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In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions. (C) 2019 Elsevier B.V. All rights reserved.

This paper considers estimation of factor-augmented panel data regression models. One of the most popular approaches towards this end is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica, 2006, 74, 967–1012, 2006). For the pooled version of this estimator to be consistent, either the number of observables must be larger than the number of unobserved common factors, or the factor loadings must be distributed independently of each other. This is a problem in the typical application involving only a small number of regressors and/or correlated loadings. The current paper proposes a simple extension to the CCE procedure by which both requirements can be relaxed. The CCE approach is based on taking the cross-section average of the observables as an estimator of the common factors. The idea put forth in the current paper is to consider not only the average but also other cross-section combinations. Asymptotic properties of the resulting combination-augmented CCE (C 3 E) estimator are provided and tested in small samples using both simulated and real data.

The predominant way of modelling mortality rates is the lee–carter model and its many extensions. The lee–carter model and its many extensions use a latent process to forecast. These models are estimated using a two-step procedure that causes an inconsistent view on the latent variable. This paper considers identifiability issues of these models from a perspective that acknowledges the latent variable as a stochastic process from the beginning. We call this perspective the plug-in age–period or plug-in age–period–cohort model. Defining a parameter vector that includes the underlying parameters of this process rather than its realizations, we investigate whether the expected values and covariances of the plug-in lee–carter models are identifiable. It will be seen, for example, that even if in both steps of the estimation procedure we have identifiability in a certain sense it does not necessarily carry over to the plug-in models.

Economic panel data often exhibit cross-sectional dependence, even after conditioning on appropriate explanatory variables. Two approaches to modeling cross-sectional dependence in economic panel data are often used: the spatial dependence approach, which explains cross-sectional dependence in terms of distance among units, and the residual multifactor approach, which explains cross-sectional dependence by common factors that affect individuals to a different extent. This article reviews the theory on estimation and statistical inference for stationary and nonstationary panel data with cross-sectional dependence, particularly for models with a multifactor error structure. Tests and diagnostics for testing for unit roots, slope homogeneity, cointegration, and the number of factors are provided. We discuss issues such as estimating common factors, dealing with parameter plethora in practice, testing for structural stability and nonlinearity, and dealing with model and parameter uncertainty. Finally, we address issues related to the use of these economic panel models.

This paper investigates the focused information criterion and plug-in average for vector autoregressive models with local-to-zero misspecification. These methods have the advantage of focusing on a quantity of interest rather than aiming at overall model fit. Any (suxfb03;ciently regular) function of the parameters can be used as a quantity of interest. We determine the asymptotic properties and elaborate on the role of the locally misspecified parameters. In particular, we show that the inability to consistently estimate locally misspecified parameters translates into suboptimal selection and averaging. We apply this framework to impulse response analysis. A Monte Carlo simulation study supports our claims.

We extend the repeated observations forecasting analysis of Stark and Croushore (2002) to allow for regressors that may be of higher sampling frequencies than the regressand. For the U.S. GNP quarterly growth rate, we compare the forecasting performances of an autoregressive model with those of several mixed-frequency models, including the MIDAS approach. Using the additional dimension provided by different vintages, we compute several forecasts for a given calendar date with each model, then approximate the corresponding distribution of forecasts by a continuous density. Next, we combine these model-specific densities using scoring rules and analyze both the composition and the evolution of the implied weights over time. In so doing, not only do we investigate the sensitivity of model selection to the choice of which data release to consider, we also illustrate how revision process information can be incorporated into real time studies. As a consequence of these analyses, we introduce a new weighting scheme that summarizes the information contained in the revision process of the variables under consideration.

This paper develops panel data tests for the null hypothesis of no error correction in a model with common stochastic trends. The asymptotic distributions of the new test statistics are derived and simulation results are provided to suggest that they perform well in small samples. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper we propose an autoregressive wild bootstrap method to construct confidence bands around a smooth deterministic trend. The bootstrap method is easy to implement and does not require any adjustments in the presence of missing data, which makes it particularly suitable for climatological applications. We establish the asymptotic validity of the bootstrap method for both pointwise and simultaneous confidence bands under general conditions, allowing for general patterns of missing data, serial dependence and heteroskedasticity. The finite sample properties of the method are studied in a simulation study. We use the method to study the evolution of trends in daily measurements of atmospheric ethane obtained from a weather station in the Swiss Alps, where the method can easily deal with the many missing observations due to adverse weather conditions.

This paper proposes a mixed-frequency error correction model for possibly cointegrated non-stationary time series sampled at different frequencies. We highlight the impact, in terms of model specification, of the choice of the particular high-frequency explanatory variable to be included in the cointegrating relationship, which we call a dynamic mixed-frequency cointegrating relationship. The forecasting performance of aggregated models and several mixed-frequency regressions are compared in a set of Monte Carlo experiments. In particular, we look at both the unrestricted mixed-frequency model and at a more parsimonious MIDAS regression. Whereas the existing literature has only investigated the potential improvements of the MIDAS framework for stationary time series, our study emphasizes the need to include the relevant cointegrating vectors in the non-stationary case. Furthermore, it is illustrated that the choice of dynamic mixed-frequency cointegrating relationship does not matter as long as the short-run dynamics are adapted accordingly. Finally, the unrestricted model is shown to suffer from parameter proliferation for samples of relatively small size, whereas MIDAS forecasts are robust to over-parameterization. We illustrate our results for the US inflation rate. Copyright © 2014 John Wiley & Sons, Ltd.

The bulk of existing work on the statistical forecasting of air quality is based on either neural networks or linear regressions, which are both subject to important drawbacks. In particular, while neural networks are complicated and prone to in-sample overfitting, linear regressions are highly dependent on the specification of the regression function. The present paper shows how combining linear regression forecasts can be used to circumvent all of these problems. The usefulness of the proposed combination approach is verified using both Monte Carlo simulation and an extensive application to air quality in Bogota, one of the largest and most polluted cities in Latin America.

In an influential paper, Pesaran [Pesaran, M.H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 967-1012] proposes a very simple estimator of factor-augmented regressions that has since then become very popular. In this note we demonstrate how the presence of correlated factor loadings can render this estimator inconsistent. (C) 2013 Elsevier B.V. All rights reserved.

In this paper, we consider a cointegrated panel data model with non-stationary common factors, which, because of its appeal in many economic applications, has received much attention in the recent literature. By deriving a Granger-type representation theorem, we obtain several equivalent model formulations, which have differing merits for empirical work. (C) 2013 Elsevier B.V. All rights reserved.

In this article, we investigate the validity of the univariate autoregressive sieve bootstrap applied to time series panels characterized by general forms of cross-sectional dependence, including but not restricted to cointegration. Using the final equations approach we show that while it is possible to write such a panel as a collection of infinite order autoregressive equations, the innovations of these equations are not vector white noise. This causes the univariate autoregressive sieve bootstrap to be invalid in such panels. We illustrate this result with a small numerical example using a simple DGP for which the sieve bootstrap is invalid, and show that the extent of the invalidity depends on the value of specific parameters. We also show that Monte Carlo simulations in small samples can be misleading about the validity of the univariate autoregressive sieve bootstrap. The results in this article serve as a warning about the practical use of the autoregressive sieve bootstrap in panels where cross-sectional dependence of general form may be present.

Practitioners are generally well aware of the fact that most standard approaches for estimation and inference in panel data regressions are based on assuming that the cross-sectional units are independent of each other, an assumption that is surely mistaken in applications, especially in macroeconomics and finance. Yet, applications involving anything but these standard approaches are very rare. The current paper can be seen as a reaction to this. The purpose is to point to some of the recent advances in the area of factor-augmented panel regressions, and to also provide some guidance regarding their implementation.

This article makes an analytical study of the effects of the presence of both common and idiosyncratic stochastic trends on the pooled least squares estimator. The results suggest that the usual result of asymptotic normality depends critically on the absence of the common stochastic trend.

Several panel unit root tests that account for cross section dependence using a common factor structure have been proposed in the literature recently, notably Pesaran (2003), Moon and Perron (2004) and Bai and Ng (2004). This paper is aimed at comparing these three proposed unit root tests for panels with dynamic factors. It makes fourcontributions: (1) it compares the three testing procedures in terms of similarities and difference in the data generation process, tests, null and alternative hypotheses considered,(2) it compares the small sample properties of the tests usingMonte Carlo results in models with up to two common factors, (3) it provides an application which illustrates the use of the tests, and (4) finally it discusses the use of the tests in modelling in general. The main conclusions are: Pesaran’s (2003) cross-sectionally augmented (CA)DF tests are designed for cases where cross-sectional dependence is due to a single factor. The Moon and Perron (2004) tests which use defactored data is similar in spirit but can account for mutiple common factors. The Bai and Ng (2004) tests allow to tests for unit roots in the common factors and/or the idiosyncratic factors. It would therefore be natural to use the Pesaran (2003) or Moon and Perron tests in a first step to find out whether there are unit roots in the data. Then in a second step of modelling, the Bai and Ng (2004) tests could be used to determine whether the unit roots arise in the common factors or in the idiosyncratic components. It is also found that the latter behave well when the observed nonstationarity in the data series comes exclusively from nonstationary common factors, e.g. when the series cointegrate along the cross sectional dimension of the panel.

In this paper, the author discusses the appropriateness of treating explanatory variables of a single-equation error correction model as being weakly exogenous. He restates the derivation of the error correction model, and particularly the single-equation conditional error correction model, both in reduced and structural form. These allow the author to point out that the condition of weak endogeneity implicitly tested by usual orthogonality tests is generally not sufficient for single-equation conditional error correction models. The potential pitfalls of working within incomplete simultaneous dynamic equation models for exogeneity tests are also pointed out. The author illustrates this on some empirical studies. Copyright 1992 by Blackwell Publishing Ltd

Panel data framework has often been used to build Early Warning Systems for financial crises. This paper questions the implicit assumption that crises are homogenously caused by identical factors. It suggests a preliminary step aiming at forming optimal country clusters.

In spite of the increased use of factor-augmented regressions in recent years, little is known regarding the relative merits of the two main approaches to estimation and inference, namely, the cross-sectional average and principal component estimators. By providing a formal comparison of the approaches, the current paper fills this gap in the literature.

Panel unit‐root and no‐cointegration tests that rely on cross‐sectional independence of the panel unit experience severe size distortions when this assumption is violated, as has, for example, been shown by Banerjee, Marcellino and Osbat [Econometrics Journal (2004), Vol. 7, pp. 322–340; Empirical Economics (2005), Vol. 30, pp. 77–91] via Monte Carlo simulations. Several studies have recently addressed this issue for panel unit‐root tests using a common factor structure to model the cross‐sectional dependence, but not much work has been done yet for panel no‐cointegration tests. This paper proposes a model for panel no‐cointegration using an unobserved common factor structure, following the study by Bai and Ng [Econometrica (2004), Vol. 72, pp. 1127–1177] for panel unit roots. We distinguish two important cases: (i) the case when the non‐stationarity in the data is driven by a reduced number of common stochastic trends, and (ii) the case where we have common and idiosyncratic stochastic trends present in the data. We discuss the homogeneity restrictions on the cointegrating vectors resulting from the presence of common factor cointegration. Furthermore, we study the asymptotic behaviour of some existing residual‐based panel no‐cointegration tests, as suggested by Kao [Journal of Econometrics (1999), Vol. 90, pp. 1–44] and Pedroni [Econometric Theory (2004a), Vol. 20, pp. 597–625]. Under the data‐generating processes (DGP) used, the test statistics are no longer asymptotically normal, and convergence occurs at rate T rather than inline image as for independent panels. We then examine the possibilities of testing for various forms of no‐cointegration by extracting the common factors and individual components from the observed data directly and then testing for no‐cointegration using residual‐based panel tests applied to the defactored data.

In this paper we derive permanent‐transitory decompositions of non‐stationary multiple times series generated by (r)nite order Gaussian VAR(p) models with both cointegration and serial correlation common features. We extend existing analyses to the two classes of reduced rank structures discussed in Hecq, Palm and Urbain (1998). Using the corresponding state space representation of cointegrated VAR models in vector error correction form we show how decomposition can be obtained even in the case where the number of common feature and cointegration vectors are not equal to the number of variables. As empirical analysis of US business fluctuations shows the practical relevance of the approach we propose.

The effect which the oil price time series has on the long run properties of Vector AutoRegressive (VAR) models for price levels and import demand is investigated. As the oil price variable is assumed to be weakly exogenous for the long run parameters, a cointegration testing procedure allowing for weakly exogenous variables is developed using a LU decomposition of the long run multiplier matrix. The likelihood based cointegration test statistics, Wald, Likelihood Ratio and Lagrange Multiplier, are constructed and their limiting distributions derived. Using these tests, we find that incorporating the oil price in a model for the domestic or import price level of seven industrialized countries decreases the long run memory of the inflation rate. Second, we find that the results for import demand can be classified with respect to the oil importing or exporting status of the specific country. The result for Japan is typical as its import price is not influenced by GNP in the long run, which is the case for all other countries.

To study non-durable import demand, we extend previous work done by Clarida (1994) and Ceglowski (1991) by considering a two-good version of the lifecycle model in which we introduce time-non-separability in the households' preferences. The model is estimated using quarterly data for the USA and France. Using the information contained in the observed stochastic and deterministic trends, we derive a cointegration restriction used to estimate curvature parameters of the instantaneous utility function. The remaining parameters are estimated in a second step by GMM. The constancy of the different parameters is investigated, in both the long and the short run. Habit formation turns out to be an important factor of import demand. (C) 1998 John Wiley & Sons, Ltd.

SUMMARY This paper reports results of an extensive analysis of statistical demand functions for food using household survey data and aggregate time-series data on food consumption in the USA and The Netherlands. Using the model put forward by Tobin (1950) for survey data, we find that socio-economic information on the composition, education, and status of households adds little to the explanation of food consumption. The income elasticity of food consumption decreases over time in the USA but increases in The Netherlands. Applying multivariate cointegration analysis to the time-series data, we find that strict price homogeneity, structural stability, and weak exogeneity of prices have to be rejected statistically at conventional significance levels, whereas weak exogeneity of food consumption cannot be rejected. The long-run income elasticity tends to decrease over time for US data and is roughly constant for Dutch data. The findings corroborate earlier findings for the survey data. The rejection of price exogeneity is consistent with Tobin’s model which treats prices as endogenous. #1997 John Wiley & Sons, Ltd.

This paper unifies two seemingly separate approaches to test weak exogeneity in dynamic regression models with Lagrange-multiplier statistics. The first class of tests focuses on the orthogonality between innovations and conditioning variables, and thus is related to the Durbin-Wu-Hausman specification tests. The second approach has been developed more recently in the context of cointegration and error correction models, and concentrates on the question whether the conditioning variables display error correcting behaviour. It is shown that the vital difference between the two approaches stems from the choice of the parameters of interest. A new test is derived, which encompasses both its predecessors. The test is applied to an error correction model of the demand for money in Switzerland.

In a recent paper, Mah (1994) investigated the behavior of Japanese aggregate import and argued that there was no empirical evidence in favor of the existence of a traditional imperfect-substitutes long-run import demand model using cointegration analysis. In this paper we reinvestigate the problem in a coherent multivariate framework and point out that the results of Mah (1994) are very much dependent on the approach he followed.

We use recently developed time series techniques to analyse long historical data on the budget of the Court of Nivelles (Belgium) in the late Middle Ages. The unidirectional causality from receipts to expenditures supports the idea that the medieval system under consideration is a fine-focused (tax-oriented) control system. However, empirical evidence on the presensce of changes in receipt collection around 1520 favours the hypothesis of the decline of the medieval, urban based, tax oriented system and its transformation into a punishment-focused system.

In this paper we discuss and illustrate the relative merits and pitfalls of modelling cointegrated systems in partial or in complete system set-up. We follow both the complete VAR based approach advocated by Hendry and Mizon (1993) and the partial system approach based on so-called structural error correction models proposed by Boswijk (1991,1992). The issue of exogeneity is discussed and illustrated using quarterly data for Belgian aggregate imports. Several economically interesting questions related to price effects in international trade are raised in the empirical analysis.

In this paper, we investigate the long run relationship among five major Pacific-Basin stock markets. We focus on the common long run behaviour of their stock price indices over a sample period of 20 years. Using cointegration theory, we find that while there exists a rather integrated Pacific Basin financial area, the regional aspects (Asian versus Pacific) play important roles.

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the group-mean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data. originally proposed for a setting of no cross-sectional dependence beyond a common time effect. The tests, suited for testing for unit roots in the observed data, can be easily implemented as no specification or estimation of the dependence structure is required. Asymptotic properties of the tests are derived for T going to infinity and N finite. Asymptotic validity of the bootstrap tests is established in very general settings, including the presence of common factors and cointegration across units. Properties under the alternative hypothesis are also considered. In a Monte Carlo simulation, the bootstrap tests are found to have rejection frequencies that are much closer to nominal size than the rejection frequencies for the corresponding asymptotic tests. The power properties of the bootstrap tests appear to be similar to those of the asymptotic tests.

In this paper we provide some illustrative Monte Carlo evidence on the usefulness of the well-known misspecification test in the case of testing for a unit root against an exogenously determined break in the level of a series. We also investigate the small sample behaviour of Perron's ( Journal of Business and Economic Statistics , 1990, 8, 153–162) unit root test in the presence of an erroneous location of the break point.

The objective of the paper is to investigate whether price indices of different European stock markets display a common long-run trending behaviour. Using cointegration analysis, we provide empirical evidence of common stochastic trends among five important European stock markets over the period 1975-1991.

Fehlerkorrekturmodelle und aggregierte Einfuhrfunktionen, von Jean-Pierre Urbain. Gegenstand dieses Artikels ist die empirische Modellierung der aggregierten Einfuhren zweier europäischer Länder mit offenen Wirtschaftsstrukturen (Belgien und die Niederlande). Die Analyse stützt sich auf eine seit kurzem angewandte ökonometrische Méthodologie. Wir berücksichtigen insbesondere die "vqm Allgemeinen zum Besonderen" vorgehende Méthode, die unter anderem von David Hendry (1987) vorgestellt wurde, wobei die (nicht) stationären Eigenschaften der untersuchten Serien deutlich herausges- tellt werden. Die Ko-lntegration der Variablen (Engle und Granger, 1987) wird einer Analyse unterzogen. Auf der Grundlage der aussagekräftigen Daten definieren wir die kurzfristige Dynamik sowie die Kennzeichen des langfristigen Gleichgewichts. Die Verfahren der Ko-lntegration erlauben es, Langzeitrelationen für die beiden Länder nachzuweisen. Für die Niederlande wird die traditionelle Homogenitätshypothese zu den Preisen für die langfristige Perspektive eindeutig bestätigt, für die kurzfristige jedoch widerlegt. Für Belgien sind unsere Resultate weniger klar. Doch haben uns die Begriffe der multivariierten Ko-lntegration, die von Johansen und Juselius (1990) entwickelt wurden, die Voraussetzungen dazu gegeben, die Langzeitsymmetrie anzunehmen., Error Correction Models and equations for aggregate importations, by Jean-Pierre Urbain. In this paper we consider the empirical modelling of aggregate imports for two small open european economies (Belgium and the Netherlands). The analysis is conducted by means of recently developed econometric concepts. Among these we focus on the so called "general to specific" approach (see inter alia Hendry, 1987) in the context of data series whose (non) stationary properties are investigated. The notion of co-integration (Engle and Granger, 1987) of a set of variables is analysed, both in a single equation and in a multivariate framework. We allowed the data to play an important role in the dynamic specification but also the specification of the underlying long run equilibrium. Using co-integration techniques we derived long run estimates for Belgium and the Netherlands. For the latter country, the traditional hypothesis of price homogeneity was deary accepted in the long run but rejected for the short run dynamic. For Belgium, our results are more puzzling although multivariate co-integration along the lines of work of Johanson and Juselius (1990) led us to accept long run symmetry., Modèles à correction d'erreur et fonctions d'importations agrégées, par Jean-Pierre Urbain. L'objet de cet article est la modélisation empirique des importations agrégées de deux économies européennes ouvertes (Belgique et Pays-Bas). Uanalyse est basée sur une méthodologie économétrique récente. Nous retenons en particulier l'approche qui va "du général au particulier", illustrée entre autres par David Hendry (1987), les propriétés de (non)stationnarité des séries étudiées étant soigneusement établies. La co-intégration des variables (Engle et Granger, 1987) est analysée. Nous laissons les données définir la dynamique de court terme, mais aussi les caractéristiques de l'équilibre de long terme. Les techniques de la co-intégration permettent d établir les relations de long-terme pour les deux pays. Pour les Pays-Bas, l'hypothèse traditionnelle d'homogénéité des prix est clairement acceptée pour le long terme, mais rejetée pour le court terme. Pour la Belgique, nos résultats sont moins clairs. Toutefois les concepts de la co-intégration multivariée développés par Johansen et Juselius (1990) nous ont conduit à accepter la symétrie pour le long terme., Modelos con corrección de error y funciones de importación agregadas, por Jean-Pierre Urbain. Este artículo tiene por objeto presentar la modelización empírica de las importaciones agregadas de dos economías europeas abiertas (Bélgica y Holanda). Este análisis se funda en una metodología econométrica reciente. En este caso se utilizará especialmente el método que va "de lo general a lo particular", ilustrado entre otros autores por David Hendry (1987), habiéndose determinado perfectamente el carácter estacionario o variable de las series estudiadas. También se analiza la co-integración de las variables (Engle y Granger, 1987) y se deja que los datos definan la dinámica de corto plazo, así como las características del equilibrio de largo plazo. Las técnicas de la co-integración permiten establecer las relaciones de largo plazo para los dos países. Para Holanda, la hipotesis tradicional de homogeneidad de los precios se acepta claramente para el largo plazo, pero se rechaza para el corto plazo. Para Bélgica, los resultados son menos precisos. No obstante, los conceptos de la co-integración multivariada desarrollados por Johansen y Juselius (1990) nos llevaron a aceptar la simetría para el largo plazo., Urbain Jean-Pierre. Modèles à correction d'erreur et fonctions d'importations agrégées. In: Économie & prévision, n°94-95, 1990-3-4. Aspects de la contrainte extérieure. pp. 63-77.

The paper considers n-dimensional var models for variables exhibiting cointegration and common cyclical features. Two specific reduced rank vector error correction models are discussed. In one, named the “strong form” and denoted by sf, the collection of all coefficient matrices of a vecm has rank less than n, in the other, named the “weak form” and denoted by wf, the collection of all coefficient matrices except the matrix of coefficient of error correction terms has rank less than n. The paper explores the theoretical connections between these two forms, suggests asymptotic tests for each form and examines the small sample properties of these tests by monte carlo simulations.the paper proposes a sequential test procedure that is aimed at uncovering strong forms by examining weak forms. For gdp series for five latin american countries, 1950–1999, the wf appears to be supported by the data. Imposing the wf parameter restrictions leads to an improvement of forecast accuracy for these data series.

In this article, we study and compare the properties of several bootstrap unit-root tests recently proposed in the literature. The tests are Dickey–Fuller (DF) or Augmented DF, based either on residuals from an autoregression and the use of the block bootstrap or on first-differenced data and the use of the stationary bootstrap or sieve bootstrap. We extend the analysis by interchanging the data transformations (differences vs. residuals), the types of bootstrap and the presence or absence of a correction for autocorrelation in the tests. We show that two sieve bootstrap tests based on residuals remain asymptotically valid. In contrast to the literature which focuses on a comparison of the bootstrap tests with an asymptotic test, we compare the bootstrap tests among themselves using response surfaces for their size and power in a simulation study. This study leads to the following conclusions: (i) augmented DF tests are always preferred to standard DF tests; (ii) the sieve bootstrap performs better than the block bootstrap; (iii) difference-based tests appear to have slightly better size properties, but residual-based tests appear more powerful.

In this chapter we extend the concept of serial correlation common features to panel data models. This analysis is motivated both by the need to develop a methodology to systematically study and test for common structures and comovements in panel data with autocorrelation present and by an increase in efficiency coming from pooling procedures. We propose sequential testing procedures and study their properties in a small scale Monte Carlo analysis. Finally, we apply the framework to the well known permanent income hypothesis for 22 OECD countries, 1950–1992.

The purpose of this paper is to review and discuss the key improvements brought to OxGauss. Without having to install Gauss on his or her machine, the OxGauss user can run under Ox a wide range of Gauss programs and codes. Even with the console Ox version (free for academics), Gauss codes can either be called from Ox programs or run and executed on their own. While the new OxGauss version is very powerful in most circumstances, it is of little use once the purpose is to execute programs that attempt to solve optimization problems using Cml, Maxlik or Optmum. In this paper we propose a set of additional procedures that contribute to bridge the gap between Ox and three well-known Gauss application modules: Cml, Maxlik or Optmum. The effectiveness of our procedures is illustrated by revisiting a large number of freely available Gauss codes in which numerical optimization relies on the above Gauss application modules. The Gauss codes include many programs dealing with non-linear models such as the Markov regime-switching models STAR models and various GARCH-type models. These illustrations highlight a further potentially interesting implication of OxGauss: it enables non-Gauss users to replicate existing empirical results using freely available Gauss codes.

The aim of this paper is to study the concept of separability in multiple nonstationary time series displaying both common stochastic trends and common stochastic cycles. When modeling the dynamics of multiple time series for a panel of several entities such as countries, sectors, firms, imposing some form of separability and commonalities is often required to restrict the dimension of the parameter space. For this purpose we introduce the concept of common feature separation and investigate the relationships between separation in cointegration and separation in serial correlation common features. Loosely speaking we investigate whether a set of time series can be partitioned into subsets such that there are serial correlation common features in the sub-groups and that there do not exist linear combinations of the common cycles which are white noise. The paper investigates three issues. First, it provides conditions for separating joint cointegrating vectors into marginal cointegrating vectors as well as separating joint short-term dynamics into marginal short-term dynamics. Second, conditions for making permanent-transitory decompositions based on marginal systems are given. Third, issues of weak exogeneity are considered. Likelihood ratio type tests for the different hypotheses under study are proposed. An empirical analysis of the link between economic fluctuations in the U.S. and Canada shows the practical relevance of the approach proposed in this paper.

We consider VAR models for variables exhibiting cointegration and common cyclical features. While the presence of cointegration reduces the rank of the long-run multiplier matrix, other types of common features lead to rank reduction of the short-run dynamics. We distinguish between strong and weak form reduced rank structures. Strong form reduced rank structures analyzed by Engle and Kozicki (1993) arise when a linear combination of the first differenced variables in a cointegrated VAR is white noise whereas in the presence of a weak form reduced rank structure, linear combinations of the first differenced variables corrected for the long-run effects are white noise. The weak form has an interest in its own. For instance, it is a necessary condition for the existence of first order codependent cycles in a VAR(2). Also, it is a necessary condition for the strong form. We also consider the mixed form which combines strong and weak forms. We discuss the model selection issues which arise from this distinction and propose a simple approach to testing for these structures using a sequence of likelihood ratio test statistics. The finite sample behavior of the sequential approach is analyzed in a Monte Carlo experiment. Finally, we illustrate the relevance of the different forms of reduced ranks with an empirical analysis of US business uctuations over the period 1954-1996.

We present an efficiency wage model in which workers'' effort depends on the level and on the growth rate of their wage relative to an alternative wage. Using data for four countries (US, UK, FR, GY), the implications of the model are examined and are found to be in accordance with the information in the non-stationary data. The restrictions implied by the model dynamics are not rejected by the data. Moreover the structural parameters are found to be constant through time, indicating that, although very simple, the model is likely to be robust to the Lucas critique. One interesting result is that the workers'' effort depends less on relative wages growth and more on relative wage levels in the US than in the three European countries analyzed.

In this paper we extend the concept of serial correlation common features to panel data models. This analysis is motivated both by the need to develop a methodology to systematically stu dy and test for common structures and comovements in panel data with autocorrelation present and by an increase in efficiency coming from pooling procedures. We propose sequential testing procedures and study their properties in a small scale Monte Carlo analysis. Finally, we apply the framework to the well known permanent income hypothesis for 22 OECD countries, 1950-1992.

In this chapter we shall now illustrate the modelling of cointegrated systems by studying empirically Belgian’s aggregate imports. Contrary to topics such as money demand or consumption functions, the problem of the dynamic modelling of trade flows has not often been used as explanatory field for recent econometric techniques and modelling approaches. Nevertheless, we think that a refinement in the dynamic specification of trade flows may lead to a substantially different analysis of price and income effects in international trade.

In the previous chapter we have mentioned how one could investigate the presence or absence of a cointegrating vector in the generating model for the conditioning variables. In particular, Johansen (1992a) and Boswijk (1991b) have proposed to test the hypothesis of weak exogeneity w.r.t. the long run parameters but do not consider any orthogonality conditions since the fact that an explanatory variable is error correcting is sufficient to reject weak exogeneity for the long run parameters. If we are in a structural framework, this condition is however not always sufficient when we are theoretically interested in the parameters of the short run dynamic in which case an additional orthogonality condition has to be verified. Although orthogonality tests will not take into account the possible violation of the variation free condition of weak exogeneity (see Engle et al., 1983), they may remain useful if the model used in empirical analysis is a structural error correction model, if the parameters of interest include both short and long run coefficients and if the cointegrating vector is known to be absent from the marginal models.