Foreclosures, monetary policy and financial stability

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Foreclosures, monetary policy and financial stability We are grateful to the seminar participants for their helpful comments at Said Business School, Oxford University, at the X-th International Academic Conference in Moscow and to Raphael Espinoza and Udara Peiris. All remaining errors are ours.

C. Goodhart,

London School of Economics

D.P. Tsomocos, A.P. Vardoulakis Said Business School, Oxford University

The current crisis has centred on borrower defaults on mortgages, and the knock-on effects of that on banks' own credit standing (and in several cases their own default), and hence on tightened conditions for lending to new (mortgage) borrowers. No model which does not incorporate such key elements, or at least most of them, can possibly hope to capture the defining features of the current crisis, certainly not standard DSGE models which (mostly) assume away the possibility of default altogether!

As pointed out first by Irving Fisher (1933), over-indebtedness and deflationary pressures can lead to defaults and subsequently to a recession as businesses reduce their production due to bankruptcy and inability to raise capital. In this paper we concentrate on the housing market and we analyse how deflationary pressures can lead to more defaults on mortgages, foreclosures and financial instability. Default plays a central role for both borrowers and banks, and financial intermediation and money have an active role. Consumers enter a mortgage contract with a bank to buy housing which they pledge as collateral. They default on their mortgage when the value of the collateral is less than the amount they have to repay [Geanakoplos, 2003; Geanakoplos, Zame, 1995]. When they default the bank seizes the amount of housing pledged as collateral and puts it in the market. The decision to default will depend on the expected real estate prices in the future, which generally depend on the existence of first time buyers. Thus, we introduce in the model an additional agent, who is a new entrant to the housing market. We abstract from the effect of default on production and investment by considering an exchange economy, since our focus is on financial instability.

Monetary policy affects the price of housing and mortgage rates, and consequently the decision to default. Standard DSGE models cannot account for this since they assume away the possibility of default altogether and do not incorporate an optimizing heterogeneous banking sector and an interbank market. In addition, default is an incomplete markets phenomenon - not every eventuality can be hedged - and trade plays a non-trivial role in the value of collateral.

1. The model

We built a General Equilibrium Model with Incomplete Markets, Commercial banks, Fiat Money, Collateral and Default. There are two goods in the economy, a consumption good which is perishable and housing which is durable and can be used as collateral. We consider a two-period economy where agents know the present (period 0) but are uncertain about the future where one of occurs. The set of all states is given by

Consumers maximize their expected utility from consumption of the good and housing and banks maximize their expected profits. The main financial imperfection is that individual bank borrowers are assigned, by history or by informational constraints, to borrow from a single bank. Money is introduced by a cash-in-advance constraint, whereby a private agent needs money to buy goods and housing from other agents; goods and housing cannot be used to buy commodities. Similarly they assume that agents needing money can always borrow cheaper from their (assigned) bank than from other agents; banks have an informational (and perhaps scale) advantage that gives them a role as an intermediary.

Given limited participation in the loan markets in our model, we need at least four agents-households (б, в, ц, л) and two commercial banks (г, д). Mr. б and Mr. в are endowed with the good, Mr. ц with housing and Mr. л, who is born in the last period, is endowed only with the good. The time-structure of the markets is illustrated in Fig. 1. The Central Bank acts in the interbank market at t = 0 by providing liquidity and in the short-term loan markets at t = 1 by providing liquidity in those markets organized by banks separately.

Fig. 1. Timeline

1.1 Optimization problems

1.1.1 Consumers

Each consumer maximizes his payoff, which is his utility from consumption of the good and the house. He acquires housing by entering into a mortgage contract, which he has to repay in the last period. The housing he purchases is pledged as collateral. He honours his mortgage when the value of housing that he has bought is greater than the amount he has to repay. If it is lower, then he defaults on his mortgage and the bank that extended the mortgage seizes the collateral. In essence he repays the minimum between the two values, i.e. min (value of collateral, mortgage amount).

We denote by the set of states that agent h does not default on his mortgage, i.e., The maximization problem is as follows:

subject to:

(1) (expenditure for housing at t = 0) (amount borrowed short-term at t = 0) + + (mortgage amount) + (initial private monetary endowment);

(2) (short-term loan repayment) (good sales at t = 0);

(3) (expenditure for housing in the second period, state ) + (mortgage repayment) (amount borrowed short-term) + (private monetary endowment in );

(4) (expenditure for housing in the second period, state ) (amount borrowed short-term) + (private monetary endowment in );

(5) (short-term loan repayment) (good sales in );

(6) quantity of goods sold in endowment of goods in

where:

: fiat money in the housing market in

: amount of goods offered for sale in

: endowment of goods in

: price of the good in

: price of housing in

Mr. ц is endowed with housing at t = 0, some (much) of which he sells to buy goods for consumption. He then deposits a part of the sales' receipts. His maximization problem is as follows:

subject to:

(1) (expenditure for goods) + (interperiod deposits) (amount borrowed short-term) + (private monetary endowment at t = 0);

(2) (short-term loan repayment) (housing sales at t = 0);

(3) (quantity of housing sold at t = 0) (endowment of housing at t = 0);

(4) (expenditure for goods) (amount borrowed short-term) + (deposits and interest payment )+ (private monetary endowment in s);

(5) (short-term loan repayment) (housing sales in s);

(6) (quantity of housing sold in s) (endowment of housing at t = 0) - (quantity of housing sold at t = 0),

where:

: fiat money in the good's market in

: amount of housing offered for sale in

: endowment of housing at t = 0.

Mr. enters the economy in the second period and is endowed with goods. His maximization problem is as follows:

subject to:

(1) (expenditure for housing) (amount borrowed short-term) + (private monetary endowment in s);

(2) (short-term loan repayment) (good sales in s);

(3) (quantity of goods sold in s) (endowment of goods in s),

where:

: fiat money in the housing market in s,

: amount of goods offered for sale in s,

: endowment of goods in s.

1.1.2 Banks

Bank г maximizes its expected profits in the second period. In the first period it borrows from the interbank market, since it is relatively poor in initial capital, and extends credit in the short-term loan and mortgage markets. It also receives deposits from ц. In the second period it receives the repayment on the mortgage it extended (full repayment for partial elsewhere since the value of the collateral is less than the amount of the mortgage), repays its interbank and deposit borrowing and extends credit short-term. Its maximization problem is as follows:

subject to:

(1) (short-term lending) + (mortgage extension) (interbank loans) + (consumer deposits) + (initial capital endowment at t = 0);

(2) (short-term lending) + (deposit repayment) + (interbank loan repayment (effective mortgage repayment) + (initial period short-term loan repayment) + (capital endowment in s),

where:

: profits = short-term loans repayment in s;

: bank г's risk-aversion.

Bank д maximizes its expected profits in the second period. In the first period it deposits in the interbank market, since it is relatively rich in capital, and extends credit in the short-term loan and mortgage markets. In the second period it receives the repayment on the mortgage it extended (full repayment for partial elsewhere since the value of the collateral is less than the amount of the mortgage), receives payment from depositing in the interbank market and extends credit short-term. Its maximization problem is as follows:

subject to:

(1) (short-term lending) + (mortgage extension) + (interbank deposits) (initial capital endowment at t = 0);

(2) (short-term lending) (effective mortgage repayment) + (initial period short-term loan repayment) + (interbank deposits and interest payment) + (capital endowment in s),

where:

: profits = short-term loans repayment in s;

: bank г's risk-aversion.

1.2 Market clearing and equilibrium

There are seven markets where agents act and all of them clear; the goods market, the housing market, the mortgage market, the short-term loans market, the consumer deposit market, and the interbank market.

The goods market clears when the amount of money offered for goods is exchanged for the quantity of goods offered for sale. The housing market clears when the amount of money offered for housing is exchanged for the quantity of housing offered for sale. When agent h defaults on his mortgage the amount of housing pledged as collateral is offered for sale by the bank that seizes it. The mortgage market clears when the amount that agents promise to repay is equal to the amount they borrow plus interest given by the mortgage rate. The effective return on mortgages has to be equal to the mortgage rate for the states that agents do not default and equal to the value of the collateral divided by initial mortgage extension for the states that agents default. The short-term money market clears when the amount of money which consumers offer to repay at the end of the period is exchanged for the amount of money lent by the banks at the equilibrium interest rate. The same holds for the consumer deposit market and the interbank market.

Equilibrium is reached when all agents optimize subject to their constraints, expectations are rational and markets clear.

housing mortgage loan default

2. Initial equilibrium

Hereafter, we investigate a parameterised version of the model whereby in the second period only three states of nature are possible. We have chosen the exogenous parameters in our model in such a way as to be able to illustrate a housing and mortgage crisis.

In the initial equilibrium we examine three different scenarios which can occur in the second period. State 1 occurs with the highest probability and state 2 is more probable than state 3. State 1 is the good period in which neither borrower defaults. In state 2 one of the two agents, Mr. в, defaults on his mortgage debt, but the other does not. In state 3 both default. Mr. б is richer in endowments of the good in the first period, whereas Mr. в is relatively richer in the second state in the second period. Bank г has less initial capital than bank д, while it has more capital in the second period. The capital of both banks in the second period can be interpreted as outside banking profits or capital injections obtained in the second period and will play a crucial role in the comparative statics we perform. We have chosen the parameterization to motivate lending in the interbank market and in particular to motivate bank д to deposit in the interbank rate.

2.1 Comparative statics

We examine how the initial equilibrium and the level of default change when (1) the Central Bank engages in a contractionary monetary policy at t = 0 and (2) banks become more risk-loving. Finally, we simulate the model combining both shocks.

2.1.1 Contractionary monetary policy

Let the Central Bank engage in contractionary monetary policy by decreasing the money supply in the interbank market in the initial period (or equivalently increasing the interbank interest rate). This pushes the interbank rate up and bank г borrows less from the interbank market and therefore to reduce its supply of short-term loans and mortgages to Mr. б and Mr. ц pushing the corresponding lending rates up. Mr. в faces stricter credit conditions in the short-run and he demands more mortgages which pushes up the mortgage rate for him as well. Since there is less money in the economy from the Quantity Theory of Money the prices of the good and housing go down in the last period as well. Consequently, effective returns on mortgages, when agents default, go down and in combination with the higher mortgage rate, they result in higher default levels. Expected banking profits go down, since the higher mortgage rates are not enough to outweigh the negative effect of increase default on mortgages.

In sum, according to the Goodhart - Tsomocos financial stability measure, contractionary monetary policy results into higher financial instability since lower banking profits and higher default lead to welfare loses in the bad states of nature.

2.1.2 Banks become more risk-loving

The change in risk-aversion is anticipated in the initial period. Their first response will be to switch from safer to riskier investments. Consequently, extension of mortgages goes up and short-term lending goes down, which means lower mortgage and higher short-term rates in the initial period. Mr. б and Mr. в increase their mortgage borrowing and reduce the sales of their goods. Consequently, Mr. ц is forced to sell more of his housing in order to purchase goods as the total amount of the latter available for sale in the second period went down. Higher mortgage extension and more foreclosures in the last period due to more housing kept as collateral leads to lower prices and consequently to lower effective returns. Even a minimal increase in the appetite for risk results in a 0,5% increase in aggregate default. Expected banking profits go up, since banks enjoy higher expected due to increased mortgage extension. However, banking profits in the bad states of the world will go down due to increased levels of default. According to the Goodhart - Tsomocos financial stability measure, this results into higher financial instability.

2.1.3 Compounding shocks

The comparative statics we examine above do not fully exhibit what we might expect to observe in a severe mortgage crisis. For that reason we have performed an exercise of letting more than one adverse shocks occur at a time. So we allow for contractionary monetary policy and for a decrease in banks' risk-aversion simultaneously.

The reduction in the money supply yields a first order effect pushing the interbank rate up. Bank д increases its interbank lending and reduces its mortgage extension. The reduction in risk-aversion will moderate this pressure. The trade-off between these two effects will determine whether bank д will extend more mortgages or not. In our simulation we find that mortgage extension by bank д increases. The reduction is more severe for bank г, since it is more dependent on liquidity injections. Mortgage rates go up, since the demand does not decrease much due to the higher cost of short-term borrowing. Prices of goods and housing in all periods and states go down, as predicted by the Quantity Theory of Money. The pressure is greater due to lower risk-aversion (as discussed above). The result is lower expected returns on mortgages, which translate into higher defaults in conjunction with the fact that mortgage rates were higher to begin with.

Higher default should mean higher mortgage rates, other things being equal. However, a higher appetite for risk pushes mortgage rates down. Nevertheless, these second order effects are outweighed by the increased default due to a lower money supply, as analysed in the preceding section. Interestingly, default increases disproportionally when contractionary monetary policy is combined with a higher appetite for risk by banks. When these adverse shocks occur at the same time, expected repayment on mortgages falls more than the aggregate change when they happen independently. In particular, nonlinear effects are not trivial as shown in Fig. 2.

Fig. 2. Nonlinear effects

Expected banking profits go up. On the one hand lower money supply and increased default put downward pressure on expected profits and on the other lower risk-aversion pushes them up. In our exercise the latter forces prevail, but the effect of the former becomes more intense as the money supply continues to decrease. Nevertheless, profits in the states that default occurs are lower resulting into higher financial instability.

Conclusions

In order to study the current financial crisis one needs a model which at least incorporates money and monetary policy, optimizing banks, a durable good which can be used as collateral and endogenous default. We provide such a model and find that both contractionary monetary policy before uncertainty is resolved and higher appetite for risk by banks increase financial instability. If the two are combined then the effect on financial instability is more severe.

References

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