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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
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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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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  6. 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. [Downloadable!] (restricted)
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  7. Fama, Eugene F, 1990. " Stock Returns, Expected Returns, and Real Activity," Journal of Finance, American Finance Association, vol. 45(4), pages 1089-1108, September. [Downloadable!] (restricted)
  8. Martin D. D. Evans & Richard K. Lyons, 2007. "Exchange Rate Fundamentals and Order Flow," NBER Working Papers 13151, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  12. repec:fth:harver:1435 is not listed on IDEAS
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  15. 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.). [Downloadable!]
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