
Mario FORNI
Professore Ordinario Dipartimento di Economia "Marco Biagi"

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2022
 The Nonlinear Transmission of Financial Shocks: Some Evidence
[Working paper]
Forni, Mario; Gambetti, Luca; MaffeiFaccioli, Nicolò; Sala, Luca
abstract
Financial shocks generate a protracted and quantitatively important effect on real economic activity and financial markets only if the shocks are both negative and large. Otherwise, their role is quite modest. Financial shocks have become more important for economic fluctuations after the 2000 and have contributed substantially to deepening the recessions of 2001 and 2008. The evidence is obtained using a new econometric procedure based on a VMA representation that includes a nonlinear function of the financial shock.
2021
 Downside and Upside Uncertainty Shocks
[Working paper]
Forni, Mario; Gambetti, Luca; Sala, Luca
abstract
An increase in uncertainty is not contractionary per se. What generates a significant downturn of economic activity is a widening of the left tail of the expected distribution of growth, the downside uncertainty. On the contrary, an increase of the right tail, the upside uncertainty, is mildly expansionary. The reason for why uncertainty shocks have been previously found to be contractionary is because movements in downside uncertainty dominate existing empirical measures of uncertainty. The results are obtained using a new econometric approach which combines quantile regressions and structural VARs.
2021
 Macroeconomic Uncertainty and Vector Autoregressions
[Working paper]
Forni, Mario; Gambetti, Luca; Sala, Luca
abstract
We estimate measures of macroeconomic uncertainty and compute the effects of uncertainty shocks by means of a new simple procedure based on standard VARs. Uncertainty and its effects are estimated using a single model so to ensure internal consistency. Under suitable assumptions, our procedure is equivalent to using the square of the VAR forecast error as an external instrument in a proxy SVAR. Our procedure allows to add orthogonality constraints to the standard proxy SVAR identification scheme. We apply our method to a US data set; we find that uncertainty is mainly exogenous and is responsible of a large fraction of businesscycle fluctuations.
2021
 Policy and Business Cycle Shocks: A Structural Factor Model Representation of the US Economy
[Articolo su rivista]
Forni, M; Gambetti, L
abstract
We use a dynamic factor model to provide a semistructural 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 five. Focusing on the fourshock specification, we identify, using sign restrictions, two policy shocks, monetary and fiscal, and two nonpolicy shocks, demand and supply. 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) Monetary and fiscal policy shocks have sizable effects on output and prices, with no evidence of crowdingout of private aggregate demand components; both monetary and fiscal authorities implement important systematic countercyclical policies reacting to demand shocks. (iii) Negative demand shocks have a large longrun positive effect on productivity, consistently with the Schumpeterian "cleansing" view of recessions.
2020
 Asymmetric Effects of Monetary Policy
Easing and Tightening
[Working paper]
Debortoli, D.; Forni, M.; Gambetti, L.; Sala, L.
abstract
Monetary policy easing and tightening have asymmetric effects: a policy easing has large
effects on prices but small effects on real activity variables. The opposite is found for a
policy tightening: large real effects but small effects on prices. Nonlinearities are estimated
using a new and simple procedure based on linear Structural Vector Autoregressions with
exogenous variables (SVARX). We rationalize the results through the lenses of a simple
model with downward nominal wage rigidities.
2020
 Asymmetric Effects of Monetary Policy Easing and Tightening
[Working paper]
Debortoli, Davide; Forni, Mario; Gambetti, Luca; Sala, Luca
abstract
Monetary policy easing and tightening have asymmetric effects: a policy easing has large effects on prices but small effects on real activity variables. The opposite is found for a policy tightening: large real effects but small effects on prices. Nonlinearities are estimated using a new and simple procedure based on linear Strutural Vector Autoregressions with exogenous variables (SVARX). We rationalize the result through the lens of a simple model with downward nominal wage rigidities.
2020
 Common Component Structural VARs
[Working paper]
Forni, Mario; Gambetti, Luca; Lippi, Marco; Sala, Luca
abstract
Small scale VAR models are subject to two major issues: first, the information set might be too narrow; second, many macroeconomic variables are measured with error. The two features produce distorted estimates of the impulse response functions. We propose a new procedure, called Common Components Structural VARs (CCSVAR), which solves both problems. It consists in (a) treating the variables, prior to estimation, in order to extract their common components; this eliminates measurement errors; (b) estimating a VAR with m > q common components, that is a singular VAR, where q is the number of shocks driving the economy; this solves the fundamentalness problem. SVARs and CCSVARs are compared in the empirical analysis of monetary policy and technology shocks. The results obtained by SVARs are not robust, in that they strongly depend on the choice and the treatment of the variables considered. On the contrary, using CCSVARs (i) contractionary monetary shocks produce a decrease of prices independently of the variables included in the model, (ii) irrespective of whether hours worked enter the model in loglevels or growth rates, technology improvements produce an increase in hours worked.
2020
 Common Components Structural VARs
[Working paper]
Forni, M.; Gambetti, L.; Lippi, M.; Scala, L.
abstract
Small scale VAR models are subject to two major issues: first, the information set might
be too narrow; second, many macroeconomic variables are measured with error. The two
features produce distorted estimates of the impulse response functions. We propose a
new procedure, called Common Components Structural VARs (CCSVAR), which solves
both problems. It consists in (a) treating the variables, prior to estimation, in order to
extract their common components; this eliminates measurement errors; (b) estimating a
VAR with m > q common components, that is a singular VAR, where q is the number
of shocks driving the economy; this solves the fundamentalness problem. SVARs and
CCSVARs are compared in the empirical analysis of monetary policy and technology
shocks. The results obtained by SVARs are not robust, in that they strongly depend
on the choice and the treatment of the variables considered. On the contrary, using CCSVARs (i) contractionary monetary shocks produce a decrease of prices independently of
the variables included in the model, (ii) irrespective of whether hours worked enter the
model in loglevels or growth rates, technology improvements produce an increase in hours
worked
2020
 Macroeconomic Uncertainty and Vector Autoregressions
[Working paper]
Forni, M.; Gambetti, L.; Sala, L.
abstract
We estimate macroeconomic uncertainty and the effects of uncertainty shocks by
means of a new procedure based on standard VARs. Under suitable assumptions,
our procedure is equivalent to using the square of the VAR forecast error as an external instrument in a proxy SVAR. We add orthogonality constraints to the standard
proxy SVAR identification scheme. We also derive a VARbased measure of uncertainty. We apply our method to a US data set; we find that uncertainty is mainly
exogenous and is responsible of a large fraction of businesscycle fluctuations.
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 finiteorder case and study the implications of partial fundamentalness for impulseresponse and variancedecomposition 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 infinitedimensional factor space: Forecasting
[Articolo su rivista]
Forni, Mario; Giovannelli, Alessandro; Lippi, Marco; Soccorsi, Stefano
abstract
The paper compares the pseudo realtime 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 socalled 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
[Working paper]
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 realtime onemonthahead forecasts with both models for four key macroeconomic variables: the monthonmonth 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 realtime onemonthahead forecasts with both models for four key macroeconomic variables: the monthonmonth 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
realtime onemonthahead forecasts with both models for four key macroeconomic
variables: the monthonmonth 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 InfiniteDimensional 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 twosided 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 onesided 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 finitedimensional 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 outofsample 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 twostep econometric procedure to estimate the effects of news and we find
highly nonlinear 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
 News, Uncertainty and Economic Fluctuations (No News is Good News)
[Working paper]
Forni, M.; Gambetti, L.; Sala, L.
abstract
We formalize the idea that uncertainty is generated by news about future developments
in economic conditions which are not perfectly predictable by the agents. Using a simple
model of limited information, we show that uncertainty shocks can be obtained as the square
of news shocks. We develop a twostep econometric procedure to estimate the effects of
news and we find highly nonlinear effects. Large news shocks increase uncertainty. This
mitigates the effects of good news and amplifies the effects of bad news in the short run.
By contrast, small news shocks reduce uncertainty and increase output 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 nonstandard 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 dotcom 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 reducedform residuals. We find that noise shocks generate humpshaped 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 realtime forecasting performance of three Dynamic Factor Models: (i) The standard principalcomponent 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
 Eigenvalue Ratio Estimators for the Number of Dynamic Factors
[Working paper]
Cavicchioli, M.; Forni, M.; Lippi, M.; Zaffaroni, P.
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 longrun effects of technology news on TFP.
2016
 VAR Information and the Empirical Validation of DSGE Models
[Working paper]
Forni, M.; Gambetti, L.; Sala, L.
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 noninvertible or nonfundamental. 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 remarkably well for all variables, but
understates the longrun effects of technology news on TFP.
2015
 Dynamic Factor Models with InniteDimensional Factor Space:Asymptotic Analysis
[Working paper]
Forni, M.; Hallin, M.; Lippi, M.; Zaffaroni, P.
abstract
Factor models, all particular cases of the Generalized Dynamic Factor Model
(GDFM) introduced in Forni, Hallin, Lippi and Reichlin (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,
Hallin, Lippi and Reichlin (2004). Those estimators, however, rely on Brillinger’s dynamic
principal components, and thus involve twosided 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 the generality afforded by the GDFM.
This paper derives the asymptotic properties of a semiparametric estimator of the loadings
and common shocks based on onesided filters recently proposed by Forni, Hallin, Lippi and
Zaffaroni (2015). Consistency and exact rates of convergence are obtained for this estimator,
under a general class of GDFMs that does not require a finitedimensional 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
outofsample forecasting.
2015
 Dynamic factor models with infinitedimensional factor spaces: Onesided 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 twosided 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 onesided 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, M.; Gambetti, L.
abstract
We identify government spending news and surprise shocks using a novel identification
based on the Survey of Professional Forecasters. News shocks lead, through an increase of
the interest rate, to 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
 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 factoraugmented VAR model is used to evaluate the role of ‘news shocks’ in generating the business cycle. We find that existing smallscale VAR models are affected by ‘nonfundamentalness’ 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
 Noise Bubbles
[Working paper]
Forni, Mario; M., ; Gambetti; L. ; Lippi M. ; Sala, L.
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 nonstandard 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 dotcom 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.
2014
 Noisy News in Business Cycles
[Working paper]
Forni, M.; Gambetti, L.; Lippi, M.; Sala, L.
abstract
The contribution of the present paper is twofold. First, we show that in a situation where
agents can only observe a noisy signal of the shock to future economic fundamentals, the
“noisy news”, 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. Second, we use our identification approach to
investigate the role of noise and news as sources of business cycle fluctuations. We find
that noise shocks, the component of the signal unrelated to economic fundamentals, generate humpshaped responses of GDP, consumption and investment and account for a
third of their variance. Moreover, news and noise together account for more than half of
the fluctuations in GDP, consumption and investment.
2014
 On the dynamic specification of aggregated models
[Capitolo/Saggio]
Lippi, M.; Forni, M.
abstract
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 nonstandard 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 dotcom 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 humpshaped 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 InfiniteDimensional Factor Space: OneSided 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 twosided 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 onesided 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 smallscale VECM models are affected by 'nonfundamentalness' 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
 No News in Business Cycles
[Working paper]
Forni, M.; Gambetti, L.; Sala, L.
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 smallscale VECM models are affected by ‘nonfundamentalness’
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
 Sufficient Information in Structural VARs
[Working paper]
Forni, M.; Gambetti, L.
abstract
We derive necessary and sufficient conditions under which a set of variables is informationally sufficient, i.e. contains enough information to estimate the structural shocks with a VAR
model. Based on such conditions, we provide a procedure to test for informational sufficiency.
If sufficiency is rejected, we propose a strategy to amend the VAR. Our method can be applied
to FAVAR models and can be used to determine how many factors to include in such models.
We apply our procedure to a VAR including TFP, unemployment and percapita hours worked.
We find that the three variables are not informationally sufficient. When adding missing information, the effects of technology shocks change dramatically.
2011
 The general dynamic factor model: Onesided 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 finitedimensional vector space. However, this finitedimension assumption rules out very simple factorloading 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 twosided and therefore unsuitable for prediction. The present paper, assuming a rational spectral density for the common components, obtains a onesidedestimator without the finitedimension assumption.
2010
 Fiscal Foresight and the Effects of Government Spending
[Working paper]
Forni, M.; Gambetti, L.
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 nonfundamental
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
 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 nonfundamental 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 semistructural 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 fourshock specification, we identify, using sign restrictions, two nonpolicy 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 longrun positive effect on productivity, consistently with the Schumpeterian ``cleansing'' view of recessions.
2010
 Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model
[Working paper]
Forni, M.; Gambetti, L.
abstract
We use a dynamic factor model to provide a semistructural 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 fourshock specification, we identify, using sign restrictions, two nonpolicy 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
longrun 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 shortrun dynamics. Removal of shortrun dynamics from a time series, to isolate the mediumlongrun component, can be obtained by a bandpass filter. However, it is well known that bandpass filters, being twosided, perform very poorly at the end of the sample. New Eurocoin is an estimator of the medium longrun component of the GDP that only uses contemporaneous values of a large panel of macroeconomic time series, so that no endofsample 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 longrun 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 crosssections
[Articolo su rivista]
Forni, Mario; Giannone, D; Lippi, M. AND REICHLIN L.
abstract
This paper shows how largedimensional 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 impulseresponse functions are sufficiently heterogeneous. We provide consistent estimators for the impulseresponse 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.
2008
 New Eurocoin: tracking economic growth in real time
[Working paper]
Altissimo, F.; Cristadoro, R.; Forni, M.; Lippi, M.; Veronese, G.
abstract
Removal of shortrun dynamics from a stationary time series to isolate the medium to
longrun component, can be obtained by a bandpass filter. However, band pass filters are
infinite moving averages and can therefore deteriorate at the end of the sample. This is
a wellknown result in the literature isolating the business cycle in integrated series. We
show that the same problem arises with our application to stationary time series. In this
paper we develop a method to obtain smoothing of a stationary time series by using only
contemporaneous values of a large dataset, so that no endofsample deterioration occurs.
2008
 The dynamic effects of monetary policy: A structural factor model approach
[Working paper]
Forni, M.; Gambetti, L.
abstract
We use the structural factor model proposed by Forni, Giannone, Lippi and Reichlin (2007) to study the effects of monetary policy. The advantage with respect to the traditional vector autoregression model is that we can exploit information from a large data set, made up of 112 US monthly macroeconomic series. Monetary policy shocks are identified using a standard recursive scheme, in which the impact effects on both industrial production and prices are zero. Such a scheme, when applied to a VAR including a suitable selection of our variables, produces puzzling results. Our main findings are the following. (i) The maximal effect on bilateral real exchange rates is observed on impact, so that the “delayed overshooting” or “forward discount” puzzle disappears. (ii) After a contractionary shock prices fall at all horizons, so that the price puzzle is not there. (iii) Monetary policy has a sizable effect on both real and nominal variables. Such results suggest that the structural factor model is a promising tool for applied macroeconomics
2007
 Opening the Black Box: Structural Factor Models with large crosssections
[Working paper]
Forni, Mario; Giannone, D; Lippi, M. AND REICHLIN L.
abstract
This paper shows how largedimensional 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 impulseresponse functions are sufficiently heterogeneous. We provide consistent estimators for the impulseresponse 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 shortrun dynamics. Removal of shortrun dynamics from a time series, to isolate the mediumlongrun component, can be obtained by a bandpass filter. However, it is well known that bandpass filters, being twosided, perform very poorly at the end of the sample. New Eurocoin is an estimator of the medium longrun component of the GDP that only uses contemporaneous values of a large panel of macroeconomic time series, so that no endofsample 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 longrun 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 shortrun 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: Onesided 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 signaltonoise 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 SocioEconomic Models, NorthHolland, 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 outofsample predictions of the Euroarea 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 rindustry 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 3digit 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 inputoutput 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 interindustry dynamic linkages across Italian manufacturing sectors. We perform a very disaggregated analysis in order to identify, for each 3digit 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 inputoutput 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 bandpassfiltered series. Moreover, longrun correlation and cohesion relate in a simple way to cointegration. Cohesion is useful to study problems of businesscycle synchronization, to investigate shortrun and longrun 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 businesscycle 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 crosscountry as well as the withincountry correlation structure and exploit all information on dynamic crosscorrelation.
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 intermediatelevel 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, LongRun Economic Growth (special issue) 21 (1996) 2742. Review of Economic Studies 65 (1998) 453473) to propose an estimation method which exploits the large crosssectional 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, 540554), introduces a new modelthe generalized dynamic factor modelfor 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, 11811304) and Chamberlain and Rothschild (1983, Econometrica 51, 13051324) 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. 45109) and Geweke (1977, in D.J. Aigner & A.S. Goldberger (eds.), Latent Variables in SocioEconomic Models, pp. 365383) 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 nonorthogonal 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 crosssectional 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 19711991. Many of these variables appear for the first time in the Barroregression 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 mediumsized firms. Second, we find weak evidence of the importance of social capital for growth, whereas variables indicating political subcultures 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 representativeagent 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 longrun 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 crosssectionally 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 crosssections 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 economywide 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 nontechnological shock. Identification is obtained by minimizing the negative realizations of the technology shock. Empirical results on 4digit industrial output and productivity for the U.S. economy from 1958 to 1986 show that: (1) at least two economywide shocks, both having a longrun 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) sectorspecific shocks explain the main bulk of total variance but generate mainly high frequency dynamics; (4) both the technological and the nontechnological 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 theorybased models that do not fit aggregate data well in their representativeagent 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 CrossSections
[Articolo su rivista]
Forni, Mario; Reichlin, L.
abstract
This paper develops a method to analyze large crosssections with nontrivial 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.
1989
 Trend, Cycle and 'Fortuitous cancellation': a Note on a Paper by Nelson and Plosser
[Working paper]
Forni, M.
abstract
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.