Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - Nov 2020)
Chapter 2, co-authored with Vadim Marmer and Kyungchul Song, considers a general formof network dependence, where dependence between two sets of random variables becomesweaker as their network distance increases. We show that such network dependence cannotbe viewed as a random field on a lattice in a Euclidean space with a fixed dimension whenthe maximum clique increases in size as the network grows. This work applies Doukhanand Louhichi (1999)’s notion of weak dependence to networks by measuring the strength ofdependence using the covariance between nonlinearly transformed random variables. Whilethis approach covers examples such as strong mixing random fields on graphs and conditionaldependency graphs, it is most useful when dependence arises through a functional-causalsystem of equations. The main results of this chapter include a law of large numbers and acentral limit theorem for network dependent processes.Chapter 3 focuses on the bootstrap for network dependent processes studied in Chapter2. Such processes are distinct from other forms of random fields that are commonly usedin the statistics and econometrics literature so that the existing bootstrap methods cannotbe applied directly. I propose a block-based method and a modification of the dependentwild bootstrap for constructing confidence sets for the mean of a network dependent process.In addition, I establish the consistency of these methods for the smooth function modeland provide the bootstrap alternatives to the network heteroskedasticity-autocorrelationconsistent variance estimator obtained in Chapter 2.Finally, Chapter 4, co-authored with Kyungchul Song, presents a large Bayesian gamewith multiple information groups and develops a bootstrap inference method that does notrequire a common prior assumption and allows each player to form beliefs differently fromother players. By drawing on the intuition of Kalai (2004), this work introduces the notion ofa hindsight regret, which measures a player’s ex post value of other players’ type information,and obtains its belief-free bound. Using this bound, we derive testable implications andpropose a bootstrap inference procedure for the structural parameters of the game.
Chapter 2 examines the role of sales (temporary price reductions) in the pricing of perishable products. When products can be stored, periodic sales are explained using inventories: the ability to store lets consumers wait for better prices. When consumers differ in their ability to wait, ﬁrms keep prices regularly high, using sales to target the low prices to the most patient consumers. This explanation is not reasonable for perishable goods, since they cannot be stored. Using a retail dataset, I show that nonetheless a cyclic pattern of sales is a major feature of how perishable products are priced. I explain this pattern using a dynamic model of loss leadership. I then test my model using grocery store data. Chapter 3 studies large contributions to crowdfunding projects and their impact on project success. I ﬁnd large contributions display a preference for being effective in helping projects succeed: they are often pivotal in the success of a project. These ﬁndings matchpredictions from a consumer choice explanation of how large contributions are made. I then examine the role large contributions play in project success. Using an instrumental variables approach, I show the ability of a project to attract large contributors is important: a project is 40-60% more likely to succeed if they can attract a large contributor. This inverts the logic of crowdfunding: the crowd may be important, but the success of many projects is driven by large contributors. Chapter 4 develops a method for determining whether a given observation is a sale or not in the context of a sequence of prices for a retail product. This classiﬁcation, based on a hidden Markov model framework has the advantage of using all the information available or classifying sales. I develop identiﬁcation requirements for this method, and illustrate its utility in directly testing questions of correlation for sales and other variables: allowing models to be evaluated without reduced-form analysis. I perform simulations, demonstrating the method’s accuracy method in classifying sales and understanding correlations. This chapter adds to the toolbox industrial economists have for studying sales, with advantages over existing methods of sales classiﬁcation.
This thesis studies two topics in Econometric models, multiple equilibria and weak instruments. Chapter 1 is an introduction. Chapter 2 considers nonparametric structural equations which may have multiple solutions for the endogenous variables. The main finding is that multiple equilibria would reveal itself in the form of jump(s) in the density function of the endogenous variables. When there is a unique equilibrium, the density function of endogenous variables will be continuous, while when there are multiple equilibria, the density will have a jump at some point, under reasonable conditions. Our test statistic is based on maximizing local jumps over the support of endogenous variables and the critical value is computed via a Gaussian multiplier bootstrap.Chapter 3 shows that in games with incomplete information, even when the payoff functions and the latent distributions are all smooth, the observed conditional choice probabilities may have a jump with respect to continuous covariates. This chapter provides a theoretical analysis on the relationship between the equilibrium behaviour of the game and the presence of a jump in the conditional choice probabilities. Such jump(s) matters in empirical research for two reasons. Statistically, it affects the estimation of the conditional choice probabilities. Economically, whether the conditional choice probabilities have a jump or not reveals information about the equilibrium behaviour of the game. Our findings are robust to correlated private information and unobserved heterogeneity independent of covariates. Chapter 4 considers efficient inference for the coefficient of the endogenous variable in linear regression models with weak instrumental variables (Weak-IV). We focus on the power of tests for the alternative hypotheses that are determined by arbitrarily large deviations from the null. We derive the power envelope for such alternatives in the Weak-IV scenario. Then we compare the power properties of popular Weak-IV robust tests, focusing on the Anderson-Rubin (AR) and Conditional Likelihood Ratio (CLR) tests. We find that their relative performance depends on the degree of endogeniety in the model. In addition, we propose a Conditional Lagrange Multiplier (CLM) test. We also extend our analysis to heteroskedastic models.
This thesis is comprised of three essays. In the first and second essays, I examine the welfare value of return predictors in financial markets when investors possess only limited historical data. The first essay focuses on the US Treasury bond market where time series variation in the expected return is forecastable by yield curve and macroeconomic variables. The second essay shifts attention to the US stock market where cross-sectional variation in the expected return is predictable by the underlying firms' characteristics. Using monthly US data, I estimate the utility benefit of various return predictors in either the bond or stock market through a structural approach of forecast evaluation. I consider both parametric and non-parametric portfolio policies and conduct both unconditional and conditional evaluations. I find that return predictors are generally hard to exploit with limited data. Incorporating return predictors renders the portfolio strategy more sensitive to estimation errors and instability in forecast relations. The resultant negative effect on portfolio returns and welfare is not dominated by the information value of predictors. The third essay discusses the estimation of the Cox-Ingersoll-Ross interest rate model. I propose a new likelihood-based methodology that uses marginal Metropolis Hasting algorithm with particle-filter based simulated-likelihood placed in each of the iterations. The benefit of this Bayesian approach is that it bypasses the need to compute exact likelihood functions, and its validity rests upon a recent development in Bayesian statistical theory. To mitigate the inefficiency in standard bootstrap filters due to peaky measurement density of the CIR model, I design an approximated conditional optimal filter to account for the informativeness of current yields and reduce the variance of particle weights. For typical parameter values, performance is shown to be satisfactory.
This thesis consists of three research chapters on the theory of empirical likelihood (EL), which is a class of inferential methods widely used in econometrics. In Chapter 2, we focus on estimation and testing of moment restriction models with weakly dependent stationary time series data using blockwise empirical likelihood method. Empirical likelihood based methods often encounters the finite sample problem that the constraint set of the profiling step becomes empty. This issue undermines the validity of EL-based methods in empirical applications. We first show first-order validity of Chen, Variyath and Abraham (2008)'s pseudo observation adjustment, which is used to overcome this shortcoming. Under regularity conditions, key higher-order properties are found. The first property is that blockwise EL ratio statistics admit higher-order refinement and this refinement can be implemented via either mean adjustment to the EL ratio statistic or creating a pseudo observation with specific level of adjustment. By the latter approach, we address both the empty-constraint-set issue and low precision of chi-square approximation. We also find that for testing problems, the optimal block length choice that minimizes the higher-order approximation error has an order of magnitude the sample size to the power of 2/5. In Chapter 3, we focus on parameter hypothesis testing problems for moment restriction models using EL ratio tests. We substantially extend existing theorems on Bartlet correctability of EL ratio tests for parameter testing problems in Chen and Cui (2007) and Chen and Cui (2006.a). We consider tests of general nonlinear restrictions on the parameter under the null hypothesis. We show Bartlett correctability of EL ratio tests of such a large family of testing problems, which are potentially useful in many empirical applications. In Chapter 4, we focus on estimation and testing of conditional moment restrictions with i.i.d. data. Following the approach of adjusted empirical likelihood (AEL) proposed by Chen, Variyath and Abraham (2008), this paper develops AEL-based methods for conditional moment restrictions, and establishes that new methods produce semiparametrically efficient estimators and consistent specification tests. This new method shows improved computational efficiency and accuracy in finite samples, as compared to some existing alternatives.