Efficient Estimation of Data Combination Models by the Method of Auxiliary-to-Study Tilting (AST)

We propose a locally efficient estimator for a class of semiparametric data combination problems. A leading estimand in this class is the average treatment effect on the treated (ATT). Data combination problems are related to, but distinct from, the class of missing data problems with data missing at random (of which the average treatment effect (ATE) estimand is a special case). Our estimator also possesses a double robustness property. Our procedure may be used to efficiently estimate, among other objects, the ATT, the two-sample instrumental variables model (TSIV), counterfactual distributions, poverty maps, and semiparametric difference-in-differences. In an empirical application, we use our procedure to characterize residual Black–White wage inequality after flexibly controlling for “premarket” differences in measured cognitive achievement. Supplementary materials for this article are available online.

[1]  Frederick Mosteller,et al.  Identification and estimation. , 1955 .

[2]  R. Cox,et al.  Journal of the Royal Statistical Society B , 1972 .

[3]  D. Rubin.  Assignment to Treatment Group on the Basis of a Covariate , 1976 .

[4]  J. A. Anderson,et al.  7 Logistic discrimination , 1982, Classification, Pattern Recognition and Reduction of Dimensionality.

[5]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[6]  R. Lalonde.  Evaluating the Econometric Evaluations of Training Programs with Experimental Data , 1984 .

[7]  James J. Heckman,et al.  Alternative methods for evaluating the impact of interventions: An overview , 1985 .

[8]  J. Heckman,et al.  Longitudinal Analysis of Labor Market Data: Alternative methods for evaluating the impact of interventions , 1985 .

[9]  W. Newey,et al.  Large sample estimation and hypothesis testing , 1986 .

[10]  James J. Heckman,et al.  Choosing Among Alternative Nonexperimental Methods for Estimating the Impact of Social Programs: the Case of Manpower Training , 1989 .

[11]  Raymond J. Carroll,et al.  Semiparametric Estimation in Logistic Measurement Error Models , 1989 .

[12]  W. Newey,et al.  Semiparametric Efficiency Bounds , 1990 .

[13]  J. Angrist,et al.  The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples , 1990 .

[14]  R. Little,et al.  Models for Contingency Tables with Known Margins when Target and Sampled Populations Differ , 1991 .

[15]  P. Bickel,et al.  Efficient estimation of linear functionals of a probability measure P with known marginal distributions , 1991 .

[16]  J. Robins,et al.  Estimation of Regression Coefficients When Some Regressors are not Always Observed , 1994 .

[17]  Thomas Lemieux,et al.  Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach , 1995 .

[18]  William R. Johnson,et al.  The Role of Premarket Factors in Black-White Wage Differences , 1996, Journal of Political Economy.

[19]  Anders Björklund,et al.  Intergenerational Income Mobility in Sweden Compared to the United States , 1997 .

[20]  Aaron Yelowitz,et al.  Are Public Housing Projects Good for Kids? , 1997 .

[21]  Derek A. Neal,et al.  Basic Skills and the Black-White Earnings Gap , 1998 .

[22]  J. Hahn.  On the Role of the Propensity Score in Efficient Semiparametric Estimation of Average Treatment Effects , 1998 .

[23]  Donald B. Rubin,et al.  Combining Panel Data Sets with Attrition and Refreshment Samples , 1998 .

[24]  Y. Qin.  Inferences for case-control and semiparametric two-sample density ratio models , 1998 .

[25]  Subhash R. Lele,et al.  Maximum likelihood estimation in semiparametric selection bias models with application to AIDS vaccine trials , 1999 .

[26]  Guido W. Imbens,et al.  Imposing Moment Restrictions from Auxiliary Data by Weighting , 1996, Review of Economics and Statistics.

[27]  G. Imbens,et al.  Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score , 2000 .

[28]  Joseph P. Lupton,et al.  Accounting for the Black–White Wealth Gap , 2001 .

[29]  G. Imbens,et al.  Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score , 2002 .

[30]  Aviv Nevo.  Sample selection and information-theoretic alternatives to GMM , 2002 .

[31]  VACANT-PROPERTY Policy,et al.  THE BROOKINGS INSTITUTION , 2002 .

[32]  Jeffrey M. Woodbridge.  Econometric Analysis of Cross Section and Panel Data , 2002 .

[33]  Oliver Linton,et al.  Semiparametric Regression Analysis With Missing Response at Random , 2003 .

[34]  J. Lanjouw,et al.  Micro-Level Estimation of Poverty and Inequality , 2003 .

[35]  G. Imbens,et al.  Large Sample Properties of Matching Estimators for Average Treatment Effects , 2004 .

[36]  G. Imbens,et al.  Estimation of Causal Effects using Propensity Score Weighting: An Application to Data on Right Heart Catheterization , 2001, Health Services and Outcomes Research Methodology.

[37]  G. Imbens.  Nonparametric Estimation of Average Treatment Effects Under Exogeneity: A Review , 2004 .

[38]  Alberto Abadie.  Semiparametric Difference-in-Differences Estimators , 2005 .

[39]  A. Tsiatis.  Semiparametric Theory and Missing Data , 2006 .

[40]  Yuichi Kitamura,et al.  Empirical Likelihood Methods in Econometrics: Theory and Practice , 2006 .

[41]  Zhiqiang Tan,et al.  A Distributional Approach for Causal Inference Using Propensity Scores , 2006 .

[42]  G. Ridder,et al.  The Econometrics of Data Combination , 2007 .

[43]  Biao Zhang,et al.  Empirical‐likelihood‐based inference in missing response problems and its application in observational studies , 2007 .

[44]  R. Freeman.  Labor Market Institutions , 2007 .

[45]  B. Graham,et al.  Inverse Probability Tilting for Moment Condition Models with Missing Data , 2008 .

[46]  Jing Qin,et al.  Empirical‐likelihood‐based difference‐in‐differences estimators , 2008 .

[47]  A. U.S.  Efficient Nonparametric Estimation of Causal Effects in Randomized Trials with Noncompliance , 2008 .

[48]  Han Hong,et al.  Semiparametric Efficiency in GMM Models of Nonclassical Measurement Errors, Missing Data and Treatment Effects , 2008 .

[49]  Xiaohong Chen,et al.  Semiparametric efficiency in GMM models with auxiliary data , 2007, 0705.0069.

[50]  Bryan S. Graham,et al.  Efficiency Bounds for Missing Data Models with Semiparametric Restrictions , 2008 .

[51]  Dylan S. Small,et al.  Efficient nonparametric estimation of causal effects in randomized trials with noncompliance , 2009 .

[52]  Alessandro Tarozzi,et al.  Using Census and Survey Data to Estimate Poverty and Inequality for Small Areas , 2007, The Review of Economics and Statistics.

[53]  Robin Moore.  In Place Of , 2009 .

[54]  V. Chernozhukov,et al.  Inference on Counterfactual Distributions , 2009, 0904.0951.

[55]  Zhiqiang Tan,et al.  Bounded, efficient and doubly robust estimation with inverse weighting , 2010 .

[56]  Shakeeb Khan,et al.  Irregular Identification, Support Conditions, and Inverse Weight Estimation , 2010 .

[57]  Patrick M. Kline.  Oaxaca-Blinder as a Reweighting Estimator , 2011 .

[58]  E. Kitagawa,et al.  Standardized comparisons in population research , 1964, Demography.

[59]  C. Rothe,et al.  Semiparametric Estimation and Inference Using Doubly Robust Moment Conditions , 2013, SSRN Electronic Journal.