NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

When to Control for Covariates? Panel-Asymptotic Results for Estimates of Treatment Effects

Joshua D. Angrist, Jinyong Hahn

NBER Technical Working Paper No. 241
Issued in May 1999

The problem of how to control for covariates is endemic in evaluation research. Covariate-matching provides an appealing control strategy, but with continuous or high-dimensional covariate vectors, exact matching may be impossible or involve small cells. Matching observations that have the same propensity score produces unbiased estimates of causal effects whenever covariate-matching does, and also has an attractive dimension-reducing property. On the other hand, conventional asymptotic arguments show that covariate-matching is (asymptotically) more efficient that propensity score-matching. This is because the usual asymptotic sequence has cell sizes growing to infinity, with no benefit from reducing the number of cells. Here, we approximate the large sample behavior of difference matching estimators using a panel-style asymptotic sequence with fixed cell sizes and the number of cells increasing to infinity. Exact calculations in simple examples and Monte Carlo evidence suggests this generates a substantially improved approximation to actual finite-sample distributions. Under this sequence, propensity-score-matching is most likely to dominate exact matching when cell sizes are small, the explanatory power of the covariates conditional on the propensity score is low, and/or the probability of treatment is close to zero or one. Finally, we introduce a random-effects type combination estimator that provides finite-sample efficiency gains over both covariate-matching and propensity-score-matching.

download in pdf format
   (1314 K)

email paper

This paper is available as PDF (1314 K) or via email.

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/t0241

Users who downloaded this paper also downloaded these:
Angrist t0181 Conditioning on the Probability of Selection to Control Selection Bias
Abadie and Imbens t0283 Simple and Bias-Corrected Matching Estimators for Average Treatment Effects
Angrist and Kuersteiner w10975 Semiparametric Causality Tests Using the Policy Propensity Score
Angrist and Fernández-Val w16566 ExtrapoLATE-ing: External Validity and Overidentification in the LATE Framework
Angrist and Lavy w5807 The Effect of Teen Childbearing and Single Parenthood on Childhood Disabilities and Progress in School
 
Publications
Activities
Meetings
NBER Videos
Data
People
About

Support
National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email: info@nber.org

Contact Us