Abstract
This study is concerned with an examination of the finite sample behaviour of several limited information estimators in interdependent structures with error terms related over time and in certain specifications across equations. The Monte Carlo or simulation approach is adopted and applied to computationally manageable structures containing lagged dependent variables. The analysis of the Monte Carlo experiments is formulated in terms of estimating response functions, the dependent variables of which are the first two moments of target model estimators. In addition to the impact of simultaneity, autocorrelation and lagged dependent variables on the estimators, evidence is also accumulated on the small sample effects of misspecification in terms of the faulty inclusion and deletion of regressors. The results of the experiments revealed the substantial impact which autocorrelation can have on ordinary least squares (OLS) and two-stage least squares (2SLS) in terms of efficiency loss. Averaging over all the coefficients in the models, estimators which take account of both autocorrelation and simultaneity had a relative efficiency factor of about 1.5 to 1.9. Many of the parameters in the Monte Carlo model (including misspecification errors, multicollinearity) had qualitatively the same effect on bias and dispersion properties of the estimators.
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References
Amemiya, T.: Specification Analysis in the Estimation of Parameters of a Simultaneous Equation Model with Autoregressive Residuals. Econometrica34, 1966, 283–306.
Bergstrom, R.: A Comparative Study of Extensions of the Iterative Instrumental Variables (IIV) Method in the Case of Autocorrelated Residuals and Lagged Endogenous Variables. Paper presented at the Third World Congress of the Econometric Society, Toronto, August 1975.
Bronfenbrenner J.: Sources and Size of Least-Squares Bias in a Two-Equation Model. Studies in Econometric Methods. Ed. by W.D. Hood and C.T. Koopmans. Cowles Commission Monograph14, 1953, Ch. 9, 221–235.
Brundy, J. M., andD. W. Jorgenson: Efficient Estimation of Simultaneous Equations by Instrumental Variables. Review of Economics and Statistics53, 1971, 207–224.
Conlisk, J.: Optimal Response Surface Design in Monte Carlo Sampling Experiments. Annals of Economic and Social Measurement3, 1974, 463–473.
Cragg, J. G.: On the Sensitivity of Simultaneous-Equations Estimators to the Stochastic Assumptions of the Models. JASA,61, 1966, 136–151.
—: On the Relative Small-Sample Properties of Several Structural-Equation Estimators. Econometrica35, 1967, 89–110.
—: Some Effects of Incorrect Specification on the Small-Sample Properties of Several Simultaneous Equation Estimators. International Economic Review9, 1968, 63–85.
Dhrymes, P.J.: Econometrics: Statistical Foundations and Applications. New York 1970.
Dhrymes, P.J., R. Berner andD. Cummins: A Comparison of Some Limited Information Estimators for Dynamic Simultaneous Equation Models with Autocorrelated Errors. Econometrica42, 1974, 311–332.
Fair, R. C.: The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors. Econometrica,38, 1970, 507–515.
Fisher, G.R.: The Algebra of Estimation in Linear Econometric Systems. International Journal of Mathematics, Education and Science Technology3, 1972, 385–403.
Fishman, G.S.: Bias Considerations in Simulation Experiments. Operations Research20, 1972, 785–790.
Goldfeld, S.M., andR.E. Quandt: Nonlinear Methods in Econometrics. Amsterdam 1972.
Hendry, D.F.: Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process. International Economic Review12, 1971, 257–268.
—: On Asymptotic Theory and Finite Sample Experiments. Econometrica,60, 1973, 210–217.
—: The Structure of Simultaneous Equation Estimators. Journal of Econometrics4, 1976, 51–88.
Hendry, D.F., andR.W. Harrison: Monte Carlo Methodology and the Small Sample Behaviour of Ordinary and Two-Stage Least Squares. Journal of Econometrics2, 1974, 151–174.
Hendry, D.F., andP.K. Trivedi: Maximum Likelihood Estimation of Difference Equations with Moving Average Errors: A Simulation Study. Review of Economic Studies39, 1972, 117–145.
Hildreth, C., andJ.Y. Lu: Demand Relations with Autocorrelated Disturbances. Michigan State University, Agricultural Experimental Station, Technical Bulletin 276, East Lansing 1960.
Quandt, R.E.: On Certain Small Sample Properties ofk-Class Estimators. International Economic Review6, 1965, 92–104.
Sargan, J.D.: The Maximum Likelihood Estimation of Economic Relationship with Autoregressive Residuals. Econometrica29, 1961, 414–426.
Summers, R.: A Capital Intensive Approach to the Small Sample Properties of Various Simultaneous Equation Estimators. Econometrica33, 1965, 1–41.
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This paper is based on the author's doctoral dissertation at Queen's University, Kingston 1977. The author wishes to thank Charles Beach, Hiroki Tsurumi, and Gordon Fisher for comments and suggestions.
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Robertson, M. The small sample properties of several limited information estimators in interdependent structures with scalar and vector autoregressive errors. Empirical Economics 7, 63–73 (1982). https://doi.org/10.1007/BF02506825
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DOI: https://doi.org/10.1007/BF02506825