System of output supply and factor demand : equations for semi-arid tropical India

SYSTEMS OF OUTPUT SUPPLY AND FACTOR DEMAND EQUATIONS FOR SEMI-ARID TROPICAL INDIA Shantin L. Bapna, Hans Binswanger and Jaime B. Quizon Series: Studies in Employment and Rural Development No. 73 Division: Employment and Rural Development Department: Development Economics Development Policy Staff International Bank for Reconstruction and Development The authors are Assistant Professor, Indian Institute of Management, Ahmedabad; Economist, World Bank; and Visiting Fellow, Yale University. The project was supported by the International Crops Research Institute for the Semi--Arid Tropics, Hyderabad, India with which the first two authors were associated for a number of years. It was also supported by a research grant of USAID to Yale Universit:r and by the Economic Growth Center, Yale University. The generous support of these institutions is gratefully acknowledged. The views expressed in this paper, however, do not necessarily reflect those of the sponsoring institutions or the current employers of the authors. All computations in this paper used the programs "Elasticities" prepared by Sidney Feit. We are also grateful for research assistance received at various stages from M. Pereira, K. Kaboth, P. Kumar, Valasayya and Rajendran. Discussions of the project with J. Behrman, R.E. Evenson and J.G. Ryan were also particularly helpful. Washington, D.C. October 1981 SYSTEMS OF OUTPUT SUPPLY AND FACTOR DEMAND FOR SEMI-ARID TROPICAL INDIA Shanti L. Bapna, Hans P. Binswanger and Jaime B. Quizon The paper presents six systems of agricultural output supply and factor demand equations for the semi-arid tropical (SAT) parts of the states of Andhra Pradesh, Madhya Pradesh, Karnataka and Tamil Nadu.1/ Three of these systems relate to the entire SAT parts of these states and consider three different levels of commodity aggregation, i.e., seven, four, two commodity models, including fertilizer. The other three systems are all disaggregated (six or seven commodities) and relate to specific subzones of the SAT namely the rice growing subregions, the wheat growing subregions and the cotton-groundnut growing subregions. The systems are based on flexible functional forms for profit functions. Due to data limitations they are incomplete, i.e. they do not contain an exhaustive list of factors of production. Systems of output supply and factor demand equations are useful for many purposes such as (1) testing hypotheses about farmer behavior, (2) analyzing impacts of price policy changes, (3) evaluating the productivity and/or equity impact of technical changes or policies which shift supply curves for certain commodities or demand curves for certain factors etc. Work on this project started at the International Crops Research Institute 1/ In India, ten states contain semi-arid regions. In addition to the above four, these are Maharashtra, Gujarat, Rajasthan, U.P. Haryana and Punjab. Data were collected only for the first four states and therefore estimates for other states are not attempted. -2- for the Semi-Arid Tropics (ICRISAT) in Hyderabad, which is the world centre for the breeding of sorghum (jowarl,,pearl tiillet Cbajral, groundnuts, chic (bengal gram) and pigeon pea (tur). The Institute wants to use the systems along with consumer demand systems (Swamy and Binswanger (1980), Radhakrishnan and Murthy (1979)) to evaluate distributional impacts of alternative breeding strategies under different agro-economic situations. The disaggregated six and seven commodity models were estimated for the purposes of the ICRISAT and at least one of the systems specifically includes equations for three of its mandate crops, viz. sorghum, groundnuts and chickpea. -3- The current project also forms a component of a large research effort designed to build a regionally disaggregated partial equilibrium model for the agricultural sector of India as a whole. In this all India model, the SAT will be treated as a single region or possibly as two regions. The model would treat agricultural output and input prices as endogenous and would be used for purposes of evaluating the impact of price policies and of technological change. The entire four state SAT area was to be treated as a single zone and a higher level of commodity aggregaticn used. The four commodity and the two commodity models were estimated in this paper with that specific purpose in mind. In this paper we will not discuss the policy models to be constructed- but will instead concentrate on the estimation techniques used and on an evaluation of the quality of the resulting estimates. Before proceeding, two general points need to be mentioned. Early on in the project, decisions were made (a) to use systems estimates rather than single equation estimates and (b) to use combined time series and cross section data at as disaggregated level as possible. Both decisions were substantially more costly than anticipated. The first decision entailed large computation costs and programming requirements and the second led to a large data assembly effort which involved generating a nineteen year time series of dozens of variables for 94 districts.- If The reader is referred to Binswanger and Quizon (1980) for a theoretical discussion, and to Swamy and Binswanger C1980, for corresponding systems of consumer demand to be used in these models. Systems of output supply and factor demand for other regions are discussed by Evenson (1981). 2/ The project was initiated in 1975. In addition to assistant time, the project has probably absorbed five man years of professional time by now. Of course the data base and the project output can and have been used for multiple purposes. -4- In our minds there is no question that the assembly of the data base --despite its cost-- was essential. First,it lead to a very substantial gain in degrees of freedom. Second, there are substantial differences in say, fertilizer demand elasticity estimates among different agricultural subzones, which would have remained unnoticed without a disaggregated data base. Third,elasticity estimates for a number of crops could not have been achieved with more aggregative data sets. The systems feature is obviously desirable for consistency of any model to be built on the basis of the econometric estimates. We gained the impression that elasticities of individual commodities (or well defined aggregates) estimated in a system context are more stable and more in line with a priori expectations than single equation estimates. The first section discusses the theoretical framework, followed by a brief section on econometric procedures. Data sources and the agroclimatic subzones are discussed in section 3. This is followed by a section on models and commodity aggregations used for the different subzones. Section 5 discusses the results in detail, followed by a summary of main conclusions. -5- SYSTEMS OF OUTPUT SUPPLY AND FACTOR DEMAND EQUATIONS Systems of output supply and factor demand equations can be derived from a profit function. The derivation is presented below. In a later section, we test whether this derivation is consistent with the statistical evidence. At this point, however, we note that systems of output supply and factor demand equations can exist, independent of the behavioral mechanism of profit maximization, as long as the behavior of individual agents is sufficiently stable over time and can be aggregated over farmers. This implies that estimated systems are useful for economic analysis regardless of whether the theoretical restrictions of profit maximization hold. However, if profit maximization does not hold, no inferences can be made from the supply and demand equations about the production function underlying them, since behavioral and technological relationships are then confounded in those equations. Suppose now that there are n commodities, Y., of which the first m are outputs and those indexed m + 1,..., n are available inputs under the control of the individual agent. We can define a vector of commodities Y such that Y > 0 for i- 1,.., m and Y. 0 for i = m +,... n. (1) These commodities have prices P > 0 for all i. II is variable profits or i return to fixed factors of production and R - Y'P. Since inputs are defined as negative quantities,they subtract from revenues of the positive outputs. There are also k fixed factors of production, Zk, k - 1...K such as fixed capital or land quality. Let t stand for time or a technology index. If a sufficiently "well-behaved" transformation function- exists, g(Y,Z,t) - 0 and 1/ For the conditions which must be imposed on the transformation function see Diewert, 1978. -6- agents maximize variable profits n, then a profit function exists which relates maximized profits n to the prices of the variable commodities, the fixed factors and time, i. e., * *(2 1 1 n (P,Z,t) (2) The function n* has the following Dronerties (where nt and r* are derivatives and cross derivatives of the profit function with respect to the,prices of the commodities i and j). i) f* is monotonically increasing in Pi if i is an output and monotonically decreasing in P if i is an input. The output supply and factor demand curves are via Shephardts lemma- Y a n (P,Z,t) -0 i 1...m (3) S< 0 i m + 1,...n (ii) The cross derivatives of H* are symmetric, i.e., 17*. -n* (4) ii ji (iii) 1* is convex, i.e., the (singular) matrix of its cross derivatives n* is positive semi-definite or all its characteristic roots are positive or zero. (iv) H* is homogenous of degree one in P and the supply and demand equations from 11 are homogenous of degree zero in P. The matrix aY P1 [ij - defines the factor demand and output supply elasticities 1/ See Shephard (1970). -7- Table 1. Output Supply and Factor Demand Formulae and Restrictions. (a) (b) Generalized Leontief (GL) Normalized Quadratic (NQ) Form of Factor P 1/2 n-1 P Y,=b + J bjL Y,=a + .Z b Demand and i ( p i( ) ni ii ii a Output Supply +Eb Z + b t + E b Z +b t k ikZk it k ik k it Equations for i - 1, ..n. - for i - 1, .... n-1 1 n-1 n-1 P Y =a. Z Z b -tE n o n1J.. 1 Pj nn n Homogeneity Imposed not testable Imposed not testable Constraint Symmetry b ij bji i 0j b - bji 1,j 0 n Constraint and including the b of Elasticities equation n. b (P\ 1/2P Cross price - -i bi 12 n aL f n nij 2Y - --- bb P2Y i-1 n nj Own price \12 I bb ii i J jOi 2Y i P n-i iPn --1 UnMj T1n -8- and n j 1e ij m 1,9 ... n. (5) We will consider two alternative functional forms for equation (2) in our empirical work. 1/ The first, the Generalized Leontief (GL) due to Diewert (1971), is written as n* a b P1/2p1/2 + b P Z + Eb Pt () The corresponding factor demand and output supply system from this profit function is given in panel (a) of Table 1. All n equations can be estimated jointly but the profi function (6) is not linearly independent since it is the linear combination n i Y P of the individual equations. In this system, the homogeneity constraint is not testable since for each equation n ii is estimated residually and we have no other independent estimates of it. This characteristic is also a serious liability when data sets are not complete. The second functional form is derived from the Normalized Quadratic (NQ) profit function. A.normalized profit function is derived by stating the initial profit maximizing P problem in terms of normalized prices q, - where all prices and profits are n divided by the price of the n'th commodity. Normalized profits are: n-l 1lins Yvq + un (7) n 1/ Data limitations prevent us.-from a~sing the translog function. -9- Shephard's Lemma then reads that - Y . The normalized quadratic profit function (Gq), is written as ~ n-1 1 n-1 n-1 n-1 n-i n - a + Z a q +- Z b qq. + Z Z b Z + E b q (8) o -11 ij 2i i- k ik Vk i.1 iki The output supply and factor demand curves for the first n-i output and factors are given in panel (b) of Table 1. Homogeneity of degree zero in all prices is imposed on all the equations and cannot be tested. The symmetry constraint can be tested and imposed. In this system we do not have the n'th commodity equation which has to be derived from equation (8) and the commodity equations n-1 Y , a + 1 b q + kb k + bit, (9) n-i From equation (7) we can compute Y - R - E Y q . By substituting into this expression the equation (8) for I and the commodity eauations (9) for Yi we obtain - n-1 n-i Y U - ao - 1/2 Z1 j 1 bij qiq (10) The derivatives of this equation with respect to individual prices are aYn n-i -3 - Eb j< n (1 n from which we can compute the elasticities for the n'th equation as aY P P n-i A a . Pi b P 12 nj iP Y P (12) n n " 10 n-1 Finally, nn can be determined residually via equation (5) as n -j Innj* It should be noted that one could include equation (6) in the estimation process or leave it out and estimate the elasticities of the n'th equation residually. - 11 - Incomplete Systems: The data base to be discussed below is incomplete in that data on labor service flows, bullock service flows, and bullock prices 1/ are not available. Wage rate data, however, are available and have been used.- The first consequence of missing data is that profits cannot be measured and the profit function cannot be estimated directly. Second, the translog profit function cannot be used since its derived demand equations have profit shares as dependent variables. Third, the equations for the missing factors have to be left out of the system. For the normalized quadratic case one of the left out factors is the n'th factor and this more complex n'th factor equation need therefore not be estimated. Symmetry constraints can be imposed only where both price and quantity variables are available for both factors in any given factor pair. Missing quantity variables alone introduce no biases or inconsistencies into the set of coefficient estimates for the remaining equations, but make them less efficient than would be achievable in a full systems context. Missing prices on the other hand may lead to left out variable problems. If the missing bullock price is correlated with any of the other prices, the coefficient estimates on these included prices would be biased. We do not a priori expect relative bullock prices to be highly correlated with any of the other relative prices and simply neglect the problem. (Absolute prices are correlated because of inflation). A further problem arises for the generalized Leontief form. Own elasticities are computed residually from all price coefficients in an equation (see Table 1). Even if no left out variable bias arises for the included price coefficients, the residual 1/ A separate project aimed at estimating labor and bullock demand equations based on farm management data is reported in Evenson and Binswanger (1981). - 12 - computation omits the possible non-zero coefficients of a missing price and this can lead to biased own elasticities. It can be shown that these biases may go in any of the following directions: Let Xk be the commodity for which the price Pk is missng. If Xi and Xk are both competitive (complementary ) outputs then nit is biased upwards (downwards). If they are both inputs and are substitutes (complements) in production then iii will be biased upwards (downwards). If Xi is an output and Xk an input or vice versa, the direction of the bias is indeterminate. Despite this potential problem of biased own elasticities in the generalized Leontief form, we estimated systems for both forms and simply neglected the problem. - 13 - ECONOMETRIC PROCEDURES The systems are estimated with data sets (see next section) which are balanced cross sections of time series. To take account of the relationships of errors (1) among the time series in the cross section and (2) among equations,a stepwise procedure of estimation is used which leads to consistent estimators. The first step performed for each equation separately consists of the estimation of an additive error components model to pool cross section and time series data (Wallace (1977)). The model is as follows: Yirt i +iXirt + Iir +Vit + irt (13) where i stands for the i'th commodity,. r for agricultural subregions and t for time,'and where pir is the regional error component, Vit is the time error component and cirt is the residual error component. These 2 2 2 components have variances ai,,Uiv,and aic respectively which are estimated using a procedure due to Amemiya (1971). The data is first transformed via a covariance transformation (to transformed data 1) from which a consistent set of icoefficients is estimated. These ais.are then applied to the original data to estimate residuals from which the variance components are estimated. The original data is then transformed (to transformed data 2) using the estimated variance components. The second step in the estimation 1/ Maximum likelihood (ML) procedures could have been used. The research reported here is, however, a small fraction of similar estimations for other agro-climatic zones and other crov breakdowns. Given the large amounts of data and the many systems estimated,the cost of using ML procedures would have been prohibitive. - 14 - procedure consists of applying Zellner's (1962) joint estimation technique to transformed data 2 and this procedure takes account of error inter- dependence across equations. Restrictions across equations are tested and imposed in this second step. All programs used in the project were written by Sidnie Feit.1/ 1/ For more detailed discussion of the te-chniques used the reader is referred to Sidnie Feit (1980) and Appendix E of Binswanger and Swamy (1980). - 15 - DATA SOURCES AND AGROCLIMATIC SUBZONES Data were assembled for 93 districts from the four states of Tamil Nadu (Madras), Karnataka (Mysore), Andhra Pradesh and Madhya Pradesh for the years of 1955/56 to 1973/74 by the International Crops Research Institute for the Semi-Arid Tropics in Hyderabad.- Data were gathered from published Seasons and Crops Reports and/or Statistical Handbooks of each state or else were collected directly from the statistical offices in each state. Area, production and yield data for 22 principal crops come from the regular crop reporting systems which, for the major crops in each state, are based on crop cutting experiments. Prices of crops are farm harvest prices collected from major markets in each district during the main crop marketing season following the harvest of each crop. The crops covered and numbered accordingly are: Two superior cereals: 1 Rice, 2 Wheat Six Coarse cereals: 3 Sorghum (or Jowar) 4 Pearl Millet (or Bajra) 5 Maize, 6 Finger millet (or Ragi), 7 Kodon,Kutki (or Kodo and Barnycod millets 8 Other minor millets Six Pulses: 9 Chickpea (or Bengal gram) 10 Pigeonpea (tr Tur-ot Red gram), 11 Green gram,(Mung) 12 Black gram (or Urad) 13 Horsegram, (Kulthi) 14 Other pulses 1/ This work was coordinated by S.L. Bapna with the assistance of pjendran, M. Pereira, Pavan Kumar and Valasayya. - 16 - Three Oilseeds: 15 Groundnuts, 16 Sesamum, 17 Castor bean, 18 Linseed Four Other Crops: 19 Sugarcane, 20 Cotton, 21 Tobacco, 22 Chillies. The crop cutting experiments are based on a national sampling scheme designed to give estimates of state level production with certain standard errors. Since each state has between eight and 42 districts, the standard errors for the district estimates must inevitably be higher, and may even be so high as to make estimation rather meaningless. States, on the other hand are agrcclimatologically quite heterogencus since they were created on a language basis which cuts across major agroclimatological differences. States are therefore not useful as homogenous agroclimatic units. As a compromise solution we subdivided each state into agroclimatic subregions and data of the districts belonging to eaca !tragion were aggregated. Each of the 17 subregions so created consists of between 4 to 8 districts. They do not cross state boundaries because India had instituted food zones and internal trade restrictions for various crops during the period under investigation. This led to systematic price divergences across states (which were the administrative unit for the food zones). The resulting price differences in the cross sections are useful for econometric estimation and would be reduced or lost if subregions contained districts from different states. The criteria used to define subregions were based on average annual rainfall, percent of gross cropped area under irrigation and cropping patterns of the dominant crops. Average values for these variables over the 19 years were considered. The subregions and the criteria used to define each of them are listed in Appendix Table 1. Subregions 8, 12 and 17 are excluded from the - 17 - semi arid tropics. The remaining 14 subregions are either fully specialized in rice growing or in wheat growing but none of them produces both of these superior cereals in sufficient quantity to allow the estimation of the wheat-rice crop substitution. The 14 SAT districts are therefore divided into a wheat SAT (7 subregions) and a rice SAT (7 subregions) which do not overlap. Groundnut and cotton are also not produced in all subregions and a system which contains both of these crops is therefore estimated for a cotton-groundnut SAT which contains 7 agricultural subregions from both the wheat and the rice SAT. While the wheat and rice SAT zones are mutually exclusive sets of subregions, the cotton-groundnut SAT overlaps both of them. The allocation of subregions to these three SAT zones is also indicated in Appendix Table 1. Note that subregion 1,while included in the rice SAT, is excluded from the models which are estimated for the SAT as a whole, i.e. the all SAT models contain only 13 subregions. Text Table 2 characterizes the SAT and its three subzones in terms of the means of outputs, prices and other characteristics used in the analysis. We should note here that SAT wheat is primarily unirrigated wheat, grown during the cool winter months on heavy vertisoils using residual moisture. SAT rice, on the other hand, is primarily grown as an irrigated crop during the summer months with most of the irrigation from minor irrigation schemes. Finally, the subregions which are excluded from the SAT either have very high rainfall and rainfed rice or are irrigated with large scale canals such as the coastal rice zone in Andhra Pradesh. - 18 - MODELS AND COMMODITY AGGREGATION Table 3 describes the six models which were fitted to the entire SAT and to the three subregions. Model A for the entire SAT has six output commodities. Wheat and rice are aggregated into superior cereals because each of the SAT subregions do not produce both, but concentrates either on wheat or on rice alone (same treatment in model E). Sorghum (jowar) is grown in virtually all subregions and treated as a separate commodity. Each of the other coarse cereals are much less pervasive and therefore aggregated into "other coarse cereals." (The same treatment is also done for models C, D and E). None of the individual puls.s is sufficiently pervasive over all SAT subregions to be treated as an individual crop and they are therefore treated as a single aggregate. The same is done with oilseeds. Finally sugarcane, cotton,tobacco and chillies form an aggregate called "other crops A." On the production side these crops are similar in that they all require high levels of purchased inputs relative to most food crops. They also are largely produced by market oriented producers, and except for chillies, these crops are processed by separate processing industries before they enter final consumption. Fertilizers are the only variable factor input for which high quality data exist which allow estimation of a separate input demand equation., They are measured in tons of nutrients of N, P205, K20. Labor stock data are available at ten year intervals from census data but due to changes in definitions in the successive censuses and the lack of sufficient detail to construct a labor use series, this data cannot be used for our purpose. Bullock flow data are equally difficult to construct.-/ All the systems reported here are therefore systems which leave the labor and bullock demand equations unspecified. While labor flow data do not exist at the aggregate level, 1/ Labor demand and bullock demand equations have been estimated from farm management studies in a separate study (Evenson and Binswanger (1980)). - 19 - agricultural wage rate data have been systematically reported for each district (often for more than one center) in Agricultural Wages in India (various issues). All output supply equations and the fertilizer demand equation in all systems therefore include a wage rate variable which is a daily male wage rate standardized on an eight hour basis. Bullock. prices, however, are not available in a similarly consistent-manner. Each equation in each of the systems also includes variables which are not under the control of the farmers. They are listed and defined in panel III of Table 2 as rainfall (RAIN), extent of use of high yielding varieties of rice, wheat, sorghum, pearl millet and maize (HYK), road density (ROADL), regulated market density (MKTS), and extent of irrigation (IRK). Some states contain both regulated and unregulated markets and the regulated market density measures government assistance to the marketing process rather than market access. Market access is probably better measured by road density. Systems B and F are also estimated for the entire SAT at progressively higher levels of aggregation. In system B all coarse cereals are aggregated into a single equation and oilseeds, pulses and other crops A are aggregated into a single aggregate called "other crops B." Finally system F is aimed at estimating an aggregate agricultural supply equation for the SAT with one equation for "All Crops" and another equation for fertilizer demand. Systems C, D and E are aimed at estimating supply functions for individual commodities which cannot be handled for the SAT as a whole because not all 13 subregions produce the commodity to a sufficient degree. System C for the wheat SAT estimates individual equations for wheat, sorghum - 20 - and chickpeas. Chickpeas are the major pulse in the wheat SAT and compete for the same land in the winter season. Coarse cereals other than sorghum form a fourth equation. This will allow the aggregation of the estimated sorghum elasticities with those for other coarse cereals if that is desired at a later stage. The aggregate of "other crops C" includes everything not treated in separate equations. For the rice SAT, separate equations are fitted for rice, sorghum, groundnuts (produced in most but not all of the subregions of the rice SAT), and other coarse cereals. All other crops are aggregated in "other crops C." The cotton-groundnut SAT contains those subregions of the rice SAT and the wheat SAT where both cotton and groundnuts are important. Separate equations are fitted for superior cereals, sorghum, other coarse cereals, groundnuts, cotton, and an aggregate "other crops F." In interpreting the results for the equation "other crops" in each of the systems, the reader will have to bear in mind that this aggregate contains widely different crops for the different systems. It is simply the set of crops which complements those crops or crop aggregates for which individual equations have been fitted. The relative importance of the "other crops" aggregate also varies across systems and can be studied from the means table. - 21 - LAG STRUCTURE No lags are imposed on prices of fertilizer and wages or on any of the Z-variables, RAIN, HYK, IRK, ROADL and MKTS. Fertilizer prices and wage rates are largely known when these inputs are committed. However for all output prices, an expected price was formed with the following lags. E P = 0.71 Pi, t-1 + 0.29 Pi, t-2 imposing a single lag structure on all output prices was a decision made at the start for reasons of convenience. Estimating and imposing separate lag structures for each of the output prices would have substantially increased computational burdens. Furthermore, one can estimate separate lag structures for each output price from each of the equations in a system. What if the structures for the same price differed significantly among equations? And if price ratios are fornied are the expected price ratios the ratios of expected prices (formed by applying separate lag structures to each of the prices) or are they yet another lag structure for the price relative? These complications are avoided by a single lag structure on all output prices. Lag structure experiments were performed on a single equation (using the entire SAT data set) with superior cereals as the dependent variable and the relative price of superior cereals to all other crops as the independent price to be lagged. Also included as independent variables were wage rates, the fertilizer price and all Z-variables in unlagged form. The (relative) price of superior cereals was then lagged - 22 - seven times and the data set truncated to eliminate the first seven years. A form-free lag structure was then estimated by introducing all seven lagged prices (but not the current price). The generalized least squares technique discussed in the econometric section was used to pool our cross section, time series data. The variance-covariance matrix estimated across regions and time periods was saved and applied to the later regressions with shorter lag structures. This was done simply by using the same "transformed data set 2",as defined in the section on econometric estimatio4 for all regressions with shorter lag structures. Lagged prices were then successively deleted until the regressions contained only two lagged prices. F-tests for joint deletion of lags were performed comparing each length of lag to the seven lags. It turned out that all but two lagged prices could be deleted without increasing sums of squares of errors significantly at any of the conventional levels and none of the F-ratios exceeded one. Even when only two lagged Drices were i.ncluded the Cf1.eient of Pt-2 was only slightly larger than its standard error. To test whether multicollinearity among lagged prices prevented the estimation of a longer lag structure, the Almon lag procedure was also applied to the truncated data set allowing seven lags. Second, third and fourth order polynomials were tried but only the first term was ever statistically significant, and it was not possible to statistically identify a more complex lag structure. Given these experiments it was decided to use only two lagged prices. The weights on the two lags given at the beginning of this section were then estimated in a superior cereals regression including Pt_1 and Pt-2 without any restrictions on the lag form. The data set used contained - 23 - 17 of the 19 years of data and the GLS technique to combine'cross section and time series was used. TEST RESULTS Table 4 presents the summary statistics and test results about the systems. The summary statistics refer to the restricted systems where symmetry constraints are imposed. For the SAT as a whole, the disaggregate system A has the lowest goodness of fit, measured both by weighted mean 2 square and weighted R , while the most aggregative system has the best 2 goodness of fit. The highest R value (above 0.5) is achieved by the system C for the wheat SAT. The symmetry constraint is accepted for the two relatively aggregated systems B and E in the entire SAT, where only six and one constraints were imposed respectively. We noted in the introduction the special importance of these systens for modelling work at the all India level. In the other four systems, either 15 or 21 constraints were imposed and these constraint sets increase error sums of squares in a statistically significant way. For the profit function to be quasiconvex, the n-1 independent characteristic roots of the Hessian matrix (evaluated at predicted mean price levels-in the case of the GI) should all be nonnegative. This is only the case for the highly aggregative system F. In all other systems,at least one of the characteristic roots is negative. We shall see below that this is probably caused by negative own elasticities of supply (which are usually not significant) for some "awkward" aggregates. We therefore believe that the rejection of the -24- symmetry constraint is a more important issue than the rejection of quasiconvexity of the system. Rejection of symmetry constraints is usually taken as a rejection of an important constraint derived from the theory of profit maximization. However, it is clear that rejection could equally well result from using a wrong functional form (we could not use the translog form because of data limitations), or from errors in variables or left out variable biases, Furthermore we know that SAT farms are risk averse (Binswanger 1980), and may be utility maximizing rather than profit maximizing. With the data at hand,the reason for rejection of symmetry cannot be further elucidated. But whatever the reason, however, the systems of output supply and factor demand are useful even if they are not derived from a profit function, so long as the behavioral and technological relationships underlying the systems are sufficiently stable that the supply and demand curves reflect replicable responses of the farmers. Again we cannot test whether this is indeed the case. For now we can only turn to the elasticity estimates to see (a) whether they are consistent with a priori expectation and (b) whether they are fairly robust across regions and/or functional forms. Such consistency and robustness is ultimately the only way to gain confidence in a set of estimates. Table 4 provides virtually no guidance to choose between the two functional forms, since the results are very similar for both forms. For any of the equation systems A to F, we may prefer the NQ on the basis of one criterion while preferring the GL on the basis of another. We therefore opt in favor of simplicity and concentrate on reporting results from the NQ. In the few instances where elasticity estimates differ sharply between functional forms we will signal it in the text. - 25 - ESTIMATES The Appendix Tables A-4 to A-9 report both the restricted and unrestricted estimates for the NQ functions. Similar estimates for the GL forms are available from the authors. In any simulation application, the estimation equations should be used in this raw form since elasticities are not constant. The symmetry constraint is accepted for the important systems B and E and is useful in many economic applications even where it is not accepted. We therefore present the restricted NQ elasticities in Tables 5 and 6. Unrestricted NQ elasticities are easily computed from information in the Appendix Tables and in Table 2. For comparison purposes the restricted GL elasticities are reported in Appendix Table A-3 and A-4. Expected signs on own elasticities are positive for outputs and negative for inputs. Of 22 own elasticities, seven have the wrong sign but only two are statistically significant and exceed 0.1 in absolute value. The other five are thus best regarded as zero estimates. Three of the seven instances are for other coarse cereals (systems A, D, and E where it is - .37***). Two more negative values occur in other crops (-.38*** in D and -.09 in E). The other two instances are near zero values for oilseeds (-.01 in A) and for fertilizer (0.03 in C)'-/. Thus the most important difficulties arise for the most heterogenous aggregates which we will term "awkward" aggregates. 1/ For the unrestricted normalized quadratic systems, seven own price coefficients also have the wrong sign and only two of these are statistically significant. It is again other coarse cereals and other crops which account for five of the seven unexpected signs. In the restricted generalized Leontief case only five elasticities have unanticipated signs of which only one is significant. - 26 - In particular, other coarse cereals consist of several minor crops for which the data base is not particularly good. We conclude that own elasticities have the anticipated sign or zero values in all systems for all individual commodities, for fertilizer and for the aggregates superior cereals, coarse cereals, pulses and oilseeds. This conclusion is robust both across functional forms and across subregions. Of the 25 own elasticities with expected sign, 14 are statistically significant. Thus, nearly half of all own price elasticities display the expected sign and are statistically significant..L/ In what follow, we discuss the results commodity by commodity. Superior Cereals Systems A, B and E Own supply estimates vary from 0.29** to 0.36*** in the NQ form and are all statistically significant. 2/ Small but significant cross- elasticities indicating competitiveness were estimated with oilseeds in system A and other crops in system B for the NQ form (and in system A for the GL form). The All-SAT estimates indicate that all Z variables have a statistically significant positive impact on superior cereals. In the smaller cotton-groundnutregion the signs are the same but roads and markets are not significant. Irrigation and rainfall elasticities have the largest values, 1/ In the case of the generalized leontief systems, 17 of the own elasticities have correct sign and are significant. - 27 - around 0.3*** for All SAT systems and a maximum of 0.8*** for the cotton groundnut SAT. Road elasticities have a value around 0.17** wihile markets and high yielding varieties have elasticities of less than 0.1***. Wheat (System C) The supply elasticity is estimated at 0.33 i.e. the same range as for superior cereals, but is not statistically significant. On the 1/ other hand increases in jowar and fertilizer prices- significantly reduce the attractiveness of wheat cultivation while higher labor costs tend to increase it. The cross elasticity with respect to the sorghum price is especially large at -035.** In this region both these crops compete for the same land in the same postrainy season, and this finding is consistent with a priori expectation of competitiveness. Wheat cultivation is very responsive to rainfall (0.51***) and irrigation (G.31**). Its lack of responsiveness to HYV, may be because high yielding wheat varieties have not been very suitable for the unirrigated conditions in the SAT. Rice (System D) Rice supply appears to be slightly more responsive to its own price than wheat at 0.47***, It competes significantly with other crops D, 1/ This is not for the GL form. -28- which in this case includes primarily the highly input-intensive crops sugarcane, cotton, tobacco and chillies, note the small difference between OCROPSAQ and OCROPSDQ). These crops are often grown on similar land of higher quality as rice. Other cross effects are not aginificant. Rice cultivation responds primarily to rainfall (0.77***) and to high yielding varieties (0.53***). The high responsiveness to rainfall arises because SAT rice is either grown under rainfed conditions or grown with small scale irrigation directly dependent on local rainfall which covers much larger areas in high rainfall years than low rainfall years. Coastal Andhra and Tamil Nadu, which are irrigated from large canals and have benefitted much more from the green revolution, are not included in our rice SAT. Jowar (Sorghum, Systems A, C, D, E). Jowar is the most pervasive coarse cereal in the four state SAT regions. The supply elasticity is fairly low (.15) and not significant when estimated in all the SAT. However, when estimated in all three subzones, its supply appears highly price responsive with elasticity estimates ranging from 0.38** to 0.77*** i/. The responsiveness of this crop thus appears much higher than we initially expected,.given that marketed supplus of this crop - is generally quite low. Our estimates do not support die view that production of subsistence crops is not price responsive. As mentioned previously, sorghum production appears to be competitive with wheat in the wheat SAT but complementary with pulses for the SAT as a whole (0.25***). Rises in wage rates tend to reduce sorghum supply substantially (-.32 to -.45**) and 1/ The GL elasticities are all somewhat higher. - 29 - the effect is significant in three of the four systems (in the GL form it is significant in all systems). Sorghum production is reduced by RAIN and HYV.1/ The RAIN effect, however, is large and statistically significant only in system A (-.2***). The HYK effect is much smaller (-.03** to -.05***) but significant in three of the four cases. During the sample years, high yielding sorghum hybrids were not yet widely adopted in the SAT and the estimates reflect the shifts away from sorghum when technology improved in other crops. The other Z variables have no statistically significant effect on sorghum production, except for ROADL in the wheat SAT (0.36*). Coarse Cereals (System B) The coarse cereals supply elasticity is estimated at 0.2 but is not significant. Neither is any of its cross price elasttcities. With the exception of maize, the coarse cereals are fairly drought resistance crops. High rainfall, therefore, tends to reduce areas planted to these crops and the HYV effect is similar to the case of sorghum. Regulated market density has a small statistically significant positive effect on its supply Other Coarse Cerealr (Systems A, C, D, E). Other coarse cereals exclude sorghum and comprise a set of crops, each of which is only important in certain subregions of the SAT. Fingermillet is largely confined to the low rainfall areas of Karnataka, and kodon and kutkito thO higher rainfall areas of Madhya Pradesh. Pearl millet is important in certain districts of Tamil Nadu. As mentioned before, own elasticities of this "awkward" aggregate have the wrong sign in two of the three cases. The crops appear to be competitive with all pulses in system A and with bengal gram in the wheat SAT. Complementary relationships appear to exist with oilseeds in system A, with other crops in system A 1/ After a certain level of rainfall, higher rainfall causes water-logging and the crop is damaged. This was also observed in a study (Bapna, 1973) in Kota district of Rajasthan where introduction of canal water led to decline in Kharif jowar because of water logging and the fields were kept fallow. Therefore, coefficient of rain is consistent with other observations. - 30 - and C and D, and with cotton in system E. Increased fertilizer price tends to favor these crops, an effect which is significant in systems A and E (0.15**, 0.21**). This may reflect a substitution of these crops which use little fertilizer for other crops. As for jowar, higher wages tend to reduce the supply of these crops, an effect which is significant in system E only. Other coarse cereals respond negatively to rainfall, an effect which is .significant in the wheat SAT. (-0.31*). Like all coarse cereals, they also respond negatively to increases in HYV acreage, an effect which is always statistically significant and about twice the size as that for sorghum (-0.46** to-0.11**). Irrigation tends to increase areas under other coarse cereals, as do road length and markets in some cases. Oilseeds (System A) and Groundnuts (Systems D and E). Oilseeds as a whole cannot be shown to be price responsive for the SAT as a whole. Groundnut supply is elastic in the rice SAT ( .46**) but not in the cotton-groundnut SAT. Results are thus rather contradictory. The only significant cross effects are a competitive relation of oilseeds with superior cereals in system A (-.31**) and a complementary one with other coarse cereals (-.22*). The latter effect is not significant for the GL functional form. Oilseeds as a whole (.30**) and groundnuts in particular (0.41* System D, 0.76***, System E) respond sharply to increased irrigation levels,which is consistent with a priori expectations. In many SAT areas high yields of groundnuts are only achievable under irrigated conditions in the winter season. The sharp negative response in all systems A, D and E to roadlength is rather unexpected, however. But groundnuts clearly are associated with higher regulated market densities (systems D and E), whereas the same is not true for oilseeds as a whole. - 31 - Other crops A The output supply elasticity for the aggregate of these highly input-intensive crops is not significant in the NQ form, but is significant in the GL form. This arises because the price movements of the crops in this aggregate are probably not highly correlated. HYK and ROADL have significant positive effects. Other crops E This aggregate is formed by adding the pulses and three minor oilseeds to OCROPSA,increasing the latter aggregate only modestly (Table 2). The estimates for the cotton-groundnut SAT identify a negative response to increased fertilizer prices (-.19***). Such a negative response was also found for OCROPSA in the GL form, and may reflect the high fertilizer intensity of the most important cash crops forming this aggregate. OCROPSE responds positively to HYX and ROADL(O.14*** and 0.58*** respectively). Other crops B This aggregate is the sum of OCROPSE and gr-jundnuts. The importance of groundnuts as a SAT crop can be seen by noting that for the All-SAT case the addition of groundnuts nearly doubles the other crops aggregate (Table 2). A positive output supply elasticity is estimated in the NQ form (0.22**) but this effect is not significant in the GL form. OCROPSB appears to be competitive with superior cereals (-.14*) but this effect is only significant for the NQ form. On the other hand with both forms, a significant negative fertilizer price effect is identified, an effect which was discussed already for OCROPSE. The aggregate responds positively to HYK (.08***), IRK (.17*), and MKTS (.08**). The irrigation effect is probably carried into the aggregate via the addition of the groundnuts which have one of the highest irrigation response!g, - 32 - Other crops C This aggregate includes OCROPSA, rice, most pulses and all oilseeds. The major addition compared to OCROPSB therefore is rice, which in the wheat SAT leads to only a modest increase in the aggregate. None of the price effects is significant in the NQ form, probably because of the increasing heterogeneity of the aggregate. IRK and ROADL have significant and large positive effects while HYK and MKTS have smaller negative ones. These estimates now refer to only the wheat SAT, not all SAT as OCROPSB. Other crops D This aggregate contains OCROPSA, wheat (not important in the rice SAT), all pulses and the oilseeds except for groundnuts.' It is a auite different aggregate compared to OCROPSB or OCROPSC and very heterogenous. Own supply response has a statistically significant wrong elasticity. The cross effects have already been discussed under different crops. Higher wage rates tend to favor the aggregate, as do higher percentages of HYV and lower market densities. As with all "other" aggregates, not too much weight should be given to the individual coefficient estimates since the main function of the aggregate is to complete the system. All crops The aggregate output supply elasticity is low C.09) and not significant.1/ All Z-variables, however, have the expected sign. Irrigation has the highest elasticity C.17**), followed by regulated market density CO.10***) and high yielding varieties (0.5***). The other effects have about the same magnitude but are not significant. Fertilizer (All Systems) As can be secn frcm Table 2, fertilizer use per agricultural subregion is about four times as high in the rice or cotton groundnut subregions as in the wheat subregions. One might thus expect somewhat 1/ An earlier study (Bapna, 19811 found an aggregate supply elasticity of 0.20 for the semi-arid district of Ajmer in Rajhastan. While the difference between our elasticity and that of the earlier study may not be significant, one would expect aggregate supply elasticities for groups of districts such as our agroclimatic subzones to be lower than for an individual district since factor mobility among individual districts is likely to be higher than among groups of districts. - 33 - different resnnnses to fertilizer according to subregions, In the rice SAT and the cotton groundnut SAT the elasticities are large and significant (-.90***, -,62**); elasticity estimates for the GL form are even somewhat higher. However in the wheatSAT neither functional form finds fertilizer demand elasticity to be different from zero. This difference in response carries over to the fertilizer demand elasticities for the SAT as a whole. For the NQ form the estimates vary from -.28 for system A to -.65** for system F. For the GL form much higher elasticities are estimated, i.e., from -.85** for system B to -.98** for system A. The own elasticities are therefore quite sensitive to functional form, to the level of aggregation of the other crops in the system and to subregions for which estimation is undertaken. The cross elasticities with respect to other crops have already been discussed. The cross elasticity between fertilizer and labor is always positive, indicating that the two factors are substitutes. NQ estimates range from 0.10 for the cotton-groundnut SAT to 0.82** for the rice SAT. Given the importance of both labor and fertilizer in rice cultivation such strong substitutability is not surprising. For the most aggregative SAT system F, the cross elasticity estimated at .51 is not significant for the NQ form but is for the GL form, In the three "All SAT" systems, fertilizer demand responds positively to all Z variables,with remakably similar elasticities. However only the effects of HYK, ROADS and MKTS are statistically significant. A remarkable finding is the very high elasticity of fertilizer use to road density (0.99***, system E to 1.13***, system B). Given the uniform price of fertilizer across all railhead points, the roadlpmght variable may often capture the largest component of transport cost differences, -34- and stand for an additional dimension of the fertilizer elasticity with respect to the delivered price. Measured across all the SAT,regulated market density, high yielding varieties and rainfall all have much lower elasticities (between 0.2 and 0.4). In the rice SAT and the cotton-groundnut SAT these Z variables have substantially similar effects as those for the All SAT. This however is not tht case for the wheat SAT. ROADS (4.44***) and irrigation (1.53***) have substantially higher elasticities than for the SAT as a whole. Remember that the wheat SAT centers largely on Madhya Pradesh,where irrigation covers only 5.5% of gross cropped area and road density is much lower than for the rest of the SAT. It is also here that no significant own price effect could be identified for fertilizer demand. It appears that the entire price effect has been captured by the variable reflecting road transport conditions and that fertilizer -use is extremely constrained by the low irrigation leve: We conclude that fertilizer use is generally quite responsive to its delivery cost. It is also responsivet its price in areas where it has been widely adopted and road transport networks are dense. Rainfall Effects: Attempt at measuring rainfall impacts at aggregative levels have been made repeatedly. Our estimates indicate substantial sensitivity of individual crops to as crude a moisture index as average rainfall for the following commodities: rice P.79***), wheat (.51**), superior cereals (.15** to 0.33***l bengal gram 0.30***), Consistent with these estimates is also the generally positive elasticity of fertilizer use with respect to rainfall, although the effect is never significant. Sorghum, coarse cereals, and cotton, on the other hand,tend to have supplies reduced with higher rainfall. In the case of the coarse cereals this is probably a substitution effect towards less drought tolerant crops which have higher returns in the high rainfall years. For cotton it may reflect more intensive pest damage in wet years. - 35 - Discussion Three systems have been estimated for the entire SAT at different levels of aggregation. Three more systems for three different subregions were likewise estimated in order to establish supply responses for certain crops which are not pervasive across all the SAT. The following conclusions emerge the just three.of this have to do with our methodology. 1) Symmetry and convexity constraints on the profit function are only accepted at the most aggregative level (in system F). System B with four commodity equations still accepts symmetry but not convexity. The more disaggregated six and seven equation systems reject both sets of constraints. This holds for both functional forms. 2) The "best" equations in terms of a priori sign expectations are for individual commodities that are fairly widely grown (or used) over the region wherein they are estimated (rice, wheat, sorghum, fertilizer), or for commodity aggregates such as superior cereals or coarse cereals which are also grown in substantial quantities in virtually all agricultural subregions. Substantial difficulties are encountered in estimating equations for "awkward" aggregates such as other coarse cereals or other crops which are heterogenous and where the individual components are grown only in relatively small pockets of the zone for which estimates are sought. 3) There thus appears to be a tradeoff in levels of commodity aggregation. The higher the level of aggregation, the easier it is to impose constraints but the less we can say about price responsiveness of farmers with respect to individual commodities or well defined subaggregates. A second tradeoff relates to the size of subzoncs to be formed. Smaller subzones enable the estimation of elasticities with respect to individual crops or crop - 36 - aggregates which are primarily grown in just that subzone, i.e. which are not pervasive across vast zones. But if the estimates are to be used for simulation or policy work at the national level, this requires the estimation and later use of many systems for many subzones. Furthermore, if one wants to estimate elasticities for fairly location specific crops such as cotton, groundnuts or chickpea, one ends up with zones which are not mutually exclusive. These tradeoffs were known in advance but. the research reported here gives a better quantitative impression how severe they are and where they are most likely to be important. 4) On the substantive side we first note that wherever we can form fairly clear sign expectations (for own elasticities and for many of the Z variables) the estimates conform well with these a priori sign expectations. Oaly 2 of 32 own elasticities were found to have unexpected signs and they both occured for the "awkward"-aggregates OCROPS and OCRSCERY/. On the other hand 14 of the 32 ovn elasticities bad the anticipated sign and were significant, This demonstrates a remarkable extent of price responsiveness of semi-arid tropical farmers, who are generally regarded as working under very adverse climatic conditions where high yielding technologies have become available only for a restricted set of crops and cropping conditions. (For illustration of this point see the low levels of KYV adoption rates and irrigation levels shown in Table 2). 1/ The reader should note that the elasticities of these two aggregates can be added up using commodity weights from Table 2 if one wants to avoid working with them individually. It might have been better to aggregate the two "awkward" aggregates prior to estimation. But this is wisdom acquired after the fact, and the estimates are not sufficiently trouble- some to warrent costly reestimation of all systems. - 37 - 5) Particularly striking is the finding of a fairly high supply elasticity for sorghum (0.38** to 0.77***1/), the most pervasive coarse cereal. The marketed surplus of this crop is a fairly small percentage of the total harvest. Our estimates, therefore are not consistent with the view that supply of traditional subsistence crops are not responsive to price changes. We also document substantial wage impacts on sorghum supply. Higher cost of labor (or higher opportunity cost of the farmer's own time) appear to make sorghum production less attractive. Sorghum as well as the other coarse cereals also tend to be crowded out when technical change occurs in other crops. 6) The highest supply elasticity (0.70***) was found for cotton, a highly labor intensive commodity. It therefore appears to be extremely sensitive to wage rate rises with a wage elasticity of -1.37***. 7) While fertilizer demand elasticities differ across systems, they are much higher than we expected in the subregions D and E where they are widely used (-0.62** to -.90***). As discussed previously, much of the real price difference is not recorded in the fertilizer price data whiclh by and large reflect railhead prices. Transport costs to farms and fields depend shraply on the road network. The elasticity of fertilizer demand relative to road density was found to be around one except in the wheat SAT with the lowest road density where that elasticity jumps to around four and-where expansion irrigation also crucially affect fertilizer use. Again the high responsiveness of SAT farmers to price or price -like variables is quite remarkable. REFERENCES Amemiya, Y., "The Estimation of the Variances in a Variance Component Model," IER. vol. 12, pp. 1-13, 1971. Bapna, S.L. "Economic and Social Implications of Green Revolution, Vallabh Vidyanagas," Agro-Economic Research Centre, 1973 (mimeo). Bapna, S.L. Aggregate Supply Response of Crops in a Developing Region, New Delhi, Sultan Chand and Sons, 1981. Binswanger, H.P., "Attitudes Toward Risk, Experimental Measurement in Rural India," American Journal of Agricultural Economics, Vol. 62, No. 3, pp. 39a-407. 1980. - and J.B. Quizon, "Factor and Output Market Effects of Technical Change and Public Investment Policies in Agriculture," New Haven, Yale University, Econcmic Growth Center Discussion Paper 337, August 1980. Diewert, W.E., "An Application of the Shepherd Quality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, 79: 481-507, 1981. , "Duality Approaches to Microeconomic Theory," in K.J. Arrow and M.D. Intrilligator (eds.), Handbook of Mathematical Economics, (Amsterdam: North Holland Publishing Co. (1978). Evenson, R.E. and Binswanger, H.P., "Estimating Labor Demand Functions for Indian Agriculture," New Haven, Yale University, Economic Growth Center Discussion Paper 356, August 1980. Feit, Sidney, "Elasticities, A Programming Package for Estimating Linear Demand and Supply Systems with Large Data Sets," Yale University, Economic Growth.Center, Mimeo, 1980. Fertilizer Association of India, Fertilizer Statistics, New Delhi, various issues. Radhakrishna, R. and Murthy, K.N., Food Demand Model for India," Serdar Patel Institute of Economics and Social Research, Ahmedabad, India, 1978. Radhakrishna, R. Murthy, G.V.S.N., Shah, N.C., "Models of Consumer Behavior for Indian Economy," Sarder Patel Institute of Economic and Social Research, Ahmedabad, India, 1979. Shephard, R.W., Cost and Production Functions, New Jersey: Princeton University Press, 1970. Swamy, G. and H.P. Binswanger, "Flexible Consumer Demand Systems with Linear Estimation Equations: Food Demand in India," New Haven, Yale University, Economic Growth Center Paper No. 339, March 1980. Tyagi, D.S., Farmer's Response to Agricultural Prices in India, Delhi: Heritage Publishers, 1974. Wallace, T.D. "Methods for Combining Cross-Section and Time Series Data: Prepared for ICRISAT," mimeo, ICRISAT, Hyderabad, India. Woodland, A., personal communication. Zellner, A. "An Efficient Method of Estimating Seemingly Unrelated Regression and Tests for Aggregation Bias," Journal of The American Statistical Association, vol. 57, pp. 348-368, 1962. APPENDIX A Data Transformation Rules, Dimension 1. Aggregation of raw data from district level to subregion level Notation: Yirt = production of commodity i, subregion, r in year t: A = Area under the commodity irt Pirt = price of commodity i = 1, . . . . I Commodities h =.1, . . . . H districts t = 1, . . . . T time periods r = 1, . . . . R subregions Net cropped area (NCA), gross cropped area (GCA), total geographic area (TGCA), net area irrigated (NAI), total irrigated area (TIA), tons of plant nutrients (NITRO, P205, K20), number of regulated markets (TMKTS), kilometers of roads (TRDS) and area planted to high yielding varieties of rice, wheat, sorghum, pearl millet and maize (HYV) Units of measurements in source files All areas in 1000 hectares All quantities of products in 1000 tonnes All prices in Rs/quintal Road length in km, markets in actual numbers Wages in Rs/day Plant nutrients in tonnes Prices of plant nutrients in Rs/tonne Rainfall in mms/year -2- Aggregation of production areas and other quantities over districts in a sub-regions is by a simple summation Y = Y irt her iht The same system is used for all A. series and for NCA, GCA, aht TGCA, NAI, TIA, NITRO, P205, K20, TMKTS,TRDS, HYV Aggregation of Prices z Y P P irt = her iht iht her iht Aggregation of Rainfall (RAIN) RAIN. = RAIN irt her ht H r where H = Number of districts in aggregate r WAGE: Wage for male laborers in Rs per standard day of 8 hours. We do not have district labor force data, therefore we aggregate by value of total output V = E Y P V iht i iht iht Then aggregate WAGE z V WAGE irt her iht ht E V her iht -3- 2. Definition of some regression variables High yielding varieties as percent of gross cropped areas: HYK HYK = HY x 100 GCA TQtal irrigated area as % of gross cropped area IRK = TIA x 100 GCA Road length per geographic area ROADL =TDS TGCA measured in km/km2 Regulated markets per 1000 km2 of geographic area TMKTS MKTS = TGCA x 1000 TGCA 3. Price and Quantity indices: 1/ Individual crops and individual plant nutrients are aggregated to crop aggregatesand total fertilizer using chained Fisher quantity and price indexes. The quantity and price indices estimated in this manner are all equal to 1 in the base year for all the subregions and therefore do not take into account the differences in base-year prices and quantities among subregions. To account for this, the following procedure is used: 1/ For details of the computational procedures and for the programs used see Feit (1980). -4- For each commodity i contained in an aggregates, a reference price is calculated for the base year 0 which is simply the total value of the commodity across all subregions divided by the total quantity across subregions i.e. it is simply an average SAT price. E Y P Pi*0 r irO iro E Y r ir0 For each aggregate s and for each subregion we now define reference "expenditures" for the base year 0 (REFEXPS ) which is the total value srO of all commodities in the aggregate evaluated at SAT reference prices rather than the actual prices received by producers in region r. REFEXPS = E Y P ies sr0 i ir0 ir0 By multiplying REFEXPSsrO with the Fisher's quantity index we generate an adjusted quantity series for the aggregate which has a value dimension. The adjusted quantity series reflects the quantity changes of the commodities within the subregion over time, and also reflects quantity differences (not price differences) among subregions at the beginning of the period. On the other hand the ratio of observed expenditures relative to reference expenditures in each regions is a measure of the proportion by which (base year) prices of an aggregates differ across agricultural subregions. This ratio is called REFRATIO and it is an index of the prices (of an aggregate s) in subregion r relative to the average SAT prices (of the aggregate) -5- Z Y P I irO irO REFRATIO = iOPr ics We generate an adjusted price index by multiplying the Fisher price index for each subregion by the reference ratio. The adjusted price index corresponds to the adjusted quantity series and reflects both the initial price differences among subregions as well as the price changes in each subregion over time. 4. Basic normalization of quantity and price series Because of this definition explained above, the adjusted quantity series for all aggregate have the dimension of Rs. 10000 in constant 1956/57 prices. Correspondingly all adjusted price indices have a weighted average value (across subregions) of 1.0 for the base year 1956/57. Individual commodity prices and quantities are converted to the same dimensions by dividing each price series in each region by its own base year price and by multiplying each quantity series by its base year price. Thus all quality and quantity indices used as dependent variables are measured in Rs 10000 of 1956/57 purchasing power. Note however that the means given in table 1 for individual commodities are in 1000 tons and in Rs. per quintal. But that is not the fofm used in the regressions. 5. Fertilizer prices The data for the construction of prices per tonne of each-Pf the nutrients N P2 5 and K20 are taken from Fertilizer Statistics in India (various issues) published by the Fertilizer Association of India. Prices for each nutrient are based on the most common fertilizer which -6- contain only one of the nutrients. These nutrient prices are then applied to published data on nutrients use from all fertilizer (including from mixtures). District level data on use of each of the fertilizers, and fertilizer mixtures is simply not available. Fertilizer prices in India are statutarily controlled. These price data are publishe in the "fertilizer statistics of India". However price data for indivi ual states and districts are not available. Therefore, fertilizer price information does not reflects regional variation, except for Tamil Nadu. The retail prices used here do not include central and state sales taxes. Note, however, that the government also distributes fertilizers, and uses freight equalization schemes which equalize prices at railhead actual destination regardless of distance travelled. Therefore regional variations in prices are unlikely to be large, except in periods of rationing of fertilizers. Nevertheless, statutory retail prices reflect fertilizer price trends rather well. Nitrogen: The most common straight nitrogen fertilizer are Urea and Ammonium sulphate. Using the respective content of the domestically produced materials (46% and 20.6%) a price per nutrient tonne is calculated for each of these from the prices published in Fertilizer statistics in India (1972/73 p. 1-246, and 1977/78, p. 144). Where prices changed during an agricultural year, the prices for the agricultural year were computed by weighting the separate prices by the number of quarters they prevailed. Prices before 1961 are not published, but we know that they stayed virtually constant from 1956 to 1961.- Furthermore consumption was very small during that period. 1/ Price of Anmonium Sulpahte reported in the Statistical Abstract 1963-64, Govt. of India varied in a very narrow range of Rs. 338 - Rs. 343 Rs. tonne. -7- Prior to 1959, no urea was produced in India and Ammonium sulphate was the predominant straight fertilizer. By 1975 production and consumption had shifted almost completely over to urea. To capture this shift, the nutrient price of urea and ammonium sulphate were weighted by their respective share in domestic production of nutrients (in tonnes; Fertilizer Statistics of India, 77/78, pp. 1-37) to arrive at an index of nitrogen prices. Prior to 1966,statutory retail prices in Tamil Nadu and Uttar Pradesh differ from those in the other states and a separate series was constructed for these two states which take these price differences into account. Phosphorous (P205 ): The price per ton of P205 is calculated from the statutory retail price of superphosphata (16%) (Fertilizer statistics of India, 1977/78, p. 1-161). The 1960 price is used for all years prior to 1960. Potashum (K20) All potash is imported and the price of muriate of potash (60%) is used throughout. For the period 1960 to 1967 only the ex godown price at ports is available. Retail prices of pool fertilizer are available from the third quarter of 1967. Both series overlap from then until Spring 1969 and the average ratio between the two series of 1.0854 is used to adjust the port price to the retail price level. The 1960 price is used for the years from 1956/57 onwards where no price series is available. Table 2: VA?.IABLE DEFINITIONS, UNITS OF MEASUREMENT AND MEAN VALUES, BY SUBREGIONS MEANS Cotton - Variable. Dimension All 13 Wheat Rice Groundnut Definition Abbreviation Units SAT Subregions SAT Subregions SAT Subregions SAT Subregions I. Quantities 1/ 1. Rice QRICE 1000 tons T/ 439.83 127.54 2 1047.17 DZ 591.46 2. Wheat Q1HEAT 1000 cons 160.33 296.71 C 11.30 58.75 2 3. Jowar (Sorghum f QJOWAR 1000 tons 344.85 AB 374.19 C 268.41 D 444.63 E 4. Bengal gram (chickpea) QBGM 1000 tons 70.73 127.03 C 12.04 25.30 5. Groundnuts QCNUT 1000 tons 173.29 105.90 218.20 D 299.67 E 6. Cotton QCOTN 1000 tons 17.64 20.00 12.80 30.39 E 7. Allcrops ALLCROPQ 1956j57 74043.35 . F 56054.99 102778.13 95290.02 8. Superior cereals SUPCERQ Rs.10,000 29492.04 AB 19585.53 53924.53 32797.08 E 9. Coarse cereals CRSCERQ i 19914.59 B 17301.90 .20566.77 26900.57 10. Otlher coarse cereals OCRSCERQ o 7761.94 A 4017.32 C 11206.02 D 11250.09 E 11. Pulses PULSESQ " 4551.95 A 6738.18 2672.00 3130.12 12. Oilseeds OILSEEDQ " 8706.12 A 5669.76 10965.34 13957.97 13. Other crops A3 OCROPSAQ " 10396.50 A - 624L.77 13177.51 17301.72 14. Other crops B OCROPSBQ " 24084.36 B 18948.62 27366.72 35006.58 15. Other crops C OCROPSCQ ' 44309.26 2078j.99 C 81072.11 64441.31 16. Other crops D OCROPSDQ 23462.75 27383.82 18105.28 D 24577.06 17. Other crops El OCROPEIQ 1956/57 Rs 12593.79 9967.16 14909.71 15121.70 E 18. Fertilizer FERTQ 1000 cons 3114.51 ABF 1276.62 C 4865.89 D 4510.59 E II. Prices 1. Rice PRICE Rs/quintar 85.07 74.31 82.95 87.16 2. Wheat PWHEAT Rs/quintalf/ 75.02 74.94 74.58 88.03 3. Jowar (Sorghum) PJOWAR Rs/quintal, 61.82 63.11 59.99 63.56 4. Bengal gram(chickpea) PBGM Rs/quintalf/ 74.90 74.30 81.46 86.38 5. Groundnuts PGNUT Rs/quintal7- 107.28 104.79 108.49 106.94 6. Cotton PCOTN Rs/quintal 460.75 470.66 496.23 479.60 7. All crops ALLCROPP S 1.92 1.90 1.86 1.99 8. Superior cereals SUPCERP Average 1.68 1.62 1.63 1.73 9. Coarse cereals CRSCERP Price for 1.88 1.87 1.89 1.90 10. Other coarse cereals OCRSCERP 1956/57 2.07 2.19 2.03 2.04 11. Pulses - PULSESP is Equal 2.32 2.27 2.37 2.54 12. Oilseeds OILSEEDP to one 2.4 2.44 2.46 2.45 13. Other crops A OCROPSAP 1* 2.26 2.08 2.37 2.27 14. Other crops B OCROPSBP 4 2.30 2.23 2.35 2.32 15. Other crops C OCROPSCP 1.98 2.03 1.85 2.03 16. Other crops D OCROPSDP 2.08 1.95 2.30 2.21 17. Other crops El OCROPElP 2.25 2.17 2.31 2.29 18. Fertilizer FERTP " 1.40 1.52 1.36 1.39 19. Labor WAGE a 2.33 ARF 2.27 C 2.29 D 2.34 E Ilr. Other Variables 1. Rainfall RAIN =m 949.07 ABF 990.75 C 959.99 D 809.57 E 2. High yielding varieties HYK % of gross 2.02 ABF 1.22 C 2.93 D 2.37 E cropped area 3. Roads ROADL km/km 1.77 ABF 1.09 C 2.28 D 1.96 E 4. Markets MKTS No/1000 k=2 4.87 ABF 5.18 C 4.21 D 5.55 E 5. Irrigation IRK % of gross 14.89 ABF. 5.47 C 23.42 D 17.19 E cropped area 1/ These variables were not used in the regression in their natural units shown here but were transformed such that the average SAT rrice of each croo was Rs.1.00 for the year 1956/57. Thus the regression quantities were also measurei in 1956/57 Rupees.10,000. 2/ The letters indicate the system in which a quantity or a price is included. Labor quantity but the wage rate is included in all systems. 3/ See Appendix Table 3 for precise definitions. Table 3: SUMMARY OF COMMODITIES, AGGREGATES, MODELS AND REGIONS FOR VlICH ESTIMATED ALL SAT WHEAT SAT RICE SAT COTON CRNDNT SAT C ORS O1 ACIRECATES ABSREVIATION A B F C D E CROPS INCLUDED RICE RICE X IMi:AT 1llEAT X JOWAR (Sorghum) JOWAR X X X X BENCAL GRAIM (chickpea) BCM X CwUUNUIAITS CH C X X COTTON COTN X ACGREGATES ALL CROPS ALLCROP X ALL 22 SUPERIOR SUPCER X X X 1 RICE, 2 WHEAT COARSE CEREALS CRSCER X 3 SORGIUIM, 4 PEARLMILLET, 5 MAIZE, 6 FINGERMILLET, 7 KODON KUTKI (BARNYARD & KODO MILLET) 8 OTHER MINOR MILLETS OTHER COARSE CEREALS OCRSCER X X X X CRSCER except SORGUM PULSES PULSES X 9 CHICKPEA, 10 PIGEONPEA, 11 GREEN GRAM, 12 BILACKGRAM, 13 hORSE CRAM, 14 OTHER PULSES 01LSEEDS OILSEED X 15 GROUNDNUTS, 16 SESIdIUM, 7 CASTOR, 18 LINSEED OTHER CROPSA OCROPSA X 19 SUGARCANE, ?0 COTTON, 21 TOBACCO, 22 CHILLIES OTHER CROPSB OCROPSB X OCROPSA + PULSES + OfLSEEDS OTHER CrOPlSo OCROPSC X OCROPSA + RICE + OILSEEDS + 10i11+12+13+14 OTHR CROPSD OCROPSD X OCROPSA + VllEAT + PULSES + 16-17+18 OTHER CROPS El OCROPSEl X PULSES + 16+17+18+19+21+22 FERTILIZER FER X X X X X X Ntp+K in nutrient tons WAGE WAGE X X X X X X X-Crop counodity or crop aggregate is included in the system. Table 4: SUMMARY STATISTICS AND TESTS OF EQUATIONS SYSTEMS Normalized Quadratic Generalized Leontief Equation System MSEI1/ (R2 F of Negative MSE 1 (R ) 2 F of Negative Symmetry 3/ Characteristics Symmetry 3/ Characteristics roots *roots ALL SAT A 1.10 .30 3.11* 3 of 7 1.11 .30 3.50* 3 of 7 (1386) (21) B 1.06 .35 1.93 1 of 4 1.05 .35 1.34 1 of 4 (798) (6) E .1.04 .45 2.78 0 of 2 1.04 .45 1.04 0 of 2 (401) (1) WEAT SAT C 1.18 .53 3.26* 2 of 6 1.19 .54 3.71* 2 of 6 (615) (15) RICE SAT D 1.15 .40 1.93* 2 of 6 1.14 .38 1.87* 2 of 6 (615) (15) COTTON-GNUT SAT E 1.20 .41 3.99* 3 of 7 1.18 .41 2.54* 2 of 7 (714) (21) * Significant at 5. or better 11 Weightd Mean squared error. Degrees of freedom in parenthesis. 2/ This 1, corresponds to the approximate F-rest on all non-intercept variables In the system. 3/ F-value of test of symmetry constraints. Number of constraints in parenthesis. 4/ Number of negative characteristics roots of the iessian matrix evaluated at predicted weighted mean levels. All should be negative for the convL:xity condition to be satisfied. 上 Table 6: OUTPUT SUPPLY AND INPUT DEMAND ELASTICITIES WITH RESPECT TO THE Z VARIABLES, NOFUXALIZED QUADRATIC FOM l/ RAIN HYK IRK ROADL MTS System A SUPCERQ 3195*** '0675*** .321-4*** .1787*** .0710** JOW RQ -:1998*** -.0307*** -.0292 .0413 .0468 OCRSCERQ -.0869 -.0606*** .1736 .0810 .1325*** PULSESQ .2565*** .0852 .0967 -.1894** -.0239 OILSEEDQ .0715 .0352 .3000** --6758 *** -.3S07*** OCRORSAQ .1579 .1665** .2227 .7473*** -.0765 .FERTQ .2229 .2411*1** .3054 1.0387*** .3669*** System B SUPCERQ 3293*** .0589*** .3497*** .1562** .0762** CRSCERQ -:1778** -.0497*** .0311 .0113 .0955"** OCROPSBQ -.0178 .0843*** .1745* .0629 .0804** FERTQ .2509 .2548*** .247 1.1261*** .4215*** System F ALLCROPQ .0709 .0507*** .1704** .0655 .0966*** FERTQ .1351 .2289*** .2944 .9922*** .4302*** System C WHEATQ .5056*** -.0499 .3110** -.2412 .0985 JOWARQ -.0641 -.0498 .2674 .3372* -.1066 OCRSCERQ -.3090* -.1104*** .5125*** 1.4228*** .0097 BGMQ .2997*** -.0377 .2722* -.2203 -.0519 OCROPSCQ .0039 -.1079*** .5680*** 1.0446*** -.1712.* FERTQ .3598 -.0599 1.5297*** 4.4378*** .0165 System D RICEQ .7715*** .0534*** -.1760 .0893 .0586 JOWARQ -.0120 -.0507*** -.1810 .0224 -.0605 OCRSCERQ .0378 -.0456** -.0598 .0507 -.1015 .GNUTQ .1637 -.0050 .4065* -.8226*** .3379** OCROPSDQ .0888 .2069*** .2770 .1127 -.1388**" FERTQ .2204 .2688*** '.4514 .9174*** .1326 System E SUPCERQ .1519** .0713*** .8380*** .0960 .0272 JOWARQ -.1246 -.0330** 1454 -.0274 OCRSCERQ -.0636 -.0673*** .4751***,' --i- -','.3120*** .0139 CGTNQ -.3604** -.0038 .2380 :..3568* .0346 GhTTO .1021 .0263* .7624*** 5562*** .1995*,k* OCROftlQ -.0147 .1373*** .0077 .5810*** -.1018 FERTQ .2014 .1866*** -.1547 1.1478*** .3183*** l/ The corresponding derivatives from which these elasticities are derived are significant at these defined levels. Significant at .0l.level-. Significant at .05 level. Significant at .10 level. Appendix Table I THE AGRICULTURAL SUBREGIONS CRITERIA STATE SUBREGION 2 2 DISTRICTS SAT WHEAT RICE CROUJM,:UT RAIN1 IRRIG CROPPING PATTERN SAT SAT COTTON SAT NAD11YA PRADESH1 1. Rainfed Rice >950 <30 Rice > 40, Wheat < 10 Durg, Bastar, Raipur, Bilaspur, X Raigart, Surguja, Balaghac, Shadul 2. Rainf.d Wheat >950 <30 Wheat > 40 Sigar, Damoh, Schore, RaLsen X X Vidisha, Iloshangabad 3. Rainfed Wheat-Rice >950 <10 (Rice + Wheat + Jabalpur, Seont, Panna, Rewa X x Chickpe4 > 40, Rice + Satnd, Sidhi, Handle Wheat > 33 4. High Rainfall Wheat >950 <30 Wheat > 15; Sor > 10 Chinfiware, Narsingpur, Betul, X X Sorjhua, Chickpea Chickpea > 7 Tikhaiagarh, Chattarpur - 5. Low Rainfall Wheat <950 <30 Wheat > 20, Sor > 10, Gwalior, Shivpuri. Guna. Data, X X Sorghum Chickpea Chickpea > 10 Morena, Bbind. Indore, Ujajin 6. Cotton-Soi-ghum >900 <10 Cotton > 20, Sorghum > 25 Dewas, Khargone (W.N.), X X X <1200 Khan(wa (E.N.), Shajpur 7. Low Rain, Mixed Cropping <950 10 Wheat < 20, Cotton, Maize, Ratlam, Rajgarh, Jahabua, Mandsaur, X X X Groundnut, Chickpea > 5 Dhar ANDHRA PRADESH 8. High Rain, Irrigated > 950 )45 Rice > 50 Srikakulam, East Godavari, West Coastal Rice Godavari, Krishna 9. Medium Rain, Medium Irrigation, <950 >30 Rice > 30 Vizakhapatnam, Guntu; Nellore, Ix X X Rice <45 Chitcoor, Nizamabad 10. Low Rain, Low Irrig. <700 <30 5'Ride < 20, Sorghum > 15, Kurnool. Anantapur, Cuddahpah, X X x Mix.d Cropping Groundnut > 8 Mahboobnagar, Nalgonda 11. Medium Rain, Low Irrigation, >700 <30 Rice > 10, Sorghum > 20, Hyderabad, Medak, Warangal, Khacmam, X X Mixed Cropping <1100 Karlmnagar, Adilabad KARNATAKA- 12. Humid Rice >2500 Rice > 90 - South Kanara, North Kanara. Coorg 13. Transition Zone >680 >18 Rice > 25, Mandra Hasson, Shimoga, Chickmagalur X X <2000 <50 (Sorghum 4- Ragi) 25 14. Low Rainfall ->700 <25 Rice > 10, Ragi > 45 Bangalore, Kolar, Tumkur, Mysore X X X RaLi Zone <900 15. Low Rainfall >540 C15 Sorghum > 25, Groundnut 8 Chitradurga, bellary, Dharwar X X X Sorghum <860 0 4 Rice 4 10 Belg:um, Bijapur, Bidar, Ratchur, TAMIL NADU Gulb.irga 16. Low Rain Medium >670 >20 Rice > 10 Salem, Coimabaore, Tiruchirapalli X X X Irrigation, Mixed Cropping <860 <45 Hadural, Raman.athapuram, Tirunelveli 17. High Rain, Irrigated Rice >950 50 Rice > 40 Chingleput, S. Arcot, N. Arcot Thanjavur, Kanyikunari Total 13 7 7 7 Appendix Tzible 2 PRIGE ELASTICITIES FOR GENERULIZED LEONTIEF SYSTEMS! SUPCERP JOWARP OCRSCERP PULSESP OILSEEDP OCROPSAP FERTP LABOR Sv;tcm A ALL SAT SuiIiRQ . .32**2 .02 -.09 .03 -.12* -.10* .02 -007 JOWAI9 .04 .24 -.05 .21*** 0 -.15* .05 -.35** OCRý;CERQ -.28 -.07 .02 -.15 .19 .28*** .18** -.18 I'LjSE-SQ .14 .38*** -.21 .6*** .09 -.14 -.39*** -,34** OILSEEDQ -.29* 0 .15 .05 -.07 .01 -.04 .18 0CROPSAQ -.18* . -.11* .16*** -.06 0 .23* -.08** .03 FEIRTQ -.18 -.21 -.58** .89*** .16 .42** -.92** .41 System B CRSCERP OCROPSBP SUI'CERQ .27** -.12 -.12 .01 -.04 CRSCERQ -.16 .20 .06 .07 -.16 CROPIsBQ -.11 .03 .13 -.10*** .04 FERTQ -.11 -.54 1.09*** -.85** .41 System F ALLCROPP ALLCROPQ .09 -.01 -.08 FEIRTQ .27 -.91*** .64* WHEAT SAT System C WHEATP j^'-ARP BCGP OCROPSCP WIlEATQ .37 -.39* -.12 .10 ' -.24 -.03 .31* 30WRQ -.42* .95*** .10 -.03 -.30 .05 -.34* OCRSCERQ -.35 .27 .22 -.65*** .60** .10 -.19 BCHQ .24 -.08 -.56*** .54* -.29 .10 .05 OCROPSCQ -.13 -.15 .11** -.06 .27* -.05** 0 FERTQ .38 -.51 -.44 -.49 1.06** -.19 .18 RICE SAT System D RICEP GNUTP OCROPSDP RICEQ .44*** -.05 -.08 .02 -.16** -.03 -.14 30WARQ -.27 .49*** .20 -.24 .03 .26** -.46*** OCRSCERQ -.-32 .14 .01 .04 .20 .06 -.13 GUTQ .09 -.17 .04 .38* .02 -.13 -.23 OCROPSDQ -.36** .01 .13 .01 -.24* -.08 .53*** FERTQ .34 -.55** -.20 .41 .39 -1.03*** .64* COTTON-GROUJIIDNUT SAT System E SUPCERP COTNP CMUTP OCROPEIP SUPCERQ .44*** -.05 -.12 -.02 -.05 .02 -.03 -.19 JOWARQ -.10 .40** .08 0 .05 -.06 -.07 -.31* OCRSCERQ -.29 .10 - .17 .35*** .18 .09 .26** -.52*** COTNQ -.09 .01 .52*** .72;** -.12 .16 .02 -1.23*** GNUTQ -.09 .05 .13 -.06 -.06 .02 0 .01 OCROPEIQ .03 -.05 .06 .07 YO' -.04 -.25*** .15 FEIQ- .23 .26 -.85** -.04 .01 1.18*** -.92*** .12 1/ The corresponding derivatives from which these elasticities are derived are signIficant at these definéd levels. Significance levels for elasticities are not comput:ed. SignIficant at .01 level. ÅA fI:n t f~ Appendix Tablc 3: OUTPUT SUPPLY AND INPUT DFXAND EL&STTCITIES WIT RESPECT TO THE Z VARIABLES GENERALIZED LEONTIEF SYSM:S 1/ RAIN YK IRK ROADL MKTS System A ALL SAT SUPCERQ 0.3268*** 0.0550*** 0.3116*** 0.1754** 0.0671* JOWARQ -0.2107** -0.0286** -0.0532 0.0157 0.0452 OCRSCERQ * -0.0984 -0.0502*** 0.1611 0.0775 0.0947* PULSESQ 0.2566*** 0.0021 0.0552 .-0.1664* -0.0182 OILSEEDQ 0.0805 0.0301** 0.3123** -0.6610*** 0.3277*** OCROPSAQ -0.0915 0.1244*** 0.1687 0.7080*** -0.1155* FERTQ 0.2801 0.1891*** 0.2567 l1.1674*** 0.3053*** System B ALL SAT SUPCERQ 0.3373*** 0.0485*** 0.3330*** 0.1703** 0.0681* CRSCERQ -0.1810** -0.0383*** 0.0353 -0.0003 0.0841** OCROPSBQ 0.0279 0.0694*** 0.1949* 0.0568 0.0721* FERTQ 0.2849 0.2021*** 0.2334 1.1529*** 0.3465*** .System F ALL SAT ALL CROPQ 0.0879 0.0427*** 0.1655** 0.0696 0.0833** FERTQ 0.1558 0.1940*** 0.2739 1.0590*** 03668*** System C WP.EAT SAT WHEATQ 0.5114*** -0.0304 0.2883** -0.2065 0.1015 JOWARQ -0.0702 -0.0416 0.2235 0.3606* -0.1185 OCRSCERQ -0.2654* -0.0961** 0.4734** 1.4319*** 0.0011 BGMQ 0.3189*** -0.0364 0.2482* -0.1568 -0.0424 OCROPSCQ 0.0195 -0.0914*** 0.5291*** 0.9576*** -0.1382 FERTQ 0.3258 -0.0553 1.4665*** 4.2934*** 0.0659 SSystem D RTCE SAT RICEQ 0.7910*** 0.0423*** -0.134 0.1097 0.0593 JOWARQ -0.0280 -0.0361** -0.1775 0.0316 -0.0392 OCRSCERQ 0.0250 -0.0360** -0.0251 0.0034 -0.0990* GNUTQ 0.1652 -0.0049 0.4345* -0.8000*** 0.2847*** OCROPSDQ 0.1358 0.1783*** 0.2574 0.1894 -0.1175** FERTQ 0.2710 0.2159*** 0.3914 0.9338*** 0.0863 System E COTTON-GROUNDNUT SAT SUPCERQ 0.1482* 0.0571*** 0.7559*** 0.1352 0.0231 JOWARQ -0.1481 -0.0340*** 0.1190 0.0555 -0.0160 OCRSCERQ -0.0797 -0.0557*** 0.4803*** 0.2749*** -0.0169 COTNQ -0.3778** -0.0054 0.1752 0.3541* 0.0214 GNOTQ 0.0656 0.0222* 0.6517*** -0.6106*** 0.2201*** OCROPE1Q -0.0029 0.1109*** -0.0142 0.6061*** -0.0959 FERTQ 0.1995 0.1548*** -0.2770 1.2733*** 0.2613** I/ The corresponding derivatives from which these elasticities are derived are significant at these defined levels. significant at .01 level. ** * significant at .05 level. * - significant at .10 level. Table A4: Restricted and Unrestricted Coefficient Estimates of the Output Supply and Input Demand Y,uations, System A (1959-1974) Restricted Estimate 1/ Independent Variables- Dependent ESUPCER/ EJOWAR/ EDCRSCER/ EPULSES/ EOILSEED/ EOCROPSA/ FERTP/ Variables WAGE WAGE WAGE WAGE WAGE WAGE WAGE INTERCEPT RAIN HYK IRK ROADL MKTS SUPCERQ 14927.66 81.69. -2895.10 408.95 -3702.04 -1825.89 2330.34 -209.72 10.38 857.39 646.46 2992.11 406.80 (2.64) (0.03) (-1.50) (0.31) (-1.95) (-1.31) (1.11) (-0.40) (4.48) (6.21) (3.54) (2.39) (1.87) JOWARQ 81.69 2516.42 164.55 2891.09 -404.68 -610.74 703.55 583.00 -2.65 -159.38 -23.96 282.86 109.51 (0.03) (0.99) (0.13) (3.00) (-0.34) (-0.79) (0.48) (2.55) (-2.33) (-2.32) (-0.24) (0.42) (0.96) OCRSCERQ -2895.10 164.55 -1052.32 -1150.27 1695.32 1717.65 1971.13 290.35 -0.73 -197.53 89.43 348.01 194.68 (-1.50) (0.13) (-0.90) (-1.76) (2.04) (3.33) (1.94) (1.87) (-0.92) (-4.20) (1.31) (0.76) (2.54) PULSESQ 408.95 2891.09 -1150.27 1913.97 436.96 -340.54 -2771.99 134.14 1.32 17.09 30.69 -501.06 -21.62 (0.31) (3.00) (-1.76) (2.46) (0.70) (-1.11) (-3.25) (1.58) (3.16) (0.68) (0.86) (-2.02) (-0.53) OILSEEDQ -3702.04 -404.68 1695.32 436.96 -98.22 587.62 -821.07 423.72 0.66 126.93 171.00 -3212.89 570.31 (-1.95) (-0.34) (2.04) (0.70) (-0.09 (1.00) (-0,87) (2.52) (0.77) (2.44) (2.10) (-6.03) (6.44) OCROPSAQ -1825.89 -610.74 1717.65 -340.54 587.62 561.90 -590.94 45.70 -1.81 747.03 158.01 4422.09 -154.84 (-1.31) (-0.79) (3.33) (-1.11) (1.00) (0.52) (-1.09) (J.14) (-1.13) (7.89) (1.21) (5.22) (-1.04) -FERTQ 2330.34 703.55 1971.13 -2771.99 -821.07 -590.94 1730.03 317.81 -0.89 -378.11 -75.73 -2148.39 -259.60 (1.11) (0.48) (1.94) (-3.25) (-0.87) (-1.09) (0.82) (1.83) (-1.20) (-8.34) (-1.31) (-5.20) (-3.67) Unrestricted Estimates SUPCERQ 12706.88 13543.93 -14004.10 -9893.67 8239.53 -1484.54 1094.80 -175.47 *10.24 870.15 684.06 2161.88 370.46 (1.50) (1.97) (-2.97) (-2.09) (1.98) (-0.85) (0.14) (-0.32) (4.36) (6.02)' (3.70) (2.09) (1.63) JOWARQ -5340.10 4119.38 -799.27 -3600.95 6583.20 -412.72 5779.05 605.17 -2.62 -142.66 5.45 -430.64 130.87 (-1.28) (1.21) (-0.35) (-1.58) (3.48) (-0.47) - (1.84) (2.56) (-2.28) (-2.02) (0.05) . (-0.60) (1.13) OCRSCERQ -4065.19 -1319.56 -3060.70 -3885.04 7146.70 1575.79 5796.21 239.56 -0.81 -209.41 99.19 107.12 202.54 (-1.42) (-0.57) (-1.94) (-2.45) (5.34) (2.61) (2.50) (1.50) (-1.02) (-4.29) (1.44) (0.22) (2.56) PULSESQ -451.88 4527.04 -1869.23 811.88 1232.73 -318.36 -1705.59 132.45 1.31 28.35 31.40 -638.01 -29.50 (-0.30) (3.69) (-2.25) (0.97) (1.73) (-1.01) (-1.37) (1.53) (3.13) (1.10) (0.88) (-2.48) (-0.71) OILSEEDQ -185.11 -2618.22 -3502.94 -1039.83 3833.27 569.06 2807.96 371.96 0.55 85.27 167.35 -3050.10 600.20 (-0.06) (-1.00) (-2.07.) (-0.61) (2.78) (3.83) (1.32) (2.14) (0.64) (1.57) (2.03) (-5.31) (6.53) OCROPSAQ -3803.43 -2697.73 -2343.96 2800.05 3846.32 169.10 8196.44 -201.94 -2.17 758.54 149.56 4251.29 -239.14 (-0.65) (-0.57) (-0.72) (0.85) (1.31) (0.14) (1.45) (-0.58) (-1.33) (7.58) (1.13) (4.38) (-1.51) -vrl.RTQ 3427.78 1711.35 2572.50 -5469.77 -963.54 -479.13 339.58 410.35 -0.74 -375.95 -68.34 -2148.23 -223.68 (1.27) (0.78) (1.71) (-3.62) (-0.72) (-0.86) (0.14) (2.28) (-0.99) (-8.14) (-1.17) (-4.96) (-3.09) 1/ t - statistics in parenthesis Table AS: Restricted and Unrestricted Coefficient Estimates of the Output Supply and Input Demand Equations, System B (1959-1974) Restricted Estimates Dependent Independent Variables- / Variables ESUPCER/ ECRSCER/ EOCROPSB/ FERTP/ WAGE WAGE WAGE WAGE INTERCEPT RAIN HYK IRK ROADL MKTS SUPCERQ 12015.99 -3714.03 -4878.57 1679.41 -77.50 10.71 747.60 702.39 2615.91 436.45 (2.21) (-1.14) (-1.90) (0.86) (-0.14) (4.74) (5.55) (3.70) (2.02) (1.98) CRSCERQ -3714.03 1976.91 2173.40 1944.24 1139.44 -3.85 -420.87 41.64 126.63 364.47 (-1.14) (0.70) (1.10) (1.37) (3.28) (-2.16) (-3.92) (0.28) (0.13) (2.16) OCROPSBQ -4878.57 2173.40 5455.80 -3950.28 751.63 0.47 869.19 284.35 855.22 373.60 (-1.90) (1.10) (2.16) (-3.32) (1.94) (0.24) (7.65) (1.66) (0.77) (1.97) -FERTQ 1679.41 1944.24 -3950.28 2752.30 395.64 -0.95 -375.77 -57.71 -2189.68 -280.36 (0.86) (1.37) (-3.32) (1.47) (1.95) (-1.27) (-8.35) (-1.05) (-5.40) (-4.04) Unrestricted Estimates SUPCERQ - 13653.04 -6888.06 -2958.57 2594.63 -241.67 10.74 743.25 711.65 3086.75 425.89 (1.82) (-1.32) (-0.78) (0.45) (-0.42) (4.71) (5.36) (3.72) (2.25) (1.91) CRSCERQ -5225.92 -1635.80 3398.94 15420.13 906.37 -4.27 -362.72 33.08 -299.26 325.70 (--0.91) (-0.41) (1.09) (2.43) (2.50) (-2.38) (-3.29) (0.22) (-0.27) (1.90) OCROPSBQ -6230.71 -2063.76 7569.34 6960.75 478.74 0.18 908.05 311.64 1039.10 347.82 (-0.98) (-0.47) (2.36) (1.36) (1.18) (0.09) (7.70) (1.79) (0.85) (1.81) -FERTQ 3512.13 1526.65 -4665.27 1351.87 446.32 -0.87 -386.67 -65.22 -2162.27 -263.58 (1.45) (0.91) (-3.75) (0.62) (2.12) .(-1.17) (-8.49) (-1.17) (-5.15) (-3.76) Table A6: Restricted and Unrestricted Coefficient Estimates of the Output Supply and Input De"and Equations, System C (1959-1974) Dependent .Restricted Estimates Variables Independent Variablesi/ EWUEAT EJOINAR EOCRSCER ERCH EOCROPSC FERTP I1TERCEPT RAIN HYK IRK ROADL WAGE WAGE WAGE WAGE WAGE WAGEI WIEEATQ 5374.60 -6330.25 -689.42 435.56 -1695.76 -2664.41 487.31 6.92 -451.96 728.62 -2875.09 241.30 (1.54) (-1.94) (-0.58) (0.33) (-0.68) (-2.74) (1.84) (4.73) (-1.33) (2.12) (-1.35) (1.20) JOWARQ -6330.25 13794.29 912.20 16.34 -3528.54 2901.75 211.34 -0.88 -463.34 626.19 4023.52 -261.29 (-1.94) (2.87) (0.64) (0.01) (-1.30) (2.25) (0.66) (-0.51) (-1.24) (1.55) (1.63) ?-1.08) OCRSCERQ -6d9.42 912.20 1021.46 -1902.44 1716.49 466.25 -367.21 -1.31 -377.91 372.33 5259.43 7.38 (-0.58) (0.64) (1.29) (-2.95) (1.55) (0.90) (-1.85) (-1.88) (-2.65) (2.51) (5.84) (0.06) BG'Q 435.56 16.34 -1902.44 1896.29 -603.28 653.18 179.32 1.33 -113.43 206.41 -849.87 -41.12 (0.33) (0.01) (-2.95) (1.54) (-0.59) (0.83) (1.82) (2.62) (-0.97) (1.74) (-1.16) (-0.53) 0CKCPSCQ -1695.76 -3528.54 1716.49 -603.28 5299.56 -963.49 -548.68 0.83 -1563.09 2074.16 19409.21 -653.75 (-0.6b) (-1.30) (1.55) (-0.59) (1.48) (-1.23) (-1.10) (0.35) (-3.22) (3.53) (5.44) (-1.84) -FEqTQ -26b4.41 2901.75 466.25 653.18 -963.49 -63.08 596.70 -0.54 61.55 -396.12 -5847.36 -4.46 (-2.74) (2.25) (0.90) (0.83) (-1.23): (-0.06) (7.48) (-1.48) (0.73) (-4.70) (-11.11) (-0.08) Unrestricted Estimates WiEAT Q 2062.64 171.39 -2325.89 2701.21 -3607.05 -3932.22 475.32 6.85 -511.20 775.32 -2052.44 59.27 (0.47) (0.03) (-0.97) (0.65) (-0.98) (-0.68) (1.76) (4.52) (-1.43) (2.18) (-0.89) (0.25) JOARQ -13840.80 11627.57 -4977.61 11972.25 3571.83 -3733.32 154.53 -1.31 -1065.23 933.86 5766.98 -752.64 (-2.58) (1.61) (-1.73) (2.49) (0.86) (-0.64) (0.48) (-0.73) (-2.49) (2.17) (2.15) (-2.60) OCKSCERQ 663.82 2333.66 -1620.29 -3658.52 3425.07 2063.95 -477.54 -1.33 -304.39 328.36 5776.54 1.95 (0.31) (0.79) (-1.39) (-1.88) (2.07) (0.90) (-2.30) (-1.83) (-1.84) (2.07) (5.96) (0.02) bwCIQ -167.36 -2018.83 -952.98 4146.25 -205.21 -2765.61 222.99 1.21 -217.93 254.75 -645.5d -92.94 (-0.11) (-0.97) (-1.16) (2.98) (-0.17) (-1.56) (2.24) (2.35) (-1.78) (2.10) (-0.85) (-1.14) OCROPSCQ -1613.04 -6357.27 -11193.80 7091.15 137ki.55 13,6.65 -722.00 0.56 -1848.10 2184.97 21420.41 -1102.32 (-0.20) (-0.65) (-2.69) (1.07) (2.35) (0.19) (-1.41) (0.23) f-3.03) (3.43) (5.49) (-2.55) FERTQ -3152.16 2510.06 997.85 1378.97 -1288.94 -522.30 611.75 -0.55 36.02 -383.04 -5928.66 -13.63 (-2.u9) (1.65) (1.b7) (1.37) (-1.48) (-0.41) (7.59) (-1.47) (0.41) (-4.45) (-11.00) (-0.24) !L-statiatics in parentheses Table A7: Restricted and Unrestricted Coefficient Estimates of the Output Supply and Input Demand Equations, System D (1959 - 1974) Restricted Estimate Independent Variablesi/ ERICEl EJOWAR/ EOCRSCER/ ECNUT/ EOCROPSD/ FERTP/ WAGE WAGE WAGE WAGE WAGE WAGE INTERCEPT RAIN HYK IRK ROADL MKTS Independent Variables RICEQ 36190.33 -4081.47 -4431.53 222.40 -12725.80 -1975.54 256.81 44.72 837.88 -406.13 2076.17 675.31 (3.27) (-1.26) (-1.23) (0.07) (-3.23) (-0.56) (0.25) (7.16) (3.05) (-0.98) (0.86) (1.08) JOWARQ -4081.47 5755.10 1550.74 -1702.25 386.89 4943.38 308.12 -0.12 -137.65 -72.24 90.29 -120.71 (-1.26) (2.40) (0.93) (-1.19) (0.27) (2.10) (1.65) (-0.1Q) (-2.50) (-0.89) (0.17) (-0.39) OCRSCERQ -4431.53 1550.74 -56.53 -418.19 3998.27 541.53 584.40 0.45 -147.16 -28.35 242.29 -240.20 (-1.23) (0.93) (-0.03) (-0.31) (2.65) (0.27) (2.38) (0.32) (-2.31) (-0.31) (0.41) (-1.55) GNUTQ 222.40 1702.25 -418.19 4055.24 1291.68 -1776.85 216.58 1.66 -13.70 16-3.80 -3353.53 680.18 (0.07) (-1.19) (-0.31) (2.28) (0.83) (-1.18) (0.98) (1.16) (-0.22) (1.65) (-5.58) (5.01) 0CROPSDq -12725.80 386.89 3998.27 1291.68 -8019.13 -1475.80 958.95 1.81 1144.39 225.12 922.87 -563.36 (-3.23) (0.27) (2.65) (0.83) (-2.74) (-0.90) (2.34) (0.73) (10.69) (1.35) (0.94) (-2.35) -FERTQ -1975.54 4943.38 541.53 -1776.85 -1475.80 8548.27 49.52 -1.29 -426.32 -105.22 -2154.65 -154.44 (-0.56) (2.10) (0.27) (-1.18) (-0.90) (2.63) (0.17) (-0.96) (-7.04) (-1.21) (-3.88) (-1.15) Unrestricted Estimate RICEQ 19912.11 20228.02 -19148.60 30336.06 -25412.00 -1688.02 -199.64 44.70 689.80 -286.66 -621,O5 682.86 (1.02) (1.30) (-1.49) (3.29) (2.97) (-0.08) (-0.18) (7.11) (2.41) (-0.68) (-022) (1.02) JOWARQ -8316.76 3158.43 4154.12 434.20 178.10 8301.62 298.07 -0.22 -142.33 -69.59 -364.74 -141.21 (-2.17) (1.05) (1.59) (0.23) (0.10) (1.70) (1.57) (-0.18) (-2.55) (-0.85) (-0.64) (-1.01) OCRSCERQ -6736.30 -3021.17 1080.77 3712.92 3140.42 4758.59 527.52 0.19 -169.56 -27.51 -122.72 -197.28 (-1.51) (-0.85) (0.36) (1.73) (1.59) (0.89) (2.08) (0.13) (-2.60) (-0.29) (-0.19) (-1.24) GC1UTS -908.42 -2377.22 -3211.23 6180.33 1560.44 4922.15 144.32 1.59 -25.72 150.77 -3611.81 755.18 (-0.22) (-0.66) (-1.19) (3.15) (0.83) (1.38) (0.64) (1.11) (-0.40) (1.50) (-5.63) (5.29) OCROPSDQ -6525.83 -2512.92 3770.69 -179.21 -8013.00 -7908.16 1023.62 1.74 1120.84 231.11 1719.43 -547.96 (-0.87) (-0.41) (0.78) (-0.05) (-2.41) (-1.12) (2.44) (0.70) (10.02) (1.36) (1.56) (-2.16) -FERTQ -2438.47 2006.76 2161.20 -2138.34 -747.93 10011.87 44.92 -1.30 -414.72 -116.90 -2145.45 -119.44 (-0.60) (0.59) (0.82) (-1.11) (-0.41) (2.63) (0.15) (-0.97) (-6.76) (-1.33) (-3.75) (-0.87) -t - statistics in parenthesis Table AS: Restricted and Unrestricted Coefficient Estimates of the Output Supply and Input Demand Equations, System E (1959-1974) Dependent Restricted EstimatesI/ Variables Independent Variables-- ESUPCER/ EJOWAR/ EDCRSCER/ EGNUT/ ECOTN/ E0CROPE1/ FERTP/ WAGE WAGE WAGE WAGE WAGE WAGE WAGE INTERCEPT RAIN HYK IRK ROADL HKTS SUPCERQ 15998.72 -2416.13 -1676.30 1288.89 -2080.39 -2684.80 1417.73 -1406.33 6.45 861.02 1625.53 1614.85 150.15 (2.17) (,0.60) (-0.57) (0.47) (-0.97) (-0.86) (0.41) (-1.48) (2.00) (5.74) (7.14) (1.11) (0.62) JOWARQ -2416.13 8019.20 2066.39 -1011.86 979.88 1177.32 -2732.76 472.15 -2.50 -188.05 133.08 941.31 -71.37 (-0.60) (2.14) (0.88) (-0.58) (0.67) (0.59) (-1.14) (1.28) (-1.35) (-2.19) (0.68) (0.94) (-0.46) OCRSCERQ -1676.30 2066.39 -4654.07 1054.55 3681.55 197G.62 4014.56 -182.87 -0.90 -270.78 306.85 1746.71 25.47 (-0.57) (0.88) (-1.86) (0.78) (3.54) (1.39) (1.92) (-0.54) (-0.76) (-4.93) (3.44) (3.14) (0.28) GNUTQ 1288.89 -1011.86 1054.55 -14.20 600.93 -171.43 -1013.51 262.79 1.63 119.70 556.24 -3517.92 414.48 (0.47) (-0.58) (0.78) (-0.01) (0.51) (-0.11) (-0.73) (0.91) (1.22) (1.87) (3.69) (-4.49) (3.40) COTNQ -2080.39 979.88 3681.55 600.93 4362.78 841.68 557.42 -276.66 -2.93 -8.81 88.46 1149.33 36.65 (-0.97) (0.67) . (3.54) (0.51) (3.17) (0.58) (0.43) (-0.89) (-2.13) (-0.14) (0.68) (1.65) (0.34) OCROPElQ -2684.80 -1177.32 1970.62 -171.43 841.68 -1571.47 -5142.37 600.46 -0.29 780.39 7.04 4593.92 -264.50 (-0.86) (0.59) (1.39) (-0.11) (0.58) (-0.53) (-3.06) (1.33) (-0.14) (8.12) (0.03) (4.25) (-1.54) -FERTQ 1417.73 -2732.76 4014.56 -1013.51 557.42 -5142.37 5681.80 313.39 -1.36 -358.83 47.74 -3070.02 -279.68 (0.41) (-1.14) (1.92) (-0.73) (0.43) (-3.06) (1.88) (0.92) (-1.10) (-6.15) (0.45) (-4.75) (-2.86) Unrestricted Estimates SUPCERQ 13223.86 1838.67 -18851.10 16860.37 -1943.16 -12421.30 25823.24 -2308.62 7.57 910.22 1686.84 991.57 14.30 (1.15) (0.18) (-1.88) (3.03) (-0.50) (-2.44) (2.10) (-2.19) (2.27) * (5.67) (6.96) (0.59) (0.06) JOWARQ -8864.36 2579.34 2166.03 7260.33 201.30 -2790.46 8876.22 441.74 -1.84 -188.09 120.29 -85.19 -76.82 (-1.34) (0.43) (0.39) (2.55) (0.09) (-0.99) (1.71) (1.14) (-0.98) '(-2.09) (0.59) (-0.08) (-0.48) OCRSCERQ -5655.79 -2603.54 -4566.67 7469.61 2794.47 -1116.31 13926.54 -382.32 -0.65 -264.42 331.92 1144.88 0.22 (-1.37) (-0.70) (-1.28) (3.89) (1.98) (-0.62) (3.51) (-1.04) (-0.54) (-4.63) (3.59) (1.86) (0.00) CNUTQ 3979.12 137.62 -9334.57 4846.25 -244.79 -1241.82 5156.32 289.19 2.33 52.80 484.51 -3779.54 489.47 (0.80) (0.01) (-2.271 (2.42) (--0.14) (-0.60) (1.68) (0.95) (1.69) (0.77) (3.07) (-4.36) (3.86) COTNQ -11623.60 -1799.37 2413.56 2267.82 3209.81 -160.52 25964.57 -390.21 -2.43 66.91 41.59 -106.78 -1.77 (-2.34) (-0.41) . (0.55) (0.92) (1.89) (-0.07) (4.31) (-1.19) (-1.72) (0.98) (0.31) (-0.13) (-0.02) OCROPE1Q 2455.13 5634.56 -6160.78 4196.41 -1107.52 -4328.47 -2184.25 515.06 0.05 759.05 5.78 4493.12 -303.54 (0.32) (0.82) (-0.95) (1.25) (--0.42) (-1.33) (-0.34) (1.05) (0.02) (7.37) (0.03) (3.61) (-1.72) -FERTQ 1546.88 -3907.32 5731.62 -1272.52 18.81 -5043.02 3942.29 415.36 -1.43 -363.20 51.44 -3147.60 -258.63 (0.35) (-0.99) (1.55) (-0.66) (0.01) (-2.68) (1.10) (1.17) (-1.14) (-6.08) (0.48) (-4.65) (-2.60) Y/ statistics in parenthesis Table A9: Restricted and Unrestricted Coefficient Estimate of the Output Supply and Input Demand Equation, System F (1959 - 1974) Restricted Estimate Independent VTriables- EALLCROP/ FERTP/ WAGE WAGE INTERCEPT RAIN H1YK IRK ROADL MKTS ALLCROPQ 8279.34 -611.59 1881.94 5.76 1609.70 855.31 2743.80 1383.29 (1.06) (-0.44) (2.20) (1.28) (6.00) (2.13) (1.09) (3.13) -FERTQ -611.59 4010.72 223.72 -0.53 -353.67 -71.89 -2021.28 -299.84 (-0.44) (2.32) (1.11) (-0.73) (-8.07) (-1.23) (-5.19) (-4.19) Unrestricted Estimates ALLCROPQ 437.03 21463.46 1527.11 5.28 1697.41 935.79 2085.59 1330.54 (0.05) (1.63) (1.75) (1.16) (6.24) (2.31) (0.80) (3.01) -FERTQ -562.26 3454.65 264.99 -0.52 -356.47 -78.51 -2030.62 -294.82 (-0.40) (1.94) (1.31) (-0.72) (-8.12) (-1.34) (-5.20) (-4.11) 1/ -t-statistics in parenthesis Appendix Table 10 - Intercept terms used to compute predicted quantities, using the Data - 1 file (Raw data), Normalized Quadratic form. Dependent Variable Intercept T Stat System A SUPCERQ * -2654.6 -0.54646 JOTARQ 10113.4 4.13181 OCRSCERQ 5137.8 3.04565 PULSESQ 2226.4 2.42306 OILSEEDQ 8815.2 4.71524 OCROPSAQ 681.8 0.21063 -FERTQ 3876.7 2.45412 System B SUPCERQ -937.3 -0.19454 CRSCERQ 19880.4 5.14646 OCROPSBQ 13089.6 3.21282 -FERTQ 11093.0 6.99104 System F ALLCROPQ 350F1.2 3.79249 -FERTQ 2113.4 1.40889 System C WHEATQ 8898.3 2.9367 JOWARQ 3980.1 1.1202 OCRSCERQ -3179.5 -2.2866 BGMQ 2846.5 2.7271 OCROPSCQ -9370.8 -1.8605 -FERTQ 7741.5 10.2474