Panel Data Estimation Methods on Supply and Demand Elasticities: The Case of Cotton in Greece

Headnote

This article examines the effects of the application of panel data estimation methods on a system of equations with unbalanced panel data. We apply pooled, random-effects, and fixed-effects estimation in three data sets: small, medium, and large farms to examine the relationship between farm size and the elasticity of cotton supply with respect to cotton price. Our results indicate that the adoption of various estimation methods entails different estimated parameters both in terms of their absolute value and in terms of their statistical significance. Additionally, the elasticity of cotton supply with respect to price varies according to farm size.

Key Words: farm size, panel data, supply elasticity, systems of equations

JEL Classifications: C33, D21, Q18

In recent years, many empirical studies that evaluate the effects of agricultural policies in Europe and United States have relied on data sets that are balanced or unbalanced panels. The use of farm-level data implies that we have to consider the application of proper panel data estimation methods so as to obtain estimates of parameters. The adoption of the appropriate estimation method is crucial because the estimated parameters are used for policy evaluation. Consequently, the increased reliability of the estimated parameters ensures that the policy evaluation will be more accurate.

Although there are a significant number of empirical papers that rely on the estimation of a system of equations with balanced or unbalanced panel data to evaluate agricultural policies, they do not use panel data estimation methods. Serra et al. (2005a, 2006) examined the effects of agricultural policies in the United States. They have estimated a system of equations using a balanced panel with farm-level data collected in Kansas. As for the unbalanced panel data sets, the most frequently used in agricultural economics in the European Union is the Farm Accountancy Data Network (FADN), which consists of farm-level data collected every year (Bakucs and Fertô, 2009; Csajbok, Lansink, and Huirne, 2005; Karagiannis and S arris, 2005; Melfou, Theocharopoulos, and Papanagiotou, 2009; Reidsma et al., 2009; Rezitis, Tsiboukas, and Tsoukalas, 2002). Many studies that evaluate the effects of Common Agricultural Policy estimate a system of equations and make use of the FADN data set. However, they do not take into account the panel structure of the data (Moro and Sckokai, 1999; Sckokai and Moro, 2006; Serra et al., 2005b).

In this study we focus on the estimation of a Seemingly Unrelated Regression System (SUR) with unbalanced panel data applying three estimation techniques: pooled, randomeffects (RE), and fixed-effects (FE) estimation. We apply these methods to underline the different results obtained by adopting them. The effects of panel data estimation methods on estimated parameters have also been examined by Platoni, Sckokai, and Moro (2008). However, although they apply FE and RE estimation in a single equation, in a system of equations only, the RE method is applied. In this study, we apply all the different estimation techniques in a system of equations, i.e., in the same model. Thus, the difference in the estimated parameters is exclusively attributed to the estimation method.

In terms of economic analysis, the objective of this study is to examine the relationship between farm size and the elasticity of cotton supply with respect to its own price. The elasticities we estimate are short-run elasticities, which, generally, are smaller than the long-run supply elasticities as a result of the existence of fixed costs. Although producers in the short run can increase production by increasing variable inputs, in the long run, producers can adjust all input quantities. Small farmers use more variable inputs than medium and large farmers (European Commission, 2007, pp. A6-A13). This way, small farmers gain in terms of flexibility and therefore can better accommodate to output variation in the presence of price fluctuations (Mills and Schumann, 1985). Therefore, we expect the elasticity of the cotton supply to be decreasing with respect to farm size. This result was found by Adesoji (1991), who examined the relation of farm size and supply elasticity for U.S. dairy farms. He found that they move in the opposite direction in the short run but the reverse holds during the long-run period.

Table 1. Distribution of Cotton Farms per Size Category in Greece and Spain

The European Union Cotton Market

The cotton sector is of limited importance to the European Union (EU) as a whole because cotton contributes only 0.5% to the final agricultural output. However, cotton production has strong regional importance to Greece and Spain, which are the main EU cotton producers. Greece is the major cotton-producing Member State of the EU given that 76% of the EU's total cotton output is grown in Greece. The share of cotton to total agricultural output in Greece is 9. 1 % and in Spain 1.3% (European Commission, 2007).

In terms of economic size classes, i.e., the classification that is used in the present study, the distribution of small-, medium-, and largesized cotton farms in Greece and Spain is presented in Table 1.

In light of these results, it is quite clear that the number of cotton farmers in Greece is much larger than in Spain. For example, the total number of cotton farms in Greece in 2000 is 42.050, in which 16.600 are small and 14.930 and 10.250 are medium and large, respectively. The total number of cotton farms in Spain in 2000 is 4.260, which corresponds to 840 small, 1.490 medium, and 1.930 large farms. In both countries, the number of cotton farms decreases from 2000 to 2003 but in Greece remains relatively stable after 2003. On the other hand, the number of cotton farms in Spain reduces greatly in 2007. This result can be attributed to the change in the cotton policy regime that took place in the EU from 2006. In Spain, during the cultivation year 2006-2007, there was a decrease in the area under cotton by 45%. On the contrary, in Greece, the cotton area increased by 4% (European Commission, 2007).

Taking into consideration the share of farms per size, it is clear that there is small change from year to year in Greece. However, the situation in Spain is completely different. The share of small and medium farms to total cotton producers gradually decreases and the corresponding share of large farms is almost doubled from 2000 to 2007. According to the FADN data, the total cost of production is higher in Spain, 3.037 euro/ha, than in Greece, 2565 euro/ha. Additionally, the total profit is larger in Spain, 745.5 euro/ha, than in Greece, 596.8 euro/ha (European Commission, 2007).

Theoretical Framework

In this section, we present the theoretical framework that we used in this study. To compute the supply and the derived demand elasticities, we use duality theory and particularly a flexible functional form of profit function. Flexible functional forms of profit functions have been widely used in agricultural economics research (Abrar, Morrissey, and Rayner, 2004 Arnade and Kelch, 2007; Pope et al., 2007 Shumway, 1983; Sidhu and Baanante, 1981 Vilezca-Becerra and Shumway, 1994; Weaver, 1983). We choose the normalized quadratic profit function, which is one of the flexible functional forms that exist.

To be consistent with competitive theory, the profit function must satisfy the following properties: linear homogeneity in prices, symmetry, i.e., α^sub ij^ = α^sub ji^ monotonicity in prices and fixed inputs, convexity in prices, and concavity in quantities of fixed inputs. We impose linear homogeneity by dividing the profit function with the price of m netput (in our case input)1 and symmetry before estimation. Convexity and monotonicity were checked after estimation.

Econometric Techniques

In this section, we present the econometric techniques that we applied to obtain estimators of the coefficients. As we noted in the introductory comments, we estimate a system of equations using three different econometric techniques. In the first case, we estimate the system without taking into consideration the panel specification of our data, i.e., pooled estimation. In the second case, we estimate the system using the one-way error components method for unbalanced panel data proposed by Bi0rn (2004) so as to obtain RE estimators. Finally, we use the least-squares dummy-variable approach to obtain the FE estimators.2

A. Pooled Data Estimation

It is well known that the appropriate way to estimate a system of M equations is the SUR proposed by Zellner (1962). In this case, the best linear unbiased estimator is the Generalized Least Squares (GLS). Up to now, this method has been used by various researchers in agricultural economics (Carlberg, 2002; Fousekis and Revell, 2000; Lee, Kennedy, and Fletcher, 2006).

B. Panel Data Estimation

The panel data estimation relies on the hypothesis that in the estimation procedure, we take into account the "heterogeneity" of each crosssectional unit. Because it is well known by previous studies (Baltagi, 1985; Cai et al., 2008; El-Osta and Mishra, 2005; Kaltsas, Bosch, and McGuirk, 2008; Poudel, Paudel, and Bhattarai, 2009), the most frequently used models in panel data are the one-way RE and FE models. These models rely on the hypothesis that differences among cross-sectional units can be captured by means of an intercept term, which is specific for each cross-sectional unit. This specific intercept term is considered as a random disturbance in the RE model and as a fixed parameter in the FE model.

Step 4: Using the results from the previous step and equation (7), we calculate the variancecovariance matrix Ω^sub u(s)^

Step 5: We compute the matrix Ω^sup -1^^sub u(s)^, which is inserted in equations (12) and (13) so as to calculate the GLS estimators as well as their variance-covariance matrix.

Data

The data we use are from the EU FADN, National Statistical Service of Greece and Eurostat during the period 1991-2002. From the entire sample of farms that are characterized as cotton producers, we use the farms that produce only cotton as well as the farms that the proportion of cotton revenue to total revenue is equal or larger than 95%, so they are considered as pure cotton producers. According to standard FADN methodology, there are ten categories of farm size and our sample consists of farms that belong to first nine categories.4 Details about the way that farms are grouping into nine categories are provided in Table 2 in the Appendix. However, as a result of limitations in the number of observations in each category, we grouped the farms into three size categories. First, the farms that belong to the first three categories are considered small-sized. Second, the farms that belong to the next three categories are considered as medium-sized and finally the farms of the three last categories as large-sized. After this grouping, we obtain three samples of unbalanced panel data. The sample of small-sized firms consists of 28 farms, the sample of medium-sized farms involves 206 farms, and finally the sample of large-sized includes 282 agricultural enterprises.5 The number of observations of each sample is 108, 752, and 986 for small, medium, and large farms, respectively. The descriptive statistics of the variables are provided in Table 3.

Cotton farmers produce cotton using four variable inputs: labor, fertilizer, energy, and other intermediate inputs6 and two quasi fixed inputs: land and capital. Cotton quantity and revenue are available from FADN data so we obtain cotton price by dividing revenue with quantity. As for the variable inputs, the FADN sample contains expenditures and quantity of labor, but only expenditures for fertilizer, energy, and the other intermediate inputs. Prices for energy and fertilizer are provided by Eurostat and the price index for the other intermediate inputs is provided by the National Statistical Service of Greece. To obtain quantities of energy and fertilizer, we divide the expenditures by the corresponding prices. The expenditures of the other intermediate inputs are divided by their price index so as to obtain their quantity measure. The quantity of land is available from FADN data and the value of capital is deflated by the capital price index to obtain its quantity measure. Finally, we include a time trend to take into account the effect of technology change in the cotton production.

Table 3. Descriptive Statistics of the Variables

For each sample of farms we estimate a system of four equations: cotton supply and the derived demands of fertilizer, energy, and the other intermediate inputs. Labor is our numeraire input. STATA 10 (College Station, TX) econometrics software is used for the estimations.

Estimation Results

In this section we present the estimated supply and derived demand functions, which are obtained by applying all estimation techniques, the results of which are obtained by the statistical tests as well as the elasticities for small-, medium-, and large-sized farms. Initially, we pooled the data for all farms to test if the parameter estimates differ by size. Using the dummy variables approach, under the hypothesis that farm size affects both constant terms and slopes, we found that the differences in parameters are statistically significant. The χ^sup 2^^sub 52^ statistic is equal to 965.73 at the 5% level of significance with the corresponding critical value 69.83. Estimation results for small-, medium-, and large-sized farms are reported in Tables 4, 5, and 6, respectively.

The absolute value of the estimated coefficients is fairly different when either comparing the coefficients of pooled with the corresponding RE and FE or the coefficients of RE with the FE. For example, the coefficient of cotton supply with respect to cotton price for large-sized farms is equal to 0.145, 0.244, and 0.330 when we apply the pooled, RE, and FE methods, respectively. The statistical significance of the estimated parameters is improved when we apply the panel data estimation methods. The standard errors of the RE coefficients are smaller than the standard errors of the pooled coefficients in 59 of 78 cases. The result is similar when we compare the standard errors of the FE estimators with the corresponding of pooled estimators because they are smaller in 43 of 66 cases. The obtained results make clear that when we take into account the panel specification of our data, the statistical significance of the estimated parameters is increased.

Additionally, we checked if the properties of the profit function are satisfied. According to the obtained results, the profit function is increasing in the price of output and decreasing in input prices. We also checked the eigenvalues and the determinants of the principal minors of Hessian matrix and we found that the only case that the convexity property is not satisfied as for small farms in the RE model.7 These results are reported in the Table 7 in the Appendix.

Table 4. Estimated Parameters of Supply and Demand, Small-Sized Farms

Table 5. Estimated Parameters of Supply and Demand, Medium-sized Farms

Table 6. Estimated Parameters of Supply and Demand, Large-sized Farms

Taking into consideration the previously mentioned analysis about the estimated coefficients in all cases, it is clear that their values are affected by the estimation method. Therefore, our conclusions about cotton supply and input demands depend on the estimation method. To examine the appropriate specification of our model and as a result the appropriate estimation method, we applied two statistical tests. First, we test the pooled model against the FE model; thus, we computed the F-statistic for all samples. The values of F-statistic are reported in the Table 8 that follows.

In view of these results, it is clear that the null hypothesis about the common constant term for all farms is rejected in all cases. This means that the FE model is more preferable than the pooled model so in the estimation procedure, we have to take into account the "heterogeneity" of each cross-sectional unit.

Afterward, the question that arises is which of two panel models is the most appropriate. In this case we have to test the FE model against the RE model using the Hausman test. We computed the h-statistic for all samples and we found that the appropriate specification of our model is the FE because the H^sub 0^ hypothesis is strongly rejected. The values of h-statistic are presented in the Table 9.

Because h is distributed asymptotically as χ^sup 2^^sub 22^, which has a critical value of 33.9 at 5% level of significance, it is evident that the RE model is not appropriate.

In view of this analysis, we conclude that the right specification of our model and our data are the FE and as a result, the FE estimators are consistent. In terms of policy analysis, this means that we have to use the elasticities based on FE estimators in case we want to make policy simulations.

We now turn the analysis to our estimated elasticities. The elasticities of supply and derived demands for each sample and all estimation methods are reported in Tables 10, 11, and 12, respectively.

Table 8. F Test Statistic for All Samples

All own price elasticities have the correct sign, i.e., cotton supply elasticity is positive and input demand elasticities are negative. However, there is strong variability in the value of the estimated elasticities, which depends on the farm size and the estimation method.

Our results indicate that the elasticity of cotton supply with respect to cotton price is larger in value for small farms than for medium- and large-sized farms. In the case of pooled estimation, the elasticity of cotton supply with respect to cotton price decreases as farm size increases. The calculated cotton supply elasticities for small-, medium-, and large-sized farms are 0.861, 0.272, and 0.149, respectively. In the RE and FE models, this elasticity is also larger in value for small farms than for medium and large farms; however, it is not smaller for large farms relative to the medium farms. For example, in the RE model, the elasticity of the cotton supply with respect to cotton price is equal to 2.202, 0.239, and 0.251 for small, medium, and large farms, respectively. In the FE model, the corresponding values are 0.914, 0.255, and 0.339. Previous studies for Greece (Katranidis and Velentzas, 2000; Lianos and Rizopoulos, 1988; Zanias, 1981) estimated that the elasticity of cotton supply with respect to cotton price varies from 0.41 to 0.70.

These results are in accordance with the past literature, which found an inverse relation between the farm size and the elasticity of supply with respect to price. Mills and Schumann (1985) find that there is an inverse relation between the degree of output variation and capital intensity of a firm, so small firms have the ability to vary production more intensely than large firms. Following this result, short-run supply elasticities are lower for larger farms.

Table 9. Hausman Test Statistic for All Samples

Table 10. Elasticities of Supply and Demand, Pooled Estimation

Own price elasticities for inputs are different in three samples and different estimation methods. Specifically, the elasticity of fertilizer with respect to its price range from -0.540 to -1.971, the corresponding elasticity for energy range from -0.956 to -2.091, and the elasticity of other intermediate inputs with respect to its price varies from -0.447 to -1.192. Additionally, in some cases, the demand changes from elastic to inelastic and vice versa. This change is attributed to the different estimation method. For example, the demand for other intermediate inputs in medium-sized farms is elastic when we apply the pooled estimation method and inelastic in case of RE and FE estimation. This practically means that the adoption of the right estimation method is crucial to arrive at a right conclusion about the magnitude of the elasticities.

Table 11. Elasticities of Supply and Demand, Random-Effects Estimation

Table 12. Elasticities of Supply and Demand, Fixed-Effects Estimation

All in all, considering the aforementioned discussion as well as the results of specifications tests, we conclude that the right specification of our model and our data are the FE and as a result, the FE estimators are consistent. Consequently, the elasticities based on FE estimators are the accurate policy variables in case we want to make policy simulations.

Concluding Remarks

In this study, we have attempted to evaluate the results of three different estimation methods when they are applied in a system of equations and the dataset is an unbalanced panel. These methods are applied in three data sets named small-, medium-, and large-sized farms because we also wanted to examine the relation between the own price elasticity of supply and the farm size.

According to our results, the adoption of different estimation techniques leads to quite different results in terms of the absolute value of the estimated parameters as well as in terms of their statistical significance. The absolute value of the estimated parameters is fairly different when either comparing the coefficients of pooled with the corresponding FE and RE or the coefficients of FE with the RE. In view of the fact that the estimated parameters are affected by the estimation method, it was necessary to examine the appropriate specification of our model and as a result the appropriate estimation method. We test the pooled against FE model and we found that the FE model is preferable, i.e., in the estimation procedure, we have to applied panel data estimation methods. Afterward, we test the FE against the RE model and we found that the FE estimators are consistent. Therefore, we conclude that the classical regression model with a single constant term is inappropriate for our model and our data because among all estimators, the FE estimators are consistent.

As for the elasticity of cotton with respect to its own price, we found that it varies according to farm size. The elasticity of cotton supply with respect to cotton price is larger in value for small farms in all cases. In the case that we apply the pooled estimation method, it becomes apparent that as the farm size increases, the elasticity of cotton supply decreases. In the FE and RE models, the elasticity of cotton supply is larger for small farms than for medium and large farms; however, it is not smaller for large farms relative to the medium farms. As we mentioned earlier, the consistent estimators are the FE, so we come to the conclusion that the elasticity of cotton supply with respect to cotton price is not smaller for large farms relative to the medium farms. According to this result, it is evident that it is important to apply the appropriate estimation method to come to the right conclusions about the key policy parameters.

All in all, the estimation method matters to come to the right conclusions about the estimated coefficients and the estimated elasticities based on them. Moreover, the elasticity of cotton supply with respect to cotton price is larger for small farms relative to their larger "counterparts." In terms of policy, this practically means that small farmers will be expected to produce more when, for example, the applied policy tends to increase product price.

[Received September 2009; Accepted July 2010.]

Table 7. Principal Minors and Eigenvalues of the Hessian Determinants

Footnote

2To apply the FE estimation method, we had to eliminate all the farms that appeared only once in the samples.

Footnote

3In this case, t is a sequence index, not a time index.

Footnote

4 Our sample does not contain farms that belong to the tenth category because there are no so large cotton producers in Greece.

5 The initial number of farms in each sample was 75 small, 349 medium, and 456 large. However, we eliminated the farms that appeared only once in each sample to apply the FE estimation method.

6This category includes all other intermediate inputs of production like water, pesticides, etc.

Footnote

7 This result may provide some indication that small farmers are not profit maximizers.

References

References

Abrar, S., O. Morrissey, and T. Rayner. "Aggregate Agricultural Supply Response in Ethiopia: A Farm-level Analysis." Journal of International Development 16(2004):605-20.

Adesoji, O.A. "Price Changes, Supply Elasticities, Industry Organization, and Dairy Output Distribution." American Journal of Agricultural Economics 73(1991):89-102.

Arnade, C., and D. Kelch. "Estimation of Area Elasticities from a Standard Profit Function." American Journal of Agricultural Economics 89(2007) :727-37.

Avery, B. R. "Error Components and Seemingly Unrelated Regressions." Econometrica 45(1977): 199-209.

Bakucs, Z., and I. Fertõ. "The Growth of Family Farms in Hungary." Agricultural Economics 40(2009):789-95.

Baltagi, B. H. "Pooling Cross-sections with Unequal Time-series Lengths." Economics Letters 18(1985):133-36.

_____. Econometric Analysis of Panel Data. London: John Wiley & Sons, Ltd., 2005.

Biørn, E. "Regression Systems for Unbalanced Panel Data: A Stepwise Maximum Likelihood Procedure." Journal of Econometrics 122(2004): 281-91.

Bun, J.G.M. "Testing Poolability in a System of Dynamic Regressions with Nonspherical Disturbances." Empirical Economics 29(2004): 89-106.

Cai, Y., P.A. Alviola, R.M. Nayga, and X. Wu. "The Effect of Food-Away-from-Home and Food-at-Home Expenditures on Obesity Rates: A State-Level Analysis." Journal of Agricultural and Applied Economics 40(2008):507-21.

Carlberg, J.G. "Effect of Ownership Restrictions on Farmland Values in Saskatchewan." Journal of Agricultural and Applied Economics 34(2002): 248-358.

Csajbok, I., A.O. Lansink, and R. Huirne. "Effects of Management Information from FADN on Profitability of Dutch Potted-Plant Firms." Agricultural Economics 33(2005):325-31.

El-Osta, H.S., and A.K. Mishra. "Dimensions of Wealth Dispersion among Farm Operator Households: An Assessment of the Impact Farm Subsidies." Journal of Agricultural and Applied Economics 37(2005): 187-208.

European Commission. "Study on the Cotton Sector in the European Union." Final Report, 2007. Internet site: http://ec.europa.eu/agriculture/ analysis/external/cotton/index_en.htm (Accessed February 12, 2010).

Fousekis, P., and B.J. Revell. "Meat Demand in the UK: A Differential Approach." Journal of Agricultural and Applied Economics 32(2000): 11-19.

Guajarati, D. "Use of Dummy Variables in Testing for Equality between Two Sets of Coefficients in Two Linear Regressions: A Note." The American Statistician 24(1970):50-52.

Hausman, J.A. "Specification Tests in Econometrics." Econometrica 46( 1 978): 1251-71.

Hsiao, C. Analysis of Panel Data. Cambridge, MA: Cambridge University Press, 1986.

Kaltsas, I.K., DJ. Bosch, and A. McGuirk. "Residential Land Values in Urbanizing Areas." Journal of Agricultural and Applied Economics 40(2008):635-47.

Karagiannis, G., and A. Sarris. "Measuring and Explaining Scale Efficiency with the Parametric Approach: The Case of Greek Tobacco Growers." Agricultural Economics 33(2005): 441-51.

Katranidis, S., and K. Velentzas. "The Markets of Cotton Seed and Maize in Greece: Welfare Implications of the Common Agricultural Policy." Agricultural Economics Research 1(2000): 82-95.

Lee, D.S., PL. Kennedy, and S.M. Fletcher. "An Analysis of Latin American Peanut Trade." Journal of Agricultural and Applied Economics 38(2006): 1-16.

Lianos, T., and G. Rizopoulos. "Estimation of Social Welfare Weights in Agricultural Policy: The Case of Greek Cotton." Journal of Agricultural Economics 39(1988):61-68.

Melfou, K., A. Theocharopoulos, and E. Papanagiotou. "Assessing Productivity Change with SFA in the Sheep Sector in Greece." Operations Research 9(2009):281-92.

Mills, E.D., and L. Schumann. "Industry Structure with Fluctuating Demand." The American Economic Review 75(1985):758-67.

Moro, D., and P. Sckokai. "Modelling the CAP Arable Crop Regime in Italy: Degree of Decoupling and Impact of AGENDA 2000." Cahiers D'économie et Sociologie Rurales 53(1999):50-73.

Papke, L.E., and J.M. Wooldridge. "A Computational Trick for Delta-Method Standard Errors." Economics Letters 86(2005):413-17.

Platoni, S., P. Sckokai, and D. Moro. "Panel Data Estimation Techniques for Farm-level Data Model." Paper presented at the 12th Congress of the European Association of Agricultural Economists, Ghent, Belgium, August 26-29, 2008.

Pope, R.D., J.T. LaFrance, and R.E. Just. "Imperfect Price Deflation in Production Systems." American Journal of Agricultural Economics 89(2007):738-54.

Poudel, B.N., K.P. Paudel, and K. Bhattarai. "Searching for an Environmental Kuznets Curve in Carbon Dioxide Pollutant in Latin American Countries." Journal of Agricultural and Applied Economics 4 1(2009): 13-27.

Reidsma, P., F. Ewert, H. Boogaard, and K. van Diepen. "Regional Crop Modelling in Europe: The Impact of Climatic Conditions and Farm Characteristics on Maize Yields." Agricultural Systems 100(2009):51-60.

Rezitis, A.N., K Tsiboukas, and S. Tsoukalas. "Measuring Technical Efficiency in the Greek Agricultural Sector." Applied Economies 34(2002): 1345-57.

Sckokai, P., and D. Moro. "Modeling the Reforms of the Common Agricultural Policy for Arable Crops under Uncertainty." American Journal of Agricultural Economics 88(2006):43- 56.

Serra, T., D. Zilberman, B. K. Goodwin, and A.M. Featherstone. "Decoupling Farm Policies: How Does This Affect Production?" Paper presented at the American Agricultural Economics Association Annual Meeting, Providence, RI, July 24-27, 2005a.

Serra, T., D. Zilberman, B. K. Goodwin, and K. Hyvonen. "Replacement of Agricultural Price Supports by Area Payments in the European Union and the Effects of Pesticide Use." American Journal of Agricultural Economics 87(2005b):870-84.

Serra, T., D. Zilberman, B. K. Goodwin, and A.M. Featherstone. "Effects of Decoupling on the Mean and Variability of Output." European Review of Agriculture Economics 33(2006): 269-88.

Shumway, CR. "Supply, Demand and Technology in a Multiproduct Industry: Texas Field Crops." American Journal of Agricultural Economics 65(1983):748-60.

Sidhu, S.S., and A.C. Baanante. "Estimating FarmLevel Demand and Wheat Supply in the Indian Punjab Using a Translog Profit Function." American Journal of Agricultural Economics 63(1981):237-46.

Vilezca-Becerra, A.P., and CR. Shumway. "State-Level Output Supply and Input Demand Elasticities for Agricultural Commodities." Journal of Agricultural Economics Research 44(1 994): 22-34.

Weaver, D.R. "Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region." American Journal of Agricultural Economics 65(1983):45- 56.

Zanias, G. "An Estimation of the Supply Response of Cotton in Greece from 1950-1979." Oxford Agrarian Studies 10(1981): 196-211.

Zellner, A. "An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests for Aggregation Bias." Journal of the American Statistical Association 57(1962):348-68.

Appendix

Appendix

Each farm in the FADN sample has its own size which is determined by the Standard Gross Margin (SGM) of the output that produces. The SGM is defined as: SGM = value of output from one hectare or animal - cost of variable inputs required producing that output. The SGM is expressed in terms of European Size Units (ESU), which value is expressed as fixed number of Euro. One ESU corresponds to 1200 Euros. The economic size classes in terms of ESU are presented in Table 2.

Table 2. Size Class per Category