  Dynamic discrete choice models are widely employed to answer substantive and
policy questions in settings where individuals' current choices have future
implications. However, estimation of these models is often computationally
intensive and/or infeasible in high-dimensional settings. Indeed, even
specifying the structure for how the utilities/state transitions enter the
agent's decision is challenging in high-dimensional settings when we have no
guiding theory. In this paper, we present a semi-parametric formulation of
dynamic discrete choice models that incorporates a high-dimensional set of
state variables, in addition to the standard variables used in a parametric
utility function. The high-dimensional variable can include all the variables
that are not the main variables of interest but may potentially affect people's
choices and must be included in the estimation procedure, i.e., control
variables. We present a data-driven recursive partitioning algorithm that
reduces the dimensionality of the high-dimensional state space by taking the
variation in choices and state transition into account. Researchers can then
use the method of their choice to estimate the problem using the discretized
state space from the first stage. Our approach can reduce the estimation bias
and make estimation feasible at the same time. We present Monte Carlo
simulations to demonstrate the performance of our method compared to standard
estimation methods where we ignore the high-dimensional explanatory variable
set.
