Bounds on the Variances of Specification Errors in Models with Expectations, Issue 2936
National Bureau of Economic Research, 1989 - Analysis of covariance - 33 pages
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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1050 Massachusetts Avenue absent noise arbitrage condition bound is attained Bureau of Economic Cauchy-Schwartz Cauchy-Schwartz inequality coefficient constant discount rate covariance Durlauf and Hall econometrician Economic Research error or noise ERRORS IN MODELS excess holding returns excess returns excess volatility test expectation error expectational models expectations based models fitted value flow approach flow noise forecast errors forward exchange rate hyperinflations information set instrumental variable Louis Scott lower bound Lp(t Lx(t measure MODELS WITH EXPECTATIONS NBER noise bound noise in expectation noise variance null hypothesis observed variable optimal orthogonal paper perfect-foresight variable projection of Pt random variable rational expectations regression test regressors right-hand variable Robert Shiller Sebastian Edwards Section Shiller specification error specification tests stock approach stock market stock price model testable implications Theorem 2.1 true expectation uncorrelated uncovering model noise variables known variance of noise variance of St VARIANCES OF SPECIFICATION z-variables