A Tutorial on the Generalized Method of Moments (GMM) in Finance
Main Article Content
Abstract
Context: empirical problems in which the researcher is faced with a model that is partially specified. In these cases, the GMM method is the natural alternative for estimating the parameters of interest. Objective: the goal of this paper is to offer a tutorial that allows the researcher to understand both the theory and empirical aspects of the GMM method. Methods: we discuss the GMM concepts, forms of estimation, and limitations associated with the method. As a way of illustrating the method, we use two applications in the area of empirical finance. The first application is the estimation of the parameters of a consumption-based asset pricing models; the second is the estimation of the parameters of the evolution of the interest rate in continuous time. The data and codes in R are provided as online appendices. Conclusion: the GMM method can be used in problems where other methods such as maximum likelihood are not feasible, or even when the researcher wants to estimate a model partially specified.
Download data is not yet available.
Article Details
Since mid-February of 2023, the authors retain the copyright relating to their article and grant the journal RAC, from ANPAD, the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution 4.0 International license (CC BY 4.0), as stated in the article’s PDF document. This license provides that the article published can be shared (allows you to copy and redistribute the material in any medium or format) and adapted (allows you to remix, transform, and create from the material for any purpose, even commercial) by anyone.
After article acceptance, the authors must sign a Term of Authorization for Publication, which is sent to the authors by e-mail for electronic signature before publication.
References
Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59(3), 817-858. https://doi.org/10.2307/2938229
Arellano, M., & Bond, S. (1991). Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations. The Review of Economic Studies, 58(2), 277-297. https://doi.org/10.2307/2297968
Banz, R. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3–18. https://doi.org/10.1016/0304-405X(81)90018-0
Brandt, M. W., & Santa-Clara, P. (2002). Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. Journal of Financial Economics, 63, 161–212. Retrieved from https://ideas.repec.org/a/eee/jfinec/v63y2002i2p161-210.html
Campbell, J. Y. (2018). Financial decisions and markets: A course in asset pricing. Princeton, NJ: Princeton University Press.
Cameron, A. C., & Trivedi, P. (2005). Microeconometrics: Methods and applications. New York: Cambridge University Press.
Chan, K. C., Karolyi, G. A., Longstaff, F. A., & Sanders A. B. (1992). An empirical comparison of alternative models of the short-term interest rate. Journal of Finance, 47(3), 1209-1227. https://doi.org/10.1111/j.1540-6261.1992.tb04011.x
Cochrane, J. (1996). A cross-sectional test of an investment-based asset pricing model. Journal of Political Economy, 104(3), 572-621. https://doi.org/10.1086/262034
Cox, J. C., Ingersoll, J. E., & Ross, S. A. (1985). A theory of the term structure of interest rates. Econometrica, 53(2), 385-407. https://doi.org/10.2307/1911242
Cysne, R. (2006). Equity-premium puzzle: Evidence from Brazilian data. Economia Aplicada, 10(2), 161-180. https://doi.org/10.1590/S1413-80502006000200001
Duffie, D., & Singleton, K. (1993). Simulated moments estimation of Markov models of asset prices. Econometrica, 61(4), 929-952. https://doi.org/10.2307/2951768
Gallant, A. R. (1977). Three-stage least-squares estimation for a system of simultaneous, nonlinear, implicit equations. Journal of Econometrics, 5(1), 71-88. https://doi.org/10.1016/0304-4076(77)90035-5
Genaro, A., & Avellaneda, M. (2018). Does the lending rate impact ETF’s prices? Brazilian Review of Econometrics, 38(2), 287-319. https://doi.org/10.12660/bre.v38n22018.31732
Hall, A. R. (2005). Generalized method of moments. Oxford, UK: Oxford University Press.
Hansen, L. P. (2013). Uncertainty outside and inside economic models. Retrieved from https://www.nobelprize.org/uploads/2018/06/hansen-lecture.pdf
Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, 50(4), 1029-1054. https://doi.org/10.2307/1912775
Hansen, L. P., & Singleton, K. J. (1982). Generalized instrumental variables estimation of nonlinear rational expectations models. Econometrica, 50(5), 1269-1286. https://doi.org/10.2307/1911873
Hansen, L. P., Heaton, J., & Yaron, A. (1996). Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics, 14(3), 262-280. https://doi.org/10.1080/07350015.1996.10524656
Issler, J. V., & Piqueira, N. S. (2000). Estimating relative risk aversion, the discount rate, and the intertemporal elasticity of substitution in consumption for Brazil using three types of utility function. Brazilian Review of Econometrics, 20(2), 201-239. https://doi.org/10.12660/bre.v20n22000.2758
Jagannathan, R., Skoulakis, G., & Wang, Z. (2002). Generalized methods of moments: Applications in finance. Journal of Business and Economic Statistics, 20(4), 470-481. https://doi.org/10.1198/073500102288618612
Lucas, R. E., Jr. (1978). Asset prices in an exchange economy. Econometrica, 46(6), 1429-1445. https://doi.org/10.2307/1913837
Martins, H. C. (2021). Tutorial-articles: The importance of data and code sharing. Revista de Administração Contemporânea, 25(1), e200212. https://doi.org/10.1590/1982-7849rac2021200212
McFadden, D. (1989). A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica, 57(5), 995-1026. https://doi.org/10.2307/1913621
Mehra, R., & Prescott, E. C. (1985). The equity premium: A puzzle. Journal of Monetary Economics, 15(2), 145-161. https://doi.org/10.1016/0304-3932(85)90061-3
Nickell, S. (1981). Biases in dynamic models with fixed effects. Econometrica, 49(6), 1417–1426. https://doi.org/10.2307/1911408
Pedersen, A. R. (1995). A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scandinavian Journal of Statistics, 22(1), 55–71. Retrieved from https://www.jstor.org/stable/4616340
Stock, J. H., Wright, J., & Yogo, M. (2002). A survey of weak instruments and weak identification in generalized method of moments. Journal of Business & Economic Statistics, 20(4), 518-529.
Verbeek, M. (2004). A guide to modern econometrics. Chichester, England: John Wiley & Sons