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Bounds on the Variances of Specification Errors in Models with Expectations

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  • Steven N. Durlauf
  • Robert E. Hall

Abstract

Under rather general conditions, observed covariances place a useful lower bound on the variance of the misspecification or noise III models based on expectations. Such models are widely used for securities prices, exchange rates, consumption, and output. For a correctly specified model, the lower bound will be zero. We construct an optimal bound on model noise that captures the complete set of testable restrictions on an expectations based model. Many specification tests for asset prices are easily interpreted as estimates of this lower bound. As a result, the power of different tests may be ranked according to the information restrictions employed in constructing noise estimates. Our results show that specification tests which use the history of lagged dependent variables are usually better able to uncover model noise than based on information sets that exclude those variables.

Suggested Citation

  • Steven N. Durlauf & Robert E. Hall, 1989. "Bounds on the Variances of Specification Errors in Models with Expectations," NBER Working Papers 2936, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:2936 Note: EFG
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    Cited by:

    1. Engsted, Tom, 2003. "Misspecification versus bubbles in hyperinflation data: comment," Journal of International Money and Finance, Elsevier, vol. 22(4), pages 441-451, August.
    2. Hansen, Lars Peter & Jagannathan, Ravi, 1997. " Assessing Specification Errors in Stochastic Discount Factor Models," Journal of Finance, American Finance Association, vol. 52(2), pages 557-590, June.
    3. Mark A. Hooker, 1997. "Misspecification versus bubbles in hyperinflation data: Monte Carlo and interwar European evidence," Finance and Economics Discussion Series 1997-49, Board of Governors of the Federal Reserve System (U.S.).
    4. Engsted, Tom, 2002. "Measuring noise in the Permanent Income Hypothesis," Journal of Macroeconomics, Elsevier, vol. 24(3), pages 353-370, September.
    5. Hooker, Mark A., 2000. "Misspecification versus bubbles in hyperinflation data: Monte Carlo and interwar European evidence," Journal of International Money and Finance, Elsevier, vol. 19(4), pages 583-600, August.
    6. Qin Xiao & Gee Kwang Randolph Tan, 2007. "Signal Extraction with Kalman Filter: A Study of the Hong Kong Property Price Bubbles," Urban Studies, Urban Studies Journal Limited, vol. 44(4), pages 865-888, April.
    7. Engsted, Tom, 2002. " Measures of Fit for Rational Expectations Models," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 301-355, July.
    8. Fahmy, Yasser A. F. & Kandil, Magda, 2003. "The Fisher effect: new evidence and implications," International Review of Economics & Finance, Elsevier, vol. 12(4), pages 451-465.
    9. Engsted, Tom & Tanggaard, Carsten, 2001. "The Danish stock and bond markets: comovement, return predictability and variance decomposition," Journal of Empirical Finance, Elsevier, vol. 8(3), pages 243-271, July.
    10. Robert E. Hall, 1989. "Spontaneous Volatility of Output and Investment," NBER Working Papers 3144, National Bureau of Economic Research, Inc.
    11. Engsted, Tom, 1998. "Money Demand During Hyperinflation: Cointegration, Rational Expectations, and the Importance of Money Demand Shocks," Journal of Macroeconomics, Elsevier, vol. 20(3), pages 533-552, July.

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