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Simulated Score Methods and Indirect Inference for Continuous-time Models


  • Gallant, A. Ronald
  • Tauchen, George


We describe a simulated method of moments estimator that is implemented by choosing the vector valued moment function to be the expectation under the structural model of the score function of an auxiliary model, where the parameters of the auxiliary model are eliminated by replacing them with their quasi-maximum likelihood estimates. This leaves a moment vector depending only the parameters of the structural model. Structural parameter estimates are those parameter values that put the moment vector as closely to zero as possible in a suitable GMM metric. This methodology can also be interpreted as a practical computational strategy for implementing indirect inference. We argue that considerations from statistical science dictate that the auxiliary model should approximate the true data generating process as closely as possible and show that using the SNP model is one means to that end. When the view of close approximation is accepted in implementation, the methodology described is usually referred to as Efficient Method of Moments (EMM) in the literature because (i) the estimator is asymptotically as efficient as maximum likelihood under correct specification, and (ii) detection of model error is assured under incorrect specification. There are alternative views toward the desirability of close approximation to the data, which we discuss.

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  • Gallant, A. Ronald & Tauchen, George, 2002. "Simulated Score Methods and Indirect Inference for Continuous-time Models," Working Papers 02-09, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:02-09

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    1. Jean Imbs & Haroon Mumtaz & Morten O. Ravn & Hélène Rey, 2005. "PPP Strikes Back: Aggregation And the Real Exchange Rate," The Quarterly Journal of Economics, Oxford University Press, vol. 120(1), pages 1-43.
    2. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June.
    3. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January.
    4. Engel, Charles, 2000. "Long-run PPP may not hold after all," Journal of International Economics, Elsevier, vol. 51(2), pages 243-273, August.
    5. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    6. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
    7. Frankel, Jeffrey A. & Rose, Andrew K., 1996. "A panel project on purchasing power parity: Mean reversion within and between countries," Journal of International Economics, Elsevier, vol. 40(1-2), pages 209-224, February.
    8. Abuaf, Niso & Jorion, Philippe, 1990. " Purchasing Power Parity in the Long Run," Journal of Finance, American Finance Association, vol. 45(1), pages 157-174, March.
    9. Perron, Pierre & Rodriguez, Gabriel, 2003. "GLS detrending, efficient unit root tests and structural change," Journal of Econometrics, Elsevier, vol. 115(1), pages 1-27, July.
    10. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56.
    11. Lopez, Claude & Murray, Christian J & Papell, David H, 2005. "State of the Art Unit Root Tests and Purchasing Power Parity," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(2), pages 361-369, April.
    12. Elliott, Graham & Stock, James H., 2001. "Confidence intervals for autoregressive coefficients near one," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 155-181, July.
    13. Nikolay Gospodinov, 2001. "Asymptotic Confidence Intervals for Impulse Responses of Near-Integrated Processes: An Application to Purchasing Power Parity," Computing in Economics and Finance 2001 136, Society for Computational Economics.
    14. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    15. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    16. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
    17. Cheung, Yin-Wong & Lai, Kon S., 2000. "On the purchasing power parity puzzle," Journal of International Economics, Elsevier, vol. 52(2), pages 321-330, December.
    18. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    19. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June.
    20. Graham Elliott & Elena Pesavento, 2005. "Higher Power Tests for Bilateral Failure of PPP after 1973," Emory Economics 0502, Department of Economics, Emory University (Atlanta).
    21. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    22. Lutz Kilian & Tao Zha, 2002. "Quantifying the uncertainty about the half-life of deviations from PPP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 107-125.
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    Cited by:

    1. Peter Fuleky & Eric Zivot, 2014. "Indirect inference based on the score," Econometrics Journal, Royal Economic Society, vol. 17(3), pages 383-393, October.
    2. Manuel Santos, 2007. "Consistency Properties of a Simulation-Based Estimator for Dynamic Processes," Working Papers 0705, University of Miami, Department of Economics.
    3. Jón Daníelsson & Francisco Peñaranda, 2011. "On The Impact Of Fundamentals, Liquidity, And Coordination On Market Stability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(3), pages 621-638, August.
    4. Ravi Bansal & A. Ronald Gallant & George Tauchen, 2007. "Rational Pessimism, Rational Exuberance, and Asset Pricing Models," Review of Economic Studies, Oxford University Press, vol. 74(4), pages 1005-1033.
    5. In Kim & In-Seok Baek & Jaesun Noh & Sol Kim, 2007. "The role of stochastic volatility and return jumps: reproducing volatility and higher moments in the KOSPI 200 returns dynamics," Review of Quantitative Finance and Accounting, Springer, vol. 29(1), pages 69-110, July.
    6. Michael Creel, 2008. "Estimation of Dynamic Latent Variable Models Using Simulated Nonparametric Moments," UFAE and IAE Working Papers 725.08, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC), revised 02 Jun 2008.
    7. Torben G. Andersen & Tim Bollerslev & Nour Meddahi, 2004. "Analytical Evaluation Of Volatility Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(4), pages 1079-1110, November.
    8. Detemple, Jerome & Garcia, Rene & Rindisbacher, Marcel, 2006. "Asymptotic properties of Monte Carlo estimators of diffusion processes," Journal of Econometrics, Elsevier, vol. 134(1), pages 1-68, September.

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