A Study of the Finite Sample Properties of EMM, GMM, QMLE, and MLE for a Square-Root Interest Rate Diffusion Model

Abstract

This paper performs a Monte Carlo study on Efficient Method of Moments (EMM), Generalized Method of Moments (GMM), Quasi-Maximum Likelihood Estimation (QMLE), and Maximum Likelihood Estimation (MLE) for a continuous-time square-root model under two challenging scenarios--high persistence in mean and strong conditional volatility--that are commonly found in estimating the interest rate process. MLE turns out to be the most efficient of the four methods, but its finite sample inference and convergence rate suffer severely from approximating the likelihood function, especially in the scenario of highly persistent mean. QMLE comes second in terms of estimation efficiency, but it is the most reliable in generating inferences. GMM with lag-augmented moments has overall the lowest estimation efficiency, possibly due to the ad hoc choice of moment conditions. EMM shows an accelerated convergence rate in the high volatility scenario, while its overrejection bias in the mean persistence scenario is unacceptably large. Finally, under a stylized alternative model of the US interest rates, the overidentification test of EMM obtains the ultimate power for detecting misspecification, while the GMM J-test is increasingly biased downward in finite samples.