IDEAS home Printed from https://ideas.repec.org/p/umc/wpaper/0722.html
   My bibliography  Save this paper

Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error

Author

Abstract

We consider a cointegrating regression in which the integrated regressors are messy in the sense that they contain data that may be mismeasured, missing, observed at mixed frequencies, or have other irregularities that cause the econometrician to observe them with mildly nonstationary noise. Least squares estimation of the cointegrating vector is consistent. Existing prototypical variancebased estimation techniques, such as canonical cointegrating regression (CCR), are both consistent and asymptotically mixed normal. This result is robust to weakly dependent but possibly nonstationary disturbances.

Suggested Citation

  • J. Isaac Miller, 2007. "Cointegrating Regressions with Messy Regressors: Missingness, Mixed Frequency, and Measurement Error," Working Papers 0722, Department of Economics, University of Missouri, revised 15 Apr 2009.
    • Handle: RePEc:umc:wpaper:0722
    as

    Download full text from publisher

    File URL: https://drive.google.com/file/d/1STT29yfRsiZ2H4plMGnifi-nIG9GPhwp/view?usp=sharing
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Park, Joon Y, 1992. "Canonical Cointegrating Regressions," Econometrica, Econometric Society, vol. 60(1), pages 119-143, January.
    2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    3. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-1078, September.
    4. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    5. James Davidson & Robert de Jong, 1997. "Strong laws of large numbers for dependent heterogeneous processes: a synthesis of recent and new results," Econometric Reviews, Taylor & Francis Journals, vol. 16(3), pages 251-279.
    6. 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.
    7. Milton Friedman, 1962. "The Interpolation of Time Series by Related Series," NBER Books, National Bureau of Economic Research, Inc, number frie62-1.
    8. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-375, November.
    9. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    10. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    11. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    12. 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.
    13. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    14. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
    15. Fischer, Andreas M., 1990. "Cointegration and I(0) measurement error bias," Economics Letters, Elsevier, vol. 34(3), pages 255-259, November.
    16. Griliches, Zvi, 1986. "Economic data issues," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 3, chapter 25, pages 1465-1514, Elsevier.
    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. Mishra, Vinod & Smyth, Russell, 2010. "Female labor force participation and total fertility rates in the OECD: New evidence from panel cointegration and Granger causality testing," Journal of Economics and Business, Elsevier, vol. 62(1), pages 48-64, January.
    2. Andres, Antonio Rodriguez & Otero, Abraham & Amavilah, Voxi Heinrich, 2021. "Using Deep Learning Neural Networks to Predict the Knowledge Economy Index for Developing and Emerging Economies," MPRA Paper 109137, University Library of Munich, Germany.

    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. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed‐frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    2. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    3. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    4. Minxian, Yang, 1998. "System estimators of cointegrating matrix in absence of normalising information," Journal of Econometrics, Elsevier, vol. 85(2), pages 317-337, August.
    5. Li, Jia & Liao, Zhipeng, 2020. "Uniform nonparametric inference for time series," Journal of Econometrics, Elsevier, vol. 219(1), pages 38-51.
    6. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    7. Stypka, Oliver & Wagner, Martin & Grabarczyk, Peter & Kawka, Rafael, 2017. "The Asymptotic Validity of "Standard" Fully Modified OLS Estimation and Inference in Cointegrating Polynomial Regressions," Economics Series 333, Institute for Advanced Studies.
    8. Cheol-Keun Cho & Timothy J. Vogelsang, 2016. "Fixed- b Inference for Testing Structural Change in a Time Series Regression," Econometrics, MDPI, vol. 5(1), pages 1-26, December.
    9. Yicong Lin & Hanno Reuvers, 2019. "Efficient Estimation by Fully Modified GLS with an Application to the Environmental Kuznets Curve," Papers 1908.02552, arXiv.org, revised Aug 2020.
    10. Ghysels, Eric & Hill, Jonathan B. & Motegi, Kaiji, 2016. "Testing for Granger causality with mixed frequency data," Journal of Econometrics, Elsevier, vol. 192(1), pages 207-230.
    11. Aparicio, Felipe M. & Escribano, Álvaro & Mármol, Francesc, 1999. "A new instrumental variable approach for estimation and testing in fractional cointegrating regressions," DES - Working Papers. Statistics and Econometrics. WS 6298, Universidad Carlos III de Madrid. Departamento de Estadística.
    12. Davidson, James, 2020. "A new consistency proof for HAC variance estimators," Economics Letters, Elsevier, vol. 186(C).
    13. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    14. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    15. Bunzel, Helle, 2006. "FIXED-b ASYMPTOTICS IN SINGLE-EQUATION COINTEGRATION MODELS WITH ENDOGENOUS REGRESSORS," Econometric Theory, Cambridge University Press, vol. 22(4), pages 743-755, August.
    16. de Mello Luiz & Moccero Diego & Mogliani Matteo, 2013. "Do Latin American Central Bankers Behave Non-Linearly? The Experiences of Brazil, Chile, Colombia and Mexico," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 141-165, April.
    17. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    18. Erik Hjalmarsson, 2006. "Inference in Long-Horizon Regressions," International Finance Discussion Papers 853, Board of Governors of the Federal Reserve System (U.S.).
    19. Freeman, Mark C. & Groom, Ben & Panopoulou, Ekaterini & Pantelidis, Theologos, 2015. "Declining discount rates and the Fisher Effect: Inflated past, discounted future?," Journal of Environmental Economics and Management, Elsevier, vol. 73(C), pages 32-49.
    20. Kejriwal, Mohitosh & Perron, Pierre, 2010. "Testing for Multiple Structural Changes in Cointegrated Regression Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 503-522.

    More about this item

    Keywords

    cointegration; canonical cointegrating regression; near-epoch dependence; messy data; missing data; mixed-frequency data; measurement error; interpolation;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:umc:wpaper:0722. 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: Chao Gu (email available below). General contact details of provider: https://edirc.repec.org/data/edumous.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.