Semiparametric Identification of the Discount Factor and Payoff Function in Dynamic Discrete Choice Models

TL;DR

This paper demonstrates how nonparametric assumptions in stationary infinite-horizon dynamic discrete choice models can identify the discount factor and payoff functions, providing new insights into economic modeling.

Contribution

It introduces novel polynomial restrictions derived from common assumptions that identify key parameters in both single-agent and dynamic game models.

Findings

Polynomial equalities and inequalities for discount factor identification

Identification of payoff functions under standard normalization

Firm-specific discount factors can be identified using specific assumptions

Abstract

This paper investigates how the discount factor and payoff functions can be identified in stationary infinite-horizon dynamic discrete choice models. In single-agent models, we show that common nonparametric assumptions on per-period payoffs -- such as homogeneity of degree one, monotonicity, concavity, zero cross-differences, and complementarity -- provide identifying restrictions on the discount factor. These restrictions take the form of polynomial equalities and inequalities with degrees bounded by the cardinality of the state space. These restrictions also identify payoff functions under standard normalization at one action. In dynamic game models, we show that firm-specific discount factors can be identified using assumptions such as irrelevance of other firms' lagged actions, exchangeability, and the independence of adjustment costs from other firms' actions. Our results demonstrate that widely used nonparametric assumptions in economic analysis can provide substantial identifying power in dynamic structural models.