Essays in Industrial Organization and Econometrics

This dissertation consists of three chapters relating to

identification and inference in dynamic microeconometric models

including dynamic discrete games with many players, dynamic games with

discrete and continuous choices, and semiparametric binary choice and

duration panel data models.

The first chapter provides a framework for estimating large-scale

dynamic discrete choice models (both single- and multi-agent models)

in continuous time. The advantage of working in continuous time is

that state changes occur sequentially, rather than simultaneously,

avoiding a substantial curse of dimensionality that arises in

multi-agent settings. Eliminating this computational bottleneck is

the key to providing a seamless link between estimating the model and

performing post-estimation counterfactuals. While recently developed

two-step estimation techniques have made it possible to estimate

large-scale problems, solving for equilibria remains computationally

challenging. In many cases, the models that applied researchers

estimate do not match the models that are then used to perform

counterfactuals. By modeling decisions in continuous time, we are able

to take advantage of the recent advances in estimation while

preserving a tight link between estimation and policy experiments. We

also consider estimation in situations with imperfectly sampled data,

such as when we do not observe the decision not to move, or when data

is aggregated over time, such as when only discrete-time data are

available at regularly spaced intervals. We illustrate the power of

our framework using several large-scale Monte Carlo experiments.

The second chapter considers semiparametric panel data binary choice

and duration models with fixed effects. Such models are point

identified when at least one regressor has full support on the real

line. It is common in practice, however, to have only discrete or

continuous, but possibly bounded, regressors. We focus on

identification, estimation, and inference for the identified set in

such cases, when the parameters of interest may only be partially

identified. We develop a set of general results for

criterion-function-based estimation and inference in partially

identified models which can be applied to both regular and irregular

models. We apply our general results first to a fixed effects binary

choice panel data model where we obtain a sharp characterization of

the identified set and propose a consistent set estimator,

establishing its rate of convergence under different conditions.

Rates arbitrarily close to n-1/3 are

possible when a continuous, but possibly bounded, regressor is

present. When all regressors are discrete the estimates converge

arbitrarily fast to the identified set. We also propose a

subsampling-based procedure for constructing confidence regions in the

models we consider. Finally, we carry out a series of Monte Carlo

experiments to illustrate and evaluate the proposed procedures. We

also consider extensions to other fixed effects panel data models such

as binary choice models with lagged dependent variables and duration

models.

The third chapter considers nonparametric identification of dynamic

games of incomplete information in which players make both discrete

and continuous choices. Such models are commonly used in applied work

in industrial organization where, for example, firms make discrete

entry and exit decisions followed by continuous investment decisions.

We first review existing identification results for single agent

dynamic discrete choice models before turning to single-agent models

with an additional continuous choice variable and finally to

multi-agent models with both discrete and continuous choices. We

provide conditions for nonparametric identification of the utility

function in both cases.