Testing for unit roots in bounded time series

Many key economic and financial series are bounded either by construction or through policy controls. Conventional unit root tests are potentially unreliable in the presence of bounds, since they tend to over-reject the null hypothesis of a unit root, even asymptotically. So far, very little work has been undertaken to develop unit root tests which can be applied to bounded time series. In this paper we address this gap in the literature by proposing unit root tests which are valid in the presence of bounds. We present new augmented Dickey–Fuller type tests as well as new versions of the modified ‘M’ tests developed by Ng and Perron [Ng, S., Perron, P., 2001. LAG length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554] and demonstrate how these tests, combined with a simulation-based method to retrieve the relevant critical values, make it possible to control size asymptotically. A Monte Carlo study suggests that the proposed tests perform well in finite samples. Moreover, the tests outperform the Phillips–Perron type tests originally proposed in Cavaliere [Cavaliere, G., 2005. Limited time series with a unit root. Econometric Theory 21, 907–945]. An illustrative application to U.S. interest rate data is provided

Testing Seasonal Unit Roots in Data at Any Frequency, an HEGY approach

This paper generalizes the HEGY-type test to detect seasonal unit roots in data at any frequency, based on the seasonal unit root tests in univariate time series by Hylleberg, Engle, Granger and Yoo (1990). We introduce the seasonal unit roots at first, and then derive the mechanism of the HEGY-type test for data with any frequency. Thereafter we provide the asymptotic distributions of our test statistics when different test regressions are employed. We find that the F-statistics for testing conjugation unit roots have the same asymptotic distributions. Then we compute the finite-sample and asymptotic critical values for daily and hourly data by a Monte Carlo method. The power and size properties of our test for hourly data is investigated, and we find that including lag augmentations in auxiliary regression without lag elimination have the smallest size distortion and tests with seasonal dummies included in auxiliary regression have more power than the tests without seasonal dummies. At last we apply the our test to hourly wind power production data in Sweden and shows there are no seasonal unit roots in the series.

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.

Modeling the spatial dynamics of economic models

The advances that have been characterizing spatial econometrics in recent years are mostly theoretical and have not found an extensive empirical application yet. In this work we aim at supplying a review of the main tools of spatial econometrics and to show an empirical application for one of the most recently introduced estimators. Despite the numerous alternatives that the econometric theory provides for the treatment of spatial (and spatiotemporal) data, empirical analyses are still limited by the lack of availability of the correspondent routines in statistical and econometric software. Spatiotemporal modeling represents one of the most recent developments in spatial econometric theory and the finite sample properties of the estimators that have been proposed are currently being tested in the literature. We provide a comparison between some estimators (a quasi-maximum likelihood, QML, estimator and some GMM-type estimators) for a fixed effects dynamic panel data model under certain conditions, by means of a Monte Carlo simulation analysis. We focus on different settings, which are characterized either by fully stable or quasi-unit root series. We also investigate the extent of the bias that is caused by a non-spatial estimation of a model when the data are characterized by different degrees of spatial dependence. Finally, we provide an empirical application of a QML estimator for a time-space dynamic model which includes a temporal, a spatial and a spatiotemporal lag of the dependent variable. This is done by choosing a relevant and prolific field of analysis, in which spatial econometrics has only found limited space so far, in order to explore the value-added of considering the spatial dimension of the data. In particular, we study the determinants of cropland value in Midwestern U.S.A. in the years 1971-2009, by taking the present value model (PVM) as the theoretical framework of analysis.

Estimating short and long-term residential demand for electricity : new evidence from Sri Lanka

This study investigates the short-run dynamics and long-run equilibrium relationship between residential electricity demand and factors influencing demand - per capita income, price of electricity, price of kerosene oil and price of liquefied petroleum gas - using annual data for Sri Lanka for the period, 1960-2007. The study uses unit root, cointegration and error-correction models. The long-run demand elasticities of income, own price and price of kerosene oil (substitute) were estimated to be 0.78, - 0.62, and 0.14 respectively. The short-run elasticities for the same variables were estimated to be 032, - 0.16 and 0.10 respectively. Liquefied petroleum (LP) gas is a substitute for electricity only in the short-run with an elasticity 0.09. The main findings of the paper support the following (1) increasing the price of electricity is not the most effective tool to reduce electricity consumption (2) existing subsidies on electricity consumption can be removed without reducing government revenue (3) the long-run income elasticity of demand shows that any future increase in household incomes is likely to significantly increase the demand for electricity and(4) any power generation plans which consider only current per capita consumption and population growth should be revised taking into account the potential future income increases in order to avoid power shortages ill the country.

Exploring the nexus between tourism and output in Cook Islands: An ARDL bounds approach

Tourism plays an important role in the development of Cook Islands. In this paper we examine the nexus between tourism and growth using quarterly data over the period 2009Q1–2014Q2 using the recently upgraded ARDL bounds test to cointegration tool, Microfit 5.01, which provides sample adjusted bounds and hence is more reliable for small sample size studies. We perform the cointegration using the ARDL bounds test and examine the direction of causality. Using visitor arrival and output in per capita terms as respective proxy for tourism development and growth, we examine the long-run association and report the elasticity coefficient of tourism and causality nexus, accordingly. Using unit root break tests, we note that 2011Q1 and 2011Q2 are two structural break periods in the output series. However, we note that this period is not statistically significant in the ARDL model and hence excluded from the estimation. Subsequently, the regression results show the two series are cointegrated. The long-run elasticity coefficient of tourism is estimated to be 0.83 and the short-run is 0.73. A bidirectional causality between tourism and income is noted for Cook Islands which indicates that tourism development and income mutually reinforce each other. In light of this, socio-economic policies need to focus on broad-based, inclusive and income-generating tourism development projects which are expected to have feedback effect.

Toxic effects of Pb2+ on growth of cowpea (Vigna unguiculata)

A concentration as low as 1 μM lead (Pb) is highly toxic to plants, but previous studies have typically related plant growth to the total amount of Pb added to a solution. In the present experiment, the relative fresh mass of cowpea (Vigna unguiculata) was reduced by 10% at a Pb2+ activity of 0.2 μM for the shoots and at a Pb2+ activity of 0.06 μM for the roots. The primary site of Pb2+ toxicity was the root, causing severe reductions in root growth, loss of apical dominance (shown by an increase in branching per unit root length), the formation of localized swellings behind the root tips (due to the initiation of lateral roots), and the bending of some root tips. In the root, Pb was found to accumulate primarily within the cell walls and intercellular spaces.

Can technology provide a glimmer of hope for economic growth in the midst of chaos? A case of Zimbabwe

In this paper we examine the effect of technology on economic growth in Zimbabwe over the period 1975–2014 whilst accounting for structural breaks. We use the extended Cobb–Douglas type Solow (Q J Econ 70(1):65–94, 1956) framework and the ARDL bounds procedure to examine cointegration and short run and long run effects. Using unit root tests, we note that structural changes in Zimbabwe are generally marked by the period 1982 onwards. We find that mobile technology has a positive short-run (0.09 %) and long-run (0.08 %) impact on the output per capita. The structural changes post-1982 periods show positive impact in the short-run (0.06) and the long-run (0.09), whereas the coefficient of trend in the short-run (−0.03) and the long-run (−0.04) is negative. The Granger non-causality test shows a unidirectional causality from capital stock (investment) per capita to output per capita and a bi-directional causality between mobile cellular technology and output per capita. The plausible reasons for estimated magnitude effects and the direction of causality are explained for policy deliberation.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.

Do technology shocks drive hours up or down? A little evidence from an agnostic procedure

This paper analyzes the robustness of the estimate of a positive productivity shock on hours to the presence of a possible unit root in hours. Estimations in levels or in first differences provide opposite conclusions. We rely on an agnostic procedure in which the researcher does not have to choose between a specification in levels or in first differences. We find that a positive productivity shock has a negative impact effect on hours, but the effect is much shorter lived, and disappears after two quarters. The effect becomes positive at business-cycle frequencies, although it is not significant. © 2005 Cambridge University Press.

Does final demand for energy in Portugal exhibit long memory

In this paper, we measure the degree of fractional integration in final energy demand in Portugal using an ARFIMA model with and without adjustments for seasonality. We consider aggregate energy demand as well as final demand for petroleum, electricity, coal, and natural gas. Our findings suggest the presence of long memory in all of the energy demand variables, that the series are stationary, although the mean reversion process will be slower than in the typical short run processes. These results have important implications for the design of energy policies. The effects of temporary policy shocks on final energy demand will tend to disappear slowly. This means that even transitory shocks have long lasting effects. Given the temporary nature of these effects, however, permanent effects require permanent policies. This is unlike what would be suggested by the more standard but much more limited unit root approach, which would incorrectly indicate that even transitory policies would have permanent effects.

What causes economic growth in Portugal: exports or inward FDI?

The purpose of this paper is to analyse possible casual relationships between exports, inward foreign investment and economic growth in Portugal and identify their direction. The paper uses the three stage procedure based on unit root, cointegration and causalty tests applied to annual data from 1977 to 2004.

Testing for volatility persistence change: The effect of the credit crisis on the Portuguese banks

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Logique et tests d'hypotheses: reflexions sur les problemes mal poses en econometrie

Dans ce texte, nous analysons les développements récents de l’économétrie à la lumière de la théorie des tests statistiques. Nous revoyons d’abord quelques principes fondamentaux de philosophie des sciences et de théorie statistique, en mettant l’accent sur la parcimonie et la falsifiabilité comme critères d’évaluation des modèles, sur le rôle de la théorie des tests comme formalisation du principe de falsification de modèles probabilistes, ainsi que sur la justification logique des notions de base de la théorie des tests (tel le niveau d’un test). Nous montrons ensuite que certaines des méthodes statistiques et économétriques les plus utilisées sont fondamentalement inappropriées pour les problèmes et modèles considérés, tandis que de nombreuses hypothèses, pour lesquelles des procédures de test sont communément proposées, ne sont en fait pas du tout testables. De telles situations conduisent à des problèmes statistiques mal posés. Nous analysons quelques cas particuliers de tels problèmes : (1) la construction d’intervalles de confiance dans le cadre de modèles structurels qui posent des problèmes d’identification; (2) la construction de tests pour des hypothèses non paramétriques, incluant la construction de procédures robustes à l’hétéroscédasticité, à la non-normalité ou à la spécification dynamique. Nous indiquons que ces difficultés proviennent souvent de l’ambition d’affaiblir les conditions de régularité nécessaires à toute analyse statistique ainsi que d’une utilisation inappropriée de résultats de théorie distributionnelle asymptotique. Enfin, nous soulignons l’importance de formuler des hypothèses et modèles testables, et de proposer des techniques économétriques dont les propriétés sont démontrables dans les échantillons finis.

Identification, Weak Instruments and Statistical Inference in Econometrics

We discuss statistical inference problems associated with identification and testability in econometrics, and we emphasize the common nature of the two issues. After reviewing the relevant statistical notions, we consider in turn inference in nonparametric models and recent developments on weakly identified models (or weak instruments). We point out that many hypotheses, for which test procedures are commonly proposed, are not testable at all, while some frequently used econometric methods are fundamentally inappropriate for the models considered. Such situations lead to ill-defined statistical problems and are often associated with a misguided use of asymptotic distributional results. Concerning nonparametric hypotheses, we discuss three basic problems for which such difficulties occur: (1) testing a mean (or a moment) under (too) weak distributional assumptions; (2) inference under heteroskedasticity of unknown form; (3) inference in dynamic models with an unlimited number of parameters. Concerning weakly identified models, we stress that valid inference should be based on proper pivotal functions —a condition not satisfied by standard Wald-type methods based on standard errors — and we discuss recent developments in this field, mainly from the viewpoint of building valid tests and confidence sets. The techniques discussed include alternative proposed statistics, bounds, projection, split-sampling, conditioning, Monte Carlo tests. The possibility of deriving a finite-sample distributional theory, robustness to the presence of weak instruments, and robustness to the specification of a model for endogenous explanatory variables are stressed as important criteria assessing alternative procedures.