UCLA

This dissertation is divided into three chapters. In Chapter 1, I propose a nonparametric estimator for the bidders' utility function and the density of private values in a first-price sealed-bid auction model. Specifically, I study a setting with risk-averse bidders within the independent private value paradigm. I adopt a fully nonparametric approach by not placing any restrictions on the shape of the bidders' utility function beyond strict monotonicity, concavity, and differentiability. In contrast to previous literature, I characterize such utility function and the density of private values by a minimizer of a certain functional. I estimate this minimizer, which is a smooth real-valued function, in two steps by the method of sieves. Then, the estimators for the bidders' utility function and the density of private values are smooth functionals of the estimator for the minimizer. The estimator for the utility function is uniformly consistent and shape-preserving, while the estimator for the density is uniformly consistent and asymptotically normal.

Chapter 2, which is a joint paper with I. Obara, studies a model of repeated Bertrand competition among asymmetric firms that produce a homogeneous product. The discounting rates and marginal costs may vary across firms. We identify the critical level of discount factor such that a collusive outcome can be sustained if and only if the average discount factor within the lowest cost firms is above the critical level. We also characterize the set of all efficient collusive equilibria when firms differ only in their discounting rates. Due to differential discounting, impatient firms gain a larger share of the market at an earlier stage of the game and patient firms gain a larger share at a later stage in efficient equilibrium. Although there are many efficient collusive equilibria, our model provides a unique prediction in the long run in the sense that every efficient collusive equilibrium converges to the unique efficient stationary collusive equilibrium within finite time.

Chapter 3 develops a weighted average derivative estimator for &beta in the context E(y|x^c,x^d) = G(x^c|&beta,x^d), where x^c and x^d are continuous and discrete random vectors, respectively, and G is an unknown function. A distinguishing feature of the proposed estimator is the use of kernel smoothing for the discrete covariates. Under standard regularity conditions, such an estimator is root-N-consistent, asymptotically normal, and non-iterative.