A Monte Carlo evaluation of the power of some tests for heteroscedasticity

doi:10.1016/0304-4076(86)90049-7

Journal of Econometrics

Volume 31, Issue 2, March 1986, Pages 219-231

https://doi.org/10.1016/0304-4076(86)90049-7 Get rights and content

Abstract

Szroeter's asymptotically normal test outperforms the Goldfeld-Qu2ndt test, the Breusch-Pagan Lagrange multiplier test and BAMSET, when it is possible to order the observations according to increasing variance. With no prior information on variance ordering, BAMSET is best. Some observations concerning degree of heteroscedasticity and model specification are made.

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Cited by (24)

Simulation-based finite-sample tests for heteroskedasticity and ARCH effects
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Citation Excerpt :
In addition, most of the references cited above include Monte Carlo evidence on the relative performance of various tests. The main findings that emerge from these studies are the following: (i) no single test has the greatest power against all alternatives; (ii) tests based on OLS residuals perform best; (iii) the actual level of asymptotically justified tests is often quite far from the nominal level: some are over-sized (see, for example, Honda, 1988; Ali and Giaccotto, 1984; Binkley, 1992), while others are heavily under-sized, leading to important power losses (see Lee and King, 1993; Evans, 1992; Honda, 1988, Griffiths and Surekha, 1986; Binkley, 1992); (iv) the incidence of inconclusiveness is high among the bounds tests; (v) the exact tests compare favorably with asymptotic tests but can be quite difficult to implement in practice. Of course, these conclusions may be influenced by the special assumptions and simulation designs that were considered.
Tests for heteroskedasticity in linear regressions are typically based on asymptotic approximations. We show that the size of such tests can be perfectly controlled in finite samples through Monte Carlo test techniques, with both Gaussian and non-Gaussian (heavy-tailed) disturbance distributions. The procedures studied include standard heteroskedasticity tests [e.g., Glejser, Bartlett, Cochran, Hartley, Breusch–Pagan–Godfrey, White, Szroeter] as well as tests for ARCH-type heteroskedasticity. Sup-type and combined tests are also proposed to allow for unknown breakpoints in the variance. The fact that the proposed procedures achieve size control and have good power is demonstrated in a Monte Carlo simulation.
Smoking-attributable medical care costs in the USA
1999, Social Science and Medicine
Medical care costs attributable to cigarette smoking are estimated using an econometric model of annual individual expenditures for four types of medical services: ambulatory, hospital, prescription drug, and other (which includes home health and durable medical equipment and excludes dental and mental health). The model follows the two-part specification of Duan et al. (1983). Estimation is carried out using the 1987 National Medical Expenditure Survey. Fitted values are used to calculate smoking-attributable fractions (SAFs) of expense by type of service and by age and gender category. The overall weighted average SAF is 6.54%. SAFs are generally largest for ambulatory and smallest for hospital expenses. They are larger for males and for the older age categories. The model is analyzed for heteroscedasticity and goodness of fit. Additional analysis using the National Health Interview Survey is conducted to test for the possible effect of not being able to include alcohol consumption in the primary model. A balanced repeated replication analysis is conducted to evaluate the variance of the SAFs. Variances are found to be acceptably small. An extension of the model to support evaluation of smoking-attributable costs for special populations such as individual states, and special insurance pools such as Medicaid recipients, is described. Results for the fifty states are presented. Conclusions and subjects for further research are discussed.
Marginal-likelihood score-based tests of regression disturbances in the presence of nuisance parameters
1997, Journal of Econometrics
This paper is concerned with tests of the covariance matrix of the disturbances in the linear regression model that involves nuisance parameters which cannot be eliminated by the usual invariance arguments. Score-based tests, namely, Lagrange multiplier (LM) and locally most mean-powerful (LMMP) tests are derived from the marginal likelihood. Applications considered include (i) testing for random regression coefficients, (ii) testing for second-order autoregressive (AR(2)) disturbances and (iii) testing for ARMA (1.1) disturbances, each in the presence of AR(1) disturbances. An empirical size and power comparison shows that the new tests typically have more accurate asymptotic critical values and slightly more power than their respective conventional counterparts.
18 Testing for heteroskedasticity
1993, Handbook of Statistics
This chapter discusses the methods of testing for heteroskedasticity in a variety of models. Some of these tests are routinely provided as the standard output of computer packages, whilst others still only have spasmodic use. All existing tests can be regarded as “conditional moment tests” (CM tests) with the differences between them revolving around the nature of the moments used, how nuisance parameters are dealt with, and the extent to which a full sample of observations is exploited. Early interest in heteroskedasticity arose from the concerns of users of the linear regression model. It is demonstrated that the ordinary least-squares (OLS) estimator is not efficient if the errors in the regression model are heteroskedastic, and any inferences made with standard errors computed from standard formulae would be incorrect. To obviate the latter problem, methods were derived to make valid inferences in the presence of heteroskedasticity. Binary, count and censored regression models can be regarded as specialized nonlinear regression models, implying that approaches developed for the linear model will have extensions. What differentiates the models is that these exhibit intrinsic heteroskedasticity, and the prime question is whether there is any “extra” heteroskedasticity that is not in the maintained model.
Robustness of size of tests of autocorrelation and heteroscedasticity to nonnormality
1992, Journal of Econometrics
'Profit' variability in for-profit and not-for-profit hospitals
1991, Journal of Health Economics
This paper proposes two tests of the hypothesis that not-for-profit hospitals (NFPs) behave differently than for-profit hospitals. The profit variability test states that the profits of an NFP will be less variable over time than profits of a for-profit hospital if the NFP maximizes utility subject to a profit constraint. The second test examines whether NFP profits respond less to change in exogenous factors, such as Medicare reimbursement rates, than profits of for-profit hospitals. Both tests, performed on panel data from 1983 to 1988, support the hypothesis that NFPs behave differently than for-profit hospitals.

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^☆: The authors gratefully acknowledge Shahidur Rahman's efficient and enthusiastic research assistance. An earlier version of this paper was written while Griffiths was visiting the Department of Economics, University of Illinois, Urbana-Champaign.

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A Monte Carlo evaluation of the power of some tests for heteroscedasticity☆

Abstract

Journal of Econometrics

A study of several new and existing tests for heteroscedasticity in the general linear model

Journal of Econometrics

Market models and heteroscedasticity of residual security returns

Journal of Business and Economic Statistics

Using residuals robustly I: Tests for heteroscedasticity, nonlinearity

Annals of Statistics

A simple test for heteroscedasticity and random coefficient variation

Econometrica

Tests for additive heteroskedasticity: Goldfeld and Quant revisited

Empirical Economics

On robust tests for heteroscedasticity

Annals of Statistics

A note on residual heterovariance and estimation efficiency in regressions

American Statistician

A new test for heteroscedasticity

Journal of the American Statistical Association

Testing for multiplicative heteroscedasticity

Journal of Econometrics

Some tests for homoscedasticity

Journal of the American Statistical Association

Nonlinear methods in econometrics

A test for heteroscedasticity based on ordinary least squares residuals

Journal of the American Statistical Association

Estimation of parameters in a heteroscedastic regression model

European Meeting of the Econometric Society,