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Lack of signal error (LoSE) and implications for OLS regression: measurement error for macro data

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  • Jeremy J. Nalewaik
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    Abstract

    This paper proposes a simple generalization of the classical measurement error model, introducing new measurement errors that subtract signal from the true variable of interest, in addition to the usual classical measurement errors (CME) that add noise. The effect on OLS regression of these lack of signal errors (LoSE) is opposite the conventional wisdom about CME: while CME in the explanatory variables causes attenuation bias, LoSE in the dependent variable, not the explanatory variables, causes a similar bias under some conditions. In addition, LoSE in the dependent variable shrinks the variance of the regression residuals, making inference potentially misleading. The paper provides evidence that LoSE is an important source of error in US macroeconomic quantity data such as GDP growth, illustrates downward bias in regressions of GDP growth on asset prices, and provides recommendations for econometric practice.

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    Bibliographic Info

    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2008-15.

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    Date of creation: 2008
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    Handle: RePEc:fip:fedgfe:2008-15

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    Keywords: Error analysis (Mathematics) ; Gross domestic product;

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    1. Fama, Eugene F, 1990. " Stock Returns, Expected Returns, and Real Activity," Journal of Finance, American Finance Association, vol. 45(4), pages 1089-1108, September.
    2. Jon Faust & John H. Rogers & Shing-Yi B. Wang & Jonathan H. Wright, 2003. "The high-frequency response of exchange rates and interest rates to macroeconomic announcements," International Finance Discussion Papers 784, Board of Governors of the Federal Reserve System (U.S.).
    3. repec:fth:harver:1435 is not listed on IDEAS
    4. Dennis J. Fixler & Jeremy Nalewaik, 2010. "News, Noise, and Estimates of the "True" Unobserved State of the Economy," BEA Working Papers 0068, Bureau of Economic Analysis.
    5. Martin D.D. Evans & Richard K. Lyons, 2005. "Meese-Rogoff Redux: Micro-Based Exchange Rate Forecasting," NBER Working Papers 11042, National Bureau of Economic Research, Inc.
    6. Dennis Fixler & Bruce Grimm, 2006. "GDP Estimates: Rationality Tests and Turning Point Performance," Journal of Productivity Analysis, Springer, vol. 25(3), pages 213-229, 06.
    7. Christian Broda & David E. Weinstein, 2010. "Product Creation and Destruction: Evidence and Price Implications," American Economic Review, American Economic Association, vol. 100(3), pages 691-723, June.
    8. Miles S. Kimball & Claudia R. Sahm & Matthew D. Shapiro, 2007. "Imputing Risk Tolerance from Survey Responses," NBER Working Papers 13337, National Bureau of Economic Research, Inc.
    9. John Y. Campbell & N. Gregory Mankiw, 1989. "Consumption, Income, and Interest Rates: Reinterpreting the Time Series Evidence," NBER Working Papers 2924, National Bureau of Economic Research, Inc.
    10. Estrella, Arturo & Hardouvelis, Gikas A, 1991. " The Term Structure as a Predictor of Real Economic Activity," Journal of Finance, American Finance Association, vol. 46(2), pages 555-76, June.
    11. N. Gregory Mankiw & Matthew D. Shapiro, 1986. "News or Noise? An Analysis of GNP Revisions," NBER Working Papers 1939, National Bureau of Economic Research, Inc.
    12. Karen E. Dynan & Douglas Elmendorf, 2001. "Do provisional estimates of output miss economic turning points?," Finance and Economics Discussion Series 2001-52, Board of Governors of the Federal Reserve System (U.S.).
    13. Martin D. D. Evans & Richard K. Lyons, 2007. "Exchange Rate Fundamentals and Order Flow," NBER Working Papers 13151, National Bureau of Economic Research, Inc.
    14. Chen, Nai-Fu, 1991. " Financial Investment Opportunities and the Macroeconomy," Journal of Finance, American Finance Association, vol. 46(2), pages 529-54, June.
    15. Jeremy J. Nalewaik, 2007. "Incorporating vintage differences and forecasts into Markov switching models," Finance and Economics Discussion Series 2007-23, Board of Governors of the Federal Reserve System (U.S.).
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