Skip to main content


  • Vishal Kamat (a1)

This paper studies the validity of nonparametric tests used in the regression discontinuity design. The null hypothesis of interest is that the average treatment effect at the threshold in the so-called sharp design equals a pre-specified value. We first show that, under assumptions used in the majority of the literature, for any test the power against any alternative is bounded above by its size. This result implies that, under these assumptions, any test with nontrivial power will exhibit size distortions. We next provide a sufficient strengthening of the standard assumptions under which we show that a version of a test suggested in Calonico, Cattaneo, and Titiunik (2014) can control limiting size.

Corresponding author
*Address correspondence to Vishal Kamat, Department of Economics, Northwestern University, Evanston, IL 60208, USA; e-mail:
Hide All

I am grateful to Ivan Canay for his valuable guidance and suggestions. I thank the Co-Editor, two anonymous referees, Matias Cattaneo, Joel Horowitz, Pedro Sant’Anna and Max Tabord-Meehan for their helpful comments.

Hide All
Andrews, D.W. & Guggenberger, P. (2009a) Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators. Journal of Econometrics 152, 1927.
Andrews, D.W. & Guggenberger, P. (2009b) Validity of subsampling and plug-in asymptotic inference for parameters defined by moment inequalities. Econometric Theory 25, 669709.
Armstrong, T. & Kolesar, M. (2016) Optimal inference in a class of regression models. Manuscript.
Bahadur, R.R. & Savage, L.J. (1956) The nonexistence of certain statistical procedures in nonparametric problems. Annals of Mathematical Statistics 27, 11151122.
Calonico, S., Cattaneo, M.D., & Farrell, M.H. (2016) Coverage error optimal confidence intervals for regression discontinuity designs. Manuscript.
Calonico, S., Cattaneo, M.D., & Titiunik, R. (2014) Robust nonparametric confidence intervals for regression-discontinuity designs. Econometrica 82, 22952326.
Canay, I.A., Santos, A., & Shaikh, A.M. (2013) On the testability of identification in some non-parametric models with endogeneity. Econometrica 81, 25352559.
Card, D., Lee, D.S., Pei, Z., & Weber, A. (2015) Inference on causal effects in a generalized regression kink design. Econometrica 83, 24532483.
Dufour, J.-M. (1997) Some impossibility theorems in econometrics with applications to structural and dynamic models. Econometrica 65, 13651387.
Dufour, J.-M. (2003) Identification, weak instruments, and statistical inference in econometrics. Canadian Journal of Economics/Revue canadienne d’conomique 36, 767808.
Frandsen, B.R., Frlich, M., & Melly, B. (2012) Quantile treatment effects in the regression discontinuity design. Journal of Econometrics 168, 382395.
Guggenberger, P. (2010a) The impact of a Hausman pretest on the asymptotic size of a hypothesis test. Econometric Theory 26, 369382.
Guggenberger, P. (2010b) The impact of a Hausman pretest on the size of a hypothesis test: The panel data case. Journal of Econometrics 156, 337343.
Hahn, J., Todd, P., & Van der Klaauw, W. (2001) Identification and estimation of treatment effects with a regression-discontinuity design. Econometrica 69, 201209.
Imbens, G. & Kalyanaraman, K. (2012) Optimal bandwidth choice for the regression discontinuity estimator. The Review of Economic Studies 79, 933959.
Imbens, G.W. & Lemieux, T. (2008) Regression discontinuity designs: A guide to practice. Journal of Econometrics 142, 615635.
Lee, D.S. & Lemieux, T. (2010) Regression discontinuity designs in economics. Journal of Economic Literature 48, 281355.
Leeb, H. & Pötscher, B.M. (2005) Model selection and inference: Facts and fiction. Econometric Theory 21(01), 2159.
Leeb, H. & Pötscher, B.M. (2008) Can one estimate the unconditional distribution of post-model-selection estimators? Econometric Theory 24, 338376.
Lehmann, E.L. & Loh, W.-Y. (1990) Pointwise versus uniform robustness of some large-sample tests and confidence intervals. Scandinavian Journal of Statistics 17, 177187.
McCrary, J. (2008) Manipulation of the running variable in the regression discontinuity design: A density test. Journal of Econometrics 142, 698714.
Mikusheva, A. (2007) Uniform inference in autoregressive models. Econometrica 75, 14111452.
Mikusheva, A. (2010) Robust confidence sets in the presence of weak instruments. Journal of Econometrics 157, 236247.
Mikusheva, A. (2012) One-dimensional inference in autoregressive models with the potential presence of a unit root. Econometrica 80, 173212.
Müller, U.K. (2008) The impossibility of consistent discrimination between i(0) and i(1) processes. Econometric Theory 24, 616630.
Otsu, T., Xu, K.-L., & Matsushita, Y. (2015) Empirical likelihood for regression discontinuity design. Journal of Econometrics 186, 94112.
Romano, J.P. (2004) On non-parametric testing, the uniform behaviour of the t-test, and related problems. Scandinavian Journal of Statistics 31, 567584.
Romano, J.P. & Shaikh, A.M. (2008) Inference for identifiable parameters in partially identified econometric models. Journal of Statistical Planning and Inference 138, 27862807.
van der Vaart, A.W. (1998) Asymptotic Statistics. Cambridge University Press.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
  • URL: /core/journals/econometric-theory
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
Type Description Title
Supplementary materials

Kamat supplementary material
Kamat supplementary material 1

 Unknown (21 KB)
21 KB
Supplementary materials

Kamat supplementary material
Kamat supplementary material 2

 Unknown (1 KB)
1 KB
Supplementary materials

Kamat supplementary material
Kamat supplementary material 3

 PDF (224 KB)
224 KB


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed