Multicointegration, polynomial cointegration and I(2) cointegration with structural breaks. An application to the sustainability of the US external deficit

In this paper we model the multicointegration relation, allowing for one structural break. Since multicointegration is a particular case of polynomial or I(2) cointegration, our proposal can also be applied in these cases. The paper proposes the use of a residualbased Dickey-Fuller class of statistic that accounts for one known or unknown structural break. Finite sample performance of the proposed statistic is investigated by using Monte Carlo simulations, which reveals that the statistic shows good properties in terms of empirical size and power. We complete the study with an empirical application of the sustainability of the US external deficit. Contrary to existing evidence, the consideration of one structural break leads to conclude in favour of the sustainability of the US external deficit.

Real equilibrium exchange rates. A panel data approach for advanced and emerging economies.

Based on an behavioral equilibrium exchange rate model, this paper examines the determinants of the real effective exchange rate and evaluates the degree of misalignment of a group of currencies since 1980. Within a panel cointegration setting, we estimate the relationship between exchange rate and a set of economic fundamentals, such as traded-nontraded productivity differentials and the stock of foreign assets. Having ascertained the variables are integrated and cointegrated, the long-run equilibrium value of the fundamentals are estimated and used to derive equilibrium exchange rates and misalignments. Although there is statistical homogeneity, some structural differences were found to exist between advanced and emerging economies.

CO2 emissions and economic activity: heterogeneity across countries and non stationary series

This paper explores the homogeneity of the functional form, the parameters, and the turning point, when appropriate, of the relationship between CO2 emissions and economic activity for 31 countries (28 OECD, Brazil, China, and India) during the period 1950 to 2006 using cointegration analysis. With a sample highly overlapped over time between countries, the result reveals that the homogeneity across countries is rejected, both in functional form and in the parameters of long term relationship. This confirms the relevance of considering the heterogeneity in exploring the relationship between air pollution and economic activity to avoid spurious parameter estimates and infer a wrong behavior of the functional form, which could lead to induce that the relationship is reversed when in fact it is direct.

Geometric and long run aspects of Granger causality

This paper extends multivariate Granger causality to take into account the subspacesalong which Granger causality occurs as well as long run Granger causality. The propertiesof these new notions of Granger causality, along with the requisite restrictions, are derivedand extensively studied for a wide variety of time series processes including linear invertibleprocess and VARMA. Using the proposed extensions, the paper demonstrates that: (i) meanreversion in L2 is an instance of long run Granger non-causality, (ii) cointegration is a specialcase of long run Granger non-causality along a subspace, (iii) controllability is a special caseof Granger causality, and finally (iv) linear rational expectations entail (possibly testable)Granger causality restriction along subspaces.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Using the HEGY Procedure When Not All Roots Are Present

Empirical studies have shown little evidence to support the presence of all unit roots present in the $^{\Delta_4}$ filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present. We exploit the Vector of Quarters representation and cointegration relationship between the quarters when factors $(1-L),(1+L),\bigg(1+L^2\bigg),\bigg(1-L^2\bigg) y \bigg(1+L+L^2+L^3\bigg)$ are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency $^{\pi/2}$ and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios $^{t_{{\hat\pi}_1}}$ and $^{t_{{\hat\pi}_2}}$ and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is/are present, although this is not the case for the t-ratio tests associated with unit roots at frequency $^{\pi/2}$.

Testing for multicointegration in panel data with common factors

The paper addresses the concept of multicointegration in panel data frame- work. The proposal builds upon the panel data cointegration procedures developed in Pedroni (2004), for which we compute the moments of the parametric statistics. When individuals are either cross-section independent or cross-section dependence can be re- moved by cross-section demeaning, our approach can be applied to the wider framework of mixed I(2) and I(1) stochastic processes analysis. The paper also deals with the issue of cross-section dependence using approximate common factor models. Finite sample performance is investigated through Monte Carlo simulations. Finally, we illustrate the use of the procedure investigating inventories, sales and production relationship for a panel of US industries.

Using the HEGY Procedure When Not All Roots Are Present

Empirical studies have shown little evidence to support the presence of all unit roots present in the $^{\Delta_4}$ filter in quarterly seasonal time series. This paper analyses the performance of the Hylleberg, Engle, Granger and Yoo (1990) (HEGY) procedure when the roots under the null are not all present. We exploit the Vector of Quarters representation and cointegration relationship between the quarters when factors $(1-L),(1+L),\bigg(1+L^2\bigg),\bigg(1-L^2\bigg) y \bigg(1+L+L^2+L^3\bigg)$ are a source of nonstationarity in a process in order to obtain the distribution of tests of the HEGY procedure when the underlying processes have a root at the zero, Nyquist frequency, two complex conjugates of frequency $^{\pi/2}$ and two combinations of the previous cases. We show both theoretically and through a Monte-Carlo analysis that the t-ratios $^{t_{{\hat\pi}_1}}$ and $^{t_{{\hat\pi}_2}}$ and the F-type tests used in the HEGY procedure have the same distribution as under the null of a seasonal random walk when the root(s) is/are present, although this is not the case for the t-ratio tests associated with unit roots at frequency $^{\pi/2}$.

A general theory of rank testing

This paper develops an approach to rank testing that nests all existing rank tests andsimplifies their asymptotics. The approach is based on the fact that implicit in every ranktest there are estimators of the null spaces of the matrix in question. The approach yieldsmany new insights about the behavior of rank testing statistics under the null as well as localand global alternatives in both the standard and the cointegration setting. The approach alsosuggests many new rank tests based on alternative estimates of the null spaces as well as thenew fixed-b theory. A brief Monte Carlo study illustrates the results.

Tourism and Exports as a means of Growth

This study expands existing research by considering both exports and tourism as potential influencing factors for economic growth. While trade of goods has been proven as a means of growth for countries, inbound tourism as non-traditional exports, has been scarcely examined in the literature. Using data for Italy and Spain over the period 1954-2000 and 1964-2000 respectively, both exports of goods and tourism exports are included in the same model. Standard cointegration and Granger causality techniques are applied. The main results reveal the significance of both exports and tourism towards longterm growth with some peculiarities for each country.

Sustainability of EU fiscal policies. A panel test

The fiscal policy rule implicit in the Stability and Growth Pact, has been rationalised as a way to ensure that national fiscal policies remain sustainable within the EU, thereby endorsing the independence of the ECB. We empirically examine the sustainability of European fiscal policies over the period 1970-2001. The intertemporal government budget constraint provides a test based on the cointegration relation between government revenues, expenditures and interest payments. Sustainability is analysed at both the national level and for a European panel. Results show that European fiscal policy has been sustainable overall, yet national experiences differ considerably.