# Divide and Conquer: A New Approach to Dynamic Discrete Choice with Serial Correlation - Zurich Open Repository and Archive

Reich, Gregor Philipp (2013). Divide and Conquer: A New Approach to Dynamic Discrete Choice with Serial Correlation. SSRN, University of Zurich.

## Abstract

In this paper, we develop a method to efficiently estimate dynamic discrete choice models with AR(n) type serial correlation of the errors. First, to approximate the expected value function of the underlying dynamic problem, we use Gaussian quadrature, interpolation over an adaptively refined grid, and solve a potentially large non-linear system of equations. Second, to evaluate the likelihood function, we decompose the integral over the unobserved state variables in the likelihood function into a series of lower dimensional integrals, and successively approximate them using Gaussian quadrature rules. Finally, we solve the maximum likelihood problem using a nested fixed point algorithm. We then apply this method to obtain point estimates of the parameters of the bus engine replacement model of Rust [Econometrica, 55 (5): 999–1033, (1987)]: First, we verify the algorithm's ability to recover the parameters of an artificial data set, and second, we estimate the model using the original data, finding significant serial correlation for some subsamples.

## Abstract

In this paper, we develop a method to efficiently estimate dynamic discrete choice models with AR(n) type serial correlation of the errors. First, to approximate the expected value function of the underlying dynamic problem, we use Gaussian quadrature, interpolation over an adaptively refined grid, and solve a potentially large non-linear system of equations. Second, to evaluate the likelihood function, we decompose the integral over the unobserved state variables in the likelihood function into a series of lower dimensional integrals, and successively approximate them using Gaussian quadrature rules. Finally, we solve the maximum likelihood problem using a nested fixed point algorithm. We then apply this method to obtain point estimates of the parameters of the bus engine replacement model of Rust [Econometrica, 55 (5): 999–1033, (1987)]: First, we verify the algorithm's ability to recover the parameters of an artificial data set, and second, we estimate the model using the original data, finding significant serial correlation for some subsamples.

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Item Type: Working Paper 03 Faculty of Economics > Department of Business Administration 330 Economics English 2013 28 Jan 2014 17:00 31 May 2017 03:44 SSRN 19 Official URL. An embargo period may apply. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2371592 merlin-id:8813