United States

Department of

Agriculture First-Handler Grain

Agriculturpl

030&~$a:“‘“” Cooperative Elasticit
Abstract

First-Handler Grain Cooperative Elasticities:

Output Supply, Factor Demands, and Factor Substitution, 1983-1991

Anthony C. Crooks

David E. Cummins

Agricultural Economists

Agricultural Cooperative Service

United States Department of Agriculture

This report is the first of a multi-part investigation that attempts to

quantify the impacts of market and policy changes upon first-handler grain

cooperatives in the United States The response of grain cooperatives to

their changing market and policy environment from 1983 to 1991 is

quantified.

An economic model is constructed to measure grain cooperative

output supply response, changes in grain cooperative factor demands, and

substitution rates among the factors of production employed by grain

cooperatives in four major United States grain producing regions. The

model assumes that grain cooperatives employ three basic factors of

production (intermediate inputs, labor, and capital) to provide three

services/products (grain sales or merchandising, grain storage, and farm

supply sales). A discussion of the important findings of the model in the

light of the events transpiring in the grain industry during the study period

and important model implications is also included.

Keywords: Farmer cooperatives, grain, elasticities, policy analysis, duality,

translog profit function

ACS Research Report 128

March 1994
This report is based on balance sheet and operating statement data from

annual cooperative reports requested by USDA’s Agricultural Cooperative

Service (ACS) as part of an annual survey of grain marketing cooperatives. By

ACS definition, grain cooperatives are those whose sales of grains and

oilseeds account for more than half of total sales. Other types of information

such as volume of grain handled and storage capacity were obtained directly

from first-handler cooperatives.

Report estimates were obtained from local first-handler associations

having $5 million or more in total sales during the study period, and four types:

corn-soybean, wheat-sorghum, wheat-barley-oats, and wheat-barley. This

group accounted for an estimated 90 to 95 percent of total grains and oilseeds

sales by local grain cooperatives. Most cooperatives were diversified, also

handling farm supplies. All provided related services.

Information for this report is based on condensed balance sheets and

operating statements. Adjustments were made in financial reports to ensure

data comparability because of variations in accounting, auditing practices, and

terminology. Some detail was lost in the process.

Information in this report can help cooperative managers and boards

make sound business decisions as they adjust to variations of old problems

and consider the need for increased capital for improved or new facilities and/

or services. Information can be used to compare your cooperative with others

of similar size.
Contents

Highlights ........................................................................................................ iv

Introduction ....................................................................................................... 1

Materials and Methods.. .................................................................................... 2

Measuring Cooperative Response to Market Changes:

A Duality Approach ..................................................................................... 2

Testing the Hypothesis of Net Savings Maximization

Among United States Grain Cooperatives ................................................ 3

The Data Set ........................................................................................ -3

Nonparametric Test Results ................................................................ 3

A Data Exploration Strategy for the Cooperative Net Savings Function... 4

Model Validation.. ....................................................................................... 7

Empirical Results ............................................................................................. 8

Corn Belt (corn-soybeans) ......................................................................... 8

Northern Plains (wheat-barley-oats) .......................................................... 8

Southern Plains (wheat-sorghum). ............................................................. 8

Pacific Northwest (wheat-barley) ............................................................. 1 1

Grain Cooperative Factor Substitution ..................................................... 14

Discussion ...................................................................................................... 14

Model Implications ................................................................................... 14

Historical Context ...................................................................................... 14

Conclusions.. .................................................................................................. 16

References ..................................................................................................... 16

Appendix ........................................................................................................ 19

iii
Highlights

This report is the first of a multi-part investigation that attempts to

quantify the impacts of market and policy changes upon first-handler grain

cooperatives in the United States from 1983 to 1991.

l Varian’s (1985) nonparametric test was performed for behavioral

consistency with the hypothesis that grain cooperatives in the United States

maximize net savings. The execution of Varian’s test generated a failure

rate of less than 0.6 percent among cooperatives within each region

(provided in Table 2). The hypothesis of net savings rationality cannot be

rejected, therefore, among first-handler grain cooperatives in the United

States

l An economic model was constructed to measure grain cooperative

output supply response, changes in grain cooperative factor demands, and

substitution rates among the factors of production employed by grain

cooperatives in four major grain producing regions in the United States, the

Corn Belt (corn-soybeans), Northern Plains (wheat-barley-oats), Southern

Plains (wheat-sorghum), and the Pacific Northwest (wheat-barley).

l Evidence of technical change and of factor reallocation were also

examined. Technical change occurring in the Corn Belt region had a

pronounced impact on the substitution of capital for labor. Evidence for the

impact of technical change in the other three regions was inconclusive.
First-Handler Grain Cooperative Elasticities:

Output Supply, Factor Demands, and Factor Substitution, 19834991

Anthony C. Crooks, David E. Cummins

Agricultural Economists

INTRODUCTION

This report is the first of a multi-part

investigation that attempts to quantify the

impacts of market and policy changes upon firsthandler grain cooperatives in the United States

This paper reports how grain cooperatives

responded to their changing market and policy

environment from 1983 to 1991. An economic

model is constructed to measure grain

cooperative output supply response, changes in

grain cooperative factor demands, and

substitution rates among the factors of production

employed by grain cooperatives in four major

grain producing regions in the United States

(figure 1).

Figure 1

The model assumes that grain cooperatives

employ three basic factors of production

(intermediate inputs, labor, and capital) to

provide three services/products (grain sales or

merchandising, grain storage, and farm supplies

sales). The estimation technique uses a flexible

functional form approach to permit a more

disaggregated analysis of the structural changes

occurring among grain cooperatives during the

study period and a way to measure the impacts of

technological change upon factor use and factor

substitution. The technique also has the feature of

exploiting the duality relationship between the

cooperative’s production and net savings

functions.

Location of Selected Types of First-handler Grain Cooperatives

1
The report provides a brief history and

justification of the method of analyses used, a

description of a procedure to test the hypothesis

of net savings maximization among cooperatives,

a description of the data set, the results of a

nonparametric testing, a data exploration strategy

for the cooperative net savings function, and

model validation efforts. The third section

reports empirical results for the econometric

model. A discussion of the important findings of

the model in the light of the events transpiring in

the grain industry during the study period and

important model implications follows in the

fourth section. The fifth section provides a

summary of results and important conclusions for

first-handler grain cooperatives in the United

States

MATERIALS AND METHODS

Measuring Cooperative Response to Market

Changes: A Duality Approach

The application of duality theory to

empirical analysis has long been appealing as a

way to bring theoretical coherence to empirical

estimation. The dual approach offers researchers

a method of ensuring theoretical consistency of

cross-commodity relationships. The practice has

often been overlooked with non-dual approaches

(Taylor, 1990). The application of duality also

allows the empirical estimation of producers’

output supply and factor demand functions.

Without understanding these two aspects of

producer response, any analysis of a policy

regime or market structure change is critically

hindered.

The first applications of duality to economic

analysis were Hotelling (1932) and Roy (1942) for

consumer demand, and Shephard (1953) and

Samuelson (1953) for cost and production

functions. McFadden (1973) generalized the

work of Shephard to include net savings and

revenue functions.

Another advantage of the dual approach is

that it provides the researcher with a richer class

of operational functional forms. Investigation of

production in a multi-product and multi-factor

framework was made possible with this

framework. The work of Diewert (1971,1973,

1974); Lau (1972); Lau and Yotopolous (1972); and

Jorgensen and Lau (1973); to develop flexible

functional forms permits a highly disaggregated

analysis of production structure.

Traditional approaches required the

aggregation of heterogeneous exogenous factors

that may effect factor demands and output

supplies differently. The combined use of duality

theory with the flexible forms makes it possible to

trace the impact of an array of environmental

factors simultaneously (Sidhu and Banaante,

1981).

However, the dual approach is not without

its “pitfalls” (Taylor, 1990). Duality results are

obtained by applying the envelope theorem to the

classical models of net savings maximization

(Hotelling’s lema) or cost minimization

(Shephard’s lema). And while the envelope

theorem always holds for optimizing behavior, it

has been demonstrated that the duality results

may not. Lee and Chambers (1986) show this

general failing in the case of constraints on net

savings maximization. The general duality

results are also shown to not hold in the cases of

uncertainty (Pope, 1980,1982a, 198213) and

stochastic dynamic problems (Taylor, 1984).

Furthermore, questions regarding the

validity of the neoclassical maximization

hypothesis have also been raised (MacCrimmon

and Larson, 1979; De Alessi, 1983; Shoemaker,

1982). Because any empirical application of

duality theory rests on the assumption of net

savings maximization, suspecting the validity of

the maintained hypothesis presents a more

fundamental problem. If, however, the

maximization hypothesis is testable, and there

seems to be no consensus even on this point,’ then

perhaps some conclusions may be drawn as to the

applicability of the duality approach to a

particular empirical question.

‘Consider the spirited debate between Boland (1981,1983) and

Caldwell (1983).

2
Several approaches for testing the net

savings maximization hypothesis have been

offered. These tests are both parametric (Dillon

and Anderson, 1971) and nonparametric (Varian,

1984; Chavas and Cox, 1988; Fawson and

Shumway, 1988) in nature.

Parametric testing is based on comparing

marginal physical productivities to price ratios.

These tests suffer from the same shortcoming

faced by all parametric tests of being conditional

on the selected functional form. Because neither

theoretical nor biological relationships provide

any criteria for the selection of functional form,

the researcher is often left to his own device

(intuition). Nonparametric testing has the

advantage of allowing hypothesis testing without

imposing any assumptions on functional form or

the technology. However, nonparametric tests

also have an heuristic base and can only

determine whether or not observed behavior is

consistent with the null hypothesis (Taylor, 1990).

It seems reasonable, therefore, to combine

parametric and nonparametric tests. Information

gained from both tests stands to be

complementary and should provide the

researcher with a stronger sense of the validity of

the maintained hypothesis.

Testing the Hypothesis of Net Savings

Maximization Among United States Grain

Cooperatives

Following Varian (1984,1985), a

nonparametric test was performed for behavioral

consistency with the hypothesis that grain

cooperatives in the United States maximize net

savings. In general, the Varian test is a pragmatic

comparison of current period net savings against

the net savings that would result from current

year prices and wages with output and factor

quantities of all other periods. More precisely, a

production set Y is said to be net savings rational

for the observed behavior if for a net-output price

vector P

pi yi > pi yj for i,j = 1, . . . ,n; p >> 0, y 2 0.

The Data Set-This report is based on balance

sheet and operating statement data from

cooperatives’ annual reports requested by ACS as

part of an annual survey of grain marketing

cooperatives. By ACS definition, grain

cooperatives are those whose sales of grains and

oilseeds account for more than half of total sales.

Other types of information such as volume of

grain handled and storage capacity were obtained

directly from first-handler cooperatives.

Report estimates were obtained from local

first-handler associations having $5 million or

more in total sales during the study period, and

four types: corn-soybean, wheat-sorghum,

wheat-barley-oats, and wheat-barley. This group

accounted for an estimated 90 to 95 percent of

total grains and oilseeds sales by local grain

cooperatives. Most cooperatives were diversified,

also handling farm supplies. All provided related

services. Information for this report is based on

condensed balance sheets and operating

statements.

Revenues and expenditures from grain sales

and storage and farm supply sales, and grain

volume data from farmer cooperatives designated

as grain handlers (at least 60 percent of income in

grain sales) from prominent grain regions from

1983 to 1991. This data set was employed for

the nonparametric tests of the net savings

maximization hypothesis and all parametric

estimates. Descriptive statistics of the data set are

provided by region and for all regions in

table 1.

Nonparu?netric Test Results-The computer

algorithm used to perform the nonparametric test

for net savings maximization among grain

cooperatives in the United States is provided in

the appendix. The nonparametric test of Varian is

distributed as an F-statistic with (n-k,n-k) degrees

of freedom; a critical-F value of 1 for each region.

Execution of Varian’s test generated a failure rate

of less than 0.6 among cooperatives within each

region (table 2). Therefore, the hypothesis of

cooperative net savings rationality cannot be

rejected.
Table 1 -Descriptive statistics for grain cooperative data set, by region

Region

Corn Belt

Northern Plains

Southern Plains

Pacific NW

All

Number Grain Storage

of Income Income

Observations - $1000 - -$lOOO1,169 11,780 597

549 10,060 369

327 10,520 774

88 14,210 970

2,143 11,350 581

Farm

SUPPlY

Income

-$lOOO3,470

2,189

3,617

2,282

3,114

Grain

Volume

- 1000

bushels -

3,496

3,214

3,598

4,236

3,485

Table 2-Varian’s test of the weak axiom of profit (net savings) maximization for U.S. grain

cooperatives, by region, 1983-91

Region

Corn Belt

Northern Plains

Southern Plains

Pacific NW

Critical F,, (-, -) = 1 .OO

Number of Number of

Observations Failures

1,168 3,173

548 719

326 274

87 22

Number of Rate of Failures/

Comparisons Comparisons (%)

682,696 0.46

150,426 0.48

53,301 0.51

3,828 0.57

A Data Exploration Strategy for the

Cooperative Net Savings Function

Just as the net savings function for

cooperatives is more complicated than the

analogous profit specification for the proprietary

firm, estimation of the indirect net savings

function for cooperatives is also more complex

than a similar estimate for investor-owned firms.

An estimate of cooperative indirect net savings

must account for both total private profits

(farmer-member profits) and collective profits

(net savings) of the cooperative. Fortunately, the

collective net savings of the cooperative may be

incorporated into the estimate of an indirect net

savings function in a relatively simple manner.

From Royer (1978), the net savings function for a

cooperative that maximizes the total net savings

of all member patrons may be written as:

x = RY - PX t s’(RY - PX - FCC), (1)

where:

p is a vector of the expected net savings of a

member patron,

R is a matrix of product prices,

Y is a matrix of total product quantities,

P is a matrix of factor prices,

X is a matrix of factor quantities,

4
FCC is the total fixed costs to the

cooperative, and for s, the porportion of

patronage refunds paid in cash, and

s’ = s + (l-s) / (1 + d)‘,

where:

d is the member patron’s discount rate, and

t is the number of years that (l-s) portion of

patronage refunds is deferred. Because estimates

of the indirect net savings function include only

variable costs, the fixed costs to the cooperative

term (FCC) may be excluded for econometric

estimates such that (1) may be rewritten as:

x = (1 t s’) RY - PX, (2)

and s’ becomes a constant for given values of s, d

and z.

Following Mountain and Hsaio (1989), a

specification search for the “correct” functional

form was performed beginning with the simplest

flexible parametric specifications and proceeded

in increasing order of complexity. When

compared with the more popular general-tospecific approach this technique reduced the

computational burden because in the former

approach there could be many more different

routes of imposing restrictions. To choose the

most appropriate specification, we began by

testing the most restrictive hypothesis. Thus,

testing began with the Cobb-Douglas

specification, proceeded with the translog, and

culminated with the Fourier functional form. For

all tests the alternate hypothesis was the

homogeneous unrestricted functional form of

equations (3) and (4), below.

In n = (1 t a) a t Zi pi In Pi’ t xi Zi fIii In Pi’ In Pi* (3)

- 2 (Ei [Si sin(ln Pi” ) t qi codln Pi’ )I)

!Yi = (1 t a) (pi t Xi bij In Fj t 2 (Xi [Si sin(lnp’J

- Qi Codlnp’JlI). (4)

For the above system to be derived from a

viable net savings function, one of the following

sets of restrictions must hold:

(a) constant (Cobb-Douglas) case, 2ji = @ = bij = 0,

all i,j;.

(b) linear (translog) case, 6, = $ = 0, bij = B,,, all i,j;

or

(c) Fourier case hi = -6, Qi = -Qj, Bii = Bji, all i,j.

From the general function (l), the

normalized flexible net savings function for grain

cooperatives is specified:

ln~‘=(lt~)(at~,lnP’,t~~lnP’~t~~InP*k (5)

t ‘/, B,, In P’X In PsX t b,, In PsX In P’w t Bxk In Fx In P’,

t ‘/, B,, In PSw In Psw t p,, In P‘w In PX t bwk In P’w In P’,

t‘/, f3, In P’, In P’, tf3, In P’, In PgX t Bkw In P’, In P’w

- 2 [@ix sin In Pox t Q, cos In p:) t (SW sin In PSw t $, cos

In P’,) t (6, sin In P’, t Qk cos In P,)])

where:

8 is a constant defined by the cash portion of

patronage refunds and the discount rate (s’

above);

rc’ is normalized net savings with output price PY

as the numeraire, evaluated as total revenue per

unit (bushel) of grain (sold and or stored);

P’X is the normalized intermediate inputs cost per

bushel of grain;

P’w is the normalized wages expenditure per

bushel of grain;

P’, is the normalized price of capital, i.e., interest

expense per bushel of grain.

Following the development of (4), the S

function for intermediate inputs (including grain

purchases and storage), wages, and capital

expenditures can be obtained by differentiating

(5) with respect to PX, Pw and I’,.

S, = (lt 0) @, t B,, In Fx t p,, In Fw t bxk In P’, (6)

t 2 [S, sin In Plx - 0, cos In P*.J t y,Q t ET

SW = (lt 0) {f3, t f3_ In Fw t B,, In Fx t pwk In P’, (7)

t 2 [F, sin In I”,,, - $,,, cos In P’J t y,Q t ET

5
S’, = (1 t 0) ( Bk t pkk In P’, t f& In P’, t Bkw In Pw (8)

t 2 [6, sin In I”, - ok cos In I”,11 t ykQ t ET

where: SX = - rXX / TC’;

s*, = - Pw xw / lr*;

s”, = - r*, x, / ?r*;

1z, for i = x,w, and k, is a coefficient to estimate

neutral and non-neutral efficiency differences in

factor allocation; and

E a coefficient to proxy technical change.

Following Binswanger, the model includes a

coefficient <$ to capture any factor reallocation

that occurs during the study period and a proxy

measure for technical change (E). Binswanger

described a non-neutral efficiency difference (in

the sense of Hicks) as one in which the isoquant

does not shift inward homothetically, i.e., the

factor price ratio does not remain constant. In

such an event g is significantly different from

zero. If for example, the capital-labor ratio

increased during the period, then estimates of rk

>O, and r, ~0, would be expected. Since the

variable T is a simple linear trend (T=l, 2, . . . . lo),

if its coefficient (E) is significantly different from

zero, then certain time periods contributed more

to the outcome of the estimate than others. Such

an outcome strongly suggests that technical

change occurred during the period. When the

results of y and E are combined, inferences may be

drawn not only on the existence of technical

change but also on impacts of such change upon

factor reallocation among grain cooperatives.

Given the estimated parameters of equations

(5) - (B), the elasticities of output supply and

factor demands, evaluated at the simple mean of

S, are linear transformations of the parameter

estimates.

The own-price elasticity of demand (hii) for

each factor becomes:

llii = (-s’i /(l+ e)) - I - (Bii / (s’i /(l+ e))), (9)

for inputs i = x, w, and k. Similarly, the crosselasticity of demand (r+) for input i with respect

to a l-percent change in the price of the jth input

is:

‘lij = -sj /Cl+ e) - ‘Pii / si /Cl+ w, m

for i and j = x, w, and k; and i fj. The elasticity of

demand for input i (TQ with respect to an output

price, Py, is:

niy = Xi si /(lt Cl) t 1 t xj cpij / si /Cl+ co), (11)

for i = x, w, and k. The elasticity of output supply

(EJ with respect to the price of the input is given

by:

&yi = - Si /(It e) - zj pii / (1 t xj s; /(it e)), (12)

for i and j = x, w, and k. The own-elasticity of

output supply (EyV) is:

Eyy = xi s’i /(it 0) t xi xi pij / (1 t zj s’j /(It o)), 03)

for i and j = x, w, and k. Finally, the elasticity of

substitution (oij) is:

oij = qii / Sj me), (14)

for i and j = x, w, and k.

Each model was estimated by the iterative

Zellner (1962) efficient technique. SASO Proc

SYSNLIN, SUR was employed for each regional

estimate. Because the profit function is

homogeneous of degree 1 in P and W, the share

equations must also be homogeneous of degree 0

in P and W. This implies that while the profit

function may be estimated using a constant term,

the share equations may not. This condition is

satisfied in each system of equations by the use of

a matrix of linear restrictions. In addition to other

previously mentioned imposed conditions, each

price variable in the profit equation (I’,, Pw, PJ is

forced to equal the constant term in its respective

share equation.

6
Table 3-Critical and Wald statistics for specification search procedure

Region

CobbDouglas Translog Fourier

Critical Value Wald Critical Value Wald Critical Value Wald

Stat. Stat. Stat.

Corn Belt

Northern Plains

Pacific NW

Southern Plains

F.05(26.1695)= 1.46

F.05(26,545j = 1.48

F.05(26,323) = 1'47

F,05c26,s~, = 1.94

lm4'* F.05(16.1695) = 1.87 F -

1.66 1'81'

.01(12,1695) = *.18

F.01(12.545) = *.*

1.49

;.05(16.545) 1 ; .;;

.05(16,323) ' 1.47*

2.08 F.O5(16,64) = 2.1'

F.01(12,323) = 2.23

1.99* F,o,(,2s4J = 2.41 -

*Accept Null Hypothesis that the given parametric specification conforms to the information contained in the data set. (Specification search stops

upon acceptance of the Null Hypothesis.)

Model Validation

These estimates form the basis for deriving

output supply elasticity estimates for grain sales,

grain storage, and farm supplies sales and the

associated factor demand elasticities for

intermediate inputs, capital expenditures, and

labor. All elasticities are evaluated at simple

averages for Si, the variable input price, and of

the level of the fixed input.

Belt region, the translog specification for the

Northern Plains, Southern Plains, and Pacific NW

regions.

The Wald statistic with an F-distribution was

used for all statistical tests. To balance the

desirability of not estimating an

overparameterized model with the sensitivity of

the procedure for rejecting a false null hypothesis,

a monotonically non-decreasing significance level

for the more restrictive null hypothesis was

employed. Therefore, a 5 percent significance

level was used for testing the Cobb-Douglas and

translog specifications, and a 1 percent level of

significance was used to test the Fourier

specification. Once the null hypothesis could not

be rejected for a particular specification, the

search procedure stopped for that region.

Following Lopez, and Siddhu and Baanante,

validation tests were performed for symmetry,

negative semi-definiteness of the function

gradients, and convexity, to examine the

specification’s consistency with the properties of

the underlying net savings function. The test of

symmetry is a joint test on the validity of the

symmetry and parametric constraints across the

estimated net savings and share equations

(Siddhu and Baanante). The null hypothesis is

that the parameters of the share equations are

equal to the corresponding shares of the net

savings equation and that bij = bli for all i,j.

The condition of negative semi-definiteness

requires that the net savings function gradients be

positive regarding output prices and negative

with respect to factor prices (Lopez). And as in

Lopez, this condition is satisfied at each sample

point since the functional gradients are positive

with respect to output prices and negative with

respect to input prices.

The procedure is a joint test on the validity The test for convexity is performed by

of imposing 26,18, and 12 restrictions for the examining the determinants of the principal

Cobb-Douglas, translog, Fourier specifications, minors of the Hessian matrix at each sample point

respectively, to estimate jointly the net savings (Lopez). Local convexity is established given

and three share equations. The critical F-test and that: 1) the matrix is convex at each sample

computed Wald statistics are provided in table 3 observation; and 2) the net output supply

for each specification and all regions. The Cobb- equations show the expected signs for each ownDouglas specification was accepted for the Corn price elasticity.

7
EMPIRICAL RESULTS labor, and capital) regarding a l-percent change

in the output price is the same, 1.950 percent.

Corn Belt (corn-soybeans):

Northern Plains (wheat-barley-oats):

Parameter estimates of the net savings

function and share equations for grain

cooperatives in the Corn Belt region are provided

in table 4. Nested hypothesis testing led to the

selection of the Cobb-Douglas specification to

estimate the Corn Belt region. Own-share

relationship estimates are provided for three

factors: intermediate inputs (Bll), labor (B22), and

capital( B33). All own-share parameter estimates

are significant at the 0.0001 level.

The proxy coefficient for technical change

(ET), significant at the 0.01 level, indicates the

occurrence of technical change during the period.

Furthermore, the factor share parameters (CQ2

and CQ3 significant at the 0.0001 and 0.05 level,

respectively) suggest that at constant factor

prices, the factor shares would have changed.

Such an occurrence indicates that technical

change was non-neutral or factor saving (in the

sense of Hicks) for labor (CQ2=-0.03~0) and factor

using for capital (CQ3=0.01>0). In other words,

the efficiency gains brought by technical change

were labor saving (labor’s contribution toward

the production of grain cooperative goods and

services declined), and capital using (capital’s

share gained).

Derived output supply and factor demand

elasticities for grain cooperatives in the Corn Belt

states are listed in table 5. The Cobb-Douglas

functional form, selected by search as the most

representative specification for grain cooperatives

in the Corn Belt, has the characteristic of unitary

elasticity of substitution across all factors. This

feature implies that the impacts of exogenous

changes across the input demand functions of

intermediate inputs, labor, and capital are

symmetric. For example, in grain sales the

change in the demand for intermediate inputs

regarding a l-percent change in either the output

price or any other factor (labor, capital) is the

same, -0.449 percent. Furthermore, the supply

response of each factor (intermediate inputs,

Estimated parameters for grain cooperatives

in the Northern Plains are provided in table 6.

The translog specification was selected in the

search for the appropriate functional form to

represent grain cooperatives in this region. Each

of the own-share parameter estimates (e.g., Bll,

B22, and B33) is significant at the 0.0001 level.

Two of the three cross-share parameter estimates

(B13, and B23) were significant at the 0.05 level.

However, the parameter capturing the interactive

effects among intermediate inputs and labor (B12)

was not significantly different from 0.

The proxy coefficient for technical change

(ET), significant at the 0.20 level, slightly suggests

the occurrence of technical change during the

period. However, neither of the factor share

parameters (CQ2 and CQ3) is significantly

different from 0. So any technical change in the

Northern Plains was diffused to such an extent

that any realized efficiency benefits (economies of

scale) were factor neutral, i.e., at constant factor

prices, the factor shares did not change.

Derived output supply and factor demand

elasticities for grain cooperatives in the Northern

Plains are listed in table 7. Cooperative grain

sales and farm supply sales were somewhat

unresponsive to output and factor price changes.

Cooperative grain storage however, was quite

responsive to output price (i.e., Federal policies

that established storage rates) changes and altered

factor prices. Grain storage factor demand

elasticities are greater than I1 I for all but the

demand for labor regarding a change in capital

prices.

Southern Plains (wheat-sorghum):

Parameter estimates and diagnostic statistics

for grain cooperatives in the Southern Plains

region are listed in table 8. One parameter

estimate (833) is significant at the 0.01 level.

8
Table 4-Estimated parameters of translog net savings model for grain cooperatives in the Corn

Belt (corn-soybean) region, 1983-91

Nonlinear SUR Summary of Residual Errors

Equation

DF

Model Error SSE MSE R-Square Adj R-Sq

DurbinWatson

Net Savings 4.5 1165 71352 61.27265 0.0421 0.0392 1.843

ht. Inputs 1.5 1168 40.5616 0.03474 0.0868 0.0864 1.914

Labor 3 1166 59.2043 0.05078 0.0660 0.0644 1.893

Cahtal 3 1166 124.2765 0.10658 0.3848 0.3838 1.969

Nonlinear SUR Parameter Estimates

Parameter Estimate

Approx. ‘ T Approx.

Std Err Ratio Prob> ITI

A 4.218 0.3957 10.66 0.0001

82 -0.317 0.0846 -3.75 0.0002

83 0.044 0.0580 0.76 0.4455

Bll 0.059 0.0129 4.58 0.0001

B22 0.102 0.0118 8.69 0.0001

833 0.082 0.0042 19.47 0.0001

CQ2 -0.030 0.0064 -4.79 0.0001

CQ3 0.011 0.0052 2.16 0.0309

ET 0.007 0.0027 2.72 0.0065

SAS@ Proc SYSNLIN is employed for all parametric estimates.

Table 5-Derived output supply and factor demand elasticities for grain cooperatives in the Corn

Belt (corn-soybeans) region, 1983-91

Prices

Stocks output Intermediate

Inputs

Labor Capital

Grain Sales

output

ht. Inputs

Labor

Capital

0.950

1.950

1.950

1.950

-0.449

-1.449

-0.449

-0.449

Grain Storage

-0.291 -0.210

-0.291 -0.210

-1.291 -0.210

-0.291 -1.210

output 0.218 -0.004 -0.057 -0.157

ht. Inputs 1.218 -1.004 -0.057 -0.157

Labor 1.218 -0.004 -1.057 -0.157

CaDital 1.218 -0.004 -0.057 -1.157

Farm Supplies

output 0.532 -0.311 -0.165 -0.056

Int. Inputs 1.532 -1.311 -0.165 -0.056

Labor 1.532 -0.311 -1.165 -0.056

Capital 1.532 -0.311 -0.165 -1.056

9
Table 6-Estimated parameters of translog net savings function for grain cooperatives in the

Northern Plains (wheat-barley-oats) region, 1983-91

Nonlinear SUR Summary of Residual Errors

Equation

DF DF

Model Error SSE MSE R-Square Adj R-Sq

DurbinWatson

Net Savings

ht. Inputs

Labor

Capital

4.5 544.5 22754 41.78945 0.0367 0.0305 1.854

1.5 547.5 18.6700 0.03410 0.1190 0.1182 1.858

546 25.8980 0.04743 0.0753 0.0719 1.860

z 546 52.6348 0.09640 0.6418 0.6405 1.957

Nonlinear SUR Parameter Estimates

Parameter Estimate Approx. Std Err ‘T’ Ratio Approx. Prob> ITI

A 6.415 0.5178 12.39 0.0001

82 -0.028 0.1223 -0.24 0.8130

83 -0.095 0.0447 -2.13 0.0338

Bl 1 0.070 0.0155 4.53 0.0001

B12 0.010 0.0138 0.77 0.4425

B13 0.005 0.0022 2.33 0.0199

B22 0.093 0.158 5.93 0.0001

B23 0.004 0.0020 2.31 0.0214

833 0.082 0.0034 23.69 0.0001

CQ2 0.007 0.0091 0.81 0.4203

CQ3 0.003 0.0041 0.78 0.4361

ET 0.003 0.0022 1.36 0.1733

Table 7-Derived output supply factor demand elasticities for grain cooperatives in the Northern

Plains (wheat-barley-oats) region, 1983-91

Stocks output

Prices

Intermediate

Inputs

Grain Sales

Labor Capital

output 0.080

ht. Inputs 0.088

Labor 0.079

Capital -0.262

0.263

-0.460

0.263

0.177

Grain Storage

0.211 1.417

0.294 -0.087

-0.372 -0.092

0.207 -0.587

output 0.152

Int. Inputs 2.312

Labor -0.561

Capital 3.434

-0.004

-3.625

-4.477

-0.454

Farm Supplies

-0.119 0.033

2.576 -1.373

4.250 0.671

-0.163 -1.896

output 0.148 0.043 0.198 1.875

ht. Inputs 0.004 -0.256 0.257 -0.210

Labor 0.022 0.200 -0.347 -0.220

Capital -0.174 0.041 0.063 -1.019

10
Table 8-Estimated parameters of translog net savings function for grain cooperatives in the

Southern Plains (wheat-sorghum) region, 1983-91

Nonlinear SUR Summary of Residual Errors

Equation

DF DF Durbin

Model Error SSE MSE R-Square Adj R-Sq

DurbinWatson

Net Savings 4.5 322.5

ht. Inputs 1.5 325.5

Labor 3 324

Capital 3 324

17861 55.38232

9.9014 0.03042

11.3061 0.03490

36.6437 0.11310

Nonlinear SUR Parameter Estimates

0.0374 0.0270 2.090

0.0783 0.0768 2.096

0.0732 0.0675 2.083

0.0371 0.0311 2.109

Parameter Estimate

Approx. ‘ T Approx.

Std Err Ratio Prob> ITI

A

62

83

Bl 1

812

813

B22

823

833

CQ2

CQ3

E T

0.502 1.6715 0.30 0.7638

-0.103 0.4496 -0.23 0.8176

-0.670 0.2616 -2.56 0.0109

0.060 0.0448 1.35 0.1778

0.033 0.0412 0.82 0.4155

-0.016 0.0170 -0.99 0.3215

0.078 0.0532 1.48 0.1397

0.063 0.0465 1.37 0.1718

0.174 0.0608 2.87 0.0043

0.038 0.0471 0.82 0.4116

0.094 0.0330 2.85 0.0-046

-0.001 0.0031 -0.36 0.7223

Three parameters (Bll, B22, and B23) are

significant at the 0.20 level, or better. The proxy

coefficient for technical change (ET) is

insignificantly different from 0. However, the

factor share coefficient for capital (CQ3) is

significant at the 0.005 level.

Derived output supply and factor demand

elasticities are given in table 9. Grain sales and

farm supplies sales elasticities are relatively

inelastic. One exception for both was the change

output related to a change in the price of capital;

both have elasticities greater than 1 at 1.21 and

1.56 for grain sales and farm supplies sales,

respectively. Grain storage output and factor use,

however, are more responsive to relative price

changes. The grain storage own-elasticity of

demand for intermediate inputs and labor are

quite elastic at 2.61 and 3.85, respectively.

Pacific Northwest (wheat-barley):

Table 10 lists parameter estimates for grain

cooperatives in the Pacific Northwest. While the

translog was selected to be the most appropriate

specification, the relative fit of the estimate might

be questioned. Only two of the parameter

estimates (Bl 1 and B22) have T-values greater

than 1 and these estimates are significant at the

0.20 level only. The coefficient to proxy technical

change (ET) was insignificantly different from

zero (significant at 0.66), as were the factor share

parameters (CQ2 and CQ3, significant at 0.66 and

0.49, respectively). These results may be the

consequence of the relatively low number of

observations available for this region.

11
Table g--Derived output supply and factor demand elasticities for grain cooperatives in the

Southern Plains (wheat-sorghum) region, 1983-91

Prices

Stocks output Intermediate

Inputs

Labor Capital

Grain Sales

output 0.291

ht. Outputs 0.084

Labor 0.063

Capital -0.332

0.449

-0.477

0.238

0.169

Grain Storage

0.291 1.210

0.276 0.042

-0.274 0.039

0.202 0.034

output 0.210

ht. Inputs -0.571

Labor -4.555

Capital 2.009

0.004

2.614

0.500

-0.101

Farm Supplies

-0.057 -0.157

-0.910 -0.876

3.850 0.458

-0.033 -0.528

output 0.234 -0.311 0.165 1.556

Int. Inputs -0.016 0.075 0.311 0.026

Labor 0.012 0.223 -0.235 -0.050

Capital -0.230 0.026 0.075 -0.342

Table 1 O-Estimated parameters of translog net savings function for grain cooperatives in the

Pacific Northwest (wheat-barley) region, 1983-91

Nonlinear SUR Summary of Residual Errors

Equation

Net Savings

Int. Inputs

Labor

Capital

D F DF

Model Error

4.5 83.5

1.5 86.5

3 85

3 85

SSE MSE

3864 46.27282

2.4717 0.02857

3.3508 0.03942

10.4020 0.12238

Nonlinear SUR Parameter Estimates

R-Square Adj R-Sq

0.0525 0.0289

0.1723 0.1675

0.1006 0.0794

0.0068 0.0166

DurbinWatson

2.196

2.249

2.222

2.238

Parameter Estimate

Approx. ‘T Approx.

Std Err Ratio Prob> ITI

A 3.859 4.2909 0.90 0.3711

82 0.376 0.6452 0.58 0.5610

B3 -0.692 0.5553 -1.25 0.2157

Bll 0.083 0.0590 1.41 0.1626

812 -0.007 0.0571 -0.13 0.8961

B13 0.002 0.0276 0.08 0.9394

822 0.090 0.0667 1.35 0.1794

B23 -0.008 0.0633 -0.13 0.8933

B33 0.086 0.1296 0.67 0.5055

CQ2 -0.026 0.0611 -0.44 0.6604

CQ3 0.049 0.0710 0.70 0.4886

ET 0.005 0.0119 0.44 0.6625

12
Table 1 l-Derived output supply and factor demand elasticities for grain cooperatives in the

Pacific Northwest (wheat-barley) region, 1983-91

Prices

Stocks output Intermediate

Inputs

Grain Sales

Labor Capital

output 0.096

Int. Inputs 0.083

Labor 0.108

Capital -0.286

0.282

-0.391

0.205

0.176

Grain Storage

0.317 1.329

0.239 -0.076

-0.389 -0.082

0.210 -0.422

output 0.257

Int. Inputs -4.148

Labor -1.879

Capital 2.428

-0.062

1.070

1.150

0.033

Farm Supplies

-0.077 -0.118

3.186 -0.256

0.824 -0.241

0.080 -1.617

output 0.148 -0.426 0.364 1.943

Int. Inputs -0.016 -3.893 4.328 -0.332

Labor 0.021 2.726 -3.016 -0.396

Capital -0.154 0.004 0.054 -1.220

Table 12-Elasticities of substitution for U.S. grain cooperatives, 1983-1991

Prices

Stocks Intermediate

Inputs

Labor

Corn Belt (corn-soybeans)

Capital

Int. Inputs

Labor

Capital

-1 .oo 1 .oo

-1 .oo

Northern Plains (wheat-barley-oats)

1 .oo

1.00

-1 .oo

Int. Inputs

Labor

Capital

-1.43 0.92

-0.72

Pacific Northwest (wheat-barley)

-0.27

-0.18

-2.06

Int. Inputs

Labor

Capital

-1.82 0.78

-0.81

Southern Plains (wheat-sorghum)

-0.25

-0.17

-1.62

Int. Inputs -2.10 1.20 0.07

Labor -0.19 0.03

Capital -1.09

13
Derived output supply and factor demand

elasticities for grain cooperatives in the Pacific

Northwest region are provided in table 11. These

estimates should be used/viewed with caution

given the relatively loose fit of the model used to

derive them. Grain sales and farm supplies

elasticities of factor demand were highly inelastic.

However, grain cooperative use of intermediate

inputs and of labor in grain storage was highly

responsive to factor price changes.

Grain Cooperative Factor Substitution:

Table 12 presents elasticities of substitution

for each of the four regions. Because the Corn

Belt region was estimated using a Cobb-Douglas

specification, the elasticities of substitution all

have an absolute value of 1. In this case, the

impact across all variable inputs of an exogenous

price change is symmetric. On the other hand,

the impact of a similar exogenous price change in

the case of the translog specification varies across

input demand equations. The own-elasticities of

substitution have little economic meaning except

that each must obey the constraint X, C’; x oii = 0.

Cross-elasticities of substitution are positive for

substitutes and negative for complements. The

elasticity of substitution of intermediate inputs,

given a l-percent change in the price of labor, is

unitary or approaches unity in each of the four

regions. Labor and intermediate inputs appear,

therefore, to be the best substitutes. Intermediate

inputs and capital and labor and capital are

complementary in both the Northern Plains and

Pacific Northwest regions.

Model Implications

A variety of policy analyses are possible

given these estimates of cooperative output

supply and factor demand response to market

changes by product and region. For example, a lpercent reduction in the target price of wheat for

grain cooperatives in the Northern Plains will

simultaneously reduce grain sales by 0.08 percent,

grain purchases by 0.09-percent, and labor by

0.08- percent, and increase capital use by 0.26-

percent. In another example, suppose that loan

rates are reduced by 1 percent, reflecting a lpercent reduction in the cost of intermediate

inputs. Considering the same region, grain

cooperatives in the Northern Plains would then

increase their demand for intermediate inputs by

0.46- percent and reduce their demand for labor

and capital by 0.26- and 0.18-percent,

respectively.

Additionally, policy analysts may, in this

same manner, consider the impacts of minimum

wage laws (so long as the proposed policy is

effective to change wages paid), changing interest

rates, or a wide array of instruments that affect

the grain prices at the farmgate. Furthermore, it

is also possible to trace and compare the relative

impacts regarding grain cooperative products/

services (grain sales and storage, and farm

supplies sales) and across regions.

Historical Context

The dramatic changes of the past 20 years,

endured by the United States grain industry in

general, and grain cooperatives in particular, are

well documented (Dahl, 1990,1991a, 1991b;

Warman, 1993). In the 197Os, regional grain

cooperatives enjoyed almost a decade of export

expansion. Increased marketing margins

stimulated cooperatives to invest in the

infrastructure - rail cars, storage, and port

facilities seen then as necessary to meet

widespread expectations of expanding markets

(Dahl, 1991a).

However, just as these facilities were coming

on line in the early 198Os, the grain industry hit a

decade of declining export demand. Competition

for the markets that remained squeezed

marketing margins ever tighter (Dahl, 1991a).

Because of the investment surge, export

infrastructure was now in surplus. And given

that this new capital was mortgaged at unusually

14
high rates of interest, many grain cooperatives

became increasingly stressed financially.

The grain industry adjusted to reduced

export demand by major consolidations,

transforming the way the industry in general and

grain cooperatives in particular do business

(Warman, 1993a).

Grain marketing is now highly

decentralized, with the futures market as the basis

for pricing cash grain. Grain is no longer bought

and sold on a sample basis, but by forward cash

contracts that specify price, grade, and quality

premiums and discounts. Consignment

marketing of grain has mostly disappeared (Dahl,

1991b).

Innovations in grain transportation

contributed to the industry’s restructuring.

Because of the increased use of trucks and

multiple-car railroad shipping rates, local

elevators now ship grain directly to port and

bypass subterminal and terminal markets. The

Staggers Act (1980) deregulated railroad shipping

rates and allowed them to be negotiated among

grain handlers and shippers.

Although its broad powers were enhanced

by other transportation legislation of the period

(The Conrail Privatization Act of 1986), the

Staggers Act encouraged the direct movement of

grain from originator to final destination

(Warman, 1993). The combined affect of these

transportation innovations and railroad

deregula lion was to hasten the decline of grain

exchanges and terminal markets for cash grain

(Dahl, 1991b).

Furthermore, the farm financial crisis

coupled with United States farm policies

accelerated the present restructuring of grain

cooperatives. During the early 198Os, high

interest rates coupled with depressed land values

and low commodity prices forced many

agricultural producers out of the industry.

Moreover, as Government policies shifted

toward more market-oriented programs (e.g.,

lowering loan rates and target prices), grain

producers and handlers were forced to operate as

efficiently and cost-effectively as possible. Those

producers who remained in the industry tended

to be larger. More sophisticated operators

managed their own marketing programs.

Consequently, grain cooperatives not only lost

membership but saw competitors (now producers

as well as investor-owned firms) gain strength.

The impacts of this eventful period on grain

cooperatives in the United States are reflected in

the elasticity estimates of capital, particularly for

storage income but also for grain sales and farm

supplies sales. Payment made to elevators to

store grain held by Commodity Credit

Corporation (CCC) was a welcome additional

source of income to cooperative elevators during

a period of narrow margins.

About 4 percent of grain cooperative gross

income was storage income during the 1983-90

period. However, these Government programs

encouraged grain storage capacity expansion

during a period of excess capacity and delayed a

needed industry-wide consolidation (Gunn and

Cobia). Given that lucrative storage and handling

fees for Government-held grain are now greatly

reduced, cooperative elevators are under pressure

to substantially adjust capacity.

The impacts of other Government payment

programs (Payment-In-Kind, Acreage Reduction

Program, Conservation Reserve Program, PIK

and roll) are also reflected in the grain

cooperative elasticities. The PIK and roll program

increased grain sales volume and encouraged

managers to alter their method of acquiring grain.

PIK and roll increased the use of cash purchases

and the use of Delayed Price Contracts (DPC)2

(Gunn and Cobia).

The impacts of changes in the rail

transportation industry, also reflected in the grain

cooperative elasticities, were somewhat offsetting

in effect. The savings associated with unit-train

rates encouraged elevators to add load-out

capacity. However, rail line abandonment caused

many cooperative elevators to loose business to

their competitors (who retained rail shipping

ability), to become supplemental storage units for

elevators with rail, or even to exit the industry.

2 A practice of grain acquisition in which the elevator takes

possession of and title to the grain, but the price is not determined

until a later date.

15
CONCLUSIONS

This study derived important economic

information regarding the input and output

responses to market changes for grain

cooperatives in the United States The elasticity

estimates are derived for output supplies, factor

demands, and factor substitution, for three grain

cooperative products/services (grain sales, grain

storage, and farm supplies sales) and three

factors, intermediate inputs, labor, and capital;

and for the four major grain producing regions in

the United States (Corn Belt, Northern Plains,

Southern Plains, and Pacific Northwest). The

existence and impacts of technical change upon

cooperative input demand was also derived.

Although important in their own right, these

estimates also make an array of policy analyses

possible. Elasticities provide a way to trace the

impacts of cooperative adjustments to market and

policy changes. These estimates also provide a

way of projecting grain cooperative response to

anticipated market and policy changes.

The next report in this series will combine

the elasticity estimates derived in this report with

additional information to quantify the impacts of

the significant market and policy changes that

occurred during the 1980s.

Boland, L.A. 1981. “On the Futility of Criticizing

the Neoclassical Maximization Hypothesis.”

American Economic Review. 71(3):1031-1036.

. 1983. “The Neoclassical

Maximization Hypothesis: A Reply.” American

Economic Review. 73(3):831-833.

Caldwell, B.J. 1983. “The Neoclassical

Maximization Hypothesis: Comment.” American

Economic Review. 73(3):828-830.

Chambers, R. 1984. “Agricultural and Financial

Market Interdependence in the Short Run.”

American Journal of Agricultural Economics. 66(l):

12-24.

Chavas, J.P. and T.L. Cox. 1988. “Nonparametric

Analysis of Agricultural Technology.” American

Journal of Agricultural Economics. 70(1):303-310.

Cochrane, D. and G.H. Orcutt. 1949. “Application

of Least Squares Regressions to Relationships

Containing Auto Correlated Error Terms.”

Journal of the American Statistical Association.

44(1):32-61.

Dahl, R.P. 1990. “Structural Change and

Performance of Grain Marketing Cooperatives.”

Department of Agricultural and Applied

Economics, University of Minnesota, Staff Papers

Series, Staff Paper P90-54, October.

. 1991a. “Structural Changes in the

United States Grain Marketing System.”

Department of Agricultural and Applied

Economics, University of Minnesota, Staff Papers

Series, Staff Paper P91-35, September.

. 1991b. “Structural Change and

Performance of Grain Marketing Cooperatives.”

Journal of Agricultural Cooperation. 5:66-80.

16
De Alessi, L. 1983. “Property Rights, Transactions

Costs, and X-Efficiency: An Essay in Economic

Theory.” American Economic Review. 73(1):64-81.

Diewert, D.L. 1971. “An Application of Shepherd

Duality Theorem.” Journal of Political Economy.

79(2):481-507.

.1972. “Functional Forms for Profit and

Transformation Functions.” Journal of Economic

Theory 5(l):

A1974. “Applications of Duality Theory.”

In Frontiers of Quantitative Economics, vol. 2. ed.

M.D. Intrilligator and D.A. Kendrick, Amsterdam:

North-Holland Pub. Co.

Dillon, J.L. and J.R. Anderson. 1971. “Allocative

Efficiency Traditional Agriculture, and Risk.”

American Journal of Agricultural Economics.

53(1):26-32.

Durbin, J. and G.S. Watson. 1950. “Testing for

Serial Correlation in Least

Squares Regression.” Biometriku. 37(2):409-428.

. 1951. “Testing for Serial Correlation

in Least Squares Regression.” Biometriku.

38(1):159-17&x

Fawson, C. and C.R. Shumway. 1988. “A

Nonparametric Investigation of Agricultural

Production Behavior for United States

Subregions.” American Journal of Agricultural

Economics. 70(1):311-317.

Gunn, S.P. and D.W. Cobia. 1992. “Grain

Marketing Cooperatives’ Adjustments to Farm

Programs.” Department of Agricultural

Economics, Agricultural Experiment Station,

North Dakota University, Agricultural Economics

Report No. 291, September.

Harvey, A.C. 1981. The Econometric Analysis of

Time Series. Deddington: Philip Alan Publishers.

Hotelling, H. 1932. “Edgeworth’s Taxation

Paradox and the Nature of Demand and Supply

Functions.” Journal of Political Economy. 40(2):577-

616.

Jeffreys, H. 1967. London:

Oxford University Press.

Jorgensen D.W. and L.J. Lau. 1973. “The Duality

of Technology and Economic Behavior.”

Discussion Paper No. 252, Cambridge HIER.

Judge, G.E., W.E. Griffiths, R.C. Hill, H.

The Theory and Prac

2d Edition. New York: J

and Sons.

Lau, L.J. 1972. “Profit Functions of Technologies

Review of

Economics and S tis tics. 54(2):281-289.

and P.A. Youtopolos. 197

Supply and Factor Demand Functions.”

American Journal of Agricultural Economics 56(1):11-

18.

Learner, E.E. 1983. “Let’s Take the Con Out of

American Economic Rev

78(1):31-43.

Lee, H. and R.G. Chambers. 1986. “Expenditure

Constraints and Profit Maximization in U.S.

American Journal of Agri

Economics, 68(3):857-865.

Lopez, R.E. “Estimating Substitution and

Expansion Effects Using a Profit Function

American Journal of Agri

Economics. 66(1984):358-367.

 K.R. and S. Larson. 199

Expected

 Paradox. and 0.

 p. 33-409. Dordrecht Holla

Jour. of Agric

14(1):200-212.

17
McFadden, D.L. 1973. “Cost, Revenue and Profit

Functions.” In An Econometric Approach to

Production Theory, D.L. McFadden ed.,

Amsterdam: North-Holland Pub. Co.

Mountain, D. and Cheng, H. 1989. “A Combined

Structural and Flexible Functional Approach for

Modeling Energy Substitution.” Journal of the

American Statistical Assoc. 84(1):76-87.

Pope, R.D. 1980. “The Generalized Envelope

Theorem and Price Uncertainty.” Znternutionul

Economic Review. 21(1):75-85.

. 1982a. “Expected Profit, Price Change,

and Risk Aversion.” American ]ournul of

Agricultural Economics. 64(2):581-584.

. 1982b. “To Dual or Not to Dual.”

Western Journal of Agricultural Economics. 7(1):337-

351.

Roy, A. 1942. “Del’ Utilitie: Contribution de La

Theorie de Choix.” Paris: Hermann, et Cie.

Royer, J.S. 1978. “A General Nonlinear

Programming Model of a Producers Cooperative

in the Short-Run.” Unpublished Ph.D. thesis,

Iowa State University.

Samuelson, P.A. 1953. “Prices of Factors and

Goods in General Equilibrium.” Review of

Economic Studies. 2(1):1-20.

SAS Institute Inc. SAS/ETSTM User’s Guide,

Version 5 Edition, Car, NC: SAS Institute Inc.,

1984, pp 505-550.

Shapiro, S.S. and M.B. Wilks. 1965. “An Analysis

of Variance Test for Normality (Complete

Samples).” Biometrika. 52(2):591-611.

Shepard, R.W. 1953. “Cost and Production

Functions.” Princeton: Princeton University Press.

Shoemaker, P.J.H. 1982. “The Expected Utility

Model: Its Variants, Purposes, Evidence and

Limitations.” Journal of Economic Literature.

20(2):529-563.

Siddhu, S.S. and CA. Banaante. 1981. “Estimating

Farm Level Input Demand and Wheat Supply in

the Indian Punjab Using a Translog Profit

Function.” American Iournul of Agricultural

Economics. 63(1):237-246.

Taylor, C.R. 1984. “Stochastic Dynamic Duality:

Theory and Empirical Applicability.” American

Journal of Agricultural Economics. 66(2):351-357.

.1990. “Duality, Optimization and

Microeconomic Theory: Pitfalls for the Applied

Researcher.” Western Journal of Agricultural

Economics. 14(1):200-212.

Varian, H.R. 1984. “The Nonparametric Approach

to Production Analysis.” Econometrica. 52(3):579-

597.

. 1985. “Non-parametric Analysis of

Optimizing Behavior with Measurement Error.”

Journal of Econometrics. 30(2):445-458.

Warman, M. 1993. “Changing Grain Market

Structure Poses Challenge to Cooperatives.”

Farmer Cooperatives 59(10):4-8, January.

Wold, H. 1938. “The Analysis of Stationary Time

Series”, 1st ed. Uppsala: Almquist and Wicksell

Wu, De-Min. 1983. “Tests of Causality

Predeterminedness and Exogeneity.” International

Economic Review. 24(2):347-358.

Zellner, A. 1962. “An Efficient Method of

Estimating Seemingly Unrelated Regression and

Tests of Aggregation Bias.” Journal of the American

Statistical Association. 57(2):348-375.

18
Appendix

(SAS code for Varian’s non-parametric test of the profit maximization hypothesis.)

DATA WORK1 ; SET GRAINS.MASTER;

WHERE GRAINVOL GT 0 AND GRAINSLS GT 0

AND LABOREXP GT 0 AND NETINTRS NE.

AND TOTEXPNS GT 0 AND NETINCOM NE. ;

%MACRO WAPM(REG);

DATA WORKZ; SET WORKl;

WHERE REGION=®

*SET IMPLIED FACTOR PRICES;

*

PSALES = GRAINSLS / GRAINVOL;

PSTORE = SUM(GROSSINC, -GROSSMGN) / GRAINVOL;

PY = SUM(PSALES,PSTORE);

PW = LABOREXP / GRAINVOL;

PK = NETINTRS / GRAINVOL;

PX = (TOTEXPNS - SUM(LABOREXP,NETINTRS))/ GRAINVOL; PROC PRINT;

DATA WORK3;

SET WORK2 NOBS=TOTOBS;

IF -ERROR_=1 THEN ABORT ABEND;

FLAG=O; COUNT=O; TEST1 =O;

DO I = 1 TO TOTOBS-1;

SET WORK2 POINT=I;

NSI=NETINCOM; PI=PY; YI=GRAINVOL;

WI=SUM(PW,PK,PX); L=TOTOBS-I;

DO J = 1 TO L; K=J+I;

SET WORK2 POINT=K;

IF -ERROR_=1 THEN ABORT ABEND;

NSK=NETINCOM; XK=GRAINVOL;

IF NSI GT NSK AND PI*YI-WI*XK GT 0 THEN FLAG=FLAG+l;

COUNT=COUNT+l ;

END;

END;

PUT REGION TOTOBS FLAG COUNT; STOP;

%MEND WAPM;

%WAPM(‘CORN BELT’);

%WAPM(‘NORTHRN PLA’);

%WAPM(‘PACIFIC NW’);

%WAPM(‘SOUTHRN PLA’);

RUN;

19
U.S. Department of Agriculture

Agricultural Cooperative Service

P.O. Box 96576

Washington, D.C. 20090-6576

Agricultural Cooperative Service (ACS) provides research, management, and

educational assistance to cooperatives to strengthen the economic position of farmers

and other rural residents. It woks directly with cooperative leaders and Federal and

State agencies to improve organization, leadership, and operation of cooperatives and

to give guidance to further development.

The agency (1 ) helps farmers and other rural residents develop cooperatives to obtain

supplies and services at lower cost and to get better prices for products they sell; (2)

advises rural residents on developing existing resources through cooperative action to

enhance rural living; (3) helps cooperatives improve services and operating efficiency;

(4) informs members, directors, employees, and the public on how cooperatives work

and benefit their members and their communities; and (5) encourages international

cooperative programs.

ACS publishes research and educational materials and issues Fanner Cooperatives

magazine. The United States Department of Agriculture (USDA) prohibits discrimination

in its programs on the basis of race, color, national origin, sex, religion, age, disability,

political beliefs and marital or familial status. (Not all prohibited bases apply to all

programs). Persons with disabilities who require alternative means for communication of

program information (braille, large print, audiotape, etc.) should contact the USDA Office

of Communications at (202) 720-7808 (TDD).

To file a complaint, write the Secretary of Agriculture, U.S. Department of Agriculture,

Washington, D.C. 20250, or call (202) 720-7327 (voice) or (202) 720-l 127 (TDD). USDA

is an equal employment opportunity employer.