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DYNAMIC SUPPLY ESTIMATION:
THEORETIC AND EMPIRIC REFINEMENTS
APPLIED TO U.S. CASH GRAIN PRODUCTION:
1965-1984

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DYNAMIC SUPPLY ESTIMATION:
THEORETIC AND EMPIRIC REFINEMENTS
APPLIED TO U.S. CASH GRAIN PRODUCTION:
1965-1984

By

Harold William Rockwell. Jr.

A DISSERTATION

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

DOCTOR OF PHILOSOPHY

Department of Agricultural Economics

1988

ABSTRACT
DYNAMIC SUPPLY ESTIMATION:
THEORETIC AND ENPIRIC REFINENENTS
APPLIED TO U.S. CASH GRAIN PRODUCTION,
1965—1984
BY

Harold William Rockwell, Jr.

Agricultural supply relations are commonly characterized as
"dynamic" in terms of "lagged adjustment" to price signals and "irre-
versible" expansions that occur more readily than contractions. The
examination of these relations, however, has been rather §g_ Egg in
relation to theory. This study attempts to put such examinations on
more secure foundations by introducing lagged adjustment derived from
upward-sloping input supply curves and irreversibility derived from
input supply constraints.

Mathematic development of a model incorporating flexible input
prices points to problems of econometric estimation that are generally
ignored. Extension to the case of input supply constraints shows even
greater difficulties for econometric applications.

These problems. however, do not make it impossible to test the
standard irreversiblity hypothesis. The fact that input suppliers’
normal capacity utilization rate is well in excess of fifty percent
suggests that input supply is more likely to be constrained by input
capacity than input disposal is to be constrained by a lack of desired
salvage markets. The resulting conclusion that irreversibility is
likely to be the opposite of common belief (that supply. in fact,
contracts on average more readily than its expands) is still difficult

to measure in terms of magnitude.

Structurally-ordered instrumental variables econometric measure-
ments of dynamic supply relations for acreage planted to feed grains,
wheat, and soybeans and for four classes of inputs supplied to agricul-
ture in the United States (1965-1984) was attempted in spite of the
theoretic implications that such measurement would be of questionable
validity. Some evidence of lagged adjustment was found and some weak
irreversibility of the type suggested was detected rather inconclusive-
ly.

This study concludes that eclectic studies of complex supply
relations may be more reliable and useful than narrow, formal economet-
rics, and that the question of irreversibility could be a major
stumbling-block for any examination of supply. A number of other
observations regarding cobweb cycles and other phenomena are also

offered to make the study’s findings more generally useful.

to Ruth, whose help and support made this effort possible

and whose presence made it seem worth doing

iv

ACKNOWLEDGMENTS

Special thanks to Eileen 0. van Ravenswaay for continued support
and encouragement and to J. Roy Black for providing an opportunity to
work and develop. Thanks also to Hsin Hui-Hsu, for repeated discus-
sions of important theoretical considerations and to Wayne N. Nhitman
for technical assistance. Thanks to the USDA Economic Research
Service for funding the original study on which this dissertation is

based.

TABLE OF CONTENTS

Chapter

Table of Contents. . . . . . . . . . . . .
Table of Figures . . . . . . . . . . . .

1. Problem Statement. . . . . . . . . . .

Policy Considerations. . . . . .
Analytic Considerations. . . . .
Overview of the Argument . . . .
Outline of the Presentation. . .

8. Dynamic Supply Theory. . . . . . . . .

Statics. . . . . . . . . . . . .
Multiple outputs . . . . . . .
Endogenous prices. . . . . . .

Dynamics with Quasi-Fixed Inputs

Dynamics with Occasionally-Fixed
No available salvage market. .
Input capacity constrained . .
Salvaging inputs . . . . . . .
Summary of the cases . . . . .

3. Characteristics of Agricultural Supply

Input Supply in Agriculture. . .
Labor. . . . . . . . . . . . .
Machinery and buildings. . . .
Purchased non-durables . . . .
Farm-produced durables . . . .
Farm-produced non-durables . .
Land . . . . . . . . . . . .
Inputs in combination. . . . .
Summary. . . . . . . . . . . .

Implications for Agricultural Output

Long-run supply. . . . . . . .
Supply with quasi-fixity . . .
Supply with occasional-fixity.
Implications for cyclicality .
The Supply of Cash Grains. . . .
Other Factors Affecting Supply .

vi

Page

ix
xi

UlOJnJH

\l

11
IA
81
82
EB
30
31

33

33
3c.
37
«o
«a
«a
4.3
43
as
A7
4.7
as
49
so
51
57

Chapter Page

4. Econometric Methods. . . . . . . . . . . . . . . . . . . 60

Introduction . . . . . . . . . . . . . . . . . . . 60
Dependent Variables. . . . . . . . . . . . . . . . 61
Crop Prices. . . . . . . . . . . . . . . . . . . . 65
Input Prices . . . . . . . . . . . . . . . . . . . 68
Legged Endogenous Variables. . . . . . . . . . . . 71
Credit, Debt, and Income . . . . . . . . . . . . . 74
Cross-equation Restrictions. . . . . . . . . . . . 75
Coefficient Shifting . . . . . . . . . . . . . . . 77
Methodological Note. . . . . . . . . . . . . . . . 79

S. Econometric Results. . . . . . . . . . . . . . . . . . . 92

Output . . . . . . . . . . . . . . . . . . . . . . 84
Independent variables used . . . . . . . . . . . BS
Regressions reported . . . . . . . . . . . . . . 88
Regression results . . . . . . . . . . . . . . . 89
Conclusions. . . . . . . . . . . . . . . . . . . 93

Farm Machinery and Equipment . . . . . . . . . . . 93
Price. . . . . . . . . . . . . . . . . . . . . . 94
Demand . . . . . . . . . . . . . . . . . . . . . 98

Fertilizer . . . . . . . . . . . . . . . . . . . . 100
Price. . . . . . . . . . . . . . . . . . . . . . 102
Demand . . . . . . . . . . . . . . . . . . . . . 104

Pesticides . . . . . . . . . . . . . . . . . . . . 107
Price. . . . . . . . . . . . . . . . . . . . . . 109
Demand . . . . . . . . . . . . . . . . . . . . . 110

Fuel . . . . . . . . . . . . . . . . . . . . . . . 112
Price. . . . . . . . . . . . . . . . . . . . . . 112
Demand . . . . . . . . . . . . . . . . . . . . . 114

Cross-Equation Restrictions. . . . . . . . . . . . 116

6. Conclusions and Implications . . . . . . . . . . . . . . 117

General Conclusions Regarding U.S. Agriculture . . 117
Extensions to Other CBSESm . . . . . . . . . . . . 120
Similarities and differences . . . . . . . . . . 120
Alternate land uses. . . . . . . . . . . . . . . 121
New input capacity, processing, and
infrastructure. . . . . . . . . . . . . . . . 121
Credit . . . . . . . . . . . . . . . . . . . . . 122
Other policy changes . . . . . . . . . . . . . . 122
Technological change . . . . . . . . . . . . . . 123
Treating the special cases . . . . . . . . 123
Examples for U. S. agricultural history and
other industries. . . . . . . . . . . . . . . 124

vii

Chapter Page

a. (continued)
Strengths and Weaknesses of the Analysis . . . . . 124
Strengths. . . . . . . . . . . . . . . . . . . . 124
weaknesses . . . . . . . . . . . . . . . . . . . 125
Policy Implications. . . . . . . . . . . . . . . . 126
Suggestions for Further Work . . . . . . . . . . . 129

Theory . . . . . . . . . . . . . . . . . . . . . 129
Data . . . . . . . . . . . . . . . . . . . . . . 130
Econometric techniques . . . . . . . . . . . . . 130
Other approachess and improved priors. . . . . . 131
Clarifying goals . . . . . . . . . . . . . . . . 131

Appendix A (to Chapter 2, p. 14) . . . . . . . . . . . . . . 132

Models of Depreciation

Appendix B (to Chapter 2, pp. 23-29) . . . . . . . . . . . . 134

Derivation of Supply/Demand Functions
with Occasional Input Fixity

Appendix C (to Chapter 4, p. 70) . . . . . . . . . . . . . . 138
Coefficient Matrix Symmetry for Imposing

Econometric Cross-equation Restrictions

Appendix D (to Chapter 5). . . . . . . . . . . . . . . . . . 140

Variable Definition and Data Sources

Appendix E (to Chapter 5, pp. 96ff.) . . . . . . . . . . . . 143

Policy for the Selection of Instrumental Variables

Appendix F (to Chapter 5, p. 116, and Appendix E). . . . . . 145

Results of Regressions with Cross-Equations Restrictions

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . 14S

viii

LIST OF TABLES

Table Page

3.1 Labor used in U.S. farming (millions of hours), 1965-83. . . 35

3.2 Gross investment in farm machinery and equipment, 1965-84,
and that industry’s fourth-quarter quarter practical capacity
utilization rate, 1974-84, and new capital expenditures,
1972-82. . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3 Practical capacity utilization rates for the agricultural
chemical industries, fourth quarter, 1974-84 . . . . . . . . 41

3.4 New capital expenditures in the agricultural chemical
industries, (millions of 1967 CPI dollars), 1972-82. . . . . 41

3.5 Regression on input use of lagged prices and inputs. . . . . 46
5.1 Dummy variable coefficient shifter forms representing the pos-
sibility of acreage-related fixity, and the total and change
in planted acreages (in millions) of feed grains, soybeans,

and wheat from which the shifters were derived, 1965-84. . . 88

5.2 Results of OLS regressions on total acreage of the
six study crops (millions of acres), 1965-84 . . . . . . . . 90

5.3 Results of regressions on the normalized price
of farm machinery and equipment (1967=1.00), 1965-84 . . . . 95

5.4 Results of regressions on farm machinery and equipment
purchases (billions of 1967 dollars), 1965-84. . . . . . . . 99

5.5 Results of instrumental variables regressions on
normalized fertilizer price (1967=1.47), 1965-84 . . . . . . 103

5.6 Results of instrumental variables regressions on
fertilizer purchases (expenditures divided by price,
1910-14=100), 1965-84. . . . . . . . . . . . . . . . . . . . 105

5.7 Results of regressions on real pesticide price, 1965-84. . . 109

ix

Table Page

 

5.8 Results of regressions on pesticide purchases
(expenditures divided by price, 1910-14=100), 1965-84. . . . 110

5.9 Results of regressions on discounted fuel price
and fuel purchases (expenditures divided by price,
1910-14'2100)’ 1965-84e e e e e e e e e e e e e e e e e e e e 115

F.1 Results of tests on one symmetry condition . . . . . . . . . 145

F.2 Results of acres planted regressions using
three different estimators . . . . . . . . . . . . . . . . . 147

LIST OF FIGURES

Figure

1.1

2.1

2.2

2.3

2.5

2.6

3.2

3.3

3.5

3.6

Conditions affecting dynamic agricultural supply . . . . .
Exogenous prices of outputs and inputs . . . . . . . . . .
Endogenous prices of outputs and inputs. . . . . . . . .

Endogenous price of a durable. . . . . . . . . . . . . . .

Cases of input supply: quasi-fixity, salvage-constrained
fixity, input-capacity-constrained fixity, and salvaging

Dynamic adjustment to increased output prices
with input quasi-fixity. . . . . . . . . . . . . . . . . .

Dynamic adjustment to decreased output prices
With input fixity (1:0). 0 O O O I O O I O I I

Dynamic adjustment to increased output prices
with capacity-constrained input supply . . . . . . . . . .

Salvage and acquisition markets with different
price flexibilities. . . . . . . . . . . . . . . . . . .

Agriculture as a net supplier of laborers to other sectors

The relative likelihood of two cases of occasional-fixity
given the frequency distribution of demand for I . . . .

Long-run output supply given endogenous prices of inputs
and other outputs. . . . . . . . . . . . . . . . . . . . .

Long-run and short-run output supply with
unconstrained input quasi-fixity . . . . . . . . . . . . .

Constrained short-run output supply with
input occasional-fixity. . . . . . . . . . . . . . . . .

Limit cycles with input occasional-fixity. . . . . . .

xi

Page

11
12

18

23

27

28

29

3O

35

38

48

4,9

50

57

Figure

3.7 Land use equilibrium without conversion costs.

3.8

3.9

5.3

5.4

5.5

5.6

5.7

Land use shifts with conversion costs.

Land use shift to corn without conversion costs.

The effect of durable land improvements on land supply .

Acreage planted to studied crops in the U.S.,

crop years 1965-84 . . .

Normalized price of farm machinery and equipment,

Farm machinery and equipment purchases and stocks,
1965-84 . . .

fitted and actual,

Normalized prices of crops (lagged, 1967=2.38)
and fertilizer (1967=1.47),

Fertilizer purchases (expenditures divided by price,

19lO-14=100), 1965-84. .

Normalized prices of crops (lagged, 1967=2.38)

1965-84.

and pesticides (1967=2.77), 1965-84.

Normalized price of fuel

(1967=1.77)

and fuel purchases (1910-14=100),

Models of depreciation: geometric decay, engineering

and their difference .

xii

1965-84.

data,

54

55

56

57

85

9:,

101

102

108

108

113

132

CHAPTER ONE

PROBLEM STATEMENT

This chapter discusses the policy concerns motivating this study
and the analytic concerns that shaped it. It then turns to an overview
of the study’s central arguments and an outline of the remaining

chapters.

Policy Considerations

The high grain prices and related policy decisions of the mid- and
late-1970’s stimulated considerable expansion of world grain produc-
tion. When prices then fell, many people debated the merits of raising
support prices or restricting domestic production to raise market
prices (or both) to increase U.S. farm incomes. Because production
responses to such measures would affect their costs and effectiveness,
the nature of agricultural supply became a major topic for discussion.

Specifically, attention focused on the difference between short-
run and long-run supply response and on whether agricultural supply
expands more readily than it contracts. The first issue is often
referred to in terms of "length-of-run", ”lagged-adjustment", or
“partial-adjustment". The second issue is often called "reversibility”
or "irreversibility".

These issues were commonly discussed before the 1970’s, but were
generally limited to domestic considerations (e.g., Tweeten and
Ouance, 1969, and others cited there.) The expansion of competing

foreign productive capacity and export facilities in the 1970’s,

however, seemed to call for an extension of these concerns to the
analysis of world markets. If foreign supply would contract slowly or

very little, U.S. policy effectiveness could be seriously impaired.

Analytic Considerations

Because much of the early work on these issues preceeded wide
knowledge of appropriate analytic techniques, the adequacy and applic-
ability of available tools has been unclear. Furthermore, empirical
studies of these dynamic characteristics of domestic agricultural
supply have been far from conclusive. Claims have not been supported
by strong evidence, and the empirical evidence that existed has not
been built on strong analytic foundations.

Econometric work has been based on two standard models. Partial-
adjustment is typically modeled by estimating production as a function
of prices, policy variables, and the previous period’s production
(e.g., Tweeten and Ouance, 1969). Irreversibility is modeled with
different ("shifted") price coefficients in periods of expansion versus
periods of contraction (e.g., Tweeten and Ouance; Wolffram, 1971;
Houck, 1977). In general, large adjustment lags (the first issue) are
not apparent in the findings, but some evidence of expansions occuring
more quickly than contractions (the second issue) have been found. The
latter conclusion may have been strengthened by the fact that a
hypothesis of faster contractions (as opposed to faster expansions) was
not considered to be important; statistical results to this effect may
well have been considered support for a null hypothesis of no differ-
ence in the speed of adjustment.

A belief in faster expansions may also have been fostered by a

3
number of studies of perennial and fruit tree supply (Arak, 1969;
French and Matthews, 1971; Baritelle and Price, 1974; Saylor, 1974;
Gemmill, 1978; French, King, and Minami, 1985). More responsive
expansions are easier to demonstrate in these cases, and the technical
uniqueness of these crops may have been overlooked. Rather than
deducing that the rest of agriculture would be less responsive in its
expansion as a result, the findings may have been uncritically extended

to other crops and possibly to agriculture as a whole.

ngrvigw of thggArqugpp

More detailed examinations of the dynamics of agricultural supply
have traditionally centered on the analysis of inputs to agriculture
(e.g., G. L. Johnson, 1958, and others cited there.) In one approach,
agricultural supply elasticity has been explained in terms of the
elasticity of the supply of inputs to agriculture (perhaps most notably
by D. G. Johnson, 1950). In this view, the more inelastic the supply
of inputs, the more inelastic the supply of outputs. A second approach
focuses on durable inputs (e.g., G. L. Johnson, 1958). In this view,
output supply is more elastic when quantities of durables vary than
when they are fixed, so attention shifts to the conditions and time
frame that determine fixity.

These two approaches to the question of agricultural supply
elasticity are not really at odds, but the focus on durables in the
second approach is significant. Whereas the first view does not
explicitly include time, the second leads directly to the subject of
length-of-run in supply adjustment. A focus on durables also suggests

the question of irreversibility: because stocks of durables are often

4
seen as variable in expansions but fixed in contractions, agricultural
supply is often held to expand more quickly than it contracts.

This study integrates these two approaches by examining dynamic
agricultural supply in relation to the elasticity of inputs supplied to
agriculture. It concentrates on: 1) a less-than-perfectly-elastic
supply of durable inputs as a source of the "quasi-fixity" of input use
that results in partial adjustment, and 2) conditions of perfectly
inelastic input supply that result in irreversibility. These condi-

tions are shown in Figure 1.1.

U1

IN

D:\\\\\\\\\\

 

Cl

".9
I.
\

 

Figure 1.1. Conditions affecting dynamic agricultural supply.

In Figure 1.1, the demand (D) for new purchases (1) of an input is
shown as a function of that input’s price (w). When input supply is

less-than-perfectly elastic (upward sloping), input price is affected

5
by demand (is endogenous) and thereby affects the quantity purchased.
When the input in question is a durable, the demand curve is affected
by the Quantity of input stocks held by farmers, resulting in quasi-
fixity and lagged adjustment (as discussed in more detail in Chapter
Two).

1f demand (0’) falls to a point at which no new purchases are
desired but at which no salvage market is available, input use becomes
perfectly price-inelastic and fixed. Similarly, if demand (0") rises
to use all available input production capacity (C), input use is again
perfectly inelastic and fixed. As explained in Chapter Two, it is
these conditions of "occasional-fixity" that lead to irreversibility of
agricultural supply.

The econometric evidence presented in Chapter Five does not
suggest that lagged adjustment is a major force in agricultural supply.
Furthermore, it is argued below that if either condition of occasional-
fixity is more prominent in agriculture, it is likely to be that of the
input capacity constraint. This implies that, if a difference exists
between the rates of expansion and contraction, it is more likely to be
the case that agricultural production contracts more readily than it
expands, the opposite of the standard view described in the previous
section. This hypothesis is weakly supported by the econometric

evidence presented in Chapter Five.

Outline of the Presentation
The remainder of this study consists of five chapters. Chapter
Two presents a formal theoretical treatment of quasi-fixity and the two

conditions of occasional fixity, and this treatment is related to other

6
literature on economic dynamics. In Chapter Three, characteristics of
agricultural production and its input supply are examined to provide
informal support for the idea of a more probable capacity-constrained
occasional-fixity. Other observations about production cycles, the
supply of cash grains, and other factors affecting supply are also made
there.

Chapter Four includes a survey of methodological considerations
involved in any attempt to examine the ideas of Chapters Two and Three
econometrically. This chapter covers both domestic and foreign
applications, and concludes with a philosophic note about methods used.
Chapter Six draws general conclusions and implications of the study.
Six appendices provide details of much of the theoretic and econometric

presentations.

CHAPTER TWO

DYNAMIC SUPPLY THEORY

The analysis of dynamic agricultural supply must be based in
economic dynamics. That base is developed in this theoretical chapter.
A beginning definition of terms and principles in statics is followed
by a discussion of quasi-fixed inputs and occasionally-fixed inputs.
This will set a foundation for the empirical investigations of the

later chapters by showing the role of input fixity in supply elastici-

ty.

Stgtics

In static ("timeless", per Hicks, 1946, p.115) production theory,
a firm’s optimum output supply (0) and variable input demand (vector1
L) are determined by prices (P for output and vector W for inputs),
given decreasing returns at some level of fixed inputs (K). Assuming

profit (R) maximization:

max R = P0 - W’L
L

subject to Q = F(L;K)

Optimum factor demand is given by simultaneous solution of the first-

order conditions:

 

‘ All vectors are column vectors unless transposed
(Eege’ u’)e

RL PQL‘H=0

01':

UL W/P = w
where RL and UL are first partial derivatives2 of R and Q with respect
to L, and w is a vector of input prices ”normalized" by output price.
The matrix of second partial derivatives (FLL) must be negative
definite as a second-order condition and symmetric by Young’s Theorem
(Chiang, 1974, p. 324). (See Varian, 1984, Chapter 1 for a standard
treatment.)

For exposition and econometric estimation, a convenient second-
order approximation of the production function F is the quadratic

functional form (Lau, 1978, p. 194):

D
N

c + a’L + 1/2 L’FLLL

This approximation is g priori as a good as any second-order approxima-

tion, and leads to linear input demand functions as follows: the

first-order conditions derived from the quadratic production function

become:

QL=a+FLLL=W

When solved simultaneously for input levels:

 

& Capital subscripts denote first partial derivatives. Double
capital subscripts denote second partial derivatives. Small
case subscripts are labels, unless noted otherwise.

FLLL : W - a
01":

L“ = FLL-1(W-a)

The resulting set of optimum input demand equations (L*) are linear in
normalized input prices and have symmetric cross-price effects (due to
symmetric FLL‘I). This symmetry is important because it can provide a
basis for more efficient econometric coefficient estimates through
cross-equation constraints on parameters.

Optimum output supply in this case is expressed as:

0* F(L*;K)

C + a’L* + 1/2 L*’FLLL*

which is quadratic in normalized input prices:

0* = C + a,FL_L-1(W-a) + 1/2 (W-a)’FLL-1(W-a)

C - l/a a,F1_L-la + 1/8 W’FLL—IW

Summing the coefficient matrices (FLL'I) across firms yields
aggregate input demand and output supply relations.

Multiplg_gutputs. Because of the multiple commodities under
consideration in the cash grain sector, a single-aggregate-output
analysis is not adequate. To develop the static multi-product case, we
shall assume that some output (0“) is additively separable from a
quadratic function (F) in other outputs (vector 0) and inputs (L and

K). (The plausibility of this assumption for agriculture is explained

10
in Chapter 4.) Normalizing prices by the price of On (PH) at the
outset and maximizing the resulting normalized profit function (r =

R/Pn, i.e., profits expressed as units of On):

max r = 0n + p’O - w’L

subject to 0n = F(Q,L;K)

with Fvv [Y = (O’ L’), the vector of 0’s and L’s] again symmetric

negative definite, the first-order conditions:

are again solved simultaneously to get optimum non-numeraire outputs

and inputs that are linear and symmetric in prices:

(O*' L*’)’ = th”‘ (-p-aq’ w-a,’)‘

and 0*" quadratic in prices. Although 0*n can be expressed in terms Of
0* and L*, it is no longer possible to express 0* in terms of L*
(except under very restrictive conditions). Once again, aggregate
relations result from summing across firms.

Hotelling’s Lemma (Diewert, 1982, p. 581; Nadiri, 1982, p. 452;
Varian, 1984, p. 52) is demonstrated by taking the first partial
derivatives of the resulting indirect profit function in normalized

output and input prices, which is:

11
r* = 0*n + (p’ -w’) (0*’ L*’)‘
= C - a,Fvv—1a + 1/2 (‘p’ W,)Fyv-‘(-p’ W’),

+ (p’ ’W,)Fyv-1('p’ w’)’ - (p’ -w’)Fyy“a

in which a = (aq’ a,’)’, and which reduces to:

r* = C - a’Fvv-la + a’Fvv-1('p, W,)’

- 1/2 (p’ -w’)Fyy‘1(-p’ w’)’

By Hotelling’s Lemma, the first partial derivatives of r* with respect

to p and -w yield 0* and L*:

(0*’ L*’)’ = (r*,’ -r*~’)’ = Fyy“ [(-p’ w’)’ - a]

as shown above.

Endogenous prices. With exogenously determined prices, this
competitive supply model is the same for both the firm and the aggre—
gate industry. In this case, output and input prices are not influ-

enced by output supply or input demand, as in Figure 2.1.

 

 

 

 

 

 

(a) (b)

Figure 2.1. Exogenous prices for outputs (a) and inputs (b).

12
With downward-sloping output demand and upward-sloping input
supply curves, however, the analysis becomes more complex at the level
of the industry. (The case of the competitive model with exogenous
prices would still apply for the firm.) Fee-1 is now the aggregate
derived from the sum of individual functions. Dropping (*) for
simplicity’s sake, endogenous prices resulting from less-than-totally-

elastic output demand and input supply are represented most simply by:

On + qu

13
11

w = w,. + m,L

in which intercepts pa and w" are functions of exogenous price shift-

ers, and mq and m, are the slopes of output demand and input supply

curves, respectively, as shown in Figure 2.2.

pm ”It

 

 

 

 

(a) (b)

Figure 2.2. Endogenous prices of outputs (a) and inputs (b).

Equating these prices with marginal products:

(aq’ a,’)’ + Fyy(0’ L’)’ = (-pm’ ww’)’ + ( )(0’ L’)’

13

or:

(Fey-m)(0’ L’)’ = (-pw’-aq’ wM'-a,’)’ where m = ( )

optimum quantities become:

(0’ L’)’ = (FYv-m)“(-pK’-aq’ wm’-a,’)’

By endogenizing induced price changes, this relationship expresses
output supply and input demand as functions of exogenous price shifters
only.

With expected signs on the elements of m, 0 and L are less
responsive to pa and w, the more p and w respond to 0 and L, demon-
strating D.G. Johnson’s (1950) major point about output supply elastic-
ity depending on input supply elasticity. (Note that there is no
implication of irreversibility.)

If m is diagonal, or at least symmetric, cross-price effects are
still symmetric, a case which seems likely. Note that if all inputs
were variable, even one upward-sloping input supply curve or one
downward-sloping output demand curve would serve the same purpose as
diminishing returns in making the coefficient matrix non-singular and
invertible, i.e., in uniquely determining quantities. The similarity
of the effects of endogenous output and input prices is interesting,
but it is not essential to this study. Endogenous input prices will be
the focus of the remainer of this work, therefore, and the endogeneity

of output prices will be ignored.

14
Dynamics with Quasi-Fixed Inputs

Time has not been explicitly part of the above static analysis, so
no distinction has been drawn between stocks and flows. Simply
indexing quantities for time does not alter this approach (Arrow,
1964). When an outcome depends on outcomes in other periods, however,
the problem becomes dynamic, and the distinction between stocks and
flows becomes important. Such is the case when the problem above
includes changing prices and durable inputs with upward-sloping supply
curves, known in the literature as "quasi-fixed" inputs. (Good
references include: Nerlove, 1972; Treadway, 1970 and 1974; Epstein,
1981; and Nariri, 1982, pp. 477-9). The notion of quasi-fixity is best
seen as the analog of quasi-rent: rent is earned by fixed assets,
quasi-rent by durable assets which are varied only by affecting their
prices (Marshall, 1982(1920), p. 358). The resulting model of dynamic
adjustment is the core of the "flexible accelerator” model of macroeco-
nomic dynamics (Lucas, 1967a).

For present purposes, a durable is defined as an input with less-
than-total depreciation in a production period. (In the discrete
analysis used below, a period is one year.) Depreciation is defined as
the periodic reduction in the value and service-yielding ability of
inputs. The common rule that depreciation is a constant proportion (d)
of the durable stock will be assumed, although this proportion can vary
by type of input. (See, e.g., Jorgensen, 1971, pp. 1112 and 1141;
Nickell, 1978, p. 8; Burmeister, 1980, p. 42; Gunjal and Heady, 1984:
and Appendix A.) This simplification makes it straight-forward to
aggregate an input of different vintages after an uneven history of

acquisition. It is also assumed that service flows are constant

15
proportions of durable stocks, another very common assumption, which
makes it irrelevant whether production function arguments are denomin-
ated in stocks or flows. (See, e.g., Treadway, 1970, p. 331, and 1974,
p. 19.)

Because the distinction between variable and fixed inputs becomes
blurred in this model, the vector L will now be used to represent
stocks (after new purchases) of all inputs at the beginning of the
production period. (For simplicity, all input purchases are assumed to
occur at that time.) Vector 1 represents new purchases, and vector (1-
d)L is stocks at the end of the production period (i.e., after depreci-

ation). By definition, then:

Lo, : 1,, + (l-d)L,,_,

For durables:

For the special case of non-durable inputs:

50:

(For the following analyses, the subscript t will be suppressed in all
unambiguous cases.)

In the multi-period model needed for dynamic analysis, first-order

16
conditions are derived by maximizing the present value of future
profits (J) with respect to current decision variables (00, Lo). That
is, in each period, output and input levels are chosen so as to

maximize the infinite sum:

max J = INFSUM (1/(1+i))“(0n + p0 -wI)
Oo,Lo t=0

subject to 0 = F(0,L)

L I + (1-d1La-,

in which i is the opportunity cost of capital funds, so that 1/(1+i) is
a discount factor; and w is the vector of input prices. (Acquisition
and salvage prices are assumed to be equal for each input.) This is
the discrete version of a standard problem in optimal control theory
and the calculus of variations. (See, e.e., Gould, 1968; Nerlove,
1972; Kamien and Schwartz, 1981, pp. 7 and 113; and Kendrick, 1982.)
The dynamic analysis does not alter the first-order conditions for

outputs (currently assumed to be non-durable):

11
0

39° = F006 ‘1’ P

except that p must now be considered to be prices expected to prevail
when outputs go to market. With stationary price expectations, the

first-order condition for each input becomes:

3L9 = INFSUM (1/(1+i))”FL° - onL0 = 0

=> INFSUM (1/(1+i))"F,_L,,O = onLo

17

With FL constant and IOLo=1:

[INFSUM (1/(1+i))”LL°] FL = w

Replacing L with (1-d)”Lo, and with LoL.=1:

[INFSUM (l/(l+i))t(l-d)tLoLol FL = w

[INFSUM (l/(l+i))”(l-d)”l FL = w

Calling the constant summation term (which reduces to (1+i)/(i+d)) “B":

BFL = w

This is the dynamic first-order condition for each input. Note that
i+d is the sum of the interest and depreciation cost rates of durable
use. When d=l, B=1 and the case of non-durable inputs is still
analogous to that of the static analysis. When O<d<1, B is a multi-
plier of the annual productive services of an input. When d=0, the
multiplier is (1+i)/i.

With exogenous input prices, the first-order conditions:

(Fa, (BF|-),)‘ = (-p’ Hy),

can be transformed into:

(Fa, FL’)’ = (-p’ (B‘lw)’)’

18
in which B‘1w is the annual user cost of inputs. The dynamic case then
reduces to the static case, as mentioned above, and some fixed input

(or downward-sloping output demand) is required to determine equilibri-

um.

With endogenous input prices linear in purchase quantities (for a

justification, see Gould, 1968, p. 49):

w“: + Nil

1
II

as in Figure 2.3, this simple transformation is not possible.

NX

 

 

Figure 2.3. Endogenous price of a durable.

Instead:

(Fo’ BFL’)’ = (-p’ (w.+w.l)‘)'

With quadratic F and I=L-(1-d)L,-,:

(iaq‘i'FHIHQT'FnLL), (8(a,+FL,-,G+F,_LL‘I)’)' = (‘9. (W..*W,L-W,‘:l“d:'Le-1)I).

19
Collecting endogenous terms on the left-hand side and predetermined

terms on the right-hand side:

((FQQG+FQLL), (BFLQQ+BFLLL'WgL),), =

((-p-aq)’ (we-Ba,)’)’ - (0’ (w,(l-d)Lb_,)’)'

Factoring out the endogenous variables 0 and L yields:

F am, Fan.
( ) (0’ L’)’ =
BFLI: BFLL. “W:

((-p-aq)’ (w.-Ba,)’)’ - (0' (w,(l-d)L.e,)’)’

Let E be the matrix:

F 136'! F6“-

BFLQ BFLL ”N;

then:
E (0’ L’)‘ = ((-p-aq)’ (we-Ba,)’)’ - (0’ (w.(1-d)L.-,)’)’
and:
(0’ L’)’ = E‘1(-p’ wn’)’ — E"(aq’ Ba,’)’
0 O
—E"1( )(O’ Lh-I')‘

0 ”5(1-d)

20
Under these conditions, the short-run price coefficient matrix (E“) is
no longer symmetric. As in the exogenous price case, it could be
rendered symmetric if B or the resulting user costs of durables were
known.

In this model, long-run profit maximation results from balancing
fluctuations in the value of the marginal product of inputs with
correlated fluctuations in their costs. In the case of durable inputs,
purchases are timed to reduce these costs by smoothing the scheduling
of acquisitions. This is the partial-adjustment model of asset
acquisition, shown here as theorectically grounded in external (to the
industry) adjustment costs. (For further exposition of this concept,
see Alchian, 1977, Proposition 8.)

Note that a common partial-adjustment output supply model (Ner-

love, 1958b, p. 26):

Q = 0(pQW’Og—1)

does not follow from durable-stock-adjustment model just derived:

L = L‘pgt'i’Lg—I)

Instead, output supply is a function of leftover durable quantities:

Q = 0(ng’Lt—1)

Whether 0._, can serve as reasonable proxy for L._, in econometric

estimation is largely an empirical question. It appears that there is

21
no way to derive a theoretical basis for this substitution.

As an alternative to the external adjustment costs derived above,
adjustment costs could also be considered to be internal to the firm or
industry. Such costs might be thought of as production lost to
planning, purchasing, and installing new assets. (See, e.g., Gould,
1968.) Linearly increasing unit costs would be precisely analagous to
the linearly increasing unit prices analyzed above (Treadway, 1974, p.
29), and they would produce the same results. If these costs were
affected by (or affected) the level of input use (or, for that matter,
levels of output production), any symmetry left in the coefficient
matrices would be lost (Mortensen, 1973). Such adjustment costs are
known in the literature as "non-separable" (Nerlove, 1972), and are
included in the analysis in Appendix 8.

Although it is often stated that it is irrelevant whether adjust—
ment costs are stated in terms of gross or net (gross minus deprecia-
tion) investment (e.g., Lucas, 1967b; Treadway, 1972, p.847), the two
are not equivalent. There are reasons to prefer the use of gross
investment (Gould, 1968); lacking a reason to also consider net

investment, this convention will be used here.

Dynamics with Ocpsiqully-Fixgg Inputs

In the above analysis, all inputs were treated as either variable
or quasi-fixed, with the implicit possibility of the existence of fixed
factors. In this section, factors that are "occasionally-fixed" (fixed
in some periods but not in others) are described and related to
irreversibility.

It is worthwhile at this point to emphasize that the term "fixity"

22
means that the level of use of an input is not an endogenous decision
at the margin in the current period, although the fact of fixity may be
endogenous; fixity does not imply the same level of input use in all
periods. It follows, then, that an input that is fixed in one period
may be variable or quasi-fixed in another, i.e., occasionally-fixed.

Two constraints that can cause factors to be occasionally-fixed
are discussed in this section. They are:

1. the absence of a salvage market for durables, which

causes 1=0 when it would otherwise be negative; and

2. an input supply capacity constraint that limits I to a

level less than otherwise desired.
Note that the first constraint applies to durables, whereas the second
could apply to any input. Although such constraints could be thought
of merely as more sharply-sloped portions of input supply curves,
absolute constraints (vertical portions of supply curves) serve better
for exposition purposes. In these cases, the level of I is predeter-
mined, and the price of inputs becomes wholely endogenous.

These cases are exhibited graphically in Figure 2.4. Panel (a)
shows the normal case of a quasi-fixed input, with both prices and
purchases endogenous to the level of input demand. In panel (b), input
demand is so low that none of the durable is purchased, and had price
not fallen precipitously as a result of no alternate use, some of the
durable would have been sold. In panel (c), demand has risen to and
above the point of total input supply capacity utilization, thereby
driving up prices to maintain short-run equilibrium. Finally, in panel
(d), the input is quasi-fixed, but its marginal value product has

fallen below its opportunity value in another use; the sector in

23
question has become a net supplier of the "input”, and the rest of the
economy has become a net demander. These last three cases are des-

cribed in more detail below.

 

 

 

 

 

 

 

 

I*>0 I I*=0 I
(a) (b)
w 5 w
S
\\D
D
I*=C I*<O L

(c) (d)
Figure 2.4. Cases of input supply: quasi-fixity (a),

salvage-constrained fixity (b), input-capacity-
constrained fixity (c), and salvaging (d).

No available salvage market. Although alternative approaches are
possible (e.g., Hartman, 1972), it is most common to constrain the
model with quasi-fixity to non-negative gross investment solutions.
Although this condition need not apply for each firm, it must hold in
aggregate unless some external market exists for disposing of assets.
(See, e.g., Taylor, 1984, p.353.) There are two approaches to applying
this constraint.

'The first approach is merely to assume that the constraint is

never binding. This approach is justified by observing that, for the

24
sectors examined empirically at the level of aggregation used, gross
investment has always been positive (e.g., Treadway, 1971, p. 847;
Epstein, 1981, p. 91). This allows for use of the above model without
modification, which is the standard approach in the literature. (See
also, e.g., Nadiri and Rosen, 1969; Schramm, 1970; and Epstein and
Denny, 1983.)

The second approach admits that there will be times when the
constraint will bind for at least one significant input for which, at
other times, it does not bind (Arrow, 1968). This input will then be
occasionally-fixed. In periods in which it is variable or quasi-fixed,
its input level will be a function of prices and other fixed input
levels. In periods in which it is fixed (at L = (1-d)L._,), its price
will be a function of other prices and its own and other fixed input
levels. This situation is represented by the equation (see Appendix B

for derivation):

0 Fan (FaLi'Fatle '1
( 1 = ( )
DVLT'DQPW", B(Dv-Dv)FLQ (8(FLL+FLr)-W;)DV+D(
'P aq FGIDv-FGLDf
[( ) - ( ) + ( ) (l-d)La_, J
DVW-u B(D..-D,r)a, B‘FL,LDf+F|__tDV)
in which:

Dv is a diagonal matrix of:

ones for inputs that vary in the period,

zeros for inputs that are fixed in the period,
D, is the identity matrix minus D3, and

F9, and FL, represent non-separable internal adjustment costs.

85
In this system of equations, output (0), some input quantities (L), and
some fixed-input rent levels (w,) are determined simulataneously by
exogenous price effects and durable input stocks. The pattern of
effects is determined by, F’s second partial derivatives and the input
supply curve slope (w.).

This model is important to analyses of agricultural supply because
it shows how standard "irreversibility" occurs, with some inputs
occasionally-fixed in contractions and occasionally-variable (or quasi-
fixed) in expansions. Before explaining how this model generates
irreversibilities, four major points about the model should be men-
tioned:

First, the inverted coefficient matrix includes dummy variables
(zero representing fixity of an input, or one for others) in all its
elements. (This can be shown by taking the inverse by partitioning.
See Appendix 8 and Ayres, 1968, p. 57.) This means that fixing the
level of an input changes the values of all coefficients, not just
those of, say, own prices. This is an important finding because not
all studies recognize this fact.

Second, as each additional input is fixed, each element of the
coefficient matrix shifts to a different value, as implied by Samuel-
son’s (1967, p. 38) Le Chatelier Principle (Varian, 1984. p. 58).
(Contrary to this principle, the possibility of internal cross-input
adjustment cost terms makes the a priori direction of some of these
shifts somewhat ambiguous (Treadway, 1970, p. 329); because the
conditions for such ambiguity are unlikely, however, this study will
assume that shifts have normal signs.) This point (and the previous

point) create great problems for econometric estimation.

86

Third, although this model accounts for the endogenous level of
variable and quasi-fixed input use and the endogenous rental value of
fixed inputs, it does not endogenize the occurrence of fixity. Because
the variables that represent this occurrence (Dv and D1) appear on the
right-hand side of the equation, this is not a true reduced-form.
Unless a way can be found to endogenize the fixity decision, there is
no clear way to avoid the resulting inconsistent parameter estimates in
econometric work.

Fourth, because nothing in this model changes long-run effects, it
is generally only the speed of adjustment that changes when inputs
become fixed; long run equilibria are not affected. The exception is
when occasionally-fixed inputs have a zero depreciation rate, which
implies no determinant long-run response to prices. (In other words,
input quantities only affect long-run responses when depreciation or
price changes give them occasion to vary.)

The dynamics of adjustment with occasionally-fixed inputs may
become clearer with an explanation of how occasional-fixity and
irreversibility could occur. The reference point for this exposition
is the "normal" condition of quasi-fixity for all durable inputs as
shown in Figure 8.4, panel (a). Equilibrium in this condition occurs
when, for given prices, new purchases simply replace depreciation,
i.e., L=L.-, when I=dL.-,. (Without loss of generality, this analysis
ignores input use trends resulting from changing technology.)

It is easy and important to show that this is a stable equilibri-
um, as follows: If, with given prices and endogenous price effects,
input purchases are greater (less) than depreciation, input use will

increase (decrease):

27

I > dLfi—l ""> L > Lg—j
(<) (<)

Because input purchase demand (Di) is a decreasing function of input

stocks, i.e.:

Dice-1 < 0

the resulting rise (fall) in input use and depreciation cause input

purchases to fall (rise) until they equal depreciation:

I = dL,_,

and thereby establish equilibrium, at least in the limit.

Graphically (see Figure 2.5), a displacement from equilibrium (0*)
could be caused, for example, by a rise in output prices implying a new
equilibrium (D**). Adjustment would take place, however, by a larger
initial shift in input demand (0’), which would then eventually

converge to D**.

D’ t=1
D** t=infinite

0* t=0

 

 

I

Figure 2.5. Dynamic adjustment to increased
output prices with input quasi-fixity.

28
With input fixity caused by the constraint of non-negative
purchases, however, this adjustment process is altered (see Figure
2.6). with output prices falling, D’ could fall to the point that new

purchases of that input cease (I=0).

0*

D**

\<D,

Figure 8.6. Dynamic adjustment to decreased
output prices with input fixity (I=0).

 

 

I

In this case, input use cannot fall as fast and, therefore, D’ cannot
shift back as fast as when I is unconstrained. As a result, adjustment
occurs more slowly until the constraint no longer holds; adjustment
then proceeds at a "normal" rate.

Depreciation determines the nature of supply irreversibility in
the absence of salvage markets. (For a definition of depreciation, see
page 14, above.) Because depreciation tends to shift D’ out of the
condition of fixity, fixity is more likely to occur in contractions
than in expansions. If such fixity is a possible occurrence, there-
fore, contractions will occur more slowly on average than expansions.
This is the link between input fixity and the supply irreversibility

that is so commonly cited in the literature of agricultural economics.

89

Input capacity constrained. The obverse of the case just des-
cribed is that in which input purchases are constrained by the capacity
of input-producing industries (I=C), as shown in Figure 8.4, panel (c).
The price response of output and the input price flexibility of input
demand would be the same, with magnitudes differing only by intercept
shifters.

In this case, all the observations made above apply, except that
adjustment would occur more slowly in expansions than in contractions,
the opposite of the kind of irreversibility found when purchases are
occasionally-fixed at zero (I=0). This time, increased stocks tend to
shift D’ back into the "normal" unconstrained range of the input supply
curve following such fixity (see Figure 8.7). (Capacity (C) would tend
to shift out through time (C’) as long as capacity utilization (I/C) is
high.) These factors would tend to make expansions more constrained
than contractions. It is also important to note that this analysis
applies both to purchased durables and non-durables, whereas the

salvage-constrained analysis applies only to durables.

D?

D**

 

 

 

Figure 8.7. Dynamic adjustment to increased
output prices with capacity-constrained input supply.

30

If input supply is constrained by either non-negativity or
capacity (0315;), adjustment could be "abnormally" slow in either
contractions or expansions. Slow adjustment would result whenever a
constraint is binding. Whether contractions or expansions are slower
on average would depend on which constraint binds more often. If
unavailable salvage markets were more common, contractions, on average,
would be more sluggish. If input capacity constraints were more likely
to bind, however, expansions would appear more sluggish on average. If
neither constraint bound, or if they bound equally often, expansions
and contractions would proceed at the same pace on average. In the
former case, the speed would not vary; in the latter, it would.

galvgginq inputs. A third type of input occasional-fixity is that
shown in Figure 8.4, panel (d), in which an input’s stocks are sold to
another sector whenever its value in production falls to some base
salvage price. Because the salvage market is liable to differ from the
acquisition market (in aggregate), price response to quantities sold
(if any) generally would differ in magnitude from that to quantities
purchased. In other words, as in Figure 8.8, the two curves would not

generally have the same slope. (Either could be steeper.)

Wu,-

.—————’”"'——————‘—‘d ""‘

D

 

 

I

Figure 8.8. Salvage and acquisition markets with
different price flexibilities.

31

Note the distinction between base acquisition and salvage prices
(wm. and wx.) in Figure 8.8. This distinction is essential for there
to be occasional-fixity in the presence of a salvage market. If the
two prices were equal, output response to prices would still differ
between acquisition and salvage cases as long as the slopes were
unequal. If, on the other hand, slopes were equal and base prices
differed, output price response would be the same for the two cases,
differing by only an intercept shifter. If base prices were also the
same, the shifter would be zero, and the analysis collapses to that of
an unconstrained quasi-fixed input.

In terms of adjustment speed, occasional-fixity in the vicinity of
w.. would be similar to that with input supply constraints and opposite
to that of unavailable salvage markets (the vicinity of w,-). The
result, of course, would be to make expansions occur more slowly than
contractions.

This analysis is a generalization to an industry aggregate of G.L.
Johnson’s (1958) notion of asset fixity, which is of most immediate
application for individual firms. This generalization works on the
assumption that salvage markets generally differ from acquisition
markets. If this were not the case, the idea of unconstrained quasi—
fixity would be sufficient. Transaction costs, which are the core of
Johnson’s base-price distinction, are not part of this approach.

Summary of the cases. In summary, four conditions described above
could obtain for each input:

1. The case of new purchases (I) constrained by input

supply capacity.

8. The "normal" case of I greater than zero.

38

3. The fixity case of I equal to zero.

4. The salvage case of I less than zero.
Except as qualified above (coefficient equality for parallel vertical
or sloped input supply segments), all coefficients would shift for each
of these cases for each input. With more complex input supply con-
straints (e.g., a gradually steeper upwardly-bending supply curve), the
number of possible coefficient shifts become infinite. In the case of
multiple inputs, possible combinations of these cases multiply as each
case for each input implies a different value for each coefficient.

The occurrence of these cases in agriculture, and their effects on

agricultural supply, is the subject of the next chapter.

CHAPTER THREE

CHARACTERISTICS OF AGRICULTURAL SUPPLY

The theory just developed can be used to examine agricultural
supply elasticity and reversibility in the light of available facts and
data. Theoretical guidance is necessary because results depend to a
large extent on the form in which data are analyzed.1 Theory will
serve as a guide in this chapter in discussions of agricultural input
supply, implications for agricultural output supply, the supply of
exported grains, and other factors affecting supply. Although the
discussion will be couched in terms of U.S. agriculture, most observa-
tions will also apply to agriculture elsewhere; many will apply to
other sectors as well. Specific points relevant to other cash grain
and oilseed exporters will be covered in the next chapter on empirical

methods.

Input Sgpply in Agriculture

As mentioned in the Introduction, input supply inelasticity has
long been used to explain agricultural supply inelasticity. As des-
cribed above, short-run input supply inelasticity can be related to l)
long-run supply inelasticity, 8) short-run fixity or quasi-fixity of
inputs which are supplied elastically in the long run, or 3) input
supply shifters (such as non-agricultural demand) that correlate with

agricultural input demand. Characteristics of agricultural inputs that

 

‘ Intriligater, 1978, pp. 187-90. For a related example of
such dependence, see Woods et al. (1981), in which empirical
results vary with the empirical formulations used.

33

34
produce such supply behavior will be discussed in this section. A
position compatible with this discussion can be found in Tweeten

(1969). The following categories of inputs are considered:

labor;

machinery and buildings;
purchased non-durables;
farm-produced durables;
farm-produced non-durables; and

land.

The section concludes with an overview of the interactions of inputs,
and a summary analysis of agricultural input supply.

nggg. Economists commonly think of labor as a variable input;
whether variable or not, laborers are durable assets. Although labor
is an important input in agriculture, the sector does not require a net
input of new workers and managers, because production of potential
farmers within the secor, labor-saving technical change, and low farmer
"depreciation rates" make agriculture a net supplier of people to other
sectors. As shown in Figure 3.1, the demand for new laborers is so low
that the labor demand curve becomes a supply curve for net disinvest—
ment of laborers (1(0), and the labor supply curve from other sectors
becomes an input demand curve (D) for laborers. Even in the odd
periods in which agricultural labor use does not fall, there is a

continuous movement of people out of the sector.

35

”it:

 

 

0 I

Figure 3.1. Agriculture as a net supplier (S) of
laborers (I) to other sectors (D).

Table 3.1. Labor used in U.S. farming (millions of hours), 1965-83.

Source:

 

Year All Farm Work All Crops
1965 7,335 3,416
1966 6,858 3,148
1967 6,677 3,104
1968 6,416 3,013
1969 6,198 8,973
1970 5,896 8,788
1971 5,741 8,757
1978 5,433 8,681
1973 5,381 8,667
1974 5,178 8,657
1975 4,975 8,630
1976 4,788 8,556
1977 4,654 8,530
1978 4,946 8,449
1979 4,347 8,436
1980 4,881 8,443
1981 4,808 8,446
1988 4,035 8,378
1983 3,681 8,186

 

USDA-ERS, 1985b.

36

The decline in labor use is show in Table 3.1. The slight
increases in crop labor in 1973 and 1981 do not necessarily contradict
the notion of continuous salvaging for three reasons. First, the labor
increases could have come from non-crop farm uses. Second, labor hours
per worker may have increased at these times, so worker numbers still
could have fallen. Third, even if numbers did not fall, they would not
have fallen enough to cut off net out-migration.

Although mobility is easier for young people who prepare for other
work, out-migration is more difficult for older people without nonfarm
skills. The specialized knowledge and self-discipline of farm man—
agers, in particular, limit their substitutability for other workers
both on and off the farm. Spatial isolation, cultural differences, and
ingrained preferences are further bottlenecks to movement. In effect,
as the demand for farm labor falls and more workers move out of
agriculture, the characteristics of the marginal out-migrant change:
the base earning potential (wm) of migrants falls, so demand is
lowered, even though the demand curve for any particular kind of worker
may be quite flat (due to the greater size of the nonfarm economy).
Hiring costs (Nadiri and Rosen, 1969) and labor unions may also
constrict movement, as does the correlation of the demands for agricul-
tural and non-agricultural labor (D.G. Johnson, 1950).

The effect of all these factors is to make labor a quasi-fixed
input in agriculture. Because workers are constantly leaving the
sector, occasional-fixity would not be expected. Such a condition is
conceivable, however. In this case, a base acquisition wage higher
than the base salvage wage, as in Figure 8.8, would lead to slower

expansions than contractions. (The case of net acquisition is so

37
unlikely as to make the counter-case irrelevant.)

flachingryuand Buildings. These purchased durables represent, for
agriculture, the classic case of quasi-fixity discussed in the litera-
ture and reviewed in the previous chapter. They might be considered,
therefore, to be a major source of lagged adjustment in agricultural
supply. Two factors alter this analysis, however, and will be consid-
ered in more detail in the next two chapters. First, the fact that
service flows from stocks are actually more flexible than assumed so
far may make machinery stocks and purchases less of an influence on
machinery use, and, hence, on agriculture supply and supply adjustment.
Second, credit availability may affect machinery purchases to an extent
that diminishes the role of farmers’ machinery stocks, thus consider-
ably complicating the analysis of lagged adjustment. (Buildings can
best be thought of as a complement to machinery, animals, or storable
output. The latter case is discussed below under Egrmiproduced
durables.)

Regarding constraints on investment, a lack of aggregate salvage
markets for agricultural machinery precludes gross disinvestment.
Constrained occasional-fixity does not result, however, because gross
investment has never fallen nearly to zero (Tostlebe, 1957, p. 146;
Table 3.8, below). (Although this may not be true for all types of
machines in all areas, it is true for aggregate statistical purposes.)
Even in the worst of times, mechanization has been a major force
displacing labor.

Even if history were not a guide, capacity-constrained purchases,
as in Figure 8.7, would seem to be the more probable case of occasion-

al-fixity. One reason is that plant capacity expansion responses

38
require considerably more than one year for completion. The other
reason is that normal plant operation (N on Figure 3.8) is well above
50 percent of capacity (C). (For historical evidence, see Table 3.8.)
With symmetrically-distributedE random demand (f) centered on normal
capacity utilization, the capacity constraint (I*=C) would occur more
often than the no-salvage constraint (I*=0). (This can be seen by the

relative thickness of the two tails at these points.)

 

// f

—-—" f(I*=C)
-——---;--—-. ----- _ f(l*=0)

 

Z
('1
0—0

Figure 3.8. The relative likelihood of two cases of occasional-fixity
given the frequency distribution of demand for I (f).

As explained in the previous chapter, the net effect would be for
supply of these inputs to respond more slowly in expansion than in
contraction at the high end of booms and, therefore, on average.
Available capacity expenditure data (Table 3.8) show that the supplying
industry itself has not experienced significant no-salvage constraints.
Because imports and exports are each only about 10 percent of U.S.
machinery production (USDA-ERS, 1985a), it is sufficient to consider

only domestic capacity and its utilization.

 

r This would be true with demand distributed at all symmetric-
ally.

Table 3.8.

(deflated by its Producer’s Price Index),

39

Gross investment in farm machinery and equipment

1965-84,

and that industry’s fourth-quarter practical capacity

utilization rate,

(deflated by CPI), 1978—88.

 

Year Investment Capacity
(millions of 1967 Utilization
dollars)

1965 3,431 -
1966 3,830 -
1967 4,171 -
1968 3,581 -
1969 3,313 -
1970 3,550 -
1971 3,348 -
1978 3,801 -
1973 5,166 -
1974 4,886 .86
1975 4,318 .78
1976 4,394 .66
1977 4,861 .65
1978 4,900 .58
1979 5,068 .58
1980 4,105 .68
1981 3,545 .48
1988 8,565 .31
1983 8,334 .38
1984 8,166 .48

1974-84, and new capital expenditures

New Capacity
(millions of 1967
dollars)

---d‘“-_---‘-------

Sources: USDA-ERS, 1986; USDC, 1984 and earlier issues; USDc, 1988a.

No earlier comparable numbers for capacity utilization and new capacity

are available, due to changes in responsibility for data collection.

40

Purchased non-durables. Non durables purchased by farmers include
materials like fertilizers, herbicides, insecticides, and fuel.
Although these inputs are variable to farmers, they come from plants
whose capacity is not. Input prices, therefore, can generally be
expected to respond to changing demand. For some inputs, like fuel,
alternative uses make this price response low. For specialized inputs
without alternative uses, like fertilizer, price response can be high,
For other inputs with specialized uses but non-specialized feeder
stocks or fixed plants, response would be intermediate.

As described in the previous chapter, such endogenous prices for
variable inputs will reduce the price elasticity of agricultural
supply. With lagged capacity adjustment in the input-supplying
industries, however, lagged adjustment and greater long—run elasticity
are induced in agricultural supply. (The analysis would be the same if
the assets of the input industries were considered to be a part of
agriculture itself.) The above conclusions regarding machinery would
then also apply to these inputs.

These conclusions would hold both for quasi-fixity and occasional-
fixity. Normal operating capacity greater than 50 percent of capacity
would constrain input production and use more often in expansion than
in contraction, thereby affecting agricultural production in the same
way. (See Table 3.3.) The fact of continuous investment in these

industries demonstrates a lack of no-salvage fixity (Table 3.4).

41

Table 3.3. Practical capacity utilization rates for the
agricultural chemical industries, fourth quarter, 1974-84.

_—-‘--——--_--—--—-—-—--——-———----—--——-—-——-——_—-—--—-—--—----—--————.

Nitrogen Phosphate Fertilizer
Year Fertilizers Fertilizers Mixing Pesticides
1974 .71 .98 .49 .71
1975 .81 .76 .55 .81
1976 .88 .56 .66 .84
1977 .98 .73 .60 .69
1978 .97 .77 .75 .87
1979 .89 .98 .61 .70
1980 .88 .89 .70 .58
1981 .86 .61 48 .58
1988 .74 .59 .58 .49
1983 .84 .87 .67 .56
1984 .84 .79 - 61

Source: U.S. Department of Commerce, 1984 and earlier issues.

Table 3.4. New capital expenditures in the agricultural chemical
industries, (millions of 1967 CPI dollars), 1978-88.

 

 

Nitrogen Phosphate Fertilizer
Year fertilizers fertilizers mixing Pesticides
1978 86 53 14 38
1973 78 66 17 41
1974 105 808 84 66
1975 848 188 31 189
1976 355 138 80 110
1977 405 68 83 181
1978 154 113 85 189
1979 91 54 39 96
1980 46 130 85 87
1981 56 858 18 93
1988 50 79 18 98

Source: U.S. Department of Commerce, 1988b.

48

Farm-produced durables. Farm-produced durables are predominantly
of two kinds: breeding livestock and land improvements. Breeding
livestock are generally acquirable from (or salvagable to) the produc-
tion of the same marketable output that they produce. Market prices
may be affected thereby, but this is not of immediate consequence to
the purposes of this study. Unless a whole population (and more) was
desired for breeding, no constraint would bind, and this would be an
extremely unlikely event.

Land improvements generally involve the application of purchased
durables or their services to alter the productivity characteristics of
land. Examples include clearing, draining, irrigating, and fencing.
The effect is to make improved land behave like a specialized durable.
Because the supply of purchased durables would be capacity-constrained,
expansions could be slowed relative to contractions. Although salvage
markets for farm land exist, improved land could be occasionally-fixed
if improvements caused base acquisition and salvage rents to differ.
This topic is discussed in more detail below.

Farmiproduggd non-durables. Farm-produced non-durables, like feed

 

and seed, are variable at given prices for individual production
processes. Because of year-long production lags, however, their short-
run supplies are virtually inelastic. (Storage possibilities alter
this somewhat.) Because prices for these inputs are derived from
demands for end products, they are, in effect, goods-in-process.
Although such multi-stage production is of interest in itself (see,
e.g., Chavas and Johnson, 1988; Chambers and Vasavada, 1983), it is not
of particular interst to the problem at hand. Knowing that these

inputs are fixed in the short run allows ignoring them for present

43
purposes.

Land. Land is the most problematic input category, because,

 

although total area is fixed, usable area and productivity can vary
greatly. Because this variation is accompanied by use of inputs that
are durable, depreciable, and bound to the soil (fertilizer residues,
irrigation and drainage improvements, fencing and windbreaks, etc.),
land might behave like a quasi-fixed input. On the other hand, some
empirical results indicate that land is a freely variable input in crop
production (Karp, Fawson, and Shumway, 1985), probably due to alternate
uses like grazing and timber production.

Whether fixed, quasi-fixed, or variable, it is shifts in the
supply response of land that interests us here. These hinge on
behavior of land in the vicinity of I*=0. (Although capacity-con-
strained purchases of durable improvements may limit land use expan-
sion, this is merely as a complement, as with machinery; in neither
case is land fixed in itself.) This case depends on the effect of
durable improvements on the difference between base acquisition and
salvage prices, as mentioned above. For now we will state that this
effect is basically neutral, as will be discussed below under The
§gpply gf Exported Engigg.

Inputs in combination. As discussed in the previous chapter and
alluded to in the previous paragraph, supply elasticities of agricul-
tural inputs affect one another’s levels of use. (This is evident from
both the input price response (w,) and fixity (Dv and D.) terms in the
coefficient matrices on page 84.) These interrelationships are
affected as well by characteristics of the technical production process

(the original a and Fvv terms). Because reliable measurement of these

4‘,
technical relations depends on proper identification of the other
components of the agricultural supply system (and because all these
relations change through time), it is not clear that we really know
much about these terms. Some specific representative observations can,
however, be made.

If, for example, tractors and tractor drivers are complements in
production, increasing the use of one factor raises the marginal
product of the other (i.e., their Fyv term is positive). With the
quantities of other inputs held constant, this implies that an exogen-
ous price decrease for either factor would lead to an increased use of
both. An endogenous input price limits this effect, however, by
decreasing the own-price response of own-quantity and, thereby, the
other-quantity’s marginal product. The more severe the quasi-fixity of
any factor, the more severe the resulting quasi-fixity of its comple-
ments, even to their own exogenous price changes and even if they
themselves are perfectly variable. The fixity of an input is the
extreme case of limiting the price response of its complements, but the
result would not be to eliminate it. Complementarity, by the way, is
the most common type of relationship between inputs (Hicks, 1946, pp.
94—98).

If, for another example, cultivating machinery and herbicides were
substitutes, increased use of one would lower the marginal product of
the other (a negative Fvv term). With other inputs constant, a
decreased price for one increases its use and lowers that of the other.
In this case, endogenous prices accentuate these effects, with fixity
again the extreme case. (As one input becomes less responsive to

exogenous changes, its substitutes become more responsive.)

45

The actual measuring of these effects becomes more complex when
other quantities can vary, but the theoretic work of this paper makes
it possible to structure the econometric estimation of these relation-
ships, among others. For a good example of such work, see Hsu (1984).

Summary. On average, then, the use of the inputs described above
is more likely to be constrained in expansion than in contraction. All
inputs are either neutral with respect to occasional-fixity or more
prone to capacity constraints. None are more likely to be subject to
the no-salvage constraint.

Among the apparently neutral factors are labor, breeding stock,
farm-produced non-durables, and land. Labor is always quasi-fixed and
salvaging (through, if occasionally-fixed, it would be expansion-
constraining). Breeding stock is quasi-fixed and unlikely to be
constrained. Farm-produced non-durables are fixed for our short-run
purposes. Land is a special case, shown below to be neutral. For the
most part, these are farm produced factors.

The more occasionally capacity-constrained inputs are the pur-
chased factors. Machinery and buildings are quasi-fixed. Purchased
durables fixed to land become quasi-fixed. Purchased non-durables are
from fixed plant and equipment. All of these inputs are possibly
occasionally subject to capacity constraints. They can be expected to
dominate the neutral factors, thereby making their complements more
sluggish to expand in use than to contract. Although use of substi-
tutes will become more responsive as that of constrained factors
becomes less responsive, the net effect on output must be to become
less responsive.

The conclusion that expansions are likely to occur more slowly

46
than contractions is supported by empirical results reported in Woods
et al. (1981, p. 17). 0f the many empirical tests of irreversibility
attempted in that paper, one is compatible with the theoretic findings
in this study’s previous chapter (as justified in more detail in the
following chapter). That equation uses a "shifter" for each coeffi-
cient in a regression of aggregate agricultural input use on: 1) that
measure, lagged, and 8) the lagged aggregate output-to-input price
ratio. The study covered the U.S. from 1948 to 1977. (Note, however,
that the price ratio is the inverse of that which was judged to be
appropriate in the previous chapter.) Simultaneity problems were
avoided by using last period’s input prices, and by segmenting the
period according to rising and falling price ratios rather than rising
and falling input use. (The latter technique can only be used when

there is only one price variable.) The results are shown in Table 3.5.

Table 3.5. Regression on input use of lagged prices and inputs.

Intercept (P/W)...1 Inputszu,
Coefficient** 87.885 .038 .681
(s.e.)* (13.80) (.086) (.155)
Shifterxxx -16.353 -.014 .187
(s.e.)* (88.94) (.039) (.857)
R3 = .885 Durbin-h = 1.813 (reject hypothesis of serial

correlation at alpha = .05)

* Standard error of estimates.
** Coefficients for periods of falling price ratios.
*** Add-on to coefficients in periods of rising price ratios.

47
Implicptions for Aqriculturpl Output Supply

It should now be possible to draw some conclusions about agricul-
tural output supply based on the above conclusions regarding agricul-
tural input supply. This will be done first by establishing a theoret-
ic basis in long-run agriculture, second by introducing unconstrained
quasi-fixity, and third by introducing input occasional-fixity. The
section will conclude with a discussion of cobweb-like cycles.

Long-run supply. It would be helpful to establish a concept of
long-run supply to serve as a basis for short-run supply analysis. The
most obvious initial base is the horizontal long-run curve with all
factors variable. Whether or not fixed factors exist in agriculture in
the long run, this model is not sufficient for present p‘rposes.
Because of the consideration of endogenous (upward-sloping) input
prices and opportunity costs in the production of joint outputs, it
would not be useful to assume the prices of all inputs and other
outputs constant for the aggregate industry. To show both short- and
long-run effects together, the supply of an output will be shown as an
(inverse) function of its price, assuming fixed exogenous other-price
factors but variable endogenous other-price effects. Such an upward-

sloping long-run supply curve is shown in Figure 3.3.

«a

0,»

 

 

0

Figure 3.3. Long-run output supply given endogenous
prices of inputs and other outputs.

§gpbly with quasi-fixity. In the theoretical model developed in
the previous chapter, a linear short-run supply curve with linear long—
run supply and linear input adjustment costs was derived. Short-run
supply would then be a steeper intersection of the long-run supply
curve, as shown in Figure 3.4. The position of the short-run curve on
the long-run curve would be an increasing function of input stocks left
over from the previous period. Movement of the short-run curve along
the long-run curve from one period to the next is a linear function of
the deviation of price in the first period from that of the intersec-
tion of the two curves in that period (equilibrium). Equilibrium is
the limit of the adjustment process given price. With linear input
supply curves adjustment to equilibrium would be of equal speed

regardless of the direction of adjustment.

49

08". I

Dca

 

 

D

Figure 3.4. Long-run (QLR) and short-run (Dawn)
output supply with unconstrained input quasi-fixity.

Sppply with ocgpsigppl-fixity. With input occasional-fixity, as
described in the previous section, movement along the quasi-fixed
short-run supply curve can be constrained. As more inputs become fixed
with larger departures from equilibrium, supply becomes increasingly
constrained, as shown by the sigmoid curve (Gene) in Figure 3.5. Note
that, in keeping with the assumption of more binding capacity con-
straints in expansions than no-salvage constraints in contractions, the
curve "turns up” nearer to equilibrium than it ”turns down." Similar-
ly, the shorterun curve will shift out more slowly along the long-run
curve (for a given departure of price from equilibrium) than it will

shift in, again reflecting asymmetric constraints on quasi-fixity.

50

 

 

 

0

Figure 3.5. Constrained short-run supply with
input occasional-fixity.

Lgplicptiong_for cyclicplity. With the cobweb assumption of
expected price equal to last period’s price, the constrained short-run
curves just developed have interesting implications for agricultural
cycles. Because demand for agricultural inputs is generally thought to
be inelastic, it is entirely possible that the demand curve is steeper
than the supply curve at equilibrium, as shown in Figure 3.6. In this
neighborhood, therefore, a cobweb is liable to be explosive, although
convergent to a stable cycle as prices move away from equilibrium.
This possibility, cited by Waugh (1964) is known as a ”limit cycle"
(Baumol, 1959, pp. 873-877). It would be further dampened by adjusting
shifts in the short-run supply curve or by rational price expectations,
but it would not necessarily be eliminated. This is an interesting
observation, because it helps to explain the existence of agriculture
cycles (even after long experience and supposed learning), and also
explains some regularity in their amplitude. Notably, Waugh believed
"that the lagged-output curves for most commodities are shaped somewhat
like the one shown in Figure [3.61" (1964, p. 749). Conclusions about

limit cycles are not affected by the fact that he was referring to the

51

sigmoid shape rather than irreversibility.

 

 

 

 

Figure 3.6. Limit cycles with input occasional-fixity.

The Supply of Cash Grain;

The theory presented in the previous chapter and the observations
of this chapter set the stage for discussing the supply of cash grains
and establishing a link between theory and econometric specification in
this section. Supply analyses for numerous countries would be neces-
sary to accomplish the broad task of examining world price and trade
prospects under various policy regimes. This section focuses on the
United States as an example of how these examinations can begin.
Specific points about other nations will be covered in the next chapter
on gppirippl Mgthpds.

The multi-output analysis outlined above could be applied to U.S.
agriculture as a whole. If a part of the sector could be separated
from the rest without losing much information, the analysis could also
be applied to that subsector. Cash grains meet this criterion: they
are grown jointly and are essentially non-joint with the rest of

agriculture. Therefore, our theory can be applied to estimating their

58
supply.

Wheat, feed grains, and soybeans (the last not a grain) are the
crops of interest. They are generally grown in the same parts of the
country (the Corn Belt and the Plains) and they share extensive margins
of cultivation. Many of the same durable inputs are used for more than
one of these crops, and their different temporal demands facilitate
this joint use. As a result, many firms grow more than one of these
crops. (Risk reduction may also help explain crop diversification, but
risk is not dealt with here.) These characteristics suggest the
existence of a joint technology, as attested to by the common presence
of each other’s cross-price terms in supply estimation. (See, e.g.,
the MSU Agriculture Model.)

The limitation of joint production to include only these crops
(i.e., separability) can also be defended. Substitution with other
crops is too slight to measure with national data. Although some
inputs may be shared with other crops, the degree of such sharing is
generally small enough to ignore.

One group of products, forage crops, may be an exception to this
rule. They are grown in the same regions as the cash grains and use
some of the same durable inputs. Furthermore, forage crops are often
used in rotation with exported grains, although the increased use of
chemical fertilizers and pesticides has diminished this practice. For
these reasons, wheat, feed grains, soybeans, and forage crops will be
considered the joint technology for supply analysis.

The inclusion of forage crops in the joint technology raises the
important issue of land conversion costs. These include extraordinary

land preparation costs and opportunity costs of scrapped forage

53
production. More ‘durable land improvement costs that may accompany
land use changes are also pertinent, as mentioned above. These issues
determine the reversibility of land use decisions, and thereby affect
the reversibility of crop supply. They are the focus of the remainder
of this section.

For the purposes of this analysis, the total supply of land to the
subsector is considered fixed. In other words, the effects of non-
subsector land use values on current production decisions will be
ignored. This approach is particularly safe if it can be assumed that
other land uses impinge primarily on forage, because the supply of
forage is not of direct concern. The focus of this study is grains and
soybeans, and the only relevant other land use effects are assumed to
be those of forage price and presence on these land uses. The land use
decision, then, is the allocation of the fixed land base between
alternate subsector crops.

For analyzing this decision, the same graphs will be used as for
other inputs. In this case, gross investment (I) will be considered to
be an increase in a non-forage crop use (L). The depreciation rate on

land is assumed to be zero, so:

I = L - (1-d)L._, = L - L,-,

This terminology is consistent with definitions used for other inputs.
(Depreciable land improvements will be considered below.)

For alternate land uses without conversion costs, the graphical
analysis is quite simple (see Figure 3.7). The marginal value of land

for, say, corn (MVC) is the demand curve for more corn land in the

54
right-hand quadrant and the supply curve of more forage land in the
left-hand quadrant. The marginal value of land for forage (MVf ), on
the other hand, shows the reverse: net land supply in the right-hand
quadrant and net land demand on the left. The curves slope as they do
(decreasing marginal returns) due to specialized quasi-fixed factors.
If land is of non-uniform quality and the better land is used for corn,
both curves would be lower on the left-hand end than if land were

uniform.

MV,

MVc

 

 

0 I

Figure 3.7. Land use equilibrium without conversion costs
(w = the price of land).

The intersection of the marginal value curves in Figure 3.7 shows
land use in equilibrium (no net change). If the price of corn were to
rise, its marginal value curve would shift to the right (MV,’ in Figure
3.8), and land would shift into corn use. With the same corn price in
the next period and all quasi-fixed inputs in equilibrium, a new land
equilibrium (like Figure 3.7, but with a higher land price) would
result. If quasi-fixed factors took longer to adjust, gradually

smaller additions to corn land would continue as the system converges

55
to equilibrium. If the price of corn had fallen instead of risen, this
same analysis would simply have been reversed, with the speed of

adjustment unchanged.

\ \ MVf
\
\

\( MVc’

\

\ MVC

 

 

0 I

Figure 3.8. Land use shift to corn without conversion costs.

This is the case of an input with a salvage market with price
flexibility equal to that of the acquisition market and equal base
salvage and acquisition prices (unconstrained quasi-fixity). This
analysis is sufficient for land use changes between wheat, feed grains,
and soybeans, for which there are no significant conversion costs.
With conversion costs, however, the analysis becomes more complex. In
Figure 3.9, conversion costs are added to the marginal value of forage
curve in the right-hand quadrant to derive the supply curve of new corn

land. (There are no conversion costs for new forage land.)

56

 

"V: n

 

 

0 I

Figure 3.9. Land use shifts with conversion costs.

In this case, corn-price changes in the neighborhood of MVC will
produce no change in land use. Corn price changes resulting in MVC’
(or MVC") will produce additions to (or subtractions from) corn land
with the same marginal sensitivity to corn price. This is the case of
corn land with a salvage market with base acquisition price greater
than base salvage price and equal price flexibilities in the two
markets.

The net result of this analysis is that, unless land use changes
are strongly uni-directional, the net effect of conversion-cost-based
occasional-fixity is neutral. With land use conversion going back and
forth, as they have in the United States, conversion costs would at
times constrain expansions and at other times constrain contractions.
Although the actual effect at particular times might be identified, the
average effect, as stated in the section on agricultural inputs, would

be neutral.

57

As mentioned above, land use improvements are also pertinent to
this analysis, because they are durable, are fixed to the land, and
affect land productivity. If such improvements raise the marginal
productivity of land for one use more than for the other, the above
analysis is altered by inserting durable "kinks" in the marginal
product curve. Their durability means that land use changes can move
such kinks off the vertical axis, as in Figure 3.10. Because of the
reasons cited above, such kinks would tend to have a neutral effect
unless land use changes were strongly uni-directional. Depreciation of
improvements would tend to make the kinks shrink through time. More
divisibility of improvements would tend to make them not appear as

kinks at all.

 

 

0 I

Figure 3.10. The effect of durable land improvements on land supply.

Other;Egctors,Affgctinq Supply
In addition to the items mentioned above, other factors affect the
supply of exported grains. These include export infrastructure, input

imports, credit, government policies, and technical change.

58

In addition to the effects of durable inputs to farming, new fixed
infrastructural investments are often cited as causes of irreversible
export supply. For a combined production/export system responding to
port prices, this would be the case of occasionally-fixed inputs
(communication, processing, transportation, and port facilities) as
discussed in the previous chapter. Identifying the system in this way
could lead to no-salvage constraints (on these facilities) as well as
to capacity constraints. Since periods of such constraints might be
identifiable, segmentation of the data set to allow for them might be
advisable. In any event, new lower-variable-cost infrastructure would
then pass on higher prices to the farm; the analysis of farm-level
supply response to farm-level prices, however, would not be affected.
Complete analysis of export supply, therefore, must distinguish between
these two levels of analysis.

Import possibilities for inputs could change the shape of input
supply curves. If imports are a continuous permanent part of the input
market (e.g., potassium from Canada), they would create no problems.
If new sources enter the market as domestic input capacity is reached,
however, supply curves could have additional kinks and new slopes.
These would suggest a need for additional coefficient shifters in the
analysis. Obviously, changing policy with respect to these imports
could have similar effects.

Farm credit availability has a major effect on durable input
purchases. In addition to the effects of prices and market interest
rates, farm income strongly influences investment due to imperfect
capital markets and a high degree of internal financing (Johnson, 1947;

Tostlebe, 1957). In effect, constricted capital flows cause a

59
separate, endogenous interest rate to prevail in farming. One approach
might be to consider cash balances and capital gains to be factors of
production that influence adjustment costs, but this could be quite
complex. In any event, government policies with respect to income,
'credit, and insurance must be kept in mind.

Numerous other government policies also affect agricultural
supply. To the extent that these policies work directly on prices, no
special analysis is required; the use of prices in the analysis is
sufficient. Land set-aside requirements and diversion programs,
however, work directly on supply. Variables representing these
policies have been useful in empirical work (see, e.g., Houck and Ryan,
1978; Wailes, 1983). To the extent that these policy variables are
over-simplified, omitted, and autocorrelated, their effects will bias
the parameter estimates for lagged endogenous variables (Griliches,
1967, pp. 33-34).

Technical change that increases the efficiency of certain inputs
will tend to change the relative demand for inputs and the supply of
outputs. To the extent that input mixes differ by output, the supply
of some outputs will increase more than that of others (some of which
may fall). It is standard to represent such changes with time trends,
and that approach could be useful here. To the extent that other
variables (especially lagged endogenous variables) embody these trends,

seperate representation may not be necessary.

CHAPTER FOUR

ECONOMETRIC METHODS

Introduction

Now that the problem for study has been defined, a body of
applicable theory identified, and a sense for its application to the
problem established, it is possible to specify techniques for measuring
parameters and testing hypotheses econometrically. Major hypotheses to

be tested include:

H1. For wheat, feed grains, and soybeans in the United States,
short-run and long-run supply responses differ.

H8. For these crops, supply response is constrained more by input
capacity in expansions than by lack of salvage markets for

durable inputs in contractions.

These hypotheses were examined somewhat informally in the previous
chapter. The purpose of this chapter is to examine methods for testing
these hypotheses more formally. These methods might also be applied to
measure other foreign and domestic supply response for projecting the
effects of alternative U.S. policy proposals.

To test these hypotheses, it has been theorized above that supply
of each of these crops can be approximated by a linear function of
their own prices, input prices, and quantities of durables used in the

previous period:

60

61

Q = f(P’”9L9—1)

According to the theory, all prices can be normalized by the price of a
numeraire: forage. (Another alternative, normalization by the Consum-
er’s Price Index, is discussed below.)

To generate useful econometric specifications, it will be neces-
sary to couch this relation more precisely according to statistical
principles for the examination of available data. That will be done in
this chapter by the application of a priori knowledge and the design of
minor hypothesis tests. These minor tests will be used to sort out
appropriate forms and techniques for testing the major hypotheses.

The chapter begins with a section on each of the above four
variable vectors, including discussion of relevant policy and struc-
tural change where appropriate. Then, after a section on the role of
credit, debt loads, and income, opportunities for efficiency gains via
cross-equation restrictions will be explored. The chapter concludes
with a review of approaches to handling the need for coefficient

shifters, and a methodological note.

Dependent Variables

Although the language of this study has been couched in terms of
supply, it is not clear which supply variables are most important. If
export supply is of concern, the role of export facilities (in addition
to farm production) must also be considered. This would be possible
for a country (e.g., Argentina) in which there are no significant
stocks and consumption is sufficiently predetermined; it would simply

be a case of a more comprehensive production analysis. In the U.S.,

68
where considerable stocks are held and grain feeding rates are endogen-
ous, the problem is much more difficult; although farm production is
predetermined, stockholding and consumption are determined simultane-
ously with prices. Such a model would be too complex for this study.

Even if looking only at farm-gate supply, the proper choice of
dependent variables is not straightforward. Because such a large
component of crop supply variation is caused by random weather-deter-
mined yield variation, it has become standard in supply estimation to
use planted acreage to represent intended production. (See, e.g.,
Nerlove, 1958b, pp. 66-68; Behrman, 1968, pp. 151-154.) Assuming
predetermined growth of expected random yield, quantity supplied is
proportional to planted acreage and no information is lost. This
assumption has been challenged by Houck and Gallagher (1976), who found
U.S. corn yields to be responsive to a corn-to-nitrogen price ratio
from 1951 to 1971. This relationship apparently disappeared for the
period 1978 to 1980 (Menz and Pardey, 1983), and was never found for
any of ten regions of Kentucky, 1960 to 1979 (Reed and Riggins, 1988).
Perhaps because such relationships are even harder to find for other
crops and other yield components, the assumption of predetermined yield
growth is still quite common (e.g., the MSU Agricultural Model; Lee and
Helmberger, 1985, p. 195).

One approach to supply analysis with planted acreage estimation is
to define supply as acreage multiplied by yield. This ignores,
however, that yield is normally expressed in terms of acres harvested,
and that the harvested-to-planted acreage ratio is not constant. Not
only has this ratio varied considerably; it can be thought of as

determined by current price and yield. The facts that these latter two

63
variables are related and that harvested acreage and price are deter-
mined simultaneously complicates the empirical estimation of these
relations. For present purposes, therefore, this study will focus only
on planted acreage and yield as measures of supply.

Before leaving the topic of yield, two important considerations
remain. The first is that yield growth represents a technical change
that should affect the response of acreage to price. The general topic
of technical change is covered below under Lagged Endogenous Variables,
but it should be mentioned here that, because yield growth has not been
constant (see Menz and Pardey, 1983), such change may not be adequately
modeled by simple time trends. Second, because the unavailability of
planted acreage data in many countries necessitates the use of harvest-
ed area data instead, some of the above-mentioned caveats of using such
data should then be born in mind.

There should be no confusion that acreage planted by crop is input
demand rather than output supply; nothing in the theory of Chapter Two
suggests that the joint-production model is capable of generating the
allocation of input demands to specific outputs. (Also see Shumway,
Pope, and Nash, 1984.) Because the subsector under consideration is
assumed to face fixed land supply, its only land demand equation would
be for the determination of land rent. It should be noted that forage
acreage is the remainder of total acreage after accounting for acreage
planted to other crops. If these equations are estimated simultaneous-
ly, the forage equation must be left out to impose the restriction of a
fixed land base.

As implied by the theory, variable and quasi-fixed input use and

price equations can also be estimated to provide additional evidence

64
about input supply elasticities and reversibilities. If cross-equation
restrictions can be imposed with supply equations, estimates of all
equations can be made more efficient. (See Cross-equation Restrictions
below.) If restrictions cannot be imposed, the independently estimated
equations can still yield valuable results, and might even reveal
effects not detectable in supply estimation.

This raises another important point about input use. Both input
use and output supply equations are assumed to incorporate information
about input supply. In the theory chapter, input supply relations were
assumed to be stationary because the theoretical analysis was intended
to show how equilibrium is determined in one period. When time series
data are used in estimation, however, this stationarity assumption may
be inadequate. Trend shifts in otherwise-stationary input supply
curves present no special problems, but shifts based on short-run
capacity utilization, for example, can introduce complications. One
approach to the solution of this problem might be to also estimate
explicit input supply functions, inculding their own short- and long~
run components. This approach is discussed below on page 70, and is
relevant to the section on ngffipignt Shifting.

Finally, because U.S. acreage set-aside and diversion programs
(including the 1983 PIK program) have been shown to be effective (e.g.,
Houck and Ryan, 1978), acreage "supplied" to these programs (or
separate participant and non-participant planted acreage equations)
might also be estimated. The alternative followed in this study is to
include seperate price-like policy variables in the standard acreage-
planted equations (see Crpp Prices, below). Too much information is

lost by simply ignoring the programs (see Lagged Endogenous Variables,

65

below).

Crop Prices

Appropriate output prices to use for this exercise include the
non-forage crop prices normalized (divided) by the price of the
numeraire (forage). This normalization deflates prices, accounts for
the price of an alternate output (without using another degree of
freedom), and is consistent with the above theory. In a case where
forage is not an alternative crop, of course, another numeraire must be
identified.

As an alternative approach to the normalization of crop prices,
the joint technology under consideration could be thought of as
including the rest of the total economy as the numeraire good. The
result of this approach would be to use a general price level indicat-
or, such as the Consumer’s Price Index, as the numeraire price for
normalization. This approach provides theoretical justification for
the common practice of estimating supply and demand functions of
discounted prices. Such a justification makes sense if, in fact,
important input and output prices have been excluded from an analysis
due to lack of data or problems of multicollinearity and degrees of
freedom, especially if the price index used is a reasonable measure of
price changes for these goods. If these goods provide a major share of
costs or revenues, as does labor in our case, this approach should be
preferred.

So far, the term "forage“ has been used somewhat indefinitely. In
fact, "forage" is being used to stand for a number of different outputs

including hay, pasture, and range. It is assumed for the purpose of

66
this study that these outputs are close enough substitutes in produc-
tion to be considered one output and close enough substitutes in
consumption for one price, that of hay, to represent them all. In
other cases, pasture rental or beef price data may be more readily
available.

Similarly, feed grains (corn, sorghum, barley, and oats) are quite
ready substitutes in consumption, somewhat less so in production.
Because of the collinearity of feed prices (simple correlations of
discounted prices range from .88 to .96 for the period 1955-83), it
will generally be advisable to use the price of only one feed grain,
usually that of corn, the most commonly traded. (See McKinzie, 1983.)
Because acreages of other feed grains in the United States are rela-
tively small, little damage is done by aggregating all feed grain
acreages into one measure as well. This will also facilitate the
imposition of symmetry conditions between supply equations when
appropriate.

Because of the time required for growing crops, expected prices at
times of input purchase and use are the relevant determinants of supply
response. These expected prices, however, are not observed. In their
place, prices received for the previous year’s crop are often used.
Alternatives include the use of futures prices or, for example, posted
Wheat Board prices in Canada. (U.S. loan rates, for that matter, could
also be considered as expected prices or determinants of expected
prices.)

Another common model of price expectations impose an infinite
geometric lag on past prices to derive "adaptive expectations” for the

future (Nerlove, 1958b). In reduced form, this model is similar to a

67

partial-adjustment model in one-period lagged price and output terms,
except that econometric error terms would be expected to be serially
correlated. A combined partial-adjustment/adaptive-expectations model,
which reduces to a form with two-years of lags in quantities (Nerlove,
1958b, p. 64), would consume too many degrees of freedom to be used
here. In any event, anticipating Muth (1961), the adaptive-expecta-
tions approach was disclaimed by Nerlove (1958c, p. 784) in favor of
the partial-adjustment approach.

None of these models takes advantage of forecasted supply informa-
tion directly, as would a rational expectations approach (Begg, 1988),
although futures price would be expected to include such considera-
tions. In spite of the usefulness of this approach in some cases
(e.g., Eckstein, 1984), the more involved modeling procedures have not
produced significantly different results in others (e.g., Karp, Fawson,
and Shumway, 1985). This is perhaps as should be expected given the
similarity of rational expectations reduced forms to those of other
distributed lag models (Tomek, 1985, p. 906).

As a result of these considerations of expectations, last-period’s
price is used in this study. Policy prices are incorporated into
program variables, which are minimized in number to avoid problems of
collinearity and degrees of freedom.

For the analysis of farm supply, farm-level prices are obviously
most appropriate. In other cases, world or port prices may have to
suffice, with the implicit assumption of constant marketing margins.
In this case, either official or black market exchange rates may be
required to convert prices to the same terms as numeraire prices.

As an alternative to the use of crop prices, some researchers have

68

used gross margins per acre as supply determinants (e.g., Salathe,
Price, and Gadson, 1988). This approach combines information on
yields, input prices, and technical change to restrict coefficient
relations and save degrees of freedom. Unfortunately, it runs the risk
of simultaneity problems by its inclusion of endogenous input price and
use information. The use of gross returns per acre avoids this problem
for inputs and for yield changes when treated as a trend.

Finally, it should be mentioned that the use of single price
expectations in a dynamic model implicitly assumes the stationarity of
current expectations over relevant time horizons. Although a rational
expectations approach could alter this, the marginal benefit of such a

model would not justify its cost.

Input Prices

The heart of this study’s concern with input prices is related to
their endogeneity. This is both the major source of its models’
dynamics and the primary cause of problems of estimation. These
problems result from the simultaneity associated with endogeneity.
(Expectations are not a major problem with inputs, because farmers
generally know prices when they make production decisions and order and
purchase inputs.) Prices are endogenous because, though often set by
manufacturers at the beginning of the season, they are set with
"rational expectations";‘ in other words, manufacturers have the same
information as farmers, and forecase demand accordingly. Endogeneity
also occurs because these prices can respond to demand somewhat during
the purchase season.

In the theoretical model, endogenous input price effects were

"reduced

69

into" the coefficient matrix. To implement this model

econometrically, only exogenous input price shifters would be used on

the right-hand side. This approach has four advantages:

The model can be estimated using ordinary least squares (at
least as considered so far).

The coefficients of output prices are mutatis mutandis with
respect to input prices, that is, they show the response of
supply to output price changes given induced changes in input
prices. Unless one was interested in modeling a whole
production system, there are obvious advantages; after all,
of what use are ceteris paribus coefficients for policy
analysis when the option of fixing input prices does not
exist? (A more general case for this position is presented
by Leamer, 1978, p. 808.)

The effects of exogenous input price shifters, such as their
respective input prices, can be identified separately.

These latter variables can be left out without biasing output
price coefficients (if orthogonal to them). This is helpful
because input price data often will not be available. If
these data add little information anyway, degrees of freedom

can be saved.

A second approach would be to simply use input prices as if they

were predetermined in ordinary least squares. The gains in terms of

low-cost estimations would be offset by inconsistent estimates, but

especially if the latter were not greatly in error, estimates could

7O
later be improved via two-stage least squares. This approach is
particularly attractive when the system to be estimated is not well
specified at the outset (Intriligator, 1978, p. 419).

A third approach would be to model input price directly. For one
advantage, this would provide a basis for specifying instrumental
variables for the first-stage estimates of input prices in two-stage
least squares regressions of input demand. In addition, input price
regressions can contribute to the efficiency of input demand estimators
via generalized least squares consideration of cross-equation error
correlations. (See Cross-eguation 3gptrictions, below.) Finally, this
approach allows for the direct examination of lagged adjustment in
input supply capacity, which is, for all practical purposes, just
another part of lagged adjustment in agricultural production. (For
non-durables, this is the same "first-order" quasi-fixity as provided
by durables whose supply is less than perfectly elastic; for durables,
lagged capacity adjustment introduces a "second-order" form of quasi-
fixity into agricultural production.) This is the approach taken in
this study.

An important question arises as to whether and how to include the
price of time (interest rates) in the analysis. If interest costs
vary, the present value of (and hence demand for) durables is affected.
This is shown in the theory chapter by the presence of i in the 8 term
on page 17. If B is part of the coefficient matrix, then that matrix
is clearly not constant (although this complication is frequently
ignored, e.g., by Karp, Fawson, and Shumway, 1985); annualizing durable
prices (w) by dividing by B does not solve the problem if i is erron-

eously assumed constant. One approach to this problem is to calculate

71
an annual user cost assuming expected interest and depreciation rates.
This approach is imperfect, however, since the endogenous component of
durable prices must remain in the coefficient matrix anyway. Another
approach would be simply to retain the 8"1 term in estimating equations
in a rather pg _pp way, and leave it in if it proves to be statistical-
ly significant, a particularly good strategy if durable use equations
are also estimated. The effect of these approaches on the imposition
of symmetry conditions is addressed below under Cross-equation Restric-

tions.

gagged Endogenous Variables

As shown in the theory chapter, lagged input quantities could be
important determinants of agricultural supply in a dynamic context.
Not only are they the base stock to which new durables are added, but
by establishing one end of the gap between current and desired stocks,
they also affect the level of new input prices and purchases. The
coefficients derived in Chapter Two (and to be estimated) include both
of these effects. (If depreciation rates were not known or undepreci-
ated lagged stocks used, the coefficients would also include deductions
for depreciation.)

To provide for comparison of durable stocks across time and to
adequately represent technical change in input industries, both prices
and quantities of inputs must be stated in terms of their service-
yielding capacities (e.g., horse-power of tractors). (For detailed
discussions of this point, see Griliches, 1963, and Jorgenson and
Griliches, 1967.) If, in addition, technical change in farming itself

changes the demands for various inputs, it would be reflected in output

78

supply and input demand shifts. If such shifts were fairly constant
over time (in absolute terms), they could be represented by simple time
trends. Such terms, however, would tend to be highly collinear with
terms representing percentage growth in input use. Because these
latter terms would be a part of measured coefficients of lagged input
quantities, simple trend terms would be highly collinear with input
quantities. As a result, the addition of trend terms to estimating
equations would show little statistical significance, so it might be
most useful to ignore such terms and accept their inclusion in the
coefficients of lagged input quantities. Both approaches can, of
course, be tried and tested; time might even prove to be the more
significant variable.

The U.S. Department of Agriculture maintains domestic input stock
data series, but such series may not be available for other countries.
Given this fact and the common use of the partial-adjustment model in
lagged output quantities (Askari and Cummings, 1976), it could be
helpful to use lagged output quantities as proxies for lagged input
quantities. This comparison is predicated on the assumption that the
use of lagged input variables is the preferred alternative. This
assumption is based on the fact that a lagged output vector cannot be
derived directly from a lagged input vector (at least not without the
additional information of a lagged expected output price vector). This
is because any given combination of inputs could produce many different
combinations of outputs and any given combination of outputs could have
been produced by many different combinations of inputs.

As it turns out, however, there may be good reasons for including

lagged output quantities as legitimate regressors in their own right.

73

One justificaiton would be the assumption of the adaptative expecta-
tions model described above (under Crop Prices). Although that notion
is not accepted for this study, others may be applicable. For one,
technical change that is very crop specific may show up more clearly in
the effect of lagged output than in that of lagged input. Second, the
complementarity of sequential cropping that leads to crop rotation
would only be expected to appear as a function of lagged output
quantities (Eckstein, 1985). Third, as a sort of combination of these
two effects, trends toward double-cropping or inter-cropping (such as
with wheat and soybeans in the U.S.) would be revealed in these terms.
There may be reasons to include both lagged input and output quantities
as regressors. Collinearity between the two could force a choice of
one, however; its coefficients would then be recognized as including
the effects of the other.

Regardless of which lagged endogenous regressors are used, they
will tend to pick up the effects of serially correlated excluded
regressors (Griliches, 1967, pp. 33-34). Because the included coeffi-
cients will be biased (upward for positive serial correlation in the
excluded variable), their standard errors biased down, and the standard
error of the regression too low, the partial adjustment specification
will generally look better than it would with a proper specification.
Perhaps the most obvious candidates for such omission already mentioned
are variables representing government policies and programs in the
U.S., but any serially correlated omitted variable that should be
included would have the same effect. This should serve as a general
caveat to the use of lagged endogenous variables as regressors, and may

help to explain the wide use of the partial adjustment model in

74

econometric work.

Qgedit, Debt, end Income

Little mention has been made so far of credit availability and the
effects of imperfect capital markets on investment and production. As
evidenced by current distress among U.S. farmers, however, these are
important and complex topics. (For a more complete treatment, see,
e.g., Cochrane, 1958; Hathaway, 1963.)

The pure interest rate effects of credit availability are ad-
dressed above under Input Prices. Because of imperfect capital
markets, however, the effective interest rate in farming is, for all
practical purposes, endogenous.

Capital market imperfections may be based partly on resistance to
flow of funds in and out of farm debt markets, but it is more funda-
mentally caused by the virtual absence of external equity financing
(Johnson, 1947, pp. 65-66). The total funds available for asset
acquisition and crop production, then, are determined by a desire to
maintain moderate debt-to-equity ratios (Weston and Brigham, 1975).

A number of factors affect debt-to-equity ratios. Income flow
changes, whether from price or policy shifts, affect the level of cash
on hand. When such variables affect perceived land values, asset and
equity holdings change. Finally, unanticipated inflation rate changes
alter the relative value of existing debt.

Since a composite cost of capital is both endogenous and unavail-
able as an historical data series, any attempt to include these
considerations in explanatory variables will require another approach.

Possible predetermined proxy variables include the previous period’s

75
income, capital gains, and year-end debt-to-equity ratio. The lag
period of these variables would seem to be appropriate as determinants
of current investment.
Shifts in policy with respect to credit markets and insurance
could also be expected to have effects on investment and production,

but they will not be considered in this study.

Cross-eguation Reetrictione

The theory developed in Chapter Two provides a basis for specify-
ing output supply and input use equations for econometric estimation.
It also provides a basis for relating coefficients in one equation to
those of others and may thereby justify cross-equation restrictions for
estimation. Such restrictions, if true, are a basis for a more
effective use of information in producing statistically efficient
parameter estimates. In addition to this minimum-variance-of—para-
meter-estimate sense of efficiency (Pindyck and Rubinfeld, 1981, p.
88), this section considers the benefits of such restrictions in
relation to their costs.

Before proceeding to cross-equation restrictions, it should be
emphasized that certain "zero" restrictions have already been imposed
on our estimating forms. By deriving linear supply and demand equa-
tions from a quadratic production function, we have implicitly assumed
the adequacy of these first- and second-order approximations. As
emphasized by Mortenson (1973), Treadway (1974), and Epstein (1981),
however, this assumption is rather restrictive in terms of assumed
forms of adjustment costs. Although this form is generally defended by

Gould (1968), it represents a considerably stronger simplification than

76
does, for example, a second-order approximation of a static production
function. Although a more flexible specification may be preferred, the
costs in terms of degrees of freedom probably do not justify such an
approach (Epstein and Denny, 1983).

The most obvious source of useful cross-equation restrictions is
knowledge of the symmetry of the original Fvv matrix (p. 10). Once
transformed to account for dynamic considerations, however, this matrix
can lose some of its symmetry. In the absence of internal adjustment
costs, it can be shown that cross-crop-price effects on crop supply are
still equal regardless of how input prices are expressed (see Appendix
C). Input prices must be converted to annual user prices, however, for
the effects of crop prices on input use to equal those of input prices
on crop supply, and for cross-input price effects on input use to be
equal. Symmetry still will not hold, however, if the second-order
approximation is inadequate or if variations in the input supply
relations embodied in the coefficient matrix are insufficiently
accounted for.

For somewhat obvious reasons, error terms are likely to be
contemporaneously correlated between estimating equations. If all
estimated equations include the same regressors as theory suggests they
should, no additional information can be gained from this fact (Pindyck
and Rubinfeld, 1981, p. 334). Under other circumstances, this condi-
tion would suggest the possibility of improving coefficient estimates
by the use of generalized least squares and Zellner estimation. If
multicollinearity leads to the imposition of zero restrictions that
limit the list of regressors, for example, Zellner estimation or three-

stage least squares could be used to produce more efficient parameter

77

estimates.

Qpefficient Shifting

Given the methods just described for measuring production re-
sponse, the groundwork is laid for testing reversibility hypotheses.
According to theory, output irreversibility exists when input occasion-
al-fixity is more common for either supply expansions or contractions.
Because no way has been found to endogenize the fact of fixity and
because some way must be found to relate supply movements to fixity,
specifications for reversibility hypothesis tests must still be
derived.

The simplest approach, as suggested by the discussion of theory,
is to compare average rates of price response in periods of expansion
versus periods of contraction. Although each average would include
periods of different extents of input fixity, at least this partition-
ing would indicate which direction of supply shift is more likely to
produce fixity. Because this is the basic reversibility question, this
direct test might be the most meaningful.

The major problem with this approach with a multi-output techno-
logy is that it is not clear what constitutes a supply expansion or
contraction. Each crop could be dealt with individually--essentially
a test for the fixity of specialized inputs--but this would ignore the
effect of shifts in the production of substitute crops. Especially
because the common acreage measure of supply provides a clear basis for
aggregation, shifts in total supply would be used to define periods of
expansion and contraction as they relate to unspecialized inputs. A

combination of these two methods could also be applied, but the cost in

78
terms of degrees of freedom would be high, since all coefficients must
shift for each combination of situations.

Alternative approaches to indexing fixity center on examining
input supply directly. For rough approximation, periods of expansion
or contraction can be identified in terms of input aggregates. This
approach has the advantage of readily available data series in the U.S.
Although these inputs cannot be identified in terms of crop use, it is
not necessarily use in the subsector of concern that determines fixity
anyway.

If more detailed information about input industries is available,
direct information about capacity utilization could be used to identify
periods of input fixity. Although this approach offers the advantage of
using direct information on sources of fixity, degrees of freedom could
be consumed quickly if there are too many combinations of cases for
different input industries. On the other hand, if periods of expansion
of input industries are clear enough, strong support could be provided
for fairly simply partition of the period under investigation. Care
must be exercised, however, because (as mentioned above) domestic input
supply might not be the relevant level for examination; if inputs are
imported in significant quantities, foreign producers must also be
studied. Furthermore, capacity utilization figures are characteristic-
ally unreliable.

All of the approaches discussed above hinge on the notion of
segmenting the sample period for the application of dummy variables
defining coefficient shifters in ordinary least squares regression.
More complex approaches are possible if consideration is given to the

point made in the previous chapter that the extent of input fixity is

79

proportional to the magnitude of output supply changes. To incorporate
the implication that short-run supply is sigmoid, two techniques are
possible. The first would be simply to add non-linear price terms as
regressors to produce the desired functional form. Ordinary least
squares could still be used, but it would cost additional degrees of
freedom and probable collinearity. The second technique would be to
impose a restriction that causes input prices (and, hence, linear
coefficients) to change proportionately to shifts in supply. This
would save degrees of freedom, but the resulting highly non-linear
specification would require costly iterative estimation techniques that
might not even yield stable parameter estimates.

Finally, it should be pointed out that, as stated in Chapter Two,
none of these approaches solves the simultaneity problem of using the
observation of D-matrix-type variables to segment the sample period.
No way has been found so far to solve the resulting problem of biased

estimators.

Methodological Note

It is common to use theory to structure econometric specifica-
tions. The extent and form of such structuring, however, varies. At
one extreme, a simple belief that some variables affect others provides
the basis for ordinary least squares estimation. At the other extreme,
variable choices, functional forms, and appropriate estimators are
derived from economic theory, statistical principles, and a set of
assumptions about the processes that generated the data.

The first approach is predicated on the belief that it is a low-

cost way to apply prior knowledge to statistical estimates, that

80
theoretical restrictions are generally arbitrary and are harmful if
untrue, and that complex estimation procedures usually offer little
advantage over ordinary least squares and may make estimates worse if
inappropriate. The second approach assumes that prior knowledge
includes some axioms and structure of economic behavior whose contribu-
tion to estimation can be tested and used if appropriate.

This study takes an intermediate position between these two. It
assumes that hypotheses about economic behavior can be examined to see
how they influence results, but that such examinations cannot tell much
by themselves. In this view, legitimate hypotheses are so numerous and
complex that none can be tested apart from a background of untested
maintained hypotheses that influence outcomes in unknown ways. Because
only a limited set of combinations of hypotheses can be tested (and
because this set itself is frequently large), choices between competing
hypotheses are generally inconclusive and often predetermined by prior
beliefs. As a result, the researcher’s judgement and experience are a
major and inseparable part of research conclusions, the acceptance of
which is conditional to researcher’s preconceptions and to other
theoretical and empirical evidence. A more complex statement of a
similar outlook is found in Leamer (1978).

The practical significance of this position is that many of the
results in the next chapter are presented somewhat tentatively. They
were obtained from extensive “specification searches" (the title of
Leamer’s book), which, though informed by prior hypotheses, were not
strictly limited by them. Summary and test statistics are considered
to be measures of "fit," not firm indicators of statistical signifi-

cance. The data analysis, then, represents an attempt to see whether

81
the data can fit the theory, not whether certain hypotheses are
"falsified." Finally, the sensitivity of important results to equation
specification and the influence of other evidence and theoretical
convictions on conclusions are discussed in the following chapter as
explicitly as is practicable.

In spite of these caveats, the standard language of statistical
significance is still used in Chapter Five. A parameter estimate at
least twice as big as its standard error is called "significant," and
"significance levels" of .05 and .01 refer to this ratio and a corre-
sponding ratio of three, respectively. t-ratios between 8 and 5 are
called "quite" significant, and those above 5 are called "very" or
"highly" significant. Those between 1 and 8 are called "fairly"
significant, although some between 1 and 1.5 are considered ”not high."
Those below 1 are considreed "low," "rather low," or "not very signifi-
cant," with those below .5 generally considered insignificant. This
terminology is adopted for convenience only, and does not reflect an

assertion regarding the probability of Type I error.

CHAPTER FIVE

ECONOMETRIC RESULTS

In this chapter, data, econometric specifications, and regression
results are reported, and preliminary specific conclusions are drawn
about the hypotheses and methods examined in the earlier chapters. In
general, the approach taken is to determine whether the world is simple
enough and the data definitive enough to yield useful econometric
results regarding these hypotheses. Specifically, various specifica-
tions are tested to detect dynamic effects and input supply constraints
(the major hypotheses outlined at the beginning of Chapter Four). This
exercise will also help to determine whether the methods described in
the previous chapter are capable of yielding useful results in other
applications.

By and large, the results reported below are not very definitive
regarding the major hypotheses. This may be because the hypotheses are
not true, or may be the result of complex adjustment processes,
difficulty in modeling policy effects, and collinearity between
independent variables. In addition, specification problems mentioned
in the previous chapter and other problems discussed below probably
took a considerable toll.

In summary, certain results provide some support for the notion of
lagged adjustment, particularly with respect to machinery production
capacity. There was little evidence of occasional fixity, except for
possible resistance to expansion of planted acreage, which could be

caused by constrained fertilizer supplies. If there are additional

88

83
problems of irreversibility, they are either so complex or so minor (or
both) as to be quite unmeasurable given the difficulties mentioned
above.

More extensive general conclusions and the possible usefulness of
this mode of analaysis for other applications are addressed (along with
other topics) in the final chapter. The remainder of this chapter is
devoted to examining specific results of regressions on output and the
prices of and demands for farm machinery, fertilizers, pesticides, and
fuel; a final section focuses on the joint estimation of equations.

The output analysis below is based on the set of crops discussed
in the previous chapters. The input analyses, however, are performed
for agriculture as a whole, due to data, econometric, and theoretical
considerations. Ready data availability did not permit otherwise,
although detailed data might be acquirable from the USDA. Econometric-
ally, the use of the individual crop prices did not produce significant
effects (possibly due in part to collinearity), so the USDA all-crop
price index was used instead. Finally, the afore-mentioned problem of
stability in the coefficient matrix caused by endogenous prices of
durables was alleviated by normalizing all prices by the Consumers’
Price Index as discussed in Chapter Four. Data availability also
constrained the input analyses to a calendar-year, rather than crop-
year, basis.

The regression results reported in this chapter are for the
following dependent and independent variables. (Not all independent
variables shown for an equation are necessarily included in any one
regression.) In addition, a time trend and an intercept shifter were

included in most regressions.

84

Total acres planted = f (corn and wheat diversion variables, wheat
allotment, machinery carry-in)

Machinery and equipment price index = f (own lagged value, lagged
steel price, lagged crop price, fertilizer price, wheat
allotment, lagged machinery purchases)

Machinery and equipment purchases = f (own user price, lagged crop
price, fertilizer price, wheat allotment, debt capacity, own
lagged value, machinery carry-in)

Fertilizer price index = f (lagged natural gas price, lagged crop
price, machinery user price, corn diversion variable)

Fertilizer pruchases = f (own lagged value, own price, lagged crop
price, machinery user price, corn and wheat diversion
variables, machinery carry-in)

Pesticide price index = f (own lagged value, lagged crop price)

Pesticide purchases = f (own price, lagged crop price, machinery
carry~in)

Fuel price index = f (crude oil price, lagged crop price, wheat
allotment, machinery carry-in)

Fuel purchases = f (own price, lagged crop price, wheat allotment,

machinery carry-in)

Output

Most of the analysis of output was focused on total U.S. acreage
planted to feed grains, soybeans, and wheat (see Figure 5.1). Acreage
planted to these individual crops was also examined. In addition, some
attention was paid to crop yields and to quantities produced (yields

times harvested acreage). More detailed data descriptions and sources

85

are provided in Appendix D.

seen-

 

. k"
:— fi 1

1980 1984

-- A A A a L L A n_ 1 L e A L A A
"' f v v r 1 fi v v

Figure 5.1. Acreage planted to studied crops in the U.S.,
crop years 1965-84.

The period 1965-1984 was chosen for the analysis because of the
availability of data for most variables for the period and because of
major changes in the terms of government programs prior to 1965.

Independent variables used. Output prices for planted acres were
expressed in terms of expected gross returns per acre (i.e., expected
price times expected yield), and were normalized by the same values for
hay and by the Consumer’s Price Index. Expected prices were taken to
be prices for the previous year’s crop prior to planting this year’s
crop; expected yields were calculated as averages of the previous five
years’ yields adjusted for yield growth trends. (This approach
implicitly assumes constant planted-to-harvested-acreage ratios, the
value of which would be a component of estimated coefficients.) These

variables worked well to explain individual crop choices, but had

86
little measurable effect on total acreage. The USDA price index for
all crops (discounted by hay price and the CPI) was also tried with
little success. As a result, no returns variables were retained in
total acreage specifications.

Policy variables were used in a number of ways. First, corn and
wheat gross returns per program acre were calculated as above, but with
adjustments for program payments and acreage set-asides and diversions.
These variables were used in conjunction with average (of minimum and
maximum) diversion rates to guage the programs’ acreage reducing
effects. Second, the effects of both variables for each crop were
combined by multiplying them together to conserve degrees of freedom.
Third, this second approach was modified by dividing by market gross
returns per acre; the result was the average diversion rate times the
ratio of program-to-market returns. Finally, the wheat allotment was
also used. (Most work to develop these approaches was done by John N.
Ferris of Michigan State University.)

A number of input price variables were used in the analysis of
planted acreage, but generally poor results (wrong signs and collinear—
ity with other variables) led to their exclusion. This decision was
supported by the resulting relief from simultaneity concerns stemming
from input price endogeneity. Coefficients of the remaining indepen-
dent variables, therefore, should be considered as mutatis mutandis, as
discussed in Chapter Four. The input variables used are addressed in
the corresponding input sections of this chapter.

Dynamic adjustment variables used in the analysis included the
January stock of machinery and equipment ("machinery carry-in") and the

debt capacity of farmers. (Both variables--which apply to all of

87
agriculture, not just the subsector under consideration--are described
more fully in the machinery section.) The effect of debt capacity on
new purchases of machinery was too slight to lead to a detectable
effect on acreage planted, so it was dropped from consideration.

A trend variable is included in most relations estimated; it is
justified as a proxy for technical change, and it generally tends to
improve fits. Lagged acreage variables were tried in certain specific-
ations (see page 73); they did not improve fits well enough to compen-
sate for their generally eg pee nature, so results of their use are not
reported here.

Finally, to test the hypothesis of occasional fixity, "shift"
variables were included. These variables serve as proxies for the D
matrices (page 84) in time series to represent occasional-fixity as it
changes through time. As the theory chapter suggests (page 38), these
shifters should account for all conditions of occasional-fixity for all
coefficients estimated. To keep them simple enough to be useful,
however, only zero/one dummy intercept shifters were used. Three forms
were tried. The first focused on a prior belief that the years 1973
and 1974 were strongly predetremined to be years of expansion by
increased prices in 1978 and 1973 and diversion relaxation in 1973 and
suspension in 1974; a seperate dummy variable was used for each year.
The other two forms were eg pee (and endogenously determined):
significant changes (more than four million acres) in total acreage
planted to the six crops were taken to indicate the possibility of
land-use-related fixity. The second form included negative one for
years of contraction, zero for years of little change, and one for

years of expansion. The third form dropped the negative values for

88

years of contraction. These latter two forms are shown in Table 5.1.

Table 5.1. Dummy variable coefficient shifter forms representing
the possibility of acreage-related fixity, and the total and change
in planted acreage (in millions) of feed grains, soybeans, and wheat

from which the shifters were derived, 1965-84.

 

Total Change in +/- +
Year acreage acreage shifter Shifter
1965 809.9 + 1.7 0 O
1966 808.6 - 0.4 0 0
1967 889.0 +80.4 1 1
1968 880.9 - 8.1 -1 0
1969 811.4 - 9.5 -1 0
1970 810.6 - 0.8 0 0
1971 884.9 +14.3 1 1
1978 816.5 - 8.4 -1 0
1973 836.7 +80.8 l 1
1974 844.7 + 8.0 1 1
1975 858.1 + 7.4 1 1
1976 859.3 + 7.8 1 1
1977 863.3 + 4.0 1 1
1978 855.0 - 8.3 -1 O
1979 861.6 + 6.6 l l
1980 878.0 +10.4 1 1
1981 879.0 + 7.0 1 1
1988 878.5 - 0.5 0 0
1983 834.6 -43.9 -1 0
1984 868.8 +34.8 1 1

Regressione reporteg. Because it was neither desirable nor

 

possible to investigate all possible combinations of the above vari-
ables, only the combinations that made the most sense were estimated.
Similarly, only those judged to be the most important of those esti-
mated are reported here.

Generally, the most meaningful results to report are regressions
on total acreage in the six crops. Results for individual crop

acreages were rather predictable and lead to no useful information

89
regarding production dynamics. Yield and quantities-produced regres-
sions on normalized crop prices and other variables did not produce
useful results; this may underline the advantage of focusing attention
on variables that are relatively easy to model and understand.

Policy variables used tended to be dominated by the average
diversion rate. The choice of policy variable retained, therefore, is
that in which the average diversion rate is multiplied by the ratio of
program-to-market returns. This approach made it possible to use
returns information without consuming additional degrees of freedom or
dealing with normalization questions.

Of the shift variables, results for only the expansion shift
variable (the last column of Table 5.1) are reported here. Results for
the expansion/contraction variable were clearly inferior in terms of
its own t-statistic and effects on other coefficient estimates.
(Because this variable includes the expansion variable, the comparison
can be considered a test of a nested model.) Although the dummy
variables for 1973 and 1974 were often quite statistically significant,
their values were quite sensitive to changes in specification.

Regression results. Relevant regression results are shown in

A———

 

Table 5.8. These results show the effect of the lagged adjustment
variable (machinery carry-in) and the acreage expansion constraint on
the response of total acreage planted to the policy variables.

Equation 8.1 presents the basic model without lagged adjustment
but with the expansion constraint. The coefficients of the diversion
variables represent millions of acres not planted per 100 percent of
diversion. Corn diversion is significant at the 1 percent level, wheat

at 5 percent.

90

Table 5.8. Results of OLS regressions on total acreage
of the six study crops (millions of acres), 1965-84.

 

Equation number:
Variable 8.1 8.8 8.3 8.4 8.5

Constant 89.1 33.8 84.1 149.4 173.0
(87.3) (81.3) (89.4) (45.3) (9.8)
Corn diversion -91.8 -6l.9 -64.8 -98.0 -108.9
(19.7) (19.4) (80.5) (19.1) (16.4)
Wheat diversion -88.7 -46.7 -50.5 -7.0 1.3
' (18.4) (18.4) (14.8) (17.8) (8.7)
Wheat allotment .341 .511 .584
(.187) (.160) (.079)
Machinery carry-in -.045 .153 .199
(.091) (.094) (.037)

Time 8.08 3.07 3.38 0.55

(0.43) (0.87) (0.68) (1.03)
Expansion shifter -8.16 -6.36 ~6.99 -6.93 -6.78
(3.63) (4.84) (4.53) (3.58) (3.40)
Adjusted RE .967 .953 .950 .970 .978
Durbin-Watson 1.79 1.85 1.77 8.47 8.60

Mean of dependent variable = 841.8 ; standard deviation = 84.6
Figures in parentheses are standard errors of estimates.

Note that, because the feed grain base is not even twice that of

wheat (and some of the feed grain diversion is not perfectly correlated

to that of corn), the much larger coefficient for the corn diversion

implies a more effective diversion program for feed grains. On the

other hand, the significant (at 5 percent) wheat allotment coefficient

is also part of the wheat program, a part which would appear to be

about 34 percent "effective” (since the allotment and planted acres are

91
scaled in the same units). The time trend catch-all is quite signifi-
cant. So is the expansion shift variable, which indicates an average
"cost" of eight million acres associated with an acreage expansion.

The estimated value of the shift coefficient is quite robust to
the specifications shown in Table 5.8, as it was to virtually all
specifications examined. Only in equations without the wheat allotment
is its significance level less than 5 percent. The implications of
this significance, however, are not immediately clear. It could be
associated either with the costs of breaking new ground or with input
occasional-fixity. The fact that the shift variable that allows for
contractionary land fixity showed no significance, however, suggests
that the resistance to expansion is grounded in increasingly higher
input costs. Unfortunately, no other strong evidence for this particu-
lar explanation was found. In any event, the amount of the adjustment
cost--eight million acres out of an average of 848 million--is rather
small.

Before moving on to consider lagged adjustment based on machinery
stocks, one more aspect of the acreage control programs should be
considered. Although the allotment coefficient is quite significant
and of believable magnitude, it is not evident exactly how or why the
allotment variable should have any effect. For the period of operation
of the wheat program, the allotment serves primarily as the calculated
base to which diversion rates would apply. It is not clear how the
allotment would operate to control plantings on its own. When excluded
from the regression, as in Equation 8.8, the coefficients of the
diversion variables take on values much more proportional to their

acreage bases. This fairly large change in these coefficients is not

98

totally surprising given the .66 simple correlation of the diversion
variables. The allotment, however, is only slightly correlated with
each of them (.17 with corn and -.05 with wheat). (The Durbin-Watson
statistic, by the way, takes on its only conclusive value in the table,
supporting rejection of the hypothesis of serially correlated residuals
at the 5 percent significance level.) No judgement is offered as to
which is the proper specification, a decision which is quite important
to the hypothesis of a machinery-stock-based lagged adjustment effect.

With machinery carry-in added to this second specification (see
Equation 8.3), virtually nothing changes, a tribute to the low signifi-
cance, small value, and wrong sign of the coefficient. When added to
the first specification (as in Equation 8.4), however, the wheat
diversion coefficient shrinks, the allotment effect grows, and the time
trend almost disappears. The 1.68 t-statistic on the machinery
coefficient, its proper sign, and the high correlations of both the
allotment (.77) and machinery (.90) with trend suggest eliminating the
now low-significance trend variable. The result, Equation 8.5, indeed
raises the significance level of the machinery variable to less than 1
percent. (It also costs the wheat diversion the rest of its effect,
and raises that of the corn diversion and the wheat allotment). Note
that these latter two specifications render the Durbin-Watson statistic
firmly inclusive at the 5 percent significance level.

Some support for the correctness of specifications 8.4 and 8.5
springs from the estimated value of the machinery coefficient. Since
the means of the dependent and independent variables are nearly equal,
the coefficient values (.15 and .80) are the estimated elasticities of

acreage with respect to machinery carry-in. As one would hope, these

93

values are reasonably close to the share of machinery costs in total
production costs of these crops (USDA-ERS, 1985c). Two factors which
would qualify this observation tend to be offsetting. First, the
estimate should be lower than the cost share because there is probably
some elasticity of yield to machinery use. Second, the estimate should
be higher than the cost share because machinery carry-in will induce
higher use-levels of other inputs.

Conclueione. The lagged-adjusment effect of machinery carry-in
may have some effect on the dynamics of planting. This conclusion,
however, is sensitive to the representation of the effects of acreage
control programs. The expansion shifter robustly indicates the
presence of some small constraint on expansion, which is more likely to
be based in input supply fixity. Together, these measures provide some
support for the hypothesis that dynamic adjustment of supply is

constrained somewhat more in expansion than in contraction.

Farm Machinery and Eguipment

Machinery market characteristics indeed apear to be a potential
source of lagged adjustment in agriculture, but not necessarily for the
reasons anticipated. One source of dynamics may be in lagged adjust-
ment of machinery supply, a second-order effect (see page 70) that is
probably quite minor. The endogeneity of machinery price seems quite
firmly established, but real machinery price variation is small.
Finally, the measured effect of machinery carry-in on new purchases is
insignificant, a fact which could make lagged effects larger than
theorized, unless machinery use intensity varies enough to compensate.

Farm machinery quantities used are gross investment and January 1

94
stocks (”carry-in”) of tractors and other machinery and equipment,
deflated by the Producers’ Price Index for farm machinery and equipment
(which was used as the price variable). The annual user price was
calculated as the sum of interest and depreciation rates times machin-
ery price adjusted for tax policy changes (see Appendix D).

Beige. Machinery prices in aggregate varied little with respect
to the CPI over the period studied: the coefficient of variation of
deflated price was .049 (see also Figure 5.8). The measured determin-
ants of price are shown in Table 5.3. The results reported were quite
robust to the specification used, expect that additional variables

increased standard errors of estimates somewhat.

1.3T

34

 

. g A: A A Ag A k A A L %L A¥A .L A A; A A A J
v v v v v—

Figure 5.8. Normalized price of farm machinery and equipment,
(1967=1.00), 1965-84.

Table 5.3.

95

of farm machinery and equipment (1967=1.00),

-—_-------------‘-----—_-----—-—-—-------------———--—-—-—--_‘---——---—

Variable OLS
Constant .088
(.164)
Price._, .540
(.186)
Steel price...1 .103
(.098)
Crop price._, .093
(.038)
Fertilizer price -.064
(.055)
Wheat allotment .00063
(.00044)
Machinery purchases.-, -.00088
(.00054)
Time .0081
(.0018)
Expansion shifter -.0118
(.0061)
Standard error of .011
the regression
Durbin-Watson 8.073

1.087; standard deviation = .

Mean of dependent variable =

.115
(.096)

.101
(.036)

-.079
(.063)

.00078
(.00048)

-.00090
(.00054)

.0080
(.0018)

-.0118
(.0061)

.011

Results of regressions on the normalized price

1965-1984.

IV price
flexibiity

.13

.83

.044

-.034

Figures in parentheses are standard errors of estimates.

96

Results from both ordinary least squares (adjusted R2 = .958) and
instrumental variables are shown. The two results are quite similar.
The latter technique was necessary because of the inclusion of endogen-
ous fertilizer price. Actual two-stage least squares was not used
because of the large number of predetermined variables in the system
studied. Instead, the list of instruments included: (1) the policy
variables; (8) the interest, depreciation, and tax components of the
user price of machinery; (3) the predetermined variables in the
equation; and (4) the predetermined variables in the equations of the
endogenous variables. (Justification for this selection rule is
provided in Appendix E.) The instrumental variables results are taken
to be the proper estimator of the machinery price equation.

The equations estimated are for the price of farm machinery and
equipment. The quite significant coefficient of last period’s price in
the regressions is taken to indicate a lagged endogenous effect of
machinery supply. In other words, capacity and the price-dependent
supply curve adjusts in lags to last period’s price. The possible
interpretation that this measured effect actually results from the high
serial correlation of a highly significant steel price is rejected on
the basis of the considerably more significant coefficient of lagged
own-price when both variables are included in the regression (as
shown). In addition, the more unfavorable Durbin-Watson statistic
(1.49 versus 8.17) and the higher standard error of the regression
(.014 versus .011) that resulted from excluding the lagged price of
machinery are taken to indicate the superiority of the reported
regression.

The short-run supply curve is shown to be shifted by last period’s

97

price of steel, a major input to farm machinery. The elasticity (or
"flexibility") of this measure is .13, a value that should be compar—
able to the share of steel in farm machinery manufacturing costs.
Neither this effect, not that of time, is very statistically signifi-
cant. The latter measure represents the sum of technological change in
the farm machinery industry (normally producing a negative effect on
price), the trend in other machinery input prices, the machinery-
intensifying trend of technological change in farming, and the excluded
trend in other demand shifters.

The remaining variables in the price equations are farm machinery
demand shifters. The direct use of these predetermined (and one
endogenous) instruments was necessitated by the fact that price has
such a strong effect on purchases that the use of purchases (or even
its estimated value) in the price equation consistently produced
negative coefficients. The resulting demand shifters in the price
equation are not exactly the same as those in the demand equation.
There is nothing objectionable in this if, as is likely:

(1) machinery prices are set at the beginning of the season;

(8) prices are set in response to factors known at the time;

(3) these factors imperfectly match those that actually affect

farmers’ decision; and

(4) these prices are somewhat inflexible with respect to actual

later developments.
These comments also apply to the other input analyses.

The estimates for crop and fertilizer price effects and the wheat
allotment should be self-explanatory. The lagged machinery purchases

were expected to have the depressing effect of recently purchased

98
stocks on demand. Interestingly, total machinery stocks were not a
significant factor, as will be shown below.

The expansion shifter is fairly significant statistically. The
negative value of the coefficient indicates a resistance to rising
demand for machinery, ceteris aribus, when acreage planted is expand-
ing. Such a finding would result from expansions being constrained by
some factor other than machinery demand. This finding, however, is not
supported by the results of the estimated demand function.

Demand. Farm machinery and equipment investment was estimated as
a function of the annual user price of machinery, the demand determin-
ants used in the price equation, and debt capacity (see Appendix D).
Because of the endogeneity of the prices of fertilizer and machinery,
instrumental variables estimation was used. The list of instruments
was derived according to the policy stated for machinery prices, and
was identical to that list as a result. As shown for prices, results
differed little from those for ordinary least squares (which produced
an adjusted R8 of .738). Only the instrumental variables results are
shown in Table 5.4. The first equation shown in the table is accepted
as the proper specification. The second equation demonstrates the very
low economic and statistical significance of including the machinery
carry-in variable.

The coefficients of prices and the wheat allotment in the first
regressiom are self-explanatory, although their demand elasticities
might be considered unexpectedly large. The influence of debt capacity
is a non-standard sort of dynamic effect, as discussed in the previous
chapter (pages 68-69). The course by which its effects would be played

out is difficult to grasp. Although its statistical significance is

99

Table 5.4. Results of instrumental variables regressions on farm
machinery and equipment purchases (billions of 1967 dollars), 1965-84.

 

 

Independent Equation 4.1
variable Equation 4.1 elasticities Equation 4.8

Constant 61.8 - 68.3
(38.9) (81.0)

User price -487. -1.49 -386.
(806.) (801.)

Crop price.-, 34.5 1.97 85.3
(17.7) (15.7)

Fertilizer price -58.3 -1.88 -37.8
(86.5) (83.6)

Wheat allotment .314 .56 .809
(.874) (.856)

Debt capacity 94.5 -’ 85.9
(63.7) (88.8)

Purchases._, -.516 -.58 -.441
(.581) (.598)

Machinery carry-in - .008
(.168)

Time .435 - .373
(.413) (1.45)

Expansion shifter -.699 - -.350
(8.80) (3.15)

Standard error of 4.53 4.66

the regression

Durbin-Watson 8.53 8.39

Mean of dependent variable
Figures in parentheses are standard errors of estimates.

standard deviation

*For the reason that no elasticity is reported, see Appendix D.

100
not high, it may be that this effect tended to dominate that of
machinery carry-in over the period, as is frequently discussed in
explanations for farmers’ current economic woes. As mentioned under
Prices, above, only last year’s purchases tended to discourage new
purchases, and then at the low trade-off rate of about one-half.

The effect of time in the regression would support the concept of
progressive capital intensification. The low, insignificant coeffic-
ient of the expansion shifter belies the interpretation of the price
effect offered above, as mentioned there. With exception of this
effect and that of debt capacity (which was not significant in the
price equation), the demand variables generally bear the same propor-
tion to one another in the price and demand equations. This fact would
tend to support the conclusion that their significance in the two
equations is, in fact, as demand shifters.

Note that machinery stock equals machinery carry-in plus machinery
purchases. The results of estimating a machinery stock equation (not
shown), therefore, are exactly the same as those of the second pur-
chases equation, except that the coefficient of carry-in is greater
(.990 versus .738). Graphs of the fitted and actual values of both

purchases and stocks are shown in Figure 5.3.

Fertilizer

In addition to machinery (with variable-cost expense shares of 86,
37, and 39 percent for corn, wheat, and soybeans, respectively),
fertilizer is the other major purchased input for the subsector under
consideration, with variable-cost shares of 38, 38, and 14 percent

(USDA-ERs, 1985c).

304

101

' LEGEND

actual

 

---.. fitted

 

 

 

3.0T

8801

 

1965 1970 1975 1980 1984
year
I LEGEND
actual
- - . - fitted

 

 

Figure

 

5.3. Farm machinery and equipment purchases (a) and stocks (b),
fitted and actual, 1965-84.

108
Fertilizer price is determined largely by expected crop prices,
with a simple correlation coefficient (when normalized by the CPI) of
.985 (see Figure 5.4). No evidence was found of lagged adjustment in
fertilizer capacity, however. There may be a tendency for fertilizer
supply to be constrained in acreage expansions, but this factor is

confounded by other effects and is too small to be definitively

 

measurable.
LEGEND
fertlllzer
:.o,- .'n‘. - - - .. craps

8.3"

wke

8.0-4

I.I1

 

 

 

Figure 5.4. Normalized prices of crops (lagged, 1967 = 8.38)
and fertilizer (1967 = 1.47), 1965-84.

Eglee. In addition to the highly significant crop price (with a
price flexibility of 1.05), the normalized price of fertilizer is
significantly affected by the lagged price of natural gas (price
flexibility of .887), the user price of machinery (.187), and time.
The negative coefficient of time is taken to represent a long-run fall

in the real price of fertilizer due to efficiency gains in its

103

Table 5.5 Results of instrumental variables regressions on
normalized fertilizer price (1967 = 1.47), 1965-84.

Independent Equation number
variable 5.1 5.8 5.3
Constant 1.89 1.88 1.88
(0.46) (0.48) (0.41)
Natural gas price.-, .188 .188 .188
(.034) (.034) (.033)
Crop price._, .655 .668 .688
(.039) (.041) (.035)
Machinery user price -1.96 ~1.93 -1.98
(0.80) (0.81) (0.77)
Time -0.19 -O.18 -0.18
(.006) (.006) (.005)
Corn diversion -.088 -.003
(.181) (.178)
Expansion shifter .087 .087
(.039) (.086)
Standard error of .0465 .0474 .0457
the regression
Durbin-Watson 1.74 1.88 1.88

 

 

Mean of dependent variable = 1.378; standard deviation = .888
Figures in parentheses are standard errors of estimates.
The elasticities reported in the text are for Equation 5.8.

104
manufacture. All of these measures are quite insensitive to the
specification changes shown in Table 5.5, as well as to others tried.

The equations shown in the table were estimated with instrumental
variables because of the endogeneity of machinery price. The selection
of instruments followed the same policy for both fertilizer price and
demand as for machinery. The OLS estimates, with adjusted Ra’s around
.96, were virtually identical to those shown.

The equations reported in Table 5.5 are intended to examine the
hypothesis that fertilizer supply may have been capacity-constrained in
acreage expansions during the period. This is done by testing the
sensitivity of the standard error of the coefficient of the expansion
shifter to the presence of the corn diversion variable, with which it
has a simple correlation of -.88. Only the corn diversion has been
included in Equation 5.1. It is of rather low statistical signifi-
cance, but of correct sign and reasonable magnitude. It was the most
significant policy variable in the fertilizer price regressions.

When the expansion shifter is added (in Equation 5.8), the
magnitude and significance of corn diversion virtually disappear. The
expansion shifter is of rather low significance, but its magnitude and
sign suggest that fertilizer capacity could be responsible for con-
straining planted acreage (and presumably yields as well). When the
corn diversion variable is dropped in Equation 5.3, the expansion
shifter becomes somewhat more significant, but is still not highly so.

Demand. In Equation 6.1 (Table 5.6), the demand for fertilizer is
estimated as a function of own price (elasticity of -.791), the prices
of crops (.500) and machines (-.576), diversion rates, machinery carry-

in (.178), time, and the expansion shifter. In addition, lagged

105

Table 5.6. Results of instrumental variables regressions on fertilizer
purchases (expenditures divided by price, 1910-14=100), 1965-84.

 

 

 

Independent Equetion number
variable 6.1 6.8 6.3 6.4
Constant -6.49 -8.33 -9.86 -5.53
(8.03) (8.10) (6.05) (5.80)
Purchases.-, -.317 -.319
(.179) (.176)
Price -18.1 -11.8 -18.7 -11.8
(3.3) (3.4) (3.1) (3.3)
Crop price._, 4.88 4.58 5.07 4.76
(8.11) (8.87) (3.18) (8.19)
Machinery user price -90.9 -66.9 -99.5 -74.9
(81.7) (18.4) (17.1) (11.9)
Corn diversion -6.16 -4.03 -6.11 -3.96
(3.51) (3.68) (3.46) (3.56)
Wheat diversion -3.78 -8.40 -5.07 -3.68
(3.18) (3.89) (8.37) (8.37)
Machinery carry-in .014 .014
(.088) (.084)
Time .679 .474 .789 .586
(.889) (.806) (.135) (.068)
Expansion shifter -.460 .843 -.697 .088
(.859) (.888) (.766) (.715)
Standard error of .816 .888 .804 .867
the regression
Durbin-Watson 8.84 8.67 8.90 8.73

 

Mean of dependent variable = 81.14; standard deviation = 3.79
Figures in parentheses are standard errors of estimates.

106
fertilizer expenditures are included, with a fairly significant
elasticity of -.309. The negative value, if true, could represent the
effect of last year’s residues on this year’s demand, but the measure
obtained seems a bit large.

Note that the coefficient of the expansion shifter is of low
statistical significance. A zero coefficient would be compatible with
the hypothesis of a fertilizer supply constraint, since the higher
price of fertilizer would serve to balance supply and demand. A
constraint imposed by another output would produce a negative coeffi-
cient on the shifter, but it would also make the shifter coefficient in
the price equation negative, the opposite of what was observed. These
findings, then, provide some weak support for the hypothesis that
fertilizer capacity has constrained crop supply in expansions.

The conclusion is not challenged by dropping the somewhat ques-
tionable lagged purchases variable in Equation 6.8. Little else
changes enough to assist much in choosing between the two specifica-
itons. In neither equation are the demand shifter coefficients of
comparable proportion to those' in the fertilizer price equation,
although the machinery price coefficient moves in the right direction
in Equation 6.8. The lower value of -66.9 is also closer to the
fertilizer price coefficient of -58.3 in the preferred machinery demand
equation; since the two would be equal under the symmetry condition,
some support is provided thereby for favoring Equation 6.8 as a
preferred specification.

Neither the conclusion just stated nor that regarding the expan-
sion shifter is challenged by excluding the rather low-significance

machinery carry-in variable as in Equations 6.3 and 6.4. The expansion

107

shifter becomes larger in Equation 6.3, but its still low significance
does not support concluding that an input fixity exists elsewhere.
When lagged purchases is dropped in Equation 6.4, this coefficient
falls to very near to zero. Again, the value of the machinery coeffi-
cient is more believable without lagged purchases. In both pairs of
equations, the inconclusive (at 5 percent) Durbin-Watson statistic is
more favorable without lagged purchases.

The jump in the value and significance of time resulting from the
exclusion of machinery carry-in can be thought of in two ways.
Statistically, the two are highly correlated. Economically, the
marginal productiyity of fertilizer' has been increased by genetic
improvement of crops through time and by the lowered cost of spreading
fertilizer. With machinery carry-in included, time measures only the
first effect; when it is excluded, time represents both.

Finally, the relative size of the diversion coefficients argues
for the validity of the first two specifications. Because fertilizer
use per acre is roughly three times as great for corn as for wheat
(USDA, ERS, ECIFS, 1988, Costs of Production), the roughly two-to-one
ratio of these coefficients in these equations is more expected than
the one-to-one ratio in the latter two equations.

The use of fertilizer over the sample period is shown in Figure

5.5.

Pesticides
The last two categories of inputs considered, pesticides and fuel,
represent 14, 6, and 31 and 14, 88, and 80 percent, respectively, of

the variable expenses of corn, wheat, and soybean production (USDA-ERS,

108

181'

 

A A A A

1975
year

Figure 5.5. Fertilizer purchases (expenditures divided by price,
1910-14 = 100), 1965-84.

LEGEND

peetlcldee

 

 

---. crepe

3.01-

 

Figure 5.6. Normalized prices of crops (lagged, 1967 = 8.38)
and pesticides (1967 = 8.77), 1965-84.

109
1985c). For neither input are results as satisfying as for machinery
and fertilizer.

Pesticide price is strongly endogenous and, in addition to falling
steadily in real terms, may have a lagged endogenous capacity effect.
The growth in pesticide use appears to be caused by the persistent fall
in price. No evidence of resource occasional-fixity was found in the
analysis of this input.

Beige. The normalized price of pesticides has fallen persistently
through time, except during the response to high crop prices in the
mid-1970s, as is evident in Figure 5.6.

Statistical measures of this relationship are shown in Table 5.7,

Table 5.7. Results of regressions on real pesticide price, 1965-84.

Independent
variable Equation 7.1 Equation 7.8
Constant 4.54 8.17
(0.61) (0.90)
Pesticide price.-, .487
(.136)
Crop price._, .587 .414
(.109) (.095)
elasticity .504 .396
Time -.045 -.084
(.007) (.009)
Expansion shifter -.036 -.086
(.077) (.061)
Adjusted RE .854 .906
Durbin-Watson 1.38 1.50

Mean of dependent variable = 8.89; standard deviation = .40
Figures in parentheses are standard errors of estimates.

110

in which the coefficients of crop price and time are very statistically
significant. In Equation 7.8, lagged pesticide price is added to the
simple specification of Equation 7.1 to test the hypothesis of lagged
adjustment in pesticide supply capacity. In statistical terms, the
significance of this variable would appear to support the hypothesis.
The high correlation of this variable with time, however, leaves the
question somewhat in doubt. The inclusion of no other variable
improved regression results; hence, the admissibility of the ordinary
least squares estimator.

The expansion shifter is quite insignificant statistically in each
regression. Its magnitude is also not large. The negative sign would
support the idea of expansion fixity in some other input, but this
result is not supported by the demand estimation results.

Demand. Results for pesticide demand estimation are fairly
sensitive to the specification used. (Instrumental variables are used
in each case.) Equation 8.1 in Table 5.8 includes a time trend which
dominates the effect of all other variables. When time is excluded, as
in Equation 8.8, price coefficients become quite significant and of
reasonable magnitude. The estimated own price elasticity of demand at
the means is -3.13. The elasticity with respect to crop price is 0.90.

In the last three regressions, the coefficient of time is con-
strained to equal 0.10 in recognition of the fact that the cost of
applying pesticides has probably fallen through time, but not as much
as implied by the unconstrained coefficient in Equation 8.1. The
constrained value represents a growth in demand of about 8 percent per
year over the period. This constraint lowers the estimated own-price

elasticity to 8.87 (probably a more reasonable figure), and that of

111

Table 5.8. Results of regressions on pesticide purchases
(expenditures divided by price, 1910-14 = 100), 1965-84.

----------------—----——-_—---_-—~--—-_---——--—----_—-—---_--—----—--——

 

Independent Equation number
variable 8.1 8.8 8.3 8.4 8.5
Constant -17.5 16.8 6.9 6.9 5.1
(17.9) ( 1.4) (1.0) (1.0) (3.8)
Price -.301 -7.13 -5.16 -5.07 ~4.50
(3.68) (0.98) (0.70) (0.67) (1.68)
Crop price._, -1.11 8.13 1.19 1.18 .79
(1.85) (1.00) (0.76) (0.74) (1.81)
Time .345 .100 .100 .100
(.179) -* -” -*
Expansion shifter .154 .075 .098 .118 .077
(.367) (.468) (.350) (.344) (.386)
Machinery carry-in .005
(.010)
Standard error of .683 .866 .656 .650 .688
the regression
Durbin-Watson 1.18 1.81 1.98 1.91 1.98

 

Mean of dependent variable = 5.81; standard deviation = 8.33

Figures in parentheses are standard errors of estimates.

*The time coefficient in Equations 8.3, 8.4, and 8.5 is imposed by
restricted regression.

Equations 8.4 and 8.5 use lagged price as an instrument.

118
crop price to .50.

All of the regressions use the policy mentioned in previous
sections to select instruments for estimated own price. In the first
three regressions, these instruments exclude lagged own-price, as if
Equation 7.1 were the proper price specification. The last two regres-
sions included lagged price, as if Equation 7.8 were more appropriate.
As Equations 8.3 and 8.4 show, the effects of changing this assumption
are minor.

Equation 8.5 shows the effect of including machinery carry-in.
Standard errors generally are increased, but no major changes occur.
If this variable were taken to represent the effect of lower pesticide
application costs, the restricted time variable could be omitted.
Because nothing suprising results, this specification is not reported.

Finally, the coefficient of the expansion shifter is fairly
insensitive to all these changes, especially considering its low
statistical significance. No particular meaning is seen in this
result, however, because, as mentioned above, its sign is not consis-
tent with any hypothesis of input fixity when considered in combination

with the results for pesticide price.

 

Regressions on fuel price and use yield no particularly strong or
surprising results. Fuel price is strongly determined by crude oil
price, and may be influenced by demand variables. The expansion
shifter exhibits no significant effects. For trends in price and use,
see Figure 5.7.

Beige. The price of agricultural fuels is highly determined by

113

(a)

LI!!-

 

 

 

 

,8
5.
1.0V
i.e : is. :7 r --— : . see :- :- Ase eee,;, :4, :7 ;,4,; e r- ::
1985 1970 1975 1980 1984
year
(b)
:21-
ii,»
I
:e<r
o+
. CC‘L:L:$:¢FC‘ ‘:t$%15£
1965 1970 1975 1980 1984
year

Figure 5.7. Normalized price of fuel (a, 1967 = 1.77)
and fuel purchases (b, 1910-14 = 100), 1965-84.

114

crude oil price. The elasticity of .419 should represent the share of
crude oil costs in fuel price. The price of fuel may be affected by
agricultural fuel demand, reflecting a less-than-perfectly elastic
supply of fuel processing and delivery services. Although there is no
evidence of this in the crop price coefficient, wheat allotment and
machinery carry-in effects are significant at the .05 level. It should
be born in mind, however, that both of these variables have strong
trend components.

The quite significant negative coefficient of time is taken to
indicate increasing efficiency of the fuel processing and delivery
system. The coefficient of the expansion shifter is of minimal
economic or statistical significance; the positive sign of the coeffi-
cient has no clear economic meaning. Because of the lack of endogenous
variables, the price equation was estimated with ordinary least
squares. No additional variables yielded useful results in other
specifications.

Demand. The fuel purchases equation is estimated in essentially
the same form as the fuel price equation. The replacement of crude oil
price with the endogenous fuel price required the use of instrumental
variables estimation. The choice of the list of instruments followed
by the same policy as mentioned above.

As expected, the estimated fuel price elasticity of demand is
quite low. Crop price now has a measurable and reasonable estimated
effect, though of fairly low statistical significance. The relative
magnitudes of the wheat allotment and machinery carry-in effects have
shifted, probably due in part to their high correlation. The negative

sign of the time coefficient is taken to indicate the increased fuel

115

Table 5.9. Results of regressions on discounted fuel price and fuel
purchases (expenditures divided by price, 1910-14 = 100), 1965-84.

 

 

 

Independent Price Purcheses
variable coefficients flexibilities coefficients elasticities
Constant 8.74 11.07
(0.61) ( 4.88)
Crude oil price .556 .419
(.098)
Fuel price -1.40 -.878
(1.06)
Crop priced—1 -.036 - .508 .109
(.067) (.440)
Wheat allotment .0078 .887 .035 .815
(.0030) (.086)
Machinery .0036 .475 .047 1.19
carry-in (.0013) (.011)
Time -.039 -.180
(.011) (.084)
Expansion .0057 -.815
shifter (.0439) (.889)
Durbin-Watson 8.01 1.86
Mean of 1.99 10.88

dependent variable

Standard deviation of .397 1.19
dependent variable

 

FIEBFEE'in parentheses aF'e-EI-EEEEFd—EFFEFE’ET'EEZIBSEEE'. """""""""

116
efficiency of agricultural machinery and equipment.

The negative sign on the expansion shifter could be consistent
with the hypothesis of a supply constraint for another input, but it is
of low significance both statistically and in terms of its magnitude.
Croee-Eouetion Reetrictipee

A cross-equation restriction for improving the efficiency of
parameter estimates was imposed and tested. It involved the symmetry
of cross-price effects (as discussed in Chapters Two and Four and
Appendix C). Only one symmetry condition existed--equality of machin-
ery user and fertilizer price effects on each other’s demands. This
condition was tested using instrumental variables and two-stage least
squares estimates, for both of which the null hypothesis of symmetry
could not be rejected at even the .80 level of significance. Three-
stage least squares (3SLS) estimates resulted in a higher t-statistic,
but its significance is unclear given the small sample used. Details
of the results obtained are presented in Appendix F.

The use of 3SLS improves the asymptotic efficiency of estimates
through Zellner’s technique of accounting for the correlation of error
terms between seemingly unrelated regressions. The resulting addition
of generalized least squares to two-stage least squares (Intriligator,
1978, p. 403) reduced the estimated standard errors of parameter
estimates somewhat, but no estimated coefficient changed radically. In
a sense, then, the results discussed in this chapter were strengthened,
but (due to the small sample size) it is unclear how much or how
reliably. Details of the use of this procedure are reported in

Appendix F.

CHAPTER SIX

CONCLUSIONS AND IMPLICATIONS

This chapter serves five functions in terminating this study.
Each is addressed in a seperate section.

First, general conclusions are drawn about the dynamics of cash
grain production in the United States. The previous chapters provide
the base in theory, informal knowledge, methods, and data analysis for
the period 1965-84 on which these conclusions rest.

Second, the potential and form for extension of this work to
application in other cases are described. Most such cases involve a
different scope or geographical subject, but uses for other time
periods and economic sectors are also mentioned.

Third, strengths and weaknesses of the analysis are discussed to
qualify the conclusions and assist in designing future applications.

Fourth, policy implications of the conclusions for United States
farm price and income support programs are outlined.

Finally, suggestions are made for improvements in theory, data,
econometric techniques, and other analytic approaches that could
benefit future research along the lines of this study. Ideas for

clarifying the need for and use of such studies are also proposed.

General Conclueions Regarding U.S. Agriculture

 

For the most part, such dynamics as exist in the U.S. cash grain
sector appeer to result form the classic forms of quasi-fixity (see

page 11) discussed in the literature of economics. They cause some

117

118

lagged adjustment in input use and a fairly small lag in acreage
adjustment. Yield lagged-adjustment may also occur, adding somewhat to
the total adjustment effect in production. These findings are essen-
tially compatible with those of Karp, Fawson, and Shumway (1985), who
detected minor quasi-fixity in U.S. agricultural production as a whole.
For the cash grain sector in aggregate, planted acreage appears to be
so strongly affected by program variables that crop price effects are
not detectable.

The source of this quasi-fixity is seen to be related primarily to
endogenous prices for durable inputs. In the case of the obvious
durables, farm machinery and equipment, the virtual independence of
purchases from existing stock represents an extreme case of another
source of lagged adjustment. Two factors, however, may mitigate this
effect: first, the low variability of machinery price leads to a low
degree of quasi-fixity induced by its endogeneity; second, flexibility
of stock use rates may reduce output effects. On the other hand,
second-order quasi-fixity (see page 70) resulting from lagged adjust-
ment in machinery supply capacity adds a more complex dynamic force to
the analysis. In addition, probable lagged adjustment in credit
availability (a complementary input) is another likely source of quasi-
fixity.

Although fertilizer prices are highly endogenous, the non-durabil-
ity of the input and a failure to detect lagged adjustment in supply
capacity suggest no source of quasi-fixity. On the other hand, the
possibility of fertilizer residues acting as durable stocks reintro-
duces a potential lagged effect, made greater by probable influences on

both acreage and yields.

119

Pesticide price is also quite endogenous and may exhibit lagged
capacity adjustment in supply. Because pesticides are non-durable,
this lagged effect would be a first-order quasi-fixity. If pesticides
also have a fertilizer-like multi-period lagged effect on crop produc-
tion, this first-order effect would make capacity a second-order
effect. Although fertilizer may be a more important input, the
relative magnitude of fertilizer and pesticide dynamic effects is
difficult to determine. The faster growth of pesticide use may justify
a shift in focus for future studies.

Although fuel prices show evidence of endogeneity, no lagged
adjustment effect originating from this input was detected.

Labor is a significant input that was not studied econometrically.
Prior knowledge, beliefs, and theory suggest, however, that labor is
quasi-fixed and leaving agriculture on a continuing basis.

Results with respect to occasional-fixity were not overwhelming:
A small effect was detected for acreage planted, but the nature of the
effect would imply that it does not originate in land-related costs,
per se. (Again, this is keeping with the findings of Karp, Fawson,
Shumway.) Some weak evidence suggests that this effect could have
originated in constrained fertilizer supply.

In summary, quasi-fixity adjustment effects in U.S. cash grain
production are not large, although the tendency for labor to be under
constant pressure to leave is persistent. Occasional constraints on
inputs have an even smaller role. Their effect, if any, is to make
production expand, on average, more slowly than it contracts. The most
significant characterization of the dynamics of U.S. cash grain

production, therefore, is simply that of an industry whose labor

180

productivity grows faster than does demand for its products.

Extensione to Other Ceeee

Since a original motivation for this study was to develop a method
for examining the dynamic crop supply of our major grain export
competitors, attention will now turn to possible applications to other
cases. The question of reversibility of these supply relations will be
a special focus. First, similarities and differences between the U.S.
and other areas will be examined. Then a number of potentially
important differences will be discussed in térms of their likelihood of
occurrence, their significance for supply, and the implications for
analysis. A final section will address applications to other periods
in the U.S. and to other sectors of the economy.

Similerities and differences. Aggregate farm-level analysis-~the
level of the empirical analysis of this study--seems to be much the
same everywhere. Production trends are dominated by labor-saving
mechanization, biological improvements, and increased purchases of non-
durables. Specific patterns obviously vary considerably from place to
place and time to time, as when labor demand is increased via infra-
structural development or when labor displacement is decreased as by
the agricultural policies of Japan. If anything, however, these
exceptions demonstrate the rule: efforts to mitigate labor displace-
ment are necessitated by the persistence of the problem. As a result,
farm-level differences are not seen as a major threat to the generality
of the analysis applied in this study.

On the other hand, significant variation can exist in the environ-

ments in which farming develops. Discussions of specific environmental

181
factors comprise the remainder of this section. Such factors include:
alternate land uses; the development of input industries, processing
capacity, and infrastructure; credit markets; other policy changes; and
the introduction of new technologies.

Alternate land uses. Major differences can exist in the regional
characteristics of land added to crop production. In addition to
irrigation of arid lands (addressed below), new lands used for grain
production can come from forest or brushland, or from perennial crops
of greater value than hay or pasture (such as coffee or sugarcane). As
a result, land conversion costs could be more significant elsewhere
than they appear to be in the U.S. In addition, the long-lived and
cyclic nature of foregone crops make their addition to an analysis
quite complex. In the case of timber, the variability in the value of
salvaged material creates even more difficulties.

In this study, the loss of land to urban development has been
ignored; in other cases, this alternate land use may be too important
to be overlooked. Similarly, extensive land reform might make cropping
patterns change so severely that reform itself might be considered to
be an alternate land use factor (Shabman, 1985, p. 1031).

flegiinput capacity, processing,:end infrestructure. As explained
above, opportunities always exist to draw the boundaries of the sector
under consideration to fit the needs of the study. In individual
countries, development of input and processing capacity and infrastruc-
ture may fall within these boundaries. New fertilizer plants have
sprung up around the world in recent years, many countries have entered
the ranks of farm machinery producers, and large, publicly-funded

irrigation projects, processing plants, and export facilities have long

188

been part of agricultural development programs. When such changes are
"lumpy" relative to existing capacity and economically isolated from
available foreign substitutes, they can emerge as occasionally-fixed
factors of production. While such changes simply produce price changes
at the farm level, the analysis becomes more complex for the agricul-
tural system as a whole. Furthermore, stock-holding behavior might
also have to be considered as part of the system under study, including
the effects of storage capacity and public policy.

Credit. The ability to purchase inputs, especially durables, is
affected by the availability of credit. Such effects have been shown
to be important in the U.S.; they are likely to be even more so where
credit markets are less developed. This is especially true when
government policies restructure patterns of credit availability. While
not a fixity, per se, such changes can drastically alter patterns of
input use. In some cases, different credit policy regimes might
produce a whole new pattern of purchases and production. Although
often mitigated by social factors at the village level, the possibility
for such effects must be considered when credit markets change signifi-
cantly.

thgfi policy cheegee. Like the physical and credit policy tools
mentioned above, a number of other government actions have major
effects on agricultural production. Such actions include policies with
respect to input and output prices, money supply, exchange rates,
taxes, communications, migration, and population. When these policies
shift sharply, fixity-like changes in supply parameters can result. As
discussed below, such changes must be handled on a case-by-case basis.

When change occurs gradually, time-trend representations may be

183
sufficient. Otherwise, more definitive techniques may be required.

Iechnoloqigei,chepge, Technological change is often cited as a
source of irreversibility in supply (e.g., Tomek and Robinson, 1981, p.
86). Once gained, new knowlegde is assumed to never disappear. (A
more sophisticated view recognizes that some forms of knowledge, such
as biological improvements, are subject to depreciation and require
additional investments to keep supply curves from shifting back.) If
taken as a time trend, of course, the index of technological change
does not ever change its direction of movement; even so, the velocity
of this movement might change in reality, causing problems for econo-
metric analysis.

Non-continuous effects of technical innovations can sometimes be
represented by diffusion indices. The lagged effects of further
learning are more complex to model. Although such changes may theoret-
ically resemble fixity, important differences exist. Accounting for
uneven technological change again requires special treatment on a case-
by-case basis.

Treating the special cases. Most of the factors discussed above

 

 

are strongly influenced by public policy. Although policy measures
often respond to prices and other economic signals, the actions of a
government (like those of any other single actor) are uneven and lumpy.
Such sporadic change cannot always be represented by the methods that
apply to the aggregate behavior of many individuals. In these cases,
prior knowledge regarding different conditions is necessary. To save
degrees of freedom, different rates of change or various factors must
at times be combined into single indices, much as was done with the

coefficient shifter in Chapter Five. Care must be taken to determine

184
if these indices represent simple intercept shifters, or whether more
complex coefficient shifting is involved.

Examples from U.S. agricultural history and other industries. A
longer view of the history of agriculture in the United States reveals
the occurrence of many of the kinds of issues discussed above.
Structural changes like railroad development and hybrid seed are
similar in all countries. (This is why many studies focus on short
enough periods for such factors to be considered stable.) The same
measures, of course, must be taken to deal with them, depending on the
level and purpose of a particular analysis.

In general, the analyses presented in this study might be applied
to the study of’ other sectors both within and outside of agriculture.
Among non-agricultural industries, steel, auto, textiles, chemicals,
and electronics seem to offer either sufficient instability or product
life-cycle effects for examinations of dynamic factors to yield
interesting results. Perhaps more general, factors discussed in this
study might be extended to intersectoral or aggregate macroeconomic
models to improve the conceptualization and measurement of lagged

economic adjustment.

Strengths and Weaknesses of the Analysis

As in the examples just shown, there are many qualifications and
complicating factors that make the analysis presented in this study
somewhat less straightforward than we might like. Although most of
these issues have been addressed in earlier chapters, a list of the
strengths and weaknesses of the analysis is collected here.

Strengths. Perhaps the major strength of this analysis is in

185
explicitly laying out the theory of dynamic aggregate output supply and
input demand for a sector of an economy facing endogenous input prices.
Although this has been done in the past, the addition of the considera-
tion of lagged adjustment in the input industries and possible con-
straints on input supply are novel. These additions do more than just
extend the theory; they also impose consistency and clarity on the
discussion of important issues in agricultural supply and policy
analysis and bound the process of examining data to test for correspon-
dence of theory to actual events. By specifying the effects of certain
conditions on the relationships between variables, these developments
assist in drawing conclusions from assumptions and data. The testing
of hypotheses is facilitated thereby, whether or not formal econometric

estimation is pursued or possible.

 

Weaknesses. The weaknesses of the approach taken in this study
include:
(1) the dificulty of representing commodity and other policies

and modeling their effects;

(8) the difficulty of representing uneven technological change;

. (3) the unobservability of expectations, especially regarding

future crop prices;

(4) possible errors in assuming price-taking behavior on the part
of input suppliers;

(5) failure to deal adequately with some inputs, particularly
labor;

(6) other short-cuts in system identification; and

(7) numerous other simplifications.

Most of these problems are most costly to econometric work. To the

186
extent that they impose more general limits on our ability to infer
conclusions from observations, they also restrict less formal methods.
There is nothing particularly unique about this list of weaknesses,
however, and they may be no more extensive for this study than for
others. Possibilities for getting around these weaknesses are suggest-
ed in the last section of this chapter, but they may be limitations of
the subject matter that simply must be lived with. In any event,
comparison of the costs and benefits of further refinements is also

discussed below.

Policy Implicetione

As discussed in Chapter One, inelastic supply is often cited as a
justification for government programs to stabilize agricultural
markets. Presumably, beliefs about the precise nature of supply
inelasticity have been relevant to the formulation of specific poli-
cies. To the extent that this study may change perceptions about the
nature of agricultural supply, it might be useful to examine implica-
tions for the design of policy instruments. Specifically, the signifi-
cance of beliefs about supply irreversibility is addressed below.

Whether or not the two are casually related, previous discussions
about the irreversibility of agricultural supply have occurred at the
same time that U.S. commodity policies have served to create a floor
for some agricultural prices. One might suspect other causes for this
policy design, but previous ideas about irreversibility would not
appear to fall reasonably among them. If irreversibility were charac-
terized by inputs fixed in farming, price floors would hold up incomes,

but they would not help the problem of constrained dynamic adjustment.

187
If inputs were thought to enter farming more easily than they leave,
dynamic adjustment would be better facilitated by providing price
ceilings. By keeping prices from rising too high, situations would be
less likely to occur in which a surge of new inputs are later found to
be fixed in excess use.

Ironically, if the thesis of this study (that inputs are more
likely to be fixed out of agriculture than fixed in) is accepted, the
existing policy design is rational. Price floors help to prevent a
situation in which input use falls so low that later response to high
prices becomes constrained by input supply capacity. Dynamic adjust-
ment is thereby facilitated. In any event, neither case of occasional-
fixity seems to be important in fact, so the policy significance of
this analysis is small.

Perhaps a more significant implication of this analysis derives
from the income-supporting effects of current policy design. To the
extent that target prices transfer income to farmers at rates even
higher than those associated with the supply-stimulating effects of
target prices and loan rates, resources for purchasing additional
inputs are provided. This may be particularly important for purchases
of farm machinery and equipment, which have been shown to be affected
by farmers’ asset positions and which may even be quite independent of
current machinery holdings.

Although it could be argued that such purchases would not be
affected by income given any level of price signals, two factors
counter this claim. First, at higher income levels, the farmer’s
leisure/labor trade-off will shift toward labor-saving mechanization.

Second, if farmers perceive themselves to be in competition for the

188

control of surrounding land to enable them to survive in an environment
of growing economies of scale, higher incomes could cause them to act
preemptively by purchasing land and large machinery beyond current
levels of profit maximation as insurance policies for futher employ-
ment. Although the first factor would lead to voluntary labor-saving
with little effect on output, the second factor would lead to ”excess"
competition creating even greater labor displacement than otherwise.
Ironically, by passing income through to excessive machinery purchases
and higher land prices, the income-raising effects of income supports
would be diverted from farm consumption; there still would be income
benefits for machinery manufacturers and dealers, and for farmers who
had planned to sell out anyway.

As a final note, the "cannibalism" encouraged by this second
factor is part of Willard Cochrane’s “Treadmill" (1958). This early
formulation of Cochrane’s thesis also included an element of machinery-
embodied technological change (pp. 99-100) that made matters even
worse. In a later formulation (Cochrane, 1979, Ch. 19), however, this
element is missing. (A more general treatment is found in Tomek and
Robinson, 1981, p. 86.) Although no mention of the lost element is
made, there may be good reasons for reducing its emphasis. First,
machinery-embodied technological change may be minor. Second, the
elasticity of substitution between labor and machinery may be so great
that the technical change represented by mechanization is merely a
strong substitution response to changing prices which does not produce

significant savings in total factor cost per unit of output.

189
Suggestione for Further Wgee

The theory of this study indicates a likelihood that farm produc-
tion of the crops considered expands more slowly than it contracts.
Econometric results provide weak support for this finding. If desired,
more conclusive results might be generated with improved theory, data,
and econometric techniques, or with other approaches to the problem and
better prior information. In addition, the need for and usefulness of
such analyses should be clarified to guide the choice of future
attempts at improvement and application.

Theory. The theoretical analysis for this study was performed
using fairly simple discrete dynamics. Perhaps because of the relative
difficulty of discrete analysis, this approach seems to be less
developed than continuous analysis. Further basic development of
discrete dynamic theory would appear to be of some value.

In addition, numerous aspects of applied dynamic optimization
theory deserve attention. For one thing, standards for normalization
when input supply is part of the system studied are vague; a general
price level indicator is one approach, but it is not clear whether
better options exist. Second, it is unclear how input supply capacity
changes should be handled; lagged supply was used in this study, but
this procedure was also shown to be rather ad hoc. Third, the adequacy
of the quadratic (or other second-order) approximation for dynamic
processes has been called into question (Epstsin and Denny, 1981), as
has the validity of this whole mode of analysis in the presence of
allocable joint inputs (Shumway, Pope, and Nash, 1984).

The annual user cost of durables is difficult to define when the

opportunity cost of capital is endogenous, and the adequacy of the

130
assumption of constant rates of depreciation should be examined. In
addition, credit availibility, a source of potentially major dynamic
effects, could probably be incorporated more formally and explicitly
into theoretical models, as could the role of policy variables as
independent variables.

Qeie. More definitive results regarding the dynamics of cash
grain production might be derived from input data more specific to this
sector. (Such data could probably be obtained from USDA.) Conclusions
would not necessarily change, but their standard errors might be
reduced.

Approaches to reducing levels of aggregation could also include
working at the regional level. Disaggregation of crop supply and input
purchase functions might be easier at this level. Attempts to model
other land uses would be desired, but are perhaps too difficult to
produce useful results. The labor input deserves seperate attention;
results for specific equipment inputs, like irrigation, might also
yield interesting findings. Data on double- and inter-cropping would
clarify information about land as an input.

Econometric teghnigues. More work is probably needed on the

 

theory of cross-equation restrictions in dynamics under different
circumstances, especially as they are tied to different assumptions
about the underlying functional forms of production functions and
adjustment costs. Particular attention should be applied to the role
of endogenous input prices with lagged adjustment of input supply, and
to the joint estimation of input price and demand equations. It is not
clear how the use of instrumental variables in these situations affects

restrictions, nor is the meaning of Zellner estimation when zero

131
restrictions are imposed.

Other approaches and improved prioee. Even with improvements of
the types listed above, there may be fairly firm limits to our ability
to extract information from available time series data, especially with
changes in technology and policy regimes. These limits might be
avoided by gathering cost data from farm surveys and deriving produc-
tion responses with mathematical programming, but care must be exer-
cised to avoid fallacies of composition in aggregating results to the
sectoral level. Land conversion cost data might be the most valuable
acquisition from this approach. Finally, simulations using results for
a complete system could serve to test the reasonableness of estimates,
to examine the dynamic effects of findings, and to suggest foci for
future research. Regardless of empirical approaches, however, well-
thought-out theory is the ultimate source of useful priors.

Clarifying goals. Finally, many different paths could be followed
in pursuing these proposed improvements. As with any study, the use of
and need for an analysis should be clarified to guide future model
choice, development, and application. It is incumbent that policy
makers be as clear as possible about priors and uncertainties to help
frame questions for researchers. It is likewise necesary for resear-
chers to specify the reliability of findings and be explicit about
options available for analyses. The value of future deveIOpments will

depend on the care exercised in their selection.

APPENDICES

APPENDIX A

MODELS OF DEPRECIATION

For the purposes of this study, it is assumed that depreciation is
a constant proportion of the stock value of an asset class per period.
This geometric-decay (GD) pattern may seem contrary to the finding that
the one-hoss-shay model of depreciation (OHS) is more accurate (Penson,
Hughes, and Nelson, 1977; Penson, Romain, and Hughes, 1981). The two
models are not necessarily at odds, however, because GD represents the
value of an asset before maintenance and OHS represents its value
after.

The service-yielding capacity of an asset given ED and a OHS-type
model derived (by Penson, Hughes, and Nelson, 1977) from engineering
data (ED) are both shown as functions of age in Figure A. The differ-

ence between the two, the barred area, is also shown.

\
service- ~777~\‘1‘\\‘ ED

yielding
capacity
f-\

 

\

GD

 

 

/\

 

 

K

asset age

MNTC

 

 

 

Figure A.1. Models of depreciation: geometric decay (GD),
engineering data (ED), and their difference (MNTC),
(adapted from Penson, Hughes, and Nelson, 1977, p. 384).

138

133
Note that the shape of this difference (MNTC) represents a typical form
of current annual expenses for repairs and maintenance: it rises
gradually as more major repairs and overhauls are required, until such
expenditures no longer pay and the asset is allowed to expire.

Although the ED curve may reflect the services derived from
durables given the addition of current inputs, the GD model better
reflects the service-yielding ability left over from the previous year.
Thus the two models are compatible, and GD is the more relevant for the

purposes of this study.

APPENDIX B

DERIVATION OF SUPPLY/DEMAND FUNCTIONS WITH OCCASIONAL INPUT FIXITY

As described on pages 83 to 89, the case of occasionally-fixed
inputs can lead to irreversible output supply and input demand rela-
tions. The derivation of the relations shown on page 84 is described
below.

Three sets of equations are necessary to account for all cases of
occasional input fixity. The first two are the first-order conditions

already described:

EFL w..+w, I

The third is the shadow price of fixed factors:

This is merely the reverse of the second set above, making w, rather
than L endogenous when L is predetermined.

To account for the fact that any input could be sometimes fixed
and sometimes variable, a full complement of equations (one equation
for each input) exists for each of the last two sets of equations.
Because only one condition can apply for each input at one time, we can
multiply each of these sets by a dummy matrix that indicates which

equations are ”turned on":

134

135

DVBFL Dv(wm+w,I)

DI WM = DvBFL

in which Dv+De is the identity matrix.

Because "turned-off" equations are zero, adding together these two
sets of equations produces one set in which each equation is either a
first-order condition (if that input is variable) or an endogenous

price expression (if the input is fixed):

DVBFL + 01W“ = DV(WM+N§I) + DfBFL

By solving this set of equations simultaneously with the output first-

order conditions, a handy way for representing supply and demand

relations with occasional fixity can be derived as follows. Begin

with:

(F0, (DVBFL+D'wl-‘),), = (‘p’ (DV(W,¢+WgI)+Df‘BF|_),),

Collect FL terms on the left:

(Fa’ ((DV-D,)BFL+wam)’)’ = (-p’ Da(wm+w,I)’)’

The diagonal square matrices B and (Dy-D.) can be reversed, and again

assuming a quadratic technology for expanding the partial derivatives

(this time with non-separable internal adjustment costs, Fm and FL,,

added on for exposition):

136
1 (aq+FnaQ+FaLL+Fa1I) , (B(Dv_D-f)(a1 +FLQQ+FLl-L+F|-x I )+D~rW,. ) , ) , =

(~p’ De(ww+w.1)’)’

Results are unchanged by inserting DV+D, to account for endogenous

versus predetermined L, and Dv when I#0, on the left-hand side:

aq+Fnau+FaL (Dy+Df )L+Fn1 DVI ‘p
( ) = ( )
B(DV'D() (81+FLQQ+FLL(DV+DV)L+FL:DVI )+Drw,¢ Dv(w..+w,1)

Then, after expanding all 1’s (1 = L-(l-d)L._,):

ae+FoaQ+Fac(Dv+D,)L+Fe,De(L-(1-d)L.-,)
( ) =
B(Dv-Dr) (31+FLQQ+FLL(DV+D9)L+FLIDV(L“( l"d)Lg—1) )+DrW,,
‘P
( )
Da(wu+w,(L-(l-d)L.-,))

and .noting that when D,=1, I=O, so D¢L=de(1-d)L,-,, we collect all
endogenous L terms on the left-hand side and all intercept and L._,

terms on the right-hand side:

an0+ (Fuh+FQ[) DVL
( ) =
B(Dv-D¢)FLGQ+(B(Dv-D¢)(FLL+FL;)-w,)DaL+D¢wm

’P 3g FOLDf-FGIDV

( ) - ( ) - ( ) (l‘d)Lg_1
Dy”), B‘Dv-Df)al B(Dv-D')(FLL_Df-FL_IDV)

Because D..D..=Dv and DVD,=0, the bold Dv-Dr terms can be dropped and the

sign on FLLD, changes. Then, factoring the endogenous variable matrix

137

from the left-hand side yields:

Fan (FQL+FG[) DV 0
( ) ( ) =
B(Da-D¢)FLG (8(FLL+FL;)-w,)Da+D¢ DVL+D¢wm
rp aq FOLDf-FGIDv
( ) - ( ) - ( ) (l-d)Le-,
D..w_.. 8(Dv-D¢)a, B1 ('FLL)Dr’FL[Dv)

(This factoring works because DVDV=DV, Dfo=ny and DVD,=0.) Multi-
plying both sides by the inverse of the left-hand side coefficient
matrix results in the system of output supply, input demand, and fixed-
factor shadow price relations shown on page 84. The convenience of
this form of expression is the ability to see how results change with

changing Do and Dc, as explained on pages 83 to 89.

APPENDIX C

COEFFICIENT MATRIX SYMMETRY FOR IMPOSING
ECONOMETRIC CROSS-EQUATION RESTRICTIONS

It is shown in Chapter Two and Appendix B that the coefficient
matrix of exogenous short-run output and input price effects on output
supply and input use with input quasi-fixity and possible internal

adjustment costs is:

Fun FGL+FQI ’1
( )
BFLQ B(FLL+FL: )‘Wt

Taking the inverse by partitioning (Ayres, 1968, p. 57), the southeast

submatrix is:

[B(FLL_+FLI)-WQ-BFLGFDO—1(FQ[_+FGI)J—l = (8571)“ s: 68—1

8 alone causes asymmetry, but factor out 8“1 and call the remaining
submatrix G. Even with B"1 factored out (i.e., using annual input user
costs), the effect of FL, and F91, which are generally not symmetric
(Mortenson, 1973), is to destroy the symmetry of G. If FL, is, by
chance, null, diagonal, or otherwise symmetric and F9, is null, G would
be symmetric because its inverse would be symmetric (Ayres, p. 58).
(6'1 would be symmetric because B‘lw, is diagonal, FLL and Fan‘1 are
symmetric, and FLG=F0L’.) This implies equivalent input cross-price
effects on input use if and only if FL, is symmetric, F0, is null, and
prices are expressed in terms of annual user costs (B‘lwu).

138

139
Similarly, cross-price effects of output a and input b are equal
under and only under the same conditions. This is true because the
southwest and northwest submatrices of the original inverted matrix,

which are, respectively:

‘68— 1 BFLGFDG- 1'

and:

-FQG’1(FQL+FQI )GBH1

are each other’s transposes under and only under these conditions

(since using B‘lw“ removes all 8 terms).

Finally, the northwest submatrix is symmetric if and only if there

are no Fa, adjustment costs and no assymmetric Fe, adjustment costs,

regardless of how input prices are expressed. This is because its

term:

FOG-1+FOO—1(FQL+FGI)GB_lBFLQFGG_L

has 8‘1 and 8 terms that cancel each other out. Hence, the equality of

crop cross-price effects depends only on adjustment costs.

APPENDIX D

VARIABLE DEFINITION AND DATA SOURCES

The variables used in the econometric analyses of Chapter 5 are, in

order of appearance:

Acres planted to the six study crops = the sum of acres planted to
barley, corn, oats, sorghum, soybeans, and wheat (double-
cropped acres counted twice).

Source: numerous USDA publications.

Yields per harvested acre - in bushels.

Source: numerous USDA publications.

Expected yield = mean of five previous years, Plus three times the

average annual yield increase over the study period.

Crop price = prices-received index, all crops (1910-14 = 100).

Source: Agricultural Statistics.

Diversion variables = mean of minimum and maximum program diversion and
set-aside rates, times the ratio of program to non-program
gross returns per planted acre.

Gross returns = sum of crop returns and government payments.

Source: Ferris, 1986.

140

141
Machinery and equipment purchases, depreciation, and January 1 stocks
(carry-in).

Source: USDA-ERS, 1986.

Machinery and equipment price - Producer Price Index 11-1, agricultural
machinery and equipment. (For stocks, mean of December and
January indices.)

Source: USDL-BLS.

Steel price = Producer Price Index 10-1, iron and steel.

Source: USDL-BLS.

User price of machinery and equipment = BA(1-TX)PKC in which:
BA = (DR+d)/(1+DR)

in which:

DR 3 Federal Intermediate Credit Bank interest rate
(USDC-BEA, Survey of Current Business), less last
year’s rate of change of the CPI.

d = mean depreciation rate over the study period =
.1843 (standard deviation = .0085).

TX = a measure of tax preference due to investment tax

credits and accelerated depreciation (Mumin, 1985).

PKC = machinery and equipment price (above), normalized by the

CPI.

148

Debt capacity ASS(.1688-DAR)/PK in which:

ASS = values of assets (excluding farm households) held by
farmers, January 1.
DAR = debt-to-asset ratio of farmers, January 1.
.1688 = mean DAR, 1965-81 (standard deviation = .0054),
taken to be a norm.
PK = machinery and equipment price (above).

Source: USDA—ERS, 1986.

Fertilizer purchases = fertilizer expenses (USDA-ERS, 1986)
divided by fertilizer prices-paid index (below).
Fertilizer price = fertilizer prices-paid index (1910-14 = 100).

Source: Agricultural Statistics.

Pesticide purchases = pesticide expenses (USDA-ERS, 1986) divided
by pesticide prices-paid index (below).

Pesticide price = agricultural chemicals prices-paid index
(1910-14 = 100).

Source: Agricultural Statistics.

Fuel purchases = petroleum fuels and oils expenses (USDA-ERG, 1986)
divided by fuels prices-paid index (below).
Fuel price = fuels and energy prices-paid index (1910-14 = 100).
Source: Agricultural Statistics.
Crude oil price 3 Producer Price Index 5-61, crude petroleum.

Source: USDL-BLS.

APPENDIX E

POLICY FOR THE SELECTION OF INDEPENDENT VARIABLES

Although the final number (19) of predetermined variables in the
system of equations in this study was fewer than the number of observa-
tions (80), actual two-stage least squares was not used. Technically,
two-stage least squares could have been employed by using all 19
instruments in the first-stage determination of the estimated values of
endogenous independent variables. These values would have been so
close to the actual values, however, as to make second-stage estimates
virtually identical to ordinary least squares results. The obvious but
often-overlooked question (an exception is Intrilligator, 1978, p. 398)
would then have been, "has two-staged least squares actually eliminated
the inconsistency introduced by using endogenous variables as regres-
sors?"

The policy reported in Chapter Five (p. 96) was chosen because it
was decided that this was not the case. This decision was based on the

following logic:

(1) The variables used as instruments have been shown to have (or
can be reasonably assumed to have) significant influences on
the relevant endogenous variable.

(8) Although all predetermined variables in the system affect all
endogenous variables in theory, the effects of the other
predetermined variables on the relevant endogenous variable

have not been measurable.

143

144

(3) Although on average and in the limit, these other variables
can add more information, their ability to explain variation
in the endogenous variable in any given small sample will be
over-shadowed by spurious correlations with first-stage error
terms resulting from the more limited choice of instruments.

(4) As a result, the use of all possible instruments simply
restores correlation between the estimated values of endogen-
ous variables and second-stage error terms.

(5) The resulting spuriously-restored bias would outweigh any
gain from the use of additional true information, producing
estimates that would be worse than those produced under the

chosen policy.

Although this position has not been shown to be valid either
mathematically or in Monte Carlo simulations, it is presented here as a
reasonable and pragmatic solution to an otherwise ignored problem.
This is in keeping with the Methodological Note at the end of Chapter
Four, and is compatible with the criteria established by McCarthy
(1971). It is very close to the "structurally-ordered instrumental
variables" approach recommended by Fisher (1965) and used frequently in
large econometric models (Pindyck and Rubinfeld, 1981, p. 330). It
should be pointed out, however, that this policy could not be followed
in the use of BSLS (see Appendix F), because this estimator requires
the use of the same instruments for all endogenous variables. For this
reason, this system estimator is not strictly comparable to the results

reported in Chapter Five.

APPENDIX F

RESULTS OF REGRESSIONS WITH CROSS-EQUATION RESTRICTIONS

Tests of the symmetry of the effects of fertilizer and machinery
prices on each other’s demands were mentioned in Chapter Five (p. 116).
These tests were performed on instrumental variables (IV), two-stage
least squares (8SLS), and three-stage least squares (3SLS) estimates by
calculating t-statistics as the difference of the two coefficient
estimates in the unrestricted specification divided by the standard
error of the difference. (The standard error is equal to the square
root of the sum of the variances of the two estimates less thCe their
covariance in BSLS.) Results for the regressions that are most
inclusive of independent variables are shown in Table F.1. (Other
coefficient estimates were not materially affected by the imposed

restriction in 3SLS.)

Table F.1. Results of tests of the symmetry condition.

 

Statistical Estimator
result IV 8SLS BSLS
Coefficient of fertilizer -50.6 -45.7 -43.4
price effect on (87.6) (84.0) (15.5)
machinery demand
Coefficient of machinery -90.9 -85.0 -91.1
price effect on (81.7) (81.3) (10.6)
fertilizer demand
Difference 40.3 39.3 47.7
Covariance - - 13.1
Standard error (35.1) (38.1) (18.1)
t-statistic 1.15 1.88 8.64

145

146

Three-stage least squares estimates are asympototically efficient
relative to IV and 8SLS. This improvement is slight in small sample
sizes, however (Thiel, 1971, p. 588), and specification errors diffused
throughout the equation system may actually produce worse estimates
(Intriligator, 1978, p. 480). Non-iterative 3SLS suffers from the same
problems discussed in Appendix E with respect to 8SLS; a Fisher-like
SOIV 3SLS option to avoid this problem was not available in the
statistical package used (Hall, 1983), and the iterative 3SLS alterna-
tive (Brundy and Jorgenson, 1971) was judged to be too expensive given
the problems mentioned above. A similar (Hausman, 1975) solution,
FIML, would have also been costly; it could not actually even be
estimated due to a greater number of variables in the system than
observations (Sargan, 1975, appendix).

The results of non-iterative 3SLS were not markedly different from
those for IV or 8SLS. Table F.8 shows these estimates for the acreage
planted equation, which varied more in results than most other equa-
tions. Although SSLS standard errors are lower than for IV and 8SL5,
the reliability of this apparent efficiency in small samples is

unknown.

147

Table F.8. Results of acres planted regressions
using three different estimators.

Independent
variable

 

 

Constant

Corn diversion

Wheat diversion

Wheat allotment

Machinery carry-in

Time

Expansion shifter

Standard error of

the regression

Durbin-Watson

 

Eetimetor

IV ESLS 3SLS
149.4 149.5 113.9
(45.3) (45.3) (88.3)
-98.0 -99.8 -93.3
(19.1) (19.1) (18.4)
-7.0 -7.1 -l9.0
(17.8) (17.8) (10.8)
.511 .511 .349
(.160) (.160) (.098)
.153 .151 .090
(.094) (.094) (.061)
.55 .56 1.41
(1.03) (1.03) (0.64)
-6.93 -7.31 -8.04
(3.58) (3.54) (8.68)
4.86 4.86 3.59
8.47 8.46 8.18

Mean-af—dependent variable = 841.8; standard deviation = 84.6
Figures in parentheses are standard errors of estimates.

 

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