Gordon Fisher

On the interpretation of the cox test in econometrics

This note seeks to clarify whether applications of Coxs (1961) modified likelihood ratio principle logically require a two- or one-tailed test. Logic requires the test of discrimination be one-tailed and the significance test for non-nested hypotheses be two-tailed. The significance test of a pair of non-nested hypotheses involves another extraneous hypothesis to which the cause of deviation from the tested hypothesis away from the alternative may be attributed.

An empirical analysis of term premiums using significance tests for stochastic dominance

Abstract The economic significance of term premiums in real returns on US Treasury Bills is examined using recently developed tests for first- and second-order stochastic dominance. The tests place only general restrictions on the preferences of individuals and on the distribution of returns. The results indicate that the two-month real return is preferred to the one-month real return based on both dominance criteria. Other term premiums do not appear to be economically significant.

Tests for two separate regressions

Several recently proposed tests for separate regressions are examined in light of recommendations by Cox (1961). This points to simplified criteria and emphasizes the unity underlying the tests. The exact distributions of some of the tests are developed and given a geometrical characterization. An orthogonal decomposition is proposed which provides a direct link between the F-test and tests based upon artificial nesting.

A Discriminant Analysis of Reporting Errors in Health Interviews

In this article the author makes use of data collected for the U.S. National Health Survey in a survey, by interview, of the hospitalisation of persons. Using a least‐squares technique, involving dummy variables, he derives a discriminating function which permits the prediction of accurate reporting of hospitalisation according to criteria such as the income and race of the respondent. The estimated effects of these and other criteria upon the accuracy with which hospitalisations are reported are discussed in some detail.

Myopic loss aversion and margin of safety: the risk of value investing

This paper examines the risk of value investing from the point of view of a myopic loss-averse investor holding a diversified portfolio and relying on infrequent portfolio rebalancing. This closely resembles purchasing a large portfolio, such as those created by BARRA, and following a buy-and-hold investment strategy. In these circumstances, which portfolio, value or growth, is riskier to a myopic loss-averse investor? To facilitate analysis, a myopic loss ranking and a corresponding statistical procedure are developed and applied to investment-style data provided by BARRA. The paper qualifies the conditions under which value investing is more risky in North American financial markets.

Testing First- and Second-Order Stochastic Dominance

Tests for stochastic dominance are important tools for the comparison of distributions between pairs of random variables. In finance, dominance criteria can potentially provide an unambiguous ranking of the desirability of different assets while placing only general restrictions on the preferences of investors. In welfare economics, dominance concepts allow for the ranking of income distributions using generally accepted welfare criteria. Existing dominance test procedures suffer from a number of weaknesses. One weakness concerns restrictions on the class of distribution functions that may be used as a basis for testing. While early literature in this area typically ignored sampling errors, this issue has been addressed in more recent literature, but only at the cost of restricting the class of parametric distributions discussed; see e.g. Stein and Pfaffenberger (1986). Since dominance criteria are attractive primarily because they allow for a ranking of returns on risky assets or income distributions, while placing only weak restrictions on preferences, it is important that dominance tests retain a degree of generality, and hence remain nonparametric in nature. Another weakness of existing dominance tests is that these often specify the null hypothesis improperly; see e.g. Bishop et al. (1989). For example, most test procedures make use of the null hypothesis that two distribution or quantile functions are identical. The hypothesis of dominance may be viewed as an hypothesis of inequality in a particular direction between two distribution or quantile functions. If such an hypothesis is rejected, then dominance cannot be sustained, a result that may or may not be caused by the equality of the two distribution or quantile functions. On the other hand, if the null hypothesis of equality is rejected, then the two distributions cannot be said to be equal, but the cause may or may not be that one dominates the other. Thus the null hypothesis of equality is not very helpful in providing information about dominance; see Levy (1992, p. 574).

Some finite sample theory for bootstrap regression estimates

Abstract Existing justifications for applying the bootstrap to linear regressions rely on the asymptotic properties of the estimates, as the parent sample size increases indefinitely, and on the evidence from Monte Carlo experiments. In this paper, the properties of various bootstrap regression estimates are developed, as the number of bootstrap replications increases indefinitely, the sample size remaining fixed and finite. Various theoretical results that serve to reinforce results previously obtained only from Monte Carlo experimentation are obtained.

The Algebra of Estimation in Linear Econometric Systems

Summary In econometrics it is common for variables to be related together in a set of linear, multilateral and causal interdependencies. This type of system generally has properties which are unsatisfactory for application of classical regression techniques. Consequently, alternative estimation methods have been developed. This paper explores the relations between several such methods in terms of symmetric idempotents of predetermined variables and their orthogonal complements. Generalizations of two‐ and three‐stage least squares and instrumental variables are considered, including Wickens estimator.2 The relative efficiencies of the estimators are also discussed. ∗ Some of the ideas in this paper appeared in Reference 1(a), a later version of which was presented to the World Congress of the Econometric Society, Rome, 1965.1(b) Since these papers appeared, the mathematical exposition has been improved, the results made more general and some new results (on efficiency) added. Some of the results reported...