Tests for additive heteroskedasticity: Goldfeld and Quandt revisited

A number of new tests for heteroskedasticity have recently become available. Using Monte Carlo methods this paper explores the small sample properties of some of these tests in the context of additive heteroskedasticity. Lagrange multiplier and Wald tests (and variants thereof) are found to be inferior to the likelihood ratio and Goldfeld and QuandtF tests. This is a reconfirmation of the conclusions obtained byGoldfeld/Quandt [1972] in their study of additive heteroskedasticity. The paper also contains some new results onAmemiya's GLS estimator of the additive heteroskedastic structure.     

An augmented autoregressive distributed lag bounds test for cointegration

An augmented autoregressive distributed lag (ARDL) bounds test for cointegration involves an extra F-test on the lagged levels of the independent variable(s) in the ARDL equation. Originally, this testing strategy was introduced using the bootstrap procedure. This paper provides both the small sample and asymptotic critical values for easier implementation of the test, making it applicable for a broader range of researchers. Two advantages of this augmented ARDL bounds test are that the assumption of an I(1) dependent variable is not necessary, and a clear conclusion on the cointegration status is provided by the three tests. The augmented ARDL bounds test is demonstrated using an empirical study on government taxation and expenditures. The tests support the tax-and-spend hypothesis of the budgetary policy for the US, the UK, and France.     

Asian real interest rates, nonlinear dynamics, and international parity

This study tests for nonlinearities in the real interest differentials of four South East Asian economies with respect to Japan and the United States. The logistic and exponential smooth transition regression models are applied to monthly data over the sample period 1977M1–2000M3. There is evidence of nonlinearities in Asian real interest differentials where nonlinearities are often captured by the logistic smooth transition autoregressive (STAR) model. The extent of nonlinearities varies across the sample with the Singapore–Japan and Thailand–Japan differentials exhibiting the sharpest transition from one regime to another. Large shocks to real interest parity (RIP) are more likely to lead to the reestablishment of parity at a faster rate than small shocks. Modeling the nonlinear stochastic dynamics of RIP can thus be useful for policymaking purposes in recovering information on monetary and financial crises.     

Small sample properties of Canonical Cointegrating Regressions

Monte Carlo simulations are performed to examine small sample properties of Canonical Cointegrating Regressions (CCR). The first data generation process is designed to generate both cointegrated and non-cointegrated systems with normal disturbances. If the near-observational equivalence of the stationary and the integrated processes is not significant, both powers and empirical sizes of CCR tests are acceptable. The second data generation process is based on the error correction model. Cointegrated systems with various fat-tailed disturbances are generated and analyzed. The empirical sizes of CCR tests with studentt disturbances and GARCH disturbances are found to be reasonable under certain restrictions. The last data generation process is a generalized least squares (GLS) process that incorporates heteroskedasticity into the error correction model. Again, the empirical sizes of CCR tests are reasonable.     

Semiparametric and nonparametric testing for long memory: A Monte Carlo study

The finite sample properties of three semiparametric estimators, several versions of the modified rescaled range, MRR, and three versions of the GHURST estimator are investigated. Their power and size for testing for long memory under short-run effects, joint short and long-run effects, heteroscedasticity andt-distributions are given using Monte Carlo methods. The MRR with the Bartlett window is generally robust with the disadvantage of a relatively small power. The trimmed Whittle likelihood has high power in general and is robust except for large short-run effects. The tests are applied to changes in exchange rate series (daily data) of 6 major countries. The hypothesis of no fractional integration is rejected for none of the series.     

Tests of restrictions in large demand systems

This paper compares some asymptotic tests of linear restrictions, using exact results and Monte Carlo methods, in systems which contain the same regressors in each equation. It is found that under a variety of conditions, a statistic suggested by Deaton provides a better approximation to the true distribution in small sample situations than the Wald, likelihood ratio or Lagrange multiplier tests.     

More on the correct use of omnibus tests for normality

This Monte Carlo study compares the small sample properties of some commonly used omnibus and directional tests, based on the standardized third and fourth moments, for assessing the normality of random variables: the omnibus D'Agostino K² test and the directional components, and three versions of the Jarque–Bera test.     

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.     

Testing for Granger non-causality in heterogeneous panels

This paper proposes a very simple test of Granger (1969) non-causality for heterogeneous panel data models. Our test statistic is based on the individual Wald statistics of Granger non causality averaged across the cross-section units. First, this statistic is shown to converge sequentially to a standard normal distribution. Second, the semi-asymptotic distribution of the average statistic is characterized for a fixed T sample. A standardized statistic based on an approximation of the moments of Wald statistics is hence proposed. Third, Monte Carlo experiments show that our standardized panel statistics have very good small sample properties, even in the presence of cross-sectional dependence.     

Trade and regional growth in Spain: panel cointegration in a small sample

In this article, we test for the existence of a relationship between per capita Gross Domestic Product (GDP) and trade, for 15 Spanish Autonomous Communities between 1988 and 2004, using a panel cointegration methodology. In particular, we implement several panel unit root tests (Maddala and Wu, 1999; Levin et al., 2002; Im et al., 2003) and panel cointegration tests (Pedroni, 1999, 2004), with a special attention to their behaviour in a small sample. We also develop a Seemingly Unrelated Regression Estimation (SURE) residual based test, in order to explicitly take into account the cross regional correlation pattern. Appropriate confidence intervals are estimated with a sieve bootstrap designed for our small time sample, preserving the dependence structure among cross sectional units. Our cointegration tests reject the existence of a significant relationship between GDP per capita and exports. However, we do find some evidence of a significant relationship between GDP per capita and imports or with total trade.     

A note on the Wald,LR and LM tests and misspecification

In this note, we investigate sensitivity of the Wald, LR and LM tests to specification error. It is shown that these three tests are very sensitive to specification error, but the LM test is relatively superior to other two tests under certain situations.     

Social class, family background, and intergenerational mobility

This research examines the various approaches taken by economists and sociologists for analyzing intergenerational mobility. Social mobility models based on social classes arising from an occupational classification scheme are analysed. A test for the statistical validity of classification schemes is proposed and tested using Danish sample survey data that was first collected in 1976 and augmented in 2000. This is referred to as a homogeneity test and is a likelihood ratio test of a set of linear restrictions which define social classes. For Denmark it is shown that this test fails for an Erikson-Goldthorpe classification system, raising doubts about the statistical validity of occupational classification systems in general. We also estimate regression models of occupational earnings, household earnings, and educational attainment using family background variables as covariates controlling for unobservables, measurement error, and simultaneous equation bias. In these models homogeneity tests are also rejected. We conclude from these results that the individual's family background has a small but significant impact on lifetime chances which is not captured by the Erikson-Goldthorpe classification scheme.     

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.     

Market efficiency,purchasing power parity,and the official and parallel markets for foreign currency in Latin America

This paper examines the purchasing power parity (PPP) theory from a long-run perspective in the presence of a parallel or ‘black’ market for U.S. dollars in four Latin American countries, namely Argentina, Brazil, Chile, and Mexico, using monthly data for the recent float. Johansen's full information maximum likelihood multivariate cointegration technique is applied. Recent developments associated with this procedure are considered. First, a formal test developed by Johansen [Econometric Theory 8 (1992) 188, Econometric Theory 11 (1995) 25, Scand. J. Stat. 24 (1997) 433] for the presence of I(2) and I(1) components in a multivariate context is applied along with the estimation of the roots of the companion matrix for the correct determination of the cointegration rank. Second, given that two significant cointegration vectors were found for any country, structural restrictions identifying the long-run relations of interest are specified as proposed by Johansen and Juselius [J. Econometrics 63 (1994) 7] and Johansen [J. Econometrics 69 (1995) 111]. Thus, the joint structure of PPP and long-run informational market efficiency could not be rejected for all countries. Furthermore, estimation of the error correction terms shows that the black market rate adjusts to eliminate any deviation from long-run PPP. Finally, stability tests proposed by Hansen and Johansen [Hansen, H., & Johansen, S. (1993). Recursive estimation in cointegrated VAR-models. Working Paper, University of Copenhagen, Institute of Mathematical Statistics; Econometrics J. 2 (1999) 306] are applied and it is shown that the dimension of the cointegration space is sample dependent while the estimated coefficients do not exhibit instability in recursive estimations.     

Firm size and capital structure: evidence using dynamic panel data

This article suggests that the validity of the Trade-Off Theory (TOT) and Pecking-Order Theory (POT) to explain financing decisions varies among small, medium-sized and large firms. Using dynamic panel data tests on a sample of 3439 Spanish firms over the period 1995–2003, results are partially consistent with both explanations but suggest a greater validity of pecking-order predictions for small firms. In small firms, the negative influence of profitability and the positive influence of investment opportunities and of intangible assets on firm debt predicted by the POT are heightened. However, no differences are observed between small and large firms in their speed of adjustment to the target leverage as suggested by the TOT.     

Three tests for the existence of cycles in time series

Three tests for the presence of cycles in univariate time series are proposed. The asymptotic distribution of the tests is derived using the properties of the integrated periodogram and the small sample properties are examined using a Monte Carlo experiment. The tests are applied to U.S. data to detect the existence of significant seasonal and of other types of periodic fluctuations.     

Do we reject too often?: Small sample properties of tests of rational expectations models

We examine the small sample properties of tests of rational expectations models. We show using Monte Carlo experiments that the asymptotic distribution of test statistics can be extremely misleading when the time series examined are highly autoregressive. In particular, a practitioner relying on the asymptotic distribution will reject true models too frequently. We also show that this problem is especially severe with detrended data. We present correct small sample critical values for our canonical problem.     

Two further aspects of some new tests for structural stability

This paper presents two extensions to Hall and Sen’s [Hall, A.R. and Sen, A. 1999. Structural stability testing in models estimated via generalized method of moments. J. Bus. Econ. Stat., 17, 335–348.] analysis of their structural stability tests. First, we approximate the p-values for the non-standard asymptotic null distribution for the structural stability test statistics proposed by Hall and Sen (1999). The p-value response surfaces are approximated by a parametric function using the methodology proposed by Hansen [Hansen, B.E., 1997. Approximate asymptotic P-values for structural change tests. J. Bus. Econ. Stat, 15, 60–67.] Second, we show how Hall and Sen’s (1999) testing methodology can be used to diagnose the source of instability in Euler equation models. To illustrate this issue, we examine the stability of the dividend capital asset pricing model proposed by Hagiwara and Herce [Hagiwara, M. and Herce M.A., 1997. Risk aversion and stock price sensitivity to dividends. Am. Econ. Rev. 87, 738–745]. Hagiwara and Herce (1997) estimate the model using annual data from 1889–1994 and find the model is not rejected using the over-identifying restrictions test. Using the same data, we find some evidence of structural instability in the model. Interestingly, the tests reveal that the model appears to be correctly specified for the period up until 1942 but incorrectly specified in the post 1942 part of the sample.     

Functional sensitivity of testing the environmental Kuznets curve hypothesis

Conventional tests for the environmental Kuznets curve (EKC) hypothesis mostly apply a quadratic equation in modeling the non-linear relationship between environmental indices (such as air pollutants) and welfare measures (such as income per capita). If their inverted-U shaped pattern is empirically accepted with two significant regressors, the income per capita and its square transformation, the EKC hypothesis is supported. Using an OECD sample, this paper shows that the validity of testing the EKC hypothesis is sensitive to how we transform income non-linearly in sulfur and carbon EKC regressions. This paper carries out experiments on different powers of γ for transforming income non-linearly and concludes that only when 0 < γ < 1 and 1 < γ < 2 will the EKC regression demonstrate a testable non-linear cointegration relationship between the two air pollutants and income per capita. In the generalized EKC regressions estimated in this paper, although we find sulfur and carbon EKC patterns in the OECD sample, none of the EKC regressions using different γ is a cointegrating equation. This finding implies an inside critique to the EKC literature that failure of cointegration of the conventional EKC regression is not because of using the quadratic functional form, but because of the fundamentally spurious relationship between the trends of pollutants and income levels.     

DO REAL INTEREST RATES REALLY CONTAIN A UNIT ROOT? MORE EVIDENCE FROM A BOOTSTRAP COVARIATE UNIT ROOT TEST

This paper re‐examines the empirical finding that international real interest rates usually have a unit root. This conclusion is put forth in Rapach and Weber (2004 ), using the Ng and Perron (2001 ) tests. We use Rudebusch's (1993 ) approach to construct the small sample distributions of the Ng and Perron tests, and calculate their asymptotic sizes, size‐adjusted powers and rejection rates. These numbers show that the lack of power in the Ng and Perron tests might account for the findings of Rapach and Weber (2004 ): that the unit root null cannot be rejected for most OECD countries. Size distortions are mild in the case of Ng and Perron tests for two series, but are serious for the Phillips and Perron Z‐test on inflation rates. We then apply a powerful covariate augmented Dickey–Fuller unit root test to examine the series for which stationarity cannot be determined with the Ng and Perron tests. The bootstrap technique is also used to control possible size distortions. In contrast to the results of Rapach and Weber (2004 ), the bootstrap covariate augmented Dickey–Fuller test yields striking evidence that real interest rates are stationary for 14 of 16 OECD countries, because nominal interest rates are stationary for the 14 countries, while inflation rates are stationary for all countries.