Testing for the cointegration rank when some cointegrating directions are changing

We develop some tests for characterizing the cointegration space of a cointegrated vector autoregressive model when its long-run parameters are modified by a structural break at a known date. We first consider the case in which the break does not affect the loading factors and second the more general one in which all long-run parameters change. For each configuration, we design procedures to test for the cointegration rank as for the number of directions which are changing between the two regimes. For the simplest case, the cointegration rank test is also extended to the case of an unknown date of shift.     

Spurious Rejections by Perron Tests in the Presence of a Break

In this paper, we concentrate on the case of an exogeneously chosen break date, but entertain the possibility that an incorrect choice is made. In fact, the Perron test statistics considered are invariant to any break in the generating process at the assumed break date. Our results therefore apply equally to the case of a generating process with two breaks, only one of which is specifically accounted for in the analysis. As in Leybourne et al . (1998), we find that a neglected relatively early break can lead to spurious rejections of the unit root null hypothesis. Moreover, for all but one of the tests analyzed, spurious rejections now also arise if a true break occurs relatively soon after the assumed break date.     

Confidence sets for the date of a single break in linear time series regressions

This paper considers the problem of constructing confidence sets for the date of a single break in a linear time series regression. We establish analytically and by small sample simulation that the current standard method in econometrics for constructing such confidence intervals has a coverage rate far below nominal levels when breaks are of moderate magnitude. Given that breaks of moderate magnitude are a theoretically and empirically relevant phenomenon, we proceed to develop an appropriate alternative. We suggest constructing confidence sets by inverting a sequence of tests. Each of the tests maintains a specific break date under the null hypothesis, and rejects when a break occurs elsewhere. By inverting a certain variant of a locally best invariant test, we ensure that the asymptotic critical value does not depend on the maintained break date. A valid confidence set can hence be obtained by assessing which of the sequence of test statistics exceeds a single number.     

Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses

Perron [Perron, P., 1989. The great crash, the oil price shock and the unit root hypothesis. Econometrica 57, 1361–1401] introduced a variety of unit root tests that are valid when a break in the trend function of a time series is present. The motivation was to devise testing procedures that were invariant to the magnitude of the shift in level and/or slope. In particular, if a change is present it is allowed under both the null and alternative hypotheses. This analysis was carried under the assumption of a known break date. The subsequent literature aimed to devise testing procedures valid in the case of an unknown break date. However, in doing so, most of the literature and, in particular the commonly used test of Zivot and 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], assumed that if a break occurs, it does so only under the alternative hypothesis of stationarity. This is undesirable since (a) it imposes an asymmetric treatment when allowing for a break, so that the test may reject when the noise is integrated but the trend is changing; (b) if a break is present, this information is not exploited to improve the power of the test. In this paper, we propose a testing procedure that addresses both issues. It allows a break under both the null and alternative hypotheses and, when a break is present, the limit distribution of the test is the same as in the case of a known break date, thereby allowing increased power while maintaining the correct size. Simulation experiments confirm that our procedure offers an improvement over commonly used methods in small samples.     

The Limiting Distribution of Post-sample Stability Tests for GMM Estimation when the Potential Break Date is Unknown

Recent papers have proposed a split-sample prediction method to test for structural stability in GMM estimation when the potential break date is treated as known. In this note we derive the limiting distribution of the supremum of this test over all possible break dates, thus allowing for endogenous determination of the potential break date.     

Structural breaks in public finances in Central and Eastern European countries

This article studies the evolution of quarterly government Total Deficit (TD) to Gross Domestic Product (GDP) and debt to GDP ratios of seven Central and Eastern European member states (CEEC-7) of the European Union over the period 2000 Q1 to 2011 Q2. Alternative unit root tests are applied to identify the number and date(s) of structural break(s) in the fiscal ratios. The breakpoint date(s) are estimated endogenously. The best performing unit root test is determined by the adjusted R-squared metric. The level and trend of fiscal ratios are estimated by using breaking trend regression models. Unit root tests performed for the period 2000 Q1 to 2007 Q4 identify the number and date(s) of structural break(s) in fiscal variables before the global economic crisis. Unit root tests and breaking trend regressions are estimated for total Eurozone TD to GDP and debt to GDP to compare the evolution of total Eurozone fiscal ratios with those of each CEEC-7.     

Testing Integration of Macroeconomic Time Series in Transitional Socialist Economies. A Modification of Perron Test

The presence of structural breaks reduces the power of integration tests. A number of methods were suggested to improve the statistical properties of integration tests in the presence of structural breaks. The most known are Perron tests, which allow to test for the level of integration of time series with one structural break. Perron tests allow for two types of structural breaks: additive outlier an innovative outlier. These tests are, however, not very useful in testing the level of integration of macroeconomic time series in countries in transition from centrally-planned to market economy. In such case one should expect two structural breaks to affect the time series: one at the beginning and one at the end of the transformation process. Test that allows for two additive outlier type structural breaks in time series is developed in this paper. This test has superior power as compared to standard Dickey-Fuller and Perron tests. This paper provides asymptotic distribution as well as finite sample properties of proposed test. Therefore practitioners receive a reliable tool for analyzing macroeconomic processes in transitional economies. This revised version was published online in July 2006 with corrections to the Cover Date.     

Tests for a Break in Level when the Order of Integration is Unknown*

In this paper, we consider tests for a break in the level of a series at an unknown point in time. It is often the case that uncertainty exists concerning the order of integration of the series; consequently, we focus on tests that are applicable when the order of integration is not known. The size and power of existing tests are analysed, and a modification to one of the established sets of tests is proposed which offers improved performance in certain circumstances.     

Testing the Null of Cointegration with Structural Breaks*

We propose a Lagrange Multiplier‐type statistic to test the null hypothesis of cointegration allowing for the possibility of a structural break, in both the deterministic and the cointegration vectors. Our proposal focuses on the presence of endogenous regressors. The test complements the usual non‐cointegration tests so as to obtain stronger evidence of cointegration. We consider the cases of known and unknown dates of the break. In the latter case, we show that minimizing the Sum of Squared Residuals results in a super‐consistent estimator of the break fraction. Finally, the behaviour of the tests is studied through Monte Carlo experiments.     

Estimating a common deterministic time trend break in large panels with cross sectional dependence

This paper develops an estimation procedure for a common deterministic time trend break in large panels. The dependent variable in each equation consists of a deterministic trend and an error term. The deterministic trend is subject to a change in the intercept, slope or both, and the break date is common for all equations. The estimation method is simply minimizing the sum of squared residuals for all possible break dates. Both serial and cross sectional correlations are important factors that decide the rate of convergence and the limiting distribution of the break date estimate. The rate of convergence is faster when the errors are stationary than when they have a unit root. When there is no cross sectional dependence among the errors, the rate of convergence depends on the number of equations and thus is faster than the univariate case. When the errors have a common factor structure with factor loadings correlated with the intercept and slope change parameters, the rate of convergence does not depend on the number of equations and thus reduces to the univariate case. The limiting distribution of the break date estimate is also provided. Some Monte Carlo experiments are performed to assess the adequacy of the asymptotic results. A brief empirical example using the US GDP price index is offered.     

Structural break tests and the Greek sovereign debt crisis: revisited

Amidst the lack of consensus from previous academic studies, this paper contributes to existing literature by further examining the commencement date of the Sovereign Debt Crisis for the Greek economy. The contribution of this paper purports that the contentious issue of the start of the Greek crisis was taking place much earlier than reported by previous research. Empirical results from this paper challenge earlier studies that may have underestimated the impact of the degree of persistence in the volatility of bond returns. This analysis uses monthly 10-year Greek government bond data and three independent structural break model tests which allow for the detection of possible endogenous break dates to capture the beginning of the crisis. Each model provides empirically plausible and robust frameworks for examining the volatility of bond returns in an evolving time series behaviour. Ultimate results from a series of autoregressive EGARCH estimations, with and without dummy variables for break dates are compared. The dummy variables are incorporated within the coefficients of the mean and variance equations to validate the structural breaks in each series. Overall results show a significant presence of nonconsistent parameters capturing a structural break in the time series sample. The detection of this break, November 2009, represents a major regime change triggered by the start of the debt crisis for the Greek economy. Crucially, research implications of such excess volatilities in sovereign bond markets have poignant implications for regulators, investors and portfolio risk managers alike.     

The effects of external and internal shocks on total factor productivity

This paper examines structural changes that occur in the total factor productivity (TFP) within countries. It is possible that some episodes of high economic growth or economic decline are associated with permanent productivity shocks; therefore, this research has two objectives. The first one is to estimate the structural changes present in TFP for a sample of 77 countries between 1950 (1960) and 2000. The second one is to identify possible explanations for breaks. Two sources were analyzed: (i) episodes in political and economic history; (ii) changes in international trade – a measure of absorption of technology. The results suggest that about one-third of the TFP time-series present at least one structural break. Downwards breaks are more common, indicating that after a break the TFP has much difficulty to recover. When we investigated factors related with structural change, developed countries presented a break near the first oil shock while the developing countries’ breaks are more spread along the decades. Thus, external strikes seem to be more relevant for developed countries. However, for each country and break date, it was possible to find an event close to the break date endogenously detected. Last, the relevance of international trade, measured by trade share percentage of GDP, seems to be limited to explain abrupt changes in TFP.     

Unit roots and structural breaks in North American unemployment rates

This paper examines the univariate time-series properties of the unemployment rate in Canada, Mexico, and the United States. Tests are employed that allow for endogenously determined break dates and the results are compared to stationarity tests that assume no break in the data. The structural break unit-root tests contradict the findings of the standard tests. We conclude that North American unemployment rates are trend stationary around a breaking trend.     

Unit root testing under a local break in trend

Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in both fixed trend break and no trend break environments, in finite samples pronounced “valleys” in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem, we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without-break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights.     

Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors

We consider the problem of estimating and testing for multiple breaks in a single‐equation framework with regressors that are endogenous, i.e. correlated with the errors. We show that even in the presence of endogenous regressors it is still preferable, in most cases, to simply estimate the break dates and test for structural change using the usual ordinary least squares (OLS) framework. Except for some knife‐edge cases, it delivers estimates of the break dates with higher precision and tests with higher power compared to those obtained using an instrumental variable (IV) method. Also, the OLS method avoids potential weak identification problems caused by weak instruments. To illustrate the relevance of our theoretical results, we consider the stability of the New Keynesian hybrid Phillips curve. IV‐based methods only provide weak evidence of instability. On the other hand, OLS‐based ones strongly indicate a change in 1991:Q1 and that after this date the model loses all explanatory power. Copyright © 2013 John Wiley & Sons, Ltd.     

MULTIVARIATE METHODS FOR MONITORING STRUCTURAL CHANGE

Detection of structural change is a critical empirical activity, but continuous ‘monitoring’ for changes in real time raises well‐known econometric issues that have been explored in a single series context. If multiple series co‐break then it is possible that simultaneous examination of a set of series helps identify changes with higher probability or more rapidly than when series are examined on a case‐by‐case basis. Some asymptotic theory is developed for maximum and average CUSUM detection tests. Monte Carlo experiments suggest that these both provide an improvement in detection relative to a univariate detector over a wide range of experimental parameters, given a sufficiently large number of co‐breaking series. This is robust to a cross‐sectional correlation in the errors (a factor structure) and heterogeneity in the break dates. We apply the test to a panel of UK price indices. Copyright © 2011 John Wiley & Sons, Ltd.     

Break Point Estimation and Spurious Rejections With Endogenous Unit Root Tests

This paper examines the accuracy of break point estimation using the endogenous break unit root tests of Zivot and Andrews (1992) and Perron (1997). We find that these tests tend to identify the break point incorrectly at one-period behind ( T_B -1) the true break point ( T_B ), where bias in estimating the persistence parameter and spurious rejections are the greatest. In addition, this outcome occurs under the null and alternative hypotheses, and more so as the magnitude of the break increases. Consequences of utilizing these endogenous break tests are similar to (incorrectly) omitting the break term B_t in Perron's (1989) exogenous test.     

Unit Root Testing under a Local Break in Trend using Partial Information on the Break Date*

We consider unit root testing allowing for a break in trend when partial information is available regarding the location of the break date. This takes the form of knowledge of a relatively narrow window of data within which the break takes place, should it occur at all. For such circumstances, we suggest employing a union of rejections strategy, which combines a unit root test that allows for a trend break somewhere within the window with a unit root test that makes no allowance for a trend break. Asymptotic and finite sample evidence shows that our suggested strategy works well, provided that, when a break does occur, the partial information is correct. An empirical application to UK interest rate data containing the 1973 ‘oil shock’ is also considered.     

Confidence sets for the date of a break in level and trend when the order of integration is unknown

We propose methods for constructing confidence sets for the timing of a break in level and/or trend that have asymptotically correct coverage for both I(0) and I(1) processes. These are based on inverting a sequence of tests for the break location, evaluated across all possible break dates. We separately derive locally best invariant tests for the I(0) and I(1) cases; under their respective assumptions, the resulting confidence sets provide correct asymptotic coverage regardless of the magnitude of the break. We suggest use of a pre-test procedure to select between the I(0)- and I(1)-based confidence sets, and Monte Carlo evidence demonstrates that our recommended procedure achieves good finite sample properties in terms of coverage and length across both I(0) and I(1) environments. An application using US macroeconomic data is provided which further evinces the value of these procedures.     

Testing for structural breaks in dynamic factor models

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our Monte Carlo simulations) is generalized to test for structural breaks in factor models where the break date is unknown and the common factors and idiosyncratic components are serially correlated. The proposed test procedures are applied to datasets from the US and the euro area.