Tes ing o Su icien In o ma ion in S uc u al VARs∗
Ma io Fo ni†
Uni e si `a di Modena e Reggio Emilia
CEPR and RECen
Luca Gambe i‡
Uni e si a Au onoma de Ba celona
Feb ua y 22, 2011
Abs ac
We de i e necessa y and su icien condi ions unde which a se o a iables is in o ma-
ionally su icien , i.e. i con ains enough in o ma ion o es ima e he s uc u al shocks
wi h a VAR model. Based on such condi ions, we sugges a p ocedu e o es o in-
o ma ional su iciency. Mo eo e , we show how o amend he VAR i in o ma ional
su iciency is ejec ed. We apply ou p ocedu e o a VAR including TFP, unemploymen
and pe -capi a hou s wo ked. We ind ha he h ee a iables a e no in o ma ionally
su icien . When adding missing in o ma ion, he e ec s o echnology shocks change
d ama ically.
JEL classi ica ion: C32, E32, E62.
Keywo ds: S uc u al VAR, non- undamen alness, in o ma ion, FAVAR models, ech-
nology shocks.
∗We hank Fabio Cano a, Ma co Lippi and Luca Sala o help ul discussion.
†Financial suppo om Fondazione Cassa di Rispa mio di Modena is g a e ully acknowledged.
Con ac : Dipa imen o di Economia Poli ica, ia Be enga io 51, 41100, Modena, I aly. Tel. +39
0592056851; e-mail: [email p o ec ed]
‡The inancial suppo om he Spanish Minis y o Science and Inno a ion h ough g an ECO2009-
09847 and he Ba celona G adua e School Resea ch Ne wo k is g a e ully acknowledged. Con ac :
O ice B3.1130 Depa amen d’Economia i His o ia Economica, Edi ici B, Uni e si a Au onoma de
Ba celona, Bella e a 08193, Ba celona, Spain. Tel (+34) 935814569; e-mail: luca.gamb[email p o ec ed]
1
1 In oduc ion
Since Sims (1980)’s seminal pape , S uc u al Vec o Au o eg ession (SVAR) models
ha e become ex emely popula o s uc u al and policy analysis. The idea behind
hese models is ha s uc u al economic shocks can be ound as linea combina ions
o he esiduals o he linea p ojec ion o a ec o o a iables on o hei pas alues,
i.e. a e inno a ions wi h espec o he econome ician’s in o ma ion se . The e o e,
an ob ious equi emen o he analysis o be meaning ul is ha such an in o ma ion
se con eys all o he ele an in o ma ion. This is implici ly assumed in any VAR
applica ion.
Bu is his assump ion always sensible? Un o una ely he answe is no. The basic
p oblem is ha , while agen s ypically ha e access o ich in o ma ion, VAR echniques
allow o handle a limi ed numbe o a iables. I he econome ician’s in o ma ion
se does no span ha o he agen s he s uc u al shocks a e non- undamen al and
canno be ob ained om a VAR (Hansen and Sa gen , 1991, Lippi and Reichlin, 1993,
1994, Cha i, Kehoe and Mcg a an, 2008). Fe nandez-Villa e de e al. (2007) de i es
a simple condi ion o check whe he he shocks o a DSGE model a e eco e able om
a VAR and shows heo e ical cases in which VAR echniques ail. Fiscal o esigh and
news shocks a e wo examples, see Leepe , Walke and Yang, (2008) and Yang (2008).
Fo ni and Gambe i (2010), Fo ni and Gambe i and Sala (2010) and Gambe i (2010).
A now he e a e no es ing p ocedu es o e i y whe he a speci ic VAR su e s
om his in o ma ional p oblem. The con ibu ion o his pape is wo old. Fi s
we heo e ically cha ac e ize necessa y and su icien condi ions unde which a se o
a iables is in o ma ionally su icien in a VAR, i.e. i con ains enough in o ma ion o
es ima e he s uc u al shocks. Second, we p opose a es ing p ocedu e based on such
condi ions. When in o ma ional su iciency is ejec ed we p opose a s a egy o amend
he VAR o ill he in o ma ional gap.
We de i e wo main esul s unde he gene al assump ion he economy admi s
a s a e space ep esen a ion. Fi s , we p o ide a necessa y and su icien condi ion
o in o ma ional su iciency. The condi ion equi es ha he e a e no s a e a iables
ha G ange cause he a iables included in he VAR.1The in ui ion is ha he s a e
1The p ecise ela ion be ween ou su icien in o ma ion condi ion and Condi ion 1 o Villa e de
e al. (2007) is explained in Sec ion 2.3. An essen ial di e ence is ha ou condi ion can be es ed
wi hou eso ing o any pa icula economic model.
2
a iables con ain all o he ele an in o ma ion; he e o e, i hey do no help o p edic
a ec o , such ec o mus con ain he same in o ma ion. Second, we show ha , e en i
he VAR is no in o ma ional su icien , s ill a single shock o in e es can be co ec ly
es ima ed. In o de o his o be he case, he shock mus be o hogonal o he pas
o he s a e a iables.
Such condi ions can be es ed empi ically. Based on he o me esul , we sugges
he ollowing es ing p ocedu e. Fi s , we es ima e he space spanned by he s a e
a iables o he economy by using he p incipal componen s o a la ge da ase , con ain-
ing all a ailable mac oeconomic in o ma ion. Second, we es whe he he es ima ed
p incipal componen s G ange cause he a iables included in he VAR. The a iables
a e in o ma ionally su icien i and only i he null hypo hesis o no G ange causali y
is no ejec ed.
The la e esul can be used o e i y whe he , e en i he VAR is no in o ma ion-
ally su icien , a pa icula shock o in e es can s ill be es ima ed. The es wo ks as
ollows. Fi s , we iden i y and es ima e he s uc u al shock. Second, we pe o m a es
o o hogonali y be ween he es ima ed shock and he lags o he p incipal componen s.
I he null o o hogonali y is ejec ed, hen he shock ob ained om he VAR canno
be s uc u al.
I a se o a iables is no su icien , we sugges o es ima e ei he a s uc u al ac o
model like Fo ni e al. (2009) o a VAR augmen ed by by he p incipal componen s,
i.e. he FAVAR model p oposed by Be nanke Boi in and Eliasz (2005), whe e numbe
o p incipal componen s is de e mined by applying a sequence o su icien in o ma ion
es s.
As an applica ion we s udy echnology shocks in he US. We es whe he a small-
scale VAR model, such as hose ypically used o s udy he e ec s o echnology shocks,
is in o ma ionally su icien . Speci ically, we use a VAR wi h o al ac o p oduc i i y,
he unemploymen a e and pe -capi a hou s wo ked. We ind ha hese h ee a iables
a e G ange caused by he i s wo p incipal componen s o a la ge da ase o US mac -
coeconomic a iables. The e o e we add such p incipal componen s o he VAR and
show ha he emaining p incipal componen s do no G ange cause he augmen ed
VAR, meaning ha he in o ma ion con eyed in he augmen ed VAR is su icien . Fi-
nally, we iden i y he echnology shock as he only one d i ing o al ac o p oduc i i y
in he long un, in bo h he o iginal and he augmen ed VAR. Di e ences in he esul s
3
in he wo models a e d ama ic. While in he o iginal VAR echnology shocks inc ease
hou s and educe unemploymen , in he augmen ed VAR esul s a e e e sed: hou s
educe and unemploymen inc eases. In he augmen ed model, in es men and GDP
eac e y sluggishly o he shock, p ices all and he eal wage inc eases. O e all he
esul a e ha d o econcile wi h he iew ha echnology shocks a e an impo an
sou ce o business cycle luc ua ions.
The emainde o he pape is o ganized as ollows. Sec ion 2 p esen s heo e ical
esul s, as well as ou p oposed es ing p ocedu es. Sec ion 3 discusses he applica ion.
Sec ion 4 concludes.
2 Theo y
2.1 The mac oeconomy
Le us s a om he ollowing MA ep esen a ion o he mac oeconomy.
Assump ion 1 (MA ep esen a ion). The n-dimensional ec o x o s a iona y mac oe-
conomic ime se ies sa is ies
x =F(L)u ,(1)
whe e u is a q-dimensional, o hono mal whi e noise ec o o s uc u al mac oeco-
nomic shocks and F(L)is an n×qma ix o impulse esponse unc ions, i.e. squa e-
summable linea il e s in he non-nega i e powe s o he lag ope a o L, such ha
ank (F(z)) = q o some complex numbe z.
Rep esen a ion (1) can be hough o as he ep esen a ion o a mac oeconomic
equilib ium. Conside o ins ance he s a e-space ep esen a ion s udied in Villa e de,
Rubio-Rami ez, Sa gen and Wa son (2007), i.e.
s =As −1+Bu (2)
x =Cs −1+Du (3)
whe e s is an -dimensional ec o o s a iona y “s a e” a iables, q≤ ≤n,A,B,
Cand Da e con o mable ma ices o pa ame e s, Bhas a le in e se B−1such ha
B−1B=Iq. P e-mul iplying (2) by B−1we ge u =B−1(I−AL)s . Subs i u ing his
in o (3) and ea anging gi es
x =DB−1+ (C−DB−1A)Ls .(4)
4
S a iona i y o s ensu es in e ibili y o (2), so ha s = (I−AL)−1Bu . Combining
his wi h (4) we ge he MA ep esen a ion
x =DB−1+ (C−DB−1A)L(I−AL)−1Bu ,(5)
which is a special case o (1).
The assump ion on he ank (F(L)) ensu es ha he ep esen a ion is no edundan
in he sense ha he e is ano he ep esen a ion wi h a smalle numbe o shocks.
2.2 Su icien in o ma ion
The SVAR econome ician obse es x , possibly wi h e o . P ecisely,
Assump ion 2. (Econome ician’s in o ma ion se ) The econome ician in o ma ion
se X∗
is gi en by he closed linea space spanned by p esen and pas alues o he
a iables in x∗
(in symbols X∗
= span(x∗
1 , . . . , x∗
n )), whe e
x∗
=x +ξ =F(L)u +ξ ,(6)
ξ being a (possibly ze o) ec o o measu emen e o s, o hogonal o uj −k,j=
1, . . . , q, any k, and ξ −k,k > 0.
In p ac ice he numbe o obse able a iables nis e y la ge, so ha he econome-
ician needs o educe i in o de o es ima e a VAR. The VAR in o ma ion se is hen
spanned by an s-dimensional sub- ec o o x∗
, o mo e, gene ally, an s-dimensional
linea combina ion o x∗
, say z∗
=W x∗
(wi h sno necessa ily equal o q).
Assump ion 3 (VAR in o ma ion se ). The in o ma ion se o he VAR is Z∗
=
span(z∗
1 −k, . . . , z∗
s −k, k ≥0),z∗
=W x∗
,Wbeing s×n.
Now, conside he heo e ical p ojec ion equa ion o z∗
on i s pas his o y, i.e.
z∗
=P(z∗
|Z∗
−1) +  .(7)
The SVAR me hodology consis s in (a) es ima ing a VAR o ge  ; (b) a emp ing o
ge he s uc u al shocks as linea combina ions o he es ima ed en ies o  . Hence
a key p ope y o z∗
and he ela ed in o ma ion se , is ha he en ies o  span he
s uc u al shocks, i.e. he in o ma ion in he his o y o z∗
is su icien o es ima e he
shocks. We call such p ope y “su icien in o ma ion”.
5

De ini ion 1 (Su icien in o ma ion). We say ha z∗
and he ela ed in o ma ion se
Z∗
con ain “su icien in o ma ion” i and only i he e exis a ma ix Msuch ha
u =M .
Le us s ess ha su iciency, de ined in his way, is ela ed only o he a iables in
z∗
and has no hing o do wi h he choice o a p ope iden i ica ion scheme. The co ec
iden i ica ion o Mis a u he p oblem, which does make sense only i su iciency holds
ue.
2.3 Su icien in o ma ion and undamen alness
F om (6) and he de ini ion o z∗
we ge
z∗
=W F (L)u +W ξ =z +W ξ .(8)
S uc u alness is ela ed o “ undamen alness” o he MA ep esen a ion in (8).2
Le us i s ecall he concep o undamen alness.
De ini ion 2 (Fundamen alness). We say ha u is undamen al o w =Hx , and
he MA ep esen a ion w =HF (L)u is undamen al, i and only i u ∈ W =
span(w1 −k, . . . , wm −k, k ≥0) (i.e. U = span(u1 −k, . . . , uq −k, k ≥0) = W ).
The ollowing p oposi ion holds:
P oposi ion 1.The in o ma ion in z∗
is su icien i and only i (a) zj ∈ Z∗
o any
jand (b) u is undamen al wi h espec o z .
P oo . I (a) and (b) hold ue, hen u ∈ Z∗
=E = span(1 −k, . . . , s −k, k ≥0).
Being o hogonal o E −1,u belongs o span(1 , . . . , s ). On he o he hand, le us
assume ha z∗
is su icien , i.e. u =M . Then (a) holds, because zj ∈ U and
U ⊆ Z∗
. As o (b), le S = span(z1 −k, . . . , zs −k, W ξ −k, k ≥0). Now, uj ∈ S −1),
j= 1, . . . , q, since i belongs o Z∗
and Z∗
⊆ S . Bu uj is o hogonal o ξ −k,k≥0
by Assump ion 2. Hence uj ∈ Z ,j= 1, . . . , q. QED
P oposi ion 1 says ha , o z∗
being su icien , he e mus be a linea ans o ma ion
o z∗
which is ee o measu emen e o s and ha e a undamen al ep esen a ion in he
s uc u al shocks.
2Some impo an e e ences abou undamen alness a e Hansen and Sa gen (1991), Lippi and Re-
ichlin (1993, 1994), Cha i, Kehoe and McG a an (2008), Fe nandez-Villa e de e al. (2007).
6
To conclude his sec ion, le us obse e ha , in he pa icula case o F(L) being a
ma ix o a ional unc ions, undamen alness o u o w , along wi h undamen alness
o he associa ed MA ep esen a ion w =HF (L)u is equi alen o he ollowing
condi ion (see e.g. Rozano , 1967, Ch. 2).
Condi ion R.The ank o HF (z)is q o all zsuch ha |z|<1.
Conside ing equa ion (5) and he case w =x , condi ion R is sa is ied i and only i
Dis in e ible and he eigen alues o A−BD−1Ca e s ic ly less han one in modulus,
which is Condi ion 1 o Villa e de e al. (2007).
2.4 Tes able implica ions o su icien in o ma ion
P oposi ion 2.I x∗
G ange causes z∗
, hen z∗
is no in o ma ionally su icien .
P oo . Assume ha z∗
is su icien , so ha u =M . Then uj −k∈ Z∗
−1 o k > 0. I
ollows ha P(z∗
|Z∗
−1) = W(F1u −1+F2u −2+. . .) and  =W F0u +W ξ . Hence
 is o hogonal o bo h u −k,k > 0, and, by se ial unco ela ion o ξ (Assump ion 2),
ξ −k,k > 0. The e o e  ⊥x∗
−k,k > 0 and x∗
does no G ange cause z∗
. QED
The in ui ion is ha , i a se o a iables is su icien , han i con ains all o he
exis ing in o ma ion, so ha no o he a iable o se o a iables can G ange cause i .
P oposi ion 2 can be o some use ulness in p ac ice.3In pa icula , i he econo-
me ician belie es ha a gi en a iable in x∗
, say , con eys ele an in o ma ion, he
can check whe he G ange causes z∗
as a ec o . I G ange causes z∗
, he VAR
wi h z∗
is misspeci ied. Obse e ha , acco ding o P oposi ion 2, iden i ica ion is no
equi ed o pe o m he es , consis en ly wi h he ac ha su icien in o ma ion, as
obse ed abo e, is independen o he iden i ica ion scheme.
On he o he hand, P oposi ion 2 has an impo an limi a ion in ha , being only a
necessa y condi ion, i can be used o ejec su iciency bu no o alida e i . Clea ly,
es ing all o he a iables in x∗
would be close o a alida ion, bu un o una ely his
is no easible, since in p ac ice x∗
is o high dimension. On he one hand, we canno
use all o he a iables simul aneously; on he o he hand, es ing each one o hem
sepa a ely would yield, wi h e y high p obabili y, o ejec su iciency e en i z∗
is
in o ma ionally su icien , owing o Type I e o .
3P oposi ion 2 is de i ed (wi hin somewha di e en se ings) in Fo ni and Reichlin (1996) and
Giannone and Reichlin (2006).
7
We can p o ide a su icien condi ion by assuming he s a e space ep esen a ion
abo e, i.e. by eplacing Assump ion 1 wi h he mo e es ic i e Assump ion 10:
Assump ion 10(ABCD ep esen a ion). The ec o x o mac oeconomic ime se ies
sa is ies equa ions (2) and (3).
I is easily seen om equa ions (6) and (4) ha x∗
ollows he s a ic ac o model
x∗
=G +ξ ,(9)
whe e G=DB−1C−DB−1Aand =s0
s0
−10.
In addi ion, we need o assume ha he his o y o he s uc u al shocks helps
p edic ing z∗
, o , equi alen ly, ha z∗
is au oco ela ed o some ex en (since o he wise
no hing can G ange cause i ).
Assump ion 4 (Au oco ela ion o z∗
). The e exis s a summable sequence {ck}∞
k=1
such ha R=WP∞
k=1 ckFkhas ank q.
The ollowing p oposi ion es ablishes a necessa y and su icien condi ion o in o -
ma ional su iciency.
P oposi ion 3.Le Kbe any non-singula p×pma ix, pbeing he dimension o .
z∗
is in o ma ionally su icien i and only i g =K does no G ange cause z∗
.
P oo . Le us assume ha z∗
is su icien , i.e. u =M . Then  is o hogonal o
u −k,k > 0 and he e o e o g −k,k > 0. Hence P(z∗
|Z∗
−1) = P(z∗
|z∗
j −k, gi −k, j =
1, . . . , s, i = 1, . . . , p, k > 0), so ha g does no G ange cause z∗
. Rega ding he
opposi e implica ion, le us assume ha g does no G ange cause z∗
. We ha e
P(z∗
|Z∗
−1) = P(z∗
|z∗
j −k, gi −k, j = 1, . . . , s, i = 1, . . . , p, k > 0). Bu he la e p o-
jec ion is equal o P(z∗
|uj −k, j = 1, . . . , q, k > 0) = WP∞
k=1 Fku −k=ζ , since ζ
belongs o span(z∗
j −k, gi −k, j = 1, . . . , s, i = 1, . . . , p, k > 0) and z∗
−ζ is o hogo-
nal o such space because o Assump ion 2. On he o he hand, ζ =P(z∗
|Z∗
−1) =
P∞
k=1 Ak −k. P ojec ing bo h sums on span(i −k, ui −k, i = 1, . . . , s, j = 1, . . . , )
we ge W Fku −k=Ak −k o all k, so ha W Fku =Ak o all kand R=
(WP∞
k=1 ckFk)u = (P∞
k=1 Ak) . Assump ion 4 ensu es ha Rhas a le in e se,
so ha u =R−1(P∞
k=1 Ak) . QED
The in ui ion o su iciency is ha , unde Assump ion 1’, he ac o s con ain all o
he in o ma ion a ailable in he sys em; he e o e hey G ange cause e e y p edic able
ec o , unless such ec o con ain he same in o ma ion.
8
P oposi ion 3 is use ul in ha , besides p o iding a su icien condi ion, allows us
o summa ize he signals in he la ge dimensional ec o x in o a ela i ely small
numbe o ac o s ( he en ies o g ). Such ac o s a e unobse able, bu , unde sui able
assump ions, can be consis en ly es ima ed by he p incipal componen s ˆg , as bo h
he numbe o a iables and he numbe o ime obse a ions go o in ini y (S ock and
Wa son, 2002; Fo ni, Giannone, Lippi and Reichlin, 2009).
2.5 Tes ing o su icien in o ma ion
P oposi ion 3 p o ides he heo e ical basis o he ollowing es ing p ocedu e.
1. Take a la ge da a se x∗
cap u ing all o he ele an mac oeconomic in o ma ion.
2. Se a maximum numbe o ac o s Pand compu e he i s Pp incipal componen s
o x∗
.
3. Pe o m G ange causa ion es s o see whe he he i s hp incipal componen s,
h= 1, . . . , P, G ange cause z∗
. I he null o no G ange causali y is ne e
ejec ed, z∗
is in o ma ionally su icien . O he wise, su iciency is ejec ed.
I in o ma ional su iciency is ejec ed, we canno use he VAR o global iden i ica-
ion. Howe e , pa ial iden i ica ion could s ill p o ide co ec esul s, as shown in he
ollowing subsec ion.
2.6 S uc u alness o a single shock
E en i in o ma ional su iciency is ejec ed, z∗
could be su icien o ge a single shock
o in e es , say u1 , o a subse o shocks u1 , . . . , uj ,j < q. This is impo an in ha
o many applica ions he econome ician is in e es ed in iden i ying jus a single shock.
To see his, conside he ollowing example
z∗
1 =u1 +u2 −1
z∗
2 =u1 −u2 −1
In his case z∗
is no su icien o u by P oposi ion 1. In ac , since he de e mi-
nan o he MA il e has a ze o in ze o, he MA ep esen a ions non undamen al by
9
Appendix: Da a
T ans o ma ions: 1=le els, 2= i s di e ences o he o iginal se ies, 4 = logs o he
o iginal se ies, 5= i s di e ences o he logs o he o iginal se ies .
no.se ies T ans . Mnemonic Long Label
1 5 GDPC1 Real G oss Domes ic P oduc , 1 Decimal
2 5 GNPC96 Real G oss Na ional P oduc
3 5 NICUR/GDPDEF Na ional Income/GDPDEF
4 5 DPIC96 Real Disposable Pe sonal Income
5 5 OUTNFB Non a m Business Sec o : Ou pu
6 5 FINSLC1 Real Final Sales o Domes ic P oduc , 1 Decimal
7 5 FPIC1 Real P i a e Fixed In es men , 1 Decimal
8 5 PRFIC1 Real P i a e Residen ial Fixed In es men , 1 Decimal
9 5 PNFIC1 Real P i a e Non esiden ial Fixed In es men , 1 Decimal
10 5 GPDIC1 Real G oss P i a e Domes ic In es men , 1 Decimal
11 5 PCECC96 Real Pe sonal Consump ion Expendi u es
12 5 PCNDGC96 Real Pe sonal Consump ion Expendi u es: Nondu able Goods
13 5 PCDGCC96 Real Pe sonal Consump ion Expendi u es: Du able Goods
14 5 PCESVC96 Real Pe sonal Consump ion Expendi u es: Se ices
15 5 GPSAVE/GDPDEF G oss P i a e Sa ing/GDP De la o
16 5 FGCEC1 Real Fede al Consump ion Expendi u es & G oss In es men , 1 Decimal
17 5 FGEXPND/GDPDEF Fede al Go e nmen : Cu en Expendi u es/ GDP de la o
18 5 FGRECPT/GDPDEF Fede al Go e nmen Cu en Receip s/ GDP de la o
19 2 FGDEF Fede al Real Expend-Real Receip s
20 1 CBIC1 Real Change in P i a e In en o ies, 1 Decimal
21 5 EXPGSC1 Real Expo s o Goods & Se ices, 1 Decimal
22 5 IMPGSC1 Real Impo s o Goods & Se ices, 1 Decimal
23 5 CP/GDPDEF Co po a e P o i s A e Tax/GDP de la o
24 5 NFCPATAX/GDPDEF Non inancial Co po a e Business: P o i s A e Tax/GDP de la o
25 5 CNCF/GDPDEF Co po a e Ne Cash Flow/GDP de la o
26 5 DIVIDEND/GDPDEF Ne Co po a e Di idends/GDP de la o
27 5 HOANBS Non a m Business Sec o : Hou s o All Pe sons
28 5 OPHNFB Non a m Business Sec o : Ou pu Pe Hou o All Pe sons
29 5 UNLPNBS Non a m Business Sec o : Uni Nonlabo Paymen s
30 5 ULCNFB Non a m Business Sec o : Uni Labo Cos
31 5 WASCUR/CPI Compensa ion o Employees: Wages & Sala y Acc uals/CPI
32 1 COMPNFB Non a m Business Sec o : Compensa ion Pe Hou
33 5 COMPRNFB Non a m Business Sec o : Real Compensa ion Pe Hou
34 1 GDPCTPI G oss Domes ic P oduc : Chain- ype P ice Index
35 1 GNPCTPI G oss Na ional P oduc : Chain- ype P ice Index
36 1 GDPDEF G oss Domes ic P oduc : Implici P ice De la o
37 1 GNPDEF G oss Na ional P oduc : Implici P ice De la o
16

no.se ies T ans . Mnemonic Long Label
38 5 INDPRO Indus ial P oduc ion Index
39 5 IPBUSEQ Indus ial P oduc ion: Business Equipmen
40 5 IPCONGD Indus ial P oduc ion: Consume Goods
41 5 IPDCONGD Indus ial P oduc ion: Du able Consume Goods
42 5 IPFINAL Indus ial P oduc ion: Final P oduc s (Ma ke G oup)
43 5 IPMAT Indus ial P oduc ion: Ma e ials
44 5 IPNCONGD Indus ial P oduc ion: Nondu able Consume Goods
45 1 AWHMAN A e age Weekly Hou s: Manu ac u ing
46 1 AWOTMAN A e age Weekly Hou s: O e ime: Manu ac u ing
47 2 CIVPART Ci ilian Pa icipa ion Ra e
48 5 CLF16OV Ci ilian Labo Fo ce
49 5 CE16OV Ci ilian Employmen
50 5 USPRIV All Employees: To al P i a e Indus ies
51 5 USGOOD All Employees: Goods-P oducing Indus ies
52 5 SRVPRD All Employees: Se ice-P o iding Indus ies
53 5 UNEMPLOY Unemployed
54 1 UEMPMEAN A e age (Mean) Du a ion o Unemploymen
55 1 UNRATE Ci ilian Unemploymen Ra e
56 5 HOUST Housing S a s: To al: New P i a ely Owned Housing Uni s S a ed
57 1 FEDFUNDS E ec i e Fede al Funds Ra e
58 1 TB3MS 3-Mon h T easu y Bill: Seconda y Ma ke Ra e
59 1 GS1 1-Yea T easu y Cons an Ma u i y Ra e
60 1 GS10 10-Yea T easu y Cons an Ma u i y Ra e
61 1 AAA Moody’s Seasoned Aaa Co po a e Bond Yield
62 1 BAA Moody’s Seasoned Baa Co po a e Bond Yield
63 1 MPRIME Bank P ime Loan Ra e
64 5 BOGNONBR Non-Bo owed Rese es o Deposi o y Ins i u ions
65 5 TRARR Boa d o Go e no s To al Rese es, Adjus ed o Changes in Rese e
66 5 BOGAMBSL Boa d o Go e no s Mone a y Base, Adjus ed o Changes in Rese e
67 5 M1SL M1 Money S ock
68 5 M2MSL M2 Minus
69 5 M2SL M2 Money S ock
70 5 BUSLOANS Comme cial and Indus ial Loans a All Comme cial Banks
71 5 CONSUMER Consume (Indi idual) Loans a All Comme cial Banks
72 5 LOANINV To al Loans and In es men s a All Comme cial Banks
73 5 REALLN Real Es a e Loans a All Comme cial Banks
74 5 TOTALSL To al Consume C edi Ou s anding
75 5 CPIAUCSL Consume P ice Index Fo All U ban Consume s: All I ems
76 5 CPIULFSL Consume P ice Index o All U ban Consume s: All I ems Less Food
77 5 CPILEGSL Consume P ice Index o All U ban Consume s: All I ems Less Ene gy
17
no.se ies T ans . Mnemonic Long Label
78 5 CPILFESL Consume P ice Index o All U ban Consume s: All I ems Less Food & Ene gy
79 5 CPIENGSL Consume P ice Index o All U ban Consume s: Ene gy
80 5 CPIUFDSL Consume P ice Index o All U ban Consume s: Food
81 5 PPICPE P oduce P ice Index Finished Goods: Capi al Equipmen
82 5 PPICRM P oduce P ice Index: C ude Ma e ials o Fu he P ocessing
83 5 PPIFCG P oduce P ice Index: Finished Consume Goods
84 5 PPIFGS P oduce P ice Index: Finished Goods
85 5 OILPRICE Spo Oil P ice: Wes Texas In e media e
86 5 USSHRPRCF US Dow Jones Indus ials Sha e P ice Index (EP) NADJ
87 5 US500STK US S anda d & Poo ’s Index i 500 Common S ocks
88 5 USI62...F US Sha e P ice Index NADJ
89 5 USNOIDN.D US Manu ac u e s New O de s o Non De ense Capi al Goods (BCI 27)
90 5 USCNORCGD US New O de s o Consume Goods & Ma e ials (BCI 8) CONA
91 1 USNAPMNO US ISM Manu ac u e s Su ey: New O de s Index SADJ
92 5 USVACTOTO US Index o Help Wan ed Ad e ising VOLA
93 5 USCYLEAD US The Con e ence Boa d Leading Economic Indica o s Index SADJ
94 5 USECRIWLH US Economic Cycle Resea ch Ins i u e Weekly Leading Index
95 1 GS10-FEDFUNDS
96 1 GS1-FEDFUNDS
97 1 BAA-FEDFUNDS
98 5 GEXPND/GDPDEF Go e nmen Cu en Expendi u es/ GDP de la o
99 5 GRECPT/GDPDEF Go e nmen Cu en Receip s/ GDP de la o
100 2 GDEF Go e nnen Real Expend-Real Receip s
101 5 GCEC1 Real Go e nmen Consump ion Expendi u es & G oss In es men , 1 Decimal
102 1 Fe nald’s TFP g ow h CU adjus ed
103 1 Fe nald’s TFP g ow h
104 5 DOW JOONES/GDP DEFL
105 5 S&P/GDP DEFL
106 1 Fe nald’s TFP g ow h - In es men
107 1 Fe nald’s TFP g ow h - Consump ion
108 1 Fe nald’s TFP g ow h CU - In es men
109 1 Fe nald’s TFP g ow h CU - Consump ion
110 1 Pe sonal Finance Cu en
111 1 Pe sonal Finance Expec ed
112 1 Business Condi ion 12 Mon hs
113 1 Business Condi ion 5 Yea s
114 1 Buying Condi ions
115 1 Consume ’s sen imen : Cu en Index
116 1 Consume ’s sen imen : Expec ed Index
117 4 Pe -capi a hou s wo ked (HOANBS/Ci ilian Polula ion 16 and o e )
18
Re e ences
[1] Bai, J., and S. Ng (2002). De e mining he numbe o ac o s in app oxima e ac o
models, Econome ica 70, 191-221.
[2] Beaud y, P. and F. Po ie (2006). S ock P ices, News, and Economic Fluc ua ions
Ame ican Economic Re iew, 96(4): 1293-1307.
[3] Be nanke, B. S., J. Boi in and P. Eliasz (2005). Measu ing Mone a y Policy: A
Fac o Augmen ed Au o eg essi e (FAVAR) App oach, The Qua e ly Jou nal o
Economics 120, 387-422.
[4] Blancha d, O. J., and D. Quah (1989). The Dynamic E ec s o Agg ega e Demand
and Supply Dis u bances. Ame ican Economic Re iew, 79(4): 655-73
[5] Cha i, V.V., Kehoe, P.J. and E.R. McG a an (2008). A e s uc u al VARs wi h
long- un es ic ions use ul in de eloping business cycle heo y? Jou nal o Mon-
e a y Economics 55: 1337-1352.
[6] Ch is iano, L., M. Eichenbaum and R. Vig usson (2003), ”Wha Happens A e a
Technology Shock?”, NBER Wo king Pape s 9819.
[7] Fe nandez-Villa e de J., J.F. Rubio-Rami ez, T.J. Sa gen and M.W. Wa son
(2007). ABCs (and Ds) o Unde s anding VARs. Ame ican Economic Re iew,
Ame ican Economic Associa ion, 97(3):1021-1026.
[8] Fo ni, M. and L. Gambe i (2010). Fiscal Fo esigh and he E ec s o Go e nmen
Spending, CEPR DP se ies no. 7840.
[9] Fo ni, Gambe i, L. and L. Sala (2010). News shocks do no d i e he business
cycle. Mimeo
[10] Fo ni, M., D. Giannone, M. Lippi and L. Reichlin (2009). Opening he Black
Box: S uc u al Fac o Models wi h La ge C oss-Sec ions, Econome ic Theo y
25, 1319-1347.
[11] Fo ni M. and L., Reichlin (1996). Dynamic Common Fac o s in La ge C oss-
Sec ions, Empi ical Economics 21, 27-42.
19
[12] Gal´ı, J. (1999), ”Technology, Employmen and he Business Cycle: Do Technol-
ogy Shocks Explain Agg ega e Fluc ua ions?”, Ame ican Economic Re iew, 89(1):
249-271.
[13] Gambe i, L. (2010). Fiscal Policy, Fo esigh and he T ade Balance in he U.S.
UFAE and IAE Wo king Pape s 852.10.
[14] Gelpe , S. and C. C oux (2007), Mul i a ia e ou -o -sample es s o G ange
causali y, Compu a ional S a is ics & Da a Analysis 51, 3319-3329.
[15] Giannone, D., and L. Reichlin (2006). Does In o ma ion Help Reco e ing S uc-
u al Shocks om Pas Obse a ions? Jou nal o he Eu opean Economic Associ-
a ion, 4(2-3), 455465.
[16] Hansen, L.P., and T.J. Sa gen (1991). Two p oblems in in e p e ing ec o au o e-
g essions. In Ra ional Expec a ions Econome ics, L.P. Hansen and T.J. Sa gen ,
eds. Boulde : Wes iew, pp.77-119.
[17] Ha ey, D. I., Leybou ne, S. J. and P. Newbold, (1998) Tes s o Fo ecas Encom-
passing, Jou nal o Business & Economic S a is ics 16, 254-259.
[18] Leepe , E.M., Walke , T.B. and S.S. Yang (2008). Fiscal Fo esigh : Analy ics and
Econome ics, NBER Wo king Pape No. 14028.
[19] Leepe , E.M., Walke , T.B. (2009). In o ma ion Flows and News D i en Business
Cycles, mimeo Indiana Uni e si y
[20] Lippi, M. and L. Reichlin (1993). The Dynamic E ec s o Agg ega e Demand and
Supply Dis u bances: Commen , Ame ican Economic Re iew 83, 644-652.
[21] Lippi, M. and L. Reichlin (1994). VAR analysis, non undamen al ep esen a ion,
Blaschke ma ices, Jou nal o Econome ics 63, 307-325.
[22] Ona ski, A. (2010). De e mining he Numbe o Fac o s om Empi ical Dis ibu-
ion o Eigen alues, The Re iew o Economics and S a is ics 92, 1004-1016.
[23] Rozano , Yu. (1967). S a iona y Random p ocesses. San F ancisco: Holden Day
[24] Schmi -G ohe, S and M., U ibe (2008). Wha ’s News in Business Cycles, NBER
WP 14215
20
[25] Sims, C. A. (1980). Mac oeconomics and Reali y. Econome ica, 48(1), 148.
[26] S ock, J.H. and M.W. Wa son (2002a). Mac oeconomic Fo ecas ing Using Di u-
sion Indexes, Jou nal o Business and Economic S a is ics 20, 147-162.
[27] S ock, J.H. and M.W. Wa son (2002b). Fo ecas ing Using P incipal Componen s
om a La ge Numbe o P edic o s, Jou nal o he Ame ican S a is ical Associa-
ion 97, 1167-1179.
[28] Yang, S.S. (2008). Quan i ying ax e ec s unde policy o esigh . Jou nal o Mon-
e a y Economics, 52(8):1557-1568.
21

Tables
A B
j z∗
w1
w2
z∗
w1
w2
1 0.000 − − 0.005 − −
2−0.480 − − 0.055 −
3 0.405 0.475 −0.113 0.977
4−0.620 0.375 −0.091 0.452
5−0.125 0.250 −0.115 0.581
6−0.105 0.500 −0.142 0.641
7−0.125 0.545 −0.126 0.186
8−0.285 0.785 −0.027 0.197
9−0.125 0.705 − − 0.216
10 −0.085 0.450 − − 0.207
11 −0.050 0.660 − − 0.148
12 − − 0.355 − − 0.186
13 − − 0.395 − − 0.239
14 − − 0.560 − − 0.279
15 − − 0.720 − − 0.337
Table 1: p- alues A: Tes o in o ma ional su iciency B: Tes o s uc u alness o
he echnology shock.
22
Figu es
Figu e 1: Impulse esponse unc ions
23
Figu e 2: Impulse esponse unc ions.
24