Extrapolate-Ing: External Validity and Overidentification in the Late Framework

This paper develops a covariate-based approach to the external validity of instrumental variables (IV) estimates. Assuming that differences in observed complier characteristics are what make IV estimates differ from one another and from parameters like the effect of treatment on the treated, we show how to construct estimates for new subpopulations from a given set of covariate-specific LATEs. We also develop a reweighting procedure that uses the traditional overidentification test statistic to define a population for which a given pair of IV estimates has external validity. These ideas are illustrated through a comparison of twins and sex-composition IV estimates of the effects childbearing on labor supply.

[1]  Jonah B. Gelbach.  Public Schooling for Young Children and Maternal Labor Supply , 2002 .

[2]  Walter Zucchini,et al.  Model Selection , 2011, International Encyclopedia of Statistical Science.

[3]  Justin L. Tobias,et al.  Simple Estimators for Treatment Parameters in a Latent-Variable Framework , 2003, Review of Economics and Statistics.

[4]  Philip Oreopoulos,et al.  Estimating Average and Local Average Treatment Effects of Education when Compulsory Schooling Laws Really Matter , 2006 .

[5]  R. Olsen,et al.  A Least Squares Correction for Selectivity Bias , 1980 .

[6]  F. Vella,et al.  Estimating and interpreting models with endogenous treatment effects : The relationship between competing estimators of the union impact on wages , 1993 .

[7]  Alberto Abadie.  Semiparametric instrumental variable estimation of treatment response models , 2003 .

[8]  A. Roy.  Some thoughts on the distribution of earnings , 1951 .

[9]  D. Rubin,et al.  Principal Stratification in Causal Inference , 2002, Biometrics.

[10]  James J. Heckman,et al.  Four Parameters of Interest in the Evaluation of Social Programs , 2001 .

[11]  E. Vytlacil.  Independence, Monotonicity, and Latent Index Models: An Equivalence Result , 2002 .

[12]  J. Angrist,et al.  Identification and Estimation of Local Average Treatment Effects , 1995 .

[13]  A. Ebenstein.  When is the Local Average Treatment Close to the Average?: Evidence from Fertility and Labor Supply , 2009 .

[14]  D. Rubin.  ASSIGNMENT TO TREATMENT GROUP ON THE BASIS OF A COVARIATE , 1976 .

[15]  Markus Frölich,et al.  Nonparametric IV Estimation of Local Average Treatment Effects with Covariates , 2002, SSRN Electronic Journal.

[16]  M R Rosenzweig,et al.  Testing the quantity-quality fertility model: the use of twins as a natural experiment. , 1980, Econometrica : journal of the Econometric Society.

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

[18]  Victor Lavy,et al.  Multiple Experiments for the Causal Link between the Quantity and Quality of Children , 2006, Journal of Labor Economics.

[19]  J. Angrist,et al.  Children and Their Parents&Apos; Labor Supply: Evidence from Exogenous Variation in Family Size , 1996 .

[20]  J. Hahn.  A Note on Bootstrapping Generalized Method of Moments Estimators , 1996, Econometric Theory.

[21]  Rudolf Winter-Ebmer,et al.  Lower and Upper Bounds of Returns to Schooling: An Exercise in IV Estimation with Different Instruments , 1998 .

[22]  G. Cruces,et al.  Fertility and female labour supply in Latin America: new causal evidence , 2007 .

[23]  G. Imbens,et al.  Identification and Estimation of Triangular Simultaneous Equations Models without Additivity , 2002 .

[24]  Joshua D. Angrist,et al.  Identification of Causal Effects Using Instrumental Variables , 1993 .

[25]  Donald W. K. Andrews,et al.  Hybrid and Size-Corrected Subsampling Methods , 2007 .

[26]  A. Wald.  The Fitting of Straight Lines if Both Variables are Subject to Error , 1940 .

[27]  Richard K. Crump,et al.  Dealing with limited overlap in estimation of average treatment effects , 2009 .

[28]  K. DonaldW..  Generalized Method of Moments Estimation When a Parameter Is on a Boundary , 1999 .

[29]  Whitney K. Newey,et al.  Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference , 2002 .

[30]  Joel L. Horowitz,et al.  Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators , 1996 .

[31]  Joshua D. Angrist,et al.  Treatment Effect Heterogeneity in Theory and Practice , 2003 .

[32]  James J Heckman,et al.  Building Bridges between Structural and Program Evaluation Approaches to Evaluating Policy , 2010, Journal of economic literature.

[33]  Gary Chamberlain,et al.  BAYESIAN ASPECTS OF TREATMENT CHOICE , 2011 .