Jason R. Blevins

Nonparametric identification of dynamic decision processes with discrete and continuous choices

This paper establishes conditions for nonparametric identification of dynamic optimization models in which agents make both discrete and continuous choices. We consider identification of both the payoff function and the distribution of unobservables. Models of this kind are prevalent in applied microeconomics and many of the required conditions are standard assumptions currently used in empirical work. We focus on conditions on the model that can be implied by economic theory and assumptions about the data generating process that are likely to be satisfied in a typical application. Our analysis is intended to highlight the identifying power of each assumption individually, where possible, and our proofs are constructive in nature.

Identifying Restrictions for Finite Parameter Continuous Time Models with Discrete Time Data

When a continuous time model is sampled only at equally spaced intervals, a priori restrictions on the parameters can provide natural identifying restrictions which serve to rule out otherwise observationally equivalent parameter values. Specifically, we consider identification of the parameter matrix in a linear system of first-order stochastic differential equations, a setting which is general enough to include many common continuous time models in economics and finance. We derive a new characterization of the identification problem under a fully general class of linear restrictions on the parameter matrix and establish conditions under which only floor(n/2) restrictions are sufficient for identification when only the discrete time process is observable. Restrictions of the required kind are typically implied by economic theory and include zero restrictions that arise when some variables are excluded from an equation. We also consider identification of the intensity matrix of a discretely-sampled finite Markov jump processes, a related special case where we show that only floor((n-1)/2) restrictions are required. We demonstrate our results by applying them to two example models from economics and finance: a continuous time regression model with three equations and a continuous-time model of credit rating dynamics.

Non‐Standard Rates of Convergence of Criterion‐Function‐Based Set Estimators for Binary Response Models

This paper establishes consistency and non‐standard rates of convergence for set estimators based on contour sets of criterion functions for a semi‐parametric binary response model under a conditional median restriction. The model can be partially identified due to potentially limited‐support regressors and an unknown distribution of errors. A set estimator analogous to the maximum score estimator is essentially cube‐root consistent for the identified set when a continuous but possibly bounded regressor is present. Arbitrarily fast convergence occurs when all regressors are discrete. We also establish the validity of a subsampling procedure for constructing confidence sets for the identified set. As a technical contribution, we provide more convenient sufficient conditions on the underlying empirical processes for cube‐root convergence and a sufficient condition for arbitrarily fast convergence, both of which can be applied to other models. Finally, we carry out a series of Monte Carlo experiments, which verify our theoretical findings and shed light on the finite‐sample performance of the proposed procedures.