Nonparametric Identication of Dynamic Models with Unobserved State Variables: Supplemental Material

We provide some additional material pertaining to our paper Hu and Shum (2008). In section 1, we verify our assumptions for a dynamic discrete-choice model inspired by Rust’s (1987) bus engine replacement model. Section 2 contains a comparison of our framework with that in Kasahara and Shimotsu (2009). Section 3 contains supplemental discussion related to Example 2 in the main paper and additional discussion of Assumption 2. 1 Additional example: dynamic discrete-choice model based on Rust (1987) In addition to the two examples presented in the main paper, we present here a discussion of our assumptions in the context of a third example: Rust’s (1987) bus-engine replacement model, augmented to allow for time-varying serially-correlated unobserved state variables. In this model, Wt = (Yt;Mt), where Yt is the indicator that the bus engine was replaced in week t, and Mt is the mileage since the last engine replacement. Let St (Mt; X t ) denote the state variables in this model. The period utility from each choice is additive in a function of the state variables St, and a choice-speci…c non-persistent preference shock: ut = ( u0(St) + 0t if Yt = 0 u1(St) + 1t if Yt = 1 where 0t and 1t are i.i.d. Type I Extreme Value shocks, which are independent over time,