Maximum likelihood estimation of a stochastic frontier model with residual covariance

Simwaka, Kisu (2012): Maximum likelihood estimation of a stochastic frontier model with residual covariance.

Abstract

In theoretical literature on productivity, the disturbance terms of the stochastic frontier model are assumed to be independent random variables. In this paper, we consider a stochastic production frontier model with residuals that are both spatially and time-wise correlated. We introduce generalizations of the Maximum Likelihood Estimation procedure suggested in Cliff and Ord (1973) and Kapoor (2003). We assume the usual error component specification, but allow for possible correlation between individual specific errors components. The model combines specifications usually considered in the spatial literature with those in the error components literature. Our specifications are such that the model’s disturbances are potentially spatially correlated due to geographical or economic activity. For instance, for agricultural farmers, spatial correlations can represent productivity shock spillovers, based on geographical proximity and weather. These spillovers effect estimation of efficiency.

• Item Type: MPRA Paper
• Language: English
• Keywords: spatial stochastic production frontier models, correlated errors
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C24 - Truncated and Censored Models ; Switching Regression Models ; Threshold Regression Models; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C21 - Cross-Sectional Models ; Spatial Models ; Treatment Effect Models ; Quantile Regressions

References

Aigner, D., C.A.K. Lovell, and P. Schmidt. "Formulation and Estimation of Stochastic Frontier Production Function Models." Journal of Econometrics 6 (July 1977): 21-37.

Baltagi, B.H., 2005. Econometric Analysis of Panel Data. Wiley, New York

Battese, G.E., and T.J. Coelli. (992). "Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India." Journal of Productivity Analysis 3 (1992): 149-165.

Battese, G E & Coelli, T J, (1995). "A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data," Empirical Economics, Springer, vol. 20(2), pages 325-32.

Cliff, A. and J.K Ord. 1973. Spatial autocorrelation. London: Pion.

Cliff, A. and J.K. Ord. 1981. Spatial processes: Models and applications. London: Pion.

Cornwell, C., P. Schmidt, and R.C. Sickles.(1990) "Production Frontiers with Cross-Sectional and Time-Series Variation in Efficiency Levels." Journal of Econometrics 46: 185-200.

Das, D., Kelejian, H.H., Prucha, I.R., 2003. Small sample properties of estimators of spatial autoregressive models with autoregressive disturbances. Papers in Regional Science 82, 1–26.

Kapoor, M. (2003). Panel Data Models with Spatial Correlation: Estimation Theory and an Empirical Investigation of the US Wholesale Gasoline Industry, Department of Economics, University of Maryland, USA.

Kelejian, H.H., Prucha, I.R., 1998. A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances. Journal of Real Estate Finance and Economics 17, 99–121.

Kelejian, H.H., Prucha, I.R., 1999. A generalized moments estimator for the autoregressive parameter in a spatial model. International Economic Review 40, 509–533.

Kelejian, H.H. and Prucha, I.R., (2007). HAC Estimation in a Spatial Framework. Journal of Econometrics 140, 131-154.

Kumbhakar, S.C. (1990). "Production Frontiers, Panel Data, and Time-Varying Technical Inefficiency." Journal of Econometrics 46: 201-211.

Lee, Y.H., and P. Schmidt. "A Production Frontier Model with Flexible Temporal Variation in Technical Efficiency." The Measurement of Productive Efficiency: Techniques and Applications. H.O. Fried, C.A.K. Lovell, and S.S. Schmidt, eds., pp. 237-255. New York, Oxford: Oxford University Press, 1993.

Meeusen, W., and J. van den Broeck. (1977) "Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error." International Economic Review 18: 435-444.

Pitt, M.M. and L. Lee. (1981), "The Measurement and Sources of Technical Inefficiency in the Indonesian Weaving Industry", Journal of Development Economics, 9, 43-64.

Schmidt, P., and R.C. Sickles. (1984)"Production Frontiers and Panel Data." Journal of Business and Economic Statistics 2: 367-374.