Abstract: This chapter is concerned with methodological issues related to estimation, testing and computation in the context of structural changes in the linear models. A central theme of the review is the interplay between structural change and unit root and on methods to distinguish between the two. The topics covered are: methods related to estimation and inference about break dates for single equations with or without restrictions, with extensions to multi-equations systems where allowance is also made for changes in the variability of the shocks; tests for structural changes including tests for a single or multiple changes and tests valid with unit root or trending regressors, and tests for changes in the trend function of a series that can be integrated or trendstationary; testing for a unit root versus trend-stationarity in the presence of structural changes in the trend function; testing for cointegration in the presence of structural changes; and issues related to long memory and level shifts. Our focus is on the conceptual issues about the frameworks adopted and the assumptions imposed as they relate to potential applicability. We also highlight the potential problems that can occur with methods that are commonly used and recent work that has been done to overcome them.

Abstract: In this paper alternative approaches for testing the unit root hypothesis in panel data are considered. First, a robust version of the Dickey-Fuller t-statistic under contemporaneous correlated errors is suggested. Second, the GLS t-statistic is considered, which is based on the t-statistic of the transformed model. The asymptotic power of both tests is compared against a sequence of local alternatives. To adjust for short-run serial correlation of the errors, we propose a pre-whitening procedure that yields a test statistic with a standard normal limiting distribution as N and T tends to infinity. The test procedure is further generalized to accommodate individual specific intercepts or linear time trends. From our Monte Carlo simulations it turns out that the robust OLS t-statistic performs well with respect to size and power, whereas the GLS t-statistic may suffer from severe size distortions in small and moderate sample sizes. The tests are applied to test for a unit root in real exchange rates.

Abstract: The paper examines the sustainability of U.S. fiscal policy, finding substantial evidence in favor. I summarize the U.S. fiscal record from 1792-2003, critically review sustainability conditions and their testable implications, and apply them to U.S. data. I particularly emphasize the ramifications of economic growth. A "growth dividend" has historically covered the entire interest bill on the U.S. debt. Unit root tests on real series, unscaled by GDP, are distorted by the series' severe heteroskedasticity. The most credible evidence in favor of sustainability is the robust positive response of primary surpluses to fluctuations in the debt-GDP ratio.

Abstract: This paper proposes a new panel unit‐root test based on the Lagrangian multiplier (LM) principle. We show that the asymptotic distribution of the new panel LM test is not affected by the presence of structural shifts. This result holds under a mild condition that N/T→k, where k is any finite constant. Our simulation study shows that the panel LM unit‐root test is not only robust to the presence of structural shifts, but is more powerful than the popular Im, Pesaran and Shin (IPS) test. We apply our new test to the purchasing power parity (PPP) hypothesis and find strong evidence for PPP.

Abstract: This paper considers estimation and inference in panel vector autoregressions where (i) the individual effects are either random or fixed, (ii) the time-series properties of the model variables are unknown a priori and may feature unit roots and cointegrating relations, and (iii) the time dimension of the panel is short and its cross-sectional dimension is large. Generalized method of moments (GMM) and quasi maximum likelihood (QML) estimators are obtained and compared in terms of their asymptotic and finite-sample properties. It is shown that the asymptotic variances of the GMM estimators that are based on levels in addition to first differences of the model variables depend on the variance of the individual effects, whereas by construction the fixed effects QML estimator is not subject to this problem. Monte Carlo evidence is provided showing that the fixed effects QML estimator tends to outperform the various GMM estimators in finite sample under both normal and nonnormal errors. The paper also shows how the fixed effects QML estimator can be successfully used for unit root and cointegration tests in short panels.We are grateful to Karim Abadir, Stephen Bond, Jinyong Hahn, Marc Nerlove, Ingmar Prucha, and, especially, Manuel Arellano, Peter Schmidt, Peter Phillips (the editor), and four anonymous referees for helpful and constructive comments. We have also benefited from useful suggestions by participants at various seminars and conferences.

Abstract: In this paper, the authors simulated the ADF unit root test of finite-sample time series with GJR-GARCH error. The sample length, existence of high-order moment in disturbance, fat-tailedness and levelage effects were analyzed, which shows that the Fuller critical values of z, statistics directly under GED and t conditional distribution of the error term can be used.

Abstract: . In this paper we provide tests for the unit-root hypothesis against the occurrence of an unspecified number of breaks which may be larger than 2 but smaller that the maximum number of breaks allowed, m, in univariate time-series models. The advocated procedure is considerably less computationally intensive than those widely used in the literature. We provide critical values for the test and examine its small sample properties through Monte Carlo experiments.

Abstract: This paper investigates the link between health care expenditures and GDP for a sample of 21 OECD countries using recent developed panel cointegration techniques. In contrast to previous studies, the analysis accounts for the fact that health care expenditures are not only determined by income. The other driving force is medical progress, which is proxied by different variables, like life expectancy, infant mortality and the share of the elderly. In the extended models, a cointegration relationship can be established among the variables. The income elasticity is not different from unity, implying that health care expenditures are not a luxury good. This finding is robust for alternative measures of medical progress. The evidence is unchanged, if alternative estimators of the cointegration vector are used. Controlling for cross section dependency does not affect the principal results, as cointegration can be found even in a model among nonstationary common factors.

Abstract: This article is concerned with forecasting from nonlinear conditional mean models. First, a number of often applied nonlinear conditional mean models are introduced and their main properties discussed. The next section is devoted to techniques of building nonlinear models. Ways of computing multi-step ahead forecasts from nonlinear models are surveyed. Tests of forecast accuracy in the case where the models generating the forecasts are nested are discussed. There is a numerical example, showing that even when a stationary nonlinear process generates the observations, future obervations may in some situations be better forecast by a linear model with a unit root. Finally, some empirical studies that compare forecasts from linear and nonlinear models are discussed.

Abstract: In this paper we examine temporal properties of eleven natural resource real price series from 1870-1990. Recent studies by Ahrens and Sharma [1997], Berck and Roberts [1996], and Slade [1988], among others, find that many nonrenewable resource prices have a stochastic trend. We revisit this issue by employing a Lagrangian Multiplier unit root test that allows for two endogenously determined structural breaks with and without a quadratic trend. Contrary to previous research, we find evidence against the unit root hypothesis for all price series. Our findings support characterizing natural resource prices as stationary around deterministic trends with structural breaks. We additionally show that both pre-testing for unit roots with breaks and allowing for breaks in the forecast model can improve forecast accuracy. Overall, the results in this paper are important in both a positive and normative sense; without an appropriate understanding of the dynamics of a time series, empirical verification of theories, forecasting, and proper inference are potentially fruitless.

Abstract: The paper provides a general framework for investigating the effects of permanent changes in the variance of the errors of an autoregressive process on unit root tests. Such a framework – which is based on a novel asymptotic theory for integrated and near integrated processes with heteroskedastic errors – allows to evaluate how the variance dynamics affect the size and the power function of unit root tests. Contrary to previous studies, it is shown that non-constant variances can both inflate and deflate the rejection frequency of the commonly used unit root tests, both under the null and under the alternative, with early negative and late positive variance changes having the strongest impact on size and power. It is also shown that shifts smoothed across the sample have smaller impacts than shifts occurring as a single abrupt jump, while periodic variances have a negligible effect even when a small number of cycles take place over a given sample. Finally, it is proved that the locally best invar...

Abstract: In this paper we test for the presence of rational bubbles in the NASDAQ stock market index over the period 1994:06–2003:11 by means of a methodology based on fractional processes. The results suggest that the existence of bubbles depends on the sampling frequency used in the analysis. We cannot reject the unit root hypothesis when using monthly data on price–dividend ratios, which according to the present value model suggests the existence of rational bubbles. However, we reject this hypothesis in favor of fractional alternatives when using daily and weekly data. This might be explained by the temporal aggregation and/or the sample sizes used in the application.

Abstract: Within the multiplicative seasonal ARIMA modeling context, there are two forecasting models, RIMA14 and ARIMA1. ARIMA14 is used for modeling stochastic nonstationary seasonality and requires first and fourth differences to achieve stationarity. ARIMA1 considers the series only in first differences, and seasonality is modeled with a constant and three seasonal dummies. The selection of either model depends on the nature of seasonality. Conventional unit root tests determine the nature of seasonality and the order of integration and, therefore, the series' choice of forecasting model. To determine whether the test correctly identifies the forecasting model for tourism demand, out-of-sample forecasting performance of ARIMA1 and ARIMA14 is compared with HEGY unit root model selection method. Comparing forecasting performance of both models with HEGY unit root model selection shows that the outcome of HEGY test procedure may not be useful in the selection of a univariate time-series model for quarterly tourism demand series.

Abstract: With introduction of new estimation techniques, old theories receive a renewed attention and on this regard, trade elasticities are no exception. In this paper we employ a new cointegration technique, i.e., ARDL approach to cointegration that does not require pre-testing for unit root and estimate income and price elasticities of import and export demand for 28 countries. The results indicate that price elasticities in most instances are high enough to conclude that real depreciation could improve the trade balance.

Abstract: Tests for fractional integration in the S&P 500 log dividend yield are conducted in order to test the proposition that exogenous shocks have permanent effects. The presence of a unit root in the log dividend yield is consistent with ‘rational bubbles’ in stock prices. Our findings, based on tests for fractional integration, yield robust rejections of the null hypothesis of rational bubbles. The results strongly suggest that the log dividend yield is mean reverting.

Abstract: We propose tests for hypotheses on the parameters of the deterministic trend function of a univariate time series. The tests do not require knowledge of the form of serial correlation in the data, and they are robust to strong serial correlation. The data can contain a unit root and still have the correct size asymptotically. The tests that we analyze are standard heteroscedasticity autocorrelation robust tests based on nonparametric kernel variance estimators. We analyze these tests using the fixed-b asymptotic framework recently proposed by Kiefer and Vogelsang. This analysis allows us to analyze the power properties of the tests with regard to bandwidth and kernel choices. Our analysis shows that among popular kernels, specific kernel and bandwidth choices deliver tests with maximal power within a specific class of tests. Based on the theoretical results, we propose a data-dependent bandwidth rule that maximizes integrated power. Our recommended test is shown to have power that dominates a related test...

Abstract: The central aim of this paper is to investigate whether shocks to Fiji's tourism industry have a permanent effect or a transitory effect on tourist expenditure in Fiji. To accomplish this aim the Zivot and Andrews (1992) one break test and the Lumsdaine and Papell (1997) two break tests are used. The one break and two break tests reveal 1987 - the year of the military coups in Fiji - as the year of the break. Moreover, it is possible to reject the unit root null leading to the conclusion that shocks to Fiji's tourism industry have a transitory effect on tourist expenditure in Fiji.

Abstract: Although the question of whether Purchasing Power Parity (PPP) holds in the long run has been extensively studied, the answer is still controversial. Some of the strongest evidence is provided by Taylor (The Review of Economics and Statistics 84[[2002] 139-150), who concludes that long-run PPP held over the 20th century. We argue that this conclusion is quite sensitive to the use of sub-optimal lag selection in unit root tests. Using superior lag selection methods, we find that long-run PPP held for the real exchange rates of only 9 out of the 16 industrialized countries in Taylor's sample with the U.S. dollar as the base currency.

Abstract: The paper examines the export-led growth (ELG) paradigm for Egypt, using historical data from 1977 to 2003. During this period, Egypt changed its economic philosophy from central planning and government intervention to one based on a free market economy. The paper employs a variety of analytical tools, including cointegration analysis, Granger causality tests, and unit root tests, coupled with vector auto regression (VAR) and impulse response function (IRF) analyses. The paper sets three hypotheses for testing the ELG paradigm for Egypt, (i) whether GDP, exports and imports are cointegrated, (ii) whether exports Granger cause growth, (iii) whether exports Granger cause investment. The paper fails to reject the first two hypotheses, while it fails to accept that exports Granger cause investment. In addition to the analysis of the 1977-2003 period, the paper looks briefly also at the impact of the economic reform undertaken in 1991, and weather the ELG hypothesis still holds during the 1991-2003 sub-period.

Abstract: This paper empirically investigates the effect of corruption on economic growth for 18 African countries using panel unit root and the Phillips-Hansen fully modified OLS procedures. The results from the IPS panel unit root tests indicate that corruption, economic growth, investment, and population growth have zero order of integration [i.e. I(o)]. The results from the Phillips-Hansen fully modified OLS procedure reveal that corruption retards economic growth directly by lowering productivity, and indirectly by restricting investment. From a policy perspective, efforts should be made to discourage corruption.

Abstract: Whether or not stock prices are characterized by a unit root has important implications for policy. For instance, by applying unit root tests one can deduce whether stock returns can be predicted from previous changes in prices. A finding of a unit root implies that stock returns cannot be predicted. This paper investigates whether or not stock prices for Australia and New Zealand can be characterized by a unit root process. An unrestricted two-regime threshold autoregressive model is used with an autoregressive unit root. Among the main results, it is found that the stock prices of both countries are nonlinear processes that are characterized by a unit root process, consistent with the efficient market hypothesis.

Abstract: We consider a number of unit root tests for micro panels where the number of individuals is typically large, but the number of time periods is often very small. As we discuss, the presence of a unit root is closely related to the identification of parameters of interest in this context. Calculations of asymptotic local power and Monte Carlo evidence indicate that two simple t-tests based on ordinary least squares estimators perform particularly well.

Abstract: This paper analyses the sustainability of Portuguese public finances, making use of a long dataset with more than a full century of observations. The use of such a long dataset is appropriate because both unit root and cointegration tests require a long period of data. The sustainability testing procedure is based on unit root and cointegration tests. We find considerable evidence in favour of sustainability for the 1903-2003 period. The overall conclusion of sustainability for the 1903-2003 period is not maintained for the more recent 1975-2003 period, which is characterised by the largest GDP deficit ratios of our sample. This latter period appears to signal a shift to an unsustainable path in Portuguese fiscal policy. Hence, our results suggest that fiscal consolidation efforts must, in fact, be continued in Portugal.

Abstract: The notion of a ripple effect in the UK housing market implies stationarity in regional:national house price ratios. In this paper a new means of examining this issue is proposed which involves the joint application of a powerful unit root test and a test of stationarity. In contrast to the previous studies which have failed to detect stationarity using the Dickey–Fuller unit root test, the proposed method uncovers stationarity for a number of regions. Monte Carlo evidence is presented to support and explain the empirical findings obtained. Importantly, it is found that in comparison to previously considered joint testing approaches and individual unit root tests, the proposed method dramatically reduces the frequency with which stationary series are mistakenly concluded by practitioners to possess a unit root.