A Recursive Partitioning Approach for Dynamic Discrete Choice Modeling in High Dimensional Settings

TL;DR

This paper introduces a semi-parametric, recursive partitioning method for dynamic discrete choice models that effectively reduces high-dimensional state spaces, improving estimation feasibility and reducing bias.

Contribution

It proposes a data-driven recursive partitioning algorithm to handle high-dimensional variables in dynamic discrete choice models, enabling more accurate and feasible estimation.

Findings

The method reduces estimation bias compared to standard approaches.

It makes high-dimensional dynamic models computationally feasible.

Monte Carlo simulations demonstrate improved performance.

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.