Universidad Nacional de La Plata
Sextas Jornadas de Economía
Monetaria e Internacional
La Plata, 10 y 11 de mayo de 2001
Business cycles in a small open economy with a banking sector
Pedro Marcelo Oviedo (North Carolina State University, EEUU)
BUSINESS CYCLES IN A SMALL OPEN ECONOMY
WITH A BANKING SECTOR
Pedro Oviedo∗
North Carolina State University
Abstract
This paper studies the interest-rate-driven business cycles of a small open economy (SOE). For than end
a costly operated banking system is added to the standard real-business-cycles model. Banks are the only
domestic agents considered worthy of credit in international capital markets. They borrow from the rest of
the world and lend domestically in a competitive credit market. Existent quantitative models of business
cycles in SOE’s indicate that interest-rate shocks are unable to cast the kind of output variability produced
by productivity or terms-of-trade shocks. Contrary to this finding, it seems that the macroeconomic
performances of several SOE’s are tightly related to international interest rates and capital flows. Neumeyer
and Perri (1999) points out that the introduction of working capital needs may close the gap between the
standard model’s predictions and the observed consequences of interest-rate shocks. This paper shows
that a more careful analysis of the microfoundations of working capital may give rise to an intermediate
position where working capital matters in explaining output fluctuations, but not as much as Neumayer
and Perri suggest. For that end, the model is calibrated to the Argentinean economy.
∗
The author has benefited from the discussions held with his advisors Paul Fackler, Enrique Mendoza, and John
Seater. Jonathan Heathcote provided valuable advices at several stages of the development of the paper. The author
also thanks seminar participants at Duke University for their comments
1
1
Introduction
This paper investigates the quantitative importance of interest-rate shocks for the business cycles
of a small open economy (SOE). For that end a competitive banking system is added to the
standard neoclassical general equilibrium model. The inclusion of banks constitutes an attempt
to provide an analytical framework to study the interactions between the financial and nonfinancial sectors in SOE’s. It also helps to improve the model representation of the process of
channeling funds from surplus-spending to deficit-spending units in actual developing economies.
Typical financial phenomena with possible impacts on other sectors in the economy are sometimes treated without explicitly modeling the behavior of central players like banks. That is
the case of models with imperfect information (see for example Aghion, Bacchetta and Banerjee (2000)) or working capital needs (see Neumeyer and Perri (1999)). The exclusion of banks
from macroeconomic analysis reflects the domination that the Arrow-Debreu paradigm has had
in macroeconomics (See for example Gertler (1988) and Freixas and Rochet (1997) ).
However, as Diamond (1984) has shown, financial intermediation is the endogenous device
for carrying out borrowing and lending in the presence of asymmetric information. And working
capital loans are the typical financing provided by commercial banks.
The case of working capital is particularly interesting because it permits to address the importance of international interest-rate fluctuations for domestic output variability. In the standard
real-business-cycles model a change in the international interest rate affects production through
the supply of factor inputs. Labor supply decisions are affected by the price of future consumption
(interest rate) on one side. At the same time, a change in bond prices makes households reallocate
their savings between capital and international bonds. In this framework Mendoza (1991) points
out that interest-rate fluctuations are unable to cast the output variance observed in the Canadian
economy. Correia, Neves, and Rebelo (1995) showed that the responses of output, consumption
and labor supply to interest rate shocks were also small in the Portuguese economy.
Contrary to these results, it seems that changes in the cost of international financing may
severely affect the evolution of output in emerging economies. In the 90’s several developing
countries faced sudden capital outflows with devastating consequences for their real economies.
After the Mexican devaluation of 1994 and the Russian default of 1997, many countries viewed
how the capital inflows that shrank interest rates and fueled economic expansions, flew out giving
2
rise to recessions and unemployment.
Figure 1 shows the 3-months Argentinean interest rate, and a GDP index for the period 19811999. The contemporaneous correlation between the two variables is equal to -0.781. A similar
pattern seems to relate interest rate and output in other countries like Mexico and Brazil. It is
not less surprising the existent co-movement between banks total loans and GDP as it can be
seen in Figure 2. The correlation observed between the latter two variables is equal to 0.64.
In another context Calvo, Leiderman, and Reinhart (1993) studied the capital inflows to Latin
America at the beginning of the 90’s. These flows are associated with the decreasing interest rate
in Latin American economies (for an example see Figure 1). Two conclusions emerge from the
work of Calvo et.al. First, much of capital inflows are result of factors external to the analyzed
Latin American economies. Second, these flows have affected the economies in several ways, for
example increasing the availability of capital, facilitating the smooth of consumption over time
and giving investors the opportunity of reacting to expected changes in profitability.
Neumeyer and Perri (1999) introduced working-capital needs in the standard model in an
attempt to increase the impact of interest-rate shocks on domestic output. This is because the
model now allows for an additional source of output variability. In this setting not only factor
supplies react to interest-rate shocks but also factor demands do as the interest rate is part of
the cost of employing inputs. The introduction of working capital permits Neumeyer and Perri
to account for 55% of output variance in Argentina. However, they model working capital as
another input factor coming directly from overseas.
A subtle analysis of the nature of working capital reveals that its introduction in a macroeconomic model deserves a deeper analysis. First, working capital is associated with short-term
loans, the typical financial service banks offer to firms, and not with a long-term international
bond. Second, these loans are monitoring-intensive and so less plausible to be granted for institutions different from domestic banks. Additionally, the assumption that the amount of working
capital is equal to total factor costs means that the stock of credit is much larger than what actual
economies have. In such case, total financing is at least as high as national income even without
counting households borrowing. This is at odds with the empirical evidence since the stock of
total credit is seldom as high as the GDP in developing economies (See for example the database
in Beck, Demirüç-Kunt, and Levine).
Modeling interest-rate shocks as if they were completely independent of domestic economic
3
developments may sound unrealistic since much of the variation in interest rates is due to country
risk, as Neumeyer and Perri show. However, there are several factors (e.g. political events)
affecting interest-rate differentials. Recently the Argentinean replacement of its Finance Secretary
made country risk first decrease and then rocket as the new secretary could not get political
support for his “plan”. Additionally as Calvo et.al. (1993) documented, much of the beginningof-nineties capital flows have responded to external factors to emergent economies as mentioned
above.
In the model of section 3 banks are the only financial intermediaries in the economy and the
only domestic agents creditworthy in international capital markets1 . They issue an internationally
traded bond and the proceeds are lent to other agents in the economy: firms and households.
Firms must pay factors of production before realizing their sales and hence have a demand for
working capital. Households use bank loans to smooth consumption and to change the stock of
capital they are renting to firms and banks. Thus from the standpoint of households, bank loans
play the role international bonds do in the standard model.
The banking sector is perfectly competitive and banks are modeled to have their two actual
constraints, a financial or balance sheet constraint, and a technology constraint (Sealey and
Lindley (1977)). The latter indicates that real resources are used up in the process of granting a
loan. Banks demand labor and capital services for loans production and maximize profits, with
revenues coming from the intermediation margin. Adding deposits production is straightforward
in this context although it does not provide any extra insight to the working capital problem
addressed later on. The balance sheet constraint assures that what banks are lending is what
they are borrowing from other agents. Thus banks are modeled following Freixas and Vives (1997,
Ch.2) .
The model fits in what Baltensperger (1980) calls “real resource models” of banks because a
prominent role is assigned to the (real) production aspect of financial activities. Thus, financial
or portfolio decisions are not independent from production decisions but they are taken jointly.
2
A banking system is a more accurate description of the financial system vis-à-vis a bond
1
2
Alternatively one can assume that banks can monitor domestic agents more efficiently than any other foreign lender.
Hancock (1991) mentions some problems associated with the alternative view where “the neoclassical theory of the
firm has been supplanted by portfolio theory in analyzing the behavior of financial institutions”: there is a tendency to
omit production and cost constraints and their role in determining banks output and input mix.
4
market in some developing economies. Domestic capital markets play an almost nil role compared
to banks in the borrow-lending process in these countries, a fact early remarked by Gurley and
Shaw (1955). As they stated, in the earlier stages of financial development, commercial banking
is the main form of intermediation. As can be seen in Beck et. al (1999), while private bonds
market capitalization is around 4% of the GDP, total private credit from financial institutions is
equal to 20% of the GDP in low and lower-middle income countries. In high income countries
these ratios are equal to 20 and 60%, respectively.
Several papers have studied the relationship between financial intermediaries and firms. Williamson
(1987), constructs a business cycle model of overlapping generations in which financial intermediation plays a central role in output fluctuations. Williamson’s banks are the optimal solution
to asymmetric information and costly monitoring problems. King and Plosser (1984) include a
banking sector in the economy. They study money-output correlations and their approach implies that banks only provide transaction services. Agénor (1997) introduces banks in a model
of SOE to study the effect of an increase in the risk premium on international markets induced
by a contagion effect. However banks are modeled as a costless technology and the interest-rate
margin arises only due to the imposition of reserve requirements. None of these works offers a
quantitative analysis of the issues addressed in their models. By emphasizing the importance of
banks in the credit supply process the paper is related to Gurley and Shaw (1955).
Christiano (1992) and Christiano and Eichenbaum (1992) have investigated how workingcapital needs along with an asymmetric distribution of money inflows among firms and households
give rise to a liquidity effect. This effect opens a new channel through which monetary shocks
affect business cycles. In the model of section 3, the mechanism through which interest-rate shocks
impact on the SOE is similar to that in Cristiano, and Christiano and Eichenbaum. On one side,
a change in the domestic interest rate (due to the liquidity effect in one case and the international
interest-rate shock in the other) affects input supplies through both assets and intertemporal
substitution. On the other side, the demand for inputs is also affected. This is because the
interest rate is part of the gross cost of employing factors of production3 .
The paper follows with other four sections. Section two elaborates on the method for incorporating banks in the standard SOE model. Section three presents the model and section four
3
In the papers cited above Christiano and Eichenbaum assume that the use of working capital is only associated to
one input factor: labor.
5
contains its quantitative properties. The model is calibrated to Argentina in order to evaluate
the role of working capital in the business cycles of that economy. The final section contains
concluding remarks and some avenues that could be explored in future research. The employed
solution method is discussed in an appendix.
2
Banks in a SOE
The existence of institutions providing financial services has been commonly justified based on
the incomplete information paradigm. This approach has been extensively used to study how the
inclusion of financial constraints may amplify business cycles (see for example Aghion, Bacchetta
and Banerjee (2000) , Bacchetta and Caminal (2000), , Bernanke, Gertler, and Gilsrist (1999),
(Bernanke and Gilchrist, 1999) and the literature cited therein).
Alternatively, the industrial organization approach stresses the importance of transaction
costs. Banks provide an array of services and the financial transactions are the only tangible
counterpart of these services. The natural question that arises is then, why don’t firms and
households do what banks are doing for them? One possible answer is linked to the presence
of transaction costs. The transformation of financial securities and the access to international
financial markets are the services that banks provide in the model of the next section.
The assumption that only banks are worthy of credit in international financial markets provides a reason for banks to exist. Although not modeled explicitly, it is assumed that there
exists information problems that make bank credit special for domestic agents. This assumption
implicitly extends Fama (1985)’s idea that for certain class of borrowers bank credit is special.
These borrowers are interpreted as all agents in the economy.
The characterization made for banks disregards several aspects of the banking system. In
particular it does not address risk management in none of its variants (credit risk, liquidity risk),
insolvency costs and equity capital considerations among other things.
On the other side, the model offers an alternative to have a well defined steady state where all
variables are stationary, independent of the value of the international interest rate and the rate
of intertemporal preference.
It is well known that the standard macroeconomic model produces unsatisfactory results when
it is extended to an open economy. The fact that both the interest rate factor, 1 + r, and the
6
intertemporal discount factor, β, are given from the standpoint of a small open economy casts
unplausible results. Particularly, a finite interior solution for the marginal utility of wealth forces
to preset the value of the mentioned parameters so that their internal product is equal to one in
the nonstochastic steady state. However that presetting cannot avoid a non-stationary solution
for some variables in the model. In all cases consumption, the trade balance, and the stock of net
foreign assets are non-stationary. In other words, the steady state is independent on the initial
conditions. And once the economy is shocked, it never reaches the initial steady state, except by
chance.
Several devices has been introduced in the literature to deal with this problem. Obstfeld
(1981), extending the work of Uzawa (1968), endogeneized the discount factor and made it dependent on the level of utility reached at a given point in time. Turnovsky (1985) distinguished
between domestic and international bonds by introducing a friction in the process of accumulating
foreign bonds. Mendoza (1991) introduced a stationary cardinal utility function with includes an
impatient effect. This effect alters the standard intertemporal marginal rate of substitution in
consumption: actual consumption makes individuals discount future consumption heavily, as in
Obstfeld (1981) . In Mendoza’s paper the endogenous rate of time preference is used to determine
a stable stochastic steady state. All these approaches assure the existence of an interior solution
for the marginal utility of wealth.
Modeling banks assuming that their (physical) capital is fixed at business cycle frequencies
permits to have stationary variables. The market domestic interest rate for loans is rL,t . In
equilibrium, rL,t is equal to the sum of the cost of funds in international markets plus the marginal
operative costs of the financial system. Operative costs depend on the activity of the banking
sector, increase with the level of loans, and make rL,t an endogenous variable. This contrasts
with the standard model where rt is taken as given. The fact that the marginal cost of a loan
depends on the amount of financing is central for the dynamic properties of the model.
3
The Model
There are three agents in the economy, banks, firms and households. They interact in four
markets, labor services, capital services, loans and final output. All agents are price takers in
every market.
7
This section characterizes the agents and markets in the economy and it also defines the
competitive equilibrium. Since the model economy is growing at a constant rate, g, all non-price
variables except labor supply, have been detrended using that rate.
3.1
Households
The representative household (RH) has an infinite life and wants to maximize its objective function
given by:
E0
∞
X
β t u(ct , 1 − nt )
(1)
t=0
where ct is total consumption and nt is the total labor supplied. The time endowment is normalized to one and household’s leisure is the time not spent working. β(< 1) is the intertemporal
discount factor and E0 indicates expectations as of time t=04 . In solving its program the household faces a budget constraint. The flow-version of the latter is:
s
s
wt nt + ky,t
rky,t + k b rkb,t + πb,t + πy,t − (1 + g)Ldh,t+1 =
ct + (1 + Ht )it − Ldh,t (1 + rL,t )
(2)
The RH’s total income is given by the sum of labor and property income. Labor income depends
on both, the wage rate, wt , and the labor services supplied to banks, nb,t , and firms, ny,t . So nt =
nb,t + ny,t . Property income has three components. First, net financial income coming from net
interest earnings on household loans, (1 + rL,t )Ldh . Second, as the RH is the owner of both banks
and firms it receives profits from these two sectors, πi : (i=b, y). Third, the RH also counts on
s
income coming from renting capital to banks, k b , and firms, kys , at their market rates, rkb , and
rky .
On the other hand, the RH spends its income buying consumption and investment goods,
including installation costs, (Ht it ). Any excess of expenditures over income is covered increasing
the stock of bank debt.
Investment (net of transaction costs) and the law of motion of capital are defined by:
s
s
it = (1 + g)ky,t+1
− ky,t
(1 − δ) + kb (g + δ)
4
(3)
The true discount factor, B, is different from β since the latter also depends on g and preference parameters
8
where δ is the depreciation rate assumed to be same across sectors.
Adjusting the stock of capital is not free. Adjustment costs are assumed to be equal to zero
only at the steady state. They are defined by:
Ht = H
³k
t+1
kt
´
n
h
= h1 exp h2
³k
t+1
kt
´i
−1
h
+ exp − h2
³k
y,t+1
kyt
−1
´i
o
−2
(4)
The introduction of these distortion implies the existence of two more prices. One is the
Tobin’s Q, and it represents the consumption value-cost of a marginal unit of new capital, Ptq .
The other is the ex-rental value of a marginal unit of installed capital, Ptk . Thus5 :
Ptq = 1 + Ht + Ht′
1
it
kt
Ptk = (1 − δ)(1 + Ht ) + Ht′
(5)
kt+1
it
kt2
(6)
The transversality and the no Ponzi scheme condition, dictate that, respectively:
limt→∞
limt→∞
β t E0 uc,t (kt − Lh,t ) = 0 where k = ky + kb
kt − Lh,t
E0 Qt−1
≥0
υ=0 (1 + rL,υ )
(7)
(8)
An initial condition for the capital stock and household loans complete the description of the
RH’s problem.
(Lh,0 , k0 ) = (Lh 0, k0)
(9)
The RH’s Optimality Conditions
s
The RH chooses sequences {ct , nt , Ldh,t+1 , ky,t+1
}∞
t=0 , so as to maximize eq. (1) subject to eqs. (2)
to (4) and (7) to (9). The information set on which the RH is choosing its actions at time t is
Ωht . The set includes the historic values of all variables until time t − 1, the value of the state
variables at time t, Ldh,t , and ky,t , and the value of two shocks buffeting the economy, ǫr,t , and ǫz,t
(described below). At time t, the RH takes saving, and inputs-supply decisions based on prices
{rL,t , wt , rky,t } and the expected values of the shocks in the economy.
5
By construction these two prices are highly correlated.
9
The following optimality conditions along with eq. (2) characterize the optimal RH’s decision
process for t = 0, . . . ∞.
un,t
= −wt
uc,t
(10)
h
i
(1 + g)uc,t = βEt uc,t+1 (1 + rL,t+1 )
h
k
(1 + g)uc,t Ptq = βEt uc,t+1 (Pt+1
+ rky,t+1 )
(11)
i
(12)
where the prices defined in eqs. (5) and (6) have been substituted accordingly. In principle the
mentioned set of equations plus the constrains in eqs. (7) and (8) could be solved for {ct , nt ,
Lh,t+1 , ky,t+1 }∞
t=0 , once the sequences for rL,t and rky,t are known.
Eq. (10) equates the marginal rate of substitution of consumption for leisure to the wage rate.
Eq. (11) governs the accumulation of bank debt. The optimal borrowing behavior indicates that
the RH demands bank loans until the benefits in terms of actual utility, equals the discounted
expected cost. This cost is the future utility that will be resigned to repay the loan.
Eq. (12) characterizes the optimal saving behavior in capital goods. The utility (gross) cost of
having installed a unit of (new) capital good is given by the left hand side of (12). The expected
discounted benefits, in utility terms, are on the right hand side and have two components. The
future rental income from an extra unit of capital, (rky,t+1 ), and the future (after depreciation)
k . The latter includes the benefit of future reductions in adjustment costs
value of capital, Pt+1
(see eq. (4)).
3.2
Firms
The representative firm (RF) faces an atemporal problem. It wants to maximize its profits
choosing a combination of labor, capital and working capital, given input prices and final output
price (normalized to one). Working capital is required since the RF must pay a fraction of labor
and capital services before selling its output. Thus the RF also cares about the value of the
domestic interest rate because it affects input costs. The RF takes supply decisions in the output
market and demand decisions in inputs and loans markets.
The RF’s objective function is:
d
d
, ny,t ) − (wt ny,t + rky,t ky,t
)(1 + τ rL,t )
πy,t = ezt f (ky,t
10
(13)
where ny,t is labor demanded and τ is the fraction of factor costs paid in advance. The importance
of τ resides in the fact that assuming its value is equal to one, as it is common in the literature,
produces a level of working capital incompatible with the amount of credit available in actual
economies. In that case the stock of credit is at least as high as national income.
The term ezt is a productivity factor. The temporal evolution of zt is given by:
zt = ρz zt−1 + εz,t
(14)
where εr,t is a mean zero i.i.d. process with V ar[εr ] = σε2r .
The FOC’s of the RF’s problem are standard. For each input the marginal revenue product
is equal to its unit cost. The cost is the sum of the market price and the financing cost:
d
, ny,t ) = wt (1 + τ rL,t )
ezt fny (ky,t
(15)
d
, ny,t ) = rky,t (1 + τ rL,t )
ezt fky (ky,t
(16)
The working capital demanded (a component of bank loans), Ly,t , is equal to
d
rky,t + ny,t wt )τ
Ldy,t = (ky,t
(17)
At each instant t, the RF observes prices rL,t , wt , and rky,t , and chooses the amount of labor
and capital services according to eqs. (15) and (16). It is obvious from these conditions how
interest-rate shocks impact on production. When rL,t is positively correlated with the international rate, a fall in the latter depresses the gross cost of employing inputs and makes firms
produce more. Since τ =0 in the standard model the interest rate has no effect on the demand
side of input markets.
3.3
Banks
The representative bank (RB) is the only domestic agent borrowing and lending in international
capital markets. It faces two constraints. One is a balance sheet constraint and it dictates that
the RB lends what it borrows from someone else. The other is a technological constraint, since
loans production imposes administrative costs. The costs are modeled as requirements of capital
and labor services. A typical commercial bank hires labor (as tellers, managers, etc.) and capital
(like computers, buildings, ATM’s, etc.) for their operations. As it was described above, the
11
bank’s capital is assumed to be fixed at business cycle frequencies, leaving labor as the only
choice variable.
The RB’s problem can be set up in two different ways. The RB may choose how much labor to
hire for loans production so as to maximize profits. Alternatively, one can see the RB’s problem as
two steps one. In the first step the RB solves for a cost function. This function gives the minimum
(administrative) cost per unit of loan. In the second step, the bank observes the market interest
rates and decides its optimal amount of loans to supply6 . Under both approaches however the
RB must observe its balance sheet constraint. The second approach is followed in the paper.
The production function for loans can be stated as:
Lt = af (kb,t , nb,t )
(18)
where nb,t is labor demanded by the RB. For a given level of Lt , one can solve for the conditional
factor demands, and from there for the bank cost function, BCFt ,
BCFt = BCF (Lt , k b , wt , rkb,t ) = wt ndb,t + kb rkb,t
(19)
where ndb,t is the conditional labor demand. Replacing kb,t with kb implies recognizing the fixed
supply of bank capital and it simplifies the problem.
The balance sheet constraint dictates that the amount of loans should be equal to the amount
of bonds placed in international capital markets, that is:
bt = Lt
(20)
The RB’s profit function is then:
πb,t = (rL,t − rt )Lt − BCF (Lt , kb , wt , rkb,t )
where rt is the international interest rate, that evolves according to:
rt = ρ0 + ρr rt−1 + εr,t
(21)
ǫr,t is an i.i.d. mean zero process with V ar(ǫr,t ) = σǫr .
6
Of course it can be shown that both approaches drive to the same solution once the market interest rates and prices
are specified.
12
The optimal level of bank loans is determined maximizing πb,t with respect to Lt . This
representation of the bank problem can be easily extended to other setups where the banks are
also producing deposits and other services. At the optimal level of Lt , the intermediation spread
is equal to the marginal operative cost, that is:
rL,t − rt =
∂BCFt
∂Lt
(22)
For an alternative interpretation of eq. (22), notice that the marginal revenue, (rL,t ), is equal
to the marginal cost. The marginal cost is the sum of the marginal financial cost, rt , and the
marginal operative costs,
∂BCFt
∂Lt .
The optimal level of Lt determines the bank’s net position in international capital markets
through the balance sheet constraint, and the labor demanded through the conditional labor
demand.
Before discussing the market clearing conditions, notice that given that kb,t =k b for all t, the
RB’s marginal cost function has a finite elasticity. This is particularly important for the dynamic
of the model. It implies that the financial system acts as a buffer when the economy is affected
by an interest-rate shock. Observe that when the slope of the marginal cost approaches to zero
the marginal cost of a loan is constant. This implies that the domestic and international interest
rate vary by the same amount. In other words, the absolute interest-rate margin is constant for
all levels of Lt . In this case the economy always reaches an steady-state that is consistent with
any initial level of loans.
3.4
Market Clearing Conditions
Markets for labor services, capital services, final goods and loans must clear in every period. Some
of the market clearing conditions do not impose additional restrictions other than recognizing that
quantities supplied and demanded should be equal. Thus,
s
d
kb = kb,t
s
d
ky,t
= ky,t
(23)
is imposed hereafter. Additionally, the labor and loans market clearing conditions imply that:
ny,t + ndb,t = nt
(24)
Lt = Ldy,t + Lh,t = (ky,t rky,t + ny,t wt )τ + Lh,t
(25)
13
The system of equations that characterize the behavior of the model economy are: the four
household optimality conditions, eq. (2), and eqs. (10) to (12); the RF’s two optimality conditions,
eqs. (15) and (16); the RB’s optimality condition, eq. (22); and the loans and labor market
clearing conditions, eqs. (24), and (25). Eqs. (14), and (21) govern the temporal evolution of the
the two shocks buffeting the economy. The system has 9 (5 dynamic and 4 atemporal) equations
that holds for t = 0, 1, ..., ∞. In principle the system could be solved for the following sequence of
9 variables {ct , nt , ny,t , nb,t , Ldh,t+1 , ky,t+1 , wt , rL,t+1 , rky,t }∞
t=0 given the initial conditions stated
in eq. (9) and the forcing processes for rt and zt . However it is not possible to solve the system
analytically and a numerical method is required instead.
The competitive equilibrium for this economy is defined as a sequence of contingent allocations
∞
{ct , ny,t , nb,t , Lh,t , Lt , ky,t }∞
t=0 , and a sequence of contingent prices {rL,t , rky,t , wt }t=0 , such that
all agents solve their optimization problems and markets clear.7 The RH maximizes its expected
lifetime utility, eq. (1), subject to: a) the resource and time constraints; b) the no Ponzi scheme
and the transversality conditions; and c) the initial conditions for loans and capital. Firms and
banks maximize their respective profits at each time t subject to their respective productive
constraints. Banks must also observe the balance sheet constraint. In every period t the four
markets in the economy (goods, labor services, capital services, and loans) must clear.
4
Quantitative Analysis
The calibration of the model to Argentina and the numerical simulations are shown here. The
employed solution method is discussed in the appendix. Starting with the functional forms, the
argument of the utility index in eq. (1) and the production functions in eqs. (13) and (18) are
all Cobb Douglas,
u(ct , 1 − nt ) =
³
ct1−µ (1 − nt )µ
(26)
1−α α
ny,t
yt = ezt ky,t
(27)
1−αb αb
nb,t
(28)
Lt = ak b
7
1−σ
´1−σ
Allocations and prices are contingent since the model is stochastic. Therefore, allocations and prices are dependent
on the sequence of shocks
14
where ezt and a are specific sector productivity factors, only the former being stochastic; α and
αb are labor shares in final output and loans production, respectively. The parameter σ is the
risk aversion parameter.
Going back to the shape of the RB’s marginal cost function, notice the dependency of that
function on the parameter αb once kb,t is fixed. As it can be seen in Figure 3, the slope of the
marginal cost curve decreases with αb.
4.1
Model Calibration
In the model, the value of firms final output is different from their added value. This is due to
the use of working capital that enters into production as an intermediate input. Firms output
is measured from income sources. Banks output in turn is measured as the product of the
intermediation spread and total loans granted. In the calibrated economy banks output is equal
to 0.5% of national income. Argentinean National Accounts indicate that the output of the
financial sector is equal to 4% of GDP (in the period 1993-1999). However banks output in the
model comprises just a fraction of the services the financial system provides in the actual economy.
Argentina has grown at approximately 2.6% per year during the last 25 years, so g=0.026 on
annual basis. Following Neumeyer and Perri (1999), r is equal to 14% on annual basis8 . The
series for rt is calculated using the US-Treasure T-bills rate and the risk premium measured by
JP Morgan (Emerging Markets Bonds Index) for Argentina. Beck, Demirgüç-Kunt and Levine
(1999)’s database defines interest rate margins as the ratio of net interest income and total assets.
These authors estimate the Argentinean banks interest margin equal to 4.25% on annual basis.
Since deposits are not considered in the model the margin is set to 2.12%.
Eq. (11) implies that β is equal to 0.9693 on quarterly basis. Therefore, the true subjective
discount factor B arises from B(1 + g)(1−µ)(1−σ) = 0.9693. It implies B=0.9764 (see below for
the value of µ). The parameter σ is set equal to 5. The labor share in firms output α is equal
to 0.50 following Argentinean National accounts. Labor share in the banking industry is difficult
to calculate since what the model measures as financial activity is different from what national
accounts do, although it is known that the financial industry is labor intensive. The model was
simulated fixing αb=0.85. A tentative measure of αb however may come from financial data.
8
Andrés Neumeyer generously provided the interest rate series to the author.
15
Notice that the capital share may be written as:
1 − αb =
rk îK̂
(rL − r)L
where î is the inmovability ratio, that is the share of non-financial capital in total bank capital;
K̂ is banks’ total capital. According to model data rk /(rL − r) = 9.55. Ignoring risk adjustments,
Argentinean banks have a capital/assets ratio equal to 0.11. With î=0.8, the implied capital
share in the banking industry is equal to 0.84.
For y denoting national income, Argentinean national accounts indicate that c/y=0.79, and
i/y=0.19. The RH’s budget constrain in steady state implies that L/y takes different values
depending on the value of τ . When just 50% of the working capital must be financed in advance
it implies that L is equal to 0.96 of the national income. The value of τ =0.5 guarantees that
approximately half of banks credit is commercial credit.
As it is standard in the business cycle literature, it is assumed that 20% of the time is employed
in final output production (ny =0.2). Given banks output (defined above) and firms added value,
optimal conditions for the use of labor in both sectors imply that nb is equal to 0.026. Thus 1.29%
of the market time is allocated to the banking sector. This is a little lower than the actual labor
share in banks in Argentina (around 4%) although again it should be noted that actual banks
provide more services than what model banks do.
Eqs. (3), (12), (16), and k/y=ky /y + kb /y, along with the assumption that banks earn zero
profits in steady state, give a solution for δ, rk , and both types of capital. Hence on annual basis
δ is equal to 6.03% and rk to 23%. ky /y is equal to 2.5, and kb /y=0.02. Lh , the amount of loans
going to the RH arises from the loans market clearing condition and it is equal to 0.46 of national
income and it represents a share of 48% of total loans. The labor market clearing condition makes
n=nb + ny . Finally, the value of µ comes from eq. (10) in steady state, and it is equal to 0.7164.
4.2
Numerical Results
In this subsection the model discussed in section 3 is compared to the standard model with and
without working capital. Both interest-rate and productivity shocks are considered. From the
estimation of an AR(1) for the Argentinean interest rate, the persistence parameter, ρr is fixed to
0.918. The standard deviation of the quarterly interest rate is equal to 0.0135 (0.0608 on annual
16
basis).
Notice that the statistical properties of the interest rates differs from those used by Mendoza
(1991). Mendoza considers a value of ρr equal to 0.356 and the standard deviation of r equal to
0.0118.
Other models are nested in the discussed one. Observe that, as the interest rate margin,
rL,t − rt , approaches zero, banks play no role in the economy. Essentially it makes banks output
equal to zero. Therefore, domestic agents obtain financing placing bonds in the international
capital market. The case without working capital is obtained setting τ equal to zero. Hence the
loans market clears when households loans demand equals banks credit supply.
4.2.1
Banks Versus Direct Financing
The introduction of a banking system into the standard model of a SOE demands a re-interpretation
of the optimality and market clearing conditions. An interest-rate shock still produces the three
known results, i.e. the wealth effect, the intertemporal substitution in consumption and labor,
and the re-allocation of assets between capital and loans. However domestic interest rates are
less volatile than the international rate.
Figures 4 and 5 display the impulse response functions that follow a interest-rate shock (rt
rises). The shock raises the financial cost of the banking system and cuts down the supply of
loans. The domestic interest rate goes up and so both the production and consumption paths are
affected, as in the standard model. However the domestic interest rate, rL,t , rises less than the
international rate. Since the equilibrium level of loans is lower when the interest rate increases,
banks marginal operative costs are lower than otherwise. The importance of the last effect depends
on: a) the interest-rate elasticity of the supply of loans (affected by the value of αb); and b) the
share of operative costs on the banks interest rate.
The larger the interest-rate margin the lower the output variability. A larger interest-rate
margin is equivalent to a larger component of operative costs in determining the domestic interest
rate. Hence shocks affecting the financial marginal cost of the banking system are less important
for the variance of domestic rate and then for the output variance.
When banks intermediate in the loans market, rL,t , and not rt , is the relative price of future
consumption. Since rt is more volatile than rL,t the economy without banks observes too much
volatility vis-à-vis the economy with financial intermediaries. Of course, the result depends on
17
how banks were introduced in the economy, and the assumption of a fixed stock of bank physical
capital.
An interest-rate shock affects both, the demand and the supply for labor at a given wage
rate. On the demand side, higher financing costs makes firms slow down production cutting
down the demand for labor services. On the supply side, as the price of future leisure decreases,
households substitute present for future labor, increasing the actual labor supply. The fact that
the equilibrium amount of labor jumps on impact indicates that the latter effect dominates initially
.
For a quantitative measure of the implied volatilities some moments conditions of the calibrated model are compared to those of the Argentinean economy. It should be noted that the
Argentinean national accounts (NA) have several deficiencies. One problem is the truncation of
the series. Macroeconomics series have small number of observations. The maximum number is
80 observations on quarterly basis (20 years). Series bases change very often. The last edition
of the NA measures macroeconomic variables at 1993 prices and its sample goes from 1993.1 to
the present. However this edition has several differences with the NA’s at 1986 prices. Indeed
these two editions show differences with the NA’s at 1970 prices9 . For these reasons it may be
preferable to make explicit the differences instead of presenting a simple average. Business cycles
statistics for the main macroeconomic variables are in Table 1.
Table 2 shows model statistics comparing the economy with banks with another under direct
financing. Before commenting on the comparison, notice that some standard results arise in
both cases. The (direct or indirect) access to capital markets to smooth out consumption makes
household loans highly volatile. This is the other side of a volatile trade balance.10 On the other
side, consumption shows a low standard deviation. The low variability of consumption is due to
the Cobb-Douglas utility index as it is discussed in Correia et al. (1995).11 The trade balance is
of course countercyclical because all effects operate in the same direction for a debtor country. A
higher interest rate increases the debt burden reducing net wealth, and also leads to substitute
9
The NA’s at 1993 prices have 24 observations, between 1993.1 and 1999.4; the NA’s at 1986 prices have 64 obser-
vations between 1980.1 and 1996.4; and the NA’s at 1970 prices have 80 observations between 1970.1 and 1990.4
10
The trade balance reported in the tables is measured relative to domestic output.
11
Correia et al. state that after having experienced with several parameter values, they could not raise the volatility
of consumption above 25% of output.
18
future for present consumption and leisure.
Results differ from one model to the other because of the difference between the domestic and
international interest rate. For the same level of adjustment costs, the banking economy shows a
slightly higher investment volatility relative to output. The relative volatility of consumption is
also lower when banks intermediate in credit markets. As the domestic rate responds to change
in domestic variables, there is an extra source of variability.
The effect of interest-rate shocks on output in the previous cases contrast with those found
by Mendoza (1991). Experimenting with different interest-rate shocks, Mendoza concludes that
the effect of these shocks on output is not significative. Results shown above depend on the
autocorrelation coefficient. Mendoza sets ρr equal to 0.356. When the same value is adopted in
the model of section 3 results are comparable to those in Mendoza (1991). Particularly, keeping
constant the variance of interest rate shocks, the standard deviation of output falls below 0.3.
Now consider the case of a positive productivity shock and see Figures 6 and 7. The existence
of the banking system breaks the separation between consumption and investment decisions that
is present in the standard model. The shock makes firm demand more capital making the Tobin’s
Q higher than 1. This induces households to accumulate capital. In the standard model the trade
balance becomes coutercyclical when the pro-borrowing effect dominates the pro-saving effect.
But since the interest rate is constant in that model the price of future consumption does not
induce additional effects on intertemporal decisions.
However in the model of section 3, investment decisions also place a higher demand for loans
and induce an equilibrium rise in the domestic interest rate. This in turns makes agents substitute
future for present consumption and hence there is a an extra incentive to work that reinforces the
previous one. But there are other two additional effects operating in the opposite direction. One
is given by the fact that the gross cost of factor inputs also rises, discouraging production. The
other operates through the substitution of assets since the higher interest rate induces agents to
substitute loans for capital goods as the saving vehicle. Figure 5 illustrates the net effect of the
productivity shock on the economy and dotted lines identify again the economy without banks.
The last two commented effects of productivity shocks make the the banking economy observes
lower volatility in its macroeconomic variables. Quantitative comparisons of both models indicate
that GDP is three times more volatile in the absence of banking intermediation, although the first
order autocorrelation of output is approximately the same. Because of the separation between
19
consumption and investment decisions, consumption is less volatile in the standard model.
4.2.2
The Effect of Working Capital
The second set of results compares the importance of different values of τ , that is the size of
working capital needs. See Figures 8 and 9, and Table 3. In the figures τ was set equal to 1, 0.5
and 0.0001. Table 3 reports the results for τ equal to 1 and 0.0001. The latter value illustrates
the economy without working capital.
As expected, output variability depends on the value of τ . However there are no significative
changes in going from τ =.5 to τ =1. Domestic interest rate varies less when firms need no working
capital. The standard deviation of output rises from 3.009 to 4.218. This result indicates that for
increasing the effect of interest rate shocks on output, the value of the autocorrelation coefficient,
ρr , is as important as the introduction of working capital.
5
Concluding Remarks
The standard neoclassical model of a SOE predicts that interest rate shocks do not generate
significative output variance. Thus, country-specific (international free rate plus risk premium)
interest rate would not be an important determinant of business cycles in actual economies.
However there is a remarkable contrast between this prediction and the stress that economists in
the private sector put on financial variables, including interest rates.
Modifying the model to introduce working capital needs seems to close the gap between the
practical economists point of view and the predictions of the theory. However the nature of
working capital, a short-term loan typically provided by commercial banks, implies that the
modification deserves a deeper analysis. Therefore the paper includes a banking system that
borrows from the rest of the world and lends to both households and firms in a domestic credit
market.
Having a banking system however reduces the impact of interest rate fluctuations on output
although leaving enough variability to maintain the alignment between model predictions and
actual business cycles. Also, there are additional interactions between the financial and non
financial sectors when the economy is buffeted by a productivity shock. The separability between
20
consumption and investment decisions does not hold once the domestic interest rate reacts to a
higher demand for loans.
As for the agenda for future research, first, as King and Plosser (1984) suggest, it could be
interesting to have the financial industry holding claims on the probability distribution of output
and deposits.
The model presented here could be extended to make firms face credit limits due to some
agency costs. The borrowing constraints could be set according to firms real wealth. This would
permit to study quantitatively how firms’ wealth interact with other variables to determine output
and the demand for factor inputs. Also, it could open the possibility of explaining the credit
condition of firms of different sizes (as measured by wealth). This would imply extending the
paper along the lines suggested by Bernanke and Gertler (1989).
21
Appendix: The Solution Method
The optimal behavior of the economy was characterized by 9 equations (see section 3). Now
another equation must be added to include a dummy variable Kt = Et ky,t+1 . This permits to
reduce the system to a first order one. After substituting nt − ny,t for nb,t a system of 9 equations
in 9 variables arises again. Finally the model has two forcing processes one for zt and another for
rt .
As can be deduced from the initial conditions of the RH’s problem, both the capital stock and
the stock of household loans have an exogenous (initial) value. Thus at any time t, the value of
these two variables are known. Assume the vector kt contains these variables. There are seven
variables whose values are non-predetermined at time t, and it is assumed they are contained in
the vector ut 12 . The two exogenous variables, rt and zt , are included in the vector zt .
Log-Linearizing the system of equations around the non stochastic steady state solution of
the model, produces another system, now of linear exptectational difference equations, that can
be expressed as:
Ã
A
kt+1
Et ut+1
!
=B
Ã
kt
ut
!
+ Czt
t = 0, 1, ...
(29)
where A and B are (9×9) square matrices, and C is a (9×2) matrix. This is the typical expectational difference equations arising from the linearization of a rational expectations model.
Since some of the equations just involve atemporal relationships, the matrix A is singular.
The solution method used for solving the model dynamic is the one suggested by Klein (1998) .
It is based on the Schur decomposition of the coefficient matrices A and B. As Klein discusses,
when the shocks buffeting the economy follow a VAR(1) process, the equations in (29) can be
rewritten as:
Ã
Ae
e t+1
k
Et ut+1
!
e
=B
Ã
et
k
ut
!
(30)
where a tilde indicates the respective matrices (vectors) are being modified to include the evolution
12
e is of (4×1).
e are of (11×11) and k
of the exogenous processes. Now Ae and B
Non-predetermined variables are Kt , ct , nt , ny,t , rL,t , rky,t , and wt .
22
e there exist
By the definition of the Schur decomposition, and given the matrices Ae and B,
e = S and QBZ
e = T . Both S and T are upper
unitary (11×11) matrices Q and Z such that, QAX
triangular and for each i, sii and tii not both zero, λ(A, B) ={tii /sii : sii 6= 0} are the generalized
eigenvalues. The pairs (sii , tii ) can be arranged in any order.
Define:
H
yt = Z xt
where xt =
Ã
et
k
ut
!
where Z H is the Hermitian transpose of Z.
Consider, an arrangement of S and T such that: a) the ns stable generalized eigenvalues of
the decomposition come first13 ; and b)the following partition of Z. The upper left-hand block
is of ns by nk , where ns is the number of stable eigenvalues and nk the number of variables in
e t . The lower right-hand block of Z has nu rows, where nu is the number of unstable generalized
k
eigenvalues of the decomposition. The the number of columns in that block is the number of
variables in ut . The other two blocks follow the described two.
Making a partition of yt into ys,t and yu,t , according to the one made for Z, and premultiplying
the system by Q,
Ã
S11 S12
0
S22
!
Et
Ã
ys,t+1
yu,t+1
!
=
Ã
T11 T12
0
T22
!Ã
ys,t
yu,t
!
(31)
S11 and T22 are invertible by construction. The system (30) is thus decoupled into (31). Since
the generalized eigenvalues of the sub-system S22 Et yu,t+1 = T22 yu,t are all unstable, the unique
solution for yu,t is found solving forward. Once the solution for yu,t is gotten, the result along
with the other subsystem in (31) permits to have the solution for ys,t . Under a set of assumptions,
Klein (1988) proves that the unique solution to system (29) is (after going back from the auxiliary
variable y to the original system) given by:
and
13
−1 e
ut = Z21 Z11
kt
(32)
e
e t+1 = Z11 S −1 T11 Z −1 k
k
11
11 t + ξt+1
(33)
Unstable generalized eigenvalues are those larger or equal to one, including infinite eigenvalues.
23
which is the recursive representation of the stable solution to the system of linear difference
equation (30). ξt+1 is the mean-zero iid shock to the state variables in the system (30). It
accounts for the shocks affecting the temporal evolution of productivity and interest-rate shocks.
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25
Table 1
Argentina: Business Cycles Statistics
National Accounts at 1993, 1986 and 1970 prices
NA’s at 1993Prices
Variable*
σx /σy
ρxt ,xt−1
Output**
3.002
Cons.
Inv.
NA’s at 1986 Prices
ρxt ,yt
σx /σy
0.828
1.000
4.343
1.157
0.826
0.911
2.673
0.800
0.959
N.Exp.
1.056
0.762
Fin.Syst.
1.549
r in Pes.
0.681
ρxt ,xt−1
NA’s at 1970 Prices
ρxt ,yt
σx /σy
ρxt ,xt−1
0.780
1.000
3.121
0.675
ρxt ,yt
1.000
1.197
0.794
0.959
3.374
0.716
0.693
3.031
0.809
0.929
4.954
0.762
0.594
-0.884
2.286
0.836
-0.830
2.922
0.779
-0.649
0.702
0.809
0.487
0.739
-.—
-.—
-.—
-.—
0.185
-0.235
-.—
-.—
-.—
-.—
-.—
-.—
r in $
0.473
0.446
-0.235
-.—
-.—
-.—
-.—
-.—
-.—
Loans
1.638
0.813
0.555
14.636
0.923
-.—
-.—
-.—
-.—
Hours
1.220
0.486
0.521
-.—
-.—
-.—
-.—
-.—
-.—
*y represents GDP and x is used for all the remaining variables.
*σx /σx is the standard deviation of each variable relative to GGDP except for the own GDP where its standard deviation has been reported
26
Table 2. Model with and without Banks
Interest-Rate Shock
Variable
Model with Banks
σx
Model without Banks
σGDP
σGDP
ρxt−1 ,GDPt
ρxt ,GDPt
GDP*
4.92
0.81
1.00
7.10
0.87
1.00
Consumption
0.19
0.94
0.87
0.17
0.96
0.81
Investment
2.42
0.47
0.01
2.07
0.44
0.02
Trade Bce.
1.18
-0.19
0.32
1.04
-0.11
0.33
Intnal. r
1.14
-0.89
0.62
0.81
-0.78
-0.46
Domestic r
0.86
-0.83
-0.50
0.81
-0.78
-0.45
HH Loans
14.47
0.85
0.99
20.90
0.91
0.99
Capital
0.67
0.85
0.99
0.64
0.91
0.98
Labor
0.28
0.70
0.97
0.26
0.72
0.96
rky
0.23
-0.89
-0.97
0.20
-0.96
-0.95
Wages
0.25
0.92
0.94
0.22
0.97
0.92
Work. Cap.
0.50
0.82
1.00
0.50
0.88
1.00
Ptq
0.07
0.36
-0.14
0.09
0.30
-0.13
Saving
ρxt ,GDPt
σx
ρxt−1 ,GDPt
0.79
0.73
0.99
0.77
0.77
The standard deviation of the GDP is in absolute terms.
0.98
Table 3. Model with and without Working Capital
Interest-Rate Shock
Variable
Models with WK
σx
Model without WK
σx
σGDP
ρxt−1 ,GDPt
ρxt ,GDPt
σGDP
ρxt−1 ,GDPt
ρxt ,GDPt
GDP*
4.22
0.79
1.00
3.00
0.76
1.00
Consumption
0.22
0.92
0.91
0.21
0.90
0.91
Investment
2.68
0.46
-0.02
2.98
0.45
-0.05
Trade Bce.
1.53
-0.22
0.30
1.67
-0.24
0.30
Intnal. r
1.14
-0.90
-0.70
1.59
-0.90
-0.72
Demestic r
0.82
-0.85
-0.57
1.02
-0.81
-0.4800
HH Loans
16.93
0.82
0.99
21.23
0.80
0.99
Capital
0.80
0.82
0.99
0.80
0.80
0.99
Labor
0.33
0.70
0.98
0.33
0.66
0.98
rky
0.27
-0.86
-0.98
0.28
-0.86
-0.96
Wages
0.29
0.88
0.96
0.28
0.86
0.96
Work. Cap.
0.50
0.80
1.00
00.00
0.76
1.00
Ptq
0.05
0.37
-0.14
0.06
0.37
-0.16
Saving
0.78
0.72
0.99
0.79
0.68
The standard deviation of the GDP is in absolute terms.
27
0.99
130
0
10
20
30
40
50
60
70
1982.1 − 1999.4
80
0.4
0.35
120
GDP index
0.3
110
Interest Rate
0.25
100
0.2
90
0.15
80
70
0.1
1982.1
0
1984.1
10
1989.1
1986.3
20
30
1991.3
40
1994.1
50
1999.1
60
70
0.05
80
Figure 1
Argentina GDP index and Country-Specific Interest Rate. 1982-1999
0.06
0
5
10
15
20
25
30
0.08
0.06
0.04
0.04
0.02
0.02
0
0
−0.02
−0.02
−0.04
−0.06
−0.04
0
5
10
15
20
25
−0.06
30
Figure 2
Argentina GDP index and Country-Specific Interest Rate. 1993-1999
28
BMC
ab=.6
0.08
0.06
0.04
ab=.8
0.02
0.5
1
1.5
2
2.5
3
Loans
Figure 3
Marginal Cost of Loans for αb equal to 0.6 and 0.85
29
HH Loans
Capital
10
0.5
0
0
−10
−0.5
−20
0
20
r*
40
−1
60
1
1
0.5
0.5
0
0
20
rky
40
0
60
0.2
0
20
rL
40
60
0
20
Y
40
60
0
20
I
40
60
0
20
40
60
0.5
0
0.1
−0.5
0
0
20
40
Consumpt
−1
60
0
5
−0.1
0
−0.2
0
20
40
−5
60
Figure 4
Models with and without Banks. Interest-rate shock.
30
TB
WK
3
0.2
2
0
1
−0.2
0
−0.4
−1
0
20
Pqt
40
−0.6
60
0.1
0
20
0
20
0
20
S
40
60
40
60
40
60
0.5
0.05
0
0
−0.5
−0.05
−0.1
0
20
Labor
40
−1
60
0.1
0
0
−0.05
−0.1
−0.1
−0.2
−0.15
−0.3
0
20
40
−0.2
60
w
Figure 5
Model with and without Banks. Interest-rate shock.
31
HH Loans
Capital
1
0.04
0
0.02
−1
0
−2
−0.02
0
−15
0
x 10
20
r*
40
60
10
−3
0
x 10
20
rL
40
60
0
20
Y
40
60
0
20
I
40
60
0
20
40
60
5
−1
0
−2
0
20
rky
40
−5
60
0.04
0.2
0.02
0
0
−0.02
0
20
40
Consumpt
−0.2
60
0.02
0.5
0.01
0
0
0
20
40
−0.5
60
Figure 6
Model with and without Banks. Productivity shock.
32
TB
WK
0.05
0.06
0
0.04
−0.05
0.02
−0.1
0
−0.15
−0.02
4
0
−3
x 10
20
Pqt
40
60
0
20
0
20
0
20
S
40
60
40
60
40
60
0.15
0.1
2
0.05
0
−2
0
0
20
Labor
40
−0.05
60
0.04
0.03
0.02
0.02
0
0.01
−0.02
0
20
40
0
60
w
Figure 7
Model with and without Banks. Productivity shock.
33
HH Loans
Capital
5
0.5
0
0
−5
−10
0
20
r*
40
−0.5
60
1
1
0.5
0.5
0
0
20
rky
40
0
60
0.2
0
20
rL
40
60
0
20
Y
40
60
0
20
I
40
60
0
20
40
60
0.5
0
0
−0.5
−0.2
0
20
40
Consumpt
−1
60
0
2
0
−0.1
−2
−0.2
0
20
40
−4
60
Figure 8
Model with and without working Capital. Interest-rate shock.
34
TB
WK
2
0.2
0
1
−0.2
0
−1
−0.4
0
20
Pqt
40
−0.6
60
0.1
0.2
0.05
0
0
−0.2
−0.05
−0.4
−0.1
0
20
Labor
40
−0.6
60
0.2
0
0.1
−0.05
0
−0.1
−0.1
−0.15
−0.2
0
20
40
−0.2
60
0
20
0
20
0
20
S
w
40
60
40
60
40
60
Figure 9
Model with and without working Capital. Interest-rate shock.
35