Moffitt, Robert A.: Weighting for Nonresponse in Panel Data: A New Method
World Conference Econometric Society, 2000, Seattle

Robert A. Moffitt, Johns Hopkins University
Weighting for Nonresponse in Panel Data: A New Method
Session: C-13-20  Wednesday 16 August 2000  by Moffitt, Robert A.
In a prior paper, "Sample Attrition in Panel Data: The Role of Selection on Observables" (three copies in the mail; forthcoming in the Annales and presented in Paris in June, 1997), the author noted considered the problem of sample attrition under the assumption of selection on observables, the case which is opposite to that considered in the literature (selection on unobservables). The paper showed that using endogenous covariates from periods prior in the panel (lagged earnings, hours of work, and other such variables in a labor economics example) to construct weights for WLS estimation yields consistent estimation of structural equation coefficients.
The selection-on-observables model in the paper is mostly closely related not to the econometric literature on selection bias adjustment, but rather to the survey statistics literature on the construction of survey weights for nonresponse. Most panel data sets contain such survey weights, which are based upon adjustments using attrition rates on the basis of observable characteristics from prior in the panel.
The difference between these traditional nonresponse survey weights, and the weights proposed in the enclosed paper, is that the method proposed here is model-specific: that is, estimation of the weights requires specification of an attrition equation containing as covariates the mostly likely sources of endogenous attrition for the particular application in mind. For example, an analyst estimating a structural earnings equation would want to use lagged earnings to construct the weights; an analyst estimating a structural consumption equation would want to use lagged consumption as weights; an analyst estimating a structural model for job transitions would want to use the number of lagged job transitions as weights; and so on. The right set of covariates maximizes the amount of bias reduced.
Usual survey practice presumes that a single, "universal" weight can be constructed and appended to a survey file, and that the weight can be used for all applications. The new method proposed here is fundamentally at odds with that approach. In fact, the "universal weight" method can be shown to be extremely inefficient, if not biased, if the variables used in the universal weights are not appropriate for the application at hand.
The paper I am currently completing provides a number of analyses of this issue, using the U.S. PSID panel. (1) A GMM method for estimating the weights together with the structural equation is provided, illustrating both 2-step and joint methods; considerations of efficiency are considered; (2) methods for selecting variables for the attrition equation are considered, and tradeoffs between bias reduction and efficiency are considered in this choice; (3) specification tests for the presence of attrition bias from selection on observables are presented; and (4) the results are compared to those obtained when using the universal weights supplied by the PSID.
A computer program will be offered to all users to implement this method themselves.

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