IDEAS home Printed from https://ideas.repec.org/p/abo/neswpt/w0069.html
   My bibliography  Save this paper

Optimal Instruments in Time Series: A Survey

Author

Listed:
  • Stanislav Anatolyev

    (NES)

Abstract

This article surveys estimation in stationary time series models using the approach of optimal instrumentation. We review tools that allow construction and implementation of optimal instrumental variables estimators in various circumstances { in single- and multiperiod models, in the absence and presence of conditional heteroskedasticity, by considering linear and nonlinear instruments. We also discuss issues adjacent to the theme of optimal instruments. The article is directed primarily towards practitioners, but also may be found useful by econometric theorists and teachers of graduate econometrics.

Suggested Citation

  • Stanislav Anatolyev, 2005. "Optimal Instruments in Time Series: A Survey," Working Papers w0069, New Economic School (NES).
    • Handle: RePEc:abo:neswpt:w0069
    as

    Download full text from publisher

    File URL: https://www.nes.ru/files/Preprints-resh/WP69Anatolyev.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Stanislav Anatolyev, 2005. "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, Econometric Society, vol. 73(3), pages 983-1002, May.
    2. Smith, Richard J., 2005. "Automatic Positive Semidefinite Hac Covariance Matrix And Gmm Estimation," Econometric Theory, Cambridge University Press, vol. 21(1), pages 158-170, February.
    3. Robert F. Stambaugh, "undated". "Estimating Conditional Expectations When Volatility Fluctuates," Rodney L. White Center for Financial Research Working Papers 17-93, Wharton School Rodney L. White Center for Financial Research.
    4. Hansen, Bruce E & West, Kenneth D, 2002. "Generalized Method of Moments and Macroeconomics," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 460-469, October.
    5. Meddahi, Nour & Renault, Eric & Werker, Bas, 2006. "GARCH and irregularly spaced data," Economics Letters, Elsevier, vol. 90(2), pages 200-204, February.
    6. West, Kenneth D & Wilcox, David W, 1996. "A Comparison of Alternative Instrumental Variables Estimators of a Dynamic Linear Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 281-293, July.
    7. Martin S. Eichenbaum & Lars Peter Hansen & Kenneth J. Singleton, 1988. "A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 51-78.
    8. Broze, Laurence & Francq, Christian & Zakoian, Jean-Michel, 2001. "Non-redundancy of high order moment conditions for efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 71(3), pages 317-322, June.
    9. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(3), pages 547-583, June.
    10. Carrasco, Marine, 2004. "03.1.2 Redundancy of Lagged Regressors in a Conditionally Heteroskedastic Time Series Regression—Solution," Econometric Theory, Cambridge University Press, vol. 20(1), pages 228-229, February.
    11. Grossman, S J & Melino, Angelo & Shiller, Robert J, 1987. "Estimating the Continuous-Time Consumption-Based Asset-Pricing Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 315-327, July.
    12. Kim, Yangseon & Qian, Hailong & Schmidt, Peter, 1999. "Efficient GMM and MD estimation of autoregressive models," Economics Letters, Elsevier, vol. 62(3), pages 265-270, March.
    13. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    14. Anatolyev, Stanislav, 2003. "03.1.2. Redundancy of Lagged Regressors in a Conditionally Heteroskedastic Time Series Regression," Econometric Theory, Cambridge University Press, vol. 19(1), pages 225-226, February.
    15. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
    16. Hotz, V Joseph & Kydland, Finn E & Sedlacek, Guilherme L, 1988. "Intertemporal Preferences and Labor Supply," Econometrica, Econometric Society, vol. 56(2), pages 335-360, March.
    17. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    18. Marshall, David A, 1992. "Inflation and Asset Returns in a Monetary Economy," Journal of Finance, American Finance Association, vol. 47(4), pages 1315-1342, September.
    19. Meddahi, Nour & Renault, Eric, 2004. "Temporal aggregation of volatility models," Journal of Econometrics, Elsevier, vol. 119(2), pages 355-379, April.
    20. Heaton, John C. & Ogaki, Masao, 1991. "Efficiency bound calculations for a time series model, with conditional heteroskedasticity," Economics Letters, Elsevier, vol. 35(2), pages 167-171, February.
    21. West, Kenneth D, 2001. "On Optimal Instrumental Variables Estimation of Stationary Time Series Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 42(4), pages 1043-1050, November.
    22. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, January.
    23. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    24. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-853, October.
    25. Epstein, Larry G & Zin, Stanley E, 1991. "Substitution, Risk Aversion, and the Temporal Behavior of Consumption and Asset Returns: An Empirical Analysis," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 263-286, April.
    26. Dunn, Kenneth B. & Singleton, Kenneth J., 1986. "Modeling the term structure of interest rates under non-separable utility and durability of goods," Journal of Financial Economics, Elsevier, vol. 17(1), pages 27-55, September.
    27. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    28. Holman, Jill A, 1998. "GMM Estimation of a Money-in-the-Utility-Function Model: The Implications of Functional Forms," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 30(4), pages 679-698, November.
    29. N. Gregory Mankiw & Julio J. Rotemberg & Lawrence H. Summers, 1985. "Intertemporal Substitution in Macroeconomics," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 100(1), pages 225-251.
    30. Mark, Nelson C., 1985. "On time varying risk premia in the foreign exchange market: An econometric analysis," Journal of Monetary Economics, Elsevier, vol. 16(1), pages 3-18, July.
    31. Bates, Charles E. & White, Halbert, 1993. "Determination of Estimators with Minimum Asymptotic Covariance Matrices," Econometric Theory, Cambridge University Press, vol. 9(4), pages 633-648, August.
    32. Amemiya, Takeshi, 1974. "The nonlinear two-stage least-squares estimator," Journal of Econometrics, Elsevier, vol. 2(2), pages 105-110, July.
    33. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    34. Weber, Christian E, 2000. ""Rule-of-Thumb" Consumption, Intertemporal Substitution, and Risk Aversion," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(4), pages 497-502, October.
    35. Smith, David C., 1999. "Finite sample properties of tests of the Epstein-Zin asset pricing model," Journal of Econometrics, Elsevier, vol. 93(1), pages 113-148, November.
    36. Donald, Stephen G & Newey, Whitney K, 2001. "Choosing the Number of Instruments," Econometrica, Econometric Society, vol. 69(5), pages 1161-1191, September.
    37. Hahn, Jinyong, 1997. "Efficient estimation of panel data models with sequential moment restrictions," Journal of Econometrics, Elsevier, vol. 79(1), pages 1-21, July.
    38. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    39. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    40. Hayashi, Fumio & Sims, Christopher A, 1983. "Nearly Efficient Estimation of Time Series Models with Predetermined, but Not Exogenous, Instruments," Econometrica, Econometric Society, vol. 51(3), pages 783-798, May.
    41. Hall, Alastair R., 2004. "Generalized Method of Moments," OUP Catalogue, Oxford University Press, number 9780198775201.
    42. Alastair R. Hall & Fernanda P. M. Peixe, 2003. "A Consistent Method for the Selection of Relevant Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 22(3), pages 269-287, January.
    43. Dolado, Juan J., 1990. "Optimal Instrumental Variable Estimator of the AR Parameter of an ARMA(1.1)," Econometric Theory, Cambridge University Press, vol. 6(01), pages 117-119, March.
    44. Ghysels, Eric & Hall, Alastair, 2002. "Interview with Lars Peter Hansen," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 442-447, October.
    45. Imbens, Guido W, 2002. "Generalized Method of Moments and Empirical Likelihood," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 493-506, October.
    46. Kocherlakota, Narayana R., 1990. "On tests of representative consumer asset pricing models," Journal of Monetary Economics, Elsevier, vol. 26(2), pages 285-304, October.
    47. Weber, Christian E., 2002. "Intertemporal non-separability and "rule of thumb" consumption," Journal of Monetary Economics, Elsevier, vol. 49(2), pages 293-308, March.
    48. Mishkin, Frederic S., 1990. "What does the term structure tell us about future inflation?," Journal of Monetary Economics, Elsevier, vol. 25(1), pages 77-95, January.
    49. Anatolyev, Stanislav, 2007. "Redundancy Of Lagged Regressors Revisited," Econometric Theory, Cambridge University Press, vol. 23(2), pages 364-368, April.
    50. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    51. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    52. Donald W. K. Andrews, 1999. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 67(3), pages 543-564, May.
    53. Kuersteiner, Guido M., 2001. "Optimal instrumental variables estimation for ARMA models," Journal of Econometrics, Elsevier, vol. 104(2), pages 359-405, September.
    54. Hansen, Lars Peter & Singleton, Kenneth J, 1996. "Efficient Estimation of Linear Asset-Pricing Models with Moving Average Errors," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 53-68, January.
    55. Anatolyev, Stanislav, 1999. "Nonparametric estimation of nonlinear rational expectation models," Economics Letters, Elsevier, vol. 62(1), pages 1-6, January.
    56. Robinson, P M, 1987. "Asymptotically Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form," Econometrica, Econometric Society, vol. 55(4), pages 875-891, July.
    57. Hahn, Jinyong, 2002. "Optimal Inference With Many Instruments," Econometric Theory, Cambridge University Press, vol. 18(1), pages 140-168, February.
    58. Keane, Michael P & Runkle, David E, 1992. "On the Estimation of Panel-Data Models with Serial Correlation When Instruments Are Not Strictly Exogenous," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 1-9, January.
    59. Keane, Michael P & Runkle, David E, 1992. "On the Estimation of Panel-Data Models with Serial Correlation When Instruments Are Not Strictly Exogenous: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 26-29, January.
    60. Meddahi, N. & Renault, E. & Werker, B.J.M., 2003. "GARCH and Irregularly Spaced Data," Other publications TiSEM cde7c8bd-37ac-4692-836c-c, Tilburg University, School of Economics and Management.
    61. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521424318, September.
    62. West, Kenneth D., 2002. "Efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 75(3), pages 415-418, May.
    63. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 423-425, October.
    64. Dhaene, G., 2004. "03.1.2. Redundancy of Lagged Regressors in a Conditionally Heteroskedastic Time Series Regression—Solution," Econometric Theory, Cambridge University Press, vol. 20(1), pages 227-227, February.
    65. Fan, Yanqin & Ullah, Aman, 1999. "Asymptotic Normality of a Combined Regression Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 191-240, November.
    66. Fama, Eugene F, 1975. "Short-Term Interest Rates as Predictors of Inflation," American Economic Review, American Economic Association, vol. 65(3), pages 269-282, June.
    67. Corbae,Dean & Durlauf,Steven N. & Hansen,Bruce E. (ed.), 2006. "Econometric Theory and Practice," Cambridge Books, Cambridge University Press, number 9780521807234, September.
    68. Barnett,William A. & Powell,James & Tauchen,George E. (ed.), 1991. "Nonparametric and Semiparametric Methods in Econometrics and Statistics," Cambridge Books, Cambridge University Press, number 9780521370905, September.
    69. Ferson, Wayne E. & Constantinides, George M., 1991. "Habit persistence and durability in aggregate consumption: Empirical tests," Journal of Financial Economics, Elsevier, vol. 29(2), pages 199-240, October.
    70. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Lag Selection for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 457-487, July.
    71. Chamberlain, Gary, 1992. "Sequential Moment Restrictions in Panel Data: Comment," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(1), pages 20-26, January.
    72. Anatolyev, Stanislav, 2003. "The Form Of The Optimal Nonlinear Instrument For Multiperiod Conditional Moment Restrictions," Econometric Theory, Cambridge University Press, vol. 19(4), pages 602-609, August.
    73. Matyas,Laszlo (ed.), 1999. "Generalized Method of Moments Estimation," Cambridge Books, Cambridge University Press, number 9780521660136, September.
    74. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
    75. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    76. Tauchen, George, 1986. "Statistical Properties of Generalized Method-of-Moments Estimators of Structural Parameters Obtained from Financial Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(4), pages 397-416, October.
    77. Matyas,Laszlo (ed.), 1999. "Generalized Method of Moments Estimation," Cambridge Books, Cambridge University Press, number 9780521669672, September.
    78. Marimon, Ramon & Scott, Andrew (ed.), 1999. "Computational Methods for the Study of Dynamic Economies," OUP Catalogue, Oxford University Press, number 9780198294979.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stanislav Anatolyev, 2007. "Optimal instruments (in Russian)," Quantile, Quantile, issue 2, pages 61-69, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kenneth West & Ka-fu Wong & Stanislav Anatolyev, 2009. "Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 441-467.
    2. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    3. repec:bla:ecorec:v:91:y:2015:i::p:1-24 is not listed on IDEAS
    4. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    5. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    6. Kris Jacobs, 2001. "Estimating Nonseparable Preference Specifications for Asset Market Participants," CIRANO Working Papers 2001s-12, CIRANO.
    7. Julian Thimme, 2017. "Intertemporal Substitution In Consumption: A Literature Review," Journal of Economic Surveys, Wiley Blackwell, vol. 31(1), pages 226-257, February.
    8. Okui, Ryo, 2009. "The optimal choice of moments in dynamic panel data models," Journal of Econometrics, Elsevier, vol. 151(1), pages 1-16, July.
    9. Smith, David C., 1999. "Finite sample properties of tests of the Epstein-Zin asset pricing model," Journal of Econometrics, Elsevier, vol. 93(1), pages 113-148, November.
    10. Orazio P. Attanasio, 1998. "Consumption Demand," NBER Working Papers 6466, National Bureau of Economic Research, Inc.
    11. Gospodinov, Nikolay & Otsu, Taisuke, 2012. "Local GMM estimation of time series models with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 170(2), pages 476-490.
    12. Chamberlain, Gary, 2022. "Feedback in panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 4-20.
    13. Ferson, Wayne E. & Constantinides, George M., 1991. "Habit persistence and durability in aggregate consumption: Empirical tests," Journal of Financial Economics, Elsevier, vol. 29(2), pages 199-240, October.
    14. Jacobs, Kris, 2000. "Estimating Nonseparable Preference Specifications for Asset Market Participants," Econometric Society World Congress 2000 Contributed Papers 1472, Econometric Society.
    15. Xiaohong Chen & David Jacho-Chávez & Oliver Linton, 2012. "Averaging of moment condition estimators," CeMMAP working papers 26/12, Institute for Fiscal Studies.
    16. Hamori, Shigeyuki, 1998. "Defying the conventional wisdom: US consumers are found to be more risk averse than those of Japan," Economic Modelling, Elsevier, vol. 15(2), pages 217-235, April.
    17. Doran, Howard E. & Schmidt, Peter, 2006. "GMM estimators with improved finite sample properties using principal components of the weighting matrix, with an application to the dynamic panel data model," Journal of Econometrics, Elsevier, vol. 133(1), pages 387-409, July.
    18. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    19. Gregory, Allan W. & Lamarche, Jean-Francois & Smith, Gregor W., 2002. "Information-theoretic estimation of preference parameters: macroeconomic applications and simulation evidence," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 213-233, March.
    20. Yuichi Kitamura, 2006. "Empirical Likelihood Methods in Econometrics: Theory and Practice," CIRJE F-Series CIRJE-F-430, CIRJE, Faculty of Economics, University of Tokyo.
    21. Ai, Chunrong & Chen, Xiaohong, 2012. "The semiparametric efficiency bound for models of sequential moment restrictions containing unknown functions," Journal of Econometrics, Elsevier, vol. 170(2), pages 442-457.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:abo:neswpt:w0069. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Vladimir Ivanyukhin (email available below). General contact details of provider: https://edirc.repec.org/data/nerasru.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.