Essays on moment inequalities [electronic resource]
Keywords: Economics

This dissertation considers inference in conditional moment inequality models. Chapter 1 derives the rate of convergence and asymptotic distribution for a class of Kolmogorov-Smirnov style test statistics for conditional moment inequality models for parameters on the boundary of the identified set under general conditions. In contrast to other moment inequality settings, the rate of convergence is faster than root-n, and the asymptotic distribution depends entirely on nonbinding moments. The results require the development of new techniques that draw a connection between moment selection, irregular identification, bandwidth selection and nonstandard M-estimation. Using these results, I propose tests that are more powerful than existing approaches for choosing critical values for this test statistic. I quantify the power improvement by showing that the new tests can detect alternatives that converge to points on the identified set at a faster rate than those detected by existing approaches. A monte carlo study confirms that the tests and the asymptotic approximations they use perform well in finite samples. In an application to a regression of prescription drug expenditures on income with interval data from the Health and Retirement Study, confidence regions based on the new tests are substantially tighter than those based on existing methods. Chapter 2 proposes confidence regions for the identified set in conditional moment inequality models using Kolmogorov-Smirnov statistics with a truncated inverse variance weighting with increasing truncation points. The new weighting differs from those proposed in the literature in two important ways. First, confidence regions based on KS tests with the weighting function I propose converge to the identified set at a faster rate than existing procedures based on bounded weight functions in a broad class of models. This provides a theoretical justification for inverse variance weighting in this context, and contrasts with analogous results for conditional moment equalities in which optimal weighting only affects the asymptotic variance. Second, the new weighting changes the asymptotic behavior, including the rate of convergence, of the KS statistic itself, requiring a new asymptotic theory in choosing the critical value, which I provide. To make these comparisons, I derive rates of convergence for the confidence regions I propose along with new results for rates of convergence of existing estimators under a general set of conditions. A series of examples illustrates the broad applicability of the conditions. A monte carlo study examines the finite sample behavior of the confidence regions. Chapter 3 derives bounds in empirical models of first price auctions with unobserved heterogeneity. Many empirical studies of auctions rely on the assumption that the researcher observes all variables that make auctions differ ex ante. When there is unobserved heterogeneity, the direction of the bias this causes is known only in a few restrictive examples. In this chapter, I show that ignoring unobserved heterogeneity in a first price sealed bid auction with symmetric independent private values gives bounds on several quantities of economic interest under surprisingly general conditions. These include bidder profits (which can be used to recover bid preparation costs in entry models) and the efficiency loss of assigning the object randomly. I then turn to estimation of these bounds, and show that, when only the winning bid is available, the rate of convergence can be slower than the square root of the number of auctions observed and depends on the number of bidders. These results apply more generally to estimation of functionals of a distribution from repeated observations of an order statistic and may be of independent interest. I apply these methods to bound the efficiency loss from replacing a set of procurement auctions for highway construction in Michigan with random assignment.