Sequential Monte Carlo Methods for Estimating Dynamic Microeconomic Models

This paper develops methods for estimating dynamic structural microeconomic models with serially correlated latent state variables. The proposed estimators are based on sequential Monte Carlo methods, or particle filters, and simultaneously estimate both the structural parameters and the trajectory of the unobserved state variables for each observational unit in the dataset. We focus two important special cases: single agent dynamic discrete choice models and dynamic games of incomplete information. The methods are applicable to both discrete and continuous state space models. We first develop a broad nonlinear state space framework which includes as special cases many dynamic structural models commonly used in applied microeconomics. Next, we discuss the nonlinear filtering problem that arises due to the presence of a latent state variable and show how it can be solved using sequential Monte Carlo methods. We then turn to estimation of the structural parameters and consider two approaches: an extension of the standard full-solution maximum likelihood procedure (Rust, 1987) and an extension of the two-step estimation method of Bajari, Benkard, and Levin (2007), in which the structural parameters are estimated using revealed preference conditions. Finally, we introduce an extension of the classic bus engine replacement model of Rust (1987) and use it both to carry out a series of Monte Carlo experiments and to provide empirical results using the original data.dynamic discrete choice, latent state variables, serial correlation, sequential Monte Carlo methods, particle filtering

Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL's good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data

Local nlls estimation of semi-parametric binary choice models

Abstract In this paper, nonlinear least squares (NLLS) estimators are proposed for semiparametric binary response models under conditional median restrictions. The estimators can be identical to NLLS procedures for parametric binary response models (e.g. Probit), and consequently have the advantage of being easily implementable using standard software packages such as Stata. This is in contrast to existing estimators for the model, such as the maximum score estimator JEL Classification: C13, C14, C25

Hearing and dementia

Hearing deficits associated with cognitive impairment have attracted much recent interest, motivated by emerging evidence that impaired hearing is a risk factor for cognitive decline. However, dementia and hearing impairment present immense challenges in their own right, and their intersection in the auditory brain remains poorly understood and difficult to assess. Here, we outline a clinically oriented, symptom-based approach to the assessment of hearing in dementias, informed by recent progress in the clinical auditory neuroscience of these diseases. We consider the significance and interpretation of hearing loss and symptoms that point to a disorder of auditory cognition in patients with dementia. We identify key auditory characteristics of some important dementias and conclude with a bedside approach to assessing and managing auditory dysfunction in dementia

Local nlls estimation of semi-parametric binary choice models

Abstract In this paper, nonlinear least squares (NLLS) estimators are proposed for semiparametric binary response models under conditional median restrictions. The estimators can be identical to NLLS procedures for parametric binary response models (e.g. Probit), and consequently have the advantage of being easily implementable using standard software packages such as Stata. This is in contrast to existing estimators for the model, such as the maximum score estimator JEL Classification: C13, C14, C25

Distribution-free estimation of heteroskedastic binary response models in Stata

In this article, we consider two recently proposed semiparametric estimators for distribution-free binary response models under a conditional median restriction. We show that these estimators can be implemented in Stata by using the nl command through simple modifications to the nonlinear least-squares probit criterion function. We then introduce dfbr, a new Stata command that implements these estimators, and provide several examples of its usage. Although it is straightforward to carry out the estimation with nl, the dfbr implementation uses Mata for improved performance and robustness

Firm Expansion, Size Spillovers and Market Dominance in Retail Chain Dynamics

We develop and estimate a dynamic game of strategic firm expansion and contraction decisions to study the role of firm size on future profitability and market dominance. Modeling firm size is important because retail chain dynamics are more richly driven by expansion and contraction than de novo entry or permanent exit. Additionally, anticipated size spillovers may influence the strategies of forward looking firms making it difficult to analyze the effects of size without explicitly accounting for these in the expectations and, hence, decisions of firms. Expansion may also be profitable for some firms while detrimental for others. Thus, we explicitly model and allow for heterogeneity in the dynamic link between firm size and profits as well as potential for persistent brand effects through a firmspecific unobservable. As a methodological contribution, we surmount the hurdle of estimating the model by extending the Bajari, Benkard and Levin (2007) two-step procedure that circumvents solving the game. The first stage combines semi-parametric conditional choice probability estimation with a particle filter to integrate out the serially correlated unobservables. The second stage uses a forward simulation approach to estimate the payoff parameters. [...