Tests of specification in econometrics

This survey of recent developments in testing for misspecification of econometric models reviews procedures based on a method due to Hausman. Particular attention is given to alternative forms of the test, its relationship to classical test procedures, and its role in pre-test estimation.     

The Interpretation of R 2 in Autoregressive-Moving Average Time Series Models

It is demonstrated that factors needed to conduct tests and form confidence intervals for the ratio of two normal variances can be found using one of the new desk calculators which compute F probabilities.     

Linearly Independent,Orthogonal, and Uncorrelated Variables

Linearly independent, orthogonal, and uncorrelated are three terms used to indicate lack of relationship between variables. This short didactic article compares these three terms in both an algebraic and a geometric framework. An example is used to illustrate the differences.     

Multi - sample test of equal gamma distribution scale parameters in presence of unknown common shape parameter

Shiue and Bain proposed an approximate F statistic for testing equality of two gamma distribution scale parameters in presence of a common and unknown shape parameter. By generalizing Shiue and Bain's statistic we develop a new statistic for testing equality of L >= 2 gamma distribution scale parameters. We derive the distribution of the new statistic ESP for L = 2 and equal sample size situation. For other situations distribution of ESP is not known and test based on the ESP statistic has to be performed by using simulated critical values. We also derive a C(α) statistic CML and develop a likelihood ratio statistic, LR, two modified likelihood ratio statistics M and MLB and a quadratic statistic Q. The distribution of each of the statistics CML, LR, M, MLB and Q is asymptotically chi-square with L - 1 degrees of freedom. We then conducted a monte-carlo simulation study to compare the perfor- mance of the statistics ESP, LR, M, MLB, CML and Q in terms of size and power. The statistics LR, M, MLB and Q are in general liberal and do not show power advantage over other statistics. The statistic CML, based on its asymptotic chi-square distribution, in general, holds nominal level well. It is most powerful or nearly most powerful in most situations and is simple to use. Hence, we recommend the statistic CML for use in general. For better power the statistic ESP, based on its empirical distribution, is recommended for the special situation for which there is evidence in the data that λ₁ < … < λ_L and n₁ < … < n_L, where λ₁ …, λ_L are the scale parameters and n₁,…, n_L are the sample sizes.     

The small sample properties of the reset test as applied to systems of equations

The RESET test for functional misspecification is generalised to cover systems of equations, and the properties of 7 versions are studied using Monte Carlo methods. The Rao F -test clearly exhibits the best performance as regards correct size, whilst the commonly used LRT (uncorrected for degrees-of-freedom), and LM and Wald tests (both corrected and uncorrected) behave badly even in single equations. The Rao test exhibits correct size even in ten equation systems, which is better than previous research concerning autocorrelation tests. The power of the test is low, however, when the number of equations grows and the correlation between the omitted variables and the RESET proxies is small.     

Adaptive bootstrap tests and their competitors in the c -sample location problem

This paper deals with a power comparison of different types of tests, parametric, nonparametric, robustified and adaptive ones for the two-sided c -sample location problem. A robustness study on level f in the case of heteroscedasticity and non-normal distributions is included in our study, too. First of all, we consider an adaptive test based on Hogg's concept and two adaptive Bootstrap tests using Hogg's principle. It turns out that the adaptive Hogg-test is the best one in the case of homoscedasticity but for heteroscedasticity, an adaptive Bootstrap test using Hogg's principle is preferable.     

Maximum likelihood estimators for extended growth curve model with orthogonal between-individual design matrices

The extended growth curve model is discussed in this paper. There are two versions of the model studied in the literature, which differ in the way how the column spaces of the design matrices are nested. The nesting is applied either to the between-individual or to the within-individual design matrices. Although both versions are equivalent via reparametrization, the properties of estimators cannot be transferred directly because of non-linearity of estimators. Since in many applications the between-individual matrices are one-way ANOVA matrices, it is reasonable to assume orthogonality of the column spaces of between-individual design matrices along with nestedness of the column spaces of within-individual design matrices. We present the maximum likelihood estimators and their basic moments for the model with such orthogonality condition.