Date of Award

Spring 2021

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Economics

First Advisor

Andrews, Donald

Abstract

This dissertation studies identification and estimation in panel and network models. Panel models have long been a workhorse in empirical research. In the first two chapters, we analyze random coefficient linear panel model and panel multinomial choice model, respectively, where we incorporate features such as time-varying endogeneity and unobserved heterogeneity that are prevalent in real life into the models. We present new identification results and provide consistent estimators based on the identification strategy. Then, we apply the estimation procedures to panel data and obtain economically convincing results. The study of networks is a fast-growing area of economic research thanks to the increasing availability of network data and computing power. In the third chapter, we study network formation problems under non-transferrable utilities (NTU). We show how to identify the parameters of interest without additive separability based on “logical differencing” and provide consistent estimators. In chapter 1, we propose a random coefficient linear panel model where the regressors can depend on the time-varying random coefficients in each period, a critical feature in many economic applications including production function estimation. The random coefficients are modeled as unknown functions of a fixed effect of arbitrary dimension and a random shock. The regressors may depend on the random coefficients due to agent's optimization behavior such as profit maximization, utility maximization, among others. We use a sufficiency argument to control for the fixed effect, which enables us to construct a feasible control function for the random shock and subsequently identify the moments of the random coefficients via a sequential argument. Based on the multi-step identification argument, we propose a series estimator and prove a new inference result. Monte Carlo simulations show that the proposed method can capture the distributional properties of the random coefficients. We then apply the procedure to panel data for Chinese manufacturing firms and find significant variation in the output elasticities both across firms and through time. In chapter 2, we propose a simple yet robust method for semiparametric identification and estimation of panel multinomial choice models, where we allow infinite-dimensional fixed effects to enter consumer utilities in an additively nonseparable way, thus incorporating rich forms of unobserved heterogeneity. Such heterogeneity may take the form of, for example, brand loyalty or responsiveness to subtle flavor and packaging designs, which are hard to quantify but affect consumer choices in complex ways. Our identification strategy exploits the standard notion of multivariate monotonicity in its contrapositive form, which provides leverage for converting observable events into identifying restrictions on unknown parameters of interest. Based on our identification result, we construct consistent set (or point) estimators, together with a computational algorithm that adopts a machine learning algorithm and a new minimization procedure on the spherical-coordinate space. We demonstrate the practical advantages of our method with simulations and an empirical example using the Nielsen data. We find that special in-store displays boost sales not only through a direct promotion effect but also through the attenuation of consumers’ price sensitivity. In chapter 3, we consider a semiparametric model of dyadic network formation under NTU. NTU frequently arises in social interactions that require bilateral consent, such as Facebook friendship networks or informal risk-sharing networks in developing countries. However, NTU inherently induces additive non-separability, which makes identification challenging. Based on multivariate monotonicity, we identify structural parameters by constructing events involving the intersection of two mutually exclusive restrictions on the unobserved individual fixed effects to cancel them out. The constructive identification argument leads to a consistent estimator. We analyze the finite-sample performance of the estimator via a simulation study. Then, we apply the method to the Nyakatoke risk-sharing network data. The results show that our approach can capture the essence of the network formation process. For instance, we find that the greater the difference in wealth between two households, the lower is the probability they are connected.

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