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Abstract:
In this paper we evaluate the relative merits of three approaches to information extraction from a large data set for forecasting, namely, the use of an automated model selection procedure, the adoption of a factor model, and single-indicator-based forecast pooling. The comparison is conducted using a large set of indicators for forecasting US inflation and GDP growth. We also compare our large set of leading indicators with purely autoregressive models, using an evaluation procedure that is particularly relevant for policy making. The evaluation is conducted both ex-post and in a pseudo real time context, for several forecast horizons, and using both recursive and rolling estimation. The results indicate a preference for simple forecasting tools, with a good relative performance of pure autoregressive models, and substantial instability in the leading characteristics of the indicators.

Leading indicator, factor model, model selection, GDP growth, inflation

Abstract:
A common finding in the empirical literature on the validity of purchasing power parity (PPP) is that it holds when tested for in panel data, but not in univariate (i.e. country specific) analysis. The usual explanation for this mismatch is that panel tests for unit roots and cointegration are more powerful than their univariate counterparts. In this paper we suggest an alternative explanation for the mismatch. More generally, we warn against the use of panel methods for testing for unit roots in macroeconomic time series. Existing panel methods assume that cross-unit cointegrating or long-run relationships, that tie the units of the panel together, are not present. However, using empirical examples on PPP for a panel of OECD countries, we show that this assumption is very likely to be violated. Simulations of the properties of panel unit root tests in the presence of long-run cross-unit relationships are then presented to demonstrate the serious cost of assuming away such relationships. The empirical size of the tests is substantially higher than the nominal level, so that the null hypothesis of a unit root is rejected very often, even if correct.

PPP, unit root, panel, cointegration, cross-unit dependence

Abstract:
The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, due to the increased availability of large datasets. In this paper we propose a new methodology for estimating factors from large datasets based on state space models, discuss its theoretical properties and compare its performance with that of two alternative estimation approaches based, respectively, on static and dynamic principal components. The new method appears to perform best in recovering the factors in a set of simulation experiments, with static principal components a close second best. Dynamic principal components appear to yield the best fit, but sometimes there are leakages across the common and idiosyncratic components of the series. A similar pattern emerges in an empirical application with a large dataset of US macroeconomic time series.

Abstract:
We provide a summary updated guide for the construction, use and evaluation of leading indicators, and an assessment of the most relevant recent developments in this field of economic forecasting. To begin with, we analyze the problem of selecting a target coincident variable for the leading indicators, which requires coincident indicator selection, construction of composite coincident indexes, choice of filtering methods, and business cycle dating procedures to transform the continuous target into a binary expansion/recession indicator. Next, we deal with criteria for choosing good leading indicators, and simple non-model based methods to combine them into composite indexes. Then, we examine models and methods to transform the leading indicators into forecasts of the target variable. Finally, we consider the evaluation of the resulting leading indicator based forecasts, and review the recent literature on the forecasting performance of leading indicators.

Business cycles, leading indicators, coincident indicators, turning points, forecasting

Abstract:
We provide a summary updated guide for the construction, use and evaluation of leading indicators, and an assessment of the most relevant recent developments in this field of economic forecasting. To begin with, we analyze the problem of selecting a target coincident variable for the leading indicators, which requires coincident indicator selection, construction of composite coincident indexes, choice of filtering methods, and business cycle dating procedures to transform the continous target into a binary expansion/recession indicator. Next, we deal with criteria for choosing good leading indicators, and simple non-model based methods to combine them into composite indexes. Then, we examine models and methods to transform the leading indicators into forecasts of the target variable. Finally, we consider the evaluation of the resulting leading indicator based forecasts, and review the recent literature on the forecasting performance of leading indicators.

Business Cycles, Leading Indicators, Coincident Indicators, Turning Points, Forecasting

Abstract:
In this paper we evaluate the role of a set of variables as leading indicators for Euro-area inflation and GDP growth. Our evaluation is based on using the variables in the ECB Euro-area model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator with that of purely autoregressive models, using an evaluation procedure that is particularly relevant for policy making. The evaluation is conducted both expost and in a pseudo real time context, for several forecast horizons, and using both recursive and rolling estimation. We also analyze three different approaches to combining the information from several indicators. First, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Second, an automated model selection procedure is applied to models with a large set of indicators. Third, we consider pooling the single indicator forecasts. The results indicate that single indicator forecasts are on average better than those derived from more complicated methods, but for them to beat the autoregression a different indicator has to be used in each period. A simple real-time procedure for indicator-selection produces good results.

Leading indicator, factor model, model selection, GDP growth, inflation

Abstract:
There is a wide literature on the dynamic adjustment of employment and its relationship with the business cycle. Our aim is to propose a statistical model that offers a congruent representation of post-war UK labour market. We use a cointegrated vector autoregressive Markov-switching model where some parameters change according to the phase of the business cycle. Output, employment, labour supply and real earnings are found to have a common cyclical component. The long run dynamics are characterized by two cointegrating vectors: trend-adjusted labour productivity and the labour share. Despite there having been many changes affecting this sector of the UK economy, the Markov-switching vector-equilibrium-correction model with three regimes representing recession, growth and high growth provides a good characterization of the sample data over the period 1966(3)-1993(1). In an out-of-sample forecast experiment over the period 1991(2)-1993(1) it beats linear and non-linear model alternatives. The results of an impulse-response analysis highlight the dangers of using VARs when the constancy of the estimated coefficients has not been established.

business cycles, employment, Impulse-Response Analysis, cointegration, regime shifts, Markov switching

Abstract:
This paper studies the impact of public infrastructure on economic performance. We employ three different methodologies to estimate the returns to public investment. First, we relate growth in total factor productivity to accumulation of public capital. Second, we assess the role of public capital as an input to production. Third, we evaluate the reduction in costs that can be attributed to the presence of public infrastructure. Using regional data for Italy, we find that the aggregate impact of public capital is positive and significant under the first approach, slightly negative under the second, and virtually zero under the third. More coherent results obtain when disaggregating by geographical area and time period: under all three approaches, the effectiveness of public investment seems to be increasing over time and to be higher in Central and Southern regions than in Northern ones.

infrastructures, TFP, growth, costs

Abstract:
This paper is a general investigation of temporal aggregation in time series analysis. It encompasses traditional research on time aggregation as a particular case and extends the analysis to irregular intervals of aggregation. The Data Generating Process is allowed to evolve at regular, deterministic-irregular or even stochastic intervals of time (operational time). The time scale of this process is then transformed to generate the observational time process. This transformation can be deterministic (such as the familiar aggregation of monthly data into quarters) or more generally, stochastic (such as aggregating stock market quotes by the hour). In general, the observational time model exhibits persistence, time-varying parameters and non-spherical disturbances. Consequently, we review detection, specification, estimation and structural inference in this context, provide new solutions to these issues, and apply our results to high frequency, FX data.

Abstract:
The relationship between wages, prices, productivity, inflation, and unemployment in Italy, Poland, and the UK between the 1960's and the early 1990's is modelled as a cointegrated vector autoregression subject to regime shifts. For each of these economies there is clear evidence of a change in the underlying equilibria of this sector of the economy. Hypotheses concerning the similarity of the transition from a rigid to a flexible labour market are tested.

Abstract:
We show how the use of panel data methods such as those proposed in single equations by Kao (1999) and Pedroni (1999) or in systems by Larsson and Lyhagen (1999) to investigate economic hypotheses such as purchasing power parity or the term structure of interest rates may be affected by the existence of cross-unit cointegrating relations. The existing literature assumes that such relations, that tie the units of the panel together, are not present. Using empirical examples from a panel of OECD countries we show that this assumption is very likely to be violated. Simulations of the properties of panel cointegration tests in the presence of cross-unit relations are then presented to demonstrate the serious cost of assuming away such relations. Some fixes are proposed as a way of dealing with these more general scenarios.

Abstract:
This paper addresses the issue of whether and by how much public capital can enhance economic performance. We apply different methodologies to Italian regional data for the period 1970-1994. The results are presented for Italy as a whole and for different macroregions, and for individual categories of public capital. For the Center and the South, the methodologies employed indicate a positive contribution of infrastructure investment to TFP growth, output, and cost reduction. However, the magnitude of the cost reducing effect does not seem large enough to outweigh the social user cost of public capital. Also, we get mixed results on which types of infrastructure are most effective. Overall, investment in transportation appears to be the most productive: railways in the North and roads in the Center and South are the categories that mostly contributed to TFP growth.

Abstract:
This paper develops tests for selection of competing non-linear dynamic models. The null hypothesis is that the models are equally close the Data Generating Process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be non-nested, overlapping, or nested. They can be correctly specified or not. Their parameters can be estimated by a variety of methods, including Maximum Likelihood, Non-Linear Least Squares, Method of Moments, where the choice depends on the selected measure of closeness to the DGP. The tests are symmetric and directional. Their asymptotic distribution under the null is either normal or a weighted sum of chi-square distributions, depending on the nesting characteristics of the competing models. The comparison of ARMAX and STAR models, and of nested ARMAX-GARCH models are discussed as examples.

Abstract:
New-Keynesian models are characterized by the presence of expectations as explanatory variables. To use these models for policy evaluation, the econometrician must estimate the parameters of expectation terms. Standard estimation methods have several drawbacks, including possible lack of identification of the parameters, misspecification of the model due to omitted variables or parameter instability, and the common use of inefficient estimation methods. Several authors have raised concerns over the validity of commonly used instruments to achieve identification. In this paper we analyze the practical relevance of these problems and we propose remedies to weak identification based on recent developments in factor analysis for information extraction from large data sets. Using these techniques, we evaluate the robustness of recent findings on the importance of forward looking components in the equations of the New-Keynesian model.

New-Keynesian Phillips curve, forward looking output equation, Taylor rule, rational expectations, factor analysis, determinacy of equilibrium.

Abstract:
This paper analyzes two features of concern to policy-makers in the countries of the prospective European Monetary Union: the solvency of their government's finances and the accuracy of fiscal forecasts. Extending the existing methodology of solvency tests, the paper finds that, with few exceptions, EU governments are insolvent, albeit debt/GDP ratios show signs of stabilizing. The accuracy of official short-term fiscal forecasts (those of the OECD) is analyzed, using conventional techniques, and found to be reassuring.

Abstract:
In this paper we compare alternative approaches for dating the Euro area business cycle and analyzing its characteristics. First, we extend a commonly used dating procedure to allow for length, size and amplitude restrictions, and to compute the probability of a phase change. Second, we apply the modified algorithm for dating both the classical Euro area cycle and the deviation cycle, where the latter is obtained by a variety of methods, including a modified HP filter that reproduces the features of the BK filter but avoids end-point problems, and a production function based approach. Third, we repeat the dating exercise for the main Euro area countries, evaluate the degree of syncronization, and compare the results with the UK and the US. Fourth, we construct indices of business cycle diffusion, and assess how spread are cyclical movements throughout the economy. Finally, we repeat the dating exercise using monthly industrial production data, to evaluate whether the higher sampling frequency can compensate the higher variability of the series and produce a more accurate dating.

Business cycle, Euro area, cycle dating, cycle synchronization

Abstract:
We investigate co-movements and heterogeneity in inflation dynamics of different regions within and across euro area countries using a novel disaggregate dataset to improve the understanding of inflation differentials in the European Monetary Union. We employ a model where regional inflation dynamics are explained by common euro area and country specific factors as well as an idiosyncratic regional component. Our findings indicate a substantial common area wide component, that can be related to the common monetary policy in the euro area and to external developments, in particular exchange rate movements and changes in oil prices. The effects of the area wide factors differ across regions, however. We relate these differences to structural economic characteristics of the various regions. We also find a substantial national component. Our findings do not differ substantially before and after the formal introduction of the euro in 1999, suggesting that convergence has largely taken place before the mid 90s. Analysing US regional inflation developments yields similar results regarding the relevance of common US factors. Finally, we find that disaggregate regional inflation information, as summarised by the area wide factors, is important in explaining aggregate euro area and US inflation rates, even after conditioning on macroeconomic variables. Therefore, monitoring regional inflation rates within euro area countries can enhance the monetary policy maker's understanding of aggregate area wide inflation dynamics.

Regional inflation dynamics, euro area and US, common factor models

Abstract:
The accession of ten countries into the European Union makes the forecasting of their key macroeconomic indicators an exercise of some importance. Because of the transition period, only short spans of reliable time series are available, suggesting the adoption of simple time series models as forecasting tools. However, despite this constraint on the span of data, a large number of macroeconomic variables (for a given time span) are available, making the class of dynamic factor models a reasonable alternative forecasting tool. The relative performance of these two forecasting approaches is compared by using data for five new Member States. The role of Euro-area information for forecasting and the usefulness of robustifying techniques such as intercept corrections are also evaluated. We find that factor models work well in general, although with marked differences across countries. Robustifying techniques are useful in a few cases, while Euro-area information is virtually irrelevant.

Factor models, forecasts, time series models, new Member States

Abstract:
Existing methods for data interpolation or backdating are either univariate or based on a very limited number of series, due to data and computing constraints that were binding until the recent past. Nowadays large datasets are readily available, and models with hundreds of parameters are fastly estimated. We model these large datasets with a factor model, and develop an interpolation method that exploits the estimated factors as an efficient summary of all the available information. The method is compared with existing standard approaches from a theoretical point of view, by means of Monte Carlo simulations, and also when applied to actual macroeconomic series. The results indicate that our method is more robust to model misspecification, although traditional multivariate methods also work well while univariate approaches are systematically outperformed. When interpolated series are subsequently used in econometric analyses, biases can emerge, depending on the type of interpolation but again be reduced with multivariate approaches, including factor-based ones.

Interpolation, factor model, Kalman filter, spline

Abstract:
Existing methods for data interpolation or backdating are either univariate or based on a very limited number of series, due to data and computing constraints that were binding until recently. Nowadays large datasets are readily available, and models with hundreds of parameters fastly estimated. We model these large datasets with a factor model, and develop an interpolation method that exploits the estimated factors as an efficient summary of the available information. The method is compared with existing standard approaches from a theoretical point of view, by means of Monte Carlo simulations, and also using actual macroeconomic series. Our method seems more robust to model misspecification, although traditional multivariate methods also work well while univariate approaches are systematically outperformed. When interpolated series are subsequently used in econometric analyses, biases can emerge, depending on the type of interpolation but again be reduced with multivariate approaches, including factor-based ones.

Interpolation, factor model, Kalman filter, spline

Abstract:
'Iterated' multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas 'direct' forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if correctly specified, but direct forecasts are more robust to model misspecification. This paper compares empirical iterated and direct forecasts from linear univariate and bivariate models by applying simulated out-of-sample methods to 171 US monthly macroeconomic time series spanning 1959-2002. The iterated forecasts typically outperform the direct forecasts, particularly if the models can select long lag specifications. The relative performance of the iterated forecasts improves with the forecast horizon.

Multistep forecasts, VAR forecasts, forecast comparisons

Abstract:
"Iterated" multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas "direct" forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more efficient if correctly specified, but direct forecasts are more robust to model misspecification. This paper compares empirical iterated and direct forecasts from linear univariate and bivariate models by applying simulated out-of-sample methods to 171 U.S. monthly macroeconomic time series spanning 1959-2002. The iterated forecasts typically outperform the direct forecasts, particularly if the models can select long lag specifications. The relative performance of the iterated forecasts improves with the forecast horizon.

Multistep forecasts, VAR forecasts, forecast comparisons

Abstract:
In this paper we assess the possibility of producing unbiased forecasts for fiscal variables in the euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider ARMA models, VARs, small scale semi-structural models at the national and euro area level, institutional forecasts (OECD), and pooling. Our small scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward biased forecast for the debt-GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small scale multi country model, simple time series models can produce more accurate forecasts, due to their parsimonious specification.

Fiscal forecasting, forecast comparison, fiscal rules, euro area

Abstract:
In this paper, we assess the possibility of producing unbiased forecasts for fiscal variables in the Euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider autoregressive moving average models, Vector autoregressions, small-scale semistructural models at the national and Euro area level, institutional forecasts (Organization for Economic Co-operation and Development), and pooling. Our small-scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time-series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward-biased forecast for the debt-GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small-scale multi-country model, simple time-series models can produce more accurate forecasts, because of their parsimonious specification.

Abstract:
In this paper we assess the possibility of producing unbiased forecasts for fiscal variables in the euro area by comparing a set of procedures that rely on different information sets and econometric techniques. In particular, we consider ARMA models, VARs, small scale semi-structural models at the national and euro area level, institutional forecasts (OECD), and pooling. Our small scale models are characterized by the joint modelling of fiscal and monetary policy using simple rules, combined with equations for the evolution of all the relevant fundamentals for the Maastricht Treaty and the Stability and Growth Pact. We rank models on the basis of their forecasting performance using the mean square and mean absolute error criteria at different horizons. Overall, simple time series methods and pooling work well and are able to deliver unbiased forecasts, or slightly upward biased forecast for the debt-GDP dynamics. This result is mostly due to the short sample available, the robustness of simple methods to structural breaks, and to the difficulty of modelling the joint behaviour of several variables in a period of substantial institutional and economic changes. A bootstrap experiment highlights that, even when the data are generated using the estimated small scale multi country model, simple time series models can produce more accurate forecasts, due to their parsimonious specification.

Fiscal forecasting, forecast comparison, fiscal rules, euro area

Abstract:
We analyse the evolution of the business cycle in the accession countries, after a careful examination of the seasonal properties of the available series and the required modification of the cycle dating procedures. We then focus on the degree of cyclical concordance within the group of accession countries, which turns out to be in general lower than that between the existing EU countries (the Baltic countries constitute an exception). With respect to the Eurozone, the indications of synchronization are also generally low and lower relative to the position obtaining for countries taking part in previous enlargements (with the exceptions of Poland, Slovenia and Hungary). In the light of the optimal currency area literature, these results cast doubts on the usefulness of adopting the euro in the near future for most accession countries, though other criteria such as the extent of trade and the gains in credibility may point in a different direction.

Business cycles, dating algorithms, cycle synchronization, EU enlargement, seasonal adjustment

Abstract:
The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, because of the increased availability of large data sets. In this article we propose a new parametric methodology for estimating factors from large data sets based on state–space models and discuss its theoretical properties. In particular, we show that it is possible to estimate consistently the factor space. We also conduct a set of simulation experiments that show that our approach compares well with existing alternatives.

Abstract:
The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, due to the increased availability of large datasets. In this paper we propose a new parametric methodology for estimating factors from large datasets based on state space models and discuss its theoretical properties. In particular, we show that it is possible to estimate consistently the factor space. We also develop a consistent information criterion for the determination of the number of factors to be included in the model. Finally, we conduct a set of simulation experiments that show that our approach compares well with existing alternatives.

factor models, principal components, subspace algorithms

Abstract:
The estimation of dynamic factor models for large sets of variables has attracted considerable attention recently, due to the increased availability of large datasets. In this paper we propose a new parametric methodology for estimating factors from large datasets based on state space models and discuss its theoretical properties. In particular, we show that it is possible to estimate consistently the factor space. We also develop a consistent information criterion for the determination of the number of factors to be included in the model. Finally, we conduct a set of simulation experiments that show that our approach compares well with existing alternatives.

Factor models, Principal components, Subspace algorithms

Abstract:
In this paper we suggest a framework to assess the degree of reliability of provisional estimates as forecasts of final data, and we reexamine the question of the most appropriate way in which available data should be used for ex ante forecasting in the presence of a data revision process. Various desirable properties for provisional data are suggested, as well as procedures for testing them, taking into account the possible nonstationarity of economic variables. For illustration, the methodology is applied to assess the quality of the US M1 data production process and to derive a conditional model whose performance in forecasting is then tested against other alternatives based on simple transformations of provisional data or of past final data.

Abstract:
The estimation of structural dynamic factor models (DFMs) for large sets of variables is attracting considerable attention. In this paper we briefly review the underlying theory and then compare the impulse response functions resulting from two alternative estimation methods for the DFM. Finally, as an example, we reconsider the issue of the identification of the driving forces of the US economy, using data for about 150 macroeconomic variables.

Factor models, principal components, subspace algorithms, structural identification, structural VAR

Abstract:
The estimation of structural dynamic factor models (DFMs) for large sets of variables is attracting considerable attention. In this paper we briefly review the underlying theory and then compare the impulse response functions resulting from two alternative estimation methods for the DFM. Finally, as an example, we reconsider the issue of the identification of the driving forces of the US economy, using data for about 150 macroeconomic variables.

Factor models, Principal components, Subspace algorithms, Structural

Abstract:
We propose a general framework to study whether and how common
trends and common cycles are still present when the original variables are linearly aggregated or only a subset of them is analysed. This is particularly important because of the adoption in empirical analysis of aggregated data on a limited number of variables.

Abstract:
The accession of ten countries into the European Union makes the forecasting of their key macroeconomic indicators such as GDP growth, inflation and interest rates an exercise of some importance. Because of the transition period, only short spans of reliable time series are available which suggests the adoption of simple time series models as forecasting tools, because of their parsimonious specification and good performance. Nevertheless, despite this constraint on the span of data, a large number of macroeconomic variables (for a given time span) are available which are of potential use in forecasting, making the class of dynamic factor models a reasonable alternative forecasting tool. We compare the relative performance of the two forecasting approaches, first by means of simulation experiments and then by using data for five Acceding countries. We also evaluate the role of Euro-area information for forecasting, and the usefulness of robustifying techniques such as intercept corrections and second differencing. We find that factor models work well in general, even though there are marked differences across countries. Robustifying techniques are useful in a few cases, while Euro-area information is virtually irrelevant.

Factor models, Forecasts, Time Series Models, Acceding Countries

Abstract:
Pooling forecasts obtained from different procedures typically reduces the mean square forecast error and more generally improve the quality of the forecast. In this paper, we evaluate whether pooling-interpolated or - backdated time series obtained from different procedures can also improve the quality of the generated data. Both simulation results and empirical analyses with macroeconomic time series indicate that pooling plays a positive and important role in this context also.

Abstract:
Pooling forecasts obtained from different procedures typically reduces the mean square forecast error and more generally improves the quality of the forecast. In this paper we evaluate whether pooling interpolated or backdated time series obtained from different procedures can also improve the quality of the generated data. Both simulation results and empirical analyses with macroeconomic time series indicate that pooling plays a positive and important role also in this context.

Pooling, interpolation, factor Model, Kalman Filter, spline

Abstract:
Pooling forecasts obtained from different procedures typically reduces the mean square forecast error and more generally improves the quality of the forecast. In this paper we evaluate whether pooling interpolated or backdated time series obtained from different procedures can also improve the quality of the generated data. Both simulation results and empirical analyses with macroeconomic time series indicate that pooling plays a positive and important role also in this context.

Pooling, Interpolation, Factor Model, Kalman Filter, Spline

Abstract:
This paper investigates the effects of temporal aggregation when the aggregation frequency is variable and possibly stochastic. The results that we report include, as a particular case, the well-known results on fixed-interval aggregation, such as when monthly data is aggregated into quarters. A variable aggregation frequency implies that the aggregated process will exhibit time-varying parameters and non-spherical disturbances, even when these characteristics are absent from the original model. Consequently, we develop methods for specification and estimation of the aggregate models and show with an example how these methods perform in practice.

time aggregation, time-scale transformation, irregularly spaced data, autoregressive conditional intensity model

Abstract:
In this paper we compare alternative approaches for the construction of time series of macroeconomic variables for Unified Germany prior to 1991, and then use them for the construction of corresponding time series for the euro area. The resulting series for Germany and the euro area are compared with existing ones on the basis of both descriptive statistics and results of econometric analyses conducted with the alternative time series. We find that more sophisticated time series methods for backdating can yield sizeable gains.

Backdating, Factor Model, Unified Germany, Euro Area

Abstract:
Index tracking requires building a portfolio of stocks (a replica) whose behaviour is as close as possible to that of a given stock index. Typically, much fewer stocks should appear in the replica than in the index, and there should be no low frequency (persistent) components in the tracking error. Unfortunately, the latter property is not satisfied by many commonly used methods for index tracking. These are based on the in-sample minimization of a loss function, but do not take into account the dynamic properties of the index components. Instead, we represent the index components with a dynamic factor model, and develop a procedure that, in a first step, builds a replica that is driven by the same persistent factors as the index. In a second step, it is also possible to refine the replica so that it minimizes a loss function, as in the traditional approach. Both Monte Carlo simulations and an application to the EuroStoxx50 index provide substantial support for our approach.

Index tracing, replica, stock index, factor models

Abstract:
This paper compares different ways to estimate the current state of the economy using factor models that can handle unbalanced datasets. Due to the different release lags of business cycle indicators, data unbalancedness often emerges at the end of multivariate samples, which is sometimes referred to as the 'ragged edge' of the data. Using a large monthly dataset of the German economy, we compare the performance of different factor models in the presence of the ragged edge: static and dynamic principal components based on realigned data, the Expectation-Maximisation (EM) algorithm and the Kalman smoother in a state-space model context. The monthly factors are used to estimate current quarter GDP, called the 'nowcast', using different versions of what we call factor-based mixed-data sampling (Factor-MIDAS) approaches. We compare all possible combinations of factor estimation methods and Factor-MIDAS projections with respect to nowcast performance. Additionally, we compare the performance of the nowcast factor models with the performance of quarterly factor models based on time-aggregated and thus balanced data, which neglect the most timely observations of business cycle indicators at the end of the sample. Our empirical findings show that the factor estimation methods don't differ much with respect to nowcasting accuracy. Concerning the projections, the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the nowcast factor models that can exploit ragged-edge data.

business cycle, large factor models, MIDAS, missing values, mixed-frequency data, nowcasting

Abstract:
This paper compares different ways to estimate the current state of the economy using factor models that can handle unbalanced datasets. Due to the different release lags of business cycle indicators, data unbalancedness often emerges at the end of multivariate samples, which is sometimes referred to as the 'ragged edge' of the data. Using a large monthly dataset of the German economy, we compare the performance of different factor models in the presence of the ragged edge: static and dynamic principal components based on realigned data, the Expectation-Maximisation (EM) algorithm and the Kalman smoother in a state-space model context. The monthly factors are used to estimate current quarter GDP, called the 'nowcast', using different versions of what we call factor-based mixed-data sampling (Factor-MIDAS) approaches. We compare all possible combinations of factor estimation methods and Factor-MIDAS projections with respect to nowcast performance. Additionally, we compare the performance of the nowcast factor models with the performance of quarterly factor models based on time-aggregated and thus balanced data, which neglect the most timely observations of business cycle indicators at the end of the sample. Our empirical findings show that the factor estimation methods don't differ much with respect to nowcasting accuracy. Concerning the projections, the most parsimonious MIDAS projection performs best overall. Finally, quarterly models are in general outperformed by the nowcast factor models that can exploit ragged-edge data.

MIDAS, large factor models, nowcasting, mixed-frequency data, missing values

Abstract:
A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffé's (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.

error bands, path forecast, simultaneous confidence region

Abstract:
A path forecast refers to the sequence of forecasts 1 to H periods into the future. A summary of the range of possible paths the predicted variable may follow for a given confidence level requires construction of simultaneous confidence regions that adjust for any covariance between the elements of the path forecast. This paper shows how to construct such regions with the joint predictive density and Scheffe's (1953) S-method. In addition, the joint predictive density can be used to construct simple statistics to evaluate the local internal consistency of a forecasting exercise of a system of variables. Monte Carlo simulations demonstrate that these simultaneous confidence regions provide approximately correct coverage in situations where traditional error bands, based on the collection of marginal predictive densities for each horizon, are vastly off mark. The paper showcases these methods with an application to the most recent monetary episode of interest rate hikes in the U.S. macroeconomy.

path forecast, simultaneous confidence region, error bands

Abstract:
Existing panel cointegration tests rule out cross-unit cointegrating relationships, while economic theory and empirical observation argue strongly in favour of their presence. Using an extensive set of simulation experiments, we show that both univariate and multivariate panel cointegration tests can be substantially oversized in the presence of cross-unit cointegration. We also propose a test for cross-unit cointegration that performs well in practice and can be used to decide upon the usefulness of panel methods.

Abstract:
In this Paper we evaluate the role of a set of variables as leading indicators for Euro-area inflation and GDP growth. Our evaluation is based on using the variables in the ECB euro area model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator with that of purely autoregressive models, using an evaluation procedure that is particularly relevant for policy-making. The evaluation is conducted both ex-post and in a pseudo real time context, for several forecast horizons, and using both recursive and rolling estimation. We also analyse three different approaches to combining the information from several indicators. First, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Second, an automated model selection procedure is applied to models with a large set of indicators. Third, we consider pooling the single indicator forecasts. The results indicate that single indicator forecasts are on average better than those derived from more complicated methods, but for them to beat the autoregression a different indicator has to be used in each period. A simple real-time procedure for indicator-selection produces good results.

Leading indicator, factor model, model selection, GDP growth, inflation

Abstract:
We derive a set of stylized facts on the effects of non-systematic fiscal policy in the four largest countries of the Euro area, and discuss their implications for the fiscal policy coordination debate, for the effectiveness of fiscal shocks in stabilizing the economies, and for the interaction of fiscal and monetary policy. We find relevant differences across countries in the effects of non-systematic fiscal policy, and substantial uncertainty about the size of these effects, which casts doubts on the possibility of a fiscal coordination. Moreover, expenditure shocks are usually rather ineffective in increasing output growth or reducing its volatility, and can require deficit financing. Tax policies also appear to have minor effects on output, and tax cuts could also require deficit financing. Finally, fiscal shocks appear to have an impact on interest rates, either direct or through the output gap and inflation while, in general, the effects of monetary policy on disbursements and receipts seem to be minor.

Fiscal policy, policy coordination, stabilization policy, monetary policy

Abstract:
Nowadays a considerable amount of information on the behaviour of the economy is readily available, in the form of large datasets of macroeconomic variables. Central bankers can be expected to base their decisions on this very large information set. Yet the academic profession has shown a clear preference for using small models to highlight stylized facts and to implement policy simulation exercises. Omitted information is then a potentially relevant problem. Recent time-series techniques for the analysis of large datasets have shown how vast an amount of information can be captured by few factors. In this paper we combine factors extracted from large datasets with more traditional small-scale models to analyse monetary policy in Europe. In particular, we model hundreds of macroeconomic variables with a dynamic factor model, and summarize their informational content with a few estimated factors. These factors are then used as instruments in the estimation of forward-looking Taylor rules, and as additional regressors in structural VARs. The latter are then used to evaluate the effects of unexpected and systematic monetary policy.

Monetary policy, small models, dynamic factors

Abstract:
In this Paper we compare alternative approaches for dating the euro area business cycle and analysing its characteristics. First, we extend a commonly used dating procedure to allow for length, size and amplitude restrictions, and to compute the probability of a phase change. Second, we apply the modified algorithm for dating both the classical euro area cycle and the deviation cycle, where the latter is obtained by a variety of methods, including a modified HP filter that reproduces the features of the BK filter but avoids end-point problems, and a production function based approach. Third, we repeat the dating exercise for the main euro area countries, evaluate the degree of synchronization, and compare the results with the UK and the US. Fourth, we construct indices of business cycle diffusion, and assess how widespread are cyclical movements throughout the economy. Finally we repeat the dating exercise using monthly industrial production data, to evaluate whether the higher sampling frequency can compensate the higher variability of the series and produce a more accurate dating.

Business cycle, euro area, cycle dating, cycle synchronization

Abstract:
This Paper aims at improving the understanding of the transmission of shocks across countries and how this transmission may have changed over time. By employing a model that allows for parameter changes across regimes, we show that transmission of shocks from the US to European countries may depend on the values of transition variables such as financial prices, exchange rates, international capital flows, trade links and monetary policy instruments. We also show that transmission mechanisms estimated with the proposed models have good performance in describing the 2001 downturn in some European countries as an effect of a US shock. More generally, the models have a good forecasting performance over short horizons.

Transmission mechanism, shocks, cycles, Europe, impulse response, non-linear VAR

Abstract:
After the creation of the European Monetary Union (EMU), both the European Commission (EC) and the European Central Bank (ECB) are focusing more and more on the evolution of the EMU as a whole, rather than on single member countries. A particularly relevant issue from a policy point of view is the availability of reliable forecasts for the key macroeconomic variables. Hence, both the fiscal and the monetary authorities have developed aggregate forecasting models, along the lines previously adopted for the analysis of single countries. A similar approach will be likely followed in empirical analyses on, for example, the existence of an aggregate Taylor rule or the evaluation of the aggregate impact of monetary policy shocks, where linear specifications are usually adopted. Yet it is uncertain whether standard linear models provide the proper statistical framework to address these issues. The process of aggregation across countries can produce smoother series, better suited for the analysis with linear models, by averaging out country specific shocks. But the method of construction of the aggregate series, which often involves time-varying weights, and the presence of common shocks across the countries, such as the deflation in the early 1980s and the convergence process in the early 1990s, can introduce substantial non-linearity into the generating process of the aggregate series. To evaluate whether this is the case, we fit a variety of non-linear and time-varying models to aggregate EMU macroeconomic variables, and compare them with linear specifications. Since non-linear models often over-fit in sample, we assess their performance in a real time forecasting framework. It turns out that for several variables linear models are beaten by non-linear specifications, a result that questions the use of standard linear methods for forecasting and modeling EMU variables.

European Monetary Union, forecasting, time-varying models, non-linear models, instability, non-linearity

Abstract:
It is rather common to have several competing forecasts for the same variable, and many methods have been suggested to pick up the best, on the basis of their past forecasting performance. As an alternative, the forecasts can be combined to obtain a pooled forecast, and several options are available to select what forecasts should be pooled, and how to determine their relative weights. In this Paper we compare the relative performance of alternative pooling methods, using a very large dataset of about 500 macroeconomic variables for the countries in the European Monetary Union. In this case the forecasting exercise is further complicated by the short time span available, due to the need of collecting a homogeneous dataset. For each variable in the dataset, we consider 58 forecasts produced by a range of linear, time-varying and non-linear models, plus 16 pooled forecasts. Our results indicate that on average combination methods work well. Yet, a more disaggregate analysis reveals that single non-linear models can outperform combination forecasts for several series, even though they perform rather badly for other series so that on average their performance is not as good as that of pooled forecasts. Similar results are obtained for a subset of unstable series, the pooled forecasts behave only slightly better, and for three key macroeconomic variables, namely, industrial production, unemployment and inflation.

Time-varying models, non-linear models, forecast pooling, European Monetary Union

Abstract:
In this Paper we evaluate the relative performance of linear, non-linear and time-varying models for about 500 macroeconomic variables for the countries in the Euro area, using a real-time forecasting methodology. It turns out that linear models work well for about 35% of the series under analysis, time-varying models for another 35% and non-linear models for the remaining 30% of the series. The gains in forecasting accuracy from the choice of the best model can be substantial, in particular for longer forecast horizons. These results emerge from a detailed disaggregated analysis, while they are hidden when an average loss function is used. To explore in more detail the issue of parameter instability, we then apply a battery of tests, detecting non-constancy in about 20-30% of the time series. For these variables the forecasting performance of the time-varying and non-linear models further improves, with larger gains for a larger fraction of the series. Finally, we evaluate whether non-linear models perform better for three key macroeconomic variables: industrial production, inflation and unemployment. It turns out that this is often the case. Hence, overall, our results indicate that there is a substantial amount of instability and non-linearity in the EMU, and suggest that it can be worth going beyond linear models for several EMU macroeconomic variables.

Instability, non-linearity, time-varying models, non-linear models, European Monetary Union

Abstract:
DSGE models are characterized by the presence of expectations as explanatory variables. To use these models for policy evaluation, the econometrician must estimate the parameters of expectation terms. Standard estimation methods have several drawbacks, including possible lack or weakness of identification of the parameters, misspecification of the model due to omitted variables or parameter instability, and the common use of inefficient estimation methods. Several authors have raised concerns over the implications of using inappropriate instruments to achieve identification. In this paper we analyze the practical relevance of these problems and we propose to combine factor analysis for information extraction from large data sets and GMM to estimate the parameters of systems of forward looking equations. Using these techniques, we evaluate the robustness of recent findings on the importance of forward looking components in the equations of a standard New-Keynesian model.

Abstract:
In this paper, we evaluate the role of a set of variables as leading indicators for Euro-area inflation and GDP growth. Our leading indicators are taken from the variables in the European Central Bank's (ECB) Euro-area-wide model database, plus a set of similar variables for the US. We compare the forecasting performance of each indicator ex post with that of purely autoregressive models. We also analyse three different approaches to combining the information from several indicators. First, ex post, we discuss the use as indicators of the estimated factors from a dynamic factor model for all the indicators. Secondly, within an ex ante framework, an automated model selection procedure is applied to models with a large set of indicators. No future information is used, future values of the regressors are forecast, and the choice of the indicators is based on their past forecasting records. Finally, we consider the forecasting performance of groups of indicators and factors and methods of pooling the ex ante single-indicator or factor-based forecasts. Some sensitivity analyses are also undertaken for different forecasting horizons and weighting schemes of forecasts to assess the robustness of the results.

Abstract:
In this paper we propose a monthly measure for the euro area Gross Domestic Product (GDP) based on a small scale factor model for mixed frequency data, featuring two factors: the first is driven by hard data, whereas the second captures the contribution of survey variables as coincident indicators. Within this framework we evaluate both the in-sample contribution of the second survey-based factor, and the short term forecasting performance of the model in a pseudo-real time experiment. We find that the survey-based factor plays a significant role for two components of GDP: Industrial Value Added and Exports. Moreover, the two factor model outperforms in terms of out of sample forecasting accuracy the traditional autoregressive distributed lags (ADL) specifications and the single factor model, with few exceptions for Exports and in growth rates.

Survey data, Forecasting, Temporal Disaggregation, Dynamic factor modes, Kalman Filter and smoother

Abstract:
Time series models are often adopted for forecasting because of their simplicity and good performance. The number of parameters in these models increases quickly with the number of variables modelled, so that usually only univariate or small-scale multivariate models are considered. Yet, data are now readily available for a very large number of macroeconomic variables that are potentially useful when forecasting. Hence, in this Paper we construct a large macroeconomic data-set for the UK, with about 80 variables, model it using a dynamic factor model, and compare the resulting forecasts with those from a set of standard time series models. We find that just six factors are sufficient to explain 50 percent of the variability of all the variables in the data set. Moreover, these factors, which can be considered as the main driving forces of the economy, are related to key variables such as interest rates, monetary aggregates, prices, housing and labour market variables, and stock prices. Finally, the factor-based forecasts are shown to improve upon standard benchmarks for prices, real aggregates, and financial variables, at virtually no additional modelling or computational cost.

Factor models, forecasts, time series models

Abstract:
This paper investigates the effects of temporal aggregation when the aggregation frequency is variable and possibly stochastic. The results that we report include, as a particular case, the well-known results on fixed-interval aggregation, such as when monthly data are aggregated into quarters. A variable aggregation frequency implies that the aggregated process will exhibit time-varying parameters and non-spherical disturbances, even when these characteristics are absent from the original model. Consequently, we develop methods for specification and estimation of the aggregate models and show with an example how these methods perform in practice.

Abstract:
We compare alternative forecast pooling methods and 58 forecasts from linear, time-varying and non-linear models, using a very large dataset of about 500 macroeconomic variables for the countries in the European Monetary Union. On average, combination methods work well but single non-linear models can outperform them for several series. The performance of pooled forecasts, and of non-linear models, improves when focusing on a subset of unstable series, but the gains are minor. Finally, on average over the EMU countries, the pooled forecasts behave well for industrial production growth, unemployment and inflation, but they are often beaten by non-linear models for each country and variable.

Abstract:
This paper proposes a dating algorithm based on an appropriately defined Markov chain that enforces alternation of peaks and troughs, and duration constraints concerning the phases and the full cycle. The algorithm, which implements Harding and Pagan's non-parametric dating methodology, allows an assessment of the uncertainty of the estimated turning points caused by filtering and can be used to construct indices of business cycle diffusion, aiming at assessing how widespread are cyclical movements throughout the economy. Its adaptation to the notion of a deviation cycle and the imposition of depth constraints are also discussed. We illustrate the algorithm with reference to the issue of dating the euro-area business cycle and analysing its characteristics, both from the classical and the growth cycle perspectives.

Abstract:
We analyse the evolution of the business cycle in the accession countries, after a careful examination of the seasonal properties of the available series and the required modification of the cycle dating procedures. We then focus on the degree of cyclical concordance within the group of accession countries, which turns out to be in general lower than that between the existing EU countries (the Baltic countries constitute an exception). With respect to the euro zone, the indications of synchronization are also generally low and lower relative to the position obtaining for countries taking part in previous enlargements (with the exceptions of Poland, Slovenia and Hungary). In the light of the optimal currency area literature, these results cast doubts on the usefulness of adopting the euro in the near future for most accession countries, though other criteria, such as the extent of trade and the gains in credibility, may point in a different direction.

Business cycles, dating algorithms, cycle synchronization, EU enlargement, seasonal adjustment

Abstract:
A continuous monitoring of the evolution of the economy is fundamental for the decisions of public and private decision makers. This paper proposes a new monthly indicator of the euro area real Gross Domestic Product (GDP), with several original features. First, it considers both the output side (six branches of the NACE classification) and the expenditure side (the main GDP components) and combines the two estimates with optimal weights reflecting their relative precision. Second, the indicator is based on information at both the monthly and quarterly level, modelled with a dynamic factor specification cast in state-space form. Third, since estimation of the multivariate dynamic factor model can be numerically complex, computational efficiency is achieved by implementing univariate filtering and smoothing procedures. Finally, special attention is paid to chain-linking and its implications, via a multistep procedure that exploits the additivity of the volume measures expressed at the prices of the previous year.

Chain-linking, Dynamic factor Models, euro area GDP, Kalman filter and smoother, Multivariate State Space Models, Temporal Disaggregation

Abstract:
Our objective is to identify a way of checking empirically the extent to which expectations are de-coupled from inflation, how well they might be anchored in the long run, and at what level. This methodology allows us then to identify a measure for the degree of anchorness, and as anchored expectations are associated with credibility, this will serve as a proxy for credibility. We apply this methodology to the US history of inflation since 1963 and examine how well our measure tracks the periods for which credibility is known to be either low or high. Of particular interest to the validity of the measure is the start of the Great Moderation. Following the narrative of a number of well documented incidents in this period, we check how well our measure captures both the evolution of credibility in US monetary policy, as well as reactions to inflation scares.

anchors for expectations, credibility, Great Inflation, Great Moderation

Abstract:
This paper discusses pooling versus model selection for now- and forecasting in the presence of model uncertainty with large, unbalanced datasets. Empirically, unbalanced data is pervasive in economics and typically due to different sampling frequencies and publication delays. Two model classes suited in this context are factor models based on large datasets and mixed-data sampling (MIDAS) regressions with few predictors. The specification of these models requires several choices related to, amongst others, the factor estimation method and the number of factors, lag length and indicator selection. Thus, there are many sources of mis-specification when selecting a particular model, and an alternative could be pooling over a large set of models with different specifications. We evaluate the relative performance of pooling and model selection for now- and forecasting quarterly German GDP, a key macroeconomic indicator for the largest country in the euro area, with a large set of about one hundred monthly indicators. Our empirical findings provide strong support for pooling over many specifications rather than selecting a specific model.

factor models, forecast combination, forecast pooling, MIDAS, mixed-frequency data, model selection, nowcasting

Abstract:
Models based on economic theory have serious problems at forecasting exchange rates better than simple univariate driftless random walk models, especially at short horizons. Multivariate time series models suffer from the same problem. In this paper, we propose to forecast exchange rates with a large Bayesian VAR (BVAR), using a panel of 33 exchange rates vis-a-vis the US Dollar. Since exchange rates tend to co-move, the use of a large set of them can contain useful information for forecasting. In addition, we adopt a driftless random walk prior, so that cross-dynamics matter for forecasting only if there is strong evidence of them in the data. We produce forecasts for all the 33 exchange rates in the panel, and show that our model produces systematically better forecasts than a random walk for most of the countries, and at any forecast horizon, including at 1-step ahead.

Bayesian VAR, Exchange Rates, Forecasting

Abstract:
We conduct a detailed simulation study of the forecasting performance of diffusion index-based methods in short samples with structural change. We consider several data generation processes, to mimic different types of structural change, and compare the relative forecasting performance of factor models and more traditional time series methods. We find that changes in the loading structure of the factors into the variables of interest are extremely important in determining the performance of factor models. We complement the analysis with an empirical evaluation of forecasts for the key macroeconomic variables of the Euro area and Slovenia, for which relatively short samples are officially available and structural changes are likely. The results are coherent with the findings of the simulation exercise, and confirm the relatively good performance of factor-based forecasts in short samples with structural change.

Factor models, forecasts, parameter uncertainty, short samples, structural change, time series models

Abstract:
The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two-step procedure that applies, in turn, shrinkage and reduced rank restrictions, and the reduced rank Bayesian VAR of Geweke (1996). We find that using shrinkage and rank reduction in combination rather than separately improves substantially the accuracy of forecasts, both when the whole set of variables is to be forecast, and for key variables such as industrial production growth, inflation, and the federal funds rate. The robustness of this finding is confirmed by a Monte Carlo experiment based on bootstrapped data. We also provide a consistency result for the reduced rank regression valid when the dimension of the system tends to infinity, which opens the ground to use large scale reduced rank models for empirical analysis.

Bayesian VARs, factor models, forecasting, reduced rank

Abstract:
This paper compares the mixed-data sampling (MIDAS) and mixed-frequency VAR (MF-VAR) approaches to model specification in the presence of mixed-frequency data, e.g., monthly and quarterly series. MIDAS leads to parsimonious models based on exponential lag polynomials for the coefficients, whereas MF-VAR does not restrict the dynamics and therefore can suffer from the curse of dimensionality. But if the restrictions imposed by MIDAS are too stringent, the MF-VAR can perform better. Hence, it is difficult to rank MIDAS and MF-VAR a priori, and their relative ranking is better evaluated empirically. In this paper, we compare their performance in a relevant case for policy making, i.e., nowcasting and forecasting quarterly GDP growth in the euro area, on a monthly basis and using a set of 20 monthly indicators. It turns out that the two approaches are more complementary than substitutes, since MF-VAR tends to perform better for longer horizons, whereas MIDAS for shorter horizons.

euro area growth, MIDAS, mixed-frequency data, mixed-frequency VAR, nowcasting

Abstract:
Inflation differentials across regions of an integrated economy can reflect a proper response to demand and supply conditions, but can also indicate distortions with negative welfare implications. Using a novel dataset of regional inflation rates from six euro area countries, we examine the size and persistence of their differentials and find that they appear to be related to factor market distortions and other structural characteristics, rather than to cyclical and growth dynamics. Our empirical analysis shows that only about half of inflation rates variation is accounted for by area-wide factors such as monetary policy or oil price developments. National factors (such as labour market institutions) still play a very important role, and a regional component accounts for about 18% of inflation variability.

Abstract:
The literature on model comparison often requires the assumption that the true conditional distribution corresponds to that of one of the competing models. This strong assumption has been extended by the notion of encompassing and in likelihood based model comparisons. This paper takes the latter approach and develops tests for the comparison of competing nonlinear dynamic models, focusing on the nested and overlaping cases. The null hypothesis is that the models are equally close to the data generating process (DGP), according to a certain measure of closeness. The alternative is that one model is closer to the DGP. The models can be correctly specified or not. Their parameters can be estimated by a variety of methods, including (pseudo) maximum likelihood and ordinary least squares. The tests are symmetric and directional. Their asymptotic distribution under the null is either normal or a weighted sum of chi-squared distributions, depending on the nesting characteristics of the competing models. The comparison of nested AR models, and of nested ARMA models with GARCH errors and exogenous forcing variables (ARMAX-GARCH) are discussed as examples.

Abstract:
DSGE models are characterized by the presence of expectations as explanatory variables. To use these models for policy evaluation, the econometrician must estimate the parameters of expectation terms. Standard estimation methods have several drawbacks, including possible lack or weakness of identification of the parameters, misspecification of the model due to omitted variables or parameter instability, and the common use of inefficient estimation methods. Several authors have raised concerns over the implications of using inappropriate instruments to achieve identification. In this paper, we analyze the practical relevance of these problems and we propose to combine factor analysis for information extraction from large data sets and generalized method of moment to estimate the parameters of systems of forward-looking equations. Using these techniques, we evaluate the robustness of recent findings on the importance of forward-looking components in the equations of a standard New-Keynesian model.

Abstract:
This paper brings together several important strands of the econometrics literature: error-correction, cointegration and dynamic factor models. It introduces the Factor-augmented Error Correction Model (FECM), where the factors estimated from a large set of variables in levels are jointly modelled with a few key economic variables of interest. With respect to the standard ECM, the FECM protects, at least in part, from omitted variable bias and the dependence of cointegration analysis on the specific limited set of variables under analysis. It may also be in some cases a refinement of the standard Dynamic Factor Model (DFM), since it allows us to include the error correction terms into the equations, and by allowing for cointegration prevent the errors from being non-invertible moving average processes. In addition, the FECM is a natural generalization of factor augmented VARs (FAVAR) considered by Bernanke, Boivin and Eliasz (2005) inter alia, which are specified in first differences and are therefore misspecified in the presence of cointegration. The FECM has a vast range of applicability. A set of Monte Carlo experiments and two detailed empirical examples highlight its merits in finite samples relative to standard ECM and FAVAR models. The analysis is conducted primarily within an in-sample framework, although the out-of-sample implications are also explored.

Cointegration, Dynamic Factor Models, Error Correction Models, Factor-augmented Error Correction Models, FAVAR, VAR

Abstract:
A theoretical model for growth or inflation should be able to reproduce the empirical features of these variables better than competing alternatives. Therefore, it is common practice in the literature, whenever a new model is suggested, to compare its performance with that of a benchmark model. However, while the theoretical models become more and more sophisticated, the benchmark typically remains a simple linear time series model. Recent examples are provided, e.g., by articles in the real business cycle literature or by new-keynesian studies on inflation persistence. While a time series model can provide a reasonable benchmark to evaluate the value added of economic theory relative to the pure explanatory power of the past behavior of the variable, recent developments in time series analysis suggest that more sophisticated time series models could provide more serious benchmarks for economic models. In this paper we evaluate whether these complicated time series models can really outperform standard linear models for GDP growth and inflation, and should therefore substitute them as benchmarks for economic theory based models. Since a complicated model specification can over-fit in sample, i.e. the model can spuriously perform very well compared to simpler alternatives, we conduct the model comparison based on the out of sample forecasting performance. We consider a large variety of models and evaluation criteria, using real time data and a sophisticated bootstrap algorithm to evaluate the statistical significance of our results. Our main conclusion is that in general linear time series models can be hardly beaten if they are carefully specified, and therefore still provide a good benchmark for theoretical models of growth and inflation. However, we also identify some important cases where the adoption of a more complicated benchmark can alter the conclusions of economic analyses about the driving forces of GDP growth and inflation. Therefore, comparing theoretical models also with more sophisticated time series benchmarks can guarantee more robust conclusions.

growth, inflation, non-linear models, time-varying models

Abstract:
We investigate co-movements and heterogeneity in inflation dynamics of different regions within and across euro area countries using a novel disaggregate dataset to improve the understanding of inflation differentials in the European Monetary Union. We employ a model where regional inflation dynamics are explained by common euro area and country specific factors as well as an idiosyncratic regional component. Our findings indicate a substantial common area wide component, that can be related to the common monetary policy in the euro area and to external developments, in particular exchange rate movements and changes in oil prices. The effects of the area wide factors differ across regions, however. We relate these differences to structural economic characteristics of the various regions. We also find a substantial national component. Our findings do not differ substantially before and after the formal introduction of the euro in 1999, suggesting that convergence has largely taken place before the mid 90s. Analysing US regional inflation developments yields similar results regarding the relevance of common US factors. Finally, we find that disaggregate regional inflation information, as summarised by the area wide factors, is important in explaining aggregate euro area and US inflation rates, even after conditioning on macroeconomic variables. Therefore, monitoring regional inflation rates within euro area countries can enhance the monetary policy maker's understanding of aggregate area wide inflation dynamics.

Regional Inflation Dynamics, Euro Area and US, Common Factor Model

Abstract:
We analyse the relative performance of the IMF, OECD and EC in forecasting the government deficit, as a ratio to GDP, for the G7 countries. Interesting differences across countries emerge, sometimes supporting the hypothesis of an asymmetric loss function (i.e. of a preference for underprediction or overprediction), and potential benefits from forecast pooling.

Fiscal forecasting, Forecast comparison, Loss function

Abstract:
We show that the standard condition for MSFE encompassing is no longer valid when the forecasts to be compared are biased. We propose a simple modification of such a condition and of tests for its validity. The relationship between these tests, pooling regressions and tests for non-nested hypotheses is also analyzed, together with their multivariate versions. The theoretical results are illustrated by an empirical example on inflation and deficit forecasts, key variables for the formulation of monetary and fiscal policy.

Abstract:
We derive the generating mechanism of a temporally aggregated process when the original one belongs to the ARMA class. We then study the effects of temporal aggregation on a set of characteristics of usual interest such as exogeneity, causality, cointegration and common features. An empirical example illustrates the main issues.