Structural Estimation by Homotopy Continuation with an Application to Discount Factor Estimation

47 Pages Posted: 3 Jan 2019 Last revised: 23 Mar 2021

See all articles by Philipp Müller

Philipp Müller

University of Zurich - Department of Business Administration

Gregor Reich

Norwegian School of Economics (NHH) - Department of Strategy and Management

Date Written: March 23, 2020

Abstract

We develop a method to robustly estimate parameters of structural economic models with potential identification issues. Using homotopy path continuation applied to the MPEC formulation of the estimation problem (Su and Judd, 2012), we trace the parameter estimates and their confidence intervals as a function of a controlled parameter.
As the discount factor is commonly assumed to be poorly identified in DDCMs, we trace the parameter estimates of the bus engine replacement model by Rust (1987) as a function of the discount factor β. Applying methods developed for undiscounted dynamic programming, we find that β is well identified and statistically significantly larger than 1. We establish an economically reasonable qualitative link between the decision-maker's discounting and the real interest rates: in an extended model with an unanticipated structural break in β, the decrease in β qualitatively agrees with the macroeconomic regime change in the real interest rates during the great inflation. These rates were low or even negative and increased after Paul Volcker took office as chairman of the Fed. In this period of negative real interest rates, a time value of money argument cannot reject the estimate β ≥ 1.

Keywords: structural estimation, parametric optimization, mathematical programming with equilibrium constraints, homotopy continuation, identification, multiplicity of equilibria

Suggested Citation

Müller, Philipp and Reich, Gregor, Structural Estimation by Homotopy Continuation with an Application to Discount Factor Estimation (March 23, 2020). Available at SSRN: https://ssrn.com/abstract=3303999 or http://dx.doi.org/10.2139/ssrn.3303999

Philipp Müller

University of Zurich - Department of Business Administration ( email )

Rämistrasse 71
Zurich, CH-8006
Switzerland

Gregor Reich (Contact Author)

Norwegian School of Economics (NHH) - Department of Strategy and Management ( email )

Breiviksveien 40
N-5045 Bergen
Norway

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