1. Chapter 10
Credit Market Imperfections: Credit Frictions, Financial Crises, and Social Security
Macroeconomics
6th Edition
Stephen D. Williamson
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2. Learning Objectives, Part I
10.1 Construct the basic credit market imperfections problem for the consumer, with a kinked budget constraint.
10.2 Adapt the credit markets model to deal with asymmetric information.
10.3 Show how limited commitment makes collateral important in the credit markets model.
In this chapter we consider financial market frictions or imperfections. First, we study two frictions that come into play in financial crises, such as what occurred in Then, we will study social security – a role for a permanent government program based on financial frictions.
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3. Learning Objectives, Part II
10.4 Show how pay-as-you-go social security works, and demonstrate what conditions are required so that it increases economic welfare.
10.5 Show how fully-funded social security programs function, and explain their economic role.
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4. Credit Market Imperfections and Consumption
Assume that lenders can lend at a lower interest rate than the one faced by borrowers.
The government borrows and lends at the interest rate that lenders face.
This implies that Ricardian equivalence does not hold, in general.
The first step is to consider a general setup in which lenders face lower interest rates than borrowers. This implies a kinked budget constraint for consumers, and the failure of Ricardian equivalence.
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5. Figure 10.1 A Consumer Facing Different Lending and Borrowing Rates
In the figure, the consumer’s budget constraint is AEF, with the kink at the endowment point.
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6. Figure 10.2 Effects of a Tax Cut for a Consumer with Different Borrowing and Lending Rates
The figure shows the results of a tax cut, of the consumer facing a kinked budget constraint. The tax cut acts to shift out the budget constraint. If the consumer chose the kink in the budget constraint initially, then consumption must change. The consumer increases current consumption – consuming the whole tax cut, with savings still at zero. Effectively, the consumer would like a loan at a low rate, which is exactly what the government provided.
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7. Effects of a Tax Cut with Credit Market Imperfections
Suppose a consumer initially is credit constrained – that is, he or she saves zero.
For such a consumer, the entire tax cut will be spent on current consumption.
This is very different from the case with no credit market imperfections, where the consumer will save the entire tax cut to pay higher future taxes.
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8. Credit Market Imperfections and the Financial Crisis
Two key credit market frictions: asymmetric information and limited commitment.
Asymmetric information: Would-be borrowers know more about their characteristics than do lenders.
Limited Commitment: Borrowers may choose to default – lender can overcome limited commitment with collateral.
We consider two financial frictions: asymmetric information and limited commitment, which are the two critical frictions which come into play in all real-world credit markets.
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9. Asymmetric Information in Credit Markets
Lending carried out through banks.
Deposit rate at banks is r1, loan rate is r2.
Fraction a of borrowers never defaults, fraction 10-a always defaults – bank cannot tell the good borrowers from the bad ones.
All good borrowers identical, borrow L.
Bad borrowers mimic the good ones.
This is a simple model of asymmetric information. All lending and borrowing is conducted through banks, which borrow from ultimate lenders and lend to borrowers. The bank is large and well-diversified. There are good and bad borrowers in the population. Bad borrowers always default, but they behave exactly like good borrowers, so the bank cannot tell them apart.
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10. Asymmetric Information – Deposit Rate and Loan Rate
Zero profits for the bank implies:
Therefore, there is a default premium (r2 > r1) when a < 1. The default premium increases as a decreases.
The bank can predict that a fraction a of its borrowers will be good, so it knows what its profits will be. There is free entry into banking, implying zero profits in equilibrium, which gives us a relationship between borrowing and lending rates of interest. There is a default premium associated with the lending rate to account for the fact that some borrowers default.
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11. Figure 10.3: Asymmetric Information in the Credit Market and the Effect of a Decrease in Creditworthy Borrowers
From the point of view of a good borrower, the budget constraint is kinked. If there are more bad borrowers in the population, this shifts the budget constraint as depicted.
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12. Figure 10.4 Interest Rate Spread
In practice, we can observe increases in the interest rate spread, just as we have increases in the spread in the model. These increases happen during times of financial stress, which increase the amount of asymmetric information in credit markets.
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13. Effect of a Decrease in the Fraction of Creditworthy Borrowers
Default premium increases – even good borrowers face higher loan rates.
Budget constraint shifts in.
Consumption falls for all borrowers.
Matches observations from the current financial crisis – increase in credit market uncertainty, reduction in lending, decrease in consumption expenditures.
A key implication of an increase in friction is that consumption falls for all borrowers. The credit market stress matters for spending.
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14. Limited Commitment and Credit Markets
Borrowers need incentives not to default on their debts – these incentives typically provided by collateral requirements.
Examples: House is collateral for a mortgage loan, car is collateral for a car loan.
Limited commitment means that borrowers cannot commit to pay back their debts. To mitigate this problem, borrowers are often asked to post collateral.
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15. H = quantity of housing owned by consumer p = price of housing
Example
H = quantity of housing owned by consumer
p = price of housing
Assume: Housing is illiquid – can’t be sold in the current period. However, it is possible to borrow against housing wealth, with a collateral constraint.
In this example, a consumer has some housing, and can borrow by posting the housing as collateral. If the consumer defaults, he or she gives up the house.
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16. Consumer’s Constraints
Lifetime budget constraint:
Collateral constraint: or
The collateral constraint says that the consumer cannot borrow more than the value of the housing he or she posts as collateral – otherwise he or she would default. The consumer now has two constraints: the collateral constraint and the lifetime budget constraint.
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17. Figure 10.5 Limited Commitment with a Collateral Constraint
This implies a kinked budget constraint for the consumer. In this case, if the value of the collateral falls, the budget constraint shifts in, as depicted. If the consumer is constrained by the amount of collateral, then current consumption falls one-for-one with the decrease in the value of the collateral. This was an important factor in credit markets during the financial crisis, particularly due to the sharp drop in the price of housing.
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18. Pay-as-you-go Social Security
Taxes on the working population pay for social security transfers to the retired each period.
Suppose two generations alive at each date, young and old.
The young pay social security taxes t, the old receive social security benefits b.
We next want to examine how social security systems work. First, we look at pay-as-you-go systems, in which benefits for the old are financed by taxes on the young.
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19. Population Growth
The population grows according to the following equation. Each period, there are N’ young and N old alive.
Assume that the population is growing at rate n.
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20. The Government Balances Its Budget
Total social security benefits must equal total taxes on the young.
Also, assume in the pay-as-you-go system that total benefits to the old are just equal to total taxes on the young. There is simply an income transfer from young to old.
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21. Relationship Between Taxes for the Old and Benefits for the Young
Simplifying, this tells us how the tax per young person depends on the population growth rate and the benefit per old person.
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22. Figure 10.8 Pay-As-You-Go Social Security for Consumers Who Are Old in Period T
When social security is introduced, it clearly benefits the initial old people, who did not have to pay the tax when young, but get social security benefits. Their lifetime wealth increases.
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23. Figure 10.9 Pay-As-You-Go Social Security for Consumers Born in Period T and Later
For succeeding generations, welfare will go up if lifetime wealth goes up. For this to happen depends on the interest rate and the population growth rate.
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24. Pay-as-you-go Social Security
Pay-as-you-go is beneficial only if the population growth rate exceeds the real interest rate.
The interpretation is that the population growth rate is the implied rate of return for an individual from the social security system, so social security is only worthwhile if the return exceeds what could be obtained in private credit markets.
Pay-as-you-go is only welfare improving if the population is growing sufficiently rapidly – if the population growth rate is greater than the real interest rate. But, if this holds, then this is one of the few examples of a free lunch in economics. Intergenerational transfers forever makes everyone better off.
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25. Fully-Funded Social Security
Essentially a mandated savings program where assets are acquired by the young, with these assets sold in retirement.
Fully funded social security is essentially a program of forced savings. While working, people are required to save in some specified assets, so that they have savings accumulated at the time of retirement.
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26. Figure 10.10 Fully Funded Social Security When Mandated Retirement Saving Is Binding
In a perfect world, forced savings can never make consumers better off. They are always choosing different quantities of savings than what they would choose if they optimized. Fully funded social security could be justified by a commitment argument. Everyone knows that the government cannot bear to let senior citizens go destitute, so people don’t save, expecting the government to bail them out in old age. Forcing them to save actually improves social welfare in this case.
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