VARIANCE-RATIO TESTS OF RANDOM WALK: AN OVERVIEW

Abstract.  This paper reviews the recent developments in the field of the variance-ratio (VR) tests of the random walk and martingale hypothesis. In particular, we present the conventional individual and multiple VR tests as well as their improved modifications based on power-transformed statistics, rank and sign tests, subsampling and bootstrap methods, among others. We also re-examine the weak-form efficiency for five emerging equity markets in Latin America.     

RANK TESTS IN 2X2 DESIGNS

Abstract. In literature numerous attempts can be found for the evaluation of two factor designs with fixed effects by means of rank tests. The aim of the present article is to show the limits of these methods and to give some new procedures for 2X2 designs. First, functionals of distribution functions shall be defined whose relations to the usual parameters of the linear model are analysed. These functionals are free of nuissance parameters under the respective hypothesis; they are estimated by special ranks of the data. The asymptotic distribution of these statistics is derived by a generalization of the Chemoff–Savage theorem for correlated random variables. The asymptotic variance depends on the parent distribution function but it can be estimated by using special rank methods. Thus, one obtains asymptotically distribution–free tests for two–factor designs with fixed effects. Some counter examples show why it is not possible to construct suitable rank tests for greater designs than the 2X2 design. The paper closes with a discussion of the drawbacks of the well known rank transform.     

Some rank tests for one–sided many–one comparisons

We compare some nonparametric tests for the (/+ 1)–sample problem with additive effects under the constraint that in every sample the treatment effect is not less than that in the first sample, i.e. of some control. The behavior of the Pitman efficiency of the respective tests (essentially tests of a Kruskal–Wallis–, Wilcoxon–, Fligner–Wolfe–, Steel–, and Nemenyi–type) is discussed which turns out to depend on the level and power of the tests as well as on the directions, from which the alternative tends to the hypothesis. It will be shown that none of the tests under consideration is uniformly superior to the others.     

APPROXIMATIONS TO THE ASYMPTOTIC DISTRIBUTIONS OF COINTEGRATION TESTS

The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accurate than the standard tables previously published.     

ON COMPARING MACROECONOMIC MODELS USING FORECAST ENCOMPASSING TESTS

ABSTRACT It is clearly of interest to macroeconomists to be able to evaluate whether one large-scale macroeconometric model ‘is better’ than another. Although comparisons between models are sometimes invidious, because the purposes for which the models were built differ, it is the case that formal comparisons of two models' statistical properties are rare. This is in spite of considerable theoretical advances in the econometric methodology, namely the development and use of non-nested and encompassing tests. Chong and Hendry (1986) advocate the use of the forecast encompassing regressions, where the outturns are regressed on competing (one-step-ahead) forecasts. This paper reports the findings of applying this rather easy-to-use method of comparing large scale macroeconometric models. The forecast data we use are those published by three macroeconometric modelling groups, namely: Liverpool; the National Institute; and The London Business School. Forecasts for up to three years ahead are published for unemployment, growth, and inflation, throughout the 1980's. Forecast encompassing tests fail to separate one model from another, based on one-year-ahead forecasts. Each model ‘wins’ once. However, the conclusions are not the same as using root-mean-square-forecast-error criteria, illustrating Clements and Hendry's (1994) observation that minimum root-mean-square-forecast-error is neither necessary nor sufficient for a model to have constant parameters, to provide accurate forecasts, or to encompass its rivals.     

A REVIEW AND COMPARISON OF TESTS OF CROSS-SECTION INDEPENDENCE IN PANELS

Abstract.  In this paper we review and compare diagnostic tests of cross-section independence in the disturbances of panel regression models. We examine tests based on the sample pairwise correlation coefficient or on its transformations, and tests based on the theory of spacings. The ultimate goal is to shed some light on the appropriate use of existing diagnostic tests for cross-equation error correlation. Our discussion is supported by means of a set of Monte Carlo experiments and a small empirical study on health. Results show that tests based on the average of pairwise correlation coefficients work well when the alternative hypothesis is a factor model with non-zero mean loadings. Tests based on spacings are powerful in identifying various forms of strong cross-section dependence, but have low power when they are used to capture spatial correlation.     

HODGES-LEHMANN EFFICACIES FOR LIKELIHOOD RATIO TYPE TESTS IN CURVED BIVARIATE NORMAL FAMILIES

For hypothesis testing in curved bivariate normal families we compare various size a tests by means of their Hodges-Lehmann efficacies at fixed alternatives, in particular when these tests have equal optimal asymptotic power in the local Pitman sense. The locally most powerful tests and the likelihood ratio tests for the curve are both Pitman optimal, but the latter turn out to have higher Hodges-Lehmann efficacy. All the tests considered here, including the locally most powerful tests, are likelihood ratio tests against suitable (possibly enlarged) sets of alternatives, the curve itself being an important special case of such a subset. In passing we illustrate a general result in Brown (1971) concerning Hodges-Lehmann optimality obtained by enlarging the model.     

NUMERICAL DISTRIBUTION FUNCTIONS OF FRACTIONAL UNIT ROOT AND COINTEGRATION TESTS

We calculate, by simulations, numerical asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real‐valued parameter b which must be estimated, simple tabulation is not feasible. Partly owing to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and a value of b, provides either a set of critical values or the asymptotic P‐value for any value of the likelihood ratio statistic. Copyright © 2012 John Wiley & Sons, Ltd.     

Measure for Measure: Exact F Tests and the Mixed Models Controversy

We consider exact F tests for the hypothesis of null random factor effect in the presence of interaction under the two factor mixed models involved in the mixed models controversy. We show that under the constrained parameter ( CP ) model, even in unbalanced data situations, MSB/MSE (in the usual ANOVA notation) follows an exact F distribution when the null hypothesis holds. We also obtain an exact F test for what is generally (and erroneously) assumed to be an equivalent hypothesis under the unconstrained parameter ( UP ) model. For unbalanced data, such a corresponding test statistic does not coincide with MSB/MSAB (the test statistic advocated for balanced data cases). We compute the power of the exact test under different imbalance patterns and show that although the loss of power increases with the degree of imbalance, it still remains reasonable from a practical point of view.     

Analysis of Divergence in Loglinear Models When Expected Frequencies are Subject to Linear Constraints

Consider the loglinear model for categorical data under the assumption of multinomial sampling. We are interested in testing between various hypotheses on the parameter space when we have some hypotheses relating to the parameters of the models that can be written in terms of constraints on the frequencies. The usual likelihood ratio test, with maximum likelihood estimator for the unspecified parameters, is generalized to tests based on -divergence statistics, using minimum -divergence estimator. These tests yield the classical likelihood ratio test as a special case. Asymptotic distributions for the new -divergence test statistics are derived under the null hypothesis.     

Models of static and dynamic technical efficiency of municipal libraries in the Czech Republic

This article deals with the modelling of the static and dynamic technical efficiency under conditions of municipal libraries of municipalities with 1000–5000 inhabitants. The aim of this article is to determine the level of the technical efficiency and the factors that influence the results of modelling of the static and dynamic technical efficiency of 34 selected municipal libraries for the years of 2011 and 2015. The first model tests the technical efficiency of conventional services of public libraries. The second model tests the technical efficiency of municipal libraries’ operation. The third model tests the technical efficiency of the key revenues and expenditures. The results in the static models estimate the average technical efficiency of municipal libraries in the interval (0.691–0.759) for the input-oriented models, and in the interval (1.413–2.005) for the output-oriented models. In the dynamic models, the majority of municipal libraries in 2015 showed lower technical efficiency and productivity in comparison with the year of 2011. The factors influencing the level of efficiency and its course include the inputs and the outputs, and their combinations within individual models.     

THE CHOICE OF CELLS IN CHI–SQUARE TESTS

The choice of cells in chi–square goodness of fit tests is a classical problem. Some recent results in this area are discussed. It is shown that the likelihood ratio of alternatives w.r.t. null distributions plays a key role when judging different procedures. The discussion centers on the case of a simple hypothesis, but location–scale models and tests of independence in contingency tables are also considered.     

SPECIFICATION TESTS FOR THE COMPETING RISKS DURATION MODEL: AN APPLICATION TO UNEMPLOYMENT DURATION AND SECTORAL MOVEMENT

ABSTRACTS This study develops three specification tests for the competing risks duration model. They include a general test for misspecification and specific tests for heterogeneity and defective risk distributions. The last two tests involves null hypotheses located on the boundary of the parameter space, and we consider alternative formulations of the score test to take account of this. The tests are applied to models of unemployment duration in which displaced job seekers may become re-employed in the pre-unemployment industry or switch industries.     

TESTS OF EQUAL FORECAST ACCURACY FOR OVERLAPPING MODELS

This paper examines the asymptotic and finite‐sample properties of tests of equal forecast accuracy when the models being compared are overlapping in the sense of Vuong (Econometrica 1989; 57 : 307–333). Two models are overlapping when the true model contains just a subset of variables common to the larger sets of variables included in the competing forecasting models. We consider an out‐of‐sample version of the two‐step testing procedure recommended by Vuong but also show that an exact one‐step procedure is sometimes applicable. When the models are overlapping, we provide a simple‐to‐use fixed‐regressor wild bootstrap that can be used to conduct valid inference. Monte Carlo simulations generally support the theoretical results: the two‐step procedure is conservative, while the one‐step procedure can be accurately sized when appropriate. We conclude with an empirical application comparing the predictive content of credit spreads to growth in real stock prices for forecasting US real gross domestic product growth. Copyright © 2013 John Wiley & Sons, Ltd.     

Panel unit root tests under cross-sectional dependence

In this paper alternative approaches for testing the unit root hypothesis in panel data are considered. First, a robust version of the Dickey-Fuller t -statistic under contemporaneous correlated errors is suggested. Second, the GLS t -statistic is considered, which is based on the t -statistic of the transformed model. The asymptotic power of both tests is compared against a sequence of local alternatives. To adjust for short-run serial correlation of the errors, we propose a pre-whitening procedure that yields a test statistic with a standard normal limiting distribution as N and T tends to infinity. The test procedure is further generalized to accommodate individual specific intercepts or linear time trends. From our Monte Carlo simulations it turns out that the robust OLS t -statistic performs well with respect to size and power, whereas the GLS t -statistic may suffer from severe size distortions in small and moderate sample sizes. The tests are applied to test for a unit root in real exchange rates.     

On testing for independence against right tail increasing in bivariate models

A random variableY is right tail increasing (RTI) inX if the failure rate of the conditional distribution ofX givenY>y is uniformly smaller than that of the marginal distribution ofX for everyy0. This concept of positive dependence is not symmetric inX andY and is stronger than the notion of positive quadrant dependence. In this paper we consider the problem of testing for independence against the alternative thatY is RTI inX. We propose two distribution-free tests and obtain their limiting null distributions. The proposed tests are compared to Kendall's and Spearman's tests in terms of Pitman asymptotic relative efficiency. We have also conducted a Monte Carlo study to compare the powers of these tests.Research supported by an NSERC Canada operating grant at the University of Alberta.Part of this research was done while visiting the University of Alberta supported by the NSERC Canada grant of the first author.     

CONFIDENCE INTERVALS FOR TEST INFORMATION AND RELATIVE EFFICIENCY

In latent theory the measurement properties of a mental test can be expressed in the test information function. The relative merits of two tests for the same latent trait can be described by the relative efficiency function, i.e. the ratio of the test information functions. It is argued that these functions have to be estimated if the values of the item difficulties are unknown. Using conditional maximum likelihood estimation as indicated by Andersen (1973), pointwise asymptotic distributions of the test information and relative efficiency function are derived for the case of dichotomously scored Rasch homogeneous items. Formulas for confidence intervals are derived from the asymptotic distributions. An application to a mathematics test is given and extensions to other latent trait models are discussed.     

ECONOMETRIC TESTS OF ASSET PRICE BUBBLES: TAKING STOCK*

Abstract Can asset price bubbles be detected? This survey of econometric tests of asset price bubbles shows that, despite recent advances, econometric detection of asset price bubbles cannot be achieved with a satisfactory degree of certainty. For each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble. We are still unable to distinguish bubbles from time‐varying or regime‐switching fundamentals, while many small sample econometrics problems of bubble tests remain unresolved.     

外部融资与企业创新投资效率——基于《物权法》自然实验的经验证据

以2007年《物权法》的实施为外生事件,2003—2011年为样本期间,构造双重差分模型,通过观察我国上市公司在《物权法》实施前后创新投资效率的变化,研究物权制度改革的政策影响。研究发现,物权制度改革提高了我国上市公司的创新投资效率,但这种创新投资效率的提高主要是通过应用型创新实现的,对于开发型创新,《物权法》的促进作用并不显著;股权融资规模的差异对物权保护与创新效率关系的影响存在差异,具体表现为相比于股权融资规模较小的公司而言,股权融资规模较大的公司在物权保护强化的背景下,其开发型创新水平的提高更加显著。