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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.

Suggested Citation

  • Jeremy J. Nalewaik, 2008. "Lack of signal error (LoSE) and implications for OLS regression: measurement error for macro data," Finance and Economics Discussion Series 2008-15, Board of Governors of the Federal Reserve System (U.S.).
  • Handle: RePEc:fip:fedgfe:2008-15
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    References listed on IDEAS

    as
    1. Dennis J. Fixler & Jeremy J. Nalewaik, 2007. "News, noise, and estimates of the "true" unobserved state of the economy," Finance and Economics Discussion Series 2007-34, Board of Governors of the Federal Reserve System (U.S.).
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    4. 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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    7. Dennis Fixler & Bruce Grimm, 2006. "GDP Estimates: Rationality Tests and Turning Point Performance," Journal of Productivity Analysis, Springer, vol. 25(3), pages 213-229, June.
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    16. Chen, Nai-Fu, 1991. " Financial Investment Opportunities and the Macroeconomy," Journal of Finance, American Finance Association, vol. 46(2), pages 529-554, June.
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    Keywords

    Error analysis (Mathematics) ; Gross domestic product;

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