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LIBRARY
Michigan State
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This is to certify that the

dissertation entitled

EFFECTS OF OUTPUT CHANGES ON FACTOR DEMAND
IN JAPANESE AGRICULTURE:
A FLEXIBLE DYNAMIC COST FUNCTION APPROACH

presented by

Shunji Oniki
has been accepted towards fulﬁllment

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Ph.D. degree in Agricultural Economics

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mm'

 

 

 

 

EFFECTS OF OUTPUT CHANGES ON FACTOR DEMAND
IN JAPANESE AGRICULTURE:
A FLEXIBLE DYNAMIC COST FUNCTION APPROACH

By

Shunji Oniki

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1 996

ABSTRACT

EFFECTS OF OUTPUT CHANGES ON FACTOR DEMAND
IN JAPANESE AGRICULTURE:
A FLEXIBLE DYNAMIC COST FUNCTION APPROACH

By

Shunji Oniki

Agricultural production in Japan is anticipated to contract due to import liberalization and
this output reduction will Chang input use for the production, such as labor and chemicals.
This study explores effects of changes in output on factor demand through estimation of the
factor demand equations and simulation of factor adjustment. In Japanese agriculture, factors
are not likely to be adjusted instantaneously to their equilibrium levels due to high costs of
adjustment, habits and customs, and time lags in the transmission of information. As a result,
this study applies an error correction model based on share equations derived from a translog
cost function. The model maintains the ﬂexible properties of a translog function but also
permits short-run disequilibrium. Estimation of the dynamic model shows that output
elasticity of labor demand is greater than unity, while the elasticities of chemical and capital
use are less than unity. It implies that, in the long-run, average use of chemicals per unit of
output increases, and the labor required to produce a unit of output declines.

In order to incorporate the effects of changes in factor prices into the analysis of output
effects, a short-term factor adjustment process is simulated. Simulation of long-run
equilibrium adjustment of factor use shows that chemical use will decline little, while labor
declines greatly. Simulation using the dynamic model of factor share adjustment also shows

that shares of chemical and capital increase, while the share of labor declines. These results

are generally consistent with earlier ﬁndings on output elasticities.

Cepyright by
SHUNJI ONIKI
1996

To my parents.

ACKNOWLEDGMENTS

I wish to express my special thanks to Robert J. Myers, my dissertation supervisor, for
his invaluable support, helpful advise, and kindness. This dissertation could not be
completed without his positive and useful suggestions. Also, I owe my sincerely gratitude
to Richard H. Bernsten, an advisor throughout my graduate study, for his warm-hearted
supports, his repeated encouragement, and patient advising in my continuous study at
Michigan State University. I would like to express my appreciation to Eileen 0. van
Ravenswaay for her valuable suggestions and constructive criticism. Also, I acknowledge
David Schweikhardt and Jeffrey Wooldridge for their providing beneﬁcial ideas and
suggestions in development of the dissertation.

I would like to extend my appreciation to the Ofﬁce of lntemational Education
Exchange for providing ﬁnancial support and an opportunity to work for Japanese school
program. Also, I would like to acknowledge my parents for their general support for my

study abroad.

vi

TABLE OF CONTENTS

LIST OF TABLES .......................................... IX
LIST OF FIGURES ........................................ xii
CHAPTER 1
INTRODUCTION ........................................ 1
1.1 Problem Statement ..................................... 1
12 Research Objectives .................................... 2
1.3 Previous Studies of Aggregate Production Functions ---------------- 3
1,4 Outline of the Dissertation ................................ 10
CHAPTER 2
PROBLEM SETTING .................................... 1 I
2.1 Agricultural Trade Protection and Rural Problems ----------------- 11
22 Inputs in Japanese Agriculture ............................. 16
23 Changes in Output and Factor USC ........................... 34
CHAPTER 3
A DYNAMIC COST FIJ'NCTION MODEL ....................... 40
3.1 Duality and Cost Function ................................ 40
32 Functional Form ...................................... 43
3.3 Dynamic Models ..................................... 52
CHAPTER 4
DATA AND PRELIMINARY TESTING ......................... 64
41 Data ............................................. 64
42 Stationarity and Cointegration ............................. 66
CHAPTER 5
RESULTS ............................................ 73
5.1 Speciﬁcation Tests .................................... 73
52 Estimates and EIaStiCItICS ................................ 80

vii

CHAPTER 6

SIMULATION FOR FACTOR ADJUSTMENT -------------------- 94

6. 1 Output Path Under Trade Liberalization ---------------------- 94

6. 2 Long-Run Equilibrium Adjustment ......................... 97

6.4 Implication for Trade Liberalization ------------------------- 105
CHAPTER 7

SUMMARY AND CONCLUSIONS .......................... 1 12
APPENDIX ............................................ l 1 8
BIBLIOGRAPHY ........................................ I 34

viii

LIST OF TABLES

Table 2.2.1 Production Costs of Rice by Farm Size per Hectare, 1993, Japan ----- 18
Table 2.2.2 Number of Farms by Size in Japan, 1950-1990 (thousands) --------- 20
Table 2.2.3 Population of Farm Households -------------------------- 23
Table 2.2.4 Number of Farm Households (thousands) -------------------- 24

Table 2.2.5 Average Working Hours per Farm in Japan (hours per farm household) - 26

Table 2.2.6 Number of Temporary Workers Away From Home (thousands) ------ 27
Table 2.2.7 Consumption of Major Fertilizers in Japan (1,000 tons) ----------- 29
Table 2.2.8 Average Number of Tractors per Farm in 1992 ---------------- 32
Table 2.2.9 The Number of Maj or Machinery Items Owned by Japanese Farmers (unit: 1,000)
...................................................... 34
Table 4.2.1 The Dickey Fuller Tests and the Phillips-Perron Tests of Unit Roots in the
val'iables ooooooooooooooooooooooooooooooooooooooooooooooo 73
Table 5.2.1 Output Elasticities of Factor Demand Estimated in Various Models ' ° - 84
Table 5.2.2 The Allen’s Partial Elasticities of Factor Substitution Estimated by

the Flexible Dynamic Model ................................... 88
Table 5.2.3 Own- and Cross-Price Elasticities of Factor Demand Estimated Flexible Dynamic
MOdeI ........................................... ' ...... 8 8
Table 5.2.4 Estimates of Technological Change Bias -------------------- 92

Table A.4.2.1 Phillips-Perron Tests for Unit Roots in Individual Variables in Dickey Fuller
Equations with Constants and Time Trend ------------------------- 118

Table A.4.2.2 Dickey-Fuller Tests of the Residual from Cointegrating Regression - 119

ix

Table A.4.2.3 Phillips-Perron Tests for Residuals from Cointegration among S., L, D, CH, K,

and Q ................................................ 119
Table A5. 1 .1 Hessian Matrices of the Flexible Model ------------------ 120
Table A.5.1.2 Hessian Matrices of the Linear Dynamic Model ------------- 120
Table A.5.1.3 Hessian Matrices of the Static Model -------------------- 120
Table A5. 1 .4 Eigen Vectors of Hessian Matrices --------------------- 120
Table A.5.2.1 Parameter Estimates of Flexible Model ------------------ 121
Table A.5.2.2 Estimates of Linear Dynamic Model -------------------- 123
Table A.5.2.3 Estimates of Static Translog Models with Cost Equation -------- 125
Table A.5.2.4 Estimates of Static Translog Models with Cost Equation with “In t” for Time
Variable ............................................... 1 26
Table A.5.2.5 Parameter Estimates of Static Translog Model, Share Equations - - - 127
Table A.5.2.6 Estimates of Cobb-Douglas Models --------------------- 128

Table A.5.2.7 Allen's Partial Elasticities of Substitution Estimated by the Flexible Model
..................................................... 129

Table A.5.2.8 Allen's Partial Elasticities of Substitution Estimated by the Static Model
..................................................... 129

Table A.5.2.9 Price Elasticities of Factor Demand Estimated by the Flexible Model 130
Table A52. 10 Price Elasticities of Factor Demand Estimated by the Static Model - 130

Table A.5.2.11 Output Elasticities of Factor Demand Estimated by the Flexible Model
..................................................... I3 1

Table A52. 12 Output Elasticities of F actor Demand Estimated by the Linear Dynamic Model
..................................................... I 3 I

Table A.5.2.13 Output Elasticities of Factor Demand Estimated by Static Model - - 131
Table A.5.2.14 Elasticities of Scale with respect to Output in Static Models ----- 132

Table A.5.2.15 Elasticities of Technological Changes Estimated the Flexible Dynamic Model
..................................................... I 32

Table A.5.2.16 Elasticities of Technological Changes Estimated in the Static Model 132

Table A.5.2.17 Elasticities of Technological Changes Estimated in the Flexible Dynamic
Model with Linear Time Trend Variables -------------------------- 133

xi

LIST OF FIGURES

Figure 2.1 Effects of Changes in Output on Factor Demand ---------------- 37
Figure 6.1 Proportion of Base Output in Year 1 ----------------------- 96

Figure 6.2a Proportion of Input Use in Year 1 Estimated by Equilibrium Displacement Model
in Case I .............................................. 100

Figure 6.2b Proportion of Input Use in Year 1 Estimated by Equilibrium Displacement Model
in Case II .............................................. 101

Figure 6.2c Proportion of Input Use in Year 1 Estimated by Equilibrium Displacement Model
in Case III ............................................. 102

Figure 6.2d Proportion of Input Use in Year 1 Estimated by Equilibrium Displacement Model
in Case IV ............................................. 103

Figure 6.3a Proportion of Input Share in Year 1 Estimated by Dynamic Model in Case I
..................................................... I 08

Figure 6.3b Proportion of Input Share in Year 1 Estimated by Dynamic Model in Case 11
..................................................... I 09

Figure 6.3c Proportion of Input Share in Year 1 Estimated by Dynamic Model in Case 111
..................................................... l 10

Figure 6.3d Proportion of Input Share in Year 1 Estimated by Dynamic Model in Case IV
..................................................... l I 1

xii

CHAPTER 1

INTRODUCTION

1.1 Problem Statement

The General Agreement on Tariffs and Trade (GATT) of 1993 requires all member
countries to reduce tariff rates and non-tariff restrictions on agricultural commodities. In
Japan, agricultural import liberalization will decrease demand for domestically produced
commodities since prices of most agricultural commodities in Japan are several times higher
than their international prices.1 Policy makers are concerned how a reduction in domestic
production will affect the structure of Japanese agriculture, and in particular, the
environmental impact of a reduction in the use of agricultural chemicals, and the potential
increase in an employment problem. However, little empirical research has been done on how
changes in production affect input use in Japanese agriculture.

In order to explore the impact of output reductions induced by trade liberalization on the
structure of Japanese agriculture, this study analyzes the effects of changes in output on factor
demand. While many studies have analyzed the effects of changes in input prices on output
supply using the production function linking inputs and output, there is currently little

research on how output changes may affect the structure of input demand. For example,

 

'Another factor is the rising value of the yen. For example, the Japanese yen rose
about 50 percent in terms of the US dollar from 1990 to 1995.

1

2

although studies have evaluated the effects of environmental policies that restrict input use
on total output,2 few studies have estimated how a change in output would affect demand for
an input that is harmful to the environment. However, because environmental issues and rural
employment problems are of great policy importance, inputs, including agricultural chemicals
and labor, have become important factors for policy analysis. Thus, it is important to develop

quantitative measures of impacts of output changes on input demand.

1.2 Research Objectives

This study has three main objectives:

1. To estimate a dynamic factor demand model, using data on agricultural production and
prices in Japan for the period from 1951 to 1992.

2. To develop estimates of elasticities of input demand with respect to output levels and input
prices, as well as partial elasticities of factor substitution and the extent of biased
technological change in Japanese agriculture.

3. To simulate factor use 10 years into the future under different scenarios as to how import
liberalization would affect output levels and factor prices.

The ﬁrst objective involves developing a dynamic model that is useful for carrying out a
structural analysis of agricultural production where full input adjustment may not be assumed
in the short run. The model is speciﬁed to be as ﬂexible as possible in order to avoid a priori
assumptions on factor substitution and production homotheticity. This allows hypotheses on

the structure of production to be treated as testable rather than imposed a priori.

 

2Dean (1993) provides a extensive survey of literature on this issue.

3

In the second objective the production structure is analyzed in terms of factor demand and
bias in technological change. Although the primary interest of this study lies with the effect
of output changes on factor demand, this output effect is closely related to substitution
between factors and technological change. Therefore, it is important to analyze the whole
structure of production. Analytical tools used for this purpose include output elasticities of
factor demand, partial elasticities of factor substitution, own- and cross-price elasticities of
factor demand, and elasticities of technological change bias.

While this structural analysis deals with long-run elasticities, and therefore long-run
effects on factor demand, it is also interesting to consider the dynamic path of factor
adjustment in the context of Japanese import liberalization policy. Thus, the third and ﬁnal
goal of the study is to simulate factor adjustment, using the long-run equilibrimn model which
allows for short-run disequilibrium. These simulations, in addition to estimation of the long-
run output elasticity, will provide comprehensive insights about how output changes might

affect factor use in Japanese agriculture.

1.3 Previous Studies of Aggregate Production Functions
Aggregate production function analyses have relied on economic theory and econometric
models. In terms of economic theory, duality theory has played a major role in analyzing both
of these aspects in recent years. Indeed, in the I960S and the early 19703, production
function analysis has moved from direct estimation of production functions and ﬁrst-order
conditions to application of duality theory using Shephard’s lemma and Hotelling’s lemma.
In terms of econometric models, many different functional forms have been used in

aggregate production function analysis. Before the 19603, the Cobb-Douglas model was

4

applied extensively. Advantages of this model include simplicity, its straightforward
mathematical properties, and compatibility with actual data. In 1961, Arrow and others
raised a question about ﬂexibility of the Cobb-Douglas form and developed the constant
elasticity of substitution (CES) model. Uzawa (1962) developed the multi-factor CES model.
The CBS and its variations have been applied in a number of empirical works. For example,
studies of Japanese agriculture by Shintani and Hayami (1975), and Kawagoe (1986), applied
the two-stage CES production function. Since the 19703 various other ﬂexible models have
also been used. One of the most widely used models is the translog developed by
Christensen, Jorgenson and Lau (1971, 1973). Binswanger (1974a, 1974b) used a translog
cost functionin analyses of agricultural production in the United States and introduced a
method to measure biased technological changes in the translog model. According to his
estimation results, the usual assumption of neutral technological change was not supported
by the data. Also, he found that elasticities of substitution are not constant across factors.
These results showed that previous models, such as Cobb-Douglas and CBS, were not valid
and justiﬁed application of more ﬂexible functional forms.

Technological change bias, a nonhomothetic production process, and factor price changes
should all be incorporated in an analysis of production. In a generalized Leontief cost
function study of Canadian agriculture, Lopez (1980) showed that a change in factor shares
was not being caused by a technological change bias, but by output changes and factor price
changes. Thus, he argues that if the assumption of a homothetic production process is
imposed on the model, the effects of output changes are incorrectly attributed to biased
technological change, even if technological progress is, in fact, Hick’s neutral. This ﬁnding

raised a question regarding the measurement of technological bias in models with restrictive

5

functional forms that assume homotheticity. Binswanger implicitly imposed a homothetic
production process when he measured technological change bias. Also, Ray (1982) imposed
the assumption of Hick’s neutral technical change when using a translog cost model of US
agriculture. Assumptions in these studies may have led to misspeciﬁcation and erroneous
conclusions.

Economists have carried out many aggregate production function studies for Japanese
agriculture, many of which evaluate technological change bias and productivity. These
include pioneering works by Hayarni and Ruttan (1970, 1971), Hayanri (1973), and Shintani
and Hayarni (1975), which tested the induced innovation hypothesis initially suggested by
Hicks (1934). Hayami and Ruttan (1970, 1971) and Kawagoe, et al. (1986) compared the
paths of technological progress in Japan and in the United States. These authors found that,
since land is a relatively scarce resource in Japan, a land-saving technology, such as high-
yielding varieties, was developed. On the other hand, as labor was relatively scarce in the
US, labor-saving technology, such as large-sized mechanization, was developed. Thus, by
comparing development patterns in these distinct countries, they successfully characterized
the direction of bias in technological innovations. However, the distinction between the two
countries has recently diminished. In Japan, as the demand for labor rose in the industrial
sector, it became a relatively scarce factor in rural areas as well. In the United States, the
development of high-yielding varieties and application of fertilizers has accelerated as land has
become more scarce.

Most studies using models with ﬂexible functional forms have found the existence of both
biased technological change and nonhomotheticity in production. For example, the

generalized Leontief cost model by McLean-Meyinssee and Okrmade (1988) found labor- and

6

chemical-saving technological changes and nonhomotheticity in production process in
Louisiana rice production.

Nghiep (1979) ﬁrst applied the translog model to the study of Japanese agriculture. He
imposed a homothetic restrictions in a production process. Kako (1979) used a translog cost
model in his study of the total factor productivity, imposing a homothetic production process.
Kuroda (1988) found that the assumption of homotheticity is invalid in Japanese agriculture.
However, the data used in his study are questionable. For example, he used wages of hired
labor as a proxy for wages in the total farm sector. However, hired labor in Japan accounts
for only 2 percent of total agricultural labor and it may be hired by only large-scale farms.

In addition to the translog function, the model developed by Egaitsu and Shigeno (1983)
was applied in several works, such as Nakajima (1989) and Ohe (1990). This model is a two-
level production function. It assumes potential substitution between labor and machinery and
between land and fertilizers but no substitution or complementarity between the other
combinations of inputs.

In the past, studies on the aggregate production function for Japanese agriculture have
not dealt explicitly with effects of output on factor demand. In terms of output effects, only
economies of scale, which represent effects of output changes on total costs, have been
analyzed.

The concept of an elasticity of scale was introduced by Hanoch (1965). This elasticity
measures the proportional change in output as all inputs change at the same rate. Baumol el
al. (1982) developed a method to evaluate how a change in output affects production cost
in a multi-product production. They derived elasticities of total cost with respect to output,

which explains whether an industry exhibits increasing, decreasing, or constant economies of

7

scale. The elasticities of scale are estimated in translog studies, such as Murty, et al.(1993),
Gyapong and Gyimah-Brempong (1988), Seldon and Bullard (1992), Hoche and Adelaja
(1984), Chino (1985), and Kako (1979). Although the reciprocal of an estimated elasticity
of scale represents how much input levels would change as the output level changes, this
measurement must have the strong restriction that all inputs must change by the same
proportion.

Production functions are also used in studies that measure effects of output changes on
factor use.3 In this case, estimated parameters of a production function are used to ﬁnd the
relationship between output and input levels. In the Cobb-Douglas production function, the
reciprocal of a parameter on an input variable represents the elasticity of the output with
respect to the input. When this measure is used to evaluate the effects of changes in output
on factor demand, the model imposes another strong restriction that all input levels, other
than the input of interest, remain unchanged. That is, only one input level is allowed to
change when the output level changes; so that no factor substitution is permitted in the
analysis. However, such an assumption is not realistic. Changes in output are usually
associated with changes in the levels of all inputs. In order to examine the output effect on
demand for inputs, it is important to include substitution effects. Instead of assuming that all
inputs change by the same degree, or that only one input varies and other inputs are ﬁxed, this
study utilizes a method that permits all input to change.

So far we have only considered restrictions in static models. However, intertemporal

effects should also be considered. A static model implicitly imposes the restriction that all

 

3For example, Shintani’s studies (1970, 1972, 1978) analyze input elasticities of
output in Japanese agriculture.

8

changes in the variables of a model are resolved within a period (e. g., one year). If
production factors are adjusted over more than one period, this restriction is violated.
However, dynamic econometric models which allow for slow adjustment have rarely been
applied in Japanese agriculture. In his study on Japanese agriculture, Nghiep (1979)
incorporated a partial adjustment process in share equations derived from the translog cost
function. Although he did not test explicitly the dynamic structure of production, estimated
parameters on the lagged share variables are statistically signiﬁcant from zero, implying the
assumption of short-run equilibrium may be inappropriate for Japanese agricultural
production. However, there are very few other studies that have paid attention to the
problem of dynamic adjustment.

There are several reasons that dynamic adjustment occurs in agricultural production.
First, farmers may need time to obtain information, to learn new production practices, and to
sell or buy assets. Also, since rapid adjustment of factors often requires high adjustment
costs, the adjustment may be delayed. Thus, full cost minimization may not be achieved in
the short-run. However, it is still reasonable to assume that the long-run equilibrium will be
achieved in the long run. The model applied in this study is a dynamic model that allows
short-run disequilibrium, but captures a long-run relationship between the variables. Thus,
this study attempts to avoid prior assumptions imposed in past studies, such as instantaneous
factor adjustment, as well as constant elasticities of substitution, homothetic production
process, etc.

Besides modeling the dynamic factor adjustment process, this study extends previous
studies on the aggregate production function in terms of output effects. A production

function represents effects of factor price changes, effects of technological changes, and

9

effects of output changes; yet, the output effects have been rarely evaluated in past empirical
studies. These are explicitly expressed in this thesis as an elasticity of factor demand with
respect to output.

Also, while knowledge of the long-run effects of output changes on factor demand is
useful for a structural analysis of agricultural production, analysis on how each factor use
changes due to output changes and factor price changes is often more useﬁrl for policy
analysis. Elasticities used in a structural analysis of production assume that other factor prices
and output remain constant. However, in the real world, changes in all factor prices, as well
as output, affect factor use simultaneously. In order to consider how output changes caused
by trade liberalization might affect factor use, this study carries out a simulation which
incorporates effects of changes in factor prices associated with the output changes into the
analysis of factor use. Simulated paths of factor adjustment over 10 year period are presented
graphically. These simulations supplement the analysis of long-run effects by examining
short-run dynamics and including the effects of price changes.

Overall, past studies of aggregate production have mainly focused on changes in output
or productivity, with little attention being paid to changes in factors of production. However,
changes in demand for factors, especially agricultural chemicals and labor, have become
serious concerns in rural areas. Thus, it is important to develop a method for measuring these
effects. Also, it is important to use a ﬂexible functional form that accommodates

nonhomotheticity and bias in technological change.

10

1.4 Outline of the Dissertation

The next chapter characterizes agricultural production in Japan in terms of trade policy
and factor use. In Chapter 3, a quantitative model is developed. This chapter ﬁrst discusses
the theory of duality, functional forms and dynamic models. Then, based on these arguments,
a dynamic econometric model is derived from a translog cost model. Chapter 4 discussed
stationarity conditions. Stationarity of individual series and cointegration among the series
are tested. Using estimates from the dynamic model, Chapter 5 evaluates elasticities used in
structural analysis. Chapter 6 simulates factor adjustment associated with several different
paths of output. In this chapter, a long-run equilibrium model provides paths of factor use
in long-run equilibrium, and simulations with the dynamic model provide short-run adjustment
paths of factor shares. Finally, Chapter 7 concludes and summarizes the policy implications

of the analysis.

CHAPTER 2

PROBLEM SETTING

In order to better understand the background of this study, Chapter 2 characterizes
Japanese agricultural policy and the structure of agricultural production. Japanese trade
policy and the effects of the coming import liberalization for agricultural products are
discussed ﬁrst. Next, the characteristics of production factors are explained, followed by
discussion of their implications for productivity. These arguments are useful f0r specifying

a model of the agricultural production.

2.1 Agricultural Trade Protection and Rural Problems

Trade protection is deﬁned as a policy which sets prices on the domestic market higher
than those on the international market equilibrium by restricting imports. In this sense,
Japanese agriculture has been highly protected for many years. For example, rice, which is
the major agricultural product in Japan, had not been imported at all on a regular basis until
1996.4 Government agencies also control all imports of wheat, butter, powdered milk,

tobacco, and silk.5 Thirteen products are imported under quotas (i.e., quantity restriction).

 

‘ However, rice was imported in several bad harvest years to eliminate shortages.

’Japan Ministry of Agriculture and Forestry, Ministry of Agriculture, Forestry, and
Fishery, Statistical Yearbook of Agriculture, Forestry and Fisheries, Statistics and
Information Department, Statistical Bureau, Ministry of Agriculture, Forestry, and Fisheries,
Japan, various issues.

11

12

Under pressure ﬁ'om foreign countries, the Japanese government has been reducing these
import restrictions over time. The number of products under import quotas decreased from
102 in 1962 to 22 in 1974.6 In 1988, import quotas on nine products, including beef and
citrus, were removed.

In December of 1993, the Uruguay Round of the General Agreement on Tariffs and Trade
(GATT) determined that all member countries were to reduce tariff rates on agricultural
products by 36 percent on average, and at least, 15 percent for an individual commodity aﬁer
1995.7 The agreement determined that an option of minimum access could be granted to a
country whose current imports of the commodity were less than 3 percent of domestic
consumption, if the country did not implement export subsidies or other output enhancement
programs. The amount of minimum access was set at 4 percent of domestic consumption in
the ﬁrst year. Then, the rate is to increase by 0.8 percent of consumption every year until the
rate becomes 8 percent in the ﬁfth year. The Japanese government will apply the minimum
access option for rice imports. Thus, through tariff reduction and the minimum access policy,
imports of agricultural products will increase.

Agricultural protectionism in Japan is generally thought to be created by political forces.
With people in rural areas rapidly moving into urban areas in the last few decades, regional
imbalances of political representation have been created. Institutional changes in the election
system have lagged the continuous migration of population. In some rural areas, the number

of representatives in the National Diet (Congress) per person are more than twice the

 

°Japan Ministry of Agriculture, Forestry, and Fishery, op. cit.

7Non-tariff restrictions were converted into tariffs.

13

average. Thus, political power in rural areas remains relatively strong and the agricultural
sector has become protected.

However, persistent agricultural protectionism in Japan cannot be explained only by the
imbalance of the election system. Hayanri (1986) argued that the level of agricultural
protection is determined by political beneﬁts and costs of a policy.8 A politician would gain
support from farmers by implementing a protective policy, while losing support from
consumers. Relative protection levels are then chosen so that net political beneﬁt is
maximized. With the development of the industrial sector, farmers ﬁnd that their incomes
decline compared to the industrial sector. Then, political activities by the farmers become
intense and politicians’ marginal beneﬁts from agricultural protection is increased. On the
other hand, as the economy advances and consumers’ incomes rise, they become less
concerned with the price of food. Thus, the level of agricultural protection increases along
with economic development. This hypothesis is also supported by a cross-country
econometric study by Homma and Hayami (1986), which revealed that there is a general
tendency for agricultural policies to become more protective as national incomes increase.

There are other arguments that non-monetary factors may affect protectionism. The non-
monetary factors can be categorized as: (i) concerns about national food security, (ii) support
of rural society and the agricultural community, (iii) uncertainty about food safety of
imported rice, and (iv) preservation of rural landscapes and water systems.

In Japan, the proportion of the domestic food supply in total food consumption (i. e. , the

 

8This argument follows theories of political economy proposed by Buchanan and
Tullock (1962), and Breton (1974).

14

food self-sufﬁciency ratio) has been decreasing during the last thirty years. From 1965 to
1992, the self-sufﬁciency ratio dropped from 73 percent to 46 percent of the calorie base;
from 86 percent to 65 percent of the total value of food, and from 62 percent to 29 percent
of the total value of grains.9 Yet, the decrease in self-sufﬁciency does not necessarily imply
a decrease in national food security. As food security is deﬁned as a stable supply of food,
depending on international supply does not necessarily increase risk and uncertainty in the
food supply. There is no evidence to show that the international rice market is so risky as to
justify the complete self-sufﬁciency of rice in Japan.10

With regard to supporting rural society and the agricultural community, urban consumers
may be willing to pay a higher price for food to support farmers’ income. In the case, some
trade protection, rather than free trade, may be a rational policy both farmer and consumer
utility would be higher with the protection. Import liberalization would reduce consumer
utility as well as producer utility.ll

This issue is closely related to social problems in rural areas of Japan. In the last forty

 

9Japan Ministry of Agriculture and Forestry, Ministry of Agriculture, Forestry, and
Fishery, Statistical Yearbook of Agriculture, Forestry and Fisheries, Statistics and
Information Department, Statistical Bureau, Ministry of Agriculture, Forestry, and Fisheries,
Japan, various issues. The total value of grain includes feed grain for livestock.

'°Hayami (1985b) explained in detail the reasons why import restrictions could not be
justiﬁed by concerns about food security.

”According to Sen (1990), altruism occurs as one wants to satisfy a feeling to help
others, therefore, it is a sort of self-interest. Note that Sen (1990) distinguished
“commitment” from “altruism.” With commitment, an individual acts voluntarily to help
others. Unlike altruism, a result of action under commitment would not affect the person’s
utility, as he does just for his sense of duty. For example, if a country refuses to import from
another country that infringes certain human rights, it is considered as a commitment.
However, this is not the case of Japanese import restriction.

15

years, the rural sector experienced a rapid decrease in population, especially among the young
generation. This situation biased demographic patterns in the rural area. The rural sector
now consists of a high ratio of elderly people compared to young people. As a result of the
decrease in rural population, ﬁlnds for public services, such as education, medical service, and
infrastructures, have become scarce and business opportunities have decreased. These
developments have accelerated migration out of the rural areas.

Environmental problems may also inﬂuence agricultural protection. In general,
agricultural production has both negative and positive effects on the environment (Sakurai,
1993, and Ogura, 1990). The negative effects include contamination of soil and water, soil
erosion, and exploitation of water resources. Contamination of water in rivers, lakes, and
groundwater have come to be a serious environmental issue, because a large amount of
chemical input is used in crop production (Kumazawa, 1995). On the other hand, soil erosion
is not a serious problem in Japan, since paddy rice production prevents soil erosion. On the
positive side, agricultural production, especially rice production, contributes to the
preservation of water resources and land, provides aesthetic values of rural landscape, and
preserves biological resources (Mitsubishi Research Institute, 1991 ).‘2 In addition, consumers

are concerned with the safety of imported agricultural products, since it is difﬁcult to monitor

 

12According to a hedonic study of Mitsubishi Research Institute, the total
environmental beneﬁts of rice production in Japan is $120 billion per year. Also, in a
contingent valuation study for more aggregated values (i. e., total WTP for protecting the
landscape and natural resources), F uj irnoto estimated the total external value of Japanese rice
production in Nara Prefecture to be $439 million. A hedonic study of Urade et al.(1992)
found that the total economic values of the agricultural and forestry resource is $20 billion
each year. Yoshida (1995) estimated an economic value of the landscape of a agricultural
area--Miou, Hokkaido using the contingent valuation method. The estimated values are $150
for a resident and $80 for a visitor.

16

pesticide residues on imported food and many kinds of pesticides and other agricultural
chemicals are used in the world.

Protective trade policy is based on various problems related to rural society and the
environment. Such problems are related to production factors, such as labor, agricultural
chemicals, and farmland. Therefore, through changes in the production factors, changes in
the trade and agricultural policies inﬂuence social and environmental problems. These factors
have important implications for rural areas. The characteristics of these production factors

are explored in the next section.

2.2 Inputs in Japanese Agriculture
This section explains characteristics of production factors and related institutional and
technological issues that may affect factor adjustment. The descriptive analysis facilitates an

understanding of the adjustment mechanism.

Land

A large portion of the land in Japan is mountainous and there is only a small amount of
arable land. In 1993, the area of land used for agriculture was 5.2 million hectares or 14
percent of the total area of J apan.l3 Rice accounts for 51 percent of the total area of crop
cultivation, followed by vegetables with 15 percent, ﬁ'uits with 8 percent, and wheat with 7

percent.

 

13The agricultural land includes 1.] million hectares of pasture.

17

Land is so limited in Japan that the productivity in marginal areas can be low. There are
many terraced ﬁelds in the mountains, and these ﬁelds are the least productive. Farmland is
small and irregularly shaped so it is difficult to use large machinery. Also, when the size of
an individual farm increases as the aggregate output level increases, then there are economies
of scale in production. In Japanese agriculture, the production technology, in terms of use
of factors, varies according to the size of a farm. Table 2.2.1 shows production costs per
hectare in 1992 for each input category. Labor costs per hectare decrease greatly as farm size
expands. Labor cost per hectare for a farm with more than 5 hectares was 42.8 percent lower
than an average-sized farm. Costs per hectare for chemical inputs (i. e., fertilizer and
pesticides) decrease by 82.5 percent and costs per hectare for machinery decreases by 70.1
percent for large farms compared to the average. The total cost per hectare in a farm with
more than 5 hectares was 67.1 percent of the average. These data show economies of scale
in rice production. The proportion of cost savings for a large farm is the highest for labor
costs, followed by machinery, and chemical inputs.

Until 1965, production costs per hectare for farms for farms with more than 3 hectares
of farmland were almost the same as the costs per hectare with less than 0.3 hectares. Yet,
in the 19703, the former became approximately one half of the latter.” However, as farm size
expanded beyond a certain level, yield declines, so that the cost reduction due to economics

of scale was offset by a decrease in income due to lower yield. In terms of rice production,

 

l"Japan Ministry of Agriculture and Forestry, Ministry of Agriculture, Forestry, and
Fishery, Survey on Production Cost of Agricultural, livestock and Sericultural Products
(Tokyo: Statistics and Information Department, Statistical Bureau, Ministry of Agriculture,
Forestry, and Fisheries, Japan).

18

Table 2.2.1 Production Costs of Rice by Farm Size per Hectare, 1993, Japan

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Average 0.3 0.5 1.0 1.5 2.0 3.0 5.0+
-0.5ha‘ -1.0ha -1.5ha -2.0ha -3.0ha -5.0ha ha

Fertilizer 91.52 104.22 99.38 87.14 79.41 88.04 93.06 82.81
Other 73.08 78.24 76.35 75.26 66.89 73.33 69.11 64.06
chemical
Infra 83.38 182.76 94.69 74.77 90.71 76.63 85.98 78.57
-structure
Rents, 109.57 200.96 145.09 100.11 79.83 68.84 57.51 48.26
Fees
Machinery 266.63 285.13 299.57 274.45 270.08 246.23 233.62 184.80
Labor 561.56 769.17 679.93 578.30 487.27 452.57 405.04 327.91
Total 1,185.74 1,511.42 1,395.01 1,190.03 1,074.19 1,005.64 944.32 786.41
*ha: hectare

Source: The Japan Ministry of Agriculture, Forestry and Fisheries, Survey on Production
Costs of Agricultural, Livestock and Sericultural Products.

19

the yield of a farm with more than 5 hectares was 4.4 percent lower than a farm between 3
and 5 hectares”. While the cost of rice production per hectare for a farm of more than 5
hectares was 8.8 percent lower than a 3-5 hectare farm in 1993, due to the lower yield the
farm gross income was 1.6 percent lower and the net proﬁt was 9 percent lower.‘6 Thus,
farmers’ net incomes were not higher for a large-scale farm.

The size of farms did not increase for a long period of time in Japan. In Table 2.2.2, 80
percent of the rice farms were less than 1 hectare in 1990, while only 5 percent of the farms
were larger than 2 hectares. The reason that farm size has remained small is explained by the
fact that farmers have kept their farmland as assets for future investments. Due to the
regional development policies of the 19603 and 19703, Japanese land prices increased rapidly.
Thus, farmers expected the price of their farmland to continue to rise in the ﬁrture. This
argument, however, does not explain why land transfer remains low even when the price has
declined. Another explanation is that econorrries of scale could not be achieved even if small,
scattered farmland was gathered.'7 Therefore, farmers did not expand their farm size. Since
there are many small plots of farmland, it is difﬁcult to collect a large area of land in the
neighborhood. Even if farmland could be collected, additional investment in infrastructure
is required. Such a large-scaled investment can be done only by a large farmer who has

enough funding and productive resources. If a farmer owns farmland in several separated

 

l5op. cit.

"The net proﬁt is the gross income minus total production costs and family labor and
rents to land owner.

l7"Economies of size" means, in this section, decreasing average cost per hectare.

20

Table 2.2.2 Number of Farms by Size in Japan, 1950-1990 (thousands)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0-0.5 0.5-1.0 1.0-2.0 2.0-3.0 3.0-5.0 5.0 ha
ha' ha ha ha ha and over
1950 1,032 1,952 1,308 176 26 l
1955 1,006 1,955 1,357 179 28 2
1960 992 907 1,406 201 34 2
1965 954 1,762 1,352 215 38 2
1970 910 1,619 1,281 244 57 6
1975 865 1,436 1,076 236 57 9
1980 806 1,304 980 240 82 13
1985 753 1,182 883 234 93 19
1990 765 1,049 782 222 100 26
*hectare

Source: The Japan Ministry of Agriculture, Forestry and Fisheries, Agricultural Census

 

21

places, it is difficult to exploit economies of scale by using large-sized machinery.
Diseconomies of size might even occur if additional costs for transportation and management
are required.

A third explanation is that the land law enacted after the war restricted the transfer of
farmland. The land reform, which was a part of agricultural reform immediately after World
War II, was carried out by the postwar government under strong recommendation of the US.
General Headquarters Organization”. The objective of the land reform was to end the old
landlordism and to stabilize the rural society. The government purchased 1.9 million hectares
of farmland and sold it to tenants at very low prices. As a result, the proportion of the
number of tenants to total farmers declined from 45 percent to 9 percent during the 1945-55
period (Hayami and Ruttan, 1985). The Land Law of 1952 legally supported the land reform
and the rights for tenancy were strengthened. All land owned by absentee landlords and
landlords exceeding 1 hectare was purchased by the government, and transfer of farmland was
restricted. This land law was revised in 1962 and 1970 and the restrictions on land transfer
were liberalized in the new laws. Therefore, the transfer of farmland is no longer a signiﬁcant
obstacle.

Technology in Japanese agriculture developed under a severe constraint on available
farmland. The land constraint induced innovation of land-saving technologies, such as
introduction of new varieties responsive to fertilizers and increased yield. Innovations in land-
saving technology should reduce the price of land but prices have increased rapidly since the

19603. Tsuchiya ( 1988) argued that increasing land prices were caused by the general

 

18Kawano (1970), p. 374

22

development of agricultural technology. Since technological development reduced the
marginal cost of production, the agricultural sector grew as more farmers entered production.
Thus, demand for agricultural land increased and, therefore, the price of farmland increased.
Still, this argument is not strong enough to explain why land prices rose even when
agricultural production declined. Rather, it seems that land prices were raised due to the
development of rural areas in Japan beginning in the mid-19603 when regional development
policies were implemented. Markets for farmland are not independent of markets for land
used for other purposes.

To sum up, even though economies of size exists at the sector level, sizes of individual
farms have remained small. The small sizes of farms were originally created by the land
reform policies after the war, but they remained even after liberalization of the land market
because of high transaction costs, including investment on infrastructure. Thus, in Japan,
producers have not beneﬁtted ﬁom economies of size in terms of their farmland. However,
severe scarcity of farm land, which existed before the war, has been relaxed due to

technological development rasing yields and due to the reduction of aggregate output.

Lam:

The population of full-time and part-time farmers in Japan is 11 million, accounting for
about 10 percent of Japan’s population. The number of farmers and the number of farms
decreased rapidly in the last several decades (Table 2.2.3). From 1960 to 1994, the
population in farm households decreased by 35 percent, while the number of farms also

decreased by 54 percent (Table 2.2.4). In addition, the tables show that the average number

23

Table 2.2.3 Population of Farm Households (Unit: thousands, percent in parentheses)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total 16-29 30-39 40-49 50-59 more than
years old years old years old years old 60 years old
1960 22,622 7,293 4,359 3,428 3,218 4,218
(100)_ (32.2) (19.3) (15.2) (14.2) (18.6)
1965 20,487 5,614 3,949 1,602 3,013 4 419
j (100) (27.4) (19._3) (7.8) (14.7) (21.6)
1970 19,460 5,815 3,171 2,848 2,891 4,427
__ $100) (29.9) (16.3) (14.6) (14.9) (22.7)
1975 17,987 4,700 2,355 3,556 2,920 4,455
(I00) (26.1) (13.1) (19.8) (16.2) (24._8)
1980 17,083 3,911 2,466 2,836 3 296 4 573
(100) (22.9) (14.1) (16.6) (19.3) (26.8)
1985 15,890 3053 2 637 2,193 3,167 4,841
(100) (19.2) (166) (13._8) (19.9) (30.5)
1990 13 ,902 2,336 2,099 2,074 2,408 4,985
(100) (1618) (15.1) (14.9) (17.3) (35.9)
1994 10,516 1,078 1,452 1,702 1,635 4,033
(100) (10.3) (13.8) (15.5) (38.4)
‘ urce: . e Japan Mimstry ongricuIture, Forestry and Fisheries, Report on Movement in
ﬁgricultural Structure .
ote: People less than 16 years old are not included.

Table 2.2.4 Number of Farm Households (thousands)

24

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Total Full-tirne Part-time Part-time

Type I Type II
1960 6,057 2,078 2,036 1,942
(100) (34.3) (33.6) (32.1)
1965 5,664 1,219 2,081 2 365
_ (100) (2_1.5) (36.7) (41.8)
1970 5,260 798 1,566 2 895
(100) (15.2) (29.8) (55.0)
1975 4 891 659 1 002 3 231
(100) (13.5) (20.5) (66.1)
1980 4 614 580 829 3 205
(i 00) (12.6) (18.0) (69.5)
1985 4 331 643 660 3 028
(100) (14.8) (13.2) (69.9)
1990 2,936 460 478 1 998
(10$ (15.7) (16.3) (68.1)
1994 2,787 449 386 1,951
(100) (16.1) (13.9) (70.0)

. ote: Part-trﬁe type I: a part-time farmer farm ousehold that earns the majorfty of the

Income in farming; Part-trme Type II: a farm household which earns the majority of its
income 1n non-farmrngemplo ent. . .

Source: The Japan Mrnrstry 0 Agriculture, Forestry and Frshenes, Report on Movement in
Agricultural Structure

25

of farmers per farming household slightly increased from 3.73 in 1960 to 3.77 in 1994. This
is probably because proportion of part-time farmers increased.

The main reason for the decreasing population of farmers is migration from the
agricultural sector to the industrial sector. From 1952 to 1980, those who moved from the
agricultural sector totaled 4.3 million, accounting for 80 percent of the changes in the farm
population.” The rest is attributed to a natural increase (i.e., the number of the new borns
minus that those who had died). The outﬂow of population occurred because of a desire to
earn better incomes in the industrial sector. As Japanese industries developed in the mid-
19503, farmers sought better employment opportunities in urban areas. Thus, in addition to
the moving of whole families, the moving of many young males was especially noted.
Consequently, many old people and women remained in the rural areas. Traditionally in
Japanese agriculture, male farm owners and their oldest sons remained on the farm as the
successor of family farms, even if his brothers had to leave in order to earn money in urban
areas and send it back to the farm. However, in recent years, because of increased migration
of male farmers, the number of female farm owners increased and the number of young
successors decreased. Table 2.2.3 shows that changes in the demographic patterns occurred
as younger generations moved out of the rural areas and older generations did not. From
1960 to 1994, the number of farmers (i. e., people in farm households) less than 30 years old
decreased by 85 percent and those between 30 and 59 years old also decreased by 56 percent,

while those more than 60 years old decreased by only 4 percent. This is due to the fact that

 

l9Tsuchiya (1988) p. 15.

26

the younger generation expects greater beneﬁts from seeking off-farm employment. Also,
since the younger generation is more sensitive to differences in cultural and educational
opportunities between rural areas and urban areas, reservation wages for agricultural activities
are higher for younger generations.

The large scale migration to the urban areas resulted in a shortage of labor in the
agricultural sector, especially for young and middle-aged people. In 1990, on average 11.3
percent of farms hired seasonal laborers for 36.7 man-days per farm. This accounted for only
2.9 percent of total labor hours in Japan. Use of hired labor decreased during the 19603 and

remains very small (Table 2.2.5).

Table 2.2.5 Average Working Hours per Farm in Japan (hours per farm household)

 

 

 

 

 

 

 

 

 

 

 

 

Year 1960 1965 1970 1975 1980 1985 1990
Family 3,724 2,880 2,575 2,189 1,906 1,874 1,728
Hired 247 107 86 56 43 52 51
labor
Total 3,971 2,987 2,661 2,245 1,949 1,926 1,779

 

 

Source: The Japan Ministry of Agriculture, Foresz and Fisheries, Statistical Yearbook of
Ministry of Agriculture, Forestry, and Fisheries.

While some people quit farming and found jobs in the industrial sector, other farmers
engaged in non-agricultural jobs, yet remained in the agricultural sector. Such part-time
farming became possible as trafﬁc systems were developed and manufacturing and service
industries developed around rural areas. Consequently, fewer farmers moved into urban areas

during slack seasons and engaged in temporary non-agricultural jobs. Table 2.2.6 shows the

27

number of temporary workers away from home. Most of them engaged in farnring in the
rural areas and had seasonal jobs in urban areas. The number of temporary workers has

decreased since the 19703.

Table 2.2.6 Number of Temporary Workers Away From Home (thousands)

 

Year 1965 1970 1975 1980 1985 1990

Number of workers 230.2 291.5 190.4 133.2 89.4 58.7
away from home

Source: The Japan Ministry of Agriculture, Forestry and Fisheries, Report on Movement in
Agricultural Structure

 

 

 

 

 

 

 

 

 

 

Eighty-two percent of the part-time farmers earned more income in other jobs (Table
2.2.4). The proportion of part-time farmers increased during the 19503 and 19603. The
number of part-time farmers relative to all farmers was 55 percent in 1938 and did not
increase until 1950. However it increased rapidly in the 19503 and 19603, and it rose to 84
percent in 1970.20 This high ratio remains. In 1994, 84 percent of the total farmers were still
part-time farmers.21 A part-time farmer is able to shift working hours ﬁ'om farm production
to non-farm employment without paying the large costs of moving to new areas and seeking
a new job.

When labor is abundant, the marginal product of labor must be close to zero. Yet,
Tsuchiya’s (1988) study found that the marginal product of agricultural labor was, in general,

signiﬁcantly higher than zero in Japan. As the output level changes, the marginal product of

 

2°Misawa (1970) and The Japan Ministry of Agriculture, Forestry and Fisheries,
Agricultural Statistics Yearbook

21The numbers exclude self-sustaining farmers.

28
labor also changes. Very few studies on changes in marginal productivity of labor have been

done in the past.22 This issue, however, is useful in explaining the mechanism of

technological change in agriculture.

Chemicals

“Chemical inputs” are fertilizers, pesticides, herbicides, insecticides, and other agricultural
chemicals. Fertilizers include organic fertilizers (i. e., manure) as well as inorganic (i. e.,
chemical) fertilizers. Since this study deals with production for the last ﬁfty years, chemical
fertilizers are of main interest. Chemical fertilizers began to be used extensively in the 19503.
Compared with manure, chemical fertilizers are easily carried and applied; mixing is not
required. Also, chemical fertilizers penetrate deeper into the soil than manure and therefore,
more yield is expected.

Most chemical inputs are supplied by both domestic and foreign sources. The proportion
of imported nitrogen (N), phosphorus (P), and potassium (K) in domestic consumption was,
respectively, 30%, 18%, and 40% in 1991.23 As demand for fertilizers increased, foreign
chemical factories as well as domestic factories increase the supply. Therefore, the long-run

supply of chemicals is elastic with respect to their prices.

 

22In the study of sericultural production in Japan, Nghiep and Hayami (1979) found
that traditional sericultural production without summer-fall rearing activity exhibited lower
and more rapidly diminishing marginal productivity of labor than the later developed
production with the activity.

23The values are calculated from Poketto Hiryo Yoran (Fertilizer Statistics Abstract)
compiled by the Japan Ministry of Agriculture, Forestry and Fisheries, and Nihon Boeki
Geppo(Monthly Statistics of Japanese Trade) compiled by the Japan Ministry of Finance.

29

Increases in the quantity demanded for fertilizers are attributed primarily to declining
prices. Until the 19703, the price of agricultural chemicals declined more than other input

prices, though this has slowed during the 19705 (Table 2.2.7).

Table 2.2.7 Consumption of Major Fertilizers in Japan (1,000 tons)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Nitrogen Phosphorus Potassium

1950 466 289 98

1955 567 385 382
1960 693 486 520
1965 769 574 601
1970 866 653 606
1975 833 583 571
1980 816 690 556
1985 952 741 645
1990 942 690 567
1993 929 728 521

 

Source: The Japan Ministry of Agriculture, Forestry and Fisheries, Statistical Yearbook of
Agriculture, Forestry, and Fisheries.

Chemical demand has been closely related to improvement in crop variety. During the
period from 1890 to 1910, when Japanese agricultural development accelerated, several new
varieties of rice, such as J inriki, Aikoku, and Kamenoo, were introduced. For two decades,
the share of production of the new varieties in total output increased from nearly zero to 40
percent. As a result, the average yield of rice increased ﬁ'om 2.2 tons to 2.6 tons per hectare
(Hayami 1973, p. 161). Consumption of fertilizers increased approximately four times during
the same period.

Initially, these varieties were developed by large farmers and distributed through local

agricultural organizations and a government extension system. In 1904, the Japanese

30

government started scientiﬁc research on new varieties. Then, in 1926 the government
organized a research institution for new varieties into a national research center, regional
experimental stations, and prefectural stations. The new research .and extension system
originally started for wheat and later was expanded to rice and then other crops. This
institution successfully developed several new varieties in the 19305.

Combined with farm mechanization, technologies based on agricultural chemicals
increased the yield of crops. Mechanization, using a large tractor, enabled deep tillage which
led to more effective use of fertilizers. Cultivating crops in different seasons smoothed out
seasonal labor requirements, and enabled efficient use of the labor force. This practice was
made possible by improvement of farm facilities and infrastructures. In certain cases, early
season rice cultivation reduced chances of crop damage and contributed to increased yield and
stable production. For example, introduction of early-maturing varieties in the northern
region of Japan reduced damage from cold weather. Early cultivation became possible
through the introduction of the protected rice nursery (i. e. , bed for rice seedlings). This
cultivation technique was adopted by 80 percent of the farmers in the northern region during
the late 19605. In the southern region of Japan, early cultivation also reduced damage from
rice diseases.

Application of chemical inputs is characterized as both labor-saving and labor-using.
Application of fertilizer often requires considerable amounts of labor. As a shortage of labor
appeared aﬁer the 19605, such labor-using technology was avoided. Also, as large-sized
machinery began to be used, farmers preferred relatively short (dwarf) varieties, which are

more suitable when using machinery. Thus, introduction of the new high-yielding varieties

31

whose yield is sensitive to fertilizers was reduced.24 Application of chemical inputs in making
a protected rice nursery, spraying pesticides, and planting seedlings also require a large
amount of labor. On the other hand, pesticides, herbicides, and insecticides are effective in
reducing hours of work.

Thus, chemical inputs become substitutes or complements for other inputs by changing
production technologies. Under given production practices, however, each chemical input
has an effect on a speciﬁc role or function and it is effective for a speciﬁc amount per output.
Productivity increases, in general, are generated not by a greater amount of chemical inputs
but by technological changes, such as the introduction of a new variety that is responsive to
fertilizers. Thus, chemical inputs are used within relatively narrow ranges, since the marginal

productivity of the chemicals tends to diminish rapidly.

Capital

Capital inputs include machinery, equipment, facilities, infrastructure, and energy. Many
of the tractors used in Japanese agriculture are small. Table 2.2.8 shows the average number
of tractors per farm for all areas”. A pulling-type tractor is a small-sized tractor and a riding-
type tractor is larger-sized. The number of pulling-tractors and riding-tractors with less than
15 horsepowers per farm was 0.77, accounting for 60 percent of the total number of tractors

in Japan. Also, large-scale farms tend to own more large-size tractors. While only 5 percent

 

24Kayou, pp.60-6l.

2’T’hese number are underestimated, especially for smaller farms, since they do not
include tractors owned by communities which are shared. In 1990, tractors owned by
communities accounted for 3 percent of the total number of tractors in Japan.

32

of farms in all areas of Japan except Hokkaido have large tractors with more than 30
horsepowers, each farm in Hokkaido has more than one large tractor on average“. Thus,
larger farms have large tractors which reduce the average cost of large-scale farming.
Moreover, most power Sprayers are also small in Japan. Riding power Sprayers account for

only 3.3 percent of the total number of Sprayers.27

Table 2.2.8 Average Number of Tractors per Farm in 1992

 

 

 

 

 

 

 

 

 

 

 

 

Pulling RidiﬂTractor
Tractor 0—15PS“ 15-3ops 3OPS and
over
All areas except 0.63 0.14 0.47 0.05
Hokkaido
0 - 0.5 ha. 0.59 0.17 0.19 0.01
0.5 - 1.0 ha. 0.65 0.18 0.40 0.01
1.0 - 2.0 ha. 0.65 0.11 0.65 0.04
2.0 ha.+ 0.60 0.06 0.75 0.28
Hokkaido 0.23 0.02 0.26 1.40

 

 

 

*horse power
Sources: The Japan Ministry of Agriculture, Foresz and Fisheries, Report on Movement in
Agricultural Structure

From an international perspective, Japanese farmers have many tractors. The number of

tractors, regardless of size, was 2.12 million in Japan in 1990, compared with 4.75 million in

 

26Hokkaido is a northern island that has extraordinary large plains for Japan. The
average area per farm in Hokkaido is 4.88 hectares for rice and 8.71 hectares for other ﬁeld
crops, while the average area per farm for all of Japan is 0.77 hectares and 0.53 hectares,
respectively. Thus, Hokkaido is a good example of production in large-sized farms in Japan.

27Sources: The Japan Ministry of Agriculture, Forestry and Fisheries, Survey of
Statistics on Movement.

33

the United States, 2.61 million in the former Soviet Union, and 1.47 million in France.28 This
suggests that mechanization in Japanese agriculture is not behind but has developed as small-
scale mechanization or “mini-mechanization” takes place (Hayami and Ruttan, 1985).

Farm mechanization was induced by serious labor shortages beginning in the 19505. As
labor became a scarce resource, wages of farmers relative to machinery prices increased.
Also, technological development in the manufacturing sector reduced prices of agricultural
machinery. Thus, mechanization was accelerated by changes in relative factor prices.
Another factor that promoted farm mechanization was improvement of agricultural land and
rural roads during the last several decades. The irregular shapes of farms were arranged into
rectangular shapes so that machinery could be more easily used. Development of farm roads
in the rural areas also facilitated the introduction of machinery.

Small-sized machinery was ﬁrst introduced in the mid-19505. Table 2.2.9 shows that
small-sized machines, such as tractors and power Sprayers and power dusters, were
popularized during the 19605. In the 19705, large machines, such as combines (auto-
threshers), as well as rice planting machines, began to be used extensively. Due to
mechanization, farmers’ working hours were rapidly reduced. As a result, productivity of
labor in rice production increased by 6.9 percent a year during 1955-65 and 5.7 percent
during 1965-85.29 However, very large-sized machinery like those used in the United States,
was not widely ad0pted in Japan, since most farms were not large enough to use this type of

machinery.

 

28FAO, Production Yearbook

29Y. Hayami and associates (1974) and Yamada (1984)

While using large-sized machinery would increase yield because of deeper tillage, small-

sized machinery saves labor but does not raise the yield much.30 Thus, mechanization in Japan

34

promoted substitution of machinery for labor rather than increases in yield.

Table 2.2.9 The Number of Maj or Machinery Items Owned by Japanese Farmers (unit: 1,000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tractors Power sprayers, Rice power Combines,
power dusters planters auto threshers

1960 278 406 0 0
1965 1,919 850 0 0
1970 3,448 2,170 33 45
1975 4,014 3,060 470 525
1980 4,223 3,364 1,746 916
1985 4,387 n. a.‘ 1,993 1,150
1990 3,731 n. a. 1,904 1,179

Source: The Japan Ministry of Agriculture, Foresz and Fisheries, Annual Sample Survey of

Agriculture

*data not available.

2.3 Changes in Output and Factor Use

The previous section discussed characteristics of inputs in Japanese agriculture and showed
that the inputs may take various adjustment paths. Changes in inputs in response to a change
in output cannot be assumed the same for all inputs, and the adjustment paths cannot be
determined a priori. Adjustment of some factors may be more rigid in the short run, while
others may be adjusted ﬂexibly.

Some economists have argued that some factors are rigid or ﬁxed due to a problem of

 

3”Tsuchiya (1988) p. 217; Inarnoto (1987) p. 117

 

35

disequilibrium in agricultural production, based on a hypothesis that agricultural production
is not at the optimal level.3| However, Tweeten (1989) suggested that there is no supporting
evidence that this disequilibrium persists; and in the long run, the factor market will be
adjusted toward the equilibrium level. Also, he found that costs of input transfer are not large
enough to prevent adjustment. Thus, the problem is not a permanent disequilibrium of the
market, but a temporary disequilibrium and slow adjustment. Also, Chambers and Vasavada
( 1983) argued that producers make decisions according to their expected input prices,
however if the prices are not realized, the inputs are in short-run disequilibrium”.

Rigidity in factor adjustment is explained by delay or by characteristics of the production
technology (i. e. , nonhomotheticity). The short-run disequilibrium model can be used to deal
with the former problem. In terms of the latter problem, if production is highly non-
homothetic, adjustment of some factors may appear rigid.

As more input is used, the productivity of an input in general increases at a diminishing
rate ceteris paribus. A proﬁt maximizing ﬁrm uses inputs so that the ratio of the marginal

products of the inputs equal the ratio of factor prices. Under a given factor price ratio, a

 

3|Galbraith and Black (1938) argued that since agricultural production requires an
expensive and lumpy ﬁxed factor, producers are not able to shift ﬁxed factors in the short run.
According to Johnson (1956), this is caused by divergence between acquisition costs and
salvage value of inputs. Also, Brewster (1961) attributed ﬁxity in labor to family farm
workers’ low reservation wage. Bischoﬁ‘ (1971) proposed the so called “putty-clay
technology” hypothesis--that is, producers are free to choose any input combination, but they
are not allowed to change the input combination after they start production, therefore,
therefore leading to irreversibility.

32Chambers and Vasavada also argued that high costs of adjustment may form the
putty-clay technology (ex post asset ﬁxity) or restrict choices of inputs within a certain range
as a farmer’s organization cannot be ﬂexibly adjusted to its environment,(ex ante asset ﬁxity).

36

factor with a slowly diminishing marginal product must be used more in order to make its
marginal product equal to the others.

Graphically, nonhomothetic production shows a nonlinear expansion path”. Figure 2.1
illustrates a case of production with two factors (XA, XB). In Figure 2.1(a), as the output
increases from q” to q’ and q”, the bundle of inputs changes from (XAO XBO) to (xA’ xB’) and
(xA” xB”). Thus, the rate of change in the input XA is smaller than the rate of change in the
input X3 for a ﬁxed factor price ratio. Figure 2. l (b) shows the relationship between the input
XA and the output q under given levels of the input XB. In Figure 2.1(a) and Figure 2.1(b), if
a level of the input XB were ﬁxed at X80, then, as the output increases from q° to q’, the input
XA would increase from XAO to xA‘. If a level of the input xa is constant, the production
function exhibits diminishing marginal product, indicated by the line xa". As the output
increases from q° to q’, the inputh will shift from X80 to xB’ and the input XA will increase
from XAO to x.«’. Similarly, as q increases to q”, XA will be at xx” since XB again shifts to xB”.
Thus, the rate of an increase in input XA is smaller than the rate of change in the output. In
other words, the average level of the input per unit output declines as output increases.
Figure 2.1 (c) shows that the rate of an increase in the input X3 is greater than the rate of

increase in output.

 

33The expansion path is deﬁned as the locus of the chosen input levels at a constant
ratio of factor prices as output.

37

    

---'.-.-‘.----.'...!

 

 

 

   

 

 

B
x u
o n
B
x n
J ..
. .
. Q
. . .
.. u c
.
. .
u u u
c u -
H . n.
H n .
. . .
.. . .
u c -
. .
XA [A U r
A A
X x x
[q
,a.
----'---. ‘-.‘-----l
n 0
. a.
. r
.
.
.
u --"---I- l--.
.
_ n
.
\ _ _
. . .
u . . . .
_ u . .
. . . .
. l7 . . _
xA 1A «A I o
X X XA XA

Figure 2.1 (b)

Figure 2.l (a)

  

---------_---- .D-- -’.

  

IIIIIIIIIIIIIIIIIII

----‘.--l

 

  

Figure 2.1 (c)

Figure 2.1 Effects of Changes in Output on Factor Demand

38

Thus, a multi-factor production is in general nonhomothetic since factor adjustment
process is determined by characteristics of marginal product in terms of each factor. As
discussed in the previous section, various factor adjustment process and factor substitution
and complementarity effects are involved in Japanese agriculture. Therefore, a model for the
factor adjustment analysis should be speciﬁed to be as ﬂexible as possible, rather than a

functional form is determined a priori.

2.4 Summary
This chapter provides broad background information for the study. Since the motivation of
this study includes how the coming import liberalization policies nright affect the rural sector
by changing the demand for production factors, this chapter deals mainly with Japanese trade
policy and productive factors of agriculture

Persistent protectionism of Japanese trade is explained by perceived beneﬁts and costs
from the import protection policies. The perceived beneﬁts include national food security,
food safety, supporting farmers’ incomes and employment opportunities, and preserving the
rural landscape and water resources. The costs include higher food prices, as well as
environmental damage by farming, such as contamination of water resources by agricultural
chemicals.

A5 import liberalization changes employment opportunities and chemical contamination,
the characteristics of productive factors, such as labor and chemicals, are important to
understand the effects of policy.

As has been noted in this chapter, labor has been a scarce resource in Japanese

39

agriculture. Therefore, there may be little potential unemployment in the rural areas due to
import liberalization. It is expected that a less labor-intensive production structure will be
developed in the future as output declines due to trade liberalization. Also, the number of
part-time farmers has been increasing due to the development of regional economies, and the
trafﬁc system around rural areas. The latter has enhanced mobility of labor between the
farming sector and the off-farming sector. Rigidity in labor adj ustrnent has been diminishing
over time.

Scarcity of land, which used to be a severe problem in Japan, has been relaxed as land-
saving technology developed and the agricultural sector shrank. Since production costs per
hectare are higher for small-scale farms, the proportion of small-scale farms will decline as
the agricultural sector contracts. Because larger farms use more chemicals and machinery in
farming, there are serious concerns about contamination of water systems caused by
agricultural chemicals, especially those used in paddy rice production, as well as concerns
about pesticide residues on the harvested products. Thus, excessive use of the chemicals
might cause further environmental problems.

In terms of adjustment of factors, some inputs, such as land, machinery, infrastructures
and facilities, are difficult to adjust to their optimal levels in the short-run. Therefore, a
method which incorporates an intertemporal adjustment process is required for this study.

In the next chapter, modeling issues with such an adjustment process will be discussed.

CHAPTER 3

A DYNAMIC COST FUNCTION MODEL

This chapter discusses properties of functional forms and problems of the model selection.
First, we characterize the cost function using duality theory. Next, the properties of
functional forms and dynamic models are discussed. Then, we derive the dynamic ﬂexible

model used here, as well as discuss estimation methods for factor demand elasticities.

3.1 Duality and Cost Function
Ilualiruihecm

A cost function has the same information about the production technology as a production
function. In other words, properties of a production function are dual to properties of a cost
function. This is the principle of duality. Duality theory was ﬁrst proposed by Hotelling
(1932) but the fundamental theory was developed by Shephard (1953). In the 19705, it was
further developed by Fuss and McFadden (1978), Diewert (1971, 1973, 1974), Berndt and
Christensen (1973), and Lau (1976).

Duality functions describe results of optimizing responses to prices under certain
constraints, rather than global responses to input and output quantities as in the
corresponding production function (Young et al. 1985). While a production function

describes global output response to possible combinations of the inputs, a cost function

40

41

describes the optimal or minimum cost of producing a certain level of the output under given
input prices and the production technology. Thus, whereas production functions are primal
functions which contain all of the information about the production technology, the cost
ﬁmction, as a dual function, contains information about the behavior at the optimum (i. e. ,
cost minimization) as well as the technology. This is an advantage of using a dual function
because the homogeneity, monotonicity, and curvature properties in production are already
imposed in the cost function. Therefore, one does not have to assume these conditions to
obtain the optimizing input mix. Instead, these conditions may be tested. One does not have
to solve the maximization problems: they are already solved implicitly in the dual function.
Also, price variables used in a cost function are generally regarded as exogenous variables
in terms of a choice problem of the ﬁrm, while factor levels used in a production function are
usually decision variables for the ﬁrm (Binswanger, 1974b). This makes a cost function
useful in empirical studies because it avoids simultaneity problems. Moreover, according to
McLean-Meyinsse and Okunade (1988), input prices are less likely to have multicollinearity,
compared with input quantities, so a cost function mitigates multicollinearity problems among

the independent variables.

E . [C F. .

A set of inputs X yielding a given level of output q, is represented by a classical
production function q = f (X) where f is increasing in inputs, strictly quasi-concave,
continuous for all nonnegative input bundles, equals zero at zero inputs, and is unbounded
when all inputs are unbounded. A cost function is derived from this production function by

solving

42
C(W, q) = min [ WX If (X) 2 q]

where W is the vector of input prices. If the cost function is concave, nondecreasing, positive
linear homogeneous, and continuously differentiable in input prices for each level of output,
it is called a “quasi cost function.” Also, the quasi cost function is called a classical cost
function if it is continuous and increasing in output, equals zero at the zero output level, and
is unbounded for unbounded output (McFadden 1978)

Properties of a classical cost function can be described in detail. Obviously the classical
cost ﬁmction is nondecreasing with respect to input prices. If every input price of the vector
W’ is greater than or equal to the corresponding prices of the vector W, then the cost of using
W’ is greater than or equal to the cost of using W to produce the same level of the output.
Also, the cost function is homogeneous of degree one in the input prices. If all input prices
increase by k times, then the cost increases by k times. Thus, the cost function can be
expressed

C(kW, q) = k C(W, q).
for any k. The cost function is concave in input prices W, because if the price of an input
increases, then costs increase at a decreasing rate.

Ifthere is no substitution between the inputs, we have the case of a passive cost ﬁrnction.
The passive cost function is expressed as

C = wm' + 2 M wr’xr',
where w‘and x'are the previous prices and levels of the input, which are held constant even
after the input price w. changes. However, if the price of an input increases, the cost
minimizing ﬁrm shifts from the relatively expensive input to other inputs. Therefore, the

minimized cost C(W', q) is on or below passive cost. Mathematically, concavity means that

43

the matrix of second derivatives is negative semideﬁnite at every point. In terms of two input
price bundles W and W’, concavity is written as

C(kW + (1 - k)W’, q) 2 kC(W, q) + (1- k)C(W’, q) for 0 <k <1.

3.2 Functional Form
ChuimﬂhmsﬂhnaLEan

A functional form is a model that approximates an unobservable economic relationship.
A choice of a functional form should be based on maintained hypotheses for the study. The
maintained hypothesis is not a hypothesis to be tested as part of the analysis but a hypothesis
to be assumed true for the research process (Fuss et al. 1978). For example, if a maintained
hypothesis is that the elasticity of substitution is unity for any input combination, the Cobb-
Douglas production function may be an appropriate model, otherwise, a more ﬂexible model,
such as the CES or translog function, should be used. Examples of maintained hypotheses
often used in production analyses are concavity, homogeneity, and homotheticity of functions,
and proﬁt maximization.

Criteria in choosing a functional form include theoretical consistency, applicability
domain, ﬂexibility, and computation facility (Lau, 1986). First, theoretical consistency is the
ability of the functional form to satisfy the theoretical properties required of the particular
economic relationship. For example, a cost function is homogeneous of degree one, concave,
and non-decreasing in input prices. Thus, an algebraic functional form should be chosen to
satisfy these requirements, at least at a neighborhood of the range of data used in the
estimation.

Second, all values of variables must be used in the functional form within the domain

44

where the functional form satisﬁes all theoretical requirements in economies. In a cost
function, for example, the prices of inputs, the outputs, and the costs must be non-negative;
the ﬁrst derivatives of the cost function must be also non-negative, and the Hessian matrix of
the second derivatives must be negative semideﬁnite.

Third, ﬂexibility is an important factor in choosing a functional form. Flexibility is deﬁned
as the ability of the algebraic functional form to approximate arbitrary but theoretically
consistent behavior through an appropriate choice of the parameters. There are two kinds
of ﬂexibility: local ﬂexibility (Diewert ﬂexibility) and global ﬂexibility (Sobolev ﬂexibility).
According to Fuss, McFadden, and Mundlak (1978), local ﬂexibility implies a perfect
approximation to the true function and its ﬁrst two derivatives at a particular point. On the
other hand, global ﬂexibility approximates the true ﬁinction in any possible range. Thus, the
true ﬁmction and its ﬁrst and second derivatives are perfectly approximated.

Fourth, computational facility is another criterion in choosing a functional form. For
example, linearity in parameters or linearity in parameter restrictions is an important factor
to enable parameters to be estimated at reasonable costs of computation. Also, the number
of parameters in the functional form should be the minimum number required to achieve the
desired degree of ﬂexibility. In addition, Griffin (1987) argues that the functional form should
be selected according to general conformity of the function to given data. For example, a
data set may be ﬁt better with a logarithmic model than a linear model. That is, among
functional forms that have similar degrees of ﬂexibility, one should choose a functional form
that ﬁts better than the others.

Overall, Lau (1986) argues that satisfying all of these criteria simultaneously is, in general,

impossible. Therefore, he suggested ﬂexibility be maintained as much as possible, since

45

inﬂexibility restricts the sensitivity of the parameter estimates to the data and limits a priori
what the data are allowed to tell the econometrician. Also, he does not recommend
sacriﬁcing computational facility since nonlinear-in-parameters models are more likely to fail
in statistical estimation than linear-in-pararneter models, and statistical theory of non-linear
estimation is less developed than linear estimation.

As Grifﬁn et a1 (1987) stated, selection of a functional form should be based on
maintained hypotheses and statistical processes of parameter estimation. With few maintained
hypotheses, more ﬂexible forms may be appropriate. If the maintained hypotheses implied
by a functional form are acceptable, the function is appropriate. Also, a choice of functional
form depends on availability and properties of data used for the estimation. With a greater
number of observations a more ﬂexible form is allowed because of greater degrees of

freedom. In the rest of this section, we discuss the properties of various functional forms.

If . E . l E
The well-known approximating ﬁinctional forms, Cobb-Douglas, CES, the generalized
Leontief, and translog ﬁmctions, are forms that are linear in parameters. Let x be a vector of
independent variables. Then, the ﬁrst order Taylor’s series evaluated at x' is given by
f (x’) + 23, f ,-(x')(x,- —x.-') and the second order Taylor's series adds a second order term,
102.2, f g-(x')(xr -x.') 2 to this for ij= l, , n, where the subscript on f shows its
differentiation with respect to the corresponding x.
The Cobb-Douglas production function is a ﬁrst order Taylor’s expansion of log quantity
in powers of 1n x.-. In the case of n inputs and one output, the Cobb Douglas production

function is

46

q=a xi (n

i=1

where q is the output level, x, is the quantity of the i-th input for i= 1,---, n, a and B,-
(i = 1,- - -,n) are parameters. A Cobb-Douglas cost function dual to this production function

is expressed as

C = u‘ w aiq p; (2)

where C is the total cost of production, w. is the price of the i-th input for i = 1, , n, and the
parameter a' = l / a. The CobbcDouglas function allows free assignment of the output level,
returns to scale, and distributive shares. Also, the Cobb-Douglas function is convenient for
estimation since it is linear in logs. However, Arrow et a1 (1961) questioned the restriction
of this function that all elasticities of factor substitution are equal to one. Thus, economists
have attempted to develop new models that impose less restrictions on factor substitution.

The constant elasticity of substitution (CES) ﬁrnction corrects the problem of unit
elasticity of substitution in the Cobb-Douglas. It takes any constant value for the elasticity

of substitution. This ﬁrnction is a ﬁrst-order Taylor’s expansion of y0 in powers x.".
q = (soil, p,x.-"’1""’ (3)
and the cost function dual to this production function is
C = (rpm, p.’w."’+ts;q'°1""’ (4)

where 0'.= l / 13,-" for i = 1,---, n, and p = 1-1/o for the elasticity of substitution 0. In the

47

CES model, however, partial elasticities of substitution are equal for all input combinations.

Sato (1967) developed the nested CES fimction, which relaxes the restriction that partial
elasticities of substitution are equal across input combinations. For example, assuming four
inputs such that inputs x1 is a substitute factor of x2 and x3 is a substitute of x4, a two-level

CES production function is expressed as follows.

2,, = [B,x,"" + (1 - ppxz'Pu‘W‘
z,=[t,x,"" + (1—B,)x.""]"’°' (5)
q =[Yx,"’ + (l-Y)x,"’]""’

Let s: be the factor share of the sum of input 1 and input 2 and 52 be the factor share of inputs

3 and 4. Then, the Allen partial elasticities of substitution are

013=or4=°23 24:0

012 = o +[1/(pl +1) - o]/sl (6)
034 = o + [1/(p2 +1) - o]/s2

=0

Thus, the elasticities of substitution are constant for some of factors. The nested CBS is not
extensively used in empirical work, however, since as the number of factors increases,
estimation of the function becomes very complicated.34

Functional forms that are more ﬂexible than the Cobb-Douglas and the CES functions
include the generalized Leontief function, the generalized Cobb-Douglas function, the
generalized quadratic function, and the transcendental-logarithmic (translog) function. These
models are second-order Taylor’s approximations of arbitrary functions. These functional

forms impose no restrictions on elasticities of substitution between inputs. Also, returns to

 

3“Fuss el al. (1978), p. 242.

48

scale are allowed to vary with the level of output.
The generalized Leontief function introduced by Diewert (1971) is a Taylor’s expansion

of q in powers of x'”.
q = Bo + 27:1 535,1” + 2;! 2:1 Byxllnle/Z (7)

Also, the generalized Cobb-Douglas function production is expressed as

lnq = [30 +211 2:1 pljln[(xt+xj)/2] (8)

The generalized quadratic function is as follows
q = [2:1 2:1 pyxiarxjaﬂ-vlﬂu (9)

All of the generalized Leontief, generalized quadratic, and generalized Cobb-Douglas
production functions are homothetic.3s None of these assume concavity. The generalized
Leontief function is concave when all Dr,- in the above equation are non-negative; the
generalized Cobb-Douglas function is not concave in general; and the generalized quadratic
function is concave if all [lg-20, Osys 1, as 1, and v S] (Grifﬁn et a1, 1987).

The translog production ﬁmction was developed by Christensen el al.(1971) and can be

represented

lnq = 90 + 27:1 pi lnx! + “2 2:1 21:! Bi} lnx'. lnxj (10)

This function does not assume homotheticity, concavity, nor constant elasticity of

 

35A function is homothetic if it can be represented as a monotonic transformation of
a ﬁrnction that is homogeneous of degree one. A function f is homogeneous degree one if
it satisﬁes f (er, kicz, , kxn) = k f (x1, x2, , xn) , for an arbitrary constant k.

49

substitution, unless restrictions are imposed on parameters. While the ﬂexibility of translog
function is greater than other ﬂexible functions described above, parsimony of parameters is
less. In a case of production with n inputs, the number of parameters in this translog
production function will be '/2(n2+3n+3), while the generalized Leontief is l/2(n2+n);
generalized Cobb-Douglas is l/2(n2+n+2); and generalized quadratic function is n2+3. The

properties of the translog cost function are discussed in detail below.

MW
As stated above, the translog cost function model is derived as a second-order Taylor’s
approximation. The general form of a Taylor’s expansion for the function f (x) around
x = a is
f(x) = f(a)+ l/ l! fr(a)(x - a) + 1/ 2!f2(a) (x - a)2 +
+ l/(n-l)!fn-r (x - a)““ + l/ nlfn (a + 0(x-a)) (x-l)"
Since the last term approaches zero as n goes to the inﬁnity, this equation can be rewritten
as an inﬁnite series:
f(x) = f(a)+1/11fr(a)(x - a) + 1/ 2!f2(a) (x - a)2+ + l/ nlfn(x - a)n +
For the logarithmic form of the cost ftmction: 1n C= lnG(lnwr, 1nw:, , ann, lnq, t) where w.
is i-th input, q is output, and t is the time trend, the Taylor’s expansion with respect to lnC,

ln w.-, lnq, and t around the points of ln w.=0, lnq=0, t=0 is

lo:

581

The

incr

50

lnC- lnG(1,1,-,1)+2— ci‘lnG1n “Mama q+alnGt

   

 

 

 

 

 

i=1 611119111: ﬁlm at
III II azlnG 1 ﬂ azlnG
+ . lnw.+— mimq+ lnw.-t ll
2§§61nwplnwjln w’ ’ 224361nwalnq igarnwa: ' ( )
+1 azlnG ”+16szqu la’_ln_G 2 ROM, 1’ , n, 1nq, ,)
261nq°6t 2 aq2 2 a__2

where R is the remainder. Assuming limn... R=0, and alnG/ aln w,- = [5,, alnG/ a 1nq = [34,
alnG/ 6 Int = 13, , azlnG/ ( 6 lnw,- a anj) = Br,- , azlnG/ ( 6 111W: alnq) = Br, , azlnG/ (a lnwr at)
= Br: , azlnG/( aln q)2= qu , azlnG/ a 3:13”, the equation (1 1) will be the translog cost
function.

Also, the Translog ﬁmction is regarded as a general form of Cobb-Douglas functional
form. Imposing the restriction or.) = 0, the translog function will be a Cobb-Douglas function
in the above equation.

In order to make the translog function consistent with economic theory, it must satisfy
several restrictions. The ﬁrst restriction is symmetry. In the translog function above,

By = 13,; for i, j = 1,-~ n, i #j. It is explained mathematically such that

9y=——=——=Bﬁ (12)

The second restriction is linear homogeneity of degree 1 in factor prices. If all factor prices

increase k times, then the cost has to increase k times as well. Homogeneity implies

2;: 13, = 1’ 211 By = 0’ 24 pi} = 0 (13)

51

for all i and j. The restrictions of symmetry and homotheticity may be added in a model to
be estimated or they could be tested later. Third, since the cost ftmction must be concave in
factor prices, 62 C/ (6 wt a w,) has to be negative semideﬁnite. Also, this condition implies the
matrix of the Allen’s partial elasticities of substitution is also negative semideﬁnite
(Binswanger 1974b). Fourth, monotonicity requires that the function be increasing as factor
prices increase. Although it is desirable that this condition holds for any arbitrary values in
the independent variables, in the translog cost function the condition cannot be mathematically
imposed in the functional form. Thus, a local condition, instead of a global condition, is
tested within the range of data.

8 lnC/a In W: = [31+ 23,- [lg-1n w,+ B,qlnq + [int 2 0

a lnC/a lnq = 0., + 2,-[3,-,-1n w,+ qulnq + But 2 0

6 lnC/dt =13, + )3,- By‘ll’l w,+ qulnq +13.” 2 0
Among these, the ﬁrst equation should be generally true, since it is equal to the cost share of

the i-th factor (Sr).

Morelilezsihleliouns
There are some functions that are more ﬂexible than the translog. For example, the

generalized Box-Cox form

q(e) = (10+ a,x,(r) + 2:, 2;_1a0xi(k)xj(k)
when: 4(0) = (q’°- 1) (14)
and x,(r) = (x,"-1)/r

This functional form is a nested form of many other forms. For example, it is linear in logs

52
when 0 = 1/2, and k = 0, Cobb-Douglas when 0 = A = 0, Ewart: 1, and all or”: 0, CES when

v0 = )1, 1a,: 2a", and at, = 0, translog when 0 = A = 0, and generalized Leontief when 0

=k=‘/2.

llllSl . 'Il'Sl

So far, we have discussed criteria in selection of a functional form and properties of major
functional forms. The main objective of this study is to estimate output elasticities of factor
demand, as well as elasticities of substitution, using a dynamic econometric model. Thus, the
selected models have to be ﬂexible in terms of economic properties and relatively unrestricted
in the parameters. Thus, the models that assume constant elasticities of substitution should
be excluded. Although there are many studies using the Cobb-Douglas function in Japanese
agriculture, there is no reason to assume that elasticities of factor substitution are one. The
hypotheses of constant elasticity of substitution and homotheticity in the production process
have been rejected in some previous studies (e. g., Kuroda, 1987). As discussed above, the
translog ﬁmction does not have constant elasticity of substitution and homotheticity as
maintained hypotheses. Yet, even though ﬂexibility is desirable, more ﬂexible models, such
as the generalized Box-Cox model require an extremely large number of parameters to be

estimated. Thus, the translog appears to be the best choice for this study.

3.3 Dynamic Models
1! . E . F.
Early production and cost function models implicitly assumed production factors were in

long-run equilibrium, that is, all factors are assumed to be adjusted immediately to the cost

53

minimizing levels. The assmnption of short-run equilibrium is, however, unrealistic in many
cases, because adjustment is often slow and disequilibrium may occur in the short run. A
classical means of incorporating dynamic structures in the factor demand analysis is the partial
adjustment model (e.g., Lucas 1967, Treadway 1969 and 1974, Mortensen 1973). This
model is rationalized in the sense that it contains mechanisms consistent with dynamic
optimization behavior. A limitation of this model is that the rate of the adjustment is constant
in all factors, and therefore the short-run elasticity and the long-run elasticity are always
proportional with a constant ratio (Taylor and Monson 1985). Another model that
overcomes this problem is a static model with ad hoc dynamic terms representing adjustment
costs or expectations (e. g., Jorgenson 1965). Even though this model contains dynamic
elements, another ad hoc functional form, such as a quadratic cost of adjustment, must be
assumed. Dynamic duality models of factor demand are developed by McLaren and Cooper
(1980) and Epstein (1981). The mechanism for this model is intertemporal optimization of
a value function using the Harnilton-Jacobi-Bellman equation. This is consistent with the
theory of adjustment cost (Epstein 1981), however, using this model, one must accept
assumptions that the real discount rate is constant and that the producer uses production
factors so as to maximize the net present value for the future production process.

Dynamic econometric models, such as the distributed lag model and the ARMAX model,
explicitly incorporate intertemporal relations between the independent variables and the
dependent variables. These models are useful for empirical research where the mechanism
of the dynamic structure is unknown.

The dynamic econometric model with ad hoc dynamic terms is adequate for analysis of

Japanese agriculture, since there is no clear consensus about the mechanism of the dynamic

54

adjustment process. Slow adjustment of factors is due to either high adjustment costs in the
short run, time lags of market information transmitted to farmers, time lags of obtaining or

disposing of factors (e. g., infrastructures), the dynamics of farmer's expectation formation.

11 . E . 1 1
This section brieﬂy reviews dynamic econometric models with lag structures. Suppose

the static relationship between q(t) and x(t) is expressed such as

q(t) = a + 11x0) + ea) (15)

where [3 is the vector of coefﬁcients on the independent variables x(t) and e(t) is a
disturbance. Distributed lag models include ﬁnite lag models and geometric lag models. The

model with a p-th order lag is

q(t) = a + 22,, l3,x(t-I) + 60) (16)

In this equation, Do is the short-run multiplier (the impact multiplier) and 214-013; is the long-
run multiplier (equilibrium multiplier). In practice, this model has several problems: It
contains so many parameters that degrees of freedom are often constrained. Also, the model
may have a severe multicollinearity problem. Thus, Almon (1965) proposed a restricted
distributed lag model with polynomial distribution of lagged coefﬁcients. The polynomial
distributed lag model effectively reduces the number of parameters, although it sacriﬁces
some ﬂexibility in the lag structure. In the ﬁnite distributed lag models, an appropriate length

of the lag must be speciﬁed; however, it is often unknown.

55
The geometric lag model introduced by Koyck (1954) takes an inﬁnite order of distributed

lags as follows:

q(t) = a + 1322;0(1-1H’x0-z) + u(t) (17)

where u(t) is the possibly autocorrelated error term. This model may be translated as an
adaptive expectation model or partial adj ustrnent model, depending on the assumption in the
study. Under the assumption of adaptive expectation, u(t)=e(t)- pe(t-1), where p is a
parameter on the lagged error. In the adaptive expectation model, the current expectation
x'(t) is formed as an average of current observations x(t) and the previous expectation x'(t— 1)
with the weight A: x°(t)=(l — k)x(t)+kx'(t- 1) or x'(t)=(1- k)/(l - AL)x(t), where L is a lag
operator. Substituting this into an expectation model q(t)=a+px'(t)+e(t) will give and

autoregressive form

(hum) = (I-m + Isa—ma) + (I-AL)e(r) (13)

On the other hand, in terms of the partial adjustment model q'(t)=a+px(t)+e(t), the current
level of q(t) is a weighted average of the optimal level q‘(t) and the previous level q(t- 1),
thus, q(t)=(l — A)q'(t)+kq(t— 1). For 0< k<1, the current level is adjusted towards its optimal
level but it is also affected by the previous level. Another representation of this is
Aq(t)=(1— k)[q'(t)-q(t—1)], so that the cru'rent adjustment is made as a certain proportion of
the previous error of adjustment to the optimal level. Since q‘(t)=[(1 - AL)/(l - k)]q(t),

q‘(t)=a+px(t)+e(t) is equivalent to

56

(1 -AL)q(r) = (1 —A)a + 130 -A)x(r) + (1 -A) err) (19)

The major limitation of geometric lag models is that they take given shapes of lag
patterns. The lag weights, however, might not be consistent with the data Jorgenson (1966)
proposed more general lag model, called the rational lag model or the autoregressive

distributed lag (ARDL) model

q(t) = a + 72%);40 + ea) (20)

where 1‘(L) = [3:0 I‘,L ', and o (L) = 27:0 (biL ’. Various patterns of lag structures could be

produced by the composite lag term [I‘(L)/<D(L)]. The autoregressive form of this equation

is
ML) q(t) = I‘(L) 15(1) + ML) 6(0 (21)

Thus, the ARDL model has a restriction that the lag structure of q(t) is just the same as those
of the moving average term of the disturbance e(t). A further general form relaxing this

restriction is

ML) q(t) = I‘(L)x(f) + 9(L) 6(1) (22)

57
where 6(L) = 2' 6 L ’ . This is a general ARMAX model.36 Although an advantage of

i=0!

ARMAX is its general and ﬂexible characteristics, the number of the parameters may become
too large for small size of samples. Then, by assuming 6(L) = I, it may be transformed into

a model called the ARX model:

¢'(L)4(t) = I“(DMD + 60) (22)

The ARX model saves degrees of freedom, while keeping the ﬂexible properties of the

ARMAX model to a large extent.

IheElexihleMQdel
This section develops a dynamic model transformed from the ARX model, called the
“ﬂexible model” in the following discussion. The ﬂexible model in this study is based on a

translog cost ﬁrnction. As stated above, the cost function may be expressed in the translog

ﬁrnctional form:
n l n n
lnC(w,q,t) = lnﬂ0 + £13,111)», + Bqlnq + B‘t'. + —Zzpylnwilnwj
1-1 2r-11-1 (23)

l 1 n n
taﬂwaan +-2'l3,{1‘2 + 2 Bthﬂnq + EB“MW,-t + 5.“an + 6
1-1

l-l

where, w.- is the price of the i-th factor of production. Technological progress is assumed

exponential.” Using Shephard’s lemma, the i-th factor cost share equation is

 

36This model is transformed into ARMA by imposing I‘(L)=0.

37The original index of technology advances at a constant rate, such as e' in the year
1, e2 in the year 2, and so forth; therefore, t, which is logarithm of the original index in the

58
S1 = 13,. + gpqmwj+ [31211114 + Brit + £1 (24)
I

where S. is the share of the i-th factor in total expenditure. As stated in the previous section,
the cross-price derivatives of the cost function must be symmetric. Therefore the cost
function must be homogeneous of degree one in the factor prices, and the cost shares must
sum to l, the translog function has restrictions on the parameters such that Dr,- =0, 1‘, 2,13,, =
0, 2. B.) = 0, and Z .13; = l. The vector representation of the share equations with the

disturbance, 6(l), is

S(t) = 8X0) + err) (25)

where the vector S = [S1, 52, , Sn ]T, the vectorXr = [1, InW1,--- , ann; lnq, t], B is the n x m
matrix with the i-th row such that [ 0,, [3,1, [3.2, 0m, (in, Bu ], and the n x 1 matrix ofthe
disturbance e(t) is independently and identically distributed over time. The parentheses of t

represent the time index. In this equation, restrictions on parameters are

i’B = (1 0 m0), i’e(r) =0 for all r (26)

where i is a unit vector with appropriate dimensions.

This static share model, which is applied by previous translog studies, implicitly assumes
that S(t) and X(t) are stationary. As Harvey (1990) mentioned, many economic data are
nonstationary, so that the assumption of stationarity is invalid. If either or both of S(t) and

X(t) are nonstationary and integrated of order one, this model cannot be estimated without

 

Taylor’s approximation, grows such as 1, 2, ~.

59

testing and imposing cointegration among the variables to make the model stationary.
Stationarity issues are discussed in more detail in the chapter 4.

Also, the static model assumes that current changes in the variables affect only current
shares. However, this assumption may not hold; changes in some independent variables affect
the shares in the following periods or the levels of the current shares may be dependent in
their previous levels. Thus, the share equations are transformed into a lagged model. Let

<D'(L) and I"(L) be lag variables on S(t) and X(t).

ML) S(t) = 1“(L) X(t) + e(t) (27)

This model has ad hoc characteristics, since it is not derived from the original translog model
but from the share equations. Thus, this model has limited implications for original cost
function. However, this model is useﬁrl in estimation, since it has a relatively small munber
of parameters and maintains a linear form. Also, it still keeps many of the ﬂexible properties
of the translog model, such as variable elasticities of substitution and nonhomotheticity. A
general form of an error correction model is derived from this model as follows.

Deﬁne ¢(L) and I‘(L):

p-1 1‘ ’
<1>(L) =2 2 QB

j=l 1:0

=(¢;+¢;)L+(05+¢I+¢2‘)L2+...+(Q;+¢;+,_.+¢;_1)Lp-l
4-1 I
I‘(L) =2 2 131.1

j=0 i=0
= P0+(I‘(;+P;)L+(I‘O. +F; +P2.)L2+...+(I‘5 +I‘; +,,,+I‘;-‘)LQ‘1

(28)

for p>1 and q2 1. The differences of <1>(L) and I‘(L) are

60

mm) o(L) - o(L)L
(o; + on], + <1)ng + (by) +... + ¢;_ILP" - (a); + + ¢;_1)LP

¢‘(L) - ALP + ogL -1

(29)
o‘(L) = Ao(L) + AL” - L +1
o‘(L) S(t) = o(L) AS(t) + AS(t-p) - S(t-l) + S(t)
= o(L)AS(r) + AS(t-p) + AS(t)
where A = 25:," «b: . Similarly,
A I‘(L) a I‘(L) - I‘(L)L
= I“; + PiL + 1‘ng + ...+ 1:41,?" - (1"; + 1‘; + + 1:01,?

=I"(L)-I‘;L"-(I‘5 +I‘1' +--- +I‘;_1)L" (30)

= 1“(L) - 11 L 1
1"(L) = (I‘(L) - I‘(L)L) + UL ’
I"(1’) X (t) = I‘(L) M“) + 11X (t ‘4)

where II = 23:}; I‘,‘ . Substituting these into the original equation, it is transformed as

<1>(L) AS(t) + A S(t-p) + AS(t) = I‘(L) AX(t) + II X(t-l)

AS(t)= - <I>(L) AS(t) - A S(t-l) + I‘(L) AX(t) + II X(t—l)

AS(t)= - <1>(L) AS(t) + I‘(L) AX(t) -A [S(t-p) - B X(t-1)]
where B = A “ IT . This is a general expression of an error correction model transformed
from the ARX model. This model has the same ﬂexibility in dynamic structure as the original
ARX in terms of dynamic structure. In the case of ﬁrst-order model (i. e., p=q=l ), A = - (I

+<I>1), I‘(L)=I‘1, lI= I‘o+I‘1, and (bisnullforp= 1,sothat

AS(r) = I‘OAX(t) - A[S(r-1) — BX(r-1)] +e(t) (31)

61

In this expression, the coefﬁcients B represent the steady state relationship, S = B X and Po
and A represent terms for short-run adjustment, which will disappear in long 11.111 equilibrium.
Thus, this model is distinct from the model (26) in the sense that coefﬁcients in this model
show long-run effects of variables, while coefﬁcients in the latter model represents short-run
effects.

Since the cost shares add up to one, differences of the shares AS; add up to zero. To
insure that the sum of the right-hand side equations is equal to zero, the column sums of I‘
and A must be zero. Also, since S = B X for the steady state condition, the sum of elements
in the ﬁrst column of B is equal to one, and the other column sums of B are zero. These
restrictions are called the ‘adding-up’ restrictions. The adding-up restrictions imply that
equations in the model are singular, therefore, it cannot be estimated unless some
modiﬁcations are made. To make the estimation feasible, ﬁrst, one of the shares is dropped
from the system. As a result, AS(t) and S(t-l) will be (n-1)xl vectors, and
correspondingly, the last row of A being deleted. Since the sum of elements in the row of
nxn matrix, A also equals to zero, the ij-element of the nxn matrix A is modiﬁed as
a3, =(a1, - arm) for all i,j = 1, , n-l, so that the new matrix A' becomes (n-l) x (n-l).
Also, restrictions for symmetry and homotheticity of input prices are imposed in the matrix
B. Thus, 13., = D ,1 for all i and j, and 1n(x./ xn) is used for the independent variables (i=1,--- ,n).
In addition, since the model has lags, the ﬁrst element of AX , the constant term disappears,
and AT is equivalent to the constant, therefore, the ﬁrst and last columns of I‘ will be
deleted.

Since this model is highly non-linear, estimation may be difﬁcult. The model can be

transformed into a linear form. The ﬁrst order form of the equation

62
S(t) = - <I>1 S(t-l) + I‘o X(t) + I‘1X(t-1) + e(t) may be transformed into

(I+¢1)"S(t-l) = - (I+<I>1)"¢S(t-l) + (I+d>1)"PoX(t-l) + (I+<D1)"P1X(t-l) + e(t)
(Ii-(I31)l (I+¢1)S(t-l) = - (I+¢Dr)'l¢1AS(t) + (I+¢1)'1(F0+P1)X(t)

- (I+<1>1)"I‘1AX(t-1)+ (I+<I>1)"e(t)

S(t) = FAS(t) + BX(t) - GAX(t-1) + 5(1) (32)

where F= - (l + $1)" (Dr, B = (I + (1)1)"(1‘0 + I‘r), G = (I + (D1)“ P1, and

€(t) = (I + (D1)" e(t). Unlike the previous error correction model, this transformed model is
linear in parameters so that estimates are easily obtained. Also, this model includes
coefﬁcients representing the long-run relationship (B), which is the same as what appears in
the error correction model. Yet, compared to the error correction representation, the
functional form of this linear dynamic model expresses less explicit implications for long-run

and short-run factor adjustment.

Ccnelusinn

In this chapter, we have reviewed the theory of duality and dynamic econometric models.
Then, a dynamic model was derived from a system of share equations based on a translog cost
function. This model is ﬂexible in terms of functional properties (i. e. , elasticities of
substitution and homotheticity) and allows for a ﬂexible ad hoc dynamic adjustment process.
Also, the model is useful for estimation of long-run output elasticities since it permits short-
run disequilibrium but still imposes long-run equilibrium.

The model is implicitly assumed to be stationary so that it can be estimated using standard

econometric procedures. This model contains levels of variables as well as ﬁrst differences.

63

Thus, the model is valid only if either all data are either stationary in levels or they are not
stationary but a linear combination of the data is stationary (i.e., cointegrated). Stationarity

of data is discussed in detail in the next chapter.

CHAPTER 4

DATA AND PRELIMINARY TESTING

4.1 Data

This study uses annual data on Japanese agriculture for the period 1951 to 1992.38 It is
assumed that agricultural production in Japan uses four kinds of inputs (i. e., land, labor,
agricultural chemicals, and capital inputs) to produce a composite output.

The prices of labor and land cannot be obtained directly from a market since these prices
include opportunity costs, such as family labor and rent for own land.39 Although there is a
market for hired labor, hired labor accounts for less than 2 percent of the total farm labor in
J apan.‘° Therefore, wages for hired labor do not adequately represent wages for the total
farm sector. Rather, this study uses labor costs per working hour as labor prices. The costs
include opportunity costs of family labor and managerial labor, as well as hired labor. Labor

cost per hour is obtained by dividing labor costs per unit of production in a year by labor

 

38Japan was in disorder during an intermittent war (1 894-1945) and several years after
the war. Thus, this study uses the data after 1951 when Japan became officially independent
and the economy normalized.

39 Kuroda (1987, 1988) used wages for hired labor as a proxy for wages of family
labor, while Kako (1979) used labor costs per hour working for prices of labor. We follow
the latter in this paper.

”The proportion of hired labor in the whole farm labor is calculated by average
working days in a year of a hired worker times the number of the hired workers in Japan
divided by average working days of a farmer times the total number of farmers in Japan.

64

65

hours per unit of production in a year. Similarly, land prices are obtained as rental costs per
hectare in a year, which includes rent for farmers’ own cultivated land as well as rent paid to
other owners by the farmer. The labor and land prices are collected in terms of ﬁve product
groups--rice, wheat and barley, potatoes, vegetables, and fruits.“l Since many kinds of
vegetables are produced in Japan, costs for vegetables are estimated in terms of the ﬁve major
products-cucumbers, eggplant, tomatoes, cabbage, and Japanese radishes (Daikon).
Similarly, two major ﬁ'uit products in Japan, oranges and apples, are used to represent for
fruits. The original data are obtained from the “Survey on Production Cost of Agricultural,
livestock and Sericultural Products” collected by the Statistics and Information Department,
Ministry of Agriculture, Forestry, and Fisheries (JMAFF). Estimated labor and land prices
for each cr0p are aggregated into total labor and land prices, by the weights of values of
production for each crop.

Prices of chemical and capital inputs are collected ﬁ'om the factor price lists in the “Survey
on Prices and Wages in Rural Areas” (JMAFF). The chemical input prices are calculated by
weighted averages of the fertilizer prices and agricultural chemicals for each year."2 Prices
of capital inputs are estimated as aggregate prices of agricultural machines and tools, heat,
lights, and other energy, farm buildings, other infrastructures, seeds, fees, agricultural
clothing, and miscellaneous materials. Averages of chemical and capital input prices are

obtained by weighting by production expenditures for each item in terms of rice, wheat,

 

"Barley produced in Japan includes “two-row barley,” “six-row barley,” and “naked
barley.”

42"Agricultural chemicals” include pesticides, insectiCideS, and all other chemical inputs
but fertilizers.

66

potatoes, vegetables, and fruits, which is obtained from the “Farm Household Economy
Survey” (J MAFF).

Output quantities are estimated as the total value of output of rice, wheat and barley,
potatoes, vegetables, and fruits, divided by the prices for the products. The total values of
output are obtained from the “Agricultural Output and Income Survey” compiled by JMAF F.
Also, a time trend is used as a proxy variable for technological progress. The technology is
assumed to grow at a constant rate each year. All prices of the factors and outputs are
normalized so that values in the base year are equal to 1. Production costs for each input are
obtained from the “Survey on Production Cost of Agricultural, livestock and Sericultural
Products”(JMAFF).“3 Then, cost shares are calculated as costs for the factor used for all

products, divided by the total costs.

4.2 Stationarity and Cointegration
S . .

A series is deﬁned as stationary if the probability laws of the process do not change over
time. Let 2(a) be a distribution at time tr. Then, if the joint distribution of 2(0) 202) Z0»)
is the same as the joint distribution of Z014) Z024.) Z(t..-r) for tr and k (i = 1 n), that is,
the distribution is not changing over time, the distribution is called strictly stationary.
Whereas this condition may hold in cross-section data, it is not often applicable in time series
data. The concept of stationarity used in this study is weak stationarity, where the mean and

variance are constant over time and autocovariance depends only on the difference between

 

43The costs include opportunity costs of labor and land.

67

the two periods. For example, in the model

W) = a + 131(0) + ”(f-1) + 60), (33)

y(t) is explained by its past value, the other explanatory variables x(t), and the innovation e(t).

By transforming this equation

y(t)=2;'.ov"ra +13x(:-i)+ err-m (34)
Therefore, the variance of y(t) is

Var[y(t)l = 2?.otv‘)’= 02,“ - 7’) (35)

where 02 is the variance of the disturbance. In order to ensure a ﬁnite and positive variance
of y(t), y must be inside of the unit circle.

A stationary series and a nonstationary series have distinct empirical difference. A
stationary series move up and down around the mean, while a nonstationary series tends to
keep grong or declining. A stationary series has a ﬁnite variance and an autocorrelation
diminish as the lag increases. On the other hand, a variance of nonstationary series grows
over time and an autocorrelation stays at one. A shock on stationary series gives a transitory
effect so that the effect declines over time, and the series will return around the original mean.

However, in terms of nonstationary data, effect of a shock would be permanent.

68
1111113191
Let v(t) be a stationary process, then an AR(1) model is expressed as

y(t) = Py(t-1)+ v(t)
If p=l , it is called a unit root process:

y(t) = y(t-l)+ v(t)
Granger and Newbold (1974) pointed out that the conventional t test for a unit root would
induce an incorrect conclusion. Dickey and Fuller (1979, 1981) showed that in a case of a
unit root, estimate of p is biased downward and the variance of the estimator converged more
rapidly than the estimator in a case of the usual ordinary least squared. It implies that a
conventional test would reject hypothesis that p=1 incorrectly. They derived a set of critical
values for testing this hypothesis using a conventional t-test procedure (Dickey and Fuller,

1979) as well as a F-test (Dickey and Fuller, 1981).

Integratinn

If a variable becomes stationary after being ﬁrst differenced d times, the series is
integrated of order d, denoted 1(d). Thus, a stationary variable is integrated of order zero,
and a variable which must be differenced once to be made stationary is integrated of order
one. Most economic data are [(0) or 1(1), and many of them are 1(1) (Harvey, 1990).“ If
x(t) ~ [(1), then Ax(t) is ~ [(0), thus, differencing will create stationarity by removing

components for random walk and trend."5

 

4“ Higher order or fractional integration is also possible.

“Hendry (1991) suggested that differencing may lose some valuable information of
the data.

oir

com}
all C(

1(d).

C356.

has 1!

Nil!

if S a
all 161

and .1

apart
long-1
cOmn
mOVe;
and 11

repics

69
C . .

There are several rules in terms of linear combinations of integrated series. If all
components of the vector series, x(t) are 1(0), then any linear combination of x(t) is 1(0). If
all components of x(t) are 1(d), then it is generally true that any linear combination of x(t) is
1(d). Yet, it is possible that the linear combination will be 1(d — b), where b>0. In this special
case, the components of x(t) are said to be cointegrated of order d, b, denoted x(t) ~ CI(d,
b) and the vector to generate this linear combination is called the cointegrating vector. If x(t)
has N components, and has r linearly independent cointegrating vectors (r s N-l), a is the
N x r matrix.

In terms of the ﬂexible dynamic model presented in the previous chapter,

AS(t) = I‘ AX(t) - A[S(t-l) — BX (t-l)] + e(t),
if S and X are [(1 ), then AS and AX are I (0). Since the left-hand side of the equation is 1(0),
all terms in the right-hand side must be 1(0) to have stationary error terms e(t), thus, S(t-l)
and X(t-l) must be cointegrated with cointegrating vectors B.

In economic theory, the notion of equilibrium implies that series cannot continue to drift
apart. Indeed, nonstationary series in many cases are found to be moving together in the
long-run. This idea is captured by cointegration. For example, it is sometimes observed that
commodity prices that seem unrelated to each other move together. Such a price co-
movement may be caused by a certain common macroeconomic shock (e. g. , money supply
and interest rate) and speculation in the commodity market (Myers, 1994). Cointegration

represents a certain long-run relationship between the data.

70
I EII'E 1C. .

In order to detect the individual variables are 1(0) or 1(1), the Dickey-Fuller test for unit

roots is used as follows:

Ax) (t) = c + y t + pix.- (t—l) + e(t).
where x includes variables for prices of labor (L), land (D), chemical (Cl-I), and capital (K);
output (Q); and shares of labor (Sr), land (SD), chemical (Sen), and capital (SK).46 A constant
term c and a time trend variable t are included in the equation.

In order to investigate cointegration among variables, this study follows Engle and
Granger’s (1987) two-step estimation procedure: First, using the OLS model, one of the
variables is regressed on the other then it is tested whether there is a unit root in the residuals.
Since the OLS seeks coefﬁcients that reduce the variance of the residuals, the regression
efficiently produces the estimate of the cointegration vector. The linear combination of the
variables other than the cointegrated vector will have inﬁnite variances. If the series are not
cointegrated, there must be a unit root in the residuals, therefore, they are found to be
nonstationary. Dickey and Fuller (1979, 1981) showed that the variance of the estimate
under the null hypothesis in the unit root equation converges to its probability limit more
rapidly than the ordinary estimators. Critical values for the t-test different ﬁ'om the ordinary
tests are provided by them.

This Dickey—Fuller test requires the disturbance to be serially uncorrelated. To check

whether or not there exists any serial correlation in the error of the above equation, the Q—

 

“The augmented Dicky-Fuller tests include lags of Axr(t).

71

statistic test proposed by Ljung and Box (1979) is used."7 The Ljung-Box Q-statistics are

computed by the following equations.

Q = T(T+2)£‘,;, [vi/(T-m.
where Y- ___ 2:1.) e(t) 5“ '1) (36)

’ 2’... eat

 

and p is the number of the lags for the test.

As an alternative test for serial correlation, Breusch (1978) and Godfrey (1978) proposed
a Lagrange multiplier test. The null hypothesis of this test is that errors are not serially
correlated and the alternative hypothesis is the errors take an autoregressive or moving
average form. The test is carried out by regressing the OLS residuals e(t) on the independent
variables and the lagged errors.

As a result of the Ljung-Box tests, serial correlations are detected in the variables D, CH,
and K. Also, the serial correlations are found in L, D, CH, and K in the Breusch-Godfrey
tests. As there are no serial correlations in the share values and the output levels, the Dickey-
Fuller test can be applied directly to these variables. The critical values for this test are - 3.50
at 5 percent and -3.18 at the 10 percent in a case of T=50. All shares as well as the output
show relatively high values. However, all of these estimates but Scu do not reach to the
critical values, so that the hypothesis of a unit root is rejected only for Sen.

Also, the hypothesis of unit roots in the autocorrelated variables (i.e., L, D, CH, and K)

is tested using procedures proposed by Phillips (1987) and Perron (1988). The Phillips-

 

"The Ljung-Box Q-test is a reﬁnement of the original Q-test proposed by Box and
Pierce (1970).

72

Perron test takes account of serial correlation and potential heteroscedasticity in the errors.

Let 0p and rp be the standard error and the t-statistic of p' and s2 is the variance of the

residuals from the Dickey Fuller regression, so that

s2 = (T-2)“2f_l 5(1)’ ;

A2 = v, + 2 23;, 1,11 -j/(q +1)]

(37)

where y, is the autocovariance of the OLS residuals between the time t and the time t—j, thus,

_ -1 T _
Y, - T 2,,” 6(t)6(t 1)
Then, the Phillips-Perron t-statistic is computed by

1/2 2
Z : Yo “tp _ T.OP(A‘ -Yo)

 

 

‘ k zs-r

And, the Phillips-Perron statistic for the coefﬁcient p is

T2.02(12-Y
Z. . T,p._ . o)
252

 

(33)

(39)

(40)

In the above equations, we use truncation of 2, 4, and 6 lags. Under the limited number of

observations, we cannot use larger number of lags as it reduces efficiency in the estimation.

The critical values in the Phillips-Perron tests are equivalent to those in the Dickey-Fuller test

 

 

73

based on estimated OLS autoregressive coefﬁcients and t statistics. The critical value of the
Phillips-Perron Tp' test (Zp) at the 5 percent level is — 19.8 in a case of 50 samples, while the
critical value of the Phillips-Perron t test (Z1) is —2.93 (Fuller 1976, p.371). In the model
with 4 lags, for example, computed Zp for L, D, CH, and K are ~6.51, — 1.26, ~5.54, and
—4.54, while those of Zr are — 1.58, —0.43, — 1.71, and — 1.25, respectively. Thus, all of these
estimates are lower than the corresponding critical levels.

F-tests are also applied under the null hypotheses of zero slopes of the autoregressive
variable and the trend variable (p=y=0). As seen in the Table 4.2.1, all estimated F-statistics
are far below the critical value of 6.73. The tests do not reject the hypothesis of unit roots
in all variables, except share of chemical. Therefore, at least all series for factor prices and

output are concluded to be nonstationary.

Table 4.2.1 The Dickey Fuller Tests and the Phillips-Perron Tests of Unit Roots in the Variables.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

L D CH K Q SL Sr) SCH SK

-0.062 -0.009 -0.065 -0.029 -0.209 -0.241 -0.337 -0.576 -0.1 1 1

SE(p) 0.076 0.064 0.053 0.063 0.091 0.094 0.123 0.150 0.068
t-statistic of p -0.821 -O.135 -1.229 -0.467 -2.304 -2.575 -2.745 -3.838 -1.640
Z(p) with p=2 -3.567 -0.056 -3.764 -2.424 -7.322 -9.096 -13.578 -21.948 -4.681
Z(t) with p=2 -l.051 -0.019 -l.431 -0.804 -2.200 -2.512 -2.723 -3.745 -l.658
Z(p) with p=4 -6.509 -l.258 -5.536 -4.541 -7.003 -10.l72 -12.147 -24.142 -4.019
Z(t) with E4 -1.579 -0.429 -1.712 -l.252 -2.212 -2.589 -2.589 -3.867 -1.561
Z(p) with p=6 -7.367 -1.769 -6.345 -5.088 -6.251 -10.925 -18.706 -23.295 -3.l78
Z(t) with p=6 -1.729 -0.569 -l.827 -1.340 -2.214 -2.631 -3.152 -3.819 -1.430
F -stat_is_t_ic 0.729 1.806 0.797 0.790 3.245 3.320 3.500 5.460 2.631
Note: p=autoregressive coefﬁcient of the OLS with constant and trend variables; SE(p)=standard

 

error of p; Z( pFPhillips-Perron statistic of the autoregressive coefﬁcient with p—th order lag truncation,
p; Z(tFPhillips-Perron statistic of the t value of p with p-th order lag truncation. F-statistic is based
on the test under hypothesis of zero coefﬁcients of the autoregressive and the trend.

Critical values for Z(p) and Z(t) at 5% levels are - 19.80 and -3.50 (T=50); Critical values for the
Dickey-Fuller test based on the OLS F statistic is 6.73 (T=50).

74

In terms of stationarity of the factor shares, hypothesis of a unit root in chemical share is
rejected at 1 percent by the Phillips-Perron test, while the hypotheses of a unit root in land
share is only rejected at 10 percent in the Phillips-Perron p test with 6-lag truncation; and the
tests could not reject for labor and land shares.“8 Based on these results, and the fact that
factor shares are bounded between zero and one, we conclude that all factor shares are
stationary.

Factor shares are considered to be stationary because they ﬂuctuate within a certain range
and could not keep growing. It is always strictly bounded between 0 and 1, so that it could
not approach “too close” to the boundaries. Some temporary shocks, such as a price shock,
may change the level of share temporary but it would not remain at a new level permanently
even after the shocks are over. Variances of share would not grow toward inﬁnity over time,
since boundary of a share would not be widened over time. In this sense, the shares are
expected to be stationary.

Still, it is possible that a share is trending in sample due to bias in technological change.
Technological change bias is measured by (BS/60(1/Sr), where Si is i-th factor share and t is
the time index (Binswanger, 1974). It clearly shows that a nonzero value of this estimate
implies that the share variable has a trend, but the trend must die out as the share approaches
zero or one.

The null hypothesis of noncointegration among the variables, L, D, CH, K, and Q is

tested. The t-values of an OLS regression of the residual from the cointegrating regression

 

48The critical values for the Phillips-Perron Z. test are -4.15 at 1 percent, -3.50 at 5
percent and -3. l 8 at 10 percent for 50 samples; similarly the critical values for the Z9 test are
-25.7 at 1 percent, -l9.8 at 5 percent, and -16.8 at 10 percent (Fuller, 1976).

 

75

on its lagged value, constant, and the time trend variable are -3.28, -0.78, and 0.84, while the
t—value of the regression without the constant and the time trend is -3.27. Since the intercept
and the coefficients on the trend variable should both be zero by construction, the test for
cointegration is carried out without these variables. The Phillips-Perron Z(t) and Z(p) tests
with 4 lags are -3 .49 and -22.21, while their critical values are, respectively, -4.49 and -3 7.7
at 5 percent. Thus, the hypothesis of noncointegration is not rejected, concluding there is not
cointegration among these variables.

The Durbin-Watson statistics from the cointegrating regressions may be used as another
test of cointegration.49 The cointegrating regression Durbin-Watson test examines whether
an estimate of Durbin-Watson statistic is large enough ﬁ‘om zero to reject the null hypothesis
of noncointegration. The critical values, provided by Sargan and Bhargara (1983), are 0.446
for the lower limit and 1.518 for the upper limit for 51 observations at the 5 percent level, and
0.651 for the lower limit and 2.185 for the upper limit for 31 observations. Thus, estimated
statistics of the model in this study are 1.609, 1.361 , 1.424, and 1.488, so that the results are

inconclusive.

E . .
The models in this study have a set of the share equations. Since the share equations are

singular, one equation is omitted.’0 The major estimation methods for system equations are

 

49However, Engle and Granger (1987) argue that the test is not recommend since the
critical value is so sensitive to the particular parameters within the null, although the CRDW
tests might be used for a quick approximate result due to its simplicity.

50According to Barten (1969), the maximum likelihood estimates of the parameters
are independent of the omitted cost share equation.

 

76
the full information maximum likelihood (F IML) method. The FIML estimates are sensitive

to distribution of the errors.

Was
The dynamic adjustment process is evaluated using the data: The maximized value of the
likelihood functions (lnL) in the ﬂexible dynamic model without the restrictions on parameters
is 360.310, while the value of lnL in the static translog model without the restrictions is
336.508. Since the likelihood ratio statistic A = -2 (1n [Al—Ll) has chi-distribution with
degrees of freedom of the number of constraints, where L. and Lo are the maximized values
of the likelihood ﬁrnctions with and without constraints. The critical value of the LR test is
42.98 at the 1 percent of signiﬁcance. The computed value of the log likelihood ﬁmction is
47.604. Therefore, the hypothesis of no dynamic process is rejected at the 1 percent level.
Similarly, the value of lnL in the ﬂexible dynamic model with restrictions of symmetry and
homotheticity is 355.675, while that in the static model is 303.926. The LR ratio 103.498 is
above the critical value; thus, the dynamic process is also supported in the model with

restrictions.

Conclusion

This chapter has discussed stationarity of data, as well as estimation methods. Now, it
is well known that many time series economic data are nonstationary. If a model that contains
nonstationary series is used for an econometric analysis, a statistical test may reject incorrectly
a hypothesis, although there is, in fact, no relationship about the hypothesis. A model used

in this study contains levels of variables as well as their ﬁrst differences. Ifdata used in this

 

77

study are nonstationary, then they must be cointegrated so that linear combination of series
is stationary. Dickey Fuller tests and Phillips-Perron tests for unit roots in the data show
series of factor prices and output are not stationary, while at least one of the shares is
stationary. Although these tests could not reject hypothesis of stationarity in some share data,
stationarity of these data is suspected. Ifone of the shares is nonstationary, the sum of these
shares cannot be 1. Also, a series of share data is strictly bounded between 0 and 1, so it
cannot keep growing over time. Also, the Phillips-Perron tests for hypothesis of
noncointegration are carried out. The test results found that the data used in the estimation

are not cointegrated.

in

 

CHAPTER 5

RESULTS

This chapter presents results of estimating the model developed in previous chapters, and
then the model’s conformity with economic theory is tested. This is followed by a section
which evaluates economic implications of the results, including output elasticities of factor

demand and partial elasticities of factor substitution.

5.1 Speciﬁcation Tests
Concerto:

Cost functions are concave in factor prices. In the translog cost function, each element
of the Hessian matrix is a function of w), but the matrix is not necessarily negative semi-

deﬁnite. For i¢j, the ij-th element of the Hessian is

82C =_1__1_alnc ac ctii azrnc C=B,+Sr-‘)C (41)
aw,awj “’1‘", alnwlalnwj wiw alnwalnw wiw

 

where C, w), and s; are the total cost, the factor price, and the i-th cost share for i=l,° ' °,n.

Also, the i-th diagonal element is

air: _1_ alnc arnc

C+_1_a’1ncc 1 amc Burrs, -s,
6w“ w,“ alnwialnw, w!2 alnwl2 w2 alnw, wlw

I

 

78

 

79

The Hessian matrix is expected to be negative semi—deﬁnite at least at the neighborhood of
the base year. Since in the base year, w.= w.=1, and C is canceled in both equations, we need
only check the signs of Bg‘l‘S: s, (i #1) and Br.+sr’-s.— (i =1). Computed Hessian matrices are
presented in Appendix Tables A.5.1.1, A.5.1.1, and A.5.1.3 and the eigenvalues are in

Appendix Table A.5.1.4. The tests fail to show the concavity in the factor prices."

S 111 l"E"

Symmetry and homotheticity conditions, which must be satisﬁed for parameters
representing long-run relationships, are checked by likelihood ratio tests. Since the ﬂexible
dynamic model is based on a static translog model, the term representing the long-run
equilibrium must comply with same restrictions as the static model. The maximized values
of likelihood functions of the ﬂexible models without restrictions, with symmetry restrictions,
with homotheticity restrictions, and with symmetry and homotheticity restrictions together
are 360.310, 358.284, 357.228, 355.675, respectively. Therefore, the likelihood ratio statistic
of symmetry restrictions on unrestricted model is 4.052, and of homotheticity restrictions is
6.164. Also, the statistic of both restrictions on unrestricted model is 4.635. Since 95
percent of the critical value in the chi-squared for 9 constraints is 16.92 and the value for 18
restrictions is 28.87, the symmetry and homotheticity restrictions are not rejected at the 95
percent level. Thus, the results show that the unrestricted model conforms to economic
theory in terms of symmetry and homotheticity conditions.

Thus, both restrictions are rejected at a 5 percent level, which implies that the static

 

"Antle and Capalbo (1984, p.76) argued that many empirical applications involving
translog fail these concavity conditions.

8O

translog model does not comply with economic theory in terms of the restrictions on
parameters. The maximum value of the log likelihood of the share equations in the static
translog model without symmetry and homotheticity restrictions is 336.508, the value with
symmetry restrictions is 310.234, and the value with symmetry and homotheticity restrictions
is 302.958.

The restrictions for the Cobb-Douglas function on the translog model are rejected at 99
percent of signiﬁcance. Therefore, the translog form is supported in terms of the ﬂexibility.
The homotheticity restrictions of the Cobb-Douglas are also rejected at 99 percent. Thus, the

Cobb-Douglas model does not satisfy the homotheticity requirement.

5.2 Estimates and Elasticities

The estimated parameters in the models derived in the previous chapter are exhibited in
Appendix Tables A52. 1. Using these estimates, the following section calculates elasticities
of factor demand, substitution, and technological change. These estimates represent long-run
effects that show how shocks on an economy might change production structure after all
factors are adjusted to their equilibrium levels.

Output elasticity of factor demand is deﬁned as a percent change in the input brought
about by a 1 percent change in the output supplied. Let C(w, q) be a twice differentiable
cost ﬁmction where w and q are the n x 1 vectors of the factor prices and the output level,
respectively. With the twice differentiable production function, a cost minimization problem
is expressed as

mmC=wx

subject to f (x) = q

 

81
Then, the ﬁrst order condition is
W1 - A f(x) = 0
q - f(x) = 0

Differentiating these equations with respect to q, we have the following matrix representation:

“/11 A'f12 ”fin f1 acl/aq 0

 

 

 

 

 

 

“'fzr “I22 “f2: f2 axz/aq 0
: : : : ; = E (43)
Afu “(12 Afin f» axnlaq 0
j; f2 f; 0‘_6A/6qq _lj
Thus,
ax’ - F“ (44)
6.; IR

where IF] and F m are the determinant and the cofactor of the ni-th element of the

(n+1 )x(n+l) matrix of the above equation. Therefore, the output elasticities of factor
demand [6x1 /6q][x.=/q] cannot be assmned to be the same for all factors. Furthermore, while
the concave production function has a Hessian with a negative deterrrrinant, the sign of the
cofactor of the matrix may be positive or negative, depending on the values of the second
partial ﬂ}.52 Thus, the signs of the output elasticities of factor demand are generally

undetermined.

In the case of marginal cost of the production equal to the average cost at long-run

 

52 If it is negative, the factor is called an inferior factor. As the output level decrease, the
factor demand will increase for a certain range of the output change. Unskilled labor in

manufacturing is one of the examples.

82
equilibrium, the output elasticity of demand for the i-th factor (i. e., 1]“, =[6Xr/X1]/[aq/q]) is

obtained from the estimated parameters [3.2, and the factor share Sr as

-—1+1 (45)

This is derived as follows: From Equation (1) and Shephard’s lemma,
6C/6wr=x,°(w,q) ‘1
62C*/ [6 Wrdq] = ax.‘/aq

Thus,

 

aZC‘ q
7qu - _

- awiaq x'. (46)

Using this equation and the deﬁnition of a factor share (i. e., S.= [x1 w.]/C ), also assuming the
marginal cost equals the average cost at the equilibrium (i. e., Cq = C/q), the coefﬁcient of

1nq lnxr in the translog cost function ﬂu, is transformed as follows:

 

 

 

 

 

 

 

 

 

 

B. = 6’an '(w,q)
"1 alnwialnq
= 1 6C '(w,q) W)
aq 6w! c.0914)
_ 32C' WA _ ac‘ WA ac‘
- awiaq c‘ aw, (3'2 aq (47)
620‘ 19,4 _ x,‘W,(C‘/q)q
' 67.637 c"
= 32C. ’9'“ -s,
aw,aq C‘

Therefore,

83

azc‘ c‘

 

 

. +S.
aw,aq wiq ”3'” ') (48)

Substituting this into the deﬁnition of the output elasticity of factor demand, the equation for

the elasticity is simpliﬁed as follows:

= C‘(qu + S1) 1
ntq qu x,
CT%+&>
= (49)
was
.p_iq_ + 1

S.

 

 

If 17.:q >1, the production becomes i-th input-intensive as the output level increases, while the
production becomes less intensive in the input if I)“, <1. In other words, there are “economies
of scale with respect to the i-th input” if 1),-q < 1: The average amount of the input (i. e. , input
requirement per unit output) declines as output increases. The elasticity may be greater than
unity for one or some of the inputs, while all of them can be less than unity when there are
increasing returns to scale. Note that the idea of “economies of scale with respect to an
input” is different from usual “economies of scale,” as explained in the next section.

Table 5.2.1 shows the output elasticities of factor demand estimated by the dynamic
model with symmetry restrictions imposed on parameters (see Appendix Tables for other
models). The elasticities are obtained by using the estimates and average share values of the
inputs. Since equations for labor, land, and chemical are used in the estimation and the
estimates of capital demand are obtained by adding-up restrictions, the standard errors of

parameters in the capital equation are not available. Chemical use and capital use are inelastic

 

 

84

with respect to output, while labor use and land use are elastic with respect to output. This

result suggests that, as output increases, average use of labor and land per unit of output will

increase tmder constant factor prices, while average use of chemical and capital per unit of

output will decrease.

Table 5.2.1 Output Elasticities of Factor Demand Estimated in Various Models

 

 

 

 

 

 

 

 

 

 

 

Labor Land Chemical Capital
Flexible Dynamic 1.360 1.868 0.268 0.633
Model (0.265) (0.636) (0.375)
Linear Dynamic 1.312 1.827 0.341 0.670
Model (0.185) (0.495) (0.369)
Static 1.318 1.192 0.347 0.864
Model (0.107) (0.287) (0.204)
Note: Standard errors are in parentheses.

 

 

Although the standard errors of the output elasticities shown in Table 5.2.1 are estimated
using standard errors obtained in F IML, as well as share values, the distribution of parameter
errors in the nonlinear model is not necessarily normal (Hatanaka, 1994). Thus, conﬁdence
intervals of the elasticity estimates are obtained by a Monte Carlo simulation. In the
simulation, error terms are obtained from the ﬁtted residuals in the previous estimation,
instead of assuming a speciﬁc type of distribution.” First, a value of a residual is picked
randomly from a set of the ﬁtted residuals in the error correction model estimated above.
Then, the chosen values are inserted in the model and factor shares are calculated (i. e. ,

independent variables in the original equations). Since the model has lagged shares as

 

53This simulation is called bootstrapping (Hamilton, 1994).

 

85

dependent variables, actual lagged values of shares are used to obtain shares in the initial
period (i.e., 1952) and calculated shares are used as lagged variables in the rest of the years.
Next, using a set of calculated shares and the actual series, the parameters are reestirnated and
saved. Using estimated parameters and shares, output elasticities of the factors are estimated.
These procedures are iterated 10,000 times and the elasticities are sorted by values. Finally,
the 5 percent conﬁdence intervals of the elasticities are obtained.

Estimated 5 percent conﬁdence intervals of the output elasticities are 1.018 to 1.783 for
labor, 0.784 to 2.704 for land, and -0.303 to 0.864 for chemicals. Thus, the simulation found
that the elasticity estimates are widely distributed. Furthermore the elasticities of labor are
distributed in a relatively narrow range, while elasticities of land are distributed in a relatively

wide range.

An elasticity of substitution measures how easily a given input can substitute for another
input, holding the other input prices and the output level constant. This elasticity has
important implications for factor demand: As an input price increases, the cost-minimizing

ﬁrm replaces the input with other inputs, however the extent of this replacement varies among
inputs. Graphically, the substitutability is represented by the curvature of isoquants. The
greater is an elasticity of substitution, the ﬂatter is the isoquant. In a case of a perfect
substitute (i. e., o=oo), the isoquant is ﬂat. If no substitution between the inputs is possible
(i. e. , 0:0), the isoquant becomes perpendicular (i. e., the Leontief function).
The partial elasticity of substitution is deﬁned as the proportional change in the ratio of
amounts of input i and input j with respect to proportional change in the input price ratio

where all other input prices and output are held constant.

I - V".

 

86

6(xilxj.) wj/w'.
o”. = (50)
6091/”) xilxj

 

In an alternative form, Allen (193 8) developed the partial elasticity of substitution,

= 22.1w. 5,

xix] |F|

ll

(51)

where x; is the i-th factor of production; ﬂ. is the derivative of the production with respect

to k-th input; and F ., is the ij-th cofactor of F, which is

 

"o f: f"-
F = fl fu fr» (52)
fr. fir] ' fun,

 

Uzawa (1964) showed that the Allen’s partial elasticity of substitution (AES) is computed

from the cost function C(w, q)“:

C - (ab/(aw, aw P
0,,- - (53)
(ea/aw) (so/aw)

 

Thus, in the translog cost frmction, the AES is obtained as:

a = .E’I.+1_i foralli
StSj S,
(54)
[”11

 

+1 for all i, j; iatj

 

5“Binswanger (1974, AER) proved this without relying on homogeneity.

 

87

Own price elasticities of demand for factor i (611') and cross-elasticities of demand for factor

iand factor j (6.)) are equivalent to the corresponding AES multiplied by the cost share of the

input:

”G

e ="+S—1foralli

l

(55)

+ S}. for all i,j; irj

‘4 Is” 3 I

The ABS and price elasticities of the factor demand estimated in models with symmetry
are presented in Table 5.2.2 (see Appendix Table A.5.2.6, A.5.2.7, and A528 for detail).
Again, the average share values are used for estimation. Results suggest that labor is a
substitute for all other inputs, especially, for capital inputs. This is consistent with the
previous argument that capital goods, like machinery, are used for labor-saving purposes.
Chemical inputs are also found to be substitutes for labor and land. For instance, fertilizers
are used for land-saving purposes and herbicides are used for labor-saving. On the other

hand, land is a weak substitute for capital. Also, chemical and capital inputs are
complementary to each other. This implies that, due to mechanization, greater use of
fertilizers became available through deep tillage, as discussed in the chapter two.

In terms of price elasticities of factor demand, chemical price and capital price

signiﬁcantly affect labor demand. A one percent increase in prices of chemicals and capital
will increase labor demand by 0.55 percent and 0.35 percent. This implies that decreasing

chemical and capital prices after the 19605 contributed to reduce labor demand in Japanese

agriculture.

 

88

Table 5.2.2 The Allen’s Partial Elasticities of Factor Substitution Estimated by

 

 

 

 

 

 

 

 

 

 

 

 

the Flexible Dynamic Model
Labor Land Chemical Capital
Labor -1 .451 0.433 6.781 -2.324
(0.409) 0.688 (1.663) (1.543)
Land 1.509 -8.346 11.730 -9.165
(0.979) (1.651) (3.981) (3.696)
Chemical 1.195 1.479 -4.548 -0.153
(0.578) (0.970) (2.347) (2.181) r‘
Capital 0.699 4.459 -9.830 5.537
L: .,
Note: Standard errors are in parentheses.

Table 5.2.3 Own- and Cross-Price Elasticities of Factor Demand Estimated Flexible Dynamic

 

 

 

 

 

Model

Labor Land Chemical Capital

Labor -0.583 0.174 2.726 -0.934
(0.164) (0.277) (0.668) (0.620)

Land 0.161 -0.893 1.255 -0.981
(0.105) (0.177) (0.426) (0.395)

Chemical 0.189 0.234 -0.719 -0.024
(0.091) (0.153) (0.371) (0.345)

Capital 0.232 0.484 -3.264 1.938

 

 

 

 

 

 

 

Note: Standard errors are in parentheses.

 

 

Economies of scale are such that long-run average cost exhibits a negative slope over a
broad range of the output level.” Thus, the rate of change in total costs is less than that of
output changes. The term “economies of scale” is similar to increasing returns to scale in the

production process, although the idea is not identical. Increasing returns to scale means a

 

55Econornies of scale is important, since, if it exists, development of larger scale of
industry is justiﬁed to be appropriate for minimizing the average cost.

 

89

proportionate increase in all inputs makes the output increase in more than the same
proportion. Thus, for a ﬁrm with increasing returns to scale, if all inputs are increasing at the
same rates, more output can be produced ﬁ'om the same amount of inputs, therefore, average
cost can be decreased.

The elasticity of scale measures relative changes in output resulting from a proportional
change in all inputs. This is the reciprocal of the elasticity of total cost with respect to output

along the expansion path (Hanoch, 197 5). In the translog equation above, the cost elasticity

is

6c = -— = B. (56)

In terms of this equation, there are economies of scale if Ec<l; neutrality of scale if ec=l; and
diseconomies of scale if €c>l. In the translog model, [Sq does not appear in the share
equations; only the original translog model contains this variable. Therefore, the economies
of scale can be measured only in the static model, for which the complete translog equation
may be included at the estimation. In the results of the static estimation, 6.; is found to be not
signiﬁcantly different from zero (Appendix Table A52. 14). Thus, we conclude that there
is no evidence to show that economies of scale or diseconomies of scale exist in the Japanese
agriculture.

Next, homogeneity and homotheticity of the production process are examined. In a
production process that is homogeneous degree 1, if all inputs increase by the k times, the
output level will also increase k times. In other words, if bundles of inputs X' and X2 produce

the same level of output yo, then kX‘ and kX2 will both produce 2qo. If a production function

 

 

 

90

is homothetic, kX1 will produce the same level of output as m, but it is not necessarily 2qo."’
Homothetic production and the homogeneous production both exhibit linear expansion paths.
In such cases, factor ratios are constant as the output level changes under the constant input
price ratio.’7 In terms of the translog cost function, the production is homothetic if [3“, =0;
It is homogeneous if qu = 0 as well as [1,-q =0. Note that homotheticity in production process
is sometimes referred as separability between input prices and output. If a production is
homothetic, shares of inputs are independent of output levels.

In terms of the ﬂexible dynamic model in this study, homotheticity may be tested under
the hypothesis of Bk, =0 for all i. The hypothesis is tested by the likelihood ratio test. The
maximum value of the log likelihood function in the restricted model is 355.784, while the
value in the unrestricted dynamic model is 360.310. Thus, the hypothesis is rejected at the
5 percent level of signiﬁcance. Since homogeneity could not be tested in the dynamic model,
it is tested in the static translog model. The number of restrictions is 4 in the full set of
translog and share equations. The estimated log likelihood is 374.990 for the unrestricted
model and 381.78] for the restricted model. Therefore, the null hypothesis is rejected at a
5 percent level.

The ﬁnal part of this section discusses effects of technological change in production.

According to Solow’s (1957) study, a production function q=A(t) f (it) includes a coefficient

 

56A function is homothetic if it is a monotonic transformation of a function that is
homogeneous of degree 1.

S7I-Iomotheticity is equivalent to separability of the cost function in factor prices and
output. If the cost function is separable, C(W, q, t) =j(q) g(W, t). Thus, changes in the output
does not affect factor shares. Also, homogeneity of the function is equivalent to constant
returns to scale in the production: C(W, q, t)= q g(W, t).

 

91

to represent a function of time A(t). Technological change is deﬁned, in this study, as a
change in productivity as time passes. Hicks’ neutrality of technological change can be
measured by the marginal rate of substitution (MRS) between production factors. A
technology is Hick’s neutral if the MRS of a factor for another factor is always constant as
the ratio of amounts of factors (i. e. , the factor share) remains constant. If the MRS of the i-th
factor for another factor is increasing over time with constant factor shares, the technology
is called i-th factor-saving. On the other hand, if the MRS is decreasing, it is i-th factor using.
To put it differently, as a ratio of factor prices is constant, the i-th factor share decreases, if
the technology is i-th factor saving. Also, if the factor share increases, it is i-th factor-using.
The factor share is constant if technological change is neutral. Thus, the technological change
bias is measured by the following elasticity:

as, 1
e: = 5’ g (57)
Technological change is i-th factor saving if e.<0; i-th factor using if e.>0; and i-th factor
neutral if e.=0. Since 6Si/at = B” in the translog equation, as/ar = B", e.= Bu,/Sr.

Table 5.2.4 shows estimated elasticities of technological change bias. According to the
results, the technology has developed using more labor and less land. Hypothesis of neutral
technological change in chemical is not rejected at the 10 percent level of signiﬁcance. These
results are not consistent with the previous studies such as Kuroda (1988) and Kako (1979).
Note that the former translog cost function studies, Kuroda (1988) and Kako (1979) used a
linear time trend variable, which appears as logarithms of trend (lrrt, where t=l,2, ---) in a

translog equation. This implicitly assumes that annual growth rates of productivity declines

 

92

over time. On the other hand, the model in this study, like most of the other translog studies,
uses an exponential time variable for the technological progress. In the translog equation, the
time trend index will be linear (i=1, 2, ---). In this case, the trend is assumed to exhibit a
constant annual growth rate. Estimates in the model with linear trend are similar to those in

the above case (Appendix Tables A.5.2.17).

Table 5.2.4 Estimates of Technological Change Bias

 

 

Labor Land Chemical Capital
0.028 -0.079 -0.028 -0.046
(0.014) (0.036) (0.027)

 

 

 

 

 

 

 

Standard errors are in parentheses.

Conolusions

Estimation in this chapter shows that elasticities of factor demand with respect to output
are large for labor and land, while they are small for chemical and capital. These estimates
show that as output changes, demand for labor and land change greatly, while chemical and
capital change little. Since output of Japanese agriculture is declining, the results suggest
that labor and land will decrease rapidly. Also estimated partial elasticity of factor
substitution shows high substitutability between chemical and labor. In Japan, relative price
of labor (wage) has been increasing as labor demand for nonagricultural sector increased. If
this trend continues, more labor will be replaced by chemicals in Japanese agriculture. Due
to the effect of substitution of labor for chemicals in addition to effect of decreases in output
on labor, labor demand will decrease signiﬁcantly. Thus, output changes caused by import

liberalization will change the production structure into less labor-intensive.

93

Estimation of bias in technological change shows that the technology has developed as
using more labor. This result is probably due to increasing demand for products requiring
intensive labor use in production, such as forced vegetables and horticultural products. Yet,
the degree of the technological change bias is very small and almost negligible, compared to
the effects of changes in factor prices or output.

On the other hand, the output elasticity chemical is small, implying that chemical demand
does not decline so much when output decreases. In addition, as explained above, chemical
use increase as labor price rises. These estimates imply that although chemical demand

declines, chemical used per unit output will increase.

 

CHAPTER 6

SIMULATION FOR FACTOR ADJUSTMENT

The previous chapter estimates long-run effects of a 1 percent change in the output on
factor use, assuming factor prices are constant. Although this measurement is useful for a
structural analysis of production, measurement of short-run effects of output changes, along
with associated changes in input prices, is often more useful for a policy analysis. This is the
case for estimating how trade liberalization might change production structure in Japanese
agriculture in terms of its factor use. In this chapter, simulations are carried out to explore

impacts of output reductions due to the trade liberalization on factor adjustment.

6. 1 Output Path Under Trade Liberalization

There is uncertainty and about the output response path under liberalization of agricultural
imports. The last GATT agreement requires each country reduce tariff rates by 36 percent
on average over 6 years. Japan decided to use a minimum access option for rice imports.
However, it is not known how the Japanese government will release imported rice or what
kind of policy the government will implement after the period of minimum access. Also, the
ﬁrture demand for imported agricultural products is uncertain (i. e. , how consumers react to
newly imported food, whether they prefer foreign food, and how fast they are adapted to

these products).

94

 

 

 

95

Thus, since it is difﬁcult to predict exactly what output changes will occur in the future,
several different cases of potential output changes are set up for simulation. The ﬁrst case
assumes that output decreases by 1 percent per year, so that rates of output change are
constant over time (Case I). In the second case, output declines at faster rates at the
beginning and the rate of changes gradually declines (Case 11).58 This case considers a
situation where greater impacts occur after a shock and then smaller, delayed impacts
continue for a long term. The third and fourth cases (Case 111 and Case IV) represent upper
and lower boundaries of the ﬁrst case. The upper boundary shows the lowest possible
reduction in output, so that output is reduced by 0.5 percent a year, or approximately 5
percent after 10 years. Similarly, the lower boundary shows the highest possible reduction
in output, which is 2 percent a year or approximately 18 percent after 10 years. Although
choice of upper and lower limits are rather arbitrary, it seems unlikely that the output path will
diverge from the region between the two boundaries. A real adjustment path lies between

these four lines. Output paths of these cases are presented in Figure 6.1.

 

1"’In the case of geometric adjustment, a rate of decrease in output at period t is
assumed to be approximated as (1/2"‘; then it is normalized so that the output level after 10
years will be equal to the level in the ﬁrst case.

96

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6. 2 Long-Run Equilibrium Adjustment

An output elasticity of factor demand as discussed in the previous chapter, evaluates a
change in factor use caused by shifting the factor demand curve when an output decreases,
holding factor prices constant. However, unless factor supplies are perfectly elastic, a
reduction in output will also lead to a change in factor prices. Thus, an effect of change in
output on factor use is sum of effect of shifting factor demand curve and effect of changing
factor demand along the demand curve.

Adj ustrnent of factor price and factor use is evaluated by a linear approximation, a

so-called “equilibrium displacement” model. Deﬁne factor demand and factor supply as

= d (factordemand)

 

 

x x
x = x ’ (factor supply) (58)
By totally differentiating these, we get,
d d
.. = e.— .. - a; 4
ax. " (59)
d): = dw
6w

Now, amount of changes in supply and demand must be equal in equilibrium, thus,

ax” dw ax" dq ax‘ dw
_____.w___ + ___.q.__. = '——'W——' (60)
aw w aq q 6w w

e—+e"—=e— (61)

01’

 

l

 

98

 

w es-e“ 7 (62)
This equation represents effects of output changes on input price. Also, from this equation

and the supply function, effects of output changes on factor use is given by

a: __ a
d

x e‘-e q

(63)

This procedure requires an estimated value of factor supply and demand elasticity.
According to Masui’s estimation (1995), the elasticity of supply of labor in rice production
in Japan is 2.29. Also, in his earlier study on factor markets related to rice production
(Masui, 1984), he uses assumptions that land supply elasticity is between 010-011 and
chemical and capital supplies are perfectly elastic. The perfectly elastic supply of capital and
chemicals are explained by the fact that most chemical and capital goods are imported and
exported and manufacturing ﬁrms may have large enough capacity to increase output in the
short run. Nonetheless, even though these are manufactured goods, inﬁnite price elasticity
of supply seems too large, since some materials or parts for these inputs are used for speciﬁc
purposes for agriculture. For example, agricultural machinery is not used in other industry.
Thus, this study assumes supply elasticities of labor, land, chemical, and capital to be 2.29,
0.10, 20, and 10, respectively.

Using the long-run price elasticities of factor demand and the output elasticities estimated
in the previous chapter, elasticities of factor prices with respect to output are obtained.
Estimated elasticities of the prices of labor, land, chemical, and capital with respect to output

are respectively, 1.380, 1.881, 0.025, and 0.079. Long-run equilibrium factor uses associated

 

99

with output paths in Cases 1, II, III, and IV are presented in Figures 6.2a, 6.2b, 6.2c, and
62d, respectively.

Elasticities of factor demand with respect to output estimated by the equilibrium
displacement model are 1.084 for labor, 0.188 for land, 0.259 for chemical, and 0.785 for
capital. These output elasticities of chemical and capital are similar to the output elasticities
estimated in the previous chapter, which assume constant factor prices. It is because supply
elasticities of chemical and capital are large so that these prices barely change even when
output changes. The output elasticity of land estimated by this model is small reﬂecting

inelastic supply.

6.3 Dynamic Adjustment of the Factor Shares
E . . ED . l l l l

The previous section simulated factor use at the long-run equilibrium by assuming all
factors can be adjusted instantaneously to their long-run equilibrium. However, as we
discussed in the previous chapters, delay in factor adjustment may result in short-run
disequilibrium. This section makes a simulation of factor adjustment using a dynamic
adjustment model which allows short-run disequilibrium. Factor shares are simulated instead
of factor use, because the dynamic model used in this study is based on share equations such

that only shares can be estimated.

 

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104

The simulation is based on the following dynamic model:

S(t) = B0X(t) + B]X(t- l) + ¢,S(t-1) + e(t) (64)

where all variables as deﬁned in the previous chapter. The vector Bo represents current
effects and 131 represents lagged effects of previous changes in X(t-l) on current shares.

Figures 6.3a, 6.3b, 6,3c, 6,3d show simulated factor shares for the next 10 years’ period
in Cases 1, 11, HI, and IV, respectively. To present percentage changes from the initial levels,
each share in the ﬁrst year is set at zero. Thus, each point in graphs shows percentage
increase or decrease relative to its value in the ﬁrst year.

In the ﬁgures it is observed that the shares of chemical and capital increase over time,
while the labor share declines. These results are basically consistent with the estimation in
the previous chapter, where estimated output elasticities were larger for labor and land and
smaller for chemical and capital.

Note that, although the previous analysis found that land is elastic in terms of output, this
simulation suggests land changes very little. This result, howevei', indicate that the simulation
successfully incorporates a fact that supply of land is inelastic so that the land area rarely
changes in response to price changes. Although a long-run output elasticity of land estimated
before is signiﬁcantly large, this estimate does not represent a realistic situation for Japanese
agriculture where farmland has been hardly moved. This contradiction is caused by unrealistic
restriction that all factor price are ﬁxed, imposed on output elasticities.

Simulated factor adjustment in the four cases shows distinct differences. In Case 1,

chemical share keep increasing at a nearly constant rate. On the other hand, in Case 11,

chemical share will not increase so much. The reason of this difference is probably because

105

chemical use respond to a shock after one year so a shock in the ﬁrst year are missed in both
case. After the second year, increases in chemical shares are almost proportional to output
changes. But, rates of output changes in Case H are much lower than rates in the case I, so
that a share does not grow in Case 11. The case 111 and Case IV show distinct adjustment
path in the latter periods, although adjustment paths in the ﬁrst few years are similar.
Figures also show that while the chemical increases at a nearly constant rate, the capital
increases at diminishing rates over time. It implies that chemical demand responds quickly
to changes in prices of the factor, while adjustment of capital input has some delayed effects.
The curved path of capital adjustment shows that the adjustment is not made instantaneously.
Finally, it must be noted that cross-factor effects of demand and supply are not included
in this analysis. As the factor demand curve shifts down due to decrease in output, the factor
supply and demand curves may shift more or less than the primary effect due to secondary
effects in the factor market. For example, if there are signiﬁcant substitutional effects in a
demand, estimated factor levels without including the secondary effects will possibly be
underestimated. However, such effects are considered to be sufﬁciently small for taking a

general view of changes in the factor shares in the simulation.

6.4 Implication for Trade Liberalization

Simulation in this chapter show that trade liberalization has a signiﬁcant impact on the
structure of Japanese agriculture, especially for labor use. This signiﬁcant change in labor
demand is due to a large output elasticity and a large elasticity of labor supply. The high
output elasticity implies high absorption effects of labor. In response to output changes, labor

demand also changes by a large degree. Even though labor demand decreases signiﬁcantly,

106
wage rates will not be decreased much because labor supply is elastic enough to change labor

supplied, in response to a small change in wages.

Output elasticity of labor estimated in the long-run equilibrium adjustment model suggests
that a 1 percent decline in output results in a 1.1 percent decline in labor, which also implies
a slight increase in labor productivity (i. e. , output per labor). As producers reduce costs of
production by reducing labor, output per unit labor hour would even increase. Current part-
time farmers will spend more hours in off-farm jobs. Promotion of part-time farming has
never turned out to be a serious consequence in rural areas. Improving labor productivity is
beneﬁcial to rural areas where labor shortage appear rather problematic.

Also, some people suggest that trade liberalization would cause various environmental
problems due to a decrease in land areas, including deteriorating rural landscape, a decrease
in water preserving ﬁrnction related to rice production.” This situation is also not likely to
occur because farmland area would change very little. Even though trade liberalization leads
to decline in an output level in Japan, almost the same area of land will be used in agriculture.

Another consequence of import liberalization is a decrease in yield (i. e. , output per a unit
area of land), which occurs because output would decline but land area would hardly change.
As yield decreases, output per unit use of machinery will fall, since use of machinery, such as
reaping or planting machines, often corresponds to land area. Output elasticity of a capital
use implies that capital productivity (i. e. , output per unit capital) decreases by 0.2 percent as
output declines by 1 percent.

Output elasticity of chemicals implies that chemical use per unit output rises by 0.7

 

”An example of this argument is in Morishima (1991)

107

percent as output declines 1 percent. This may result in increasing chemical residues on
agricultural products. Production costs are reduced by cutting labor and capital inputs, not
by reducing chemicals. Then, the amount of chemical applied per unit output would increase
as output per area of land declines. However, estimated output elasticities of land and
chemical are both small, which implies that chemical use per land would remain relatively

constant. Thus, the overall environmental impact of changes in chemical use is ambiguous.

 

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CHAPTER 7

SUMMARY AND CONCLUSIONS

This study has explored the structure of agricultural production in Japan using a dynamic
cost function model. The primary focus of this study is estimation of elasticities of factor
demand with respect to output. A dynamic model is used because it is realistic to assume that
factors are not adjusted instantaneously. The adjustment may be delayed due to rigidity in
factor movement caused by high costs of adjustment, delay in obtaining necessary economic
information, farmers’ custom about production practice, and institutional problems that hinder
quick adjustment. For example, changing occupation often requires costs of searching a new
job, obtaining a new skills, and moving residence, etc. Also, adjustment of capital inputs
oﬁen requires large-scale investment on machinery and construction. Thus, changes in the
output level possibly create a short-run disequilibrium although it is assumed that a long-run
equilibrium is achieved over time. Since a major objective of this study includes estimating
long-run adjustment, we applied an econometric model that allows short-run disequilibrium
but still captures long-run relationships.

The econometric model used in this study, called the ﬂexible dynamic model, is derived
from an ARX model of a system of share equations derived from a translog cost function.
The translog model has ﬂexible properties in terms of factor substitution and nonhomothetic

production process. Static speciﬁcation of a translog model, which was applied to aggregate

112

113

production studies of Japanese agriculture in the past, is statistically rejected in favor of the
dynamic ﬂexible model. Thus, results in the past studies may be biased and therefore a
dynamic speciﬁcation is required when instantaneous factor adjustment cannot be assumed.

This study derived an estimation method to measure a long-run elasticity of factor demand
with respect to output. The elasticity measures proportional changes in factor demand with
respect to changes in output along an expansion path. In the measurement, factor prices are
ﬁxed while all factor levels are allowed to be changed. Thus, a concept of output elasticity
used in this study is similar to measurement of bias in technological change which evaluates
shifting in an isoquant holding the factor prices constant.

The estimated output elasticities of labor and land are relatively large, while the output
elasticities of chemical and capital use are relatively small. The estimation results also suggest
that shares of labor and land change greatly in response to changes in output, but shares of
chemical and capital change just a little. Also, as output decreases, labor required to produce
a unit of output decreases, while chemical and capital use per unit of output increases.
Simulation of factor share adjustment conﬁrms that chemical share grows more than the other
factors

Estimated Allan’s partial elasticities of factor substitution show that most factors are
substitutes for each other. Large values of the elasticity of substitution between labor and the
other factors imply that labor has high substitutability for the other factors. The estimated
elasticities of substitution are not constant across the inputs, supporting the ﬂexible dynamic
model against other dynamic models which are more restrictive in terms of factor substitution.

Estimated elasticities of factor demand with respect to prices of the factors also vary

among the pairs. In terms of own price elasticities of factor demand, labor is as elastic as

114

other factors. Elastic demand for land in terms of price and output implies that land can be
adjusted ﬂexibly. However, this ﬁnding is not consistent with the real situation of Japanese
agriculture, where little transfer of land has been observed in the past. It shows a major
problem for elasticity measurement.

The model used in this analysis assumes other economic factors, such as input prices, are
constant over time, which means input supply elasticities are all perfectly elastic. However,
even though factor demand changes greatly, factor use hardly changes if input supply is
inelastic. This is a case of land adjustment. Since the land supply is considered as very
inelastic, the land area hardly changes, while price of land stays at the initial level. In the very
long-run, a factor supply elasticity may be assumed to be signiﬁcantly large, then our
estimation of the elasticity in a long-run equilibrium estimated by the ﬂexible model can be
justiﬁed.

This thesis has also dealt with the issue of short-um factor adjustment in the simulation.
Each factor price is associated with output changes, so that paths of factor shares are
expressed as a function of an output path.

The simulation shows that as output decreases, the shares of chemical and capital will rise,
while the share of labor declines. Land share changes little. It is a realistic outcome for
Japanese agriculture. Estimation of bias in technological changes has found that production
is land-saving, but other effects are not conclusive. Because of rapid economic development
during the 19608 and 19705 and changing demand for food products, the technology in

agriculture had changed at the middle of the observation period. Thus, technological change

115

bias was hardly captured in the estimation.60

Estimated output elasticities of factor demand show that, due to output decrease caused
by trade liberalization, more chemical and capital will be used to produce a unit of output in
Japanese agriculture, although the total amounts of these inputs are reduced. Production
using more chemicals per unit output may worsen problems related to chemical residues on
domestic agricultural products. Also, since the output elasticity of chemicals is almost the
same as the output elasticity of land, average use of chemical per hectare of farmland will not
reduced even though the total output decreases. Currently, amount of chemical used per
hectare is very high in Japan, the high input agricultural practice will remain."

Also, this study has found that labor requirements is reduced signiﬁcantly. As long as the
current labor shortage continues, the decrease in labor requirement will not have serious
consequences for the rural sector. The majority of farm workers in Japan are elderly people
and few successors are found in the rural areas. The labor shortage will lead to a decrease
in the rural population, which could deteriorate rural economies due to lack of funding for
public services and decrease in business opportunities. Since the majority of Japanese farmers
have income sources in the non-farm sector, the decrease in working hours in farming would
give them Opportunities to allocate more hours in their non-farming works. Thus, large scale

unemployment in the rural sector is not likely to occur in most rural areas.

 

“It may be preferred to use a model with a variable parameter to represent shifting
bias in technological change over time.

6'Although more detailed data is required to explore relationships between chemical
use in agricultural production and water and soil contamination, and relationship between
chemical contamination in water systems and their effects on human body, the high level of
chemical use per hectare is a major source of chemical contamination at farming areas in
Japan.

116
1.. . IE . [11.5 1

This study relaxes restrictions maintained in most previous models, such as instantaneous
adjustment of factors and constant elasticities of factor substitution. However, there are
several restrictions in the analysis of this study. First, due to small size of the sample used in
the estimation, the tests of unit roots have limited power to reject the null hypothesis. The
hypotheses of unit roots in series of some factor shares are not rejected, although shares are
not likely to have unit roots since they are bounded on values of zero and one. However, it
is difﬁcult to collect a larger sample of data than that used in this study, since data of
agricultural production are annual and reliable data are available only after the World War H.

Also, the estimation in this study provides only rough information about changes in factor
use since the variables in the model represent highly aggregate inputs and output. For
example, 'chemical' input in the model includes pesticides and fertilizers. Although both
pesticides and fertilizers affect the environment negatively, these two types of chemical often
give different impacts on the environment. This study can only show how much aggregate
demand for chemical increases or decreases as output changes, but more speciﬁc implications
for the environment is not provided. Further dissagregating the model would be more useful
for policy analysis. However, increasing the number of variables in the model sacriﬁces the
degrees of freedom signiﬁcantly.

This study implements the simulation of short-run factor adjustment in terms of factor
shares, instead of factor use. Since the dynamic model in this study is based on share
equations, which are derived from the static translog function, the model only takes the shares
as dependent variables. Thus, the simulation does not show absolute degrees of the changes,

but just illustrates relative changes in terms of the total cost. On the other hand, the ﬁrst

117

simulation in the previous chapter (long-run equilibrium adjustment) shows absolute levels
of factor use. However, it does not represent short-run disequilibrium in the factor
adjustment, since all factors are assumed to be at the long-run equilibrium in the model.
The analytical method used in this thesis could be applied to other regions in the world.
Although this study has dealt with the case of an agricultural sector whose output is
decreasing, a similar analysis can be made for a sector with expanding output. In a country
exporting agricultural products, for example, trade liberalization would lead to an increase
in domestic production, then the country may be concerned about short-run and long-run
effects of export policies on domestic employment situation, or inputs that might have
negative impacts on the environment. Models applied in this study will provide useful

information about how production structure might be changed due to changes in output.

APPENDIX

APPENDIX

Table A.4.2.1 Phillips-Perron Tests for Unit Roots in Individual Variables in Dickey Fuller
Equations with Constants and Time Trend

 

W1.

W1)

wc._.|

WK

Q

81.

So

Sen

8. |

 

0.097263
(2.319)

0.181177
(3.655)

0.006320l
(0.233)

0.053881
(2.971)

0.082609
2.825)

0.085046
(2.243)

0.003395
(0.609)

0. 14587
(3.667)

4.729205
(2.103)

 

0.005130
(0650)

0.002889
(0.377)

0.002126
(1.221)

0.000628
(0.205)

0.000344
(0.295)

0.000487
(1.334)

0.001650
(2.875)

0.002462
(-3.SO6)

0.000680l
(4.903

 

p

0.062126
(0.821)

-0.008650I —0.065025

(0.135)

(-1229)

0.029457
(0.4670

-0.209008
(-2305)

0.241347
(-2575)

0.337237
(-2.746)

-0.576124
(.3838)

0.111154
(-1.640

 

32

0.011205

0.022444

0.004680

0.002456

0.004671

0.000756

0.000274

0.000357

0.000730

 

Y0

0.010007

0.021 173

0.004306

0.002422

0.003489

0.000683

0.000267

0.000292

0.000714

 

Y1

0.002727

0.000586

0.002368

0.001225

-0.000400

0.000024

0.000031

—0.000004

0.000085

 

Y2

0.000839

-0.003484

0.000906

0.000117

-0.000864

-0.000147

-0.000039

-0.000043

-0.000049

 

2(9)

-3.567

-0.056

-3.764

-2 .424

-7. 322

-9.096

-l3.578

-21.948

-4.681

 

Z(t)l

-l.051

-0.019

-l.431

—0.804

-2.200

-2.512

-2.723

-3.745

-1.658

 

Y0

0.008988

0.021707

0.004502

0.002302

0.002988

0.000454

0.000280

0.000292

0.000668

 

Yr

0.003113

0.000651

0.002506

0.001279

~0.000389

-0.000002

0.000036

-0.000004

0.000070

 

Y2

0.001908

-0.003020

0.000930

0.000217

0.000020

-0.000049

-0.000043

-0.000015

 

0.000050]

 

Y3

0.002872

0.010272

0.000660

0.000183

—0.000374

0.000100

-0.000033

0.000048

0.0001701

 

Y4

-0.000838

0.000508

0.000137

-0.000003

-0.000402

0.000025

-0.000036

-0.000010

I-0.000043

 

Z(p

-6.509

-l.258

-5.536

-4.541

-7.003

-10.172

42.147

-24.142

-4.019

 

Z(t)

-l.579

—0.429

-l.712

-1.252

-2.212

-2.589

-2.589

-3.867

-l.561

 

Y0

0.006841

0.021978

0.004729

0.002433

0.002976

0.000452

0.000452

0.000300

0.000699

 

Y1

0.004031

0.000866

0.002615

0.001326

-0.000006

0.000065

0.000065

0.000004

0.000093

 

Y2

0.003845

-0.002571

0.000992

0.000245

-0.000060

-0.000015

-0.000015

-0.000012

—0.000047

 

Y3

0.001571

0.010137

0.000687

0.000207

-0.000864

0.000035

0.000035

0.000028

-0.000200I

 

14

-0.001467

0.000375

0.000267

-0.000011

-0.000378

0.000041

0.000041

-0.000030| —0.000034

 

 

Y5

-0.001747

-0.002928

0.000402

-0.000149

0000029

0.000038

-0.000038

0.000015 [0.000131

 

Y6

-0.002479

0.003850

0.000610

0.000306

-0.000496

-0.000134

-0.000134

0.000038l0000067

 

 

Z(p)

-7.367

-1.769

-6.345

-5.088

-6.251

-10.925

-18.706

-23295 | -3.178

 

 

zmi -1729

 

-0.569

 

 

-l.827

-1.340

 

-2.214

 

-2.631

 

-3.152

 

-3.819 | -1430

 

 

 

Note: t-statistics are in parentheses; C: constant; t: coefﬁcient of the time trend variable; yzautoregressive
coefﬁcient of the OLS with constant and trend variables; 1]: covariance of the residuals; szzvariance of the
residuals of regression; Z(p):Phillips-Perron statistic of the coefﬁcient with p-th order lag truncation;
Z(t):Phillips-Perron statistic of the I value of with p-th order lag truncation. Critical values for Z(p) and
Z(t) at 5% levels are 19.80 and 3.50 (T=50).

118

119

Table A.4.2.2 Dickey-Fuller Tests of the Residual from Cointegrating Regression

 

 

 

 

 

 

 

 

8 8 8
p 0.438202 0.438641 0.449213
(-3.27084) (-3.22891 ) (0.28002)
constant 0.001288 0.030573
(0.072768) (0.781746)
trend 0.0012988
(0.840661)

 

Note: t-statistics are in parentheses; e is the OLS residuals from the cointegrating regression of L

on D, CH, K, and Q; p is the coeﬂ'rcient of the lagged residual.

Table A.4.2.3 Phillips-Perron Tests for Residuals from Cointegration among S, L, D, CH, K, and Q

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

SL Sr) Sc“ S:
p -0.307733 -0.288276 -0.647168 -0.224885
-2.672460 -2.411540 4.318820 -2. 155330
Yo 0.000535 0.000381 0.000254 0.000097
Y1 0.000543 0.000408 0.000277 0.001069
Y2 0.000068 0.000087 0.000008 0.000251
73 -0.000090 -0.000039 -0.000025 -0.000104
‘14 0.000070 -0.000061 0.000026 -0.000200
82 -0.000016 -0.000050 -0.000022 -0.000112
Z(p) -13.662 -1 1.824 -22.295 -15.930
Z(p) -2.767 -2.357 -4.159 -2.545

 

 

 

Note: t-statistics are in parentheses; C: constant; t: coefﬁcient of the time trend variable;
yzautoregressive coefficient of the OLS with constant and trend variables; y -: covariance of

the residuals; szzvariance of the residuals of regression; Z(p):Phillips-Perron statistic of the
coeﬁicient with p-th order lag truncation; Z(t):Phillips-Perron statistic of the I value of with

p—th order lag truncation. Critical values for Z( p) and Z(t) at 5% levels are -42.5 and -4.74 (T=50).

120

Table A5. 1.1 Hessian Matrices of the Flexible Model

 

No Restriction

Symmetric Restrictions

Homothetic Restrictions

 

L D

C K L

D C K

L D

C

K

 

-0.244 -0.005

0.481

-0.327 -0.270

0.030 0.1

25 0.284

-0.260

0.029

0.118

0.317

 

0.041

-0.039

0.191

-0.351

0.030

-0.021 0.0

21 -0.061

0.029

-0.030

0.005

0.047

 

26 0.018

-0.l6l -0.003

0.125

0.021

-0. 180

0.026

0.118

0.005

-0.l93

0.172

 

 

 

0.076

0.026

 

-0.511

 

 

0.681

0.115

 

 

-0.029 0.0

 

34 -0.249

0.112

 

 

 

-0.004

0.069

 

 

-0.535

 

 

L
D
C 0.1
K
D

L,

Table A.5.1.2 Hessian Matrices of the Linear Dynamic Model

, C, and K are respectively variables for prices of labor, land, chemical, and capital

 

No Restriction

Symmetric Restrictions

Homothetic Restrictions

 

L D

C K L

D C K

L D

C

K

 

-0.238

0.004

0.138 -0.2

20 -0.262

0.019

0.136

1.066

-0.272 -0.043

0.126

0.221

 

0.025

-0.207

0.095 -0.1

55 0.019

-0.036

0.009

0.007

-0.043 -0.041

0.012

0.054

 

0.120

0.018

-0.212

0.080

0.136

0.009 -0.1

02 -0.044

0.126

0.012

-0.015 -0.163

 

 

 

WOO!"

0.094

 

0.185

 

-0.242

 

0.294

0.107

 

 

0.007

 

-0.044 -0.006

0.221

 

 

 

0.054

 

 

-0.163 -0.113

 

 

Note:

The linear dynamic model refers to the linear model transformed from the original

ﬂexible model. L, D, C, and K are respectively variables for prices of labor, land, chemical, and capital

Table A.5.1.3 Hessian Matrices of the Static Model

 

No Restriction

Symmetric Restrictions

Homothetic Restrictions

 

L

D

C K

L

D C

K

L D

C

K

 

-0.224 -0.013

0.449

-0.343 -0.180

0.007

0.108

0.258

-0.l6l

0.033

0.087

0.041

 

0.026 -0.017

0.110

-0.168

0.007

0.007

0.041

-0.078

0.033

-0.033

0.006

-0.006

 

0.087

0.016

-0.194

0.101

0.108

0.041

-0.098 -0.075

0.087

0.006

-0.130

0.036

 

”DUI"

 

 

0.163

0.014

 

-0.364

 

 

0.410

0.066

 

 

-0.054

 

-0.050 -0.105

 

 

0.041

 

-0.006

0.036

 

 

-0.072

 

 

Note: L, D, C, and K are respectively variables for prices of labor, land, chemical, and capital

Table A5 1.4 Eigen Vectors of Hessian Matrices

 

 

 

 

 

 

 

 

 

 

 

 

 

Flexible Model Linear Dynamic Model Static Model
No Sym Symmetric No Sym Symmetric No Sym Symmetric
Restriction -metric Homothet. Restriction -metric Homothet. Restriction -metric Homothet.
077965 -0.56430 -0.75613 0.43867 056430 -0.43088 -0.76833 0.25437 0.28365
0.94277 -O.21937 -0.31984 044264 021937 017549 0.61405 -0.l9306 -0.22674
0.19082 0.07179 0.10110 -0.10066 0.07179 -0.08335 0.16551 -0.08882 -0.09378
-0.11694 -0.00819 -0.04313 025903 000812 -0.03437 -0.03623 -0.06049 -0.04412

 

 

Note: The linear dynamic model refers to the linear model transformed from the original ﬂexible model

121

Table A.5.2.l Parameter Estimates of Flexible Model

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unrestricted Symmetry Homothetic Symmetry &
Homothetic
Estimate Standard Estimate Standard Estimate Standard Estimate Standard
Error Error Error Error
[3, 0.3962 0.0256 0.3480 0.0757 0.3827 0.0348 0.3605 0.0662
[3”, 0.0059 0.0661 -0.0202 0.1145 -0.0193 0.0794 0.0392 0.1139
[5”, —0.0244 0.0296 0.0101 0.0445 -0.0172 0.0404 0.0242 0.0463
[3”; 0.3672 0.1056 0.0117 0.0371 0.2870 0.1063 0.0286 0.0382
[3,,‘ -0.4436 0.2060 0.1681 0.2678 -0.2505 n.a. -0.0920 n.a.
[3”, 0.1446 0.1066 -0. 1978 0.1620 0.0720 0.1247 -0.2087 0.1541
Bu 0.0129 0.0043 -0.0025 0.0079 0.0090 0.0042 0.0011 0.0063
[3,, 0.0203 0.0163 -0.0032 0.0344 -0.0020 0.0295 -0.0055 0.0383
[3.1 0.0219 0.0421 0.0101 0.0445 -0.0200 0.0672 0.0242 0.0463
[39,, 0.0000 0.0189 0.0180 0.0229 0.0118 0.0342 0.0093 0.0293
[30c 0.1814 0.0673 0.0113 0.0203 0.0481 0.0899 0.0001 0.0193
_le -0.361 1 0.1313 -0.07 14 0.1193 -0.0399 n.a. -0.0336 n.a.
[3m 0.0929 0.0680 -0.0734 0.0748 -0.0278 0.1054 0.0787 0.0880
[3m 0.0137 0.0028 0.0062 0.0035 0.0071 0.0035 0.0046 0.0031
BC 0.2637 0.0142 0.2609 0.0232 0.2608 0.0143 0.2625 0.0174
BC, 0.0124 0.0367 0.0117 0.0371 0.0070 0.0326 0.0286 0.0382
[3CD 0.0081 0.0164 0.0113 0.0203 0.0097 0.0166 0.0001 0.0193
[3“; 0.0195 0.0586 0.0008 0.1166 0.0022 0.0436 0.0150 0.0542
[3“ -0.0605 0.1144 -0.0312 0.2110 -0.0188 n.a. -0.0437 n.a.
[3CQ -0.1157 0.0592 -0. 1358 0.1188 -0. 1314 0.0511 -0.1165 0.0703
13¢, -0.0031 0.0024 -0.0040 0.0053 -0.0040 0.0017 -0.0043 0.0023
& 0.3198 n.a. 0.3944 n.a. 0.3585 n.a. 0.3825 n.a.
[3,,L -0.0402 n.a. -0.0016 n.a. 0.0323 n.a. -0.0920 n.a.
1310 0.0163 n.a. -0.0394 n.a. -0.0043 n.a. -0.0336 n.a.
Bxc -0.5681 n.a. -0.0238 n.a. -0.3373 n.a. -0.0437 n.a.
[in 0.8652 n.a. -0.0655 n.a. 0.3092 n.a. 0.1693 n.a.
_ng -0. 1218 n.a. 0.4070 n.a. 0.0872 n.a. 0.4038 n.a.
[3,;T -0.0235 n.a. 0.0003 n.a. -0.0121 n.a. -0.0014 n.a.
orn 0.4865 0.2326 0.1667 0.1464 0.3131 0.1720 0.1463 0.1414
an 0.2245 0.2230 0.1153 0.2153 0.1243 0.2061 0.1850 0.1895
01,, -0.2395 0.2276 -0.4259 0.2102 -0.3438 0.2095 -0.4216 0.2108
01,, 0.0137 0.1653 -0.1385 0.1285 -0.1811 0.1248 -0.1448 0.1100
_ocn 0.5788 0.1585 0.5277 0.1548 0.4663 0.1495 0.4425 0.1437
(1” -0.3155 0.1618 -0.4056 0.1520 -0.4326 0.1520 -0.4221 0.1482
_orﬂ -0.0784 0.1812 —0.0426 0.1706 -0.0731 0.1321 -0.0091 0.1285
or,2 -0.0640 0.1738 -0.0501 0.1736 -0.0609 0.1583 -0. 1227 0.1560
(1,, 0.7406 0.1773 0.7587 0.1745 0.7438 0.1609 0.7502 0.1622

 

 

Note: “11. 8.” refers to the value is not available.

Table A.5.2.1 (cont’d)

122

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unrestricted Symmetry Homothetic Symmetry &
Homothetic
Estimate Standard Estimate Standard Estimate Standard Estimate Standard
Error Error Error Error
1,, 0.0837 0.0478 0.0657 0.0471 0.0653 0.0453 0.0741 0.0452
y,, -0.0051 0.0260 -0.0031 0.0248 -0.0011 0.0261 -0.0045 0.0253
1,, 0.1828 0.1218 0.0178 0.0837 0.0804 0.0785 0.0266 0.0741
7,, -0.2912 0.1239 -0. 1663 0.1081 -0.2051 0.0968 -0. 1948 0.0991
_Zu 0.1496 0.0554 0.1200 0.0542 0.1361 0.0548 0.1128 0.0543
_12 -0.0274 0.0340 -0.03 54 0.0333 -0.0482 0.0329 -0.0479 0.0319
72, 0.0133 0.0185 0.0144 0.0182 0.0178 0.0189 0.0174 0.0186
724 0.1478 0.0866 0.0697 0.0690 0.0327 0.0570 0.0440 0.0539
1,, 01583 0.0880 -0.0999 0.0798 -0.0616 0.0702 —0.0620 0.0700
.129 0.0546 0.0394 0.0403 0.0387 0.0394 0.0397 0.0447 0.0390
.123 -0.0006 0.0372 0.0027 0.0369 0.0000 0.0348 0.0047 0.0351
7,, -0.0009 0.0202 -0.0009 0.0201 -0.0010 0.0200 -0.0040 0.0201
_113 -0.0781 0.0949 -0.0588 0.0903 -0.0750 0.0603 -0.0559 0.0600
733 0.1658 0.0965 0.1497 0.0946 0.1631 0.0743 0.1661 0.0750
.11: -0.0965 0.0432 -0.0935 0.0428 -0.0961 0.0421 -0.0863 0.0421

 

 

 

Table A.5.2.2 Estimates of Linear Dynamic Model

123

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Restrictions S etry Restrictions
Estimate Standard Estimate Standard Estimate Standard Estimate Standard
Errors Errors Errors Errors
[3, 0.1510 0.1473 g,, 0.0785 0.0414 [3, -0.0417 0.0927 ,, 0.0757 0.0408
[3,, 0.0113 0.0379 ,, 0.0122 0.0272 [3,,L -0.0120 0.0281 ,, -0.0004 0.0267
[3,JD -0.0159 0.0196 &. -0.0155 0.0808 [3,D -0.0009 0.0125 g,, 0.0107 0.0819
[3LC 0.2455 0.1356 ,, 0.0140 0.1618 [3,, 0.0221 0.0246 ,, -0. 1894 0.1057
[3,, -0.3359 0.2156 g_,, 0.0222 0.0721 [3“, 1.0000 0.0573 ,. 0.0969 0.0583
[3,,Q 0.1253 0.0744 gg2 -0.0360 0.0295 [3,,Q 0.0259 0.0443 &, -0.0380 0.0284
Bu 0.0111 0.0055 g23 0.0141 0.0194 Bu 0.0029 0.0025 & 0.0091 0.0187
[3,, -0.0909 0.1049 ga 0.0342 0.0575 [3,, -0. 1652 0.0640 . 0.0449 0.0568
[30, 0.0050 0.0270 3,, 0.0243 0.1152 [3,), -0.0009 0.0125 E}, 00500 0.0714
1366 -0. 1678 0.0139 $3 00327 0.0513 [30,, 0.0035 0.0097 ,, -0.0042 0.0404
[3,), 0.0858 0.0965 532 -0.0078 0.0324 [3DC -0.0002 0.0128 2 -0.0078 0.0317
[30,, -0. 1646 0.1534 g, -0.0095 0.0213 0,, -l.0000 0.0357 , -0.0036 0.0210
[3DQ 0.0885 0.0530 -0.0551 0.0633 [3,,Q 0.0505 0.0307 -0.0672 0.0630
[3,, 0.0085 0.0039 5,, 0.1487 0.1266 [3,, 0.0052 0.0015 g,, 0.2547 0.1072
[3C 0.1623 0.1153 g,, 0.0080 0.0565 [3C 0.2574 0.0990 -0.0294 0.0516
BC, 0.0062 0.0297 f,, 0.4921 0.2368 [3,, 0.0221 0.0246 f,, 0.8082 0.1409
[3CD 0.0083 0.0153 f,, 02539 0.2295 [3“, -0.0002 0.0128 f,, -0. 1277 0.2137
[3cc -0.0315 0.1062 f,, 0.1865 0.2443 [30, 0.0791 0.0811 f,, 0.4099 0.2118
[30, 0.0226 0.1687 f,, 00012 0.1685 [30, 0.0000 0.1280 f,_, 0.1204 0.0979
[3CQ -0. 1041 0.0583 f,, 0.4385 0.1633 [3,,2 -0.0546 0.0493 f,, 0.4918 0.1489
[3,, -0.0044 0.0043 f23 0.3466 0.1739 [3,, -0.0004 0.0035 f,, 0.4344 0.1460
[3,, 0.7776 n.a. f,, 0.0822 0.1853 [3,, 0.9495 n.a. f,, 00741 0.1572
[3,, -0.0225 n.a. f2 0.0692 0.1796 [3,,L -0.0093 n.a. f,, 0.0137 0.1724
[3,,D 0.1754 n.a. f,3 0.2689 0.1912 13.0 -0.0025 n.a. f,_, 0.1612 0.1798
13.0 0.2999 n.a. [3,, 0.1011 n.a.
[3,, 0.4778 n.a. [3,, 0.0000 n.a.
[3,,Q -0. 1097 n.a. [3,,Q -0.0217 n.a.
[3,, -0.0152 n.a. [3,,T -0.0076 n.a.
Note: The linear dynamic model refers to the linear model transformed from the original ﬂexible model.

Standard Errors are in parentheses. “n. a.” refers to the value is not available.

 

 

124

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A.5.2.2 (cont’d)
Homotheticity Restriciton Symmetry & Homotheticity
Restrictions
Estimate Standard Estimate Standard Estimate Standard Estimate Standard
Errors Errors Errors Errors
[3, 0.0257 0.1064 ,, 0.0759 0.0410 8, -0.0453 0.0890 g,2 0.0760 0.03 94
8,, -0.0102 0.0334 ,, 0.0069 0.0267 8,, -0.0045 0.0262 ,3 -0.0038 0.0251
u, «0.0074 0.0182 &, -0.0095 0.0801 [3,, 0.0004 0.0113 ,4 0.0243 0.0766
8,C 0.0957 0.0609 g_,, -0. 1297 0.1120 8,C 0.0225 0.0217 g, -0. 1802 0.1010
[3,, -0. 1038 n.a. g,, 0.0722 0.0594 8,, 0.0269 n.a. ,. 0.0968 0.0563
,, 0.0625 0.0541 E 00380 0.0292 8,, 0.0218 0.0420 , -0.0452 0.0279
,, 0.0050 0.0023 ,, 0.0099 0.0190 8,, 0.0036 0.0020 0.0154 0.0179
8, -0. 1904 0.0756 g,. 0.0390 0.0569 8,, -0. 1564 0.0628 0.0276 0.0544
BBL -0.0121 0.0238 & -0.0898 0.0796 [3,, 0.0004 0.0113 ,, -0.0525 0.0703
[3,, 0.0051 0.0129 a, 0.0070 0.0422 8,, -0.0042 0.0086 &, -0.0050 0.0400
8,,c —0.0332 0.0433 g, -0.0077 0.0320 8,, -0.0022 0.0114 2 -0.0159 0.0313
_8_,_, 0.2307 n.a. g, -0.0092 0.0208 [3,, 0. 1624 n.a. $3 00038 0.0206
8,, 0.0386 0.0385 g, -0.0555 0.0624 8,, 0.0596 0.0296 g,4 -0.0654 0.0619
D, 0.0036 0.0016 g, 0.1571 0.0873 [3,, 0.0036 0.0012 , 0.1954 0.0826
8C 0.1697 0.0829 , 0.0050 0.0462 8c 0.2021 0.0790 , -0.0065 0.0457
8,, 0.0074 0.0261 f,, 0.6920 0.1720 8,, 0.0225 0.0217 f,, 0.8203 0.1336
8CD 0.0078 0.0142 f,3 -0. 1258 0.2034 ,1, 00022 0.0114 f,, 01754 0.1852
8CC -0.0226 0.0475 f,3 0.3365 0.2106 8,, 0.0060 0.0395 f,3 0.4093 0.2048
8,, -0. 1624 n.a. fn 0.1576 0.1222 c, 02284 n.a. f,, 0.0927 0.0944
8,, -0. 1004 0.0422 f,_, 0.5403 0.1445 8,, -0.0802 0.0390 f,, 0.6036 0.1285
8,, -0.0040 0.0018 f,J 0.4657 0.1496 8,, -0.0041 0.0017 f,, 0.4419 0.1446
8, 0.9950 n.a. f,, 0.0704 0.1340 8, 0.9997 n.a. f,, 0.0079 0.1248
8,, 0.0149 n.a. f,, 0.0617 0.1584 8,, -0.0184 n.a. f,, 0.1301 0.1496
8,, -0.0055 n.a. f,, 0.2600 0.1641 8,, 0.0060 n.a. f,, 0.2397 0.1645
_[3_,c -0.0399 n.a. 8,c -0.0264 n.a.
8,, 0.0355 n.a. [3,, 0.0391 n.a.
8,, -0.0008 n.a. 8,, -0.0013 n.a.
8,T -0.0046 n.a. 8,T -0.0030 n.a.
Note: The linear dynamic model refers to the linear model transformed from the original ﬂexible model.

Standard Errors are in parentheses. “n. 8.” refers to the value is not available.

 

125

Table A.5.2.3 Estimates of Static Translog Models with Cost Equation

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Restriction Symmetry Symmetry &
Restrictions Homotheticity
Restrictions
Estimate Standard Estimate Standard Estirrrate Standard
Errors Errors Errors
01., 0.0496 0.0779 0.1702 0.1039 -0.0107 0.0966
8, 0.4278 0.0100 0.4360 0.0185 0.4477 0.0195
8,, 0.0442 0.0273 0.0766 0.0270 0.0859 0.0260
8,, -0.0319 0.0142 0.0048 0.0103 0.0111 0.0108
[3,, 0.3609 0.0370 -0.0215 0.0209 -0.0172 0.0194
8,, -0.5204 0.0636 -0. 1644 0.0608 -0.0797 n.a.
8,, 0.1441 0.0430 -0.2017 0.0608 -0.2176 0.0634
Bu 0.0128 0.0018 0.0019 0.0027 -0.0037 0.0018
[3, 0.0130 0.0072 0.0196 0.0097 0.0261 0.0097
' 8,, -0.0286 0.0199 0.0048 0.0103 0.0111 0.0108
1366 0.0214 0.0102 0.0416 0.0085 -0.0002 0.0127
8,, 0.1139 0.0266 -0.0454 0.0241 -0.0108 0.0093
136.; -0.2196 0.0460 -0.1112 0.0437 0.0000 n.a.
8,, 0.0286 0.0309 -0.1266 0.0363 -0.0688 0.0330
8,, 0.0118 0.0013 0.0067 0.0015 0.0034 0.0010
8c 0.2670 0.0076 0.2675 0.0090 0.2671 0.0082
8,, -0.0301 0.0224 -0.0215 0.0209 -0.0172 0.0194
8,, 0.0076 0.0110 -0.0454 0.0241 -0.0108 0.0093
[3,C -0.0192 0.0283 0.1028 0.0266 0.0547 0.0264
8,, 0.0527 0.0504 -0.0527 0.0488 -0.0267 n.a.
[3,, -0.1103 0.0323 -0.0103 0.0342 -0.0332 0.0338
[3,, -0.0032 0.0014 -0.0003 0.0016 -0.0013 0.0012
8, 1.0091 1.1844 1.1939 1.1224 0.2591 n.a.
[3,, 0.0578 0.4328 -0.1644 0.0608 -0.2246 n.a.
8,, 0.0344 0.2692 -0.1112 0.0437 -0.0332 n.a.
1310 4.0369 0.6195 -0.0527 0.0488 -0.0013 n.a.
8,, 12.9787 2.8350 11.0782 2.6518 0.2591 n.a.
_8_,_, -2.7992 1.7132 -l.3232 1.5937 -0.2246 n.a.
[3,T 04345 0.1248 -0.4602 0.1217 -0.0332 n.a.
8, 0.4964 0.4524 1.7407 0.4759 1.8725 0.4571
8T -0.0303 0.0585 -0.0897 0.0559 -0.0057 0.0138
8,, 3.9295 1.9852 3.8906 1.8758 2.2887 1.8512
8,, 0.0134 0.0059 0.0194 0.0056 -0.0013 0.0006
8,, 0.0605 0.0866 0.0676 0.0815 -0.0282 0.0244

 

Note: “11. a.” refers to the value is not available.

 

126

Table A.5.2.4 Estimates of Static Translog Models with Cost Equation

with “In t” for a time variable

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Restriction Symmetry Symmetry &
Restrictions Homotheticity
Restrictions
Estimate Standard Estimate Standard Estimate Standard
Errors Errors Errors
01, 0.1052 0.1605 -0.1621 0.2027 -0.2593 0.1940
8, 0.4526 0.0281 0.4998 0.0305 0.5079 0.0263
8,, 0.1446 0.0288 0.0727 0.0190 0.0514 0.0158
[3,, -0.0177 0.0190 0.0273 0.8368 0.0271 0.8646
[3,, 0.2237 0.0582 -0.0218 0.0168 -0.0323 0.0120
8,, -0.4043 0.0815 -0. 1080 0.0424 -0.0462 n.a.
[3,, 0.0127 0.0706 -0.0580 0.0842 -0.0470 0.0760
13m 0.0012 0.0269 -0.0639 0.0262 -0.0725 0.0198
[3, 0.0341 0.0232 0.0604 0.0241 0.0381 0.0179
8,, 0.0664 0.0267 0.0273 0.8368 0.0271 0.8646
8,, 0.0266 0.0166 0.0617 0.0104 0.0217 0.0132
8,C -0.0133 0.0492 -0. 1495 0.0324 -0.0258 0.8935
_[3ﬂ -0.1012 0.0768 0.0387 0.0456 -0.0231 n.a.
8,, -0.0888 0.0584 -0. 1425 0.0647 -0. 1050 0.0512
8,T 0.0029 0.0223 -0.0327 0.0217 -0.0030 0.0138
[3, 0.2531 0.0148 0.2375 0.0154 0.2491 0.0151
8,, -0.0561 0.0192 -0.0218 0.0168 -0.0323 0.0120
[3,, 0.0045 0.0113 -0.1495 0.0324 -0.0258 0.8935
8CC 0.0287 0.0325 0.1 183 0.0267 0.0700 0.0248
8,, 0.0065 0.0565 0.0050 0.0573 -0.0119 n.a.
8,, -0.0885 0.0372 -0.0799 0.0379 -0.0405 0.0369
8,.r 0.0084 0.0144 0.0319 0.0143 0.0145 0.0133
[3, 4.4604 0.8987 2.2319 0.5686 0.9559 n.a.
[3,, -1.3905 0.5046 -0.1080 0.0424 -0.9300 n.a.
8,, 0.9041 0.3766 0.0387 0.0456 -0.0405 n.a.
i, -2.2788 0.8913 0.0050 0.0573 0.0145 n.a.
[3,, 6.2239 2.0293 2.1964 0.9176 0.9559 n.a.
8,, -2.0048 1.3022 -0.8607 1.2037 -0.9300 n.a.
[3,, -2.4609 0.7906 -1.0542 0.4773 -0.0405 n.a.
8, 0.7611 1.2465 2.2287 1.2484 4.3361 0.7309
[3, -0.6758 0.3160 -0.0022 0.2845 0.2507 0.1717
8,, 1.6277 4.1669 3.8251 3.7959 8.1341 2.8545
8,, 0.5481 0.4245 0.0153 0.3548 -0. 1237 0.1074
8,, 0.6667 1.3164 -0.0612 1.2224 -1.7159 0.5598

 

Note: “It. 3.” refers to the value is not available.

 

Table [1.5.2.5 Parameter Estimates of Static Translog Model

127

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Unrestricted Symmetry Homothetic Symmetry &
Homothetic
Estimate Standard Estimate Standard Estimate Standard Estimate Standard
Error Error Error Error
8, 0.4266 0.0101 0.4219 0.0175 0.4285 0.0123 0.4252 0.0178
8,, 0.0402 0.0298 0.0056 0.0413 0.0229 0.0343 0.0202 0.0373
8,, -0.0400 0.0146 0.0168 0.0243 -0.0669 0.0165 -0.0527 0.0153
[3,C 0.3631 0.0376 -0.0409 0.0135 0.2675 0.0360 0.0077 0.0207
8,, -0.5008 0.0671 -0.0120 0.0735 -0.2236 n.a. 0.0248 n.a.
8,, 0.1568 0.0430 -0.0971 0.0611 0.1195 0.0491 -0.0939 0.0595
Bu 0.0130 0.0018 0.0053 0.0028 0.0078 0.0018 0.0037 0.0025
[3, 0.0123 0.0072 0.0110 0.0080 0.0141 0.0093 0.0122 0.0092
,, —0.03 12 0.0214 0.0168 0.0243 -0.0408 0.0255 -0.0527 0.0153
,, 0.0160 0.0105 0.0149 0.0255 -0.0035 0.0126 0.0016 0.0095
8,C 0.1147 0.0270 0.0161 0.0093 0.0163 0.0099 -0.0039 0.0096
8,, -0.2053 0.0482 -0.0657 0.0463 0.0281 n.a. 0.0549 n.a.
8,, 0.0353 0.0309 -0.0384 0.0331 0.0147 0.0312 -0.0331 0.0315
,, 0.0119 0.0013 0.0097 0.0013 0.0073 0.0012 0.0074 0.0012
8C 0.2670 0.0076 0.2733 0.0097 0.2663 0.0077 0.2731 0.0085
[3,, -0.0310 0.0224 -0.0409 0.0135 -0.0380 0.0214 0.0077 0.0207
8CD 0.0083 0.0110 0.0161 0.0093 -0.0039 0.0096 -0.0039 0.0096
[3,C -0.0188 0.0283 0.1129 0.0280 0.0012 0.0262 0.0578 0.0270
8,, 0.0519 0.0505 -0. 1831 0.0524 0.0407 n.a. -0.0617 n.a.
8,, -0.1101 0.0323 -0.0121 0.0369 -0. 1031 0.0325 -0.0475 0.0350
8,, -0.0031 0.0014 0.0012 0.0017 -0.0025 0.0012 -0.0030 0.0013
8, 0.2941 n.a. 0.2937 n.a. 0.2911 n.a. 0.2895 n.a.
8,, 0.0220 n.a. 0.0185 n.a. 0.0559 n.a. 0.0248 n.a.
8,, 0.0158 n.a. -0.0477 n.a. 0.0743 n.a. 0.0549 n.a.
131:0 0.4589 n.a. 0.0881 n.a. 0.2850 n.a. 0.0617 n.a.
8,, 0.6542 n.a. 0.2607 n.a. 0.1548 n.a. -0.0181 n.a.
8,, -0.0820 n.a. 0.1476 n.a. -0.0018 n.a. 0.1745 n.a.
8,T -0.0218 n.a. -0.0139 n.a. -0.0126 n.a. -0.0081 n.a.

 

 

 

 

 

 

 

 

 

 

Note:

“11. a.” refers to the value is not available.

 

128

Table A.5.2.6 Estimates of Cobb -Douglas Models

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Restrictions Symmetric Restrictions
Estimate Standar Error Estimates Standar Error

80 0.0827 0.0744 0.1777 0.0894
8, 0.4040 0.0070 0.4040 0.0071
8D 0.1107 0.0088 0.1104 0.0089
8C 0.1557 0.0085 0.1560 0.0086
8.< 0.4607 0.1439 0.3296 n.a.

8Q 1.1043 0.1538 0.8571 0.2207
8.r -0.0623 0.0069 -0.0001 0.0028

 

Note: “11. a.” refers to the value is not available.

 

 

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Table A.5.2.14 Elasticities of Scale with respect to Output in Static Models

132

 

 

 

 

 

 

No Symmetry Symmetry &
Restrictions Restricitons Homotheticity
Restrictions
Estimates 0.168 1.366 2.476
(0.506) (0.474) (0.480)

 

Note: Standard errors are in parantheses.

Table A.5.2.15 Elasticities of Technological Changes Estimated

 

 

 

 

 

the Flexible Dynamic Model
No Symmetry Symmetry &
Restrictions Restricitons Homotheticity
Restrictions
Labor 0.028 0.007 0.003
(0.014) (0.006) (0.016)
Land 0079 -0.049 0.043
(0.036L (0.014) (0.029)
Chemical -0.028 -0.003 -0.027
(0.027) (0.022) (0.014)
Capital 0046 -0.023 -0.004

 

 

 

 

 

 

Note: Standard errors are in parentheses.

An ordinary Time Trend Variable (T) are used.

Table A52 16 Elasticities of Technological Changes Estimated
in the Static Model

 

 

 

 

 

 

No Symmetry Symmetry &

Restrictions Restricitons Homotheticity

Restrictions
Labor 0.031 0.006 -0.010
(0.004) (0.007) (0.004)
Land 0.111 0.088 0.033
(0.012) (0.012) (0.009)
Chemical -0.001 -0.006 -0.008
(0.009) (0.009) (0.008)
Capital -1.67l -l.510 5.693

(0.458) (0.389)

 

 

 

 

 

Note: Standard errors are in parentheses.
An ordinary Time Trend Variable (T) are used.

 

133

Table A.5.2. l7 Elasticities of Technological Changes Estimated
in the Flexible Dynamic model with Linear Time Trend Variables

 

 

 

 

 

 

 

 

 

No Symmetry Symmetry &
Restrictions Restricitons Homotheticity

Restrictions
Labor 0.003 -0. 159 -0. 180
(0.067) (0.065) (0.049)
Land 0.027 -0.305 -0.028
(0.208) (0.203) Q. 129)
Chemical 0.053 0.202 0.092
(0.091) (0.090) (0.084)
Capital -6.039 -2.593 -2.801

 

Note: Stande errors are in parentheses.

The time trend variable in translog equation is In t, where t=1,2, ...,.T

 

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