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.     

Nonstationarity,cointegration and structural breaks in the Australian term structure of interest rates

This article examines the unit-root property of the Australian short- and long-term interest rates using unit-root tests that accommodate a single or two breaks under the null and/or alternative hypothesis. Two breaks in interest rates are found to coincide with the 1982/83 and 1990/91 recessions or the 1993 inflation targeting period. We further investigate the implications of these structural breaks on the cointegrating relationship implied by the single, linear expectations hypothesis of the term structure of interest rates. While there is evidence that the data are consistent with the expectations hypothesis at the shorter end of the term structure, breaks in interest rates generate a shift in the cointegrating relationship, thus altering the information content of the term structure. Failing to account for a regime shift in the cointegration regression, the data erroneously supports the expectations hypothesis at the longer end of the term structure. These results have profound implications for policy makers who may inadequately exploit the information content of the term structure to predict future changes in inflation.     

A contribution of foreign direct investment,clean energy,trade openness,carbon emissions and economic growth to energy demand in UAE

This paper investigates the relationship between foreign direct investment, clean energy, trade openness, carbon emissions and economic growth in case of UAE covering the period of 1975Q1–2011Q4. We have tested the unit properties of variables in the presence of structural breaks. The ARDL bounds testing approach is applied to examine the cointegration by accommodating structural breaks stemming in the series. The VECM Granger causality approach is also applied to investigate the causal relationship between the variables. Our empirical findings confirm the existence of cointegration between the series. We find that foreign direct investment, trade openness and carbon emissions decline energy demand. Economic growth and clean energy have positive impact on energy consumption.     

The Feldstein–Horioka Puzzle and structural breaks: Evidence from EU members

The purpose of this paper is to investigate the level of capital mobility in European Union members using the Feldstein–Horioka puzzle proposed by Feldstein and Horioka (1980) in order to investigate relations between saving and investment flows. In this paper, data for 23 European countries were used over the period of 1995–2009 on the quarterly basis. Two different tests were used to estimate the stationarity of the model variables, which are the Ng and Perron (2001) unit root test procedure and approach proposed by Zivot and Andrews (1992) for unit root test allowing for a structural shift. Then the Kejriwal and Perron (2008, 2010) structural break test was applied to determine the presence of structural breaks in series. In most countries except Belgium and Finland UDmax and WDmax tests rejected the hypothesis of no breaks. To test the cointegration relationships between investment and saving flows of European Union members three different cointegration techniques were applied to the data. Firstly, the Johansen (1988) cointegration approach was used for the case of no cointegration shifts, then the Gregory and Hansen (1996) cointegration test was applied, which allows for one structural shift. Finally, again the Johansen' cointegration approach was used; however, this time with the inclusion of dummy variables related to earlier selected structural break locations. The empirical results provided stronger evidence of cointegration between investment and saving variables in the case of structural break accommodation compared to the case where the presence of structural breaks was ignored. The estimated saving retention coefficient in the presence of structural breaks using the Kejriwal and Perron (2008, 2010) approach appeared relatively low in many cases, illustrating by this the openness of estimated countries. In general, world and European countries with time have a tendency to a higher level of their capital market openness. Estimations of a saving retention coefficient in the presence of structural changes do not support the existence of the Feldstein–Horioka Puzzle in the considered EU countries, except Belgium.     

A note on the stability of real interest rates in Australia

The stability (stationarity) of real interest rates and surveys of expected inflation in Australia is analyzed over the period 1993(10) to 2001(10). We find that the real yields on Australian 2-, 5-, and 10-year bonds are stationary in levels whereas the real overnight cash and the bank-accepted bills (BABs) 90-day real rates are stationary subject to structural breaks occurring in September 1994 and October 1994, respectively. These breaks were identified by applying tests proposed by Nunes et al. [Oxf. Bull. Econ. Stat. 59 (1997) 435]. An application of the Nunes test to the surveyed expected inflation series points to a structural break in this series in January 1998.Our results indicate that while real long-term bond yields in Australia are relatively stable, short-term yields and expected inflation are susceptible to domestic policy changes and international influences.     

Testing the validity of PPP theory for African countries

This study examines the purchasing power parity theory for 14 African countries by applying a recent composite time series method that incorporates the Fourier approximation. The structural breaks are modelled as a gradual smooth process by means of a Fourier component. The Fourier unit root test failed to find any evidence showing that real exchange rates for these 14 countries have mean-reverting tendencies. However, both cointegration and Fourier cointegration tests detect a stable long-term relation between the nominal exchange rate and relative price levels for 8 out of 14 countries; moreover, for five countries Fourier component in cointegration analysis is found to suit quite well.     

LM cointegration tests allowing for an unknown number of breaks: implications for the forward rate unbiasedness hypothesis

This article extends the Lagrange multiplier (LM) cointegration test proposed by Westerlund and Edgerton (WE 2007) by allowing for an unknown number of breaks. Monte Carlo simulations provide two main results. First, a loss of power in the LM cointegration tests is detected when potential multiple breaks are ignored. Second, the modified testing procedures do not affect the asymptotic distribution and major properties of the tests of WE under the null, but noticeably increase their testing power in presence of multiple breaks. We also provide empirical applications of the proposed tests for the forward rate unbiasedness hypothesis (FRUH). The results reveal that the FRUH does hold when the effects of the multiple structural breaks are taken into account.     

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.     

The Long Run Demand for Broad Money in Australia Subject to Regime Shifts

The goal is to determine if there is a stable Broad Money demand relationship for Australia. Previous studies have not reached a consensus on this important issue, partly because the time series techniques used do not accommodate structural breaks. A standard multivariate cointegration analysis is conducted on monthly data over the period 1976(3) to 1998(4). It reveals some evidence for the presence of cointegration since one cointegrating vector is found. This involves broad money, the spread between interest on broad money and on non-money assets and real GDP. The evidence of cointegration is again present when a structural break is found in the relationship using Gregory and Hansen (GH) methodology. This occurs in 1991 coinciding with a deep recession and policy induced, interest rate reductions. The income elasticity of demand exceeds one, reacts positively to the interest spread and negatively to inflation.     

STRUCTURAL BREAKS AND UNIT ROOTS IN AUSTRALIAN MACROECONOMIC TIME SERIES

Abstract.  We examine the unit root properties of 16 Australian macroeconomic time series using monthly data spanning the period 1960–2004. In addition to the standard Augmented Dickey Fuller (ADF) test, we implement one- and two-break endogenous structural break ADF-type unit root tests as well as one- and two-break Lagrange multiplier (LM) unit root tests. While the ADF test provides relatively little evidence against the unit root null hypothesis, once we allow for structural breaks we are able to reject the unit root null for just under half of the variables at the 10% level or better.     

Fractional cointegration,low frequency dynamics and long-run purchasing power parity: an analysis of the Australian dollar over its recent float

A relatively new but generalized concept of fractional cointegration is applied to shed some light on the validity of purchasing power parity (PPP) as a long-run equilibrium condition, by examining the long-run relationship between quarterly consumer price indices and bilateral exchange rates of the Australian dollar and seven major OECD trading partners, over Australia's recent float. The paper demonstrates that relaxing the condition that the residual from the cointegration equation must be a I(0) process, provides a wide range of cases of parity-reversion with processes that are CI(1,d) with 0 < d < 1. Findings tend to suggest that, while standard tests of cointegration fail to support cointegration between nominal exchange rates, domestic and foreign prices, and thus the empirical favour for PPP as a long-run phenomenon, the fractional cointegration analysis permits deviations from equilibrium to follow a fractionally integrated process and hence captures a much wider class of parity or mean-reversion behaviour. Results are mainly supportive of long-run PPP. Furthermore, an analysis of the short-run dynamics propelling the long-run relationship (through a VECM) reveals that domestic prices are consistently the initial receptor of an exogenous shock to the equilibrium and the long-run equilibrium is restored through the short-run adjustment of the nominal exchange rates. These findings are shown to hold clear policy implications.     

The intertemporal relation between government revenue and expenditure in the United Kingdom, 1750 to 2004

We examine the intertemporal relation between government revenue and expenditure in the UK during 1750 to 2004. We pay particular attention to long run trends by applying a battery of unit root and cointegration techniques to the data, and we use a modified Granger causality test on data spans organized around structural breaks in the series. The results suggest that, allowing for structural breaks, UK real revenue and spending are I(1) series and cointegrated and that Granger causality runs from government spending to revenue. As such, the ‘spend-tax’ hypothesis appears to best characterize the long run intertemporal relation between government revenue and spending in the UK.     

Instability tests in cointegration relationships. An application to the term structure of interest rates

This paper tries to review, from a practitioner's point of view, the recent strand of literature on cointegration tests allowing for structural changes or parameter instability. Thus, we apply several tests using as an example the expectations model of the term structure of interest rates. The results are consistent with the existence of cointegration between the long and the short run Spanish interest rates, with a vector (1,−1), as predicted by the theory. However, there is also evidence of structural instability, mainly at the beginning of 1994, that can be attributed to the financial changes that occurred in Spain as a result of its external commitments in the process of the European Monetary Union.     

Assessment of innovation and foreign direct investment: An investigation of OECD countries

Using a panel cointegration method incorporating structural breaks and cross-sectional dependence, this paper explores the long-run equilibrium relationship between innovation and foreign direct investment (FDI) in 30 OECD countries. The results from the panel stationary test show that FDI and innovation variables follow a stationary process with several structural breaks over the period 1999–2018. The results also suggest an equilibrium relationship with structural breaks between FDI and innovation in OECD countries. The panel dynamic OLS model with breaks further reveals that FDI is positively associated with innovation performance and vice versa in OECD countries. Therefore, this paper sheds light on the relationship between FDI and innovation in OECD countries.     

Foreign Direct Investment,Female Education,Capital Formation,and Economic Growth in Japan and South Korea

ABSTRACT

The influence of foreign direct investment (FDI) on host country‘s economic growth is a widely explored issues in the existing economic literature. This study attempts to examine the role of foreign direct investment, capital formation, and expansion of female education on economic growth of Japan during the period 1971–2014, using time series observations. The study further makes a comparison regarding the association with FDI and economic growth with South Korea, another major OECD economy of Asia The study utilises the auto-regressive distributed lag (ARDL) bounds approach to cointegration to examine the long run causality association among the variables. Today, for sustainable economic development the social and institutional policy issues are important. The paper explores one such social issue, namely gender and economic prosperity. This paper has novel contributions in the current research on time series, econometric analysis for the following reasons: (1) it has investigated the relationship between economic growth, foreign direct investment and capital formation in a gendered differential framework (utilising the role of human capital formation among men versus women; (2) the study covers a long period and more recent time period (till 2014), which concurs with the upsurge of world FDI movements and (3) the study also explores the major structural breaks of the two economies and how economic growth is impacted thereof.     

A Test of Long-run Purchasing Power Parity Allowing for Structural Breaks*

If exchange rates and prices are integrated processes, standard econometric tests of the purchasing power parity (PPP) hypothesis may be biased towards rejection. This paper avoids this problem by using the Engle and Granger (1987) theory of cointegrated processes. If the absolute version of purchasing power parity is true, and nominal exchange rates and prices are integrated processes, inter-commodity arbitrage should ensure that the real exchange rate is stationary. The stationarity hypothesis is tested using Australian real exchange rate data for the 1890–1984 period We find that the effective real exchange rate cannot be modelled as a stationary process and therefore reject the absolute version of PPP. We also employ a test for structural breaks due to, for instance, the oil price shock and find mixed results. Another interpretation of our results is that the real exchange rate was affected by a series of permanent, real shocks during the sample period     

Tourism revenues and residential foreign investment flows in Spain: a simultaneous model

The aim of this work is to analyse the determinants of the tourism revenues and the residential foreign investment, in Spain, during the period 1967–1998. To do so, a two equation simultaneous model is proposed to be estimated. The specification highlights the simultaneous and direct interdependence of the tourism revenues and the residential foreign investment flows. This result contrasts with the traditional standard specification of the international tourism demands in Spain. Nonlinear simultaneous estimations, cointegration techniques and a battery of specification tests are the econometric tools applied in the work.     

Intertemporal sustainability of current account imbalances: New evidence from the OECD countries

This study estimates the intertemporal model for the relationship between exports and imports and examines the sustainability of current account deficits (CADs) and the validity of intertemporal budget constraint for 24 Organisation for Economic Co‐operation and Development countries. The standard ordinary least squares (OLS)‐based two‐step Engle and Granger test, the cointegration regression Durbin–Watson (CRDW) test, and the Stock–Watson test performed on the one‐regime model with time‐invariant parameters and no structural break provide mixed support for the presence of cointegration between exports and imports. The recursive least squares‐based cumulative sum of recursive residuals (CUSUM) and the cumulative sum of squares of recursive residuals (CUSUMSQ) tests and the OLS‐based Andrews‐Quandt (AQ) and Andrews – Ploberger (AP) tests suggest the presence of structural breaks in the long‐run relationship between exports and imports for a number of countries. The end‐of‐sample new cointegration breakdown tests performed on the OLS, fully modified OLS, and full‐information maximum‐likelihood estimates of the model suggest the presence of cointegration between exports and imports for most countries. The dominant support for cointegration between trade flows points toward the sustainability of CADs and the validity of intertemporal budget constraint. The macroeconomic stabilization policies seem to have been effective in correcting the market failures and maintaining the steady‐state equilibrium relationship between trade flows in the sample countries. The findings of this study have important implications for empirical research. The structural breaks in the cointegrating vector could occur even over the short time periods and at any point in time. It is essentially important to assess the sustainability of the external position in the presence of long‐period as well as short‐period breaks in the cointegrating vector.     

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.     

Growth in a time of austerity: evidence from the UK

This paper uses an empirical approach to test the specific causal relationship between debt and growth in the UK, in the context of the debate surrounding the use of a policy known as austerity measures. This time series perspective makes use of more recent Granger causality and cointegration tests that allow for non‐stationarity in macroeconomic time series data in the presence of structural breaks. Controlling for exogenous shocks associated with the period around the financial crisis, we find no evidence of a causal relationship between economic growth and public debt for the UK.