WPS5151
Policy Research Working Paper 5151
Capital Requirements and Business Cycles
with Credit Market Imperfections
P.R. Agénor
K. Alper
L. Pereira da Silva
The World Bank
Development Economics Vice Presidency
Operations & Strategy Unit
December 2009
Policy Research Working Paper 5151
Abstract
The business cycle effects of bank capital regulatory regulatory scrutiny. Basel I and Basel IItype regulatory
regimes are examined in a New Keynesian model with regimes are defined, and the model is calibrated for
credit market imperfections and a cost channel of a middleincome country. Simulations of supply and
monetary policy. Key features of the model are that demand shocks show that, depending on the elasticity
bank capital increases incentives for banks to monitor that relates the repayment probability to the capitalloan
borrowers, thereby reducing the probability of default, ratio, a Basel IItype regime may be less procyclical than a
and excess capital generates benefits in terms of reduced Basel Itype regime.
This papera product of the Operations & Strategy, Development Economics Vice Presidencyis part of a larger effort in
the department to investigate regulatory reforms in the financial sector after the crisis. Policy Research Working Papers are
also posted on the Web at http://econ.worldbank.org. The authors may be contacted at pierrerichard.agenor@manchester.
ac.uk and Lpereiradasilva@worldbank.org.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Capital Requirements and Business Cycles
with Credit Market Imperfections
P.R. Agénor , K. Alper , and L. Pereira da Silva
JEL Classification Numbers: E44, E51, F41.
University of Manchester, United Kingdom, and Centre for Growth and Business Cycle
Research; Research Department, Central Bank of Turkey, Ankara, Turkey; World
Bank, Washington DC, USA. We are grateful to seminar participants at the University
of Manchester, the OECD, and the Banque de France for helpful comments. The views
expressed in this paper are our own.
1
Contents
1 Introduction 3
2 The Model 6
2.1 Household . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Final Good Producer . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Intermediate GoodProducing Firms . . . . . . . . . . . . . . 11
2.4 Commercial Bank . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Central Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.6 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3 Symmetric Equilibrium 22
4 Steady State and LogLinearization 24
5 Calibration 25
6 Procyclical Effects of Regulatory Regimes 27
6.1 Negative Productivity Shock . . . . . . . . . . . . . . . . . . . 27
6.2 Negative Government Spending Shock . . . . . . . . . . . . . 29
7 Summary and Extensions 30
Appendix A: SteadyState Solution 33
Appendix B: Loglinearized System 37
References 41
Table 1: Calibrated Parameter Values 43
Figures 1 to 4 44
2
1 Introduction
The role of the bank regulatory capital regime in the propagation of business
cycles has been the subject of much scrutiny since the introduction of the
Basel I regime in 1988. The adoption of the Basel II accord in 2004which
involves using marktomarket pricing rules and setting capital requirements
on the basis of asset quality rather than only on asset typeand more re
cently the global financial crisis triggered by the collapse of the U.S. subprime
mortgage market have led to renewed focus by economists and policymakers
alike on the procyclical effects of capital adequacy requirements. Indeed, it
has been argued that because of the backwardlooking nature of its risk es
timates (based on past loss experience) Basel II induces banks to hold too
little capital in economic upswings and too much during downturns. Thus,
it does not restrain lending sufficiently in boom times, while it restrains it
too much during recessions.
In a recent contribution, Agénor and Pereira da Silva (2009) argued that
much of the analytical and empirical work devoted to the analysis of cycli
cality of regulatory capital regimes focuses largely on industrialized countries
and therefore does not account for the type of financial market imperfections
that middleincome developing countries face. These include the predom
inance of banks in the financial structure, severe asymmetric information
problems and a weak judiciary (which combine to encourage highly collat
eralized lending), the absence of financial safety nets, and a high degree of
exposure and vulnerability to domestic and external shocks. In such an envi
ronment, capital buffers may play an important role by helping banks convey
a signal to depositors regarding their commitment to screening and monitor
ing their borrowers; they may therefore raise deposits at a lower cost. This
analysis shares some similarities with Meh and Moran (2008), where banks
lack the incentive to monitor borrowers adequately, because monitoring is
privately costly and any resulting increase in the risk of loan portfolios is
mostly borne by investors (households). This moral hazard problem is mit
igated when banks are wellcapitalized and have a lot to lose from loan de
fault. As a result, higher bank capital increases the ability to raise loanable
funds and facilitates bank lending. As shown by Agénor and Pereira da Silva
(2009), if capital requirements are binding, the introduction of this channel
implies that in general, it cannot be concluded a priori whether Basel II
is more procyclical than Basel Iin contrast to what a partial equilibrium
analysis would imply.
3
Despite its intuitive appeal, the model presented in Agénor and Pereira
da Silva (2009) is a static, nonoptimizing model. In this paper, we further
examine the cyclical effects of capital adequacy requirements in the New
Keynesian model with credit market imperfections developed by Agénor and
Alper (2009). An appealing feature of that framework is its explicit focus
on the type of distortions (as described earlier) that characterize the finan
cial structure in middleincome countries. It combines the cost and balance
sheet channels of monetary policy with an explicit analysis of the link be
tween collateralizable wealth and bank pricing behavior.1 Because borrowers'
ability to repay is uncertain, banks issue only collateralized loans to reduce
incentives to default and mitigate moral hazard problems; they therefore in
corporate a risk premium (which depends on the borrower's net worth and
cyclical factors) in lending rates. At the prevailing lending rate, the supply
of funds by financial intermediaries is perfectly elastic. Moreover, the central
bank fixes a policy interest rate (the refinance rate, which therefore repre
sents the marginal cost of funds), using a Taylortype rule and its supply
of liquidity to banks is perfectly elastic at the target interest rate. As a re
sult, banks are unconstrained in their lending operations. Because changes
in central bank liquidity affect the bond rate, changes in money supply play
a significant role in determining the dynamics of real variables.
Banks are also subject to riskbased capital requirements; in order to
compare Basel Itype and Basel IItype regimes, we assume that the risk
weight on loans to firms (the only risky asset for banks) is either constant
or a function of the repayment probability. This specification is based on
the assumption that this probability is positively related to the (perceived)
quality of a loan. We determine the banks' demand for capital, based on the
assumption that issuing liabilities is costly. This, together with the capital
regulation, causes deviations from the ModiglianiMiller framework.2 We also
assume that holding capital in excess of regulatory capital generates some
benefitsit represents a signal that the bank's financial position is strong,
and reduces the intensity of regulatory scrutiny.
We incorporate a bank capital channel, but we do so in a different (al
beit complementary) manner than in Agénor and Pereira da Silva (2009).
1
In turn, the models in Agénor and Alper (2009) and Agénor and Pereira da Silva
(2009) build on the static framework with monopolistic banking and full price flexibility
developed by Agénor and Montiel (2008).
2
Without these assumptions, whether bank loans are financed with deposits or debt
would be irrelevant. See Miller (1988) for instance.
4
We assume here that holding capital induces banks to screen and monitor
borrowers more carefully.3 As a result, the repayment probability tends to
increase, which in turn leads to a lower cost of borrowing. Thus, bank capital
may also play a significant cyclical rolethe higher it is, the lower the lend
ing rate, and the greater the expansionary effect on activity. Although we do
not have (yet) strong evidence on this channel for middleincome countries,
it is consistent with the evidence for the United States reported in Hubbard
et al. (2002), which suggests thatcontrolling for information costs, loan
contract terms, and borrower riskthe capital position of individual banks
affects negatively the interest rate at which their clients borrow, and in Cole
man et al. (2002), who found that capitalconstrained banks charge higher
spreads on their loans.
The main result of our simulations is that, contrary to intuition, a Basel
IItype regime may be less procyclical than a Basel Itype regime, once credit
market imperfections and general equilibrium effects are accounted for. In
our model, the repayment probability depends not only on the regulatory
regime (through the bank capitalloan ratio), but also on the cyclical po
sition of the economy (which affects cash flows and profitability) and the
collateralloan ratio (which mitigates moral hazard). Following, say, a nega
tive shock to output, a fall in the demand for productionrelated loans tends
to raise initially the collateralloan ratio, which tends to increase the re
payment probability. By contrast, the fall in cyclical output tends to lower
the repayment probability. Both of these (conflicting) effects operate in the
same manner under either regulatory regime. If the cyclical output effect
dominates the collateralloan effect on the repayment probability, and if the
fall in that probability is sufficiently large, the Basel Itype regime mitigates
the procyclicality inherent to the behavior of the repayment probability
because the cost of issuing equity falls as required capital falls; this in turn
lowers the lending rate. In addition, while the bank capitalloan ratio does
not change under a Basel Itype regime (given that risk weights are fixed),
it may either increase or fall under a Basel IItype regime, because the risk
weight is now directly related to the repayment probability. If again the
cyclical output effect dominates the collateralloan effect, so that the repay
ment probability falls, this will also lead to a higher risk weight and larger
3
Standard results suggest that a bank's incentive to monitor does not depend on its
capital if it can completely diversify the risk in its loan portfolio. However, the inability
to fully diversify risk away is one of the key features of banking in developing countries.
5
capital requirementswhich will in turn tend to mitigate the initial drop
in the repayment probability. If this "bank capital channel" is sufficiently
strong, the Basel IItype regime may be less procyclical than the Basel Itype
regime. Our numerical results suggest that this counterintuitive response can
be obtained with relatively small and plausible changes in the sensitivity of
the repayment probability to the bank capitalloan ratio.
The paper continues as follows. Section II presents the model. We keep
the presentation as brief as possible, given that many of its ingredients are
described at length in Agénor and Alper (2009); instead, we focus on how
the model presented here departs from that paper, especially with respect to
bank behavior and the regulatory capital regime. The equilibrium is char
acterized in Section III and some key features of the loglinearized version
of the model are highlighted in Section IV. After a brief discussion of the
calibrated parameters, we present the results of our experiments: temporary,
negative supply and demand shocks, to highlight the implications of the two
regulatory regimes for the economy's response to a recession. The last sec
tion provides a summary of the main results and considers some possible
extensions of the analysis.
2 The Model
We consider a closed economy populated by five types of agents: a represen
tative, infinitelylived household, intermediate goodsproducing (IGP) firms,
a finalgoodproducing firm (or, equivalently, a retailer), a commercial bank,
the government, and the central bank, which also regulates the bank. The
bank supplies credit to IGP firms to finance their shortterm working capital
needs. Its supply of loans is perfectly elastic at the prevailing lending rate.
To satisfy capital regulations, it issues shares at the beginning of time . It
pays interest on household deposits and the liquidity that it borrows from
the central bank, and dividends on the shares that it issues. We assume that,
at the end of each period, the bank is liquidated and a new bank opens at the
beginning of the next. Thus, bank shares are redeemed at the end of each
period, all its profits (including income from the redemption of oneperiod
government bonds) are distributed, and new equity is issued at the beginning
of the next period.4
4
Goodhart, Sunirand, and Tsomocos (2005) also adopt the assumption of bank liqui
dation in a twoperiod framework. Thus, there is no intrinsic distinction between issuing
6
The maturity period of bank loans to IGP firms and the maturity period of
bank deposits by households is the same. In each period, loans are extended
prior to production and paid off at the end of the period, after the sale of
output. The household deposits funds in the bank prior to production and
collects them at the end of the period, after the goods market closes. The
central bank supplies liquidity elastically to the bank and sets its refinance
rate in response to deviations of inflation from its target value and the growth
rate of output.
2.1 Household
The household consumes, holds financial assets (including securities issued
by the bank), and supplies labor to IGP firms. It also owns the economy's
stock of physical capital and rents it to IGP firms. The objective of the
household is to maximize
( )
X
[+ ]1
1
= + ln(1  + ) + ln + (1)
=0
1  1
where is the consumption bundle, working time, a composite index
R1
of real monetary assets, = 0 , with denoting the number of
hours of labor provided to the intermediategood producing firm , and
(0 1) the discount factor. is the expectation operator conditional on
the information available in period , 0 is the constant intertemporal
elasticity of substitution in consumption and 0.
The composite monetary asset is generated by combining real cash bal
ances, , and real bank deposits, , respectively (both at the beginning of
period ), through a CobbDouglas function:
= ( ) 1
(2)
where (0 1).
Nominal wealth of the household at the end of period , , is given by
= + + + + (3)
equity or debt from the perspective of the bank; capital consists therefore, in the Basel
terminology, solely of "Tier 2" capital. See Yilmaz (2009) for instance for a partial equi
librium model in which equity is accumulated over time.
7
where is the price of the final good, = nominal cash holdings,
= nominal bank deposits, holdings of oneperiod nominal gov
ernment bonds, the real stock of physical capital held by the household
at the beginning of period , the number of ownership shares issued by
the bank, and the nominal share price. As noted earlier, equity shares
are redeemed at the end of each period; this is quite convenient analytically,
because it allows us to avoid distinguishing between equity stocks and flows.
The household enters period with real units of physical capital and
1 holdings of cash. It also collects principal plus interest on bank deposits
at the rate contracted in  1, (1 + )1 , where is the interest rate
1
on deposits, principal and interest payments on maturing government bonds,
(1 + )1 , where is the bond rate prevailing at  1, as well as the
1 1
value of redeemed shares and distributed dividends (1 + )1 , where
1 1
is the nominal yield on equity shares.
At the beginning of the period, each household chooses the real levels
of cash, deposits, equity capital, and bonds, and supplies labor and capital
to intermediate goodsproducing firms, for which it receives total real factor
payment + , where is the real rental price of capital and =
the economywide real wage (with denoting the nominal wage).
The household receives all the profits made by the intermediate good
R1
producing firms, = 0 .5 In addition, it receives all the profits of
the bank, , which is liquidated at the end of the period. It also pays a
lumpsum tax, whose real value is . The household then purchases the final
good for consumption and investment, in quantities and , respectively.
Investment turns into capital available at the beginning of the next period,
+1 .
Under certainty, the household's endofperiod budget constraint is thus
+ + + (4)
= ( +  ) + (1 + )1 + (1 + )1 + (1 + )1 1
1 1 1
2
+ +  ( + ) + 1 
2
where the last term represents transactions costs (measured in terms of the
price of the good) associated with changes in the stock of equity, with 0
denoting the adjustment cost parameter.
5
As noted below, the final goodproducing firm makes zero profits.
8
The stock of capital at the beginning of period + 1 is given by
+1
+1 = (1  ) +  (  1)2 (5)
2
where (0 1) is a constant rate of depreciation and the last term is a
capital adjustment cost function specified in standard fashion, with 0
denoting the adjustment cost parameter.
Each household maximizes lifetime utility with respect to , , ,
, = , , and +1 , taking as given period  1 variables as
well as , , and . Let +1 = (+1  ) denote the inflation rate;
maximizing (1) subject to (2)(5) yields the following solutions:
¸
1 1 1 +
= (+1 ) ( ) (6)
1 + +1
( )1
= 1  (7)
( )1 (1 + )
=
(8)
(1  )( )1 (1 + )
=
(9)

½ 2 2
¸¾
+1 +2  +1
 [1+ ( 1)]+ +1 +1 + 1   ( 2
) = 0
2 +1
½ ¾ (10)
1 +
 + +1 ( )  = 0 (11)
1 + +1
where is the Lagrange multiplier associated with the budget constraint
and = is the real equity price, together with the transversality
condition
+
lim + + ( ) = 0 for = (12)
+
Equation (6) is the standard Euler equation. Equation (7) relates labor
supply positively to the real wage and negatively to consumption. Equation
(8) relates the real demand for cash positively with consumption and nega
tively with the opportunity cost of holding money, measured by the interest
rate on government bonds. Similarly, equation (9) relates the real demand
9
for deposits positively with consumption and the deposit rate, and negatively
with the bond rate. Equation (10) can be rewritten as
( ¸1 ¸)
2
1 + +1 +2
( ) = (  1) + 1 1  + +1  ( 2 )
1 + +1 2 +1
(13)
where the lefthand side is the expected real return on bonds (that is, the op
portunity cost of one unit of capital), and the righthand side is the expected
return on the last unit of physical capital invested (adjusted for adjustment
costs, incurred both in and + 1). With = 0, this expression takes the
simpler form [(1 + )(1 + +1 )] + = 1 + +1 ; put differently, in the
absence of adjustment costs, the household simply accumulates capital to
equate the (expected) rental rate with the (expected) riskfree real interest
rate on bonds, plus depreciation.
Because (+1 ) = [(1 + +1 )(1 + )], equation (11) yields
1 
= (
) (14)
1 +
which shows that the demand for equity depends positively on its rate of
return and negatively on the bond rate. In the particular case where
0, the household is indifferent between holding bank equity or government
bonds, and = .
2.2 Final Good Producer
The final good, , is divided between private consumption, government con
sumption, and investment. It is produced by assembling a continuum of
imperfectly substitutable intermediate goods , with (0 1):
½Z 1 ¾(1)
(1)
= [ ] (15)
0
where 1 is the elasticity of demand for each intermediate good.
The final goodproducing (FGP) firm sells its output to households at a
perfectly competitive price. Given the intermediategoods prices and the
finalgood price , it chooses the quantities of intermediate goods, , that
maximize its profits. The maximization problem of the FGP firm is thus
½Z 1 ¾(1) Z 1
(1)
= arg max [ ] 
0 0
10
The firstorder conditions yield

= ( ) (0 1) (16)
Imposing a zeroprofit condition leads to the following final good price:
½Z 1 ¾1(1)
1
= ( ) (17)
0
2.3 Intermediate GoodProducing Firms
There is a continuum of IGP firms, indexed by (0 1). Each firm produces
(using both labor and capital) a distinct, perishable good that is sold on a
monopolistically competitive market. Each firm must also borrow to pay
wages in advance, that is, before production and sales have taken place.
Price adjustment is subject to quadratic costs, as in Rotemberg (1982).
Production technology involves constant returns in labor and capital:
1
= (18)
where is labor hours, (0 1), and a common technology shock,
which follows the following process
ln = ln 1 +
(19)
where (0 1) and (0 ).
Each firm borrows the amount from the bank at the beginning of
the period to pay wages in advance. The amount borrowed is therefore such
that
=
(20)
for all 0. Repayment of loans occurs at the end of the period, at the
gross nominal rate (1 + ), where is the lending rate charged to firm .
As in Rotemberg (1982), IGP firms incur a cost in adjusting prices, of
the form
= (  1)2 (21)
2 1
~
where 0 is the adjustment cost parameter (or, equivalently, the degree
of price stickiness), = 1 + is the gross steadystate inflation rate, and
~ ~
aggregate output, defined in (15).
11
IGP firms are competitive in factor markets. Unit cost minimization
yields the optimal capitallabor ratio as
(1 + )
=( )[
] (22)
1
whereas the unit real marginal cost is
£ ¤1
(1 + )
( )
= (23)
(1  )1
Each firm chooses a sequence of prices so as to maximize the dis
counted real value of all its current and future real profits, where nominal
profits at , , are defined as =   . Taking
{+ + + } as given, the firstorder condition for this maximiza
=0
tion problem is:
½ ¾ ½ ¾

1  + ( ) ( )  (  1) (24)
~
1 ~
1
( )
+1 +1
+ +1 (  1)+1 ( 2 ) = 0
~
~
which gives the adjustment process of the nominal price .
2.4 Commercial Bank
At the beginning of each period , the bank collects deposits from the
household. Funds are used for loans to IGP firms, which use them to pay
labor in advance. Thus, lending, , is equal to
Z 1
= =
(25)
0
R1
where again = 0 .
Upon receiving household deposits, and given its equity and loans
, the bank borrows from the central bank, , to fund any shortfall in
deposits. At the end of the period, it repays the central bank, at the interest
rate , which we refer to as the refinance rate. It also holds required reserves
at the central bank, , and government bonds, .
12
The bank's balance sheet is thus
+ + = + +
(26)
where
= + (27)
with denoting capital requirements and excess capital. We assume in
what follows that, due to prohibitive penalty or reputational costs,
at all times. In fact, we will focus on the case where capital requirements are
not strictly binding, that is, 0.6
Reserves held at the central bank do not pay interest. They are deter
mined by:
= (28)
where (0 1) is the reserve requirement ratio.
Using (28), and given that and are determined by private agents'
behavior, the balance sheet constraint (26) can be used to determine bor
rowing from the central bank:
= +  (1  ) 
(29)
The bank is also subject to riskbased capital requirements; it must hold
an amount of equity that covers at least a given percentage of its loans,
exogenously set by the central bank. Government bonds bear no risk and
are subject to a zero weight in calculating capital requirements. The risk
weight on loans to firms is :
=
(30)
where (0 1) is the capital adequacy ratio. Under Basel I, is fixed at
1; under Basel II, in a manner similar to Agénor and Pereira da Silva
0
(2009), we relate the risk weight to the repayment probability estimated by
the bank, because it reflects its perception of default risk:7

= ( ) (31)
~
6
As documented in Pereira (2009), this is the more relevant case in practice.
7
The Standardized Approach in Basel II can be modeled by making the risk weight a
function of the output gap, under the assumption that ratings are procyclical.
13
where 0 and is the steadystate value of . In the steady state, the
~
8
risk weight is therefore equal to unity.
The bank sets both the deposit and lending rates to firms and the house
hold, equity capital, and real holdings of government bonds, = , so
as to maximize the present discounted value of its real profits,
X +
{ + }
+ + +
=0 = arg max + ( ) (32)
=0
+
where denotes current profits at the end of period .9 In the present
setting (and given in particular the assumption that the bank is liquidated
and equity is redeemed at the end of each period), this maximization problem
boils down to a periodbyperiod problem.
Real expected gross profits can be defined as
( ) = (1 + ) + (1 + )( ) + (1  )
(33)
( )2
+  (1 + )  (1 + )(
)  (1 + ) 
2
 + 2 ( )12
where (0 1), , , 0, and (0 1) is the repayment prob
ability of IGP firms, assumed identical across them. The second term in
this expression on the righthand side, (1 + )1 , represents expected
repayment if there is no default. The third term represents what the bank
expects to earn in case of default. Under limited liability, earnings if the loan
is not paid back are given by the "effective" value of collateral pledged by the
8
In practice, the capital requirements prescribed by the Internal Ratings Based (IRB)
approach of Basel II are an increasing function of banks' estimates of not only the prob
ability of default, but also loss given default (LGD) of each loanthat is, the fraction of
exposure that will not be recovered following default. Here, given the presence of collat
eral, the value of LGD for each individual IGP firm is in fact  ; as discussed
below, this is already accounted for in the repayment probability through the collateral
loan ratio. Thus, movements in LGD are also implicitly captured through the dependence
of on .
9
In equilibrium, the lending rate is also the same across borrowers; we therefore econ
omize on notation by using a lending that is independent of .
14
borrower, .10 "Raw" collateral consists therefore of the physical assets of
the firm and measures the degree of credit market imperfections.11
The fourth term, , represents the reserve requirements held at the
central bank and returned to the bank at the end of the period (prior to its
closure). The term (1 + ) represents repayment of deposits (principal
and interest) by the bank. The term (1 + ) represents the value of
shares redeemed to households and dividend payments. The term ( )2 2
captures the cost associated with transacting in government bonds (dealer
commissions, etc.); for tractability, this cost is assumed to be quadratic.
The linear term captures the cost associated with issuing shares
(cost of underwriting, issuing brochures, etc.). By contrast, the last term,
2 ( )12 , captures the view that maintaining a positive capital buffer
generates some benefitsit represents a signal that the bank's financial po
sition is strong, and reduces the intensity of regulatory scrutiny, which in
turn reduces the pecuniary cost associated with the preparation of data and
documents required by the supervision authority.12 We assume that this ef
fect on expected profits is concave, which implies that the benefits of capital
buffers diminish fairly rapidly over time.13
The maximization problem is subject, from (20) and (22), to the loan
10
Because firms are ex ante homogenous, the bank has no screening problems; ex post
monitoring costs are captured implicitly by defining as the "effective" value of collateral
(that is, net of monitoring and contract enforcement costs) that can be seized in case of
default.
11
Note that although revenues depend on whether the borrower repays or not, payments
of principal and interest to households and the central bank are not contingent on shocks
occuring during period and beyond and on firms defaulting or not. Note also that in case
of default the bank can seize only collateral, (valued at the economywide price of
the final good, ) not realized output (valued at the firmspecific intermediate price, ).
This is important because it implies that firm , which takes as given when setting its
price, does not internalize the possibility of default. See Agénor, Bratsiotis, and Pfajfar
(2009) for the alternative (and more complex) case.
12
Because required capital depends on riskweighted assets, this term accounts for a
scale effect as well. A related argumentin a stochastic environmentis provided in
Ayuso, Pérez, and Saurina (2004), in which capital buffers reduce the probability of not
complying with capital requirements.
13
Because costs asssociated with issuing capital are modeled linearly, assuming that the
benefit associated with capital buffers is quadratic would imply a profitmaximizing value
of equal to infinity. A more general specification would be to assume that the benefits
associated with capital buffers have a convexconcave shape, but this is much less tractable
numerically.
15
demand function for IGP firms
Z 1
(1 + )
= ( ) = [
; ] (34)
0
the balance sheet constraint (26), used to substitute out , the equation
defining (27), and the capital requirement constraint (30).
The bank internalizes the fact that the demand for loans (supply of de
posits) depends negatively (positively) on the lending (deposit) rate, as im
plied by (9) and (34), and that changes in the level of loans affects capital
requirements, as implied by (30). It also takes the repayment probability of
firms, the value of collateral, the contract enforcement cost, prices and the
refinance rate as given.
The firstorder conditions for maximization yield:
  [(1 + )   (1  )(1 + )](
) = 0 (35)
©
£ ¤ª
+ (1 + )  (1  )(1 + )  (1 + ) +
= 0
(36)
(1 + )  (1 + )  = 0
(37)
( )
(1 + )  (1 + ) +  p
= 0 (38)
Let = ( ) denote the constant interest elasticity of the
supply of deposits by the household. Condition (35), which can be rewritten
£ ¤
as +  (1  ) ( ) = 0, yields
1 1
= (1 + ) (1  )
(39)
which shows that the equilibrium deposit rate is set as a markup over the
refinance rate, adjusted (downward) for the implicit cost of holding reserve
requirements.
Similarly, let = [ ]( ) denote the interest elasticity of the
demand for loans. Using this definition, condition (36) yields
1 © £ ¤ª
1 + =
1 (1  )(1 + ) + (1 + ) + (40)
(1 + )
16
which implies that the gross lending rate depends negatively on the repay
ment probability, and positively on a weighted average of the marginal cost
of borrowing from the central bank (at the gross rate ) and the total cost
of issuing equity, which accounts for both the gross rate of return to be paid
to investors and issuing costs. Weights on each component of funding costs
are measured in terms of the share of equity in proportion of loans.
Now, we assume that the repayment probability depends positively on
three sets of factors. First, it depends on borrowers' net worth; it increases
with the effective collateral provided by firms, , and falls with the
amount borrowed, .14 As argued by Boot, Thakor, and Udell (1991),
Bester (1994), and Hainz (2003), by increasing borrowers' effort and reducing
their incentives to take on excessive risk, collateral reduces moral hazard and
raises the repayment probability. Second, we assume that depends on
~ ~
the cyclical position of the economy, as measured by , with denoting
the steadystate value of aggregate output. This term captures the view,
that in periods of high (low) levels of activity, profits and cash flows tend to
improve (deteriorate) and incentives to default diminish (increase). Third, we
assume that increases with the bank's capital relative to the outstanding
amount of loans, , because bank capital (irrespective of whether it
is required by regulation or chosen discretionarily) increases incentives for
the bank to screen and monitor its borrowers. In turn, greater monitoring
mitigates the risk of default and induces lenders (if marginal monitoring costs
are not prohibitive) to reduce the cost of borrowing. As noted earlier, this
is consistent with the evidence in Hubbard et al. (2002), according to which
wellcapitalized banks tend to charge lower loan rates than banks with low
capital, and the results in Coleman et al. (2002), in which capitalconstrained
banks charge higher spreads on their loans. This effect is also consistent with
the evidence in Barth, Caprio, and Levine (2004), based on crosscountry
regressions for 107 industrial and developing countries, which suggests that
all else equal capital requirements are associated with a lower share of non
performing loans in total assets (which could reflect better screening and
monitoring of loan applicants).15
14
In standard StiglitzWeiss fashion, the repayment probability could be made a de
creasing function of the lending rate itself, as a result of adverse selection and moral
hazard effects on the riskiness of the pool of borrowers.
15
Another rationale for a negative link between the bank capitalcredit ratio and the
repayment probability could result from the fact that investors, while increasing their
holdings of bank debt, may exert pressure on the bank to increase profits. Given that
17
To capture these effects, we specify the repayment probability as
1 2 3
= 0 ( ) ( ) ( ) (41)
~
with 0 .16 Note that although we use a "quasireduced form" for
the repayment probability, the impact of collateralizable net worth can be
explicitly derived as in Agénor and Aizenman (1998), under the assumption
that the distribution of the supply shock is uniform.
Combining (40) and (41) yields the following partial equilibrium result:
Result 1. An increase in bank capital (in proportion of outstanding
loans), by increasing incentives to monitor borrowers, reduces borrowers' de
fault probability and lowers the lending rate.
From (37), the demand for bonds is
= 1 (  )
(42)
which is increasing in the bond rate and decreasing in the marginal cost of
funds.
Using equation (27), (38) yields
½ ¾2
= (43)
+ 
which shows that an increase in the direct or indirect cost of issuing equity
( or ) reduces excess capital, whereas an increase in raises excess
capital. Note that required capital, by affecting the cost of issuing equity, has
an indirect effect on the capital buffer: an increase in , by raising will
lower excess capital. In that sense, there is some degree of substitutability
between required and excess capital.
From (43), (30), and (31), it can be seen that, a drop in aggregate out
put, due to a common negative productivity shock, affects the repayment
the bank has a perfectly elastic supply of credit, the only way to do so is to stimulate the
demand for loans by reducing the lending rateand this can happen only if the repayment
probability increases. However, in this interpretation, the negative link between these two
variables would reflect greater risk taking and reckless lending, rather than improved
monitoring, as emphasized in the text.
16
We assume that 0 is such that the condition (0 1) holds continuously.
18
probability through several channels. First, because the demand for labor
(and thus bank loans) falls, the collateralloan ratio rises initially; this tends
to increase the repayment probability and to lower the lending rate. Sec
ond, the fall in cyclical output tends to lower the repayment probability and
to raise the lending rate. These two (conflicting) effects operate in either
regulatory regime. Third, although bank capitalloan ratio does not change
under a Basel Itype regime (given that risk weights are fixed), it may either
increase or fall under a Basel IIregime, because the risk weight is now di
rectly related to the repayment probabilitythe initial response of which is
ambiguous, due to the conflicting effects mentioned earlier. The net, general
equilibrium effect on the repayment probability is thus also ambiguous in
generaland so is the relationship between the degree of procyclicality of
both regimes.
Suppose then that the cyclical output effect dominates the collateralloan
effect; the repayment probability falls and the lending rate tends to increase.
At the same time, the lower level of loans (which implies lower capital re
quirements) tends to lower the rate of return on equity to induce households
to reduce their demand for these assets. In turn, the lower equity rate reduces
the loan rate. As long as the risk effect is large enough compared to this cost
effect, the Basel Itype regime mitigates the procyclicality inherent to the
behavior of the repayment probability but does not reverse it. Under the
Basel IItype regime, the initial fall in the repayment probability leads also
to a higher risk weight and larger capital requirementsif actual capital can
increase to reflect higher regulatory requirements (as implied by (43))than
under Basel I. As a result of the larger increase (or smaller reduction) in the
supply of equity, the cost of issuing equity falls by less (or may even increase,
if the effect of the higher risk weight dominates the drop in the amount of
loans) as well; this tends to increase the lending rate by more, thereby mak
ing the Basel IItype regime more procyclical. This is consistent with the
view held by many observers. Thus, if we define procyclicality in terms of
the behavior of the repayment probability (in a manner akin to Agénor and
Pereira da Silva (2009), who focus on the risk premium), we can summarize
this result as follows:17
Result 2. If the cyclical output effect dominates the collateralloan effect
17
In the numerical simulations that we report next, procyclicality could be defined equiv
alently in terms of the behavior of the lending rate or aggregate output; relative rankings
of the two regimes are the same in response to the shocks that we consider.
19
on the repayment probability, and if the fall in that probability is sufficiently
large, the Basel IItype regime magnifies the procyclicality inherent to the
behavior of the credit market.
However, in the model the higher capitalloan ratio also tends to increase
the repayment probability; this will tend to mitigate the initial fall in that
variable. If the sensitivity of the repayment probability to the capitalloan
ratio (as measured by 2 ) is sufficiently high, this will tend to make the
Basel IItype regime less procyclical than the Basel Itype regime. This
fundamental ambiguity in the procyclical effects of the Basel IItype regime,
relative to the Basel Itype regime, can be summarized as follows:
Result 3. If there is no bank capital channel ( 2 = 0), the Basel IItype
regime is always more procyclical than the Basel Itype regime. If 2 0
and sufficiently large, the Basel IItype regime may be less procyclical than
the Basel Itype regime.
Finally, at the end of the period, as noted earlier, the bank pays interest
on deposits, redeems equity shares, and repays with interest loans received
from the central bank. There are no retained earnings; the profits that are
distributed to shareholders are therefore given by
= max(0 ) (44)
where ½ ¾
= (1 + ) + min (1 + )( )
( )2
+  (1 + )  (1 + )( )  (1 + ) 
2
(  )2
 
2
2.5 Central Bank
The central bank's assets consists of holdings of government bonds, ,
loans to the commercial bank, , whereas its liabilities consists of currency
supplied to households and firms, , and required reserves ; the latter
20
two make up the monetary base. The balance sheet of the central bank is
thus given by
+ = +
(45)
Using (28), (45) yields
= + 
(46)
Any income made by the central bank from loans to the commercial bank
is transferred to the government at the end of each period.
Monetary policy is operated by fixing the refinance rate, , and providing
liquidity (at the discretion of the bank) through a standing facility.18 The
refinance rate itself determined by a Taylortype policy rule:
= + (1  )[~ + + 1 (  ) + 2 ln( ¯ )] +
1 (47)
where is the steadystate value of the real interest rate on bonds, 0 the
~
¯ ¯
central bank's inflation target, and is the output gap, with denoting
the frictionless level of aggregate output (that is, corresponding to = 0).
Coefficient (0 1) measures the degree of interest rate smoothing, and
1 2 0 the relative weights on inflation deviations from target and output
growth, respectively, and ln is a serially correlated random shock with zero
mean.
2.6 Government
The government purchases the final good and issues nominal riskless one
period bonds, which are held by the central bank and households. Its budget
constraint is given by
= (1 + )1 + (  )   1
1 1 1 1
(48)
18
In several middleincome countries, as in many industrial countries, the standard
mechanism through which the central bank injects liquidity is through openmarket op
erations of various kinds, aimed at providing sufficient cash on average to maintain the
shortterm policy interest rate at its target level. Above and beyond that, banks still short
of cash can obtain additional funds at the upper band of a corridor, the discount window,
or a standing facility (typically slightly above the policy rate). Conversely, banks with
excess cash can deposit it at the central bank (at a rate typically below the policy rate).
Our specification abstracts from openmarket operations and corresponds to a "channel
system" in which deposits held at the central bank earn a zero interest rate (see Berentsen
and Monnet (2007)).
21
where = + + is the outstanding stock of government bonds,
+1 bonds issued at the end of period + 1, real government spending,
and real lumpsum tax revenues. The final term, and 1 , comes
1
from our assumption that all interest income that the central bank makes
(from its lending to the commercial bank and its holdings of government
bonds) is transferred to the government at the end of each period.
Government purchases are assumed to be a constant fraction of output
of final goods:
= (49)
where is bounded between zero and one and is assumed to follow a first
order autoregressive process of the form
ln = ln 1 +
(50)
where (0 1) and (0 ). The innovations and are also
assumed to be independent of each other.
3 Symmetric Equilibrium
In what follows we will assume that the government equilibrates its budget by
adjusting lumpsum taxes, while keeping the overall stock of bonds constant
¯ ¯
at , and that the central bank also keeps its stock of bonds constant at .
Private holdings of government bonds are thus equal to = ¯
¯   .
In a symmetric equilibrium, all firms producing intermediate goods are
identical. Thus, = , = , = , = , for all (0 1). All
firms also produce the same output, all households supply the same hours of
labour, and prices are the same across firms. In the steady state, inflation is
constant at .
~
Equilibrium conditions must also be satisfied for the credit, deposit,
goods, and cash markets.19 Because the supply of loans by the bank, and
the supply of deposits by households, are perfectly elastic at the prevailing
interest rates, the markets for loans and deposits always clear. For equilib
rium in the goods markets we require that production be equal to aggregate
19
By Walras' Law, the equilibrium condition of the market for government bonds can
be eliminated.
22
demand, that is, using (21),20
1 +
= + + + (  1)2 (51)
2 1+ ~
Equation (5) can be rewritten as
= +1  (1  ) + (+1 ) (52)
Combining (49), (51), and (52), the aggregate resource constraint then
takes the form
½ ¾
1 + 2
1 (  1) = + +1  (1  ) + (+1 ) (53)
2 1+ ~
The equilibrium condition of the market for cash is given by
= +
R1
where is defined in (46) and = 0 denotes firms' total holdings
of cash. Suppose that bank loans to firms are made only in the form of cash;
we therefore have = .21 The equilibrium condition of the market for
currency is thus given by = + , that is, using (46)
+  = +
Using (26) to eliminate in the above expression yields
¯
+ = +  (54)
Using (8) and (9) and aggregating, condition (54) becomes
¯ ½ ¾
+
1 (1  )
 = ( ) (1 + ) + (55)

which can be solved for .
As noted earlier, households take portfolio allocation decisions for period
+ 1 at the end of period . Bank equity is thus priced so that its net return
20
Implicit in (51) is the assumption that ex post bank monitoring (that is, in case of
default) does not entail real costs.
21
As discussed by Agénor and Alper (2009), condition (54) below does not change if
instead the counterpart to loans consists of deposits.
23
at + 1 equals its expected return at for + 1, which consistsgiven that
there are no capital gains, the bank lasting only on periodof expected bank
profits (which are distributed as cash dividends at the end of the period) per
share:
= +1
(56)
Finally, the equilibrium condition of the bank equity market is obtained
by equating (14) and (43):
= + (57)
4 Steady State and LogLinearization
The steadystate of the model is derived in Appendix A. With a zero inflation
target = 0, the steadystate inflation rate is also = 0. In addition to
~
standard results (the steadystate value of the marginal cost, for instance, is
given by (  1)), the steadystate value of the repayment probability is
~~
1 2~~
= 0 (
~ ) ( )
~ ~
whereas steadystate interest rates are given by
1 1 1
~ = ~ = =
~  1 ~ = (1 +
) (1  )~
~
~ =
+ 1  1 ~
and
1 © £ ¤ª
~ =
(1  ) 1 + (1 + ~ ) +  1
(1 + 1 )~
From these equations it can be shown that ~ ~ . The reason why ~
~ = is because holding equity is subject to a cost; from the perspective
~
of the household, the rate of return on equity must therefore compensate for
that and exceed the rate of return on government bonds or physical capital.
Of course, when = 0, then ~ = ~ = .22 In addition, from (42),
~
22
Thus, the arbitrage condition in Aguiar and Drumond (2007) between the rates of
return on equity and physical capital holds only when = 0.
24
the steadystate stock of bonds held by the bank is zero, given that ~ = ~ .
Equation (43) determines ~ . Because ~ ~ , 0, given that 0.
~
By implication of (31), = 1 under both Basel I (by assumption) and Basel
~
II.
To analyze how the economy responds to shocks we proceed in standard
fashion by loglinearizing it around a nonstochastic, zeroinflation steady
state. The loglinearized equations are summarized in Appendix B. In par
ticular, loglinearizing condition (24) yields the familiar form of the New
Keynesian Phillips curve (see, for instance, Galí (2008)):
1
= ( c
) + +1
c
where is the logdeviation of from its steadystate level, given by
+
= (1  )(^ + ) + (
c ^
)^
1 + 
^
where ^ and denote percentage point deviations of the lending rate
and the rental rate of capital from their steadystate levels, and the log
^
deviation of the real wage from its steadystate value. Because changes in
bank capital affect the repayment probability and the lending rate, they will
also affect the behavior of real marginal costs.
5 Calibration
To calibrate the model we dwell as much as possible on Agénor and Alper
(2009); we therefore refer to that study for a detailed discussion of some of our
choices. In addition, for some of the parameters that are "new" or specific to
this study, we consider alternative values. This is the case, in particular, for
the elasticity of the repayment probability with respect to bank capital, and
the elasticity of the risk weight with respect to the repayment probability,
given their importance for the issue at stake.
Parameter values are summarized in Table 1. The discount factor is set
at 095, which corresponds to an annual real interest rate of 5 percent. The
intertemporal elasticity of substitution, , is 06, in line with estimates for
middleincome countries (see Agénor and Montiel (2008)). The preference
parameters for leisure, , and for composite monetary assets, , are both
set at 15. The share parameter in the index of money holdings, , which
25
corresponds to the relative share of cash in narrow money, is set at 02. The
adjustment cost parameter for equity holdings, , is set at 03, whereas the
adjustment cost for investment, , is set at 86. The share of capital in
output of intermediate goods, 1  , is set at 035, whereas the elasticity of
demand for intermediate goods, , is set at 10implying a steadystate value
of the markup rate, (  1), equal to 111 percent. The adjustment cost
parameter for prices, , is set at 745. The rate of depreciation of capital
is set at 60 percent. The reserve requirement rate is set at 01, whereas
the coefficient of the lagged value is set at = 0 (which therefore implies
that we abstract from persistence stemming from the central bank's policy
response). We also set 1 = 15 and 2 = 02, which are conventional values
for Taylortype rules for middleincome countries; the relatively low value of
2 (compared to estimates for industrial countries, which are closer to 05)
is consistent with the evidence reported for Latin America by Moura and
Carvalho (2009). For the degree of persistence of supply and demand shocks,
we assume that = = 06, with standard deviations = 002 and
= 003, respectively.
For the parameters characterizing bank behavior, we assume that the
effective collateralloan ratio, , is 02. The elasticity of the repayment prob
ability with respect to collateral is set at 1 = 005, with respect to the
bank capitalloan ratio at 2 = 001, and with respect to cyclical output at
3 = 02. In the case of 2 , we also consider an alternative value of 2 = 02.
Although somewhat arbitrary (as far as we know, there is not much empir
ical evidence about this parameter for middleincome countries), these two
different values allow us to explore the extent to which procyclical effects
differ across regulatory regimes. The elasticity of the risk weight under Basel
II with respect to the repayment probability is set at a relatively low value,
= 005. The cost parameters , , and are also set at low values,
005, 01, and 0001, respectively. The capital adequacy ratio, , is set at
008, which corresponds to the target value for Basel I and the floor value for
Basel II. Finally, the steadystate value of the risk weight is calibrated
so that it is equal to unity under both regimes. For Basel I, given that the
risk weight is constant, this choice also implies that it remains continuously
equal to unity.
26
6 Procyclical Effects of Regulatory Regimes
We now consider the procyclical effectsas measured by the behavior of the
repayment probabilityof two types of shocks: a negative productivity (or
supply) shock, and a negative (or demand) shock to the share of govern
ment spending in output.23 In each case, we report the result for the two
different values of the elasticity of the repayment probability with respect to
the capitalloan ratio (2 = 001 and 2 = 02). As is made clear below,
this parameter change allows us to illustrate the ambiguity in the procyclical
effects of the two regulatory regimes.
6.1 Negative Productivity Shock
Figures 1 and 2 shows the impulse response functions of some of the main
variables of the model following a temporary, one percentage point negative
shock to productivity. The results show indeed that two different outcomes
may occur, depending on the elasticity of the repayment probability with
respect to the capitalloan ratio, 2 . In both figures, the behavior of most of
the variables (except for marginal costs) does not differ much across regimes.
This is because of the negative relation between the capital buffer and re
quired capital, as implied by (43); as a result, total capital under the two
regimes is more closely related.24
The direct effect of the shock is to lower temporarily the rental rate of
capital, which reduces investment and tends to reduce marginal production
costs. However, because the increase in borrowing costs (as discussed below)
dominates, real marginal costs go up, thereby raising inflation.25 The policy
23
Note that we do not compare the results under either regulatory regime with the case
where there is no bank capital channel (that is, = 0 ). As is made clear below, the
main factor that makes the Basel IItype regime differ from the Basel Itype regime is the
endogeneity of the risk weight in the former. This channel disappears if there is no bank
capital. Hence, in that case, we would expect the convergence path to be similiar to what
happens under the Basel Itype regime. However, because the steadystate level of the
repayment probability would be lower in the absence of bank capital, the lending rate and
real wages would be higher and aggregate output would be lower compared to what we
obtain under that regime.
24
However, by changing the parameters by more, we could magnify these differences.
25
Note that, with our costofpriceadjustment assumption, IG producers are actually
free to reset nominal prices every period, in contrast to Calvostyle specification of price
stickiness.
27
rate, which is determined by a Taylor rule, rises in response to the increase
in prices. By and large, other interest rates in the economy tend to follow
the rise in the policy rate.26 The rise in the expected real bond rate induces
intertemporal substitution in consumption toward the future, which trans
lates into a drop in current spending by households. Because government
spending is a fixed proportion of output, it falls immediately in response to
the adverse shock to aggregate supply. The net effect on aggregate demand
is thus negative as well.
The initial drop in output also lowers the repayment probability directly,
whereas the collateralloan ratio tends to increase at firstthereby raising
the repayment probability. The net effect of these two channels is therefore
ambiguous in general; given our calibration, the first effect dominates and
the repayment probability falls, thereby raising the lending rate and marginal
costs. In addition, however, there is a third channel in the model, which
operates through the bank capitalloan ratio and depends on the regulatory
regime. Under Basel I, the bank capitalloan ratio does not change by much,
because excess capital changes very little (given our calibration) and, by
definition, the risk weight is constant. There is therefore a negligible
indirect effect on the repayment probability under this regime. By contrast,
under Basel II, the initial drop in the repayment probability raises the risk
weight and therefore actual and required capital. Because credit falls, the
bank capitalloan ratio rises unambiguously, which implies an upward effect
on the repayment probability, thereby mitigating the initial downward effect
under that regime. The net effect is thus ambiguous in general and depends
on the value of 2 . In Figure 1, which corresponds to 2 = 001, the shock
lead to the conventional case where Basel II is more procyclical than Basel
I, whereas in Figure 2, which corresponds to 2 = 02, the opposite occurs.
Thus, Basel II can be less procyclical than Basel Iin the sense that the
drop in the repayment probability, the increase in the lending rate, and the
fall in output, are all of a smaller magnitude.
26
By itself, the reduction in the demand for loans and capital requirements puts down
ward pressure on the rate of return on equity; however, given that the bond rate increases
quite significantly, the rate of return on equity ends up increasing to mitigate the drop in
the demand for equity.
28
6.2 Negative Government Spending Shock
Figures 3 and 4 show the impulse response functions associated with a tem
porary, one percentage point reduction in the share of government spending
in output. In both cases the reduction in the government spending share
raises the proportion of output going to household consumption. This lowers
immediately the marginal utility of consumption and reduces on impact the
supply of labor. As a result, real wages increase initially and output falls.
The policy rate falls as well, thereby lowering the deposit rate and thus the
bond ratewhich in turn stimulates private current consumption, by induc
ing households to shift consumption toward the present. However, due to
the relatively low intertemporal elasticity of substitution in our calibration,
this offsetting effect is only partial; aggregate demand falls on impact, albeit
by less than public spending.
The fall in aggregate supply results from an increase in the real effective
cost of labor, due not only to an increase in wages (alluded to earlier), but also
from a higher lending ratewhich itself stems from the fact that, despite the
fall in the policy rate, the repayment probability falls in both regimes. Indeed,
although the drop in bank borrowing raises the collateraldebt ratio (thereby
exerting upward pressure on the repayment probability), the downward effect
due to the fall in output dominates. The increase in effective labor costs leads
to higher marginal costs (despite a reduction in the cost of capital), and this
exerts upward pressure on inflation, which increases in both regimes when
Basel II is more procyclical (Figure 3), and in Basel I, when Basel II is
less procyclical (Figure 4). In the latter case, in the Basel II regime, inflation
actually falls because the repayment probability falls by less, and the increase
in the lending rate is smaller; as a result, the "cost channel" is not as strong,
in contrast to the other cases. The increase in the marginal product of labor
dominates the increase in the cost of working capital, which leads to a fall in
inflation.
A comparison of Figures 3 and 4 also shows that, depending on the elas
ticity of the repayment probability with respect to the capitalloan ratio, 2 ,
the repayment probability may drop by less under Basel II. The reason is
the same as beforeunder Basel II, the initial fall in the repayment prob
ability leads to a higher risk weight, which increases the bank capitalloan
ratio and thereby mitigates the initial downward pressure on that probability
associated with changes in the collateralloan ratio and output. In Figure
3, which corresponds to 2 = 001, the shock generates the "conventional"
29
result, whereas in Figure 4, which corresponds to 2 = 02, Basel II is less
procyclical than Basel Iwhether this is measured in terms of the behavior
of the repayment probability, the lending rate, or aggregate output.
In addition, the increase in the lending rate may, or may not, be larger
under Basel II. This is because the (downward) response of the policy rate
is weaker under Basel I (given that inflation drops less under that regime),
but the drop in the repayment probability may or may not dominate. If
movements in the policy rate and the repayment probability tend to offset
each other, the lending rate mat not change by much under Basel II. This
pattern also explain differences in the behavior of the rate of return on equity
under the two regimes. The larger increase in the lending rate (and thus the
marginal cost of the labor) under Basel I explains why aggregate output may
contract more under that regime, despite higher consumption under Basel II.
Marginal costs may also fall by more under Basel II, which in turn accounts
for the larger drop in inflation under that regime.
7 Summary and Extensions
In this paper the business cycle effects of bank capital requirements were ex
amined in a New Keynesian model with credit market imperfections, a cost
channel of monetary policy, and a perfectly elastic supply of liquidity by the
central bank at the prevailing policy rate. In the model, which combines
elements developed in Agénor and Alper (2009) and Agénor and Pereira da
Silva (2009), Basel I and Basel IItype regulatory regimes are defined. In
the latter case, the risk weight is related directly to the repayment probabil
ity that is embedded in the loan rate that the bank imposes on borrowers.
A "bank capital channel" is introduced by assuming that higher levels of
capital (relative to the amount of loans) induce banks to screen and monitor
borrowers more carefully, thereby reducing the risk of default and increas
ing the repayment probability. The model is calibrated for a middleincome
country. Numerical simulations show that, in the absence of the bank cap
ital channel, a Basel IItype regime is always more procyclical than a Basel
Itype regime, as in the conventional, partial equilibrium view. By contrast,
if the elasticity of the repayment probability to the bank capitalloan ratio is
sufficiently high, a Basel IItype regime may be less procyclical than a Basel
Itype regime, in response to contractionary supply and demand shocks. The
key reason is that, following a negative supply shock for instance, the bank
30
capital channel mitigates the drop in the repayment probability, due to an
increased monitoring incentive effect.
The analysis in this paper can be extended in a variety of directions. First,
the assumption that the bank lasts only one period allowed us to avoid any
distinction between stocks and flows in the dynamics of bank capital. A use
ful extension would be to consider an explicit link between (flow) dividends
and banks' net worth, as for instance in Meh and Moran (2008) and Valencia
(2008). This would enrich the dynamics of the model, because changes in
banks' net worth would affect pricesetting behavior and the real economy.
Second, it could be assumed that the central bank might choose a monetary
policy that mitigates economic fluctuations arising from capital requirements.
The reason is that the objective of prudential supervision might be in conflict
with the goal of maintaining high and stable growth. For instance, Cecchetti
and Li (2008) have shown (in their specific framework) that it is possible to
derive an optimal monetary policy that reinforces prudential capital require
ments and at the same time stabilizes aggregate economic activity. Further
research, however, is needed to determine the optimal monetary policy in the
Basel II framework.
Third, by adding an objective of financial stability in the central bank's
loss function (or by adding explicitly a regulator with the same objective),
the model could be used to examine several recent policy proposals aimed at
strengthening the financial system and at encouraging more prudent lending
behavior in upturns. Indeed, several observers have argued that by raising
capital requirements in a countercyclical way, regulators could help to choke
off asset price bubblessuch as the one that developed in the US housing
marketbefore the party really got out of hand. Countercyclical bank pro
visions have already been used for some time in countries such as Spain and
Portugal. The Spanish system, for instance, requires higher provisions when
credit grows more than the historical average, thus linking provisioning to
the credit and business cycle. This discourages (although it does not elim
inate) excessive lending in booms while strengthening banks for bad times.
A more recent proposal has been put forward by Goodhart and Persaud
(2008) and involves essentially adjusting the Basel II capital requirements
to take into account the relevant point in the economic cycle. In partic
ular, in the GoodhartPersaud proposal, the capital adequacy requirement
on mortgage lending would be linked to the rise in both mortgage lending
31
and house prices.27 However, there are several potential problems with this
type of rules. For instance, the introduction of countercyclical provisions
in Spain was facilitated by the fact that the design of accounting rules falls
under the authority of the Central Bank of Spain. But accounting rules in
many other countries do not readily accept the concept of expected losses,
on which the Spanish system is based, preferring instead to focus on ac
tual lossesinformation that is more relevant for shortterm investors. This
raises therefore the question of redesigning accounting principles in ways that
balance the shortterm needs of investors with those of individualbank and
systemic bankingsector stability.
From the perspective of the appropriate design of countercyclical bank
capital requirements rules, however, a pressing task in our view is to eval
uate carefully their welfare implications. Zhu (2008) is one of the few con
tributions that focuses on this issue, but he does so in a setting that is
more appropriate for industrial economies. In the context of middleincome
countries, where credit (as is the case here) plays a critical role in financ
ing shortterm economic activity, an acrosstheboard rule could entail some
serious welfare costs. At the same time, of course, to the extent that they
succeed in reducing financial volatility, and the risk of fullblown crises, they
may also enhance welfare. A key issue therefore is to determine the net ben
efits of countercyclical bank capital rules. Our belief is that this issue can
be fruitfully addressed by extending the existing model to account explicitly
for systemic financial stability.
27
Goodhart and Persaud argue that their proposal could be introduced under the so
called "Second Pillar" of Basel 2. Unlike Pillar I, which consists of rules for requiring
minimum capital against credit, operational and market risks, Pillar II is supposed to take
into account all the additional risks to which a bank is exposed to arrive at its actual
capital needs.
32
Appendix A
SteadyState Solution
Given the parameter values, the steadystate values of all endogenous
variables (denoted by tildes) are calculated by dropping all time subscripts
from the relevant equations. Endogenous variables would converge to these
values if the system is not disturbed by shocks.
~
From (47), with ln = 0,
~ = + + 1 (~  )
~ ~ (A1)
We require inflation to be equal to its target value in the steady state:
=
~ (A2)
Substituting this result in (A1) yields therefore the steadystate value of
the refinance rate:
~ = +
~ ~ (A3)
We will focus in what follows on the case where = 0, so that = 0.
~
The steadystate value of the bond rate is determined by setting = +1
and = 0 in (6),
~
~ = = ~ = 1  1
~ (A4)
In the steady state, with +1 = , capital adjustment costs are zero:
~
~
(  1)2 = 0 (A5)
2 ~
Substituting this result in (5) yields
~
= ~ (A6)
Substituting (A5) in (10) gives
1 + (~ + 1  ) = 0
which implies that the steadystate value of the rate of return to physical
capital is
1
=  (1  )
~ (A7)
33
which is also equal to ~ if = 0, as implied by (A3).
~
From (39), the steadystate value of the desired (and actual) deposit rate
is
1 1
~ = (1 +
) (1  )(1 + ~ )  1
(A8)
~
Setting 1 = in (41), the steadystate value of the repayment proba
bility is
~~
1 2 ~~
= 0 (
~ ) ( ) (A9)
~ ~
Using (40) and (A4), the steadystate lending rate is given by
1 © £ ¤ª
1 + ~ =
(1  ) 1 + (1 + ~ ) +
(A10)
(1 + 1 )~
which is the same for Basel I and Basel II, given the assumption that is
~
also equal to unity under Basel I.
From (8), (9), and (14), the household's demand for real cash balances,
bank deposits, and equity are
~
1 (1 + ~ )
=
~ (A11)
~
~
(1  ) 1 (1 + ~ )
~
= (A12)
~  ~
~ 1 ~  ~
= ( ) (A13)
1 + ~
or equivalently, using (A3), (A4), (A7), and (A8) with = 0,
~
~
1
=
~ (A14)
1
~ 1
~ (1  )
= (A15)
(1  )
~ 1 1 + ~
= (
 1) = (~  1 + 1)
(A16)
1 + ~
~
The last equation can be solved for ~ , with given. The solution is
~
~ =
+ 1  1 (A17)
34
~
which implies, given that 0, that ~ ~ , as discussed in the text.
From (7), the steadystate value of labor supply is
~
1
~
=1 (A18)
~
From (18), steadystate output of intermediate goods is given by
~ ~ ~
= 1 (A19)
The marginal productivity conditions yield
~ 1 1 ~ ~
= ( )1 (
~ ) ~
=( )
~ ~
(1 + ~ )
These equations can be combined to give the capitallabor ratio, whose
steadystate value is
~ (1 + ~ )~
=( )[ ]
~ 1 ~
Substituting (A4) and (A7) in this expression, and solving for with
~
= 0 yields the steadystate real wage as
~
µ ¶ ~
1  ( 1  1 + )
=
~ (A20)
~
(1 + ~ )
The steadystate level of borrowing from the bank is thus
~ ~~ ~
= (A21)
From (21), and with = 0 (so that = 1), price adjustment costs are
~ ~
zero in the steady state ( = 0). From the price adjustment equation
(24),
~ ~
~ ~
~ ~
f
(1  ) +  (  1)( ) + (  1)( )( ) = 0
~ ~
~ ~
~ ~
which can be solved for the steadystate value of the marginal cost:
1
f
= (A22)
35
From (42) and (43), and using (A4), the steadystate values of the bank's
demand for bonds and supply of equity are
~ ~
= 1 (~  ~ ) = 0
(A23)
½ ¾2
~
= 1 (A24)
 1  (~ + )
where, from (30) and (31), assuming that under Basel I the constant risk
weight is also equal to unity,
~
~
= ~ ( )
= 1
~ (A25)
~
From (A24) and(A25), total capital can be calculated as
~ ~
= + ~ (A26)
From (29) and (A23), the steadystate level of the bank's borrowing from
the Central bank is
~ ~
=  (1  )  ~~ ~ ~ (A27)
The equilibrium condition of the goods market, equation (51) yields the
~ ~ ~ ~
steadystate condition = + + , which can be rearranged, using (A6)
and (49), to give
~
(1  ) = + ~ ~ (A28)
From (55) and (A23), the equilibrium condition of the market for cash
yields
¯ 1
~
= 1 (1 + ~ )( +
)
~ ~ ~  ~
which can rearranged as, using (A3), (A4), (A7), and (A8), and with = 0,
~
¯ 1~ 1
= ( + ) (A29)
~ 1
~
This equation can be solved for . Given that the overall stock of bonds
¯ ~
is also constant, and that = 0, household holdings of government
bonds are given by
¯
=  ¯ ¯ (A30)
From (48) and (49), the steadystate value of lumpsum tax to households
is thus
~ ~ ¯
= + ~  ~ ~ (A31)
36
Appendix B
LogLinearized System
Based on the results of Appendix A, the loglinearized equations of the
model are presented below. Variables with a hat denote percentage point
deviations of the related variables for interest rates and inflation, and log
deviations for the others, from steadystate levels.28
From the firstorder conditions from household optimization, equations
(6) and (8), private consumption is driven by
^ ^
+1 = + (^  +1 )
(B1)
where +1 is defined as, given that = 0,
~
^ ^
+1 = +1  (B2)
From (8) the demand for cash is
~
()1 ^
=
^ ~ [ ( )^ ]
(B3)
1 1
By using the steadystate value of cash balances from (A14), equation
(B3) can be written as
^
=
^ ( )^
(B4)
1
From (9) and (A15), the demand for deposits is
^
£ 1 ¤ ¡ ¢
^
= +  ( 1  1) ^  1  1 ^
(B5)
From (14) and (A16), the demand for equity is
¡ ¢
^
= (1  )1 ^  ^
(B6)
~
which can be used to determine the behavior of ^ .
28
Net interest rates are thus used as approximations of the log gross interest rates.
37
The Fisher equation, defined in (10), yields
^ ^ ^ ^
(1 + ) +1 + ( +2  +1 )  ( +1  ) ^ + +1 = 0 ^
(B7)
which can be used to determine the behavior of .
^
From (7), labor supply is
~
1 ~ ^
1
~^
= 
^
~
~
that is, using (A18),
~
1 ^
^
= ( )(^  )
(B8)
~ ~
 1
From (22), labor demand can be derived as
^ ^ 1 +
=  ^  + (
^
)^ (B9)
1 + 
A loglinear approximation around the steady state of the price adjust
ment equation (24) yields
1
= ( c
) + +1 (B10)
where, using (23),
+ ^
= (1  )(^ + ) + (
c ^ )^ 
(B11)
1 + 
From the production function (18), output of intermediate goods is
^ ^ ^ ^
= + (1  ) + (B12)
From (39) and (A8), the deposit rate is given by
(1  )
^ = ^ (B13)
1  (1  )
From (40), the linearized equation for the lending rate under Basel I is
½ ¾
1 (1  ) (1  )
^ =
^ + (1 + ~ )^  [
+ (1 + ~ ) + ]^
(1 + ~ )~
(B14)
38
whereas under Basel II it is given by
½
1 (1  ) (1  )
^ =
)~
^ + (1 + ~ )^  [
+ (1 + ~ ) + ]^
(1 + ~
¾ (B15)
1
+ [(1 + ~ ) +  ]^
Thus, (B14) corresponds to (B15) with = 0.
^
From (41), the linearized equation for the probability of repayment is
^ ^ ~ ^
= 1 ( +  ) + 2 + 3
^ ^ (B16)
where the term 2 on the righthand side of this expression drops out for
^
Basel I.
From (47), the central bank policy rate is determined by
^
^ = ^ + 1 + 2
1 ^ (B17)
Firms' demand for credit is, from (20),
^ ^ ^
= + + .
^ (B18)
From (42) and (43), the bank's demand for bonds and supply of capital
are given by
^ ^ (1 + ~ )^  (1 + ~ )^
= +  ~
(B19)
~
1
^ = 2 ^  (1 + ~ )^
(B20)
1 + ~ +  1
whereas, from (30)
^ ^ ^
=  (Basel I) (B21)
^ ^ ^ ^
=  + (Basel II) (B22)
For the risk weight under Basel II, linearization of (31) yields
= 
^ ^ (B23)
Equation (B20), and either (B21) or (B22), can be used to calculate ^
as
~
^ ~
^
^
= ( ) + ( )
~ ~
39
which can then be substituted in (B6) to determine ^ .
From (29), the bank's borrowing from the central bank is
" #
~
1 ~ ^ (  )
^
= + ~~ ^ ^ ~~
 (1  ) ( + )  ( + ) ^
~
(B24)
The equilibrium condition of the market for cash, equation (55), yields
( ) (
^ (1  ) ^ ^
+ ^ ( )^ +
+ (B25)
1
¸ ¾
1 1 1
+  (  1) ^  (  1)^ = 0
Equation (B25) can be solved for ^ .
The equilibrium condition of the goods market, equation (51), is, using
(49):
~
^ ~ ~
^
^ ^
(1  )( ) = + ( +1  ) + ^ (B26)
~ ~ ~
40
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42
Table 1
Calibrated Parameter Values
Parameter Value Description
Household
095 Discount factor
06 Elasticity of intertemporal substitution
15 Relative preference for leisure
15 Relative preference for money holdings
02 Share parameter in index of money holdings
03 Adjustment cost parameter, equity holdings
86 Adjustment cost parameter, investment
Production
100 Elasticity of demand, intermediate goods
065 Share of labor in output, intermediate good
745 Adjustment cost parameter, prices
006 Depreciation rate of capital
Bank
05 Effective collateralloan ratio
1 005 Elasticity of repayment prob wrt collateral
2 001,02 Elasticity of repayment prob wrt capitalloan ratio
3 02 Elasticity of repayment prob wrt cyclical output
005 Elasticity of the risk weight wrt repayment prob
005 Cost of adjustment, bond holdings
01 Cost of issuing bank capital
0001 Benefit of holding excess bank capital
008 Capital adequacy ratio
Central bank
01 Reserve requirement rate
00 Degree of persistence in interest rate rule
1 15 Response of refinance rate to inflation deviations
2 05 Response of refinance rate to output growth
Shocks
06 002 Persistence/standard dev, productivity shock
06 003 Persistence/standard dev, public spending shock
43
Figure 1
Negative Productivity Shock
Basel II more Procyclical than Basel I
(Deviations from Steady State)
Note: Interest rates, inflation rate and the repayment probability are measured in absolute
deviations, that is, in the relevant graphs, a value of 0.05 for these variables corresponds to a 5 percentage
point deviation in absolute terms.
Figure 1 (Continued)
Negative Productivity Shock
Basel II more Procyclical than Basel I
(Deviations from Steady State)
Figure 2
Negative Productivity Shock
Basel II less Procyclical than Basel I
(Deviations from Steady State)
Note: See note to Figure 1.
Figure 2 (Continued)
Negative Productivity Shock
Basel II less Procyclical than Basel I
(Deviations from Steady State)
Figure 3
Negative Government Spending Shock
Basel II more Procyclical than Basel I
(Deviations from Steady State)
Note: See note to Figure 1.
Figure 3 (Continued)
Negative Government Spending Shock
Basel II more Procyclical than Basel I
(Deviations from Steady State)
Figure 4
Negative Government Spending Shock
Basel II less Procyclical than Basel I
(Deviations from Steady State)
Note: See note to Figure 1.
Figure 4 (Continued)
Negative Government Spending Shock
Basel II less Procyclical than Basel I
(Deviations from Steady State)