# Efficiency gains due to using missing data procedures in regression models

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## Abstract

IINN IIIIVI IVI I I I II IIIII II tlI IIIIi I IIVll lllll FEW 240 ~~-:i` `!.~ï.~3.~~'~~~~ ~;;r~t St? ï'H1:~`rC~,,, ~ l~ Tlt~p~RG ~ ~ .,..-! EFFICIENCY GAINS DUE TO USING MISSING DATA PROCEDURES IN REGRESSION MODELS Th.E. Nijman F.C. Palm November 1986 EFFICIENCY GAINS DUE TO USING MISSING DATA PROCEDURES IN REGRESSION MODELS Th.E. Nijman wr F.C. Palm november 19f36 . In the chapter on "Economic Data Issues" of the Handbook of Econometrics, Griliches (1986) analyzes the asymptotic variance of an estimator of a reqression coefficient using imputations for the missing regressor values and he compares it with that of an estimation procedure based on the com- plete observations only. His derivation of an expression for the relati- ve efficiency is íncorrect. In this note, we qive the correct result and show that the relative efficiency of three estimators desiqned to handle incomplete samples depends on parameters that have a atraightforward sta- tistical interpretation. In terms of a gain of asymptotíc efficiency, the use of these estimators is equivalent to the observation of a percen- tage of the values which are actually missing. This percentage depends on three R2-measures only, which can be straiqhtforwardly computed in applied work. Therefore it should be easy in practice to check whether it is worthwhile to use a more elaborate estimator. The authors thank Professor Z. Griliches for his comments on an earlier version of this note. t rt Department of Econometrics, Tilburq University, P.O.B. 90153, 5000 LE Tilburg, The Netherlands. Department of Economics, University of Limburg, P.O.B. 616, 6200 MD Maastricht, The Netherlands. 1 Griliches (1986) considers the following regression model 2 yi - Rxi t yzi t ei . ei ~ IN(0,o ), and xi - dzi t vi , vi ~ IN(O,Q~), where the regressors xi and zi are assumed to be independent of the correspondinq disturbances ei and vi. Actually, the normality assumption is not made by Gril

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