Estimating Causal Effects With Matching Methods in the Presence and Absence of Bias Cancellation

This article explores the implications of bias cancellation on the estimate of average treatment effects using ordinary least squares (OLS) and Rubin-style matching methods. Bias cancellation (offsetting biases at high and low propensities for treatment in estimates of treatment effects that are uncorrected for nonrandom selection) has been observed when job training is the treatment variable and earnings is the outcome variable. Contrary to published assertions in the literature, bias cancellation is not explainable in terms of the standard selection model, which assumes a symmetric distribution for the errors in the structural and assignment equations. A substantive rationale for bias cancellation is offered, which conceptualizes bias cancellation as the result of a mixture process based on two distinct individual-level decision-making models. While the general properties are unknown, the existence of bias cancellation appears to reduce the average bias in both OLS and matching methods relative to the symmetric distribution case.

[1]  D B Rubin,et al.  Matching using estimated propensity scores: relating theory to practice. , 1996, Biometrics.

[2]  Jacques A. Hagenaars,et al.  Categorical Longitudinal Data: Log-Linear Panel, Trend, and Cohort Analysis , 1990 .

[3]  J. Heckman,et al.  The Economics and Econometrics of Active Labor Market Programs , 1999 .

[4]  Herbert L. Smith.  6. Matching with Multiple Controls to Estimate Treatment Effects in Observational Studies , 1997 .

[5]  D. Rubin,et al.  Constructing a Control Group Using Multivariate Matched Sampling Methods That Incorporate the Propensity Score , 1985 .

[6]  Christopher Winship,et al.  THE ESTIMATION OF CAUSAL EFFECTS FROM OBSERVATIONAL DATA , 1999 .

[7]  D. Rubin,et al.  Reducing Bias in Observational Studies Using Subclassification on the Propensity Score , 1984 .

[8]  M. Sobel.  Causal Inference in the Social and Behavioral Sciences , 1995 .

[9]  Petra E. Todd,et al.  Matching As An Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme , 1997 .

[10]  D. Rubin.  INFERENCE AND MISSING DATA , 1975 .

[11]  D B Rubin,et al.  Practical implications of modes of statistical inference for causal effects and the critical role of the assignment mechanism. , 1991, Biometrics.

[12]  Christopher Winship,et al.  Loglinear Models with Missing Data: A Latent Class Approach , 1989 .

[13]  A. Dempster.  Elements of Continuous Multivariate Analysis , 1969 .

[14]  Age , 2000, BMJ : British Medical Journal.

[15]  J. Heckman.  Sample selection bias as a specification error , 1979 .

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

[17]  Rudolf Beran,et al.  Testing for Ellipsoidal Symmetry of a Multivariate Density , 1979 .

[18]  James J. Heckman,et al.  Longitudinal Analysis of Labor Market Data , 1985 .

[19]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[20]  J. Heckman.  Instrumental Variables: A Study of Implicit Behavioral Assumptions Used in Making Program Evaluations. , 1997 .

[21]  M. Lechner.  Earnings and Employment Effects of Continuous Gff-the-Job Training in East Germany After Unification , 1995 .

[22]  P. Holland.  Statistics and Causal Inference , 1985 .

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

[24]  James J. Heckman,et al.  Characterizing Selection Bias Using Experimental Data , 1998 .

[25]  Petra E. Todd,et al.  Matching As An Econometric Evaluation Estimator , 1998 .

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