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A practical two-step method for testing moment inequalities

  • Joseph P. Romano
  • Azeem M. Shaikh
  • Michael Wolf

This paper considers the problem of testing a finite number of moment inequalities. We propose a two-step approach. In the first step, a confidence region for the moments is constructed. In the second step, this set is used to provide information about which moments are “negative.” A Bonferonni-type correction is used to account for the fact that with some probability the moments may not lie in the confidence region. It is shown that the test controls size uniformly over a large class of distributions for the observed data. An important feature of the proposal is that it remains computationally feasible, even when the number of moments is large. The finite-sample properties of the procedure are examined via a simulation study, which demonstrates, among other things, that the proposal remains competitive with existing procedures while being computationally more attractive.

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Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 090.

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Date of creation: Aug 2012
Date of revision: Apr 2014
Handle: RePEc:zur:econwp:090
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  1. Donald W. K. Andrews & Panle Jia Barwick, 2012. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Econometrica, Econometric Society, vol. 80(6), pages 2805-2826, November.
  2. Bajari, Patrick & Benkard, C. Lanier & Levin, Jonathan, 2007. "Estimating Dynamic Models of Imperfect Competition," Research Papers 1852r1, Stanford University, Graduate School of Business.
  3. Andrews, Donald W.K. & Guggenberger, Patrik, 2010. "ASYMPTOTIC SIZE AND A PROBLEM WITH SUBSAMPLING AND WITH THE m OUT OF n BOOTSTRAP," Econometric Theory, Cambridge University Press, vol. 26(02), pages 426-468, April.
  4. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  5. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," 2004 Meeting Papers 52, Society for Economic Dynamics.
  6. Douglas Staiger & James H. Stock, 1994. "Instrumental Variables Regression with Weak Instruments," NBER Technical Working Papers 0151, National Bureau of Economic Research, Inc.
  7. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  8. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation for Research in Economics, Yale University.
  9. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  10. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
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