Essays in Econometrics

Abstract

In my doctoral research, I developed econometric estimators with strong applications in analysis of heterogeneous consumer demand. The first chapter develops an estimator for grouped patterns of heterogeneity in an approximately sparse setting. This setting is used to estimate demand shocks, competition sets and own-price elasticities for different groups of consumers. The second chapter, which is joint work with Stefan Hoderlein and Alexander Meister, develops a nonparametric estimator of the marginal effects in a panel data even if there are only a small number of time periods. This is used to estimate the heterogeneous marginal effects of increasing income on consumption of junk food. The third chapter, which is joint work with Stefan Hoderlein and Solvejg Wewal, is the first difference-in-differences model for binary choice outcome variables when treatment effects are heterogeneous. We apply this estimator to examine the heterogeneous effects of a soda tax. Chapter 1: ``Approximately Sparse Models and Methods with Grouped Patterns of Heterogeneity with an Application to Consumer Demand" introduces post-Lasso methods to time-varying grouped patterns of heterogeneity in linear panel data models with heterogeneous coefficients. Group membership is left unrestricted and the model is approximately sparse, meaning the conditional expectation of the variables given the covariates can be well-approximated by a subset of the variables whose identities may be unknown. I estimate the parameters of the model using a “grouped fixed-effects” estimator that minimizes a post-Lasso least-squares criterion with respect to all possible groupings of the cross-sectional units. I provide conditions under which the estimator is consistent as both dimensions of the panel tend to infinity and provide inference methods. Under reasonable assumptions, applying this estimator to a consumer demand application allows me to partition consumers into groups, deal with price endogeneity without instrumental variables, estimate demand shocks, and identify compliments and substitutes for each group. I then use this estimator to estimate demand for soda by identifying different groups' competition sets as well as demand shocks using Homescan data. Chapter 2: In ``A Panel Data Estimator for the Distribution and Quantiles of Marginal Effects in Nonlinear Structural Models with an Application to the Demand for Junk Food", we propose a framework to estimate the distribution of marginal effects in a general class of structural models that allow for arbitrary smooth nonlinearities, high dimensional heterogeneity, and unrestricted correlation between the persistent components of this heterogeneity and all covariates. The main idea is to form a derivative dependent variable using two periods of the panel, and use differences in outcome variables of nearby subpopulations to obtain the distribution of marginal effects. We establish constructive nonparametric identification for the population of ``stayers" (Chamberlain 1982), and show generic non-identification for the ``movers". We propose natural semiparametric sample counterparts estimators, and establish that they achieve the optimal (minimax) rate. Moreover, we analyze their behavior through a Monte-Carlo study, and showcase the importance of allowing for nonlinearities and correlated heterogeneity through an application to demand for junk food. In this application, we establish profound differences in marginal income effects between poor and wealthy households, which may partially explain health issues faced by the less privileged population. Chapter 3: In ``A Binary Choice Difference-in-Differences Model with Heterogeneous Treatment Effects and an Application on Soda Taxes", we answer how should Differences-in-Differences be implemented when outcomes are binary and we expect heterogeneous effects. The scope for applications is clearly vast, including labor force participation, product purchase decisions, enrollment in health insurance and much more. However, assumptions necessary to measure heterogeneous effects in classic Difference-in-Difference models break down with a binary dependent variable. We propose a model with a nonparametric random coefficient formulation that allows for heterogeneous treatment effects with a binary dependent variable. We provide identification of the average treatment effect on the treated (ATT) along with identification of the joint distribution of the actual and counterfactual latent outcome variable in the treatment group which allows us to show the heterogenous treatment effects. We suggest an estimator for the treatment effects and evaluate its finite sample properties with the help of Monte Carlo simulations. We further provide extensions that allow for more flexible empirical applications, such as including covariates. We apply our estimator to analyze the effect of a soft drink tax on consumer's likelihood to consume soda and find heterogeneous effects. The tax reduced the likelihood of consumption for the most consumers but not for those who were most likely to be consuming previously.