DO REAL INTEREST RATES REALLY CONTAIN A UNIT ROOT? MORE EVIDENCE FROM A BOOTSTRAP COVARIATE UNIT ROOT TEST

This paper re‐examines the empirical finding that international real interest rates usually have a unit root. This conclusion is put forth in Rapach and Weber (2004 ), using the Ng and Perron (2001 ) tests. We use Rudebusch's (1993 ) approach to construct the small sample distributions of the Ng and Perron tests, and calculate their asymptotic sizes, size‐adjusted powers and rejection rates. These numbers show that the lack of power in the Ng and Perron tests might account for the findings of Rapach and Weber (2004 ): that the unit root null cannot be rejected for most OECD countries. Size distortions are mild in the case of Ng and Perron tests for two series, but are serious for the Phillips and Perron Z‐test on inflation rates. We then apply a powerful covariate augmented Dickey–Fuller unit root test to examine the series for which stationarity cannot be determined with the Ng and Perron tests. The bootstrap technique is also used to control possible size distortions. In contrast to the results of Rapach and Weber (2004 ), the bootstrap covariate augmented Dickey–Fuller test yields striking evidence that real interest rates are stationary for 14 of 16 OECD countries, because nominal interest rates are stationary for the 14 countries, while inflation rates are stationary for all countries.     

Nonlinearity and stationarity of inflation rates: evidence from the euro-zone countries

Earlier studies hardly reject the hypothesis of a unit root in inflation. Few studies have examined the possibility of nonlinearity in inflation and tested nonlinear stationarity of the inflation rates. This study thus intends to fill the gap. This study utilizes the tests for nonlinearity along with the unit root tests that allow for nonlinearity in the variables to examine the stationarity of inflation rates of 12 European countries that formed the Euro Zone (EZ) later in the sample period. The results suggest that the majority of these countries’ inflation rates can be characterized by mean reversion during the floating exchange rate period. Many of them appear to be nonlinear stationary. This finding is essential in conducting applied economic studies for these countries, when constructing models whose validity relies on whether or not inflation is stationary. The results of this study also imply that shocks to inflation have a transitory effect on inflation in the euro area. Therefore, it would be less costly in exercising the policies of disinflation for the monetary authorities of the euro area than for those of the countries with nonstationary inflation.     

Is there a unit root in the inflation rate? New evidence from panel data models with multiple structural breaks

In this article, we examine whether or not the inflation rate for 17 OECD countries can be modelled as a stationary process. We find that (1) conventional univariate unit root tests without any structural breaks generally reveal that the inflation rate contains a unit root; (2) the KPSS univariate test with multiple structural breaks reveals that for 10 out of 17 countries inflation is stationary; and (3) the KPSS panel unit root test reveals strong evidence for stationarity of the inflation rate for panels consisting of countries which were declared nonstationary by univariate tests.     

A REVISIT TO THE STATIONARITY OF OECD INFLATION: EVIDENCE FROM PANEL UNIT‐ROOT TESTS AND THE COVARIATE POINT OPTIMAL TEST*

This paper re‐examines the stationarity of inflation rates in 19 Organisation for Economic Cooperation and Development countries with the use of cross‐sectional information. We employ the panel unit‐root tests that allow for cross‐sectional dependency and the covariate point optimal test. These tests have high power in common due to the exploitation of cross‐sectional information, and they can assist mutually to draw a concrete conclusion on inflation dynamics for all series in the panel. Our empirical results show that allowing for cross‐sectional dependency rejects the null hypothesis that all series in the panel have a unit root, implying that there is at least one stationary series in the panel. With the help of the results of the covariate test, we can distinguish the panel into a group of stationary and a group of non‐stationary series. For robustness, the two groups of series are re‐confirmed by the panel tests. Our results reveal evidence of mean reversion in inflation for 15 of 19 countries, which is significantly stronger as compared to that obtained by the state‐of‐the‐art univariate unit‐root tests.     

Response of inflation to shocks: New evidence from Sub-Saharan African countries

In this paper, we investigate whether or not the inflation rate of 17 Sub-Saharan African countries can be modelled as a stationary process. We achieve this goal through using univariate and panel stationarity tests for data over the period 1966 to 2002. We use the Kwiatkowski, Phillips, Schmidt and Shin (KPSS, 1992) univariate test and allow for multiple structural breaks. We find that except for Burkina Faso, Burundi and Gambia, the inflation rate is stationary for the rest of the 14 countries. We then apply the panel version of the KPSS test, developed by Carrion-i-Silvestre et al. (2005), which accounts for multiple structural breaks. We find strong evidence of panel stationarity of the inflation rate. However, for a panel consisting of Burkina Faso, Burundi and Gambia, we could not find evidence that the inflation rate is stationary.     

Improving the Performance of a Long‐Run Variance Ratio Test for a Unit Root

Cai and Shintani (2006, Econometric Theory, 22, 347–372) considered the impact of introducing an inconsistent long‐run variance estimator when constructing a class of kernel‐based ratio tests for testing non‐stationarity in the series. They found that the quotient of two estimators with different rates of convergence under the null and the alternative hypotheses may lead to a test having an interesting size and power trade‐off. This paper develops modified versions of this test, presents new asymptotic results and tabulates critical values. The finite sample performance is explored through Monte Carlo simulations. The results show that the modifications proposed lead to more powerful unit root tests.     

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.     

A revisit on real interest rate parity hypothesis – simulation evidence from efficient unit root tests

A set of unit root tests are applied to test the existence of long-run real interest rate parity among the G-10 countries over the period 1971M1 to 2007M2. Rather than trusting the asymptotic distributions, this article uses simulation techniques to establish the small sample distributions of these tests, conditional on the stationary and nonstationary processes. The empirical results indicate that the tests have stable finite-sample sizes and higher size-adjusted powers such that the two estimated processes can be distinguished from each other. Thus, for six of the nine countries, their series are more likely to come from the estimated Autoregressive (AR) stationary process than from the nonstationary process. Noticeably, the testing results are rather different from those using the asymptotic distributions, in which only three countries support the real interest rate parity.     

How credible is inflation targeting in Asia? A quantile unit root perspective

This article examines the dynamic behavior of the inflation rate for eight Asian countries using a quantile unit root test. We advocate a three-way definition of inflation targeting based on perfect, imperfect and zero credibility and advance the analysis by incorporating a fully-fledged adoption of inflation targeting. In doing so, we offer new insights by showing that the credibility of inflation targeting and the alternative monetary policy frameworks in Asia are imperfect, except for Malaysia and South Korea under a fully-fledged adoption of inflation targeting. In contrast to past studies that focus on the mean-reversion in inflation rates, we also consider trend-reversion and find that Asian inflation targeting countries have been building up their monetary policy credibility more than the non- inflation targeting countries in terms of a faster rate of decline in inflation rate changes. Our results generally indicate the presence of mean reversion at the lower quantiles only. Where stationarity is present, we find evidence of a varied speed of adjustment process across the quantiles. Finally, we determine the threshold levels whereby inflation becomes stationary and demonstrate that Asian inflation rates generally display stationary behavior during periods of inflation declining or slowing down.     

BOOTSTRAPPING COVARIATE UNIT ROOT TESTS: AN APPLICATION TO INFLATION RATES

This paper proposes a bootstrap procedure for the covariate point optimal tests (CP_T) of Elliott and Jansson. Although the covariate tests enjoy large power gains over the traditional univariate unit root tests, our simulations show that they still suffer from severe size distortions at finite samples. Through simulations, we demonstrate the superiority of the bootstrap procedure in the sense that it can yield desirable size and power properties for the CP_T tests when the Akaike's information criterion is used. Moreover, we show the empirical relevance of the bootstrap tests by applying them to inflation in the G‐10 countries, and then obtain strong evidence against the unit root hypothesis for most countries at the 5% significance level.     

Are OECD consumption–income ratios stationary after all?

This paper investigates the stochastic properties of the consumption–income ratio for a sample of 23 OECD countries over the period 1960–2005. For that purpose, we employ a battery of recently developed panel unit root and stationarity tests. Our findings from panel unit root tests which do not control for structural breaks appear in line with those from previous studies since they are clearly supportive of the unit root hypothesis. In stark contrast stand the results obtained from the application of a panel stationarity test with multiple breaks, which support the existence of regime-wise stationarity in OECD consumption–income ratios once we control for cross-sectional dependence through bootstrap methods. These findings are reinforced by the median-unbiased estimates of half-lives obtained from impulse-response functions which are found to be finite for the 23 OECD countries.     

Are EU budget deficits stationary?

In this paper, we test for the stationarity of European Union budget deficits over the period 1971–2006, using a panel of thirteen member countries. Our testing strategy addresses two key concerns with regard to unit root panel data testing, namely (1) the presence of cross-sectional dependence among the countries in the panel and (2) the identification of potential structural breaks that might have occurred at different points in time. To address these concerns, we employ an AR-based bootstrap approach that allows us to test the null hypothesis of joint stationarity with endogenously determined structural breaks. In contrast to the existing literature, we find that the EU countries considered are characterised by fiscal stationarity over the full sample period irrespective of us allowing for structural breaks. This conclusion also holds when analysing sub-periods based on before and after the Maastricht treaty.     

To converge or not converge: unit labor cost inflation in the Euro area

In this article, convergence of unit labor cost (ULC) inflation within the Euro area is tested by means of panel unit root tests. To account for the small cross-sectional dimension, cross-sectional dependence of model innovations and time varying volatility, wild bootstrap critical values are employed for inference. Convergence is tested separately for pre- and post-Euro introduction subperiods. Moreover, we identify particular economies that are characterized by diverging ULC inflation after the introduction of the Euro. While the German economy is characterized by ULC inflation which is persistently below the sample average, Spain and Italy have suffered sustained losses of price competitiveness against their trading partners within the Euro area. ULC inflation in Finland, France, and Ireland can be classified as neutral with respect to relative competitive positions.     

Testing poolability in a system of dynamic regressions with nonspherical disturbances

This study analyzes the testing of cross-equation restrictions within a set of regression equations. Through Monte Carlo experiments we examine the actual size of various asymptotic procedures for testing the poolability hypothesis, i.e., equal slope vectors across individual equations. Regression models with both lagged dependent variable regressors and nonspherical disturbances are considered. In these models we find that the performance in finite samples of classical asymptotic test procedures using critical values from either or ² approximations is often rather poor. However, employing the original test statistics with bootstrapped critical values leads to much more accurate inference in finite samples. In an empirical analysis of panel data on GDP growth and unemployment rates in OECD countries it is shown that classical asymptotic tests and bootstrap procedures may lead to conflicting test outcomes. I am indebted to Peter Boswijk, Jan Kiviet, Peter Vlaar, the associate editor and 2 anonymous referees for their constructive comments. I want to thank Geoffrey Garrett for kindly making available his data.     

On the power of bootstrap tests for stationarity: a Monte Carlo comparison

This paper studies the behavior of recently proposed bootstrap tests for the null hypothesis of stationarity when the data are generated under the alternative hypothesis of a unit root. Using Monte Carlo experiments and empirical examples, it is shown that the power of these tests critically depends on the type of bootstrap employed. Specifically, while tests based on the stationary bootstrap have power functions that are increasing with respect to sample size, those based on the sieve bootstrap have non-monotonic power functions. We argue that this difference arises from the fact that the latter procedure does not impose the null hypothesis when generating the bootstrap samples while the former ensures that the bootstrap samples are stationary, conditional on the original data. Our results therefore suggest that while both forms of bootstrap are effective at providing improved distributional approximations under the null hypothesis, it is important to pay careful attention to the particular type of bootstrap being employed when attempting to distinguish between the unit root and stationarity hypotheses as the choice of bootstrap can have crucial implications for the power of the resulting tests.     

TESTING FOR STATIONARITY IN HETEROGENEOUS PANEL DATA IN THE CASE OF MODEL MISSPECIFICATION

This paper investigates the performance of the tests proposed by Hadri and by Hadri and Larsson for testing for stationarity in heterogeneous panel data under model misspecification. The panel tests are based on the well known KPSS test (cf. Kwiatkowski et al.) which considers two models: stationarity around a deterministic level and stationarity around a deterministic trend. There is no study, as far as we know, on the statistical properties of the test when the wrong model is used. We also consider the case of the simultaneous presence of the two types of models in a panel. We employ two asymptotics: joint asymptotic, T, N →∞ simultaneously, and T fixed and N allowed to grow indefinitely. We use Monte Carlo experiments to investigate the effects of misspecification in sample sizes usually used in practice. The results indicate that the assumption that T is fixed rather than asymptotic leads to tests that have less size distortions, particularly for relatively small T with large N panels (micro‐panels) than the tests derived under the joint asymptotics. We also find that choosing a deterministic trend when a deterministic level is true does not significantly affect the properties of the test. But, choosing a deterministic level when a deterministic trend is true leads to extreme over‐rejections. Therefore, when unsure about which model has generated the data, it is suggested to use the model with a trend. We also propose a new statistic for testing for stationarity in mixed panel data where the mixture is known. The performance of this new test is very good for both cases of T asymptotic and T fixed. The statistic for T asymptotic is slightly undersized when T is very small (≤10).     

Parity reversion persistence in real exchange rates: middle income country case

This article investigates purchasing power parity (PPP) in the specific context of middle income countries. To circumvent the low power of traditional stationarity tests (Augmented Dickey-Fuller and Phillips-Perron tests), it performs variance ratio and fractional integration tests in addition to Perron's test that accounts for potential structural changes in real exchange rate processes. Beyond estimating half-life shocks to PPP, this article attempts to explain these estimates using a set of country specific variables as suggested by economic theory. The evidence suggests that reversion to parity tends to be faster in high inflation countries and that productivity improvement leads to a higher level of persistence. Openness to trade tends to reduce the extent of deviations from parity but this result does not appear to be statistically robust. Evidence shows also that deviations are less persistent under a fixed exchange rate regime and under unrestricted capital mobility.     

Re-examining the threshold effects in the inflation–growth nexus with cross-sectionally dependent non-linear panel: Evidence from six industrialized economies

This paper analyzes the empirical relationship between inflation and output growth using a novel panel data estimation technique, Panel Smooth Transition Regression (PSTR) model, which takes account of the non-linearities in the data. By using a panel data set for 6 industrialized countries that enable us to control for unobserved heterogeneity at both country and time levels, we find that there exists a statistically significant negative relationship between inflation and growth for the inflation rates above the critical threshold level of 2.52%, which is endogenously determined. Furthermore, we also control cross-section dependency by using the CD test modified to non-linear context and remedy cross-section dependency with Seemingly Unrelated Regression Equations through Generalized Least Squares (SURE-GLS) and newly proposed Common Correlated Effects (CCE) estimation techniques. We find that these methods change the critical threshold value slightly. The estimated threshold values from these estimation methods are 3.18% and 2.42%, respectively.     

NONPARAMETRIC BOOTSTRAP PROCEDURES FOR PREDICTIVE INFERENCE BASED ON RECURSIVE ESTIMATION SCHEMES*

We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for out‐of‐sample nonlinear Granger causality, and in the other we outline a test for selecting among multiple alternative forecasting models, all of which are possibly misspecified. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (Journal of Applied Econometrics 14 (1999), 491–510), within the context of encompassing and predictive accuracy tests. In the empirical illustration, it is found that unemployment has nonlinear marginal predictive content for inflation.     

Is Asian per capita GDP panel stationary?

The goal of this paper is to examine whether per capita GDP for 15 Asian countries is panel stationary. We apply a panel test for stationarity that allows for multiple structural breaks developed by Carrion-i-Silvestre et al. (Econ J 8: 159–179, 2005). Our main findings are: (1) when we apply conventional tests, such as the ADF and KPSS univariate tests without structural breaks, we find little evidence for stationarity; (2) when we apply the KPSS univariate test with multiple structural breaks, we find evidence of stationarity for 10 out of 15 countries; and (3) when we apply the KPSS panel test with multiple structural breaks, we find overwhelming evidence of panel stationarity of per capita real GDP for different panels of Asian countries.