Linear IV regression estimators for structural dynamic discrete choice models

Abstract

In structural dynamic discrete choice models, unobserved or mis-measured state variables may lead to biased parameter estimates and misleading inference. In this paper, we show that instrumental variables can address such measurement problems when they relate to state variables that evolve exogenously from the perspective of individual agents (i.e., market-level states). We define a class of linear instrumental variables estimators that rely on Euler equations expressed in terms of conditional choice probabilities (ECCP estimators). These estimators do not require observing or modeling the agent's entire information set, nor solving or simulating a dynamic program. As such, they are simple to implement and computationally light. We provide constructive arguments for the identification of model primitives, and establish the estimator's consistency and asymptotic normality. Four applied examples serve to illustrate the ECCP approach's implementation, advantages, and limitations: dynamic demand for durable goods, agricultural land use change, technology adoption, and dynamic labor supply. We illustrate the estimator's good finite-sample performance in a Monte Carlo study, and we estimate a labor supply model empirically for taxi drivers in New York City.

An Instrumental Variable Approach to Dynamic Models

“…A recent paper by Kalouptsidi et al (2020) shares our IV intuition and is in many ways closest to our spirit. They show that in a class of dynamic discrete choice models with serially correlated market-level unobservables, one can obtain Euler equations that pointidentify some firm-specific profit parameters.…”

“…This working paper version of later published work emphasizes an indi↵erence condition interpretation of policy functions in the context of dynamic discrete choice with independent errors.18 HM andArcidiacono and Miller (2011) employed related multi-period indi↵erence conditions to simplify a second-step in problems with "finite dependenc" and independent errors. These methods could be adapted to our case as well if the underlying model featured additive independent errors in addition to any serially correlated component Kalouptsidi, Scott, and Souza-Rodrigues (2020). make use of related finite-dependence indi↵erence conditions in their special case IV method.…”

The Impact of Dollar Store Expansion on Local Market Structure and Food Access

“…Simultaneity in players' moves can cause multiplicity of equilibria in this context. The two CCP-based estimation approaches we use circumvent this difficulty by relying on the best-response mapping as estimating equations (Pesendorfer and Schmidt-Dengler (2008), Kalouptsidi et al (2020), Bugni and Bunting (2021)). For our counterfactual analysis, we initialize the computation algorithm at a large number of starting values and iterate to a fixed point.…”

“…As detailed in Section 4, this allows us to express period-t choice-specific value function as a function of period-t + 1 (known) CCPs and structural profit function. Second, we avoid numerical integration over the high-dimensional state space by using the linear IV regression approach of Kalouptsidi et al (2020). The latter paper combines insights from the finite dependence approach and the GMM-Euler approach Magesan (2013, 2018)) to construct moment restrictions for the structural parameters.…”

“…This property simplifies estimation of the game substantially as it allows us to represent the firms' value functions directly in terms of the period-ahead probability of making the terminal choice. We leverage this property and estimate the model using the linear IV strategy of Kalouptsidi et al (2020). The latter paper combines insights from the finite dependence approach and the GMM-Euler approach of Aguirregabiria and Magesan (2018) to propose a method (ECCP) that circumvent integration over the highdimensional state space.…”