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 <italic>n<super>-1/3</super></italic> 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.
continuous time
discrete choice
dynamic games
nonparametric identification
panel data
partial identification
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