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Moment inequalities in the context of simulated and predicted variables


  • Hiroaki Kaido

    () (Institute for Fiscal Studies and Boston University)

  • Jiaxuan Li

    (Institute for Fiscal Studies)

  • Marc Rysman

    (Institute for Fiscal Studies)


This paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confi dence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (fi rst-order) bias due to the simulation errors may remain in the estimated boundary of the con fidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can signi ficantly reduce the coverage probabilities of confi dence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.

Suggested Citation

  • Hiroaki Kaido & Jiaxuan Li & Marc Rysman, 2018. "Moment inequalities in the context of simulated and predicted variables," CeMMAP working papers CWP26/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:26/18

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    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    2. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(03), pages 669-709, June.
    3. Hiroaki Kaido & Francesca Molinari & Jörg Stoye, 2019. "Confidence Intervals for Projections of Partially Identified Parameters," Econometrica, Econometric Society, vol. 87(4), pages 1397-1432, July.
    4. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    7. Kei Kawai & Yasutora Watanabe, 2013. "Inferring Strategic Voting," American Economic Review, American Economic Association, vol. 103(2), pages 624-662, April.
    8. 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.
    9. repec:hrv:faseco:34728615 is not listed on IDEAS
    10. McFadden, Daniel, 1989. "A Method of Simulated Moments for Estimation of Discrete Response Models without Numerical Integration," Econometrica, Econometric Society, vol. 57(5), pages 995-1026, September.
    11. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, vol. 33(05), pages 1218-1241, October.
    12. repec:wly:emetrp:v:82:y:2014:i:5:p:1979-2002 is not listed on IDEAS
    13. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2014. "A Practical Two‐Step Method for Testing Moment Inequalities," Econometrica, Econometric Society, vol. 82(5), pages 1979-2002, September.
    14. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October.
    15. Thomas J. Holmes, 2011. "The Diffusion of Wal‐Mart and Economies of Density," Econometrica, Econometric Society, vol. 79(1), pages 253-302, January.
    16. Stephen P. Ryan, 2012. "The Costs of Environmental Regulation in a Concentrated Industry," Econometrica, Econometric Society, vol. 80(3), pages 1019-1061, May.
    17. Meredith Fowlie & Mar Reguant & Stephen P. Ryan, 2016. "Market-Based Emissions Regulation and Industry Dynamics," Journal of Political Economy, University of Chicago Press, vol. 124(1), pages 249-302.
    18. Gregory S. Crawford & Ali Yurukoglu, 2012. "The Welfare Effects of Bundling in Multichannel Television Markets," American Economic Review, American Economic Association, vol. 102(2), pages 643-685, April.
    19. Victor Chernozhukov & Emre Kocatulum & Konrad Menzel, 2015. "Inference on sets in finance," Quantitative Economics, Econometric Society, vol. 6(2), pages 309-358, July.
    20. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    21. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    22. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    23. Hausman, Jerry A., 1983. "Specification and estimation of simultaneous equation models," Handbook of Econometrics,in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 1, chapter 7, pages 391-448 Elsevier.
    24. Matthew Masten & Alexandre Poirier, 2017. "Inference on breakdown frontiers," CeMMAP working papers CWP20/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    25. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    26. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
    27. Keisuke Hirano & Jack R. Porter, 2012. "Impossibility Results for Nondifferentiable Functionals," Econometrica, Econometric Society, vol. 80(4), pages 1769-1790, July.
    28. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    29. Alon Eizenberg, 2014. "Upstream Innovation and Product Variety in the U.S. Home PC Market," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 1003-1045.
    30. Rosen, Adam M., 2008. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," Journal of Econometrics, Elsevier, vol. 146(1), pages 107-117, September.
    31. Katherine Ho, 2009. "Insurer-Provider Networks in the Medical Care Market," American Economic Review, American Economic Association, vol. 99(1), pages 393-430, March.
    32. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, January.
    33. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    34. Jean-François Houde & Peter Newberry & Katja Seim, 2017. "Economies of Density in E-Commerce: A Study of Amazon’s Fulfillment Center Network," NBER Working Papers 23361, National Bureau of Economic Research, Inc.
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