Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

Abstract

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K-stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz-Miller estimator (for K = 1) and Rust's nested fixed point estimator (in the limit when K → ). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade-off between finite sample precision and computational cost in the sequence of policy iteration estimators.

An approach for extending dynamic models to settings with multi-product firms

“…1 For related methods in the single agent context see Hotz and Miller (1993), Hotz et al (1994), and Aguirregabiria and Mira (2002). For a review of structural estimation of dynamic games see Ackerberg et al (in press).…”

Exchange rate fluctuations, plant turnover and productivity

“…In the first stage, I use the Nested Pseudo Likelihood (NPL) algorithm developed in Aguirregabiria and Mira (2002) to obtain estimates of the model's dynamic parameters that characterize variable profits, along with the per-period fixed cost of operation. In the second stage, I use the Method of Simulated Moments (MSM) to recover estimates of the cost of entry and the parameters characterizing the distribution of unobserved potential entrant productivity.…”

“…To estimate some of the dynamic parameters in the model below, I use the NPL algorithm developed in Aguirregabiria and Mira (2002), which offers a more efficient and parsimonious alternative to the estimators developed by Rust (1987) and Hotz and Miller (1993). 1 Collard-Wexler (2009) estimates a model of entry and exit using the multi-agent NPL algorithm developed in Aguirregabiria and Mira (2007) to study the role of plant productivity on turnover and profitability in the U.S. ready-mix concrete industry.…”

Prevention of Competition by Competition Law: Evidence from Unbundling Regulation on Fiber-Optic Networks in Japan

“…For example, in 2003, the United States'Federal Communication Commission (FCC) amended the law and removed unbundling regulations on …ber-optic premises in order to accelerate building competition among carriers and promote investments in …ber networks, even though many companies without facilities objected. 2 However, in relation to unbundling regulation's importance, the literature that studies it is limited. This is because the municipal level data set is rarely available and building of the new networks, such as …ber-optic networks, is uncommon.…”

“…Greenstein and Mazzeo (2006) found that unbundling widened the variety of services, and Economides, Seim and Viard (2008) found that competition in service markets induced 2 This deregulation has been continually criticized by …rms that use the regulated lines, and created a controversy between regulated …rms and the users of their facilities. For example, in December 2009, Cbeyond.Inc, supported by the Small Business Administration (SBA), …led a petition with the FCC to reverse the deregulation.…”