Abstract
The paper establishes an equivalence result in the context of anm-equation error component structural system, whose disturbances have the usual three-component structure, and whose equations feature explanatory variables of the formz i, zt andz it; the latter vary (respectively) only over individuals, only over time, and over both. Under the stochastic specification assumed, it is shown that the alternative instrumental variables (IV) estimators commonly used in the special cases of this system are all equivalent (numerically identical); the result is a generalization of the equivalences established previously for the special cases. In the single equation (m=1) context, the equivalence requires that the IV set contain variables of the formz i and/orz t, and further, in numbers determined by the ranks of (respectively) the individuals-mean and time-mean matrices of the instruments. If such an IV set is common to all equations, the equivalence also holds for the system under joint estimation. The result is used to recommend a couple of estimators for use in panel data, on grounds of computational simplicity.
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References
Amemiya T, MaCurdy TE (1986) Instrumental-variable estimation of an error component model. Econometrica 54:869–881
Balestra P (1988) Equality between ordinary and generalized procedures in econometrics. Cahier de Département d'Econométrie, Université de Genève
Baltagi BH (1981) Simultaneous equations with error components. Journal of Econometrics 17:189–200
Breusch TS, Mizon GE, Schmidt P (1989) Efficient estimation using panel data. Econometrica 57:695–700
Cornwell C, Rupert P (1988) Efficient estimation with panel data: An empirical comparison of instrumental variables estimators. Journal of Applied Econometrics 3:149–155
Cornwell C, Schmidt P, Wyhowski D (1989) Simultaneous equations and panel data. Department of Economics, Michigan State University, East Lansing, MI
Hausman JA, Taylor WE (1981) Panel data and unobservable individual effects. Econometrica 49:1377–1398
Hsiao C (1986) Analysis of Panel Data. Cambridge University Press, New York
Prucha IR (1985) Maximum likelihood and instrumental variable estimation in simultaneous equation systems with error components. International Economic Review 26:491–506
Revankar NS (1990a) Exact equivalence in instrumental variables estimation with application to an error component model. Department of Economics, State University of New York at Buffalo
Revankar NS (1990b) On the problem of forecasting prior to ‘price’ control and decontrol. Forthcoming in the Journal of Forecasting
Riddell WC (1979a) The empirical foundations of the Phillips curve: Evidence from Canadian wage contract data. Econometrica 47:1–24
Weiss R (1986) Necessary and sufficient conditions for ordinary least squares estimators to be best linear unbiased estimators. The American Statistician 40:178–179
Zyskind G (1967) On canonical forms, non-negative covariance matrices and best and simple least squares linear estimators in linear models. Annals of Mathematical Statistics 30:1092–1109
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This is a revision of the December 1990 draft with the same title, and is a substantial revision of the April 1990 version entitled: “Analysis of an error component structural system”. This revision has benefited from comments received from a referee and a editor of this journal. I came to know from an anonymous reader that the equivalence criterion developed in my 1990 a article, used here and the two earlier versions, was infact obtained previously in an unpublished paper by Balestra (1988). Balestra's paper, which was made available to me by Badi Baltagi at the time of this revision, and subsequently by Balestra, considers the equivalence ofδ b,δ c and one other estimator which differs from ourδ a. Errors, if any, are my responsibility.
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Revankar, N.S. Exact equivalence of instrumental variable estimators in an error component structural system. Empirical Economics 17, 77–84 (1992). https://doi.org/10.1007/BF01192476
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DOI: https://doi.org/10.1007/BF01192476