Jou nal o Mode n Accoun ing and Audi ing, ISSN 1548-6583
Janua y 2012, Vol. 8, No. 1, 66-76
Business Cycle and he Riskiness o I alian Fi m:
An Empi ical Analysis
Filippo Di Pie o
Uni e si y o Se ille, Spain
Giuseppe Lusignani
Uni e si y o Bologna, I aly
Dolo es Oli e Al onso
Uni e si y o Se ille, Spain
Gi en he impo ance o he ela ionship be ween de aul a es and business cycles, we examine he abili y o
mac oeconomic a iables, explaining changes on he de aul a e o I alian companies. Via a VAR ( ec o
au o eg essi e) model and an analysis o indi idual equa ions, we ind a signi ican in luence o sho - e m in e es
a es, and he g ow h a e o g oss domes ic p oduc (GDP) in he eu o a ea, on he de aul a e o I alian companies
in he pe iod 1985-2004. Using he selec ed mac oeconomic a iables, we build a c edi cycle index (CCI) in o de
o in e he s a e o c edi in he I alian ma ke in u u e pe iods. The cons uc ion o his “c edi cycle index” is
based on a obus econome ic s uc u e wi h a minimum numbe o pa ame e s and a minimum numbe o equi ed
da a.
Keywo ds: c edi isk, business cycle, econome ics, endogenous, es ima ion, o dina y leas squa es (OLS)
In oduc ion
Wha mos in luences he pe o mance o a c edi po olio is he sys ema ic isk (Ja ow, Lando, & Yu,
2000; F ey & McNeil, 2002; Lucas, Klaassen, Sp eij, & S ae mens, 2001; Giesecke, 2003). In a loan po olio,
he le el o isk is p ima ily ep esen ed h ough he c edi cycle, which in u n is cha ac e ized by de e io a ion
o imp o emen .
Despi e his, he mos popula po olio models such as hose o C edi Me ics (Gup on, Finge , & Bha ia,
1997) and C edi Risk (C edi Suisse, 1997) did no ake in o accoun he cycle and i s e ec s on isk. An
excep ion is he C edi Po a olioView (Wilson, 1997a, 1997b) model, which a emp ed o assess he
ela ionship be ween he conduc o business ailu es and he mac oeconomic indica o s o he economic cycle.
In ac , sys ema ic c edi isk ac o s a e usually associa ed wi h mac o-economic condi ions. Empi ical s udies
e ealed ha long- e m ends o he a e age de aul a es o la ge company g oups highly di e si ied be ween
each o he , ela i e o a gi en coun y a e highly ola ile and ha e cyclical ac o s.
I was ecognized, indeed, ha en i onmen al ac o s may cause a co ela ion be ween he ac ual de aul
a es o a se o companies (e.g., Asamow & Edwa ds, 1995; Wilson, 1997a, 1997b). This is e iden bo h om
heo e ical models (Williamson, 1987; Kiyo aki & Moo e, 1997; Be nanke, Ge le , & Gilch is , 1999; Kwa k,
2002) on he eal business cycle, ei he by empi ical e idence (Nickell, Pe audin, & Va o o, 2000; Bangia,
Diebold, K onimus, Schagen, & Schue mann, 2002; Ka a has, 2001; Ma cucci & Quaglia ello, 2005).
The gene al conclusion o hese models is ha he p obabili y o de aul ends o be highe in imes o
Filippo Di Pie o, assis an p o esso , Depa men o Financial Economics and Ope a ions Managemen , Uni e si y o Se ille.
Giuseppe Lusignani, p o esso , Depa men o Economics, Uni e si y o Bologna.
Dolo es Oli e Al onso, p o esso , Depa men o Financial Economics and Ope a ions Managemen , Uni e si y o Se ille.
DAVID PUBLISHING
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BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
67
economic down u n. Hence, he e is a gene al accep ance ha he s a e o he economy o a coun y has a di ec
impac on he obse ed a e o insol ency.
In his wo k, we analyze he ela ionship be ween he de aul a e and he mac oeconomic a iable,
examining how mac oeconomic a iables a ec he mo emen s in he de aul a es o I alian companies. Via a
VAR model and an analysis o indi idual equa ions, we ind a signi ican in luence o sho - e m in e es a es,
and he g ow h a e o he GDP in he eu o a ea on he de aul a e o I alian companies in pe iod 1985 o 2004.
Using he selec ed mac oeconomic a iables, we build a c edi cycle index (CCI) in o de o in e he s a e o
c edi in he I alian ma ke in u u e pe iods. The pape is o ganized as ollows.
In he second sec ion, he di icul y o good co ela ion es ima ion be ween mac oeconomic a iables and
de aul a es is explained. In he hi d sec ion, a li e a u e e iew o his i em is made. In he ou h sec ion, he
da a used o his wo k a e p esen ed. The empi ical model and he esul s a e p esen ed in sec ion i e. The
esul s a e back es ed in he six h sec ion. And he las sec ion is he conclusions o he pape .
The Di icul y o a Good Co ela ion Es ima ion
The esul s ob ained om he es ima ed co ela ion be ween mac oeconomic a iables and de aul a es a e
alid only i he s a is ical ime se ies o de aul a es o loans a e su icien ly long and su icien ly nume ous
g oups. This, un o una ely, is no equen ly ound in banks.
One o he solu ions which can be p oposed is o pe o m an analysis o he co ela ions no on he bank’s
in e nal da a, bu on e y la ge da abases, such as loans and c edi s o he whole sys em. Then, once we ge he
ma ix o a iances and co a iance, apply his o he bank’s po olio o assess he iskiness1.
The se ies ha a e a ailable o banks a e limi ed, pa ly because he na u e o non-sho - e m c edi isks
p e en daily o mon hly obse a ions, being ha ing conside ed o leng hen he ho izon o his o ical analysis
necessa ily includes dis o ions due o s uc u al modi ica ions o long- e m economies o p oduc ion and
consump ion. Ins ead, he analysis o co ela ions needs a high abundance o da a o dis inguish “s uc u al
co ela ions”, ela ed o s ong phenomena, om he “ empo a y co ela ions”, alid only a ce ain pe iods so,
in addi ion o he p oblem o being able o es ima e he co ela ion be ween he losses o loans, i is impo an o
be able o alida e he hypo hesis ha he co ela ion be ween loans ends o emain s able o e ime.
The iden i ica ion o mac oeconomic a iables ha p oduce signi ican ola ili y in de aul a es o he
economic cycle is impo an , because i can be used o condi ion he expec ed de aul a es and he ma ix
mig a ion o he s a e o he economy. Then, mac oeconomic a iables can be inse ed in o ecas ing in e nal
a ing sys ems.
Li e a u e Re iew
The main ques ion acing Nickell e al. (2000)2 in hei wo k is: gi en ha he ansi ion p obabili ies o
he a ings a y o di e en bo owe s a di e en imes o he economic cycle, wha a e he causes o hese
a ia ions?
1 A bank acco ding o Basel II, in ac , may use bo h in e nal da a and ex e nal da a, bu he popula ion o exposu es ep esen ed
in he da a, should be he same o a leas be compa able wi h ha o he ac ual exposu e o he bank; he bank mus also
demons a e ha he economic and ma ke condi ions ha unde lie he da a a e consis en wi h he cu en si ua ion and
pe spec i e.
2 Helwege and Klieman (1996); McDonald and Van de Guch (1999). The esul s o hese wo s udies ha e benn con i med and
ex ended by Nickell e al. (2000).
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
68
The issue is aced calcula ing he non-condi ional ma ix and he condi ional ma ix o ansi ion a ings in a
s anda dized manne , and h ough a model “p obi ” logical in which he ansi ions a e d i en by ealiza ions o a
la en a iable ha inco po a es a se ies o “dummies” by ypes o bo owe s and he s a us o he business cycle.
The app oach aken by Nickell e al. (2000) is o es ima e he pa ame e s by aking he en i e uni e se o
e en s o mig a ion as a single sample, and conside ing he a iables sec o /a ea/s a e o he business cycle as
dummy a iables ( he business cycle is conside ed by simply di iding he yea in o “ a o able”, “no mal” and
“un a o able”)3. The conclusions o his s udy con i med wha has p e iously been assumed. In ac , he
au ho s ound ha he equency o downg ade and de aul o coun e pa ies o coun e pa s assigned o a ing
classes wi h a high isk inc eases in he ea ly s ages o economic down u n, i is less p edic able and mo e
con adic o y han a second esul ob ained om hei model, namely, o coun e pa s wi h be e a ing he
impac o nega i e phases o he cycle seems o inc ease no only he p obabili y o “downg ade” bu also
“upg ade”, hus a ec ing he ola ili y mo e han he di ec ion o he a ing p ocess mig a ion.
Bikke and Me zemake s (2005), using a panel o 26 O ganiza ion o Economic Co-ope a ion and
De elopmen [OECD] coun ies o e he pe iod 1979-1999, ound ha he ac i i y o he bank loan is highly
dependen on he demand o money measu ed by cyclic a iables, such as he a e o eal g ow h, in la ion,
unemploymen and eal supply money.
Hackba h, Miao, and Mo ellec (2006) de eloped a amewo k o analyzing he impac o
mac oeconomic condi ions on c edi isk and he choice o he dynamic s uc u e o capi al chosen by he
company, demons a ing ha his simple obse a ion has a wide ange o implica ions o business.
Close o he I alian case we wo k on: Ma o a, Pede zoli, and To icelli (2005), applying a model
de eloped by Pede zoli and To icelli using he de aul da a o I alian i ms p o ided by he Bank o I aly.
The basic idea o he model is o use a measu e o isk ha g ows jus be o e a ecession on he c edi
ho izon, and ice e sa dec eases jus be o e a pe iod o expansion. The pu pose o he p oposed model is o
include a o ecas o he economic cycle in he measu es o c edi isk.
O he empi ical s udies inco po a e mac oeconomic a iables in o ecas ing models o c edi isk, such as
he models p oposed by H. Pla and M. Pla (1991) ha a emp ed o isola e he dynamics o sec o ial indices
h ough he use o he “ ela i e” alue calcula ed by ela ing he ob ained alue by he company and ha
obse ed by he sec o o membe ship.
Lennox (1999) used mac oeconomic a iables o imp o e he pe o mance o he models o c edi isk.
The esul s look encou aging, bo h in e ms o e iciency a ing, and o he possibili y o es ima ing he e ec
o a mac oeconomic shock on he p obabili y o company de aul .
A wo k o conside able impo ance o he analysis ca ied ou he e, and which d aws on he empi ical
analysis, is ha done by Zazza a and Ro ondi (2005a). In hei wo k, he abili y o mac oeconomic a iables o
explain he de aul a es o i ms in he I alian banking ma ke is examined. Via a VAR and analysis o
indi idual equa ions, hey ound signi ican in luences in e es a es in he sho e m, he di e ence be ween
po en ial GDP and eal GDP (ou pu gap), he eal alue o asse s, and in la ion on he de aul a e o I alian
i ms o e he pe iod 1990-2004. Using hese mac o a iables, hey buil a “C edi Cycle Index” in o de o
in e he s a e o c edi in he I alian ma ke in u u e pe iods.
3 Dummy a iables o he ou loca ions conside ed: U.S., UK, Japan, and Eu ope (including England), dummy a iables o 10
indus y ca ego ies, dummy a iables o he cu en s a e o he economy and ha which is expec ed (one yea ). See Nickell e al.
(2000), p. 216.
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
69
Da a Sample4
The da a a ailable o he p elimina y uni a ia e and mul i a ia e analysis, in o de o ind he mos
impo an mac oeconomic a iables a e yea ly. We ake 1985 as he s a ing yea o ou es ima ion pe iod,
since o he se ies o de aul a es a e no a ailable p io da a. The de aul a e se ies co e all I alian
companies. The de aul a es a e a mo ing a e age, cen e ed a h ee yea s. This allows an easie p ocessing o
such da a.
S a ing om a sample o 12 se ies o mac oeconomic a iables, we a i e a he selec ion o he mos
signi ican ones o ou analysis.
The a iables a e:
(1) Public demand (public adminis a ion expendi u e in eal e ms): DPA.
(2) Taxes paid by en e p ises (sha e o GDP): TPE.
(3) Taxes paid by households (sha e o GDP): TPH.
(4) Social secu i y con ibu ions (sha e o GDP): SC.
(5) Wages and sala ies pe capi a indus y: WpC.
(6) B en c ude oil p ices: PBC.
(7) P ice index o non-ene gy commodi ies (USD cu ency): PNC.
(8) Change $/€: CH.
(9) US GDP: USGDP.
(10) Eu o GDP: EGDP.
(11) GDP in de eloping coun ies (de eloping coun ies): DCGDP.
(12) Th ee-mon h in e es a e: IR3.
Uni a ia e analysis was based on he e i ica ion o he s a iona i y o da a ia he ADF (Augmen ed
Dickey-Fulle ) es on he le els, log-le els, i s di e ences and second di e ences, and i shocks a e pe manen
o s a iona y.
Mul i a ia e analysis was based on he signi icance o he eg esso s and he co ela ion o e o s. A his
s age, he choice o a iables o be used may be based on subjec i e assessmen s, pe haps guided by heo e ical
assessmen s o maybe jus om he esul s highligh ed by o he s udies. Then, hanks o he econome ic wo k,
i is possible o iden i y he op imal classi ica ion ule, iden i ying a iables ha can be elimina ed as no
ele an in de e mining he e ec i eness o he model. I is no ed, howe e , ha almos all p oposed s udies on
he subjec ha e used i e a i e p ocedu es ha can iden i y he signi ican a iables among a la ge se o
selec ed a iables.
A e ca ying ou an i e a i e p ocess in which all possible VAR models we e es ima ed, including he
i s wi h i e a iables, hen ou and hen h ee, and ha e el he signi icance o all a iables in he ollowing
es ima es o o dina y leas squa es (OLS).
A he end o he analysis, we conside only he ollowing a iables: he de aul a e o I alian companies,
such as he au o eg essi e e m, he loga i hm o GDP in he eu o a ea and in e es a es in he sho e m.
Es ima ion Me hodology and Resul s
S a ing om he pape s o Zazza a and Ro ondi (2005b), we build a c edi cycle index o I alian
4 Da a p o ided by P ome eia Associa ion—one o he la ges I alian companies in inancial and economic esea ch.
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
70
companies. A wo-s age app oach is used. We s a om he iden i ica ion o mac oeconomic a iables, and ia
a VAR model, we ind he numbe o a iables o use and he lag.
The VAR app oach a oids a s uc u al model, modeling each endogenous a iable in he sys em as a
unc ion o lagged alues o all endogenous a iables. The equa ion is:
-1 p -p
ΥΑΥ ΑΥ ΒΧε
=
+⋅⋅⋅+ + + (1)
A e ca e ul analysis and a ious es s we choose among all he se ies o mac oeconomic a iables.
-1
DF
DR PL
=
whe e DR is he de aul a e;
LNR is loans no epaid a ime ;
EL -1 is he exis ing loans in ime -1;
IRsho = in e es a es in he sho e m.
LEGDPEURO = he loga i hm o g oss domes ic p oduc in he eu o a ea.
The es ima ed VAR model ells us ha he bes model is one ha uses ew a iables wi h a single lag, his
ge s he mos signi icance o he eg ession. Table 1 shows he s a is ical eg ession pe o med wi h he VAR.
The i s e ms in pa en heses a e he “s anda d e o ” a iable eg ession. The second e ms in pa en heses a e
he -s a is ic.
Table 1
VAR Es ima ion
DR Tb e LPILEURO
DR (-1) 0.857553
(20.9909) -0.966055
(-1.67830) -11.99617
(-1.01158)
IRsho (-1) 0.246329
(4.93865) 0.607240
(0.86407) -0.911236
(-0.06294)
LPILEURO (-1) -0.008187
(-2.97555) 0.020297
(0.52357) 1.046109
(1.30981)
C 0.003160
(1.83458) 0.010666
(0.43951) 0.221320
(0.44265)
R-squa ed 0.981412 0.776045 0.746792
Adj. R-squa ed 0.977694 0.731254 0.696150
Sum sq. esids 1.06E-05 0.002099 0.890716
S.E. equa ion 0.000839 0.011828 0.243682
F-s a is ic 263.9913 17.32594 14.74661
Log Likelihood 196.9403
Akaike in o ma ion c i e ia -19.46740
Schwa z c i e ia -18.87091
No es. Sample (adjus ed): 1986-2004; included obse a ions: 19 a e adjus ing endpoin s. S anda d e o s and -s a is ics a e in
pa en heses.
The R-squa ed has a e y high alue con i ming he alidi y o he eg ession. In all he VAR models
es ima ed wi h mo e a iables and/o mo e “lags” we ound p oblems o low signi icance o he eg esso s and
mul icollinea i y. So, he i s esul s o es ima ion indica e ha o he cons uc ion o he CCI and, mo e
gene ally, o explain he ela ionship be ween mac oeconomic pe o mance and he de aul a es o he loans, i
is mo e e icien o wo k wi h a selec ew one-lag mac o a iables.
Figu e 1 aces he impulse esponse unc ion, he dependen a iable (in ou case, de aul a e), which

BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
71
co esponds o a shock in he s anda d de ia ion o each explana o y a iable. As expec ed, he de aul a es
espond nega i ely o an exogenous shock o he s anda d de ia ion o GDP in he eu o a ea, bu espond
posi i ely o a shock in he s anda d de ia ion o in e es a es in he sho e m.
Figu e 1. Responses on impulse unc ion o DR.
Selec ing he mac o a iables, we mono onically ans o m he de aul a es. The ans o ma ion is as
ollows:
Logi ( ) Ln( )
1
ii, -j
i
DR
DR βΧ ε
DR
α
=
=+ × +
−∑ (2)
We ans o m he a iable GDP:
1
(Ln ) Ln( )
D GDP GDP GDP−
=
− (3)
whe e D e e s o he i s di e ence, and Ln o he na u al loga i hm, so we u ned he GDP se ies in he i s
di e ence o i s na u al loga i hm.
We make his change o se e al easons. Fi s because we a e no e y in e es ed in how he le els o
GDP a ec he de aul a e bu a he han he GDP g ow h a e in luences he de aul a e. The ans o ma ion
in i s di e ences is pe o med o a be e s abiliza ion o he a iable and o make i mo e signi ican in he
eg ession.
As shown abo e he na u al loga i hm o ⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
−
DR
DR
1 is linea ly eg essed wi h mac oeconomic explana o y
a iables j i
X−,. The i
β
coe icien s a e he e o e es ima ed using he me hod o o dina y leas squa es (OLS).
1 2 3 4 5 6 7 8 9 10
0.000
1 2 3 4 5 6 7 8 9 10
1 2 3 4 5 6 7 8 9 10
Response o DR o one S.D. IR inno a ion
-0.002
-0.004
0.000
0.002
0.004
0.006
-0.003
-0.002
-0.001
0.001
0.004
0.003
0.002
0.001
0.000
-0.001
-0.002
0.002
Res
p
onse o DR o one S.D. LEGDP inno a ion
Res
p
onse o DR o one S.D. DR inno a ion
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
72
Table 2
Reg ession Analysis
Va iable Coe icien S d. e o -s a is ic P ob.
C -1.192346 0.162762 -7.325686 0.0000
Logi (DR ) (-1) 0.754341 0.040127 18.79895 0.0000
IRsho (-1) 4.940155 0.438420 11.26808 0.0000
DLGDPEURO (-1) -0.158821 0.040396 -3.931564 0.0015
R-squa ed 0.986202 Mean dependen a . -3.727850
Adjus ed R-squa ed 0.983245 S.D. dependen a . 0.242755
S.E. o eg ession 0.031423 Akaike in o c i e ion -3.889449
Sum squa ed esid. 0.013823 Schwa z c i e ion -3.691588
Log likelihood 39.00504 F-s a is ic 333.5380
Du bin-Wa son s a . 1.927173 P ob (F-s a is ic) 0.000000
No e. Included obse a ions: 18.
The s a is ical eg ession in Table 2 shows ha he -s a is ics o he coe icien s a e all signi ican , excep
he cons an . Bo h he R-squa ed and he adjus ed R-squa ed ha e e y high alues, and hen he - es s a is ic
s ongly ejec s he null hypo hesis o no signi icance o he es ima e as a whole.
A e es ima ing he equa ion abo e, i s anda dizes he Logi unc ion and adds a minus sign be o e he
equa ion, in o de o ob ain a new a iable:
Ln 1
Ln 1
Ln 1
DR
DR
DR
DR
DR
DR
Z
μ
σ
⎛⎞
⎜⎟
−
⎝⎠
⎛⎞
⎜⎟
−
⎝⎠
⎛⎞
−
⎜⎟
−
⎝⎠
=− (4)
The a iable Z ep esen s he C edi Cycle Index and indica es he s a us o c edi di ided by all he
bo owe s du ing he pe iod .
By cons uc ion, he index is ze o when he alue o all mac oeconomic se ies is exac ly equal o he
a e age o e he es ima ion pe iod.
The CCI is a he posi i e o nega i e when he mac oeconomic se ies di e om hei mean.
In pa icula , i is posi i e in he good imes o he cycle (implying a lowe p obabili y o de aul ) and
nega i e in he bad imes (implying a highe p obabili y o de aul ). See Figu e 2.
Figu e 2. Rela ion be ween DR and CCI.
-2
-1
0
1
2
0.015
0.020
0.025
0.030
0.035
86 88 90 92 94 96 98 00 02 04
CCI D
R
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
73
Visual inspec ion o he Figu e 2 (whe e CCI = CCI es ima ed, and DR = he de aul a e in he pe iod
obse ed) abo e shows an in e se ela ionship be ween he de aul a e and he CCI c edi , as assumed in he
cons uc ion o he index. You can see how he CCI app oxima es qui e well o he end o de aul a e in Table 3.
Table 3
Compa ison Be ween Ac ual CCI and CCI Es ima ed
Yea s Ac ual Es ima e Yea s Ac ual Es ima e
1987 -0.14994 -0.24479 1996 -0.99943 -0.87965
1988 0.252228 0.081049 1997 -0.54895 -0.49671
1989 0.482398 0.448169 1998 -0.05439 0.031501
1990 0.269926 0.32977 1999 0.678005 0.381685
1991 -0.19697 -0.31965 2000 1.119023 0.878269
1992 -0.99049 -0.87652 2001 1.367896 1.290381
1993 -1.47174 -1.53971 2002 1.421929 1.216358
1994 -1.65872 -1.62648 2003 1.394831 1.30301
1995 -1.31222 -1.39476 2004 1.298784 1.41808
Table 3 shows in he “Ac ual” column he ac ual alues o he index o each yea o he sample, and he
“Es ima e” column he es ima ed alue. You can see ha he e is a close p oximi y o he alues o each yea
o he sample and as o he la ge majo i y o he obse a ions he wo measu es ha e he same sign, i is e y
impo an o no e he change o sign, he es ima ed CCI app oxima es well wo on h ee, he hi d an icipa e he
obse a ion in one yea .
Back es and Fo ecas
A e building ou CCI, we es he obus ness o ou app oach h ough s a is ical back es measu es. In
pa icula , we ensu e he o esigh o ou c edi cycle index, bo h “in- he-sample” and “ou -o - he-sample”.
We use he widely used s a is ical e o “Theil Inequali y Coe icien ”5.
∑∑
∑
==
=
+
−
=
n
n
n
n
y
n
n
y
TIC
11
2
2
2
1
)(
λ
λ
(5)
whe e:
=
λ
Expec ed alue o he c edi cycle index a ime ;
=
y Realized alue o he c edi cycle index a ime ;
=n Numbe o pe iods.
∑
=
−
n
n
y
1
2
)(
λ
, he nume a o is known as he oo mean squa ed e o o he o ecas . This coe icien
a ies om 0 o 1, whe e 0 indica es a pe ec “ i ”.
Figu e 3 shows an almos alignmen o he cu e ep esen ing he expec ed CCI (ESTIMATE) wi h ha
achie ed (TRUE). Some small di icul ies in he inal es ima ion whe e he c edi cycle index ollows a sligh ly
di e en ajec o y han he c edi cycle index achie ed.
5 I p o ides a measu e o how well a ime se ies o es ima ed alues compa es o a co esponding ime se ies o obse ed alues.
BUSINESS CYCLE AND THE RISKINESS OF ITALIAN FIRM
74
Figu e 3. Compa ison be ween ac ual CCI and CCI es ima ed.
Table 4 shows a good pe o mance wi h a good “ i ” be ween he expec ed CCI and CCI ealized. These
esul s a e also due o annual da a. To “back es ” he model be e mo e ep esen a i e qua e ly da a ha bes
sui e his ype o phenomena would be use ul, bu , un o una ely, we do no ha e such da a.
Table 4
Repo o he Robus ness o CCI
Sample Pe iod Tail inequali y Same sign o index Same sign o index in change
1985-2004 0.072 95% 66%
Now we y o p o e he obus ness o ou CCI es ima ing ou -o - he-sample. To do his, we di ide he
sample pe iod (1985-2004) in wo, wi h he i s being om 1985 o 2002. We es ima e he coe icien s as
ca ied ou by he eg essing Equa ion (1), and using hese es ima e he c edi cycle index in pe iod (2002-2004).
See Figu e 4.
Figu e 4. Compa ison be ween es ima ed alue ou o he sample and ue alue.
Figu e 4 compa es he CCI es ima ed wi h he ac ual, and we can see how he wo measu es did no
subs an ially di e , and make a good o ecas ou -o - he-sample.