Panel Data Estimators for Nonseparable Models with Endogenous Regressors

By Joseph G. Altonji, Rosa L. Matzkin. 2001

46 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics

View Paper: https://www.semanticscholar.org/paper/1d9f523634e733add4a3f5863f72ee4abc2e7f52

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Citations in the corpus

Censored regression quantiles with endogenous regressors (2007, methodology): “…(Powell, 1987, 2001; Ahn and Powell, 1993; Chen and Khan, 1999; Honoré and Powell, 2004; Das et al., 2003; Blundell and Powell, 2004) and nonparametric models (e.g., Newey et al., 1999; Altonji and Matzkin, 1997; Blundell and Powell, 2001; Imbens and Newey, 2002; Florens et al., 2003).”
Inference in Censored Models with Endogenous Regressors (2003, methodology): “In panel data models, Altonji and Matzkin (1997) introduced a semiparametric estimator for nonseparable models with endogenous regressors.”
IDENTIFICATION AND INFERENCE IN NONLINEAR DIFFERENCE-IN-DIFFERENCES MODELS BY (2003, unknown): “22 For example, Altonji and Matzkin (2001) analyze a nonseparable panel data model with an endogenous regressor, x.”
Estimating Dynamic Panel Data Discrete Choice Models with Fixed Effects (2007, background): “This is the parameter of interest estimated in Altonji and Matzkin (2001).”
Identification in Nonparametric Simultaneous Equations Models (2008, background): “Altonji and Ichimura (2000) considered models with latent variables. Altonji and Matzkin (2001, 2005) provided estimators for average derivatives in nonseparable models, using conditional independence, and for nonparametric nonseparable functions, using exchangeability. Altonji and Matzkin (2003) ex”
Dummy Endogenous Variables in Weakly Separable Models (2007, methodology): “1 Assume that (D,Y ) are generated according to equations (1)-(2).”
Estimating Derivatives in Nonseparable Models with Limited Dependent Variables (2008, unknown): “We can estimate β(x) by substituting suitable parametric or nonparametric estimators for the functions on the right hand side of this equation.12 Following Altonji and Matzkin (2001, 2005), if one is willing to assume that the conditional distribution of Uit is exchangeable in (Xi1, Xi2, . . . XiT )”