Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi�cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.growth shift, level shift, structural change, trend breaks, unit root

Testing for Multiple Structural Changes in Cointegrated Regression Models

This paper considers issues related to testing for multiple structural changes in cointegrated systems. We derive the limiting distribution of the Sup-Wald test under mild conditions on the errors and regressors for a variety of testing problems. We show that even if the coefficients of the integrated regressors are held fixed but the intercept is allowed to change, the limit distributions are not the same as would prevail in a stationary framework. Including stationary regressors whose coefficients are not allowed to change does not affect the limiting distribution of the tests under the null hypothesis. We also propose a procedure that allows one to test the null hypothesis of, say, k changes, versus the alternative hypothesis of k + 1 changes. This sequential procedure is useful in that it permits consistent estimation of the number of breaks present. We show via simulations that our tests maintain the correct size in finite samples and are much more powerful than the commonly used LM tests, which suffer from important problems of non-monotonic power in the presence of serial correlation in the errors.change-point, sequential procedure, wald tests, unit roots, cointegration

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi?cation of countries according to the ?growth shift?, ?level shift? and ?linear trend? hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.growth shift, level shift, structural change, trend breaks, unit root

Wald Tests for Detecting Multiple Structural Changes in Persistence

This paper considers the problem of testing for multiple structural changes in the persistence of a univariate time series. We propose sup-Wald tests of the null hypothesis that the process has an autoregressive unit root against the alternative hypothesis that the process alternates between stationary and unit root regimes. Both non-trending and trending cases are analyzed. We derive the limit distributions of the tests under the null and establish their consistency under the relevant alternatives. The computation of the test statistics as well as asymptotic critical values is facilitated by the dynamic programming algorithm proposed in Perron and Qu (2006) which allows the minimization of the sum of squared residuals under the alternative hypothesis while imposing within and cross regime restrictions on the parameters. Finally, we present Monte Carlo evidence to show that the proposed tests perform quite well in finite samples relative to those available in the literature.structural change, persistence, Wald tests, unit root, parameter restrictions

Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation

This paper examines the Prebisch-Singer Hypothesis employing new time se- ries procedures that are robust to the nature of persistence in the commodity price shocks, thereby obviating the need for unit root pretesting. Speci…cally, the proce- dures allow consistent estimation of the number of structural breaks in the trend function as well as facilitate the distinction between trend breaks and pure level shifts. In comparison with past studies, we …nd fewer cases of commodities that display negative trends thereby weakening the case for the Prebisch-Singer Hypoth- esis. Finally, a new set of powerful unit root tests allowing for structural breaks under both the null and alternative hypotheses is applied to determine whether the underlying commodity price series can be characterized as di¤erence or trend sta- tionary processes. Relative to the extant literature, we …nd more evidence in favor of trend stationarity suggesting that real commodity price shocks are mostly of a transitory nature.primary commodity prices, structural breaks, trend functions, Prebisch- Singer Hypothesis, unit roots, Demand and Price Analysis, Marketing, Research Methods/ Statistical Methods, 013, C22,

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi�cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis

Breaking Trends and the Prebisch-Singer Hypothesis: A Further Investigation

This paper examines the Prebisch-Singer Hypothesis employing new time series procedures that are robust to the nature of persistence in the commodity price shocks, thereby obviating the need for unit root pretesting. Specifically, the procedures allow consistent estimation of the number of structural breaks in the trend function as well as facilitate the distinction between trend breaks and pure level shifts. In comparison with past studies, we find fewer cases of commodities that display negative trends thereby weakening the case for the Prebisch-Singer Hypothesis. Finally, a new set of powerful unit root tests allowing for structural breaks under both the null and alternative hypotheses is applied to determine whether the underlying commodity price series can be characterized as difference or trend stationary processes. Relative to the extant literature, we find more evidence in favor of trend stationarity suggesting that real commodity price shocks are mostly of a transitory nature

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi�cation of countries according to the "growth shift", "level shift" and "linear trend" hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis

A two step procedure for testing partial parameter stability in cointegrated regression models

Kejriwal and Perron (2010, KP) provided a comprehensive treatment for the problem of testing multiple structural changes in cointegrated regression models. A variety of models were considered depending on whether all regression coefficients are allowed to change (pure structural change) or a subset of the coefficients is held fixed (partial structural change). In this note, we first show that the limit distributions of the test statistics in the latter case are not invariant to changes in the coefficients not being tested; in fact, they diverge as the sample size increases. To address this issue, we propose a simple two step procedure to test for partial parameter stability. The first entails the application of a joint test of stability for all coefficients as in KP. Upon a rejection, the second conducts a stability test on the subset of coefficients of interest while allowing the other coefficients to change at the estimated breakpoints. Its limit distribution is standard chi-square. The relevant asymptotic theory is provided along with simulations that illustrates the usefulness of the procedure in finite samples.First author draf

Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

This article proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by non‐stationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup‐Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime‐specific bootstrap p‐values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the finite sample improvements offered by our methods. An application to OECD inflation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures.Accepted manuscrip