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Instrumental Variables Estimation of Heteroskedastic Linear Models Using All Lags of Instruments

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  • Kenneth West
  • Ka-fu Wong
  • Stanislav Anatolyev

Abstract

We propose and evaluate a technique for instrumental variables estimation of linear models with conditional heteroskedasticity. The technique uses approximating parametric models for the projection of right-hand side variables onto the instrument space, and for conditional heteroskedasticity and serial correlation of the disturbance. Use of parametric models allows one to exploit information in all lags of instruments, unconstrained by degrees of freedom limitations. Analytical calculations and simulations indicate that sometimes there are large asymptotic and finite sample efficiency gains relative to conventional estimators (Hansen, 1982), and modest gains or losses depending on data generating process and sample size relative to quasi-maximum likelihood. These results are robust to minor misspecification of the parametric models used by our estimator. [Supplemental materials are available for this article. Go to the publisher's online edition of Econometric Reviews for the following free supplemental resources: two appendices containing additional results from this article.]

Suggested Citation

  • 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.
  • Handle: RePEc:taf:emetrv:v:28:y:2009:i:5:p:441-467
    DOI: 10.1080/07474930802467241
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    as
    1. 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.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. 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.
    4. 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.
    5. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
    6. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    7. Ball, Laurence & Croushore, Dean, 2003. " Expectations and the Effects of Monetary Policy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 35(4), pages 473-484, August.
    8. 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.
    9. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May.
    10. Raquel Carrasco & José M. Labeaga & J. David López-Salido, 2005. "Consumption and Habits: Evidence from Panel Data," Economic Journal, Royal Economic Society, vol. 115(500), pages 144-165, January.
    11. Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
    12. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    13. 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.
    14. West, Kenneth D. & Wilcox, David W., 1994. "Estimation and inference in the linear-quadratic inventory model," Journal of Economic Dynamics and Control, Elsevier, vol. 18(3-4), pages 897-908.
    15. Matthew D. Shapiro, 1986. "The Dynamic Demand for Capital and Labor," The Quarterly Journal of Economics, Oxford University Press, vol. 101(3), pages 513-542.
    16. Jonathan A. Parker & Christian Julliard, 2005. "Consumption Risk and the Cross Section of Expected Returns," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 185-222, February.
    17. Hall, Robert E, 1988. "Intertemporal Substitution in Consumption," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 339-357, April.
    18. Campbell, John Y & Mankiw, N Gregory, 1990. "Permanent Income, Current Income, and Consumption," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(3), pages 265-279, July.
    19. Bates, Charles E. & White, Halbert, 1993. "Determination of Estimators with Minimum Asymptotic Covariance Matrices," Econometric Theory, Cambridge University Press, vol. 9(04), pages 633-648, August.
    20. Wouter J. Den Haan & Andrew T. Levin, 1995. "Inferences from parametric and non-parametric covariance matrix estimation procedures," International Finance Discussion Papers 504, Board of Governors of the Federal Reserve System (U.S.).
    21. Jeffrey C. Fuhrer, 2006. "Intrinsic and Inherited Inflation Persistence," International Journal of Central Banking, International Journal of Central Banking, vol. 2(3), September.
    22. Mishkin, Frederic S., 1992. "Is the Fisher effect for real? : A reexamination of the relationship between inflation and interest rates," Journal of Monetary Economics, Elsevier, vol. 30(2), pages 195-215, November.
    23. 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.
    24. Newey, Whitney K., 1988. "Adaptive estimation of regression models via moment restrictions," Journal of Econometrics, Elsevier, vol. 38(3), pages 301-339, July.
    25. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    26. Ang, Andrew & Bekaert, Geert & Wei, Min, 2007. "Do macro variables, asset markets, or surveys forecast inflation better?," Journal of Monetary Economics, Elsevier, vol. 54(4), pages 1163-1212, May.
    27. repec:cup:etheor:v:9:y:1993:i:4:p:633-48 is not listed on IDEAS
    28. Kennan, John, 1979. "The Estimation of Partial Adjustment Models with Rational Expectations," Econometrica, Econometric Society, vol. 47(6), pages 1441-1455, November.
    29. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-763, May.
    30. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    31. Stanislav Anatolyev, 2005. "GMM, GEL, Serial Correlation, and Asymptotic Bias," Econometrica, Econometric Society, vol. 73(3), pages 983-1002, May.
    32. West, Kenneth D., 1986. "Full-versus limited-information estimation of a rational-expectations model: Some numerical comparisons," Journal of Econometrics, Elsevier, vol. 33(3), pages 367-385, December.
    33. Kuersteiner, Guido M., 2002. "Efficient Iv Estimation For Autoregressive Models With Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 18(03), pages 547-583, June.
    34. 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.
    35. Breusch, Trevor & Qian, Hailong & Schmidt, Peter & Wyhowski, Donald, 1999. "Redundancy of moment conditions," Journal of Econometrics, Elsevier, vol. 91(1), pages 89-111, July.
    36. Brown, Bryan W & Maital, Shlomo, 1981. "What Do Economists Know? An Empirical Study of Experts' Expectations," Econometrica, Econometric Society, vol. 49(2), pages 491-504, March.
    37. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    38. Ramey, Valerie A, 1991. "Nonconvex Costs and the Behavior of Inventories," Journal of Political Economy, University of Chicago Press, vol. 99(2), pages 306-334, April.
    39. Oliner, Stephen D. & Rudebusch, Glenn D. & Sichel, Daniel, 1996. "The Lucas critique revisited assessing the stability of empirical Euler equations for investment," Journal of Econometrics, Elsevier, vol. 70(1), pages 291-316, January.
    40. 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.
    41. 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.
    42. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    43. Qiang Zhang & Masao Ogaki, 2004. "Decreasing Relative Risk Aversion, Risk Sharing, and the Permanent Income Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 421-430, October.
    44. McDonald, James B. & Newey, Whitney K., 1988. "Partially Adaptive Estimation of Regression Models via the Generalized T Distribution," Econometric Theory, Cambridge University Press, vol. 4(03), pages 428-457, December.
    45. Chinn, Menzie D., 2006. "The (partial) rehabilitation of interest rate parity in the floating rate era: Longer horizons, alternative expectations, and emerging markets," Journal of International Money and Finance, Elsevier, vol. 25(1), pages 7-21, February.
    46. Jacob Boudoukh & Matthew Richardson & Robert Whitelaw, 2005. "The Myth of Long-Horizon Predictability," NBER Working Papers 11841, National Bureau of Economic Research, Inc.
    47. Anatolyev, Stanislav, 2003. "The Form Of The Optimal Nonlinear Instrument For Multiperiod Conditional Moment Restrictions," Econometric Theory, Cambridge University Press, vol. 19(04), pages 602-609, August.
    48. 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.
    49. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:

    1. Hansen, Lars Peter, 2013. "Uncertainty Outside and Inside Economic Models," Nobel Prize in Economics documents 2013-7, Nobel Prize Committee.
    2. David Laibson & Andrea Repetto & Jeremy Tobacman, 2005. "Estimating Discount Functions with Consumption Choices over the Lifecycle," Levine's Bibliography 784828000000000643, UCLA Department of Economics.
    3. Salem Abo-Zaid & Anastasia Zervou, 2016. "Financing of Firms, Labor Reallocation and the Distributional Role of Monetary Policy," Working Papers 20161020_001, Texas A&M University, Department of Economics.
    4. Elena Corallo, 2005. "The effect of the war risk: a comparison of the consequences of the two Iraq wars on some financial variables," LIUC Papers in Economics 171, Cattaneo University (LIUC).
    5. Stanislav Anatolyev, 2007. "Optimal Instruments In Time Series: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 21(1), pages 143-173, February.
    6. 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.
    7. Arellano, Manuel, 2016. "Modelling optimal instrumental variables for dynamic panel data models," Research in Economics, Elsevier, vol. 70(2), pages 238-261.
    8. West, Kenneth D., 2002. "Efficient GMM estimation of weak AR processes," Economics Letters, Elsevier, vol. 75(3), pages 415-418, May.
    9. Okui, Ryo, 2011. "Instrumental variable estimation in the presence of many moment conditions," Journal of Econometrics, Elsevier, vol. 165(1), pages 70-86.
    10. Kuersteiner, Guido M., 2012. "Kernel-weighted GMM estimators for linear time series models," Journal of Econometrics, Elsevier, vol. 170(2), pages 399-421.
    11. Mardi Dungey & Vitali Alexeev & Jing Tian & Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91, pages 1-24, June.

    More about this item

    Keywords

    Efficiency; Efficiency bounds; Instrumental variables; Optimal instrument; Stationary time series;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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