13 Financial Market Frictions
Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected])
13 Financial market frictions
Index:
13 Financial market frictions ...... 1
13.1 Introduction ...... 3 13.2 The case with symmetric information...... 4
13.2.1 The lender’s risk hypothesis ...... 4 Box 1. Asset price bubbles ...... 7 13.3 Asymmetric information ...... 9
13.3.1 Adverse selection ...... 9 13.3.2 Moral hazard ...... 12 13.3.3 Collateral ...... 13 13.3.4 Rationing ...... 14 13.4 The rationed firm ...... 15
13.4.1 The value of the firm...... 15 13.4.2 The firm’ problem ...... 16 13.4.3 Non-binding constraint ...... 17 13.4.4 Binding constraint ...... 18 13.4.5 Persistence and propagation effects ...... 19 13.5 The financial accelerator ...... 21
13.5.1 The collateral in advance constraint ...... 21 13.5.2 Balance sheet effects ...... 23 13.5.3 The external finance premium ...... 25 13.6 The credit channel ...... 25
13.6.1 Indirect versus direct finance ...... 25 13.6.2 Why do we need banks? ...... 26 Box 2. Credit crunch ...... 27 13.6.3 The monetary transmission mechanism revisited ...... 28 13.6.4 Balance sheet effects on banks ...... 30 Box 3: The interbank money market during the subprime crisis ...... 31 13.7 Taking stock ...... 32 Further reading ...... 34
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Appendix 1. The household sector and equilibrium ...... 34 Appendix 2. The supply of funds without collateral ...... 35 Review questions and Exercises ...... 40
Review questions ...... 40 Exercises ...... 40
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13.1 Introduction
In the two-period model, we learned that the opportunity to borrow and lend allows agents to decide their optimal patterns of investment and consumption independently of the business cycle. In light of that model, agents take full advantage of the financial system borrowing in bad times and saving in good times, to smooth consumption. In the model without financial market failures, the financial system is a shock absorber. It allows aggregate demand to be more stable than it would be without a financial system.
In the real World, however, we observe that the availability of credit to households and firms is not independent of the business cycle. During boom phases, credit is cheap and abundant. During downturns, banking practices become more restrictive and credit gets costlier, making it difficult for households to keep the desired consumption levels and for firms to implement the desired investment plans.
In this note, we depart from the assumption that the financial system is just a veil matching borrowers and lenders. Between borrowers and lenders there is a key market failure due to asymmetric information. When the information regarding the characteristics (creditworthiness) or actions (risk taking behaviour) of the borrower are not observed by the lender, the later may respond restricting the availability of credit. This problem becomes particularly serious during economic downturns, when the general attitude towards risk becomes more conservative. When the economic conditions deteriorate, the general availability of credit to the economy tends to be reduced, and the conditions required by banks to keep lending are substantially tightened. This means that instead of making the business cycles smoother, the financial system has the potential to create more instability amplifying the business cycle. The aim of this handout is to illustrate this proposition.
The handout is organized as follows. In Section 2 we analyse the decision of lending to a risky borrower, assuming that the lender is well informed about the risk characteristics of the project. In that case, the interest rate does a good job in selecting the socially beneficial projects. In Section 3 we analyse the implications of asymmetric information, whereby the borrower knows more about its risk-taking characteristics and creditworthiness than the lender. First, we consider the case in which the lender cannot distinguish among different types of borrowers. In this case, a problem of adverse selection arises, giving rise to an equilibrium whereby bad projects are implicitly subsidized by good projects. In case the proportion of bad projects in the economy gets too high, the bank may refuse to lend at all.
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Then, we turn to the case in which a given borrower, after obtaining credit, deviates funds from the project for which the funds were earmarked, to engage in a project with higher private return, at the cost of the general interest. We show that the bank may align the borrower’ incentives with its own interest by reducing the size of the loan and requesting a collateral. In Section 4, we revisit the problem of the firm, considering a binding constraint on borrowing. When the firm is rationed in the credit market, temporary shocks affecting firm’ revenues will deliver persistent effects through lower investment. In that case, the dividends policy matters. In Section 5, we analyse the case in which the firm is subject to a collateral-in-advance constraint. Since assets prices are in general pro-cyclical, in that model the availability of credit correlates positively with the business cycle. Section 6 briefly describes the role of banks in the economy, and how monetary policy shifts are transmitted to the real economy via the so-called credit channel. Section 6 summarises the main ideas.
13.2 The case with symmetric information
13.2.1 The lender’s risk hypothesis
A main characteristic of financial contracts is that the return the lender expects to obtain in a loan typically differs from the interest rate set in the contract. The reason is that there is a probability of the loan not to be repaid.
To see this, consider the problem of a risk-neutral bank deciding the interest rate to set on a one-peso loan to a risky project. The bank knows that the probability of repayment in this project is equal to p. With probability 1-p the loan is not repaid, and the bank loses the principal. In alternative, the bank can buy a safe asset at the risk-free interest rate rf . This will be the opportunity cost of lending to the risky project.
Let r be the contractual interest rate on the risky project. Given p, the expected profit of the bank (B) is:
EB p(1 r) 1 rf 1 p0 1 rf p(1 r) 1 rf (1)
The bank will be indifferent between lending to the safe project or to the risky project if the interest rate to be charged in the risky project r is such that EB 0 , that is:
1 r 1 r f (2) p
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This condition implies that the expected return in the risky project is equal to the return in the safe project. Thus, the lower the probability of repayment in the risky asset, the higher the interest rate the bank needs to charge, to be indifferent between the two assets. This formula also shows that, when p is small, small changes in p have large impacts in the
1 default premium, r rf . The interest rate as a selection device
Consider the case in which the bank is deciding between two alternative uses for one peso available or lending. One, to buy a safe asset whereby investing one peso delivers an interest rate equal to rf . Two, lend to an entrepreneur that borrows one peso to engage in a ~ risky project. The risky project delivers z 1 rf with probability p or nothing with probability 1-p.
If the bank was able to charge an interest rate to the risky entrepreneur according to rule (2), it would be indifferent between buying the safe asset and lending to the risky borrower. A different question is whether the entrepreneur will be willing to accept the proposed interest rate, r . To examine this, let’s consider the expected profit of the entrepreneur. The entrepreneur will repay the loan only in case its project succeeds:
E~ p~z (1 r) 1 p0 (3)
Equation (3) shows that the entrepreneur is only concerned to what happens in case the good scenario materializes. In case the project fails, the loss will be taken by the bank, only. The borrower will be willing to engage in projects with a negative social value because he is cushioned on the downside.
The expected return of the entrepreneur will be positive if ~z (1 r) . This means that the maximum interest rate the bank can charge to the risky borrower is:
1 The discussion above presumes that the bank gets nothing in case of default. In alternative, one could assume that in case of default the proportion 1 of the loan would be recovered. As you may easily check, in this case the arbitrage condition becomes 1r1 1 r 1 p ' , with p´ p 1 p . This means that the only implication of allowing for partial default is to consider a higher probability value in model (1).
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1 r ~z (4)
If the proposed interest rate is higher than (4) the entrepreneur will not find profitable to invest in the project and will not take the loan.
Assuming that the bank observes the risk characteristics of the project, it will set the interest rate according to (2). Given (4), the entrepreneurs will accept the interest rate proposed by the bank if and only if: ~ pz 1 rf (5)
Equation (5) is a necessary condition for both parties to participate in the financial contract. It states that the project will be financed if its expected return is higher than the risk- free rate.
A question that immediately arises is whether condition (5) will exclude socially valuable projects. In our simple framework, a socially valuable project is one with a net gain to the aggregate consisting in the borrower and the lender. Adding up (1) and (3), the social value of the project is: ~ ~ EB E pz 1 rf (6)
Condition (6) implies that projects with positive social value are those with an expected return higher than the risk-free rate. Thus, any project with a non-negative social value will meet condition (5). Moreover, condition (5) implies that only socially valuable projects will be financed by risk neutral banks. Projects with negative social value will face prohibitive interest rates and will not be financed.
Summing up, when the bank can correctly assess the risk characteristics of each project, he will charge an interest rate that makes it indifferent between lending in the risky segment and buying the safe asset. If the interest rate is accepted by the borrower, there will be a financial transaction and a socially valuable project will be funded. When the project is socially inefficient, the risk adjusted interest rate is too high for the borrower to find it interesting. The conclusion is that under symmetric information, the interest rate plays a good job in discriminating good and bad projects.
The interesting case arises when the bank cannot accurately perceive the risk characteristics of the different projects, or when the investor is able to shift from the safe project to the risky project without the lender permission after obtaining the loan. As we see
6 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) next, under asymmetric information, the bank may respond to the problems of adverse selection and of moral hazard by restricting the availability of credit.
Box 1. Asset price bubbles
The arbitrage condition (2) can be used to interpret asset price bubbles. A bubble occurs when the price of an asset starts increasing over time, feed by the expectation that it will increase more in the future, without any fundamental reason. And yet, a bubble can emanate from rational decisions by economic agents.
To see this, consider first the price of a common stock in an infinite horizon under perfect foresight. Assuming that the stock pays dividends each year equal to t , its value today at must obey to an arbitrage condition stating that the dividend plus the capital gain must equal the return of the benchmark asset, that is,
t1a t 1 a t rf . at
Solving for at and substituting recursively, we get
at2 t 2 t1 a 1 r a tt1 1 f ttt 1 2 3 ... t 1r 1 r 1 r 2 3 f f f 1rf 1 r f
That is, the value of the stock shall be equal to the discounted sum of future dividends. For this condition to hold one must have assumed that:
aT limT 0 T 1 r f
This is the so-called non-Ponzi game condition. This condition requires that the price of the stock cannot increase faster than the interest rate. This condition is convenient, because otherwise it would pay for an investor to borrow an infinite amount of money, buy the stock and pocket the difference. The non-Ponzi game condition rules out speculative bubbles.
As an extreme case, assume that this stock paid no dividend at all, today or in the future. That is, t 0, t . Arguably, if the intrinsic value of an asset is zero, its price should be zero. However, this is only true if the non-Ponzi game condition holds. If the asset starts
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out with a positive value and is expected to appreciate over time at the rate rf , implying
at1 a t1 r f for any t, it will be indifferent for an investor to hold this asset or to hold the safe asset. The anticipation of ever-increasing prices will satisfy the arbitrage condition (2).
In reality, we know that bubbles to not last forever. To capture this, assume that there is a probability 1-p of the bubble bursting each period. Also assume that, if the bubble bursts, the price of the asset collapses to zero. A risk neutral investor would be still be indifferent between holding the asset and the risk-free asset if:
E at1 a t pat1 a t rf at a t
Another way of writing this equation is
a 1 r t1 f (2a) at p t
This is just a reincarnation of the lenders’ risk hypothesis, (2). In light of this equation, the asset price must be expected to increase – in case of no crash - at a rate that is higher than the risk-free rate and that rate is inversely proportional to the probability of the bubble to go on. Thus, the higher the probability of a burst, the higher the asset must promise in case the bubble continues one more period. This explains why during bubbles, asset prices accelerate more and more as they approach the collapse: the asset price needs to increase faster and faster, in order to deliver increasingly higher returns r when p declines, and keep risk neutral investors in.
Summing up, the materialization a bubble does not need to be an irrational phenomenon: rational investors aware of the risk evolved may be willing to keep buying the asset as long as the implied return obeys to the arbitrage condition (2a).
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Speculative bubbles are frequent and can affect a variety of assets, such as stocks, real state, gold, and cryptocurrencies2. The problem with speculative bubbles is that they cause large misalignments in asset prices, leading to significant, though unsustainable, wealth effects, that translate into consumption booms, overinvestment, and macroeconomic overheating. These episodes are followed by abrupt market corrections when the bubble collapses, causing financial distress and economic downturns.
13.3 Asymmetric information
13.3.1 Adverse selection
The discussion above presumes that the bank can observe the risk characteristics of the projects. In the real world, however, individuals know their own circumstances, but do not know those of other individuals. In the case of debt contracts, the asymmetry arises in that lenders have less information regarding the risk characteristics of the projects than borrowers. This gives rise to a problem of adverse selection.
Adverse selection is the problem created by asymmetric information that occurs before the transaction takes place. If the lender cannot observe the risk characteristics of the borrower, he cannot charge the interest rate that better matches the corresponding probability of default. The lender will set instead an average interest rate, taking into account the distribution the default risk across many borrowers. Setting an average interest rate will however change adversely the composition of the pool, as the borrowers more likely to repay the loan are priced out. In the limit, this problem may lead banks to refuse any lending, even if they know that there are safe borrowers in the market.
In order to make the explanation simple, assume again that the bank can opt between buying a safe asset paying a certain return, rf , or conceding credit to entrepreneurs. In the
2 Note that this can only happen with assets with no maturity, like stocks and real state, or without defined face value at maturity, like options.
9 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) later segment, there are only two types of borrowers, those involved in good projects (G) and those involved in bad projects (B). Projects are inherent to borrowers, so a borrower cannot engage in a project different for his type. The bad projects deliver a return ~z B with probability p B and zero with probability 1 p B . The good projects deliver a return ~z G with probability pG and nothing with probability 1 pG . Further assume that:
p B pG (7)
~ B ~G z z 1 rf (8)
B ~ B G ~G p z 1 rf p z (9)
Equation (7) established that the bad project has a lower probability of success than the good project. Equation (8) states that in case of success the bad project delivers a higher return than the good project. Equation (9) states that the expected return of the bad project is less than the return in the safe asset, which makes it a project with negative social value. The opposite holds for the good project.
Although the bank cannot distinguish the types of projects entrepreneurs are involved in, it observes the proportion of the two types in the economy. Assume that a fraction of entrepreneurs is engaged in bad projects, while the remaining fraction, 1 , is engaged in good projects.
Since the bank cannot distinguish the two types of borrowers, it cannot charge different interest rates. The question is whether it will be possible to set an average interest rate, r , such that both types of entrepreneurs are borrowing. The expected profit of the bank in the pooled equilibrium is:
B G EB p (1 r) 1 p (1 r) 1 rf (1a)
Assuming that lenders are competitive and have zero expected profit, the interest rate in the pooled equilibrium must be such that the expected profits of the bank are zero, that is:
1 r 1 r f (2b) p B 1 pG
This is another incarnation of equation (2): the interest rate to be charged in the pooled equilibrium is equal to the ratio between the return of the safe assets and the expected
10 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) probability of repayment. The later, is a weighted average of the probabilities of success of the two types of projects.
For the pooled equilibrium to exist, condition (5) must hold for both borrowers. Given (8), one must have:
1 r ~z G (5a)
Using (2b), this implies:
1 1 r pG f (10) G B ~G c p p z
Equation (10) states that the proportion of bad firms in the economy must be lower
3 than the critical level c . Whenever condition (10) is met, the bank will set an interest rate that is acceptable by both types of entrepreneurs.
The pooled equilibrium involves lending both to entrepreneurs with good projects and to entrepreneurs with bad projects. Moreover, the interest rate is such that the good projects are subsidizing the bad projects. The entrepreneur engaged in the bad project will be happy to borrow in the pooled equilibrium because it is treated as an average firm and will be paying an interest rate that is acceptable from his point of view. Had the bank correctly assessed the risk characteristics of his project, and the proposed interest rate would become prohibitive. As for the entrepreneurs engaged in good projects, the opposite is true: these are paying a higher interest rate than in the case with symmetric information. However, there is nothing they can do, because they are indistinguishable from bad borrowers.
With this model in mind, we can now guess what happens during a financial crisis. When the fraction of bad projects in the economy, , increases, the pooled interest rate (2b) increases. Thus, the transfer of resources from good borrowers to bad borrowers increases, as well as the size of the economic inefficiency (ie, the bank lending to socially undesirable
3 Note that the term in brackets is positive for sure, because we assumed that the good project is socially valuable (eq. 9).
11 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) projects). Since we only have two types of borrowers, the demand for credit by entrepreneurs will not change until the critical level implied by (10) is reached. When this critical level is surpassed, the interest rate becomes prohibitive for good projects and they will drop out of the market (adverse selection). Then, because the segment of bad borrowers is unprofitable to the bank, the bank stops lending in the risky market, turning instead to safe assets4.
This model helps explain why during economic depressions banks reduce their exposure in the credit segment, turning instead to direct finance, where lending is less information intensive. Since typically the credit segment is the one devoted to SMEs, which in general create more jobs in an economy, by squeezing the credit in this segment, banks can amplify the impact of economic downturns.
13.3.2 Moral hazard
Moral hazard is the problem created by asymmetric information that occurs after the transaction takes place. In the case of debt contracts, moral hazard refers to the risk that opportunistic borrowers engage in activities that reduce the probability of the loan being repaid. Rational borrowers may have an incentive to do so in case they face no penalty in default.
To illustrate this, consider the case of a borrower facing two alternative projects: a safe project, whereby investing one peso delivers a cash flow (before interest) equal to ~ z 1 rf for sure; and a risky project whereby investing one peso may deliver z z with probability p or zero with probability 1-p. Also assume that condition (5) does not hold,
4 In this model, there are only two types of risky borrowers. In a more general setup with many borrowers with different probabilities of default, the lender would need to balance the benefits of setting a higher interest rate to rise promised revenues with the fact that such increase would change the composition of its portfolio, with less risky borrowers dropping out. Stiglitz and Weiss (1981) showed that lenders find it more profitable to set an interest rate that is less than the market clearing level, rationing the availability of credit, than to charge an interest rate that completely eliminates the excess demand for credit, as the later would increase the riskiness of the pool, by either pricing out less risky borrowers (adverse selection) and affecting the incentive of the borrowers, inducing higher risk taking (Moral Hazard). [Stiglitz, J., Weiss, A., 1981. Credit Rationing in markets with imperfect information, American Economic Review 71 (3), 393-410).
12 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) meaning that the expected return of the project is less than the risk free rate. The bank will be willing to lend to the safe project at the risk-free interest rate, but not to the risky project.
Suppose the borrower agreed to invest in the safe project, and accordingly obtained a loan from the bank at the risk-free interest rate rf . A problem arises when the borrower cannot credibly commit to remain in the safe project once the credit is obtained.
If the borrower invests in the project for which the funds were earmarked, her expected profit will be:
z (1 rf ) 0
After the loan is obtained, however, the borrower may opportunistically change the use of money, engaging in the risky project. The borrower will have an incentive to do so, because: ~ ~ E pz (1 rf ) 1 p0 0
The borrower has an incentive to invest in the bad project, because she is not investing her own money, and because she is cushioned in the downside (it the project fails, the bank will bear the loss). In general, any risky project with promised return in the good scenario higher than the risk-free interest rate, z 1 rf , will be profitable to the entrepreneur, even if not socially desirable, 1rf pz .
In order to prevent the borrower from engaging in the risky project after the loan is conceded, the lender can impose restrictive covenants in the loan contract. Then, to ensure that the terms of the contract will prevail, the lender must incur in monitoring costs and in enforcement costs. Since these are expensive and the outcome of litigation is uncertain, the bank may also try to adjust the terms of the contract so as to turn the borrower’ incentives right. This can be done requesting a collateral and reducing the size of the loan.
13.3.3 Collateral
Collateral requirements are an important tool in credit risk management. When collateral is posted as part of a credit contract, the borrower gives the lender the right to seize the collateral in the event of default. This helps mitigate the problem of moral hazard, because the borrower has more to lose from a default.
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Suppose the borrower was requested to post a real asset T (say, land) as collateral. The future value of this asset will be qT . The question is: how much should the collateral be so that the borrower preferred the safe project? The collateral must be set such that:
E pz (1 rf ) 1 pqT 0
That is
pz z qT (11) 1 p
So, as long as the borrower can provide collateral with future value satisfying condition (11), the lender will be willing to supply the loan at the risk-free rate.
The ability of a financially healthy borrower to post collateral reduces the lender's risk and aligns the borrower's incentives with those of the lender.
13.3.4 Rationing
Suppose that the maximum collateral the borrower could arrange was smaller than the implied by (11). In this case, the lender may still fix the incentive problem by reducing the size of the loan. Setting the size of the loan L<1, the borrower will be forced to assume part of the risk, investing his own money.
The expected profit of the borrower when engaging in the risky project is:
E p z (1 r ) 1 p qT 1 L (1 r )
Getting the incentives right consists in setting L such that the expected profit of the borrower in the risky project is less than the profit in the safe project (zero). That is,
p z (1 r ) 1 p qT 1 L (1 r ) 0
qT z pz L (12) 1rf z pz
Equation (12) implies that the lender can set the incentives right by reducing the size of the loan.
An important implication of (12) is that, whenever the market price of the collateral declines, the bank must further restrict the availability of credit to prevent moral hazard.
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Credit rationing is an important mechanism through which financial crises that impact on the market value of collateralizable assets become self-feeding.
13.4 The rationed firm
13.4.1 The value of the firm
Consider a firm that needs to purchase in advance a capital good that is fully consumed in the production process, so that 1 (think, for instance, in seeds for agriculture). In alterative, you may think a capital good with 1, but that is so specific that it has no market value (human capital, for instance, cannot be traded).
K Further assume that the capital good costs p1 units of output today. The firm’ production function for the upcoming cycle is as follows:
Q2 z2FK2 (13)
Since 1, then K2 I1 .
For simplicity, we assume that the number of shares is unchanged and is set equal to 1. In order to finance investment, the firm can either use retained earnings (equity) or borrow from a bank. Let’s denote the bank loan by L. To make the story simple, we assume that the firm lasts for two periods only, so all debts must be cleared at the end of period 2.
The loan accumulates according to:
LL1 01 rIQ 0 1 1 1 (14)
Then firm savings (internally generated funds) are:
F S1 Q1 r0 L0 1 (15)
Equation (14) can also be written as
F LLIS1 0 1 1 (16)
That is: the firm’ net borrowing is equal to the difference between investment and savings. As for period t=2, the condition similar to (14) is:
L2 L1 1 r1 Q2 2 (17)
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Setting L2 0 and solving together, we get the value of the firm:
2 z2 F I 1 1 QL 1 01 r 0 I 1 (18) 1r1 1 r 1
The component in square brackets corresponds to the value of the firm without new investment, which is pre-determined. Assuming away agency problems, the objective of the firm is to choose the amount of investment today, I1 , so as to maximize the net present value of investment opportunities:
z2 F I 1 V1 I 1 (19) 1 r1
A problem arises is that the firm may lack the funds needed to implement the optimal investment. Suppose that, because of information failures, this firm faces a borrowing constraint in period 1 amounting to L1 . That is:
L1 L 1 (20)
Of course, it will make a different if the borrowing constraint (20) is binding or not. In the following, we consider the two scenarios.
13.4.2 The firm’ problem
The firm maximizes (19) subject to (16) and (20). The Lagrangian is as follows:
zFSF L L F 2 1 1 0 £ SLL1 1 0 LL 1 1 1 r1
Where is the multiplier associated to constraint (20). This multiplier measures the marginal benefit that would be achieved if the borrowing constraint was alleviated in one unit. The Kuhn-Tucker conditions for L1 and can be written as:
z2 FK K 1 1 r1 (21) p1
L1 L 1 0 (22)
There are two possible solutions to this problem, depending on whether the borrowing constraint (20) is binding or not.
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13.4.3 Non-binding constraint
Consider first the case in which equation (20) is not binding. In that case, the firm can borrow the enough to make the optimal investment. Since the constraint is not binding the value of the Lagrangian multiplier is 0 . The optimal condition (21) becomes:
* I1 : zF2K 1 r 1 (23)
In this case, investment is such that the marginal product of capital is equal to the market interest rate. This case is described by point 0 in Figure 1.
* When investment is I1 , the optimal size of the loan is:
** F LLIS1 0 1 1 (16a)
An important property of this equilibrium is that the opportunity cost of internally generated funds (retained earnings) is equal to the cost of borrowing. Thus, if the firm decided to pay more dividends today and less dividends in the future satisfying its inter- temporal budget constraint,
2 1 0 , (24) 1 r1 that would not impact on optimal investment: the fall in the firm savings today would be matched by an increase in the size of the bank loan, and the corresponding service next year would exactly match the lower future dividend payment. As long as the interest rate for the shareholder and for the firm are the same, the anticipation of dividends does not produce real effects. The dividend policy will not matter. It will be indifferent to finance investment with shareholders money or with borrowed funds.
Figure 1: optimal investment of the unconstrained firm
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* F 1 r1 II1 1 S 1 LL 0 1
1 r1 0 z2 FK
* 0 I I1 I 1 1
13.4.4 Binding constraint
Now suppose that the borrowing constraint was such that the firm could not tap the optimal amount of credit. In that case, the investment level is determined by the maximum feasible loan, that is:
F * I1 S 1 LLI 0 1 1 (23a)
Since the firm is investing less than desired, production in period 2 will be affected. Figure 2 describes the case in which the collateral in advance constraint is binding: investment will be suboptimal, future output will be affected, and there will be a wedge between the marginal product of capital and the market interest rate. In other words, the marginal value of a peso inside the firm will be more valuable than the value of a peso distributed to shareholders. In figure 2, the wedge is represented by the difference r1 r 1 .
This means that the dividends policy is no longer irrelevant. If dividends increased today by one unit, the shareholder would deposit this extra amount in the bank, obtaining r1 . This is less than the value that could generate if this resources were employed in production: the marginal product of capital. Reciprocally, if the firm decides to pay a lower dividend today in compensation for a higher dividend tomorrow while satisfying equation (24), this would imply an increase in the availability of resources inside the firm to invest today. Since
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the marginal product of capital is higher than the risk-free interest rate ( r1 ), the value of the firm would increase, and the household would be better off. By retaining earnings, the constrained firm can increase its market value5.
Figure 2: Feasible investment when the borrowing constraint is binding
1 r F * 1 I1 S 1 LLI 1 0 1
1r1 1 1 External Finance Premium
1 r1 0 z2 FK
* 0 I1 I I 1 1
13.4.5 Persistence and propagation effects
When constraint (20) is not binding, a temporary shock affecting the firm revenues Q1 (like a temporary fall in demand or a bad harvest), will not impact on investment and on the next year’ production. From (16a), the firm will optimally offset the decline in internally generated funds by hiring a higher loan and keeping investment at the optimal level. As long as there are no borrowing constraints, a temporary shock will deliver no persistent effects.
The only difference, in case r1 0 , will be on the distribution of income between shareholders and the bank, amounting to the extra interest payment.
5 See appendix 1 for the households budget constraint and equilibrium conditions.
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When the borrowing constraint is binding, otherwise short-lived economic shocks may have long-lasting effects. This is illustrated in Figure 3: when corporate savings decline, the maximum feasible investment (23a) shifts to the left, and future output will contract.
This mechanism aggravates the severity of the macroeconomic shock6. A persistence effect arises because next year production will be lower, even if the shock hitting the economy was temporary in nature. In plus, a propagation effect will arise: sellers of the capital good that our firm is not buying will be impacted and will eventually also face adverse borrowing constraints, reducing their demand to other sectors.
Figure 3: When the borrowing constraint tightens
I' SF ' LL 1 r1 1 1 0 1
1r 1 ' F 1 IS1 1 LL 0 1
1r1 1
1 r 1 1‘ 1
z2 FK
0 I ' I * I 1 1 I 1
6 Bernanke, Ben S., and Mark Gertler (1989). "Agency Costs, Net Worth, and Business Fluctuations," American Economic Review, vol. 79 (March), pp. 14-31.
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13.5 The financial accelerator
Because borrowers cannot credibly pre-commit themselves to repay their debts, lenders often request borrowers to set aside collaterals, in order to protect themselves from the risk of default. These collaterals are typically real assets or liquid financial assets. A problem is that the value of these collaterals may change over time. Because assets prices are not independent of the business cycle, this opens a channel through which economic downturns are amplified by the credit channel. This mechanism is labelled “financial accelerator” 7. This argument is examined in this section.
13.5.1 The collateral in advance constraint
Assume that the bank requires the firm to post a collateral in the debt contract. The collateral cannot be the capital good, because it erodes totally during the production process. Thus, the shareholder needs to post an asset of its personal portfolio, say a building (T), in order to obtain the desired loan. Denoting by q2 the market price of that building in period 2, the collateral-in-advance constraint takes the form:
q2 T L1 L 1 (20a) 1 r1
The term 0 1 captures the ability of the lender to enforce the collateral in the courts, in case of default. A weak rule-of-law will be reflected in a low , implying that the borrower will manage to keep most of the promised collateral in case of default. When 1 the borrower is coerced to deliver to the bank the full promised collateral.
7 The term “financial accelerator” was introduced in the literature by Bernanke, B., Gertler, M., Gilchrist, “The Financial accelerator and flight to quality”, The Review of Economics and Statistics, 78(1), 1996.
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In equation (20a), the future value of the collateral is discounted using the risk-free interest rate adjusted for the probability of enforcing the collateral.
To see how the collateral-in-advance constraint shows up in the model, we refer to figures 4 and 5. In figure 4, the borrowing constraint is described as a downwards sloping curve, reflecting the fact that the discounted value of the collateral is a decreasing function of the interest rate. Point 0 describes the exact value of the borrowing constraint, given the interest rate 1 r1 . The bank’ supply of funds is infinitely elastic at the market interest rate until the borrowing constraint (20) is met, at which point the supply of funds becomes vertical.
Figure 4 also describes the impact on the borrowing constraint of an increase in the market interest rate. All else equal, the increase in the interest rate causes the discounted value of the collateral to decrease, impacting negatively on the maximum size of the loan. Thus, the supply of credit shifts upwards and to the left.
Figure 4. The supply of funds and the market interest rate
1 r1
' 1 1 r1
1 r1 0 qT2 L1 1 r1
L' 0 1 L1 L 1
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Figure 5. The supply of funds and the value of collateral
1 r1
1 r1 1 0 qT2 L1 1 r1
L' 0 1 L1 L 1
Figure 5 describes the impact of a decrease in the future value of the collateral, q2 . In this case, the borrowing constraint schedule shifts to the left. The same will happen when the rule of law decreases, implying that a lower proportion of the collateral will be recovered by the bank: the higher the difficulty of the bank to enforce the loan contract ex post, the less the bank will agree to lend ex ante8.
An implication of this model is that bank resources are allocated to entrepreneurs according to the availability of collateral. A wealthy entrepreneur will find it easier to get funding than a poor entrepreneur, even if the later had a project with higher productivity z2 . Because of asymmetric information and costs in contract enforcement, the allocation of credit will not be efficient.
13.5.2 Balance sheet effects
8 A limitation of this model is that it produces a kinked supply of funds, rather than an upward sloping curve. Because the loan is fully collateralized, there is no scope for non-repayment, and this explains why all the credit is supplied at the risk-free rate. In Appendix 2, we show that, without a collateral constraint, the supply of funds schedule becomes positively sloped.
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Putting the pieces together, we now analyse the relationship between business cycles and the availability of resources for investment. Given (16) and the collateral in advance constraint (20a), the maximum feasible investment is determined by the availability of internally generated funds and of net borrowing, which in turn depends on the value of the collateral:
F qT2 IS1 1 L 0 (16b) 1 r1
As we already argued, during economic downturns, internally generated funds tend to decline because of lower revenues (fall in Q1 ). Now, we add a second mechanism, related to the value of the collateral: in recessions, the market prices of real estate and of liquid financial assets tend to decrease (fall in q2 ). Moreover, when the environment becomes riskier, monitoring and enforcing financial contracts becomes more costly, inducing banks to reduce the size of loans relative to the collateral (in the model, a fall in the loan-to-value ratio can be interpreted in terms of a fall in ). These factors reduce the borrowing ability of firms, affecting investment and spending decisions.
The same mechanism holds for household spending: in normal times, households are given the opportunity to borrow for consumption on favorable terms, with the equity in their home or shares serving as collateral. During financial crisis, changes in homeowners' net worth impact negatively on their borrowing ability, and thereby on consumer spending. This counter-cyclical behaviour of credit is exactly the opposite of what one would need to smooth consumption. The phenomenon through which pro-cyclical movements of the balance sheet of borrowers amplify and propagate business cycles, is known as the “financial accelerator” 9.
9 According to Ben Bernanke, the financial accelerator played a key role in the propagation of the Great Depression in the US. Massive bank failures and the decline of the financial wealth of borrowers induced a freeze the allocation of credit to households and small businesses, aggravating the recession [Bernanke, Ben S. (June 1983). "Nonmonetary Effects of the Financial Crisis in the Propagation of the Great Depression". American Economic Review. 73 (3): 257–2769].
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When a borrowing constraint tightens, the agent is forced to spend less, irrespectively of what is happening to the interest rate in the bonds market. The financial accelerator therefore implies that the IS curve will shift to the left during economic downturns and to the right during economic booms, reflecting the tightening and the lessening of borrowing conditions.
13.5.3 The external finance premium
In the model above, the collateral protects the lender from the advent of default, so the firm is given the opportunity to pay the risk-free rate. This does not mean that the cost of funds to the firm shall be measured by the risk-free rate: when the firm is rationed, the value of funds inside the firm (opportunity cost of borrowed firms) is measured by the marginal product of capital, 1 1 r1 . This exceeds the return received by lenders.
More generally, in a context of uncertainty regarding the future value of the collateral or about litigation costs, the borrower will bear the cost of the corresponding risk, paying
1 1 r1 in the loan (see Appendix 2). In that case, the cost of borrowed funds (the marginal product of capital) will exceed the cost (to the shareholder) of funds raised internally (by retaining earnings). This difference is labelled the “external finance premium”.
The “external finance premium”. reflects the deadweight loss arising because of imperfect information problems and costly contract enforcement. The external finance premium varies inversely with the borrowers’ creditworthiness, as measured by his net worth and liquidity. A higher net worth and liquidity enables the borrower either to reduce the cost of borrowed funds or to self-finance a greater share of its investment.
13.6 The credit channel
13.6.1 Indirect versus direct finance
The flow of funds from lenders to borrowers can take place directly or indirectly (see figure 6).
Figure 6 – The Flow of funds through the financial system
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Direct Finance Lenders Borrowers (net savers) Securities -Stocks Brokers - Bonds
Indirect Finance Financial Intermediaries: tY • Insurance companies,I K K • Deposits Pension funds • Loans • Contractual • Banks • Securities savings
In indirect finance, the flow of funds from savers to borrowers is mediated by financial intermediaries, such as banks and insurance companies. Financial intermediaries borrow funds from savers (deposits or contractual savings) and lend the hired funds to other borrowers at their own risk.
In direct finance, borrowers get funds directly from lenders in financial markets, selling securities. These transactions may be mediated by brokers (for instance, in the stock exchanges). Brokers are distinct from financial intermediaries in that they don’t buy and sell securities on their behalf: they only match borrowers and lenders and charge a fee for this service.
13.6.2 Why do we need banks?
A question that arises is why economic agents lend to each other through financial intermediaries such as banks, instead of engaging in direct finance. The answer is that banks have an economic role. This economic role results from the existence of frictions in financial markets.
In a frictionless world, with perfect information about each potential borrower, and with costless contract negotiation and enforcement, each lender should be able to lend directly to borrowers without transaction costs. Financial transactions would be carried out by atomistic individuals, and each small lender would be able to diversify risk, by lending small amounts of money to a large number of borrowers.
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In the real world, information failures and costs related to contract enforcement give rise to non-negligible transaction costs in financial activities. This includes the cost searching and matching borrowers and lenders; the cost of screening and evaluating projects (to mitigate adverse selection); the cost of designing contracts with the right incentives and restrictive covenants, the cost of monitoring regularly the conformity of the borrower with the contract, the cost of contract enforcement and litigation (to mitigate moral hazard). Some of these costs do not depend on the size of the loan. If these costs were incurred by each one lender, small and opaque borrowers would find the cost of external finance prohibitive.
The key function of banks is to screen and monitor borrowers in order to reduce the chance of default. Banks develop expertise in gathering relevant information, as well as maintaining ongoing relationships with customers, accumulating “informational capital”, and in designing contracts to mitigate the incentive problem. Banks take opportunity of economies of scale, reducing the transactions costs that would exist in their absence. Banks allow small savers and borrowers to engage (indirectly) in financial transactions that otherwise (directly) would not take place.
Banks have therefore comparative advantage in “information intensive loans”. Wherever the information on borrowers is easy to acquire by the public, the scope for intermediation declines. Banks do not have a special advantage with borrowers that are too transparent. In general, sovereigns and large corporations find it cheaper to engage in direct finance, issuing bonds or shares. These large borrowers can afford the high fixed costs related to making public the information regarding their creditworthiness (for instance hiring credit rating agencies). Banks hold securities, mostly government bonds, for portfolio diversification reasons, but have no comparative advantage in this market. Bank loans and funds raised in financial markets are not perfect substitutes: they target different audiences.
Box 2. Credit crunch
During episodes of financial crisis, banks typically depart from their traditional markets (information intensive loans), to invest more in market securities. The public tends to switch away from risky assets, including bonds, to hold a larger proportion of their wealth in the form of cash and deposits. In such context, financial intermediaries find it optimal to fill the gap, redirecting their lending to large borrowers and to the government, away from bank dependent borrowers (SME, households). This move materializes a credit crunch (Figure 7).
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Figure 7 – Credit crunch
Lenders Direct Finance (net savers) Securities Transparent -Stocks Brokers • Governments - Bonds • Corporations
Indirect Borrowers Finance Financial Intermediaries: tY • Insurance companies,I K K Opaque • Deposits Pension funds • SMEs • Contractual • Banks • Households savings
The 2007 financial crisis is an example of an episode when bank lending to the private sector declined significantly. This affected particularly households and SMEs, which are the segments of the credit markets where information asymmetries are more pervasive. During that crisis, banks redirected much of the credit previously allocated to SMEs to large borrowers, such as sovereigns and public companies, which are easier to monitor, and that meanwhile had lost much of their access to direct finance. Since SME are those in the economy that create more jobs, the recession was amplified.
13.6.3 The monetary transmission mechanism revisited
The discussion above weighs on our understanding of how changes in monetary policy are transmitted to the real economy (the transmission mechanism of monetary policy). The conventional (Keynesian) wisdom emphasizes the interest rate channel: open market operations alter the interbank money market interest rate, which in turn influences the long term bond yields through the term structure of interest rates. In the literature, it has been found that the investment and consumer spending respond little to changes in bond yields, while monetary policy has a very significant impact on aggregate demand. This apparent contradiction led economists to search for channels alternative to the interest rate, through which monetary policy may impact on aggregate demand. The “credit channel” is the
28 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) mechanism through which changes in monetary policy impact on the creditworthiness of bank-dependent agents, and by then, on economic activity.
Due to financial market frictions, banks play a key role in the transmission mechanism of monetary policy. Households and most SMEs lack access to direct finance and rely on banks, which have the capability to monitor and screen their actions and activities. In light of the credit view, changes in monetary policy impact on the banks’ willingness to lend (the bank lending channel) and also on the agents net worth and liquidity (the balance sheet channel), and by then on the availability of credit.
The bank lending channel refers to the supply of loans by banks. Because of moral hazard and adverse selection, banks use non-price rationing devices as part of their loan approval processes. When monetary policy is tightened, banks reserves decline, and the volume of credit is reduced through these rationing devices. The interest rate on loans does not necessarily increase, because banks know that raising lending rates would alter the risk composition of the credit portfolio (adverse selection). Thus, in result of an open market operation, the credit availability to SMEs and the public will be impacted, causing consumption and investment to fall through a channel that is distinct from the interest rate.
The balance-sheet channel refers to the impact of changes in market interest rates on the value of assets and cash flows of potential borrowers. As an example, consider a tightening of monetary policy, that causes the risk-free interest rate to increase. This is
' illustrated in Figure 8, with the move from point 1 to point 1’. With a higher interest rate r1 the borrowing constraint tightens because of a combination of different effects. First, the current value of the firm’ collateral declines (figure 4). Second, a higher interest rate may impact negatively on the firm’ savings, either via lower demand for output. The combined effect is a tightening of the borrowing constraint and a fall in the maximum feasible investment. The firm will invest less, with effects propagating to other firms and to the future.
Figure 8: Impact of an increase in the interest rate
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1 r1
1r1 1 '
1r1 1
' 1‘ 1 r1 1 1 r1
z2 FK
I ' 1 I1 I
13.6.4 Balance sheet effects on banks
Banks use short-term liabilities, such as demand deposits, to finance long-term assets, such as mortgages and business loans. With this important function of maturity transformation, banks conciliate the preferences of depositors, who desire easy access to their savings, and the long run borrowing needs of firms and households on housing and investment. The other side of the coin is that banks are exposed to a liquidity risk. The function of maturity transformation relies on the ability of bank to keep rolling over their short term liabilities.
When the public gets suspicious about the creditworthiness of a bank, a bank run may happen. Since the depositors’ resources are invested in illiquid assets, banks typically cannot liquidate all deposits at the same time. Eventually, those depositors that arrive first will be served. But if that is true, this will create the incentive for all deposits to withdraw their savings as soon as possible, precipitating the collapse. To protect depositors and to promote the stability of the financial system, regulators have developed a number of tools, such as deposit insurance, reserve requirements, minimum capital requirements, and the central bank function of lender of last resort. These institutions have helped raise confidence of depositors in banks, reducing the scope for bank runs. This, in turn, allows banks to keep the credit flowing to the economy, even during downturns.
More recently, however, a different type of bank runs has developed: banks running on other banks. The reason is that banks have become increasingly more reliant on non-
30 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) deposit funds with very short maturities, such as interbank loans and collateralized loans from other financial institutions. Loans from other financial institutions are easier to raise in large amounts than traditional deposits, but they also carry a high risk of evaporating when risk perceptions increase. In plus, the interest rate in interbank loans is much more reactive to changes in the bank net worth than traditional deposits are (Box 3 offers an illustration).
These funding conditions costs are then transmitted to the cost and availability of funds to bank-dependent borrowers. When the economy is booming, the lending activity pays off and banks make profits. Showing up high creditworthiness, banks find it cheaper to borrow in inter-bank markets, and this creates the incentives for banks to expand their activity, lending more to firms and households. When, on the contrary, the economy contracts and banks face high sinistrality in their asset portfolios, interbank funding becomes more difficult and costly. Banks trapped in a financial distress will try to reduce their financing needs, reducing credit to households and firms.
Box 3: The interbank money market during the subprime crisis
The negative relationship between the value of the collateral and the external finance premium is at the core of the theory of the financial accelerator. The subprime crisis that started in 2007 offers a good example of this phenomenon. During the crisis, there was a substantial increase in the number of non-performing loans in sub-prime mortgages, eroding the value of tradable securities backed by these mortgages. As the value of these asset-backed securities declined, it became increasingly costly for financial institutions to borrow in money markets without a collateral.
Figure 8 shows what happened to the interbank interest rates in the euro area. In the Eurosystem, banks lend to each other under two alternative modes: loans without collateral (unsecured lending), based on the perceived creditworthiness of the borrowing institution: the average interest rate of these loans is labelled EURIBOR; loans based on repurchase - agreements, whereby the borrower “sells” securities (collateral) to the lender committing to repurchase these securities when the loan matures: the average interest rate of these loans is labelled Eurepo. Figure 8 shows the evolution of the Euribor and of the Eurepo rates along 2007. Initially, the two interest rates were evolving close to each other, reflecting the high confidence among fellow banks. By mid-2007, the gap between the two interest rates increased sharply: the “balance sheet effects” of the sub-prime crises translated into a change
31 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) in risk perceptions, resulting in a significant wedge between the price of uninsured loans relative to that of collateralized loans. That difference is a measure of the external finance premium paid by banks. The freeze of inter-bank money markets during the financial crisis was the main reason why banks increased their desired reserves, cutting down credit.
Figure 8 - Money market interest rates in the Eurozone, 2007
Source: ECB.
13.7 Taking stock
Financial transactions are characterized by a problem of asymmetric information. Asymmetric information arises when one party in the transaction does not know as much as the other party in the transaction. In the case of debt contracts, the main source of asymmetry is that the borrower knows more about his attributes (creditworthiness) and his actions (risk-taking) than the lender.
In general, asymmetric information comes along with two types of problems: adverse selection, a failure that occurs before the transaction takes place, and moral hazard, a failure that occurs after the transaction takes place. These two problems help explain why consumers and firms cannot always borrow the amount of credit they would like at the prevailing interest rates.
Credit rationing becomes particularly serious during episodes of financial crisis, when the lenders’ perception regarding risk increases. Banks may optimally decide to restrict the supply of credit, particularly in the information-intensive segments, where small and medium enterprises are.
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To mitigate problems with moral hazard in lending activities, creditors often require borrowers to post an asset as collateral. During economic downturns and financial crises, however, asset prices tend to decline, lessening the capacity of borrowers to pledge collateral. This balance sheet effect causes a contraction of bank credit, leading to a further fall in consumption and in investment, amplifying the recession.
In a World with perfect information, the financial system should operate as a shcok absorber. If that was so, banking credit should be counter-cyclical. If, however borrowing is conditional on collaterals, which values fall during recessions, then credit becomes pro-cyclical. The phenomenon through which changes in financial and credit conditions translate into credit tightening during recessions, propagating the business cycle, is labelled “financial accelerator”.
When a borrowing constraint tightens, the agent is forced to spend less, irrespectively of what is happening to the interest rate in bond yields. In the bank-dependent segment, access to credit is not adequately measured by the interest rate. The financial accelerator implies that the IS curve will be shifting upwards during booms and leftwards during downwards, reflecting the lessening or tightening of borrowing constraints to bank-dependent borrowers.
Because banks play a prominent role in the intermediation process, they also play a key role in the transmission of monetary policy. The credit view contends that monetary policy alters the cost of funds to bank-dependent borrowers through balancesheet effects and via the bank willingness to lend. These effects impact on the volume of credit much more than one might guess looking at interest rates.
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Further reading
Bernanke, B., Gertler, M., Gilchrist, “The Financial accelerator and flight to quality”, The Review of Economics and Statistics, 78(1), 1996.
Brunnermeier, M., Reis, R., 2019. A crash course on the euro crisis. Mimeo. Princeton University.
Driscoll, John, 2003, Lecture notes in Macroeconomics, Brown University, Chapter 4.4.
Montiel, P. 2003. The macroeconomics of Emerging Markets, Cambridge. chapter 11.
De Gregorio, J., Macroeconomía, Pearson, 2012, Chapter 24.7.
Blanchard and Fisher, 1992, Lectures on Macroeconomics, MIT press. Chapter 5.
Romer, D., 2001. Advanced Macroeconomics. MacGraw-Hill. Chapter 8.7.
Appendix 1. The household sector and equilibrium
Households carry from period zero a given stock of financial wealth, consisting of
B securities issued by banks ( b0 ) and shares ( a0 ). At the beginning of period 1, last year’ bonds pay the market interest rate, r0 , shares pay a dividend, 1 , and worth a1 at the end of period. Ignoring taxes and other income, the individual’ net worth at the end of period 1 will be:
B B ba1 11 rba 0 0 1 1 C 1 . (a1)
The household’ savings in period 1 are:
H B S1 rb 0 0 1 C 1 . (a2)
The correspondent to (a2) in period 2 is:
B B ba2 21 rba 1 1 2 2 C 2 (a3)
B Setting b2 a 2 0 and solving together (a1) and (a2), we get the household’ lifetime budget constraint:
C2 C1 1 (a4) 1 r1
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B 2 with 1b 01 r 0 1 (a5) 1 r1
The bank raises funds from households selling its bond and lends to firms exactly the same amount, at the same interest rate. Assuming that has no other operations, the balance sheet identity implies:
B b0 L 0 (a6)
Combining (a14), (a2) and (15), private sector savings become:
S1 Q 1 C 1 (a7)
Combining (a5), (a14) and (18), the household lifetime wealth becomes:
z2 F I 1 1Q 1 I 1 (a8) 1 r1
Appendix 2. The supply of funds without collateral
Consider again the bank’ problem of setting a credit limit to an agent, but now assuming that the loan is not collateralized. In case of default, the bank doesn’t get reimbursed at all. For a given probability of repayment, p, the bank will be indifferent between lending or buying the risk-free asset if pr1 p ( 1) r1 . This implies:
1 r 1r 1 (a9) 1 p
Default involves a penalty to the borrower, . You can interpret this parameter as capturing litigation costs and pecuniary penalties. When deciding to default or not, the borrower compare the benefit of defaulting against the penalty in case of default. There will be no default if:
L11 r 1 (a10)
The amount of the penalty is not unknown. This reflects the fact that judiciary outcomes are uncertain, and more uncertain the lower the quality of institutions and the rule of law. We assume that has a uniform probability distribution in the range L, H , L
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and H refer to the highest possible and the lowest possible values, respectively. In other
1 words, each possible realization of has an equal probability, with H L .
In this case, the probability of (a10) will be equal to10:
L1 r p H 1 1 , 0p 1 (a11)
Outside this interval, the corner solutions p=0 or p=1 apply. When the minimum possible penalty L exceeds the value of the debt, the borrower pays for sure. In that case, the bank sets the risk free rate:
L C L1 L 1 , (a12) 1 r1
C Beyond the critical value ( L1 L 1 ) the interest rate in the loan will be an increasing function of the size of the loan. The interior solutions are obtained solving together (a11) and (a9), which gives11:
2 H1 H 4 1 r1 1r1 (a13) 2L1 2 L 1 L 1
This equation establishes a positive relationship between the size of the loan and the interest rate in the loan contract.
In this model, the external finance premium is equal to r1 r 1 . The difference relative to the deterministic case is that the cost of borrowed firm is no longer a shadow cost, defined by the marginal product of capital: the firm is actually charged at the interest rate r1 ,
10 This model adapts from Sachs and Cohen (1982). [Sachs, J., Cohen,, D., 1982. LDC borrowing with default risk. NBER Working Paper Series N.925. NBER, Cambridge MA]. 11 The system (a9) and (a10) is a quadratic equation, delivering two roots for the interest rate, one with low probability of repayment and high interest rate, and other with high probability of repayment and low interest rate. When the financial contract is negotiated bilaterally, only the root with low interest rate makes economic sense. The case with many (uncoordinated) lenders is examined in a different handout.
36 30/10/2020 https://mlebredefreitas.wordpress.com/ Politicas macroeconomicas, handout, Miguel Lebre de Freitas ([email protected]) reflecting the fact that the bank bears the cost in case of default. In either case, the external finance premium is equal to the difference between the marginal product of capital (shadow price of borrowed funds) and the risk-free rate.
An interior solution only exists if the term in the square root is non-negative. This condition imposes a maximum limit on the size of the loan:
2 Max H L1 L 1 (a14) 4 1 r1
This is the maximum loan the entrepreneur could be entitled with. Beyond this level,
Max the bank could not be compensated for the risk it would take. Beyond L1 a situation of credit rationing arises: the bank refuses to lend to the investor at any interest rate.
As for an numerical illustration of (a12)-(a14), assume that the risk-free rate is
1r1 1 and litigation costs range from L 20 and H 100 , implying 80 . In this
2 100 1 100 320 case, it is easy to see that (a13) becomes 1r1 . 2L1 2 L 1 L 1
Figure A1 describes how the interest rate varies with the size of the loan in this case:
C the interest rate is equal to the risk-free rate until the critical level L1 20 is reached (equation a12). Beyond this level, the interest rate is increasing. If, for instance, the firm demands a loan amounting to L1 30 , the equilibrium interest rate will be 1r1 1.33 , implying an external finance premium of 33.3%. Given the probability distribution of the
Max litigation costs, the bank will not be willing to lend more than L1 31.25 .
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Figure A1: Supply of credit in the numerical example
1 r1
1.6
1.33
1.00
LC 20 Max 1 30 L1 31.25 L 1
We now proceed, investigating how a change in a parameter affects the supply of funds to the entrepreneur.
Figure A2 describes what happens when the risk-free interest rate increase to
1r1 1.25 . As in the deterministic case, this causes the loan supply curve to shift upwards and the borrowing constraint to tighten. The segment along which the borrower faces the
C risk-free interest rate also shortens, to L1 16
Finally, figure A3 describes the implications of an increase in uncertainty regarding the penalty, to 100 . As shown in the figure, the interest rate increases for each level of
12 L the loan and the borrowing constraint tightens . Since in this example q2 0 , no loan is possible at the risk-free rate.
12 Catão, L., Kapur, S., 2004. Missing links: volatility and the debt intolerance paradox. IMF Working Paper 04/5. IMF. Washington DC.
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Figure A2: Increase in the risk-free interest rate
1 r1 2.00 1.6
' 1r1 1.25
1r1 1.00
C ' C Max L1 16 L 31.25 L1 20 1 L1 LMax ' 25 1
Figure A3: Increase in uncertainty regarding the penalty
1 r1
2.00 1.6
1r1 1.00
LC ' 0 LC 20 LMax 31.25 1 1 1 L1 L Max ' 2 5 1
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Review questions and Exercises
Review questions
13.1. Describe the different types of information failures that hinder financial markets.
13.2. What is the external finance premium? Explain how it helps explain the role of financial intermediaries.
13.3. Elaborate on the different reasons why credit to SMEs becomes tighter during financial crises.
13.4. Do banks have comparative advantages with small borrowers and specific projects or with large and well-known borrowers? Why?
13.5. The scope for financial intermediation (vs. direct financing) is expected to increase or to decrease during a financial crisis? Why?
Exercises
13.6. (The Lender’s Risk Hypothesis) Consider a project where 1 peso invested may deliver 2 pesos with 20% probability and 0 peso pesos otherwise. Assuming that the risk- free interest rate is 20%, how much should a risk-neutral lender charge in a loan to this project?
13.7. (Adverse selection): Consider an economy where all agents are risk neutral. This economy is populated by two types of borrowers: BBB, that engage in risky projects whereby 1 peso invested delivers 1.2 pesos with probability 90%, and CCC borrowers that engage in risky projects whereby 1 peso invested delivers 2 pesos with probability 40%. Further assume that borrowers cannot switch across projects; that banks operate under perfect competition; and that the risk-free interest rate is 1.5%. a) Find out the maximum interest rate each type of borrower would be able to pay for a loan. b) Assume first that banks were able to distinguish the two types of borrowers. Find out the interest rate offered to each type of borrower. Would the implied equilibrium be efficient? c) Now assume lenders could not distinguish the two types of borrowers. Banks observe, however, the proportion of CCC borrowers in the economy. If that proportion was 5%, would a pooled equilibrium exist? What would be the interest rate in that case? d) Departing from (c), examine the implications of a decline in the probability of success of BBB projects to 85%. e) Departing from (c), examine the implications of an increase in the proportion of CCC projects to 15%. Discuss.
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13.8. (Moral hazard): Consider an economy where all agents are risk neutral. There is only one lender (the bank), with 1 peso available for lending. In this economy, there are only two possible projects: AAA, a safe project, whereby the borrower invests 1 peso to obtain 1.2 for sure; and CCC, a risky project, whereby the borrower invests 1 peso to obtain 1.8 pesos with 50% probability. a) Assume that the bank sets the interest rate at 20% and lends 1 peso to a given borrower, without requesting any collateral or without imposing any restrictive covenant. If, after obtaining the loan, the borrower could choose the investment project, which project would he choose, A or B? Explain. [A: 30%>0%]. b) If the bank could request a collateral, what should be its minimum value, so as to induce the right choice on a loan amounting to L=1? [0.6] c) Now assume that the lender could reduces the size of the loan, forcing the borrower to fund the remaining with own capital. If the borrower’ collateral amounted to qT=0.36 only, what would be the maximum incentive-compatible lending?
13.9. (Moral Hazard, collateral): Consider a case where both the borrower and the lender are risk neutral. The lender (the bank) is analyzing the possibility of conceding a loan to the borrower, who can choose between two projects: a safe project, whereby the borrower invests 8 pesos to obtain 15 for sure; and a risky project, whereby the borrower invests 8 pesos to obtain 24 pesos with 50% probability. The interest rate the bank set in its loans is 25%. a) Assume first that the borrower could obtain a full loan L=8. In that case, which project would he prefer, the risky one or the safe one? [A: 5; 7]. b) Would the bank prefer the borrower to engage in the risky project or in the safe project? [A: 2; -3]. c) Now assume that the lender reduces the size of the loan to L=4, forcing the borrower to fund the remaining with own capital. In this case, which project would the borrower prefer? Is the bank better or worse than in the earlier case? [A: 1>-3]. d) Finally, assume that the bank concedes L=8, but requires a collateral from the borrower (say, a property). How much should be the minimum value of the collateral so that the right project is selected? [A: 4].
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13.10. (Collateral-in-advance constraints, consumption). Consider an household which . . life-time utility function is given by U C1C2 . The household income today is Q1 68 . As . for the future, its resources will be future income Q2 261.6 plus the selling of a real asset,
which future value is expected to be q2T 165 . a) Assuming that this consumer could borrow or lend any amount of the consumption . good at the interest rate r1 0.1 , what would be the present value of his lifetime wealth? [A: 455.8]. b) Without borrowing constraints, what would be his optimal consumption-path? [A: 227.9; 250.7]. c) Now assume that the loan was subject to a collateral-in-advance constraint, so that the amount of the loan could not exceed the present value of the real asset. How much would be current consumption in that case? How much would be shadow interest rate in that case? [A: 218; 20%]. d) Sticking with the assumption of a collateral-in-advance constraint, examine the effects of an increase in the interest rate to 25%. Represent the change in the inter-temporal budget constraint in a graph [A: 200; 30.8%].
e) Finally, assume that the future value of the collateral declined to q2 T 150 . With the interest rate equal to 25%, show, with the help of a graph, the new change in the consumption patter [A: 188, 39.1%]. f) In the context of this exercise, explain the meaning of “financial accelerator”. Discuss the effectiveness of monetary policy in mitigating its implications.
13.11. (Borrowing constraints, Financial Accelerator) Consider a firm with a production
function Qt1 zFI t 1 t , with both I and Q priced at 1 peso. The firm has own resources S F LILS F r equal to t and needs to borrow ttt1 t at the interest rate t to finance current investment. a) What is the optimal borrowing by the firm? b) Now suppose that the firm is requested to provide as collateral an asset (say, the
building), which market value is qt1 T . The borrowing constraint is therefore
Lt(1 r t ) qT t1 . Explain why a binding constraint implies an external finance premium.
c) Now suppose that a recession causes the value of the collateral qt1 to fall, as well as F the firm’ own resources, St . What will happen to the firm’ value in that case? Is that something the monetary policy could do to mitigate the bad scenario?
13.12. (Collateral-in-advance constraints, investment): Consider an entrepreneur, which 0.5 production function is given by Q2 zI1 , where I refers to an input that must be
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purchased one period in advance. The entrepreneur has initially no internal funds, so all input use must be financed by a bank. a) Assuming unrestricted access to credit, what would be the optimal demand for the input, I*? How much will be output in this case? Exemplify, assuming that z=48.4 and r=21% (A: 400; 968). b) Now assume that the loan (plus interest) cannot exceed the value of a collateral, consisting in a building valued at 146.41 pesos. Assuming r=21%, how much would output and the external finance premium be? [532.4; 99%] c) Discuss the implications of a fall in the value of the building to 121 pesos. In particular, discuss the impact in the external finance premium and on output (484, 121%). d) Suppose the central bank set the interest rate equal to 0%. Would this help mitigate the problem? Describe in a graph.
13.13. (Borrowing constraint, partial equilibrium) Consider the firm’ problem in a two-
period economy. The firm’ value is given by 1 21 r 1 , where
0.5 1QI 1 1 LL 1 01 r 0 , 2QL 2 11 r 1 , where Q1 300 and Q2 25 K 2 .
Assume that the risk-free interest rate is 1r1 1.25 , and that K2 I 1 (capital depreciates
fully each year). Initially, L01 r 0 300 . a) (a1) Find out the investment level that maximizes the value of the firm. Find out the
implied value of the firm, considering the cases with (a2) 1 0 ; (a3) 1 64 . b) Consider in alternative the case where the firm was subject to a borrowing constraint of
the form L1 qT1 r 1 , with qT 125. Describe the problem of the firm assuming
that: 1 64 . In particular: (b1) find out the implied investment level; (b2) display in a graph; (b3) quantify the External Finance Premium. (b4) Find out the value of the firm;
(b5) Would it make a difference if 1 0 ? (b6) Explain, comparing to (a).
c) Suppose this economy was closed and the real interest rate was sticky at 1r1 1.25 . Would current output in this case be invariant with the borrowing constraint? Explain the intuition.
13.14. (Borrowing constraint, IS curve) Consider a two-period closed economy, where the
preferences of the representative consumer are Uln C1 ln C 2 . Households are the owners of firms, and there is no government. The consumer’ life-time wealth is given by n 1Q 1 V 1 . In this economy, natural output in period 1 is Q1 75 , and future output 0.5 depends on current investment, according to Q2 zK 2 . Capital depreciates fully each year.
a) (Optimal consumption) (a1) Describe the consumer’ problem considering 1 as
given. Find out the expressions of: (a2) optimal C1 as a function of 1 . (a3) optimal
S1 , as a function of Q1 and V1 . Considering 1r1 1, find out the optimal C1 and S1
when: (a3) Q1 75 , V1 25 ; (a4) Q1 56 , V1 24 ; (a5) Describe the two equilibria in
the C1, C 2 locus.
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b) (Investment schedule) (b1) Assume that z 10 . Find out the optimal investment as a
function of the interest rate, as well as (b2) the implied Net Present Value, V1 . (b3)
Describe the investment function in a graph and (b4) identify the case with 1r1 1. (b5) Which factors would cause this curve to shift? c) (Saving schedule, IS curve) Given your results in (a) and (b), find out the expressions
of: (c1) household’ saving, S1 , as a function of Q1 and V1 . (c2) the IS curve. (c3) Represent the IS curve in a graph. (c4) Describe the equilibrium with flexible prices, quantifying (c5) the natural interest rate, (c6) consumption, savings and investment. d) (Collateral in advance): In the following assume that the interest rate is stuck at
1r1 1, implying that the equilibrium level of output, Q1 , is endogenous. Returning to the firm’ problem, assume that dividends are set according to the rule
1QL 1 01 r 0 implying that current investment is financed with a bank loan,
I1 L 1 . The firm is subject to a borrowing constraint of the form L1 16 . (d1) explain why this might occur. Find out the implied (d2) investment and (d3) Net Present Value,
V1 . (d4) Compare the cases (b4) and (d2) referring to the Investment schedule, and (d5)
show, quantifying, the EFP. (d6) Find out the equilibrium level of Q1 , as well as of (d7)
C1 . (d8) Explain what happened in a graph, referring to the IS curve.
13.15. [Credit supply curve under uncertainty]. Consider the bank’ problem of setting a
maximum ceiling on the agent’ loan. Assume that the default penalty ranges from L 25
to H 100 . Further assume that the risk-free rate is 1r1 1. a) What will the maximum possible loan and the risk free rate? And the maximum possible loan? And the maximum interest rate [25; 39.0625; 1.6].
b) Examine the implications of a deterioration in the rule of law such that L 0 . [0; 31.25; 2]
c) Examine the implications of an increase in the risk free rate to 1r1 1.25 [20, 31.25; 2.0] d) Examine the implications of an increase in uncertainty to 1.25 [0, 31.25; 2.0]
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