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Bounds on the Variances of Specification Errors in Models with Expectations

  • Steven N. Durlauf
  • Robert E. Hall

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.

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File URL: http://www.nber.org/papers/w2936.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 2936.

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Date of creation: Apr 1989
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Handle: RePEc:nbr:nberwo:2936
Note: EFG
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  1. Andrew W. Lo & Craig A. MacKinlay, . "Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test (Revised: 29-87)," Rodney L. White Center for Financial Research Working Papers 5-87, Wharton School Rodney L. White Center for Financial Research.
  2. Salemi, Michael K & Sargent, Thomas J, 1979. "The Demand for Money during Hyperinflation under Rational Expectations: II," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 741-58, October.
  3. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-74, May.
  4. Hodrick, Robert J. & Srivastava, Sanjay, 1984. "An investigation of risk and return in forward foreign exchange," Journal of International Money and Finance, Elsevier, vol. 3(1), pages 5-29, April.
  5. Kenneth D. West, 1986. "A Specification Test for Speculative Bubbles," NBER Working Papers 2067, National Bureau of Economic Research, Inc.
  6. John Y. Campbell & Robert J. Shiller, 1986. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  7. John F. O. Bilson, 1980. "The "Speculative Efficiency" Hypothesis," NBER Working Papers 0474, National Bureau of Economic Research, Inc.
  8. Frankel, Jeffrey A. & Stock, James H., 1987. "Regression vs. volatility tests of the efficiency of foreign exchange markets," Journal of International Money and Finance, Elsevier, vol. 6(1), pages 49-56, March.
  9. Fama, Eugene F., 1984. "Forward and spot exchange rates," Journal of Monetary Economics, Elsevier, vol. 14(3), pages 319-338, November.
  10. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-36, June.
  11. Meese, Richard A, 1986. "Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates?," Journal of Political Economy, University of Chicago Press, vol. 94(2), pages 345-73, April.
  12. Hansen, Lars Peter & Hodrick, Robert J, 1980. "Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis," Journal of Political Economy, University of Chicago Press, vol. 88(5), pages 829-53, October.
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