Testing unit root based on partially adaptive estimation

This paper proposes unit tests based on partially adaptive estimation. The proposed tests provide an intermediate class of inference procedures that are more efficient than the traditional OLS-based methods and simpler than unit root tests based on fully adptive estimation using nonparametric methods. The limiting distribution of the proposed test is a combination of standard normal and the traditional Dickey-Fuller (DF) distribution, including the traditional ADF test as a special case when using Gaussian density. Taking into a account the well documented characteristic of heavy-tail behavior in economic and financial data, we consider unit root tests coupled with a class of partially adaptive M-estimators based on the student-t distributions, wich includes te normal distribution as a limiting case. Monte Carlo Experiments indicate that, in the presence of heavy tail distributions or innovations that are contaminated by outliers, the proposed test is more powerful than the traditional ADF test. We apply the proposed test to several macroeconomic time series that have heavy-tailed distributions. The unit root hypothesis is rejected in U.S. real GNP, supporting the literature of transitory shocks in output. However, evidence against unit roots is not found in real exchange rate and nominal interest rate even haevy-tail is taken into a account.

Comparing two multivariate unit root tests

In this essay, a method for comparing the asymptotic power of the multivariate unit root tests proposed in Phillips & Durlauf (1986) and Flˆores, Preumont & Szafarz (1996) is proposed. In order to determine the asymptotic power of the tests the asymptotic distributions under the null hypothesis and under the set of alternative hypotheses described in Phillips (1988) are determined. In addition, a test which combines characteristics of both tests is proposed and its distributions under the null hypothesis and the same set of alternative hypotheses are determined. This allows us to determine what causes any difference in the asymptotic power of the two tests against the set of alternative hypotheses considered

Purchasing power parity and the unit root tests: a robust analysis

Empirical evidence suggests that real exchange rate is characterized by the presence of near-unity and additive outliers. Recent studeis have found evidence on favor PPP reversion by using the quasi-differencing (Elliott et al., 1996) unit root tests (ERS), which is more efficient against local alternatives but is still based on least squares estimation. Unit root tests basead on least saquares method usually tend to bias inference towards stationarity when additive out liers are present. In this paper, we incorporate quasi-differencing into M-estimation to construct a unit root test that is robust not only against near-unity root but also against nonGaussian behavior provoked by assitive outliers. We re-visit the PPP hypothesis and found less evidemce in favor PPP reversion when non-Gaussian behavior in real exchange rates is taken into account.

A unit root test based on partially adaptive estimation

This paper constructs a unit root test baseei on partially adaptive estimation, which is shown to be robust against non-Gaussian innovations. We show that the limiting distribution of the t-statistic is a convex combination of standard normal and DF distribution. Convergence to the DF distribution is obtaineel when the innovations are Gaussian, implying that the traditional ADF test is a special case of the proposed testo Monte Carlo Experiments indicate that, if innovation has heavy tail distribution or are contaminated by outliers, then the proposed test is more powerful than the traditional ADF testo Nominal interest rates (different maturities) are shown to be stationary according to the robust test but not stationary according to the nonrobust ADF testo This result seems to suggest that the failure of rejecting the null of unit root in nominal interest rate may be due to the use of estimation and hypothesis testing procedures that do not consider the absence of Gaussianity in the data.Our results validate practical restrictions on the behavior of the nominal interest rate imposed by CCAPM, optimal monetary policy and option pricing models.

Multivariate unit root tests

A new multivariate test for the detection ofunit roots is proposed. Use is made ofthe possible correlations between the disturbances of difIerent series, and constrained and unconstrained SURE estimators are employed. The corresponding asymptotic distributions, for the case oftwo series, are obtained and a table with criticai vaIues is generated. Some simulations indivate that the procedure performs better than the existing alternatives.

A new perspective on the PPP hypothesis

This paper the stastistical properties of the real exchange rates of G-5 countries for the Bretton-Woods peiod, and draw implications on the purchasing power parity (PPP) hypothesis. In contrast to most previous studies that consider only unit root and stationary process to describe the real exchange tae, this paper also considers two in-between processes, the locally persistent process ans the fractionally integrated process, to complement past studies. Seeking to be consistent with tha ample evidence of near unit in the real exchange rate movements very well. This finding implies that: 1) the real exchange movement is more persistent than the stationary case but less persistent than the unit root case; 2) the real exchange rate is non-stationary but the PPP reversion occurs and the PPP holds in the long run; 3) the real exchange rate does not exhibit the secular dependence of the fractional integration; 4) the real exchange rate evolves over time in a way that there is persistence over a range of time, but the effect of shocks will eventually disappear over time horizon longer than order O (nd), that is, at finite time horizon; 5) shocks dissipation is fasters than predicted by the fractional integracion, and the total sum of the effects of a unit innovation is finite, implying that a full PPP reversion occurs at finite horizons. These results may explain why pasrt empirical estudies could not provide a clear- conclusion on the real exchange rate processes and the PPP hypothesis.

Testing covariance stationarity

In this paper, we show that the widely used stationarity tests such as the KPSS test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) In the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) In the presence a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) The proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on US Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.

On the purchasing power parity for Latin-American countries

The purpose of this paper is to test the hypothesis of long-run purchasing power parity (PPP) for all Latin American countries. These countries share similar economic history and contagious effects from currency crises, which might lead to comovements in their real exchange rates. New time series unit root tests found evidence of PPP for the vast majority of countries. In the panel data framework, tests for the null of unit root, null of stationarity, and unit root under multiple structural breaks indicated stationary real exchange rates. Thus, there is convincing evidence that PPP holds for Latin-American countries in the post-1980 period.

Co-movement between two processes with local persistence

This paper introduces a residual based test where the null hypothesis of c:&InOvement between two processes with local persistenc~ can be tested, even under the presence of an endogenous regressor. It, therefore, fills in an existing lacuna in econometrics, in which longrun relationships can also be tested if the dependent and independent variables do not have a unit root, but do exhibit local persistence.

Testing covariance stationarity

In this paper, we show that the widely used stationarity tests such as the KPSS test has power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) In the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) In the presence a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) The proposed test has the same size as traditional stationarity tests under the null hypothesis of covariance stationarity. An application to daily observations of return on US Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in sub-samples.

Output convergence in Mercosur: multivariate time series evidence

The aim of this paper is to provide evidence on output convergence among the Mercosur countries and associates, using multivariate time-series tests. The methodology is based on a combination of tests and estimation procedures, both univariate and multivariate, applied to the differences in per capita real income. We use the definitions of time-series convergence proposed by Bernard & Durlauf and apply unit root and tests proposed by Abuaf & Jorion and Taylor & Sarno. In this same multivariate context, the Flôres, Preumont & Szafarz and Breuer, MbNown & Wallace tests, which allow for the existence of correlations across the series without imposing a common speed of mean reversion, identify the countries that convergence. Concerning the empirical results, there is evidence of long-run convergence or, at least, catching up, for the smaller countries, Bolivia, Paraguay, Peru and Uruguay, towards Brazil and, to some extent, Argentina. In contrast, the evidence on convergence for the larger countries is weaker, as they have followed different (or rather opposing) macroeconomic policy strategies. Thus the future of the whole area will critically depend on the ability of Brazil, Argentina and Chile to find some scope for more cooperative policy actions.

Purchasing power parity: the choice of price index

Looking closely at the PPP argument, it states that the currencies purchasing power should not change when comparing the same basket goods across countries, and these goods should all be tradable. Hence, if PPP is valid at all, it should be captured by the relative price indices that best Öts these two features. We ran a horse race among six di§erent price indices available from the IMF database to see which one would yield higher PPP evidence, and, therefore, better Öt the two features. We used RER proxies measured as the ratio of export unit values, wholesale prices, value added deáators, unit labor costs, normalized unit labor costs and consumer prices, for a sample of 16 industrial countries, with quarterly data from 1975 to 2002. PPP was tested using both the ADF and the DFGLS unit root test of the RER series. The RER measured as WPI ratios was the one for which PPP evidence was found for the larger number of countries: six out of sixteen when we use DF-GLS test with demeaned series. The worst measure of all was the RER based on the ratio of foreign CPIs and domestic WPI. No evidence of PPP at all was found for this measure.

Monetary union and productivity differences in mercosur countries

This paper investigates cross-country productivity convergence among Mercosur members plus associates (Chile and Bolivia) and Peru, during the period 1960-1999. The testing strategy is based on the definitions of time-series convergence by Bernard and Durlauf (1995), and applies sequentially the multivariate unit root tests proposed by Sarno and Taylor (1998), Flôres, Preumont and Szafarz (1995) and Breuer, Mc Nown and Wallace (1999). The last two tests allow to identify the countries that converge. Our results show evidence of convergence among the four Mercosur countries, using either Argentina or Brazil as benchmark. Weaker evidence of convergence is also found with Bolivia. The results point out that monetary union among the Southern Cone economies, though a far objective, is not without sense.

Taylor principle and inflation stability in emerging market countriesw

The goal of this paper is to evaluate the validity of the Taylor principle for inflation control in 12 developing countries that use inflation targeting regimes: Brazil, Chile, Colombia, Hungary, Israel, Mexico, Peru, Philippines, Poland, South Africa, Thailand and Turkey. The test is based on a state-space model to determine when each country has followed the principle; then a threshold unit root test is used to verify if the stationarity of the deviation of the expected inflation from its target depends on compliance with the Taylor principle. The results show that such compliance leads to the stationarity of the deviation of the expected inflation from its target in all cases. Furthermore, in most cases, non-compliance with the Taylor principle leads to nonstationary deviation of the expected inflation.