Tests for cointegration allowing for an unknown number of breaks

This paper introduces cointegration tests allowing for an unknown number of breaks. The introduced tests assume that the unspecified number of breaks is smaller than or equal to the maximum number of breaks set a priori. Monte Carlo simulations provide two main results. First, the proposed tests perform as well as the tests of Gregory and Hansen (1996a) and Hatemi-J (2008), which assume one or two breaks a priori, when the cointegration relationship has one or two breaks. Second, the proposed tests perform better than the tests of Gregory and Hansen (1996a) and Hatemi-J (2008) when the cointegration relationship has more than three breaks or persistent Markov switching shifts. We also provide empirical applications for the money demand of the U.S. The empirical results show that the proposed tests reject the null hypothesis of no cointegration as compared to other tests.     

Bootstrapping covariate stationarity tests for inflation rates

This paper investigates the stationarity properties of international inflation rates by bootstrapping two stationarity tests with covariates in Jansson (2004). When the asymptotic critical values are used, the two powerful tests are found to reject the null hypothesis less in the presence of a large negative moving-average (MA) error in inflation. To cope with this problem, a parametric bootstrap scheme is developed and then is investigated by a Monte Carlo study. The simulation results demonstrate that the bootstrap tests display a better control over the empirical rejection rates at finite samples. Furthermore, after applying these tests to the inflation in G-10 countries, we find that one of the two tests using bootstrap critical values yields inferences that differ from when using asymptotic ones, and as a whole, the bootstrap tests consistently provide strong evidence in support of mean reversion in inflation in most countries of the G-10.     

Exchange rates dynamics revisited: a panel data test of the fractional integration order

We test the possibility that exchange rates from nine developed countries have a unit root against the alternate possibility that they are fractionally integrated. Theoretically, exchange rates are only expected to follow a random walk under restrictive assumptions. However, most traditional unit root tests cannot reject a unit root in exchange rates, and time series tests that allow for fractional integration have given inconclusive results. To increase the power of the test of the integration order we develop two panel data tests of the fractional integration order. Monte Carlo simulations show that these tests are correctly sized and have relatively high power compared to other similar tests. Moreover, our empirical results show that we can reject a unit root in exchange rates with a high probability, but the integration order is close to one. This indicates that exchange rates are mean-reverting, although the reversion is slow, resulting in long swings.     

TESTING THE STRUCTURE OF CONDITIONAL CORRELATIONS IN MULTIVARIATE GARCH MODELS: A GENERALIZED CROSS‐SPECTRUM APPROACH*

We introduce a class of generally applicable specification tests for constant and dynamic structures of conditional correlations in multivariate GARCH models. The tests are robust to the presence of time‐varying higher‐order conditional moments of unknown form and are pure significance tests. The tests can identify linear and nonlinear misspecifications in conditional correlations. Our approach does not necessitate a particular parameter estimation method and distributional assumption on the error process. The asymptotic distribution of the tests is invariant to the uncertainty in parameter estimation. We assess the finite sample performance of our tests using simulated and real data.     

Tests for cointegration rank and the initial condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Such initial conditions are known to affect the power of univariate unit root tests diversely, whereas their impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on the power of tests for cointegration rank, such as Johansen??s widely used likelihood ratio test, tests with prior adjustment for deterministic terms, and a test based on the eigenvalues of the companion matrix. We find that the power of the likelihood ratio test is increasing in the magnitude of the initial condition, whereas the power of the other tests is generally decreasing. We exploit these findings in an application to price convergence.     

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.     

Robust tests for time-invariant individual heterogeneity versus dynamic state dependence

We derive tests for persistent effects in a general linear dynamic panel data context. Two sources of persistent behavior are considered: time-invariant unobserved factors (captured by an individual random effect) and dynamic persistence or “state dependence” (captured by autoregressive behavior). We will use a maximum likelihood framework to derive a family of tests that help researchers learn whether persistence is due to individual heterogeneity, dynamic effect, or both. The proposed tests have power only in the direction they are designed to perform, that is, they are locally robust to the presence of alternative sources of persistence, and consequently, are able to identify which source of persistence is active. A Monte Carlo experiment is implemented to explore the finite sample performance of the proposed procedures. The tests are applied to a panel data series of real GDP growth for the period 1960–2005.     

The stability assumption in tests of causality between money and income

This note argues that structural stability is an important condition for tests of Grangercausality. Despite this fact the standard causality tests are sometimes applied to data for which structural stability cannot be assumed a priori. Therefore the stability of GNP/M1 systems of the U.S., Canada, and West Germany in the aftermath of the 1973/74 oil crisis is analyzed using formal statistical tests. Prediction tests are particularly useful for that purpose. The stability of the model for Canadian data is rejected whereas stability is not rejected for the U.S. and West Germany.     

Digging out the PPP hypothesis: an integrated empirical coverage

We use several popular tests to test the validity of the Purchasing Power Parity (PPP) hypothesis. In particular, we analyze four classes of tests??standard univariate unit root tests, co-integration, panel unit root tests, and unit root tests for nonlinear frameworks??for a dataset consisting of 20 bilateral exchange rates. Through this approach, we ascertain the effectiveness of each methodology in assessing the validity of PPP. Overall, our results suggest little evidence to support PPP. Among the conducted tests, the Panel Analysis of Nonstationarity in the Idiosyncratic and Common components (PANIC) provides the richest insights by disentangling the possible sources of non-stationarity of real exchange rates. The relevance of using price indices with different characteristics is also pinpointed.     

A wavelet-based panel unit-root test in the presence of an unknown structural break and cross-sectional dependency,with an application of purchasing power parity theory in developing countries

This article introduces two different non-parametric wavelet-based panel unit-root tests in the presence of unknown structural breaks and cross-sectional dependencies in the data. These tests are compared with a previously suggested non-parametric wavelet test, the parameteric Im-Pesaran and Shin (IPS) test and a Wald type of test. The results from the Monte Carlo simulations clearly show that the new wavelet-ratio tests are superior to the traditional tests both in terms of size and power in panel unit-root tests because of its robustness to cross-section dependency and structural breaks. Based on an empirical Central American panel application, we can, in contrast to previous research (where bias due to structural breaks is simply disregarded), find strong, clear-cut support for purchasing power parity (PPP) in this developing region.     

Convergence in West German Regional Unemployment Rates

Abstract. Differences in regional unemployment rates are often used to describe regional economic inequality. This paper asks whether changes in regional unemployment differences in West Germany are persistent over time. Understanding the persistency of regional unemployment differences helps us to assess how effective regional policy can be. While univariate tests suggest that changes in regional unemployment differences are persistent in West Germany, more powerful panel tests lend some support to the hypothesis that regional unemployment rates converge. However, these tests reveal a moderate speed of convergence at best. Because there is a structural break following the second oil crisis, we also use tests that allow for such a break. This provides evidence for both convergence and quick adjustment to an equilibrium distribution of regional unemployment rates that is, however, subject to a structural break.     

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.     

A critical assessment of existing estimates of US core inflation

Core inflation rates are widely calculated. The perceived benefit of core inflation rates is that they help to inform monetary policy. This is achieved by uncovering the underlying trend in inflation or by helping to forecast inflation. Studies which compare core inflation rates frequently assess candidate core rates on these two criteria. Using US data, the two standard tests of core inflation – the ability to track trend inflation and the ability to forecast inflation – are applied to a more comprehensive set of core inflation rates than has been the case in the literature to date. Furthermore, the tests are applied in a more rigorous fashion. A key difference in this paper is the inclusion of benchmarks to the tests, which is non-standard in the literature. Two problems with core inflation rates emerge. Firstly, it is very difficult to distinguish between different core rates according to these tests, as they tend to perform to a very similar level. Secondly, once the benchmarks are introduced to the tests, the core inflation rates fail to outperform the benchmarks. This failure suggests that core inflation rates are of less practical usefulness than previously thought.     

Risk aversion,order strategy and price formation

Since goods classified as non-durable may, in fact, have a durable component, random-walk tests of the permanent income hypothesis using non-durable data series may yield incorrect results. This paper investigates this problem by first simulating a model of consumption to show the effects of durability on statistical tests of non-durable consumption models, and then by applying these tests to various disaggregated consumption series to determine the effect in practice. The paper finds that there are significant differences in the behaviour of the series within the non-durables and services catagories, and that these differences may be related to durability. The effect of this on standard tests of consumption is discussed.     

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.     

Meeting Maastricht: Nominal convergence of the new member states toward EMU

This paper estimates whether the new member states (NMS) that joined the EU in 2004 have achieved a form of inflation and long-term interest rate convergence. Using quarterly data from the mid-1990s, convergence is evaluated through a series of unit root and cointegration tests. Both univariate and panel tests are performed, including tests for a large number of combinations of inflation and interest rates satisfying the Maastricht inflation and long-term interest rate criteria. It is generally found that nominal convergence in inflation has been attained among the NMS. There is, however, less evidence of convergence in long-term interest rates. Possible exceptions include Estonia and the Czech Republic and, to a lesser extent, Slovakia which has since joined the euro area. There is also a large degree of consistency between the various unit root and cointegration tests in both the univariate and panel variations.     

Testing for Equilibrium in the Australian Wage Equation*

In this paper a range of unit root and cointegration tests are applied to the time-series variables most commonly found in the various specifications of the Australian wage equation. We find a contradiction between the standard Dickey-Fuller (DF) tests and the results from Johansen estimation regarding the order of integration. The conclusion we reach using tests developed by Perron (1989,1990) is that all the variables are trend stationary processes and that the cointegration framework is inappropriate in this case.     

Hysteresis in the development of unemployment: the EU and US experience

We examine hysteresis in EU and US unemployment by panel unit root tests. First generation tests indicate that unemployment is stationary. Second generation tests show mixed results. Idiosyncratic components are stationary in the US. A unit root in the US common component depends on the starting point of the sample. While the common component is nonstationary over the whole period, it is mean-reverting after initial observations are dropped. Hysteresis in EU unemployment is attributed to idiosyncratic, but not to common components. The findings might reflect a different regulation of labour markets and a lower degree of migration in the EU.     

A new test for chaos and determinism based on symbolic dynamics

We propose a novel test to determine, given a time series, if the dynamics are generated by a deterministic (including low dimensional chaos), rather than a stochastic, process. In addition, we introduce a new nonparametric bootstrap test for independence which is consistent against a broad class of alternatives. The conditions under which the tests can be applied are very weak. The advantages of the presented methods are simplicity, invariance with respect to monotonic transformations and the applicability of the tests regardless of the discrete or continuous nature of the data generating process. We conduct several simulation studies to evaluate the performance of our tests on well-known dynamic processes. Finally, our tests are applied to several sets of financial returns that have been recently studied.     

Determining market power exertion between buyers and sellers: are nonparametrics a viable alternative?

A review of recent literature reveals the development of several deterministic non-parametric (DNP) tests of market power. The performance of selected DNP market power tests is ascertained to determine their usefulness as an alternative to data-hungry parametric market power tests. This assessment is carried out through implementation of Monte Carlo experiments using data sets from ten known market structures. Only two of the six DNP tests appear able to satisfactorily identify market power.