EMM: A Program for Efficient Method of Moments

Authors: A. Ronald Gallant and George Tauchen

A. Ronald Gallant
Fuqua School of Business
Duke University
Box 90120, W425
Durham NC 27708-0120

Phone 1-919-660-7927 (Duke-Fuqua)
e-mail: ron.gallant@duke.edu

George Tauchen
Department of Economics
305 Social Science
Box 90097
Duke University
Durham NC 27708-0097

Phone: 1-919-660-1812
e-mail: george.tauchen@duke.edu

Keywords: efficient method of moments, EMM, estimation by simulation, simulated method of moments,
minimum chi-square, stochastic differential equations, and diffusions.


FORTRAN Code and a User's Guide as a PostScript file are available anonymous ftp from http://econ.duke.edu/webfiles/get in directory pub/get/emm. It runs on PC's using the free GNU g77 compiler or the Intel compiler; it also runs under UNIX/LINNUX. The GNU, Intel, and UNIX versions of EMM are posted under ftp/pub/get/emm. These versions work with SNP Versions 8.9 and earlier. The distribution software contains four worked examples.  One is for estimation of a simple stochastic volatility model to stock returns data, and the others pertain to estimation of continuous time stochastic differential equations for stock prices and the short-term interest rate.  The posted version is the last FORTRAN version and is effectively frozen, with no updates nor modifications planned.

C++ Code and a User's Guide as a PostScript file are available anonymous ftp from http://econ.duke.edu/webfiles/arg in directory /pub/arg/emm_cpp.  The C++ version is the modern version of EMM which will be maintained forward.


All code is provided at no charge for research purposes without warranty of any kind, expressed or implied.


Click here for a complete list of working papers and published papers

Gallant, A. Ronald, and George Tauchen (2002) "Simulated Score Methods and Indirect Inference for Continuous-time Models," prepared for the Handbook of Financial Econometrics, available at  http://www.econ.duke.edu/~get/wpapers

Gallant, A. R., and Long, J. R. (1997) "Estimating Stochastic Differential Equations Efficiently by Minimum Chi-Squared," Biometrika, 84, 125-141.

Tauchen, G., (1997) "New Minimum Chi-Square Methods in Empirical Finance," in Advances in Econometrics, Seventh World Congress, eds. D. Kreps, and K. Wallis, Cambridge UK: Cambridge University Press, 279-317.

Gallant, A. R., and Tauchen, G. (1996) "Which Moments to Match?," Econometric Theory, 12, 657-681.

Related References (A Few Applications of EMM):

Click here for a more complete list of working papers and published papers

Andersen, T., L. Benzoni and J. Lund (2002) "An Empirical Investigation of Continuous-Time Models for Equity Returns,"  Journal of Finance 57  1239-1284.

Bansal, Ravi and Hao Zhou (2002) "Term Structure of Interest Rates with Regime Shifts," Journal of Finance, October 2002; 57(5): 1997-2043.

Ahn,-Dong-Hyun, Dittmar, Robert-F  and Gallant, A Ronald (2002) "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Spring 2002; 15(1): 243-88.

Qiang Dai and Kenneth J. Singleton, (2001) "Specification Analysis of Affine Term Structure Models," Journal of Finance 55, 1943-1978.

Chernov, Mikhail, and Ghysels, Eric, (2000) "A Study Towards a Unified Approach to the Joint Estimation of Objective and Risk Neutral Measures for the Purpose of Options Valuation," Journal of Financial Economics 56, 407-458

Andersen, Torben G., and Lund, Jesper (1997) "Estimating Continuous Time Stochastic Volatility Models of the Short Term Interest Rate," Journal of Econometrics 77, 343--378.


The Efficient Method of Moments (EMM) is a simulation-based technique for situations where the likelihood is intractable and thus likelihood-based and Bayesian inference are infeasible. EMM would be regarded as a minimum chi-square estimator in the statistics literature and as a generalized method of moments (GMM) estimator in the econometrics literature. Among many potential applications, the technique is well suited to estimation of systems of stochastic differential equations (SDEs).

The moment equations of the EMM estimator are based on the score vector of an auxiliary model, termed the score generator. Gallant and Tauchen (1996) show that if the score generator encompasses the maintained model, then EMM is as efficient as maximum likelihood. Results of Tauchen (1997) suggest that the EMM estimator will be nearly as efficient as maximum likelihood when the score generator is a good statistical approximation to the observed process the sense of passing diagnostic tests, etc. Gallant and Long (1997) support this conjecture by showing that if the score generator is the SNP density, then efficiency of the EMM estimator can be made arbitrarily close to that of maximum likelihood.

Language: FORTRAN 77 and C++

Platforms: PCs under the free GNU g77 FORTRAN and Intel FORTRAN; UNIX/LINUX workstations including SUNs, HPs, and Intel-based boxes running either LINUX or Solaris and supporting f77 or cpp.

Support: For more information on the EMM package contact its authors:
A. Ronald Gallant (ron.gallant@duke.edu)
or George Tauchen (george.tauchen@duke.edu)