Unit Roots and Cointegration Analysis: The Impact on Empirical Analysis in Economics

The purpose of this paper is to examine some of the impacts of the theoretical literature relating to unit roots and cointegration on empirical analysis in economics. The results of a survey of time-series-related empirical papers in seven journals in 1995 indicate that about 40 per cent and 30 per cent of papers include tests for unit roots and cointegration , respectively. In testing for unit roots, the Augmented Dickey- Fuller procedure is clearly the most commonly used test. In testing for cointegration, the closely related Engle-Granger procedure is the most commonly used test but its dominance is not as pronounced.     

Are PPP tests erratically behaved? Some panel evidence

This paper examines whether, in addition to standard unit root and cointegration tests, panel approaches also produce test statistics behaving erratically when applied to tests for Purchasing Power Parity (PPP). We show that if appropriate tests (which are robust to cross‐sectional dependence) are used, any evidence of erratic behaviour disappears, and empirical support is found for PPP.     

Tests for cointegration with two unknown regime shifts with an application to financial market integration

It is widely agreed in empirical studies that allowing for potential structural change in economic processes is an important issue. In existing literature, tests for cointegration between time series data allow for one regime shift. This paper extends three residual-based test statistics for cointegration to the cases that take into account two possible regime shifts. The timing of each shift is unknown a priori and it is determined endogenously. The distributions of the tests are non-standard. We generate new critical values via simulation methods. The size and power properties of these test statistics are evaluated through Monte Carlo simulations, which show the tests have small size distortions and very good power properties. The test methods introduced in this paper are applied to determine whether the financial markets in the US and the UK are integrated.      

Testing for Unit Roots in Small Panels with Short-run and Long-run Cross-sectional Dependencies

An IV approach, using as instruments non-linear transformations of the lagged levels, is explored to test for unit roots in panels with general dependency and heterogeneity across cross-sectional units. We allow not only for the cross-sectional dependencies of innovations, but also for the presence of co-integration across cross-sectional levels. Unbalanced panels and panels with differing individual short-run dynamics and cross-sectionally related dynamics are also permitted. We also more carefully formulate the unit root hypotheses in panels. In particular, using order statistics, we make it possible to test for and against the presence of unit roots in some of the individual units for a given panel. The individual IV t -ratios, which are the bases of our tests, are asymptotically and normally distributed and cross-sectionally independent. Therefore, the critical values of the order statistics as well as the usual average statistic can be easily obtained from simple elementary probability computations. We show via a set of simulations that our tests work well, whereas other existing tests fail to perform properly. As an illustration, we apply our tests to the panels of real exchange rates, and find no evidence for the purchasing power parity hypothesis, which is in sharp contrast with the previous studies.     

Revisiting the Link Between Stock Prices and Goods Prices in OECD Countries

Fisher hypothesis postulates positive relation between stock return and inflation; however early studies document negative relationship between the two and they conclude that stock cannot be used as a hedge against inflation. In this paper we explore long‐run nonlinear relationship between stock price and goods price. Our sample consists of 19 OECD countries; all or some of these countries have been studied before with the findings of linear cointegration between the stock index and goods price index. Based on unit root tests and linear cointegration test, we apply threshold cointegration tests, Autoregressive Distributed Lag (ARDL) cointegration test and panel VAR method. With all these econometric methods we arrive at heterogeneous findings as follows: two countries have linear cointegration, five countries have threshold cointegration, nine countries do not have any cointegration and finally two countries provide inconclusive results. Estimates of Fisher coefficient provided by linear and nonlinear cointegration methods, which range between 1.27 and 1.86, are consistent with previous studies. Impulse response analysis from panel VAR for countries having no cointegrating relation shows that shock to inflation produces negative response in stock return, which supports findings of earlier studies.     

Government revenue,government expenditure,and temporal causality: evidence from China

Dissatisfied with little evidence provided on various hypotheses concerning the revenue-expenditure relation in China, this paper is an empirical endeavour to fill the gap through a battery of econometric tests for causality based on vector error correction and vector autoregression models. A more comprehensive testing strategy for unit roots and cointegration has been suggested, and a bidirectional causality pattern has been found in China's government finance. The paper thus concludes that attempts simply to change revenue or expenditure or both without taking into account of the interdependence between the two may be counter-productive, and the effects on aggregate demand of government debt-financing in the presence of inflation may not be as detrimental as some economists would expect.     

Testing for seasonal integration and cointegration: The Austrian consumption income relationship

This paper analyzes the nature of seasonal fluctuations in quarterly observations for Austrian consumption and income data. We begin with univariate tests of the order of integration and then move on to tests of cointegration. Seasonally adjusted as well as raw data are used in these tests. in univariate tests, the outcome for seasonally adjusted and raw data is in line. The unit roots at the zero frequency found in the seasonally adjusted series are also present in the raw data. In bivariate tests, the results for seasonally adjusted and raw data differ. While we find cointegration at the zero frequency between consumption and income for seasonally adjusted series, this hypothesis is generally rejected for the raw data.     

Do Financial and Institutional Variables Enhance the Impact of Remittances on Economic Growth in Latin America and the Caribbean? A Panel Cointegration Analysis

Using recently developed panel unit root and panel cointegration tests and the Fully-Modified OLS methodology (FMOLS), this paper estimates the impact of remittances on the economic growth of selected upper and lower income Latin American & Caribbean (LAC) countries over the 1990–2007 period. Despite the large flow of remittances to the region, there have been relatively few empirical studies assessing the impact of remittances on economic growth in LAC. Panel unit root tests suggest that several of the macro variables included in the model exhibit unit roots, yet, at the same time, Pedroni’s panel cointegration test determined that there is a cointegrating relationship among the variables in the estimated model. The FMOLS estimates suggest that remittances have a positive and significant effect on economic growth in both groups of countries. The estimates also indicate that both the degree of economic freedom and credit provided by the banking system have a positive and significant effect on economic growth in upper (middle) income LAC countries. The sign of the interaction term between remittances and the credit (and EFI) variables suggest that remittances act as substitutes for these variables. Finally, the effect of remittances on both sets of countries is stronger in the presence of a financial (credit) variable.     

Detecting cointegration relationships under nonlinear models: Monte Carlo analysis and some applications

Testing for cointegration in the presence of nonlinear adjustments or structural breaks is important for examining the equilibrium relationship among economic variables. It is known that standard cointegration tests perform poorly when a cointegration relationship has nonlinear adjustments or structural breaks. However, it is not clear how some cointegration tests allowing for nonlinearity perform under other classes of nonlinear cointegration models. This paper investigates which cointegration tests help detect a cointegration relationship with nonlinear adjustments or structural breaks. Our Monte Carlo simulation results demonstrate that the cointegration test with threshold adjustment generally has better power performance under most cointegration relationships with nonlinearity. We also provide empirical applications to the money demand and term structure of the U.S. interest rates. The empirical results show that the test allowing for threshold adjustment provides strong evidence of the cointegration relationships of money demand and the term structure of interest rates.     

Long‐Run PPP under the Presence of Near‐to‐Unit Roots: The Case of the British Pound–US Dollar Rate*

Empirical tests typically provide evidence that the British pound–US dollar exchange rate and the relative wholesale price index contain exact unit roots and exhibit cointegration. However, the cointegrating vector is significantly different from [1, ?1], thus raising doubts on the validity of the purchasing power parity (PPP) hypothesis. Following Elliott (1998 ), we show that if the exchange rate and relative price series contain near‐to‐unit roots in the context of a bivariate system, then any inference on the “cointegrating” vector and consequently on PPP, which is based on standard cointegration estimation methods, will be misleading. We then argue that the existing evidence against the PPP hypothesis in the British pound–US dollar market can be attributed to the finite sample bias of the standard cointegration estimators, arising from an endogenous and “nearly” nonstationary regressor. We also show that when robust procedures are employed the evidence favors the PPP hypothesis.     

Cointegration and causality in the exports-GDP nexus: The post-war evidence for Canada

This paper tests for unit roots, cointegration, and Granger-causality in the exports-GDP nexus in Canada 1947–96, using both bivariate and trivariate models. Contrary to previous studies we cannot conclude that economic growth is either export-led, or output-driven, but rather that strong bi-directional causality exists between Canadian exports and GDP, and the GDP of its main trading partner, the United States. First version received: April 1998/final version received: March 1999     

On the Robustness of Robustness Checks of the Environmental Kuznets Curve Hypothesis

Since its first inception in the debate on the relationship between environment and growth in 1992, the Environmental Kuznets Curve hypothesis (EKC hereafter) has been subject of continuous and intense scrutiny. The most recent line of investigation criticizes the EKC hypothesis on more fundamental grounds, in that it stresses the lack of sufficient statistical testing of the empirical relationship and questions the very existence of the notion of EKC. Attention is in particular drawn on the stationarity properties of the series involved—per capita emissions or concentrations and per capita GDP—and, in case of presence of unit roots, on the cointegration property that must be present for the EKC to be a well-defined concept. Only at that point can the researcher ask whether the long-run relationship exhibits an inverted-U pattern. On the basis of panel integration and cointegration tests for sulfur, Stern (2004) and Perman and Stern (1999, 2003) have presented evidence and forcefully stated that the EKC hypothesis does not exist. In this paper we ask whether similar strong conclusions can be arrived at when carrying out tests of system fractional integration and cointegration. As an example we use the controversial case of carbon dioxide emissions. The results show that more EKCs come back into life relative to traditional integration/cointegration tests. However, we confirm that the EKC hypothesis remains a fragile concept.      

A managerial model of investment: overlooked alternatives

The long-run purchasing power parity (PPP) hypothesis is tested for nine bilateral sterling exchange rates, using recently developed techniques on cointegration and seasonal integration. The empirical findings show that none of the exchange rates and relative prices contain seasonal unit roots, but all have an autoregressive unit root. The cointegration tests overwhelmingly reject the PPP hypothesis as a long-run equilibrium condition for all countries concerned.     

The Feldstein–Horioka model re-visited for African countries

We study the relationship between the saving and investment rates for 20 African countries using a long period of data. A high correlation between saving and investment is often taken as evidence of capital immobility. We use the new Ng–Perron unit root tests to examine the stationarity of saving and investment rates. Both Johansen cointegration tests and fractional cointegration tests are used. The results are mixed. The Johansen cointegration tests show that the saving and investment rates are cointegrated only for Rwanda and South Africa. This implies that for the other 18 countries, there is evidence of capital mobility. The fractional cointegration test results are different. The two rates are found to be fractionally cointegrated for the following 12 countries: Algeria, Burundi, Egypt, Morocco, Niger, Rwanda, Senegal, South Africa, Swaziland, Tunisia, Tanzania and Zimbabwe. For Cote d’Ivoire, Kenya, Lesotho and Sierra Leone there is some evidence of capital mobility while the results for Ethiopia, Malawi, Mauritius and Nigeria are mixed.     

The seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

Efficient Tests for a Unit Root When the Initial Observation is Drawn From Its Unconditional Distribution

Researchers desire powerful tests for unit roots. This paper derives the family of asymptotically most powerful tests for unit roots when the initial condition is drawn from its unconditional distribution under the alternative. This enables both the examination of previously proposed statistics and the construction of powerful tests against this alternative model.     

Unit Root Analyses of the Causality Between Japanese Money and Income

Unit root techniques and cointegration analysis have develop ed considerably in the last ten years. At the same time, the nonstationary test for Granger causality has been developed. We shed some new light on Japanese money supply and income causality by using nonstationary techniques. We specify univariate ARMA models of money, income, GNP deflator and rate of interest, initially by using the Dickey and Fuller (DF) or the augmented DF (ADF) tests. Two diagnostic tests are applied to each selected ARMA regression. One is the residual DF test, and the other is the moving average (MA) unit root test of residuals . After selecting the ARMA model, some causality tests are applied to the error correction model (ECM) of a vector autoregression (VAR) one of which is ordinary least squares (OLS) and another is the maximum likelihood (ML) method. The former requires only the standard F -test on the deleted variables in the ECM. The latter requires the Johansen's ML method in estimating cointegration. Causality is found to go from income to money supply but not the other way. Appendices include a simple implementation of the MA unit root test, a pedagogical proof of the Granger causality tests developed by Toda and Phillips (1993) and an interpretation of the test proposed by Toda and Yamamoto (1995).
JEL Classification Numbers: C32, E50     

Structural Changes, Common Stochastic Trends, and Unit Roots in Panel Data

This paper studies the problem of unit root testing in the presence of multiple structural changes and common dynamic factors. Structural breaks represent infrequent regime shifts, while dynamic factors capture common shocks underlying the comovement of economic time series. We examine the modified Sargan–Bhargava (MSB) test in the panel data setting and propose ways to handle multiple structural changes and dynamic factors. Properties of the MSB test under these non-standard conditions are derived. For example, the test statistics are shown to be invariant, in the limit, to mean breaks. This invariance does not carry over to breaks in linear trends, where the test statistics will converge to functionals of weighted Brownian bridges. A simplified test statistic is then proposed, which is invariant to both mean and trend breaks. We further study pooled test statistic based on standardization and combination of p -values. Response surfaces for p -values of all test statistics are computed to facilitate the empirical implementation of the proposed methodology. The pooled tests are shown to have good finite sample performance.     

Granger Causality Between Money and Income for the Japanese Economy in the Presence of a Structural Change

This paper examines Granger causality between money and income in the Japanese economy based upon a bivariate VAR model with a structural change in the trend function. We employ a stratified testing strategy incorporating preliminary tests for a unit root and for the order of cointegration rank. Our study reveals that the choice of either trend stationarity or difference stationarity, as well as the order of cointegration rank, crucially affect the test results for Granger causality. It is found that the causality from money to income was strong before 1980 but weakened or virtually disappeared after 1980; the opposite causality existed weakly before 1980 but not after 1980. The result confirms the claim by the Bank of Japan (1992) and Honda et al . (1995) among others that the role of money as a leading indicator for predicting movements in income has weakened or even disappeared in the 1980s.
JEL Classification Numbers: C32, E40     

A panel cointegration approach to the investment-saving correlation

This paper augments the empirical literature concerning the Feldstein-Horioka puzzle using non-stationary panel data. Recently developed tests for panel cointegration and panel unit root tests are employed. We find substantial evidence to support the hypothesis of no cointegration in this panel, implying a high degree of international capital mobility. Our results suggest that tests for cointegration in panel data provides a better methodological focus than the magnitude of saving-retention coefficients. First version received: August 1999/Final version accepted: December 2000