Bank Capital Regulation, Lending Channel and

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propagate the business cycles. The model builds on Bernanke, Gertler and Gilchrist (1999), where credit demand friction due to agency cost is considered, but it ...
Bank Capital Regulation, Lending Channel and Business Cycles Longmei Zhang1 Institute for Monetary and Financial Stability Goethe University, Frankfurt

Preliminary Draft May 2009

Abstract This paper develops a dynamic stochastic general equilibrium model to study how the instability of the banking sector can accelerate and propagate the business cycles. The model builds on Bernanke, Gertler and Gilchrist (1999), where credit demand friction due to agency cost is considered, but it deviates from BGG in that financial intermediaries have to share aggregate risk with entrepreneurs, and therefore bear uncertainty in their loan portfolios. After signing a loan contract based on two parties’s expectation of the economic situation in the future, an unexpected negative shock will lead to higher ex-post loan default rates, and the bank’s capital faces larger write-offs because of unexpected loan losses. Given the bank capital regulation established by the Basel Accord (where banks have to hold a minimum capital to asset ratio), banks will face difficulty in the next period to raise capital because households perceive a higher bank default probability i.e., its capital level will fall below the regulatory threshold. Model simulations show that instability in the banking sector alone can create strong credit supply friction, and have a significant effect on accelerating short run cycles. In the long run, instability of the banking sector implies a lower capital stock in the economy and therefore a lower level of investment and output. 1

The author thanks Deutsche Bundesbank for research support,thanks seminar participants at Deutsche Bundesbank and Hong Kong Monetary Autority for discussions, thanks Hans Genberg, Eric Van Wincoop, Haibin Zhu for useful comments. The author is especially grateful to Thomas Laubach, Falko Fecht, Alex Ho, Alexander L. Wolman for detailed suggestions. Contact information: IMFS, Goethe University, Grueneburgplatz 1 (Box H 12), 60629 Frankfurt/Main, Germany, email: [email protected].

Non-Technical Summary Dynamic Stochastic General Equilibrium (DSGE) models have long been criticized for lacking an appropriate way of modeling the financial markets and, as a result, fail to explain important regularities of business cycles. Given the historically repetitive waves of financial crises and the current worldwide deep recession triggered by the U.S. subprime mortgage market and the subsequent banking instability, it has become abundantly clear how relevant financial frictions are in business cycle transmission and amplifications. Among the existing literature that focuses on the role of financial frictions, credit demand frictions are the most extensively studied. Representative work from Bernanke, Gertler and Gilchrist (1999, BGG thereafter) establishes a link between the borrowing cost of firms and their net worth, which can generate counter-cyclical external finance premium and amplify various macro shocks. Yet the financial friction coming from the supply side or the vulnerability of the financial intermediary itself has so far received very little attention and has not yet been incorporated into stylized DSGE models. Recent literatures have tried to link the financial structure of banks to their lending rate to motivate the role of bank capital (e.g Markovic (2006), Aguiar and Drumond (2007) ) or have modeled the function of banks in a detailed manner (Gerali, Neri, Signoretti (2007), Christiano, Motto, and Rostagno (2007)). But they have all refrained from the key issue of endogenously deriving uncertainty in banks’ loan default rates and the related banking instability which will then be passed on to the whole economy through the credit market. This paper sheds new light on how the instability of the banking sector can accelerate and propagate the business cycles in a general equilibrium setting. The model builds on BGG, where credit demand friction due to agency cost is considered, but it deviates from BGG in that financial intermediaries have to share aggregate risk with entrepreneurs, and therefore bear uncertainty in their loan portfolios. After signing a loan contract based on two parties’ expectation of the economic situation in the future, unexpected negative shock will lead to higher ex-post loan default rates, and the bank’s capital faces larger write-offs because of unexpected loan losses. Given the bank capital regulation established by the Basel Accord (where banks have to hold a minimum capital to asset ratio), banks will face difficulties in the next period in raising capital because households perceive a higher bank default probability i.e., its capital level will fall below the regulatory threshold. The higher cost of raising funds for banks will be passed

through to their lending decision, which will cause aggregate investment and output to contract even further. Model simulation shows that instability of the banking sector alone can create strong credit supply friction, and has a significant effect on accelerating short run cycles. Asset prices and investment become much more volatile after the additional bank capital channel is considered. In the long run, instability of the banking sector implies a lower capital stock in the economy and therefore a lower level of investment and output. This paper also compares the relative contribution of various frictions in shock transmission. Three cases are considered: In the first case, only norminal rigidity and capital adjustment cost is considered; In the second case, credit demand friction, or financial accelerator effect is added on top of the existing frictions; In the third case, credit supply friction, or the bank balance sheet channel is incorporated. Model simulations show that bank capital channel is more important than the financial accelerator in amplifying policy shocks. This is consistent with previous foundings in the literature that financial accelerator only has marginal contribution to the monetary policy transmission. However, the relative importance of the two channels is reversed when a positive technology shock hits the economy, where strong corporate balance sheet is playing an important role in driving up asset price and aggregate investment. As the degree of financial frictions is determined to a large extent by the firm’s balance sheet and the bank’s balance sheet, whose performances are very closely related to the movement of asset prices, whether the monetary authority should respond to asset prices in their policy rule becomes an important question. As a scenario analysis, this paper compares the model impulse responses under two alternative policy rules: one responds to lagged inflation only, while the other also 0 leans against the wind 0 . Model simulations show that monetary policy that reacts to asset prices has strong stabilizing effects in the short run. Another highlight of the model is that it can replicate a long-established empirical observation hitherto unexplained in a theoretical model that aggregate lending does not go down immediately following a contractionary monetary policy shock, but increases for 4-6 quarters and then falls. (Christiano, Eichenbaum and Evans (1996)). The mechanism behind this phenomenon is shown to be that firm net worth contracts faster than the asset 2

price in the initial period following a negative policy shock, and that therefore firms have to rely more on external financing. In the following period, however, the speed of adjustment reverses, and shrinking aggregate lending occurs.

3

Contents 1 Introduction 2 Model 2.1 The Financial Contract . 2.2 General Equilibrium . . . 2.2.1 Households . . . . 2.2.2 Entrepreneurs . . . 2.2.3 Capital Producers 2.2.4 Banking Sector . . 2.2.5 Retail Sector . . . 2.2.6 Monetary Policy .

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3 Calibration

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4 Simulation 4.1 Technology shock . . . . . . . . . . . . 4.2 Monetary policy shock . . . . . . . . . 4.3 Model Comparison: Marginal Effect of 4.3.1 Long run effect . . . . . . . . . 4.3.2 Short run effect . . . . . . . . .

14 14 17 19 19 20

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5 Policy Rule Comparison

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6 Conclusion

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1

Introduction

The role of financial friction in business cycle propagation has long been ignored in the literature. The main theoretical justification behind the omission is the Modigliani-Miller proposition that in a frictionless world of full information and complete markets, a firm’s value is independent of its capital structure. A more specific interpretation of the theorem in the credit market would be: on the demand side, the firm’s leverage ratio does not influence its borrowing capacity; on the supply side, bank’s lending decisions are not influenced by their capital ratio. It is clear that the world we are living in is far from perfect, yet it is not clear whether the deviation from the perfect world is big enough to make Modigliani-Miller proposition nontrivial. Earlier work by Bernanke and Gertler ( 1989), Bernanke et al (1999) (BGG there after) starts to look at the role of asymmetric information from credit demand side. Their model established a link between the borrowing cost of firms and their networth. In economic downturn, firm’s leverage ratio increases, which makes them face a higher external finance premium in borrowing because of exacerbation of information asymmetry and thus drives down capital demand. The drop in capital demand reinforces the decline of firm’s net worth and the business cycle is propagated. This mechanism is known as 0 financial accelerator 0 in the literature. Meier and Muller (2006) estimates model with BGG type of financial accelerator by matching impulse response of a monetary policy shock from a vector autoregression, and they find that financial accelerator only has marginal contribution to monetary policy transmission. Therefore they argue that little is lost if DSGE models do not incorporate financial accelerator effects. Christensen and Dib (2008) bring BGG type of DSGE model to the data, and estimate the model with maximum likelihood, they find that the model without a financial accelerator is statistically rejected in favor of a model with it, but they also report that the importance of the financial accelerator for output fluctuation is relatively minor. One possible reason for the under performance of DSGE models with financial accelerator is that they only pay attention to the financial friction from credit demand side, but oversight the frictions coming from the credit supply side. Just as firm leverage ratio is important in deciding its borrow cost, bank’s leverage ratio also determines how costly it is to raise external capital. Given the heavy regulation on banking sector, especially minimum capital ratio at 8 percent required by Basel Accord, when the bank’s capital ratio goes down, households will expect a higher probability of bank being 1

shut down by supervisory agency for not fulfilling the regulatory requirement, therefore demand a higher return for holding the bank equity. Higher cost of fund from the bank’s side will be carried on to a higher loan rate, and drives down aggregate credit. The importance of bank capital position in determining credit supply can not be demonstrated more from the crisis that we are now experiencing. The financial turmoil that began in 2007 in the U.S. subprime market, spreading to broader credit and funding market afterwards, is now developing into a world wide recession. As IMF mentioned in its latest Global Financial Stability Report ( International Monetary Fund, 2008), this financial turmoil has weakened the capital and funding of large systematically important financial institutions, which then needed to raise capital or cut back assets to cope with the strains. Markvoic (2007) extended BGG (1999) to analyse the macroeconomic consequences of changes in the cost of bank capital, and distinguish among three subchannels, namely default risk channel, adjustment cost channel, and capital loss channel. He finds that those channels have relative important propagation effect of business cycles. But the model suffers from many imposed empirical functional form, like bank default propability and the evolution rule of bank share price. Aguiar and Drumond (2007) show that procycliality effect of bank capital is stronger under Basel II compared to Basel I. The propagation mainly come from a counter-cyclical liquidity premium that the bank has to pay on raising equity. But in this model it is assumed that capital requirement is always binding, which means bank capital ratio remains constant cross cycles, which is a nontrivial assumption to make. Meh and Moran (2007) embed Holstrom and Tirole (1997)’s framework within a dynamic general equilibrium model, where no regulatory rule is composed, banks hold capital simply for market reasons. Given the heavy banking regulation today and the importance of banking sector in monetary policy transmission, it is probably more relevant to incorporate the banking regulation into general equilibrium model and study the implication of policy shock or other macro shocks. At the same time, it is important to demonstrate the interaction between the financial friction coming from both credit supply and demand side. Therefore, this model choose BGG (1999) as a starting point. The most important deviation of this model from BGG is to bring uncertainty to the banking sector. In BGG and the previous mentioned two papers which build on BGG, bank can write state-contigent contract to entrepreneurs, which means the contract loan rate will change according to economic situation. By making the entrepreneus take all the aggregate risk, bank always obtain a riskless loan portfolio, and ex-post default rate is exactly equal to ex-ante default 2

rate. It is obvious how far away this assumption is from reality. If banks can always have riskfree loan porfolio,and ex-post default rate never diviate from ex-ante default rate, we won’t have a financial crisis to start with. The innovation of this model is to rewrite the financial contract so that the contractual loan rate is based on the agents’ expectation of economic condition in next period, but once it is signed, the contract loan ate is fixed. In the next period, if an unexpected negative shock hits the economy, there will be more entrepreneurs default than the bank expected, and creats unexpected loss in loan portfolio, this will eat off bank’s capital and push bank into a bad situation in equity market because of higher default probability perceived by the households. The difficulty in raising external capital will make the bank be more stringent in extending credit in the following period, they are only willing to offer credit at a higher rate. On the other hand, after the negative shock hits the economy, net worth of entrepreneurs goes down, leverage ratio goes up, which makes them less attractive in the credit market and have to pay a higher external finance premium. The shift in credit supply from bank’s side and credit demand from entrepreneur’s side will drive down aggregate investment to a even further degree which leads to a deeper recession. The remainder of the paper is as follows. Section 2 presents the model. Section 3 describes the calibration strategy. Section 4 discusses the effect of bank capital channel on long run steady states and short run dynamics. Section 5 compares the model dynamics under two alternative policy rules: one that reacts only to inflation rate, while the other ”leans against the wind”. Section 6 concludes.

2 2.1

Model The Financial Contract

In this section, optimal financial contract is derived in a partial equilibirum setting, taking the price of capital goods, entrepreneur net worth, cost of deposit and bank capital as given. In the next section, these variables will be endogenously determined in the general equilibrium. The contract consists of two parties: an entrepreneur with net worth n, and a bank, which can raise funds from the household either in the form of deposit or equity and may wish to lend to the entrepreneur. Both parties are assumed to be risk-neutral. At the end of period t,a continuum of 3

entrepreneurs (indexed by i ∈ (0, 1)) need to purchases capital for use at i , and the real price t + 1. The quantity of capital purchased is denoted Kt+1 paid per unit of capital in period t is qt . The return of capital is subject to both idiosyncratic risk and aggregate risk. The ex-post gross return to k , where ω is an idiosyncratic shock to entrepreneur entrepreneur i is ωi Rt+1 i k i, and Rt+1 is the ex-post aggregate return to capital. The idiosyncratic shock ωi is i.i.d (across time and entrepreneurs) distributed with lognormal distribution and mean of unit. In order to purchase capital, entrepreneurs use their internal fund (net i worth), and borrow the rest from a bank. Let Nt+1 denotes the net worth of entrepreneur at the end of period of t, then it has to borrow the following amount from the bank: i i Lit+1 = qt Kt+1 − Nt+1

(1)

The bank obtain funds from households either in the form of deposit or equity. Because of regulation rules, the bank is obliged to hold some equity, therefore the opportunity of funds equals to a linear combination of the cost of raising deposit and the cost of raising equity. The exact combination is determined by bank’s capital ratio. Agency problem is introduced into the model by assuming that ωi is private information, costless observed only by entrepreneur i, while bank has to pay a monitoring cost to observe it. 2 This information assymetry creates a moral hazard problem that entrepreneurs may misreport the value of ωi . As Gale and Hellwig (1985) showed, under this enviroment, the optimal contract between lender and borrower is risky debt. i.e. When the idiosycratic shock is above certain threshold, the entrepreneurs pay a L ; On the contrary, if the idiosycratic shock fall below fixed amount Rt+1 the threshold, entrepreneurs will default, the bank monitors the result and obtain the the remaining assets of the entrepreneur. This type of debt structure can motivate the entrepreneurs always to report the true value of L ωi . Let ω denotes the threshold value, and Rt+1 the contractual loan rate, following condition has to hold: k L ω i Rt+1 qt Kt+1 = Rt+1 Lit+1

(2)

The contract can thus be characterized by ω, Lit+1 . Gale and Hellwig (1985) only derived the optimal debt structure subject to idiosycratic shock, 

2



This type of ’costly state verification’ has been used in a number of papers, first analysed by Townsend (1979)

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where banks can perfectly diversify idiosycratic risk and hold a risk-free loan portfolio. But under the presence of aggregate risk, it is not yet clear how the risk should be allocated. BGG (1999) assumes that entrepreneurs will absorb all the aggregate risk, and bank can still have risk-free loan portfolio. The way to realize this type of risk allocation is to enable bank to write statecontingent loan contract. More specifically, ω can be written as a function of aggregate shocks. The implication for this is that loan rate is not fixed in the contract, but changes according to the realization of aggregate shocks. The risk-sharing assumption in BGG has very unrealistic implications, i.e. there’s no uncertainty in bank’s loan portfolio, ex-ante default rate is alway equal to ex-post default. However, in reality, unexpected change in default rate is the major, if not the biggest uncertainty that banks are facing today. Unlike BGG, this model assumes that aggregate risk is shared between banks and entrepreneurs. The financial contract cannot contigent on realized capital return, rather it has to be written based on the two parties’ expectation of capital return in the next period. The implication for this type of risk sharing is that aggregate shock will drive ex-post default rate away from ex-ante rate, and creat unexpected loss or gain to bank’s loan portfolio. k let Et Rt+1 denotes the expected capital return at the end of period t when the financial contract is signed, the expected return to the entrepreneur is given by :

Z ∞ ωa

k k ωEt Rt+1 qt Kt+1 f (ω)dω − (1 − F (ω a ))ω a Et Rt+1 qt Kt+1

(3)

where the first part is the gross return the entrepreneur obtains from capital return, the second part is the loan that it has to pay back. f (ω) and F (ω a ) are respectively the density function and cumulative distribution function of ω (also the probability of default). Note that if the the realization of ωi is below the threshold value ω a , the entrepreneur gets nothing. The bank will monitor the project return and confiscate everything that is left. The entrepreneur maximize its expected return subject to the participation constraint of the bank, which is characterized as following: L (1 − F (ω a ))Rt+1 Lit+1 + (1 − µ)

Z ωa 0

f k ωEt Rt+1 qt Kt+1 f (ω)dω = Rt+1 Lit+1 (4)

Bank’s return from loan portfolio come from two parts, the first part is 5

the loan amount that paid back by the entrepreneurs, the second part is in the default space, aquisition of remained assets of firm after paying off the monitoring cost, which is a linear function of capital return. µ is a parameter that captures the degree of monitoring cost or information asymmetry. If µ is set to zero, there will be no information asymmetry between lenders and borrowers, the firm balance sheet channel won’t exist. By solving the contract we can derive the following credit demand equation: ( See Appendix for details) k Et Rt+1 = S(

i qt Kt+1 )Rtf i Nt+1

(5)

S 0  0, Where S denotes the external finance premium, which captures the wedge ( driven by the exsitence of monitoring cost) between the cost of finance from firm’s side and the cost of funds from the bank’s side. Note that there exists a one-to-one relationship between leverage ratio and default threshold or default probability. The more heavily is the firm leveraged, the higher is default probability, agency cost goes up, bank thus charge a higher external finance premium to compensate for it. After solving for the default threshold in the optimal contract, contractual loan rate could be solved as. L Rt+1 =

k q K ω a Rt+1 t t+1 Lit+1

(6)

Notice that in this model, the contract loan rate is fixed, the default rate could deviate from expected value,whereas in BGG the loan rate is state-contigent, but the default rate remains constant regardless what shocks hit the economy after the contract is signed. At the end of period t, entreprenuers sign the contract with bank, in which a fixed loan amount and a fixed loan rate are provided. In the next session, we will endogenize all the variables that we treat exogenous in solving the optimal contract.

2.2 2.2.1

General Equilibrium Households

There is a continuum of households in the economy, each indexed by i ∈ (0, 1). They consume the final good, ct , invest in safe bank deposits, dt , bank equity, et , supply labor lt and own shares of a monopolistic competitive sector that produces differentiated varieties of goods. The households 6

maximize follwing utility function: d1+ϕ max Et β [ln(ct+k ) + t+k + ρ ln(1 − ht+k )] 1+ϕ k=0 ∞ X

k

(7)

subject to the sequence of budget constraint: dt+1 + et+1 + ct = wt lt + Rtd dt + Rte (1 − pdt )et + Πt

(8)

d e dt+1 and et+1 are deposit and bank equity in real terms. Rt+1 and Rt+1 reflect the gross real return of holding deposit and bank equity, and pdt+1 is the default rate of bank capital. lt is household labor supply, wt is real wage for household labor, Πt is dividends received from ownership of retail firms. Following Van den Heuvel (2007), the liquidity services of bank deposits are modeled by assuming that the household has a derived unitility function that is increasing in the amount of deposits. The optimization problem of the households yields following first-order conditions: e Uc (ct , dt ) = βEt Rt+1 (1 − pdt+1 )Uc (ct+1 , dt+1 )

(9)

d Uc (ct , dt ) − Ud (ct , dt ) = βEt Rt+1 Uc (ct+1 , dt+1 )

(10)

−Uc /Uh = wt

(11)

Equation (9) shows that the intertemporal consumption decision of households are determined by the default adjusted return on holding bank equity. Equ ation (10) implies that the wedge between bank equity return and deposit return are composed of two parts. One is liquidity premium, as captured in Ud (ct , dt )/Uc (ct , dt ). Since deposit can provide households extra utiliy besides carrying on monetary reward, bank equity has to provide a higher return to compete against deposit for households’s willingness to hold. The second part comes from the default risk of bank capital. Whenever the capital ratio fall below the regulatory threshold, bank will be shut down and default on capital return. Since bank default is a steady state phenomenon, bank equity has to provide higher return over deposit to compensate for default risk. 2.2.2

Entrepreneurs

After signing the financial contract, entrepreneurs combine loans acquired from the bank and its own net worth to purchase capital. They use capital and labor produce wholesale goods and sell it on a perfect competitive 7

market for a price that equal to its norminal marginal cost. The aggregate production function is given by the following: Yt = At Ktαk hαt h (lte )αe (ltb )αb

(12)

Following BGG (1999), it is assumed that in addition to operating firms, entrepreneurs also supply labor service in the general labor market. The same is assumed for the bankers. As will be see later, αe and αb are calibrate so that these two additional labor force has neglibile effect on output level and model dynamics. The salary that bankers earn from labor supply could be understood as fee income from transaction service, a funtion of financial intermediaries that is not modelled in the paper. The optimization problem of production remains standard: Yt Kt

(13)

wth = αh mct

Yt ht

(14)

wte = αe mct

Yt lte

(15)

wtb = αh mct

Yt ltb

(16)

zt = αk mct

where zt is the real rental rate of capital,wth ,wte and wtb are respectively the real wage of households, entrepreneurs and bankers. mct denotes real marginal cost. The expected capital return is then: k Et Rt+1



= Et

zt+1 + (1 − δ)qt+1 qt



(17)

The accumulation of entrepreneurs’ net worth come from two parts, one is the operation of the firms, the other is labor income. It is assumed that in every period, entrepreneur will die with the probability 1 − γ. This assumption is to make sure that entrepreneurs can never accumulate enough net worth to finance a project without external financing. Those entrepreneurs who die at time t will consume (1 − γ)Vt . The evolution of aggregate net worth is therefore given by the following: Nt+1 = γVt + wte 8

(18)

where Vt represents net return of operating business. It is the difference between gross capital return and loan payment. Z ∞

Vt =

ωb

k L ωRt+1 qt Kt+1 f (ω)dω − (1 − F (ω b ))Rt+1 Lit+1

(19)

ω b denotes the ex-post default threshold, which could be derived by following condition: k ω a Et Rt+1 ωb = (20) k Rt+1 From the expression, we can easily see that if ex-post capital return is higher than previous expectation, loan default rate is also lower than expected. Since in the default space, entrepreneur does not get anything, therefore, when more entreprenuers move to the non-default space, aggregate net worth will go up. 2.2.3

Capital Producers

Capital producers purchase a fraction of final goods from the retailer as investment goods it , and combine this with existing capital stock to create new capital stock. A quadratic capital adjustment cost is included to motivate a variable price of capital, which contributes to the volatility of net worth of entrepreneurs. Capital producers will choose the quantity of investment goods to maximize profit subject to adjustment cost: "

max Et

χ qt it − it − 2



it −δ kt

#

2

kt

(21)

where qt is the real price of capital. The optimization problem yields the following capital supply curve: qt = 1 + χ(

it − δ) kt

(22)

χ is a parameter that captures the degree of capital adjustment cost. The higher is χ, the more volatile is capital price. If χ is set to zero, capital price will be constant at 1. The aggregate capital stock evolves according to: kt+1 = it + (1 − δ)kt where δ is the depreciation rate.

9

(23)

2.2.4

Banking Sector

Bank’s equity value are accumulated through retained earnings, as shown in the following equation: L et+1 = (1 − pdt )et + Rt+1 Lit+1 (F (ω a ) − F (ω b ))

+(1 − µ)

Z ωb 0

−(1 − µ)

Z ωa 0

k ωRt+1 qt Kt+1 f (ω)dω

k ωEt Rt+1 qt Kt+1 f (ω)dω + wte

where pdt is the bank default rate, which will be explained in the bank regulation section. Aggregate bank equity at time t+1 come from three parts: remained equity from those banks who didn’t default at time t, unexpected gain or loss in loan portfolio, and transaction fees collected from the aggregate production function. Given the amount of loan portfolio on bank’s balance sheet Lt derived from the optimal debt contract, and the amount of bank equity, we can caculate the aggregate bank capital ratio: ∆t =

et Lt

(24)

The rest of bank fund dt = Lt − et

(25)

will be collected from the households’ in the form of deposit. Therefore, from a aggregate level, the opportunity cost of bank fund is a linear combination of cost of bank equity and cost deposit, where the proportion of each fund vary according to the bank capital ratio. f e d Rt+1 = ∆t Rt+1 + (1 − ∆t )Rt+1

(26)

d e The respective cost of deposit Rt+1 and equity Rt+1 are derived endogenously from households’ optimization problem.

Bank regulation In modern banking regulation, capital requirement has become the focal point. Given the implict or explicit government gurantee on bank deposit, and a 0 lender-of-last-resort 0 facility, bank capital regulation is imposed to restrict banks from excessive risk-taking. In 1987, Bank

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for International Settlement (BIS) established Basel I Accord, which provides a uniform capital standard for all banks in the 12 member countries. In Basel I, it was required that bank’s capital to risk-weighted assets ratio reaches a minimum of 8 percent, with at least 50 percent of Tier-1 capital. By 1993, nearly all of the world’s big banks had satisfied the Basel capital requirement. Many of them have been increasing their capital ratio. Figure 1 presents a histogram of the risk-based total capital ratios of U.S. commercial banks in the fourth quarter of the year 2000. As we can see from the figure, capital ratios vary cross banks, with most of them lie between the ratio of 10 and 11 percent, and very few lie below.

Figure 1: Distribution of Bank Capital Ratio of U.S. Banks in 2000:4

Source: Federal Reserve Bank of Chicago Motivated by this empirical observation, the capital ratio cross banks in the model is assumed to have lognormal distribution. The mode of the distribution is given by the aggregate capital ratio derived above. ∆i,t lognormal (∆t , σ). The health condition of the whole banking sector will depend largely on the variation of aggregate capital ratio. With a higher aggregate ratio, the distribution move rightward, and fewer banks will fall short of the 8 percent threshold and default, and vice versa. The default probability is given by the cumulative distribution function up to the regulatory threshold: pdt = cdf (∆t , σ) 11

(27)

The higher the default probability, the higher the cost for banks to raise equity. Therefore, low capital ratio today will lead to higher equity cost in the next period. This increase funding cost will decrease credit supply, and decrease aggregate investment. 2.2.5

Retail Sector

The retail sector is introduced into the model to motivate sticky prices.As is standard in literature. monopolistic competition and calvo pricing are assumed in this sector. Retailers purchase the wholesale good from entrepreneurs at a price equal to its norminal marginal cost, and differentiate them at no cost. They then sell these differentiated retail goods in a monopolistically competitive market. Let Yt (i) be the quantity of output sold be retailer i, measured in units of wholesale goods, and let Pt (i) be the norminal price. Total final usable goods, Yt are the following composite of retail goods: Z 1

Yt =

Yt (i)

(−1)/

/(−1)

di

(28)

0

with  ≥ 1 and represents the degree of monopolistic competition. The corresponding orice index is given by Z 1

Pt =

1/(1−)

Pt (i)(1−) di

(29)

0

Following Calvo (1983), in a given period, the retailer receive the signal to adjust price with probability 1 − θ, otherwise the retailer has to carry on the previous price. Let Pt∗ (i) denote the price set by retailers who are able to change price at t, and Yt∗ (i) the demand given this price. Retailer will thus choose this price to maxmize future expected discounted real profits, given by: max Et

∞ h X

θk Λt,k Ωt+k (i)/Pt+k

i

(30)

k=0

subject to the demand function ∗ Yt+k (i)

=

 ∗ − Pt (i)

Pt+k

Yt+k

(31)

where the discount rate Λt,k = β k Ct /Ct+k (given assumed log utility in consumption) is the household intertemporal marginal rate of substitution,

12

which the retailer takes as given. Ωt+k is norminal profits given by (Pt∗ (i) − ∗ (i). The optimization problem yields the following condition: M Ct+k )Yt+k Pt∗ (i) =

θ Et θ−1

P∞

k=0 θ

Et

∗ t,k M Ct+k (i)Yt+k (i)/Pt+k k k=0 θ Λt,k Yt+k (i)/Pt+k



P∞

(32)

Given that the fraction θ of retailers do not change their price in period t, the aggregate price evolves according to: h

1− Pt = θPt−1 + (1 − θ)(Pt∗ )1−

i

1 1−

(33)

Combining the optimal pricing and the evolution of aggregate price, then loglinearize, we obtain a standard phillips curve,where mc ˆ t represents the real marginal cost gap. βEt πt+1 = πt − (1 − βθ) 2.2.6

1−θ mc ˆ t θ

(34)

Monetary Policy

Following BGG (1999), the model consider a simple rule, according to which the central bank adjusts the current norminal interest rate in response to the lagged inflation rate and the lagged interest rate. n rtn = ρr rt−1 + ρπ πt−1 + t

3

(35)

Calibration

In the household utility function, ρ is chosen so that steady state labor is 0.3. ϕ is calibrated so that steady state liquidity premium is 380 bp on an annual base. β is calibrate at 0.988. In the aggregate production function, capital share is 0.33, the share of household labor is 0.66, the share of entreprneur labor is 0.00956 and the share of banking labor is 0.00044. Capital depreciate at 2.5 percent quarterly. In the retail sector, the degree of mopolistic competition  is calibrated at 6, which implies a steady state mark-up of 20 percent. The calvo probability that a firm does not change price in a given period θ is calibrate at 0.75, which implies on average prices are adjusted every four quarters in the economy. In monetary policy, the autoregressive coefficient is set to 0.65 and the coefficient of lagged inflation 1.2. These calibrations are standard in the literature.

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In the financial contract, monitoring cost parameter µ is set to 0.12, following (BGG 1999). The probability that entrepreneurs die in a given period 1 − γ is set to 0.019. The variance of idiosyncratic productivity is set to 0.265. These parametrization leads to following steady state values: capital to net worth ratio equals to 2 ( leverage ratio of 0.5), annual loan default rate of 2.56 percent, annual external finance premium of 180 bp. In the distribution of bank capital ratio, steady state ratio is calibrate at 10 percent, the variance of the distribution is set to match a steady state bank default rate of 1 percent. Aggregate productivity shock follow AR (1) process as usual, with coefficient of 0.9, standard deviation of 0.0056. Another parameter important for the model dynamics is the capital adjustment parameter χ. Chirinko (1993)’ estimates based on aggregate data shows a value of 2, which was used then used in King and Wolman (1996). Therefore, in this model, χ is calibrated at 2.

4

Simulation

In the simulation, two shocks are considered: technology shock and monetary policy shock. first, the impulse response to shocks are analysed; then the model is compared to a baseline model where the only financial friction comes from the credit supply side. The marginal contributions of bank capital channel on long-run steady state and short-run dynamics are studied.

4.1

Technology shock

After a positive technology shock, realized capital return is higher than expected, this means ex-post loan default rate is lower than ex-ante, the unexpected gain from loan portfolio will strengthen bank’s capital and increase bank’s capital ratio. Given the improvement in bank’s balance sheet, households expecte a lower bank default rate in the next period, therefore is willing to hold bank capital with a lower return. The reduction of cost of funds from the bank’s side will push up credit supply and drive up investment in equilibirum. On the other hand, after a positive technology shock, firm’s net worth increases, leverage ratio goes down, this makes them facing less agency cost in the credit market, and can obtain loan by paying less external finance premium. The positive reaction both from credit supply and credit demand side drive up aggregate lending to a large extent, which implies a investment boom. This leads to higher output, consumption, and

14

asset prices. The marginal cost of production falls after productivity increases, therefore inflation goes down.

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Figure 2: Impulse responses to productivity shock Output

−3

x 10

Investment

−3

x 10

8

7 6

6

5 4

4

3 2

2

1 0

5

15

0

20

Inflation

−4

0

10

x 10

5

10

15

20

Consumption

−3

x 10 8

−1 −2

6

−3 −4

4

−5 2

−6 −7 5

10

15

0

20

Asset Price

5

15

20

Risk Premium

−4

0

0.015

10

x 10

−1 0.01

−2 −3

0.005 −4 −5 0

5

10

15

20

5

Leverage Ratio

10

15

20

15

20

Net worth

0 −0.002

0.025

−0.004

0.02

−0.006

0.015

−0.008 0.01

−0.01

0.005

−0.012 5

10

15

0

20

16

5

10

−3

x 10

Aggregate Lending

Bank Capital

−3

x 10 2

1.5 1.5 1

1

0.5

0.5

0

5 −3

0

x 10

10

15

0

20

Bank Default Rate

5 −3

x 10

10

15

20

Cost of Bank Capital

0 −0.5 −1 −1

−2

−1.5 5

10

15

20

5

Expected Loan Default Rate 0

0

−0.005

−0.005

−0.01

−0.01

5

4.2

10

15

10

15

20

Realized Loan Default Rate

20

5

10

15

20

Monetary policy shock

After a monetary policy tightening,the cost of deposit becomes higher, bank credit supply does down, ex-post loan default rate goes up. The unexpected loss in loan portfolio will write off bank’s capital, and decrease bank capital ratio. The deteriation in bank’s balance sheet will therefore make households to require higher return to hold bank capital in the next period. The difficulty in raising capital will further depress bank’s credit supply and propaganda the monetary policy shock. On the other hand, the net worth of entrepreneurs goes below the equibilrium level, leverage ratio goes up. This makes them look less attractive in the credit market and have to pay a higher external finance premium. Notice that despite the contraction in both credit supply and credit demand, the aggregate lending goes up for about quarters and then does down. This kind of loan behavior has been well documented in empirical studies. Christiano, Eichenbaum and Evans (1996) shows that ’Following a contractionary monetary shock, net funds raised by the business sector increase for roughly a year, after which it falls.’ The reason for the temporary increase in loan amount is that: After a monetary policy tightening, networth goes down, and capital and asset price also goes down. The adjustment speed of capital is small, therefore the change of aggregate lending depends on the adjustment speed of net worth and asset

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price. Since at the beginning, net worth decrease much faster than the asset price, so the firm has to borrow more external funds in financing the reduced amount of investment. The rest of dynamics are standard, after increase in interest rate, inflation goes down, consumption goes down. Contraction in both output and consumption drives down output level. Figure 3: Impulse responses to monetary policy shock Output

Investment

0

0

−0.02

−0.02

−0.04

−0.04 −0.06

−0.06

−0.08

−0.08

−0.1 −0.1 −0.12 −0.12

−0.14 5

10

15

20

5

Inflation

10

15

20

Consumption

0

0 −0.02

−0.02

−0.04 −0.04

−0.06 −0.08

−0.06

−0.1 −0.08 −0.12 5

10

15

20

5

Asset Price

15

20

Risk Premium

−3

x 10

0

10

10

−0.05

8

−0.1

6

−0.15

4

−0.2

2

−0.25 5

10

15

0

20

5

Leverage Ratio

10

15

20

15

20

Net worth 0

0.25

−0.1

0.2

−0.2

0.15

−0.3

0.1

−0.4

0.05

−0.5

0

5

10

15

20

5

18

10

Aggregate Lending

Bank Capital 0

0.01

−0.01 0

−0.02

−0.01

−0.03

−0.02

−0.04 5

10

15

20

5

Bank Default Rate

10

15

20

Cost of Bank Capital 0

0.1

−0.2 −0.4

0.05

−0.6 −0.8

0

5

10

15

20

5

Expected Loan Default Rate 0.2

0.1

0.1

4.3

5

10

15

15

20

Realized Loan Default Rate

0.2

0

10

0

20

5

10

15

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Model Comparison: Marginal Effect of Banking Instability

Next, we consider this model with a baseline model where only the BGG type of financial friction exists. The results show that additional instability of banking sector will decrease aggregate capital stock and investment level, and have accerleration effect on the short-run dynamics of the models. 4.3.1

Long run effect

In this model, bank default is a equilibirum phenomenon. That is, the proportion of banks whose capital ratio falls below 8 percent, will be shut down by regulatory agency. If we consider a model where there’s no regulatory requirement, which means capital ratio remains changable, yet bank does not default. From the following table, we can see that the default probability of banks leads to lower output level in the steady state. The reason is that given the default possiblity of bank capital, households will require a higher return to hold bank capital, the increase in cost of fund will drives down bank credit supply and therefore investment in the equilibirum.

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Table 1: Steady states comparison Variable Zhang BGG Capital 7.1621 7.4116 Investment 0.17905 0.1853 Output 0.86509 0.875 Consumption 0.68604 0.68964

4.3.2

Short run effect

Figure 4 and Figure 5 compare the relative importance of various frictions in shock transmission. The green line describes impulse responses in a standard DSGE model, where only norminal rigidity and capital adjustment cost is considered. The red line considers an additional friction coming from the credit demand side, or the financial accelerator effect. The blue line captures the model dynamics where bank capital channel is added on top of the previous frictions. As we can see from the graphs, bank capital channel has strong acceleration effect on both impulse response to technology shock and monetary policy shock. The most significant effect of bank capital is on investment, asset price, and external finance premium. The instability in the banking sector brings extral volatility in these varabiles. The reason that output seems to be not so dramatically influenced is that consumption, which accounts for 80 percent of output in the model calibration, is not strongly subject to the influence of banking instability. Things would be very different if we consider that households also have to rely on credit to sustain consumption, which is a very relevant case in many countries. As long as households also borrow from banks, banking instability will have a huge effect on the consumption level, and a significant change in output due to bank capital channel along would be expected. Another observation from figure 4 is that bank capital channel is more important than the financial accelerator in amplifying policy shocks. This is consistent with previous foundings in the literature that financial accelerator only has marginal contribution to the monetary policy transmission. However, the relative importance of the two channels is reversed when a positive technology shock hits the economy, where strong corporate balance sheet is playing an important role in driving up asset price and aggregate investment. 20

Figure 4: Impulse responses to monetary policy shock Output

Investment

0

0

−0.02

−0.02

−0.04

−0.04

Asset price 0 −0.05 −0.1

−0.06

−0.06

−0.15

−0.08

−0.08 Zhang BGG No financial friction

−0.1 −0.12 0

10

−0.1

−0.2

−0.12

−0.25

−0.14

20

0

10

Risk Premium

20

0

10

Inflation

20

Consumption

0

0

0.25

−0.02 −0.02 −0.04

0.2

−0.06

−0.04

0.15

−0.08 0.1

−0.06

0.05 0

−0.1 −0.12

−0.08 0

10

20

0

10

20

0

10

20

Figure 5: Impulse responses to productivity shock −3

x 10

Output

−3

x 10

Investment

Asset price 0.015

8

7 6

6

5

0.01

4

4

3 0.005 Zhang BGG No financial friction

2

0

0

10

x 10Risk −3

0

20

2 1 0

Premium

0

10

−4

0

x 10

20

0

Inflation

0

10

20

x 10 Consumption −3

8

−2 −2

−4

6 −6

−4 4

−8 −10

−6

2

−12 −8 0

10

20

0

10

21

20

0

0

10

20

5

Policy Rule Comparison

This part compares the monetary policy rule which only reacts to inflation rate with a policy rule that ’leaning against the wind’. There’s a big debate in the literature whether monetary policy should react to asset price in order to stablize inflation and output. This paper does not aim to derive an optimal monetary policy based on welfare criteria. Rather, it provides insights on how the economy differ under alternative policy rules. Figure 6: Impulse responses to monetary policy shock output

Investment

0

0

−0.02

−0.02

−0.04

−0.04

Asset price 0 −0.05 −0.1

−0.06

−0.06

−0.15

−0.08

−0.08

−0.1

−0.2

−0.1 Benchmark −0.12 −0.12 Monetary Policy reacts to asset price −0.14 0 10 20 0

Risk Premium

−0.25 10

20

Inflation

10

20

Consumption

0

0

0.25 −0.02

−0.02 0.2

−0.04 −0.04

0.15 0.1

−0.06 −0.08

−0.06

−0.1

0.05 0

0

−0.08 −0.12 0

10

20

0

10

20

0

10

20

We can see from the impulse reponse that if monetary policy responds to asset price, then given a negative policy shock, output and investment contracts less than the alternative senario where policy only reacts to inflation rate, also, credit market does not tight as much as the previous case. On the other hand, inflation goes down more and much faster after asset price is controlled. After a positive technology shock, output, investment and consumption are booming and inflation rate is picking up. Especially, asset price experience pronouced increase. Monetary policy that responds to asset price could avoid over-heating of the real economy since dampened asset price increase would lead to less investment and therefore output boom. But on the 22

Figure 7: Impulse responses to productivity shock −3

x 10

Output

−3

x 10

Investment

Asset price 0.015

8

7 6

6

5

0.01

4

4

3 0.005 2

2

Benchmark 1 Monetary Policy reacts to asset price 0 0 0 10 20 0

x 10Risk −3

0

Premium

10

−3

0

x 10

20

0

Inflation

0

10

20

x 10 Consumption −3

8

−2 −1 −4

6 −2

−6

4

−8 −3 −10

2 −4

−12 0

10

20

0

10

20

0

0

10

20

other hand, the monetary authority does face the trade-off that while the real side is stabilizing, the inflation rate contracts stronger after the positive technology shock. Which type of policy rule is welfare improving demands a serious comparison based on welfare criteria. However, from previous comparison we can see that, policy rule reacting to asset price has stronger stabilizing effect both on the norminal side and the real side of the economy after a policy shock. Yet, the same policy rule faces trade-offs in reducing the volatility of real variable and increasing the volatility of inflation rate if a technology shock hits the economy.

6

Conclusion

This paper extends a general equilibrium model with BGG type of financial accelerator to a model in which financial friction coming from both credit supply and credit demand side are considered. Previous literatures (BGG (1999), Carlstrom and Faust (1997)) have emphasized the credit demand friction under information assymetry, where borrowers have to pay an external finance premium to compensate lenders for the monitoring cost, which 23

is spent to identify project return in the loan default case. The economic implication for this agency problem is that the highly leveraged the firm is, the higher external finance premium it has to pay due to the increased agency cost. In economic downturn, shrinked net worth of firms leads to higher borrowing cost in the next period, which drives investment down even further and propagates the business cycle. The biggest drawback in these earlier literature is that the instability of financial interdemediary and related credit supply friction are ignored. In earlier models, bank can diversify idiosyncratic risk. and can avoid aggregate risk by writing state-contigent loan contract, therefore, the financial intermediary is always on a safe position. The economic crisis in 2008 has made us realized how important is instability of banking sector in accelerating business cycles. It is therefore crucial to demonstrate this significant role that financial intermediary plays in models we used to do policy analysis. In the model, banks can still diversify idiosyncratic risk, but they have to share with the borrowers the aggregate risk. The loan contract is written based on two parties’ expectation of economic situation in the next period. When an unexpected negative shock hits the economy, not only is the net worth of firms goes down, but also are banks facing large equity write-offs because of unexpected losses from loan portoflio. Given the bank capital regulation, where banks have to hold a minimum capital to asset ratio, in the next period, banks have to pay higher cost to raise funds from households because of their perceived higher bank default probability. The difficulty for banks to raise funds themselves and the higher agency cost firms have to pay to obtain credit given increased leverag ratio will interact and drive down the economy much deeper. Model simulation has shown that instability of banking sector along creats strong credit supply friction, and has significant effect in accerlerating short run cycles; In the long run, the instability of banking sector implies a lower capital stock in the economy, and therefore a lower level of investment and output. In future research, this model could be extended to consider consumer loan. Since consumption is the major component of output, once the feedback from banking instability to consumption is incorporated, the effect on output will be much significant compared to the case that only industrial loans are made. The model could also be extended to an open economy case, and study how the instability of financial intermediary in one country could influence the real sector in the other economy.

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References Aguiar, A. and Drumond, I.(2007),‘Business cycle and bank capital: monetary policy transmission under the basel accords’, FEP Working Paper Series 242. Bernanke, B., Gertler, M. and Gilchrist, S. (1999), ‘The financial accelerator in a quantitative business cycles frame work’, in Taylor, J and Woodford, M, Handbook of macroeconomis, page 1341-1393. Carlstrom, C.,Fuerst, T.(1997), ‘Agency cost, net worth and business fluctuations: a computable general equilibrium analysis’, American Economic Review 87, 893-910. Christensen, I.,Dib, Ali (2008), ‘The financial accelerator in an estimated New Keynesian model’, Review of Economic Dynamics 11, 155-178. Christiano, L., Eichenbaum, M. and Evans, C.(1996),‘ The effect of monetary policy shocks: evidence from the flow of funds’, Review of Economics and Statistics 78, 16-34. Faia, E.,Monacelli, T.(2007),‘Optimal interest rules,asset prices and credit friction’, Journal of Economic Dynamics and Control. Gale, D.,Hellwig, M.,(1985), ‘Incentive-compatible debt contracts: the oneperiod problem’, Review of Economic Studies 52,647-664. Markovic,B.,(2006),‘Bank capital channels in the monetary transmission mechanism’, Bank of England Working Paper No. 313 Meh, M.,Moran,K.,(2008), ‘The role of Bank Capital in the Propagation of Shocks’, Bank of Canada Working Paper No. 36. Meier, A., Mueller,G.,(2006),‘Fleshing out the monetary transmission mechanism: output composition and the role of financial frictions. Journal of Money, Credit and Banking 38, 1999-2133. Townsend, Robert(1979), ‘Optimal contracts and competitive market with costly state verification’, Journal of Economic Theory 21, 265-293.

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Van den Heuvel (2007), ‘ The bank capital channel of Monetary Policy’. Society for Economic Dynamics Meeting Papers No.512. Van den Heuvel (2002), ‘Does Bank capital matter for monetary transmission’, Economic Policy Review, Federal Reserve Bank of New York, issue May, pages 259-265.

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