Cost Function Estimation with Proportional Errors in Variables

Yıl 2012, Cilt: 4 Sayı: 2, 59 - 81, 01.09.2012

Richard E. Just Rulon D. Pope

Öz

A model with proportional errors in variables arising naturally in microeconomics is considered. Unlike the classical additive errors case, all OLS parameter estimates exhibit attenuation bias that does not depend on the limiting distribution of the data. The distribution of OLS estimators is developed. With no intercept, a simple correction of OLS based on mean predictions is identified that is consistent and asymptotically normal. With an intercept, a readily available additional moment based on sample data identifies the parameters. In neither case are additional restrictions or use of extra-sample data as instruments required as for common errors-in-variables methods.

Anahtar Kelimeler

Errors in variables, Proportional errors, Estimation

Kaynakça

• Amemiya, Y. (1990). Two-stage instrumental variable estimators for the nonlinear errors- in-variables model, Journal of Econometrics, 44, 311-332.
• Antle, J.M. (1984). The structure of U.S. agricultural technology, 1910-78, American Journal of Agricultural Economics, 66, 414-421.
• Ball, E. V., Bureau, J-C., Nehring, R. and Somwaru, A. (1997). Agricultural productivity revisited, American Journal of Agricultural Economics, 79, 1045-1063.
• Berndt, E. R. and Wood, D.O. (1975). Technology, prices, and the derived demand for energy, Review of Economics and Statistics, 57, 259-268.
• Binswanger, H. (1974). The Measurement of technical change biases with many factors of production, American Economic Review, 64, 964-976.
• Blundell, R. (1988). Consumer Behavior, Theory and empirical evidence—a survey, Economic Journal, 98, 16-65.
• Briggs, F.E.A. (1962).The influence of errors on the correlation of ratios, Econometrica, 30, 162-177.
• Burt, O.R. and Brewer, D. (1971). Estimation of net social benefits from outdoor recreation, Econometrica, 39, 813-827.
• Casson, M.C. (1973). Linear regression with error in the deflating variable, Econometrica, 41, 751-759.
• Cragg, J.G. (1997). Using higher moments to estimate the simple errors-in variables model, Rand Journal, 28, S71-S90.
• Diewert, W.E. (1971). An application of the Shephard duality theorem: a generalized Leontief, Journal of Political Economy, 79, 481-507.
• Donald, S.G. and Newey, W.K. (2001). Choosing the number of instruments, Econometrica, 69, 1161-1191.
• Dhrymes, P. (1978). Mathematics for Econometrics. Springer-Verlag: New York.
• Fuss, M. (1977). The structure of technology over time: a model for testing the "putty-clay" hypothesis, Econometrica, 45, 1797-1821.
• Garber, S. and Klepper, S. (1980). Extending the classical normal errors in variables model, Econometrica, 48, 1541-1546.
• Gorman, W.M. (1959). Separable utility and aggregation, Econometrica, 27, 469-481.
• Griliches, Z. and Ringstad, V. (1970). Error-in-variables bias in nonlinear contexts, Econometrica, 38, 368-370.
• Hansen, L. P. (1982). Large sample properties of method of moments estimators, Econometrica, 50, 1029-1054.
• Hausman, J. (2001). Mismeasured variables in econometric analysis: problems from the right and problems from the left, Journal of Economic Perspectives, 15, 57-67.
• Hausman, J.A., Newey, W. K., Ichimura, H. and Powell, J.L. (1991). Identification and estimation of polynomial errors-in variables models, Journal of Econometrics, 50, 273-295.
• Heien, D. (1977). The cost of the U.S. dairy price support program: 1949-1974, Review of Economics and Statistics, 59, 1-8.
• Humphrey, D.B. (1975). Estimates of factor-intermediate substitution and separability, Southern Economic Journal, 41, 531-534.
• Izumida, N., Urushi, H. and Nakanishi, S. (1999). An empirical study of the physican- induced demand hypothesis—the cost function approach to medical expenditure of the elderly in
• Japan, Review of Population and Social Policy, 8, 11-25.
• Kuh, E. and Meyer, J. (1955). Correlation and regression estimates when the data are ratios, Econometrica, 23, 400-416.
• Lewbel, A. (1987). Characterizing some Gorman Engel curves, Econometrica, 55, 1451- 1459.
• Loève, M. (1977). Probability Theory. 4th edn. Van Nostrand: Princeton.
• Nelson, D. B. (1995). Vector attenuation bias in the classical errors-in-variables model, Economics Letters, 49, 345-349.
• Newey, W. and McFadden, D. (1994). Large sample estimation and hypothesis testing. In Handbook of Econometrics, Vol. 4, eds. R.F. Engle, R.F., D. McFadden, Elsevier: New York, 2111-2245.
• Newey, W. (2001). Flexible simulated moment estimation of nonlinear errors-in-variables models, Review of Economics and Statistics, 83, 616-627.
• Newey, W.K. and West, K.D. (1987). A simple positive definite heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica, 55, 703-8.
• Pope, R.D. and Just, R.E. (1996). Empirical implementation of ex ante cost functions, Journal of Econometrics, 72, 231-49.
• Riersol, O. (1950). Identifiability of a linear relation between variables which are subject to error, Econometrica, 18, 375-89.
• Shephard, R. (1970). Cost and Production Functions. Princeton University Press: Princeton, NJ.
• Song, D. and Hallberg, M. (1982). Measuring producers' advantage from classified pricing of milk, American Journal of Agricultural Economics, 64, 1-8.
• Theil, H. (1961). Economic Forecasts and Policy. North-Holland: Amsterdam.
• White, H. (1984). Asymptotic Theory for Econometricians. Academic Press: New York.