Abstract
This paper considers methods of estimating a static correlated random coefficient model with panel data. We mainly focus on comparing two approaches of estimating unconditional mean of the coefficients for the correlated random coefficients models, the group mean estimator and the generalized least squares estimator. For the group mean estimator, we show that it achieves Chamberlain (1992) semi-parametric efficiency bound asymptotically. For the generalized least squares estimator, we show that when T is large, a generalized least squares estimator that ignores the correlation between the individual coefficients and regressors is asymptotically equivalent to the group mean estimator. In addition, we give conditions where the standard within estimator of the mean of the coefficients is consistent. Moreover, with additional assumptions on the known correlation pattern, we derive the asymptotic properties of panel least squares estimators. Simulations are used to examine the finite sample performances of different estimators.
Highlights
IntroductionOne useful tool for reducing real-world details for econometric modeling is through “suitable”
One useful tool for reducing real-world details for econometric modeling is through “suitable”aggregations of micro data
Parameter heterogeneity among micro units is quite common and a random coefficients model is a convenient way to take into account unobserved heterogeneity in pooling the panel data (e.g., Hsiao and Tahmiscioglu 1997; Hsiao et al 2005)
Summary
One useful tool for reducing real-world details for econometric modeling is through “suitable”. Heckman and Vytlacil (1998) propose an instrumental variable method for the population mean of slope coefficients but not the intercept in the cross sectional correlated random coefficients model. We consider the parametric identification and estimation of the unconditional mean of the random coefficients using panel data when the regularity conditions hold. When only cross-sectional data are available, the identification conditions of average effects for a correlated random coefficients model require the existence of instrumental variables, which are very stringent and may not be satisfied for many data sets. When panel data are available, it is possible to obtain a consistent estimator of the population mean of random coefficients without the existence of instrumental variables. We discuss different conditions and estimations in the following subsections
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