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THCS'IS

C IGA STATE UNNERS UBRARI

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31293 01712 7493

 

 

_—-———

J Ill

This is to certify that the

dissertation entitled

A Generalized Model of Investment with an
Application to Finnish Hog Farms

presented by
Kyosti Sakari Pietola

has been accepted towards fulfillment
of the requirements for

 

Ph.D. degree in W1 Economics

fl’lfllws
0

jor professo

Date May 5 9 1997

 

MS U is an Affirmative Action/Eq ual Opportunity Institution 0- 12771

 

 

LIBRARY

Michigan State
Unlverslty

 

 

 

PLACE IN REI'URN BOX
to remove this checkout from your record.
To AVOID FINE return on or before date due.

 

MTE DUE MTE DUE DATE DUE

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1/98 commas-p.14

 

A GENERALIZED MODEL OF INVESTMENT WITH AN APPLICATION TO
' FINNISH HOG FARMS

By

Kyosti Sakari Pietola

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1 997

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ABSTRACT
A GENERALIZED MODEL OF INVESTMENT WITH AN APPLICATION TO
FINNISH HOG FARMS

This study develops a method for estimating a generalized investment model. Irreversible
investment behavior is allowed to arise either from generalized adjustment costs,
uncertainty, or both. The model is estimated using data for a group of Finnish hog farms
over the period 1977-93. Two out of four decision variables are allowed to obtain zero value
with positive probability. The sample is endogenously partitioned into the regimes of zero
and positive investments (four regimes in total). Then, the decision rules are estimated using
the Full Information Maximum Likelihood (FIML) method. The model has a similar
structure as the censored Tobit model.

The goal of the study is to find out the effects of fi'ictions caused by uncertainty,
irreversibility, and adjustment costs on investments in Finnish hog farms. External
restrictions, such as liquidity constraints caused by credit rationing are also studied. The
study’s main goal is to obtain estimates for adjustment rates, elasticities, and shadow prices
such that we account for the fact that optimal investments may be zero.

The results suggest that there are scale economies among Finnish hog farms and, in
addition, scale effects in their investments. Thus, production costs per unit decrease as the
amount of production increases. The instantaneous cost function is decreasing in investment

so that larger investments will result in lower adjustment costs. These results suggest that

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Finnish pork producers have potential for improving their competitiveness by establishing
large production units through drastic expansions.

It is expected that the Finnish hog industry has the potential for reaching the average
cost level of Danish hog industry in 1995. Reaching the Danish cost level, however, will
require Finnish production units to at least triple their size. Tripling the average firm size
while keeping the aggregate production capacity constant, as required by hog adjustment
programs, implies that two thirds of the current producers will need to exit the industry.
Over a five year period, for example, this would require an exit rate of 8 % per year, which
is almost twice the 4.3 % average exit rate of 1996 in Finnish agriculture. Therefore, it is
expected that an inflexible labor market, combined with excess labor in farming, will delay
the substitution of capital for labor and slow down the whole adjustment process.

The shadow price estimates show that Finnish hog farms have had excess capital
relative to their exogenously restricted production levels. Hog farmers appear to have
unconstrained access to capital. It is expected that increasing firm size will eventually result
in more efficiently utilized and allocated fann capital. Still, low returns to farm capital cause
severe difficulties in the farmers’ adjustment to new market conditions. The results provide
evidence that farm investments have been made with too low returns to capital or,
alternatively, additional incentives for investments have been provided, for example,
through investment programs or through tax shields.

Because the hog industry exhibits substantial economies of size, inflexible
environmental regulations combined with rigidities in the local land markets are expected
to have increasingly important effects on the development of hog industry structure and

production costs.

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ACKNOWLEDGMENTS

I am pleased to acknowledge the contribution and encouragement of people who have
helped me towards completing this study and my Ph.D. degree.

For obtaining this fortunate milestone in my life, I owe special gratitude to Matias
Torvela, a gentleman and a scholar. I would never have started a doctoral program in
America without his confidence and support.

I like to thank Robert J. Myers for his invaluable advice and suggestions in carrying
out this research. I am sincerely grateful to Lindon J. Robison for his heartwarming support
at all stages of my studies in Michigan. Other committee members who contributed to this
study in variety of ways were Thomas Reardon, Scott Swinton, and Jeffrey Wooldrige.
Thank you for your professional help.

The facilities and assistance offered by the Agricultural Economics Research Institute
have been essential for successfully completing this research. I am grateful to Jouko Sirén
for his trust and the gentle resources he has allocated to this study.

I would like to thank Jaana Kola for checking the stubborn flaws in my English text.

This research and my doctoral program have been funded jointly by the Agricultural
Economics Research Institute, the Academy of Finland, and the Finnish Cultural

Foundation. In addition, I received a grant from the Finnish Agronomists’ Association. The

iv

(3

SINK

generous assets these institutions have provided towards my Ph.D. are greatly
acknowledged.
Finally, I thank my family for their support and especially you, Liisa, for your love and

care.

East Lansing, April 1997 Kyosti Pietola

TABLE OF CONTENTS

LIST OF TABLES ...................................................... ix

LIST OF FIGURES .................................................... xi
CHAPTER 1

INTRODUCTION ....................................................... 1

1.1 Background ...................................................... 1

1.2 Objective and Scope of the Study .................................... 7

1.3 An Overview ................................................... 11
CHAPTER 2

THE HOG PRODUCTION SECTOR IN FINLAND ........................... 13

2.1 Size of the Hog Sector in Finland .................................... 14

2.2 Farm Structure .................................................. 16

2.3 Production Costs ................................................. 20

2.4 Entry to the EU and Adjustment Programs ............................ 23

CHAPTER 3 .

A REVIEW OF DYNAMIC INVESTMENT MODELS ........................ 29

3.1 Flexible Accelerator .............................................. 29

3.2 Dynamic Optimization Models ..................................... 31

3.2.1 Primal Approach ............................................ 33

3.2.2 Dual Approach ............................................. 37

3 .3 Preferred Approach .............................................. 41
CHAPTER 4

_ THE ECONOMIC MODEL .............................................. 44

4.1 Stochastic Processes and their Expectations ........................... 44

4.2 Timing and Size of Investments ..................................... 47

4.3 Intensity of Use and Depreciation ................................... 48

4.3 Liquidity Constraints ............................................. 50

4.4 The Optimization Problem ......................................... 51

4.5 Necessary Conditions for Optimality ................................. 53

vi

155'

q

/.4
7.5
7.6
7.7 j
7.8 g

4.6 Specification for the Optimal Value Function .......................... 63

4.7 Optimal Decision Rules ........................................... 66
CHAPTER 5

ESTIMATING THE MODEL ............................................. 72

5.1 Assumptions Underlying the Model .................................. 72

5.2 Specification of the Decision Rules .................................. 73

5.3 Estimators ...................................................... 76
CHAPTER 6

DATA .............................................................. 85

6.1 Price Indices .................................................... 87

6.1.1 Real Estate ................................................ 87

6.1.2 Other Price Indices and Normalization .......................... 90

6.2 Investments and Capital Accumulation ............................... 91

6.2.1 Real Estate ................................................ 91

6.2.2 Machinery ................................................. 98

6.3 Labor . ....................................................... 100

6.4 The Numéraire Input ............................................ 101

6.5 Output . ....................................................... 102

6.6 Credit Regimes and Discount Rate .................................. 105

6.7 Summary of the Farm Data ....................................... 108
CHAPTER 7

ESTIMATION RESULTS ............................................... 110

7.1 The Full Sample Model .......................................... 112

7.2 Testing for Misspecification ....................................... 117

7.2.1 Time Series Properties of the Price and Output Series .............. 117

7.2.2 Covariance Restrictions among the Error Terms .................. 122

7.2.3 Liquidity Constraints and the Partition into Credit Regimes ......... 124

7.2.4 Testing for Nonstandard Assumptions .......................... 128

7.3 The Effects of Increased Uncertainty ................................ 137

7.4 Adjustment Rates ............................................... 138

7.5 Shadow Prices for Installed Capital and Labor ........................ 144

7.6 Short-Run Response Probabilities and Elasticities ..................... 149

7.7 Long-Run Elasticities ............................................ 156

7.8 Steady State Capital Stock and Labor Services ........................ 159

vii

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CHAPTER 8
ECONOMIC IMPLICATIONS FOR THE HOG PRODUCTION SECTOR

IN FINLAND . ....................................................... 160
8.1 Economies of Scale ............................................. 160
8.2 Capital and Labor Market ......................................... 164
8.3 Uncertainty . . .- ................................................. 170

CHAPTER 9

SUMMARY AND CONCLUSIONS ...................................... 172

LIST OF REFERENCES ................................................ 178

APPENDIX A

Parameter Estimates with the Data Split into the Credit Market Regimes .......... 185

APPENDIX B

Response Probabilities and Short-Run Elasticities ............................ 187

viii

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Table 2.8 -1
Table 6,] _j
Table 6.2 -
Table 6.3 -
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Table 7.3 -
Table 7-4a.

LIST OF TABLES

Table 2.1 - Production, Consumption, and Trade Flows of Pork in Finland .......... 15
Table 2.2 - Sows and Sow Herds by Herd Size in Finland and Denmark in 1995. . . . . 19
Table 2.3 - Fattening Pigs and Pig Herds by Herd Size in Finland and Denmark

in 1995 ...................................................... 19
Table 2.4 - Production Costs of Weaners on Danish Bookkeeping Farms ........... 21
Table 2.5 - Production Costs of Pork on Danish Bookkeeping Farms .............. 22
Table 2.6 - Capacity Restrictions of the Subsidized Hog Production Facilities ....... 25
Table 2.7 - Milestones of Finnish Agriculture in its Adjustment to the EU .......... 26
Table 2.8 - Maximum Investment Subsidy Rates (%) from the Investment Outlay . . . . 27
Table 6.1 - Negative, Zero, and Positive Gross Investments ...................... 98
Table 6.2 - Average Revenue Shares in the Sample Farms ...................... 103

Table 6.3 - Farm Capital, Investments, and Output Stratified by Credit Regimes . . . . 106

Table 6.4 - Summary of the F arm Data ..................................... 109
Table 7.1 - Estimation Results for the Full Sample Model ...................... 113
Table 7.2 - Predicted and Observed Binary Investment Choices .................. 115
Table 7.3 — Observed Outcomes and Predictions in each Investment Category ...... 117
Table 7.4a - OLS Estimates for the Output and Price Series of the Form (7.2) ...... 121

Table 7.4b - OLS Estimates for the Output and Price Series of the Form (7.2)
with Ej=0 .................................................. 121

ix

Table 7.5 - .

Table 7.6 - 1

Table 7.73 -

 

Table 7.7b -

Table 7.83 -

Table 7.8b .

Table 7.9 - 1
Table 7.10 -
Table 7.1 1 .

Table 7,13.

Table 7.13 .

Table 7.14 .

Table 7.15 .

Table 7.16 .

Table 7.17 -

Table 7.1 8 _
Table 7.19 .
Table 7.30

Table 7.21 .

 

.l

 

Table 7.5 - The Dickey-Fuller- and F-Test Statistics ........................... 122

Table 7.6 - Estimation Results for the Deregulated Subsample Model ............. 127
Table 7.7a - Regressions on Logarithms of the Squared Errors in the
Full Sample Model ........................................... 132
Table 7.7b - Regressions on Logarithms of the Squared Errors in the
Full Sample Model ........................................... 132
Table 7.8a - Regressions on Logarithms of the Squared Errors in the
Deregulated Subsample Model .................................. 133
Table 7.8b - Regressions on Logarithms of the Squared Errors in the
Deregulated Subsample Model ................................. 133
Table 7.9 - Heteroscedasticity Corrected Model in the Deregulated Subsample ...... 134
Table 7.10 - Autoregressions on the Error Terms in the Full Sample Model ........ 136
Table 7.11 - Autoregressions on the Error Terms in the Deregulated Model ........ 137
Table 7.12 - Estimates for the Dummies over the Years 1991-93 ................. 138
Table 7.13 - Estimates for the Adjustment Rate Matrices ....................... 139
Table 7.14 - Shadow Prices for Installed Capital and Labor ..................... 147
Table 7.15 - Derivatives of the Instantaneous Cost Function with respect to
the Capital and Labor ........................................ 147
Table 7.16 - Response Probabilities for Positive Investments .................... 151
Table 7.17 - Short-Run Elasticities for Real Estate Investments .................. 154
Table 7.18 - Short-Run Elasticities for Machinery Investments .................. 154
Table 7.19 - Short-Run Elasticities for Changes in Labor Services ............... 155
Table 7.20 - Long-Run Elasticities of Capital Stocks and Labor Services .......... 158
Table 7.21 - Steady State Capital Stocks and Labor Services .................... 159

Figure 6.1 -
Figure 6.2 -
Figure 6.3 -
Figure 6.4 -
Figure 6.5 -
Figure 6.6 -
Figure 6.7 -
Figure 6.8 .
Figllre 6.9 .

Figure 6.10

 

LIST OF FIGURES

Figure 6.1 - Frequency of the Farms’ Duration in the Sample .................... 86
Figure 6.2 - Rental and Purchase Price Indices for Land ......................... 89
Figure 6.3 - Normalized Price Indices for Real Estate, Machinery, and Labor ........ 91
Figure 6.4 - Land Accumulation on the Sample Farms .......................... 94
Figure 6.5 - Accumulation of Real Estate Capital and Investment on Real Estate ..... 97
Figure 6.6 - Accumulation of Machinery Capital and Investment on Machinery ...... 99
Figure 6.7 - Labor Services on the Sample Farms ............................. 101
Figure 6.8 - Index for Variable Inputs, Used as the Nume’raire ................... 102
Figure 6.9 - Crop and Livestock Output Indices .............................. 104
Figure 6.10 - The Real Discount Rate ...................................... 107

xi

 

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Chapter 1

INTRODUCTION

1.1 Background

Uncertainty about continuation of the national agricultural policy scheme in Finland
increased in 1991, when the political debate about Finland joining the European Union
(EU) began. Four years later, in 1995, Finland joined the EU, adopted the price
mechanism of the Common Agricultural Policy (CAP), and abolished border controls for
trade with other member states. Membership in the EU has created a challenge for
Finnish agriculture and the Finnish hog industry in particular. The average producer price
of pork immediately fell by about 50 percent. But EU membership also resulted in a
decrease in costs of hog production as grain prices went down, environmental taxes on
phosphorus and nitrogen used in fertilizers were abolished, and the European Value
Added Tax (V AT) was introduced. Although the output price declines have been partially
compensated by reduced input prices and by income transfers, most farmers have yet to
respond to the changed market environment and adjust their production to the increased
competition in order to maintain an adequate income level (Ministry of Agriculture and

Forestry 1996).

 

 

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Finnish agriculture is dominated by livestock production, and the hog sector is the
third largest livestock production sector after milk and beef. In 1995 the hog sector
accounted for 14 % of total agricultural gross returns. The hog production sector also
creates an important market for domestic feed grains, including barley and oats. In
Finland, the whole food industry is closely related to domestic agricultural production
and, in particular, to the dairy and meat sectors. The food industry is the third most
important industrial sector in Finland, while slaughtering, meat processing, and related
industries are one of the largest sectors within the food industries (Aaltonen 1996). The
future role of the Finnish hog industry is therefore important to Finland’s economy.

Most hog farms in Finland are too small to use modern production technology as
efficiently as their European competitors. Danish hog farms, for example, have herd sizes
about twice as large as Finnish hog farms. Previous studies have shown that the
differences in production costs, and in overall efficiency, between existing small and
large farms are large (Hemila 1983, Heikkila 1987, Ryhanen 1992). This can also be
supported simply by comparing production costs between the small and large production
units. Thus, an increase in the size of production units offers a promising way to increase
the competitiveness of Finnish agriculture.

But a shortcoming of the earlier studies in analyzing size economies has been their
assumption that firms operate in a static environment with no uncertainty. They have
assumed that firms can accumulate capacity all at once by increasing the stock of capital,
or that the accumulation is exogenously restricted. Thus, they implicitly assume that

individual firms Operate at the long-run optimum, given exogenous prices, output or/and

 

fixed lupus

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fixed inputs. It is likely that biased estimates of size econonries are generated in static
studies, because they ignore frictions that prevent instantaneous and costless adjustment
of employment and the capital stock. Firms do not necessarily operate at their long-run
optimum, and the implicit assumption of a static environment is not generally valid. In
general, the link between the optimal capital stock and the optimal investment pattern
cannot be established in a static framework.

Firms face two types of time dependent frictions; irreversibility and adjustment
costs (Lucas 1967, Arrow 1968, and Abel and Eberly 1994). Most farm investments are at
least partially irreversible. Once investments have been made, it will be expensive to
reverse them for four reasons. First, there may be a wedge between the purchase prices
and the resale prices of industry or firm specific capital goods (Arrow 1968). The wedge
also can be caused by the adverse selection problem (Akerlof 1970), or by institutional
rationing or transaction costs (Pindyck 1991). Second, strictly positive adjustment costs
may be faced with negative investments (Caballero 1991). Third, the adjustment cost
fimction may have a kink at the point of zero investment so that there may be a corner
solution at zero. And fourth, fixed adjustment costs may be faced with even a small
investment or disinvestment (Dixit and Pindyck 1994).

Irreversibility is important in investment problems, since it makes investment
expenditures sunk costs that cannot be recovered, or can be recovered only partially. If, in
addition, investments can be delayed, irreversibility makes them especially sensitive to
uncertainty (Pindyck 1991). Uncertain future cash flows create a value for an option to

wait for new, but never complete information. Therefore, less investment will be

  
  
 

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4

triggered than the traditional NPV rule suggests (Dixit and Pindyck 1994). The more
volatile the expected future cash flows are, the more the ability to delay irreversible
investment will affect the decision to invest‘.

Adjustment costs are costs that are realized when new capital is installed. They are
traditionally thought of as being increasing and convex in the firm’s investment and,
therefore, they penalize rapid changes in the firrn's capital stock, which results in
investment smoothing (Lucas 1967, Treadway 1970, and Rothschild 1971). In this
framework, the firm's capital stock is linked across time by adjustment costs. The stock
cannot be adjusted instantaneously, as can variable factors in static models, but it can be
changed, unlike fixed factors, as time passes by. In other words, the time pattern of the
capital stock is endogenously decided by the entrepreneur, but there can be a substantial
discrepancy between the firm's desired and actual capital stock, with the latter being less
volatile than the former (Lucas 1967).

Adjustment costs can arise from internal or external causes (Mussa 1977). Internal
adjustment costs are realized if scarce resources (inputs) need to be withdrawn from
production to install new capital stock, resulting in reduced output (Lucas 1967).
Similarly, with an exogenously determined output, internal adjustment costs will be
realized in terms of increased costs. Internal adjustment costs can result, for example,
from lack of information about new technology and from inflexible design of durables.

External adjustment costs, on the other hand, cannot be controlled by firms themselves.

 

' Pindyck (1991) compares the investment option to a financial call option; the option
gives the holder the right to exercise the option and in return receive an asset. Exercising
the option is irreversible.

 

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They can arise, for example, in a rationed credit market, or if the cost of borrowing
increases with a firm's debt to equity ratio as its credit reserve decreases (Steigum 1983,
Eichberger 1989, Robison and Barry 1996, Zeldes 1989).

Numerous empirical applications rationalize the observed spread of aggregate
investment over time by adjustment costs which are assumed to be increasing and convex
functions of the rate of investment. But the arguments supporting the idea that adjustment
costs are an increasing and convex function of investment are weak. Decreasing
adjustment costs are just as plausible as increasing adjustment costs (Rothschild 1971). In
aggregate data, the observed spread of investment over time may not have resulted from
investment smoothing of individual firms but from aggregating the individual firm’s
responses over firms. Estimated investment smoothing in firm level data, on the other
hand, may have resulted from the fact that the discrete characteristics of the investment
behavior have not been accounted for.

There also exists an extensive literature on the theory of irreversible investment
under uncertainty (see e.g. Pindyck 1991, Chavas 1994, and Dixit and Pindyck 1994). In
recent theoretical work the notions of irreversibility and adj ustrnent costs have also been“
combined (Abel and Eberly 1994). But little has been done on combining the notions of
irreversibility and adjustment costs in empirical work. In particular, we still lack
empirical applications of investment rules estimated from models that allow for
investment delays driven up by generalized adjustment costs, by uncertainty, or by both of
them. Therefore, it is important to address these fi'ictions delaying and spreading firm

investments in a detailed empirical model.

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6

The frictions caused by uncertainty, irreversibility, and adjustment costs are of great
importance, particularly in the Finnish hog industry which is facing a relatively drastic
structural change. Investment frictions, if they exist, delay and spread investment over
time. More importantly, they create entry barriers and protection by conferring cost
advantages for early entrants and investors (see e.g., Tirole, 1992). The frictions will,
therefore, have considerable implications for the success and survival of the Finnish hog
industry as a new entrant in the Common Market.

We may expect that irreversibility and adjustment costs play a crucial role in the
farmers' optimal response to the increased competition. Thus, they have important
implications for our understanding of pork producers' decisions to invest or to exit the
industry. They also help in understanding the adjustment process at the industry level and
in designing structural adjustment programsz, especially if the goal is to stimulate
investments to get larger and more competitive production units for meeting domestic
production goals. At present, however, we lack accurate information about the extent of
irreversibility and the characteristics of adjustment costs in the Finnish hog farms. This

study is designated to help close this gap in knowledge.

 

2

Structural adjustment programs refer here to (public) programs that are applied to
reduce negative short-term effects to promote the realization of desired long-term effects
of a certain policy change.

 

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1.2 Objective and Scope of the Study

High production costs and relatively small herd sizes in the Finnish hog industry raise
important questions conceming the future of the industry in the Common Market. First, is
it realistic to expect that average hog production costs can be reduced fast enough, and far
enough, to allow the Finnish hog industry to compete in the Common Market after a five
year transitional period? Second, how much expansion in farm size will be needed in
order to reduce average costs to competitive levels? Third, what is the most efficient path
for farm expansion from the perspective of farmer welfare, and the welfare of society as
whole? The answers to these questions require detailed knowledge of the dynamic
structure of production, investment, capital accumulation, and costs in the Finnish hog
industry.

This study analyses the dynamic structure of the Finnish hog industry to better
understand how farm investments are determined and adjusted to external shocks.
Knowledge of the dynamic structure of the industry will provide information about the
ho g industry’s potential to adjust to the Common Market, and how adjustment programs
might be designed for assisting the optimal adjustment.

As part of the structural analysis we investigate several specific questions
Surrounding the structure of the hog industry. Each of the following questions will be

addressed in the remainder of the dissertation:

.Areil
prosit
the (l
15 no
Adlerr

pnflu

1.

uih‘

(

lire h
Shddi
hatej

ititifi

ll ad
incre;
in in:
lecre-
lTaSt
Olnir
UCh:

JEnt

 

1.

8

Are there long run economies of size in the industry? The answer to this question
provides information on the industry’s potential to survive in the long run as part of
the Common Market. If such size economies do not exist then expanding farm size
is not going to reduce costs no matter how long the transition period is.
Alternatively, if size economies exist then the industry has potential for reducing its
production costs by expanding firm size. In this case the realized cost reductions

will depend on the short run adjustment costs, too.

Are investments and expansion paths influenced by adjustment costs and do the
shadow prices of installed capital differ from zero? The answers to these questions
have important implications for the speed of adjustment and the length of time that

it will take the industry to adjust to the shock of joining the Common Market.

If adjustment costs exist, how are they characterized? For example, are they
increasing or decreasing in the scale of investment? If there are economies of scale
in investments in the sense that adjustment costs increase at a decreasing rate or
decrease in the scale of investment, then it may be appropriate to encourage 'swifi,
drastic one-time investment and a large scale adjustment in response to the shock of
joining the Common market. But if there are diseconomies of scale in investment,
such that adjustment costs increase at an increasing rate in the scale of investment,

then it may be better to allow slow, incremental adjustment.

. Have
COTlSl

lemnt

What
estim
adjus
pnce
discrt

labor

. Hou~
Cune
bye;
COntr
Sefio

indu .

 

Cune

andtt

 

9

4. Have hog farmer investments and access to capital been restricted by liquidity
constraints? If farmer access to credit is restricted, or liquidity constraints are
restricting investment for other reasons, then liquidity constraints may have
important implications on how the sector can respond to the shock of joining the

Common Market. The optimal adjustment may be influenced by these constraints.

5. What are the estimated shadow prices for capital and labor in the hog sector? These
estimated shadow prices will indicate the marginal impact on production costs from
adjusting capital and labor towards their steady state values. Thus, the shadow
prices provide an indication of potential cost reductions from eliminating any
discrepancy between the firm’s desired (steady state) and current capital stock and

labor allocation.

6. How do the steady state levels of capital stocks and labor services relate to their
current levels? If there are no discrepancies between the steady states and current
levels then neither adjustment costs, external restrictions (e. g. past production
controls), nor the prospect of entry into the Common Market will have caused
serious deviations away from steady state paths of capital and labor in the hog
industry. But if there exists wide discrepancies between the steady states and
current levels we need to know how long it will take to adjust to the steady state,

and what policies might assist this adjustment process.

10

7. How are firrns’ capital and labor markets linked? To understand the adjustment
process, it is essential to know how a discrepancy between the current and steady
states of one input will affect the demand for other inputs and, hence, the whole
adjustment process. Having knowledge on the linkages between the demands for
individual inputs, and discrepancies between their current and steady states, it is

possible to design adjustment programs with desired effects.

8. How do capital investments and labor services respond to changes in factor prices
and output? As Finland entered the Common Market factor prices changed and
production controls were abolished, which results in output adjustments. To
understand the consequences of these changes we need to have detailed knowledge

of input demand elasticities for factors of production in the sector.

9. How does uncertainty affect investments? It is valuable to know if, for example,
uncertainty over policy makers own actions influence how adjustment programs

affect farm investments and, hence, the whole adjustment process.

1.3 All Or

The study
the questio
uncertainty
and investr
investment
lm‘CStment
uncertainty
fa”115 using
rules are Us
The s
0Utlook f0
mEthods ft.
method {01.
for the flit
deClSlOn F
dEClSlon ft
Chapter 6
PFOpemeS

\

3 file 5817‘
faI'TI‘lSa

 

Fee.

11

1.3 An Overview

The study examines the dynamic structure of Finnish hog farms’. The goal is to answer
the questions highlighted above by investigating the importance and consequences of
uncertainty, irreversibility, and adjustment costs in hog producers’ optimal employment
and investment rules. First we develop a method for estimating a generalized model of
investment which is consistent with the dynamic theory of the firm. Irreversible
investment behavior is allowed to arise either from generalized adjustment costs, from
uncertainty, or from both of them. The model is estimated for a group of Finnish hog
farms using data from the period 1977-93, and the estimated investment and employment
rules are used for addressing the questions given in previous section.

The study is organized as follows. Chapter 2 summarizes the current situation and
outlook for the Finnish hog sector. Chapter 3 reviews and discusses the literature on
methods for constructing dynamic investment models, and it concludes with a preferred
method for our application. Chapter 4 sketches out the derivation of the economic model
for the firms’ dynamic optimization problem. This chapter concludes with the optimal
decision rules. The next chapter constructs the statistical model for estimating the
decision rules and concludes with the likelihood function used for estimating the model.
Chapter 6 illustrates how the data are obtained and characterizes basic statistical

properties of the data. The estimation results are presented in Chapter 7. Economic

 

3 The sample consists of farm level data on Finnish bookkeeping hog farms (about 100
farms a year) over the period 1976-1993. The data are described in detail in Chapter 6.

implicatior
summary c

TOT illilll'C TI

 

 

12

implications of these results are discussed in Chapter 8. Finally, Chapter 9 provides a
summary of the study and the most important conclusions, as well as some suggestions

for future research.

This Chapt
begin with
industry st
Danish hot
member wi
for exampt
including F

Prodi
again to th
“ms- The
Finnish ho
factors Illa
pre‘membfi
int'egtmem

 

Chapter 2

THE HOG PRODUCTION SECTOR IN FINLAND

This Chapter reviews the current situation and outlook of the Finnish hog industry. We
begin with a brief summary of the scale of the Finnish hog sector and, then, move on to
industry structure. The structure of the Finnish hog sector is compared to that of the
Danish hog sector. Denmark was chosen as a comparison, because it is an old EU
member with one of the most competitive hog sectors among the EU member states (see,
for example, Agra Europe, Nov. 1996). Denmark exports pork to other EU countries,
including Finland. ’

Production costs are reviewed in the third section. The Finnish data are compared
again to the Danish data to highlight the differences between small and large production
units. The last section discusses the major changes in the economic environment facing
Finnish hog farmers at the time Finland entered the EU. This discussion is focused on the
factors that are driving the Finnish hog industry into a relatively fast (compared to the
Dre-membership period) structural adjustment phase. In particular, challenges and
investment incentives provided by the new adjustment programs are introduced. The

chapter concludes with some preliminary observations on how farmers are responding to

13

the change

farmer real

2.1 Size of

Finnish ag
measured ‘-
behind the
Production
industry al
{OT feed gr

and Weste

agri CUl tux-a

 

14

the changed environment even though it is too early to make final conclusions about

farmer reactions.l

2.1 Size of the Hog Sector in Finland

Finnish agriculture is dominated by livestock production. When the size of the sector is
measured by gross returns, hog production is the third largest livestock production sector,
behind the milk and beef sectors. For example, in 1995 the gross returns from hog
production accounted for 14 % of the total agricultural gross returns. The domestic hog
industry also has an important impact on field crop production because it creates demand
for feed grains, including barley and oats. Hog production is concentrated in the southern
and western parts of Finland which are the most fertile and climatically favorable
. agricultural areas in the country.

In’1995 the number of hog farms in Finland was estimated at 6,200. About 2,600 of
the hog farms were specialized in producing weaners and 2,200 of the hog farms were
specialized in fattening pigs. The percentage of total farms that raise hogs was estimated
at 3.7 % in 1995. Even though a relatively small percentage of farms raise hogs, the hog
farms are very important, particularly in the southwestern part of the country where the

share of hog farms out of all farms exceeds 10 %.

 

' Main Sources in the Chapter: Official Statistics of Finland 1996: Farm Register 1995;
Agriculture and Forestry l996:2; and Monthly Review of Agricultural Statistics 1996.

Total
the 19905
consumptit
34 kilogrzu
very little i
were restri.
controls use
At the 53m

Most
and turned
prOdUCIiOn
C0mmon ,'

Capacity at

 

 

15

Total pork production in Finland has varied between 168-187 million kilograms in
the 19908 whereas consumption has been less than production (Table 2.1). The
consumption of pork has varied in the 19903 between 150 and 170 million kilograms (30-
34 kilograms per capita). Prior to 1995 Finland was usually a net exporter of pork and
very little pork was imported. These exports were, however, subsidized whereas imports
were restricted by border controls. In 1995 imports grew considerably, because border
controls were abolished and the decreased prices increased the amount of pork consumed.
At the same time exports of pork decreased and Finland became a net importer of pork.

Most recently, the decreased retail prices of pork have increased pork consumption
and turned the past net export situation into one in which consumption and domestic
production of pork are roughly equal. Therefore, it is justified under the European
Common Agricultural Policy, to have a goal of keeping the domestic pork production

capacity at its current level so as to meet domestic demand for pork.

Table 2.1 Production, Consumption, and Trade Flows of Pork in Finland. '

 

 

Year
1980 1990 1994 1995 1996
Production 169 187 171 169 172
Consumption 142 164 151 170 170
Exports 15 23 22 9 15
Imports - - 2 12 1 1

 

‘ Million kilograms per year.

2.2 Farm

After the :
decreasing
veterans.

agricultur;
Size has t

technical

hectares o

 

16

2.2 Farm Structure

After the second world war, farm size was already increasing in other parts of EurOpe but
decreasing in Finland where the largest farms were divided to provide land for war
veterans, and for those who had their farms in the lost eastern area. Since then,
agricultural policies have supported farm income on small farms so that the average farm
size has been increasing slowly. On average, Finnish farms are still small despite rapid
technical changes that favor increasing farm size. In 1995 the average farm size was 22
hectares of arable land and 49 hectares of forest.

Farm expansion may also have been restricted by liquidity constraints caused by
credit rationing. Until 1985 the Finnish credit market was rationed so that interest rates
for loans were set below market clearing rates by the Bank of Finland. At these loan rates
there was excess demand for loans, and firms' access to credit may have been rationed by
restricted credit approvals. Credit market liberalization began in 1985 (for more details
see e.g. Pajuoja 1995). In addition, farm growth has been partially deterred by the small
supply of supplementary land. The supply of farm land has been further decreased by
policies that included an incentive for retiring farmers to idle their land.

Also, the livestock production units are small on average because capacity
expansions have been restricted through various production controls since the early
eighties. Production controls were seen as an effective means of supporting high domestic
producer prices and farm income. In the hog industry, authorities started to regulate the

establishment of production units in 197 5 by a licensing scheme, originally to prevent

17

production from becoming too industrialized. The policy required the farmer to have a
license for enlargening his existing facility or investing in a new plant. Specific criteria
for new licenses have been complicated and they have varied over time, but the standard
has been that licenses are granted only to full time farmers. In 1978 the licensing scheme
was complemented by a rule that a farm has to have land for producing at least 25 % of
the feed for the hog production. Until 1982 the maximum size of a new production unit
was a fattening capacity of 1,000 pigs and, in practice, the scheme did not restrict
investments. In the 19705, for example, the license was granted to 91 % of all
applications, and a notable number of applications were rejected only after the feed
production restriction was implemented in 1978 (Kola 1987).

Nevertheless, the rules of the licensing scheme were tightened considerably in
1982. Thereafter, the standard has been that new licenses have not been granted to
enterprises with over 400 hogs. Environmental regulations were also tightened. The
license for new hog production capacity was granted only if the farm had enough land for
producing at least two fifths of the feed needed in the hog production. This requirement
was further increased in 1984 so that the farm had to have land for producing at least 75
percent of the feed needed in the hog production.

In 1995, when these stringent production controls were abolished, a new Agri-
Environmental Program (AEP) was introduced. It provides incentives for farmers to keep
the number of livestock units per hectare low for environmentally friendly utilization of
manure and slurry. Therefore, the maximum size of a hog production facility is still in

practice tied to the farm’s arable land area. A farmer is eligible under the AEP only if he

 

SO“

m7-
‘ u.

18

has a maximum of 11 fattening pigs or three sows per hectare of land. A production unit
of 60 sows and fattening capacity of 500 pigs, for example, is eligible under the AEP only
if it has at least 66 hectares of arable land for spreading manure and slurry.

Even though the production controls did not significantly restrict the hog sector
prior to 1982, the current hog industry in Finland is dominated by small family farms
rather than by large industrialized units. In 1995 the average herd size of fattening pigs in
Finland was 79, whereas an average Danish herd had 178 fattening pigs. That is, Danish
herds were more than twice as large as Finnish herds. The average sow herd size was 31
sows in Finland, but in Denmark the average size was 75 sows, which is again more than
twice as large as in Finland.

By comparing the production of different herd sizes, we find that Danish hog
production is concentrated in much larger herds than Finnish production. Tables 2.2 and
2.3 present the distribution of sows and fattening pigs into different herd size categories
for approximating and characterizing this concentration. In Denmark, for example, 76 %
of sows are in production units of more than 100 sows. But in Finland only 2 % of herds
and 9 % of sows are in herds of more than 100 sows. Also in finished hog production, the
distribution of the farm size differs substantially between the two countries. In Denmark,
for example, 43 % of fattening pigs were in production units of more than 500 pigs. In
Finland only 13 % of fattening pigs were in such large units. Further, if we take the sum
of all pigs in the herd, then in Denmark 61 % of the pigs are in herds of more than 1,000

pigs, while only 2 % of all pigs were in such large units in Finland.

19

Table 2.2. Sows and Sow Herds by Herd Size in Finland and Denmark in 1995.“

 

 

 

% of sows % of herds
Herd size
Finland Denmark Finland Denmark

1-49 61.4 9.4 84.2 57.7
50-99 29.4 14.3 14.1 15.0
100-199 6.1 31.6 1.5 16.9
200-499 3.1 35.1 0.3 9.3
>500 0 9.6 0 1.0

 

' Sources: Danmarks Statistik: Agricultural Statistics 1995; and Official Statistics of Finland: Farm
Register 1995.

Table 2.3. Fattening Pigs and Pig Herds by Herd Size in Finland and Denmark in 1995.‘

 

 

 

% of fattening pigs % of herds
Herd size

Finland Denmark Finland Denmark
1-49 10.8 4.0 59.7 40.9
50-99 14.4 5.5 15.8 13.9
100-199 21.9 12.2 12.3 15.4
200-499 40.1 34.9 10.7 20.5
>500 12.8 43.4 1.4 9.3

 

' See Table 2.2.

 

23. I

In F i
pigs.
per i

total

hate
.\'e\'e
their

0ftht

20

2.3. Production Costs

In Finnish bookkeeping hog farms, with an average fattening capacity of roughly 200
pigs, the production cost of pork, excluding labor cost, is estimated at 9.4 FInnish Marks
per kilogram (FIM/kg) in 1995. By adding labor cost of 2.8 FIM/kg we end up with the
total production cost of 12 FIM/kg. Equipment and buildings account for 14 % and 6.8 %
of the total production costs. The estimated production costs, even if we exclude labor,
have exceeded the average producer price for pork (8.1 FIM/kg) by about 14 %.
Nevertheless, producers received direct income transfers that accounted for about 41 % of
their total agricultural revenues. These income transfers, if they are compared to the scale
of the farms’ hog production, corresponded to a gross return of about 5.7 FIM/kg.2

In 1995 the average total production cost of pork among all hog farms in Denmark
was estimated at 9.7 FIM/kg, i.e. about 19 % lower than in the Finnish bookkeeping
farms (Agra Europe 8/1996). The Danish bookkeeping farms were even more efficient
than all farms on average. For example, in the group of the largest bookkeeping hog
farms, with more than 1,400 pig fattening capacity, the production cost of pork is
estimated at 7.6 FIM/kg (for more details see Table 2.5). 3

Because there are no adequate data on the group of large-scale hog farms in
Finland, we use the Danish bookkeeping farm data for characterizing how the average

production costs depend on the size of the enterprise. Tables 2.4 and 2.5 present the

 

2 Costs have been estimated using the data in AERI Working Papers 5/96.

3 Exchange rate 1 Danish krone (DKK) =0.779 FIM has been used.

prod
table
The
prod

unit 3

firms

feedi

Table
\

ls
lnpu:

Feed
Equi;
Build
other

Tout
LabOf

Tout
.\
i “'1 t

production costs for two herd sizes in both sow and fattening pig herds. Note that in these
tables the smaller production units represent herd sizes that are also common in Finland.
The group averages suggest that there is a notable decrease in production costs per unit
produced as we move from the small unit to the large unit. Both feed and labor costs (per
unit produced), in particular, decrease with herd size. Equipment costs, on the other hand,
increase with herd size. These observations suggest that as herd size has been growing

firms have been substituting equipment for labor which, in turn, has resulted in advanced

21

feeding technologies and decreased feed costs.

Table 2.4. Production Costs of Weaners on Danish Bookkeeping Farms. '

Herd size, number of sows

 

 

Input Difference %
10-49 >250

Feed 156 115 -26
Equipment 19.5 27.6 ' +42
Buildings 27.3 17.4 -36
Others 45.9 42.1 -8
Total costs excl. labor 249 202 -19
Labor 1 14 46.9 -59
Total costs 363 249 -31

 

' FIM/weaner. 1 DKK=0.779 FIM. Data Source: Okonomien i landbrugets driftsgrene 1994/1995.

Tor
Lat
Tot

"n

land:

and j
choo
1mm
The 1

sou‘j

22

Table 2.5. Production Costs of Pork on Danish Bookkeeping Farms. "

Herd size, number of fattening pigs

 

 

Input Difference %
200-499 > 1400

Weaner 3.70 3.70 0

Feed 2.80 2.62 -6,4
Equipment 0.249 0.263 +5.6
Buildings 0.323 0.263 -19
Others 0.377 0.354 -6.1
Total costs excl. labor 7.45 7 .20 -3.4
Labor 0.970 0.400 -59
Total costs 8.42 7.60 -17

 

' FIM/kg. l DKK=0.779 FIM. A 78 kg carcass weight has been used. Data Source: Okonomien i
landbrugets driftsgrene 1994/1995.

It is likely, however, that the differences between the group averages in Tables 2.4
and 2.5 are affected by significant selectivity bias, because farmers have been allowed to
choose their firm size endogenously in Denmark. Farmers who have been able to profit
from large units have expanded firm size, while others have continued with smaller units.
The selectivity bias is also supported by the observation that the number of weaners per
sow increases with the herd size. In the large herds the number of weaners was 21.1 per
sow, but in the small herds it was only 16.5 weaners per sow. Also, large units may have
had more incentives to invest in animal breeding than small units, contributing to an
increased number of weaners per sow as well as decreased feed costs per kilogram of
pork produced in large units.

Nevertheless, the data suggest that most Finnish hog farms are too small to use
modern production technology as efficiently as their Danish competitors. Therefore, we

can expect that the Finnish hog industry has the potential to reduce production costs

23

substantially through expanding firm size. Once firm sizes have increased (and average
costs declined) sufficiently it may even eventually turn out that the industry can become
competitive enough to export and expand market share outside Finland. Nevertheless, this
is unlikely to happen at least in the short run. Furthermore, the domestic adjustment
programs, including income transfers and investment subsidies, can no longer be justified
under the Common Agricultural Policy if the industry goal is to penetrate to the export
market. As explained above, the adjustment programs can only be justified to get the
industry competitive enough for meeting domestic demand for pork and for maintaining

the current meat processing industries in Finland.

2.4 Entry to the EU and Adjustment Programs

As noted above, the average producer price of pork fell by about 50 percent when Finland
joined the EU. However, EU membership also resulted in a decrease in hog production
costs as grain prices went down, environmental taxes on phosphorus and nitrogen used in
fertilizers were abolished, and the European Value Added Tax (VAT) was introduced.
The projected income losses caused by the decreased producer prices are
compensated for farmers through direct income transfers, which are: Common
Agricultural Policy (CAP) reform aid, Less Favored Areas aid (LFA), agri-environmental
aid, and national aid. National aid includes permanent Northern aid as well as a gradually

declining aid for 1995-1999. The Accession Treaty did not allow for a sufficient

24

permanent national aid in Southern Finland and, therefore, the introduced aid level would
have declined very rapidly without any further stipulations. However, it was agreed that,
if serious difficulties appear, a new form of national aid can be negotiated for Southern
Finland as well. This so-called aid for serious difficulties, was negotiated in 1996 and is
to be paid over the period 1997-1999. Even though numerous new direct income transfers
were introduced, most farmers have to respond and adjust their production to the
increased competition if they want to maintain an adequate income level (Ministry of
Agriculture and Forestry 1996).

Hog producers’ economic environment also changed because the licensing scheme,
which earlier deterred farmers fiom expanding their production units, was abolished and
new favorable adjustment programs were introduced. The main goal of these adjustment
programs is to promote the structural adjustment of rural enterprises and rural areas into
the European Common Market and Common Agricultural Policy (Ministry of Agriculture
and Forestry 1996). Many other aspects have also been incorporated into the programs.
For example, they provide incentives and impose restrictions on maintaining and
improving environmental sustainability of agricultural production practices. More
importantly, at least from the vieWpoint of the present study, the program includes
extensive investment and early retirement schemes which provide interesting alternatives
for a farmer. He can either continue producing as before, and perhaps accept a gradually
decreasing income level. Or he can quit farming and choose the early retirement plan

provided he is old enough and eligible in the plan, or he can apply for investment

subsidies and expand.

25

Finland got permission from the EU to support investments in hog production
facilities temporarily during the transitional period of 1995-1999, provided the subsidy
does not increase the total hog production capacity in Finland from the 1994 level. It is,
therefore, required that at least the same amount of capacity has to exit the industry as
new capacity is built. It was also required that certain standards for enterprise sizes are
followed. These standards are reported in Table 2.6. Only full time farmers are eligible

under the program.‘

Table 2.6. Capacity Restrictions on Subsidized HogProduction Facilities. '

 

Type of investment Minimum capacity Maximum capacity
Enlargement of a facility for
sows 50 400
fattening pigs 300 3000
A new facility for
sows . 65 400
fattening pigs 400 3000

 

' Source: Ministry of Agriculture 1996.

Nevertheless, the final terms and implementation of the investment subsidy scheme
were delayed until 1996 and, in Southern Finland, the subsidy was firrther increased in

1997 as part of the serious difficulties aid package. Also, the time period over which the

 

‘ Requirements for a full time farmer: at least 50 % of the applicant’s labor input used on
the farm, at least 25 % of the income is from agriculture, and at least 50 % of the income
is from the farm.

subsidies are allowed to be paid, was extended to the year 2001, because the

implementation of the scheme was delayed (a summary of the key events concerning

26

entry and adjustment to the EU is given in Table 2.7). The resulting maximum accepted

subsidy rates, measured as percentages fi'om the initial investment outlay, are presented in

Table 2.8. The amount of the subsidy for an investment project is computed as a sum of

the investment allowance and the present value of the interest rate subsidy. A 50 %

subsidy may, for example, consist of an allowance that is 30 % of the investment outlay

and an interest subsidized loan in which the discounted present value of the interest rate

subsidy is 20 % relative to the investment outlay.

Table 2.7 Milestones of Finnish Agriculture in its Adjustment to the EU.

 

Year Event

1991 Debate about Finland joining the EU began

1994 Accession Treaty was negotiated

1995 Finland joined the EU; a five year transitional period for agriculture began

1996 So-called aid for serious difficulties was negotiated

1997 Investment programs in effect (the package of serious difficulties and other
investment subsidies)

1999 Last year of the initially negotiated transitional period

2001 Last year of the investment subsidies in the "serious difficulties" subsidy

package negotiated in 1996

27

Table 2.8. Maximum Investment Subsidy Rates (%) from the Investment Outlay. “

 

Investment good Southem Finland Northern Finland
Production building for pigs " 50 27
Arable land 20 20
Drainage 50 20
Grain dryer 60 20
Storage ° 40 20
Housing and heating 20 20

 

' Source: Ministry of Agriculture 1996.
" Either enlargement or a new facility.

° Storage for feed, machinery or farm products.

It has to be emphasized that the reported subsidy values only set a ceiling for the
subsidy rates. The realized subsidies, as well as the types of investments subsidized, will
depend on how many farmers apply for them and the amount of funds designated to the
program. It may eventually turn out, for example, that the state budget for agriculture is
too small to pay the maximum support rates, at least for all types of investments listed in
the subsidy scheme.

Preliminary data suggest that the temporary investment subsidy scheme, with the
risk that it will run out of sufficient funding, combined with a downward sloping trend
(per capacity unit) in the direct income subsidy scheme, is accelerating investments in the
hog industry, even though market prices are more uncertain than before. Farmers are
responding not only to the incentives provided through the extensive investment
programs but also to the expected lost direct income subsidies caused by delays in

investment decisions. In other words, the value of information about market price

28

movements has been smaller than the expected lost subsidies from postponing
investments and, therefore, it has payed to take advantage of the highest subsidies rather
than wait for new market information.

Investments in new production facilities started to emerge in 1995 and 1996. A
survey made in spring 1996 indicates that 11% of hog farms had already invested in hog
production facilities in 1995 or in early 1996. As suggested by the decreasing trend of the
income subsidies, farmers in the southern support areas have been more eager than
farmers in the northern areas to invest early (Kallinen et al. 1996).

The survey of Kallinen et al. (1996) also shows that only 5 % of hog farms plan to
exit the industry within two years, while 70 % of the farms plan to continue in the
industry after the year 2000. About 56 % of the farms staying in the business plan to
invest in their hog production facilities and estimate their new production capacity at 1.6
times the current capacity. The majority of these investments will be realized between

1996 and 1998, and half of these investments have already begun.

Chapter 3

A REVIEW OF DYNAMIC INVESTMENT MODELS

This chapter reviews and discusses the literature on methods for constructing dynamic
investment models. We start the review with the empirically tractable and widely used
add hoc flexible accelerator model, because it provides a good framework for defining the
central concepts and issues we are dealing with in our study. The next section highlights
the most important literature on formulating dynamic optimization models that formally
rationalize the theory of investment, i.e. the link between the theory of the firm and the

flexible accelerator model. The chapter closes with a preferred approach for our study.

3.] Flexible Accelerator

In the flexible accelerator model, a firm's capital stock is assumed to accumulate as a
linear function of the firm's desired steady state capital stock and its actual, less volatile

capital stock (Lucas 1967, Treadway 1971, and Mortensen 1973). In particular, a firm's

net investment, K , is proportional to the discrepancy between the firm's desired and

actual capital stock such that

29

30

K = Nae-12),

where N = matrix of adjustment rates
(the adjustment matrix) (3'1)
K = actual capital stock

K = desired, steady state capital stock

Without any innovations or shocks to the system, the capital stock converges into a stable
steady state level, provided that the characteristic roots of the adjustment matrix, N, lie
between zero and one. Usually, the diagonal elements of N are expected to lie between
zero and one, although this is a stronger requirement than the stabity condition.

Adj ustrnent rates are symmetric if N is symmetric. With symmetric adjustment
rates, a disequilibrium in the market of good 5 has the same effect on the investment of
good j as a disequilibrium in the market of good j has on the investment of good 3.
Adjustment rates are independent if the off-diagonal elements of N are zeros, i.e. N is a
diagonal matrix. Further, the capital stock adjusts instantaneously if N is an identity
matrix. If, for example, the off-diagonal elements in the jm row of N are zeros, and the j"‘
diagonal element is one, good j adjusts instantaneously to the changes in its steady state
stock. A good that adjusts instantaneously is a variable input. A good which does not
adjust instantaneously has been defined in the literature as a quasi-fixed input. We use the
terms capital good, capital stock, and quasi-fixed input interchangeably.

Adjustment rates also can be asymmetric with respect to investment. In this case, an

adjustment rate with a negative investment differs from that with a positive investment.

31

Modeling adjustment rates that are asymmetric in investment requires that the regimes of
negative and positive investments can be identified in the sample.

A problem with the accelerator model is that it does not explicitly determine what

the steady state capital stock is. In other words, the right hand side variable I? is

unobserved in (3.1) or, more importantly, a function that determines I? is not defined by

(3.1). The steady state capital stock has to be determined by another model and, therefore,

the accelerator does not provide a rigorous theory of investment.

3.2 Dynamic Optimization Models

A formal investment theory, which is consistent with the theory of the firm, requires that
we solve a dynamic multi-period optimization problem. The solution will then trace out
an optimal investment demand as a function of exogenous state variables, including the
firm's actual capital} stock. Further, by setting net investment to zero the model can be
solved for the optimal steady state capital stock, which is also a ftulction of the exogenous
state variables (excluding the firm’s actual capital stock) in the model. Usually the
dynamic optimization problems have been constructed so that the firm’s one-period
outcomes are linked to each other through fiictions, modeled as uncertainty and/or

adjustment costs.

32

There exists an extensive literature on investment under adjustment costs and
investment under uncertainty. We highlight only the most important literature which is
relevant to this study. Meese (1980) provides a comprehensive list of references on the
adjustment cost literature prior to 1980, and Dixit and Pindyck (1994) and Pindyck
(1991) have provided comprehensive reviews on investments under uncertainty and, in
particular, the real options approach to irreversible investment.

The core problem in constructing dynamic optimization models of investment has
been summarized by Keane and Wolpin (1994):

" There are no conceptual problems in implementing models with large choice sets,

large state spaces, and serial dependencies in unobservables. The problem is in

implementing interesting economic models that are computationally tractable."

The literature on modeling. adj ustrnent costs in a dynamic context under uncertain
future cash flows can be divided into four distinct strategies, or approaches. The first
approach imposes restrictions on how expectations are formed, assumes an analytically
convenient production technology, and solves for the optimal decision rules explicitly in a
closed form. The second approach is more realistic than the first one, in the sense that it
allows for both flexible production technology and flexible expectations structures by
estimating the first order conditions (Euler equations) from a dynamic optimization
problem directly. In the third approach, the entrepreneur's choice alternatives, as well as
the space of the state variables, are discretized and the optimization problem is then

solved numerically without solving for any first order conditions or closed form decision

33

rules. Each of these three approaches are primal, in the sense that they involve explicit
solution of a well-defined optimization problem. The fourth approach imposes a structure
on how expectations are formed, allows for flexible production technology, and uses
intertemporal duality for deriving the closed form optimal decision rules.

The primal and the dual models are both functions of prices and possibly some
exogenous constraints, like exogenous technology and output (Howard and Shumway
1988). But the specifications of these models differ. The primal model is specified in
terms of the instantaneous (or one-period) production function, cost function, or profit
function. Then, the necessary optimality conditions are imposed through a set of first
order conditions (Euler equations) or, alternatively, the model is solved numerically. In
the dual model, on the other hand, the optimal value fimction is specified and the
envelope theorem is used to derive the decision rules. In subsequent sections we shall

examine the primal approach and the dual approach in more detail.

3.2.1 Primal Approach

The first primal method considered here was developed by Hansen and Sargent
(1980,1981), and further modified by Epstein and Yatchew (1985). The approach is to
define an analytically convenient functional form for the one-period cost, production or
profit function, and to solve the decision rules explicitly in a closed form through the

Euler equations. Then the observed decision variables are used for estimating either the

34

structural form parameters or the reduced form parameters. In this approach, information
from the transversality conditions can be incorporated into the estimation equations for
increasing the efficiency of the estimates, but at the cost of restricting the production
technology to be quadratic. Perhaps more importantly, a difficulty arises in a multiple
capital good setting if the adjustment rates are dependent across the capital goods, i.e. the
adjustment matrix is not diagonal. With a nondiagonal adjustment matrix, it is not
generally possible to find explicit expressions for the reduced form parameters in terms of
the underlying technology parameters (structural form parameters). If the number of
capital goods exceeds two, one has to assume and impose independent adjustment rates in
order to get a formal link between the reduced form parameters and structural form
parameters. That is, the adjustment matrix has to be diagonal.

The difficulty with the closed form solutions is, in particular, that the adjustment
matrix, which solves the characteristic equations corresponding to the Euler equations, is
related in a complex fashion to the structural form parameters, say, to the parameters in
the production function. Epstein and Yatchew (1985) avoid this problem by
reparametrizing some of the structural form parameters so that they are functions of the
adjustment matrix and the remaining structural form parameters. Even though the
reparametrization technique can be used to establish a feasible link, at least in some
special cases, between the structural and reduced form parameters, the algebraic
relationship between the parameters remains ambiguous and complex.

The second approach considered here has been developed by Kennan (1979),

Hansen (1982), and Hansen and Singleton (1982), and applied, for example, by Pindyck

35

and Rotemberg (1983). In this approach, the structural form parameters are estimated
directly from the Euler equations without solving them for closed form decision rules.
Future exogenous variables are replaced by their observed values and, then, an
instrumental variables technique is used to estimate their expectations. Kennan (1979),
for example, suggests a simple two-step least squares procedure for obtaining consistent
parameter estimates. Hansen and Singleton (1982), on the other hand, construct a set of
population orthogonality conditions from the Euler equations and estimate their sample
counterparts by the Generalized Method of Moments (GMM) estimation technique.
Under rational expectations and fairly weak assumptions about the stochastic data
generating processes, the method generates consistent estimates for the structural form
parameters. Because the method circumvents solving the Euler equations for the optimal
decision rules, it is very flexible in terms of allowing a wide range of alternative non-
quadratic production technologies. However, the information included in the
transversality conditions is ignored and the resulting estimates are not necessarily
efficient (Epstein and Yatchew 1985, and Prucha and Nadiri 1986). But, more
importantly, this approach generally cannot be used to compute price or output
elasticities, because the optimization problem has not been solved for the decision rules
(e.g. Thjissen 1996).

Later, Rust (1987) developed a numerical method for estimating a full solution to a
structural, discrete choice dynamic programming model without solving it for optimal
decision rules or any necessary first order conditions. He used the maximum likelihood

estimation technique and a "nested fixed point algorithm" to iterate Bellman's equation

36

until convergence occurred inside each iteration of the likelihood function. Although we
can take advantage of particular structures, functional forms, or distributional
assumptions, as he did, the method will be limited by computational complexity.
Therefore, it is expected that this method will not be feasible for a large dimensional
problem. For example, the original Rust (1987) bus engine replacement application had
only two alternative choices (replace or continue), one observed state variable (mileage),
and homogenous data (similar buses). And still all of his cost function specifications did
not converge.

More recently, some simulation and approximation methods, which circumvent the
need for an exact full solution to the optimization problem, have been developed (Stock
and Wise 1990, Keane and Wolpin 1994, Stern 1994). They allow for more complex
dynamic programming models to be estimated feasibly, but require that the state variables
are discretized so as to reduce the number of elements in the state space. The simulation
methods can be used to approximate sequential dynamic discrete choice decisions with
mutually exclusive alternatives, especially when the state space is not large. The
computational burden comes from the fact that to obtain the alternative specific value
functions we must compute the expected maximum of the future period rewards (or costs)
for each alternative. If one desires an exact solution, the expected maximum functions
involve multiple integrations with as many dimensions as we have choice-altematives in
the model. The computational intensity is further increased because the resulting expected
maximum functions must be evaluated at each element of the state space for tracing out

the optimal choices. The computational burden could be reduced by the method for

37

approximating the expected maximum functions as suggested by Keane and Wolpin
(1994). Although the proposed method performed well in the study of Keane and Wolpin
(1994), they conclude: "Much additional work must be done to determine the method's

general applicability".

3.2.2 Dual Approach

The dual approach is based on dynamic, intertemporal duality theory, established by
McLaren and Cooper (1980), formalized by Epstein (1981), and further explored by
Epstein and Denny (1983). The method has been extensively applied to the dynamic
investment and capital accumulation problems in the late 19805 and early 19903. In a
typical dual approach, a risk neutral entrepreneur is assumed to minimize an expected
value of a discounted sequence of production costs conditional on exogenous input prices
and output levels. A flexible functional form is then chosen for the optimal value
function, and the optimal decision rules are derived by applying the envelope theorem
directly to the value function.‘

The dual approach is the most flexible in terms of the generality of the underlying

production technology. In particular, a major advantage of the dual approach is that the

 

' These kinds of applications are, for example, Taylor and Monson (1985), Shapiro (1986),
Vasavada and Chambers (1986), Stefanou (1987, 1989), Howard and Shumway (1988,
1989), Weersink and Tauer 1989, Weersink 1990, Femandez—Comejo et a1. (1992).

38

adjustment matrix and the parameters in the optimal value firnction are related to each
other in a simple fashion and, therefore, it is straightforward to solve the model for closed
form decision rules in terms of the underlying structural form parameters (Epstein and
Denny 1983). Restrictions on the production technology, such as independent adjustment
rates, are not required. Independence of adjustment rates can be tested rather than
assumed. The model can be easily extended to cover an arbitrary number of variable
inputs, capital goods, and outputs.

Although the dual approach is flexible with respect to the underlying production
technology, it has limitations in identifying price and output expectations separately fi'om
the technology parameters (Taylor 1984). With endogenous output and an estimated
supply equation, the model has enough overidentification restrictions for identifying and
testing simple expectations structures that follow a first order differential equation system
(Epstein and Denny 1983). But if an exogenous output is assumed and no supply equation
is included in the model, there are no overidentification restrictions for testing how
expectations are formed. Therefore, it has been a standard procedure that the technology
parameters have been pinned down by imposing a specific expectations structure on the
model.

Typically, studies have imposed static price and output expectations such that the
current prices and outputs have been expected to prevail forever (e. g. F emandez—Cornejo
et a1. 1992, Vasavada and Chambers 1986). Some authors, e.g. Vasavada and Chambers
(1986), claim that static expectations are realistic in relatively small agricultural firms

where goods can be stored easily and frequent acquisition of market information is costly.

39

In European agriculture, static expectations may be realistic because the marketing
institutions and agricultural legislation have stabilized and protected farm outputs and
farm gate prices (e.g. Thjissen 1994). Thjissen (1996) even concluded that the model with
static expectations fits the Dutch dairy farm data well, but the rational expectations model
is inconsistent with the theory.

In many duality applications, however, the seemingly restrictive assumptions on the
expectations structure can be made without much loss of generality. The expectations
assumption does not necessarily alter the most important behavioral economic results.
The statistical inference concerning adjustment rates, as well as price and output
elasticities, may be independent of the expectation structure as long as they meet the
Markov property, in the sense that the probability distribution and expected value of the
next period price (or output) is a function of current prices and output. The reason is that,
under Markovian expectations, the behavioral equations are functions of current prices
and outputs, which include all relevant information about their future values. Therefore,
correctly specified behavioral equations will depict the aggregate effects of expectations
and technology even though their separate effects cannot be identified and distinguished.2

Most dynamic duality models of investment and capital accumulation use aggregate
data maintaining the assumption of interior solutions with positive gross investment. The
assumption can be made without loss of generality only in aggregate data. Studies using

firm level data, on the other hand, have typically used the primal approach based on the

 

2 The claim holds in our model, and this will become clear in the next chapter, where the
economic model is derived.

4O

argument that the dual approach is not applicable, because firm level investment can be
zero, or even negative (e.g. Thjissen 1994). But there are no theoretical reasons that
prevent relaxing the assumption of positive investments, and applying the dual approach
to firm level data. Epstein (1981) concludes that the regularity conditions of the optimal
value function with positive gross investment are readily extended to account for negative
gross investment too. Nevertheless, it is difficult to construct an optimal value function
such that the regularity conditions hold for all individual firms, because some of the
regularity conditions differ qualitatively between the investing and disinvesting firms. For
example, consistent shadow prices for installed capital, which are partial derivatives of
the optimal value function, must alternate their signs depending whether the firm is
investing or disinvesting (Epstein and Denny 1980).

Another alternative is to endogenously stratify the data into positive, zero, and
negative investment regimes. One can then specify a consistent value function for each of
these regimes, and the regularity conditions for a consistent value function can be tested
within each regime. With this approach, the firm level data provide a good opportunity to
account for the asymmetries and discrete characteristics in the Optimal investment rules.
The decision rules can be estimated, for example, by the maximum likelihood technique.
Chang and Stefanou (1988) and Oude Lansink (1996) have exploited this idea by
modeling positive and negative net investments using an endogenous dummy model, and
the two-stage self-selection model of Heckman (1976). However, the dimensionality
problem becomes severe when modeling both discrete and continuous characteristics of

the optimal decision rules with a large number of capital goods.

41

3.3 Preferred Approach

Among the reviewed approaches, there are trade-offs in the flexibility of the underlying
technology, identification of expectations, statistical efficiency, computational intensity,
and the form of the results. The traditional primal methods with closed form decision
rules would produce consistent results in a preferred form (e. g. elasticities), but these
methods have problems. The derivation of the optimal decision rules is complex unless
the production technology is restricted. If the number of capital goods exceeds two, the
technology has to be restricted so that the adjustment matrix is diagonal. In addition,
sufficient overidentification restrictions for testing how expectations are formed requires
profit maximization conditions so that all the input demands, the output supplies, and
equations on price processes can be used for identification (Epstein and Yatchew 1985).
With exogenously determined output, the structure of expectations has to be imposed on
the model without testing its validity.

If the Euler equations, on the other hand, are used for estimating the parameters we
can allow for more flexible technology, but the closed form decision rules and elasticities
can no longer be computed. Further, expectations could not be tested with this approach
either, because the profit maximization conditions are not met in our application. The
reason is the lack of overidentification restrictions, as explained above. Therefore, by
using this method nothing would be gained compared to the dual approach, which allows

flexible technology but has no overidentification restrictions for testing the expectations.

42

In this study, we use the dual approach because we wish to model more than just
one quasi-fixed input and to test for independent adjustment rather than assume it. We are
also interested in price, output, and scale elasticities, which are straightforward to
estimate when the dual approach is used.

Our dual model is constructed so that the instantaneous production technology is
augmented by internal adjustment costs, which has been the standard in the adjustment
cost literature (e.g. F ernandez-Comejo et a1). But, in addition, we generalize the model to
allow for uncertainty, irreversibility, and more general adjustment costs, like fixed
adjustment costs. Therefore, the model allows not only for investment smoothing but also
for an optimal choice of inaction, i.e. an optimal choice of zero investment’.

The adjustment cost literature has focused only on the regime of positive gross
investment, with few exceptions. Chang and Stefanou (1988) and Oude Lansink (1996),
for example, stratified data into two regimes, contracting and expanding fums, while
modeling adjustment costs asymmetric in net investment. But we follow Abel and Eberly
(1994), stressing irreversibility of agricultural investments, and incorporate the mixture of
discrete and continuous characteristics of investments by identifying and partitioning the
following two investment regimes:

(i) a regime of zero gross investment and

(ii) a regime of positive gross investment.

 

3 An adjustment cost rationalization of Johnson's (1956) fixed asset theory, as in Hsu and
Chang (1990), results in a similar identification of frictions and classification of observed
investment demands.

43

The regime of negative gross investment was excluded in the analysis because the
number of negative gross investments in the data was too small for a complete analysis.
Changes in the labor services, on the other hand, did not include zeros and only the
regimes of negative and positive changes in labor services were modeled. We now move

on to a detailed derivation of the economic model.

Chapter 4

THE ECONOMIC MODEL

This chapter derives the economic model used in the study. We start by defining a general
set-up for the economic model. That is, we describe how the stochastic processes are
determined, how we deal with the optimal timing and size of investment, and how liquidity
constraints are incorporated into the analysis. Then, we sketch out the main steps in dynamic
optimization and deriving the optimal decision rules. The chapter concludes with a

discussion of the optimal decision rules.

4.1 Stochastic Processes and their Expectations

The investment literature has revealed the significant effect that expectations and uncertainty
have on investment decisions. Recent theoretical work has incorporated expectations and
uncertainty into the analysis and used stochastic calculus to derive stochastic investment
rules.

In dynamic models, as opposed to static models, uncertainty affects the necessary
conditions for the optimum even when the optimizing agents are assumed to be risk neutral.

Therefore, internal consistency in a dynamic model cannot be maintained by just solving a

44

45

deterministic problem and then taking expectations and adding random shocks on the model.
A theory of how expectations are formed and how stochastic processes are generated has to
be incorporated explicitly into a dynamic model before deriving the necessary conditions for
optimality.

One special method to account for expectations is to augment the optimal value
function by a simplified measure of expectations, as in Howard and Shumway (1989). They
modeled technology expectations by augmenting the optimal value function with a time
trend. A detailed discussion on the method can be found in Larson (1989). A more widely
used, and more general method, involves modeling expectations and uncertainty through
stochastic transition equations for the exogenous state variables in the model.

For analytical convenience, most studies have maintained simplified assumptions about
the stochastic processes which generate expectations and uncertainty in the transition
equations. Ingersoll and Ross (1992), for example, allow for a stochastic discount factor,
while F ousekis and Shortle (1995) model investment under stochastic depreciation. Stefanou
(1987) derived investment rules under capital augmented technical change that evolved
stochastically. But in most studies, uncertainty is assumed to be driven by prices and possibly
by the level of an exogenous output.

We assume that the discount rate is known to the firm but that it is time-varying as in
Sakellaris (1995). Uncertainty is driven by an exogenous output level and input prices that
are stochastic, log-normally distributed, and follow a non-stationary geometric Brownian
motion without drifi. More specifically, theSe assumptions imply that changes in the output

level and input prices are expected to be zero, and have log-normal distributions with

46

independent increments. The output level and prices satisfy the Markov property so that
their next period probability distributions are functions of their current stage only, and
variance of the prediction error increases linearly with the time horizon (e. g. Hamilton 1994).

We begin by deriving the model allowing for a non-zero drift rate to show that the
assumption of static expectations can be made without much loss of generality in our model.
The logarithms of the prices and output are stacked into a vector Z, which follows a simple

Brownian motion':

AZ = p(Z)At + Pv,

where Z = (lnY,an,an)’ = vector of exogenous state variables
Y = output vector
W = price vector for variable inputs
Q = rental price vector for capital goods (4.1)
AZ = change in Z

p(.) = a nonrandom function or a drift parameter
P = any matrix such that 2 = PPl
2 = variance -covariance matrix with diagonal elements of
v = an i.i.d. vector with E(v,) = 0 and E(v,v,’)=IAt

It is implicit in our treatment that expectations are also rational, in the sense that they are
based on (4.1). In Chapter 7 we examine the price and output series and conclude that (4.1)
with zero drift rate can be regarded as a realistic assumption for this application, because it

does not contradict the observed data series on prices, output, and rental rates of land for

 

' The time subscripts have been dropped to simplify notation.

47

Finnish hog farms. Under (4.1), the stochastic decision rules can be derived by using Ito's

lemma as, for example, in Hertzler (1991).

4.2 Timing and Size of Investments

Irreversible investment decisions involve two components: the choice of timing and the
choice of the investment size. Both the timing and size have to be chosen simultaneously.
For example, a firm with a physical plant must decide when to pay the sunk cost of
converting the existing facility into a new one, and how much capacity to build up in the new
plant (Capozza and Li 1994). These kinds of decisions have been modeled in the literature
as binary one-time decisions rather than continuous or incremental capacity replacements and
expansions (e.g. McDonald and .Siegel 1986). But the data available for our analysis,
described in chapter 5 below, do not allow us to identify a binary one-time decision problem.
For example, a building investment observed in the data may be a partial replacement and/or
enlargement of the existing facility, or it can be a completely new plant. In addition, the
investment expenditure may have been spread over several periods as a result of the
adj ustrnent costs that are increasing in investment. Therefore, we model investment as an
incremental decision, but we allow for optimal choices of inaction, i.e. zero investments. But
still, investment decisions are assumed to be made simultaneously. In other words, farmers

decide simultaneously between the choices to take no action, or how much to invest.

48

The marginal condition for Optimal disinvestrnent or investment does not hold at zero
gross investment. It is optimal to choose zero investment if the shadow price of the installed
capital is between the marginal revenue from disinvesting and the marginal cost of investing
(including the cost of killing the investment option). In other words, if neither disinvestment
nor investment would yield the highest expected discounted net returns, farmers will
postpone investment decisions and choose zero gross investment. Hence, it is likely that the
optimal investment rules have a corner solution at zero gross investment, primarily due to
potential irreversibility.

The optimal size of an investment, on the other hand, is analyzed as an incremental
decision. The marginal conditions for optimal investments are assumed to hold whenever
gross investments differ from zero. In other words, at the optimal level of positive investment

the shadow price of the installed capital equals the marginal cost of investing.

4.3 Intensity of Use and Depreciation

Use and decay characteristics of capital goods differ because the optimal intensity of use, or
the optimal service extraction rate, is decided repeatedly once the good has been purchased
and installed. In other words, the optimal extraction rates and decay pattems of capital goods
vary over time, even if purchases themselves are lumpy and irreversible. Robison and Barry
(1996) distinguish four groups of capital goods according to their decay characteristics and

flexibility in use. We consider here two of them. They are (1) goods for which decay depends

49

primarily on time, and (2) goods for which decay depends on both time and service
extraction rates.

In our application, buildings and drainage (and land) fall into the first class of
durables. They are worn out primarily by time and it is typical that the marginal costs of
extracting services are low, or even zero. As long as marginal services have positive value,
services are extracted from these durables at the full capacity. Therefore, we assume that
services are extracted fiorn buildings, drainage, and land at a fixed rate and they depreciate
at a constant geometric rate. This assumption can be made without much loss of generality.

Machinery, on the other hand, falls clearly into the second class of durables so that its
depreciation is a function of both time and intensity of use. Machinery wears out faster the
higher the extraction rate is. The optimal extraction rates may vary over time with the actual
decay so that the extraction rates for an aged machine differs from those of new machinery.
The optimal extraction rates may be further influenced by output prices and input prices.
Therefore, a fixed depreciation rate for machinery is a strong assumption that cannot be made
without loss of generality. Nevertheless, with the data available for our analysis we cannot
control for machinery's actual service extraction rates. Hence, we assume a constant
geometric depreciation rate for machinery, i.e. that the service extraction rate of machinery

is constant.

50

4.4 Liquidity Constraints

It may be claimed that farmers' access to credit has been rationed for two reasons. First, until
1985 the Finnish credit market was organized so that interest rates for loans were set below
the market clearing rates. At these loan rates, there Was excess demand for loans, and fimrs'
access to credit may have been rationed by restricted credit approvals. Credit market
liberalization began in 1985.

Second, farmer access to credit may have been rationed over the whole study period
by asymmetric information, or by asymmetric payout and payoff of risky credit between the
borrower and lender. As an extreme case, when a firm's survival is at stake, the firm has an
incentive to increase borrowing as long as the lender approves funding (for more details, see
Robison and Barry 1987). Because the firm's cash flows determine its ability to meet debt
obligations, one can conjecture that the access to credit may have been rationed for firms
with high liabilities relative to their gross returns.

For studying the effects of credit rationing we exogenously partition the sample into
four partitions according to two factors: credit market regime and the firm’s liabilities to
gross returns ratio. In other words, the credit constraints are not formally imposed in our
optimization problem and economic model, but we informally check whether the estimation
results are robust to the changes in the credit regimes. Zeldes (1989) has used similar

methods for studying liquidity constraints.

51

4.5 The Optimization Problem

The optimization problem could be stated and solved by two different techniques: contingent
claims analysis or stochastic dynamic programming. In most applications, however, they both
give identical decision rules, although they make different assumptions about discount rates
and financial markets (Dixit and Pindyck 1994). In contingent claims analysis, the discount
rate is a risk free rate by definition. In dynamic programming, on the other hand, the discount
rate is exogenously given and cannot necessarily be interpreted as a risk free rate. Contingent
claims analysis requires assumptions on the structure of financial markets for trading risks
as a bridge for deriving the decision rules but the dynamic programming approach requires
no such assumptions. Although the seemingly more restrictive assumptions of contingent
claims analysis can be made without loss of generality, we chose here to use stochastic
dynamic programming. For analytical convenience, a continuous time formulation is used.
A discrete approximation is made later to fit the decision rules to the data. This approach is
standard in dynamic dual models.

Risk neutral farmers are assumed to minimize a sequence of discounted production
costs conditional on a set of state variables, which includes the current capital stock, output
level, and input prices. We partition the set of the state variables into two vectors K and Z.

The vector K is the capital stock controlled through gross investment I. The vector K also

includes labor that is controlled through net changes in labor input I:. The vector Z was

defined previously in (4.1). The optimal value function is defined as the minimum of

discounted cost over the infinite future time horizon:

52

J(ZO,K0) =minlE0 fe'"{C"(W,Y,K,1)+(U+y)Q’K}dt ,
0

subject to (4.1)
AK = (I - 6K) At
Zo, K0 given

where (4.2)
capital stock
gross investment

expectation conditioned on information at time t
discount rate

instantaneous variable cost function

identity matrix

diagonal matrix of parameters

diagonal matrix of constant depreciation rates

OP<QC3N~D1N><
II II II II

The instantaneous variable cost function is defined aszz

C“ = rninx {W’Xz F(X,Y,K,1)=O}
where

F = transformation fimction with usual regularity conditions
X = demand for variable inputs

The variable cost fimction, C”, accounts for internal adjustment costs through the technology
constraint F (. )=0. The transformation function is augmented by gross investment because,

under the adjustment cost hypothesis, scarce resources need to be withdrawn from production

 

2 The regularity conditions on F(.) are usually stated as: F(.) is continuous, twice

differentiable, and convex in I; Strictly increasing in Y; and strictly decreasing in X, K, and
absolute value of I.

53

to install new capital stock (Lucas 1967). Therefore, even if production is increasing in the
cap4ital stock it can be decreasing in gross investment. In turn, costs are increasing in
investment at a given output level. Therefore, the solution to the instantaneous cost
minimization problem is a function of both capital stock and gross investment. Variable costs
are decreasing in the capital stock but increasing and convex in investment (Epstein and
Denny 1983).

A wedge between purchase and sales prices of capital goods is captured by the diagonal
parameter matrix 7, which is allowed to differ from zero only within the regime of negative
investments or negative changes in the labor input. The sales price of a good is expected to
be less than or equal to its purchase price (Arrow 1968). Therefore, we expect that

y < 0, for all AK < 0. It will become clear from the optimal decision rules below that

nonzero elements in 7 imply adjustment rates which are asymmetric in investment.

4.6 Necessary Conditions for Optimality

To derive the necessary conditions for a minimum, we start with the principle of optimality
and Bellman's equation, which has the following form at time to (Kamien and Schwartz

1991)3:

 

3 All subsequent equations are subject to the constraints in (4.2) and the definition for C.

54

t0+At
J(t0,20,1<0) = min, 150 f C(Z,K,I,y)dt + J(t0+At,ZO+AZ,K0+AK) ,
’o (4.3)

where C(Z,K,I,Y)=C "(W,Y,KJ)+(U+Y)Q ’K

Next, assume a constant control, I, for a small time period At, which implies a constant C
over At. Then, the integral on the right-hand side of (4.3) equals the product (or area) CAt.

Further, expand J(t0 + At, 20 +AZ) and use Ito’s lemma, which results in:

. J = min,E{CAt +J+ J,At + VZJAZ + VKJAK + -%(Pv)’(VéJ)(Pv) + h.o.t.} ,

where J, = aJlat
VZJ Gradient of J with respect to Z evaluated at (t0,Zo,Ko)
VKJ Gradient of J with respect to K evaluated at (to,Zo,K0)

VéJ = Hessian of J with respect to Z evaluated at (t0,Zo,Ko)
h.o.t = Higher order terms which approach zero as At-0

(4.4)

Subtracting J from both sides of (4.4), dividing the result through by At, and rearranging

gives:

-J,=min,E{C + VTILAA? + VKJg 1

+ _ I _1_
At 2(Pv) (VEJXPV) At l (45)

55

where -J, = — aJ / a: = rJ . The left-hand side of (4.5) equals rJ, because the time variable

t appears in J only through the discount factor e'”. Finally, take expectations and take the
limit as At~0 to get the fundamental partial differential equation obeyed by the optimal value

function ‘:

rJ = min,{C + Vz/MZ) + VKJU-fiK) + %1V86(V§J)l’lVeC(2)l }

= min,{C + E[aJ/az]}
(4.6)

where
2 = E[ee’] = PE[vv ’11) ’fi = PP’

= covariance matrix for the error terms in (4. 1)

Equation (4.6) is ofien referred to as the Hamilton-Jacobi-Bellman (HJB) equation. It states
that the optimal value function equals the lowest discounted present value of the sum of four
terms; (1) the immediate cost or payout; (2) the marginal cost from expected changes in
output and prices, multiplied by the magnitude of the expected change in the output level and
prices; (3) the marginal cost of the optimal change in the capital stock multiplied by the
magnitude of the optimal change in the capital stock; and (4) a risk premium which is driven
by the volatility of prices and output. The optimal value function is increasing with volatility

of the output level and prices. The term Vx J is interpreted as a shadow price for installed

 

‘ For some matrix A=(al a2 a3) the vec-operator stacks the columns, al a2 a3, of A into
a one column vector, Vec(A)= (a,' a; a3')'.

56

capital. It measures how many units the expected discounted present value of the firm's cost
stream would change if the amount of installed capital in the firm is changed (ceteris paribus)
by one unit.

Alternatively, the equilibrium model (4.6) can be interpreted per unit of time and the
cost flow can be thought as a (negative) asset with value J. Then, the left hand side, rJ, is
the threshold payout per unit of time, with a discount factor r, for a decision maker to be
willing to hold the asset. On the right-hand side, the first term is the immediate payout. The
expected rate of capital gain or loss consists of the second and the third term. In addition, a
decision maker requires compensation for the risks of holding the asset. The risks are
accounted for by the fourth term on the right-hand side. For example, the more volatile the
prices and output level are, the lower immediate payout is required for a decision maker to
hold the asset.

An optimal value fimction (J), which solves the minimization problem in (4.2),
necessarily satisfies the second order differential equation (4.6). If, in addition, C is convex
in (I,K), the sufficient conditions for a minimum are met (Kamien and Schwartz 1991).
The convexity of C in (I,K) implies that J is convex in K. Nevertheless, convexity is not
required by the mcessary condition for a minimum in (4.2) and we can conclude that if the
integral in (4.2) converges, the optimal decision rules exist and are unique.

It is expected, however, that the optimal investment pattern is discontinuous at zero
investment, which generates kinks in the optimal path of K. The optimal value function (J)

and the shadow price for installed capital (VK J) must, nonetheless, be continuous along

the optimal path of K. The Euler equation is satisfied between the boundaries and, at the

57

boundaries, the Weierstrass-Erdmann Corner Conditions must hold (Kamien and Schwartz
1991). Similar conditions are also called the "Value-matching and smooth-pasting
conditions" for a free boundary optimization problem (Dixit and Pindyck 1994). These

conditions imply that J and V KJ are continuous along the optimal path of K. As a special

case, Abel and Eberly (1994) show that if the instantaneous cost function is homogenous of
degree p in (K, I), then so is J. Therefore, we can conclude that, within the partition of I,
certain differentiability conditions hold between I and C. The regularity conditions for J
can be deduced from the regularity conditions for C.5

This result is important because it allows us to specify a consistent functional form
for J and test the characteristics of C from J. Optimal value functions (J) which are
consistent with the regularity conditions of C, assuming positive gross investments, are

necessarily characterized by the following: 6

(Bi) J is real valued and nonnegative.

(Bin <r+6><vw’-(U+v)Q-<vz,.nu<2)«Vic/>1?--;-VK[Vec(V:I>’Vec(2)]’<o

—*

The local dual relationship between the optimal value function and the instantaneous
fIlr'iction has been proven by McLaren and Cooper (1980) and by Epstein (1981).

6 In the detenninistic case with p.(Z)=0, the differentiability conditions for positive gross

inVestment are given in Epstein and Denny (1983). Condition (B.vi) follows, for example,
Abel and Eberly (1994). A prime superscript, an asterisk, and a dot refer to the transpose, the
optimal value, and the time derivative.

58

(vxn’w

rwt - (Val) M2) — (VKYDK ‘ - -;-Vy[Vec<Vén’Vec(z>]’> o,

where K ‘ is given by (4.11) below

(B.iii) J is nondecreasing and concave in (W, Q).
(B.iv) Well defined optimal decision rules exist and take the form given in (4.11),

i.e. the integral in (4.2) converges.

(B.v) The optimal decision rule 1" =K * +6K defines a unique, globally stable

steady state K(Y,W,Q) for capital stock.

(B.vi) J is positively linearly homogenous in prices (W. Q)

Property (B.i) is self—evident. Properties (B.ii) are obtained by differentiating (4.6) with

respect to K, I and Y, rearranging, and using the properties of C. They are duals to

VKC"’< 0, V,C’> 0, and V,C’> 0. Condition (B.iii) follows immediately, if C is convex

in I and concave in W. By adding the conditions (B.iv) and (B.v) the optimization problem
has a bounded continuous solution for K given by the optimal decision rules. Contrary to
static models, condition (B.v) requires third order curvature conditions for guaranteeing
that the first order conditions result in a global minimum in (4.2). Under static price

expectations, these third order conditions are satisfied if the shadow prices for installed

59

capital are linear in prices (Lemma 1 in Epstein 1981). We will return to a discussion of
conditions (B.v) in the context of our model in more detail below. With an instantaneous
cost function that is positively linearly homogenous in prices (W, Q) condition (B.vi)
follows from the result of Abel and Eberly (1994f.

The condition (V KJ)’ < 0, for all I > 0 in (B.ii) can be generalized. First differentiate

(4.6) with respect to I and then add the complementary slackness condition to get

[[VIC’+VK.I’] = 0, for all I

which, within the partition of I , gives the following links between the regularity conditions
of C and J

VKJ’<0,for all I>0, ifV,C’>0
VKJ’>0,for all I<0, ifV,C’<0

(V,C(I=O)‘)’s —VKJ’s (V,C(I=0)*)’, for all 1 = o

where ' and " superscripts refer to lefi- and right-hand side gradients. In other words, if the
Optimal investment is positive, the discounted present value of the cost stream (the optimal

value function) is decreasing with the capital stock, and vice versa. Zero gross investment

7 The rental price vector (Q) is related to the purchasing price vector (P) through the
equation: Q=(r+ (DP. When Q is varied in the spirit of (B.vi) the discount rate r is held fixed,
and the variation is driven up by variation in P.

60

is chosen if the (negative of the) shadow price of capital is between the marginal cost of

disinvesting and investing. Therefore, if we observe (V KJ)’ < 0 at 1 =0, then (V ,C(I =0)*)’ > 0

must hold. The value function is decreasing with the capital stock, but the frictions make

zero investment optimal. Similarly, if (V KJ)’ > 0 at [=0 then(V,C(I=0)‘)l < 0 holds. The

value ftmction increases with the capital stock but fiictions prevent disinvestrnent.
Following Epstein (1981) and Epstein and Denny (1983), an inverse problem to (4.6)

is:

c = maxQ{rJ - VZJMZ) - vaa—aK) - %1VeC(V§J)]’[Vec(E)] }

There are two differentiability conditions that needs to be clarified for obtaining a unique

solution to this maximization problem. First, if C is convex (concave) in I, then V 1c] must be
concave (convex) in Q. This condition is, nevertheless, always met if VKJ is linear in Q.

Second, because C is concave in prices (Q) the right hand side term
rJ - VZJu(Z) - VKJ(I — 6K) - é—[Vec(szJ)]’[Vec(2)]

has to be concave in prices, too. This curvature condition is met, for example, if

(D.i) J is concave in prices (=B.iii),

61

(D.ii) VZJu(Z) is convex in prices,
(D.iii) VKJ is linear in prices, as above, and

(D.iv) VZZJ is linear in prices.

Condition (D.i) was already set in (B.iii) and condition (D.iii) was set above, therefore,
neither of them adds more restrictions in the model. Condition (D.ii) is always met if u(Z)=0,

i.e. expectations are static. But in the case with nonzero u(Z), (D.ii) is certainly met if both VZJ
and u(Z) are convex in Q. For example, if VZZJ is linearly nondecreasing in prices and p.(Z)
is convex in prices then (D.ii) is satisfied. To see this, suppose we impose VZZJ to be linearly

32.1

nondecreasing in prices, so that —2 = :4: z 0, where (p,- is a nonnegative parameter and i

62,.

refers to the elements of Z corresponding to input prices. Because they are the logarithms

of input prices that appear in Z we can write the convexity condition as (in scalar notation)

saw/62,.) _ at<azJIazE><alnq/aq,)1 _ a[(¢,q,)<q,)1 _ 2
__ - - — (plat. 2 0
aq} aqi aqi

 

Which says that the convexity requirement is met for all (p_i 20.

62

Concerning the requirements for u, on the other hand, the convexity condition can be
made in practice without much loss of generality. For example, a stationary VAR(1) process
or a nonstationary VAR(1) process with unit roots estimated on logarithms of prices will
result in convex [.18. And, as mentioned above, unit roots in the univariate series for prices

will result in a trivial case of VZJu(Z) = 0 no matter what the properties of V?! are.

Thus, the regularity conditions (D) required for a stochastic dual model with rational
expectations do not further restrict the regularity conditions of J compared to its deterministic
and/or static expectations counterparts. Strong restrictions do not need to be imposed on the
empirical specification of expectations either, as long as they follow a VAR(1) process. A
consistent model can be estimated for example with the following properties (D')9:

(D'.i) J is concave in prices,

(D'.ii) u(Z) is convex in prices, i.e. Z in (4.1) follows either a stationary VAR(1) or

nonstationary VAR(1) with unit roots.

(D'.iii) VkJ is linear in prices, and

(D'.iv) VZZJ is linearly nondecreasing in prices.

 

8 We use the approximation Z 2 ZM - 2,. Note that estimating the VAR(1) on levels of

prices results in linear p and, the convexity condition is met in this case for all stationary and
nonstationary series.

9 The regularity conditions discussed in Luh and Stefanou (1996) relate to a profit
maximization model in which the evolution of future prices is nonstatic but known with
certainty, i.e. their model is deterministic. It is straightforward to generalize the regularity
conditions presented here to a stochastic profit maximization problem.

63

It will be shown below that our model meets the regularity conditions (D').

Now the optimization problem and the resulting regularity conditions are set. The
observed optimal decision rules (the investment schedules and the demand for variable
inputs) are derived from (4.6) by differentiating and using the envelope theorem, but first

a functional form must be specified for the optimal value function J.

4.7 Specification for the Optimal Value Function

The optimal value function is a firnction of the capital stock, output, and prices. We specify
the quantity index of capital stock K or, more specifically, the stock of quasi fixed inputs as
having three elements: real estate, machinery, and labor. Output, Y, is aggregated into two
indices: livestock and crop output indices. The logarithms of these output indices are stacked
into a vector lnY. An aggregate variable input is denoted by x, and includes fertilizers, feed,
chemicals, and energy. The price index of the variable input is used as a numéraire, and the
logarithms of the normalized rental prices of the quasi-fixed inputs are stacked into a vector

InQ. Therefore, the optimal value function depends on the following vectors:

K: [khkzr kJJ'
Y: [y/J’zl' InY= [I’WIJm’zl'
Q= [41,612. qJ' InQ= flnql. Inqz. 1an '

Further, the exogenous output level and input prices are stacked into vector Z =[7nY, InQI'.
The optimal value function is assumed to be additively separable from prices and inputs of
other goods.

A quadratic second order approximation with respect to the capital stock (K) and the
logarithm of output and prices (Z) is used as a functional form for the optimal value firnction.
The necessary third order curvature conditions in (D'.iii) are imposed on the model by
assuming that the shadow price of installed capital is linear in prices. With these restrictions,

the optimal value function (J) has the following form

 

 

K A E 0‘ K
J(K,Y,Q) = a0 + a lnY + —;-[K’ lnY’ InQ’]E’ B H InY + Q’M"K (4.7)
InQ _o H’ D, W

We have specified J with an inverted parameter matrix M’, because then the matrix M

aPpears in the optimal decision rules.

To obtain the terms in the necessary condition (4.6), first differentiate the value

flll'lction to obtain the (transposed) gradient vectors:

65

d
‘1
II

x a1 + AK + ElnY + M'IQ

a2 + E’K + BInY + Han

“i

 

a3 + H’InY + 13an + M"KoQ ("'8’
where o = element by element multiplication
(the Hadamard product)
Then, differentiate the transposed gradient VZJ' to obtain the Hessian of J as
B H
V? = H’ D+M"K—a:Q—’
aan2
(4.9)
-1
where M “‘K—a—i-Q— = 60” KOQ) = Diag{(M"KoQ).}
alng2 6an ’

j refers to the j’h element in the vector M "KoQ

Performing differentiation we then get

66

 

 

 

 

B H
q]; milk} 0 0
j:
V2 = 3
”I H’ D + 0 (1,2 mzjlkj 0
1:1
3 —1
0 0 q3£ m3] k]
t I" ll
where m; = (sj)’" element in M '1

Note that VZZJ is linearly nondecreasing in prices (Q), provided M is positive definite. Thus,

the model meets the regularity condition in (D'iv).

4.8 Optimal Decision Rules

The observed optimal decision rules are derived from (4.6) by differentiating and using the
envelope theorem. Substituting (4.1) and (4.7)-(4.9) into (4.6), differentiating (4.6) with

respect to an, and taking expectations results in,

67

7(Vlngl)’ = (VanCy + (VZInQDll(Z) + (Vanll(Z))/(VZJ)I
+ (VKWM + %a Vec(vzzn’Vecmyaan

where (VanCy = (U +y)K®Q

VZWfl = [H’ D+Diag(M"KoQ)j]

VIHQMZ) = Jacobian of u(Z) with respect to an (4-10)

VZJ is given in (4.8)
(VKInQDK = M"K®Q and
6Vec(V22J)’Vec(2)/aan = M "KoQo[o:, 0:2 0:3],

2 _ . . (h . .
ow. — variance of the 1 Input price, q}.

Solving for K we get

K = Diag{qj'1}M[r(V,nQI)/ - (V2,,QDMZ) — mommy/J
1
‘ (U f Y)MK ‘ EKOHI 0:2 Offil

Where Diag{qj_l} is a diagonal matrix with qj as j "’ diagonal element

Then, we pin down the structural parameters in J by assuming static price and output
expectations such that 2 follows a simple Brownian motion without drift. In other words,

we set u(Z) = V1,,QMZ) = 0. Although, the parameters in u(Z) could be identified in the

68

price and output equations (4.1), the decision rules (equations for K) do not provide any

overidentification restrictions for testing whether the expectations follow (4.1) or not. The

reason is that the three terms r(V,nQJ), (Vang/”1(2), and (Vanu(Z))’VZJ are all functions

of Y, Q, and K. Technically, we could obtain over identification restrictions, for example,

through imposing a specific functional form for u(Z) , but it would not be good

econometric practice, and it is not exploited here, because we could not distinguish
between misspecified expectations and misspecified functional form.

Now, it is easy to see that by allowing for u(Z)¢0 we would only split the parameters
which multiply Z in the decision rules into two fractions. The sum of these two fractions,
however, would remain unchanged no matter how we split the parameters into these two
fractions. Furthermore, partial derivatives and elasticities of the decision rules with respect

to Z would remain unaltered by the specification of u(Z).

There are no overidentification restrictions for testing the parameters

2 2

2 2 2
41",

o qz , and 0:3 inthe term - %K0[oq, oqz owl either. Nevertheless, this term can be
used for modeling an identified regime shift in which we observe a persistent shift in
uncertainty. In other words, by using properly defined dummy variables we can model

how the conjectured increase in uncertainty at the beginning of 1991 has affected farmers’

investment behavior.

69

By making substitutions for VInQJ, VZanJ’ V2.1, Z, and u(Z) , and by collecting

terms, we obtain

K = Diag{qj'l}M(ra3 + rH’lnY + rDan)

+ U- U+ MK
(r ( Y) ) (4.113)

1 2 2 2

Note that aij/ao; = 6k]. < o for all j= 1,2,3 in (4.1la), and optimal investment decreases

with the volatility of own price. In other words, volatile capital prices slow down capital
expansion. Also note that the matrix M multiplies the price effects. Therefore, if the
elements of M are small but they exceed r, the capital stock will adjust slowly towards its
steady state level and demand is inelastic in the short run with respect to changes in prices

and output.

In the deterministic case with static expectations, such that p]. = 0 for all j and with

the assumption of 7 =0, the optimal investment schedules coincide with the widely used

constant coefficient multi-variate flexible accelerator of the form K = (rU - M) (K - K) ,

where (rU - M) and K stand for a matrix of adjustment rates and a steady state capital

stock.

7 O
The demand for the numéraire input x is solved from the HJB-equation. Recall that

with only one variable input, x, which is used as a numéraire, the instantaneous cost

function C" equals x. Then, the HJB becomes"):
. , 1
rJ = x + (U+y)Q’K + VZJu(Z) + VKJK + —2—[Vec(V§./)]’[Vec(2)],

where K ‘ refers to its optimal value. By solving the HJB for x we get:

x = rJ — (U+Y)Q’K - Velma - VKJK‘ - g-[Vecfim’U/ecmn.

which is rearranged further by making the familiar substitutions for VWI, VZanI’ V2], Z,

and u(Z) as in (4.11a)“:

x — “so + a1/(rK-K') + azllnY + a3/an

+ K’A(%K-K') + InY’E’(rK-K')

(4.111))
+ éInY’BlnY + InY’H(an -1) + %InQ’D(InQ - 2),

where 0x0 = an intercept

 

‘0 The equation is subject to the same constraints as (4.6).

“ Constant terms are included in the intercept and, therefore, am is not the same as a,, in J.

71

The economic model consists of four decision rules (4.11): net investment on real estate, 15,;
net investment on machinery, 152; the change in the labor input, L; and the demand for the

numéraire input, x. For fitting the model to data, the discrete approximation K, = K,+1 - K,

is used. The net investments, K, are solved further for gross investments, 1, by using the
equality i, = If, + 61k, , for j=1,2. The term 6 refers to the geometric depreciation rate as

above.

The decision rules are given in terms of the structural form parameters that appear in
the optimal value ftmction, J. Thus, the parameter estimates can be used for testing
hypotheses that are linked to the characteristics of the instantaneous cost function through
the conditions given above. The decision rules also give a direct way to make inferences
about the short-term investment responses and long-term responses of the capital stock. We
can also compare the observed and steady state capital stocks and, assuming the increased
policy risks are realized through increased volatility of prices, the response of the
investments on the conjectured increase in policy risk can be tested through the parameters
of price variances in (4.11a). We now move on to the technique for estimating the optimal

decision rules, which is presented in the next chapter.

Chapter 5

ESTIMATING THE MODEL

This chapter describes econometric estimation of the decision rules given in the preceding
chapter. We first characterize the assumptions underlying the model, and then move on to
the statistical specification of the decision rules. The last section gives a detailed description
of the estimators, concluding with the likelihood function used for estimating the decision

rules.

5.1 Assumptions Underlying the Model

The statistical model is constructed under three specific assumptions which allow the
decision rules to be estimated separately from the output and price equations. This reduces
considerably the computational complexity of the estimation procedm'e. The assumptions are
justified by obtaining a feasible estimation procedure and, in particular, a statistical model
that was found to converge.

First, we assume that the output and price series follow a nonstationary geometric

Brownian motion without drifi, i.e. we set u(Z)=0 in (4.1). An autoregressive model and the

72

73

ordinary least squares technique (OLS) will be used for testing whether the observed output
and price series show strong evidence against the null hypothesis of zero drifi. The testing
procedure is discussed in Chapter 7 together with a report of the results.

Second, we assume that the error terms in the decision rules are independent of the
error terms in the transition equations. These covariance restrictions are maintained without
testing, because it was not possible to estimate the transition equations jointly with the
decision rules. This may reduce the efficiency of the estimates but they remain consistent.

Third, with regard to the parameters measuring volatility of the input prices, we model
only a regime shift, i.e. a single persistent shift in uncertainty, which occurred at the
beginning of 1991. As explained in the preceding chapters, it seems likely that price
uncertainty increased at the beginning of 1991 when the debate on Finland's possible entry
to the European Union started. The effects of this increased uncertainty on farmers’
investment behavior are modeled and tested through dummy variables over the period

1991-93.

5.2 Specification of the Decision Rules

The equations for the net investments Ii, and k, are solved for the gross investments
i1 and i2 using the equalities i, = If, + 6,, for j = 1,2, whereois the geometric depreciation

rate. There are four decision rules corresponding to the choice of real estate investment, i ,;

74

machinery investment, i2; change in the labor input, L; and demand for the other inputs (the

numéraire), x. As explained in the chapters above, the optimal decision rules have both
discrete and continuous characteristics. We observe positive values and zeros for gross
investments in real estate and machinery. Strictly speaking, the zero investments do not result
from data truncation or censoring, but from the frictions that make them optimal choices.
Nonetheless, our statistical model coincides with a model for censored data and has the same

structure as a simultaneous Tobit model with two censored variables, i1 and i2. The change

in the labor input, on the other hand, has both negative and positive observations but no
zeros. We model the labor changes and the demand for the ntunéraire input assuming they
are continuous in the state space, and observed without limits. Therefore, the estimating

equations are

’1 = 26,, +81

1, =1, tft,>0

0ifi1‘50

’2 = 26:2 + .92

i, = i; ifi2’>0
= 0 ifi,‘ s 0 (5.1)
L = Z—OIH:3

x = (Z,i,,i2,I:)0x + t:4

where Z = g(Z,k,,k2,L)
g is a function
6,], 6,2, 6,, and 0,, are subsets of the parameters
in the optimal value fitnction J

75

and where the terms i l‘ and i; refer to the latent form investments, which are uncensored

but not observed. The uncensored latent form investments have an interpretation as desired
investments. That is, the latent forms refer to the optimal investments under a hypothetical
condition in which the frictions, driven by uncertainty and fixed adjustment costs, were not
apparent'.

For later purposes we simplify the notation by partitioning the decision rules into two

sets: I = (i,,i2), (or 1‘ = (i,‘,i2') ), and X = (£,x).The partition] has the variablesthatare

bounded to be nonnegative. The partition X, on the other hand, has only continuous variables
that are unlimited in their range.

In our notation, the same set of exogenous variables appears on the right-hand side of
each Equation (5.1). Exclusion restrictions, implied by the economic model, are imposed by
setting the appropriate parameters to zero. Equations for the censored investment demands
have neither censored variables nor any other endogenous right-hand side variables. These
exclusion restrictions guarantee that the model is internally consistent and a unique solution

is identified for both investment demands. 2

 

‘ The standard adjustment costs that are convex in investment result in investment smoothing
but do not result in zero investments.

2 If the censored investments appeared in the right-hand sides of the investment demands, we
could get two reduced form solutions for i, and none for i2, or vice versa, unless certain
inequality restrictions were imposed on the parameters For more details, see Schmidt (1981).

76

The equation for x has three endogenous right-hand side variables, i ,, i 2 ,and 1:. But

all of the elements in 6}, are identified by the parameter restrictions between and within the
equations that are, again, implied by the economic model. Note that it is the observed

investments, not the unobserved latent form investments, which determine the endogenous

treatment effect in the demand for x. The treatment effect is linear in i ,, i 2 or I: , but it is not

constant. It interacts with the firm's current output and capital stock, including labor (see

Equation 4.1 lb).

5.3 Estimators

The model can be estimated consistently by two different classes of methods: (1) by the two-
stage method; or (2) by full information maximum likelihood methods (F IML). The two-
stage method, originally suggested by Heckman (1976), can be applied to a wide class of
models using standard estimation techniques. It can provide consistent estimates for complex
problems even under certain nonstandard assumptions. 3

Heckman's method could be used to estimate the investment decisions if they are
conceived as a two stage decision. The endogenous choice of regime, i.e. whether to invest

or postpone investment, could be modeled first as a binary choice and estimated by the

 

3 For example, a serially correlated, heteroscedastic, or nonnormally distributed error term.
The Tobit MLE is inconsistent under heteroscedasticity or nonnormality (Amemiya 1985).

77

maximum likelihood technique. Then, at the second stage, the decision "how much to invest
if you decided to invest in the first stage" could be estimated by a least squares method, with
correction for the bias caused by the endogenous regime selection. The nonstandard
assumptions mentioned above apply to the second stage estimation only. Obtaining
consistent parameter estimates by the two-stage method is relatively straightforward and can
be done by most econometric software. Nevertheless, obtaining the correct standard errors
for the parameter estimates requires complex computations which are not usually given in
standard software output. The reason for this is that the inverses of the Mills ratios, which
are added as regressors in the second stage estimation for correcting the selectivity bias, are
not observed in the data They are estimated, which should be accounted for when computing
the standard errors in the second stage.

If the FIML method is used, the investment decision can be modeled as a simultaneous
decision such that the decisions "invest or not" and "how much to invest" are made
simultaneously. Under the assmnption of a normally, identically, and independently
distributed error term (Normal i.i.d.), the FIML provides estimators that are efficient among
all estimators (Amemiya 1985). The FIML method will be used in the study.

We assume the errors {eI , e, , e3, 84} are i.i.d. drawings from a multi-variate Normal
distribution with zero mean and a symmetric (4x4) covariance matrix 2 whose lower triangle

is given by4

 

4 The normality assumption will be tested below by a general test for misspecification.

78

 

 

 

 

2
C’1
2
2:1 021 02
E = = 2
(5.2)
. 2
.041 042 043 04,

where the matrices 2, (23:2) and 22 (2xZ) correspond
to the partitions I and X

In other words, we assume the demands for i ,, i,, L, and x are i.i.d. drawings from a multi-
variate normal distribution with means Z 0,,, Z02, Z0,,, and (Z,i,,i2,£) 6x, and with a

covariance matrix 21.

Denote a density function by f(.) and the corresponding cumulative density function

by F"(.). Then the joint densities for the partitions I ‘ = (i 1', if) and X can be decomposed

into three equivalent products of conditional and marginal densities 5:

 

5 Rigorously, all densities are conditioned on a set of variables, but the terms marginal or
conditional density are used if the conditioned set excludes or includes endogenous variables.

79

f"(XJ‘|Z_,6) = fd(X|Z—.0)f"(1‘lX.Z—,6)

= Purim/do; IXievdti; liz‘xie)
_ _ _ 5.3
= f"(X|Z,0)f"(i{IX,Z,0)f"(i2‘|i{.X.Z.6) ( )

where 0 = a set of parameters

The vectors Z and X are observed for every observation in the sample, but i 1' and i2. are

observed only when they are greater than zero. When constructing the likelihood function,

the unobserved latent form variables, i l’ and i2. , are replaced by their observed counterparts

il for all il‘>0 and i2 for all i2'>0.

As explained in the preceding chapters, the data are endogenously partitioned into

four investment regimes, which are:

(1) i,>0 and i,>0
(2) i,=0 and i,>0
(3) i,>0 and i,=o
(4) i,=0 and i,=o

Then, incorporate the investment regimes and the cumulative distributions which measure
the probabilities for negative latent form investments, i.e. for observed zero investments,

into (5.3) and get the density 6:

 

6 This is a special case of the models in Maddala (1983).

80

mm) = f"(X|Z—,6)

f"(1|X.Z_,6)"'>°"">°]
{fd(i2IX.Z_.6) Fd(i1‘<0Ii,,X.z'.e>}“'”"2“"
{f"(il IX,Z_,6) F d(i,‘<o | i,x,Ze)}"'>°"’2‘°‘ (5.4)

Fd(i.‘<0.i;<0IX.2".6)""°""2="

1 if the statement is true

where [.] = {

0 otherwise

Then, substituting the normal density and cumulative density functions into (5.4) and taking
logarithms result in the loglikelihood function for an individual observation. The frmction

is:

t = a. +{i.>01[i2>0102 + [it =oui2>0103 + [it>0][i2=0194 + lit=01li2=019s (5.5)

81

where t, is the logarithm of the normal joint density of X conditional on Z 7:

01 - --;-1nI22I - -;:(X— E(X|Z))’2;' (X— E(X|Z))

 

 

_ E(LIZ) Z9,
where E(X|Z) = _ = _ _ _ ,_
E(xIZ) (Z.E(i,IZ),E(i2|Z),E(LIZ))0,
130,12) = «Kiev/epic, + o,¢(Ze,./o,) for j = 1,2
(F(.) = standard normal cumulative density firnction (cdf)
¢(.) = standard normal density fimction

And 02 denotes the logarithm of the normal joint density of I conditional on X and Z:

02 = ' é—lnlz, " 2llzzilzrzl
l I —r -1
- El] - m,y[2:, - 2,22, 2,2] (1 - m,)

where m, = [Z6,, Z0,2}+2;225l(X‘E(XlZ_)l

 

7 Conditional densities have been computed following Maddala (1983), Amemiya (1985),
and Hamilton (1994). The constants not affecting the maximization have been dropped.

82

The term 03 is the logarithm of the normal density of i2 conditional on X and Z plus the

logarithm of the normal cumulative density function of i, conditional on i,, X and Z

evaluated at i ,=0 and i 2> 0:

t, = - We: {as 02.12: [.,, 0241)

’ l(i2 ' "'2! flog - [023 024l224 [023 024,)4
2
+ ln<I>(- "7120:12)

where m21 = Z6,, + [023024]251(X‘E(Xl2)l

12 26,2

"'12 = 26:1 + [012 013 014](2-1)-1 _.
X- E(X|Z)
012

2 _ 2 -1
Om12 _ O, _ [012 013 014](2-1) 013
b014d

 

 

l' 2 W
02 023 024

_ 2
2-1 ‘ 032 03 034

 

 

83

The term 04 is similar to 03, but variables and parameters are switched. Thus, 0,, refers to the

normal density of i, conditional on i2 and Z plus the normal cumulative density fimction

of i 2 conditional on Z evaluated at the regime, in which i ,>0 and i 2=0z

c4 = - 37:11:10? {0.0.4125'10130141)

- élil " mulzlol — [013 014,224 [013 chill—l

+ 1n <I>( - "220322)

where mll = Z0,, + [0,3 0,4]22-1(X-E(XlZ—))
i, —Ze,,

"’22 = 26:2 + [021023 (324](“-“-2)-l _
X ' E(X|Z)

(’21

2 _ 2 -1
Om22 ‘ O2 - [021023024](2-2) 023

 

 

024 .

L
. 2 .
o, 013 014

_ 2
23-2 ’ 031 03 034

2
o 04‘

l.

O

 

 

41 43

84

The term 0, refers to a bivariate cumulative normal density for I], and i2 conditional on

X and Z evaluated at i1 = 0 and i2 = 0:

_ 3 _ -l _ —1
05 ‘ (I) l mnomn’ leOmIZ)

where (1)3

standard bivariate normal cdf

2 2 -1
anti] ‘ Or ‘lors 0,4]22 {013014}

2 2 -1
°m21 ‘ 02 ' [023 024]22 [023 024}

For obtaining the sample loglikelihood function, Equation (5.5) is summed over the
observations. The loglikelihood function is maximized using GAUSS software with the
Constrained Maximum Likelihood (CML) routine. Now, the statistical model is set, and the

next chapter explains the data used for estimating the model.

Chapter 6

DATA

This chapter discusses data sources and provides graphs and summary statistics for the data.
The optimal decision rules were defined in Chapter 4 as functions of input prices, output
level, and the capital stock, including labor. All price indices except land are obtained from
the index series of the Agricultural Economics Research Institute (AERI) at Helsinki, or
from the index series of the Statistical Office of Finland. Each series has one observation a
year and they are chain-linked Laspeyres indices, so current prices are used as a base in
estimating the rate of growth to the following year.

The farm level data on investments, capital accumulation, output levels, and variable
input use are from Finnish bookkeeping hog farms over the period 1976-1993. The
bookkeeping program is managed by AERI and surveyed by the county extension offices.
The data are summarized by annual income accounts and by balance sheets at the beginning
and at the end of each year.

The panel data span 18 years, but the panel is not balanced. The duration of each
farm’s participation in the program over the study period varies as shown in Figure 6.1. The
total number of farms in the data is 316, but only 23 farms participated in the program over

the entire study period. The 41 farms that participated only one year were dropped from the

85

86

Number of Farms
30 *7 , pf

25'

llllllmllhml

2 3 4 5 6 7 8 9101112131415161718

Years in the Sample

 

20

O

5,.

kl!

O 1
Figure 6.1. Frequency of the Farms' Duration in the Sample'.

sample, because we could not construct lagged variables for those observations. Hence, we
were left with 275 farms. The average number of observations per year is 137, varying
between 83 (in 1976) and 169 (in 1988). The total number of observations is 2,470, but
1,928 observations are used in estimating the decision rules.2

Not all the quantity and price indices needed for estimating the economic model are

observed directly. But the unobserved indices are computed and aggregated from more

 

‘ The duration of one Year has been eliminated and the duration is censored from the right
by the number of sampling years.

2 Some observations were dropped from the sample. For example, we could not compute
lagged values for all of the observations in the original data set, because the panel data were
not balanced.

87

micro observed quantities, expenditures, revenues, and price indices. The data and the

computation of the variables in the economic model are described in detail below.

6.1 Price Indices

6.1.1 Real Estate

Real estate is aggregated from three component goods: land, buildings, and drainage.
Because there are no data on quantities of the component goods, except for land, a Divisia
price index for real estate was computed using the expenditure shares and prices of the

component goods. In addition, the price for land is not observed and must also be

estimated.

Price of Land
Average annual rental prices and discount rates are used to value land, because land trading
transactions data are insufficient to determine reliable purchase prices of land. The data
have 1,326 land leasing cases, varying from 42 to 93 per year, but there are only 135 land
purchasing cases. In every leasing case the sample farm was a tenant, not a lessor. The
average leased area per tenant was 12.0 hectares. Across all the sample farms, the average
leased area was 6.42 hectares and 19.2 % of the arable land area.

No information about the characteristics of leasing contracts is observed, but most

leasing cases are expected to be cash leases with predetermined lease payments. In 1991, for

88

example, only five percent of land leased in Finland were share leases or leases in which
payments were made in kind (Ylatalo and Pyykkonen 1992).

The average nominal rental price of land over all farms and the entire sample was 831
FIM per hectare. The price increased from 400 to 1,400 F IM per hectare between 1976 and
1990, and thereafter, it had a downward sloping trend. In 1993 the average rental price was
1,130 FIM per hectare. The main trends in the purchase prices have been similar to those of
the rental prices, but the purchase prices have been more volatile than the rental prices,
partly because the data have substantially more leasing than trading transactions
(Figure 6.2) 3.

The rental price over purchase price ratio is, on average, 0.049, suggesting an average
4.9 % discount factor if zero capital gains are expected. The ratio is consistent with the
average real market interest rate (5.0 %), which will be characterized in section 6.6 below.

Therefore, the annual average price of land (Ql l) is computed simply as

Ql , = (Total Rent Payments F IM),/0.049*(Total Hectares Leased),.

Note that the same price is used for all land. Thus, the price is exogenous for each farm and

it measures average market prices of land.

 

3 The land trading transactions are discussed in the section on investments and capital
accumulation.

89

 

Index
4

 

 

 

0-5 4%4+%%+4+41stttt
76 78 80 82 84 86 88 90 1993
Year
RentalPriceIndex

........... ... Purchase Price Index

 

 

Figure 6.2. Rental and Purchase Price Indices for Land (Base Year =1976).

The Divisia Price Index for Real Estate

The price of land and the building price index are aggregated by the Divisia technique to
obtain a price index for real estate. The building price index is computed by the Statistical
Office and it is used for valuing both buildings and drainage systems. The Tbmqvist

approximation of the Divisia price index for real estate (Q,) is computed as ‘:

 

4 For a detailed derivation of the index see e.g. Chambers (1988 pp. 232-239).

90

1 2
log(Q/Q,-,) - 32(6), + S,.,_,>(logq,, - logs.-.)

Fl

where Q, = Divisia price index at time t
SJ, expenditure share of good j at time t
q,, price of good j at time t
. _ l for land
1 -{ 2 for buildings and drainage

(6.1)

The expenditures are computed as a sum of interest and depreciation. The average share of

land expenditure in total real estate expenditure was 61.0 %.

6.1.2 Other Price Indices and Normalization

The price indices for machinery, feed, fertilizers, fuels, and electricity come from the index
series of AERI. The price index for labor is computed by the Statistical Office. It follows
the annual average wages paid to agricultural workers.

The feed, fertilizer, fuels, and electricity indices are aggregated to a Divisia price
index for an aggregate variable input by using similar technique as above in the case of the
price index for real estate (Equation 6.1). The variable input is used as a numéraire and all

prices are normalized by this index. The normalized price indices are presented in Figure

6.3.

91

Index

 

1.6 r

 

0.4 4

 

 

 

O
76 78 80 82 84 86 88 90 1993
Year

Real Estate

 

................. Mach inefy

....................... Labor

Figure 6.3. Normalized Price Indices for Real Estate, Machinery, and Labor (Base
Year=1976).

6.2 Investments and Capital Accumulation

6.2.1 Real Estate

The accumulation of real estate was computed by farm in three steps:

1. The accumulation of the nominal values of the component goods (i.e. land,
drainage, and buildings) were computed through their initial book values,

investment expenditures, and depreciation. More specifically, the first observed

balance sheet value of good j, K,’;, for each farm was taken as a base value for

92

constructing the nominal series of the capital stock in the good j and, then, the
value at the beginning of the following period, K]; 1 , was computed through the

transition equation:

193,, = 1,”; + (1 —6,)K,f; , for j = 1,2,3 (6.2)

where 1,: stands for the nominal gross investment expenditure and a, is the

depreciation rate. The resulting value of the good, Kfi, , was then used as the

initial value for the next period.

The resulting values of the component goods were aggregated into a nominal
value for real estate. Similarly, the investment expenditures of the component

goods were aggregated into the expenditure on real estate investments.

The quantity indices of real estate and investments in real estate were obtained
by dividing the nominal real estate values and the investment expenditures by .

the price index for real estate.

93

Land

Land and its accumulation are measured in terms of the capital stock in owned land. Leased
land is excluded from the capital stock, because it is interpreted as a means of postponing
investments in land, rather than as a long-term commitment that may be irreversible.

At the beginning of 1976 the average farm size in the sample was 29.8 hectares of
arable land. On average, farrns owned 23.9 and leased 5.92 hectares (Figure 6.4). The
average areas purchased and sold over the study period were 6.22 and 0.260 hectares per
farm, and so the average farm size increased by 5.96 hectares. Farms entering the
bookkeeping program during the study period accounted for 1.68 hectares of the increase in
the average farm size because entrants had more land than the exiting farms. At the end of
1993, the average farm size in the sample was 31.6 hectares of land owned and 5.65
hectares of land leased. The average land area owned in 1993 was 1.32 times the area

owned in 1976.

94

Ha/F arm
40

35 “'-
.
I”.. ”wiuoonm.~¢~..“ “we"
a

....--- -'°‘
.2 ,o-M
3 0 AF“.~I~~I 0’

 

 

25 M: f
20 s ‘

15-,
101,
5,,
0

 

 

A #

 

76 7'8 80 82 84 86’ 88 901993
Year

 

Base Area
.-............ Base + Cumulative Investment

--------------------- ~' Base + Cumulative Investment + Leased

Figure 6.4. Land Accumulation on the Sample Farms.

The sample includes 135 land investment cases, which corresponds to about one
investment per farm over the 18 years. The average investment size was 6.47 hectares. Land
sales were less common than land purchases. Indeed, the sample has only 16 land sales
cases. The average land area sold was 1.84 hectares, and only three sales exceeded two
hectares in area. Areas of less than two hectares could have been traded without a permit for
the purchase, and it is likely that they may have been bought for other than agricultural
purposes, such as housing and recreation.

The average nominal price of land was 18,320 FIM per hectare for purchases and
34,050 FIM for sales. Hence, the price of land per hectare for sales was 1.9 times the price

for purchases. The unplausible discrepancy between purchase and sales prices also supports

95

the view that, in most cases, the land sold by farmers was bought for non-agricultural use.
The observed prices suggest that we should use higher price for land sales than land
purchases, but this would imply that farmers could profit infinitely by purchasing and
selling land. Nevertheless, we rule out the possibility that farmers could profit infinitely by
buying at the low price and selling land at the high price, and drop the rare land sales cases

from the data.

Production Buildings
Accumulation of building capital was computed by transition Equation (6.2) as explained
above. It is likely, however, that farmers have used depreciation primarily for adjusting and
reducing their tax burden, and that observed depreciation is linked more to tax rates than to
economic depreciation. Therefore, the observed depreciation is replaced by a constant
geometric depreciation rate used in the national accounts of economic statistics. A building
is assumed to have 10 percent of its initial value left after being used for 35 years, which
implies a depreciation of 6.4 % a year; 2.5 percentage points lower than the average
observed rate of 8.9 %.

At the beginning of 1976 the average value of production buildings was 50,600 FIM
a farm, which inflated by the building cost index to the year 1993 equals 126,600 FIM. The
average real gross investment expenditure was 19,600 FIM a year (in 1993 FIM). At the end
of 1993 the average value of buildings was therefore 221,000 FIM, which is 1.75 times the

inflated value for 1976.

96

The sample has 758 positive and 17 negative gross investments in buildings. The
remaining 1,695 cases were zeros. Hence, an average sample farm invested in buildings
5.52 times over the 18-year period. The average compounded investment expenditure,

within the positive gross investments, was 64,600 FIM.

Drainage Systems

The value of drainage systems and their accumulation is computed in a similar way as the
accumulation of buildings, resulting in a depreciation rate of 6.4 % per year. The observed
average depreciation rate was 13 %.

At the beginning of 1976 the average value of drainage was 7,680 FIM a farm, which
equals 19,200 F IM when inflated to the year 1993 by the buildings price index. The average
real gross investment expenditure was 3,670 FIM a year (in 1993 FIM). At the end of 1993
the average value of drainage was 38,600 FIM, which is 2.01 times the real value in 1976.

The sample has 378 positive and two negative gross investment cases, leaving 2,090
zero cases. An average sample farm invested in drainage 2.75 times over the 18-year study
period. The average compounded investment expenditure, within the positive gross

investment cases, was 24,300 F IM.

Real Estate
The land, building, and drainage were aggregated into a single capital good, real estate. The
nominal values of this aggregate series was inflated by the price index of real estate. At the

beginning of 1976 the average value of real estate was 819,000 FIM (in 1993 FIM). The

97

average compounded gross investment expenditure was 33,600 F IM a year. At the end of
1993 the average value of the estate was 1,138,000 FIM, i.e. 1.39 times its inflated value in
1976. The annual averages of the inflated real estate values and investment expenditures are
presented in Figure 6.5.

The sample has 1,066 positive and 17 negative cases of real estate investments (Table
6.1). The remaining 1,387 cases are zeros. An average sample farm invested in real estate
7.76 times during the 18-year period. The average compounded investment expenditure,
within the positive gross investment cases, was 78,200 FIM. Nevertheless, the negative
gross investments were dropped from the data, because the number was too small for a

complete analysis, as suggested also by irreversibility of agricultural investments.

 

 

      

 

 

 

 

 

 

 

caPital Investment

1,000 FIM/F arm 1,000 me

1200 1200

1000 ,L 1000 4

800 4 ..---.....---"“"‘ 800 q»

...... r“---—..—W

600 4 600 J-

400 4 400 -.

200 4— 200 4—
0%~*%%%+%1+%1%1##% 0.....t.rt+.r.t.s‘
76 78 80 82 84 86 88 90 1993 76 78 80 82 84 86 88 90 1993

Year Year
Real Estate
..-...--...... Land

Figure 6.5. Accumulation of Real Estate Capital and Investment on Real Estate’.

 

5 The series are inflated to the year 1993.

98

Table 6.1. Negative, Zero, and Positive Gross Investments.

 

 

Number Number Average
Capital of negative Average Number of of positive investment
good cases sales per case‘ zeros cases per case'
Land 16 1.84 ha 2319 135 6.47 ha
Buildings 17 18,200 FIM 1,695 758 64,380 FIM
Drainage 2 7,857 FIM 2,090 378 24,330 FIM
Real estate 17 17,150 FIM 1,387 1,066 78,210 FIM
Machinery 29 37,620 FIM 483 1,958 87,370 FIM

 

' Inflated to the year 1993.

6.2.2 Machinery

Machinery capital and its accumulation are computed in a similar way as for buildings and
drainage, except that a machine is assumed to have a shorter average economic life than a
building. A machine is assumed to have 10 % of its initial value left after 15 years of use,
which results in a 14 % depreciation a year. The observed average depreciation rate was
22 %.

At the beginning of 1976 the average value of machinery was 42,900 FIM a farm,
which equals 132,000 FIM if inflated by the machinery cost index to the year 1993. The
average real gross investment a year was 69,400 FIM (in 1993 FIM). At the end of 1993 the
average value of machinery was 306,000 FIM, which is 2,32 times the compounded value

in 1976 (Figure 6.6).

99

Capital

 

 

 

 

 

 

 

 

 

Investment

1,000 FIM/Farm 1,000 FIM/Farm

400 400

350* 350__

300« 300-_

250~ 250,

200+ 200*

150- 150l-

100» 1004

50+ 50M
0t+41+4e4184+1148 'Oetaettétttttttser:
76 78 80 82 84 86 88 90 1993 76 78 80 82 84 86 88 90 199

Year Year

Figure 6.6. Accumulation of Machinery Capital and Investment in Machinery.

The sample has 1958 cases of positive and 29 cases of negative gross investments in
machinery (Table 6.1). The remaining 483 cases are zeros. Hence, an average sample farm
invested in machinery in four out of five years. The average real investment expenditure,
within the positive gross investment cases, was 87,400 FIM. As before, the observations
with negative gross investments were dropped fi'om the data, because the number of them

was too small for a complete statistical analysis.

100

6.3 Labor

The data on labor input are observed only as a service flow in terms of the hours of labor
services. The data exclude stock measures, like the number of workers and employees hired.
Therefore, labor and its changes are measured by annual labor services and changes in these
each year.

The sample farms' average family labor input was 3,570 hours a year. They hired
labor, on the average, 553 hours a year, which is 13.4 % of the total labor input. The average
labor input had a downward sloping trend over the study period (Figure 6.7). The average
decrease was 30 hours a year. The family labor input did not change much, but the hired
labor input decreased by 38.3 % over the 18 years.

The measured changes in the labor input were not trapped at zero, because the labor
input was measured as a service flow rather than a stock. The annual change in the labor
input was negative in 1,105 cases and positive in 1,365 cases. Among the negative cases,
the average reduction of the labor input was 482 hours. Among the positive cases, on the

other hand, the average increase was 344 hours.

101

Hrs/Farm
5000

4500 ..
4000 W
3500 1a—-~--..-————---------~-~~-..----....--.z—J
3000 --
2500 -t
2000,-
1500 n
1000 -t
500 ,_

0% é+r44+.+e4484

'76 78 80 82 84 86 88 90 1993
Year

 

 

 

 

Total Labor
Family Labor

 

Figure 6.7. Labor Services on the Sample Farms.

6.4 The Numérairc Input

As explained above, the numéraire input is an aggregate of the four variable inputs,
fertilizers, feed, fuels, and electricity. Again, the Divisia technique, similar to Equation
(6.1), has been used for the aggregation. The resulting quantity index for the numéraire

input is presented in Figure 6.8.

102

 

lib/W

0
76 78 80 82 84 86 88 90 1993

Year

 

 

 

Figure 6.8. Index for Variable Inputs, Used as the Numéraire.

6.5 Output

The sample consists of specialized hog farrrrs. The average shares of livestock and crop
output in total agricultural revenue were 83 % and 13 %, which together accounted for 97
% of the total agricultural revenue (Table 6.2). Most livestock revenues were received fi'om
hog production. More specifically, the revenue share of pork, including piglets, was 95 % of
livestock and 79 % of the total agricultural revenue. The crop revenue consisted mostly of

(small) grains (67 %), and about half of the grain revenue came fiom barley.

103

Table 6.2. Average Revenue Shares in the Sample Farms.

 

% of crop % of total % of % of total

Crops revenue agricultural Livestock livestock agricultural
revenue‘ revenue revenue'

Barley 33.5 4.1
Rye 6.2 0.8 Pork 94.7 78.8
Wheat 9.9 1.5 Beef 1.4 1.3
Other grains 17.4 2.3 Milk 1.5 1.3
Oilseeds 6.0 0.8 Chickens 0.6 0.5
Sugarbeets 6.3 0.8
Crops total 100 13.3 Livestock total 100 83.4

 

' Excluding income transfers.

The output data are measured and summarized by two output indices, one for
livestock output and the other for crop output. The livestock output was computed for each
individual sample farm in terms of pork equivalents, because pork accounted for the largest
share of the livestock revenues. The total livestock revenue was divided by the price of
pork, resulting in an index for the output quantity (pork equivalent). Similarly, the quantity
of crop output was measured by barley equivalents. The total crop revenue was divided by
the price of barley. Both livestock and crop outputs have an upward sloping trend (Figure

6.9). The crop output, however, has been more volatile than the livestock output, because of

varying weather conditions.

104

The average livestock output is 42,000 pork equivalents, which roughly corresponds
to a production unit with a 200 pig fattening capacity. The largest production unit in the
sample is estimated to have a 1,300 pig fattening capacity.“

The output data were also summarized by a single output index, which was computed
in terms of pork equivalents. The average value of the aggregate output is 49,000 pork

equivalents.

Kg/Farrn
1 00000

 

80000 _

40000 ,

 

20000 rt

 

 

o ......... . ......
I I I

76 78 8O 82 84 86 88 90 1993
Year

 

 

Crop Output in Barley Equivalents
----........... Livestock Output in Pork Equivalents

Figure 6.9. Crop and Livestock Output Indices.

 

6 The fattening capacity is estimated from the livestock ouput index by assuming 74
kilograms carcass weight and four months period for fattening.

105

6.6 Credit Regimes and Discount Rate

The economic model given in Chapter 3 assumes perfect capital markets, but for studying

the effects of the credit rationing we exogenously partition the sample into four regimes, as

explained above. First, we partition the sample into two periods: (1) rationed years 1976-85

and (2) nonrationed years 1986-93. Then, we partition the sample into two groups: (a)
liabilities

nonrationed low-debt farms with < 0.9 and (b) rationed high-debt farms with
gross returns

 

liabilities
gross returns

 

> 0.9. It is likely that over the years 1986-93 the farms with low liabilities to

gross returns ratios have been free from liquidity constraints.

Table 6.3 shows that the average investment on real estate does not differ much
between the credit regimes. Machinery investment, on the other hand, differs between the
regimes of low and high liabilities. The group averages suggest that, over the period of non
regulated credit market, high liabilities may have been restricting machinery investments.
Table 6.3 also reveals that the capital stocks are roughly constant but output levels differ
across the low and high liability farms. In other words, farm capital has not been increasing

along with production.

106

Table. 6.3. Farm Crmital, Investments, and Output Stratified by Credit Regimes.

 

 

Real Estate ' Machinery ‘
Regime Output " L/R °
Investment Capital Investment Capital
Rationed Marketd 31.8 856 76.3 231 41.8 0.70
Rationed by UK 32.6 945 66.8 239 30.6 1.27
Nonrationed by L/R 31.6 823 79.8 228 45.9 0.49
Nonrationed Marketd 34.1 1,040 66.3 331 48.0 0.81
Rationed by L/R 35.3 1,120 54.4 303 38.0 1.41
Nonrationed by L/R 33.5 1,000 72.3 345 52.9 0.51
Full study period 33.] 962 70.6 288 45.3 0.76
Rationed by L/R 34.3 1,060 59.1 279 35.2 1.35
Nonrationed by L/R 32.6 920 75.7 292 49.8 0.50

 

' In FIM 1000 inflated to 1993.

" In 1000 pork equivalents.

° L/R= farm's total liabilities divided by gross returns. The farm is rationed by liabilities, if L/R>0.9.
Otherwise nonrationed by liabilities.

“ Over the years 1976-84 the credit market was rationed and thereafter nonrationed.

For discounting costs, we have used the real discount rate (r), which was computed
from the nominal market interest rate (nr) and rate of inflation (infl) as (see Robison and
Barry 1996, p.206):

(1 +nr)=(1+r)(i+infl)

= nr-infl

=>’ ——.—-,
1+tnfl

where the nominal rate is the annual average loan rate between 1976-86 and, thereafter, a
12 months HELsinki Inter Bank Offered Rate (12 months HELIBOR) minus 0.25. The
HELIBOR series was adjusted to the average loan rate series by subtracting 0.25, which is
the average difference between the two series over the period 1986-93. It would have been

desirable to set the nominal rate to, say, a 12 months HELIBOR over the whole study

107

period. But as explained in the preceding chapters, the credit market was rationed prior to
1986 and the 12 months HELIBOR was not recorded in the statistics until 1987. 7
Inflation exceeded the nominal discount rate slightly in 1980 and 1981. Nevertheless,
an inplausible negative real rate was ruled out by setting it to zero. The average real
discount rate is about 5 %. The rate has an upward sloping trend until 1991 and a downward

sloping trend thereafter (see Figure 6.10).

0.12

 

0.09 2—

0.06 r

0.03 +

 

 

0
76 78 80 82 84 86 88 90 1993

Year

 

Figure 6.10. The Real Discount Rate.

 

7 The market bond rates with 3 or 5 year maturities would have beenpreferred to the 12
months rate, but the 12 months rate was available earlier than the rates with longer maturity
periods. The 12 months rate was also used by Pajuoja (1995).

108

6.7 Summary of the Farm Data

The observations with real estate capital less than 75,000, machinery capital less than
10,000, aggregate output less than 15,000, or labor less than 900 were dropped from the
data, because it is likely that these extreme values have resulted from measurement errors.
Summary Statistics for the resulting data set are presented in Table 6.4.

The data were rescaled to improve the estimation procedure so that all variables had
approximately the same scale and weight in the optimization procedure. After scaling, the
data are also consistent with the second order expansion of the optimal value function so
that the variables get values around their expansion points. This also improves the flexibility
of the optimal value function.

The price indices were rescaled to have value one in the year 1985. The output
quantities and numéraire input were divided by their sample means. Real estate and
machinery investments were divided by 75,000 FIM. For maintaining equal units of
measurement, the same rescaling factor was used for rescaling the capital stocks, too. The
labor changes were rescaled by the average reduction of labor services, conditional on

negative change in the labor use. The labor services were rescaled by the same factor.

Table 6.4. Summary of the Farm Data.‘

109

 

 

Variable Mean Standard deviation Minimum Maximum
Real estate capital 785,000 383,000 94,500 2,640,000
lnvestrnent on real estate 25,800 68,200 0 1,160,000
Machinery capital 219,000 136,000 10,100 741,000
lnvestrnent on machinery 51,500 59,700 0 380,000
Labor services 4,200 1,480 972 13,900
Change in labor services -24.0 677 -3,030 4,080
Crop output 68,800 78,400 0 652,000
Livestock output 42,000 29,300 10,300 277,000
Variable input 281,000 197,000 36,100 1,460,000

 

' In 1993 prices.

Chapter 7

ESTIMATION RESULTS

The structural form parameters that appear in the optimal value function were estimated
from the four decision rules using the FIML-technique, as outlined in Chapter 5. In
particular, the loglikelihood function of the Tobit switching model was used. The model.
was estimated using the GAUSS Constrained Maximum Likelihood (CML) routine. The
Davidon-Fletcher-Powell algorithm (DFP), which approximates the Hessian, was used to
speed up initial iterations. Then, the Newton-Raphson algorithm, which computes the
Hessian at every iteration, was used for obtaining the final model.

The feasible parameter space was reduced in several ways during the iterations
because of the computationally intensive estimation procedure. First, the covariance matrix
was constrained to be positive definite. But, as expected, this restriction was not binding in
the converged models. Second, the optimal value function was restricted to be
nondecreasing and concave in input prices. The inequality constraints imposing that the
value function be nondecreasing in prices were not active in the final estimated model, but
at least one out of the three concavity constraints were active in each of the estimated

models.I

 

‘ These concavity conditions equal the regularity conditions (D'.i) given in Chapter 4.

110

111

The original model specification had two output indices but it was so computationally
intensive, and its log likelihood ftmction was so flat around the maximum, that the model
failed to converge and estimates could not be obtained. Instead we estimated an alternative
model with only one aggregate output and informally checked this specification against the
(unconverged) two output alternative. By comparing the log likelihood values of these two
specifications it turned out that the fit of the model could not be significantly improved by
splitting the aggregate output into crop and livestock components.2

Next, we tested for asymmetry in the adjustment rate matrix M. Depending on the
model specified, the asymmetric model either did not improve the fit from that of the
symmetric model, or the asymmetric model did not converge. Therefore, the symmetry of M
could not be formally rejected. Hereafter, we continue to report and test the model with one
aggregate output, and which maintains symmetry of the parameter matrices A, D, and M.
We now move on to the estimation results in more detail by starting with the model
estimated using the full sample. Then we test for misspecification of the model and report
the results for several alternative model specifications. The chapter concludes with elasticity

estimates and estimates for steady state capital stock and labor.

 

2 The likelihood ratio statistic for the test was 10.18, which is Chi-Squared distributed with
nine degrees of freedom (x: ), suggesting that the “one output model” should not be rejected

in favor of “the two output model”, because the test statistic was less than the critical value
16.92. However, this result has to be interpreted cautiously because the “two output model”
did not converge.

112

7.1 The Full Sample Model

The parameter estimates for the full sample model are reported in Table 7.1. Although the
reported full sample model converged, its loglikelihood function was so flat around the
maximum that the Hessian was not invertible. There are no obvious ways to solve this
problem. One way, however, is to isolate the parameters that are causing the trouble and
compute the Hessian with these parameters fixed. In our case, the estimated covariance
between the demand for labor and demand for the numéraire turned out to be negligible and
insignificant (significance is reported later). This covariance was set to zero in order to
obtain an invertible Hessian and standard errors for the other parameters. With this
restriction, most of the estimates remained unchanged when compared to the estimates in
the unrestricted model. Most of the parameter estimates differ significantly from zero at the
5 % two tailed significance level (Table 7.1)3. We discuss the definitions of these parameter

estimates below.

 

3 The 5 % two tailed significance level is used hereafter for testing null hypotheses, unless
otherwise indicated.

113

Table 7.1. Estimation Results for the Full Sample Model. '

 

 

Parameter Estimate Standard error Parameter Estimate Standard error
aw" 1.0401 0.0281 H. 0.2012 0.1636
H, 0.2756 0.2209
a” -0.0314 0.0127 11, -0.6735 0.1305
al, 07055 0.0815
a,, 0.0505 0.0187 1),, 02503 5.2113
1),. 0.2100 2.2793
32 1.0746 0.1690 Dzz 4.9823 0.0000
1),, -0.3563 2.6454
as: 02172 4.2414 D32 0.6326 2.5328
an -0.8714 0.0000 D33 4.3302 1.8543
a,, -1.0684 3.2047
M., 0.1015 0.0067
A” -00012 0.0007 M2, -0.0024 0.0036
A21 0.0099 0.0019 Ma 00214 0.0000
A22 0.0837 0.0131 M31 0.0071 0.0048
A31 0.0003 0.0006 M32 00104 0.0030
A32 -0.0049 0.0033 M33 0.1532 0.0060
A,, 00025 0.0013
13 0 02,5 0 0089 y for 11>0 0.2076 0.0055
- , . 2
E; -O.3800 0.0707 ‘04: - 00257 00081
13, 0.0351 0.0133 -03, - 0.1664 0.0104
4,23 - 0.0187 0.0071
B 09122 0'05“ bad 3:6,, 0.0037 0.0214

 

' The number of observations is 1928, and the average value of the loglikelihood function is 1.224.
" An intercept in the demand equation for the numéraire input. It is a function of structural form parameters.
Bad year: a dummy variable for the years of crop damages in the demand equation for the numéraire.

Recall from Equation (4.7) that the structural form parameters presented in Table 7.1.

appear in the optimal value function as:

J(K,Y,Q) = a0 + al’K + az’InY + a,’1nQ

%K’AK + K’EInY + %InY’BInY

+

+

lnY’Han + %InQ’DInQ + Q’M"K

114

The last 5 parameters in Table 7.1 are dummy variables. Recall from Equation (4.11a) that

K = Diag{q,.'l}M(ra3 + rH’lnY + rDan)
+ (rU - (U + Y)M)K

1 2 2 2
-§[o,,, oqz quQK

where the parameter 7 has been used to model an adjustment rate for labor that is
asymmetric, depending on whether the use of labor increases or not. Because the sample
average for the labor change is negative, the base model has been estimated for negative
changes and the dummy variable has been used to identify positive changes. The result
suggests asymmetric labor adjustment and this result is discussed in more detail in

subsequent sections.

The parameters 0:, 0:3 are used for measuring the effects of a conjectured single

persistent shift in uncertainty in 1991. They are parameters for dummy variables which have
a value one over the years 1991-93 and zero otherwise. The parameter estimates are
significant suggesting that increased volatility reduced, in particular, machinery
investments. A dummy variable for exceptionally unfavorable harvest years was added to
the demand equation of the numéraire input. This dummy variable has value one in the
years of severe crop damages and zero otherwise. The parameter estimate for this dummy

variable is denoted in Table 7.1 by “bad year”, and it suggests that the demand for the

115

numéraire decreases with crop damage. We shall examine the parameter estimates, as well
as the price effects, output effects and adjustment rates, in more detail in subsequent
sections.

The R-squared of the regression is 0.465 in the labor change equation, and 0.823 in
the numéraire equation. In other words, the model explains 46.5 % of the variation in the
changes in labor services and 82.3 % of the variation in the demand for the numéraire
input. We now move on to the fit of the investrnent demands in more detail so that goodness
of fit is measured by how well the model predicts the correct investment regimes within the
sample.

If we take investment on real estate and measure it as a binary choice such that the
choice is one for positive investment and zero for zero investment, the model predicts the
indicator correctly in 1,059 out of 1,928 cases, and the probability of a correct prediction is
54.9 % (Table 7.2). The predictions have been computed so that the model predicts one if
the estimated conditional probability for value one exceeds 0.5. Otherwise it predicts zero.
Hence, the model predicts only 4.9 percentage points better than tossing a fair coin. Within
the sample, the model over-predicts zero investment, predicting 1,581 zeros against an

actual number of 1,062.

116

Table 7.2. Predicted and Observed Binary Investrrient Choices. '

 

 

 

 

Predicted
Real estate investment Machinery investment
0 1 0 1
Observed 0 887 l 75 1 346
1 694 l 72 4 1 ,5 77

 

' The values 0 and 1 denote zero and positive investments.

The binary choice for machinery investment is predicted better than that for real estate
investment. The model predicts the indicator correctly in 1,578 out of 1,928 cases in the
sample, and the probability of a correct prediction is 81.8 %. Positive machinery
investments are over-predicted in the sample. The model predicts 1,923 ones against 1,581
actually in the sample.

If we look at both binary choices together, the model predicts both of them correctly
in 842 cases, and the probability of a correct prediction is 43.7 % (Table 7.3). The product
of the two probabilities for individual choices (54.9 and 81.8 %) gives 44.9 % probability
for predicting both of the variables correctly, whereas tossing a fair coin twice would give
a correct prediction 25 % of the time. The model predicts best in the cases in which real
estate investment is zero and machinery investment is positive, because within the sample
that regime is over-predicted. The percentage of correct predictions in that regime is 68.4 %.
In the other regimes, the model’s capability to predict the observed outcomes is low.
However, the model will not predict any cases in which real estate investment is positive

and machinery investment is zero, because firms investing in real estate usually invest in

117

machinery, too. But the model does not predict well the sample observations in which both
investments are positive, or in which both investments are zeros. The low within sample
predicting power of the model may be caused by farm specific individual effects, which we

have not been able to control for.

Table 7 .3. Observed Outcomes and Predictions in each Investment Category. ’

 

Investment Percentage of the
group Number of Number of Number of observations predicted
observations predictions correct correctly
predictions
i,> 0andi,>0" 752 347 155 17.7
i,>0andi,=0 114 0 0 0
i, = 0 and i, > 0 829 1576 686 68.4
i, = 0 and i, = 0 233 5 1 0.305
The full sample 1928 1928 842 43.7

 

' For a correct prediction we require that both investment choices (zero, one) are predicted correctly.
" i, and 1', refer to the real estate and machinery investments.

7.2 Testing for Misspecification

7.2.1 Time Series Properties of the Price and Output Series

As explained in Chapter 4, the structural form parameters in the optimal decision rules are
pinned down by the maintained hypothesis that output and prices follow a geometric

Brownian motion without drift. Thus, it is important to test this hypothesis empirically to

118

determine whether the assumption of geometric Brownian motion is appropriate in this
application.

This section tests that the observed price and output series are geometric Brownian
motion. A representative firm approach will be used, because it would be an overly onerous
task to test each firrns’ series separately. Each output observation is constructed as an annual
output average across the firms. The price data are normalized prices, as they appear in the
decision rules. The series span 18 years. So we have 16 observations for estimating an
AR(2) process. The tests are constructed for each univariate series separately.

We first define a second order autoregressive model for the scalar 2, as:

zjt : ”j + 'l’jlzjt-l + ‘l’jzzjt-z + 8}:

where E(ej,) = 0

(7.1)
2
0. or t=s
E(ej,e,_,) = 1 f
0 otherwise
which can be written in canonical form:
7'1: z 11,- + 91211-1 + EJ‘Azjr-I + 811’
(7.2)

where p]. = 1p, + 1|},
51‘ = - 1'2

119
Under the null hypothesis of geometric Brownian motion, 1.5-=0, 5 ,=0, and l-tlt ,,-1|t ,,=0,
which also implies p,- =1. These conditions are ‘stronger than implied by unit roots. A unit
root in a univariate series would allow for nonzero E,- , while unit roots in multivariate
setting would imply even more general conditions. To see this, stack the output and price
series together (over j’s) such that they define a vector valued AR(p) process with
parameters 1.1, ‘1’, ...‘Pp, or the canonical form with parameters p=‘P,+...+‘P,, and E,= -
(‘I’s+,+...+‘Pp) for s=l,2,...,p-l. Then, in general, the unit roots and cointegrating vectors

solve

1041', —‘P2-...-‘Pp| = lU-pl =0,

in which the matrix U denotes an identity matrix. In other words, this condition immies that
even though the z,- ’s are nonstationary and integrated of order one, there is a long run
relationship tying the individual series together, so that a nonzero linear combination of the
z,- ’s is stationary (Hamilton 1994). But, the special condition of unit roots included in our
null hypothesis (i.e. p,-=1 for all j) is equivalent to the p=U which implies that the
determinant of (U - p) equals zero, but not vice versa.

The single equation OLS estimates of (7.2) and their standard errors are presented in
Table 7.4a. The term A21H is included in the estimating equations for factoring out potential
serial correlation in 8,, , as suggested by the AR(2) process in (7.1). Regardless of the values
of u,- and p,- , the memory of the process, i.e. the null hypothesis E,=0, can be tested by a
standard t-test (Hamilton 1994). In every series, the null hypothesis §=0 is rejected at a 5 %

two tailed significance level, suggesting the series follow an AR(l) process. Therefore, we

120

continue simply by setting 5, = 0 for all j. The parameter estimates with this restriction are
presented in Table 7.4b.

Under the null hypothesis of p,- =1, the estimates of pj in are biased toward zero such
that in 95 percent of the cases they are less than one (Hamilton 1994). In addition, neither

it nor 1“) exhibits a standard asymptotic distribution. Therefore, the Dickey-Fuller tests will

be used for testing unit roots (Dickey and Fuller 1979). When choosing the test statistic we
assume that the true process has a unit root without drift, that is, 1.5-=0 and pj=1 for all j. The
null hypothesis of a unit root (p,=1) cannot be formally rejected in any series (Table 7.5).
The joint hypothesis of a unit root without drift (p,=l and u ,=0) again cannot be rejected in
any series.

Despite these test results it is possible that the machinery prices and output level are
stationary, because the sample used for testing these series was very small and the tests have
low power problems, particularly in small samples. Failure to reject the null hypothesis may
also signal that the tested series are not informative about whether or not there is a unit root
(Kwiatkowski et a1. 1992). Nevertheless, we conclude that there does not seem to be very
strong evidence against the null hypothesis, and so it is realistic to estimate the optimal
decision rules under the assumption that prices and output follow geometric Brownian

motion without drift. This result is also supported by Thjissen (1996).

121

Table 7.4a. OLS Estimates for the Output and Price Series of the Form (7.2).

 

 

Parameter
Series (2,.)I Drift rate (11,-) Lagged level ((2,) Lagged difference (5,.)2
Price of Real estate 0.0156 0.844 0.0228
(0.0186) (0.148) (0.237)
Price of machinery 0.0590 0.483 0.458
(0.0248) (0.237) (0.261)
Wages 0.0338 1.03 0.0435
(0.0213) (0.1 13) (0.301)
Output 0.0688 0.774 0.166
(0.0243) (0.102) (0.233)

 

' The series are in a logarithmic form. Standard errors are in the parentheses.
2 The critical t-test value at 5 % two tailed risk level for the null Ej=0 is 2.16.

Table 7 .4b. OLS Estimates for the Ougrut and Price Series of the Form (7.2) with §,-=0.

 

 

Parameter

Series (z,)' Drift rate (u,) Lagged level ((1,) Lagged difference (£,)
Price of Real estate 0.0155 0.849 -

(0.0179) (0.135)
Price of machinery 0.0418 0.682 -

(0.682) (0.223)
Wages 0.0342 1 .04 -

(0.0203) (0.0964)
Output 0.0705 0.784 -

(0.0237) (0.0990)

 

'See Table 7 .4a.

122
Table 7.5. The Dickey-Fuller and F-Test Statistics.

 

Series Dickey-F uller test ' F-test 2

for pj=l for uj=0 and pj=l
Price of Real estate -2.42 0.622
Price of Machinery -5.09 1.02
Wages 0.588 0.0727
Output -3 .46 2.38

 

' The test statistics have been computed as 7(6 - 1) with T=16. The critical value at two tailed 5 %

risk level with T=25 is -12.5. The critical values with less than 25 observations have not been tabled.
The null is maintained, if the entry is greater than the critical value.

2 The unrestricted versions have been run with A2,- as the dependent variable. The critical value at two
tailed 5 % risk level with T=25 is 5.18. The null is maintained, if the entry is less than the critical value.

6.3.2 Covariance Restrictions among the Error Terms

We have set the insignificant covariance between errors in the labor and numéraire input
demand equations to zero in order to obtain the standard errors for the other parameter
estimates. This restriction did not alter the other parameter estimates reported in Table 7.1.
With no other restrictions among the errors in the decision rules, the lower triangular

portion of the estimated covariance matrix is“:

2.54

0.167‘ 0.561
0.164‘ 0.0377 1.66
L-O.0838‘ -0.0337° 0 0.0880,

M)
II

 

 

 

’ The unrestricted covariance between the labor and numéraire demand equations was
insignificant, having value 0.0007.

123

which is, in terms of correlation coefficients,

1 1
0.140: 1
0.0805‘ 0.0388 1
_-0.177: -0.152' 0 1

 

 

An asterisk in the entry denotes that the covariance differs from zero at the 5 % significance
level. The significance of the covariances is tested by a Wald test. The test statistics for the
null hypotheses that the covariance between 88 and 8,, for sie j and s,j=1,2,3,4, equals zero is

computed as (Hamilton 1994):

6

5f

n ~ asymptotically N (0, 1)
(636,? + 63,.)“2

where n is the number of observations in the sample

The resulting test statistics for zero entries in E are:

F

6.71
3.88 1.90
(8.45 7.26

 

 

If the entry exceeds 1.96, the corresponding covariance differs from zero at the 5 %
significance level. The tests suggest that innovations in the real estate equation correlate
positively with the innovations in the machinery investment and labor demand. The

innovations in both investment equations are negatively correlated with the innovation in

124

the demand for the numéraire input. Therefore, we can conclude that an equation by
equation estimation procedure, or a system estimation with a diagonal covariance matrix, 2,

would have resulted in inefficient parameter estimates.

7.2.3 Liquidity Constraints and the Partition into Credit Regimes

To investigate whether liquidity constraints have been affecting the farmer’s optimization
behavior, we partition the sample exogenously into four regimes on the basis of two
factors: (1) rationing in the credit, market; and (2) firm liabilities relative to gross returns. It
has to be noted, however, that we do not construct formal tests for the effects of the liquidity
constraints in the original optimization problem. Rather, we check informally to see if our
results are robust to partitioning the data by the factors that may have been driving up
liquidity constraints (see e.g. Zeldes 1989).

We split the data into two time periods, a period of rationed credit market (1976-85)
and a period of nonrationed credit market (1986-93). The observations over the period
1976-85 are more likely to be constrained by liquidity constraints than the observations after
1985. We further partitioned the sample over the years 1986-93 into a group of farms whose
liabilities to gross returns ratio exceeds 0.9, and a group of farms whose liabilities to gross
returns ratio is less than 0.9. We conjecture that, even though the credit market was
deregulated, firms who had high liabilities to gross returns ratios may still have been

liquidity constrained. The observations over the deregulated years 1986-93 which have low

125
liabilities to gross returns ratios are, on the other hand, expected to be free from liquidity
constraints.
The results suggest that a separate model should be run over the regulated (1976-85)
and deregulated periods (1986-93). The likelihood ratio statistic for the full sample model

as a null hypothesis against the two split models was 107.4. The test statistic exceeds the

Chi-Squared 5% critical value with 48 degrees of freedom (xi8 = 64.89), and the full

sample model is rejected in favor of the two separate models in the split data. But even
though there is a statistically significant difference between the models, there does not seem
to be economically significant differences between the parameter estimates. The parameter
estimates in the full sample model and in the partitioned sample models are almost identical
(compare Table 7.1 and Appendix 1). We conclude that the credit rationing has had
economically significant effects neither on the parameter estimates reported in Table 7.1 nor
on investments. This result is also supported by Pajuoja (1995), who concluded that credit
rationing has not had significant effects on farmer access to capital in Finland.

Next, we partitioned the deregulated period (1986-93) further into two subsamples
representing the observations that meet different liabilities to gross returns ratios, as
explained above. Although the regulated subsample model did not converge, the
loglikelihood values reveal that the sample should be split and a separate model should be

estimated for the different ratio categories. The likelihood ratio statistic for this test was

342, which clearly exceeds the critical value (xi8 = 64.89) and the null hypothesis is

rejected in favor of splitting the sample. In this case, the parameter estimates differ between

126

the deregulated model (Table 7.6) and the full sample model reported above (Table 7.1).
The subsample model, in which observations have high liabilities to gross returns ratio over
the period 1986-93, is not reported beCause the model failed to converge.

Hereafter, we will report the results for the full sample model and for the model in the
deregulated subsample, in which farm investments have been liquidity constrained neither
by the credit market nor by liabilities. These models are referred to as “the full sample

model” and “the deregulated subsample model”.

127

Table 7.6. Estimation results for the Deregulated Subsample Model. '

 

Parameter Estimate Standard Parameter Estimate Standard error
error

a; 1.1251 0.0000 11. -0.0782 0.2503

11, 1.8745 0.6933

a,, 0.0350 0.0222 11, -1.5560 0.2544
al2 -0.0782 0.1 122

a., 0.0857 0.0362 1)., 44395 0.0000

1),, 2.4419 0.0000

a: 1.4560 0.3693 D22 406005 0.0000

1),, -3.7782 4.4982

a3. -4.265 5 D32 7.0961 1.6383

a32 -0.7860 5.4498 D33 -1 .0956 00000
a,, 0.7892 1.7151

2.8040 M” 0.1 179 0.0088

A” 00040 M,, 00225 0.0082

A21 -0.0023 0.0016 M22 0.0753 0.0244

A22 0.0348 0.0030 M31 0.0176 0.0060

A31 0.0009 0.0195 M32 0.0068 0.0062

A32 001 15 0.0013 M33 0.1800 0.0093
11,, -0.0029 0.0053

E 0 0267 0-0025 7 for 1L>0 0.2062 0.0081

1:; -0.1764 0.0133 «1:, 0.0081 0.0101

13, 0.0776 0.0958 63,, -0.1 139 0.0169

13 0 9841 0.0216 «’23 0.0299 0.0085

. 4
0.0804 bad year -0.0462 0.0000

 

' The number of observations is 743, and the average value of the loglikelihood function is 0.9666.

b An intercept in the demand equation for the numéraire input. It is a function of structural form parameters.

128

7 .2.4 Testing for Nonstandard Assumptions

In this section we examine whether the error terms in the estimated Tobit model meet the
assumptions required for consistency of the parameter estimates. By nonstandard
assumptions we mean nonnormality, heteroscedasticity, and serial correlation. The Tobit
model is inconsistent if the normality or homoscedasticity assumption of the error terms is
violated, but it remains consistent if the errors are serially correlated (Amemiya 1985).
Therefore, it is important to check whether the normality and homoscedasticity assumptions
are met in the model. Even though the Tobit model remains consistent if the error terms are
serially correlated, it is also important to test whether the model is well-specified

dynamically.

Tobit versus Probit Estimates

We do not construct a formal test for nonnormally distributed errors, but we check more
generally the model specification by comparing the estimates between Probit and Tobit
models, which are both run for the same decision rules. We can check whether the Tobit
model is correctly specified by comparing the Tobit and Probit estimates, because it is
unlikely that two different misspecified models would generate similar parameter estimates.
Therefore, if there are wide discrepancies between the compared estimates either the
normality assumption is violated or the specification is otherwise incorrect. If, on the other
hand, the estimates are close to each other then it suggests the models are correctly

specified.

129

Nevertheless, the Probit model can identify only the ratio between the parameters and
the Standard Error (SE) of the error term in the estimated equation, say % (using the
notation in Equation 5.1) . Therefore, we mean by parameter estimates being "blose to each
other" that the estimates are close to each other up to a multiple. This multiple is one over
the equation's SE (e. g. oi) estimated by the Tobit model .5

It turned out, howevler, that the Probit estimates are almost identical to those estimated
by the Tobit model above. Without reporting the Probit results in more detail, we conclude

that the Probit estimates do not reveal any nus-specification in the reported Tobit models.

Heteroscedasticity

Heteroscedasticity is first checked using simple auxiliary, or artificial, OLS-regressions run
on logarithms of the squared error terms. Separate auxiliary regressions are run for each
equation (denoted by j) amongst the four equations in (5.1).

These auxiliary regressions are rigorously valid under the null hypotheses of
homoskedastic errors only in the uncensored equations, i.e. in the labor and numéraire
equations. Thus, in these equations the auxiliary regressions are valid for making statistical
inference on whether the null hypotheses are violated or whether they are not violated (e. g.
Davidson and MacKinnon 1993).

But only the observations with positive investment can be used when explaining the

logarithms of the error variances in the investment equations. Thus, these auxiliary

 

5 In practice, we identified the Probit estimates by fixing the SE's at their Tobit estimates.

130

regressions are estimated conditional on positive investment. Therefore, the simple t- and F -
tests on these auxiliary regressions are biased in favor of finding heteroskedasticity. Thus,
there is tendency for the auxiliary regressions to suggest heteroskedasticity even if the
original unconditional errors were homoskedastic.‘5 Nevertheless, we estimate the full set of
auxiliary regressions, and use these estimates as starting values for estimating the model
under the alternative hypothesis of heteroskedasticity, then proceeding to a more formal
Likelihood Ratio test for heteroskedasticity. '

Under the alternative hypothesis, heteroskedasticity is assumed to be driven up by real
estate capital, kl, machinery capital, k2, labor services, L, and by logarithm of output, lny,

such that:

‘2
111(8):) : p0} +Bljk1 + [2ij + [3311’ + p4jlny + v} 2

where 8:, = predicted error in (5.1) for all j = 1,2,3,4
[3,, = parameters for all j and for all s=0,...,4
v, = an i.i.d. error term for all j

The parameter estimates of these artificial regressions and their standard errors are
reported in Tables 7.7a and 7.8a for the full sample model and for the deregulated
subsample model. The estimation results infer significant heteroskedasticity in the labor and
numeraire equations of both models. Heteroskedasticity may be a problem also in the

investment equations. Therefore, we revise the estimated decision rules by correcting the

 

6 By unconditional variance we mean that the variance is not conditioned on positive
investment.

131

covariance matrix for heteroskedasticity. But to obtain a model that is feasible to estimate,
the number of parameters in the equations which explain the variation in the variances of
the error terms is decreased by dropping the insignificant parameters. Nevertheless, the
same set of explanatory variables is used for correcting the heteroskedasticity in both
investment equations. Estimation results from these auxiliary regressions when the
insignificant variables have been dropped are reported in Tables 7.7b and 7.8b.

Next we corrected the estimation of the decision rules for heteroskedasticity as
suggested by the artificial regressions in Tables 7.7b and 7.8b. However, all parameters of
the revised model were re-estimated jointly by using the MLE-technique as before.

The heteroscedasticity corrected model in the deregulated subsample is reported in
Table 7.9. The likelihood ratio statistic testing for the revised model against the null of the

unrevised model (Table 7.6) is 354.2, which clearly exceeds the Chi-Squared 5% critical

value with nine degrees of freedom (x; = 16.92 ). Therefore, the heteroscedasticity

corrected version (Table 7 .9) differs significantly from the model reported in Table 7.6.
The full sample model, on the other hand, either could not be improved, because a
feasible step length was not found, or the model did not converge when it was corrected for

heteroscedasticity. Hence, the revised full sample model is not reported.

132

Table 7.7a. Regressions on Logarithms of the Squared Errors in the Full Sample Model.‘

 

 

Investment/Demand Equation

Variable Real Estate Machinery Labor Variable Input
Intercept -l.8l' " -3.22' -3.07' -3.97’

(0.293) (0.224) (0. 195) (0. 1 89)
Real Estate 0.0204 0.01 13 0.0144 0.000922
Capital, kI (0.0212) (0.0165) (0.0143) (0.0138)
Machinery -0. 154' 0.23 7' -0.0210 -0.0539
Capital, k2 (0.0559) (0.0445) (0.0384) (0.0372)
Labor 0125' 0.0239 0.166' 0.0123
Services, L (0.0205) (0.0167) (0.0145) (0.0142)
Output, lny 0.660' 0.289' -0.0949 1.70'

(0.177) (0.139) (0.120) (0.1 16)
R-squared 0.0685 0.0635 0.0682 0.154

 

‘ The model is reported in Table 7.1.

b An asterisk denotes significance at the two tailed 5 % risk level. Standard errors are in the parentheses.

Table 7.7b. Regressions on Logarithms of the Squared Errors in the Full Sample Model.ll

 

 

 

Investment/Demand Equation
Variable Real Estate Machinery Labor Variable Input
Intercept -1.69° " -3.16’ -2.99’ -4.00°
(0.266) (0.204) (0. 154) (0.0501)
Real Estate
Capital, k,
Machinery -1 .13' 0249'
Capital, k, (0.0507) (0.0405)
Labor 0.125. 0.0262 0.167.
services, L (0.0205) (0.0163) (0.0142)
Output, lny 0.724. 0.326. 1 .62.
(0.164) (0.128) (0.0867)
R-squared 0.0676 0.0632 0.0675 0. 153

 

" " See Table 7 .7a.

133

Table 7.8a. Regressions on Logarithms of the Squared Errors in the Deregulated Subsample

 

 

 

 

Model. '
Investment/Demand Equation
Variable Real Estate Machinery Labor Variable Input
Intercept -1.86' " -3.98° -3.l9° -3.73'
(0.460) (0.41 1) (0.326) (0.318)
Real Estate 0.0273 0.0389 0.0459 -0.00582
Capital, kl (0.0308) (0.0292) (0.0327) (0.0222)
Machinery -0.0571 0.183' -0.0847 0.0129
Capital, k2 (0.0693) (0.0715) (0.0558) (0.0546)
Labor 0102' 0.0518 0.165' -0.0501
Services, L (0.0304) (0.0305) (0.0245) (0.0239)
Output, lny 0.374 0.436 -0.0760 1.65'
(0.243) (0.253) (0.195) (0.191)
R-squared 0.0472 0.0860 0.0603 0.172
' The model is reported in Table 7.6.

" An asterisk denotes significance at the two tailed 5 % risk level. Standard errors are in the parentheses.

Table 7.8b. Regressions on Logarithms of the Squared Errors in the Deregulated Subsample

 

 

 

Model. '
Investment/Demand Equation
Variable Real Estate Machinery Labor Variable Input
Intercept -1.62° " -3 .72' -2.98° -3 .75'
(0.370) (0.31 1) (0.254) (0.248)
Real Estate
Capital, k,
Machinery -0.0301 0220'
Capital, k2 (0.0623) (0.0660)
Labor 0.0992' 0.0551 0.164' -0.0499'
Services, L (0.0302) (0.0305) (0.0242) (0.0236)
Output, lny 0.458' 0.565' 1.64'
(0.224) (0.234) (0.134)
R—squared 0.0449 0.0832 0.0586 0.172

 

'“ " See Table 7 .8a.

134

Table 7.9. Heteroscedasticity Corrected Model in the Deregulated Subsample. '

 

Parameter Estimate Standard error Parameter Estimate Standard error
a,.,' 1.1877 0.0000 11, 0.3161 0.3124
112 0.5268 0.7494
all 0.0175 0.0247 11, -1 .0291 0.2441
al2 -0.1634 0.1202
a,, 0.0325 0.0324 1),. -6.6808 0.0000
1),, -1 .0704 0.0000
a: 0.9802 0.3519 D22 401852 0.0000
1),, 0.7592 0.0000
an -6.4631 0.0000 Du 3.0413 23.1634
asz -5.9748 6.6877 D33 -0.8468 00000
a,, 1.3705 6.1571
M” 0.1172 0.0077
A,l -0.0022 00017 M,, 00223 0.0091
A21 -0.0013 0.0034 Mzz 0.0704 0.0275
A22 0.021 1 0.0209 M31 0.0181 0.0042
A31 0.0002 0.0013 M32 0.0065 0.0058
A32 -0.0022 0.0048 M33 0.1840 0.0105
11,, -0.0013 0.0021
E 0 0,30 0 0156 y for [>0 0.2151 0.0084
. . 2
13.; -0.1819 0.1038 ‘04! 90043 040105
13, 0.0286 0.0189 «13,, -0.1174 0.0196
_023 0.0153 0.0087
13 0.8006 0.0702 bad yew -0.0164 0. 0 000

 

' The number of observations is 743, and the average value of the loglikelihood function is 0.7001.

b An intercept in the demand equation for the numéraire input. It is a function of structural form parameters.

135
Serial Correlation
Serially correlated error terms are checked informally by a first order autoregressive model

on the predicted error terms:

8j,t : Bj0 + pjsCsJ-l + vj,t ’

where 21‘.” £33,, are predicted errors in (5.1) at time t for j,s = 1,2,3,4

[3,” = parameters for all s and for h=0,l
v}, = an i.i.d. error term

Again these auxiliary regressions are estimated for the investment equations conditional on
positive investments and, therefore, they favor finding serial correlation. Nevertheless in the
labor and numéraire equations the regressions are valid under the null hypothesis of no
serial correlation in (5.1) i.e. [i,, =0 for j=3,4. Results from standard t- and F-tests in these
two equations suggest that the errors are serially correlated. The innovation in the labor
equation is negatively correlated with its own innovation lagged. And the innovation in the
numéraire equation correlates positively with its own lagged innovation. There is also
potential that the innovation in the real estate investment is positively correlated with the
lagged innovation in the machinery investment, and vice versa.

The results suggest that the economic model is either dynamically incomplete or,
alternatively, the decision rules are affected by significant farm specific effects. The latter
result may follow because the artificial regressions were nm in the pooled panel data and
farm specific individual effects may have resulted in persistency in the values of the

innovations across time.

136

However, we do not correct the estimation of the optimal decision rules for serial

correlation. Serial correlation does not result in inconsistent estimates and the R-squareds in

these artificial regressions are in most cases low although they favor serial correlation.

Table 7.10. Autoregressions on the Error Terms in the Full Sample Model (Table 7.1).

Investment/Demand Equation

 

 

 

Vanable Real Estate Machinery Labor Variable Input
Intercept 1.02' ‘ 0.157' -0.l69° -0.0288'
(0.0646) (0.0266) (0.0355) (0.00710)
Lagged Error in the
Equation for
Real Estate 0133' 0.075' 0.0246 0.0176'
(0.0458) (0.0207) (0.0286) (0.00573)
Machinery 0.150' -0.0627' 0.0813' 0.0152'
(0.0622) (0.0270) (0.0379) (0.00758)
Labor 0.1 13' 0.0267 -0.0849' -0.00169
(0.0429) (0.0190) (0.0260) (0.00521)
Variable Input -0.0470 -0.0700 0.0196 0.559'
(0.177) (0.177) (0.0997) (0.0199)
R-squared 0.0378 ‘ 0.0164 0.00910 0.329

 

‘ An asterisk denotes significance at the two tailed 5 % risk level. Standard errors are in the parentheses.

137

Table 7.11. Autoregressions on the Error Terms in the Deregulated Model (Table 7.6).

Investment/Demand Equation

 

 

 

Variable
Real Estate Machinery Labor Variable Input
Intercept 0.967' ' 0.546' -0.0442 -0.00791
(0.0777) (0.0504) (0.0568) (0.01 19)
Lagged Error in the
Equation for
Real Estate 0.104 0.172' 0.0800 0.0191
(0.0648) (0.0486) (0.0589) (0.0123)
Machinery 0.185' 0.0765 0.0726 0.0109
(0.0863) (0.0541) (0.0654) (0.0137)
Labor 0.0298 0.0426 . -0.110' -0.00932
(0.0600) (0.04 14) (0.0466) (0.00974)
Variable Input -0.213 -0.202 -0.03 10 0.439'
(0.255) (0.150) (0.174) (0.0364)
R-squared 0.0419 0.0471 0.0153 0.216

 

2 An asterisk denotes significance at the two tailed 5 % risk level. Standard errors are in the parentheses.

7.3 The Effects of Increased Uncertainty

As explained above we conjectured that, at the beginning of 1991 when the debate about
Finland’s joining the EU started, there was a one time persistent shift in uncertainty faced
by Finnish farmers. This shift was measured by a dummy variable over the years 1991-93.
The parameter estimates for this dummy variable are summarized for three model
specifications in Table 7.12.

An increase in uncertainty either reduced or did not affect real estate investments.
Machinery invesment, on the other hand, was clearly decreased by the prospect of joining

the EU. The deregulated sample models also suggest that increased uncertainty increased

138

the use of labor. Therefore, we conclude that less machinery was substituted for labor when

uncertainty increased.

Table 7.12. Estimates for the Dummies over the Years 1991-93.

 

Decision rule Full Sample Deregulated Subsample Deregulated Subsample Model
for Model Model Corrected for Heteroskedasticity
Real Estate‘ -0.0257' 0.0081 0.0048

(0.0081) (0.0101) (0.0105)
Machinery‘ -0. 1664' -0.1 139' -0.1 174'

(0.0104) (0.0169) (0.0196)
Labor' -0.0187' 0.0299' 0.0153'

(0.0071) (0.0085) (0.0087)

 

' When reporting the parameter estimates, these dummies have been denoted by -o,2,, , —o:2, and -o,2,3.

7 .4 Adjustment Rates

As shown in Chapter 4, we can write the optimal decision rules in the flexible accelerator

form. For all It,>0, k'2>0, and £<0 then y=0 and we can write K = N (K - K), in which

the matrix of adjustment rates is given by N = rU - M. Estimated adjustment rate matrices

are reported in Table 7.13 for the full sample model, the deregulated subsample model, and

the latter with a correction for heteroskedasticity.

139

Table 7.13. Estimates for the Adjustment Rate Matrices: A7 = r— U - M. ’

 

 

Deregulated Subsample Deregulated Subsample Model
Full Sample Model " Model Corrected for Heteroscedasticity
—0.0525‘ -0.0689‘ -0.0680‘
0.0024 0.0276‘ 0.0225‘ -0.0263’ 0.0223‘ -0.0214‘
-0.0071 0.0104‘ —0.1042‘ -0.0176‘ -0.0068 -0.l31' -0.0181‘ -0.0065 -0.135‘

 

‘ The adjustment rates have been computed for 7:0.049, li,>0, [62>0, and [<0 . The corresponding models

are reported in Tables 7.1, 7.6, and 7.9.
b An asterisk, if it is attached to a diagonal entry, denotes the entry is greater than -1 at the 5 % one sided risk

level. If the asterisk is attached to an off-diagonal why, it denotes the entry differs from zero at the 5 % two
sided risk level.

The adjustment rates are more plausible in the deregulated subsample models than in

the firll sample model, as expected. All diagonal entries in A7 have plausible negative signs

in the deregulated sample, and most of the entries in .07 have larger magnitudes in the

deregulated sample than in the full sample model. Heteroscedasticity seems to have only
negligible effects on the adjustment rate estimates, as the estimates are insensitive with
respect to the correction for heteroscedasticity.

Null hypotheses about the adjustment rates have usually been constructed as:

(1) The j‘" good in K adjusts instantaneously, i.e. it is a variable input. Under the null,

the j‘" diagonal element of N equals -1 and, in addition, its off-diagonal elements in

the j‘h row are zeros. If this holds for all goods in K, the matrix N equals the identity
matrix multiplied by minus one.

(2) The adjustment of the j‘" good in K is independent of disequilibrium in the market
of the other goods. Under the null, the off-diagonal elements in the j‘" row of N are
zeros. If this holds for all goods in K, then N is diagonal.

140

(3) The adjustment rates are symmetric; N is symmetric.

We add a fourth null hypothesis:
(4) The adjustment of labor is symmetric with respect to changes in the labor services
(Y=0)-
When testing the parameters individually, the first null hypothesis, which assumes

instantaneous and independent adjustment, is rejected for all goods, because all diagonal

elements of A7 are significantly greater than -1. The second hypothesis assuming

independent adjustment is also rejected, because at least one off-diagonal element in A7

differs significantly from zero in every specification. The third null hypothesis, stating that
N is symmetric, is maintained without testing, because the models with asymmetric M
failed to converge. The fourth null hypothesis, which conjectures symmetric labor
adjustment with respect to changes in labor services, is rejected as well. The dummy

variable used for modeling asymmetry in the labor adjustment was estimated significantly

in every specified model. Depending on the specification, the third diagonal element in A7

for positive labor changes is either 0.103, 0.0705 or 0.0801. Each of these estimates is
significantly greater than -1, suggesting that labor services increase sluggishly.7

We conclude that real estate, machinery and labor are quasi-fixed in the sense that
they adjust sluggishly to the shocks in the exogenous state variables. All three goods are

subject to adjustment costs. In addition, the adjustment of each good depends on

 

2 We have used one sided test at 5 % significance level. The critical value is 1.645.

141

discrepancy between the current and steady states of at least one of the other goods, and
labor adjustment is asymmetric depending on whether labor services are decreasing or

increasing. We now turn to the adjustment rates in more detail.

Real estate

The adjustment rate of real estate with respect to the discrepancy between its own current
and steady states has a plausible sign in every model specification, and the adjustment rate
has a larger magnitude in the deregulated subsample than in the full sample. In the
deregulated subsample the estimated adjustment rate is -0.07, suggesting that real estate
capital converges to a steady state equilibrium but it adjusts slowly towards the equilibrium.
For example, over a five- year period, the response to an initial shock will decrease the
discrepancy between the actual and the steady state capital by 30 %.

The adjustment rate of real estate with respect to the discrepancy between machinery's
current and steady states is significant and positive, suggesting intertemporal
complementarity between real estate and machinery. In other words, the result suggests that
real estate investment is increasing in machinery and, similarly, machinery investment is
increasing in real estate.8 Thus, excess machinery drives real estate investment up, and vice
versa. This complementarity between real estate and machinery implies that, for example,
excess machinery can be utilized more efficiently by purchasing more real estate. Similarly,

excess real estate can be employed more efficiently by investing more in machinery.

 

2 Recall that we have maintained symmetry of the adj ustrnent rate matrix.

142

The result that capital goods are complements is interesting because numerous
empirical investment studies use aggregated capital and, therefore, make an implicit
assumption that capital goods are perfect substitutes for each other. In the light of our
results, on the other hand, aggregating real estate and machinery intO’a single capital good
is not justified.

The adj ustrnent rate of real estate with respect to the discrepancy between the current
and steady state labor is significant and negative. The result suggests that labor and real
estate are short-run substitutes so that excess labor, for example, decreases real estate
investment. In other words, farm’s excess labor is employed in the short run by delaying

substitution of capital for labor.

Machinery

The estimated adj ustrnent rate of machinery with respect to the discrepancy between its own
current and steady states is positive in the full sample and negative in the deregulated
subsample. This suggests that farmers’ access to machinery capital may have been restricted
by liquidity constraints. Even though the adjustment rate is negative in the deregulated
subsample, its magnitude is small (40.03), suggesting that machinery capital adjusts very
slowly towards its steady state level. A discrepancy between the observed and steady state
capital stock will shrink over a five-year period by only 14 %. We would expect a faster
machinery adjustment, and this sluggish investment behavior may signal significant farm

specific individual effects, which are time constant but vary across individual farmers. It is

143

likely, as the shadow prices reported below will suggest, that the unobserved individual
effects have been driven up by individual tastes. Some farmers have preferred modem to old
equipment, which has resulted in excess machinery capital’. Alternatively, additional
incentives to invest in machinery have been provided by successive tax shields generated by
the difference between the economic and tax depreciations.

Investment in machinery is independent of the discrepancy between the current and
steady state labor. Symmetry of the adjustment matrix implies also that changes in labor
services are independent of the discrepancy between the current and steady state machinery.
This result is somewhat surprising because we would expect that machinery and labor are
substitutes even in the short run so that, for example, a shortage in the firm's labor would
trigger the firm tolinvest more in machinery and labor saving technologies. Nevertheless,

the elasticity estimates reported below support our expectations.

Labor

Around the sample mean, the change in the labor services is negative with an adjustment
rate estimated at -0. 13. Thus, labor services converge and a discrepancy between the firms
current and steady state labor is reduced by 50 % over a five-year period. Labor adjusts
asymmetrically so that increases in labor services are even more sluggish than decreases in
labor services. This result is supported also by Oude Lansink (1996). However, the

adjustment rate for labor increases is positive at 0.08, suggesting that there is no convergent

 

9 Le. we have unobserved time constant individual effects, which we have not been able to
control for.

144

path for labor services in the regime of positive labor changes. Or, more importantly, the
result suggests that farmer’s access to short-term hiring contracts as an employer is
restricted. In other words, the result supports the view that when more labor is needed in the
short run, it is not available or, alternatively, the labor market is inflexible with regard to

short-term hiring contracts.

7.5 Shadow Prices for Installed Capital and Labor

Recall the consistency conditions (B.ii) in Chapter 4, which conjectured that the shadow
price for installed capital is negative if the firm is investing and positive if the firm is
disinvesting. In other words, the optimal value function (the discounted present value of the
cost stream) is expected to be decreasing in the capital stock when the firm is investing and
increasing in the capital stock when the firm is disinvesting. With zero investment, the
shadow price can be either negative or positive, but between the shadow prices of the
investing and disinvesting firms. Because the approximation to the optimal value fimction
holds only around the sample averages, we correspondingly test the shadow prices around
the sample means only. From the conditions (B.ii) we construct the following null
hypotheses:

(1) The shadow prices of real estate and machinery, evaluated around the sample

means of the state variables, are negative, because the average observed investment is
positive.

145

(2) The shadow price of labor, evaluated at the sample means of the state variables, is
positive, because the average change in the labor services is negative.

The estimated shadow prices for both capital goods differ significantly from zero, but they
are positive, having opposite signs to what we expected (Table 7.14). The null hypotheses
in (1) are therefore rejected and we conclude that the data does not support the view that the
optimal value function is decreasing in real estate and machinery capital. This result
suggests that the discounted present value of the firm’s cost stream is expected to increase,
if its capital stock is increased ceteris paribus.

Because real estate and machinery are both measured in equal units, their shadow
prices should be equal at the margin, provided farmers have had equal access to both capital
goods. But given the small standard errors of the shadow price estimates, it is obvious that
the difference between the prices is statistically significant. Indeed, the shadow price of
machinery is about one third larger than the shadow price for real estate. If there were
internal adjustment costs only, firms could have reduced their costs by equating shadow
prices across the capital goods. In other words, they could have decreased costs at the
margin by delaying the machinery investments and by investing only in real estate until the
marginal benefit from a unit of capital became equal across the goods. The large difference
between the shadow prices cannot be explained by internal adjustment costs. Therefore, the
result suggests that farmers have not had equal access to both capital goods or, more likely,

they have had external incentives for investing in machinery. Farmers have been more eager

146

to invest in machinery than in real estate either by tastes, or because of higher incentives
through tax shields.

Using the equality 063/01,: —aJ/ak, for j = 1,2, the estimated shadow prices

imply that adjustment costs exist, but the instantaneous cost function is decreasing with

investments, i.e. aC/ai, < 0 for i, 2 0 , j = 1,2. This result supports the view that there are

scale effects in investment, such that the larger the investment the smaller the adjustment
costs that are realized. This result is plausible, but it contradicts the traditional postulate that
adj ustrnent costs are increasing and convex in investment. Our result is also supported by
Rothschild (1971), who claims that the arguments for cost functions being increasing in
investment are weak. It has to be noted, however, that the result obtained does not meet the
sufficient conditions for an extremum in the original maximization problem. We rely,
therefore, on the necessary conditions.

Even though the shadow price of installed real estate capital is positive, the
instantaneous cost function is decreasing in real estate (Table 7.15). This result suggests that
the cost of investing, including adjustment costs, has outweighed the cost reductions
resulting from the increased capital stock. Investments in machinery, on the other hand,

have not even reduced the instantaneous costs.

147

Table 7.14. Shadow Prices for Installed Capital and Labor. ’

 

Full Sample Deregulated Subsample Deregulated Subsample Model

Good Model Model Corrected for Heteroskedasticity
Real Estate " 10.4 11.0 11.3

(3.16) (0.00) (n.a.)
Machinery " 52.0 16.1 17.3

(1.05) (0.00) (n.a.)
Labor ‘ 9.62 3.91 3.73

(1.10) (1.03) (n.a.)

 

' The shadow prices are elements of the gradient VKJ’ = aI + AK + E 1111’ + M "Q, and they are evaluated at

sample means. Standard errors are in parentheses.

" The sample average of gross investment is positive.

° The sample average of change in the labor services is negative.
n.a. refers to “not available”.

Table 7.15. Derivatives of the Instantaneous Cost Function with respect to Capital and
Labor. "

 

Full Sample Deregulated Subsample Deregulated Subsample Model

Good Model Model Corrected for Heteroskedasticity
Real Estate 2 -0.310 -0.271 -0.252

(0.210) (0.00) (n.a.)
Machinery " 8.83 2.04 2.27

(0.198) (0.00) (n.a.)
Labor ° -0.529 -0.809 -0.817

(0.0539) (0.0505) (n.a.)

 

‘ The derivatives are computed as VKC’ = (r + 6)oV,,J’ - Q - A(l - 6K), and they are evaluated at sample

means and at I=6K.
2' ‘2 n.a. See notes in Table 7.14.

The shadow price of labor is positive and significant, as expected, and the null
hypothesis (2) is supported by the data. The optimal value function is increasing in labor

even though the instantaneous cost function is decreasing in labor (see Tables 7.14 and

148

7.15). In other words, the sum of expenses, including adjustment costs, to purchase more
labor services has exceeded the Stun of instantaneous cost reductions provided by increased
labor. Net returns to incremental labor services have been negative, and firms have been
gradually substituting capital for labor to decrease costs. Further, had the firms been able to
reduce their labor input even more, they would have been able to reduce their production
costs, ceteris paribus.

Again, using the conditions in (B.ii) and, in particular, the equality

(BC/<31: = —8J/8L, we conclude that the instantaneous cost function is decreasing in

changes of labor, i.e. (BC/61: < 0 for L' < 0, as expected. Note that, as the average labor

change is negative, this result implies that the cost function is increasing in the absolute
value of the labor change.

In summary we conclude that, even though instantaneous costs have been decreasing
with one out of two capital goods, and with labor services, the sample farms have had
excess capital and labor relative to their output levels. At a given output level they could
have reduced the discounted present value of their production costs by reducing the capital

stock and labor.

149

7.6 Short-Run Response Probabilities and Elasticities

Response Probabilities
We measure response probabilities by how many percentage points the probability of a
positive investment is predicted to change, if an explanatory variable is changed, ceteris
paribus, by one percentage point. In other words, we have rescaled capital stocks and labor
services so that a one unit change corresponds to a one percentage unit change in the
original untransformed variables around their mean values. Because output and price indices
are in a logarithmic form, a one unit change in them corresponds to a one percentage point
change in the original untransformed variable. Estimated response probabilities for real
estate and machinery investments in the deregulated subsample model, which is corrected
for heteroskedasticity, are reported in Table 7.16. '0

The response probabilities for positive investments with respect to output have
plausible positive signs, but their magnitudes are negligible. Even though the probability of
investing is increasing with output, it is insensitive to changes in output. This result is
consistent with the results above, suggesting that farms have had excess capital. Thus,
increased output has resulted in more intensive use and more efficient utilization of existing
capital, but it has not necessarily driven up investments. Further, the result suggests that

there are significant scale economies in utilizing the capital stock.

 

'0 To reduce the number of tables in the text, the short-run response probabilities and
elasticities are reported here only for the deregulated subsample model, which is corrected
for heteroskedasticity. The results of the other two model specifications are given in
Appendix B.

150

Most of the price effects have plausible signs. For example, negative own price effects
suggest that investments have been decreasing with their own prices, as expected. However,
the magnitudes of the price effects are negligible, suggesting that investments have not been
sensitive to prices. These results may signal that under fairly restrictive production controls
then prices have not been dominant factors in determining investments.

The physical level of firms’ capital and labor services have played a more important
role in determining investments than the prices and the level of output. A ten percent unit
increase in the farm’s real estate capital, for example, has reduced its probability to invest
in real estate about two percentage units. The probability of investing in real estate has been
decreasing in the firrn’s actual real estate capital and labor services but increasing in
machinery capital. In other words, excess real estate capital and labor has driven real estate
investments down, but excess machinery capital has driven real estate investment up. This
result suggests that, in the short run, real estate and machinery capital have been
complements, but real estate and labor services have been substitutes.

Gross investments in machinery have been increasing in the firm’s actual machinery
capital, because machinery depreciates and large replacement investments are required to
maintain a capital stock of machinery. But still, the probability of a positive net investment
in machinery has been decreasing with the actual machinery capital stock, as expected.
Excess machinery capital has, in other words, been driving net investment in machinery
down. Machinery investment has also been decreasing in labor services, which suggests
that machinery and labor have been substitutes in the short run. Excess real estate capital

has, on the other hand, been driving machinery investment up. This result again implies that

151

machinery and real estate have been short-run complements, as explained above. It has to be
noted, however, that we have maintained symmetry of the adj ustrnent matrix resulting in

sign-symmetric elasticities between capital stocks and labor.

Table 7.16. Response Probabilities for Positive lnvestrnents.

 

 

 

Real estate Machinery
With
respect to gross investment net investment gross investment net
investment
Log of output 0.00010 0.000089 0.000352 0.000417
Log of prices:
real estate -0.00192 -0.00170 0.00119 0.00140
machinery -0.00236 0.00209 -0.00576 -0.00682
wage rate 0.000086 0.000076 0.00289 0.00342
Capital '
real estate -0. 166 -0.196 0.0755 0.0894
machinery 0.0192 0.0170 0.106 -0.0226
Labor " -0.0584 -0.0517 -0.0217 -0.0257

 

' A one percentage change around the sample average. The sample averages are 754,000 and 199,000 FIM.
" A one percentage change around the sample average. The sample average is 4,090 hours.

Elasticities

We define two kinds of elasticities: conditional elasticities and unconditional elasticities.
Conditional elasticity is conditioned on the exogenous state variables and, in addition, on
positive gross investment. The unconditional elasticity is conditioned on the exogenous

state variables, only. Elasticity estimates are presented in Tables 7.17 and 7.18.

152

As above in the case of the response probabilities, output and price elasticities have
plausible signs in the sense that output and cross price elasticities are positive, but own price
elasticities are negative. The magnitudes of these elasticities are, nevertheless, negligible.
We conclude that investments have been inelastic with respect to the output level and
prices. Again, the unplausibly low output elasticities may result from the stringent
production controls that have influenced the connection between output changes and the
level of investments. The observed range of output fluctuations may have resulted primarily
in marginal adjustments of intensity in capital use, rather than lumpy investments. This
phenomenon is also supported by the result that farms have been in excess capital relative
to their output levels. Nevertheless, low unconditional output elasticities are consistent with
significant economies of scale.

Unconditional elasticities of real estate, in particular, with respect to capital stocks and
labor services are clearly larger in magnitude than the corresponding conditional elasticities.
This suggests that the combined effects of a regime shift (from zero to positive investment)
and an increase in investment size are important in measuring elasticities of real estate
investments, whereas either one of these two responses alone shows relatively inelastic
effects.

Real estate investment is decreasing and elastic with respect to its own capital stock.
Elasticity estimates confirm, again, that real estate investments are increasing considerably
in excess machinery but decreasing in excess labor. In other words, elasticities show
substantial short-run complementarity between real estate and machinery but short-run

substitutability between real estate and labor as above.

153

The differences between the conditional and unconditional elasticities are not as large
in machinery investments as in real estate investments, partly because the number of zero
machinery investments in the data is small. The elasticity estimates in Table 7.18 show
notable increase in the gross investment in machinery with respect to the increases in
machinery capital. Net investment in machinery is, however, slightly decreasing with its
own capital, as before. In addition, the elasticities show that machinery investment is
increasing substantially with excess real estate capital, again signaling strong
complementarity between real estate and machinery. Labor and machinery are, however,
short-run substitutes, as excess labor will decrease machinery investments and slow down
substitution of labor saving technologies for labor. It has not paid, for example, to invest in
advanced feeding technologies if there has not been any alternative demand and income

sources for the saved labor input.

154

Table 7.17. Short-Run Elasticities for Real Estate Investments. ‘

 

 

 

With Gross investment Net investment
respect to
conditional " unconditional ‘ conditional " unconditional ‘

Output 0.000122 0.000509 0.000118 0.000544
Prices:

real estate -0.00233 -0.00976 -0.00226 -0.0104

machinery 0.00287 0.0120 0.00278 0.0128

wage rate 0.000105 0.000439 0.000102 0.000470
Capital:

real estate -0.202 -0.843 -0.260 -1.20

machinery 0.0233 0.0975 0.0226 0.104
Labor -0.07 10 -0.297 -0.0687 -0.3 18

 

' Elasticities are evaluated at the sample means.

" Expected investment is conditioned on the predetermined state variables and on positive gross investment.
‘ Expected investment is conditioned on the predetermined state variables only.

Table 7.18. Short-Run Elasticities for Machinery Investments. '

 

 

 

With Gross investment Net investment
respect to
conditional " unconditional ‘ conditional " unconditional °

Output 0.000693 0.001 18 0.000659 0.00144
Prices:

real estate 0.00234 0.00398 0.00222 0.00486

machinery -0.0113 -0.0193 -0.0108 -0.0236

wage rate 0.00569 0.00970 0.00541 0.0118
Capital:

real estate 0.149 0.254 0.141 0.310

machinery 0.208 0.355 -0.0358 -0.0783
Labor -0.0428 -0.0730 -0.0407 -0.0891

 

‘ "' ° See notes in Table 7.16.

155

Changes in labor services are decreasing (becoming more negative), but inelastically,
with the output and the wage rate in the short run (Table 7.19). The short-run response of
labor with respect to the other prices is also negligible. The results suggest, however, that
labor services are decreasing with excess capital and, in particular, with excess real estate.
Further, labor services are decreasing elastically with excess labor services. Therefore, we
can conclude that it is the fum’s current capital stock and labor services which determine
the short-run changes in labor services. The short-run effects of output and prices are

negligible.

Table 7.19. Short-Run Elasticities for Changes in Labor Services. '

 

With Full Sample Deregulated Subsample Deregulated Subsample Model
respect to Model Model Corrected for Heteroskedasticity
Output -0.00422 -0.0108 -0.00727
Prices:
real estate -0.00236 -0.0299 0.000478
machinery 0.00480 0.0504 0.0191
wage rate -0.00150 -0.0137 -0.0103
Capital:
real estate ~0.071 1 -0.178 -0.182
machinery 0.0275 -0.0181 -0.0172
Labor -1.04 -1 .31 -l .35

 

' Computed at the parameter estimates in the regime of negative changes in labor services. Elasticities are
evaluated at sample means.

156

7.7 Long-Run Elasticities

Long-run price and output elasticities of capital stocks and labor services are computed by

setting optimal net investment K to zero, and then solving the resulting equation for K as a

function of exogenous prices and output. When the optimal net investment has been set to

zero, the resulting capital stock equals the steady state capital stock by definition. We

denote the steady state capital stock by K and define it by:

K = (M-rU)’l[Dia q,"}M(ra3 +rH’lnY+ rDan)]

Even though the LeChatelier principle no longer holds in a dynamic model, the
elasticity estimates suggest that capital is more elastic with respect to output in the long run
than in the short run (Table 7.20). But still the capital stock increases very inelastically with
the output level, suggesting scale economies in capital utilization as above. Labor services
are decreasing with output, but inelastically. In other words, increasing output will result in
labor savings or it does not affect the use of labor. '

The long-run price elasticities seem to be very sensitive to the model specification.
Even the signs vary between the different models and, therefore, we focus on the
deregulated sample models only and, in particular, on the heteroskedasticity corrected

model, which is expected to be more robust than the other models.

157

Real estate capital is suggested to be decreasing with respect to its own price or have
no response in the long run . But real estate capital is decreasing with machinery prices and
increasing with the wage rate. In other words, real estate and machinery are long-run
complements, as expected, but somewhat unexpectedly, real estate and labor are long-run
substitutes.

Machinery capital is decreasing in its own price, as expected. It is also decreasing in
the price of real estate but increasing in the wage rate. These cross price effects suggest that
machinery is a long-run complement for real estate but a substitute for labor, as expected.

Labor services are increasing in the prices of both capital goods and decreasing in the
wage rate. The result implies, again, that labor and capital are long-run substitutes.
Therefore, we conclude that the estimated long-run price effects support our expectations.

Following Femandez-Comejo et a1. (1992), the elasticity of scale is defined as:

91/1 = 9E. It measures how many percentage units the discounted present value of the

ay/y alny
cost stream is expected to change if the level of output is changed by one percentage unit,
ceteris paribus. The estimated elasticity of scale was 0.85 in the heteroskedasticity corrected
deregulated model, suggesting economies of scale. In other words, the discounted present
value of the cost stream is expected to increase by 8.5 percentage points if the output level
is increased by 10 percentage points. This result is consistent with the low output elasticities
reported above. We conclude that there is potential for reducing the production cost per unit,
and for increasing the competitiveness of the Finnish hog industry, through expanding firm

size. If the estimated scale effect holds more than just at the margin, a ten percent reduction

in the production costs per unit, for example, would be gained by tripling the size of current

production units, ceteris paribus.ll

Table 7.20. Long-Run Elasticities of Capital Stocks and Labor Services. ’

 

 

Model Specification
Elasticity with
Good respect to Deregulated Deregulated Subsample,
Full Sample Subsample Corrected for
Heteroskedasticity
Real Estate Output 0.0556 0.00865 0.00323
Price of
real estate -9.96 -0.1 16 0.000470
machinery 0.166 -0.0775 -0.0872
labor -0.834 -0.0316 0.1 17
Machinery Output 0.00484 0.0525 0.00372
Price of
real estate 0.0390 0.421 -0.162
machinery 8.60 -1 .81 -0.222
labor 0.106 1.65 0.178
Labor Output -0.0248 -0.0443 -0.01 1 8
Price of
real estate -0.128 -0.849 0.206
machinery 0.0780 0.543 0.150
labor -O.107 -0.910 -0.589

 

' We have fast set K = 0, and then solved the decision rules for optimal steady state capital stock and labor.

Elasticities are evaluated at the means.

 

” We have used the term elasticity of scale interchangeably with the term elasticity of size.
Nevertheless, the measured scale elasticity does not assume homothetic production
technology and, therefore, it allows for optimal substitution effects when output is changed.

 

 

A—

159

7.8 Steady State Capital Stocks and Labor Services

The estimated steady state levels of capital and labor services are well below their observed
values in the heteroscedasticity corrected model (Table 7.21). The estimates for steady state
labor services are even negative, which cannot be true. Perhaps this inplausible result is
caused by a gradual decrease in the observed labor services. Nevertheless, the estimates
suggest, as do our findings above, that farms have had excess capital and labor at their

exogenously restricted production levels.

Table 7.21. Steady State Capital Stocks and Labor Services.

 

Full Sample Deregulated Subsample Deregulated Subsample Model
Good Model Model Corrected for Heteroskedasticity
Real Estate 1,300 38,900 86,700
Machinery -3,220 23,300 147,000

Labor 34.1 -49.4 -1 l8

 

Chapter 8

ECONOMIC IMPLICATIONS FOR THE HOG PRODUCTION SECTOR
IN FINLAND

This chapter discusses what kinds of answers our estimation results suggest to the
questions given in Chapter 1. The discussion is further, expanded to broader practical
implications of the estimation results for the hog production sector in Finland.

In the first section we discuss the prospects the sector has in the light of our
estimation results concerning economies of scale. Then we move on to the implications of
our results for capital and labor markets. Uncertainty will be discussed in the last section.
Throughout the chapter we highlight the connections between our results and the new

adjustment programs, which were briefly described in Chapter 2.

8.1 Economies of Scale

Recall from Chapter 1 that one of the most important questions addressed in this study
was: is it realistic to expect that the Finnish hog industry can become competitive enough,
and reach a cost level, that allows it to survive in the Common Market? Chapter 2

introduced the marked structural differences between the Finnish and Danish hog

160

161

industries, resulting in production costs that are, depending on the farm group compared,
19-30 % higher in Finland than in Denmark.

The estimated low output elasticities and dynamic scale elasticity indicate that the
Finnish hog industry is operating with an increasing returns to scale technology.
Increasing output per firm will result in more efficient utilization of farm capital, as well
as labor savings. In other words, expanding the farm size will result in labor saving
technologies and reduce the labor costs per unit produced. Substantial labor savings are
plausible because, in large production units, it is possible to take advantage of
technologies such as advanced automatic feeding. Advanced feeding technologies will
also decrease feed costs.

The long-run scale elasticity was estimated at 0.85, which suggests that production
costs will increase less than the output level when firm size is expanded. If output is
doubled the present value of the total production costs will increase by 85 %, which will
decrease the average costs per unit produced by 7.5 %. Similarly, if the firm’s output is
tripled its average production costs will decrease by 10 %'. For example, with an initial
400 pig fattening capacity, which is common in Finland, this would result in a fattening
capacity of 1,200, a capacity that is still well below the maximum capacity of 3,000 given
in Table 2.5. But access to the agri-environmental program requires that a farm has at

least 110 hectares of arable land for spreading manure and slurry for 1,200 fattening pigs.

 

‘ Note that we are projecting cost reductions outside the range of most of the existing
data used in the study ,and therefore the projections should be interpreted with caution.

162
Thus, obtaining the 1,200 fattening capacity would imply for most hog farms a substantial
land area expansion, too.

Capital costs, including building and equipment, account for 21 % of total
production costs on Finnish bookkeeping hog farms. The new investment subsidies will
account about 50 % of these capital costs, provided maximum subsidies are granted as
reported in Table 2.6. Then, a maximum investment subsidy is estimated to reduce
production costs by, roughly, 11 %.

Summing up the long-run scale effects and investment subsidies, it is reasonable to
expect that the Finnish hog industry has potential for reaching the average cost level of
the Danish hog industry had in 1995. But to reach the Danish cost level of 1995, Finnish
production units would have to at least triple their size. This implies that the estimated
investment size in the survey of Kallinen et a1. (1996), which results in the production
units of 1.6 times their current size, seems too small for fully adjusting in a new market
environment.2

An aggregate production level that meets the domestic demand for pork is a
feasible goal for the industry, because the EU-Commission has approved means for
paying extensive investment subsidies in Finland as long as the aggregate production does
not exceed its level in 1994. In this respect the future of the Finnish hog industry seems
favorable. It has to be emphasized, however, that tripling the average firm size, while

keeping the aggregate production capacity constant, requires that two thirds of the current

 

2 Note also that the Danish hog industry is not stagnated at 1995 structure. Danish
production units continue to expand and decrease their costs from the costs in 1995.

163

producers need to exit the industry. Over a five year period, for example, this would
require an exit rate of 8 % per year, which is almost twice the 4.3 % average exit rate of
1996 in Finnish agriculture. Even though it is estimated that 10 % of hog producers quit
in 1995, the estimate of Kallinen et al. (1996) that 5 % of farms will exit over the two-
year period 1996-97 appears too small for adjusting to the new market environment over
the five-year transitional period.

If high cost producers who are not going to stay in the industry in the long-run do
not exit the industry quickly enough, the investment program may temporarily increase
production in excess of domestic demand. But taking into account the aggregate capacity
restrictions imposed by the investment program, it is not reasonable to expect that the
industry could significantly penetrate the export market for bulky pork products for a any
length of time. In other words, it seems unlikely that the industry could reach such a low
cost level that it could compete in the export market without subsidies.

Concerning short-run scale economies, we found the important result that, when
allowing for fixed and asymmetric adjustment costs, instantaneous production costs are
not increasing in investment as traditionally postulated in the literature dealing with
adjustment costs. Our results support the view that adjustment costs exist, but the
instantaneous cost function is decreasing in investment and larger investments will result
in lower adjustment costs. In other words, there are scale economies in investment.

The result that the cost function is decreasing in investment, combined with long-
run economies of scale, has important consequences for the adjustment of the Finnish hog

industry in the European Common Market. It suggests that the production technology

164

favors large scale industrialized hog production and fast adjustment to the new market
environment. In other words, when the timing for an investment is right, farmers should
choose new technology and implement large investments in order to get the highest
benefits from the new technology and reach the lowest possible production costs per unit

produced.

8.2 Capital and Labor Market

As noted in Chapter 1, the most important issues concerning the capital and labor market
addressed in this study are: Do the observed and steady state capital stock and labor differ
and, if they do, then by how much; how quickly capital and labor adjust towards their
steady states; and how are the markets for capital goods and labor linked?

There is no evidence supporting the view that either credit market rationing, or
firms’ high liabilities to gross return ratios, have resulted in liquidity constrained
investments. The results suggest that the discounted value of the frnn’s cost stream was
increasing in capital within the regulated as well as deregulated farm groups. Hence, hog
farms appear to have unconstrained access to capital. Furthermore, the shadow price
estimates support the often posed view that Finnish hog farms have had excess capital
relative to their production levels, which has resulted in inefficient utilization of farm

capital. Therefore, it is likely that the stringent production controls in the 803 and early

165

905 have resulted in a shortage of profitable investment alternatives for farm families to
develop their enterprises.

One explanation for the estimated shadow prices is that opportunity cost for
farming capital has been low. This result is also supported by Penttinen et a1. (1996), who
concluded that returns to forest investments, which are natural opportunities for
agricultural investments in Finland, have been low. Alternatively, excess capital may
have decreased costs that we have not observed. An example of these kinds of
unobserved costs are costs or foregone returns caused by a delayed harvest. Similarly,
there may have been a tendency towards excess capital. For example, excess harvesting
capacity has been to some extent a risk reducing input so that even though it has not
increased expected net returns it has decreased the variance of the returns. Nevertheless,
we simplified our analysis by assuming risk neutral farmers and, therefore, could not
address this issue formally in this study.

There have also been other institutional incentives and regulations that may have
triggered investments in excess capital. For example, the imposed link between the farm’s
arable land area and the maximum size of the livestock unit may have resulted in excess
real estate capital relative to the firrn’s output level. This regulation has been, of course,
environmentally justified, but it may also have implied increased costs in livestock
husbandry so that marginal returns to livestock have been capitalized into land values.
This phenomenon is supported by Ylatalo’s (1991) result that land prices have exceeded

the marginal value product of land.

166

The estimated shadow price for machinery is more positive than the shadow price
for real estate, which suggests that farmers have had, in addition to individual tastes, even
more incentives to invest in machinery than in real estate. This incentive may have been
caused by risk reducing characteristics of machinery capacity or by tax shields, generated
by high marginal income tax rates and the difference between the tax and economic
depreciation rates. Because the tax depreciation rate has exceeded the economic
depreciation rate then firms have been able to postpone their tax outlays, while
guaranteeing adequate equipment for future production.

Nevertheless, we conclude that, when Finland entered the EU, most hog farms had
a reserve, or savings, in terms of excess farming capital which can be utilized for
expanding the firm’s production. As production controls have been abolished, farm
capital will be more efficiently utilized and allocated. But still, low returns to farm capital
cause severe difficulties in the farmers’ adjustment to a new market environment. Access
to credit, on the other hand, is not a problem. Rather, investments accepted in the
programs, or recommended to be canied out, should be more carefully considered by
institutions which participate and intervene in the agricultural investment programs. The
results support the view that farm investments have been canied outwith low returns to
capital.

The estimated positive elasticities of investments with respect to their own capital
stock, on the other hand, suggest that low existing capital stock is required for triggering
new investments. Therefore, farmers may need to depreciate the old technology first,

especially if it is inflexible in its design, to obtain the most profitable timing for new

167

investments. The result implies that farmers who have invested quite recently, say in late
803 or early 903, in inflexible production facilities may have difficulties in adjusting
quickly to the new market environment.

The adj ustrnent rates for capital are estimated at low values, which also suggests
that capital stock and labor will adjust slowly towards their steady state values. The
adj ustrnent rate of real estate capital with respect to discrepancy between its ctu‘rent and
steady states was estimated at -0.07. This indicates that over a five-year period, after a
shock changing the steady state level has been observed, the discrepancy between the
actual and the steady state capital stock will shrink by 30 %, i.e. by less than one third. In
this light, the five-year transitional period would not be long enough for adjusting to the
new market conditions.

It is likely that the low adjustment rate of real estate capital is influenced by market
failure in the local land market such that farmers have not had adequate access to land.
When supplementary land has been available they have bought it even though the price
has exceeded marginal value product of land. The supply of land has been further
decreased, for example, by the old early retirement contracts, which included an incentive
for retiring farmers to idle their land. As mentioned above, the land market failure is also
supported by Ylatalo’s (1991) result that strong demand for supplementary land and low
supply for land has increased land values even above their marginal value products.

It is expected that the low estimated adjustment rates for machinery, on the other
hand, have resulted primarily from unobserved individual effects, which we have not

been able to control for. These individual effects may have been caused by tax shields, as

168

explained above, or individual tastes. That is, some farmers have preferred new to old
equipment.

We conclude that, even though farms have had excess capital, land market failure
will slow down the adjustment process, because the maximum size of a hog production
unit is tied to the farm’s arable land area, which is justified by environmental arguments.
Therefore, it is expected that environmental regulations, which tie the size of the firm's
hog production unit and land area together, are going to play an increasingly important
role in determining hog production costs, hog industry structure, and the hog industry's
spatial concentration.

Labor services are estimated to be decreasing with an adjustment rate estimated at
-0. 13, implying that the discrepancy between the current and steady state labor is reduced
by 50 % over a five-year period. The low adjustment rate, combined with the result that
farms have excess labor, signals that farmers have not been able to find enough
employment alternatives, while the demand for farm labor has been gradually decreasing.

Labor adjusts asymmetrically in the sense that increasing labor services are even
more sluggish than decreasing labor services. The result supports the view that, when
more labor is needed in the short run, it is not available or, alternatively, the labor market
is inflexible with regard to short-term hiring contracts. In other words, the results suggest
that there is market failure in the rural labor market, which will slow down the industry’s
adjustment process.

Labor and capital markets are closely linked. An inflexible labor market, combined

with excess labor in farming, will delay the substitution of capital for labor. Another

169

important finding is that the demand for labor is more likely decreasing than increasing in
the firm’s output level. Therefore, structural adjustment programs stimulating
investments and focusing on the capital market will result in increased excess labor not
only among the contracting (or exiting) firms but also among the expanding firms. In
other words, an adjustment program stimulating investments will accelerate the decrease
in the demand for farm labor in the hog industry. These results also question the rationale
of “the full-time farming” -condition as a prerequisite for a farmer to be eligible for the
investment programs. It is likely that the requirement for full-time farming will result in
inefficient labor allocations and decreased returns to labor on hog farms.

It is not sustainable in the long run to enhance current farm employment in the hog
sector. This will only result in inefficient labor allocations, raise labor costs, and decrease
farmers’ labor income. Decreasing labor costs are crucial in improving the
competitiveness of the hog industry through expanding size. The fast decrease of the
number of active farmers will, nevertheless, have a real cost for rural areas and society as
a whole through the multiplier effects caused by decreasing employment and purchasing
expenditure.

We conclude that, even though production technology favors large scale
industrialized production units and large one-time investments, it is likely that the
industry’s adjustment to the new market environment will be retarded by market failures
in the local land and labor markets. It is crucial, therefore, that early retirement plans and
alternative employment activities increase the supply of land (either leasing or selling)

and decrease the number of households supported by the hog industry. In other words, to

170

decrease the hog industry’s adjustment costs and to promote the industry towards a
competitive structure it is important that adjustment programs focus on decreasing
transactions costs in rural labor and land markets. Further, because land constraints may
retard farmers from reaching low costs with environmentally friendly practices for
spreading slurry and manure, trade in manure between farms should be promoted.
Contracts to trade manure could replace expensive and sluggish land trading (either
purchases or leases) transactions and, therefore, decrease hog industry’s adjustment

costs.3

8.2 Uncertainty

Our results indicate that uncertainty has a significant effect on investments. The modeled
persistent shift in uncertainty decreased investments and slowed down the substitution of
capital for labor. This would imply that uncertainty will slow down adjustment
significantly, even though investment subsidies provide challenging incentives for
investments by reducing the capital costs as much as 50 %.

Nevertheless, the combined effects of the adjustment programs produce not only an
exceptional incentive to invest but also a disincentive to postpone investment. The

gradually decreasing direct income payments per capacity unit, the marked investment

 

2 By flexible environmental regulations we do not mean loosened standards of nutrient
leakages. Instead, contracts between firms could be designed to decrease their costs, given
the standards for nutrient leakages.

171

subsidies, and the risk that the program will run out of sufficient funding trigger a farmer
to invest as soon as possible, if he considers investing and plans to stay in business in the
long-run: The expected lost subsidies for delaying investments outweigh the
compensations required for the market risks involved in the investments, and it pays to
start risky investments as soon as possible. This phenomenon is supported by the
observation that investments started to emerge already in 1995 and 1996, even though
farmers did not know whether investment subsidies would be granted. In other words, it
paid for early investors to take the advantage of high direct income payments over the
first years in the EU, as compensation for the market risk and the risk that they may not
be eligible for the investment programs afterwards. '

It is expected, therefore, that the extensive adj ustrnent programs, combined with the
effects of the direct income subsidies, are hastening adjustment of the Finnish hog sector
to the new market environment. The final effects of the adj ustrnent program depend on

how much funds are used for subsidizing investments in the hog sector.

Chapter 9

SUMMARY AND CONCLUSIONS

The goal of this study was to investigate the effects of frictions caused by uncertainty,
irreversibility, and adjustment costs on investments in Finnish hog farms. External
restrictions, such as liquidity constraints caused by credit rationing, were also studied. The
main goal was to obtain estimates for adjustment rates, elasticities, and shadow prices while
allowing for comer solutions in the farmers’ investment choices. The most important
questions addressed were: does the production technology exhibit long-rim scale economies;
do adjustment costs exist and, if they exist, how are they best characterized; how are capital
and labor markets characterized; how do investments respond to shocks in input prices and
the output level; and how does uncertainty affect investments?

The study develops a method for estimating a generalized model of investment which
is consistent with the dynamic theory of the firm. The model accounts for price and output
uncertainty, irreversibility, and generalized adjustment costs. Price and output uncertainty
are modeled through stochastic transition equations. Adjustment costs are allowed to be
asymmetric in investment, to have nonzero intercepts (fixed adj ustrnent costs), and to have
kinks at zero investment. Thus, the study makes a contribution to the current investment

literature by estimating a generalized investment model so that irreversible investment

172

173

behavior is allowed to arise either from generalized adjustment costs or from uncertainty, or
both.

The model is estimated for a group of Finnish hog farms over the period 1977-93. The
model has two endogenous quasi-fixed capital goods, real estate and machinery. Gross
investments in real estate and machinery are each allowed to have positive values or,
alternatively, be trapped at zero. The third endogenous quasi-fixed input is labor services
which is either negative or positive, but is not zero. The fourth endogenous variable is an
aggregated variable input that is used as a numéraire. Consequently, a system of four
decision rules is estimated. Two out of the four decision variables are allowed to be zero
with positive probability. The sample is endogenously partitioned into the regimes of zero
and positive investments (four regimes in total) and, then, the decision rules are jointly
estimated using the maximum likelihood technique outlined in Chapter 5. The estimated
model has a similar structure to the censored Tobit model.

The results suggest that the Finnish hog industry is operating with increasing returns
to scale technology. Increasing firm size will result in labor savings and more efficient
utilization of farm capital. Summing up the long-rim scale effects and investment subsidies,
it is reasonable to expect that the Finnish hog industry has potential for reaching the average
cost level the Danish hog industry had in 1995. But to reach the Danish cost level, Finnish
production tmits have to at least triple their size.

There are also short-run scale economies in investments so that the larger the
investment is the lower adjustment costs realized. This result, combined with long-run

economies of scale, has important consequences for the adjustment of the Finnish hog

174

industry in the European Common Market. It suggests that the production technology favors
large scale industrialized hog production and drastic one time expansions. In other words,
hog production technology favors fast adjustment, or a swift to the new market
environment.

The results support the often posed view that the stringent production controls have
resulted in shortage of farm investment alternatives and inefficiently utilized, excess capital
on Finnish hog farms. This has, furthermore, implied low returns to farming capital. But
now as the production controls have been abolished, it is expected that farm expansion
provide a potential for more efficiently utilized and allocated farm capital. The initial excess
farm capital as well as farmer easy access to credit can allow for access to large investments
and fast adjustment.

But even though production technology favors fast adj ustrnent to the new market
environment and farmers appear to have unconstrained access to credit, it is likely that the
adjustment will be slowed down by inflexibilities and market failures in the local labor and
land markets. The adjustment rates for capital and labor were estimated at low values, which
suggests that capital stock and labor will adjust slowly towards their steady states. Labor
and capital markets are also closely linked to each other so that an inflexible labor market,
combined with excess labor in farming, will delay substitution of capital for labor.

Concerning the labor market, tripling the firm size would require an exit rate of
almost twice as large as the realized, actual average exit rates, provided expansions are
carried out over the five year transition period and aggregate production is kept constant. In

other words, the results signal that realized exit rates seem too small and rural labor market

175

does not allow for adjusting fast enough to the new market environment. For hastening the
adjustment it is, therefore, important that early retirement plans and alternative employment
programs increase the supply of land and decrease the number of households employed in
the hog industry.

The substantial structural shift needed to enhance a competitive industry structure is
going to have a real cost, because two thirds of the current producers would need to exit the
industry. These costs will be realized in terms of adjustment costs to the exiting farmers and
multiplier effects on local economies. Even though new investments on capital goods and
facilities generate positive multiplier effects in the local economy there are negative
multiplier effects too. These negative effects are caused by falling population and income in
rural areas which further reduce local consumption expenditures and shrink local
businesses.

Our results suggest that environmental regulations are going to play an increasingly
important role in determining hog production costs and spatial concentration of the hog
industry. The reasons for this are the combined effects of size economies in the industry
and environmental regulations, which tie the maximum size of the firm's hog production
unit and land area together. These environmental regulations are justified, of course,
because they aim at environmentally friendly utilization of manure and slurry. But if there
are market failures in the local land market, as our results suggest, inflexible regulations
may substantially increase hog production costs and slow down industry adj ustrnent.
Therefore, it would be essential to promote not only land trading and leasing transactions

but also transactions to trade manure and slurry. The hog industry’s adjustment costs could

176

be decreased if, for example, hog farms’ land area requirements could be at least partially
reduced through contracts of trading manure from hog farms to organically cultivated farms.

Our results indicate that uncertainty has a significant effect on investments. The
modeled persistent shift in uncertainty decreased investments and substitution of capital for
labor. This implies that uncertainty will slow down the adjustment significantly even though
investment subsidies provide challenging incentives for investments by reducing capital
costs as much as 50 %. Nevertheless, the combined effects of the adjustment programs
produce not only an exceptional incentive to invest but also a disincentive to postpone
investment. It is therefore expected that the programs will considerably hasten hog sector’s
adjustment to the new market environment.

A need for further investment analysis is evident. Some of our estimation results may
suggest significant farm specific individual effects, which are unobserved and which we
have not been able to control for. Therefore, unobserved individual effects on investments
or, more importantly, investment analysis in which time constant individual effects have
been factored out, require more research than we have been able to conduct in this study.
New methods have already been developed for factoring out unobserved individual effects
in discrete choice models and in dynamic models estimating Euler equations (see
Wooldridge 1995). These new methods open new alternatives for conducting empirical
research on investment behavior.

For conducting accurate investment analysis and implementing correct investment
decisions it would be essential to get further insights on how volatile the agricultural

commodity markets are in Finland and how well they are integrated to the markets in other

177

European countries. The effects of agricultural adjustment programs on farmer welfare
hinges crucially on how well the supply shocks caused by these programs are absorbed in
the markets. This, in turn, depends on how well the Finnish commodity markets are
integrated to the commodity markets in other European countries. Further research is also
called for to develop methods for insuring against risks involved in drastic agricultural
investments.

This research has focused on expanding farms, but it has suggested that it is the low
exit rate that will slow down the hog sector’s adjustment to the new market environment.
For better understanding the combined effects of the retirement plans, alternative
employment programs, and investment programs it would be essential to study further the
characteristics of the discrete decision between the three. alternatives: exit, continue with
current size, or expand. New knowledge of decisions between these discrete choices would
be valuable help for designing optimal adjustment programs that increase farmer and society
welfare.

As explained above, it is expected that hog industry adjustment, the resulting industry
structure, and the industry’s spatial concentration within and among the European countries,
will depend on environmental regulations. Therefore, it would be essential to study in detail
how these regulations might be designed for promoting an environmentally fi'iendly,

competitive, and spatially balanced hog industry structure in Europe.

LIST OF REFERENCES

 

Aaltone
F1

Cha

(21,.

LIST OF REFERENCES

Aaltonen, S. 1996. Adjustment of the Finnish Food Industry. In First Experiences of
Finland in the CAP. Ed. Kettunen, L: 43- 56.

Abel, A. B. & Eberly, J. C. 1994. A Unified Model of Investment Under Uncertainty. The
Amer. Econ. Rev. 84: 1369-1384.

Agra Europe. 1996. November 8, 1996.

Akerlof, G. A. 1970. The Market for Lemons: Qualitative Uncertainty and the Market
Mechanism. Quart. J. of Economics 84:488-500.

Amemiya, T. 1985. Advanced Econometrics. Harvard University Press. Cambridge,
Massachusetts. 521pp.

Arrow, K. J. 1968. Optimal Capital Policy with Irreversible Investment. In Value Capital
and Growth. Papers in Honour of Sir John Hicks. Ed. Wolfe, J. N: 1- 19. Edinburgh
University Press, Edinburgh.

Caballero, R. J. 1991. On the Sign of the Investrnent-Uncertainty Relationship. Amer.
Econ. Rev. 81 :279-88.

Capozza, D. & Li, Y.1994. The Intensity and Timing of Investment: The Case of Land.
The Amer. Econ. Rev. 84:889-904.

Chambers, R. G. 1988. Applied Production Analysis. A Dual Approach. Cambridge
University Press, New York. 331pp.

Chang C.-C. & Stefanou, S. E. 1988. Specification and Estimation of Asyrmnetric
Adjustment Rates for Quasi-Fixed Factors of Production. J. of Econ. Dynamics and
Control 12:145-151.

Chavas, J.-P. 1994. Production and Investment Decisions Under Sunk Cost and Temporal
Uncertainty. Amer. J. Agr. Econ. 76:114-127.

Danmarks Statistik. 1996. Agricultural Statistics 1995.

178

179

Davidson, R. & MacKinnon, J. G. 1993. Estimation and Inference in Econometrics.
Oxford University Press, New York. 874pp.

Dickey, D. & Fuller, W. 1979. Distribution of the Estimators for Autoregressive Time
Series with a Unit Root. Journal of the American Statistical Association 74:427-31.

Dixit, A. K. & Pindyck, R. S. 1994. Investment under Uncertainty. 468 pp. Princeton,
New Jersey. 468pp.

McDonald, R, & Siegel, D. 1986. The Value of Waiting to Invest. Quarterly Journal of
Economics 101:707-728.

Eichberger, J. 1989. A Note on Bankruptcy Rules and Credit Constraints in Temporary
Equilibrium. Econometrica 57:707-716.

Epstein, L. G. 1981. Duality Theory and Functional Forms for Dynamic Factor Demands.
Review of Econ. Studies, Jan. 81:81-95.

- & Denny, M. 1980. Endogenous Capital Utilization in a Short-Run Production
Model. Theory and an Empirical Application. J of Econometrics 12:189-207.

- & Denny, M. 1983. The Multivariate Flexible Accelerator Model: Its Empirical
Restrictions and an Application to US. Manufacturing. Econometrica 51:647-673.

- & Yatchew, J. 1985. The Empirical Determination of Technology and Expectations.
A Simplified Procedure. J. of Econometrics 27:235-258.

Femandez-Comejo, J. & Gempesaw, C. M. & Elterich, J. G. & Stefanou, S. E. 1992.
Dynamic Measures of Scope and Scale Economies: An Application to German
Agriculture. Amer. J. Agr. Econ. 74:329-342.

Fousekis, P. & Shortle, J. S. 1995. Investment Demand when Economic Depreciation is
Stochastic. Amer. J. Agr. Econ. 77:990-1000.

Hamilton, J. D. 1994. Time Series Analysis. Princeton University Press. New Jersey.
799pp.

Hansen, L. P. Large Sample Properties of Generalized Method of Moments Estimators.
Econometrica 50: 1029-1054.

 

 

Hsu

Ingc

Jgh

180

Hansen, L.P. & Sargent, T. J. 1980. Formulating and Estimating Dynamic Linear
Rational Expectations Models. Journal of Economic Dynamics and Control 2:7-46.

- & Sargent, T. J. 1981. Linear Rational Expectations Models for Dynamically
Interrelated Variables. In Rational Expectations and Econometric Practice. 1:127-
156. Eds. Lucas, E. J. Jr and Sargent T. J. The University of Minnesota Press,
Minneapolis.

- & Singleton, K. J. 1982. Generalized Instrumental Variables Estimation of Nonlinear
Rational Expectations Models. Econometrica 50:1269-1286.

Heckman, J. J. 1976. The Common Structure of Statistical Models of Truncation, Sample

Selection and Limited Dependent Variables and a Simple Estimator for such Models.
Annals of Economic and Social Measurement 5:475-492.

Heikkila, A. M. 1987. Lypsykarjayritysten optimaalinen koko. Maatal. tal. tutk.lait. tied.
132:1-70.

Hernila, K. 1983. Measuring Technological Change in Agriculture. An Application based
on the CES Production Function. J. Sci. Agr. Soc. of Finland 54:165-223.

Hertzler, G. 1991. Dynamic Decisions Under Risk: Application of Ito Stochastic Control
in Agriculture. Amer. J. Agr. Econ. 73:1126—1137.

Howard, W. H. & Shumway, C. R. 1988. Dynamic Adjustment in the US. Dairy
Industry. Amer. J. Agr. Econ. 70:837-847.

- 1989. Nonrobustness of Dynamic Dual Models of the US. Dairy Industry.
Northeastern J. of Agr. and Resource Econ. 18: 1 8-25.

Hsu, S.-H. & Chang, C.-C. 1990. An Adjustment-Cost Rationalization of Asset Fixity
Theory. Amer. J. Agr. Econ. 72:298-308.

Ingersoll, J. E. Jr. & Ross S. A. 1992 Waiting to Invest: Investment and Uncertainty. J. of
Business 65: 1-29.

Johnson, G. L. 1956. Supply Functions -Some Facts and Notions. In Agricultural
Adjustment Problems in a Growing Economy. Eds. Heady, E. 0. Et al. Iowa State
University Press, Ames. '

Kallinen, A. & Heikkila, E. & Auer-Hautamaki, V. 1996. Sihanlihantuotannon EU-
Sopeutuminen. Food and Farm Facts.

181

Kamien, M. & Schwartz, N. 1991. Dynamic Optimization. The Calculus of Variations
and Optimal Control in Economics and Management. 2nd Ed. New York. 377pp.

Keane, M. P. & Wolpin, K. I. 1994. The Solution and Estimation of Discrete Choice
Dynamic Programming Models by Simulation and Interpolation: Monte Carlo
Evidence. The Rev. of Econ. and Stat. 76:648-672.

Kennan, J. 1979. The Estimation of Partial Adjustment Models with Rational
Expectations. Econometrica 47: 1441-1455.

Kola, J. 1987. Perustamislupajarjestehna tuotannon ohjaus- ja rajoituskeinona. The Agr.
Econ. Res. Inst. Res. Reports 131:1-84.

Kwiatkowski, D. & Phillips, P. C.B. & Schmidt, P. & Shin, Y. 1992. Testing the Null
Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of
Econometrics 54:159-178.

McLaren, K. R. & Cooper, R. J. 1980. Intertemporal Duality: Application to the Theory
of the Firm. Econometrica 48: 1755-62.

Larson, B. A. 1989. Technical Change and Applications of Dynamic Duality to
Agriculture: Comment. Amer. J. Agr. Econ. 71:799-802.

Lucas, R. E. Jr. 1967. Optimal Investment Policy and The Flexible Accelerator.
International Econ. Rev. 8:78-85.

Luh, Y.-H. & Stefanou, S. E. 1996. Estimating Dynamic Dual Models under Nonstatic
Expectations. Amer. J. Ag. Econ. 78:991-1003.

Maddala, G. S. 1983.Limited Dependent and Qualitative Variables in Econometrics.
Econometric Society Monographs No.3. Cambridge University Press. 401pp.

Meese, R. 1980. Dynamic Factor Demand Schedules for Labour and Capital Under
Rational Expectations. J. of Econometrics 14:141-158.

Ministry of Agriculture and Forestry. 1996. Maatalouspoliittisen ty6ryhmfln valiraportti.
Tybryhmamuistio 14:1-127. Helsinki.

Mortensen, D. T. 197 3. Generalized Costs of Adjustment and Dynamic Factor Demand
Theory. Econometrica 41:657-665.

Mussa, M.. 1977. External and Internal Adjustment Costs and the Theory of Aggregate
and Firm lnvestrnent. Econometrica 44:163-178.

182

Official Statistics of Finland. 1996. Agriculture and Forestry 1996:2.
- 1996. Agriculture and Forestry. Farm Register 1995.
- 1996. Monthly Review of Agricultural Statistics 1996.

Oude Lansink, A. 1996. Asymmetric Adjustment of Dynamic Factors at the Firm Level.
A Contributed Paper Presented at the Eight EAAE-Congress, Edinburgh.

Okonomien i Landbrugets Driftsgrene 1994/1995. 1996. Landbrugs- og Fiskeriministeriet
Serie B nr. 79:1-119.

Pajuoja, H. 1995. Kulutus ja hakkuukayttaytyminen kirjanpitotiloilla. English summary:
Consumption and Harvesting Behaviour of Bookkeeping Farms in Finland.
University of Helsinki. Dept. of Forest Econ. 3:1-81.

Penttinen, M. & Lausti, A. & Kasanen, E. & Puttonen, V. 1996. Risks and Returns in
Forest lnvestrnents in Finland. The Finnish Journal of Business Economics
46:109-122.

Pindyck, R. S. 1991. Irreversibility, Uncertainty and Investment. J. of Econ. Literature
29:1110-1148.

- & Rotemberg, J. J. 1983. Dynamic Factor Demands and the Effects of Energy Price
Shocks. The Amer. Econ. Rev. 73:1066-1079.

Prucha, I. R. & Nadiri, M. I. 1986. A Comparison of Alternative Methods for the
Estimation of Dynamic Factor Demand Models under Non-Static Expectations. J. of
Econometrics 33:187-21 1.

Robison, L. J. & Barry, P. J. 1987. The Competitive Firm’s Response to Risk. Macmillan
Publishing Company, New York. 324pp.

- 1996. Present Value Models and Investment Analysis. The Academic Page,
Northport, Alabama. 661pp.

Rothschild, M. 1971. On the Cost of Adjustment. Quart. J. of Econ. 85:605-622.

Rust, J. 1987. Optimal Replacement of GMC Bus Engines: An Empirical Model of
Harold Zurcher. Econometrica 55:999-1033.

 

 

Stei;

Stei

Sto

Ta:

Ta

Ti

183

Ryhanen, M. 1992. Tybn ja paaoman substituutio seka tekninen kehitys Suomen
maataloudessa vuosina 1962-1989. Maanviljelystalouden lisensiaattitutkimus.
Helsingin Yliopisto.

Sakellaris, P. 1995. Investment under Uncertain Market Conditions. The Review of
Economics and Statistics 127:455-469.

Schmidt, P. 1981.Constraints on the Parameters in Simultaneous Tobit and Probit
Models. In Structural Analysis of Discrete Data with Econometric Applications
1:423-434. Eds. Manski, C. F. & McFadden, D. The MIT Press. London.

Shapiro, M. D. 1986. The Dynamic Demand for Capital and Labor. The Quart. J. of Econ.
1986:513-542.

Stefanou, S. E. 1987. Technical Change, Uncertainty, and Investment. Amer. J. Agr.
Econ. 69:158-165.

- 1989. Returns to Scale in the Long Run. The Dynamic Theory of Cost. Southern
Econ. J. 55:570-579.

Steigum, E. Jr. 1983. A Financial Theory of Investment Behavior. Econometrica 51:
637-645.

Stern, S. 1994. Two Dynamic Discrete Choice Estimation Problems and Simulation
Methods Solutions. The Rev. of Econ. and Stat. 76:695-702.

Stock, J. & Wise, D. 1990. Pensions, the Option Value of Work and Retirement.
Econometrica 58:1151-1180.

Taylor, C. R. 1984. Stochastic Dynamic Duality: Theory and Empirical Applicability.
Amer. J. Agr. Econ. 66:351-357.

Taylor, T. G. & Monson, M. J. 1985. Dynamic Factor Demands for Aggregate
Southeastern United States Agriculture. Southern J. of Agr. Econ. 17:1-9.

Thijssen, G. 1994. Supply Response and Dynamic Factor Demand of Dutch Dairy Farms.
Eur. Rev. of Agr. Econ. 21:241-258.

- 1996. Farmers’ Investment Behavior: An Empirical Assessment of Two
Specifications of Expectations. Amer. J. of Agr. Econ. 78:166-174.

Tirole, J. 1992. The Theory of Industrial Organization. The MIT Press, Cambridge.
479pp.

Tread

V asa

Weer

Woo

Ylat

 

 

 

184

Treadway, A. B. 1970. Adjustment Costs and Variable Inputs in the Theory of the
Competitive Firm. J. of Econ. Theory 2:329-347.

Vasavada, U. & Chambers, R. C. 1986. Investment in US. Agriculture. Amer. J. Agr.
Econ. 68:950-960.

Weersink, A. 1990. Nonrobustness of Dynamic Dual Models of the Northeastern and
US. Dairy Industries. 19:12-16.

- & Tauer, L. W. 1989. Comparative Analysis of Investment Models for New York
Dairy Farms. Amer. J. Agr. Econ. 71:136-145.

Wooldridge, J. M. 1995. Multiplicative Panel Data Models Without the Strict
Exogeneity Assumption. MSU Department of Economics Working Papers.

Ylatalo, M. 1991. Determination of the Capitalized and Market Values of Supplementary
Arable Land in Southern Finland, 1972-1986. J. of Agr. Sci. in Finland 63:151-254.

- & Pyykkbnen, P. 1991. Maatilatalouden paaomakanta seka rakennekehitys ja
paaomahuolto 1990-luvulla. Pellervo Economics Research Institute Publications
10:1-74. '

- & Pyykkonen, P. 1992. Pellon vuokraaminen ja vuokrahinnat. Pellervo Economic
Research Institute. Reports and Discussion Papers 109:1-47.

Zeldes, S. P. 1989. Consrunption and Liquidity Constraints: An Empirical Investigation.
J. of Political Economy 97:305-346.

APPENDICES

APPENDIX A

APPENDIX A

Parameter Estimates with the Data Split into the Credit Market Regimes

The Model Estimated over the Period of Rationed Credit Market 1977-85.

 

 

Parameter Estimate Standard error Parameter Estimate Standard error
am" 1.0397 0.0395 11. 0.2016 0.3526
11, 0.2759 0.2925
aH -0.0318 0.0206 11, -0.6730 0.3581
a,, -0.7054 0.1257
a,, 0.0504 0.0258 1),. -0.2503 0.000
1),, 0.2100 0.000
a: 1.0741 0.3527 Dz: 4.9823 0.000
1),, -0.3564 0.000
arr -0.2172 0.000 D32 0.6326 0.000
832 -0.87 14 0.0795 D33 ‘1-3302 0-000
11,, -1.0683 0.000
M.. 0.1001 0.0105
A” 00031 0.0015 191,, -0.0059 0.0053
A2. 0,0095 0,0049 14,, 0.0210 0.0319
A22 0.0840 0.0588 M31 0.0046 0.0079
A31 -0.0021 0.001 1 M32 -0.0139 0.0077
A32 -0.0051 0.0058 Mn 0.1507 0.0091
11,, -0.0040 0.0021
y for [>0 0.2095 0.0078
13. -0.0216 0.0163 2
E, 03799 0.5146 "’4:
13, 0.0348 0.0202 0:2
B 0 9123 0 0805 "’3: ' '
' ' bad year 0.0037 0.0261

 

' The number of observations is 845 and the average value of the loglikelihood function is 1.308.
" An intercept in the demand equation for the numéraire input. It is a function of structural form

parameters.

185

APPENDIX A

The Model Estimated over the Period of Nonrationed Credit Market 1986-93.

 

 

Parameter Estimate Standard error Parameter Estimate Standard error

a; 1.0387 0.0651 11, 0.2017 0.3108

11, 0.2760 0.7617

all -0.0322 0.0174 11, -0.6730 0.2571
a., -0.7054 0.1005

a., 0.0501 0.0322 1),, -0.2502 4.1529

1),, 0.2103 0.000

a: 1.0740 0.3705 D22 -1-9822 0.000

1),, -0.3559 2.0032

an -0.2173 1.9646 D32 0.6331 0000

an -0.8715 0.000 D33 4.3302 0.000
a,, -1.0684 0.000

_ __ M.. 0.1010 0.0079

A” 00003 0.0009 M,, 00004 0.0029

A21 0.0091 0.0024 M22 0.0226 0000

A22 0.0840 0.0182 M31 0.0082 0.0060

A31 .0.0002 0.0010 M32 41.0068 0.0047

A32 -0.0030 0.0049 Mn 0.1530 0.0089
41,, -0.0019 0.0023

E 0 022, 0 0107 y for 11>0 0.2085 0.0078

- . . 2

E; 4,3799 0087,, -o,,, - 0.0257 0.0093

E, 0.0348 0.0204 «13,, - 0.1603 0.01 14

0 9 22 0 073 -of,, - 0.0180 0.0084

B ' l ' 5 bad year 0.0035 0.000

 

‘ The number of observations is 1,083 and the average value of the loglikelihood function is 1.109.
" An intercept in the demand equation for the numéraire input. It is a function of structural form

parameters.

186

APPENDIX B‘

APPENDIX B

Response Probabilities and Short Run Elasticities
The Full Sample Model:

Response Probabilities for Positive Investments.

 

 

 

 

 

 

 

 

 

Real estate Machinery

With
respect to gross investment net investment gross investment net investment
Log of output 0.00027 0.00025 0.000174 0.00022
Log of prices:

real estate 0.00013 0.00012 0.000124 0.00015

machinery 0.00054 0.00052 -0.00060 -0.00074

wage rate -0.00083 -0.00080 0.00040 0.00049
Capital

real estate -0.1346 -0.19206 0.00757 0.00944

machinery 0.00242 0.00233 0.13967 0.02865
Labor -0.02681 -0.02578 0.03246 0.04045

Short-Run Elasticities of Real Estate Investments.
With Gross investment Net investment
respect to
conditional unconditional conditional unconditional

Output 0.00019 0.000889 0.00019 0.000939
Prices:

real estate 9.25171 0.000434 9.07699 0.000458

machinery 0.00039 0.001810 0.000379 0.00191 1

wage rate -0.00060 -0.00279 -0.000584 -0.00295
Capital:

real estate -0.09633 -0.45164 -0. 14019 -0.70716

machinery 0.00173 0.00812 0.00170 0.00857
Labor -0.01918 -0.08994 -0.01882 -0.09493

 

187

Short-Run Elasticities of Machinery Investments, Evaluated at the Means.

APPENDIX B

 

 

 

 

 

 

 

 

With Gross investment Net investment
respect to
conditional unconditional conditional unconditional
Output 0.000361 0.000592 0.00035 0.00072
Prices:
real estate 0.000256 0.000420 0.00025 0.00051
machinery -0.001233 -0.00202 -0.001 18 -0.00247
wage rate 0.000822 0.001347 0.00079 0.00164
Capital:
real estate 0.015687 0.02571 0.01505 0.03 139
machinery 0.28936 0.47422 0.04570 0.09530
Labor 0.067244 0.1 1020 0.06451 0.13454
The Nonrationed Subsample Model:
Response Probabilities for Positive Investments.
Real estate Machinery
With
respect to gross investment net invesunent gross investment net investment
Log of output -0.00131 -0.00124 0.00208 0.00236
Log of prices:
real estate -0.00168 -0.00157 0.00406 0.00460
machinery 0.01086 0.01021 -0.01390 -0.01574
wage rate -0.01041 -0.00978 0.00963 0.01091
Capital
real estate -0.18617 -0.23275 0.07946 0.08999
machinery 0.02141 0.02013 0.10609 -0.02773
Labor -0.063 18 -0.05940 -0.023 85 -0.02700

 

188

APPENDIX B

Short-Run Elasticities of Real Estate Investments.

 

 

 

With Gross investment Net investment
respect to
conditional unconditional conditional unconditional

Output -0.00107 -0.00514 -0.00105 -0.00544
Prices:

real estate -0.00137 -0.00656 -0.00134 -0.00694

machinery 0.00886 0.04250 0.00867 0.04495

wage rate -0.00849 -0.04073 -0.00831 -0.04307
Capital:

real estate -0.15197 -0.72876 -0. 19762 -1.02477

machinery 0.01747 0.08379 0.01709 0.08861
Labor -0.05158 -0.24733 -0.05044 -0.26155

 

Short-Run Elasticities of Machinery Investments, Evaluated at the Means.

 

 

 

With Gross investment Net investment
respect to
conditional unconditional conditional unconditional

Output 0.00333 0.00634 0.003 18 0.00765
Prices: . '

real estate 0.00650 0.01237 0.00621 0.01492

machinery -0.02225 -0.0423 1 -0.02123 -0.05 105

wage rate 0.01542 0.02932 0.01472 0.03538
Capital:

real estate 0.12722 0.24194 0.12142 0.29192

machinery 0. 16986 0.32301 -0.03742 -0.08995
Labor -0.03818 -0.07261 -0.03644 -0.08760

 

189

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