🤖 AI Summary
Estimating high-dimensional dynamic discrete choice models is often computationally infeasible due to the curse of dimensionality, and identification of the true decision-relevant structure among covariates is challenging without strong theoretical priors. This paper proposes a semiparametric recursive partitioning framework: it employs data-driven recursive splitting to automatically reduce dimensionality while preserving salient behavioral heterogeneity, discretizing the high-dimensional state space; integrates semiparametric utility modeling with Monte Carlo simulation-based evaluation to ensure unbiased estimation and computational tractability. It is the first work to introduce recursive partitioning into dynamic choice modeling, enabling data-driven discovery of the true decision structure in high-dimensional covariate spaces without theoretical pre-specification. Simulation results demonstrate substantial reductions in estimation bias, rendering previously intractable high-dimensional models estimable, and outperform standard approaches that ignore or inadequately handle high-dimensional covariates.
📝 Abstract
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.
