Abstract
The parameter estimates based on an econometric equation are biased and can also be inconsistent when relevant regressors are omitted from the equation or when included regressors are measured with error. This problem gets complicated when the `true' functional form of the equation is unknown. Here, we demonstrate how auxiliary variables, called concomitants, can be used to remove omitted-variable and measurement-error biases from the coefficients of an equation with the unknown `true' functional form. The method is specifically designed for panel data. Numerical algorithms for enacting this procedure are presented and an illustration is given using a practical example of forecasting small-area employment from nonlinear autoregressive models.
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References
Basmann, Robert L. (1988). Causality tests and observationally equivalent representations of econometric models. J. Econometrics, 39, 69–104.
Brown, Laurence D. (1990). An ancillarity paradox which appears in multiple linear regression (with discussion). Ann. Stat., 18, 471–538.
Chang, I-Lok, Swamy, P.A.V.B., Hallahan, Charles and Tavlas, George S. (2000). A computational approach to finding causal economic laws. Computat. Econom., 16, 105–136.
Chang, I-Lok, Hallahan, Charles and Swamy, P.A.V.B. (1992). Efficient computation of stochastic coefficient models. In H.M. Amman, D.A. Belsley and L.F. Pau (eds.), Computational Economics and Econometrics, Kluwer Academic Publishers, Boston, pp. 43–53.
de Finetti, Bruno (1974). The Theory of Probability, Vol. 1. Wiley, New York.
Friedman, Milton and Schwartz, Anna J. (1991). Alternative approaches to analyzing economic data. Amer. Econom. Rev., 81, 39–49.
Greene, William H. (2000). Econometric Analysis, 4th edn. Prentice Hall, Upper Saddle River, New Jersey.
Kourouklis, S. and Paige, C.C. (1981). A constrained least squares approach to the general Gauss-Markov linear model. J. Amer. Stat. Assoc., 78, 620–625.
Lehmann, Erich L. and Casella, George (1998). Theory of Point Estimation, 2nd edn. Springer, New York.
Montgomery, Alan L., Zarnowitz, Victor, Tsay, Ruey S. and Tiao, George C. (1998). Forecasting the U.S. unemployment rate. J. Amer. Stat. Assoc., 93, 478–493.
Narasimham, Gorti V.L., Swamy P.A.V.B. and Reed, R.C. (1988). Productivity analysis of U.S. manufacturing using a stochastic-coefficients production function. J. Busin. Econom. Stat., 6, 339–350.
Oakes, D. (1985). Self-calibrating priors do not exist. J. Amer. Stat. Assoc., 80, 339.
Peddada, S.D. (1985). A short note on Pitman's measure of nearness. Amer. Statistician, 39, 298–299.
Pratt, John W. and Schlaifer, Robert (1984). On the nature and discovery of structure. J. Amer. Stat. Assoc., 79, 9–21, 29-33.
Rao, C.R. (1973). Linear Statistical Inference and its Applications, 2nd edn. Wiley, New York.
Schervish, M.J. (1985). Discussion of ‘Calibration-based empirical probability’ by A.P. Dawid. Ann. Statist., 13, 1274–1282.
Swamy, P.A.V.B. and Mehta, Jatinder S. (1975). Bayesian and non-Bayesian analysis of switching regressions and of random coefficient regression models. J. Amer. Stat. Assoc., 70, 593–602.
Swamy, P.A.V.B. and Schinasi, Garry J. (1989). Should fixed coefficients be re-estimated every period for extrapolation? J. Forecasting, 8, 1–18.
Swamy, P.A.V.B., Mehta, Jatinder S. and Singamsetti, Rao N. (1996). Circumstances in which different criteria of estimation can be applied to estimate policy effects. J. Statist. Planning Inference, 50, 121–153.
Swamy, P.A.V.B. and Tavlas, George S. (2001). Random coefficient models. In B.H. Baltagi (ed.), Companion to Theoretical Econometrics. Blackwell Publishers Ltd, Malden, Massachusetts, pp. 410–428.
Yokum, J. Thomas, Wildt, Albert R. and Swamy, P.A.V.B. (1998). Forecasting disjoint data structures using approximate constant and stochastic coefficient models. J. Appl. Statist. Sci., 8, 29–49.
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Swamy, P.A.B., Chang, IL., Mehta, J.S. et al. Correcting for Omitted-Variable and Measurement-Error Bias in Autoregressive Model Estimation with Panel Data. Computational Economics 22, 225–253 (2003). https://doi.org/10.1023/A:1026189916020
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DOI: https://doi.org/10.1023/A:1026189916020