Estimating Peanut Production Efficiency and Assessing

Estimating Peanut Production Efficiency and Assessing Farm-Level Impacts of the 2002 Farm Act Paper prepared for presentation at the 2004 AAEA Meetings in Denver, Colorado Authors Denis A. Nadolnyak Department of Agricultural and Applied Economics University of Georgia [email protected] Valentina M. Hartarska Department of Agricultural Economics and Rural Sociology Auburn University [email protected] Stanley M. Fletcher Department of Agricultural and Applied Economics University of Georgia [email protected] Copyright 2000 by D. Nadolnyak, V.M. Hartarska, and S.M. Fletcher. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies. 1 ABSTRACT The paper presents preliminary results of the analysis of cost efficiency of peanut production in the South-Eastern region utilizing data from the 2001 Peanut Farm Costs and Returns Survey. Stochastic cost frontier analysis using both Cobb-Douglas and translog functional forms is used as the most suitable given data availability and the nature of the industry. Estimation results are used in a discussion of the likely farm-level effects of the 2002 Farm Act, which substituted quota support with marketing assistance loan program. Contrary to our expectations, quota ownership did not significantly affect cost efficiency, which implies that quota ownership is not a discriminating factor in considering the effects of the Farm Act. Other producer characteristics, such as farm size and operator’s age have significant effect on cost efficiency. These findings, however, must be treated with caution, as the survey data appears to be too noisy, and the underlying assumptions may not be appropriate due to highly regulated nature of peanut production. We plan to further refine the data, as well as to use the DEA methodology which, due to its unrestricted and flexible nature, might provide more conclusive results and deeper insights. 2 1. Introduction This paper presents an analysis of peanut production efficiency in the South-Eastern region of the U.S. and uses the results in a discussion of the likely effects of changes in farm legislation on farm income and on peanut production. Peanuts are one of several crops whose production was, until recently, regulated by a quota system which was, essentially, a pricequantity policy control. The 2002 Farm Act dealt away with quantity controls and significantly lowered price support by replacing the quota system with the marketing loan program. As a result, quota holders lost the quota rental payments, whereas quota renters were relieved of them, and farmers are no longer constrained in production quantities or output destination. These changes might have significant redistributive and income effects, and they affect producers with different efficiency characteristics differently: while a decrease in output price and elimination of quantity controls drives less efficient growers out of peanut production, it benefits more efficient ones. That is why it is important to evaluate peanut production efficiency and use the results to assess the farm-level impact of the recent changes in the industry. The data used in the efficiency estimation come from a 2001 Peanut Farm Costs and Returns Survey conducted in the spring of 2002 and sponsored by the National Center for Peanut Competitiveness, the National Peanut Board, the Southern Peanut Farmers Federation, University of Georgia, Auburn University, and the University of Florida. The last peanut production survey in the South-East was conducted in 1996 and, to the best of our knowledge, no comprehensive peanut surveys have recently taken place in other peanut growing regions. While the 2001 survey does not capture the effects of the 2002 Farm Bill, efficiency analysis permits construction of cost frontier, which makes it possible to study the effect of quota ownership on efficiency, and thus derive implications for the effects of the policy changes on different farms. 1 Based on the analysis of relative (dis-)advantages of the methodologies used for estimating efficiency, two methods—stochastic cost frontier analysis and data envelopment analysis—are chosen as most suitable approaches to estimating the available survey data. The stochastic cost frontier analysis is chosen because the survey data provides the variables required for estimation and because the nature of competitive but regulated farm production satisfies the assumptions required for cost efficiency estimation better than those of profit maximization. The data envelopment analysis (DEA) is used for checking the results of the stochastic frontier analysis, as it defines efficiency frontier based only on the observed firm-level data, thus being the most flexible and assumption-free. The results of the estimation of cost efficiency are used in a discussion of the likely farmlevel effects of the 2002 Farm Act, which eliminated quota support policies and introduced a price floor in the form of the marketing assistance loan rate. We find that, contrary to our expectations, there is no significant difference in cost efficiency between quota owners and quota renters, i.e., quota ownership does not affect cost efficiency. This finding implies that quota ownership is not a discriminating factor in considering farm-level effects of the Farm Act. Other producer characteristics have significant effect on cost efficiency. The efficiency increases with operator’s age up to about 50 years and decreases henceforth, and operation’s size has positive impact on efficiency. These findings must be treated with caution, as the survey data appears to be too noisy and do not always conform to the properties of cost function. This might be a result of a highly regulated nature of peanut production before 2002 and of rigidities in the input markets, which may violate the assumptions of the stochastic frontier models, particularly cost minimization. These issues will be dealt with by further refining the data, and possibly collecting 2 extra data for operator location and other attributes. Besides, using more unrestricted and flexible DEA methodology might provide deeper and more conclusive insights. The rest of the paper is structured as follows. Section 2 provides a brief overview of peanut farm support policies and discusses how they affect production and cost efficiency. Section 3 describes different efficiency estimation methodologies and motivation of the choice of analytical techniques. Section 4 describes the data and presents preliminary estimation results, together with discussion of policy implications. Section 5 concludes. 2. Changes in Peanut Farm Support Policies The analysis of peanut production efficiency is done with a view of assessing the likely impacts of the changes in the peanut and other oilseed farm support policies introduced by the 2002 Farm Act. The 2002 Farm Act dealt away with the quota support system that existed for a number of years before 2002. Under the quota support, both price and quantity controls were imposed on peanut production. The quantity of peanuts grown for “edible purposes” was limited by the annual quota size, which was fixed as the quota was actually an asset that belonged to some farmers (and non-farmers) and did not to others. As a result, some producers rented quota quantities (in lbs) from quota owners, which meant that they were buying the right to grow “edible” peanuts. The advantage of growing “quota” peanuts was in the fact that these peanuts could be sold at a high price that varied between $600 and $680 over the years. Any additional quantities not covered by the quota (so-called “additionals”) had to be sold at much lower market prices for non-edible purposes only. The Farm Act replaced the quota system with a marketing assistance loan program (MLP) that lifted the quantity restrictions on peanut production and introduced a price floor in 3 the form of marketing loan rate. Under the MLP, producers can, instead of selling the crop at harvest, move it into the marketing loan (government storage) as a pledge for a loan rate of $314 per metric ton (the price floor). During the post-harvest period, farmers can either forfeit the loan (give up the “collaterized” peanuts and keep the loan rate) or repay the loan at the lower of the loan rate and a loan repayment rate that is set equal to “weekly posted county prices” and announced by the USDA. While the mechanics of the interaction among the producers, crop processors, and the government within the framework of the MLP are quite complicated leaving a researcher with a lot of ambiguities (see Nadolnyak, Revoredo, and Fletcher, 2004), it is clear that lifting the quantity restrictions and substituting the fixed support price with a much lower price floor is going to affect farmers, and most likely affect them differently. More precisely, the legislative change described above may leads to deprivation of quota owners of the quota ownership and thus dealt away with quota rental payments by those producers who rented quota to grow edible peanuts. Introducing/unleashing some put market forces emphasizes cost and production efficiency and is likely to lead to production expansion by more efficient and contraction by less efficient producers. This makes efficiency analysis of peanut production particularly timely and important. 2. Methodology The current version of the paper uses stochastic cost frontier methodology for estimating cost efficiency. Economic efficiency is usually estimated by stochastic frontier methods and by data envelopment analysis (DEA). While the former is an econometric technique, the latter represents/utilizes a non-parametric approach. As results from this paper are somewhat weak, the 4 next step is to validate them by DEA analysis. The use of the two approaches is justified by the fact that they complement each other and can be compared in terms of the ranking of the operators in the sample. In particular, robustness of the results may be checked by comparing efficiency rankings produced by the two methods using Spearman correlation coefficient. Consistency of the results may indicate that inefficiency is more important than random events in the explanation of deviations from the efficiency frontier. This section provides a short description of the two methodologies, identifies their advantages and disadvantages, but focuses on reasons for choosing stochastic frontier cost function and on the specification used in the estimation.1 The DEA defines efficiency frontier based solely on the observed firm-level data, i.e., without assuming any specific functional form. The resulting production (cost) frontier is constructed by solving profit maximization (cost minimization) LP for every firm and represents a piece-wise set of production or cost vectors observed as best practices. Firm-level efficiency is computed by comparing the datum to the “best practice” defined by the frontier. This information is used for identifying characteristics of the most and the least efficient firms, as well as for recovering technological information and forecasting firm behavior (Varian, 1984). The main limitation of the DEA model is that any deviation from the frontier is interpreted as an indication of inefficiency. In the presence of random disturbances that affect farm operations, such as weather, farms may be erroneously labeled as inefficient. This inflexibility of deterministic DEA may lead to systematic overestimation of inefficiency (Cooper, Seiford, and Tone, 1999). However, since most farmers in the sample operate in similar geographical location, these effects could be attenuated. 1 The description follows Kumbhakar and Lovell (2000), Coelli, Rao, and Battese (1998), and Chambers (1988). 5 The stochastic frontier approach is based on assuming a specific functional form for the cost/production frontier. In its simplest form, the approach posits a stochastic model for a cross-sectional frontier with a distinct two-component disturbance specification: one error term is the usual two-sided noise component, while the other is a one-sided disturbance component explicitly associated with inefficiency (Fare, Grosskopf, and Lovell, 1994). The main advantage of this approach is that it accommodates statistical noise, thus avoiding possible overestimation of cost inefficiency by allowing deviations from the frontier to be associated with both inefficiency and random factors. In the choice of a stochastic frontier estimation method, it is important to consider the differences between the output- and output-oriented approaches. The former corresponds to the production frontier estimation of output-oriented technical inefficiency, and the latter corresponds to the cost frontier estimation of cost efficiency that incorporates both input-oriented technical and allocative inefficiencies. The two approaches have important differences. Most importantly, they differ in terms of data requirements. While production efficiency analysis requires data on input use and output provision, cost efficiency analysis requires input prices, output quantities, and total input expenditure. For decomposition of the inefficiency term into technical and allocative inefficiency components in the cost efficiency analysis, data on output quantities or cost shares are also required. The survey data in question provides detailed information on input expenditure, cost shares, and output value. The survey does not, however, contain data on input quantities, which makes cost efficiency analysis the only viable choice of methodology. The cost and production efficiency estimation also rely on different behavioral assumptions. In fact, the production frontier analysis does not impose any behavioral 6 assumptions because it is concerned with technical efficiency only. The cost frontier analysis, however, implies cost minimization. While this assumption may be unrealistic if the agents are constrained in the ability to adjust the use of inputs and the constraints are not modeled, it is very appropriate in competitive environments where input prices are exogenous and in which output prices are demand driven, which makes them exogenous. Kumbhakar and Lovell, 2000, note that many regulated industries also satisfy these exogeneity criteria. The assumption of cost minimization is also applicable in industries where output is not storable (as is the case with onfarm peanut storage) so that output maximization objective underlying output-oriented technical efficiency is inappropriate. Peanut producers are competitive, which implies that input and output prices are indeed exogenous. Besides, the producers’ ability to rent quota before 2002 meant that the influence of quantity constraints was significantly reduced. This makes cost frontier analysis a more suitable choice of methodology. Results of estimation of cost and production models also contain different information. While the technical efficiency resulting from the production frontier analysis cannot be decomposed, the cost efficiency resulting from the cost frontier analysis can be decomposed into allocative and technical components. As these two inefficiencies have different causes, decomposition can be desirable in many circumstances. Since output-oriented efficiency is necessary, but not sufficient, for cost efficiency, the degree of input-oriented technical efficiency is smaller than the cost efficiency by the magnitude of input allocative efficiency. Also, measures of input-oriented technical efficiency can differ from those of output-oriented technical efficiency. The two measures are equal if either equals one (production is technically efficient or production is technically inefficient but exhibits constant returns to scale). If the two are not equal, then input-oriented technical efficiency is greater (less) than output-oriented technical 7 efficiency if returns to scale are increasing (decreasing) over the relevant region of production technology. In the current version of the paper, decomposition of the inefficiency term is not performed due to the data problems discussed in the next section. Stochastic cost frontier estimation allows incorporation of quasi-fixed inputs, i.e., inputs that are not variable during the time period under consideration. While all inputs are treated equally in the stochastic production frontier analysis, as the efficiency measurement is output oriented, the cost frontier analysis treats variable and quasi-fixed inputs differently because its efficiency measurement is input oriented. In this case, knowledge of quasi-fixity of some inputs is exploited by replacing cost frontier with a variable cost frontier. Finally, cost frontier analysis accommodates multiple outputs. Based on these considerations, the stochastic cost frontier analysis is used for estimating peanut production efficiency. In the stochastic frontier analysis, the cost function is of the form Ci ≥ c( yi , wi , β ) , where Ci is the actual (variable) cost of producer i, and c(.) is the efficient cost function of the output yi, input prices wi, and a vector of coefficients. The difference between the actual and the efficient cost is captured in the error term ei that consists of two parts, the truly random shock vi and the cost inefficiency term ui that is random but non-negative. While several distributional assumptions about u and v are possible, they are always assumed to be independently distributed and vi ~ iid N (0, σ v2 ) ; (1) ui ~ iid N + (0, σ u2 ) ; With these specifications, it is possible to derive marginal density, mean, and variance of ei = ui + vi. Using these, an expression for conditional distribution of u given e can be obtained, f(u|e). Thus, estimating the cost function that incorporates ei using either MLE or method of 8 moments provides estimates of the cost inefficiency term, ui. The measure of cost inefficiency, CEi, can be expressed as CEi = c( yi , wi ; β ) = E (exp{−ui } | ei ) . Ei (2) This measure provides inefficiency information that is limited to producer-specific estimates of the cost of inefficiency. Estimation of ui can be followed by estimation of equation: uˆi = ∑ γ i zi + ε i , (3) l where zi’s are the variables that explain the inefficiency. The models in the paper are first estimated by this two-stage method, consisting of ML estimation of a stochastic cost frontier followed by OLS estimation of an equation relating predicted cost inefficiency to its potential determinants. This approach has been criticized because the model of predicted inefficiency effects contradicts the assumption of identically distributed ui’s from the first stage. Battese and Coelli (1995) combined the estimation into a single step by assuming that ui is distributed independently but not identically as truncations of the normal distribution, N + ( Z i γ ,σ u ) . Thus, the mean of the cost inefficiency effect is a function of variables Zi. This specification permits the coefficients γ to be estimated together with the coefficients of the cost frontier. These one stage estimation is also performed for each of the models estimated. The functional forms most commonly used for cost frontier estimation are Cobb-Douglas and translog. The Cobb-Douglas specification is very simple and allows the focus to be on the error term (Kumbhakar and Lovell, 2000) normally takes the following form: 9 ln Ei = β 0 + β y ln yi + ∑ β n ln wni + vi + ui . (4) n Since a cost frontier must be linearly homogeneous in input prices, either the parameter restriction β k = 1 − ∑n ≠ k β n must be imposed prior to estimation, or the equation above must be reformulated as ⎛w ⎞ ⎛E ⎞ ln⎜⎜ i ⎟⎟ = β 0 + β y ln yi + ∑ β n ln⎜⎜ ni ⎟⎟ + vi + ui . n ⎝ wki ⎠ ⎝ wki ⎠ (5) A single input translog cost frontier takes the form: 1 ln VEi = β 0 + β y ln yi + ∑α n ln wni + β yy (ln yi ) 2 2 n + 1 ∑∑α nk ln wni ln wki + ∑n α yn ln yi ln wni + vi + ui 2 n k (6) where w consists of two subgroups Wi and zi , where Wi is a vector of input prices and zi is a vector of quasi-fixed inputs involved in production of a single output, yi. While the usual symmetry and linear homogeneity parameter restrictions can be imposed prior to estimation, a number of regularity conditions can be tested after estimation. The advantage of the translog specification over that of Cobb-Douglas is that the one-sided error component ui now captures both input oriented technical and allocative inefficiency. Decomposing it into the two inefficiency measures requires additional data on input prices or cost shares. Derivations of the decomposed measures require the use of complex numerical techniques. The translog specification also provides a more flexible functional form that is a second-order approximation of the true cost function and that it exploits some information that Cobb-Douglas specification does not. Inclusion of the quasi-fixed inputs permits calculation of their shadow prices after estimation. The expression for a shadow price is 10 ( ) ∂VEi VEˆ i exp(−ui ) ˆ = β q + ∑r βˆqr ln zri + ∑n γˆqn ln wni + βˆ yq ln yi . ∂z qi z qi (7) If the actual prices of the quasi-fixed inputs are known, their comparison with predicted shadow prices provides an indication of over- and underutilization of the inputs: a quasi-efficient input is overutilized (underutilized) if ∂VEi ∂zqi < (>) pqi (Kumbhakar and Lovell, 2000). This information is important because misallocation of quasi-fixed inputs constitutes another type of inefficiency. However, the translog specification suffers from high data volume requirements: estimation requires a very large sample size for relatively large number of inputs (and outputs for multi-output models). Besides, multi-collinearity among the regressors may lead to imprecise estimates of many parameters in the model, which may offset the benefit of flexibility. 4. Data and Empirical Results The data used in the analysis was taken from the 2001 peanut farm costs and returns survey. The survey was sponsored by the National Center for Peanut Competitiveness, National Peanut Board, Southern Peanut Farmers Federation, University of Georgia, Auburn University, and the University of Florida. The survey was conducted between March and April of 2002. The original sample size was 740, out of which only about 80 respondents provided valid responses that entered the dataset. Most of the respondents were from Georgia, the largest peanut producing state in the country. The survey questionnaire contains a wide array of questions grouped by several topics organized by the following cost components: land operated and commodities produced, peanut marketing and miscellaneous expenses, peanut acreage and seeding, peanut quota, fertilizer, chemicals and pesticides, vehicles and tractors, field operations, labor, custom and technical 11 services, irrigation, landlord shares, farm production costs and returns, farm assets and debts, farm operator and household, and other crop costs and production. Altogether, the questionnaire is quite comprehensive and contains 2000 entries. However, the choice of estimation methodology was largely dictated by availability of relevant data as, regardless of the comprehensive nature of the survey, it did not furnish some of the important market and input price data. Thus, both methodological concerns and the data quality dictated the use of stochastic cost, and not production, frontier analysis. Both Cobb-Douglas (equations 4 and 5) and translog (equation 6) functional forms were estimated. The two approaches described in the methodology section are applied to each functional form. In the first approach, a stochastic frontier model assuming a half-normal distribution is estimated. Estimation results are used to predict the inefficiency term, which is then regressed on quota ownership and other variables that are expected to affect inefficiency. As this approach has been criticized on the grounds of violating the assumption of identical distribution of ui’s, a second approach to inefficiency estimation was applied, which follows Battise and Coelli (1995) and estimates inefficiency and its dependence on a set of covariates jointly by assuming that ui’s are not identically distributed but that ui ~ N + ( Z iγ , σ u ) . The variables used in the stochastic frontier analysis are summarized in Table 1. The cost variable represents variable costs per acre and includes the value of paid labor and the costs of seeds, fertilizer, pesticides, fuel, electricity, farm supplies, and marketing.2 Output is measured as 2 Estimation of total cost function was also experimented with but the results do not seem to fit any of the functional forms described in this section. The model failed to converge when homogeneity restrictions were imposed on the cost function. In the version where input prices were divided by an input price, the output was negative and statistically significant, which clearly violates the basic properties of a cost function. Results of this estimation are presented in the Appendix. Some challenges and potential pitfalls of the total cost model clearly come from data quality and the treatment of quasi-fixed inputs. The value of the land was measured by multiplying the land area in acres by a weighted index of the price of the reported and imputed land rent (for rented and owned land shares respectively). Owned land was valued at $50 per acre, which was the average value reported by renters, although the standard deviation was relatively high (31). Capital costs were calculated as the sum of the depreciation, lease 12 the per acre value of the total peanut production. The input prices in log form are per hour wage to paid labor, and per acre costs of seeds, fertilizers, pesticides, and materials. The last category groups together fuel, electricity, farm supplies, and marketing costs. In order to impose the homogeneity restriction, the cost variable and all input prices were divided by the cost of materials. The variables hypothesized to affect inefficiency are QUOTA, measured as the percentage of peanut quota owned relative to the total peanut quota used (own and rented); SIZE, measuring the size of the peanut operation as the log of peanut acres planted/harvested.3 Also included are operator age, measured by OAGE, and education level OEDU, measured by an index of education varying from 1 to 5, where 1 stands for incomplete high school, 2 stands for completed high school, 3 stands for some college education, 4 stands for completed Bachelor degree, and 5 stands for graduate school.4 The results from estimation of the two-stage regression model are given in Table 2, Panel A. The data do not seem to fit perfectly into the Cobb-Douglas function estimated by the halfnormal stochastic frontier model approach. As expected, all input prices have positive coefficients but only the coefficients of the price of paid labor and of price of seeds are statistically significant. The coefficients of fertilizers and pesticides are close to but not significant. One reason for this result could be the relatively small number of observations, as expenses, and other quasi-fixed expenses related to peanuts, and the respective per acre cost was this value divided by acres of peanuts planted/harvested. Own labor was also included and was valued by the number of unpaid hours worked by the operator, partners, and family multiplied by the average value of the per hour own labor rate. The latter was calculated on the basis of the value reported as the average per hour rate. Only 18 operators reported this value and its average was $32, although the standard deviation was also very high (29). Due to these data deficiencies and functional form problems, the total cost function is only reported in the Appendix, as the search for a better estimation method, functional form, and better approximations of the prices of the quasi-fixed assets continues. 3 There is no difference between the two variables reported by farmers. 4 Specifications with dummies for each educational level, as well as with the numbers of years of education, were also experimented with but none of these variables were significant. 13 only 66 observations could be used in this model. The output coefficient does not conform to the requirements of the cost function, as it is negative although statistically insignificant. In the estimation of a stochastic frontier model, the variance parameters are also important. The estimates of the variance of the inefficiency component σ u2 (0.378) and of the random disturbance to the cost σ v2 (0.219) show that deviations from the frontier due to inefficiency error are higher (1.73 times as great) than deviations due to factors outside of operators’ control. The hypothesis that producers are inefficient (that is, σ u2 = 0 ) is rejected at 5 percent level. Panel B of Table 2 shows the results from the second stage estimation, where the inefficiency estimate is regressed on QUOTA, SIZE, OAGE, OAGE2, and OEDU. While the ownership of quota has a positive effect on inefficiency, it is not significant. However, larger peanut operators seem to be less inefficient, which suggests possible “efficiency economies of scale”. In addition, experience affects inefficiency as inefficiency decreases with age up to about 51, since when the trend is reversed. However, operator’s educational level does not seem to be significant. Results of the single-stage truncated-normal stochastic frontier model are presented in Table 3. This model estimates the mean of the cost inefficiency effect as a function of the quota and demographic variables. As should be expected, the data seem to fit this functional form better. All coefficients of input prices are positive and statistically significant. The coefficient of the output price is now positive but still insignificant. The variance of the inefficiency term is significantly reduced and most of the deviations from the frontier are now due to factors outside of operators’ control. Quota ownership, the main variable of interest, still does not affect efficiency, while larger peanut producers are again less inefficient. The effect of age is similar to 14 the results from the two-stage model, but now the reversal of the age effect is estimated to occur much later, at 61 years. Since the data did not seem to support well the Cobb-Douglas functional form, results of estimating the translog functional are presented next. A major limitation of the trasnlog form applied to small datasets as the one used in this paper is that only a few input prices/cost shares can be used. To limit the number of explanatory variables, inputs were aggregated in three groups: (1) paid labor, (2) seeds, fertilizers and pesticides, and (3) materials as defined in the Cobb-Douglass specification. Homogeniety restrictions were imposed by dividing input prices and the cost variable by the input price of the “materials” cost component. Table 4, Panel A shows the results of the first stage half-normal stochastic frontier cost function estimation. As it turns out, the data fits the translog functional form even worse. The coefficient of the price of paid labor is positive and significant as expected, and its second derivative is negative, but not significant. The coefficient of the input price of seeds, fertilizers, and pesticides is not significant and its second derivative is positive and significant, which violates the standard properties of a cost function. The coefficient of the output value also violates basic cost function properties as the signs are incorrect and the coefficients are not statistically significant. The inefficiency hypothesis ( σ u2 = 0 ) is rejected here only at 8 percent level and deviation from the cost frontier due to inefficiency are 1.5 times as high as deviations due to the exogenous shocks to producers’ costs. Panel B of Table 4 shows the results of the second stage estimation. Ownership of quota still does not seem to influence inefficiency while, again, the results show that larger producers are less inefficient than smaller producers. Also, according to this specification, operator age and education level do not explain cost inefficiencies. 15 Table 5 shows the results of the truncated-normal stochastic frontier model with translog specification estimated in a single step using Battese and Coelli (1995) technique. There are no qualitative differences between this model and the model shown in Table 4. Although disappointing, these results are not unusual. Chambers (1991) states that, in empirical work, stochastic cost frontier models are usually not estimated either because the functional forms are inappropriate of because of limited data availability and/or quality constraints. In addition, some of the reasons behind the results could be due precisely to the fact that ownership of quota, as well as the quota support system, may have induced non-optimizing behavior. If this is the case, then it is hard to estimate the role of the quota ownership using a stochastic frontier cost function since is requires cost minimizing behavior. 4. Conclusion The paper presents preliminary results of the analysis of cost efficiency of peanut production in the South-Eastern region of the U.S. in 2001. The analysis utilized data from the 2001 Peanut Farm Costs and Returns Survey. Stochastic cost frontier analysis using both CobbDouglas and translog functional forms were used for the estimation. This approach was chosen because the survey data provides the variables required for estimation and because the nature of competitive but regulated farm production satisfies the assumptions of cost minimization required for cost efficiency estimation better than those of profit maximization, which is a prerequisite for production efficiency analysis. The results of the estimation of cost efficiency were intended to be used in a discussion of the likely farm-level effects of the 2002 Farm Act, which dealt away with the quota support policies and introduced a price floor in the form of the marketing assistance loan rate. However, 16 it was found that, contrary to the initial expectations, the results of the frontier analysis did not show any significant difference in cost efficiency between quota owners and quota renters, i.e., quota ownership did not affect cost efficiency. This may imply that the advent of the 2002 Farm Act did not discriminate significantly against quota owners. Results show that some producer characteristics affect cost efficiency. For example, larger farms are less inefficient. In addition, there is some evidence that efficiency increases with operator’s age up to about between 50 to 60 years and decreases henceforth, while the education level, as measured by the index of education, does not affect inefficiency. These findings must be treated with caution, as the survey data appears to be too noisy. In all estimated models, there is at least one variable whose coefficient is either statistically insignificant or has the wrong sign thus not conforming to the standard cost function properties. In particular, output per acre is never positive and statistically significant and, in some specifications, even has a negative sign. This might be a result of a highly regulated nature of peanut production before 2002 and of rigidities in the input markets, which may violate the assumptions of the stochastic frontier models. As methods of cost frontier estimation imply cost minimizing behavior, failure of the data to support the cost functions experimented with may imply that the cost minimization assumption was not satisfied. These problems will be addressed by further refining the data, including dummies for location, land type, and other attributes. In addition, the less restrictive and more flexible data envelopment analysis, which it defines efficiency frontier based solely on the observed firmlevel data without imposing assumptions, might provide deeper and more conclusive insights. 17 TABLES Table 1. Data description and summary statistics Output (value of peanutes in $ per acre) Total Cost (value in $ per acre) Price of capital ($ per acre) Price of own labor (per hour wage rate) Price of land ($ per acre) Price of fertiliser ($ per acre) Price of seeds ($ per acre) Price pf pesticide ($ per acre) Price of paid labor (per hour wage) Price of materials ($ per acre) QUOTA (% of quota owned) SIZE (log of acres planted) OAGE (Operator age in years) OEDU (Index of education) Mean Std. Dev. Min Max 722 658 139 31 51 40 64 121 12 61 43 4.88 50 2.72 226 246 114 13 20 31 38 131 9 38 38 1.03 13 0.92 312 320 41 2 21 0 7 0 3 15 0 1.79 25 1.00 1514 1812 987 126 134 135 131 377 70 184 100 7.31 81 5.00 18 Table 2. Panel A. Cobb-Douglas stochastic frontier—normal/half-normal model. Lnvc lny w4 w5 w6 w7 Constant sigma_v sigma_u Chi2 Log-Likelihood Observations Coef. -0.091 0.285 0.084 0.074 0.318 -3.029 0.219 0.378 Std. Err. 0.159 0.051 0.055 0.046 0.055 1.028 0.051 0.097 z -0.57 5.59 1.52 1.58 5.81 -2.95 P>z 0.566 0 0.129 0.113 0 0.003 133.83 -16.767 66 Table 2 Panel B. OLS on the predicted inefficiency term Lnvc QUOTA OEDU OAGE OAGE2 Constant R-squared Adj R-sq Observations Coef. 0.000 0.013 -0.026 0.000 1.203 Std. Err. 0.001 0.022 0.011 0.000 0.263 z -0.16 0.57 -2.47 2.51 4.57 P>z 0.875 0.573 0.017 0.015 0 0.28 0.22 66.00 19 Table 3. Cobb-Douglas stochastic frontier—normal/truncated-normal model lnvc Coef. Std. Err. z P>z w7 Constant 0.0966 0.2426 0.0832 0.0606 0.3791 -3.9554 0.1359 0.0359 0.0444 0.0279 0.0463 0.8953 0.71 6.76 1.87 2.17 8.18 -4.42 0.477 0.000 0.061 0.03 0.000 0.000 QUOTA SIZE OAGE OAGE2 OEDU Constant sigma_u2 sigma_v2 0.0010 -0.3941 -0.0579 0.0005 -0.0877 3.5747 0.0008 0.0563 0.0016 0.0864 0.0271 0.0002 0.0820 0.8700 0.0040 0.0096 0.63 -4.56 -2.14 1.89 -1.07 4.11 0.531 0.000 0.032 0.059 0.284 0.000 lnvc lny w4 w5 mu Chi2 LogLikelihood Observations 233 -0.914 65 20 Table 4. Panel A. Translog stochastic frontier—normal/half-normal model lnvc lny lny2 Labor Supplies LS LY SY LL SS Constant sigma_v sigma_u Coef. -4.2672 0.5055 2.1385 -0.6707 0.0204 -0.3075 0.1310 -0.0834 0.2073 12.8137 0.2397 0.3577 Chi2 Log-Likelihood Observations 257.09 -27.863 70 Std. Err. 3.3590 0.4970 1.1900 1.2588 0.1288 0.1896 0.1948 0.0821 0.0481 11.5408 0.0515 0.1055 z -1.27 1.02 1.8 -0.53 0.16 -1.62 0.67 -1.02 4.31 1.11 P>z 0.204 0.309 0.072 0.594 0.874 0.105 0.501 0.309 0 0.267 Table 4. Panel B. OLS on the predicted inefficiency term u_h QUOTA SIZE OEDU OAGE Constant R-squared Adj R-squared Obs Coef. Std. Err. 0.0000 -0.0688 0.0069 0.0016 0.5181 t 0.0004 0.0138 0.0147 0.0011 0.0916 P>t 0.00 -4.97 0.47 1.49 5.66 0.997 0.000 0.640 0.139 0.000 0.247 0.215 70 21 Table 5. Translog stochastic frontier—normal/truncated-normal model Lnvc Coef. Std. Err. z P>z Lny lny2 Labor Supplies LS LY SY LL SS Constant -1.5419 0.0499 2.5002 -1.6665 0.0086 -0.3524 0.2800 -0.0793 0.1840 5.1088 2.8193 0.4184 0.9788 1.0550 0.0966 0.1528 0.1620 0.0659 0.0403 9.6789 -0.55 0.12 2.55 -1.58 0.09 -2.31 1.73 -1.20 4.56 0.53 0.584 0.905 0.011 0.114 0.929 0.021 0.084 0.229 0.000 0.598 QUOTA SIZE OEDU OAGE Constant sigma2 gamma 0.0021 -0.5934 0.0489 0.0041 1.8537 0.0666 0.0490 0.0024 0.1402 0.0878 0.0064 0.6085 0.0117 0.1052 0.88 -4.23 0.56 0.65 3.05 0.378 0.000 0.577 0.518 0.002 Lnvc mu Chi2 Log-Likelihood Observations 376 -4.015 70 22 References: Battese, G.E., Coelli, T.J. 1995. “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data,” Empirical Economics, 20:325-332. Chambers, R. “Applied Production Analysis: A Dual Approach.” Cambridge University Press, 1991. Coelli, T., D.S. Prasada Rao, and G.E. Battese. An Introduction to Efficiency and Productivity Analysis. Kluwer Academic Publishers, 1998. Cooper, W., Seiford, L. and Tone, K. (1999). Data Envelopment Analysis. Kluwer Academic Publishers. Fare, R., S. Grosskopf and C.K. Lovell (1994). Production Frontiers. Cambridge University Press. Hazarika, G., and J. Alwang. 2003. “Smallholder Tobacco Cultivators in Malawi,” Agricultural Economics, 29, pp.99-109. Kumbhakar, S. C., and C. A. Knox Lovell. Stochastic Frontier Analysis. Cambridge University Press, 2000. Nadolnyak, D., C. Revoredo, and S. Fletcher. 2004. “Option-Based Forward Contracting under the Marketing Loan Program,” Working Paper, Department of Agricultural and Applied Economics, University of Georgia. Shi, Z., and S. Fletcher. 2003. “Georgia Peanut Cost Structure: A Preliminary Analysis from 2001 Survey”, working paper, Department of Agricultural and Applied Economics, University of Georgia. Varian, H. (1984). The Non-Parametric Approach to Production Analysis. Econometrica, Vol. 52(3):579-597. 23 Appendix Table 1. Panel A. Cobb-Douglas stochastic frontier model-normal/half normal lnc Coef. Std. Err. z P>z -0.2040 0.0995 -2.05 0.040 lny 0.3112 0.0384 8.09 0.000 w1 0.2523 0.0537 4.70 0.000 w2 -0.0306 0.0713 -0.43 0.668 w3 0.0403 0.0306 1.32 0.188 w4 0.0400 0.0315 1.27 0.205 w5 0.0987 0.0256 3.85 0.000 w6 0.0566 0.0528 1.07 0.284 w7 3.5460 0.6852 5.18 0.000 Constant sigma_v 0.0985 0.0331 sigma_u 0.2399 0.0535 Chi2 Log-likelihood Observations 551.34 21.859 61 Table 1. Panel B. OLS on the predicted inefficiency term u_h Coef. Std. Err. 0.0402 0.0048 QUOTA -0.0472 0.0151 SIZE 0.0402 0.0169 OEDU 0.0010 0.0013 OAGE 0.2883 0.1058 Constant R-squared Adj R-squared Obs t 0.84 -3.13 2.38 0.72 2.72 P>t 0.405 0.003 0.021 0.472 0.009 0.1961 0.1387 61 24 Table 1. Panel A. Cobb-Douglas stochastic frontier model-normal/truncated-normal model lnc Coef. Std. Err. z P>z lny w1 w2 w3 w4 w5 w6 w7 Constant -0.2571 0.2424 0.2791 0.0025 0.0205 0.0272 0.0926 0.1066 4.1280 0.0914 0.0397 0.0519 0.0616 0.0253 0.0263 0.0179 0.0422 0.6173 -2.81 6.10 5.37 0.04 0.81 1.03 5.18 2.53 6.69 0.005 0.000 0.000 0.967 0.418 0.301 0.000 0.011 0.000 QUOTA SIZE OEDU OAGE Constant sigma_u2 sigma_v2 -0.0019 -0.2634 0.2411 0.0040 0.4016 0.0164 0.0164 0.0015 0.1245 0.1116 0.0047 0.4117 0.0193 0.0063 -1.24 -2.12 2.16 0.86 0.98 0.216 0.034 0.031 0.388 0.329 Chi2 Log-Likelihood Observations 623 -31.322 61 lnc mu 25