A test for the ex ante efficiency of a given portfolio of assets is analyzed. The relevant statistic has a tractable small sample distribution. Its power function is derived and used to study the sensitivity of the test to the portfolio choice and to the number of assets used to determine the ex post mean-variance efficient frontier. Several intuitive interpretations of the test are provided, including a simple mean-standard deviation geometric explanation. A univariate test, equivalent to our multivariate-based method, is derived, and it suggests some useful diagnostic tools which may explain why the null hypothesis is rejected. Empirical examples suggest that the multivariate approach can lead to more appropriate conclusions than those based on traditional inference which relies on a set of dependent univariate statistics.

https://www.jstor.org/stable/pdfplus/1913625.pdf

A test of the efficiency of a given portfolio

Current 1 -year forward rates on 1 - to 5-year U.S. Treasury bonds are information about the current term structure of 1-year expected returns on the bonds, and forward rates track variation through time in 1-year expected returns. More interesting, 1 -year forward rates forecast changes in the 1 -year interest rate 2- to l-years ahead, and forecast power increases with the forecast horizon. We attribute this forecast power to a mean-reverting tendency in the 1-year interest rate

The Information in Long-Maturity Forward Rates

Efficient method of moments estimation techniques include many commonly used techniques, including ordinary least squares, two- and three-stage least squares, quasi maximum likelihood, and versions of these for nonlinear environments. For models estimated by any efficient method of moments technique, the authors define analogues to the maximum likelihood based Wald, likelihood ratio, Lagrange multiplier, and minimum chi-squared statistics. They prove the mutual asymptotic equivalence of the four in an environment that allows for disturbances that are auto correlated and heteroskedastic. They also describe a very convenient way to test a linear hypothesis in a linear model. Copyright 1987 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Hypothesis Testing with Efficient Method of Moments Estimation

In this landmark book, Scott Page redefines the way we understand ourselves in relation to one another. The Difference is about how we think in groups--and how our collective wisdom exceeds the sum of its parts. Why can teams of people find better solutions than brilliant individuals working alone? And why are the best group decisions and predictions those that draw upon the very qualities that make each of us unique? The answers lie in diversity--not what we look like outside, but what we look like within, our distinct tools and abilities. The Difference reveals that progress and innovation may depend less on lone thinkers with enormous IQs than on diverse people working together and capitalizing on their individuality. Page shows how groups that display a range of perspectives outperform groups of like-minded experts. Diversity yields superior outcomes, and Page proves it using his own cutting-edge research. Moving beyond the politics that cloud standard debates about diversity, he explains why difference beats out homogeneity, whether you're talking about citizens in a democracy or scientists in the laboratory. He examines practical ways to apply diversity's logic to a host of problems, and along the way offers fascinating and surprising examples, from the redesign of the Chicago "El" to the truth about where we store our ketchup. Page changes the way we understand diversity--how to harness its untapped potential, how to understand and avoid its traps, and how we can leverage our differences for the benefit of all.

Prologue to The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies

: Scientific learning is an iterative process employing Criticism and Estimation. Correspondingly the formulated model factors into two complimentary parts - a predictive part allowing model criticism, and a Bayes posterior part allowing estimation. Implications for significance tests, the theory of precise measurement, and for ridge estimates are considered. Predictive checking functions for transformation, serial correlation, bad values, and their relation with Bayesian options are considered. Robustness is seen from a Bayesian viewpoint and examples are given. For the bad value problem a comparison with M estimators is made. (Author)

Sampling and Bayes' inference in scientific modelling and robustness

Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances

This paper surveys alternative testing criteria in the linear multivariate regression model, and investigates the possibility of conflict among them. We consider the asymptotic Wald, likelihood ratio (LR), and Lagrange multiplier (LM) tests. These three test statistics have identical limiting chi-square distributions; thus their critical regions coincide. A strong result we obtain is that a systematic numerical inequality relationship exists; specifically, Wald , LRa LM. Since the equality relationship holds only if the null hypothesis is exactly true in the sample, in practice there will always exist a significance level for which the asymptotic Wald, LR, and LM tests will yield conflicting inference. However, when the null hypothesis is true, the dispersion among the teststatistics will tend to decrease as the sample size increases. We illustrate relationships among the alternative testing criteria with an empirical example based on the three reduced form equations of Klein's Model I of the United States economy, 1921-1941.

Conflict among criteria for testing hypotheses in the multivariate linear regression model

In this paper, we examine the robust Wald test statistic for SUR systems with adding up restrictions where the same explanatory variables are present in all equations and where heteroskedasticity and/or autocorrelation of unknown forms may be present. For this case, the coefficients are usually estimated by least squares, equation by equation. For testing the typical hypotheses of interest, we show that the robust Wald statistic, i.e., the statistic based on the heteroskedasticity and autocorrelation consistent covariance matrix estimator, is invariant to the equation deleted. Our proof of invariance is algebraic and does not rely on parametric assumptions or on the knowledge of the covariance matrix of disturbances. Furthermore, the adding-up restrictions we consider are of a general form: the weighted sum of the dependent variables adds up to one of the explanatory variables, not necessarily a constant. We illustrate our results using the Capital Asset Pricing Model.

Robust Wald Tests in Sur Systems with Adding‐up Restrictions

This paper re-examines the tests of the Sharpe-Lintner Capital Asset Pricing Model (CAPM). The null that the CAPM intercepts are zero is tested for ten size-based stock portfolios and for twenty five book-to-market sorted portfolios using five-year, ten-year and longer sub-periods during 1965-2004. The paper shows that the evidence for rejecting the CAPM on statistical grounds is weaker than the consensus view suggests, and highlights the pitfalls of testing multiple hypotheses with the conventional heteroskedasticity and autocorrelation robust (HAR) test with asymptotic P-values. The conventional test rejects the null for almost all sub-periods, which is consistent with the evidence in the literature. By contrast, the null is not rejected for most of the sub-periods by the new HAR tests developed by Keifer, Vogelsang and Bunzel (2000), Kiefer and Vogelsang (2005), and Sun, Phillips and Jin (2008).

https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=1517874

Testing the CAPM Revisited

Model selection, i.e., the choice of an asset pricing model to the exclusion of competing models, is an inherently misguided strategy when the true model is unavailable to the researcher. This paper illustrates the advantages of a model pooling approach in characterizing the cross section of stock returns. The optimal pool combines models using the log predictive score criterion, a measure of the out-of-sample performance of each model, and consistently outperforms the best individual model. The bene fits to model pooling are most pronounced during periods of economic stress and it is a valuable tool for asset allocation decisions.

N. Eugene Savin

Papers

Estimation and Hypothesis Testing in Singular Equation Systems with Autoregressive Disturbances

Conflict among criteria for testing hypotheses in the multivariate linear regression model

Robust Wald Tests in Sur Systems with Adding‐up Restrictions

Testing the CAPM Revisited

Modeling the Cross Section of Stock Returns: A Model Pooling Approach