Bounds on the Variances of Specification Errors in Models with Expectations

35 Pages Posted: 29 Dec 2006 Last revised: 13 Jul 2010

See all articles by Steven N. Durlauf

Steven N. Durlauf

University of Chicago; National Bureau of Economic Research (NBER)

Robert E. Hall

Hoover Institution and Department of Economics, Stanford University; National Bureau of Economic Research (NBER)

Date Written: April 1989

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

Durlauf, Steven N. and Hall, Robert E., Bounds on the Variances of Specification Errors in Models with Expectations (April 1989). NBER Working Paper No. w2936. Available at SSRN: https://ssrn.com/abstract=461376

Steven N. Durlauf (Contact Author)

University of Chicago ( email )

1155 East 60th Street
Chicago, IL 60637
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Robert E. Hall

Hoover Institution and Department of Economics, Stanford University ( email )

Stanford, CA 94305-6010
United States
650-723-2215 (Phone)

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States
650-723-2215 (Phone)

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