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

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Joshua D. Angrist
Jinyong Hahn

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Abstract

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.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0241.

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Date of creation: May 1999
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Handle: RePEc:nbr:nberte:0241

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data

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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Mueser, Peter & Troske, Kenneth R. & Gorislavsky, Alexey, 2003. "Using State Administrative Data to Measure Program Performance," IZA Discussion Papers 786, Institute for the Study of Labor (IZA). [Downloadable!]
    Other versions:
  2. Jochen Kluve & Hartmut Lehmann & Christoph M. Schmidt, 2002. "Disentangling Treatment Effects of Polish Active Labor Market Policies: Evidence from Matched Samples," William Davidson Institute Working Papers Series 447, William Davidson Institute at the University of Michigan Stephen M. Ross Business School. [Downloadable!]
    Other versions:
  3. Jochen Kluve & Boris Augurzky, 2005. "Assessing the performance of matching algorithms when selection into treatment is strong," RWI Discussion Papers 0021, Rheinisch-Westfälisches Institut für Wirtschaftsforschung. [Downloadable!]
    Other versions:
  4. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2000. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," NBER Technical Working Papers 0251, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  5. Angrist, Joshua & Lavy, Victor, 2002. "The Effect of High School Matriculation Awards: Evidence from Randomized Trials," CEPR Discussion Papers 3827, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
    Other versions:
  6. Paula Veiga & Ronald P. Wilder, 2006. "Maternal smoking during pregnancy and birthweight - A propensity score matching approach," Working Papers 32, Núcleo de Investigação em Microeconomia Aplicada (NIMA), Universidade do Minho. [Downloadable!]
  7. Joshua Angrist & Victor Lavy, 2003. "Achievement Awards for High School Matriculation: Evidence from Randomized Trials," Natural Field Experiments 0003, The Field Experiments Website. [Downloadable!]
  8. Fajnzylber, Pablo & Maloney, William F. & Rojas, Gabriel V. Montes, 2006. "Releasing constraints to growth or pushing on a string ? the impact of credit, training, business associations, and taxes on the performance of Mexican micro-firms," Policy Research Working Paper Series 3807, The World Bank. [Downloadable!]
  9. Angrist, Joshua D. & Lavy, Victor, 2004. "The Effect of High Stakes High School Achievement Awards: Evidence from a School-Centered Randomized Trial," IZA Discussion Papers 1146, Institute for the Study of Labor (IZA). [Downloadable!]
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