Asymmetric Information in Credit Markets and Monetary Policy Ulrike Neyer* Martin-Luther-University Halle-Wittenberg, Germany 1 September 2000

Abstract This paper analyses the consequences of asymmetric information in credit markets. Its particular focus lies on monetary transmission mechanisms and the impact of a monetary impulse on inefficiencies in form of under- and overinvestment caused by the asymmetric information. The main results are: Asymmetric information can amplify, modify or – under extreme circumstances - overcompensate the conventional interest rate channel, in other words there is a credit channel of monetary policy due to asymmetric information in credit markets, but its direction of influence is ambiguous. Furthermore a contractionary monetary impulse aggravates underinvestment whereas the impact on overinvestment is ambiguous.

JEL classification: D 82, E 44, E 51 Key Words: Asymmetric Information, Monetary Policy, Capital Allocation, Credit Channel

* Corresponding author: Martin-Luther-University Halle-Wittenberg, Department of Economics, 06099 Halle/Saale, Germany, Tel.: +49/345/552 33 33, Fax.: +49/345/552 71 90, E-mail: [email protected]

1

Introduction

Asymmetric information in credit markets might play a crucial role for monetary transmission mechanisms and capital allocation. In this context this paper analyses two aspects: 1. Do informational asymmetries on credit markets amplify the effects of the conventional interest rate channel or do they dampen the effects, i. e. into which direction does the so called credit channel of monetary policy operate? 2. Under which conditions do informational asymmetries on credit markets lead to inefficient capital allocations in form of under- and overinvestment and what are the consequences for monetary policy? Monetary Policy Transmission Mechanisms In recent years consequences of asymmetric information in credit markets on monetary policy transmission mechanisms have received a growing attention. The conventional interest rate channel says that - due to sticky prices - a contractionary monetary impulse leads to higher real capital costs in the short run and therefore to decreasing aggregate investment spending. According to the credit channel of monetary policy asymmetric information in credit markets amplify and propagate the conventional interest rate effects. The credit channel theory can be divided into the bank lending channel and the balance sheet channel. According to the bank lending channel, bank dependent borrowers (especially small firms or start ups, which are especially burdened with informational problems and which therefore cannot access the credit market directly) are affected by a declining supply of bank loans, caused by a contractionary monetary impulse, that decreases bank reserves and bank deposits. According to the balance sheet channel a tight monetary policy weakens the borrower´s financial position (reduced cash flow due to higher interest payments on short term liabilities and a reduced net worth due to decreasing asset prices), which raises adverse selection and moral hazard problems on credit markets burdened with informational asymmetries. These problems reduce bank lending and consequently aggregate investment. [Bernanke and Gertler (1995), Mishkin (1995).] Therefore in the credit channel theory asymmetric information on credit markets operate as a financial accelerator. [Compare Bernanke, Gertler and Gilchrist (1996).] Empirical analyses indicate that there might be a credit channel, amplifying the effect of a tight monetary policy in the USA [see for example Kashyap and Stein (1994), Bernanke, Gertler and Gilchrist (1996)]. But most empirical studies analysing the German credit market find little evidence for the existence of a credit channel [see for example Stöß (1996), Guender and Moersch (1997)]. An exception is the study of de Bondt (2000). De Bondt examines among other things the existence of a credit channel of monetary policy in six European countries. His regression results confirm the existence of a credit channel in some countries (for example Germany) but rejects the existence of a credit channel in others, for example in UK.

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This paper focuses on the balance sheet channel of monetary policy, which is built into two different credit markets models. The main result is that asymmetric information in credit markets can amplify, dampen or – in an extreme case – even overcompensate the effect of the conventional interest rate channel of monetary policy.1 Therefore this paper might give a further theoretical explanation why empirical analyses cannot find a credit channel of monetary policy in some countries. Further Capital Allocation Since the seminal paper of Stiglitz and Weiss (1981) a vast literature regarding the consequences of asymmetric information in credit markets has emerged. A major part of this literature shows that informational asymmetries between banks and firms, with the firms having the informational edge, can lead to credit rationing as a consequence of adverse selections, adverse incentives, moral hazard or costly state verification problems. Another part of this literature describes how these informational asymmetries can lead to overinvestment resulting from selection and incentive effects.2 This paper identifies the conditions under which asymmetric information in credit markets lead to underand/or overinvestment, with the underinvestment not going hand in hand with credit rationing, and analyses the consequences of a contractionary monetary impulse on these inefficiencies. The main results are: Depending on the risk-return-combination of investment projects informational asymmetries can lead to selection effects, which result in under- and/or overinvestment. Informational asymmetries are not sufficient for these inefficiencies to occur, but the extent of informational problems must be sufficiently high, the rate of internal finance must be sufficiently low and entrepreneurs must operate near the break even point. A tight monetary policy aggravates underinvestment , whereas the consequences on overinvestment are ambiguous. The rest of this paper is organised as follows: Section 2 presents the underinvestment set up. Firstly the credit market with informational asymmetries and the benchmark case, a credit market not burdened with informational problems, are modelled. Afterwards the outcome of the two markets is compared and finally the implications are discussed. Section 3 describes analogously the overinvestment set up. Section 4 analyses the consequences for monetary policy. The paper ends with a summary and a conclusion.

1

Compare Bacchetta and Caminal (2000), who show that that the output response to shocks is not necessarily amplified but can be dampened by the presence of asymmetric information on credit markets, depending on the kind of shock. 2 Concerning the credit rationing result see Stiglitz and Weiss (1981), Clemenz (1986), Williamson (1986, 1987), for the overinvestment result de Meza and Webb (1987, 1999). For a survey see for example Hillier (1997), chapter 1. In most studies it is assumed that entrepreneurs are better informed than banks. De Meza and Southey (1996) on contrary analyse the consequences of asymmetric information, with the banks having the informational edge.

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2

Underinvestment

2.1

The Credit Market with Asymmetric Information

The credit market burdened with informational asymmetries is modelled similar to the one described by Stiglitz and Weiss (1981). The main differences are: Banks are able to divide the entrepreneurs into risk categories; collateral is considered; the distribution of the probability of success of the projects is specified; and there are constant marginal costs of loanable funds. The latter implies that the credit market equilibrium cannot be characterized by credit rationing,3 and that there cannot be a bank lending channel of monetary policy, so in this paper the focus is on the balance sheet channel. Demand Side There is a continuum of entrepreneurs, of which every single entrepreneur has an initial endowment of liquid assets W (a bar above a variable indicates an exogenous variable) he can either invest in his project or on the capital market. Investing on the capital market the entrepreneur receives a riskfree rate of return ρ . Furthermore each entrepreneur has marketable collateral S as land or buildings for example. His project can either succeed, yielding a return Ris , or fail, yielding no return. Since the investment project is indivisible and requires an investment I , with I > W , the entrepreneur must borrow from a bank to realise his project. The entrepreneurs only differ in the risk of their project, which is expressed by different probabilities of success pi , and the return of their project in case of success Ris . So the index i indicates entrepreneur- respectively project-specific variables and variables without an index are the same for each entrepreneur. The probabilities are distributed uniformly across the entrepreneurs. An entrepreneur realises his project, if the expected profit E ( PE ) i is at least as high as the profit of the alternative investment (equation 1). If the project succeeds, the entrepreneur´s profit is Ris minus principal and interest payments (1 + rk ) ⋅ ( I − W ) and minus the invested wealth. In case of failure the entrepreneur simply loses all his wealth. Therefore equation 2 describes the expected profit of an entrepreneur realising his project. In this equation the asymmetric information in credit markets become already obvious. Banks are unable to distinguish the entrepreneurs with regard to the specific risk of their project. The probability of success pi is private information of the entrepreneurs. One of the often discussed reasons for the existence of banks as intermediaries is their capability to reduce informational asymmetries between deficit and surplus units.4 Here it is assumed that banks know the distribution of pi and that they obtain the necessary information to classify the entrepreneurs into risk categories, relating to the pi of their project. The continuum of 3

In the Stiglitz-Weiss-world a “restriction” on loanable funds is a necessary condition for credit rationing to occur. Stiglitz and Weiss modelled this restriction in form of increasing marginal costs for loanable funds. Another possibility is for example the consideration of capital adequacy requirements for banks [for respective analyses see for example Blum and Hellwig (1994), Brinkmann and Horvitz (1995)]. 4 See for example Leland and Pyle (1977), Diamond (1984), Mayer (1988), Hellwig (1991), von Thadden (1995).

4

entrepreneurs of each risk category is normalized to one. Each entrepreneur within a specific category receives the same interest rate rk , so the index k indicates risk category specific variables. The stronger the informational asymmetries in the credit markets the more heterogenous are the entrepreneurs within a risk category. Therefore the variance σ p2i ,k of the uniformly distributed probabilities of success within a category is a measure for the extent of the informational problems. σ p2i ,k reflects the capability of banks to reduce the informational asymmetries in the credit markets. The mean µ pi , k reflects the average risk over the projects within a category. The expected return R is the same for all projects, but as the projects differ in their probability of success pi and their return in case of success Ris , there exists a mean preserving spread (equation 3).5 Substituting equation 3 into equation 2 reveals that c. p. there is a positive relationship between the entrepreneur´s expected profit and the risk of his project (equation 4). From this follows that a critical value of the probability of success p kcrit exists (equation 5). Only the entrepreneurs having a project which does not exhibit a higher p i than p kcrit want to realise their project. If pi > p kcrit the expected profit is smaller than from the investment on the capital market, so that they prefer the latter. Dividing denominator and numerator by I , equation 5 shows that p kcrit depends on the project´s rate of return q , the rate of internal finance w , the rate of collateral s and the risk free interest rate ρ , which are all exogenous variables, and on the charged interest rate rk , which is an endogenous variable. Since a rising interest rate rk results in higher costs for the entrepreneur, it is obvious that p kcrit decreases if rk increases. Equation 6 maps the density function of the uniformly distributed pi . The most risky project in a risk category has a probability of success pka , the probability of success of the safest project is pkz . Since only those entrepreneurs realise their project whose project has a pi which does not exceed pkcrit , three possible states for the credit demand for D z each risk category K asym , k depending on the interest rate rk can be identified (equation 7). ( rk is the

reservation interest rate of the entrepreneurs with the safest project, rka is the reservation interest rate of the entrepreneurs with the most risky project in a risk category.) If rk ≤ rkz , all entrepreneurs of a risk category will realise their project, i. e. pkcrit ≥ p kz , the credit demand is one. If rka ≥ rk > rkz , the investment on the capital market will be the better alternative for the entrepreneurs having the relatively safe projects, i. e. pka ≤ pkcrit < pkz . The credit demand of the group will be smaller than one but higher than zero. If rk ≥ rka , even the entrepreneurs with the most risky projects will prefer the investment on the capital market, i. e. pkcrit < pka , the credit demand of this risk category is zero.

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E ( PE ) i ≥ W ⋅ ρ

(1)

E ( PE ) i = p i ⋅ ( Ris − (1 + rk ) ⋅ ( I − W ) − W ) + (1 − p i ) ⋅ (−W − S )

(2)

R = p i ⋅ Ris

(3)

This implies that the risk of a project is measured in the sense of Rothschild and Stiglitz (1970).

5

E ( PE ) i = R − p i ⋅ (1 + rk ) ⋅ ( I − W ) − W − S + p i ⋅ S

(4)

R − W ⋅ (1 + ρ ) − S 1 + q − w ⋅ (1 + ρ ) − s = (1 + rk ) ⋅ (1 − w ) − s (1 + rk ) ⋅ ( I − W ) − S

(5)

p kcrit =

 1 = d k if p ka ≤ pi ≤ p kz  g k ( pi ) =  p kz − p ka  0 otherwise 

(6)

This leads to:

µ pi ,k

pkz + pka = 2

D K asym ,k

σ

2 pi ,k

( pkz − pka ) 2 = 12

pkz = µ pi ,k + 3σ p2i k

1 if p kcrit ≥ p kz  p kcrit  = ∫ g k ( p i ) ⋅ dp i =  x, x ∈ ] 0,1 [ if p ka ≤ p kcrit < p kz o  0 if p kcrit < p ka

pka = µ pi ,k − 3σ p2i k

(7)

Credit Supply – Determining the Interest Rate The supply of loanable funds to the banks is absolutely elastic to the risk free interest rate ρ (equation 8). This implies that the quantity of credit supply plays no central role in this model. The crucial fact is the price, the interest rate rk . If a financed project succeeds, the bank will get principal and interest payments. Should a project fail, the bank will receive collateral S , with S < I − W . The resulting expected rate of return (before the costs of loanable funds) of a credit granted to an entrepreneur i is shown in equation 9. Banks do not know the project specific probability of success pi , which corresponds with the project specific probability of repayment. Banks can only assess the average probability of repayment of a risk category, expressed by the expected probability of success E ( p i ) k . Therefore an identical interest rate rk is offered to all entrepreneurs in the same risk category. This interest rate is adequate to the average risk over the financed projects in a category. This identical interest rate implies that there is an interest subsidy of the entrepreneurs with relatively risky projects by those with relatively safe projects. Since the marginal entrepreneurs are those with the relatively safe projects, the marginal entrepreneurs are those who subsidise. This subsidy effect is crucial in this model. Since rk and E ( p i ) k are the same for all entrepreneurs in a risk category, E ( PB) i equals E ( PB) k . Equation 10 shows that the expected probability of repayment E ( p i ) k depends on the offered interest rate rk : If rk ≤ rkz , all entrepreneurs of the category apply for credit, which implies that that E ( p i ) k equals µ pi , k . If rka > rk > rkz , the expected probability of success is smaller than

µ pi ,k , since the entrepreneurs with the relatively safe projects prefer the investment on the capital market. From the banks´ point of view an increasing interest rate between rkz and rka leads to an adverse selection, as more and more entrepreneurs with relatively safe projects prefer the alternative 6

investment. This means that there is a negative relationship between rk and E ( p i ) k . If rk > rka , no entrepreneur asks for a credit i. e. p kcrit < p ka . Equation 10 shows that in this case E ( p i ) k is not defined. It is assumed that the banks suppose that an increase in the interest rate beyond the reservation interest rate of the entrepreneurs with the most risky projects rka will not deteriorate their risk position any more, so that E ( p i ) k equals pka if rk ≥ rka . Considering these aspects a two times kinked function of the expected rate of return depending on the offered interest rate E ( PB) k (rk ) results (equation 11). For rka > rk > rkz an increase of rk has two effects on E ( PB) k : a positive effect due to higher interest revenues and a negative effect due to the higher risk, resulting from the adverse selection, expressed by a decreasing E ( p i ) k .6 Due to the competitive banking industry banks can only yield the normal profit, which means that E ( PB) k equals their costs of loanable funds ρ (equation 12). Solving the equations describing the supply side of the credit market, an absolutely elastic credit supply to the offered interest rate rk results (equations 13 and 14), with rk covering the banks´ costs for loanable funds ρ and a risk premium, expressed by 1 / E ( p i ) k . Furthermore the interest rate will decrease, if the secured part of the loan s /(1 − w ) increases.

η LS , ρ → ∞

(8)

E ( PB) i = (1 + rk ) ⋅ E ( pi ) k + [1 − E ( pi )] ⋅ p kcrit

E ( pi ) k =

∫p

i

⋅ g k ( pi ) ⋅ dpi

0

p kcrit

∫g

k

( pi ) ⋅ dpi

s − 1 = E ( PB) k 1− w

 µ pi , k if p kcrit ≥ p kz  a =  p + p crit (r ) k k k if p ka < p kcrit < p kz  2 

(9)

(10)

0

Assumption: E ( pi ) k = p ka

if pkcrit ≤ pka

s  if p kcrit ≥ p kz (1 + rk ) ⋅ µ pi , k + (1 − µ pi , k ) ⋅ (1 − w ) − 1   p a + p kcrit (rk )  p a + p kcrit (rk )  s ⋅ + 1 − k − 1 if p ka < p kcrit < p kz E ( PB) k (rk ) = (1 + rk ) ⋅ k  2 2   (1 − w )   s (1 + rk ) ⋅ p ka + (1 − p ka ) ⋅ if p ka ≥ p kcrit −1  (1 − w )

(11)

E ( PB) k = ρ

(12)

η K S ,r → ∞

(13)

k

6

k

In the world of Stiglitz and Weiss (1981) this adverse selection leads to an optimal interest rate for the bank, which is a further necessary condition for an equilibrium on the credit market characterised by credit rationing. But in this setting no optimal interest rate in the sense of Stiglitz and Weiss and therefore no credit rationing in the sense of Stiglitz

7

rk =

1 + ρ − [1 − E ( p i )]⋅ E ( pi ) k

s 1− w −1

(14)

Equilibrium Bringing demand and supply side of a credit market together, the equilibrium critical probability of * success pkcrit* , and therefore the equilibrium number of concluded credit contracts K asym ,k and the * equilibrium interest rate rasym ,k can be determined for each risk category (equations 15, 16 and 17).

Equations 15 and 16 reveal that there can be three possible outcomes in each risk category: all entrepreneurs conclude a credit contract ( pkcrit* ≥ pkz , equilibrium Asym I), only a share of the entrepreneurs conclude a credit contract ( pka ≤ pkcrit* < pkz , equilibrium Asym II) or no entrepreneur realises his project ( pka > pkcrit* , equilibrium Asym III). The equations 15 to 17 show that the equilibrium variables depend on the average risk µ pi ,k , the extent of informational problems σ p2i ,k , the expected success of the projects q , the rate of internal finance w , the costs of loanable funds, respectively the opportunity costs of the entrepreneurs ρ and the collateral s .

p

crit * k

( µ pi ,k − 3 ⋅ σ p2i ,k ) ⋅ (1 + q − w ⋅ (1 + ρ ) − s )

=

(15)

(1 + ρ ) ⋅ (2 − w ) − (1 + q ) − s 1 if p kcrit * ≥ p kz  = ∫ g k ( pi ) ⋅ dpi =  x, x ∈ ] 0,1 [ if p ka ≤ p kcrit* < p kz o  if p kcrit* < p ka 0 p kcrit *

* K asym ,k

* rasym ,k =

[

] 1 −s w

1 + ρ − 1 − E ( pi )*k ⋅ E ( pi )*k

µ pi ,k  * with E ( pi ) k =  p a + p crit* k k  2  2.2

Asym I Asym II

(16)

Asym III

−1

(17)

if p kcrit* ≥ p kz if p ka ≤ p kcrit* < p kz

Credit Markets without Informational Problems: The Benchmark Case

On credit markets not burdened with informational problems, banks know the probability of success pi of any project, which means that they can offer each entrepreneur a risk adequate interest rate ri . In order to analyse, which entrepreneurs conclude a credit contract if the credit market is not burdened with informational asymmetries, the reservation interest rates of entrepreneurs and banks

and Weiss exists, since the uniform distribution of the probabilities of success p i implies that between rkz and rka the banks´ expected rate of return E ( PB ) k is a linear function of rk .

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are determined. Considering equations (1) to (4) one gets equation (18) for an entrepreneur´s reservation interest rate. ri ResE =

1 + q − w ⋅ (1 + ρ ) − s s + −1 (1 − w ) ⋅ pi (1 − wk )

(18)

It can be seen that there is a positive relationship between the risk of an entrepreneur´s project (1 − p i ) and the highest interest rate he is willing to pay. By the help of equations 9 and 12, considering that in this situation without informational problems the expected probability of repayment is pi instead of E ( pi ) , the banks´ reservation interest rate can be determined. Equation 19 shows that the banks´ reservation interest rate covers the costs for loanable funds ρ and a risk premium 1 / pi . The interest rate is further negatively influenced by s /(1 − w ) . There is a positive relationship between the banks´ reservation interest rate and the risk of the project. ri ResB =

1 + ρ − (1 − pi ) ⋅ pi

s 1 − w −1 = r * sym ,i

(19)

Only those entrepreneurs, whose reservation interest rate is not smaller than the reservation interest rate of the banks realise their project ( ri ResB ≤ ri ResE ). Therefore all projects are financed, whose expected rate of return is not smaller than the risk free interest rate. This implies that there are two possible outcomes in each “risk category”, if the credit market is not burdened with informational asymmetries (equation 20):7 either all entrepreneurs conclude a credit contract ( ρ ≤ q , equilibrium Sym I) or no credit contract is concluded ( ρ > q , equilibrium Sym II). Due to the competitive banking industry the equilibrium interest rate in Sym I corresponds with the banks´ reservation interest rate (equation 19). 1 if ρ ≤ q Sym I * K sym ,k =  0 if ρ > q Sym II 2.3

(20)

Comparison – Underinvestment Is Possible

In order to identify which of the outcomes Asym I to Asym III is characterised by underinvestment, it is analysed how many projects would have been realised under the same conditions without asymmetric information. Equilibrium Asym II – Underinvestment: In Asym II only a share of the entrepreneurs realises their project, with the marginal entrepreneurs subsidising the entrepreneurs with the relatively risky projects. This means that the marginal entrepreneurs face higher financing costs than on a credit market

7

Since banks know the specific risk of each project, they do not have to form risk categories. But in order to compare the number of concluded credit contracts under both scenarios (with and without asymmetric information) the entrepreneurs are grouped in the same fashion in both scenarios.

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not burdened with informational problems. This implies that they would have realised their project in the benchmark case as well, the corresponding equilibrium must be Sym I. Thus the only reason for not realising a project in Asym II are the additional financing costs due to the informational problems on the credit market. Entrepreneurs are not able to bear these additional costs. Equation (21) describes the extent of this underinvestment. Uk =

pkz

∫g

k

( pi )dpi

(21)

pkcrit *

Figure 1 illustrates the underinvestment problem. The upper part shows the entrepreneurs´ and the banks´ reservation interest rate depending on p i (compare equations 18 and 19).8 The lower part of figure 1 illustrates the density function of the uniformly distributed p i of a risk category. The upper part shows that at any pi the reservation interest rate of the banks is smaller than that of the entrepreneurs, which implies that in the benchmark case all projects are financed (areas 5 and 6). For realising all projects in the situation with informational problems the for all entrepreneurs identical interest rate must not exceed rkcrit . But at this and lower interest rates the banks calculate with a loss, as figure 1 shows: Area 1 illustrates the expected profit above the normal profit at the interest rate rkcrit , the areas 2 and 3 present the expected loss at this rate. Since area 1 is smaller than the sum of the areas 2 and 3, there is an expected loss in total. The equilibrium interest rate must be rk* . At this rate the expected profit above the normal profit (area 4) is as high as the expected loss (area 3). The normal profit condition is fulfilled. But at rk* only the entrepreneurs represented by area 6 realise their project, which means that there is an underinvestment to the extent represented by area 5.

Figure 1: Underinvestment as a Consequence of Asymmetric Information

8

For simplicity reasons a linear relationship between p i and the reservation interest rates is assumed in figure 1. Actually the relationship is hyperbolic as equations 18 and 19 indicate. The linearity can be justified, if only a section, as in the figure, is looked at. Simulations confirm this aspect

10

Equilibrium Asym I - No Underinvestment: In Asym I all entrepreneurs of the risk category conclude a credit contract. That means that the entrepreneurs with the safest projects are willing to bear the additional financing costs resulting from the informational asymmetries. That means that these entrepreneurs would have realised their project as well in the benchmark case, where no subsidy costs occur. Therefore the corresponding equilibrium is Sym I. Equilibrium Asym III – No Underinvestment: In Asym III no entrepreneur of the risk category realises his project. But this does not imply underinvestment. The corresponding equilibrium in the benchmark case is Sym II, in which no entrepreneur realises his project either: The interest rate, which implies that pkcrit* = p ka does not include a subsidy effect any more, since only entrepreneurs with a project having the same risk apply for credit. But this interest rate does not cover the banks´ costs for loanable funds and the necessary risk premium. That means that the banks must charge these entrepreneurs a higher interest rate. Yet, at this higher interest rate these entrepreneurs do not want to invest into their project anymore. That means that in Asym III entrepreneurs do not realise their project because of additional financing costs resulting from the informational problems, but the projects´ expected rate of return does not cover risk adequate financing costs. That means in the benchmark case no project would have been realised either. The corresponding equilibrium must be Sym II. 2.4

Implications

Necessary and Sufficient Conditions for Underinvestment Underinvestment is characterised by the non realisation of efficient projects as a consequence of informational problems. Referring to the equation 20 the necessary condition for underinvestment must be therefore: q≥ρ

(22)

But this condition is not sufficient, since if all projects are financed in the benchmark case, it is still possible that all of them are realised in a situation with asymmetric information as well (Asym I). Therefore the sufficient condition for underinvestment is that the entrepreneurs with the relatively safe projects cannot bear the additional costs resulting from the subsidy effect due to the informational problems. This means that p kcrit* < p kz , which leads to the following sufficient condition for the occurrence of underinvestment: 3 ⋅ σ p2i ,k [(1 + ρ ) ⋅ (1 − w ) − s ] > µ pi ,k ⋅ (q − ρ )

(23)

Magnitude of the Model Variables in Case of Underinvestment Equations 22 and 23 imply: Typically, the expected rate of return q and the capital costs ρ lie in a specific corridor: q is not that low and ρ is not that high that the entrepreneurs would not have realised their project in the reference situation, but they are not that high respectively that low that 11

all entrepreneurs can bear the additional costs. The rate of internal finance w , the rate of collateral s , the average risk µ pi ,k and the extent of the informational problems σ p2i ,k have no effect on a project´s efficiency, and therefore on the necessary condition. But they play a central role for the sufficient condition: The subsidy effect is linked to the external capital. This means that the lower the rate of internal finance and/or the rate of collateral are, the higher is the subsidy effect and therefore the capital costs of the entrepreneurs with the relatively safe projects. The same argument holds analogously for µ pi ,k and σ p2i ,k . The higher the average risk (1 − µ pi ,k ) and the higher the extent of the informational problems the higher is the subsidy effect and therefore the additional costs for the entrepreneurs with the relatively safe projects. This means that in case of underinvestment w and

µ pi ,k are typically low and σ p2i ,k is typically high. External Finance Premium Banks screen potential borrowers to assess the risk of potential loans, i. e. banks reduce asymmetric information in credit markets (compare page 4). This assessment generates costs, which make external capital more expensive than internal funds. But assuming that these costs of intermediation are not influenced by monetary policy, they are not considered in the described credit market models. Therefore these costs are not included in the discussed external finance premium either. The external finance premium considers only the costs due to non reduceable asymmetric information, i. e. the difference between the costs of external finance in the case the credit market is burdened with asymmetric information (section 2.1) and in the benchmark case (section 2.2). Subtracting the * * interest rate rsym ,i (equation 19) from rasym ,k (equation 17) reveals the external finance premium ei

due to non reduceable asymmetric information in credit markets:

[

 S  * 1 + ρ + I − W  ⋅ pi − E ( pi ) k  ei =  E ( pi ) *k ⋅ pi µ pi ,k  * with E ( pi ) k =  a p p crit*  k+ k 2 

and p

crit * k

=

] (24)

if p kcrit* ≥ p kz if p ka ≤ pkcrit* < p kz

( µ pi ,k − 3 ⋅ σ p2i ,k ) ⋅ (1 + q − w ⋅ (1 + ρ ) − s ) (1 + ρ ) ⋅ (2 − w ) − (1 + q ) − s

Equation 24 shows that ei is positive for entrepreneurs (projects) only, possessing a risk smaller than the average risk of all financed projects ( pi > E ( pi )*k ). Entrepreneurs whose project has a higher risk, do actually benefit from the informational problems on the credit market, their external finance premium is negative. This is logical, since the informational asymmetries lead to the de-

12

scribed subsidy effect. Crucial is that the external finance premium is therefore positive for the marginal entrepreneurs. 3 3.1

Overinvestment The Credit Market with Asymmetric Information

The only difference between the overinvestment set up and the one describing a possible underinvestment is the risk-return-combination of the investment projects: In the underinvestment model all projects have the same expected return R but may differ in the probability of success. In the overinvestment set up all projects yield the same return in case of success R s , but may differ in the probability of success. This idea goes back to de Meza and Webb (1987). In what follows the main differences to the de Meza-Webb-Model are: Banks are able to divide the entrepreneurs into risk categories; collateral is considered; the distribution of the probability of success of the projects is specified; and there are constant marginal costs of loanable funds. Since the overinvestment set up differs from the underinvestment set up only in the risk-return-combination of the projects, only those equations which differ from the respective equations of the underinvestment set up are presented in the following formal description of the credit market. Credit Demand In this set up all projects exhibit the same return in case of success R s . Equation 25 shows that therefore due to different probabilities of success there is, on contrary to the underinvestment set up, no mean preserving spread. This implies c. p. a negative relationship between an entrepreneur´s expected profit and the risk of his project (equation 26). This results again in a critical probability of crit success pasym ,k . But on contrary to the underinvestment model an entrepreneur only realises his pro-

ject, if the probability of success of his project is not lower than this critical value. As can be seen crit s from equation 27 pasym ,k depends on the project´s rate of return in case of success q , the rate of

internal finance w , the rate of collateral s and the risk free interest rate ρ , which are all exogenous, and the interest rate rk , which is endogenous. Since an increasing interest rate results in crit higher costs for the entrepreneurs, it is obvious that ∂pasym ,k / ∂rk > 0 . Since only those entrepreneurs crit ask for credit, whose project´s pi is not lower than pasym ,k , there are - analogously to the underin-

vestment model - three possible states of credit demand in each risk category, depending on rk (equation 28). Ri = pi R s

(25)

E ( PE ) i = pi [ R s − (1 + rk ) ⋅ ( I − W ) −W ] + (1 − pi ) ⋅ (−W − S )

(26)

crit p asym ,k =

(1 + ρ ) ⋅ w + s (1 + ρ ) ⋅ W + S = s R − (1 + rk ) ⋅ ( I − W ) + S q − rk + w ⋅ (1 + rk ) + s s

13

(27)

crit a 1 if p asym ,k ≤ p k  crit z = ∫ g k ( pi ) ⋅dpi =  x, x ∈ ] 0,1 [ if p ak < p asym ,k ≤ p k crit pasym  ,k crit z if p asym 0 ,k > pk 1

D K asym ,k

(28)

Credit Supply – Determining the Interest Rate In the overinvestment set up there are the same informational problems as in the underinvestment model, which leads as well to an identical interest rate for all entrepreneurs belonging to the same risk category. This implies again that the entrepreneurs with the relatively safe projects subsidise those with the relatively risky ones. But an important fact is that due to the different modelling of the risk-return-combination of the investment projects, in this set up the entrepreneurs with the relatively risky projects are the marginal entrepreneurs. This means that - on contrary to the underinvestment set up - the marginal entrepreneurs are those who are subsidised. The different modelling of the risk-return-combination of the projects results in a different expression for E ( pi ) k (equation 29). A rising interest rate implies that in the first place those entrepreneurs with the relatively risky projects prefer the alternative investment on the capital market. This implies that as long as the offered interest rate does not exceed the reservation interest rate of those entrepreneurs with the most risky projects rka all entrepreneurs in a risk category ask for a credit, so that E ( pi ) k = µ pi ,k . Further increases of rk imply that more and more entrepreneurs with relatively risky projects do not ask for a credit any more, which means that E ( pi ) k rises as well as long as rk < rkz . This means that E ( pi ) k > µ pi ,k if rka < rk < rkz . For rk ≥ rkz E ( pi ) k is not defined by equation 29. For the sake of simplicity it is assumed that in this case E ( pi ) k = Pkz , which says that banks suppose that an increasing of rk above rkz does not lead to a further improvement of their risk position. As can be seen from equation 30 these aspects result again in a two times kinked function of the banks´ expected rate of return depending on the offered interest rate E ( PB) k (rk ) . For increases of the interest rate between rka and rkz there are two positive effects on the banks´ expected rate of return of their credit business: one positive effect due to higher interest revenues and a second positive effect resulting from the favourable selection of the entrepreneurs. Solving the supply side equations an absolutely elastic credit supply to the offered interest rate rk results, covering the banks´ refinancing costs ρ and a risk premium, expressed by 1 / E ( p i ) k . Collateral influences the offered interest rate negatively (equation 31). 1

∫ p ⋅g i

E ( pi ) k =

k

( pi ) ⋅ dpi

crit pasym ,k

1

∫g

k

( pi ) ⋅ dpi

crit pasym ,k

Assumption:

 µ pi , k  =  crit (r ) + p kz p  asym,k k  2

crit a if pasym ,k ≤ p k

(29) if p < p a k

E ( pi ) k = p kz

crit asym ,k

if p kcrit ≥ p kz

14

p kz

Asym III

−1

(32)

(33)

(34)

if p kcrit* ≤ p ka if p ka < p kcrit * ≤ p kz

The Credit Market without Asymmetric Information

Analogously to the underinvestment model the entrepreneurs´ reservation interest in this set up is: ri ResE =

(1 + q s ) (1 − w )

−

(1 + ρ ) ⋅ w + s s + −1 (1 − w ) pi (1 − w )

(35)

Equation 35 shows that there is a negative relationship between ri ResE and the risk of a project. Since there is positive relationship between the banks´ reservation interest rate (which is the same 15

as in the benchmark case in the underinvestment set up, see equation 19) and the risk of a project, crit * there exists a critical pi : The projects must have at least a probability of success p sym ,k otherwise

ri ResE < ri ResB , and the project is not realised. crit * psym ,k =

1+ ρ 1+ q s

(36)

This means that in the situation without informational problems there can be three possible outcomes for each “risk category”.9 Either all entrepreneur conclude a credit contract (Sym I), a part of the group members receive a loan (Sym II) or no entrepreneur realises his project (Sym III):

* K sym ,k

1  1  = ∫ g k ( pi ) ⋅ dpi =  x, x ∈ ]0,1 [ crit * p sym  ,k 0 

crit * a if p sym ,k ≤ pk

Sym I

crit* z if pka < p sym ,k ≤ p k

Sym II

crit * z if p sym ,k > pk

(37)

Sym III

Due to the competitive banking industry the equilibrium interest rate corresponds with the banks´ reservation interest rate in the equilibria Sym I and Sym II. 3.3

Comparison – Overinvestment Is Possible

In order to identify which of the outcomes Asym I to Asym III is characterised by overinvestment, it is analysed how many credit contracts would have been concluded under the same conditions if the credit market had not been burdened with asymmetric information. If the latter is smaller, the equilibrium will be characterised by overinvestment. Equilibrium Asym II - Overinvestment: The corresponding equilibrium in the benchmark case is SYM II. In both situations only a share of the entrepreneurs of a risk category realise the project. But the number of realised projects in the situation with asymmetric information must be higher crit * crit* ( pasym ,k < p sym ,k ), due to the subsidy effect combined with the competitive banking industry, as fig-

ure 2 illustrates.

9

Compare footnote 7.

16

Figure 2: Overinvestment as a Consequence of Asymmetric Information

The upper part shows the entrepreneurs´ and the banks´ reservation interest rates depending on pi (compare equations 19 and 35).10 The lower part illustrates the density function of the uniformly crit * distributed pi . In the benchmark case all projects, whose probability of success is at least p sym ,k are

financed. The size of the realised projects therefore corresponds with area 5 under the density function. Due to the competitive banking industry the whole surplus (the area between the two “reservation interest rate curves”) accrues to the entrepreneurs. Realising the same projects in the situation with informational asymmetries demands an equilibrium interest rate rk ,1 . But with this interest rate the banks would expect a profit above their normal profit (areas 3 and 4). Therefore the interest rate decreases to rk , 2 , where the expected profit above the normal level (area 4) equals the expected loss (areas 1 and 2). But rk , 2 is that low, that more entrepreneurs than in the situation without informational problems realise their project. The size of this overinvestment corresponds with area 6 under the density function. Therefore Asym II always implies overinvestment. Equation 38 describes this overinvestment formally. crit * p sym ,k

O II , k =

∫g

k

( p i ) ⋅ dp i

(38)

crit * p asym ,k

Equilibrium Asym I – Overinvestment Is Possible: Under Asym I all projects are financed. This situation

10

can

imply

overinvestment.

It

implies

an

inefficient

capital

allocation,

if

For simplicity reasons a linear relationship between p i and the reservation interest rates is assumed in figure 2. Actually the relationship is hyperbolic as equations 19 and 35 indicate. The linearity can be justified, if only a section, as in the figure, is looked at. Simulations confirm this aspect.

17

crit * a crit* pasym ,k ≤ p k < p sym ,k . In this case the corresponding equilibrium in the benchmark case is Sym II, so

that the number of realised projects is higher with informational asymmetries. Equation 39 decrit * a crit * a scribes this overinvestment formally. But if pasym ,k < p k and p sym ,k ≤ p k , the corresponding equilib-

rium is SYM I, which means that in both situations all projects are financed, the informational asymmetries do not lead to overinvestment. crit * p sym ,k

OI ,k =

∫g

k

( p i ) ⋅ dp i

(39)

p ka

Equilibrium Asym III – No Overinvestment: Under Asym III no project is realised. In this case no project would have been financed in the benchmark case either, the corresponding equilibrium is crit * z crit* z Sym III ( pasym ,k > p k and p sym ,k > p k ). The expected profit from the projects is so small, that the

alternative investment on the capital market is more favourable for all entrepreneurs of the group in any case. 3.4

Implications

Necessary and Sufficient Conditions for Overinvestment In this set up overinvestment is characterised by the realisation of inefficient projects. Inefficient projects are financed, because there is an interest subsidy of the marginal entrepreneurs due to asymmetric information. The necessary and the sufficient condition for overinvestment is that in a risk category there are efficient and inefficient projects. Formally does this mean that crit * z p ka < p sym , k ≤ p k , which leads to:

µ pi ,k − 3 ⋅ σ p2i ,k