Tests For Cointegration In Models Research Articles

Testing for cointegration with threshold adjustment in the presence of structural breaks

Abstract In this paper, we develop new threshold cointegration tests with SETAR and MTAR adjustment allowing for the presence of structural breaks in the equilibrium equation. We propose a simple procedure to simultaneously estimate the previously unknown breakpoint and test the null hypothesis of no cointegration. Thereby, we extend the well-known residual-based cointegration test with regime shift introduced by (Gregory, A. W., and B. E. Hansen. 1996a. “Residual-based Tests for Cointegration in Models with Regime Shifts.” Journal of Econometrics 70: 99–126) to include forms of nonlinear adjustment. We derive the asymptotic distribution of the test statistics and demonstrate the finite-sample performance of the tests in a series of Monte Carlo experiments. We find a substantial decrease of power of the conventional threshold cointegration tests caused by a shift in the slope coefficient of the equilibrium equation. The proposed tests perform superior in these situations. An application to the “rockets and feathers” hypothesis of price adjustment in the US gasoline market provides empirical support for this methodology.

Trade-threshold Effect on Inflation in Tunisia: New Evidence Resulting from a Nonlinear Approach

ABSTRACTTrade openness is an important determinant of the inflation process. The effect of trade openness on inflation, however, is still an issue of debate at both theoretical and empirical levels. This study tried to provide a contribution to the literature by examining the relationship between inflation and trade openness in Tunisia over the period 1975Q1-2015Q4 using a nonlinear model. The originality of this study stems from the fact that it is the first investigation considering both the Residual-Based Tests for Cointegration in Models with the Regime Shifts and Threshold Regression model. The linear model confirms the existence of a positive relationship between inflation and trade in Tunisia. Yet, considering the nonlinear model, trade openness growth and Consumer Price Index (CPI) inflation growth show a statistically significant negative link as long as the trade openness evolution does not exceed the threshold. Nevertheless, if the trade openness growth is higher than the threshold, integrating the trade positively affects CPI inflation. Furthermore, a positive influence of Money supply growth on this type of inflation was noticed in Tunisia in all the considered regimes proving the effect of monetary factors on inflation level. Consequently, trade openness could be used to control inflation in Tunisia.

Is the US demand for money unstable?

The demand for money (M1) for the US is estimated with annual data from 1960 to 2008 and its stability is analysed with the extended Gregory and Hansen (1996b Gregory, AW and Hansen, BE. 1996b. Tests for cointegration in models with regime and trend shifts. Oxford Bulletin of Economics and Statistics, 58: 555–9. [Crossref], [Web of Science ®] , [Google Scholar]) test. In addition to estimating the canonical specification, alternative specifications are estimated which include a trend and additional variables to proxy the cost of holding money. Results with our extended specification showed that there has been a structural change in 1998 and the constraint that income elasticity is unity could not be rejected by subsample estimates. Short run dynamic adjustment equations are estimated with the lagged residuals from the Fully Modified Ordinary Least Squares (FMOLS) estimates of cointegrating equation and also with the General to Specific (GETS) approach.

Regime switches between dividend and bond yields

The relation between bond and equity returns serves as a proxy for estimating the premia investors' demand on their equity portfolio holdings and assessing the substitution effects between the two markets. With this in mind, we examine empirically the co-movements and the underlying information between equities and bonds. Our approach relies on the comparison between bond and dividend yields — a relation better known as the gilt-equity yield ratio–GEYR — by examining the characteristics of the cointegration relation between the bond and equity yields. In this context, this paper's contribution is that it lifts the restrictions of linearity both in the long-run cointegration relations and in the underlying short-run relations presented in the VECM. Specifically, we apply the regime-switching framework of Gregory and Hansen (Gregory, A. W. & Hansen, B. E. (1996). Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126) for the long-run equilibriums and the Markov Switching VECM, established by Krolzig (Krolzig, H.M., 1997. Markov switching vector autoregressions. Modelling statistical inference and application to business cycle analysis. Springer, Verlag) for the short run ones. Our aim is to examine the allocation of capital among the UK bond (or else, gilt) and stock markets for the period of 01-1987 to 01-2007, in a fashion that better reflects the structural breaks and regime shifts of the underlying market conditions. Our findings confirm the substitution effects among stocks and bonds in the long run and highlight the importance of market conditions for the allocation of capital among stocks and bonds.

Testing for capital mobility: New evidence from a panel of G7 countries

In this paper, we test the savings–investment relationship for the G7 countries. Upon applying the Gregory and Hansen [Gregory, A.W., Hansen, B.E., 1996. Residual-based tests for cointegration in models with regime shifts, J. Econ. 70, 99–126] residual-based structural break test for cointegration for each of the G7 countries, we did not find any evidence of a cointegrating relationship between savings and investment. Extending the analysis to a panel framework, we could not establish any evidence of panel cointegration. Taken together, our findings suggest that capital in these G7 countries is highly mobile since no long-term relationship exists between savings and investment.

Residual-based tests for cointegration in models with multi-breaks

In this article, we propose residual-based tests for cointegration in models with multi-breaks. Cointegration can be tested regardless of whether there exist structural breaks. For a one-point break, we usually use the test proposed by Gregory and Hansen (1996). However, this test has not been considered in the case of multistructural breaks. Therefore, we extend this test by considering multi-point breaks. We derive the asymptotic distribution and critical values of the test statistics. Since the critical values of the test statistics are not exact values, we derive these using the Monte Carlo simulation.

Russian equity market linkages before and after the 1998 crisis: Evidence from stochastic and regime-switching cointegration tests

This paper examines the relationships between Russian and other equity markets over the period of 1995–2004. To account for potential instability in the market relationships we apply a number of cointegration approaches: Gregory–Hansen [1996. Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126] test, which allows for a structural break in the relationships, a stochastic cointegration framework by McCabe [2003. Testing for Stochastic Cointegration and Evidence for Present Value Models. Working Paper], the non-parametric test by Breitung [2002. Nonparametric tests for unit roots and cointegration. Journal of Econometrics 108(2), 343–363] and a regime-switching cointegration model in the spirit of Ho [1999. Financial liberalization and international capital mobility of Taiwan: a regime-switching approach. Asian Economic Journal 13(4), 407–417]. The tests point to a significant agreement that the Russian equity market remained isolated from the influence by international markets in the long run and that while a structural break might have occurred in August 1998 this did not alter the nature of long-run relationships.

Residual-based tests forcointegration with gradual switching

In this article, we propose residual-based tests for cointegration in models with gradual switching. The cointegration test proposed by Gregory and Hansen (1996) is employed to consider the structural break. However, this test has not been considered in the case of gradual switching. Therefore, we extend this test by considering gradual switching. We derive the asymptotic distribution and critical values of the test statistics.

Estimating energy elasticity with structural changes in Japan

The purpose of this paper is to estimate energy elasticity in Japan taking into account structural changes. We employ a residual-based cointegration model developed by Gregory and Hansen [Gregory, Allan W., Hansen, Bruce E., 1996. Residual-based tests for cointegration in models with regime shifts, Journal of Econometrics. 70, 99–126]. The empirical results show that the three variables have a stable relationship in the long term when considering structural changes in the second quarter of 1993. As compared with the values obtained in previous studies, the income elasticity is higher and the price elasticity is lower. From our analysis, we can confirm whether a carbon tax will meet the objective of the Kyoto Protocol. In conclusion, the tax rate required in the case without structural changes is lower than that in the case with structural changes.

Modeling the long-run sustainability of Turkish external debt with structural changes

The paper examines the solvency of Turkey regarding its external debts. Recent economic crises Turkey faced in last decade raised concerns on the issue of external debt sustainability. Using the usual intertemporal budget constraint, a statistically testable measure of solvency is derived and the methodology of Hakkio and Rush (Hakkio, C.S., Rush, M., 1991. Is the budget deficit ‘too large’? Economic Inquiry 29, 429–445.) is followed to evaluate the sustainability of the external debt of Turkey. In addition to the conventional cointegration tests, Zivot–Andrews (Zivot, E., Andrews, D.W.K., 1992. Further evidence on the great crash, the oil price shock, and the unit root hypothesis. Journal of Business and Economic Statistics 10, 251–270.) unit root test and Gregory–Hansen (Gregory, A., Hansen, B., 1996. Residual based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126.) cointegration test are also employed to find out whether a possible structural break that may be due to the recent economic crises in Turkey changes the empirical results. The findings show that with or without considering any structural break, Turkish external debt is weakly sustainable.

Spot-forward cointegration, structural breaks and FX market unbiasedness

FX market unbiasedness requires spot-forward cointegration with unitary vector, or a stationary forward-premium (FP). These conditions have found mixed support, which recent research explains via FP fractional integration. An alternative explanation is breaks in spot-forward cointegration regressions, so that I apply Gregory and Hansen [Gregory, A.W., Hansen, B.E., 1996a. Residual-based tests for cointegration in models with regime shifts. Journal of Econometrics 70, 99–126; 1996b. Tests for cointegration in models with regime and trend shifts. Oxford Bulletin of Economics and Statistics 58, 555–560] models to DM, Yen and Pound data, allowing for intercept, slope, and time-trend shifts. I adapt the procedure of Bai [Bai, J., 1997. Estimation of a change point in multiple regression models. Review of Economics and Statistics 79, 551–563] to sequentially search for multiple breaks, and find evidence of cointegration with “regime-and-trend shifts” for the three currencies. Cointegration-with-breaks regressions show stationary residuals and unitary slopes across regimes, consistent with long-run unbiasedness overall. Forward-premium regressions estimated for subsamples determined by cointegration-regression break dates find support for short-run unbiasedness in some regimes but not others.

Modelling the linkages between the Australian and G7 stock markets: common stochastic trends and regime shifts

This paper examines whether the Australian equity market is integrated with the equity markets of the G7 economies by applying both the Johansen (Statistical analysis of conintegrating vectors, Journal of Economic Dynamics and Control, 12, 231–54, ) and Gregory and Hansen (Residual-based tests for cointegration in models with regime shifts, Journal of Econometrics, 70, 99–126, ) approaches to cointegration. Some evidence of a pairwise long-run relationship between the Australian stock market and the stock markets of Canada, Italy, Japan and the United Kingdom is found, but the Australian equity market is not pairwise cointegrated with the equity markets of France, Germany or the USA.

PRACTITIONERS CORNER: Tests for Cointegration in Models with Regime and Trend Shifts

ABSTRACTRecently Gregory and Hansen (1996) proposed a number of residual‐based tests for cointegration in models with the possibility of a structural break. They considered three models: (i) level shift; (ii) level shift with trend; and (iii) regime shift (both level shift and slope coefficients can change). We introduce a more general model that permits a trend shift as well as a regime shift and we provide the critical values appropriate for testing this hypothesis.

Residual-based tests for cointegration in models with regime shifts

In this paper we examine tests for cointegration which allow for the possibility of regime shifts. We propose ADF-, Z α-, and Z t -type tests designed to test the null of no cointegration against the alternative of cointegration in the presence of a possible regime shift. In particular we consider cases where the intercept and/or slope coefficients have a single break of unknown timing. A formal proof is provided for the limiting distributions of the various tests for the regime shift model (both a level and slope change). Critical values are calculated for the tests by simulation methods and a simple Monte Carlo experiment is conducted to evaluate finite-sample performance. In the limited set of experiments, we find that the tests can detect cointegrating relations when there is a break in the intercept and/or slope coefficient. For these same experiments, the power of the conventional ADF test with no allowance for regime shifts falls sharply. As an illustration we test for structural breaks in the U.S. long-run money-demand equation using annual and quarterly data.