Structural Estimation by Homotopy Continuation with an Application to Discount Factor Estimation
47 Pages Posted: 3 Jan 2019 Last revised: 23 Mar 2021
Date Written: March 23, 2020
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
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