Abstract A fixed effect production function model is adopted and estimated in this paper for evaluating the agricultural policies of the Soviet planners in Russia (formerly RSFSR) and Kazakhstan from 1953 to 1980. In particular, the functional form allows the variance of output to increase or decrease as one input is increased. Our estimates suggest the following assessment of the Soviet planners' agricultural policies during the command economy days: First, the extension of farming in Kazakhstan with generally inferior soils and climate resulted in lower crop levels (with identical input applications). Second, the massive inflow of capital resources and sharp rise in fertilizer use in agriculture during the Brezhnev years (1964-1982) did not contribute significantly to crop levels in the two republics. Finally, the extension of the cultivated area into marginal lands generally, and of fertilizer use in wrong mix and form contributed to the instability of agricultural output. In conclusion, we emphasize the need for specifying and estimating appropriate models for evaluating Soviet agricultural policies especially because farm-level data are rapidly becoming available in the republics of the former Soviet Union.

February 16, 1994 Preliminary Comments welcome Modeling Soviet Agriculture for Assessing Command Economy Policies by Padma Desai Columbia University and Balbir Sihag University of Lowell

The increasing availability of firm and farm level data in Russia and other republics of the former Soviet Union is contributing to scholarly research in several directions. In particular, the use of the production function as a microeconomic tool of empirical analysis with the aim of drawing policy conclusions in specific activities is much in evidence. Thus, Danilin, Materov, Rosefielde and Lovell (1984) estimate technical efficiency in Soviet cotton refining from a 1974 sample of 151 enterprises and conclude that its production efficiency is high in relation to the estimated stochastic frontier, and exhibits little inter-enterprise dispersion. Johnson et al. (1994) employ a similar stochastic frontier analysis to data for 11,400 farms for six years (from 1986 to 1991) and provide measures of technical efficiency and its inter-farm variation. Both studies draw on current estimation procedures and extend them to increasingly complex functional specifications. At the same time, they speculate on the impact of Soviet planning procedures and managerial incentive systems on the performance, as indicated by their estimates, of the relevant activity. These pioneering studies herald the liberation of planned economy empirical research from its early efforts constrained by the paucity of data, and their availability by industrial branches and sectors of economy. The use of large, microeconomic data set for econometric estimation with continuing refinements in the functional form and estimation procedures makes the estimates credible. When these are employed for explaining the role of the planners in influencing the performance of this or that activity,

the exercise comes closer to being authentic. As these economies

move to free markets, the initial studies can also provide a

meaningful anchor for contrasting the performance of the original

production units (in the panel data set) with their fortunes at a

future date.

While such data are becoming increasingly available for post-

Soviet agriculture, the critical issue consists in linking the

proposed analysis with the available, state-of-the-art scientific

work. The important contributions of Anderson, Buccola, Griffiths,

Just, McCarl and Pope provide the necessary foundations from two

perspectives.

First, the production function must be defined such that it

captures the peculiarity of agricultural activity. In the standard

production function with the multiplicative error term, the

marginal risk defined as the partial derivative of the variance of

output with respect to a given input is positive for all inputs.1

This implies that the reduction at the margin of, say, pesticide

use will reduce crop variability whereas actually it might raise

such variability. Therefore, the functional form must permit the

variance of output to increase or decrease as one input is

increased. Following Just and Pope (1978, 1979), and Griffiths and

Anderson (1982), it can be stated as follows:

k «.

k fl.

Q = f(X) + h(X) = T T X 1 + T T X 1

(1)

where Q is the level of output, X^ is the level o-f the ith

input and is a stochastic error term with zero mean and

variance of"

For a rigorous proof, see Just and Pope (1979, p. 277) .

This more general formulation permits greater analytical flexibility with respect to the effect of an input on mean farm output and its variance.2 Second, Griffiths and Anderson (1982) suggest that time series data may be needed to estimate / V s in equation (1) since in a cross-section series, much of the variation in output "...can be attributed to weather variation and if the increased use of some inputs is to have mitigating effect on output variation, observations over time are likely to be needed to capture this effect." (p. 529). On the other hand, cross-section data are necessary, in their view, to estimateoc/s in equation (1) because input levels in a farm may not vary significantly over time to allow estimation ofcC/s. Therefore, they recommend the pooling of cross-section and time-series data to estimate equation (1). However, appropriate statistical tests must be undertaken to justify such pooling. Additionally, the model in (1) , which is nonlinear and includes the stochastic function h(X) can be specified in various ways. Therefore, in Section I, we state our model and discuss the statistical tests necessary for accepting the parametric estimates. The sequence of steps for estimating the model is stated in Section However, the residual h(Xt, ft )Јt is generally heteroscedastic and therefore creates problems about hypothesis testing and the statistical properties of the estimates of °C. and /3t. Despite the presence of heteroscedasticity, the ordinary least squares (OLS) and nonlinear least squares (NLS) estimates of eCj are unbiased and consistent; however, they are asymptotically inefficient. (Buccola and McCarl, 1986, p. 732.)

II. In Section III, we present some estimates for the two republics of RSFSR (currently Russia) and Kazakhstan based on our (fixed effect) specification. In conclusion, we interprete our results and link them to the decisions implemented by Soviet planners in the command economy days. In particular, our estimates suggest that while increased fertilizer use raised mean agricultural output modestly, it increased its variance.3 In conclusion, we emphasize that the policies of planners in Soviet agriculture cannot be assessed properly without incorporating the special features of farming in the model. More so as detailed, farm-level information becomes available. I. The Model and the Required Statistical Tests The fixed effect model (alternatively known as the covarinace model) adopted by us is stated as follows:

.N

T

K *k

K #k

Qit =

1 -- C.

t-- C.

K--1

K=l

where

Z j t = 1 for the ith cross-sectional unit = 0 otherwise (i=2,3...N) Wit = 1 "f°r t n G * t h time period = 0 otherwise (t=2,3 T) $i measures the unit-specific effect and S^. measures the time--specific effect E(it) = 0, Var

In a pathbreaking study of Indian foodgrain production,

Mehra (1981) showed that the improved seed/fertilizer-

based technologies (beginning from the mid-1960s) raised

grain yields but increased their instability compared to

the earlier years.

Note that in this fixed effect model, the dummy variables Zit and Wit are included to allow for, say, differences in soil quality in the two republics and of weather over time.4 What are the implications of this procedure? Suppose we adopt a dummy of 1 for soil quality in the RSFSR and 0 in Kazakhstan.5 The soil quality of the RSFSR agricultural belt is a mixture of the chernozem (black), forest-steppe and steppe soils.6 On average, the soils in Kazakhstan are inferior with a combination of steppe and semi-desert soils. The adoption of the dummies here implies that It must be emphasized that soil quality is mentioned here as an illustrative feature distinguishing one republic from the other. Another distinguishing element can be the extent of irrigation facilities. The relative breakdown of farms in collective (kolkhoz) and state (sovkhoz) types with differing incentives to farm workers is yet another aspect. Again, these features can be measured in the unitspecific effect for a set of farms when they are pooled together according to a distinguishing characteristic such as a soil zone. Instead of the 0-1 dummies, one can devise soil indexes for the republics (or for a group of farms in a given soil zone) based on a detailed mapping of soil types in their agricultural belts. Such an index will reflect soil differences in a republic (or the selected farms) in relation to average soil. It is also possible to construct an irrigation index reflecting the availability of irrigation water in a republic (or in a set of farms) . Similarly, time series of weather indexes can be constructed for a republic (or farms in a climate zone) on the basis of weather data used by Desai (1986). For a discussion of the variety of soils in the Soviet agricultural belt, see Desai (1986, Chapter 3 ) .

the soil differences in the two republics and their impact on output are nonrandom.7 In any case, it is necessary to test if there are systematic differences between the two republics with respect to, say, soil quality and other features, or weather, or both. For this purpose, it is necessary to apply appropriate tests. Statistical Tests: Suppose we want to establish in our fixed effect model that there are no systematic differences of soil quality and weather (from year to year) between the two republics. For this purpose, we must test the null hypothesis that 0; = 0, St = 0. Additionally, we must test the hypothesis that the coefficients ock are identical for each republic in order to justify the pooling of the time-series and cross-section data. The detailed steps of applying these tests for the fixed effect model are stated in the Appendix. II. Estimation Methodology The procedure for estimating the fixed effect model is essentially similar to those for estimating the random effect model By contrast, in the random effect model (discussed extensively by Just and Pope, and Anderson and Griffiths) the likely magnitude of the impact of republic-specific feature such as soil quality is included in the error term and is random. Among the statistical differences of the two models, note that the fixed effect model adopted by us sacrifices many degrees of freedom whereas the random effect specification saves degrees of freedom and the estimators are, therefore, likely to be efficient. On the other hand, its major limitation is that if the omitted variables, such as soil quality and weather, are related to the explicitly specified inputs on the right hand side of the equation, the estimated coefficients can be biased and inconsistent implying a misspecification.

developed by Just and Pope (1979) and further refined by Griffiths and Anderson (1982). We state the sequence of steps for our fixed effect model because we have employed the first two steps for deriving the results reported in Tables 1 and 2. Step 1. Run a nonlinear regression on the first part of K #k equation <2) (i.e. without j,Ј TT X ^ J ^ and compute the residuals

K uit =

Step 5. Regress the residuals

on the inputs as follows

2

K

and transform equation < 2)

k=l

by dividing both sides by h^t. Run again a nonlinear regression as in step 1 to obtain X, 6^, 6'^ and ocik?ns equation (2) . §tep__Јt. iterate the above steps two or three times to obtain e-fficient estimators of

cn LO

en

en

o

LO

cn

CM LO CO

o cn CO

r-- LO ·

· cn

1--·

CM CM

i

1

1

CO

ct:

CO

co

00

CO

oo

LO

ro

CM

cu «a-1-- a ··- i_ cu

CO o O i en r-- CO LO CO i-- oo

CO

cr>

CM CO

c

CM

LD o CO <

oo LO co CM C\J LO o <--

o *d- CO i-- O UD oo

cr» o e CO CM i-- CM O CM

CO CM

«3- CO

OJ

LO vo

oo vo C\J

LO en

O co

o co

O CM

oooo

00 O cn o

en vo

o co CO «3" c n r*>. LO en CM i--

13

cu

G.

o

oo

o

o a:

o

CM

CM

LO

CO

i--

CO

CM

co

CO

o

LO o

LLJ oo

CO

o

o

o

CM LO

CM

LO

^

I

, 7832 7662 4143 ,2783

,1016) ,1405 ,0178)

LO en o

CM ca O

LO LO

r-o.

oo

o i--

L O r-> CM O CO .a r»» co CM co r-» co CO LO o CM

econ *3o- UD CO

CO. -i- ca

vo en r-- O CO LO I-- LO CM CM

r«. O LO CM .-- LO cn r** oo

o rv. en o en «acn r»« oo

C M co CO CO cr-o» ^or CO

(0 +-> CM -r- o -a r-- C en a3

co CM i CM LO oo

oo i oo

3

o 00.

CM CO en L O LO r-^

co r*. i-- 00 en r--

CO r-^

LO o

oo

o a:

10 Notes to Tables i and 2 1. The estimates in rows <1) and (2) of Table i are derived by fitting equation (2*), and in rows <3) and (4) by fitting equation (2") with pooled data for the two republics of Kazakhstan and RSFSR. However, as stated in the text* »g is constrained to be zero in row (3) and is estimated iv» row (4). The estimates of Table 2 are derived by fitting the equation in step 2 on page 7 . The equations in Table 1 are nonlinear whereas in Table 2? they are specified in double--log formulation- Furthermore? the dependent variables in the equations of rows (1?) and (2*) are the (natural) log of the absolute values of the error terms estimated from the equations in rows (1) and (2)? and the explanatory variables are also in (natural) log. Finally? the estimates in row ( V ) of Table 2 are derived by pooling the data of the two republics- Here the dependent variable is the (natural) log of the absolute values of the error terms of the equation in row 2. Values in parentheses are t values of the estimated parameters. SER is the standard error of the regression, LLF is the log of likelihood function? DW is the Durbin--Watson statistic and R1- is (correlation coefficient)^.

11

carried out. In other words? we have not corrected for

heteroscedasticity to achieve efficient estimates- Also? the

statistical test with regard to the equality of ot^'s

(k=l?2?3?4) across the republics in justification of pooling

the data for the two republics has not been performed. In

Table 1? S«^f=l and in Table 2? (Sjf'sj as already stated? are

not constrained to be non--negative. Finally? the dummy

variables Wjj- representing time--related effects such as

year--to--year variations in weather are not included

111 the

estimation. However? the dummy variable Z^t

representing republic-specific effect such as different soil

quality is incorporated. This implies that the equation for

estimating the parameters for Kazakhstan (specified as

republic 1) and RSFSR (specified as republic 2) in rows <1)

and (2) of Table 1 is:

K aki

K ^ki

where i = l?S and k=l?2?3?^f Tor the four inputs? whereas the specification for estimating the parameters for the pooled data of the two republics in rows <3) and <^> is:

.

K ak

K #k

a i t = iX+ e a z a t > " / k i t + i t ' / k i t

<2">

where i=l,2? k=l?2?3?4? and Z 2 t is the dummy of 1 for RSFSR and 0 for Kazakhstan. However? note that in row (3) of the

12

Table? &g=Q implying that- X is identical for the two

republics whereas in row (4), 0= is estimated which implies

that if A is the constant term for Kazakhstan? then the

constant term for RSFSR is

In row (2) of Table 1? the coefficients «^. have

positive signs but in row

is negative. The estimating equation for both is < 2 =· ) . When

the data for the two republics are pooled in row <3> and 8p

is constrained to be zero implying that the values of ot^'s

and the constant term \ are equal for both the republics?

the estimates of the coefficients otj, change significantly

and the coefficient with respect, to capital becomes

negative- On the other hand? in row (4)? 0g is allowed to

vary. As a result? the standard error of the regression

falls? all the coefficients have expected signs? and most of

the coefficients and? in particular? 8g? are statistically

significant. In view of the statistically significant value

of Op? we reject the null hypothesis that Gg = 0 .

What do the results of row <4) in Table 1 imply? First?

the coefficient of (A+82) for RSFSR estimated at 1.0366 <0.6639 + 0.37S7) exceeds the corresponding term in

Kazakhstan with a value of 0.6639. This implies that? for

identical input levels? crop levels in RSFSR would be higher

than in Kazakhstan. This may result from say the superior

soils in RSFSR. Or perhaps in the RSFSR? relatively more

farms are organized along collective lines implying an ed«je

in farm incentives. "the dummy

=-?=*·

13

with an estimated parameter of 0.3727 incorporates the

combined impact of several such features. Clearly, it is

important to separate these by employing properly--specified

indexes each incorporating these aspects for the republics.

Second* the ·

*" estimates suggest very small output

elasticities with respect to capital and fertilizers. If

these estimates are correct? a further application of

capital and fertilizers does not contribute significantly to

augmenting crop levels. (Note that the impact of these

inpubs on crop variabi1i ty is a separate issue and is

analyzed in terms of the estimates of

The estimates of ft^ °"r Table 2 are derived on the basis

of step 2 on page 7 . The estimated constant term here is

jSo. The results in row (4*) with the pooled data provide a

better fit than in rows (1) and (2). Most of the

coefficients are statistically significant. Also? the signs

of the coefficients &re in line with our expectations: the

variance in output increases with increases in the area

under cultivation and fertilizers? and the variance

decreases with increases in capital and labor.

The presumption here is that increased use of fertilizers without matching applications of new seed varieties? pesticides and water can raise crop variability. For evidence in support of this argument with respect to Soviet- graingrowing, see Desai (1937, chapter 6 ) .

14 Our estimates throw light on the agricultural policies pursued by the Soviet planners in RSFSR and Kazakhstan for almost three decades ending in 1980. First, the extension of farming in Kazakhstan with generally inferior soils and climate resulted in lower crop levels (with identical input applications). Second, the massive inflow of capital resources and sharp rise in fertilizer use in agriculture during the Brezhnev years (19641982) did not contribute significantly to increased crop levels in the two republics. Investments were channeled into agriculture, without consideration of costs or returns, over wide-ranging activities such as land drainage and reclamation, rural roadbuilding and provision of social infrastructure, increasing the supplies of machines without regard to quality or spare parts, and setting up agroindustrial complexes. By 1982, outlays in agriculture had reached 27 percent of total investment in the economy. At the same time, fertilizer use per kilogram of hectare under grain had jumped sixfold from 8.9 kilograms in 1964 at the start of the Brezhnev leadership to 54 kilograms in 1982. Finally, the extension of the cultivated area into the marginal lands generally, and fertilizer use in wrong mix and form contributed to instability of agricultural output. Even at the republic level, our results can be improved by including suitable soil features and weather indexes. However, our preliminary estimates mark a significant step in specifying and estimating an appropriate model for evaluating Soviet agricultural Details are in Desai (1987 p. 243, and 1992)

15 policies. These refinements are equally important when farm-level data are used for assessing agricultural policies in the former Soviet Union.

16 Appendix METHOD OF HYPOTHESIS TESTING Testing the Assumptions of the Fixed Effect Model Testing the Null Hypothesis 6^=0 We estimate equation (2) with and without the constraint. For example? the null hypothesis $2=O means that the second republic (RSFSR) is not different from the first (Kazakhstan) and a rejection of the null hypothesis implies that RSFSR is diffrent from Kazakhstan. We apply the likelihood ratio test to test the null hypothesis. That is LR = -2CL(o(,iT2> - L ( « , L T 2 ) D -V X ^ where L(«,ff2) is the log of likelihood function with the constraint (i.e. &g=0) and L < « , cr'^) is the log of likelihood function without the constraint. Similarly, the likelihood ratio test can be used to test the null hypothesis <5"t=0 and the equal i ty (between the republics) of the coefficients oc^,.

17 References Buccola, Steven T. and Bruce A. McCarl (1986), "Small-Sample Evaluation of Mean-Variance Production Function Estimators," American Journal of Agricultural Economics. August, pp. 73238. Danilin, V. I., Ivan S. Materov, Steven Rosefielde and C.A. Knox Lovell (1984), Measuring Enterprise Efficiency in the Soviet Union: A Stochastic Frontier Analysis," Economica, May, pp. 225-33. Desai, Padma (1986), Weather and Grain Yields in the Soviet Union, Washington, D.C.: International Food Policy Research Institute. (1987), The Soviet Economy: Problems and Prospects, Oxford: Basil Blackwell. (1992), "Reforming the Soviet Grain Economy: Performance, Problems, and Solutions," The American Economic Review. May, pp. 49-54. Griffiths, William E. and Jock R. Anderson (1982), "Using TimeSeries and Cross-Section Data to Estimate a Production Function with Positive and Negative Marginal Risks," Journal of American Statistical Association, September, pp. 529-36. Johnson, Stanley R. , Aziz Bouzaher, Alicia Carriquiry, Helen Jensen, P.G. Lakshminarayan and Peter Sabluk (1994), "Production Efficiency and Agricultural Reform in Ukraine," American Journal of Agricultural Economics, forthcoming. Just, R.E. and R.D. Pope (1978), "Stochastic Specification of Production Functions and Economic Implications," Journal of Econometrics. June, pp. 67-86. (1979), "Production Function Estimation and Related Risk Considerations," American Journal of Agricultural Economics, May, pp. 276-84. Mehra, Shakuntla (1981), Instability in Indian Agriculture in the Context of the New Technology, Washington, D.C.: International Food Policy Research Institute.

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