  We study dynamic discrete choice models, where a commonly studied problem
involves estimating parameters of agent reward functions (also known as
"structural" parameters), using agent behavioral data. Maximum likelihood
estimation for such models requires dynamic programming, which is limited by
the curse of dimensionality. In this work, we present a novel algorithm that
provides a data-driven method for selecting and aggregating states, which
lowers the computational and sample complexity of estimation. Our method works
in two stages. In the first stage, we use a flexible inverse reinforcement
learning approach to estimate agent Q-functions. We use these estimated
Q-functions, along with a clustering algorithm, to select a subset of states
that are the most pivotal for driving changes in Q-functions. In the second
stage, with these selected "aggregated" states, we conduct maximum likelihood
estimation using a commonly used nested fixed-point algorithm. The proposed
two-stage approach mitigates the curse of dimensionality by reducing the
problem dimension. Theoretically, we derive finite-sample bounds on the
associated estimation error, which also characterize the trade-off of
computational complexity, estimation error, and sample complexity. We
demonstrate the empirical performance of the algorithm in two classic dynamic
discrete choice estimation applications.
