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Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parameters

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  • Benedikt M. Poetscher

    () (Institut für Statistik, Universitat Wien, Austria)

Abstract

Important estimation problems in econometrics like estimating the value of a spectral density at frequency zero, which appears in the econometrics literature in the guises of heteroskedasticity and autocorrelation consistent variance estimation and long run variance estimation, are shown to be "ill-posed" estimation problems. A prototypical result obtained in the paper is that the minimax risk for estimating the value of the spectral density at frequency zero is infinite regardless of sample size, and that confidence sets are close to being uninformative. In this result the maximum risk is over commonly used specifications for the set of feasible data generating processes. The consequences for inference on unit roots and cointegration are discussed. Similar results for persistence estimation and estimation of the long memory parameter are given. All these results are obtained as special cases of a more general theory developed for abstract estimation problems, which readily also allows for the treatment of other ill-posed estimation problems such as, e.g., nonparametric regression or density estimation. Copyright The Econometric Society 2002.

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  • Benedikt M. Poetscher, 2002. "Lower Risk Bounds and Properties of Confidence Sets for Ill-Posed Estimation Problems with Applications to Spectral Density and Persistence Estimation, Unit Roots, and Estimation of Long Memory Parame," Econometrica, Econometric Society, vol. 70(3), pages 1035-1065, May.
  • Handle: RePEc:ecm:emetrp:v:70:y:2002:i:3:p:1035-1065
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    1. Härdle, W. & Marron, S.J., "undated". "Semiparametric comparison of regression curves," CORE Discussion Papers RP 890, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, pages 945-973.
    3. Hal R. Varian, 1983. "Non-parametric Tests of Consumer Behaviour," Review of Economic Studies, Oxford University Press, vol. 50(1), pages 99-110.
    4. Wolfgang HÄRDLE & O. LINTON, 1995. "Nonparametric Regression," SFB 373 Discussion Papers 1995,29, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    5. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    6. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, pages 931-954.
    7. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, pages 611-618.
    8. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, pages 565-604.
    9. A. P. Lerner, 1935. "A Note on the Theory of Price Index Numbers," Review of Economic Studies, Oxford University Press, vol. 3(1), pages 50-56.
    10. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    11. James J. Heckman, 1974. "Effects of Child-Care Programs on Women's Work Effort," NBER Chapters,in: Marriage, Family, Human Capital, and Fertility, pages 136-169 National Bureau of Economic Research, Inc.
    12. Diewert, Erwin, 2007. "Index Numbers," Economics working papers diewert-07-01-03-08-17-23, Vancouver School of Economics, revised 31 Jan 2007.
    13. Hausman, Jerry A & Newey, Whitney K, 1995. "Nonparametric Estimation of Exact Consumers Surplus and Deadweight Loss," Econometrica, Econometric Society, vol. 63(6), pages 1445-1476, November.
    14. Afriat, S N, 1973. "On a System of Inequalities in Demand Analysis: An Extension of the Classical Method," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(2), pages 460-472, June.
    15. James Banks & Richard Blundell & Arthur Lewbel, 1994. "Tax reform and welfare measurement: do we need demand system estimation?," IFS Working Papers W94/11, Institute for Fiscal Studies.
    16. Holly, Alberto, 1982. "A Remark on Hausman's Specification Test," Econometrica, Econometric Society, vol. 50(3), pages 749-759, May.
    17. Banks, James & Blundell, Richard & Lewbel, Arthur, 1996. "Tax Reform and Welfare Measurement: Do We Need Demand System Estimation?," Economic Journal, Royal Economic Society, vol. 106(438), pages 1227-1241, September.
    18. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, pages 115-145.
    19. Pendakur, Krishna, 1998. "Semiparametric estimates and tests of base-independent equivalence scales," Journal of Econometrics, Elsevier, pages 1-40.
    20. Sippel, Reinhard, 1997. "An Experiment on the Pure Theory of Consumer's Behaviour," Economic Journal, Royal Economic Society, vol. 107(444), pages 1431-1444, September.
    21. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation for Research in Economics, Yale University.
    22. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics,in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339 Elsevier.
    23. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, pages 711-730.
    24. Brown, Bryan W & Walker, Mary Beth, 1989. "The Random Utility Hypothesis and Inference in Demand Systems," Econometrica, Econometric Society, vol. 57(4), pages 815-829, July.
    25. Diewert, W. E. & Parkan, C., 1985. "Tests for the consistency of consumer data," Journal of Econometrics, Elsevier, pages 127-147.
    26. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-999, September.
    27. Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
    28. W. E. Diewert, 1973. "Afriat and Revealed Preference Theory," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 419-425.
    29. Famulari, Melissa, 1995. "A Household-Based, Nonparametric Test of Demand Theory," The Review of Economics and Statistics, MIT Press, pages 372-382.
    30. Richard Blundell & Alan Duncan, 1998. "Kernel Regression in Empirical Microeconomics," Journal of Human Resources, University of Wisconsin Press, pages 62-87.
    31. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, pages 312-326.
    32. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., pages 435-461.
    33. Whitney K. Newey & James L. Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-6, Massachusetts Institute of Technology (MIT), Department of Economics.
    34. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, pages 445-458.
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    Cited by:

    1. DUFOUR, Jean-Marie & JOUINI, Tarek, 2005. "Finite-Sample Simulation-Based Inference in VAR Models with Applications to Order Selection and Causality Testing," Cahiers de recherche 16-2005, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Zhijie Xiao & Luiz Renato Lima, 2007. "Testing Covariance Stationarity," Econometric Reviews, Taylor & Francis Journals, pages 643-667.
    3. Dufour, Jean-Marie & Jouini, Tarek, 2006. "Finite-sample simulation-based inference in VAR models with application to Granger causality testing," Journal of Econometrics, Elsevier, pages 229-254.
    4. Davidson James & Rambaccussing Dooruj, 2015. "A Test of the Long Memory Hypothesis Based on Self-Similarity," Journal of Time Series Econometrics, De Gruyter, pages 115-141.
    5. Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2007. "A simple, robust and powerful test of the trend hypothesis," Journal of Econometrics, Elsevier, pages 1302-1330.
    6. Preinerstorfer, David & Pötscher, Benedikt M., 2016. "On Size And Power Of Heteroskedasticity And Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, pages 261-358.
    7. Muller, Ulrich K., 2007. "A theory of robust long-run variance estimation," Journal of Econometrics, Elsevier, pages 1331-1352.
    8. Xiao, Zhijie, 2012. "Robust inference in nonstationary time series models," Journal of Econometrics, Elsevier, pages 211-223.
    9. Tsay, Wen-Jen, 2004. "Testing for contemporaneous correlation of disturbances in seemingly unrelated regressions with serial dependence," Economics Letters, Elsevier, pages 69-76.

    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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