Discussion Paper No. 276
How Important are Financial Shocks for the
Canadian Business Cycle?
Shin-Ichi Nishiyama

September 2011

TOHOKU ECONOMICS RESEARCH GROUPGRADUATE SCHOOL OF ECONOMICS AND

MANAGEMENT TOHOKU UNIVERSITY
KAWAUCHI, AOBA-KU, SENDAI,
980-8576 JAPANHow Important are Financial Shocks for the Canadian Business
Cycle?
Shin-Ichi Nishiyamay
Graduate School of Economics and Management,
Tohoku University
This Version: September, 2011
First Version: August, 2009

Abstract
In this paper, we investigate the importance of …nancial shocks for the Canadian business cycle
employing the …nancial friction DSGE framework following Bernanke, Gertler, and Gilchrist (1999)
with an extension of a small-open economy feature. In particular, we explored the importance ofan external …nance premium shock and an aggregate net worth shock. In order to identify …nancial
shocks in the model, we utilized …nancial data in estimating our model. Our variance decomposition
results showed that the external …nance premium shock to account about 7.5% and the aggregate net
worth shock to account about 5.6% of the variance of the business …xed investment in Canada. Also,
our historical decomposition results and smoothing of the various …nancial variables showed that dataon corporate leverage ratio to be particularly useful in identifying the …nancial shocks in the model.
Finally, when the …nancial shocks were present in the model, relative importance of the investmentspeci…c technology shock was substantially subdued that it accounted for only 17% of the varianceof the business …xed investment –much lower than the results reported in the former empirical studies.
Keywords: Canadian economy, …nancial friction, …nancial shock, business cycle
JEL Classi…cation: E1, E3, G1

The author of this paper would like to thank Ian Christensen, Paul Corrigan, Ippei Fujiwara, Takatoshi Ito, Kazumasa
Iwata, Yasuharu Iwata, Takashi Kano, Ryo Kato, Oleksiy Kryvtsov, Cesaire Meh, Rhys Mendes, Masao Ogaki, Yasushi
Okada, Giorgio Primiceri, Christopher Sims, Bryan Smith, Daniel Solomon, Nao Sudo, Yaz Terajima, Hajime Tomura, Taka
Tsuruga, Koichi Yano, and Yahong Zhang for their valuable comments and discussions. Any remaining errors are theresponsibility of the author. The …rst version of this paper was written when the author was at Bank of Canada. The
views expressed in this paper are those of the author and do not necessarily re‡ect those of Bank of Canada.
y 27-1 Kawauchi, Aoba-ku, Sendai-shi, Miyagi-ken, 980-8576, JAPAN, Tel.: +81-22-795-3471,
E-mail: nishiyama@econ.tohoku.ac.jp1

1

Introduction

Given the on-going …nancial crisis precipitated by the sub-prime loan problem in the U.S. …nancial sector,
there has been an increased interest in the linkage between …nancial activity and real economic activity. In
particular, there is a heightened interest in how the shocks occurring in the direct and/or indirect …nancial
market can a¤ect real economic activity. Although the Canadian banking sector seems to be weathering
the current …nancial crisis (Northcott et al. (2009)) and have not experienced a major …nancial turmoil inrecent decades1 , there is no guarantee that the Canadian economy will be free from a large shock in the…nancial sector in a near future. In order to help the policy makers to understand the consequences ofsuch contingency and to facilitate them in forming a counter-measure, it is crucial to assess how vulnerable(or robust) the Canadian economy is to the shocks originating in the …nancial sector. As such, we ask thefollowing question in this paper; how important are …nancial shocks for the Canadian business cycle?
To answer the above question, we need to decide how to model the …nancial friction and …nancial shocks.
In modeling the …nancial friction in a general equilibrium setting, there are mainly two approaches. One
way is to impose collateral constraint as in Kiyotaki and Moore (1997). This collateral constraint approachis becoming a popular choice2 , especially when modelling the …nancial friction in a mortgage loan market
where residential asset is customarily withheld as collateral until the mortgage loan is repaid in full.
Another approach is to model an external …nance premium as in Bernanke and Gertler (1989), Carlstrom
and Fuerst (1997), and Bernanke, Gertler, and Gilchrist (1999). This approach proved extremely useful3
in modelling the standard debt contract between the corporate sector and …nancial intermediary whichallows us to analyze the relationship between business …xed investment and external …nancing cost. Bothtypes of …nancial friction –collateral constraint and external …nance premium –are useful in addressing thelinkage between the …nancial market and real economic activity such as …nancial acceleration mechanism
in residential investment and business …xed investment. However, since we are more interested in the‡uctuation of the business …xed investment – the most important factor in output ‡uctuation –, we will
be adopting the external …nance premium as the …nancial friction mechanism in this paper. In particular,
we construct a medium-scale dynamic stochastic general equilibrium (denoted DSGE, hereafter) modelwith …nancial friction à la Bernanke, Gertler, and Gilchrist (1999) (denoted BGG, hereafter). Further,re‡ecting the Canadian context, we extend the model to incorporate a small-open economy feature.
Next, we need to decide the speci…cations of the …nancial shocks. In addition to the standard macroeconomic shocks adopted in the empirical DSGE literature, we adopt two types of …nancial shocks: external…nance premium shock and corporate net worth shock. The importance of the external …nance premium
shock has been pointed out by Smets and Wouters (2003, 2007)4 , while the importance of the corporate net
1 Except for the episode of failures by two small banks – the Canadian Commercial Bank and the Northland Bank, bothof them located at the western provinces and heavily invested in oil related sectors – which occurred in September 1985.
Due to the economic recession in the early 80’s, which hit the oil related sectors in the western provinces especially hard,
two banks eventually defaulted and were pushed out from the …nancial system. Although some …nancial ‘contagion’ (i.e.,
eventual acquisitions of the Bank of British Columbia and the Continental Bank of Canada by today’s HSBC Bank Canada)followed after the failures, since the combined asset of two banks was less than 1% of the entire banking industry, theCanadian …nancial system remained pretty much intact. For more details on the episode of the bank failures in 1985, see
Dingle (2003, Ch.5). Surprisingly, a bank failure episode in Canada preceeding to 1985 goes back as far to the episode of
the Home Bank failure in August, 1923.
2 For instance, Iacoviello (2005), Iacoviello and Neri (2008), Christensen et al. (2008) among others.
3 For empirical DSGE papers with this type of …nancial friction, see, for instance, Meier and Müller (2005), De Graeve(2008), Christiano et al. (2007), and Christensen and Dib (2008). On a di¤erent note, Aoki et al. (2002) adopts an external…nance premium in modelling residential investment.
4 Smets and Wouters (2003, 2007) refer to the external …nance premium shock as ‘risk’premium shock or ‘equity’premium2worth shock has been emphasized by Christiano, Motto, and Rostagno (2007) (denoted CMR, hereafter).
In the context of this paper, the external …nance premium shock is an exogenous shock that a¤ects theexternal …nance premium (or credit spread) irrespective of corporate leverage ratio and can be interpreted
as any shock a¤ecting the credit spread without initially a¤ecting the corporate balance sheet, such as…nancial market condition or …nancial intermediary’s lending attitude. The corporate net worth shock,in our context, is an exogenous shock to turn-over rate of entrepreneurs which, in turn, a¤ects the credit
spread through the aggregate leverage ratio of the corporate sector. Following CMR, this shock can
be interpreted as an aggregate shock to the entrepreneurial net worth in the economy. Considering theimportance of both types of …nancial shock as in Smets and Wouters (2003, 2007) and CMR, we embedboth of them to our benchmark model and compare which type of shock, external …nance premium shock
or corporate net worth shock, are relatively important in accounting for the Canadian business cycle.
As for the estimation of the model, we adopt the Bayesian estimation methodology which is becoming
a standard tool in the empirical DSGE literature. Now, an issue remains. When there are two typesof …nancial shock in the model and both shocks a¤ect the non-…nancial variables via an external …nancepremium –the only channel that links non-…nancial variables and …nancial variables in BGG-type model–, inevitably, the qualitative pattern of the impulse response functions under both types of …nancial shock
become similar, especially for the non-…nancial endogenous variables. Consequently, if the observabledata in the estimation are con…ned to non-…nancial variables, we will face a di¢ culty in identifying
the two …nancial shocks. In order to avoid this identi…cation problem of the two …nancial shocks, we
include …nancial variables (i.e., leverage ratio) to our observable data set, in addition to the standard
non-…nancial data adopted in the empirical DSGE literature. Since the impulse response functions under
the two …nancial shocks imply qualitatively di¤erent patterns for these …nancial variables, we claim that
inclusion of …nancial variables to observed data will ensure the identi…cation of two …nancial shocks in theestimation.
The main empirical …ndings of this paper can be summarized as follows. Under the shock speci…cation
where both …nancial shocks –external …nance premium shock and aggregate net worth shock –are present
in the model, it turns out that both …nancial shocks are quite important in accounting for the Canadianbusiness cycle. Taking the case of business …xed investment in Canada, our variance decomposition for
unconditional forecast error show that the external …nance premium shock to account for as much as 7.5%
and the aggregate net worth shock to account for as much as 5.6% of the variance. In total, the …nancial
shocks account for more than 13% of the variance of the business …xed investment and this magnitude
is comparable to that of an investment-speci…c technology shock. Based on this result, it will not be
an over-statement to say that the …nancial shocks are as important as the investment-speci…c technology
shock in accounting for the movement in the business …xed investment in Canada.
The remainder of this paper is organized as follows. Section 2 describes the model structure and theshock structure adopted in this paper. Section 3 explains the estimation strategies and also describes
the data adopted in this paper. Section 4 reports the estimation results under four di¤erent shockspeci…cations of the …nancial shocks. In particular, the posterior means of the parameters, estimatedIRF, variance decompositions and historical decompositions will be reported. Section 5 explores theconsequences of using alternative data set. In particular, this section demonstrates the importance ofutilization of the …nancial data, especially leverage ratio data, in identifying the …nancial shocks. Section
6 summarizes and concludes the paper.
shock in their context. In our context, we will refer to this shock as external …nance premium shock.

3

2

Model Description

We basically adopt BGG as the workhorse in modelling …nancial frictions in the economy and extend it toincorporate the small open economy features –a necessary extension when analyzing the Canadian businesscycle. The economy is populated by households consuming …nal goods and supplying labour inputs,
entrepreneurs producing domestic intermediate goods, capital producers, monopolistically competitive
wholesalers of domestic intermediate goods and imported goods, perfectly competitive retailers of …nal
goods, a government and a monetary authority. The factor markets (capital market and labour market)
are perfectly competitive. There are four types of rigidities in the economy: nominal price rigidity
for wholesalers, external habit formation of consumption for households, investment adjustment costs
for capital producers, and external …nance premiums for entrepreneurs when borrowing credits. In thissection, we describe the problem settings and the equilibrium conditions for each agent in turn.

2.1

Household’s Problem

The representative household derives utility from …nal goods consumption and disutility from supplying
labour inputs. The household strives to maximize their utility over time and their expected discounted
sum of period-by-period utility function is speci…ed as follows,
E0

1
X

t
t

ln(cH
t

(ltH )1+
1+

hCtH 1 )

t=0

;

(1)

where parameter stands for the discount rate by the household, cH
t stands for …nal goods consumption,
Hparameter h stands for habit persistence coe¢ cient, and Ct 1 represents external habit formation whichH
is exogenously given to the household at period t, but cH
t = Ct in equilibrium. Turning to the labourH
supply side of the utility function, lt stands for the supply of labour inputs by the household, andparameter stands for labour supply elasticity. Now, t represents an intertemporal preference shockto the household’s current and future consumption and labour supply and it follows AR(1) stochastic
process.
Next, let us turn to the budget constraint of the representative household. By supplying the labour
inputs, ltH , to the entrepreneur, the representative household can earn the real wage, wt , for each unit of
input. They can also deposit their …nal goods, bt , at period t and earn real interest rate, Rt = t+1 ; next
period where Rt stands for gross nominal interest rate at period t and t+1 stands for gross in‡ation rate
at period t + 1. Further, the household has access to the international …nancial market and can borrow
the amount of et bft units of domestic …nal goods, where et stands for real exchange rate measuring therelative price of foreign goods in terms of domestic goods and bft stands for the amount of foreign debt
at period t. Next period, the household will repay the gross real interest rate of et+1 Rtf t = ft+1 to theinternational …nancial market for each unit of foreign debt, where Rtf stands for gross foreign nominalinterest rate, t stands for country speci…c risk premium which is exogenous to the household’s decision,and ft+1 stands for gross foreign in‡ation rate in period t + 1. Finally, the household pays the lump sum
tax of t to the government and earns the combined dividend of t from domestic and imported goods
wholesalers every period. Thus, the household’s budget constraint at period t can be expressed, in realterms, as follows,cH
t + bt + et

Rtf 1 t 1 f
Rt 1
bt 1 = wt ltH +bt 1 + et bft
f
t

t

4

t+

t:

(2)

Given the above budget constraint (2), the representative household maximizes intertemporal utilityfHfunction (1) with respect to cH
t , lt , bt , and bt . The …rst order conditions for this dynamic optimization
problem are:
cH
t

1
;
hcH
t 1

(3)

=

(ltH )

;

(4)

H
t t

=

Et t+1 Ht+1

Ht t et

=

H
t

=

wt

H
t

Rt

; and

(5)

Rtf

(6)

t+1

Et t+1 H
t+1 et+1

t
;
f
t+1

where Ht stands for the Lagrangian multiplier associated with the budget constraint (2). From eq. (3),Ht can be interpreted as the marginal utility of consumption at period t. Here, note that we used theHproperty of external habit formation and the equilibrium condition, cH
t 1 = Ct 1 ; to derive eq. (3). Eq.
H(4) is the …rst order condition with respect to lt and it can be interpreted as the labour supply function
by the household. Eq. (5) is the …rst order condition (or Benveniste-Scheinkman equation) with respect
to bt and can be interpreted as an implicit credit supply function by the household. It should be notedthat intertemporal preference shock, t , a¤ects the decision of credit supply (or saving) by the household
signi…cantly. For instance, if the ratio of intertemporal shocks, t+1 = t , is expected to be temporarily
larger than one, the household will temporarily put higher weight on the future marginal utility, H
t+1 ,and, therefore, decide to consume more in the future. In other words, in such situation, the household
will decide to save more and supply more credit at current period. Thus, ratio of intertemporal shocks
play an important role for the supply of credit, bt . Finally, eq. (6) is the …rst order condition (orBenveniste-Scheinkman equation) with respect to foreign debt, bft , and can be interpreted as an implicit
foreign credit demand function by the household. By the same token, the ratio of intertemporal shocksa¤ect the decision of foreign credit demand by the household signi…cantly.

2.2

Entrepreneur’s Problem

2.2.1

Individual Entrepreneur’s Problem

Following BGG, there is a continuum of entrepreneurs indexed by j 2 [0; 1] where each entrepreneur
is risk neutral and has a …nite expected horizon. As in BGG, these assumptions will ensure that eachentrepreneur will not accumulate enough net worth to self-…nance their new capital –i.e., each entrepreneur
will rely on external …nance to purchase new capital to some extent in equilibrium. In a spirit of CMR,
each entrepreneur faces an exogenous time-varying stochastic survival rate of t+1 from period t to t + 1
which is common across all entrepreneurs5 . We assume that the stochastic process of t is uncorrelatedwith any other shocks in the economy and has its mean equal to – i.e., E[ t ] = . Between periodt and t + 1, after 1
t+1 fraction of entrepreneurs have disappeared from the business, exactly thesame amount of new entrepreneurs will enter the business so that the population of entrepreneurs in theeconomy remains the same from period t to t + 1. Each entrepreneur entering period t + 1 is endowedEwith …xed units of entrepreneurial labour, lfEix ; and receive compensation of wt+1
for each unit of labour.
5 CMR interprets this stochastic survival rate,
t+1 , as reduced form way to capture shocks unrelated to preference or
technology in the economy. They name ‘asset price bubble’and ‘irrational exuberance’for such examples.

5This endowment ensures the new entrepreneurs entering the intermediate goods industry to have strictly
positive net worth to start up their business and issue their debts.
For 1
t+1 fraction of entrepreneurs who happened to exit the business between period t and t + 1,
they will sell o¤ the capital they purchased at the end of period t and retire all of their debts before
maturity6 . They will simply consume their remaining net worth, nt (j), and cease to exist from theeconomy at the beginning of period t + 1.
Turning to the production technology, each entrepreneur produces homogeneous domestic intermediate
goods, ytD (j), and they are perfectly competitive when selling their products to the wholesalers. Each
entrepreneur uses capital inputs and labour inputs and has a constant-return-to-scale technology in producing intermediate goods. Following Gertler, Gilchrist, and Natalucci (2007), the production function7
for the intermediate goods is given byytD (j) = ! t (j)At kt (j) lt (j)1;(7)

where kt (j) stands for capital holding by an entrepreneur j at period t and lt (j) stands for labour inputs
composed of household labour, ltH (j), and entrepreneurial labour, ltE (j), which is de…ned aslt (j) = ltH (j)1

ltE (j) :(8)Here, it should be noted that the aggregate technology shock, At , is common across all entrepreneurs.
Also, the capital share parameter, , and the entrepreneurial labour share parameter, , are common
across all entrepreneurs as well. Following CF and BGG, we assume each entrepreneur is subject to an
idiosyncratic shock, ! t (j), which a¤ects the total factor productivity of intermediate goods, yt (j). The
idiosyncratic shock, ! t (j), is a private information to entrepreneur j and assumed to be i.i.d. shock withmean equal to one –i.e., E[! t (j)] = 1:
The corporate balance sheet of each entrepreneur at the end of period t can be expressed as
qt kt+1 (j) = bt (j) + nt+1 (j)(9)

where qt stands for the relative price of capital, kt+1 (j) stands for the capital which will be used for
production in period t + 1 but purchased at period t, bt (j) stands for the real debt issued at period t andnt+1 (j) stands for the net worth at the end of period t. Basically, left-hand side of eq. (9) represents
the total asset of the entrepreneur and right-hand side represents the liability and the net worth of theentrepreneur at the end of period t. As can be seen from this balance sheet equation, capital, kt+1 (j),which is purchased at the end of period t is partially …nanced by issuing the debt, bt (j) at period t. With
the assumptions of risk neutrality and …nite planning horizon, net worth (or internal …nance) itself is neverenough in …nancing the cost of capital purchase and, thus, each entrepreneur will rely on external …nancein equilibrium.
The corporate income statement (or using alternative accounting terminology; pro…t and loss statement) for entrepreneur j entering period t is speci…ed as follows
nt+1 (j) = mct (j)ytD (j)wt ltH (j)wtE ltE (j)Rt 1 st 1 (j)tbt 1 (j) + qt (1)kt (j) + wtE lfEix(10)

where mct (j) stands for marginal cost of intermediate goods j, wt stands for real wage of householdlabour, wtE stands for real wage of entrepreneurial labour, parameter stands for capital depreciation rate,
6 We assume no penalty rate is charged by the …nancial intermediary.
7 To be accurate, GNN incorporates capital utilization in their production function speci…cation.

will assume that capital is fully utilized at any time for any entrepreneur.

6Here, for simplicity, weand st 1 stands for external …nance premium charged by …nancial intermediary at period t 1. Each
entrepreneur is a price-taker in the …nancial market and, thus, external …nance premium is exogenously
given to each entrepreneur8 .
Let us look at the corporate income statement more closely. At the beginning of period t, eachentrepreneur will use capital kt (j) –which was purchased at the end of period t 1 –and employ household
and entrepreneurial labour. Then, each entrepreneur will produce intermediate goods j according to
production function (7) and sell them o¤ to the wholesalers in a perfectly competitive manner. Thus,
the revenue for each entrepreneur will be equal to marginal cost multiplied by the amount of intermediate
goods produced as can be seen in eq. (10). Each entrepreneur will pay the labour cost and also repay
the debt to …nancial intermediary. The gross repayment rate is given by Rt 1 st 1 = t which includes theexternal …nance premium in addition to the realized real interest rate. Finally, each entrepreneur will sello¤ depreciated capital to the capital market earning qt (1)kt (j) and provide endowed entrepreneurial
E E
labour to other entrepreneurs earning wt lf ix as an income. The net income after these activities arecaptured by nt+1 (j) and will be a net worth for the entrepreneur j at the end of period t. Given this net
worth, each entrepreneur will plan for the next period and decide how much capital to purchase and how
much debt to issue at the end of period t as we have seen in balance sheet equation (9).
For each entrepreneur entering period t, they will maximize their expected discounted sum of pro…ts
by choosing capital inputs, labour inputs, and debt issuance subject to eq. (7), (8), (9), and (10). The…rst order conditions for each entrepreneur j are given by

Et

wt

=

(1

wtE

=

(1

Rt st (j)
t+1

t+1

= Et

mct (j)ytD (j);ltH (j)mct (j)ytD (j); and)ltE (j)D
mct+1 (j)yt+1(j)=kt+1 (j) + (1
t+1
qt
)(1

(11)

)

(12)
)qt+1

:

(13)

Eq. (11) equates marginal cost of employing household labour to marginal product of household labour.
This equation can be thought of as a demand function for household labour by entrepreneur j. By thesame token, eq. (12) can be thought of as a demand function for entrepreneurial labour. Eq. (13) equates
the expected marginal cost of capital …nanced by debt to the expected marginal return of capital …nanced
by debt and can be thought of as the Euler equation of capital for entrepreneur j. Since stochastic
survival rate, t+1 ; is uncorrelated to any other shocks in the economy, eq. (13) can be further rearrangedasD
mct+1 (j)yt+1(j)=kt+1 (j) + (1)qt+1
Rt st (j)
= Et
(14)
Et
q
t+1
t
which is the standard result as in BGG. Thus, the introduction of stochastic survival rate will not alter
the Euler equation of capital for any entrepreneur j compared to the case with constant survival rate asin BGG.
8 We will elaborate more on this external …nance premium when explaining …nancial intermediary’s behaviour.

72.2.2Financial Intermediary

We now turn to the …nancial intermediary’s problem9 . Following BGG, the idiosyncratic total factor productivity shock, ! t (j), is private information for entrepreneur j that there exists information asymmetry
between entrepreneur (borrower) and …nancial intermediary (lender). Due to costly state veri…cation, the…nancial intermediary cannot observe entrepreneur j’s output, ytD (j), costlessly, but need to incur a …xed
monitoring cost to observe entrepreneur’s output. The entrepreneur, after observing project outcome,will decide whether to repay the debt or default at period t. If the entrepreneur decides to repay, the…nancial intermediary will receive gross repayment of Rt 1tst 1 for each unit of credits outstanding at
period t regardless of the realization of idiosyncratic shock, ! t (j). On the other hand, if the entrepreneur
decides to default, the …nancial intermediary will pay a …xed monitoring cost to observe ytD (j) and seize
the project outcome from the entrepreneur.
Under this problem set up, BGG shows that the optimal debt contract implies that the external …nancepremium, st , to depend upon the entrepreneur’s overall balance sheet condition. Speci…cally, they showthat the external …nance premium to be a function of the leverage ratio and increasing with respect tothe ratio. The reduced form function can be characterized byst (j) = s

qt kt+1 (j)nt+1 (j)(15)

where s0 ( ) > 0 and s(1) = 0.
For estimation purpose, we follow Covas and Zhang (2007) and Dib et al. (2008) and adopt thefollowing functional form
qt kt+1 (j)st (j) =exp(ust )(16)
nt+1 (j)where parameter can be interpreted as the elasticity of external …nance premium with respect to theleverage ratio and is strictly positive and ust stands for an exogenous external …nance premium shock
which is common across all entrepreneurs. Thus, for the empirical purpose of this paper, the movement
in external …nance premium can be decomposed into two factors –1) a movement due to a change in theleverage ratio (i.e., qt kt+1 =nt+1 ) which is endogenously determined in the model and 2) a movement due
to a change in the external …nance premium shock (i.e., ust ) which is exogenously given outside of themodel.
2.2.3

Aggregate Net Worth Transition

As shown by CF and BGG, the assumptions of constant-return-to-scale production technology and risk
neutrality will render marginal product of labour, marginal product of capital, marginal cost, and leverage
ratio to be equal across all solvent entrepreneurs in equilibrium10 . Further, since bankruptcy cost is
constant-return-to-scale and leverage ratio are equal for all j, the external …nance premium will be equal
across all solvent entrepreneurs in equilibrium. This property will make aggregation very simple which
renders eq. (11), eq. (12), eq. (14), and eq. (15) to hold in aggregate level as well.
9 Here, we will exactly follow the results presented by BGG and, thus, will be brief in explaining the behaviour of …nanicial

intermediary. Interested readers should refer to BGG for more details on optimal contracting problem between entrepreneurs
and …nancial intermediary.
1 0 As analyzed in Covas (2006), when production technology is decreasing-return-to-scale, leverage ratio will not be equal
across the entrepreneurs. In such a case, heterogeneity across the entrepreneurs and distribution of leverage ratio should be
explictly taken into account.

8

Next, we derive the law of motion of the aggregate net worth. Aggregating over corporate income
statement eq. (10) and taking into account of stochastic survival rate of entrepreneurs from period t 1
to t, we obtain the following aggregate net worth transition equation11
nt+1 =

t

Rt 1 st 1

1 + rtk qt 1 kttt

bt 1 + wtE lfEix(17)

where realized gross return from capital, 1 + rtk , is de…ned as
1 + rtk

mct y Dt =kt + qt (1
qt 1

)

:

D
E
and y Dt stands for the average of realized yt (j) across all entrepreneurs. By normalizing lf ix to one andusing corporate balance sheet eq. (9), eq. (17) can be rearranged as

nt+1 =t

1 + rtk qt 1 kt

Rt 1 st 1(qt 1 kttnt ) + wtE :(18)

Finally, aggregate consumption of entrepreneurs going out of business can be expressed ascE
t = (1

2.3

t)

1 + rtk qt 1 kt

Rt 1 st 1(qt 1 ktnt ) :(19)t

Capital Producer’s Problem

We now turn to a capital producer’s problem. Capital producers are perfectly competitive and risk neutral.
They purchase ikt amount of …nal goods from the retailer, convert them to ikt amount of capital goods,
and combine them with existing capital stock (purchased from entrepreneurs), (1)kt , to produce newcapital stock, kt+1 . Capital producers will, then, sell o¤ new capital stock to entrepreneurs in a perfectlycompetitive manner. Capital producers have linear production technology in converting …nal goods tocapital goods. However, following CEE and SW, when they change the production capacity of capital
goods from previous period, they will incur quadratic investment adjustment cost. Given this set up, thepro…t function for each capital producer at period t can be expressed as follows,
8
2
39
!2
1
<
=
k
X
i
1
t+i
i H
k
k
k 5
4
i
+
q
i
1
i
(20)
Et
t+i
t+i
t+i
t+i
:
;
Akt+i t+i 2 ikt+i 1
i=0kwhere i H
t+i stands for discount factor imposed by the representative household who owns the …rm, At
stands for investment speci…c technology shock and stands for adjustment cost parameter. Each capital
producer will maximize the expected discounted sum of the pro…ts with respect to ikt . The …rst ordercondition is given by
"
#
2
2
ikt+1
ikt+1
ikt
ikt
ikt
1
H
1
+
1
1
:
(21)
qt = k 1 +t+1 k
2 ikt 1
At
ikt 1
ikt 1
At+1
ikt
ikt

Finally, aggregate capital accumulation equation is given by
kt+1 = ikt + (1

)kt :

(22)

1 1 As for notation, aggregate variable is expressed by suppressing the argument j. For instance, variable n ; where argumenttj is suppressed, stands for aggregate net worth instead of entrepreneur j’s net worth.

9

2.4

Wholesaler and Retailer’s Problem

2.4.1

Wholesaler of Domestic Intermediate Goods

Here, we describe the optimal price setting behavior of the continuum of wholesalers of domestic intermediate goods, z D 2 [0; 1], who purchase domestic intermediate goods at perfectly competitive price fromthe entrepreneurs and resale them monopolistically (perhaps by attaching their brand name z D ) in thewholesale market. The demand function for domestic intermediate goods sold by the wholesaler z D isgiven byytD (z D ) =D

pt (z D )
PtD

YtD ;

where YtD stands for CES-aggregated domestic intermediate goods à la Dixit-Stiglitz, pt (z D ) stands fornominal price of intermediate goods ytD (z D ), PtD stands for aggregate price index of domestic intermediate
goods YtD , and parameter D stands for the relative price elasticity for ytD (z D ). We assume Calvo (1983)- Yun (1996) type sticky price setting for the wholesaler where, for any given period t, fraction D of theentire wholesalers cannot freely revise their price. Further, following the treatment of CEE (2005) andSmets and Wouters (2003, 2007) in modelling in‡ation persistence12 , we allow for the partial indexation
for the wholesalers who were not able to revise their prices freely at period t. In particular, D fractionof the wholesalers who did not receive a ‘signal of price change’will partially index their price to lagged
in‡ation of domestic intermediate goods as follows,D

pt+1 (z ) =

PtD
PtD 1

D

pt (z D )where parameter D 2 [0; 1] controls the magnitude of indexation to the past in‡ation rate.
D
Under this setting, for 1
fraction of the wholesalers who received a ‘price changing signal’at
period t, they will maximize their expected present value of pro…ts by setting the price such that
2
3
D
1
D
D
D
X
P
p
e
t 1+i
D i4 ti H
D)Et
mct+i 5 yt+i(z D ) = 0
t+i (
D
D
D
1
P
P
t 1
t+i
i=0

H
where peDt stands for the optimal price chosen by the ‘price changing’wholesalers at period t, t+i stands
for marginal utility of consumption by the household at period t + i, and mct+i stands for the purchasing
cost of domestic intermediate goods from the entrepreneurs which are purchased at perfectly competitive
price (i.e., the real cost of purchase equals marginal cost of producing domestic intermediate goods) at
period t + i.
From the de…nition of the aggregate price index, it can be shown that the law of motion of PtD to be
as follows
2
31 D
D
D
D
D
Pt 1
1
1
D
5
PtD
= D 4PtD 1
+ (1
) peD
:
t
D
Pt 2

2.4.2

Wholesaler of Imported Intermediate Goods

The optimal price setting behavior by the wholesalers of imported intermediate goods will be similar tothat of domestic wholesalers. There is a continuum of imported goods wholesalers, z M 2 [0; 1], who
1 2 Recently, Dupor, Kitamura, and Tsuruga (2008) show that in‡ation persistence can be motivated by a micro-foundedmodel which integrates sticky price and sticky information.

10

purchase imported intermediate goods at the purchasing cost equal to real exchange rate, et , and resell
them monopolistically in the wholesale market. The demand function for imported intermediate goods
sold by the wholesaler z M is given byytM (z M ) =M

pt (z M )
PtM

YtM ;

where YtM stands for CES-aggregated imported intermediate goods, pt (z M ) stands for nominal price ofimported intermediate goods, ytM (z M ), PtM stands for aggregate price index of imported intermediate
goods YtM , and parameter M stands for the relative price elasticity for ytM (z M ). By the same token as
Min domestic intermediate goods, we assume Calvo-Yun type sticky price setting where fraction (1)
of the wholesalers of imported intermediate goods can freely re-optimize their prices at any given periodt. For the rest of fraction M of the wholesalers, they will partially index their price to lagged in‡ationof imported intermediate goods as follows,M

pt+1 (z ) =

PtM
PtM1

M

pt (z M )where parameter M 2 [0; 1] controls the magnitude of indexation.
M
Under this setting, (1) fraction of the wholesalers at period t will set the price such that
2
3
M
1
M
M
M
X
P
et
t 1+i
M i4 pi H
M)Et
et+i 5 yt+i
(z M ) = 0
t+i (
M
M
M
1
P
P
t 1
t+i
i=0

where peMt stands for the optimal price by the imported goods wholesalers who re-optimize at period t andet+i stands for the real exchange rate which is equal to the purchasing cost of the imported intermediate
goods at period t + i. Thus, the only di¤erence (except for the parameter values and superscripts)
between domestic wholesalers and imported goods wholesalers is the purchasing cost of the intermediate
goods. The domestic wholesalers pay the marginal cost of producing domestic intermediate goods as thepurchasing cost, while the wholesalers of imported goods pay the real exchange rate as the purchasing
cost.
Again, from the de…nition of the aggregate price index, it can be shown that the law of motion of PtM
to be as follows
PtM

2.4.3

1

M

=

2

M 4

PtM1

PtM1
PtM2

M

31
5

M

+ (1

M

) peM
t

1

M

.

Retailer of Final Goods

Next, we describe the behavior of the …nal good retailer. The retailer combines domestic intermediate
goods and imported intermediate goods to form the …nal goods, Yt , using the following CES aggregation
technology
h
i 1
1
1
1
1
Yt = (1 !) (YtD )+ ! (YtM )where parameter ! 2 [0; 1] stands for the share of imported goods in the …nal goods production andparameter stands for the elasticity of substitution between domestic intermediate goods and imported

11

intermediate goods. The retailer is perfectly competitive in the …nal goods market and the cost minimization yields the following demand functions for YtD and YtM ;
YtD

=

(1

!)

YtM

= !

PtM
Pt

PtD
Pt

Yt

Yt :

Finally, the price index, Pt , corresponding to to the …nal goods can be shown to be as follow
Pt = (1

2.5!)(PtD )1+ !(PtM )1

1
1:

Small Open Economy Features

Here, we describe the small-open economy feature of the model. Substituting eq. (5) into eq. (6) and
log-linearization around the steady state yields a modi…ed version of the uncovered interest rate parity
condition^ t Et ^ t+1 = R^ tf Et ^ f + Et e^t+1 + ^ tRt+1
where the log-deviation from the steady state is denoted by the hat-form. Following Adolfson et al.
(2007), the country risk premium is assumed to depend on the level of the net foreign debt and thechanges in the real exchange rate as follows^ t = ' ^bf + 'e (Et e^t+1 +te^t ) + ut

where parameters ' and 'e control the sensitivity of country risk premium in response to the level ofnet foreign debt and changes in real exchange rate and ut is an AR(1) exogenous shock to the country
risk premium.
The demand of …nal goods by the foreign sector, YtX , which is to be exported to foreign sector is given
by
'f
1
X
Yt =
Ytf
et
where the inverse of real exchange rate stands for the relative price of Canadian …nal goods in terms offoreign goods, parameter f stands for the relative price elasticity of exported …nal goods, and Ytf stands
for foreign GDP.
The balance of payment accounting identity is given as!
Rtf 1 t 1 ff
XMYt
et Yt = etbt 1 b tftwhere the left-hand side stands for the trade surplus and the right-hand side stands for foreign investment
income de…cit combined with the change in net foreign debt position. By the accounting identity, bothsides should be balanced as above.
In order to keep the foreign sector as simple as possible, we assume ARMA(1,1) process for loglinearized foreign GDP, foreign in‡ation, and foreign interest rate as follows:
Y^tf

=

^ ft
^ tf
R

=
=

Yf ^f
Yt 1 + uYt f where uYt f = uY f uYt f1 + "Yt f ;
f
f
f
Pf
Pf f
^ t 1 + uP
where uP
= uP f uPttt 1 + "t ; andRf
Rf ^ f
Rt 1 + uRf
where uRf
= uRf uRfttt 1 + "t :12Thus, the structure of the foreign sector is exogenous to the domestic sector – i.e., the exogenous shock
originating in the foreign sector will a¤ect Canadian endogenous variables, but the shock originating in
the Canadian sector will not a¤ect foreign variables.

2.6

The Rest of the Model Structure

In closing the model, we describe the rest of the model structure here. The central bank is assumed tofollow a simple Taylor-type monetary policy rule and the nominal interest rate is adjusted in response toin‡ation gap and GDP gap with some interest rate smoothing. In the log-deviation form, the monetary
policy rule is speci…ed as followhiR^t = RR^ t 1 + (1d t + "RR)
^ t + GDP GDP(23)twhere parameter R controls the magnitude of interest smoothing, parameterstands for the Taylor
GDPcoe¢ cient in response to in‡ation gap,
stands for the Taylor coe¢ cient in response to GDP gap(the variable GDPt will be de…ned shortly), and "Rt stands for i.i.d. monetary policy shock. The central
bank is assumed to react to the short-run in‡ation gap which is a deviation of in‡ation rate from thein‡ation target.
The government budget constraint is speci…ed as
gt =

(24)

t

which is simply saying that the government expenditure, gt , is …nanced solely by lump-sum tax, t , whichappears in the representative household’s budget constraint eq. (2). Thus, the government is assumed tooperate on a balanced budget every period without accumulating debt (or assets) over time.
Next, the market clearing condition for …nal goods is given as follows
EkX
Yt = cHt + ct + it + gt + Yt :(25)

Now, it should be noted that the above market clearing condition does not conform with the de…nition of(real) GDP since the net export does not appear in the equation. In order to conform with the de…nitionof real GDP (which will be the observed data in the estimation), we de…ne the auxiliary variable, GDPt ,by subtracting the value of imported intermediate goods from the value of …nal goods as follow
GDPt

Yt

et YtM :(26)

We use this auxiliary variable, GDPt , to match the actual real GDP data in our estimation section.

2.7

The Shock Structure

There are a total of 12 shocks speci…ed in the model. For convenience, these shocks are classi…ed into two
categories: …nancial shocks and non-…nancial shocks. We specify the stochastic process of each shock, inthe log-linearized form, as follows:
Financial Shocks

Aggregate net worth shock ("Nt ):N^ t = "Nt where "tExternal …nance premium shock ("St ):

u
^st =
13

i:i:d:

2
N)
i:i:d:S s
u^t 1 + "St where "St
N (0;

N (0;

2
S)

Non-Financial Shocks

A i:i:d:A^t = A A^t 1 + "A
N (0; 2A )t where "ti:i:d:^ = D^+ "D where "DN (0; 2 )Aggregate technology shock ("At ):Intertemporal preference shock ("Dt ):tGovernment expenditure shock ("G
t ):

t 1

Investment-speci…c tech. shock ("K
t ):

g^t =
A^K =

Country risk premium shock ("L
t ):

^t =

L^

C
Marginal cost shock ("M
):
t

C
"M
t

i:i:d:

Monetary policy shock ("R
t ):

"R
t

f
Foreign in‡ation shock ("P
t ):

f
"P
t

i:i:d:

Foreign interest rate shock ("Rf
t ):

"Rf
t

i:i:d:

Foreign GDP shock ("Yt f ):"Yt f

i:i:d:

t

i:i:d:tt

D

G i:i:d:g^t 1 + "G
N (0; 2G )t where "t
K ^K
K i:i:d:At 1 + "K
N (0; 2K )t where "tGL
L i:i:d:N (0;t 1 + "t where "t

N (0;

N (0;

2
L)

2
MC )

2
R)

N (0;

2
Pf)

N (0;

2
Rf )

N (0;

2
Y f) .

3

Estimation Strategies and Data Description

3.1

Motivation of having two …nancial shocks in the model

As we have seen in Section 2, in addition to standard macroeconomic shocks adopted in the empirical
DSGE literature, we adopt two types of …nancial shocks in this paper: 1) external …nance premium shockand 2) aggregate net worth shock. The importance of the external …nance premium shock has been
pointed out by Smets and Wouters (2003, 2007)13 and Dib et al. (2008), among others. In a similar
fashion, CMR emphasized the importance of the role of the aggregate net worth shock14 to economic‡uctuations based on U.S. data. Considering the potential importance of both …nancial shocks to the
Canadian business cycle, the approach of this paper is to incorporate only one or both or even none of
the …nancial shocks in the estimation models and to assess the relative importance of the two shocks.
In our model setup, an intrinsic di¤erence between the external …nance premium shock and the aggregate net worth shock is as follows: the former shock directly a¤ects the …nancing cost of capital goods,
but does not a¤ect the balance sheet of the entrepreneurs directly, whereas the latter shock a¤ects theaggregate net worth directly, which in turn a¤ects the …nancing cost of capital goods via change in leverage
ratio. In other words, the former shock is an exogenous shock to the …nancing cost, whereas the lattershock is an exogenous shock to the aggregate net worth position which, in turn, a¤ects the …nancing costendogenously. In a sense that the external …nance premium shock a¤ects the external …nance premium(or credit spread) regardless of the conditions in corporate balance sheets, this shock can be interpreted asa shock occurring in the …nancial market or a shock to …nancial intermediary’s lending attitude. Likewise,
the aggregate net worth shock can be interpreted as a shock occurring in the corporate sector a¤ecting
the aggregate net worth position of the economy.
1 3 To be accurate, Smets and Wouters (2003, 2007) refer to their …nancial shock as ‘equity premium shock’.

However, thisshock is essentially the same as external …nance premium shock in our model, in the sense that it a¤ects the …nancing costof capital goods exogenously.
1 4 To be accurate, CMR refers to this shock as ‘…nancial wealth shock.’ In our paper, however, noting an importanceof this shock to the entrepreneurial aggregate net worth, we will simply refer to this shock as ‘aggregate net worth,’ unlessotherwise noted.

14

In order to compare the relative importance (or unimportance) of these two …nancial shocks, weestimate several versions of the model speci…ed in Section 2. Speci…cally, we employ four versions ofempirical models where 1) there are no …nancial shocks in the model (referred as NoFin-Shock model),2) the aggregate net worth shock is the only …nancial shock in the model (referred as eN-only model), 3)
the external …nance premium shock is the only …nancial shock in the model (referred as eS-only model),and 4) both shocks are incorporated into the model (referred as Full-Shock model).

3.2

Motivation of the usage of …nancial data

In addition to the standard macroeconomic data, such as GDP, consumption, business …xed investment,
in‡ation rate, etc., used in the empirical DSGE literature (such as in SW and Adolfson et al. (2007),
among others), we use additional …nancial data to estimate the model. Since the main objective of thispaper is to assess the link of …nancial variables and shocks to real economic activity in the Canadianbusiness cycle, it is imperative that we include some additional …nancial data to identify the shocks and,further, to assess the …nancial shock propagation mechanism more accurately. Following CMR, we include
credit spread data as a proxy for external …nance premium. Provided that credit spread data is a goodproxy of the external …nance premium, inclusion of such data should help assessing the dynamic linkage(if any) between the external …nance premium and business …xed investment more accurately.
In addition to credit spread data, we add another …nancial data for model estimation. Speci…cally, we
include leverage ratio data from the National Balance Sheet Accounts as a proxy for the leverage de…nedin the model. The reason for this inclusion is as follows. There are two …nancial shocks in the benchmark
model in this paper: external premium shock and aggregate net worth shock. As we will see later inthe estimation section, both shocks imply qualitatively similar, if not quantitatively, shape of impulse
response functions for the non-…nancial variables such as GDP, consumption, business …xed investment,
capital price, in‡ation, and trade surplus. Further, even for impulse response functions of external …nancepremium, both shocks imply qualitatively similar shape. Thus, if the observable variables are con…ned tothese variables, it will be di¢ cult, if not impossible, to discern the external …nance premium shock fromthe aggregate net worth shock from the observed data. In order to facilitate identi…cation of two shocks,
we include additional …nancial data, such as leverage ratio data, for the model estimation.

3.3

Data description

We estimate the model using 12 series of quarterly Canadian and U.S. data: Canadian GDP, consumption
expenditure, business …xed investment, in‡ation rate, trade surplus, U.S.-Canada real exchange rate, yieldspread, credit spread, leverage ratio, U.S. GDP, U.S. in‡ation, and U.S. nominal interest rate. Due to theavailability of leverage ratio data, the sample period spans from 1990Q1 to 2007Q4 (total 72 observations).
The data series of Canadian GDP, consumption expenditure, business …xed investment, and trade
surplus are from Statistics Canada’s National Income and Expenditure Accounts (NIEA). All the expenditure series are measured in seasonally adjusted, real terms, and per capita base using Canadian
population aged 15 years and above. Consumption expenditure is measured by real personal expenditure
on consumer goods and services, while business …xed investment is measured by non-residential structuresand equipment. The series for trade surplus is constructed from exports and imports measured by goods
and services. Canadian in‡ation rate is based on the Bank of Canada’s measure of core-CPI index,
excluding eight most volatile components of CPI and adjusted for indirect tax e¤ects.

15

The data series of credit spread is based on the index15 of BBB medium term corporate bond spreadvis-à-vis medium term government bond. This credit spread data will be matched to the model’s external…nance premium, st 16 . The data series of leverage ratio is simply the ratio of total asset over net
worth where both data are adopted from the National Balance Sheet Accounts (NBSA, non-…nancial
corporations including government business enterprises). This leverage ratio data will be matched to themodel’s leverage ratio, qt 1 kt =nt , with some measurement error. Again, it should be noted that, due tothe data restriction arising from the NBSA, the sample period of leverage ratio is con…ned to 1990Q1 to
2007Q4.
The data series of U.S. GDP is from the U.S. National Income and Product Accounts (NIPA) andis measured in seasonally adjusted, real terms, and per capita base using U.S. total population. U.S.
in‡ation rate is based on seasonally adjusted U.S. core-CPI, excluding food and energy components. U.S.
nominal interest rate is measured by the U.S. Federal Funds target rate. U.S.-Canada real exchange rateis calculated as the nominal exchange rate (Canadian$/US$) multiplied by the ratio of U.S. CPI overCanadian CPI. Thus, the U.S.-Canada real exchange rate measures the relative price of U.S. goods andservices in terms of Canadian goods and services which is consistent with the unit of real exchange rate,
et , de…ned in this paper.
The data series for yield spread is calculated by subtracting the yield rate from a 10-year Government of
Canada Bond from the interbank overnight rate, which is the policy instrument for the Bank of Canada.
^ in the model according to the following
Then, this yield spread data is matched with the variable R
equation
39
1 X ^
^t
Et Rt+i(27)
Y Stobs = R
40 i=0where Y Stobs stands for yield spread data observed at period t. The reason why we do not simply match^ t is that R^ t in the model represents the (log) deviation of short-term nominal
the overnight rate to R
interest rate from its steady state (i.e., Rss = ss = in our model). Now, if, in reality, the expectedin‡ation rate is stationary over time without having any trend, then usage of overnight rate data can^ t to the demeaned overnight rate data. Unfortunately, however, thebe justi…ed by matching model’s R
expected in‡ation rate may possess a trend over time. In order to match the overnight rate data with^ t , then, it requires appropriate detrending which is a formidable task to attain. Rather,
the model’s R
in our paper, we take a di¤erent path and construct the yield spread by subtracting 10-year government
bond yield from the overnight rate. Under the assumption that the term premium on a 10-year bond isappropriately eliminated17 and the expected in‡ation component being cancelled out by subtraction, theyield spread data represents the gap between the short-term monetary policy stance and long-term (or10-year-averaged) monetary policy stance. In our model, this gap can be formulated by the right handside of eq. (27). Similar methodology has been adopted by DeGraeve et al. (2007) and Wouters (????).
1 5 The sources of this index are due to Scotia Bank for the period of 1980Q1 to 1999Q3 and Merrill Lynch for the periodof 1999Q3 to 2007Q4. Two indices by Scotia Bank and Merrill Lynch were equalized and connected at 1999Q3.
1 6 Dib et al. (2008) adopts business prime rate less real interest rate as a proxy for external …nance premium. By adopting
corporate BBB bond spread in this paper, we believe that we can capture the ‘average’ credit spread of the business sector
rather than ‘prime’ credit spread. Further, credit spread based on business prime rate reveals signi…cant persistence since
the late 90’s in Canada, behaving as if it is …xed and independent of the corporate balance sheet. This is another reason
why we adopt BBB corporate bond spread as a proxy for the credit spread.
1 7 In our paper, we attempt to eliminate the term premium by demeaning the raw yield spread data where the raw yieldspread is simply equal to the overnight rate less 10-year government bond yield. Implicit assumption we make here is thatthe term premium is stationary during the sample period.

16

Finally, the structure of the model assumes that all the variables possess a stationary processes aroundthe steady states. Further, since we log-linearize the model around the steady state and convert all
the variables into the log-deviation form with mean zero, the observed data need to be transformed
accordingly. Speci…cally, we (log) linearly detrend the following series; Canadian GDP, consumption
expenditure, business …xed investment, trade surplus, real exchange rate and U.S. GDP. Also, we demean
the following series; Canadian in‡ation18 , yield spread, credit spread, U.S. in‡ation, and U.S. nominalinterest rate.

3.4

Measurement Errors

We allow for the existence of measurement errors for the following variables: trade surplus and leverage
ratio. The reason is purely empirical. For the trade surplus data series adopted from NIEA, it includes
the trade surplus from the U.S. as well as the rest of the world. However, the foreign GDP, foreignin‡ation, and foreign interest rate in the model are matched to the U.S. data only that there may be adiscrepancy between the model’s de…nition of trade surplus vis-a-vis the actual trade surplus from thedata. In order to subdue the e¤ect from this possible discrepancy empirically, we impose the measurement
error to the model’s de…nition of trade surplus as follows
T Stobs = (YtX

et YtM ) exp(uTt S )where T Stobs stands for the observed trade surplus data and uTt S stands for the measurement error for the
trade surplus. We allow the measurement error to follow AR(1) process as follows;
Measurement error in trade surplus ("Tt S ): uTt S =i:i:d:TS TS
ut 1 + "Tt S where "Tt S
N (0;2
T S ):The reason for imposing measurement errors on leverage ratio is similar. For leverage ratio, we adopt
the data from the NBSA where the de…nition of the asset, liability and net worth may be di¤erent fromthe model’s de…nitions of those variables. Again, in order to subdue the possible empirical e¤ects arisingfrom these discrepancies, we impose the measurement errors to the model’s de…nition of leverage ratio as
follows
qt 1 kt
LVtobs =exp(uLVt )ntstand for the measurement errors for leverage
where LVtobs stand for observed leverage ratio data and uLVtratio. Again, we allow the measurement error to follow AR(1) process as follow;
LV
Measurement error in leverage ratio ("LV=t ): ut

3.5

T S LVut 1 + "LVtwhere "LVt

i:i:d:

N (0;

2
LV ):

Calibrated parameters and Priors

We calibrate the subset of the parameters in the model that are not identi…able (i.e., the parameters only
pertinent to the steady states) or are di¢ cult to identify from the observed data. Calibrated parameters
are reported in Table 1. From Christensen and Dib (2008), the discount factor, , is set to 0.9928, thecapital share, , is set to 0.3384, and the capital depreciation rate, , is set to 0.025. Following BGG,
the survival rate of the entrepreneurs, , is set to 0.9728. Likewise, the speci…cation of the priors arereported in Table 2.
1 8 To be accurate, we did not demean the Canadian in‡ation, but rather we subtracted 2% (or 0.5 quarterly percentagerate) from the in‡ation rate series. This is due to the modeling assumption such that the steady state of the moving in‡ation
target, t , is equal to 2%. This assumption is based on the fact that the Bank of Canada has …xed the in‡ation target at
2% since the end of 1995.

17

Parameters

!
D
M
IT

kss =nss
gss =GDPss

Table 1: Calibrated Parameters
Description
discount factor
capital share in production
mean survival rate of entrepreneurs
capital depreciation rateshare of imported goods in …nal goods production
elasticity of substitution between domestic and imported goods
relative price elasticity of domestic goods
relative price elasticity of imported goods
persistence parameter of in‡ation target shockgross steady state in‡ation target
steady state leverage ratio
steady state ratio of government expenditure to GDP

Values
0.99280.3384
0.97280.025
0.2479
1
20
20
0.975
1.005
1.991
0.2201

4

Estimation Results with Various Shock Speci…cations

4.1

Posteriors

Table 3 reports the posterior distributions of the parameters for the benchmark model described in Section
2. For the sake of comparison, the estimation results for three alternative versions of the model arereported as well – i.e., 1) the model without …nancial shocks (denoted NoFin-Shock model, hereafter),2) the model with only aggregate net worth shock as …nancial shock (denoted eN-only model, hereafter),and 3) the model with only external …nance premium shock as …nancial shock (denoted eS-only model,
hereafter). It should be noted that, here, the basic structure of four models are exactly the same, except
for the speci…cation of the …nancial shocks. The idea in comparing the estimation result of the benchmark
model against those from three di¤erent models is to see whether the estimation result is sensitive to thespeci…cation of the …nancial shock structure.
The most notable results are for the estimates of elasticity of external …nance premium, . It turns outthat the posterior means for are very close under benchmark model, NoFin-Shock model, and eS-onlymodel (0.0267, 0.0263, and 0.0267, respectively), while the posterior mean under eN-only model turns out
to be quite di¤erent (which is 0.0630). Compared to BGG’s original calibration (which was 0.05) andChristensen and Dib’s (2008) estimate (which was 0.042 based on U.S. data), the estimates of underbenchmark model, NoFin-Shock model, and eS-only model are relatively low. In contrast, under eN-onlymodel, the estimate of turned out to be relatively high. This contrast in the estimates of indicatesthat the estimation result can be sensitive to the speci…cation of the shock structure. Since is the
key parameter in controlling the …nancial accelerator e¤ect, this gap in the estimates of will make themagnitude of propagation from monetary policy shock quite di¤erent, especially for the business …xed
investment, as we will see later in the estimated IRF.
Turning to the elasticity of capital goods production, , the posterior means are more or less similar
among four models. The posterior mean of NoFin-Shock model turns out to be slightly higher (whichis 2.0657) than other three models, but it is not signi…cantly di¤erent based on the con…dence intervalreported. The di¤erences in shock structures do not seem to matter for the estimate of , at least in ourestimates.
18

Table 2: Speci…cation of the Priors
Parameters
GDP

h

D
M
D
M

'e
'
'f
all ’sall ’sDescription
Taylor coe¢ cient of in‡ation gap
Taylor coe¢ cient of GDP gap
habit formation parameterelasticity of labour supply
elasticity of external …nance premium
investment adjustment cost parameter
Calvo parameter for domestic goods
Calvo parameter for imported goods
in‡ation persistence param. for domestic goods
in‡ation persistence param. for imported goods
elasticity of country risk premium w.r.t. eelasticity of country risk premium w.r.t. bf
relative price elasticity of exported goods
all AR(1) persistence parametersstd. deviation for all shocks

Dist. Type
gamma
gamma
beta
gamma
inv. gamma
gamma
beta
beta
beta
beta
beta
inv. gamma
gamma
beta
inv. gamma

Mean
2.00
0.50
0.5
0.5
0.05
1.00
0.50
0.50
0.50
0.50
0.50
0.001
2.00
0.5
0.01 or
0.001

Std.
0.5
0.25
0.25
0.35
0.025
0.5
0.25
0.25
0.25
0.25
0.25
Inf
0.75
0.25
Inf

Next, the estimation results of the standard deviation of the shocks which are reported at the lower
panel of Table 3. In this paper, since the focus is on the …nancial shocks, we restrict our attention to theaggregate net worth shock and external …nance premium shock. Taking a look at the estimates of thestandard deviation of the aggregate net worth shock, "Nt , we notice a di¤erence between the benchmark
model and the eN-only model. Under benchmark model, the estimate is relatively small (which is 0.0051),
while under the eN-only model, the estimate is relatively large (which is 0.0089) and the di¤erence in theestimate seems to be signi…cant based on the con…dence interval. In contrast, turning to the estimatesof the standard deviation of the external …nance premium shock, "St , we …nd the estimates under thebenchmark model and the eS-only model to be very close with each other.
Finally, we now turn to the marginal likelihoods of each model. As can be seen from Table 3, thebenchmark model has the highest marginal likelihood among three models (we exclude the NoFin-Shockmodel since we cannot compare it on equal footing). This result is not surprising. Since the benchmark
model incorporates both …nancial shocks, it should have higher ‡exibility in ‘matching’the model to theobserved data compared to the eN-only or eS-only models.19 Now, the marginal likelihood of the eN-onlymodel was sizably lower than those of the benchmark model and eS-only model. If we are to take marginal
likelihood as a model selection criteria, the …nancial shock structure only with the aggregate net worth
shock may not be appropriate in accounting for the observed data compared to the benchmark model or
eS-only model. Also, relatively low marginal likelihood under the eN-only model may, in part, explain
why the eN-only model yielded a very di¤erent estimate for compared to other models.
1 9 However, it is worth noting that the marginal likelihood of eSonly model was strikingly close to that of benchmark
model.

19

4.2

Estimated IRF

Next, we report the estimated IRF from our four model speci…cations. Since the dimension of endogenous
variables and shocks are large, we restrict our attention to selected shocks and variables. Speci…cally, forthe variables we restrict our attention to the followings; GDP, consumption, business …xed investment,
capital price, in‡ation rate, external …nance premium, business credit, net worth, and leverage ratio.
For the shocks, we restrict our attention to the followings; aggregate technology shock, intertemporal
preference shock, investment-speci…c technology shock, monetary policy shock, external …nance premium
shock, and aggregate net worth shock.
Figure 1 reports the estimated IRF of the aggregate technology shock for the four model speci…cations.
As can be seen from the …gure, the benchmark model, NoFin-Shock model, and eS-only model have similar
magnitudes and patterns of IRF, while the IRF of the eN-only model reveals some di¤erence in magnitude
of response although the qualitative patterns are the same. The reason behind this di¤erence is dueto the di¤erence in the estimate of . The interpretation of the IRFs are as follows. After a positive
aggregate technology shock which, in turn, raises the marginal productivity of capital, entrepreneurs willaccumulate the net worth above the steady state. Consequently, the leverage ratio decreases and, thus,
the external …nance premium will decline. Now, since the estimate of is larger in the eN-only model,
the magnitude of decline in the external …nance premium is deeper under the eN-only model compared toother models. This deeper decline in the external …nance premium will, in turn, contribute to a larger
response in the business …xed investment – i.e., a stronger …nancial accelerator e¤ect vis-à-vis aggregate
technology shock under the eN-only model.
Figure 2 reports the estimated IRFs of the intertemporal preference shock. For this particular shock, allfour models have more or less reveal the same magnitudes and patterns of the IRFs. The interpretationof the IRFs are as follows. Given the intertemporal preference shock, consumers become temporarily
impatient that they decide to substitute future consumption for current consumption. As a consequence,
because of crowding-out e¤ect due to aggregate resource constraint, business …xed investment will fall.
Figure 3 reports the estimated IRF of the investment-speci…c technology shock. As can be seen fromthe …gure, positive investment-speci…c technology shock will lower the cost of producing capital goods,
thereby, boosting the business …xed investment. This qualitative pattern is common for all four models,
except that the magnitude is slightly di¤erent for the NoFin-Shock model due to a di¤erence in theestimate of investment adjustment cost parameter, . Turning to the external …nance premium, IRF of
the eN-only model reveals a larger increase compared to other models. Again, this is due to a di¤erencein the estimate of .
Figure 4 reports the estimated IRF of the monetary policy shock. The magnitude of ampli…cation in
IRFs are similar among the benchmark model, NoFin-Shock model, and eS-only model, while the eN-onlymodel reveals larger …nancial acceleration. The reason behind this di¤erence is obviously attributable
to the di¤erence in the estimates of . An interpretation is as follow. After a tightening in monetary
policy, the aggregate net worth will fall due to higher debt repayment cost, causing the leverage ratio torise. Consequently, the entrepreneurs will be facing a higher external …nance premium. Here, since
the elasticity of external …nance premium is higher under the eN-only model, the rise in the premium
under the eN-only model will be higher compared to other models. As a result, the …nancial acceleratione¤ect will be stronger and the decline in business …xed investment will be deeper under the eN-only modelcompared to other models.
Figure 5 reports the estimated IRF of the external …nance premium shock. Note that IRFs are only

20

shown for the Full-Shock and eS-only model since external …nance premium shock is absent in eN-onlyor NoFin-Shock by construction. As can be seen from the …gure, a positive external …nance premium
shock raises the cost of …nancing that the corporate sector reduces the amount of borrowing (or businesscredit) and, thus, cuts back on the business …xed investment. Further, as a result of prolonged reduction
in borrowing, corporate leverage ratio eventually (approximately …ve quarters after the shock) falls below
the initial level. This fall in leverage ratio will contribute to lower the external …nance premium, thus
partially o¤setting the impact from the external …nance premium shock. Indeed, business …xed investment
starts to recover approximately …ve quarters after the shock and quickly returns to the initial level.
Figure 6 reports the estimated IRF for a negative aggregate net worth shock. Since aggregate net
worth shock is absent in eS-only or NoFin-Shock model, IRFs are only shown for Full-Shock and eN-onlymodel. After a negative net worth shock, the entrepreneur is faced with a need to square the balance
sheet equation (9). As a result, the entrepreneur will reduce the capital stock (or reduce the asset side ofbalance sheet) by reducing the business …xed investment as can be seen from the …gure. Now, in orderto square the balance sheet, the entrepreneur will increase the borrowing (or increase the liability side ofbalance sheet) as well. This increase in borrowing will occur because if the entrepreneur tries to square
the balance sheet only by reducing the capital stock, then the opportinity cost from forgone investment
will be too high. Thus, it is in an interest of the entrepreneur to strike a balance between reductionof asset side and increase in liability side by reducing business …xed investment and by increasing debt.
Now, due to an increase in borrowing and decrease in net worth, the leverage ratio will rise. This risein leverage ratio will contribute to raise the external …nance premium, thus prolonging the impact fromthe aggregate net worth shock. Consequently, it will have a prolonged e¤ect on business …xed investment
which is in contrast to the external …nance premium shock.
For Figure 5 and Figure 6, one important observation should be made. Turning to the IRF of theexternal …nance premium, it is rising both in Figure 5 and Figure 6. However, turning to the IRF
of business credit, it is falling after the shock in Figure 5 and it is rising in Figure 6. Based on thisobservation, the external …nance premium shock can be classi…ed as a ‘supply-side’ shock in the credit
market and the aggregate net worth shock can be classi…ed as a ‘demand-side’shock in the credit market.
Thanks to this qualitatively di¤erence between the external …nance premium shock and the aggregate net
worth shock, two …nancial shocks in the model can be identi…ed once the relevant …nancial data (especiallyrelated to external …nance premium and business credit) are supplied.20

4.3

Variance Decomposition

We next consider the forecast-error variance decompositions for selected variables under all four model
speci…cations. For each decomposition, we decompose the variance of forecast-error at the horizon of
1-quarter, 4-quarter, 8-quarter, and 16-quarter. In addition, unconditional variance decomposition ofeach variable will also be reported.
Table 4 reports the forecast-error variance decomposition based on the benchmark model. Turning to
the variance decomposition of GDP, most of the movement in GDP is accounted by aggregate technology
2 0 Notice that it will be extremely di¢ cult to identify two …nancial shocks just based on real-side (as opposed to …nancial-side) data. This is because, by construction, the qualitative pattern of IRFs related to real-side variables will be similar forboth …nancial shocks – i.e., real-side economy and …nancial-side economy are linked by the external …nance premium whichis the only real-…nancial linkage in the model. Indeed, if we take a close look at the IRFs of real-side variables such as GDP,
consumption, business …xed investment, captial price and in‡ation in Figure 5 and Figure 6, we notice that the directions of
IRF movements are the same for both …nancial shocks.

21

shock which is in line with the empirical evidence of the empirical DSGE literature. Financial shocks(aggregate net worth shock and external …nance premium shock) accounts for a small portion (1% to 2%)of the movement in GDP. For the business …xed investment, the picture is quite di¤erent. As can beseen from the table, the variation of business …xed investment is largely accounted by the investmentspeci…c technology shock, especially on a shorter forecast horizon, while the …nancial shocks account for
non-negligible portion of the variation, especially in a longer horizon. In a longer forecast horizon, theaggregate net worth shock accounts for about 5.6% and the external …nance premium shock accounts forabout 7.5% of the variation in the business …xed investment. In total, …nancial shocks accounts for about
13% of the variation in business …xed investment in a longer forecast horizon and this is not a negligible
size. Turning to the variance decomposition of the external …nance premium, most of the movement
is accounted by the external …nance premium shock. However, sizable portion of the movement in theexternal …nance premium is attributable to the aggregate net worth shock, especially in a longer forecasthorizon. Indeed, the aggregate net worth shock accounts for more than the aggregate technology shock,investment-speci…c technology shock, and monetary policy shock in all forecast horizon. Finally, let us
turn to the variance decomposition of leverage ratio. Here, recall that we have allowed for a measurement
error when observing this variable. With no surprise, large portion of the variation of leverage ratio data
is attributed to a measurement error, especially in a shorter forecast horizon. However, it should bealso be noted that the share of a measurement error in variance decomposition decreases as the forecasthorizon gets longer. For an unconditional forecast-error horizon, measurement error accounts for lessthan 10% of the movement in leverage ratio data. Aside from a measurement error, it turns out that theaggregate net worth shock is an important shock in accounting for the variation in leverage ratio both in
the short and long forecast horizon. The external …nance premium shock also turns out to be important,especially in the longer horizon, in accounting for the variation.
Table 5 reports the forecast-error variance decomposition based on the eN-only model. Let us …rst
turn to the variance decomposition of GDP. In contrast to the benchmark model, sizable portion of thevariation in GDP is now accounted by the aggregate net worth shock – as much as 10% in the longer
horizon. This is more evident if we turn to the variance decomposition of the business …xed investment.
The aggregate net worth shock accounts for more than 10% in the shorter horizon and more than 30% in
the longer horizon. Literary taking the result under the eN-only model, the aggregate net worth shockaccounts for the variation in the business …xed investment more than the investment-speci…c technology
shock in the longer horizon. Compared to the benchmark model where the investment-speci…c technology
shock accounted for more than the …nancial shocks, this is a very di¤erent result. Turning to the variancedecomposition of the external …nance premium, astonishingly, majority of the variation is accounted by
the aggregate net worth shock in all forecast horizon. Since the aggregate net worth shock is the only
…nancial shock under the eN-only model, perhaps, this restrictive shock structure forced the aggregate net
worth shock to account for the variation in the external …nance premium. This is one particular example
where a di¤erence in shock structure signi…cantly alters the result of variance decomposition. Finally,turning to the variance decomposition of the leverage ratio, the aggregate net worth shock accounts forlarge portion of the variation. One notable di¤erence compared to the benchmark model is that the shareof a measurement error in variance decomposition remains to be large even in the longer forecast horizon
which stands in sharp contrast to the benchmark case. This can be considered as an evidence that the…nancial shock structure under the eN-only model is not capable in accounting for the movement in theleverage ratio data appropriately.
Table 6 reports the forecast-error variance decomposition based on the eS-only model. For GDP,22

the external …nance premium shock accounts for small portion of the variation (1% to 2%). Turning to
the business …xed investment, the external …nance premium shock accounts for non-negligible size of thevariation especially in the longer horizon, although its size is not as large as that of the investment-speci…ctechnology shock. This result under the eS-only model is similar to the result under the benchmark
model both qualitatively and quantitatively. Now, turning to the external …nance premium, nearly 90%of the variation is accounted by the external …nance premium shock for 1-quarter to 16-quarter forecasthorizon. Even for unconditional forecast horizon, approximately 60% of the variation is accounted by
the shock. Taking this result for a face value, this implies that the exogenous component in eq. (16)is accounting for most of the movement in the external …nance premium and the endogenous component
in eq. (16) is accounting for only a minor share. Interpreting di¤erently, this result suggest that theeS-only model is not successful in capturing the movement in the external …nance premium endogenously
and need to rely on the exogenous factor to …t the data. Lastly, turning to the leverage ratio data, ameasurement error accounts for most of the variation in the shorter horizon and still a large portion evenin the longer horizon. Compared to the benchmark model, the share of a measurement error in variancedecomposition is larger both in short and long horizon which indicates a poor performance of the eS-onlymodel in accounting for the variation in leverage ratio data.
Finally, we touch on the variance decomposition result under NoFin-Shock model which is reported
in Table 7.21 For GDP, the share of the investment-speci…c technology shock in variance decompositionis larger compared to that of the benchmark model, both in short and long horizon. Perhaps thevariation in GDP which was accounted by …nancial shocks under the benchmark model is now picked upby the investment-speci…c technology shock under the NoFin-Shock model. Turning to the business …xed
investment, the variation is largely accounted by the investment-speci…c technology shock. This result
is similar with the empirical DSGE literature which emphasize the importance of the investment-speci…ctechnology shock. Now, compared with the benchmark model in this paper, di¤erence in the importanceof the investment-speci…c technology shock is stark especially in the long horizon. Under the benchmark
model, the investment-speci…c technology shock, in the unconditional forecast horizon, accounts for about
17% of the variation in the business …xed investment whereas, under the NoFin-Shock model, it accounts
as much as 49% of the variation. Assuming that the benchmark model is the correctly speci…ed model,
an omission of the …nancial shocks will render the model to rely too much on the investment-speci…ctechnology shock in accounting for the variation in the business …xed investment, which results into an‘over-accounting’by this particular shock. In principle, a question asking which model –the benchmark
model, NoFin-Shock model or perhaps other kind of model – is the ‘correct’model is an open question.
However, the result reported in Table 7 points for a potential pitfall of ‘over-accounting’by a particular
shock, especially when the shock structure is misspeci…ed.

4.4

Historical Decomposition

Following SW(2003, 2007), we conduct a historical decomposition for selected observed variables: GDP,business …xed investment, external …nance premium and leverage ratio. Theoretically speaking, themovement (or deviation from steady state) of any endogenous variable can be ultimately attributed tothe movement in exogenous shocks in the model. The aim of the historical decomposition exercise isto account for the historical movement of the endogenous variables by the exogenous shocks from the2 1 Here in Table 7, since …nancial shocks are absent and …nancial data (i.e., credit spread and leverage ratio data) are notobservable in NoFinshock model, the variance decomposition for external …nance premium and leverage ratio will not bereported.

23

estimated model. One advantage of the historical decomposition exercise is that it allows us to see thedirection and the magnitude22 of contribution of each exogenous shock to the movement of endogenous
variables. Keeping this advantage in mind, we now turn to the historical decomposition results underfour model speci…cations.
Figure 7 shows the historical decomposition of four observed variables based on the benchmark model
estimation result. The observed data is indicated by a solid line and the contribution of each shock to thehistorical movement of the data is shown in the form of a bar chart. For GDP historical decomposition,
we notice that most of the movement in 1990’s and early 2000’s is accounted by the aggregate technology
shock, while the movement in late 2000’s are largely accounted by the country-speci…c risk premium shock.
Notice here that the …nancial shocks are playing non-negligible role in accounting for the movement, whichis consistent with the variance decomposition result reported in Table 4.
Turning to the business …xed investment, we observe that several shocks are contributing to the
movement. The aggregate technology shock, investment-speci…c technology shock, and country-speci…crisk premium shock are all contributing largely, although the contribution from the investment-speci…ctechnology shock is not as large as expected. Now, for the …nancial shocks, we observe that both shocks(aggregate net worth shock and external …nance premium shock) are playing a non-negligible role inaccounting for the movement in the business …xed investment. Further, we observe that two shocks
account for the movement in opposite direction from time to time. For instance, in the middle of1990’s, the external …nance premium shock contributes positively to the movement of the business …xed
investment, while the aggregate net worth shock contributes negatively. But then, in the early 2000’s,
both shocks contribute negatively to the movement. The fact that two shocks occasionally contribute in
the opposite direction and occasionally contribute in the same direction can be perceived as an evidence
that two shocks are well identi…ed in the estimation. It should be kept in mind that when the shocks are
not well identi…ed, as we will see later, two shocks are not able to account in opposite direction.
To see the details of how the …nancial shocks are a¤ecting the movement of business …xed investment, it
is useful to look at the historical decompositions of the external …nance premium and leverage ratio. First,
for the external …nance premium, we observe that the external …nance premium shock (which enters to eq.
(16) exogenously) is contributing for lower premium in the mid 1990’s and contributing for higher premiumin the early 2000’s, corresponding to the historical movement in the business …xed investment. Taking
a look at the contribution from the aggregate net worth shock, we observe that the shock is contributing
to raise the premium from early 1990’s to early 2000’s and then we see reversal of that contribution
in the middle of 2000’s. This pattern corresponds with the historical movement in the business …xed
investment as well. Second, turning to the leverage ratio, we observe that the aggregate net worth shock(which exogenously enters to the aggregate net worth transition equation (18)) is contributing to raise
the leverage ratio throughout early 1990’s to early 2000’s and then contributes to lower the leverage ratio
after mid 2000’s. This pattern is basically the same pattern observed in the historical decomposition of
the external …nance premium.
Figure 8 shows the historical decomposition under the eN-only model. Comparing the historicaldecomposition results of GDP and the business …xed investment against those under the Full-shock model(Figure 7), we observe that the aggregate net worth shock is taking a larger role under the eN-only model.
Indeed, the aggregate net worth shock is one of the main factors in determining the movement of GDP
2 2 In variance decomposition exercise, we have seen how each shock has contributed to the variance (i.e., second moment)of the endogenous variables. In contrast, historical decomposition exercise allows us to see how each has contributed to the…rst moment of the endogenous variables.

24and the business …xed investment under the eN-only, which stands in contrast to the results under the
Full-shock model. Further, under the eN-only model, the aggregate net worth shock tends to contributenegatively to the movement in GDP and the business …xed investment from late 1990’s to the middle of2000’s, but have almost no contribution in the early 1990’s and late 2000’s which stands in contrast to
the Full-shock model.
Turning to the historical decomposition results for the external …nance premium and the leverage ratio
under the eN-only model, we see a deeper mechanism of how the aggregate net worth shock is a¤ecting to
the movement of the business …xed investment. Basically, the aggregate net worth shock contributed toraise the premium from late 1990’s to the middle of 2000’s and this rise in the premium corresponds to therise in the leverage ratio (after smoothing) as we observe in the historical decomposition of the leverage
ratio. Indeed, we observe that the historical decomposition pattern of the premium and the leverage
ratio to be almost identical under the eN-only model. The reason behind this identical pattern can be
attributed to the omission of the external …nance premium shock. Without the external …nance premium
shock, the premium and the leverage ratio are forced to move in tandem (see eq. (15)) resulting to theidentical historical decomposition pattern. Not only that, by suppressing the external …nance premium
shock, the smoothed leverage ratio (not the observed leverage ratio) is forced to move in tandem with thecredit spread data as we can see from the …gure. Here, we see an example where the error structure of themodel (in this case, lack of the external …nance premium shock) matters substantially for the accountingof the business cycle.
Figure 9 shows the historical decomposition under the eS-only model. As can be seen, the …nancial
shock (in this case the external …nance premium shock) does not play a major role in the historicaldecomposition of GDP or the business …xed investment. For the business …xed investment, the external…nance premium shock plays some role in accounting for the historical movement and the pattern ofcontribution is similar to that under the Full-shock model, except for the period in the late 2000’s. Thisdi¤erence in the pattern of shock contribution in the late 2000’s can be attributed to the omission of theaggregate net worth shock under the eS-only model.
To see where the di¤erence in the pattern is arising, it is useful to check the historical decompositionof the external …nance premium and the leverage ratio data. Let us …rst focus our attention at the late2000’s of the historical decomposition result of the external …nance premium. Compared to the result
under the Full-shock model (see …gure 7), we notice that the magnitude of contribution from the external…nance premium shock is weaker under the eS-only model especially in 2007 when the sub-prime loan
problem broke out. This discrepancy between two models is stemming from the omission of the aggregate
net worth shock. Under the Full-shock model, since there is a substantial negative contribution fromthe aggregate net worth shock, the model is identifying relatively strong e¤ect from the external …nanceshock to account for the movement in the credit spread. In contrast, under the eS-only model, since
there is no contribution from the aggregate net worth shock, the model is identifying relatively weak e¤ectfrom the external …nance premium shock. In retrospect, considering the aftermath of the sub-prime loan
problem, the Full-shock model (i.e., the model containing two …nancial shocks) seems to be accounting forthe movement in the credit spread more plausibly. Finally, turning to the historical decomposition result
for the leverage ratio data, we observe that the e¤ect from the government expenditure shock is somehow
exaggerated under the eS-only model compared to that of Full-shock model. Further, as we see later,
the magnitude of a measurement error in leverage ratio is substantial under the eS-only model rendering
the gap between the smoothed leverage ratio and observed to leverage ratio to be quite large. Again,
these discrepancies can be attributed to the omission of the aggregate net worth shock under the eS-only25

model.

4.5

Smoothed and Observed Leverage Ratio

Here we check how three shock-speci…cations of the model – i.e., Full-shock model, eN-only model, andeS-only model –are …tting the …nancial data, in particular the leverage ratio data.23 First, let us take alook at Figure 10 which shows the smoothed and observed leverage ratio data under the Full-shock model.
As can be seen from the …gure, the smoothed leverage ratio under the Full-shock model …ts the observed
data quite well. This means that the Full-shock model was capable to account for the movement in theobserved leverage ratio data without relying too much on a measurement error. Next, let us take a lookat Figure 11 which shows the smoothed leverage ratio under the eN-only model. As can be seen from the…gure, the smoothed and observed leverage ratio reveal substantial discrepancy with each other. Thisis largely due to the omission of the external …nance premium shock. Without the premium shock, theleverage ratio de…ned in the model is forced to move in tandem with the credit spread data and this willcause a gap between the smoothed leverage ratio and observed leverage ratio. As a result, the model will
largely rely on a measurement error in accounting for this gap. Obviously, reliance on a measurement
error is not a convincing way of accounting for the historical movement in the leverage ratio data. Finally,
let us turn to Figure 12 which shows the smoothed leverage ratio under the eS-only model. As can beseen, the smoothed and observed leverage ratio reveal considerable discrepancy though not as bad as thecase under eN-only model. Qualitatively speaking, the smoothed leverage ratio under the eS-only model
does move in the same direction with the historical data most of the time, except for the late 2000’s when
the sub-prime loan problem broke out. Quantitatively speaking, however, the gap between the smoothedand observed leverage ratio is considerable. Again, the reason for this considerable discrepancy can be
attributed to the omission of the aggregate net worth shock under the eS-only model.
In sum, both the eN-only and the eS-only model revealed a considerable discrepancy between thesmoothed and observed leverage ratio, heavily relying on a measurement error in accounting for the
movement of the data. Failure of the eN-only and the eS-only model is basically due to the omissionof either the external …nance premium shock or the aggregate net worth shock. In contrast, we observethat the Full-shock model to have relatively small gap between the smoothed and observed leverage ratio.
This means that the Full-shock model did not have to rely on a measurement error in accounting for the
movement in the leverage ratio data. This result exempli…es the importance of embedding two …nancial
shocks (external …nance premium shock and aggregate net worth shock) into the model in accounting forthe movement in …nancial data. In other words, shock speci…cation does matter in accounting for the
movement in …nancial data.

5

Alternative Estimation Results with Various Data Sets

In section 4, we reported the estimation results of the model with various shock speci…cations. The
estimation results in section 4, however, were based on the …xed data set. In particular, …nancial data
were limited to credit spread data and leverage ratio data. What if the …nancial data were not con…ned
to credit spread or leverage ratio data? Does the result change substantially from the case where the
2 3 Another …nancial data used for estimation is the credit spread data.

However, since we assume that the credit spread
data can be observed without measurement errors, by construction, the estimated models have a perfect …t with the observed
data. In other words, smoothed credit spread and observed credit spread data matches perfectly.

26

…nancial data are …xed? In this section, we explore the estimation results based on the benchmark model(i.e., Full-shock model) by altering the data set.

5.1

Why do we need …nancial data?

We …rst ask why do we need …nancial data for estimating the model. What if we do not utilize …nancial
data at all or only utilize limited …nancial data? In order to answer the question, we take up three
versions of data sets where – A) both credit spread data and leverage ratio data are absent, B) credit
spread data is utilized, but leverage ratio data is absent, and C) both credit spread data and leverage
ratio data are utilized.24 We refer to these three versions of data set as version A, version B, and version
C, respectively.
Table 8 reports the maximum likelihood estimation (MLE) results regarding the standard deviationsof the shocks for each version of data set. In theory, if the shock is well-identi…ed in the estimation,
the t-statistics of the standard deviation of the shocks will have high values.25 Keeping this in mind,
let us see the top panel in Table 8 where the estimation result from version A data set is reported. As
can be seen, t-statistics of the standard deviation of the aggregate net worth shock (denoted eN in thetable) is not statistically signi…cant. While t-statistics of the standard deviation of the external …nancepremium shock (denoted eS in the table) is statistically signi…cant, it is not as high as usually reported in
the empirical DSGE literature. These low t-statistics may be the sign of ill-identi…cation of the …nancial
shocks under version A data set. Another observation we should note is that t-statistics for all othershocks tend to be low as well. It may be the case that without …nancial data, the …nancial shocks are
ill-identi…ed and this ill-identi…cation of the …nancial shocks is ‘contaminating’the identi…cation of othernon-…nancial shocks. Turning to the middle panel where the estimation result from version B data set isreported, we see that t-statistics for the …nancial shocks to be higher than those under version A. Also, we
observe that t-statistics for other shocks to be substantially higher than those under version A –indeed,
the standard deviations of all shocks are statistically signi…cant. Finally, turning to the bottom panel
where the estimation result from version C data set is reported, we see even higher t-statistics for the…nancial shocks compared to version B data set. This is more or less so for other shocks as well. It
may be the case that, by utilizing more …nancial data in the estimation (recall that version B utilizes
more …nancial data than version A and version C more than version B), the …nancial shocks become more
identi…able yielding higher t-statistics and the identi…cation of …nancial shocks is helping to identify othershocks in the model as well.
In order to illustrate the consequences from ill-identi…cation of the …nancial shocks, we show thehistorical decomposition of business …xed investment under version A, B, and C. In the top panel of Figure
13, the historical decomposition result under version A data set is shown. We notice that the aggregate
net worth shock plays a major role in accounting for the movement in the business …xed investment, while
the external …nance premium shock plays almost no role. This is in sharp contrast with the historicaldecomposition result reported in Section 4 under the Full-shock model –the result which is re-posted at
the bottom panel of Figure 13 under version C data set – where both …nancial shocks played a role in
2 4 Thus, the estimation result under version C will be exactly the same with fullshock model estimation result reported in

Section 4. We report the result under version C to facilitate the comparison against version A and B.
2 5 Recall that identi…cation of the parameters in the maximum likelihood estimation is closely linked with the curvature of
the likelihood surface around the mode. For instance, ill-identi…ed parameters may have a loose curvature around the modeor the likelihood function may be multi-modal. Well-identi…ed parameters will have uni-modal likelihood function withsharp curvature. Consequently, well-identi…ed parameters will have relatively small standard error and high t-statistics.

27

accounting for the movement in the business …xed investment. Perhaps the ill-identi…cation of the …nancial
shocks, especially for the external …nance premium shock, under version A data set is the culprit behind
this odd historical decomposition result. Turning to the middle panel of Figure 13 where the historicaldecomposition result under version B data set is shown, this time, we notice that the aggregate net worth
shock is playing almost no role in accounting for the movement. Again, this is in sharp contrast with theresult reported in Section 4 (i.e., version C data set). As we have seen in the MLE result reported in Table
8, the t-statistics of the standard deviations of both …nancial shocks were statistically signi…cant that there
seemed to be no problem regarding the identi…cation of the …nancial shocks when we, at least, utilized
the credit spread data. Yet, we observe this odd historical decomposition result where the aggregate net
worth shock is playing almost no role even under version B data set. It may be the case that limited
utilization of …nancial data (recall that version B data set only utilize credit spread for …nancial data) was
not enough to provide su¢ cient information in identifying the …nancial shocks.
In sum, when there are multiple …nancial shocks in the model, it is essential to utilize multiple series of…nancial data to identify …nancial shocks in the estimation. As we have illustrated in this section, when
no …nancial data is utilized or if there are insu¢ cient series of …nancial data, it can be potentially di¢ cultto identify the …nancial shocks. Further, an ill-identi…ed …nancial shock may a¤ect the identi…cationof other shocks negatively and can yield misleading historical decomposition result as we have seen inthis section. For this reason, in order to identify the …nancial shocks and to reach a reliable historicaldecomposition, it is crucial to utilize su¢ cient series of …nancial data in the estimation.

5.2

Why do we use leverage ratio data?

Next, we ask why we select particular …nancial data for the estimation, speci…cally, the leverage ratio
data. What if we use some other type of …nancial data? Here, in order to answer this question, we
drop leverage ratio data from the data set and replace it, one after another, with the following …nancial
data; investment de‡ator, business credit, and stock price index. Thus, three di¤erent data sets werecreated and Full-shock model was re-estimated using three versions of the data set. For each estimation,
the investment de‡ator was matched with the price of capital, qt , business credit data from NBSA wasmatched with the corporate debt, bt , and, following CMR, the stock price index (TSX) was matched withthe corporate net worth, nt , in the model. Following the treatment for the leverage ratio, we allow for ameasurement error in each of the observed data.
Figure 14 shows the comparison of smoothed and observed data for the investment de‡ator, businesscredit, stock price index, and leverage ratio. The gap between smoothed and observed data represents themagnitude of measurement error. As can be seen from the …gures, all three …nancial data – investment
de‡ator, business credit, and stock price index – reveal a wide gap between smoothed and observed data,
heavily relying on measurement error to account for the historical movement. Although we do not reporta formal statistics regarding the goodness-of-…t to the observed data, a cursory visual inspection of Figure
14 should be enough to judge that the leverage ratio has the best …t.
There may be several reasons why the …nancial data considered here revealed a substantial gap between
smoothed and observed data. One reason may be that, conceptually, the de…nition of the variables in
the model and the de…nition of the data may not be consistent with each other. For instance, the stock
price may be re‡ecting the net present value of future pro…ts for …rms and may not be compatible withthe de…nition of the corporate net worth prescribed in the model. Indeed, as can be seen from the…gure, the observed stock price index tends to be volatile possibly re‡ecting the forward-lookingness of28

the variable, while the smoothed variable tend to be more stable perhaps re‡ecting the nature of net worth
being a state variable in the model. Another reason for the gap may arise from the detrending of theobserved data. For the estimation here, the investment de‡ator, business credit, and the stock price index
were log-linearly detrended. However, log-linear detrending of the …nancial data may be inappropriate
and some other methods of detrending, possibly non-linear detrending, may be necessary. In contrast,
leverage ratio data is a ratio of total asset over net worth that, as long as total asset and net worth arecointegrated, there is no issue of detrending for this data. This can be thought of as another advantage
of using leverage ratio data.
Whatever the reason may be, it is clear from Figure 14 that the leverage ratio reveal the best …t to thedata among the four …nancial data considered here. Of course this is not to claim that the leverage ratio
has the best …t for any countries or has the best …t under any kind of …nancial friction model. However, atleast for the Canadian case and for the model considered in this paper –i.e., a small-open economy versionof BGG model –, leverage ratio data, among other …nancial data, seems to be a promising candidate to
be included in an estimation data set.

6

Conclusion

In this paper, we have investigated the importance of …nancial shocks for the Canadian business cycle
employing the dynamic stochastic general equilibrium framework à la BGG with an extension of smallopen economy feature. In particular, in the spirit of Smets and Wouters and CMR, we explored theimportance of the external …nance premium shock and the aggregate net worth shock as two …nancial
shocks in the model.
In order to answer the question ‘how important are …nancial shocks’, it requires caution when choosing
the speci…cation of the shock structure. Or to rephrase the statement, we need to validate that both…nancial shocks – external …nance premium shock and aggregate net worth shock – are quantitatively
important for the business cycle. As such, we estimated the model under four speci…cations of …nancial
shocks – 1) the model without …nancial shocks, 2) the model with only aggregate net worth shock, 3)
the model with only external …nance premium shock, and 4) the model with both …nancial shock. It
turned out that the speci…cation of the …nancial shocks matters more or less for the estimation of theparameters and, hence, for the estimated impulse response functions. Further, it turned out that theresult of the variance decomposition and historical decomposition can dramatically change depending on
which shock speci…cation is adopted. Thus, the shock speci…cation does matter when making inferencewith the estimation results.
Based on the marginal likelihood statistics and the goodness-of-…t vis-à-vis the …nancial data, the modelwith both …nancial shocks fared better than other shock speci…cations. In other words, we con…rmed that,indeed, both shocks are quite important and none of them are redundant in accounting for the Canadianbusiness cycle. Taking the case of the business …xed investment in Canada, our variance decomposition
for unconditional forecast error showed that the external …nance premium shock to account for as muchas 7.5% and the aggregate net worth shock to account for as much as 5.6% of the variance of the business…xed investment. Combined, the …nancial shocks accounted for more than 13% of the variance and we
regard the size to be non-negligible when accounting for the business cycle.
Before we close the paper, one remark should follow. Former studies in the empirical DSGE literature have emphasized the importance of the investment-speci…c technology shock in accounting for the
movement in the business …xed investment. When we suppressed the …nancial shocks in our model, we
29

did …nd the investment-speci…c technology shock to be important –accounting for 49% of the variance ofunconditional forecast error. However, when the …nancial shocks were present in our model, the relative
importance of the investment-speci…c technology shock was subdued substantially. Indeed, the shockaccounted for only 17% of the variance and the size was not too di¤erent from those from the …nancial
shocks combined. Of course, our results are con…ned to Canadian case and it is too early to judge theimportance (or unimportance) of the investment-speci…c technology shock in other countries. Nevertheless, our evidence points to a potential importance of the …nancial shocks in other countries and are-examination of the role of the investment-speci…c technology shock in the empirical DSGE literature
may be warranted.

30

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31[17] Gertler, Mark, Simon Gilchrist, and Fabio Natalucci. 2007. External constraints on monetary policy
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32

Table 3: Posterior Estimates of Parameter Means Under Four Model Specifications
Full Shocks
Parameter

Prior
Mean

Post.
Mean

rho_A
rho_Akrho_lambda
rho_ED
rho_S
rho_EG
rho_Yfrho_pif
rho_EYF
rho_Epif
rho_ETS
rho_ELEV
rho_R
mu_pi
mu_Y
rho_Rfrho_ERfhabit
eta_pluschipsitheta_D
theta_M
iota_D
iota_M
phi_e
phi_lambda
phi_f0.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50002.00000.50000.50000.50000.50000.50000.05001.00000.50000.50000.50000.50000.50000.00102.00000.9926
0.3674
0.94820.72660.91790.89450.64120.80480.65000.04750.31950.91830.37632.8076
0.05500.72800.73710.16840.15910.02671.63990.05050.92000.48470.19310.11550.00111.6048eN Shock Only

5% Conf. 95% Conf.
0.9856
0.18920.93220.62530.85770.83750.32720.71380.32970.00020.01220.81040.1653
2.17120.02960.62290.63670.06460.01690.01930.90040.00040.89550.07410.03510.01310.00031.48300.99970.54530.96510.8366
0.97560.95070.9716
0.89400.9721
0.09740.6134
0.99750.57013.43760.08030.84000.84600.27300.28370.03422.41820.1016
0.94520.87830.34030.20570.0021
1.7321

Prior
Dist.

Prior
Mean

Post.
Mean

beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
gamm
gamm
beta
beta
beta
gamm
invg
gamm
beta
beta
beta
beta
beta
invg
gamm

0.50000.50000.50000.5000N/A
0.50000.50000.50000.50000.50000.50000.50000.50002.00000.50000.50000.50000.50000.50000.05001.00000.50000.50000.50000.50000.50000.00102.00000.97430.46980.95170.7045
N/A
0.87170.65650.77870.64460.06070.76120.9686
0.64282.58300.05360.73310.73470.36220.72490.06301.41180.55000.94210.2866
0.34220.08230.00061.5661eS Shock Only

5% Conf.

95%
Conf.

Prior
Dist.

Prior
Mean

Post.
Mean

0.95030.29910.93480.5356N/A
0.81500.34750.6866
0.33810.0001
0.5431
0.94200.55332.03210.02830.62950.63150.18210.03920.05280.50700.34540.91000.00600.12100.00020.0002
1.43770.99900.65520.96920.8823
N/A
0.9366
0.95620.88450.95000.12780.97790.99600.73383.13620.07720.84250.84160.53461.41560.07292.17300.76340.9786
0.59800.66810.17080.00101.6939

beta
beta
beta
beta
N/A
beta
beta
beta
beta
beta
beta
beta
beta
gamm
gamm
beta
beta
beta
gamm
invg
gamm
beta
beta
beta
beta
beta
invg
gamm

0.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50000.50002.00000.50000.50000.50000.50000.50000.05001.00000.50000.50000.50000.50000.50000.00102.00000.99130.42790.94770.72090.93540.88560.65910.80740.63950.05080.49030.96230.41272.73950.05340.73360.73010.18410.22030.02671.65580.11880.92850.53030.2564
0.10850.00101.5978

No Fin Shock

5% Conf.

95%
Conf.

Prior
Dist.

Prior
Mean

Post.
Mean

5% Conf.

95%
Conf.

Prior
Dist.

0.98270.25850.9316
0.60350.88940.81900.35170.72380.33640.00010.12090.93200.15572.14670.03200.62760.63030.05630.02530.01960.83620.00030.89560.13630.02390.00880.00031.47080.99950.59740.96310.83670.9864
0.95370.96290.89630.95320.10940.8801
0.9964
0.66143.32520.07630.83860.84210.29470.41750.03462.46810.35340.96400.91990.54360.19070.00191.7221

beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
beta
gamm
gamm
beta
beta
beta
gamm
invg
gamm
beta
beta
beta
beta
beta
invg
gamm

0.50000.50000.50000.5000N/A
0.50000.50000.50000.50000.50000.5000N/A
0.50002.00000.50000.50000.50000.50000.50000.05001.00000.50000.50000.50000.50000.50000.00102.00000.9846
0.61700.95970.7138N/A
0.84920.66570.79160.64550.05890.7570N/A
0.62332.81490.05130.73560.72780.23790.37790.02632.06570.36210.96680.42710.45850.15900.00091.6434

0.97170.48430.94130.5761
N/A
0.78850.3612
0.69800.34640.00030.6113
N/A
0.50892.19810.02700.62100.61250.09280.07750.01850.96710.1682
0.94890.03740.06720.01530.0002
1.5326

0.99840.76700.97630.8600N/A
0.9104
0.95110.88110.94040.12750.9244N/A
0.74073.38870.07540.84600.84480.38050.66970.0336
3.12670.54480.98650.80450.82030.29510.00171.7548

beta
beta
beta
beta
N/A
beta
beta
beta
beta
beta
beta
N/A
beta
gamm
gamm
beta
beta
beta
gamm
invg
gamm
beta
beta
beta
beta
beta
invg
gamm

Table 3 (ctd): Posterior Estimates of Shock Standard Deviations Under Four Model Specifications
Full Shocks
Shock
eA
eD
eG
eK
eL
eLV
eMC
eN
ePf
eR
eRf
eS
eTS
eYf

Prior
Mean
0.010
0.010
0.010
0.010
0.001
0.010
0.001
0.010
0.001
0.001
0.001
0.001
0.010
0.001

Post.
Mean
0.00800.00550.02230.01180.00310.00830.00980.00510.00150.00410.00090.00060.00920.0049eN Shock Only

5% Conf. 95% Conf.
0.00680.00390.01790.00950.00230.00620.00660.00280.00130.00270.00080.00050.00610.00420.00920.00700.02650.01410.00380.01040.01270.00730.00170.00520.00100.00070.01190.0055

Prior
Dist.
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg

Prior
Mean
0.010
0.010
0.010
0.010
0.001
0.010
0.001
0.010
0.001
0.001
0.001
N/A
0.010
0.001

eS Shock Only

Post.
Mean

5% Conf.

95%
Conf.

0.00940.01110.02980.01240.00270.01200.00140.00890.00150.00240.0009N/A
0.01640.00490.00730.00660.02530.00960.00190.01000.00020.00710.00130.00190.0008N/A
0.01330.00420.01160.01580.03420.01510.00350.01410.00310.01070.00170.00290.0010N/A
0.01950.0056

Prior
Dist.
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
N/A
invg
invg

Prior
Mean
0.010
0.010
0.010
0.010
0.001
0.010
0.001
N/A
0.001
0.001
0.001
0.001
0.010
0.001

No Fin Shock

Post.
Mean

5% Conf.

95%
Conf.

0.00810.00570.02380.01160.00300.00980.0082
N/A
0.00150.00380.00090.00060.01640.00490.00680.00360.01730.00930.00220.00830.0004N/A
0.00130.00220.00080.00050.00690.00420.00930.00780.03110.01390.00370.01120.0125N/A
0.00170.00530.00100.00070.01710.0055

Prior
Dist.
invg
invg
invg
invg
invg
invg
invg
N/A
invg
invg
invg
invg
invg
invg

Prior
Mean
0.010
0.010
0.010
0.010
0.001
N/A
0.001
N/A
0.001
0.001
0.001
N/A
0.010
0.001

Post.
Mean

5% Conf.

95%
Conf.

0.00820.00750.03000.01030.0025N/A
0.0011
N/A
0.00150.00260.0009N/A
0.01610.00490.00680.00480.02560.00800.0017N/A
0.0002
N/A
0.00130.00190.0008N/A
0.01360.00430.00960.01010.03440.01250.0032
N/A
0.0026N/A
0.00170.00330.0010N/A
0.01870.0056

Prior
Dist.
invg
invg
invg
invg
invg
N/A
invg
N/A
invg
invg
invg
N/A
invg
invg

Table 4: Variance Decomposition under Full-shock ModelGDP
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
57.99
73.01
79.12
83.08
93.07

eD
0.63
1.66
1.49
1.03
0.25

eG
24.13
12.92
8.72
5.61
1.32

eK
12.17
6.5
3.81
2.38
0.75

eL
0.21
0.1
0.09
0.19
0.36

eLV

Business Fixed Investment
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
9.21
24.94
36.47
42
50.83

eD
2.64
4.03
3.55
2.38
1.7

eG

eK
78.28
47.77
27.24
17.76
16.72

eL

eLV

0
0.02
0.08
0.17
0.26

External Finance Premium
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
1.54
1.75
1.88
1.89
1.24

eD
0.76
0.75
0.72
0.66
0.93

eG
0.01
0.04
0.09
0.2
0.76

eK
1.67
2.88
4.37
6.01
6.91

eL
0.32
0.81
2.26
6.53
21.12

eLV

Leverage Ratio
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA

eD

eG

eK

eL

0
7.88
10.74
12.27
9.43

0
3.81
7.89
14.96
28.8

eLV
72.59
39.28
31.01
23.75
9.73

0
6.03
6.39
5.49
1.7

0
2.43
2.04
1.5
1.28

0
0.14
0.27
0.42
1.03

0
0.07
1.09
3.15
3.75

eMC
1.68
0.45
0.99
1.45
0.67

eN
0.21
1.47
2.04
2.46
1.52

ePf
0.05
0.07
0.05
0.03
0.01

eR
0.01
0.35
0.66
0.88
0.52

eRf
0.13
0.26
0.24
0.19
0.03

eS

0
0
0
0
0

eMC
5.13
12.39
16.32
16.43
10.26

eN
1.17
3.18
4.82
5.81
5.61

ePf
0.06
0.11
0.12
0.11
0.07

eR
0.93
2.27
3.14
3.4
2.68

eRf
0.23
0.52
0.72
0.76
0.47

eS
2.29
4.56
6.29
7.88
7.55

eTS

0
0
0
0
0

eMC
1.17
1.27
1.26
1.1
2.13

eN
5.65
6.94
8.06
9.11
13.26

ePf

eR

eRf

eS
87.18
83.5
78.96
71.73
49.52

eTS

0
0
0
0
0

eMC

eN
27.41
23.98
22.08
19.89
18.66

ePf

eS

eTS

0
4.18
3.93
2.82
2.91

0
0
0.01
0.02
0.03

0
0.03
0.05
0.06
0.04

1.7
2.05
2.31
2.48
3.77
eR
0
5.88
5.86
5.21
5.14

0
0.01
0.08
0.22
0.32
eRf
0
0.2
0.38
0.54
0.43

eTS

0.4
1.26
1.64
2.13
1.41

0
6.13
9.31
13.01
20.84

0
0
0
0
0

eYf
2.39
1.96
1.15
0.56
0.11

0
0
0
0
0

eYf
0.05
0.13
0.17
0.15
0.09
eYf

0
0
0
0
0

0
0
0.01
0.02
0.02
eYf

0
0
0
0
0

0
0.04
0.06
0.06
0.03

Table 5: Variance Decomposition under eN-only ModelGDP
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
49.31
69.69
74.87
77.57
80.91

eD
0.25
0.7
0.75
0.55
0.24

eG
31.73
10.74
6.36
3.82
2.1

eK
10.68
3.69
2.12
1.62
1.41

eL

Business Fixed Investment
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
15.17
31.02
38.45
40.44
38.82

eD
3.66
4.55
3.46
2.2
1.94

eG
0.12
0.12
0.17
0.3
0.39

eK
64.61
32.74
18.12
13.63
15.65

eL
0.03
0.04
0.16
0.5
1.7

eLV

External Finance Premium
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
5.22
4.39
3.83
3.44
2.19

eD
0.88
0.47
0.29
0.19
0.15

eG
0.01
0.1
0.28
0.55
0.78

eK
9.21
11.72
14.11
15.72
12.54

eL

eLV

Leverage Ratio
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA

eD

eG

eK

eL

0
3.08
3.42
3.11
1.23

0
0.44
0.33
0.19
0.08

0
0.09
0.19
0.31
0.44

0
5.84
7.85
9.06
7.06

eLV

3.3
5.1
4.22
3.48
2.15

1.4
2.48
4.51
9.14
20.13

0
1.45
2.76
5.16
11.34

eMC
0.25
0.11
0.09
0.09
0.09

eN
0.82
6.36
8.51
10.14
10.75

ePf
0.06
0.13
0.09
0.05
0.03

eR
1.5
1.42
1.58
1.81
1.92

eRf
0.43
0.91
0.75
0.52
0.22

eTS

0
0
0
0
0

eMC
0.52
0.73
0.78
0.75
0.65

eN
11.35
23.68
30.57
33.62
32.87

ePf
0.04
0.05
0.04
0.04
0.05

eR
4.17
6.53
7.66
7.92
7.4

eRf
0.26
0.39
0.44
0.47
0.43

eTS

0
0
0
0
0

eMC
0.5
0.49
0.44
0.37
0.34

eN
70.68
68.53
65.2
60.05
54.29

ePf

eR
12.06
11.68
10.94
9.8
8.9

eRf
0.01
0.11
0.32
0.62
0.6

eTS

0
0
0
0
0

eMC

eN
35.49
42.16
41.02
38.03
32.02

ePf

eR

eRf

eTS

eLV
64.51
40.27
37.37
37.45
42.22

0
0.27
0.28
0.24
0.19

0
0.02
0.04
0.07
0.06

0
0.01
0.03
0.04
0.04

0
6.25
6.49
6.02
5.02

0
0.11
0.23
0.36
0.34

0
0
0
0
0

eYf
1.68
1.14
0.67
0.35
0.18

0
0
0
0
0

eYf
0.08
0.15
0.16
0.13
0.11

0
0
0
0
0

eYf
0.02
0.01
0.02
0.05
0.03
eYf

0
0
0
0
0

0
0.02
0.03
0.03
0.02

Table 6: Variance Decomposition under eS-only ModelGDP
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
57.25
73.4
80.4
84.87
93.01

eD
0.43
1.42
1.29
0.9
0.24

eG
25.54
12.85
8.44
5.23
1.34

eK
12.52
7.37
4.56
2.89
0.99

eL
0.83
0.62
0.42
0.45
0.45

eLV

Business Fixed Investment
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
9.15
24.13
36.66
43.25
49.82

eD
2.35
3.44
3.09
2.08
1.51

eG

eK
80.35
54.25
33.52
22.38
20.92

eL
0.03
0.15
1.1
3.01
3.7

eLV

External Finance Premium
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
1.66
1.83
1.92
1.9
1.3

eD
0.7
0.68
0.62
0.56
0.82

eG

eK
2.19
3.68
5.51
7.49
9.11

eL
0.27
0.7
2.04
5.89
20.48

eLV

Leverage Ratio
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA

eD

eG

eK

eL

0
9.93
13.1
14.27
10.3

0
3.49
7.09
12.74
23.17

eLV
100
59.82
49.31
40.99
24.21

0
6.25
6.38
5.2
1.48

0
2.16
1.72
1.18
0.93

0
0
0.04
0.12
0.21

0
0.03
0.08
0.19
0.72

0
0.13
0.26
0.39
0.81

eMC
0.4
0.15
0.63
1.06
0.6

ePf
0.08
0.1
0.08
0.05
0.01

eR
0
0.31
0.62
0.85
0.58

eRf
0.23
0.4
0.35
0.26
0.05

eS
0.45
1.49
2.07
2.89
2.61

eTS

0
0
0
0
0

eMC
4.19
9.73
13.49
14.13
9.09

ePf
0.07
0.11
0.12
0.11
0.08

eR
0.94
2.16
3.11
3.47
2.82

eRf
0.25
0.53
0.73
0.75
0.49

eS
2.61
5.35
7.95
10.51
11.25

eTS

0
0
0
0
0

eMC
1.14
1.22
1.2
1.03
2.02

ePf

eR
1.91
2.23
2.46
2.58
4.1

eRf

eS
92.12
89.63
86.08
80.1
61.07

eTS

0
0
0
0
0

eMC

ePf

eR

eRf

eS

eTS

0
3.9
3.55
2.44
2.28

0
0
0.01
0.02
0.03

0
0.03
0.05
0.06
0.04

0
6.32
6.05
5.08
4.64

0
0.01
0.07
0.21
0.31

0
0.2
0.36
0.48
0.35

0
7.72
12.07
17.1
31.76

0
0
0
0
0

eYf
2.27
1.88
1.13
0.56
0.12

0
0
0
0
0

eYf
0.06
0.15
0.19
0.17
0.11
eYf

0
0
0
0
0

0
0
0.01
0.02
0.02
eYf

0
0
0
0
0

0
0.05
0.06
0.06
0.02

Table 7: Variance Decomposition under NoFinShock ModelGDP
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
48.18
68
76.72
84.1
91.9

eD
0.01
1.09
1.07
0.78
0.27

eG
34.84
14.64
8.78
4.95
1.93

eK
13.8
12.25
10.16
7.34
3.21

eL
0.68
1.43
1.12
1
1.19

eMC
0.03
0.01
0.02
0.04
0.05

ePf
0.03
0.09
0.07
0.05
0.02

eR

eRf
0.14
0.48
0.43
0.32
0.1

eTS

0.4
0.33
0.58
0.88
1.15

Business Fixed Investment
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
7.14
16.15
27.66
39.65
43.31

eD
1.68
2.09
2.03
1.6
1.24

eG
0.09
0.1
0.15
0.26
0.34

eK
89.78
79.29
66.34
53.18
48.57

eL
0.01
0.04
0.09
0.2
1.57

eMC
0.13
0.26
0.44
0.62
0.53

ePf
0.03
0.03
0.04
0.04
0.04

eR
0.95
1.7
2.79
3.9
3.97

eRf
0.14
0.22
0.31
0.37
0.32

eTS

External Finance Premium
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
16.48
12.85
9.57
6.9
2.5

eD
5.02
3.11
1.84
1.02
0.77

eG

eK
48.67
55.97
61.01
61.44
42.48

eL
4.41
6.56
10.26
17.27
42.33

eMC
0.59
0.48
0.35
0.22
0.21

ePf

eTS

0
0.01
0.04
0.07
0.06

eR
24.76
20.74
16.02
11.55
9.76

eRf

0
0.15
0.48
0.79
1.27

Leverage Ratio
1 period ahead forecast error (%)
4 periods ahead forecast error (%)
8 periods ahead forecast error (%)
16 periods ahead forecast error (%)
unconditional forecast error (%)

eA
14.11
9.51
4.9
2.5
1.48

eD
3.62
2.1
1.19
0.77
0.93

eG
0.09
0.38
0.82
1.27
0.81

eK
53.64
61.11
63.91
42.48
10.3

eL
5.84
8.73
15.25
42.33
23.17

eMC
0.52
0.38
0.22
0.21
2.28

ePf
0.01
0.03
0.07
0.06
0.04

eR
22.08
17.44
12.95
9.76
4.64

eRf
0.05
0.29
0.63
0.57
0.35

0
0.1
0.39
0.65
0.57

0
0
0
0
0

eYf
1.88
1.69
1.06
0.55
0.19

0
0
0
0
0

eYf
0.05
0.11
0.16
0.17
0.12

0
0
0
0
0

eYf
0.07
0.02
0.05
0.08
0.04

0
0
0
0
0

eYf
0.03
0.03
0.06
0.04
0.02

eTS

Tabe 8: MLE results of stadard deviations of shocks under various data sets
Full Shocks, Version A
Shock
eA
eD
eG
eK
eL
eLV
eMC
eN
ePf
eR
eRf
eS
eTS
eYf

Prior
Mean
0.010
0.010
0.010
0.010
0.001
N/A
0.001
0.010
0.001
0.001
0.001
0.001
0.010
0.001

Mode

S.D.

t-Stat.

0.00970.00700.02920.00830.0016N/A
0.00180.02680.00150.00190.00090.00050.01560.00480.00840.08390.00600.01280.0023
N/A
0.01280.01610.00020.00070.00010.00010.00240.00041.16060.08314.87530.64430.6818N/A
0.13701.66958.78422.8461
12.3280
3.4674
6.397812.1019

Full Shocks, Version B
Prior
Dist.
invg
invg
invg
invg
invg
N/A
invg
invg
invg
invg
invg
invg
invg
invg

Prior
Mean
0.010
0.010
0.010
0.010
0.001
N/A
0.001
0.010
0.001
0.001
0.001
0.001
0.010
0.001

Mode

S.D.

t-Stat.

0.00820.00670.02970.00980.0021
N/A
0.00050.00440.00150.00250.00090.00060.01580.00480.00090.00170.00250.00120.0004N/A
0.00010.00170.00010.00040.00010.00000.00130.00048.83543.953011.87148.12034.7524N/A
3.44202.581712.30615.856713.042212.9181
11.9240
12.1540

Full Shocks, Version C
Prior
Dist.
invg
invg
invg
invg
invg
N/A
invg
invg
invg
invg
invg
invg
invg
invg

Prior
Mean
0.010
0.010
0.010
0.010
0.001
0.010
0.001
0.010
0.001
0.001
0.001
0.001
0.010
0.001

Mode

S.D.

t-Stat.

0.00810.00670.02970.01120.00240.00890.00050.00400.00150.00270.00090.00060.01610.00480.00090.00160.00250.00140.00040.00100.00010.00120.00010.00050.00010.00000.00140.00049.15794.225211.80718.26535.36868.61423.42303.332512.35105.818213.0453
13.2592
11.7871
12.1736

Prior
Dist.
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg
invg

Figure 1: Estimated IRF of Aggregate Technology ShockConsumption

0.7

0.8

0.6
0.5

0.4

0

5

10

15

0.7
0.6

0.5

20

Business Fixed Investment
3

percent deviation

0.9

percent deviation

percent deviation

GDP
0.8

0

5

Capital Price

10

15

2.5
2
1.5
1
0.5

20

0

Inflation

0.6

5

10

15

20

External Finance Premium

0

0.01

−0.02

0.2
0

0

percent deviation

percent deviation

percent deviation

0.4

−0.04
−0.06
−0.08

−0.01
−0.02

−0.1
−0.2

0

5

10

15

20

−0.12

0

5

15

−0.03

20

0.8

0.8

0

0.6
0.4
0.2

5

10

15

20
fullshockpercent deviation

0.1

0

5

0.6
0.4
0.2
0

0

5
eSonly

10

10

15

20

15

20

Leverage

100

Net Worth1

percent deviation

percent deviation

Business Credit

10

15
eNonly

20

−0.1
−0.2
−0.3
−0.4

0

NoFinshock

5

10

Figure 2: Estimated IRF of Intertemporal Preference ShockGDP

Consumption

−0.05
−0.1

0

5

10

15

0.3
0.2
0.1
0
−0.1

20

0.5

percent deviation

0

−0.15

0

5

Capital Price

−1

20

5

10

15

20

−3

10

−0.2
−0.3

0.1

percent deviation−0.1

External Finance Premium
x 10

0.05
0

6
4
2
0

0

5

10

15

−0.05

20

0

5

10

15

−2

20

−0.2

0.2

−0.1
−0.2

10

15

20

percent deviation

0

percent deviation

0.3

5

5

−0.4
−0.6

−0.8

fullshock0

5
eSonly

10

10

15

20

15

20

Leverage000

Net Worth

0.1

−0.3

0

8

0

percent deviation

percent deviation

15

−0.5

0.15

Business Credit

percent deviation

10

0

Inflation

0.1

−0.4

Business Fixed Investment

0.4

percent deviation

percent deviation

0.05

15
eNonly

20

0.1
0

−0.1

0

NoFinshock

5

10

Figure 3: Estimated IRF of Investment−specific Technology ShockGDP

Consumption

0.1
0

−0.1

0

5

10

15

4

0.1

3

0
−0.1
−0.2
−0.3

20

1
0

0

5

10

15

−2

20

0

0.06

0.03

−0.4
−0.6

0

5

10

15

0.04
0.02
0
−0.02

20

percent deviation

0.035

−0.2

0.015

0

5

10

15

0.005

20

0

5

10

15

0

5

20

−1

fullshock

15

20

15

20

Leverage

−0.5

−1.5

10

0.8

percent deviation

percent deviation

0

20

0.02

Net Worth

0.5

15

0.025

0

1

10

0.01

Business Credit
1.5

−0.5

5

External Finance Premium

0.08

−0.8

0

Inflation

0.2

percent deviation

percent deviation

2−1

Capital Price

percent deviation

Business Fixed Investment

0.2

percent deviation

0.2

percent deviation

percent deviation

0.3

0

5
eSonly10

15
eNonly

20

0.6
0.4
0.2
0
−0.2

0

NoFinshock

5

10

Figure 4: Estimated IRF of Monetary Policy ShockGDP

Consumption

0.05

Business Fixed Investment

0

0

−0.05
−0.1

percent deviation

percent deviation

percent deviation

−0.02
0

−0.04
−0.06
−0.08

−0.5

−1

−0.1
−0.15

0

5

10

15

−0.12

20

0

5

−1.5

20

0

0.03

−0.4

5

10

15

−0.1
−0.2

−0.3

20

percent deviation

0

−0.2

0

5

Business Credit

15

0

0

5

10

15

0

5

−0.4
−0.6
−0.8

fullshock

−1

10

15

20

15

20

Leverage

−0.2

20

20

0.6

percent deviation

percent deviation

0.2

15

0.01

0

20

0

0.4

10

0.02

Net Worth

0.6

−0.2

10

5

External Finance Premium
0.04

0

0

Inflation
0.1

−0.6

percent deviation

15

0.2

percent deviation

percent deviation

Capital Price

10

0

5
eSonly10

15
eNonly

20

0.4

0.2
0

−0.2

0

NoFinshock

5

10

Figure 5: Estimated IRF of External Finance Premium ShockGDP

Consumption

0.1

Business Fixed Investment

0.02

1

0

−0.05

percent deviation

percent deviation

percent deviation

0.01
0.05

0
−0.01
−0.02

0.5

0

−0.5

−0.03
−0.1

0

5

10

15

−0.04

20

0

5

0

0.005

−0.1

−0.2

0

5

10

15

−0.01

20

0

5

−0.4

−0.6

10

15

10

15

20

20

0.02
0

0

5

10

15

20

15

20

Leverage
0.4

0

−0.5

−1

15

0.04

−0.02

20

percent deviation

0.5

percent deviation

percent deviation

−0.2

10

0.06

Net Worth155External Finance Premium−0.005Business Credit

0

0

0.08

0

0

−0.8

−1

20

percent deviation

0.01

−0.3

15

Inflation

0.1

percent deviation

percent deviation

Capital Price

10

0

5
fullshock

10

15

20

eSonly

0.2
0
−0.2
−0.4
−0.6

0

5

10

Figure 6: Estimated IRF of Aggregate Net Worth ShockGDP

Consumption

−0.2

−0.3

−0.4

0

5

10

15

0

0.1

−0.5

0
−0.1
−0.2
−0.3

20

−0.4

10

15

0

5

15

−3

20

0.02

0.08

0.01
0
−0.01

0

5

10

15

10

15

20

20

0.02

0

5

10

15

20

15

20

Leverage

−1

−1.5

−2

15

1.5

percent deviation

percent deviation

0

10

0.04

Net Worth

0.5

5

5

0.06

0

20

−0.5

0

0

External Finance Premium
0.1

Business Credit

percent deviation

10

0.03

−0.02

20

1

−0.5

−2

percent deviation

percent deviation

percent deviation

−0.2

5

−1.5

Inflation

0

0

−1

−2.5

Capital Price
0.2

−0.6

Business Fixed Investment

0.2

percent deviation−0.1

percent deviation

percent deviation

0

0

5
fullshock

10

15

20
eNonly

1

0.5

0

0

5

10

eA

eD

eG

eK

eL

eMC

eN

ePf

eR

eRf

0.1

0.05

-0.05

0

-0.1

-0.15

-0.2
Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990eS
Q1 2004
Q3 2004
Q1 2005
Q3 2005
Q1 2006
Q3 2006
Q1 2007
Q3 2007

Q1 2004

Q3 2004

Q1 2005

Q3 2005

Q1 2006

Q3 2006

Q1 2007

Q3 2007

Q3 20030.2

Q3 20030.15
Q1 2003

Smoothed Leverage Ratio Historical Decomposition (Full-Shock Model)

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

0.3

0.2

0.1

-0.1
0

-0.2

-0.3

-0.4
Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

eYf

Lev. smoothed

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2003

0.4

Q3 20030.5
Q1 2003

Business Fixed Investment Historical Decomposition (Full-Shock Model)

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Figure 7: Historical Decomposition under Full-Shock Model
GDP Historical Decomposition (Full-Shock Model)

0.08

0.06

0.04

0.02

-0.02
0

-0.04

-0.06

-0.08

-0.1

External Fiannce Premium Historical Decomposition (Full-Shock Model)

0.008

0.006

0.004

0.002

0

-0.002-0.004-0.006

eA

eD

eG

eK

eL

eMC

eN

ePf

eR

eRf
Q3 2005
Q1 2006
Q3 2006
Q1 2007
Q3 2007

Q1 2006

Q3 2006

Q1 2007

Q3 2007

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Q1 2005-0.4

Q3 2005-0.3
Q3 2004-0.2

Q1 2005

0

Q3 2004-0.1
Q1 2004

0.1
Q3 20030.2

Q1 2004

0.3

Q3 2003

0.4
Q1 2003

Smoothed Leverage Ratio Historical Decomposition (eN-only Model)

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

-0.6

-0.8

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

eYf

Lev. smoothed

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

Q1 2005-0.4

Q3 2004

0

Q1 2005-0.2

Q3 2004

0.2

Q1 2004

0.4

Q3 2003

0.6

Q1 2004

1

Q3 20030.8

Q1 2003

Business Fixed Investment Historical Decomposition (eN-only Model)

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Figure 8: Historical Decomposition under eN-only Model
GDP Historical Decomposition (eN-only Model)

0.15

0.1

0.05

0

-0.05

-0.1

-0.15

External Finance Premuim Historical Decomposition (eN-only Model)

0.015
0.02

0.005
0.01

-0.0050-0.015-0.01-0.025
-0.02

eA

eD

eG

eK

eL

eMC

ePf

eR

eRf

eS

Q1 2006
Q3 2006

Q1 2006
Q3 2006

Q3 2007

Q3 2005

Q3 2005

Q1 2007-0.2
Q3 2007-0.25
Q1 2007-0.1

Q3 2007-0.15

Q1 20070

Q3 2007-0.05

Q1 2007

0.1

Q3 2006

0.05

Q1 2006

0.15

Q3 2006

Smoothed Leverage Ratio Historical Decomposition (eS-only Model)

Q1 2006-0.006
Q3 2005-0.004Q3 2005-0.002Q1 2005

0

Q1 2005

0.002

Q3 2004

0.004

Q3 2004

0.006

Q1 2004

0.01

Q1 2004

0.008

Q3 2003

External Finance Premium Historical Decomposition (eS-only Model)

Q3 2003

Q1 2005

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Q3 2004-0.4
Q1 2005-0.3

Q3 2004-0.2
Q1 2004

0
Q3 2003-0.1

Q1 2004

0.1

Q3 20030.2
Q1 2003

0.3

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

0.4

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Business Fixed Investment Historical Decomposition (eS-only Model)

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Figure 9: Historical Decomposition under eS-only Model
GDP Historical Decomposition (eS-only Model)

0.08

0.06

0.04

0.02

-0.02
0

-0.04

-0.06

-0.08

-0.1

eYf

Lev. smoothedQ3 2007

Q1 2007

Q3 2006

0.1

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

0.1

Q1 2006

Q1 2005

Q3 2004

Q1 2004

Q3 2003

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Q3 2007

Q1 2007

Q3 2006

Q1 2006

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2003

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

0.1

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2003

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Figure 10: Smoothed and Observed Leverage Ratio under Full-Shock Model
Full-Shock Model

0.15
Leverage Smoothed

Leverage Observed

0.05

0

-0.05

-0.1

-0.15

Figure 11: Smoothed and Observed Leverage Ratio under eN-only ModeleN-only Model

0.15
Leverage Smoothed

Leverage Observed

0.05

0

-0.05

-0.1

-0.15

Figure 12: Smoothed and Observed Leverage Ratio under eS-only ModeleS-only Model

0.15
Leverage Smoothed

Leverage Observed

0.05

0

-0.05

-0.1

-0.15

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

Q3 2006
Q3 2007

0.5

Q3 2007

Business Fixed Investment Historical Decomposition (Full-Shock, Ver. C)
Q1 2007

Ik data

Q1 2007

Q3 2006

eYf

Q1 2006

Q3 2005

eYf

Q1 2006

Q3 2005

eS
Q1 2005

Q3 2004

Q1 2004eS

Q1 2005

Q3 2004

Q1 2004

eRf
Q3 2003

Q1 2003

Q3 2002eRf

Q3 2003eR

Q1 2003

Q1 2002eR

Q3 2002

Q1 2002ePf
Q3 2001

Q1 2001

Q3 2000

ePf

Q3 2001

Q1 2001

Q3 2000

eN
Q1 2000

Q3 1999

Q1 1999eN

Q1 2000

eMC

Q3 1999

Q3 1998

Q1 1998

Q3 1997

eMC

Q1 1999

Q3 1998eL

Q1 1998

Q1 1997eL

Q3 1997

Q1 1997eK
Q3 1996

Q1 1996

Q3 1995

eK

Q3 1996

Q1 1996

Q3 1995

eG
Q1 1995

Q3 1994eG

Q1 1995

Q3 1994eD
Q1 1994

Q3 1993

Q1 1993eD

Q1 1994eA

Q3 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990eA

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990

Q1 1990

Q2 2007

Q3 2006

Q4 2005

Q1 2005

Q2 2004

Q3 2003

Q4 2002

Q1 2002

Q2 2001

Q3 2000

Q4 1999

Q1 1999

Q2 1998

Q3 1997

Q4 1996

Q1 1996

Q2 1995

Q3 1994

Q4 1993

Q1 1993

Q2 1992

Q3 1991

Q4 1990

Q1 1990

Figure 13: Historical Decomposition using Ver.A, Ver.B, and Ver. C Data Sets
Business Fixed Investment Historical Decomposition (Full-Shock, Ver.A)

0.5

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.5

Ik dataBusiness Fixed Investment Historical Decomposition (Full-Shock, Ver.B)

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

-0.4

-0.15Q3 2007

Q1 2007

0.1

Q3 2006

Q3 2007

Q1 2007

Q3 2006

0.3

Q1 2006

0.4

Q1 2006

Q4 2007

Q1 2007

Q2 2006

Q3 2005

0.1

Q4 2004

Q1 2004

Q2 2003

Q3 2002

Q4 2001

Q1 2001

Q2 2000

Q3 1999

Q4 1998

Q1 1998

Q2 1997

Q3 1996

Q4 1995

Q1 1995

Q2 1994

Q3 1993

Q4 1992

Q1 1992

Q2 1991

Q3 1990

Q4 1989

Q1 1989

Q2 1988

Q3 1987

Q4 1986

Q1 1986

Q2 1985

Q3 1984

Q4 1983

Q1 1983

Q2 1982

Q3 1981

Q4 2007

Q1 2007

Q2 2006

Q3 2005

Q4 2004

Q1 2004

Q2 2003

Q3 2002

Q4 2001

Q1 2001

Q2 2000

Q3 1999

Q4 1998

Q1 1998

Q2 1997

Q3 1996

Q4 1995

Q1 1995

Q2 1994

Q3 1993

Q4 1992

Q1 1992

Q2 1991

Q3 1990

Q4 1989

Q1 1989

Q2 1988

Q3 1987

Q4 1986

Q1 1986

Q2 1985

Q3 1984

Q4 1983

Q1 1983

Q2 1982

Q3 1981

Q4 1980

Q1 1980-0.08

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2003

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q4 1980

Q1 1980-0.06

Q3 2005

Q1 2005

Q3 2004

Q1 2004

Q3 2003

Q1 2003

Q3 2002

Q1 2002

Q3 2001

Q1 2001

Q3 2000

Q1 2000

Q3 1999

Q1 1999

Q3 1998

Q1 1998

Q3 1997

Q1 1997

Q3 1996

Q1 1996

Q3 1995

Q1 1995

Q3 1994

Q1 1994

Q3 1993

Q1 1993

Q3 1992

Q1 1992

Q3 1991

Q1 1991

Q3 1990-0.15

Q3 1990-0.4

Q1 1990-0.1

Q1 1990

Figure 14: Smoothed and Observed Variables using Various Financial Data
Investment Deflator

0.08

0.06

0.04

0.02

-0.02
0

-0.04

Observed

Smoothed

Business Credit

0.15

Observed

Smoothed

0.05

0

-0.05

-0.1

Stock Price Index

0.5

Smoothed
Observed

0.2

0.1

-0.1
0

-0.2

-0.3

Leverage Ratio

0.15

Observed

Smoothed

0.05

0

-0.05

-0.1