Conditional Choice Probabilities: The Shortcut Revolutionizing Dynamic Discrete Choice Estimation

Описание: Estimation of dynamic discrete choice models can take days or even weeks. But what if there were a smarter way? In this video, we introduce Conditional Choice Probability (CCP) estimation, the landmark computational contribution by Hotz and Miller (1993) that transformed how economists estimate forward-looking structural models.

Slides used in the video are available here: https://raw.githack.com/tyleransom/st...
Source code for the slides is here: https://github.com/tyleransom/structu...

Scientific Reference: Hotz, V.J. and Miller, R.A. (1993). "Conditional Choice Probabilities and the Estimation of Dynamic Models." The Review of Economic Studies, 60(3), 497–529. https://doi.org/10.2307/2298122

We start by recalling why dynamic discrete choice models are computationally brutal: agents are forward-looking, their decisions satisfy a Bellman equation, and solving that equation via backward recursion (repeated for every parameter guess during estimation) leads to an exponentially growing computational burden as the state space expands. This is the infamous "curse of dimensionality."

The key insight of Hotz and Miller (1993) is that you don't need to solve the dynamic programming problem at every parameter guess. Instead, you can:
1. Estimate conditional choice probabilities (CCPs) directly from the data
2. Invert those probabilities using the Hotz-Miller inversion formula
3. Use a dramatically simplified likelihood to recover the structural parameters

When choice shocks are Type I Extreme Value, the log-odds ratio between any two choice probabilities equals the difference in their conditional value functions. This means that the data itself reveals the value function differences. No full solution of the Bellman equation is required!

We also discuss the key limitations of the CCP approach: the need for clever normalizations to break the recursive structure, and the fact that CCPs cannot be used directly for counterfactual or policy exercises (since we don't observe choices in the counterfactual world).

Tyler Ransom is an Associate Professor of Economics at the University of Oklahoma. Subscribe for more videos on data science, econometrics, and research methods!

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