IDENTIFICATION OF INCOMPLETE INFORMATION GAMES WITH MULTIPLE EQUILIBRIA AND UNOBSERVED HETEROGENEITY

This dissertation mainly studies identification of finite action games with incomplete information. The essential contribution of this dissertation is to allow for the presence of multiple equilibria and/or unobserved market-level heterogeneity. Chapter 2 provides a novel methodology to nonparametrically identify static games with multiple equilibria. Exploiting the results in mis-classification error models, I show that the number of equilibria, the equilibrium selection mechanism and individual equilibrium strategies associated with all positively employed equilibria can be nonparametrically identified from the distributions of the game outcomes. Provide the equilibrium conditional choice probabilities, payoffs then can be identified nonparametrically with exclusion restrictions. A natural estimator is also proposed following the constructive identification procedure. The empirical application investigates the strategic interaction among radio stations when they choose commercial timings, which provides evidence that two equilibria exist. Chapter 3 extends chapter 2 to incorporate unobserved market-level heterogeneity. This chapter assumes that the market-level latent type is discrete and has a finite support. With the discrete feature, the presence of unobserved heterogeneity generates similar finite mixture feature as the presence of multiple equilibria. The combination of both payoff-relevant and payoff un-relevant latent factor complicates the identification because of lacking information to disentangle the two. Consequently, instead of providing point identification, I provide set identification for the payoff parameters in chapter 3. To understand the trade-off between point identification and extra assumptions, I also provide conditions under which the identified set shrinks to a point. Chapter 4 considers identification in dynamic settings. If only Markov Perfect Equilibria being considered, observables including actions and payoff relevant covariates in period $t$ follow a first-order Markov process in time series by a market. This Markov property is a key condition under which dynamic games can be nonparametric identified with four periods of data. In particular, the law of motion associated with every possible combination of equilibria and the unobserved market-types can be nonparametrically identified. Additionally, payoffs can be identified nonparametrically with exclusion restrictions. More importantly, multiple equilibria and unobserved heterogeneity can be distinguished from the test with the null that payoffs associated with two levels of latent factor are the same. Specifically, if two payoffs are the same, then they should belong to the same latent market type but different equilibria. On the other hand, if two payoffs are different, they should be driven by the heterogeneity. Chapter 5 concludes and proposes possible avenues for future research based on this dissertation

Peer Effects in Consideration and Preferences

We develop a general model of discrete choice that incorporates peer effects in preferences and consideration sets. We characterize the equilibrium behavior and establish conditions under which all parts of the model can be recovered from a sequence of choices. We allow peers to affect only preferences, only consideration, or both. We exploit different types of variations to separate the peer effects in preferences and consideration sets. This allows us to recover the set (and type) of connections between the agents in the network. We then use this information to recover the random preferences and the attention mechanisms of each agent. These nonparametric identification results allow unrestricted heterogeneity across agents and do not rely on the variation of either covariates or the set of available options (or menus). We apply our results to model expansion decisions by coffee chains and find evidence of limited consideration. We simulate counterfactual predictions and show how limited consideration slows down competition

Order Statistics Approaches to Unobserved Heterogeneity in Auctions

We establish nonparametric identification of auction models with continuous and nonseparable unobserved heterogeneity using three consecutive order statistics of bids. We then propose sieve maximum likelihood estimators for the joint distribution of unobserved heterogeneity and the private value, as well as their conditional and marginal distributions. Lastly, we apply our methodology to a novel dataset from judicial auctions in China. Our estimates suggest substantial gains from accounting for unobserved heterogeneity when setting reserve prices. We propose a simple scheme that achieves nearly optimal revenue by using the appraisal value as the reserve price

Anaplastic Transformation in Thyroid Cancer Revealed by Single-Cell Transcriptomics

The deadliest anaplastic thyroid cancer (ATC) often transforms from indolent differentiated thyroid cancer (DTC); however, the complex intratumor transformation process is poorly understood. We investigated an anaplastic transformation model by dissecting both cell lineage and cell fate transitions using single-cell transcriptomic and genetic alteration data from patients with different subtypes of thyroid cancer. The resulting spectrum of ATC transformation included stress-responsive DTC cells, inflammatory ATC cells (iATCs), and mitotic-defective ATC cells and extended all the way to mesenchymal ATC cells (mATCs). Furthermore, our analysis identified 2 important milestones: (a) a diploid stage, in which iATC cells were diploids with inflammatory phenotypes and (b) an aneuploid stage, in which mATCs gained aneuploid genomes and mesenchymal phenotypes, producing excessive amounts of collagen and collagen-interacting receptors. In parallel, cancer-associated fibroblasts showed strong interactions among mesenchymal cell types, macrophages shifted from M1 to M2 states, and T cells reprogrammed from cytotoxic to exhausted states, highlighting new therapeutic opportunities for the treatment of ATC

Global estimation of finite mixture and misclassification models with an application to multiple equilibria

We show that the identification results of finite mixture and misclassification models are equivalent in a widely-used scenario except an extra ordering assumption. In the misclassification model, an ordering condition is imposed to pin down the precise values of the latent variable, which are also of researchers' interests and need to be identified. In contrast, the identification of finite mixture models is usually up to permutations of a latent index. This local identification is satisfactory because the latent index does not convey any economic meaning. However, reaching global identifition is important for estimation, especially, when researchers use bootstrap to estimate standard errors, which may be wrong without a global estimator. We provide a theoretical framework and Monte Carlo evidences to show that imposing an ordering condition to achieve a global estimator innocuously improves the estimation of fine mixture models. As a natural application, we show that games with multiple equilibria fit in our framework and the global estimator with ordering assumptions provides more reliable estimates

Identification of Auction Models Using Order Statistics

Auction data often contain information on only the most competitive bids as opposed to all bids. The usual measurement error approaches to unobserved heterogeneity are inapplicable due to dependence among order statistics. We bridge this gap by providing a set of positive identification results. First, we show that symmetric auctions with discrete unobserved heterogeneity are identifiable using two consecutive order statistics and an instrument or three consecutive ones. Second, we extend the results to ascending auctions with unknown competition and unobserved heterogeneity

Dynamic decisions under subjective expectations: A structural analysis

This paper studies dynamic discrete choices by relaxing the assumption of rational expectations. That is, agents' subjective expectations about the state transition are unknown and allowed to differ from their objectively estimable counterparts. We show that agents' subjective expectations and preferences can be identified and estimated from the observed conditional choice probabilities in both finite and infinite horizon cases. Our identification of subjective expectations is nonparametric and can be expressed as a closed-form function of the observed conditional choice probabilities. We estimate the model primitives using maximum likelihood estimation and illustrate the good performance of estimators using Monte Carlo experiments. We apply our model to Panel Study of Income Dynamics (PSID) data and analyze women's labor participation. We find systematic differences between agents' subjective expectations about their income transition from those under rational expectations. A counterfactual analysis suggests that women with low and medium incomes would increase the probability of working under rational expectations, and that the probability would decrease for women with high income

Gender Differences in Persistence in a Field of Study

Weaker retention of women in quantitatively oriented fields, particularly STEM* is widely seen in US higher education. This persistence gap is often explained by less generous grading in these fields and the conjectured tendency of female students to generally exhibit stronger “sensitivity” to grades. We examine student persistence in a wide spectrum of academic fields using a rich Indiana University Learning Analytics dataset. We find that the phenomenon of women’s relatively lower persistence in STEM in response to lower grades does not universally extend to other disciplines. Further, a stronger response, in terms of attrition, to grades received is not a gender-specific characteristic but more likely to reflect gender differences in the underlying field preferences. In other words, it is a weaker preference for a field of study that is likely to make students more responsive to grades received in it, rather than the other way around as is commonly suggested

Subjective or Objective? Nonparametric Estimation of Misreporting and Mis-Assessment in Corporate Credit Rating

∗Comments and suggestions are welcomed

A Simple Estimator for Dynamic Models with Serially Correlated Unobservables

We present a method for estimating Markov dynamic models with unobserved state variables which can be serially correlated over time. We focus on the case where all the model variables have discrete support. Our estimator is simple to compute because it is noniterative, and involves only elementary matrix manipulations. Our estimation method is nonparametric, in that no parametric assumptions on the distributions of the unobserved state variables or the laws of motions of the state variables are required. Monte Carlo simulations show that the estimator performs well in practice, and we illustrate its use with a dataset of doctors’ prescription of pharmaceutical drugs