Moran's I test of spatial panel data model — Based on bootstrap method

Under the condition of the finite sample or the unknown distributed error term, testing for spatial dependence in panel data models is an unresolved problem in spatial econometrics. In this paper, a fast double bootstrap (FDB) method is used to construct bootstrap Moran's I tests for Moran's I test in spatial panel data models, and Monte Carlo simulation experiments are used to prove the effectiveness from two aspects including size distortion and power. The experiment results show that, in asymptotic Moran's I test, there is serious size distortion, which could be rectified in bootstrap Moran's I test.     

LM cointegration tests allowing for an unknown number of breaks: implications for the forward rate unbiasedness hypothesis

This article extends the Lagrange multiplier (LM) cointegration test proposed by Westerlund and Edgerton (WE 2007) by allowing for an unknown number of breaks. Monte Carlo simulations provide two main results. First, a loss of power in the LM cointegration tests is detected when potential multiple breaks are ignored. Second, the modified testing procedures do not affect the asymptotic distribution and major properties of the tests of WE under the null, but noticeably increase their testing power in presence of multiple breaks. We also provide empirical applications of the proposed tests for the forward rate unbiasedness hypothesis (FRUH). The results reveal that the FRUH does hold when the effects of the multiple structural breaks are taken into account.     

Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form

Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be infinite. Both linear and nonlinear conditional mean specifications are covered. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroscedasticity and higher order time-varying moments of unknown form. They check a large number of lags, but naturally discount higher order lags, which is consistent with the stylized fact that economic behaviours are more affected by the recent past events than by the remote past events. No specific estimation method is required, and the tests have the appealing „nuisance parameter free” property that parameter estimation uncertainty has no impact on the limit distribution of the tests. A simulation study shows that it is important to take into account the impact of conditional heteroscedasticity; failure to do so will cause overrejection of a correct conditional mean model. In a horse race competition on testing linearity in mean, our tests have omnibus and robust power against a variety of alternatives relative to some existing tests. In an application, we find that after removing significant but possibly spurious autocorrelations due to nonsynchronous trading, there still exists significant predictable nonlinearity in mean for S&P 500 and NASDAQ daily returns.     

On the choice of regularization parameters in specification testing: a critical discussion

This article reviews and discusses the problem of choosing smoothing parameters and resampling schemes for specification tests in econometrics. While smoothing is used for the regularization of the non-specified parts of the null hypothesis and omnibus alternatives, the resampling serves for determining the critical value. Several of the existing selection methods are discussed, implemented, and compared. This has been done for cross-sectional data along the example of additivity testing. Doubtless, all problems considered here carry over to specification testing with dependent data. Intensive simulations illustrate that this is still an open problem that easily corrupts these tests in practice. Possible ways out of the dilemma are proposed.     

Careers guidance,psychometric testing and unemployment amongst young people: an empirical analysis for Northern Ireland

Psychometric tests continue to form an important part of careers guidance for young people of school leaving age throughout the UK. In the existing literature, there is little evidence about the impact of testing on subsequent labour market success. This paper presents a quantitative analysis of the effect of testing in Northern Ireland on young people's subsequent experiences of unemployment and long-term unemployment between the ages of 16 and 18. On account of the sample selection problem, standard single equation estimates of the effects of testing are likely to give biased results, and so the bivariate probit model is used in the estimation. The results suggest that although testing is not having an adverse impact, it is not having a statistically significant positive effect. This may be attributable to some aspects of test administration in Northern Ireland which, in many cases, seems to fall short of recommended guidelines.     

A test for the presence of central bank intervention in the foreign exchange market with an application to the Bank of Canada

In this article, a general nonlinear simultaneous equations framework for the econometric analysis of models of intervention in foreign exchange markets by central banks in response to deviations of exchange rates from target levels is proposed. The instrumental variables estimation of possibly nonlinear response functions and tests of intervention, when the functional form may be nonlinear, asymmetric, and may contain unknown shape parameters, is considered. The methodology applies techniques developed for testing in the presence of nuisance parameters unidentified under a null hypothesis to a nonlinear simultaneous equations model. The results of an empirical analysis of stabilization activity of the Bank of Canada, for the period from 1953 to 2009, with regard to the Canada–U.S exchange rate are reported here. A nonlinear specification is found necessary to capture activity after 1998.     

On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea

Much interest has been paid recently to the nonlinear cointegrating relations existing among economic variables. Various testing procedures are already available to test for the existence of nonlinear cointegration. For example, Breitung (2001) proposes rank tests and his testing procedure has been broadly applied. In this study, we warn against a blind application of the rank cointegration tests, particularly to economic variables that evidence certain behavior. As an illustration, we employ the nominal exchange rates and relative prices of Papua New Guinea against her major trading partners with the objective of testing the validity of purchasing power parity for the country. Our simulation results also confirm our warnings. Additionally, we provide some simple solutions to the problem we encounter herein.     

Bootstrap Testing in Nonlinear Models

Bootstrap testing of nonlinear models normally requires at least one nonlinear estimation for every bootstrap sample. We show how to reduce computational costs by performing only a fixed, small number of Newton or quasi-Newton steps for each bootstrap sample. The number of steps is smaller for likelihood ratio tests than for other types of classical tests and smaller for Newton's method than for quasi-Newton methods. The suggested procedures are applied to tests of slope coefficients in the tobit model and to tests of common factor restrictions. In both cases, bootstrap tests work well, and very few steps are needed.     

Testing for Convergence Clubs in Income Per Capita: A Predictive Density Approach*

The article proposes a technique, based on the predictive density of the data, conditional on the parameters of the model, to jointly tests for groups of unknown size in a panel and to estimate the parameters of each group. The procedure is applied to the problem of identifying convergence clubs in scaled income per capita data. The steady‐state distribution of European regional data clusters around four poles of attraction with different economic features. The distribution of income per capita of OECD countries has two poles of attraction and each group clearly identifiable economic characteristics. We share the uncommonness of being different. J. P. Roche     

Bootstrap LM tests for higher-order spatial effects in spatial linear regression models

This paper first extends the methodology of Yang (J Econom 185:33–59, 2015) to allow for non-normality and/or unknown heteroskedasticity in obtaining asymptotically refined critical values for the LM-type tests through bootstrap. Bootstrap refinements in critical values require the LM test statistics to be asymptotically pivotal under the null hypothesis, and for this we provide a set of general methods for constructing LM and robust LM tests. We then give detailed treatments for two general higher-order spatial linear regression models: namely the \(\mathtt{SARAR}(p,q)\) model and the \(\mathtt{MESS}(p,q)\) model, by providing a complete set of non-normality robust LM and bootstrap LM tests for higher-order spatial effects, and a complete set of LM and bootstrap LM tests robust against both unknown heteroskedasticity and non-normality. Monte Carlo experiments are run, and results show an excellent performance of the bootstrap LM-type tests.     

Diagnostic Testing in Applied Econometrics*

Economic policy formation and the development of economic theory both rely ultimately upon empirical analysis for their direction and sustenance. Recent contributions from econometric theory suggest that the quality of the advice obtained from applied econometric research can be considerably improved by more systematic testing of empirical models. These new tests help identify both strengths and weaknesses of the models. Though fundamental economic theory and good knowledge of data are the primary ingredients of applied economic research, these new diagnostic tests are an important adjunct to existing methodology. This survey introduces the non-specialist econometrician to diagnostic model testing, and thoughout emphasizes the heuristic rather than the mathematical underpinnings of the testing strategy.     

Testing for normality in linear regression models using regression and scale equivariant estimators

In this paper we provide a general solution to the problem of controlling the probability of a type I error in normality tests for the disturbances in linear regressions when using robust-regression residuals. We show that many classes of well-known robust regression estimators belong to the class of regression and scale equivariant estimators. It is these equivariance properties that are used to reduce the nuisance parameter space under the null, from which we develop Monte Carlo and Maximized Monte Carlo tests for the null of disturbance normality. Finally, we illustrate in a simulation experiment the potential power gains from using robust-regression residuals in testing this null hypothesis.     

Panel cointegration and the neutrality of money

Most econometric methods for testing the proposition of long-run monetary neutrality rely on the assumption that money and real output do not cointegrate, a result that is usually supported by the data. This paper argues that these results can be attributed in part to the low power of univariate tests, and that a violation of the noncointegration assumption is likely to result in a nonrejection of the neutrality proposition. To alleviate this problem, two new and more powerful panel cointegration tests are proposed that can be used under quite general conditions. The empirical results obtained from applying these tests to a panel covering ten countries between 1870 and 1986 suggest money and real output are cointegrated, and hence that the neutrality proposition must be rejected.      

Simple Procedures for Testing Autoregressive Versus Moving Average Errors in Regression Models

This paper develops several simple separate (or non-nested) procedures for testing autoregressive versus moving average errors in regression models. These asymptotically valid tests are straightforward to calculate: after estimating both models by maximum likelihood methods, the procedure involves testing the significance of variables added to a linearized version of the null model, the added variables being the predictions, or the residuals from the specified alternative model, or the difference of the predictions of the two models. Some small sample evidence on the properties of the tests is presented, as is an empirical application on the Australian unexpected inflation rate series.
JEL Classification Numbers: C12, C22, C52, E31.     

TESTS OF UNIT ROOTS AND COINTEGRATION HYPOTHESES IN ECONOMETRIC MODELS*

A number of statistical procedures for testing the unit roots hypotheses and the cointegration hypothesis have been proposed by statisticians and econometricians. This paper unifies many of the previous studies on unit roots tests and cointegration tests in the framework of a multivariate regression model and develops some new test statistics. We give a convenient quadratic representation of the limiting distributions of test statistics using stochastic integrals with respect to Brownian motions. The test procedures in this paper include the statistics for testing the unit root, the double unit roots, the seasonal unit roots, and the cointegrating relations for special cases. We also discuss some useful generalizations of unit roots tests and cointegration tests for empirical studies.     

TESTING THE SEQUENTIAL LOGIT MODEL AGAINST THE NESTED LOGIT MODEL*

In this paper, we show that the sequential logit (SL) model, in which a choice process is characterized as a sequence of independent multinomial logit models, is a limiting case of the nested logit (NL) model. For testing the SL model against the NL model, we propose Wald, likelihood ratio and Lagrange multiplier tests after suitably reparameterizing the NL model. It is found that when the NL model parameters are “weakly identified”, the Wald test severely underrejects the true model, whereas the sizes of the LR and LM tests are not significantly affected.     

Bayesian analysis of periodic unit roots in the presence of a break

A Bayesian testing approach for a periodic unit root in quarterly and monthly data is presented. Further a Bayesian test is introduced to test for unit roots at (non)seasonal spectral frequencies. All procedures admit one structural break in the periodic trend function, where the occurrence of a break and the associated timing are treated as additional model parameters. A Bayesian model averaging (BMA) approach is proposed and power functions of the tests are computed. Overall the results indicate that the BMA periodic unit root test exhibits favourable test properties even in small samples. In an empirical application the presented testing procedures are used to test for (non)seasonal forms of unemployment persistence among OECD countries.     

Rationality tests in the presence of instabilities in finite samples

The importance of expectations in modern macroeconomic models and in particular of policy makers expectations for forward looking policy rules has generated a lot of interest in time series of professional forecasts (including central bank staff forecasts). This has spawned a large literature on the evaluation of forecasts that are not model based or where the model is unknown. Although, the available time series of historical forecasts are typically short, this literature has so far mostly disregarded the small sample properties of the proposed tests and estimators. In this paper we fill this gap in the literature, focusing on a set of recently proposed rationality tests for unstable environments. Using a Monte Carlo study we demonstrate that the asymptotic tests are substantially oversized in finite samples including any sample size that is practically available. We provide finite sample adjusted critical values, that allow those tests to be properly applied to sample sizes of typically available forecasts such as the Survey of Professional Forecasters, the Federal Open Market Committee. The critical values we provide will help to avoid false rejections using those data.     

A time series model of fertility and female labour supply in the UK

Multiple time series procedures suitable for estimation and testing with nonstationary data are applied to UK data on age-specific fertility rates, age-specific female labour force participation rates, and women's and men's wages. Cointegration tests establish the existence of two long-run equilibrium relations, identified as a fertility relation and a labour supply equation, for each age group. Maximum likelihood estimates of these equations are consistent with the new home economics model of fertility, and tests of Granger-causality show evidence of extensive feedback among the variables.     

Enhancing the local power of IVX-based tests in predictive regressions

IVX estimation is used increasingly often in predictive regressions with regressors of unknown persistence. While not exhibiting the second-order bias the OLS estimator has in this setup, IVX estimators have reduced rates of convergence when the regressors are highly persistent. The reduced convergence rates may sometimes lead to power losses in finite samples when testing for no predictability, for instance. The note discusses a simple way of improving the local power of IVX-based tests, consisting of augmenting the predictive regression with the lagged dependent variable. This implies a feed-back loop which strengthens the signal of the IVX instrument without changing its dynamic properties. The proposed augmentation works best when the power loss of IVX would have been maximal compared to the infeasible OLS-based test.