This dissertation studies how to leverage the unique characteristics of panel and network data, particularly repeated observations and symmetries, to recover the structural parameters of three econometric models of theoretical and applied interest.
In Chapter 1, I study parameter identifiablility and estimation of dynamic discrete choice models with strictly exogenous regressors, fixed effects and logistic errors. Specifications of this kind are popular in Labor Economics and Industrial Organization to disentangle the sources of serial persistence in agents’ decisions. The primary challenge lies in the nonlinearity of these models, making the treatment of fixed effects difficult in short panel settings. I introduce a new method that exploits the structure of logit-type probabilities and elementary properties of rational fractions to derive moment restrictions in a broad class of models. This includes binary response models of arbitrary lag order as well as first-order panel vector autoregressions and dynamic multinomial logit models. These moment restrictions are free from the fixed effects and provide a natural way to estimate the common parameters via the Generalized Method of Moments. I further establish the identification of a class of average marginal effects which are often of importance in empirical work. The approach is illustrated through an analysis of the dynamics of drug consumption amongst young people in a nationally representative sample.
In Chapter 2, coauthored with Stéphane Bonhomme and Bryan Graham, we study identification in a binary choice panel data model with a single predetermined binary covariate (i.e., a covariate sequentially exogenous conditional on lagged outcomes and covariates). The choice model is indexed by a scalar parameter θ, whereas the distribution of unit-specific heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, are left unrestricted. This setup departs from Chapter 1 which imposed strict exogeneity of explanatory variables, effectively ruling out any influence of past outcomes oncovariates. In this framework, we provide a simple condition under which θ is never point-identified, no matter the number of time periods available. This condition is satisfied in most models, including the logit one. We also characterize the identified set of θ and show how to compute it using linear programming techniques. While θ is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about θ may be possible even in short panels with feedback. As a complement, we report calculations of identified sets for an average partial effect, and find informative sets in this case as well.
In Chapter 3, I present an approach to address network endogeneity in a linear social interaction model. I consider a setting wherein individual-specific latent random effects influence both outcomes and link formation modelled as a conditionally independent dyad process. Using the exchangeability properties of the framework, I show that controlling or matching individuals by degree-centrality can be sufficient to eliminate the omitted variable bias induced by endogenous peer selection. I leverage this result and insights from Bramoullé et al. (2009) for the case of exogenous friendships to present two simple strategies for the identification and estimation of social effects. Asymptotic properties of the proposed estimators are derived for clustered samples and I illustrate their performance in Monte Carlo simulations.
