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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.

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Bibliographic Info

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

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  1. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(3), pages 741-58, October.
  2. Kenneth D. West, 1986. "A Specification Test for Speculative Bubbles," NBER Working Papers 2067, National Bureau of Economic Research, Inc.
  3. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, American Economic Association, vol. 71(3), pages 421-36, June.
  4. 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, Wharton School Rodney L. White Center for Financial Research 05-87, Wharton School Rodney L. White Center for Financial Research.
  5. Campbell, John Y & Shiller, Robert J, 1987. "Cointegration and Tests of Present Value Models," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 95(5), pages 1062-88, October.
  6. 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, University of Chicago Press, vol. 88(5), pages 829-53, October.
  7. Fama, Eugene F., 1984. "Forward and spot exchange rates," Journal of Monetary Economics, Elsevier, Elsevier, vol. 14(3), pages 319-338, November.
  8. John F. O. Bilson, 1980. "The "Speculative Efficiency" Hypothesis," NBER Working Papers 0474, National Bureau of Economic Research, Inc.
  9. Hodrick, Robert J. & Srivastava, Sanjay, 1984. "An investigation of risk and return in forward foreign exchange," Journal of International Money and Finance, Elsevier, Elsevier, vol. 3(1), pages 5-29, April.
  10. Frankel, Jeffrey A. & Stock, James H., 1987. "Regression vs. Volatility Tests of the Efficiency of Foreign Exchange Markets," Department of Economics, Working Paper Series, Department of Economics, Institute for Business and Economic Research, UC Berkeley qt4t87m30k, Department of Economics, Institute for Business and Economic Research, UC Berkeley.
  11. Meese, Richard A, 1986. "Testing for Bubbles in Exchange Markets: A Case of Sparkling Rates?," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 94(2), pages 345-73, April.
  12. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, Econometric Society, vol. 49(3), pages 555-74, May.
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Cited by:
  1. Qin Xiao & Randolph Gee Kwang Tan, 2006. "Signal Extraction with Kalman Filter: A Study of the Hong Kong Property Price Bubbles," Economic Growth centre Working Paper Series, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre 0601, Nanyang Technolgical University, School of Humanities and Social Sciences, Economic Growth centre.
  2. Lars Peter Hansen & Ravi Jagannathan, 1994. "Assessing specification errors in stochastic discount factor models," Staff Report, Federal Reserve Bank of Minneapolis 167, Federal Reserve Bank of Minneapolis.
  3. Engsted, Tom, 2003. "Misspecification versus bubbles in hyperinflation data: comment," Journal of International Money and Finance, Elsevier, Elsevier, vol. 22(4), pages 441-451, August.
  4. Engsted, Tom & Tanggaard, Carsten, 2001. "The Danish stock and bond markets: comovement, return predictability and variance decomposition," Journal of Empirical Finance, Elsevier, Elsevier, vol. 8(3), pages 243-271, July.
  5. Engsted, Tom, 2002. " Measures of Fit for Rational Expectations Models," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 16(3), pages 301-55, July.
  6. Hooker, Mark A., 2000. "Misspecification versus bubbles in hyperinflation data: Monte Carlo and interwar European evidence," Journal of International Money and Finance, Elsevier, Elsevier, vol. 19(4), pages 583-600, August.
  7. Robert E. Hall, 1989. "Spontaneous Volatility of Output and Investment," NBER Working Papers 3144, National Bureau of Economic Research, Inc.
  8. Fahmy, Yasser A. F. & Kandil, Magda, 2003. "The Fisher effect: new evidence and implications," International Review of Economics & Finance, Elsevier, Elsevier, vol. 12(4), pages 451-465.
  9. Mark A. Hooker, 1997. "Misspecification versus bubbles in hyperinflation data: Monte Carlo and interwar European evidence," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 1997-49, Board of Governors of the Federal Reserve System (U.S.).
  10. Engsted, Tom, 2000. "Measuring Noise in the Permanent Income Hypothesis," Finance Working Papers, University of Aarhus, Aarhus School of Business, Department of Business Studies 00-8, University of Aarhus, Aarhus School of Business, Department of Business Studies.
  11. Engsted, Tom, 1998. "Money Demand During Hyperinflation: Cointegration, Rational Expectations, and the Importance of Money Demand Shocks," Journal of Macroeconomics, Elsevier, Elsevier, vol. 20(3), pages 533-552, July.

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