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A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information

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  • Atukorala, Ranjani
  • Sriananthakumar, Sivagowry

Abstract

In order to better understand the economy and conduct policy analysis, both econometricians and decision makers are interested in effective inferences using econometric models. Because of the complexity of economic data, econometricians heavily rely on asymptotic theory when making statistical inferences. However, the use of asymptotic approximations to the distributions of test statistics and estimators is not always successful. This paper illustrates the use of the Kullback-Leibler information (KLI) measure to assess the relative quality of two asymptotic approximations to an unknown distribution from which we can obtain simple random drawings. The illustration involves comparing the large-sample and small-disturbance asymptotic distributions under the null hypothesis of a t statistic from the dynamic linear regression model. We find convincing evidence in favour of the use of p values and critical values from the small-disturbance Student's t distribution, rather than from the large-sample standard normal distribution, in this case. This simple KLI measure has considerable potential. For example, it can guide us to conditions under which asymptotic approximations are reasonable and to circumstances when it may be inappropriate to rely totally on asymptotic approximations.

Suggested Citation

  • Atukorala, Ranjani & Sriananthakumar, Sivagowry, 2015. "A comparison of the accuracy of asymptotic approximations in the dynamic regression model using Kullback-Leibler information," Economic Modelling, Elsevier, vol. 45(C), pages 169-174.
    • Handle: RePEc:eee:ecmode:v:45:y:2015:i:c:p:169-174
    DOI: 10.1016/j.econmod.2014.11.021
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    as
    1. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    2. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    3. King, Maxwell L., 1983. "Testing for autoregressive against moving average errors in the linear regression model," Journal of Econometrics, Elsevier, vol. 21(1), pages 35-51, January.
    4. Maxwell L. King & Michael McAleer, 1987. "Further Results on Testing AR (1) Against MA (1) Disturbances in the Linear Regression Model," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 649-663.
    5. Kiviet, Jan F. & Phillips, Garry D.A., 2012. "Higher-order asymptotic expansions of the least-squares estimation bias in first-order dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3705-3729.
    6. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, January.
    7. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    8. Kadane, Joseph B, 1974. "Testing a Subset of the Overidentifying Restrictions," Econometrica, Econometric Society, vol. 42(5), pages 853-867, September.
    9. King, M.L. & Harris, D.C., 1995. "The Applications of the Durbin-Watson Test to the Dynamic Regression Model Under Normal and Non-Normal Errors," Monash Econometrics and Business Statistics Working Papers 6/95, Monash University, Department of Econometrics and Business Statistics.
    10. Kiviet, J.F. & Phillips, G.D.A., 1998. "Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root," Discussion Papers 9909, University of Exeter, Department of Economics.
    11. repec:ilo:ilowps:168467 is not listed on IDEAS
    12. Nankervis, J.C. & Savin, N.E., 1987. "Finite Sample Distributions of t and F Statistics in an AR(1) Model with Anexogenous Variable," Econometric Theory, Cambridge University Press, vol. 3(3), pages 387-408, June.
    13. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    14. Vougas, Dimitrios V., 2006. "Remark on the asymptotic distribution of the OLS estimator in a simple Gaussian unit-root autoregression," Statistics & Probability Letters, Elsevier, vol. 76(1), pages 27-34, January.
    15. Srivastava, V K, et al, 1980. "A Numerical Comparison of Exact, Large-Sample and Small Disturbance Approximations of Properties of k-Class Estimators," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 249-252, February.
    16. Sriananthakumar, Sivagowry & King, Maxwell L., 2006. "A new approximate point optimal test of a composite null hypothesis," Journal of Econometrics, Elsevier, vol. 130(1), pages 101-122, January.
    17. Inder, Brett, 1986. "An Approximation to the Null Distribution of the Durbin-Watson Statistic in Models Containing Lagged Dependent Variables," Econometric Theory, Cambridge University Press, vol. 2(3), pages 413-428, December.
    18. Kiviet, Jan F. & Phillips, Garry D.A., 1993. "Alternative Bias Approximations in Regressions with a Lagged-Dependent Variable," Econometric Theory, Cambridge University Press, vol. 9(1), pages 62-80, January.
    19. King, Maxwell L. & Wu, Ping X., 1991. "Small-disturbance asymptotics and the Durbin-Watson and related tests in the dynamic regression model," Journal of Econometrics, Elsevier, vol. 47(1), pages 145-152, January.
    20. anonymous, 1976. "The economy in 1975," Federal Reserve Bulletin, Board of Governors of the Federal Reserve System (U.S.), issue Feb, pages 71-81.
    21. Morimune, Kimio & Tsukuda, Yoshihiko, 1984. "Testing a Subset of Coefficients in a Structural Equation," Econometrica, Econometric Society, vol. 52(2), pages 427-448, March.
    22. Lô, Serigne N. & Ronchetti, Elvezio, 2012. "Robust small sample accurate inference in moment condition models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3182-3197.
    23. Sriananthakumar, Sivagowry, 2013. "Testing linear regression model with AR(1) errors against a first-order dynamic linear regression model with white noise errors: A point optimal testing approach," Economic Modelling, Elsevier, vol. 33(C), pages 126-136.
    24. Ullah, Aman, 2002. "Uses of entropy and divergence measures for evaluating econometric approximations and inference," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 313-326, March.
    25. Inder, Brett A, 1990. "A New Test for Autocorrelation in the Disturbances of the Dynamic Linear Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 341-354, May.
    26. Silvapulle, Paramsothy & King, Maxwell L, 1991. "Testing Moving Average against Autoregressive Disturbances in the Linear-Regression Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(3), pages 329-335, July.
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