Disturbance Variance Research Articles

A further class of tests for heteroscedasticity

This paper considers the problem of testing for heteroscedasticity in the linear regression model when one is willing to postulate only the ranking of the disturbance variances under the alternative hypothesis. A new class of tests is proposed and methods of finding the tests' critical values are discussed. An empirical power comparison with other tests that have found favor in the literature demonstrates the potential power advantage of these new tests and results in particular versions being recommended for practical use.

Testing the disturbance variance after a pre-test for a linear hypothesis on coefficients in a linear regression

In this paper, we examine the sampling performance of a two-stage test which consists of a pre-test for a linear hypothesis on regression coeffiecients followed by a main-test for a disturbance variance in a linear regression. It is shown that the actual size of the two-stage test can be well-controlled around the normal size if the suggested sizes presented in this paper are used in the pre-test. It is also shown that the two-stage test when the suggested sizes are used in the preferable to the usual test for the disturbance variable which incorporates no pre-test in terms of the power.

Optimal levels of significance of a pre-test in estimating the disturbance variance after the pre-test for a linear hypothesis on coefficients in a linear regression

In this note, we compare sampling properties of a pre-test estimator of the disturbance variance in a linear regression after a pre-test for a linear hypothesis on coefficients with those of an improved estimator of the variance proposed by Stein (1964). It is shown that the pre-test estimator with an optimal level of the pre-test is in fact the improved estimator proposed by Stein (1964).

On pooling disturbance variances when the goal is testing restrictions on regression coefficients

In this paper, we examine the problem of pooling variances from the viewpoint of testing linear restrictions on regression coefficients. That is, we examine the sampling performance of the two-stage test which consists of the pre-test for equality of disturbance variances followed by the main-test for linear restrictions on regression coefficients. It is shown that the bias in the size of the two-stage test may not be important and the two-stage test can be more powerful than the usual test which does not conduct the pre-test, if the size of the pre-test is chosen appropriately.

Introducing a Disturbance into Logit and Probit Regression Models

Logit and probit regression models for dichotomous data make no explicit allowance for heterogeneity induced by omitted explanatory variables or by random fluctuations. This article considers several alternative models for incorporating heterogeneity by the inclusion of a disturbance term. When all the observations are independent, the presence of the disturbance has few empirical consequences. In particular, the variance of the observed counts does not increase and conventional estimators are still appropriate. For some models, however, the disturbance variance may invalidate cross-population comparisons. Quite different implications arise with grouped data when there is a single realization of the disturbance for each group. The observed variance is increased and conventional estimators are inefficient. Several alternative estimators are considered.

Some Macro Implications of Risk

Using the capital asset pricing model as the financial sector of a conventional rational-expectations macro model, an increase in expected inflation reduces the long-run capital stock, contrary to the usual result. This occurs because the induced fall in real balances increases equity's share in the market, raises equity's beta and discount rate, and reduces investment. Increases in the variance of disturbances to aggregate demand reduce the capital stock, while increases in the variance of inflation raise the stock. A proportionate increase in both variances reduces the captial stock. Copyright 1987 by Ohio State University Press.

Analysis of polarization fluctuation in single-mode optical fibers with continuous random coupling

A new analysis method is developed to study the polarization fluctuation in conventional single-mode optical fibers. A random partial differential equation is derived to describe the continuous random coupling between two eigenpolarization modes caused by the perturbation of permittivity along fibers. The calculation formulas for the polarization fluctuation are given. By these formulas, it is proved that the average noise power of the fluctuation at the fiber output depends on the fiber length, the correlation length of perturbation, and the variance of disturbances.

Some sampling properties of the two-stage test in a linear regression with a proxy variable

In thia paper, we examine the sampling properties of the two-stage test which consists of a pre-test for disturbance variance followed by a main-test a regression coefficient of an unobservable variable when a proxy variable is used instead of the unobservable variable. It is shown that the pre-test works effectively if the significance level of the pre-test is appropriately chosen.

Testing For Structural Change Under Heteroscedasticity A Note And An Application

Testing for structural change or the Chow Test enjoyed numerous applications since its introduction by Chow. There have also been several extentions of this test. One of the more re- cent extentions is to the case of structures with unequal disturbance variances. This paper ex- tends the computationally sîmple Lagrange Multiplier test of structural change under hetero- scedasticity introduced by Erlat to the case of several structures. The result is then used in testing the Life-Cycle Hypothesis of saving utilizing household expenditure survey data of Ankara.

Inadmissibility of the iterative Stein-rule estimator of the disturbance variance in a linear regression

In this paper, we consider the estimator of the disturbance variance in a linear regression when the Stein-rule estimator is used in place of the OLS estimator (the iterative Stein-rule estimator of the disturbance variance). It is shown that the iterative Stein-rule estimator of the disturbance variance is dominated by the usual estimator of the disturbance variance based on the OLS estimator under the squared error loss criterion, if the number of regressors is greater than or equal to five.

The illusion of stabilization policy?

For the period 1959-1972 money growth in the United States was positively correlated with past inflation and negatively correlated with past unemployment, whereas for the period 1973-1984 this correlation pattern was reversed. International data, moreover, show that the eight largest western economies exhibit a wide variety of patterns for these correlations, and these patterns seem to be unrelated to average inflation. Theoretical analysis reveals that a model in which the monetary authority is concerned only with controlling inflation is consistent with any pattern of sample correlations of money growth with past inflation and past unemployment. This analysis suggests that international differences in these sample correlations result from differences in the sample variances of disturbances to productivity growth and to aggregate demand. Specifically, the analysis suggests that the critical difference between the pre-1973 and post-1973 periods for the United States was a decrease in the importance of transitory disturbances to aggregate demand relative to permanent disturbances to productivity growth. More generally, these results imply that we cannot readily infer the objectives of the monetary authority from observed patterns of monetary policy.(This abstract was borrowed from another version of this item.)

A Bounds Test for Equality Between Sets of Coefficients in Two Linear Regression Models Under Heteroscedasticity

This article proposes a small sample bounds test for equality between sets of coefficients in two linear regressions with unequal disturbance variances. The probability that our test is inconclusive is given under the null hypothesis. It is also shown that our test is more powerful than the Jayatissa test when the regression coefficients differ substantially.

A Bounds Test of Equality between Sets of Coefficients in Two Linear Regressions When Disturbance Variances are Unequal

Abstract This article considers the Wald test statistic for testing equality between sets of coefficients in two linear regressions when the disturbance variances are unequal. It is shown that the distribution of the test statistic under the null hypothesis is bounded, asymptotically up to the second order, by the distributions of two F variates multiplied by the number of the regressors.

A Bounds Test of Equality Between Sets of Coefficients in Two Linear Regressions When Disturbance Variances are Unequal

Abstract This article considers the Wald test statistic for testing equality between sets of coefficients in two linear regressions when the disturbance variances are unequal. It is shown that the distribution of the test statistic under the null hypothesis is bounded, asymptotically up to the second order, by the distributions of two F variates multiplied by the number of the regressors.

Comparing Single-Equation Estimators in a Simultaneous Equation System

Comparisons of estimators are made on the basis of their mean squared errors and their concentrations of probability computed by means of asymptotic expansions of their distributions when the disturbance variance tends to zero and alternatively when the sample size increases indefinitely. The estimators include k-class estimators (limited information maximum likelihood, two-stage least squares, and ordinary least squares) and linear combinations of them as well as modifications of the limited information maximum likelihood estimator and several Bayes' estimators. Many inequalities between the asymptotic mean squared errors and concentrations of probability are given. Among medianunbiasedestimators, the limited information maximum likelihood estimator dominates the median-unbiased fixed k-class estimator.

The Effect of Measurement Error in Structural Equation Modeling

It is commonly believed that measurement error is accounted for when utilizing the LISREL approach. The purpose of the present research was to utilize the expanded factor analysis model to examine the effects of unreliability on the various parameter estimates yielded from structural models. In other words, the relationships between “true score” latent variables was considered under a range of assumed values of reliability. The results indicate that the amount of measurement error, as defined by specific variance, does have certain effects upon the estimates of structural equation models. When the level of specific variance is reduced (due to decreased reliability) for only one of the exogenous variables, the following can occur: Error variance for that variable increases systematically since specific and error variance are analytically, inversely related; the remaining parameters of the measurement models remain unchanged; the maximum-likelihood estimate and standard error for the relevant structure coefficient increase at the same rate; the maximum-likelihood estimate of the disturbance variance also decreases; and goodness of fit of the model is unchanged. Thus, in those situations where indicator variable reliability differs substantially from unity, say 0.8 or less, consideration needs to be given to taking the unreliability into account in the analysis; otherwise, certain important parameter estimates may be biased leading to possible model misinterpretation.

Testing equality between sets of coefficients after a preliminary test for equality of disturbance variances in two linear regressions

Abstract In this paper we propose a two-stage test which consists of testing equality of regression coefficients after a preliminary test for equality of disturbance variances in two linear regressions. The optimal procedure of the two-stage test is presented. The sampling performance of the optimal two-stage test is compared with that of the Jayatissa test and with that of the size-corrected Wald test.

Algebraic equivalences among Wald, LM and Hausman's tests in the linear regression model

Under certain conditions, the Hausman's statistic is identical to the Wald statistic, if we use the unconstrained maximum likelihood estimate for the variance of disturbances, while it becomes identical to the LM statistic, if we use the constrained maximum likelihood estimate for the variance.

Testing linear hypothesis on regression coefficients after a pre-test for disturbance variance

In this note, we analyze the sampling performance of the two-stage test that tests the linear hypothesis on regression coefficients after a pre-test for disturbance variance. It is shown that the two-stage test has a serious upward bias in size when the degrees of freedom is small, but it gets smaller as the degrees of freedom gets larger and the power of the two-stage test is higher than that of the conventional F test for the linear hypothesis which does not conduct the pre-test.

A New Approach to Estimation of the Term Structure of Interest Rates

The purpose of this study is to extend the analysis of estimation of the term structure. The ability of the exponential/polynomial present-value function of equation (5) to approximate the theoretical present-value function is analyzed empirically. This study confirms previous results that indicate that the function does not provide an acceptable fit using least squares regression. In most samples, the near end of the estimated term structure appears substantially in error. Lengthening the polynomial tends to improve the fit only at the far end. Since the data appear to be subject to maturity-related heteroschedasticity, we have generalized the disturbance variance specification to allow for this possibility.Our correction permits determination of sample-specific degrees of heteroschedasticity. The reason is that the intensity of the heteroschedasticity appears to change from period to period. Although previous studies have attempted heteroschedasticity corrections (see [4]), the same specification was imposed on each sample in such studies. Maximum likelihood estimation was proposed and implemented in this paper. The results indicate that the difficulties of providing a good fit using the exponential/polynomial function are substantially eliminated.Recent literature regarding term structure estimation emphasizes the selection of more sophisticated estimating functions to provide a reasonable fit throughout the entire maturity range. This study emphasizes more careful modeling of the pricing disturbances. The prior approach involves somewhat complicated estimating functions and a potential loss of efficiency due to the lack of influence that each portion of the term structure is able to exert on other portions (with spline functions, for example.) Our maximum likelihood approach is somewhat difficult to implement and computationally burdensome. Nevertheless, it appears to provide a useful term structure estimation procedure.