Unobserved heterogeneity is common in economic data and has nontrivial impacts on modeling, estimation and statistical inference. This dissertation consists of three chapters that explore and illustrate the implications of unobserved heterogeneity for different types of data. The first two chapters focus on panel data, and the third chapter focuses on cross--sectional data.
A popular way to control for unobserved heterogeneity in panel data models is to include fixed effects, but fixed effect estimators of dynamic and nonlinear panel models are subject to the incidental parameter problem. This problem has two implications for applied research: (1) point estimators are largely biased, and (2) confidence intervals have incorrect coverages. Chapter 1 proposes a new method for bias reduction based on indirect inference. The method simulates data using the model with estimated individual effects, and finds estimators of the model parameters by equating the fixed effect estimates obtained from observed and simulated data. The asymptotic framework provides consistency, bias correction, and asymptotic normality results. An application to female labor force participation and numerical simulations illustrate the finite--sample performance of the method.
Chapter 2 is coauthored with Victor Chernozhukov at MIT, Iván Fernández-Val at BU, and Hiroyuki Kasahara and Paul Schrimpf at The University of British Columbia. It is based on the observation that existing jackknife methods that deal with the incidental parameter problem require stationary variables. However, many applications feature covariates of interests that have trends or structural breaks. This chapter proposes a new jackknife bias correction method that relaxes stationarity. The method is named crossover jackknife because it partitions the panel in two halves, each including half of the time series observations for each cross sectional unit, but where the time periods are crossed over between the two halves of the cross section units. We derive the theoretical properties of this method and illustrate its finite--sample performance via calibrated numerical simulations.
Chapter 3 is coauthored with Hiroaki Kaido at BU. In many important discrete choice models, whether the model makes a unique prediction or not depends on its policy-relevant features and can be examined by testing restrictions on underlying structural parameters. Imposing strong assumptions completes the model and allows to predict unique outcomes, but it masks heterogeneity of the data and affects statistical inference. We provide a new test of model incompleteness using a score-based statistic. Our test statistic remains computationally tractable even with a moderate number of nuisance parameters because they only need to be estimated in the restricted complete model. Two empirical applications illustrate the computational feasibility of the method. A Monte Carlo experiment shows the score test outperforms existing tests in terms of local power.
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/45233 |
| Date | 04 October 2022 |
| Creators | Chen, Shuowen |
| Contributors | Fernandez-Val, Ivan |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
| Rights | Attribution 4.0 International, http://creativecommons.org/licenses/by/4.0/ |
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