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Errors-in-Variables Estimation with No Instruments

Author

Listed:
  • Ramazan Gencay

    (Department of Economics, Simon Fraser University)

  • Nikola Gradojevic

    (Faculty of Business Administration, Lakehead University)

Abstract

This paper develops a wavelet (spectral) approach to estimate the parameters of a linear regression model where the regress and and the regressors are persistent processes and contain a measurement error. We propose a wavelet filtering approach which does not require instruments and yields unbiased and consistent estimates for the intercept and the slope parameters. Our Monte Carlo results also show that the wavelet approach is particularly effective when measurement errors for the regress and and the regressor are serially correlated. With this paper, we hope to bring a fresh perspective and stimulate further theoretical research in this area.

Suggested Citation

  • Ramazan Gencay & Nikola Gradojevic, 2009. "Errors-in-Variables Estimation with No Instruments," Working Paper series 30_09, Rimini Centre for Economic Analysis.
    • Handle: RePEc:rim:rimwps:30_09
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    References listed on IDEAS

    as
    1. Yongmiao Hong & Jin Lee, 2000. "Wavelet-based Estimation for Heteroskedasticity and Autocorrelation Consistent Variance-Covariance Matrices," Econometric Society World Congress 2000 Contributed Papers 1211, Econometric Society.
    2. Amemiya, Yasuo, 1985. "Instrumental variable estimator for the nonlinear errors-in-variables model," Journal of Econometrics, Elsevier, vol. 28(3), pages 273-289, June.
    3. Ramsey, James B. & Zhang, Zhifeng, 1997. "The analysis of foreign exchange data using waveform dictionaries," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 341-372, December.
    4. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    5. Ramazan Genay & Faruk Seļuk & Brandon Whitcher, 2003. "Systematic risk and timescales," Quantitative Finance, Taylor & Francis Journals, vol. 3(2), pages 108-116.
    6. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    7. Shanken, Jay, 1992. "On the Estimation of Beta-Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 5(1), pages 1-33.
    8. Elliott, Graham & Stock, James H., 1994. "Inference in Time Series Regression When the Order of Integration of a Regressor is Unknown," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 672-700, August.
    9. Schennach, Susanne M., 2004. "Exponential specifications and measurement error," Economics Letters, Elsevier, vol. 85(1), pages 85-91, October.
    10. Ramsey, J.B., 2002. "Wavelets in Economics and Finance: Past and Future," Working Papers 02-02, C.V. Starr Center for Applied Economics, New York University.
    11. Cashin, Paul & McDermott, C. John & Pattillo, Catherine, 2004. "Terms of trade shocks in Africa: are they short-lived or long-lived?," Journal of Development Economics, Elsevier, vol. 73(2), pages 727-744, April.
    12. Ľuboš Pástor & Robert F. Stambaugh, 1999. "Costs of Equity Capital and Model Mispricing," Journal of Finance, American Finance Association, vol. 54(1), pages 67-121, February.
    13. Sepanski, J. H. & Carroll, R. J., 1993. "Semiparametric quasilikelihood and variance function estimation in measurement error models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 223-256, July.
    14. Duchesne, Pierre, 2006. "On Testing For Serial Correlation With A Wavelet-Based Spectral Density Estimator In Multivariate Time Series," Econometric Theory, Cambridge University Press, vol. 22(4), pages 633-676, August.
    15. Gencay, Ramazan & Selcuk, Faruk & Whitcher, Brandon, 2005. "Multiscale systematic risk," Journal of International Money and Finance, Elsevier, vol. 24(1), pages 55-70, February.
    16. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(2), pages 343-366.
    17. Carmichael, Benoît & Coën, Alain, 2008. "Asset pricing models with errors-in-variables," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 778-788, September.
    18. Molinari, Francesca, 2008. "Partial identification of probability distributions with misclassified data," Journal of Econometrics, Elsevier, vol. 144(1), pages 81-117, May.
    19. Hong, Yongmiao & Lee, Jin, 2001. "One-Sided Testing For Arch Effects Using Wavelets," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1051-1081, December.
    20. Whitney K. Newey, 2001. "Flexible Simulated Moment Estimation Of Nonlinear Errors-In-Variables Models," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 616-627, November.
    21. Dagenais, Marcel G. & Dagenais, Denyse L., 1997. "Higher moment estimators for linear regression models with errors in the variables," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 193-221.
    22. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    23. John G. Cragg, 1994. "Making Good Inferences from Bad Data," Canadian Journal of Economics, Canadian Economics Association, vol. 27(4), pages 776-800, November.
    24. Duchesne, Pierre, 2006. "Testing for multivariate autoregressive conditional heteroskedasticity using wavelets," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2142-2163, December.
    25. Wayne E. Ferson & Dennis H. Locke, 1998. "Estimating the Cost of Capital Through Time: An Analysis of the Sources of Error," Management Science, INFORMS, vol. 44(4), pages 485-500, April.
    26. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    27. Yongmiao Hong & Chihwa Kao, 2004. "Wavelet-Based Testing for Serial Correlation of Unknown Form in Panel Models," Econometrica, Econometric Society, vol. 72(5), pages 1519-1563, September.
    28. Lee, Jin & Hong, Yongmiao, 2001. "Testing For Serial Correlation Of Unknown Form Using Wavelet Methods," Econometric Theory, Cambridge University Press, vol. 17(2), pages 386-423, April.
    29. Ramsey James B., 2002. "Wavelets in Economics and Finance: Past and Future," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 6(3), pages 1-29, November.
    30. Levi, Maurice D, 1973. "Errors in the Variables Bias in the Presence of Correctly Measured Variables," Econometrica, Econometric Society, vol. 41(5), pages 985-986, September.
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    Citations

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    Cited by:

    1. Huijun Guo & Youming Liu, 2017. "Strong consistency of wavelet estimators for errors-in-variables regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 121-144, February.
    2. Yi-Ting Chen & Edward W. Sun & Min-Teh Yu, 2018. "Risk Assessment with Wavelet Feature Engineering for High-Frequency Portfolio Trading," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 653-684, August.
    3. Reese, Simon & Li, Yushu, 2013. "Testing for Structural Breaks in the Presence of Data Perturbations: Impacts and Wavelet Based Improvements," Working Papers 2013:36, Lund University, Department of Economics.
    4. Chen Yi-Ting & Sun Edward W. & Yu Min-Teh, 2015. "Improving model performance with the integrated wavelet denoising method," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(4), pages 445-467, September.
    5. Yazgan, M. Ege & Özkan, Harun, 2015. "Detecting structural changes using wavelets," Finance Research Letters, Elsevier, vol. 12(C), pages 23-37.
    6. Bekiros Stelios & Nguyen Duc Khuong & Uddin Gazi Salah & Sjö Bo, 2015. "Business cycle (de)synchronization in the aftermath of the global financial crisis: implications for the Euro area," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 609-624, December.
    7. Gallegati, Marco & Ramsey, James B., 2013. "Bond vs stock market's Q: Testing for stability across frequencies and over time," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 138-150.
    8. Chakrabarty, Anindya & De, Anupam & Gunasekaran, Angappa & Dubey, Rameshwar, 2015. "Investment horizon heterogeneity and wavelet: Overview and further research directions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 45-61.
    9. Bruzda Joanna, 2015. "Amplitude and phase synchronization of European business cycles: a wavelet approach," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 625-655, December.

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    More about this item

    Keywords

    Cointegration; discrete wavelet transformation; maximum overlap wavelet transformation; energy decomposition; errors-in-variables; persistence;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • F31 - International Economics - - International Finance - - - Foreign Exchange
    • G0 - Financial Economics - - General
    • G1 - Financial Economics - - General Financial Markets

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