Matching Estimators and Their Applications to Social Work Research

Purpose: Methods of causal inference have undergone a significant change in the past 25 years as researchers have recognized the need to develop more efficient approaches to control extraneous factors. The interest in seeking consistent and efficient estimators of program effectiveness has led to a surge in work focusing on estimating average treatment effects under various sets of assumptions. This workshop aims to introduce a newly developed approach called “matching estimators” by Abadie and Imbens (2002, 2006), including the simple matching estimator, the bias-corrected matching estimator, the variance estimator assuming a constant treatment effect and homoscedasticity, and the variance estimator allowing for heteroscedasticity. Applications of the matching estimators to social work research are illustrated.

Contents: The workshop will focus on the following topics: (1) review of the Neyman-Rubin's counterfactual framework for causal inference with observational data, (2) examination of the core idea of matching with vector norm, (3) a step-by-step demonstration of running Stata program nnmatch to evaluate the sample and population average treatment effect, the average treatment effect for the treated, and the average treatment effect for the control, (4) illustration of applying the method to a social work study evaluating the impact of childhood poverty on children's academic achievement, and (5) a discussion of strengths and limitations of the method.

Findings: Using the 1997 CDS and 30 years PSID data, the illustrating example shows that the estimates of poverty effects produced by conventional methods are biased and exaggerated. A t-test shows that the mean difference of passage comprehension standardized score between children who ever used AFDC and children who never used is -11.35 points (p<.0001). An OLS regression estimates the difference as -5.87 points (p<.0001). However, matching estimator indicates that such difference is only -4.70 points (p<.01).

Implications: The workshop concludes by discussing the seminal paper of Abadie and Imbens (2006), which underscores the importance of using robust correction methods to study causality. Contributions of the Abadie and Imbens's model include: (1) it uses a simpler mechanism for matching (i.e., vector norm), which makes the approach much easier to implement than other correction methods such as propensity score matching or Heckman's kernel-based matching, (2) it does not require postmatching analysis, and therefore, reduces the number of subjective decisions a researcher has to make, and (3) it permits statistical significance testing that does not rely on bootstrap. Although the method offers several advantages, its large sample properties are not attractive. As such, users should be cautious when applying the method to studies with many matching variables but small sample sizes.

Pedagogical Techniques: Teaching methods include lecture, PowerPoint presentation, and computer demonstration of running the Stata program nnmatch.