Inference Based on Conditional Moment Inequalities

Set identification of the censored quantile regression model for short panels with fixed effects

“…Alternatively, one can estimate the identified set by converting the conditional moment inequalities implied by (8) to the unconditional ones, following the approach taken by Andrews and Shi (2013). Similar approaches can be found in Bierens (1982) and Bierens and Ploberger (1997) for consistent specification tests, Dominguez and Lobato (2004) for GMM estimation based on moment equalities, Khan and Tamer (2009) for a point-identified model based on moment inequalities for censored regression, and Linton et al (2013) for a nonparametric test of a leverage hypothesis with conditional inequalities among others.…”

“…The literature on unconditional inequality models includes Andrews and Soares (2010), Beresteanu and Molinari (2008), Bontemps et al (2012), Bugni (2010), Canay (2010), Shaikh (2008, 2010), Rosen (2008) and Stoye (2009) among others. The contribution to the literature on conditional inequality models includes Andrews and Shi (2013), , Kim (2009), Ponomareva (2010 and Armstrong (2011a,b) among others.…”

“…This is because our two-step estimation method excludes trivial bounds for the estimation at the first step and thus all probability bounds are not always used for constructing the set estimator. Instead of the inference based on conditional quantile functions, one can take an approach based on pairs of conditional inequalities in (8), using the results for conditional moment inequalities in Andrews and Shi (2013) and Lee et al (2013). 3 Also, as shown in Theorem 1, the identified set is convex and the dual problem may provide convenient solution in practice, see Beresteanu and Molinari (2008), Bontemps et al (2012) and Kaido (2012).…”

Examining the Distributional Effects of Military Service on Earnings: A Test of Initial Dominance

“…We note that it is also possible to implement a bootstrap procedure that uses the estimator x m,n in place of x * m,n in Step 3 of Algorithm 2.1. However, implementing this modified bootstrap procedure would require us to incorporate Downloaded by [University of North Dakota] at 01:24 20 December 2014 Andrews and Shi's (2010) infinitesimal uniformity factor, or a similar method used by Donald and Hsu (2010), to well control the size of the test since both the test statistic and the bootstrap critical value based on * m,n (x m,n ) would converge to zero whenever x 1 = 0. Because the additional complexity (e.g., the introduction of an additional tuning parameter) would invariably cause us to stray from the main contribution of this article, we do not adopt such a procedure in the present article.…”

Sharp Identification Regions in Models With Convex Moment Predictions

“…This sample analog is given by the set of minimizers of a sample criterion function. In the Supplemental Material (Beresteanu, Molchanov, and Molinari (2011, Appendix B)), we establish that the methodology of Andrews and Shi (2009) can be applied in our context to obtain confidence sets that uniformly cover each element of the sharp identification region with a prespecified asymptotic probability. Related methods for statistical inference in partially identified models include, among others, Chernozhukov, Hong, andTamer (2004, 2007), Pakes, Porter, Ho, and Ishii (2006), , Rosen (2008), Chernozhukov, Lee, and Rosen (2009), Galichon and Henry (2009b), Kim (2009), Andrews and Soares (2010), Bugni (2010), Canay (2010), Romano and Shaikh (2010), and Ponomareva (2010).…”