Journal of Financial Econometrics Advance Access originally published online on August 22, 2007
Journal of Financial Econometrics 2008 6(1):108-142; doi:10.1093/jjfinec/nbm014
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Evidence on Simulation Inference for Near Unit-Root Processes with Implications for Term Structure Estimation
Haas School of Business, University of California at Berkeley
Address correspondence to Richard H. Stanton, Haas School of Business, U.C. Berkeley, 545 Student Services Building #1900 Berkeley, CA 94720-1900, or e-mail: stanton{at}haas.berkeley.edu
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Abstract |
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The high persistence of interest rates has important implications for the preferred method used to estimate term structure models. We study the finite-sample properties of two standard dynamic simulation methods—efficient method of moments (EMM) and indirect inference—when they are applied to an first order autoregressive (AR[1]) process with Gaussian innovations. When simulated data are as persistent as interest rates, the finite-sample properties of EMM differ both from their asymptotic properties and from the finite-sample properties of indirect inference and maximum likelihood. EMM produces larger confidence bounds than indirect inference and maximum likelihood, yet is much less likely to contain the true parameter value. This is primarily because the population variance of the data plays a much larger role in the EMM conditions than in the moment conditions for either indirect inference or maximum likelihood. These results suggest that, under Gaussian assumptions, indirect inference (if practical) is preferable to EMM when working with persistent data such as interest rates. EMM's emphasis on the population variance strongly enforces stationarity on the underlying process, so this same reasoning suggests that EMM may be preferable in settings where stability and stationarity are important and difficult to impose.
KEYWORDS: AR process, unit root, EMM, indirect inference
We thank Eric Renault, George Tauchen (the editor) and Hao Zhou for helpful discussions, and two anonymous referees for helpful comments. We are grateful for financial support from the Fisher Center for Real Estate and Urban Economics.
Received October 2, 2006; revised March 12, 2007; accepted July 24, 2007
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