Advances in Nowcasting Economic Activity:Secular Trends, Large Shocks and New Data

Juan Antolın-Dıaz1 Thomas Drechsel2 Ivan Petrella3

World Congress of the Econometric Society 2020

1London Business School2University of Maryland3Warwick Business School and CEPR

contribution of this paper

I This paper is about nowcasting economic activity

I Propose Bayesian dynamic factor model (DFM), which takes seriously keyfeatures of macroeconomic data:

1. Low-frequency variation in the mean and variance2. Heterogeneous responses to common shocks (leads/lags)3. Fat tails (outliers and “large” shocks)

I Evaluate model and its components in comprehensive out-of-sample exercise

I On fully real-time, unrevised data US data 2000-2019I Point and density forecastingI Taking advantage of cloud computing

I Apply model out of sample to track the Great Lockdown of 2020 (in progress)

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motivation #1trend and volatility changes in us real gdp growth

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020-4

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motivation #2lead and lag dynamics in macro data

2000 2002 2004 2006 2008 2010

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2Industrial Production

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2000 2002 2004 2006 2008 2010

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2Civilian Employment

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motivation #3outliers in macro data

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

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Light Weight Vehicle Sales (% MoM Change)

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015-6

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Real Personal Disposable Income (% MoM Change)

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plan of the talk

1. The Model

I Lay out how data features are formally captured in DFM

I Highlight what the related novel model components achieve

2. Data and estimation algorithm

3. Setup of comprehensive real-time evaluation exercise

4. Evaluation results

5. Application to the Great Lockdown (in progress)

6. Conclusion

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the model

the model: specification of baseline

I Start from familiar specification of a DFM (e.g. Giannone, Reichlin, and Small,2008 and Banbura, Giannone, and Reichlin, 2010)

I An n-dimensional vector of quarterly and monthly observables yt follows

∆(yt) = c + λft + ut

(I − Φ(L))ft = εt

(1− ρi(L))ui,t = ηi,t, i = 1, . . . , n

εtiid∼ N(0,Σε)

ηi,tiid∼ N(0, σ2

ηi), i = 1, . . . , n

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the model: specification of trend

I Consider n-dimensional vector of observables yt, which follows

∆(yt) = ct + λft + ut,

with

ct =

[B 00 c

] [at1

],

I Common factor and idiosyncratic components follow

(I − Φ(L))ft = εt,

(1− ρi(L))ui,t = ηi,t, i = 1, . . . , n

I Builds on Antolin-Diaz, Drechsel, and Petrella (2017)

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estimated trend

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 2020-4

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the model: specification of sv

I Consider n-dimensional vector of observables yt, which follows

∆(yt) = ct + λft + ut,

with

ct =

[B 00 c

] [at1

],

and

(I − Φ(L))ft = σεtεt,

(1− ρi(L))ui,t = σηi,tηi,t, i = 1, . . . , n

I The time-varying parameters are specified as random walk processes TVP processes

I Builds on Antolin-Diaz, Drechsel, and Petrella (2017)

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estimated volatility of the factor

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 20200

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2

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7

I SV captures both secular (McConnell and Perez-Quiros, 2000) and cyclical(Jurado et al., 2014) movements in volatility

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the model: adding heterogeneous dynamics

I Modify the observation equation to be

∆(yt) = ct + Λ(L)ft + ut,

where Λ(L) contains the loadings on contemporaneous and lagged factors

I Camacho and Perez-Quiros (2010) first noticed that survey data was betteraligned with a distributed lag of GDP

I D’Agostino et al. (2015) show that adding lags improves performance in thecontext of a small model

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estimated heterogeneous dynamics

0 5 10 15 20

Months

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1Monotonic

GDPINDPROCONSUMPTION

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Months

-1

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3Reversing

CARSALESHOUSINGSTARTSNEWHOMESALES

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Months

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1

1.5

2

2.5

3Hump Shaped

ISMMANUFPHILLYFEDCHICAGO

I Substantial heterogeneity in IRFs of to innovations in the cyclical factor

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the model: allowing for outliers

I Modify the observation equation to be

∆(yt − ot) = ct + Λ(L)ft + ut,

where the elements of ot follow t-distributions:

oi,tiid∼ tνi(0, ω2

o,i), i = 1, . . . , n

I The degrees of freedom of the t-distributions, νi, are estimated jointly with theother parameters of the model

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news decompositions: what fat tails achieve

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Forecast Error for Industrial Production (standard deviations)

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0

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Now

cast

Upd

ate

(per

cent

age

poin

ts a

nn.)

Basic DFM (Gaussian) Full Model (Student-t outliers)

News decomposition details All variables

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the model: summary of novel features

1. Macro data: low-frequency variation in mean and variance

I Model: time-varying parameters

2. Macro data: different leads and lags across indicators

I Model: variables load on factor lags

3. Macro data: recurring outliers in level and difference

I Model: t-distributed component

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estimation

estimation: data sets

I We construct a data set comprising US quarterly and monthly time series

I Indicators of real economic activity, excluding prices and financial variables

I We use both hard and soft indicators and

I Choice is guided by timeliness and coincidence with GDP

I In each economic category we include series at the highest level of aggregation

I This results in a panel of 28 series

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us data setFrequency

Hard IndicatorsGDP (Chained $) QGDI (Chained $) QConsumption (Chained $, Non Dur. + Serv.) QInvestment (Chained $, Fixed + Cons. Dur.) QAggregate Hours Worked (Total Economy) QIndustrial Production MPayroll Employment (Establishment Survey) MReal Retail Sales Food Services MReal Personal Income less Transfer Payments MNew Orders of Capital Goods MLight Weight Vehicle Sales MReal Exports of Goods MReal Imports of Goods MBuilding Permits MHousing Starts MNew Home Sales MCivilian Employment (Household Survey) MUnemployed MInitial Claims for Unemployment Insurance M

Soft IndicatorsMarkit Manufacturing PMI MISM Manufacturing PMI MISM Non-manufacturing PMI MConference Board: Consumer Confidence MUniversity of Michigan: Consumer Sentiment MRichmond Fed Mfg Survey MPhiladelphia Fed Business Outlook MChicago PMI MNFIB: Small Business Optimism Index MEmpire State Manufacturing Survey M

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estimation: settings and priors

I Our methods are Bayesian

I We use conservative priors that shrink the model towards a more parsimoniousspecification without the new features

I This has the appeal that we can let the data speak about to what extent theadditional components are required

More details

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estimation: algorithm

I Model specified at monthly frequency. Observed quarterly growth rates related tounobserved monthly ones using weighted mean (Mariano and Murasawa, 2003)

I Hierarchical implementation of a Gibbs Sampler (Moench, Ng, and Potter, 2013)which iterates between

I Small DFM on the outlier adjusted dataI Univariate measurement equations

⇒ large computational gains from parallelization

I SVs are sampled following Kim et al. (1998), the Student-t component is sampledfollowing Jacquier et al. (2004)

I Vectorized implementation of the Kalman filter

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real-time out-of-sample evaluation

details of data base construction

I We construct a real-time data base for the US from ALFRED

I For each vintage, sample start is Jan 1960, appending missing observations to anyseries which starts after that date

I Use appropriate deflators for nominal-only vintages

I Splice data for series with methodological changes

I Apply seasonal adjustment in real time for survey data

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implementation of the exercise

I The model is fully re-estimated every time new data is released/revised

I The exercise starts in Jan 2000 and ends in Dec 2019: on average there is a datarelease on 15 different dates every month ⇒ 3600 vintages of data

I Thanks to efficient implementation, it takes just 20 min Gibbs sampler on a singlecomputer (we use 8,000 iterations/draws)

I However this would mean almost 2 months of time to run the evaluation

I Made feasible by using Amazon Web Services cloud computing platform

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selected evaluation results

evaluation resultsforecasts vs. actual over time (us)

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019-10

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Actual Basic DFM Full Model

I Long run trend eliminates the upward bias in GDP forecasts after the crisisI Lead-lag dynamics improve the mode’s performance around turning points

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gdp point forecastsrmse across horizons

NowcastForecast Backcast

-180 -150 -120 -90 -60 -30 0 30Forecast Horizon (days after end of reference quarter)

1.4

1.6

1.8

2

2.2

2.4

2.6

Roo

t Mea

n Sq

uare

Err

or

Basic DFM Full Model

I Point forecasting performance significantly improved across horizons Results for MAE

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gdp density forecastslog score across horizons

NowcastForecast Backcast

-180 -150 -120 -90 -60 -30 0 30Forecast Horizon (days after end of reference quarter)

-2.5

-2.4

-2.3

-2.2

-2.1

-2

-1.9

-1.8

-1.7

Log

Sco

re

Basic DFM Full Model

I Density forecasting performance significantly improved across horizons Results for CRPS

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gdp point forecastsrmse through time

20012002200320042005200620072008200920102011201220132014201520162017201820191

1.2

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1.6

1.8

2

2.2

2.4

2.6

2.8

Basic DFM Full Model

I Proposed model is favored early on in the evaluation period Results for MAE

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gdp density forecastslog score through time

2001200220032004200520062007200820092010201120122013201420152016201720182019-2.5

-2.4

-2.3

-2.2

-2.1

-2

-1.9

-1.8

-1.7

Basic DFM Full Model

I Proposed model is favored early on in the evaluation period Results for CRPS

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contribution of different model components

RMSE across horizons[p-value against AR(1)] AR(1) Basic DFM Trend & SV Lead/lag Fat tails-180 days 2.4 2.5 2.4 2.3 2.3

[0.80] [0.63] [0.37] [0.36]-90 days (start reference quarter) 2.3 2.6 2.4 2.2 2.1

[0.75] [0.59] [0.30] [0.28]-60 days 2.1 2.2 2.0 1.9 1.9

[0.58] [0.39] [0.25] [0.23]-30 days 2.1 2.1 1.9 1.7 1.7

[0.48] [0.29] [0.12] [0.10]0 days (end reference quarter) 2.1 2.0 1.8 1.5 1.5

[0.33] [0.18] [0.05] [0.04]+30 days (first release) 2.1 1.9 1.8 1.5 1.5

[0.28] [0.13] [0.04] [0.03]

Table for Log Score

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the great lockdown

nowcasting during the great lockdown

I Covid-19 pandemic caused recession of unprecedented magnitude

I Many formal models simply produce nonsensical results

I We have been exploring two avenues

1. How novel model components help tracking activity in 2020

I In particular heterogeneous dynamics and fat tails

2. How to incorporate ‘alternative data’ in the DFM machinery

I Novel data sources with very small history have become available

I Both avenues are work in progress

I A few pictures to on no 1. to follow ...

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nowcasts as of 30 march 2020

I SV captures massive increase in uncertainty

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fat tailed observations

I Model correctly captured rebound in retail sales based on history of similar outliers

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nowcasts as of june 2020basic dfm (left) vs. full model (right)

2008 2010 2012 2014 2016 2018 2020-60

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2008 2010 2012 2014 2016 2018 2020-20

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I Persistent decline or more V-shaped recovery?

I Heterogeneous dynamics capture rebound in GDP despite persistent decline inother series (in particular surveys)

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conclusion

conclusion

I We propose a bayesian DFM, which explicitly incorporates:

1. Low-frequency variation in the mean and variance

2. Heterogeneous responses to common shocks

3. Outlier observations and fat tails

I We provide a thorough evaluation of the novel model features for the nowcastingprocess and demonstrate how they improve point and density nowcasts in real time

I Assessment of US activity in 2020 is in progress

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references

Antolin-Diaz, J., T. Drechsel, and I. Petrella (2017): “Tracking the slowdown in long-run GDPgrowth,” Review of Economics and Statistics, 99.

Banbura, M., D. Giannone, and L. Reichlin (2010): “Nowcasting,” CEPR Discussion Papers 7883,C.E.P.R. Discussion Papers.

Banbura, M. and M. Modugno (2014): “Maximum Likelihood Estimation of Factor Models on Datasetswith Arbitrary Pattern of Missing Data,” Journal of Applied Econometrics, 29, 133–160.

Camacho, M. and G. Perez-Quiros (2010): “Introducing the euro-sting: Short-term indicator of euro areagrowth,” Journal of Applied Econometrics, 25, 663–694.

D’Agostino, A., D. Giannone, M. Lenza, and M. Modugno (2015): “Nowcasting Business Cycles: ABayesian Approach to Dynamic Heterogeneous Factor Models,” Tech. rep.

Giannone, D., L. Reichlin, and D. Small (2008): “Nowcasting: The real-time informational content ofmacroeconomic data,” Journal of Monetary Economics, 55, 665–676.

Jurado, K., S. C. Ludvigson, and S. Ng (2014): “Measuring Uncertainty,” American Economic Review,Forthcoming.

McConnell, M. M. and G. Perez-Quiros (2000): “Output Fluctuations in the United States: What HasChanged since the Early 1980’s?” American Economic Review, 90, 1464–1476.

Moench, E., S. Ng, and S. Potter (2013): “Dynamic hierarchical factor models,” Review of Economics andStatistics, 95, 1811–1817.

appendix slides

the model: time-varying parameter processes

I Model’s time-varying parameters are specified to follow driftless random walks:

aj,t = aj,t−1 + vaj,t , vaj,tiid∼ N(0, ω2

a,j) j = 1, . . . , r

log σεt = log σεt−1 + vε,t, vε,tiid∼ N(0, ω2

ε)

log σηi,t = log σηi,t−1 + vηi,t , vηi,tiid∼ N(0, ω2

η,i) i = 1, . . . , n

Back to main slides

news decompositions

Banbura and Modugno (2014) show in a Gaussian model that the impact of a newrelease on the nowcasts can be written as a linear function of the news:

E(yk,tk|Ω2)− E(yk,tk|Ω1) = wj (yj,tj − E(yj,tj |Ω))

wj =ΛkE

((ftk − ftk|Ω)(ftj − ftjΩ)

)Λ′j

ΛjE(

(ftj − ftj |Ω)(ftj − ftjΩ))

Λ′j + σ2ηj,tj

Back to main slides

news decompositions

We show that with the Student-t distribution the weights are no longer linear, butdepend on the value of the forecast error itself:

E(yk,tk|Ω2)− E(yk,tk|Ω1) = wj(yj,tj) (yj,tj − E(yj,tj |Ω))

wj(yj,tj) =ΛkE

((ftk−ftk|Ω)(ftj−ftjΩ)

)Λ′j

ΛjE(

(ftj−ftj |Ω)(ftj−ftjΩ))

Λ′j+σ2ηj,tj

δj,tj

δj,tj = (((yj,tj − E(yj,tj |Ω))2/σ2ηj,tj + vo,j)/(vo,i + 1)

Large errors are discounted as outlier observations containing less information.

Back to main slides

influence functions for all variables

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0.5INDPRO

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Back to main slides

estimationdetails on model settings and priors (1/2)

I Number of lags in polynomials Λ(L), φ(L), and ρ(L): Set to m = 1, p = 2, andq = 2

I For Λ(L), prior mean is set to 1 for first lag, and zero in subsequent lags, whichshrinks factor to being cross-sectional average, see D’Agostino et al. (2015)

I For φ(L) prior mean is set to 0.9 for first lag, and zero in subsequent lags, whichreflects a belief that factor captures highly persistent but stationary business cycleprocess

I For AR coefficients of idiosyncratic components, ρi(L) prior is set to zero for alllags, shrinking model towards no serial correlation in ui,t

Back to main

estimationdetails on model settings and priors (2/2)

I Variance on priors set to τh2 , where τ governs tightness of prior, and h ranges over

lag numbers 1 : p, 1 : q, 1 : m+ 1.

I Following D’Agostino et al. (2015), we set τ = 0.2, a value which is standard inthe Bayesian VAR literature.

I Shrink ω2a, ω2

ε and ω2η,i towards zero (standard DFM). For ω2

a set IG prior with one

d.f. and scale 1e-3. For ω2ε and ω2

η,i set IG prior with one d.f. and scale 1e-4 (seePrimiceri, 2005)

Back to main

mae instead of rmse (across horizon)

NowcastForecast Backcast

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1.8

2

2.2

Mea

n A

bsol

ute

Err

or

Basic DFM Full Model

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crps instead of log score (across horizon)

NowcastForecast Backcast

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Con

tinuo

us R

ank

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abili

ty S

core

Basic DFM Full Model

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mae instead of rmse (through time)

20012002200320042005200620072008200920102011201220132014201520162017201820190.8

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1.1

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Basic DFM Full Model

Back to main

crps instead of log score (through time)

20012002200320042005200620072008200920102011201220132014201520162017201820190.7

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Basic DFM Full Model

Back to main

contribution of different model components

Logscore across horizons[p-value against AR(1)] AR(1) Basic DFM Trend & SV Lead/lag Fat tails-180 days −2.42 −2.40 −2.16 −2.16 −2.16

[0.36] [0.00] [0.00] [0.00]-90 days (start reference quarter) −2.40 −2.37 −2.21 −2.10 −2.09

[0.33] [0.03] [0.00] [0.00]-60 days −2.34 −2.24 −2.05 −1.99 −1.98

[0.09] [0.00] [0.00] [0.00]-30 days −2.34 −2.18 −2.00 −1.90 −1.88

[0.02] [0.00] [0.00] [0.00]0 days (end reference quarter) −2.34 −2.14 −1.98 −1.83 −1.81

[0.00] [0.00] [0.00] [0.00]+30 days (first release) −2.35 −2.13 −1.96 −1.81 −1.80

[0.00] [0.00] [0.00] [0.00]

Back to main

dynamic vs. static factorsan alternative benchmark?

I A dynamic factor model (with 1 lag and 1 factor) can be always rewritten as astatic factor model (with 2 static factors, with a rank restriction on the varianceof the transition equation).

I So the question is: How close to rank deficient is the static factor representation?

I To answer this question we look at the relative size of the eigenvalues of thevariance in the transition equation of the (unrestricted) static factorrepresentation of the model (a) using real data and (b) from data simulated froma (s=1, r=1) dynamic factor model (with parameters chosen so as to be in linewith the estimation of our model).

dynamic vs. static factorsan alternative benchmark?

I Two static factors: [F 1t

F 2t

]=

[φ11 φ12

φ21 φ22

] [F 1t−1

F 2t−1

]+

[ε1,tε2,t

],

I One Dynamic factor: [ftft−1

]=

[φ11 φ12

1 0

] [ft−1

ft−2

]+

[10

]ηt,

I The latter specification implies 2 static factors representation, with a reduced rankcovariance matrix restriction on the shocks εt

I A static factor model can always be rotated into a dynamic factor provided thatthe rank restriction is satisfied.

dynamic vs. static factorsan alternative benchmark?

I Two static factors: [F 1t

F 2t

]=

[φ11 φ12

φ21 φ22

] [F 1t−1

F 2t−1

]+

[ε1,tε2,t

],

I One Dynamic factor: [ftft−1

]=

[φ11 φ12

1 0

] [ft−1

ft−2

]+

[10

]ηt,

I The latter specification implies 2 static factors representation, with a reduced rankcovariance matrix restriction on the shocks εt

I A static factor model can always be rotated into a dynamic factor provided thatthe rank restriction is satisfied.

which specification is preferred by the data?evidence that single dynamic factor is preferred

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Share of the Maximum Eigenvalue

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