TY - JOUR
AU - Altonji,Joseph G.
AU - Matzkin,Rosa L.
TI - Panel Data Estimators for Nonseparable Models with Endogenous Regressors
JF - National Bureau of Economic Research Technical Working Paper Series
VL - No. 267
PY - 2001
Y2 - March 2001
DO - 10.3386/t0267
UR - http://www.nber.org/papers/t0267
L1 - http://www.nber.org/papers/t0267.pdf
N1 - Author contact info:
Joseph G. Altonji
Department of Economics
Yale University
Box 208264
New Haven, CT 06520-8264
Tel: 203/432-6285
Fax: 203/432-5591
E-Mail: joseph.altonji@yale.edu
Rosa Matzkin
Department of Economics
University of California, Los Angeles
8283 Bunche Hall
Mail Stop 147703
Los Angeles CA 90095
E-Mail: matzkin@econ.ucla.edu
AB - We propose two new estimators for a wide class of panel data models with nonseparable error terms and endogenous explanatory variables. The first estimator covers qualitative choice models and both estimators cover models with continuous dependent variables. The first estimator requires the existence of a vector z such that the density of the error term does not depend on the explanatory variables once one conditions on z. In some panel data cases we may find z by making the assumption that the distribution of the error term conditional on the vector of the explanatory variables for each cross-section' unit in the panel is exchangeable in the values of those explanatory variables. This situation may be realistic, in particular, when each unit is a group of individuals, so that the observations are across groups and for different individuals in each group. The basic idea is to first estimate the slope of the mean of the dependent variable conditional on both the explanatory variable and z and then undo the effect of conditioning on z by taking the average of the slope over the distribution of z conditional on a particular value of the explanatory variable. We also extend the procedure to the case in which the explanatory variable is endogenous conditional on z but an instrumental variable is available. The second estimator is based on the assumption that the error distribution is exchangeable in the explanatory variables of each unit. It applies to models that are monotone in the error term. A shift in the value of an explanatory variable for member 1 of a group has both a direct effect on the distribution of the dependent variable for member 1 and an indirect effect through the distribution of the error. A shift in the explanatory variable has an indirect effect on the dependent variable for other members of the panel but no direct effect. We isolate the direct effect by comparing the effect of the explanatory variable on the distribution of the dependent variable for member 1 to its effect on the distribution for the other panel members.
ER -