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Mario FORNI

Professore Ordinario presso: Dipartimento di Economia "Marco Biagi"


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Pubblicazioni

2019 - Structural VARs and noninvertible macroeconomic models [Articolo su rivista]
Forni, M.; Gambetti, L.; Sala, L.
abstract

We resume the line of research pioneered by C. A. Sims and Zha (Macroeconomic Dynamics, 2006, 10, 231–272) and make two novel contributions. First, we provide a formal treatment of partial fundamentalness—that is, the idea that a structural vector autoregression (VAR) can recover, either exactly or with good approximation, a single shock or a subset of shocks, even when the underlying model is nonfundamental. In particular, we extend the measure of partial fundamentalness proposed by Sims and Zha to the finite-order case and study the implications of partial fundamentalness for impulse-response and variance-decomposition analysis. Second, we present an application where we validate a theory of news shocks and find it to be in line with the empirical evidence.


2018 - Dynamic factor model with infinite-dimensional factor space: Forecasting [Articolo su rivista]
Forni, Mario; Giovannelli, Alessandro; Lippi, Marco; Soccorsi, Stefano
abstract

The paper compares the pseudo real-time forecasting performance of three dynamic factor models: (i) the standard principal component model introduced by Stock and Watson in 2002; (ii) the model based on generalized principal components, introduced by Forni, Hallin, Lippi, and Reichlin in 2005; (iii) the model recently proposed by Forni, Hallin, Lippi, and Zaffaroni in 2015. We employ a large monthly dataset of macroeconomic and financial time series for the US economy, which includes the Great Moderation, the Great Recession and the subsequent recovery (an update of the so-called Stock and Watson dataset). Using a rolling window for estimation and prediction, we find that model (iii) significantly outperforms models (i) and (ii) in the Great Moderation period for both industrial production and inflation, and that model (iii) is also the best method for inflation over the full sample. However, model (iii) is outperformed by models (ii) and (i) over the full sample for industrial production.


2018 - The Forcasting Performance of Dynamic Factor Models with Vintage Data [Articolo su rivista]
Di Bonaventura, Luca; Forni, Mario; Pattarin, Francesco
abstract

We present a comparative analysis of the forecasting performance of two dynamic factor models, the Stock and Watson (2002a, b) model and the Forni, Hallin, Lippi and Reichlin (2005) model, based on vintage data. Our dataset contains 107 monthly US "first release" macroeconomic and financial vintage time series, spanning the 1996:12 to 2017:6 period with monthly periodicity, extracted from the Bloomberg database. We compute real-time one-month-ahead forecasts with both models for four key macroeconomic variables: the month-on-month change in industrial production, the unemployment rate, the core consumer price index and the ISM Purchasing Managers' Index. First, we find that both the Stock and Watson and the Forni, Hallin, Lippi and Reichlin models outperform simple autoregressions for industrial production, unemployment rate and consumer prices, but that only the first model does so for the PMI. Second, we find that neither models always outperform the other. While Forni, Hallin, Lippi and Reichlin's beats Stock and Watson's in forecasting industrial production and consumer prices, the opposite happens for the unemployment rate and the PMI.


2018 - The Forecasting Performance of Dynamic Factor Models with Vintage Data [Working paper]
Di Bonaventura, L.; Forni, M.; Pattarin, F.
abstract

We present a comparative analysis of the forecasting performance of two dynamic factor models, the Stock and Watson (2002a, b) model and the Forni, Hallin, Lippi and Reichlin (2005) model, based on vintage data. Our dataset that contains 107 monthly US “first release” macroeconomic and financial vintage time series, spanning the 1996:12 to 2017:6 period with monthly periodicity, extracted from the Bloomberg database† . We compute real-time one-month-ahead forecasts with both models for four key macroeconomic variables: the month-on-month change in industrial production, the unemployment rate, the core consumer price index and the ISM Purchasing Managers’ Index. First, we find that both the Stock and Watson and the Forni, Hallin, Lippi and Reichlin models outperform simple autoregressions for industrial production, unemployment rate and consumer prices, but that only the first model does so for the PMI. Second, we find that neither models always outperform the other. While Forni, Hallin, Lippi and Reichlin’s beats Stock and Watson’s in forecasting industrial production and consumer prices, the opposite happens for the unemployment rate and the PMI.


2017 - Dynamic Factor Models with Infinite-Dimensional Factor Space: Asymptotic Analysis [Articolo su rivista]
Forni, Mario; Hallin, Marc; Lippi, Marco; Zaffaroni, Paolo
abstract

Factor models, all particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forni et al., (2000), have become extremely popular in the theory and practice of large panels of time series data. The asymptotic properties (consistency and rates) of the corresponding estimators have been studied in Forni et al. (2004). Those estimators, however, rely on Brillinger’s concept of dynamic principal components, and thus involve two-sided filters, which leads to rather poor forecasting performances. No such problem arises with estimators based on standard (static) principal components, which have been dominant in this literature. On the other hand, the consistency of those static estimators requires the assumption that the space spanned by the factors has finite dimension, which severely restricts their generality—prohibiting, for instance, autoregressive factor loadings. This paper derives the asymptotic properties of a semiparametric estimator of the loadings and common shocks based on one-sided filters recently proposed by Forni et al., (2015). Consistency and exact rates of convergence are obtained for this estimator, under a general class of GDFMs that does not require a finite-dimensional factor space. A Monte Carlo experiment and an empirical exercise on US macroeconomic data corroborate those theoretical results and demonstrate the excellent performance of those estimators in out-of-sample forecasting.


2017 - News, Uncertainty and Economic Fluctuations (No News Is Good News) [Articolo su rivista]
Forni, Mario; Gambetti, Luca; Sala, Luca
abstract

We formalize the idea that uncertainty is generated by news about future developments in economic conditions which are not perfectly predictable. Using a simple model of limited information, we show that uncertainty shocks can be obtained as the square of news shocks. We develop a two-step econometric procedure to estimate the effects of news and we find highly non-linear effects. Large news shocks increase uncertainty. This mitigates the effects of good news and amplies the effects of bad news in the short run. The Volcker recession and the Great Recession were exacerbated by the uncertainty effects of news.


2017 - Noise Bubbles [Articolo su rivista]
Forni, Mario; Gambetti, Luca; Lippi, Marco; Sala, Luca
abstract

We introduce imperfect information in stock prices determination. Agents, whose expectations are not assumed to be rational, receive a noisy signal about the structural shock driving future dividend variations. Equilibrium stock prices are decomposed into a fundamental component and a transitory ‘noise bubble’ which can be responsible for boom and bust episodes unrelated to economic fundamentals. We propose a non-standard VAR procedure to estimate the effects of noise shocks as well as bubble episodes. Noise explains a large fraction of US stock prices. In particular the dot-com bubble is almost entirely explained by noise.


2017 - Noisy News in Business Cycles [Articolo su rivista]
Forni, Mario; Gambetti, Luca; Lippi, Marco; Sala, Luca
abstract

We investigate the role of "noise" shocks as a source of business cycle fluctuations. To do so we set up a simple model of imperfect information and derive restrictions for identifying the noise shock in a VAR model. The novelty of our approach is that identification is reached by means of dynamic rotations of the reduced-form residuals. We find that noise shocks generate hump-shaped responses of GDP, consumption and investment, and account for a sizable fraction of their prediction error variance at business cycle horizons.


2016 - DYNAMIC FACTOR MODEL WITH INFINITE DIMENSIONAL FACTOR SPACE: FORECASTING [Articolo su rivista]
Forni, Mario; Giovannelli, Alessandro; Lippi, Marco; Soccorsi, Stefano
abstract

The paper compares the pseudo real-time forecasting performance of three Dynamic Factor Models: (i) The standard principal-component model, Stock and Watson (2002a), (ii) The model based on generalized principal components, Forni et al. (2005), (iii) The model recently proposed in Forni et al. (2015b) and Forni et al. (2015a). We employ a large monthly dataset of macroeconomic and financial time series for the US economy, which includes the Great Moderation, the Great Recession and the subsequent recovery. Using a rolling window for estimation and prediction, we find that (iii) neatly outperforms (i) and (ii) in the Great Moderation period for both Industrial Production and Inflation, and for Inflation over the full sample. However, (iii) is outperfomed by (i) and (ii) over the full sample for Industrial Production.


2016 - Eigenvalue Ratio Estimators for the Number of Common Factors [Articolo su rivista]
Cavicchioli, Maddalena; Forni, Mario; Lippi, Marco; Zaffaroni, Paolo
abstract

In this paper we introduce three dynamic eigenvalue ratio estimators for the number of dynamic factors. Two of them, the Dynamic Eigenvalue Ratio (DER) and the Dynamic Growth Ratio (DGR) are dynamic counterparts of the eigenvalue ratio estimators (ER and GR) proposed by Ahn and Horenstein (2013). The third, the Dynamic eigenvalue Difference Ratio (DDR), is a new one but closely related to the test statistic proposed by Onatsky (2009). The advantage of such estimators is that they do not require preliminary determination of discretionary parameters. Finally, a static counterpart of the latter estimator, called eigenvalue Difference Ratio estimator (DR), is also proposed. We prove consistency of such estimators and evaluate their performance under simulation. We conclude that both DDR and DR are valid alternatives to existing criteria. Application to real data gives new insights on the number of factors driving the US economy.


2016 - Government spending shocks in open economy VARs [Articolo su rivista]
Forni, Mario; Gambetti, Luca
abstract

By using the Survey of Professional Forecasters, we provide new evidence on the open economy effects of government spending, focusing on a key puzzle in the literature, that the real exchange rate depreciates in response to a scal expansion. Much of government spending is well anticipated over a one year horizon. Once news and surprise shocks are treated as ddifferent shocks, there is no depreciation puzzle for news shocks while it is still there with surprise shocks. Fiscal foresight seems to lie at the heart of the different exchange rate responses to news and surprise shocks, depending on the timing of the anticipated budget adjustment following the shock. Indeed, the results are broadly consistent with the prediction of a DSGE model with spending reversals.


2016 - VAR Information and the Empirical Validation of DSGE Models [Articolo su rivista]
Forni, Mario; Gambetti, Luca; Sala, Luca
abstract

A shock of interest can be recovered, either exactly or with a good approximation, by means of standard VAR techniques even when the structural MA representation is non- invertible. We propose a measure of how informative a VAR model is for a specific shock of interest. We show how to use such a measure for the validation of shocks' transmission mechanism of DSGE models through VARs. In an application, we validate a theory of news shocks. The theory does fairly well for all variables, but understates the long-run effects of technology news on TFP.


2015 - Dynamic factor models with infinite-dimensional factor spaces: One-sided representations [Articolo su rivista]
Forni, Mario; Hallin, Marc; Lippi, Marco; Zaffaroni, Paolo
abstract

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced in Forniet al. (2000). That paper, however, rests on Brillinger’s dynamic principal components. The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have been dominant in this literature. On the other hand, those estimators require the assumption that the space spanned by the factors has finite dimension. In the present paper, we argue that such an assumption is extremely restrictive and potentially quite harmful. Elaborating upon recent results by Anderson and Deistler (2008a, b) on singular stationary processes with rational spectrum, we obtain one-sided representations for the GDFM without assuming finite dimension of the factor space. Construction of the corresponding estimators is also briefly outlined. In a companion paper, we establish consistency and rates for such estimators, and provide Monte Carlo results further motivating our approach.


2014 - Government Spending Shocks in Open Economy VARs [Working paper]
Forni, Mario; Gambetti, Luca
abstract

We identify government spending news and surprise shocks using a novel identification based on the Survey of Professional Forecasters. News shocks lead to an increase of the interest rate, a real appreciation of US dollar and a worsening of the trade balance. The opposite is found for the standard surprise shock which raises government spending on impact: the currency depreciates and net exports improve. We reconcile the two conflicting results showing the different timing of the spending reversals associated with the two shocks. The effects of the news shock on government spending are much more persistent and the reversal occurs much later.


2014 - No News in Business Cycles [Articolo su rivista]
Forni, Mario; Gambetti, Luca; Sala, Luca
abstract

A structural factor-augmented VAR model is used to evaluate the role of ‘news shocks’ in generating the business cycle. We find that existing small-scale VAR models are affected by ‘non-fundamentalness’ and therefore fail to recover the correct shock and impulse response functions; news shocks have a smaller role in explaining the business cycle than previously found in the literature; their effects are essentially in line with what predicted by standard theories and a substantial fraction of business cycle fluctuations are explained by shocks unrelated to technology.


2014 - Sufficient information in structural VARs [Articolo su rivista]
Forni, Mario; Gambetti, Luca
abstract

Necessary and sufficient conditions under which a VAR contains sufficient information to estimate the structural shocks are derived. On the basis of this theoretical result we propose two simple tests to detect informational deficiency and a procedure to amend a deficient VAR. A simulation based on a DSGE model with fiscal foresight suggests that our method correctly identifies and fixes the informational problem. In an empirical application, we show that a bivariate VAR including unemployment and labor productivity is informationally deficient. Once the relevant information is included into the model, technology shocks appear to be contractionary.


2013 - Noise Bubbles [Working paper]
Forni, Mario; Gambetti, Luca; Lippi, Marco; Sala, Luca
abstract

We introduce noisy information into a standard present value stock price model. Agents receive a noisy signal about the structural shock driving future dividend variations. The resulting equilibrium stock price includes a transitory component — the "noise bubble" — which can be responsible for boom and bust episodes unrelated to economic fundamentals. We propose a non-standard VAR procedure to estimate the structural shock and the "noise" shock, their impulse response functions and the bubble component of stock prices. We apply such procedure to US data and find that noise explains a large fraction of stock price volatility. In particular the dot-com bubble is entirely explained by noise. On the contrary the stock price boom peaking in 2007 is not a bubble, whereas the following stock market crisis is largely due to negative noise shocks.


2013 - Noisy News in Business Cycles [Working paper]
Forni, Mario; Gambetti, L.; Lippi, M; Sala, L.
abstract

In a situation where agents can only observe a noisy signal of the shock to future economic fundamentals, SVAR models can still be successfully employed to estimate the shock and the associated impulse response functions. Identification is reached by means of dynamic rotations of the reduced form residuals. We use our identification approach to investigate the role of the "noise" shock the component of the signal observed by agents which is unrelated to economic fundamentals as a source of business cycle fluctuations. We find that noise shocks generate hump-shaped responses of GDP, consumption and investment and account for about a third of their prediction error variance at business cycle horizons.


2012 - Dynamic Factor Models with Infinite-Dimensional Factor Space: One-Sided Representations [Working paper]
Forni, Mario; Marc, Hallin; Lippi, Marco; Paolo, Zaffaroni
abstract

Factor model methods recently have become extremely popular in the theory and practice of large panels of time series data. Those methods rely on various factor models which all are particular cases of the Generalized Dynamic Factor Model (GDFM) introduced inForni, Hallin, Lippi and Reichlin (2000). That paper, however, relies on Brillinger's dynamic principal components. The corresponding estimators are two-sided filters whose performance at the end of the observation period or for forecasting purposes is rather poor. No such problem arises with estimators based on standard principal components, which have been dominant in this literature. On the other hand, those estimators require the assumption that the space spanned by the factors has finite dimension. In the present paper, we argue that such an assumption is extremely restrictive and potentially quite harmful. Elaborating upon recent results by Anderson and Deistler (2008a, b) on singular stationary processes withrational spectrum, we obtain one-sided representations for the GDFM without assuming finite dimension of the factor space. Construction of the corresponding estimators is also briefly outlined. In a companion paper, we establish consistency and rates for such estimators, and provide Monte Carlo results further motivating our approach.


2011 - No News in Business Cycles [Working paper]
Forni, Mario; Luca, Gambetti; Luca, Sala
abstract

This paper uses a structural, large dimensional factor model to evaluate the role of 'news' shocks (shocks with a delayed effect on productivity) in generating the business cycle. We find that (i) existing small-scale VECM models are affected by 'non-fundamentalness' and therefore fail to recover the correct shock and impulse response functions; (ii) news shocks have a limited role in explaining the business cycle; (iii) their effects are in line with what predicted by standard neoclassical theory; (iv) the bulk of business cycle fluctuations is explained by shocks unrelated to technology.


2011 - The general dynamic factor model: One-sided representation results [Articolo su rivista]
M., Lippi; Forni, Mario
abstract

Recent dynamic factor models have been almost exclusively developed under the assumption that the common components span a finite-dimensional vector space. However, this finite-dimension assumption rules out very simple factor-loading patterns and is therefore severely restrictive. The general case has been studied, using a frequency domain approach, in Forni, Hallin, Lippi and Reichlin (2000). That paper produces an estimator of the common components that is consistent but is based on filters that are two-sided and therefore unsuitable for prediction. The present paper, assuming a rational spectral density for the common components, obtains a one-sidedestimator without the finite-dimension assumption.


2010 - Fiscal Foresight and the Effects of Government Spending [Articolo su rivista]
Forni, Mario; Gambetti, Luca
abstract

We study the effects of government spending by using a structural, large dimensional, dynamic factor model. We find that the government spending shock is non-fundamental for the variables commonly used in the structural VAR literature, so that its impulse response functions cannot be consistently estimated by means of a VAR. Government spending raises both consumption and investment, with no evidence of crowding out. The impact multiplier is 1.7 and the long run multiplier is 0.6.


2010 - Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model [Articolo su rivista]
Forni, Mario; Gambetti, L.
abstract

We use a dynamic factor model to provide a semi-structural representation for 101 quarterly US macroeconomic series. We find that (i) the US economy is well described by a number of structural shocks between two and six. Focusing on the four-shock specification, we identify, using sign restrictions, two non-policy shocks, demand and supply, and two policy shocks, monetary and fiscal. We obtain the following results. (ii) Both supply and demand shocks are important sources of fluctuations; supply prevails for GDP, while demand prevails for employment and inflation. (ii) Policy matters: Both monetary and fiscal policy shocks have sizeable effects on output and prices, with little evidence of crowding out; both monetary and fiscal authorities implement important systematic countercyclical policies reacting to demand shocks. (iii) Negative demand shocks have a large long-run positive effect on productivity, consistently with the Schumpeterian ``cleansing'' view of recessions.


2010 - New Eurocoin: Tracking Economic Growth in Real Time [Articolo su rivista]
Altissimo, F; Cristadoro, R; Forni, Mario; Lippi, M; Veronese, G.
abstract

This paper presents ideas and methods underlying the construction of an indicator that tracks the euroarea GDP growth, but, unlike GDP growth, (i) is updated monthly and almost in real time; (ii) is free from short-run dynamics. Removal of short-run dynamics from a time series, to isolate the mediumlong-run component, can be obtained by a band-pass filter. However, it is well known that band-pass filters, being two-sided, perform very poorly at the end of the sample. New Eurocoin is an estimator of the medium- long-run component of the GDP that only uses contemporaneous values of a large panel of macroeconomic time series, so that no end-of-sample deterioration occurs. Moreover, as our dataset is monthly, New Eurocoin can be updated each month and with a very short delay. Our method is based on generalized principal components that are designed to use leading variables in the dataset as proxies for future values of the GDP growth. As the medium- long-run component of the GDP is observable, although with delay, the performance of New Eurocoin at the end of the sample can be measured.


2010 - The Dynamic Effects of Monetary Policy: A Structural Factor Model Approach [Articolo su rivista]
Forni, Mario; Gambetti, L.
abstract

A structural factor model for 112 US monthly macroeconomic series is used tostudy the effects of monetary policy. Monetary policy shocks are identified usinga standard recursive scheme, in which the impact effects on both industrial productionand prices are zero. The main findings are the following. (i) The maximaleffect on bilateral real exchange rates is observed on impact, so that the “delayedovershooting” puzzle disappears. (ii) After a contractionary shock prices fall at allhorizons, so that the price puzzle is not there. (iii) Monetary policy has a sizableeffect on both real and nominal variables.


2009 - Opening the Black Box: Structural Factor Models with large cross-sections [Articolo su rivista]
Forni, Mario; Giannone, D; Lippi, M. AND REICHLIN L.
abstract

This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We argue that all identification schemes employed in SVAR analysis can be easily adapted in dynamic factor models. Moreover, the ``problem of fundamentalness'', which is intractable in structural VARs, can be solved, provided that the impulse-response functions are sufficiently heterogeneous. We provide consistent estimators for the impulse-response functions, as well as (n,T) rates of convergence. An exercise with US macroeconomic data shows that our solution of the fundamentalness problem may have important empirical consequences.


2007 - Opening the Black Box: Structural Factor Models with large cross-sections [Working paper]
Forni, Mario; Giannone, D; Lippi, M. AND REICHLIN L.
abstract

This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We argue that all identification schemes employed in SVAR analysis can be easily adapted in dynamic factor models. Moreover, the ``problem of fundamentalness'', which is intractable in structural VARs, can be solved, provided that the impulse-response functions are sufficiently heterogeneous. We provide consistent estimators for the impulse-response functions, as well as $(n,T)$ rates of convergence. An exercise with US macroeconomic data shows that our solution of the fundamentalness problem may have important empirical consequences.


2006 - New Eurocoin: Tracking Economic Growth in Real Time [Working paper]
Altissimo, F; Cristadoro, R; Forni, Mario; Lippi, M; Veronese, G.
abstract

This paper presents ideas and methods underlying the construction of an indicator that tracks the euroarea GDP growth, but, unlike GDP growth, (i) is updated monthly and almost in real time; (ii) is free from short-run dynamics. Removal of short-run dynamics from a time series, to isolate the mediumlong-run component, can be obtained by a band-pass filter. However, it is well known that band-pass filters, being two-sided, perform very poorly at the end of the sample. New Eurocoin is an estimator of the medium- long-run component of the GDP that only uses contemporaneous values of a large panel of macroeconomic time series, so that no end-of-sample deterioration occurs. Moreover, as our dataset is monthly, New Eurocoin can be updated each month and with a very short delay. Our method is based on generalized principal components that are designed to use leading variables in the dataset as proxies for future values of the GDP growth. As the medium- long-run component of the GDP is observable, although with delay, the performance of New Eurocoin at the end of the sample can be measured.


2005 - A core inflation indicator for the euro area [Articolo su rivista]
R., Cristadoro; Forni, Mario; L., Reichlin; G., Veronese
abstract

This paper proposes a new core inflation indicator for the euro area, obtained by 'cleaning' monthly price changes from short-run volatility, idiosyncratic, and measurement errors. We use a factor model to project monthly inflation on a large panel of time series. Exploiting multivariate information we obtain a satisfactory degree of smoothing without using backward looking moving averages, which induce a time delay in the signal. The indicator forecasts inflation and is a useful tool for policy makers. It outperforms other commonly used predictors at 6 months and longer horizons. It tracks past policy interventions of the ECB.


2005 - The generalized dynamic factor model: One-sided estimation and forecasting [Articolo su rivista]
Forni, Mario; M., Hallin; M., Lippi; L., Reichlin
abstract

This article proposes a new forecasting method that makes use of information from a large panel of time series. Like earlier methods, our method is based on a dynamic factor model. We argue that our method improves on a standard principal component predictor in that it fully exploits all the dynamic covariance structure of the panel and also weights the variables according to their estimated signal-to-noise ratio. We provide asymptotic results for our optimal forecast estimator and show that in finite samples, our forecast outperforms the standard principal components predictor.


2004 - Antitrust Policy and national growth: Some Evidence form Italy [Articolo su rivista]
Allegra, E; Forni, Mario; Grillo, M; Magnani, L.
abstract

Antitrust problems affecting markets for intermediate goods or services raise the input costs of firms operating in the downstream sectors, which often face tough international competition. Such firms lose market shares, thus worsening the economic performance of the country. We try to document the importance of this link between competition problems and growth by analysing Italian sectoral data. We find that sectors which depend more heavily on inputs and services produced in sectors suffering from competition problems perform worse in terms of net exports, export growth and output growth.


2004 - The generalized dynamic factor model: consistency and rates [Articolo su rivista]
Forni, Mario; M., Hallin; M., Lippi; L., Reichlin
abstract

A factor model generalizing those proposed by Geweke (in: D.J. Aigner and A.S. Goldberger, Latent Variables in Socio-Economic Models, North-Holland, Amsterdam, 1977), Sargent and Sims (New Methods in Business Research, Federal Reserve Bank of Minneapolis, Minneapolis, 1977), Engle and Watson (J. Amer. Statist. Assoc. 76 (1981) 774) and Stock and Watson (J. Business. Econom. Statist. 20 (2002) 147) has been introduced in Form et a]. (Rev. Econ. Statist. 80 (2000) 540), where consistent (as the number n of series and the number T of observations both tend to infinity along appropriate paths (n, T(n))) estimation methods for the common component are proposed. Rates of convergence associated with these methods are obtained here as functions of the paths (n, T(n)) along which n and T go to infinity. These results show that, under suitable assumptions, consistency requires T(n) to be at least of the same order as n, whereas an optimal rate of rootn is reached for T(n) of the order of n(2). if convergence to the space of common components is considered, consistency holds irrespective of the path (T(n) thus can be arbitrarily slow); the optimal rate is still rootn, but only requires T(n) to be of the order of n.


2004 - Using Stationarity Tests in Antitrust Market Definition [Working paper]
Forni, Mario
abstract

In this paper it is argued that, if two products or geographic areas belong in the same market, their relative price must be stationary. Hence stationarity tests like the ADF and the KPSS can be helpful in delineating the relevant market for Antitrust purposes, particularly for abuses of dominant positions and agreements between competitors. The proposed procedure is closely related with cointegration analysis but has more general validity. An application to the Italian milk market illustrates the technique.


2004 - Using Stationarity Tests in Antitrust Market Definition [Articolo su rivista]
Forni, Mario
abstract

In this paper it is argued that, if two products or geographic areas belong in the same market, their relative price must be stationary. Hence stationarity tests like the ADF and the KPSS can be helpful in delineating the relevant market for Antitrust purposes, particularly for abuses of dominant positions and agreements between competitors. The proposed procedure is strictly relatedwith cointegration analysis but is simpler and has more general validity. An application to the Italian milk market illustrates the technique.


2003 - Do financial variables help forecasting inflation and real activity in the euro area? [Articolo su rivista]
Forni, Mario; M., Hallin; M., Lippi; L., Reichlin
abstract

This paper uses a large data set, consisting of 447 monthly macroeconomic time series concerning the main countries of the Euro area to simulate out-of-sample predictions of the Euro-area industrial production and the harmonized inflation index and to evaluate the role of financial variables in forecasting. We considered two models which allow forecasting based on large panels of time series: Forni et al. (Rev. Econom. Statist. 82 (2000) 540; Mimeo (2001b)) and Stock and Watson (Mimeo (1999)). Performance of both models were compared to that of a simple univariate AR model. Results show that multivariate methods outperform univariate methods for forecasting inflation at one, three, six, and twelve months and industrial production at one and three months. We find that financial variables do help forecasting inflation, but do not help forecasting industrial production.


2002 - Knowledge Spillovers and the Growth of Local Industries [Articolo su rivista]
Forni, Mario; Paba, Sergio
abstract

The literature on localized knowledge spillovers and growth focuses on the relative importance of intra vs. inte r-industry externalities, but the nature and the characteristics of the dynamic linkages across manufacturing sectors are not investigated. In this paper we perform a very disaggregated analysis in order to identify, for each 3-digit industry, which composition of industrial activity is more conducive to growth. We find that diversity matters for growth, but each industry needs its own diversity. We provide some evidence of clustering of industries based on dynamic externalities. We find that many spillovers occur within input-output relationships. They often originate in downstream sectors favoring the growth of upstream industries. Lastly, the importance of spillovers does not depend on the technological intensity of the industry.


2002 - Spillovers and the growth of local industries [Articolo su rivista]
Forni, Mario; Paba, Sergio
abstract

In this paper we investigate the nature and directions of inter-industry dynamic linkages across Italian manufacturing sectors. We perform a very disaggregated analysis in order to identify, for each 3-digit industry, which composition of industrial activity is more conducive to growth. We find that diversity matters for growth, but each industry needs its own diversity. We provide some evidence of clustering of industries based on dynamic externalities. We find that many spillovers occur within input-output relationships. They often originate in downstream sectors favouring the growth of upstream industries. Lastly, the importance of spillovers does not depend on the technological intensity of the industry.


2001 - A measure of comovement for economic variables: Theory and empirics [Articolo su rivista]
Croux, C; Forni, Mario; Reichlin, L.
abstract

This paper proposes a measure of dynamic comovement between (possibly many) time series and names it cohesion. The measure is defined in the frequency domain and is appropriate for processes that are costationary, possibly after suitable transformations. In the bivariate case, the measure reduces to dynamic correlation and is related, but not equal, to the well known quantities of coherence and coherency. Dynamic correlation on a frequency band equals (static) correlation of bandpass-filtered series. Moreover, long-run correlation and cohesion relate in a simple way to co-integration. Cohesion is useful to study problems of business-cycle synchronization, to investigate short-run and long-run dynamic properties of multiple time series, and to identify dynamic clusters. We use state income data for the United States and GDP data far European nations to provide an empirical illustration that is focused on the geographical aspects of business-cycle fluctuations.


2001 - Coincident and leading indicators for the EURO area [Articolo su rivista]
Forni, Mario; Hallin, M; Lippi, M; Reichlin, L.
abstract

This paper proposes a new way to compute a coincident and a leading indicator of economic activity. Our methodology, based on Forni, Hallin, Lippi and Reichlin (2000), reconciles dynamic principal components analysis with dynamic factor analysis. it allows us to extract indicators from a large panel of economic variables (many variables Tot many countries). The procedure is used to estimate coincident and leading indicators fut the EURO area. Unlike other methods used in the literature, the procedure takes into consideration the cross-country as well as the within-country correlation structure and exploit all information on dynamic cross-correlation.


2001 - Federal policies and local economies: Europe and the US [Articolo su rivista]
Forni, Mario; Reichlin, Lucrezia
abstract

This paper establishes stylized facts on regional output fluctuations in Europe and the US. Moreover, it proposes a measure of the potential output target of the future European central bank, estimates the potential variance stabilization of a fiscal federation and constructs a regional map of the potential beneficiaries of monetary and fiscal federal policies. The econometric model is an extention of the dynamic factor model a la Sargent and Sims (1977. In: Sims, C.A. (Ed.), New Methods in Business Research. Federal Reserve Bank of Minneapolis) where we introduce an intermediate-level shock, which is common to all regions (counties) in each country (state), but it is not common to Europe (US) as a whole. We build on Forni and Reichlin (1996. Empirical Economics, Long-Run Economic Growth (special issue) 21 (1996) 27-42. Review of Economic Studies 65 (1998) 453-473) to propose an estimation method which exploits the large cross-sectional dimension of our data set. Our analysis shows that (i) Europe has a level of integration similar to that of the US and that national shocks are not a sizeable source of fluctuations: around 75% of output variance is explained by global and purely local dynamics; (ii) Europe, unlike the US, has no traditional business cycle; (iii) the core of the most integrated regions in Europe does not have national boundaries;(iv) the future European Central Bank has a potential stabilization target of about 18% of total output fluctuations; (v) a fiscal federation, if implemented, could have a smoothing effect on output in addition to what done by national fiscal policy, which accounts also for about 18% of total output fluctuations. (C) 2001 Elsevier Science B.V. All rights reserved. JEL classification: C51; E32; O30.


2001 - The generalized dynamic factor model: Representation theory [Articolo su rivista]
Forni, Mario; Lippi, Marco
abstract

This paper, along with the companion paper Forni, Hallin, Lippi, and Reichlin (2000, Review of Economics and Statistics 82, 540-554), introduces a new model-the generalized dynamic factor model-for the empirical analysis of financial and macroeconomic data sets characterized by a large number of observations both cross section and over time. This model provides a generalization of the static approximate factor model of Chamberlain (1983, Econometrica 51, 1181-1304) and Chamberlain and Rothschild (1983, Econometrica 51, 1305-1324) by allowing serial correlation within and across individual processes and of the dynamic factor model of Sargent and Sims (1977, in C.A. Sims (ed.), New Methods in Business Cycle Research, pp. 45-109) and Geweke (1977, in D.J. Aigner & A.S. Goldberger (eds.), Latent Variables in Socio-Economic Models, pp. 365-383) by allowing for nonorthogonal idiosyncratic terms. Whereas the companion paper concentrates on identification and estimation, here we give a full characterization of the generalized dynamic factor model in terms of observable spectral density matrices, thus laying a firm basis for empirical implementation of the model. Moreover, the common factors are obtained as limits of linear combinations of dynamic principal components. Thus the paper reconciles two seemingly unrelated statistical constructions.


2000 - The Generalized Factor Model: Identification and Estimation [Articolo su rivista]
Forni, Mario; Hallin, M.; Lippi, M.; Reichlin, L.
abstract

This paper proposes a factor model with infinite dynamics and non-orthogonal idiosyncratic components. The model, which we call the generalized dynamic factor model, is novel to the literature, and generalizes the static approximate factor model of Chamberlain and Rothschild (1983), as well as the exact factor model `a la Sargent and Sims (1977). We provide identification conditions, propose an estimator of the common components, prove convergence as both time and cross-sectional size go to infinity at appropriate rates and present simulation results. We use our model to construct a coincident index for the European Union. Such index is defined as the common component of real GDP within a model including several macroeconomic variables for each European country.


2000 - The sources of local growth: evidence from Italy [Articolo su rivista]
Forni, Mario; Paba, Sergio
abstract

The aim of this paper it to identify the main determinants of growth for local areas belonging to the same country. We examine the impact of a number of social, structural, and political variables on the economic performance of the Italian provinces during the period 1971-1991. Many of these variables appear for the first time in the Barro-regression literature. We analyze growth not only in terms of income, but also in terms of employment and population. First, we find that local growth is strongly affected by the diffusion of specialized industrial districts made up of small and medium-sized firms. Second, we find weak evidence of the importance of social capital for growth, whereas variables indicating political sub-cultures and social cohesion are strongly related with economic performance. Lastly, we show that crime and labor conflicts have a clear negative impact on employment.


1999 - Aggregation of Linear Dynamic Microeconomic Models [Articolo su rivista]
Forni, Mario; Lippi, M.
abstract

We survey a number of important results concerning aggregation of dynamic, stochastic relations. We do not aim at a comprehensive review; instead, we focus heavily on the results collected in Forni and Lippi [Forni, M., Lippi, M., 1997. Aggregation and the Microfoundations of Dynamic Macroeconomics. Oxford University Press, Oxford]. We argue that the representative-agent assumption is misleading and the microfoundation of dynamic macroeconomics should be based on explicit modeling of heterogeneity across agents. An unpleasant aspect of this modeling strategy is that macroeconomic implications of micro theory are difficult to obtain. However, difficulties are reduced by large number results. Moreover, puzzling implications of existing theories could be reconciled with empirical evidence on macro data. © 1999 Elsevier Science S.A. All rights reserved


1999 - Risk and potential insurance in Europe [Articolo su rivista]
Forni, Mario; Reichlin, Lucrezia
abstract

This paper argues that risk is related to long-run volatility of income and therefore stabilization policies should target permanent fluctuations. We show that such fluctuations can, in principle, be insured away by a multinational fiscal federation which smooths income cross-sectionally and has no ex ante permanent redistribution effects. We propose a measure of risk and a measure of potential insurable risk. We estimate these measures for the European countries and compare results with the US. Results show that potential insurable income risk in Europe is about 45%. Most countries will benefit from an average income tax of 10%, but gains differ widely across countries. (C) 1999 Elsevier Science B.V. All rights reserved.


1998 - Let's get real: A factor analytical approach to disaggregated business cycle dynamics [Articolo su rivista]
Forni, Mario; Reichlin, Lucrezia
abstract

This paper develops a method for analysing the dynamics of large cross-sections based on a factor analytic model. We use law of large numbers arguments to show that the number of common factors can be determined by a principal components method, the economy-wide shocks can be identified by means of simple structural VAR techniques and that the parameters of the unobserved factor model can be estimated consistently by applying OLS equation by equation. We distinguish between a technological and a non-technological shock. Identification is obtained by minimizing the negative realizations of the technology shock. Empirical results on 4-digit industrial output and productivity for the U.S. economy from 1958 to 1986 show that: (1) at least two economy-wide shocks, both having a long-run effect on sectoral output, are needed to explain the common dynamics; (2) although the technological shock accounts for at least 50% of the aggregate dynamics of output, it cannot by itself explain dynamics at business cycle frequencies; (3) sector-specific shocks explain the main bulk of total variance but generate mainly high frequency dynamics; (4) both the technological and the non-technological component of output show a peak for positive sectoral comovements of output at business cycle frequencies; (5) technological shocks are strongly correlated with the growth rates of the investment in machinery and equipment sectors and their inputs.


1997 - Aggregation and the Microfoundations of Dynamic Macroeconomics [Monografia/Trattato scientifico]
Forni, Mario; Lippi, M.
abstract

This book argues that modern macroeconomics has completely overlooked the aggregate nature of the data. Standard models start with intertemporally maximizing agents and obtain dynamic equations linking economic variables like consumption, income, investment, interest rates and employment. Such equations exhibit testable properties like cointegration, definite patterns of Granger causality, and restrictions on the parameters. The usual simplification that agents are identical leads to testing these properties directly on aggregate data. Here this simplification is systematically questioned. In Part I the homogeneity assumption is tested using disaggregate data and strongly rejected. As shown in Part II, the consequence of introducing heterogeneity is that, apart from flukes, cointegration, unidirectional Granger causality and restrictions on the parameters do not survive aggregation: thus the claim that modern macroeconomics has solid microfoundations is unwarranted. However, it is argued in Part III that aggregation is not necessarily bad. Some important theory-based models that do not fit aggregate data well in their representative-agent version can be reconciled with aggregate data by introducing heterogeneity.


1996 - Consumption Volatility and Income Persistence in the Permanent Income Model [Articolo su rivista]
Forni, Mario
abstract

Deaton's (1987) "excess smoothness" question can be reformulated by focusing attention on total income rather than labor income: the permanent income theory predicts that the relative volatility of consumption is equal to total income persistence, a fact that is contradicted by empirical evidence. This formulation is more general than the original one in that it is independent of the value of the interest rate, the univariate dynamics of labor income and the information set of the representative consumer. When properly formulated, the excess smoothness problem cannot be solved within Quah's (1990) superior information model; as a consequence, the interest of alternative solutions such as aggregation models is increased.


1996 - Dynamic Common Factors in Large Cross-Sections [Articolo su rivista]
Forni, Mario; Reichlin, L.
abstract

This paper develops a method to analyze large cross-sections with non-trivial time dimension.The method (i) identifies the number of common shocks in a factor analytic model; (ii) estimates the unobserved common dynamic component; (iii) shows how to test for fundamentalness of the common shocks; (iv) quantifies negative and positive comovements at each frequency. We illustrate how the prposed techniques can be used for analyzing features of the business cycle and economic growth.


1991 - Aggregation Across Agents in Demand Ssystems [Articolo su rivista]
Brighi, Luigi; Forni, Mario
abstract

In this survey we present the main results on the problem of aggregation across agents in demand systems, when no restrictions are placed on income distribution. The focus is on the theoretical aspects of the results. The implications for empirical work are made explicit, but not dealt with in detail.


1990 - L'aggregazione nei modelli dinamici [Monografia/Trattato scientifico]
Forni, Mario
abstract

Il libro discute la relazione tra le reazioni microeconomiche e le relazioni macroeconomiche. Le condizioni di aggregazione perfetta sono estremamente restrittive. In generale, le relazioni macroeconomiche sono mal specificate e l'agente rappresentativo invocato da gran parte della macroeconomia moderna non esiste.


1987 - Storie familiari e storie di proprieta': la scomparsa della mezzadria in Italia [Monografia/Trattato scientifico]
Forni, Mario
abstract

Il libro descrive i processi che hanno generato la scomparsa della mezzadria in Italia attraverso l'analisi di storie familiari e storie di proprieta' raccolte attraverso interviste dirette a Modena e nei comuni limitrofi.