Inverse Probability Weighted

Inverse Probability Weighted - INVERSE PROBABILITY WEIGHTED...

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INVERSE PROBABILITY WEIGHTED ESTIMATION FOR GENERAL MISSING DATA PROBLEMS Jeffrey M. Wooldridge Department of Economics Michigan State University East Lansing, MI 48824-1038 (517) 353-5972 [email protected] This version: April 2003 1
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ABSTRACT I study inverse probability weighted M-estimation under a general missing data scheme. The cases covered that do not previously appear in the literature include M-estimation with missing data due to a censored survival time, propensity score estimation of the average treatment effect for linear exponential family quasi-log-likelihood functions, and variable probability sampling with observed retainment frequencies. I extend an important result known to hold in special cases: estimating the selection probabilities is generally more efficient than if the known selection probabilities could be used in estimation. For the treatment effect case, the setup allows for a simple characterization of a “double robustness” result due to Scharfstein, Rotnitzky, and Robins (1999): given appropriate choices for the conditional mean function and quasi-log-likelihood function, only one of the conditional mean or selection probability needs to be correctly specified in order to consistently estimate the average treatment effect. Keywords: Inverse Probability Weighting; M-Estimator; Censored Duration; Average Treatment Effect; Propensity Score JEL Classification Codes: C13, C21, C23 2
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1. INTRODUCTION In this paper I further study inverse probability weighted (IPW) M-estimation in the context of nonrandomly missing data. In previous work, I considered IPW M-estimation to account for variable probability sampling [Wooldridge (1999)] and for attrition and nonresponse [Wooldridge (2002a)]. The current paper extends this work by allowing a more general class of missing data mechanisms. In particular, I allow the selection probabilities to come from a conditional maximum likelihood estimation problem that does not necessarily require that the conditioning variables to always be observed. In addition, for the case of exogenous selection – to be defined precisely in Section 4 – I study the properties of the IPW M-estimator when the selection probability model is misspecified. In Wooldridge (2002a), I adopted essentially the same selection framework as Robins and Rotnitzky (1995), Rotnitzky and Robins (1995), and Robins, Rotnitzky, and Zhao (1995). Namely, under an ignorability assumption, the probability of selection is obtained from a probit or logit on a set of always observed variables. A key restriction, that the conditioning variables are always observed, rules out some interesting cases. A leading one is where the response variable is a censored survival time or duration, where the censoring times are random and vary across individual; see, for example, Koul, Susarla, and van Ryzin (1981) and Honoré, Khan, and Powell (2002). A related problem arises when one variable, say, medical cost or welfare cost, is unobserved because a duration,
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.

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Inverse Probability Weighted - INVERSE PROBABILITY WEIGHTED...

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