An Integrated Framework for Multiple Financial Regulations*

Charles A. E. Goodhart 

Financial Markets Group, London School of Economics 

Anil K Kashyap 

University of Chicago Booth School of Business, Federal Reserve Bank of Chicago, 

and National Bureau of Economic Research 

Dimitrios P. Tsomocos 

Said Business School and St Edmund Hall, University of Oxford 

Alexandros P. Vardoulakis 

Banque de France 

First draft: March 2012 

Abstract 

In this companion paper to Goodhart, Kashyap, Tsomocos and Vardoulakis (2012), we explore 

the interactions of various types of financial regulation. We find that regulations that control fire 

sale risk are critical for delivering financial stability and improving the welfare of savers and 

borrowers. We describe the combinations of capital regulations, margin requirements, liquidity 

regulation and dynamic provisioning that are most effective in this respect. A policy featuring 

margin requirements together with counter-cyclical capital requirements delivers equal or better 

outcomes for the economy than does an unregulated financial system. But it is easy to produce 

combinations of regulation that look sensible but when combined have adverse effects on the 

economy. 

* Prepared for the Board of Governors of the Federal Reserve System and International Journal of 

Central Banking conference on “Central Banking: Before, During, and After the Crisis”, March 23/24, 2012. 

The views in this paper are those of the authors only and not necessarily of the institutions with 

which they are affiliated. Kashyap thanks the Initiative on Global Markets and the Center for 

Research on Securities Prices at Chicago Booth for research support. For information on his 

outside compensated activities, see http://faculty.chicagobooth.edu/anil.kashyap/. All errors are 

our own. 
1

1. Introduction 

Donald Kohn has a remarkable ability to attack problems using many approaches and 

incorporating insights from a variety of perspectives. This flexibility was critical to the success 

of his leadership within the Federal Reserve during a period when both the economy and our 

understanding of the economy were constantly evolving. When his career began the concept of 

“macroprudential financial regulation” did not exist. Instead, the U.S. and much of developed 

world was saddled with a set of outdated regulations that contributed to macroeconomic 

instability in the 1970s. By the time Don retired from the Federal Reserve the landscape of 

central banking had changed and the term macroprudential was part of the standard lexicon of 

central bankers. We share the Kohn (2011) view that “the consistent and systematic application 

of this [macroprudential] perspective to highly sophisticated globally integrated markets and 

institutions as is now being undertaken in the UK, US, and other advanced economies is in its 

infancy.” 

Kohn (2010) argued that policymakers should “use regulation and supervision to 

strengthen the financial system and lean against developing problems. Given our current state of 

knowledge, monetary policy would be used only if imbalances were building and regulatory 

policies were either unavailable or had been shown to be ineffective. But, of course, we should all 

be working to improve our state of knowledge, so as to better understand economic and financial 

behavior and to further expand the range of policy tools that can be employed to enhance 

macroeconomic performance.” 

In this paper we take up Don’s challenge to explore the range of policy tools beyond the 

short-term interest rate that can be used to contribute to macroeconomic stability. Our starting 

point is the framework introduced in Goodhart, Kashyap, Tsomocos and Vardoulakis (2012) 

(henceforth GKTV (2012)). That model was built to study an economy that is at risk of an 

occasional asset price collapse. The novel feature of the model is the inclusion of both a 

traditional banking and a “shadow banking system” that each helps households finance their 

expenditures and smooth their consumption inter-temporally. But if asset prices collapse, the 

consumers default and the financial system amplifies of the default. The financial amplification 

creates a number of distortions. 
2

In our initial paper we mostly concentrated on how a range of regulatory tools, used in 

isolation, could enhance stability. One of the main lessons from that exercise was that tools 

should be grouped according to the distortions that they addressed, rather than on the incidence of 

the regulation. For example, a loan to value regulation that reduces the leverage that a consumer 

can take on and margin requirements on repurchase agreements between banks and shadow banks 

share an important similarity. Both of these regulations limit the extent to which risks can build 

up ahead of an asset price collapse by limiting credit availability. So even though their 

immediate effect is to constrain different agents in the economy from taking risks, in general 

equilibrium the price effects transmit the constraints across the entire economy. Therefore, in 

many respects these two tools are closer to being substitutes than complements because their 

first-order impact is to limit the buildup of risks. Other tools might slow an asset price boom that 

is already underway, or serve to strengthen the financial system after an asset price collapse. 

In this paper we explore the interactions between different tools much more 

comprehensively than in our earlier work. In particular, we focus on combining regulations to 

study their joint effects when they are simultaneously deployed. We find that controlling fire-sale 

risk is critical to improving overall economic performance. But not all strategies of controlling 

for this risk are equally effective. The intuition for why some combinations work better than 

others is subtle and depends critically on the channels through which different tools operate. 

While this research program is still very early, we believe it is also already showing signs of the 

promise of pursuing the Kohn agenda of considering alternative tools for financial stability. 

Section 2 of the paper briefly reviews the modeling philosophy that distinguishes our 

approach from the orthodox approach that prevailed prior to the financial crisis. Section 3 

reviews the model in general terms, although for details the reader should consult GKTV (2012). 

Section 4 presents the baseline equilibrium in the economy and briefly shows how the 

equilibrium is altered by the five regulatory tools we consider in this paper. Section 5 provides 

the new contributions from this paper that relate to combination policies of the different tools, 

including some intuition that we believe is helpful for more general settings than those we are 

currently able to model. Section 6 concludes. 
3

2. Modeling Philosophy 

The ruling workhorse models used by central banks prior to the financial crisis that began in 2008 

essentially ignored the financial system (see for example, Woodford (2003)). This was especially 

ironic since the four professional economists who were Governors of the Federal Reserve System 

in 2007 (Bernanke, Kohn, Kroszner and Mishkin) each gave at least one speech in 2007 

emphasizing the risks that financial instability posed for the economy.1 But the fact remains that 

in journals and the leading graduate programs this view was not widely shared. 

 Subsequent to the crisis the profession has scrambled to correct this problem. But in our 

view most of the responses continue to carry the baggage that had built up prior to the crisis when 

financial factors were considered a side-show. So before getting into the details of our approach, 

it is helpful to review of the direction followed by most people working on these issues. The core 

question is how to model default. 

The typical assumption in most of the literature is that economic agents will always honor 

their contractual obligations in all cases. One reason for the “no default” assumption is the 

argument that the appropriate design of contracts will include sanctions that diminish the 

incentives of debtors to default. Indeed, a large literature following Kiyotaki and Moore (1997) 

presumes that borrowers pledge a level of collateral that fully protects lenders even in the most 

adverse scenario. However, such exhaustive terms can impede more efficient levels of intertemporal smoothing and result in lower welfare. As shown in Dubey et al. (2005), positive 

default in equilibrium can be welfare improving when asset markets are incomplete and 

economic agents cannot write comprehensive contracts. 

The standard approach in the macroeconomics literature that includes monetary policy 

decisions and financial frictions began with Bernanke et al. (1999). In that set up the fundament 

financing problem comes because a borrower’s net worth would be too low to permit repayment. 

So shocks to borrowers’ net worth become a central driving factor in the economy. But financial 

                                                            

1 See for example Bernanke (2007), Kohn (2007), Kroszner (2007) and Mishkin (2007) and in fact most of them 

gave more than one speech on this topic. 
4

intermediaries can hedge against (aggregate) default coming from the real sector and thus avoid 

losses. 

Moreover, the easiest way to incorporate financial frictions into a macro model without 

elaborating on the structure of the financial system is to add an exogenous credit-risk premium 

into the expenditure function, a la Curdia-Woodford (2010). But the exogeneity of that creditrisk premium means that such an approach offers no guidance about the factors that cause 

financial crises. 

Our analysis goes in a different direction by allowing for default by financial 

intermediaries themselves. This implies that defaults can directly interfere with the supply of 

credit. This raises a host of new distortions and potential scope for regulatory interventions. We 

think that satisfactory models for studying macroprudential regulation must include the 

possibility of credit supply shocks. 

3. Model Structure 

We analyze a specific parameterization of the GKTV (2012) model. The full notation (see Table 

A-1) and model equations are given in appendix I and II, but for a longer explanation of the 

details see GKTV( 2102). So what follows is a brief, intuitive summary of the model and its 

properties. The model describes a two period endowment economy with two goods and 

heterogeneous agents. In the first period, households trade to rebalance their endowments. In the 

second period a shock occurs which determines whether that period’s endowments will be high 

or low. Households seek to smooth their consumption over time (and across goods). 

One household type (R) is very well endowed with “housing”, which is a durable good. A 

second household type is less well endowed with “potatoes”, a non-durable. Some of the agents 

who are endowed with potatoes (P) live and consume in both periods, and others (F) enter the 

economy in the second period as first time buyers and serve the role of supporting the demand for 

housing.2 

                                                            

2 If the first time home buyers were absent, then in the event of default all the goods would wind up being by the 

same agents, in which case default is much less important than in real situations where defaulting agents do not 

merely get to reacquire any assets against which they had borrowed. 
5

The two types of households trade with each other using money as the stipulated means of 

exchange. The role of the financial system is to intermediate funds between borrowers and 

lenders. Most importantly, it supplies credit to support purchases and facilitate the inter-temporal 

smoothing of consumption. 

In the benchmark equilibrium that we study the R households are relatively rich. For 

these households the combination of their endowment and their monetary holdings are sufficient 

to allow them to fully smooth their consumption (across potatoes and houses in each period and 

between periods). In contrast, the other households need access to the financial system to avoid 

having large swings in consumption. This asymmetry is important because it means that 

regulation will mostly not affect the welfare of the R households, because they can use other 

strategies besides relying on the financial system to achieve their goals. But the defensive 

response of the rich households to regulation can have potentially important effects of the other 

households. 

The desire to study the potential effects of regulatory arbitrage leads us to allow for two 

types of financial institutions, a commercial bank (B) and a shadow bank (or equivalently a nonbank, N). Household R, being the natural lender, deposits some of the revenues from housing 

sales with a commercial bank, which extends credit to household P in order to accommodate its 

housing purchases in the initial period. Deposits are unsecured, while credit to household P takes 

the form of a mortgage contract with the houses bought pledged as collateral in the event of 

default. Mortgages mature at the end of the second period while deposits are optimally withdrawn 

in the beginning of that period, thus creating a maturity mismatch and a need for liquidity by the 

commercial bank. 

Apart from collecting deposits and extending mortgages, the commercial bank offers 

short-term loans to all households to facilitate their transactions in every period. Short-term loans 

are repaid at the end of the respective period and are free of credit risk. B faces a portfolio 

problem and can choose to securitize some of the mortgages it extended and package them in 

mortgage backed securities (MBS). The shadow bank having a higher appetite for risk is the 

natural buyer of these securities. Securitization allows the commercial bank to extend more credit 

without compromising its liquidity position. In addition, the introduction of a new asset (MBS) 
6

enhances the hedging opportunities of the commercial bank. N finances its MBS purchases with 

its own capital and a repo loan from the commercial bank. The purchased MBS are pledged as 

collateral in the event of default. 

Notice that this formalization of the shadow banks system delivers two nice properties. 

First, the regulatory structure can play a role in governing the extent of securitization and hence 

the size of the shadow banking system (see Tucker (2010)). In particular, differences in the risk 

weights associated with mortgages and MBS for purposes of bank capital assessments will be one 

factor that determines whether housing finance is provided by the banking system or the shadow 

banking system.3 Moreover, in the event of default on the mortgages the impaired MBS are at 

risk for flowing back onto the books of the banks. This was an important accelerant in the crisis, 

at least in the U.S. (Adrian and Shin (2009)). 

 Finally, the bank funds its operations with its equity capital, deposits and with short-term 

borrowing (dubbed discount window loans) from the “central bank”, which stands in for the rest 

of the world. The borrowing from the central bank is always limited to what can completely be 

repaid. 

One important simplification is to assume that both the bank and non-bank are risk averse. 

If we assumed the financial institutions were risk neutral then their willingness to take risk would 

lead to a number of extreme portfolio choices. We view the risk aversion as a short hand way of 

modeling the many efficiency costs and managerial reputational costs that accompany a default 

and limit risk-taking. 

The decision to default is endogenous and depends on the relative value of collateral to 

the value of the loan obligation. Accounting for additional costs of default, such as reputational 

penalties, it is individually optimal for household P to default on its mortgage and have its house 

foreclosed when the market value of collateral is low enough. Similarly, the shadow bank may 

choose to surrender the MBS it holds when mortgages, which are the underlying asset, are in 

default. As discussed below, the fall in housing prices and the subsequent defaults on mortgages 

                                                            

3 This is not the only reason why shadow banks exist. Even with identical capital charges for mortgages and MBS, 

their assumed differences in risk aversion create an incentive to securitize and even with no differences in risk 

aversion, there would still be pure diversification benefits to sharing the housing risk. 
7

creates a number of knock-on effects: fire-sales, margin spirals, and a credit-crunch. Financial 

regulation tries to mitigate the adverse effects of default due to a fall in asset/house prices. 

Regulation can be imposed either on the contributors to risk, i.e. household P and the shadow 

bank, or instead on the commercial bank, which is directly exposed to housing price risk and can 

amplify this risk when it defaults on its depositors. 

Figure 1 presents the structure of the model, the financial relationships and the flow of 

goods and houses in the real economy. We should note that this research program is just 

beginning and the modeling approach is very flexible. The general equilibrium setup with fully 

endogenous prices, portfolio decisions and default allows for this. So this model is better thought 

of as a framework for comparing different potential financial externalities under various market 

structures. Hence the longer term conclusions about regulatory design will depend on analyzing 

many variants of the model and determining which are robust to the many possible formalizations 

of the financial system. 

Figure 1: Structure of the Economy 

To understand the model it is helpful to realize that the only uncertainty in the model 

stems from whether the quantity of potatoes in period two is high or low relative to the amount of 

houses. When potatoes are abundant then the borrowers from the first period can repay their 

loans and potentially even acquire more housing. So in this case there is no default and instead 
8

the financial institutions (and agents R and P who are also housing owners) experience capital 

gains on those assets. The only actor that suffers in this case are the new homebuyers, F, who 

face high home prices and have to compete to rent it with others in the economy who are 

rebalancing their portfolios to reflect the capital gains. 

The outcomes are much more subtle and complicated when the endowment of potatoes is 

low because in this case house prices will collapse. This collapse is unavoidable and default on 

mortgages is optimal from an individual’s point of view. However, there are several channels 

through which the financial system may amplify the initial impulse that will lead to other 

inefficiencies. Regulations may be useful if they can limit this amplification. 

The trigger for any amplification starts with the choice of the non-bank over whether to 

repay the repo loan or return the MBS which serve as collateral on the loan. Arbitrage guarantees 

that the effective return from buying MBS backed by defaulted mortgages must be same as 

buying the underlying houses. So mortgage default must depress MBS prices. When the fall in 

housing prices is big enough, it becomes rational for the N to suffer the reputational penalty 

associated with defaulting and return the collateral rather than repay the loan. In this case, the 

bank not only sees its asset values drop because of its losses on the mortgages that it retained, but 

also because the MBS it finds returned are worth less than the loan it was carrying on its books. 

Given the asset impairment, B faces a decision over whether to default on its deposit 

obligations. In deciding whether to honor its deposit contracts the bank trades off a reputational 

penalty associated with default, against the profits that can be had from deploying the resources 

for other investments. 

One alternative to defaulting is for the bank to sell assets to pay off the deposits. 

However, the only assets which can potentially be sold at the time when the deposits are due are 

the MBS that have been returned by the shadow banks. Depending on the availability of buyers to 

purchase MBS, selling assets may contribute to a fire-sale. 

We assume that MBS prices are subject to cash-in-the-market pricing (Allen and Gale 

(1994)) whereby that the value of the MBS is determined by the wealth of the potential buyers of 

the assets rather than the future cash flows generated by the assets. The shadow bank, which is 
9

the natural buyer of mortgage backed securities, finds its capital depleted in the state of the world 

where housing prices collapse. Thus, given the limited resources of the shadow banks, the more 

MBS that the commercial bank returns to the market, the lower is the price of MBS. This simple 

formulation is intended to capture the Shleifer and Vishny (2011) characterization of a fire sale 

whereby prices for assets are depressed because the natural buyers of the assets are impaired at 

the time of sale. Obviously, any regulation that limits the size of the initial repo default can 

potentially influence the size of the fire sale. 

But the presence of the fire sale also creates three follow-on effects. The first comes 

because banks must make an active portfolio choice between holding onto its mortgage backed 

securities and extending new loans. The bank is assumed to be unable to issue equity (in the 

immediate aftermath of the bad shock), so its balance sheet capacity is limited. Thus, the bank 

must trade off using its capital to hold a mortgage backed security or to initiate new loans. So the 

losses on the MBS sales from the cash-in-the-market pricing tighten this capital constraint and 

potentially create a “credit crunch” for new borrowers (in that the bank’s capital problem reduces 

the supply of loans that are available). 

The second potential inefficiency comes because the repo default also raises the incentive 

for the bank to default on its deposit contracts. The losses to the depositor (R) reduce his wealth, 

causing him to sell additional housing to finance his purchases of goods. The additional housing 

sales will lead to lower housing prices. 

Finally, there is a third channel that arises from the interaction of the cash-in-the-market 

fire sale and the other two follow-on effects. B always considers the arbitrage relation between 

MBS prices and the price of houses. When the bank receives the MBS that are issued against 

defaulted mortgages (from the shadow bank), either it can hold the MBS to maturity or it can sell 

the MBS right away, which depresses further not only MBS but also house prices. Therefore, the 

model also embodies the kind of downward spiral described in Brunnermeier and Pedersen 

(2009). 

One prominent feature of the model is the asymmetry between the rich households and 

the other agents in the model. The combination of the risky deposit, money which can be used as 

a store of value, and the durable asset means that household R can invest in ways that protect 
10

itself from financial problems. But the way in which R responds to different risks or regulations 

will matter for the other agents. To take one particularly important example, depending on the 

extent of fire sale risk, R will decide whether to retain some housing that can be sold in the 

second period (rather than saving through the banking system or with money). If R is selling 

more housing in the second period and the good state materializes, then the extent of the house 

appreciation in that scenario is limited (relative to the case where R is selling less). The relative 

price of housing is a key factor in determining whether P and F’s welfare rises or falls. So even 

though R may be relatively immune to interventions that alter the financial system, R’s response 

to these developments can be critical. This is why a full general equilibrium model is needed to 

study regulation and why partial equilibrium reasoning can be potentially misleading. 

4. The Baseline Equilibrium and the Role of Financial Regulation 

The remainder of our analysis proceeds using particular choices for the model parameters. The 

assumed values for endowments, wealth, financial institution’s capital, central bank lending rates, 

default penalties, risk aversion, probabilities of good and bad states, discount rates and housing 

depreciation rates are given in Table A-2 in appendix I. 

In reviewing the calibration keep in mind that a period is presumed to be 5 years, so with 

the probability of the bad state being 10 percent, a crisis would be expected roughly every 50 

years. We see the key choices in Table A-2 as relating to those that directly govern the size of 

the fire sale in the bad state. As we just explained, when the fire sale risk is large then financial 

sector amplification of the initial house price decline is strong (and vice versa). 

The two most important factors directly affecting the fire sale are the wealth of N 

(because that influences the degree of cash-in-the-market pricing) and the endowments of P and F 

who are the house price buyers. The baseline version of the model (see Table A-3) is calibrated 

so that MBS prices fall by 26% in the crisis (and rise by 44% in the boom), so that the real estate 

collapse is very much in line with the recent U.S. experience; the fire sale involves the bank 

selling only six percent of the MBS that it receives back as collateral. 

In a crisis households default on mortgages by only repaying 45 cents on each 1 dollar 

borrowed. The down payment that they make is assumed to 37% of the mortgage. The bank’s 
11

willingness to permit the household to have more leverage is tempered by the bank’s own risk 

aversion. One direction for future work is to explore the effects of presuming more willingness 

to take risks by the banks and non-banks. The banks in the current version repay 60 cents on 

every dollar of deposits.4

 

Before exploring the effects of regulation on the equilibrium it is helpful to note the 

channels through which regulation can improve the welfare of the households and financial 

institutions. Cataloging the various channels makes it easier to see the distributional effects of 

different policies. 

R’s welfare is almost immune to regulatory interventions as he can undo almost all 

adverse effects by re-optimizing his mix of deposits and housing sales. However, as demonstrated 

above his actions create pecuniary externalities through relative prices on P and F because they 

do not face complete markets. As a rule he will save more through the banking system when 

defaults are less severe. But, the attractiveness of retaining housing and selling the extra housing 

also depends on the size of the fire-sale and the house price collapse in the bad state. In order for 

a policy to make R definitely worse off, it must effectively reduce his wealth by making his 

endowment less valuable by changing the relative price of potatoes and houses, otherwise he can 

adjust his savings strategy to evade the effects – we will see that there are regulations that can 

operate this way. 

P can gain if he can get more housing in period 1 or 2, (or if in a crisis he defaults less). 

He can increase his first period housing if more short-term lending in period 1 becomes available 

or more mortgage lending in period 1 is available. He can acquire more housing in the good 

state in period 2 if its relative price is lower because R is selling more, or if short-term lending 

terms are better. 

F’s gains depend solely on the relative price of potatoes to houses. In the good state, he 

can get more housing if potatoes prices are high, either because R is selling more housing or if 

short term lending terms are better so that the same amount of potatoes can support a higher 

                                                            

4

 The repayment rate can also be thought of as the expected probability of default when the decision to default is 

endogenous and there is no repayment on deposits in the event of default. 
12

housing purchase. In the bad state, if the relative price of housing is lower, then he can buy more 

of it. 

B gains in the good state when it makes more capital gains on the mortgages that it holds 

on the balance sheet. So, ceteris paribus, this can happen if it retains more mortgages or if it sees 

a bigger price appreciation on houses. Its welfare in the bad state depends on the size of its 

default. It also gains whenever the spread between its lending rate and its cost of funding is 

higher (in either period 1 or 2). 

Finally the shadow bank gains in the good state when it makes more capital gains on its 

MBS holdings. These gains come from being able to hold more MBS or from larger house price 

appreciation. In the bad state, the non-bank gains if its default is smaller. 

With these mechanisms in mind we explore the potential effects five regulatory tools: 

limits on loan to value ratios, capital requirements for banks, liquidity coverage ratios for banks, 

dynamic loan loss provisioning for banks, and margin requirement on repurchase agreements 

used by shadow banks. The point of each of the regulations is to limit the consequences of the 

housing price collapse. Each of these interventions will limit fire sales in the bad state by 

reducing either the size of the non-bank’s default on its repo loan or the size of the bank deposit 

default. 

But because they differ in ways of inducing this stability the effects can differ across 

agents. In particular, margin requirements, liquidity requirements, loan to value and initial 

capital requirements all directly reduce mortgage lending in period 1. They differ in whether 

their incidence limits bank or non-bank lending more. The capital requirements in period 2 

guarantee that banks are healthier after a default occurs to reduce directly the costs of the default; 

the equilibrium adjustments though involve large lending changes in period 1. Dynamic 

provisioning damps the credit boom in the good state and thus only indirectly influences the 

fallout from a house price drop. The precise mathematical formulas for the regulations are given 

in appendix III. In the text we focus on the key prices and quantities that govern welfare for the 

households and financial institutions. 
13

Loan to value (LTV) requirements force households to use more of their own wealth to 

obtain a mortgage loan. The effects on the key endogenous variables in the model are shown in 

Table 1. This regulation is unique among those we consider because it directly acts on P to limit 

his ability to obtain credit, rather than creating incentives for the bank or non-bank to extend less 

credit. Because the bank is risk-averse it will prefer smoother profit streams to more variable 

ones, so given that P will be able to obtain less total credit B will spread this reduction over both 

the first and second period. Since the households endowed with potatoes are the primary 

borrowers in the economy, this credit contraction forces them to sell more potatoes which lowers 

the price of potatoes relative to houses in both periods. 

Table 1: Impact of Alternative Regulations on Key Endogenous Variables 

 (Change relative to baseline equilibrium) 

 LTV MR CR1 CR2b LCR1 DP 

Securitization - - + + + + 

Relative price of potatoes to housing-good state - ≈0 ≈0 + + + 

Profits of the Bank period 1 + + + - - - 

Profits of Bank good state + + - - - - 

+ indicates increase, - indicates decrease, ≈0 indicates no change 

Table 2: Impact of Alternative Regulations on Household Utilities and Financial Institutions’ 

Welfare (Change relative to baseline equilibrium) 

 LTV MR CR1 CR2b LCR1 DP 

P’s Utility - ≈0 + + + + 

F’s Utility - ≈0 ≈0 + + + 

R’s Utility ≈0 ≈0 ≈0 ≈0 - - 

B’s Payoff + + + - - - 

N’s Payoff + + ≈0 - ≈0 - 

+ indicates increase, - indicates decrease, ≈0 indicates no change 

The impact on the different agents is shown in Table 2. Given the reduction in relative 

price of potatoes, both P and F suffer from increasing the down-payment requirements on houses. 

The higher relative prices of houses deliver slightly higher capital gains on mortgages and MBS 

for the financial institutions in the good state. But more importantly, the lower loan to value ratio 

makes the homeowner absorb more of the losses from a home price collapse, so that the financial 

institutions’ defaults are much lower than without the loan to value regulation. 
14

Margin requirements force non-banks to pledge more equity to secure their repo loans. 

This reduces the attractiveness of securitization and so that relatively more of the housing 

financing that occurs comes via mortgages that remain on the balance sheets of the banks. These 

changes in the structure of financing benefit the banks in two ways. First, by virtue of a higher 

market share in housing financing the banks capture more of the gains from the house price 

appreciation in boom scenario. Second, the non-banks’ higher equity contribution reduces the 

size of their repo default. This latter effect also benefits the bank. Households are essentially 

unaffected by the imposition of margin requirements: the relative price of houses is not much 

affected, and while P has a smaller default that is because he was able to acquire less housing in 

period 1. 

Capital ratios for banks in the baseline equilibrium are higher in period 1 than in the bad 

state.5

 The starting capital positions, therefore, are counter-cyclical. So, care must be taken in 

thinking about which comparative static exercise to consider: a local perturbation to either the 

first period ratio or ratio in the bad state will mean that the counter-cyclical rule would still be in 

place. Alternatively, one can examine a large enough change in the capital requirement in the 

bad state so that it becomes equal to the level observed in the good state. We first describe the 

local experiments and explore combined changes in the last section of the paper. 

Raising the capital requirement in period 1 induces the bank to hold fewer mortgages on 

its balance sheet. It substitutes by securitizing more of the mortgages it originates and by making 

more short-term loans in period 1. This portfolio shift generates slightly more profits in period 1 

and fewer profits in the good state. But the bank’s default is much lower in the bad state, which 

makes B better off. Because P is able to obtain less mortgage credit his default is less severe, so 

he also is better off. As usual R is essentially unaffected. The relative price of houses and 

potatoes are not altered enough to change the outcomes for F. The non-bank becomes riskier by 

virtue of the additional MBS that it is holding: this generates additional profits in the good state 

and default in the bad state larger. On net N’s welfare is about the same. 

                                                            

5

 In the good state all assets are essentially risk-less so capital ratios are technically infinite. 
15

Raising capital requirements in the bad state triggers several general equilibrium 

responses. First, the bank does less mortgage lending in period 1 to avoid losses in period 2. The 

bank’s reduction in mortgage financing means that the bank also needs fewer deposits, so that R 

saves more using his housing endowment. This leads R to sell more houses in period 2, raising 

the relative price of potatoes in both states, making both P and F better off. The lower relative 

price of houses in the good state, and the lower overall reduction in first period mortgages means 

N is worse off. B suffers for these reasons (and also because its profits are lower in period 1), but 

does default by less when house prices crash. The net effect is still negative for the bank. 

Liquidity requirements can also be applied in the first period or during the second period. 

Imposing liquidity requirements in the bad state leads to a massive fire sale because the only way 

for the bank to obtain liquidity is to sell its MBS. So this regulation makes no sense to consider.6

 

Imposing liquidity requirements during the good state runs into the same problem as imposing 

capital requirements during booms. When asset prices are high many assets can be easily sold. 

So to make this ratio bind, the regulation would have to be extremely aggressive, changing 

substantially as a boom developed. Since we do not view this as plausible we also do not 

consider this regulation. 

These choices leave a first period liquidity requirement for consideration. Banks meet 

this kind of liquidity requirement by making more short term loans in period 1 and by 

securitizing the mortgages it does make – notice the similarity to the period 1 choices that are 

made by the bank when it is faced with an ex-post capital requirement. The bank sees profits fall 

in period 1 and the good state, and it is not better protected against default in the bad state. So the 

bank sees its payoffs reduced. The non-bank (just as with the initial capital requirement) sees its 

risk rise due to the additional securitization, but on net its overall payoff is not much affected. 

Because it has reduced mortgage issuance the bank also reduces its deposit taking, which pushes 

R to do more saving using its housing endowment. The additional housing sales in the second 

period make F and P better off; P also benefits from defaulting less due to having less housing 

                                                            

6

 We conjecture that this intuition that it is dangerous to impose a common liquidity requirement all the way through 

a credit cycle will carry over to other versions of the model. 
16

credit. R’s utility drops very slightly because the housing sales in the good state are so large that 

they create a big decline the relative price of houses, reducing his purchasing power. 

Finally, it is possible to use dynamic provisioning, which we formalize as a direct tax on 

increasing real estate related lending in the good state. This makes it very different than the other 

tools in two respects. First, it is the only one of the regulatory options that it is targeted directly 

at leaning against the credit boom. Second, it is the only regulation that by construction must 

impair R. Normally R has portfolio substitution possibilities involving shifting savings between 

deposits and housing that allow him side-step regulation. But by making real estate lending more 

expensive in the good state, dynamic provision acts as a tax on R’s endowment and forces him to 

sell more houses at a lower price. This leaves R worse off and P and F better off. Because the 

bank and non-bank both make much lower capital gains in the good state their profits suffer as 

well. 

5. Combined Regulations 

The foregoing results suggest combinations of regulation that should work well together and 

those that would not be expected to interact well. We proceed under the assumption that the goal 

of financial regulation to increase stability and credit availability so that both the financial 

institutions and the households are better off relative to the unregulated equilibrium. As a 

practical matter we have seen that R’s utility is very insensitive to regulation, so we concentrate 

on the other agents. 

 From Table 2 we can see that certain tools are likely to be more effective than others. In 

particular, both margin requirements and loan to value regulations increase financial stability by 

making defaults less traumatic, and in doing so make the payoffs to the financial institutions 

higher than in the absence of regulation. But loan to value regulation depresses credit supply 

making borrowers worse off, while margin requirements are much less restrictive. So it appears 

easier to find a bundle that makes everyone better off when margin requirements are used instead 

of requiring larger down payments. 

 Likewise, raising capital requirements in the bad state and dynamic provisioning each 

reduce the relative price of houses in the good state. This benefits P and F at the expense of the 

financial institutions. But dynamic provisioning operates as a tax on R, while the capital 
17

requirements do not. So using ex-post capital requirements should be more attractive than using 

our depiction of provisioning. 

 Capital requirements and liquidity requirements in the initial period are similar in that 

both reduce mortgage extensions and prevent P from defaulting as much in the bust. Capital 

requirements reduce the bank’s default as well, while a liquidity requirement does not. In 

contrast, a higher liquidity ratio raises the relative price of potatoes in the good state which 

benefits F. 

 Taken together these observations suggest that combinations of regulation involving 

margins, capital ratios and the initial liquidity ratio are the most promising to explore. The same 

reasoning suggests that substituting LTV requirements for margin requirements should deliver 

worse outcomes. Table 3 shows the change in welfare relative to the baseline from different 

regulatory packages of this sort – the three-way combinations dominate the two way versions, so 

to limit the possibilities we concentrate on these. 

Table 3: Impact of Combining Regulations on Household Utilities and Financial Institutions’ 

Welfare (Change relative to baseline equilibrium) 

 CR1& CR2b &MR CR1& LCR1 &MR CR1& CR2b <V

P’s Utility + + ≈0 

F’s Utility + - - 

R’s Utility ≈0 ≈0 ≈0 

B’s Payoff + + + 

N’s Payoff + + + 

+ indicates increase, - indicates decrease, ≈0 indicates no change 

 The column one combination includes margins and the two capital ratios. When all three 

are in place, R’s utility is equivalent to that of the baseline and the other agents are better off. 

The regulations interact in interesting ways. In particular, raising capital requirements in period 1 

leads to a carryover of capital into the second period, so that the incremental increase of capital 

needed in the bad state is reduced (relative to the case when capital requirements in the first 

period are not altered). This endogenous response weakens the adverse effects of ex-post capital 

requirements on financial institutions payoffs. Therefore, putting these two requirements 

together a small margin requirement makes everyone at least as well off as in the baseline case. 

 We also considered a combination that involves margins, along with period 1 liquidity 

requirements and capital requirements in the bad state. Any time a liquidity requirement is 
18

imposed, it triggers the same portfolio adjustments by the bank in period 1 as if the bank had its 

capital requirement in the bad state increased. This effect proves so powerful that the capital 

ratio in the bad state becomes so much higher that the regulation is not binding. Hence, these 

bundles amount to studying liquidity requirements, with margin requirements, and a less countercyclical set of capital standards; the capital ratio in period 1 is little affected, but remains above 

the capital ratio in period 2. So it is not really possible to do an isolated experiment that moves 

only margins, ex-ante liquidity and ex-post capital regulations. 

 The second column of table 3 shows a regulatory bundle featuring higher margins, along 

with increased ex-ante capital and liquidity regulations. This combination leaves F worse off. 

Based purely on the individual effects from table 2 this might at first seem surprising. The reason 

why this combination delivers a strange interaction is because it stifles the bank’s ability to 

expand credit. On the one hand, the liquidity requirements forces it to expand short term lending 

(which is naturally limited by the first period wealth of the R and P), while on the other, the 

margin requirements limit the shadow bank’s ability to absorb securitization. Faced with these 

roadblocks the bank cuts total credit, and because of its preference for smooth profits it spreads 

the credit reduction over both period 1 and period 2. P benefits partly because the lower loan 

limits reduce the size of this default in the bad state, but F only sees the reduction in credit and 

winds up worse off. 

 The last combination considered in table 3 shows the effects of packaging capital 

requirements in both periods with tighter loan to value regulation. This amounts to substituting a 

loan to value restriction for a margin requirement. From our analysis of the one-at-a-time 

regulatory interventions we would expect this to be a less good permutation. This intuition is 

confirmed as the welfare of both P and F drop when the LTV rules are imposed.7

 The losses are 

attributable to the reduction in total credit that is induced by the increased down-payment 

requirements – just as when it was imposed as a single regulation. Credit availability falls in both 

periods, so P sees a sharp drop in mortgage credit and F is able to borrow less in the boom state. 

Thus, both borrowers are made worse off by raising down payment requirements instead of 

margin requirements. 

                                                            

7

 To make sure the comparison between columns 1 and 3 is reasonable, we calibrate the increase in LTV in column 3 

to match the endogenous change in the LTV that occurs naturally in column 1. If the LTV and margins were 

identical tools then the equilibrium should not change, but as seen in the table things change considerably. 
19

 We draw three conclusions from the results from analyzing the results in Table 3. First, 

while this model has multiple ways in which the financial system can amplify shocks, it is not the 

case that regulatory interventions with multiple tools is necessarily welfare enhancing. One of 

the more obvious policy packaging that at first glance might be appealing actually is welfarereducing. Indeed, it is easy to put together many other combinations of policies that have 

unintended effects. 

Second, the reason why some of the policy bundles in Table 3 did not work accords with 

the intuition we have emphasized about paying attention to the channels through which 

regulations operate. For example, combining two ex-ante regulations that control bank risktaking is unnatural when considering their expected economic effects, even though blindly using 

the results in Table 2 might suggest trying this combination. The more successful package 

combines regulations that operate via fairly different channels. 

 Finally, and most importantly, the only way to conduct this type of exercise is to use a full 

general equilibrium model. There would simply be no way to guess confidently based on partial 

equilibrium hunches which policies would be complements and substitutes and which ones would 

have unfortunate interactions when they are implemented simultaneously. 

 

6. Conclusions 

Our approach to studying financial regulation highlights the substantial payoff to having a formal 

general equilibrium model that takes a clear stand on the purpose and risks associated with 

having a financial system that includes both banks and shadow banks that deliver funding to the 

economy. Given many complex interactions between the various agents in the model, no single 

regulatory tool is going to be sufficient to offset the many distortions arising from a default. But 

it does appear that a bundle of tools can improve outcomes relative to the unregulated equilibrium 

that the economy would reach. 

 We highlight groups of regulations that work in harmony towards alleviating the knockon effects from asset fire sales. Margin requirements are a valuable complement to other 

regulations because they contribute to the stability of shadow banking system. Similarly, capital 

requirements that force banks to be better capitalized after an asset price collapse also work well 

with other regulatory tools. The ex-post requirement on bank health reduces bank risk-taking and 
20

thereby contributes to the stability of the banking system. It also creates incentives for savers to 

diversify their portfolio choices which bring other benefits. 

 The best regulatory combination that we identify also includes raising capital 

requirements ahead of an asset price boom or bust. This restriction reduces bank risk-taking 

without too severely limiting overall credit supply and also lowers the burden of requiring higher 

capital during bad times. 

 Importantly, we find that indiscriminate combinations of regulations can easily be welfare 

reducing. Simply piling on multiple regulations because there are multiple channels of financial 

contagion is not necessarily good. Instead, wise regulation requires that considerable care is 

taken to anticipate the ways in which policies will interact and to guard against creating perverse 

incentives and reactions. 

 As Kohn (2010, 2011) emphasized, we are in the early days of macroprudential analysis. 

There are still many unanswered questions. But the prospects of addressing these questions using 

this style of general equilibrium model are bright. 
21

References 

Adrian, Tobias and Hyun Song Shin. 2009, “The Shadow Banking System: Implications for 

Financial Regulation”, Federal Reserve Bank of New York Staff Reports, no. 382. 

Allen, Franklin and Douglas Gale. 1994, “Liquidity Preference, Market Participation and Asset 

Price Volatility,” American Economic Review, 84, 933-955. 

Bernanke, Ben S. 2007, “The Financial Accelerator and the Credit Channel” speech at the Credit 

Channel of Monetary Policy in the Twenty-first Century Conference, Federal Reserve Bank 

of Atlanta, Atlanta, Georgia, June 15, 2007 

Bernanke, Ben S., Mark Gertler, and Simon Gilchrist. 1999. "The financial accelerator in a 

quantitative business cycle framework," in: John. B. Taylor & Michael Woodford (ed.), 

Handbook of Macroeconomics, edition 1, volume 1, chapter 21, pp. 1341-1393, Elsevier 

Brunnermeier, Markus and Lasse H. Pedersen, 2009, “Market Liquidity and Funding Liquidity”, 

Review of Financial Studies 22 (6), pp. 2201-2238. 

Curdia, Vasco and Michael Woodford, 2010, “Credit Spreads and Monetary Policy”, Journal of 

Money, Credit and Banking, 42(1), 3-35 

Dubey, Pradeep, Geanakoplos, John, and Martin Shubik (2005), Default and Punishment in 

General Equilibrium, Econometrica 73(1), pp. 1-37. 

Goodhart, Charles A.E., Anil K Kashyap, Dimitrios P. Tsomocos, and Alexandros P. 

Vardoulakis, 2012, “Financial Regulation in General Equilibrium”, National Bureau of 

Economic Research Working Paper Number 17909. 

Kashyap, Anil K, Berner, Richard, and Charles A.E. Goodhart, 2011, “The macroprudential 

toolkit”, IMF Economic Review,59(2), 145–161. doi:10.1057/imfer.2011.4. 

Kohn, Donald, L., 2011, “The Financial Policy Committee at the Bank of England” speech at the 

U.S. Department of the Treasury Conference, 2 December 2011 

http://www.bankofengland.co.uk/publications/Documents/speeches/2011/speech536.pdf 

Kohn, Donald, L., 2010, “Monetary Policy in the Crisis: Past, Present, and Future” speech at the 

Brimmer Policy Forum, American Economic Association Annual Meeting, Atlanta, 

Georgia, January 3, 2010 

http://www.federalreserve.gov/newsevents/speech/kohn20100103a.htm 

Kohn, Donald, L., 2007, “Financial stability and policy issues” speech at the Federal Reserve 

Bank of Atlanta's 2007 Financial Markets Conference, Sea Island, Georgia, May 16, 2007 
22

Kroszner, Randall S., 2007, “Analyzing and Assessing Banking Crises” speech at the Federal 

Reserve Bank of San Francisco, Conference on the Asian Financial Crisis Revisited, San 

Francisco, California (via videoconference), September 6, 2007 

Mishkin, Frederic S., 2007, “Will Monetary Policy Become More of a Science?” Finance and 

Economics Discussion Series: 2007-44, Board of Governors of the Federal Reserve System 

Shleifer, Andrei and Robert Vishny, 2011, “ Fire Sales in Finance and Macroeconomics”, 

Journal of Economic Perspectives, 25(1), pp. 29-48. 

Tucker, Paul 2010. “Shadow Banking: Financing Markets and Financial Stability”, speech at the 

BCG Partners Seminar, London, January 21, 2010 

Woodford, Michael. 2003, Interest and Prices: Foundations of a Theory of Monetary Policy. 

Princeton: Princeton University Press. 

 
23

Appendix I: Notation and Parameterization 

The labeling convention indentifies agents with superscripts (ܲ, ܨ, ܴ, ܤ, ܰሻ, and goods (݌	ܽ݊݀	݄ሻ, 

and periods/states (1, 2݃, 2ܾሻ with subscripts. The following table presents the notation used for 

the exogenous and endogenous variables in the model. Superscripts and subscripts are not shown 

to save space. 

Table A-1: List of variables 

ࢋ Endowments of potatoes or houses ࢉ Consumption of potatoes or housing 

࢟ࢋ࢔࢕ࡹ Monetary endowments of households ࢗ Quantity of potatoes or housing sold 

ࡱ Capital of financial institutions ࢀࡿࡸ Quantity of short-term loans 

ࡼ Prices of potatoes, housing or MBS ࢀࡾࡻࡹ Quantity of mortgages 

࢘

Interest rates on short-term loans, on 

discount window borrowing, on deposits, 

on mortgages or on repo loans 

ࡻࡼࡱࡾ Quantity of repo loans 

࣎

Marginal non-pecuniary penalty for 

default on mortgages, deposits or repo 

loans 

ࡰ Quantity of deposits 

ࢽ Risk aversion coefficients ࡯ࡿࡵࡰ

Quantity of discount window loans 

made by the central bank to the 

commercial bank 

࣓ Probability of good or bad state ࡿ࡮ࡹ Quantity of mortgage backed securities 

sold 

ࣈ Time discount factor ࣌ Percentage of retained mortgages sold 

ࢾ Depreciation rate ࣖ Percentage of returned MBS that are 

re-sold (Rate of fire-sales) 

ࢁ Utility of households ࢂ Repayment rate on mortgages or 

deposits 

ࢌ࢕࢘ࡼ Profit function ࡯࡯ Cash committed for mortgage 

extension by the commercial bank 

࣊ Profits of financial institutions ࢎ࢙ࢇࢉ Cash assets held by the commercial 

bank 

 
24

Table A-2: Exogenous variables 

Endowments of 

goods 

Households’ wealth F.I. capital CB rates Default 

penalties 

Risk aversion Other 

parameters 

݁ଵ,௣

ଵݕ݊݁݋ܯ 10 ൌ௉ 

௉ ൌ 4.1 ܧଵ

஻ ൌ 0.5 ݎଵ

஼஻ ൌ 0.12 ߬ଶ௕

௉ ൌ 4 ߛ ௉ൌ 2.1 ߱ଶ௕ ൌ 0.1

݁ଶ௚,௣

௚ଶݕ݊݁݋ܯ 32 ൌ௉ 

௉ ൌ 4.1 ܧଶ௚஻ ൌ 0.5 ݎଶ௚

஼஻ ൌ 0.12 ߬ଶ௚

஻ ൌ 1.2 ߛி ൌ 2.1 ߦ ൌ 0.85

݁ଶ௕,௣

௕ଶݕ݊݁݋ܯ 5.8 ൌ௉ 

௉ ൌ 0.1 ܧଶ௕஻ ൌ 0 ݎଶ௕

஼஻ ൌ 0.20 ߬ଶ௕

ఉ ൌ 1.2 ߛோ ൌ 2.4 ߜ ൌ 0.15

݁ଶ௚,௣

ி ൌ 11 ݋ܯ݊݁ݕଶ௚ி ൌ 4.1 ܧଵ

ே ൌ 1 ߬ଶ௕

ே ൌ 0.2 ߛ ஻ൌ 1.4

݁ଶ௕,௣

ி ൌ 11 ݋ܯ݊݁ݕଶ௕

ி ൌ 2.1 ܧଶ௚

ே ൌ 2 ߛே ൌ0.7 

݁ଵ,௛

ோ ൌ 1 ݋ܯ݊݁ݕଵ

ோ ൌ 6.5 ܧଶ௕

ே ൌ 1 

݁ଶ௚,௛

ோ ൌ 0 ݋ܯ݊݁ݕଶ௚

ோ ൌ 0 

݁ଶ௕,௛

ோ ൌ 0 ݋ܯ݊݁ݕଶ௕

ோ ൌ 0 

Table A-3: Initial Equilibrium variables 

Prices Interest 

rates 

Aggregate Consumption Loans Securitization Delivery 

rates 

F.I. 

profits 

ܲଵ,௣ ൌ 1.48 ݎଵ

ௌ் ൌ 0.12 ܿଵ,௣

௉

ൌ 0.827 ܿଵ,௣

ோ ൌ 9.173 ܮܵܶଵ

௉

ൌ 12.10

ଵܵܶܮ

஻

ൌ 50.70

ଵܵܤܯ

஻

ൌ 21.95 ܸଶ௚

ெைோ் ൌ 1 ߨଵ

஻ ൌ 0.68

ܲଶ௚,௣ ൌ 1.33 ݎଶ௚

ௌ் ൌ 0.12 ܿଶ௚,௣

௉

ൌ 1.289

ܿଶ௚,௣

ோ

ൌ 41.320

௚ଶܵܶܮ

௉

ൌ 38.48

௚ଶܵܶܮ

஻

ൌ 64.11 ߪଶ௚

஻ ൌ 0.281 ܸଶ௕

ெைோ்

ൌ 0.55

௚ଶߨ

஻

ൌ 1.01

ܲଶ௕,௣ ൌ 1.60 ݎଶ௕

ௌ் ൌ 0.20 ܿଶ௕,௣

௉

ൌ 0.295

ܿଶ௕,௣

ோ

ൌ 15.874

௕ଶܵܶܮ

௉

ൌ 7.33

௕ଶܵܶܮ

஻

ൌ 21.13 ߪ ଶ௕

஻ ൌ 0 ܸଶ௚

஽ ൌ 1 ߨଶ௕

஻

ൌ 1.00

ܲଵ,௛ ൌ 676.02 ݎ ஽ൌ 0.34 ܿଵ,௛

௉

ൌ 0.064 ܿଵ,௛

ோ ൌ 0.936 ܯܱܴܶ௉

ൌ 27.02

ଵܥܵܫܦ

஻

ൌ 44.68 ߴଶ௕

஻ ൌ 0.063 ܸଶ௕

஻ܥܥ 0.60 ൌ஽ 

ൌ 5.60

ܲଶ௚,௛

ൌ 1,111.18

்ெைோݎ

ൌ 0.58

ܿଶ௚,௛

௉

ൌ 0.052

ܿଶ௚,௛

ோ

ൌ 0.783

௚ଶܵܶܮ

ி

ൌ 12.63

௚ଶܥܵܫܦ

஻

ൌ 96.94

௚ଶܵܤܯ

ே ൌ 1.42 ܿܽݏ݄ଵ

஻

ൌ 6.74

ܲଶ௕,௛

ൌ 362.83

ݎோா௉ை

ൌ 0.57

ܿଶ௕,௛

௉

ൌ 0.020

ܿଶ௕,௛

ோ

ൌ 0.796

௕ଶܵܶܮ

ி

ൌ 13.80

௕ଶܥܵܫܦ

஻

ൌ 38.74 ܤܯܵଶ௕

ே ൌ 1.39 ߨଶ௚

ே

ൌ 4.82

ܲଵ,ெ஻ௌ ൌ 0.98 ܯଵ

஼஻

ൌ 44.68

ܿଶ௚,௣

ி

ൌ 0.391

ଵܵܶܮ

ோ

ൌ 38.59

஻ܱܲܧܴ

ൌ 20.41     ߨଶ௕

ே

ൌ 1.20

ܲଶ௚,ெ஻ௌ

ൌ 1.41

௚ଶܯ

஼஻

ൌ 96.94

ܿଶ௕,௣

ி

ൌ 0.631

௚ଶܵܶܮ

ோ

ൌ 13.00       

ܲଶ௕,ெ஻ௌ

ൌ 0.72

௕ଶܯ

஼஻

ൌ 38.74

ܿଶ௚,௛

ி

ൌ 0.015

௕ଶܵܶܮ

ோ

ൌ 0.005       

    ܿଶ௕,௛

ி

ൌ 0.044 ܦோ ൌ 31.53       
25

Appendix II: Optimization and Equilibrium 

This section presents the objective functions and budget constraints for the main actors in the 

model. For full details see GKTV (2012). 

Household P’s optimization problem 

Household P maximizes its intertemporal expected utility from the consumption of potatoes and 

housing. The last term in the utility function represents the reputational penalty from default, 

which is proportional to the loss given default on mortgages. 

max ܷഥ௉ ൌ ܷ௉൫ܿଵ,௣

௉ , ܿଵ,௛

௉ ൯൅ߦ∙߱ଶ௚ൣܷ௉൫ܿଶ௚,௣	

௉ , ሺ1െߜሻܿଵ,௛

௉ ൅ ܿଶ௚,௛௉ ൯൧ ൅	

ߦ∙߱ଶ௕ ቂܷ௉൫ܿଶ௕,௣

௉ , ܿଶ௕,௛௉ ൯െ߬ଶ௕௉ ൣܯܱܴܶ௉ሺ1൅ݎெைோ்ሻ െ ܲଶ௕,௛ܿଵ,௛௉ ൧ቃ

where       1 1

,, , ,

1 1 , 1 1

P P

PP P P P Uc c c c ts p ts h ts p ts h P P

 

 

 

   

subject to the following budget constraints 

ܲଵ,௛ܿଵ,௛

ଵݕ݊݁݋ܯ ൑ ௉ଵܵܶܮ ൅ ௉ܱܴܶܯ ൅ ௉

௉

i.e. the purchase of housing in the initial period is funded by own monetary endowments, a 

mortgage and short-term borrowing 

ଵܵܶܮ

௉ሺ1 ൅ ݎଵ

ௌ்ሻ ൑	ܲଵ,௣ݍଵ,௣

௉

i.e. the revenues from potatoes sales are used to repay the short-term loans at the end of the 

initial period 

ܯܱܴܶ௉ሺ1൅ݎெைோ்ሻ ൅ ܲଶ௚,௛ܿଶ௚,௛

௚ଶݕ݊݁݋ܯ ൑ ௉௚ଶܵܶܮ ൅ ௉

௉

i.e. the repayment of the mortgage in the good state and the new housing purchases are funded by 

own monetary endowments and short-term borrowing 

௚ଶܵܶܮ

௉ ሺ1 ൅ ݎଶ௚

ௌ்ሻ ൑	ܲଶ௚,௣ݍଶ௚,௣

௉

i.e. the revenues from potatoes sales in the good state are used to repay the short-term loans at 

the end of the second period 

ܲଶ௕,௛ܿଶ௕,௛

௕ଶݕ݊݁݋ܯ ൑ ௉௕ଶܵܶܮ ൅ ௉

௉

i.e. own monetary endowments and short-term borrowing are the only funds used for the new 

housing purchases in the bad state, since households default on their mortgages 

௕ଶܵܶܮ

௉ ሺ1 ൅ ݎଶ௕

ௌ்ሻ ൑	ܲଶ௕,௣ݍଶ௕,௣

௉
26

i.e. the revenues from potatoes sales in the bad state are used to repay the short-term loans at the 

end of the second period 

Household F’s optimization problem 

Household F enters the economy only in the second period. Thus, it lives either in the good or in 

the bad state and it aims at maximizing utility in either state from the consumption of potatoes 

and housing. 

max 	ܷி൫ܿଶ௦,௣

ி , ܿଶ௦,௛

ி ൯

where       1 1

22 2 2

1 1 , 1 1

F F

F

ph p

FF F F Ucc c c F F h

 

 

 

   

subject to the following budget constraints 

ܲଶ௦,௛ܿଶ௦,௛

ଶ௦ݕ݊݁݋ܯ ൑ ி

ி ൅ ܮܵܶଶ௦ி

i.e. housing purchases are funded by own monetary endowments and short-term borrowing 

ଶ௦ܵܶܮ

ி ሺ1 ൅ ݎଶ௦

ௌ்ሻ ൑	ܲଶ௦,௣ݍଶ௦,௣

ி

i.e. the revenues from potatoes sales are used to repay the short-term loans 

Household R’s optimization problem 

Household R maximizes its intertemporal expected utility from the consumption of potatoes and 

houses. 

max ܷഥோ ൌ ܷோ൫ܿଵ,௣

ோ , ܿଵ,௛

ோ ൯ ൅ 	ߦ ∙ ߱ଶ௚ൣܷோ൫ܿଶ௚,௣

ோ , ሺ1െߜሻܿଵ,௛

ோ ൅ ܿଶ௚,௛ோ ൯൧ ൅ ߦ

∙ ߱ଶ௕ൣܷோ൫ܿଶ௕,௣

ோ , ሺ1െߜሻܿଵ,௛ோ ൅ ܿଶ௕,௛ோ ൯൧

where       1 1

,, , ,

1 1 , 1 1

R R

sp sh sp sh R

RR R R R Ucc c c R

 

 

 

   

subject to the following budget constraints 

ܲଵ,௣ܿଵ,௣

ଵݕ݊݁݋ܯ ൑ ோܦ ൅ ோ

ோ ൅ ܮܵܶଵோ

i.e. potatoes purchases and deposits at the commercial bank are funded by own monetary 

endowments and short-term borrowing 

ଵܵܶܮ

ோሺ1 ൅ ݎଵ

ௌ்ሻ ൑	ܲଵ,௛ݍଵ,௛

ோ
27

i.e. the revenues from housing sales are used to repay the short-term loans at the end of the 

initial period 

ܲଶ௦,௣ܿଶ௦,௣

ଶ௦ݕ݊݁݋ܯ ൑ ோ

ோ ൅ ܮܵܶଶ௦ோ ൅ ܸଶ௦

ሻ஽ݎ൅1ோሺܦ ஽

i.e. potatoes purchases in state s in the second period are funded by own monetary endowments, 

short-term borrowing and the received repayment on deposits 

ଶ௦ܵܶܮ

ோ ሺ1 ൅ ݎଶ௦

ௌ்ሻ ൑	ܲଶ௦,௛ݍଶ௦,௛

ோ

i.e. the revenues from housing sales in state s are used to repay the short-term loans at the end of 

the second period 

Commercial bank B’s optimization problem 

The commercial bank aims at maximizing a concave function of profits made in both periods. 

The last term in the payoff function represents the reputational loss from default, which is 

proportional to the loss given default on deposits. 

max ܲ݋ݎ݂ തതതതതതത஻ ൌ ܲ݋ݎ݂஻ሺߨଵ

஻ሻ ൅ߦ෍߱ଶ௦ሾܲ݋ݎ݂஻ሺߨଶ௦

஻ ሻ െ ߬ଶ௦஻ ሾ1െݒଶ௦஻ ሿܦ஻ሺ1 ൅ ݎ஽ሻሿ

௦

where     1 1

1 

B

ts

B B Prof B ts



 





 

subject to the following budget constraints 

ଵܵܶܮଵܧ	൑ ஻ܥܥ ൅ ஻ܱܲܧܴ ൅ ஻ଵܥܵܫܦ ൅ ஻

஻ܦ ൅ ஻

i.e. the commercial bank uses its own capital together with funds borrowed from the discount 

window and deposits to supply short-term and repo loans and to hold a cash amount committed 

to the extension of mortgages 

ܯܱܴܶ ൑ ஻ܥܥ ൅ ஻ܲଵ,ெ஻ௌܤܯܵଵ

஻

i.e. the commercial bank funds the extension of mortgages with its own committed cash and with 

the proceeds from the securitization of mortgages 

ଵܥܵܫܦ

஻ሺ1൅ݎଵ

஼஻ሻ ൅ ܿܽݏ݄ଵ

ଵܵܶܮ ൑ ஻

஻ሺ1 ൅ ݎଵ

ௌ்ሻ

i.e. a part of the proceeds from the repayment of short-term loans are used to repay the loans 

from the discount window and the rest is held as cash reserves 

௚ଶܵܶܮ௚ଶݒ ൅ ஻

ଵ݄ݏܿܽ 	 ൑ ሻ஽ݎ൅1ሺ஻ܦ ஻

௚ଶܧ ൅ ஻௚ଶܥܵܫܦ ൅ ஻

஻ ൅ ܲଶ௚,ெ஻ௌ	ߪଶ௚஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻ
28

i.e. the commercial bank uses its cash reserves and new capital together with borrowed funds 

from the discount window and revenues from further securitization of retained mortgages to 

repay depositors and extend new short-term lending in the good state in the second period 

௚ଶߨ௚ଶܵܶܮ ൑ ஻

஻ ൫1 ൅ ݎଶ௚

ௌ்൯ ൅ ܴܧܱܲ஻ሺ1 ൅ ݎோா௉ைሻ ൅ ሺ1 െ 	ߪଶ௚

஻ ሻሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻሺ1 ൅ ݎெைோ்ሻ

௚ଶܥܵܫܦ െ

஻ ሺ1 ൅ ݎଶ௚

஼஻ሻ

i.e. the profits in the good state are equal to the profit on short-term lending plus the repayment 

on repo loans and the mortgages remaing in the balance sheet less the loans that must be repaid 

to the central bank 

௕ଶܵܶܮ௕ଶݒ ൅ ஻

ሻ஽ݎ൅1ሺ஻ܦ ஻

ଵ݄ݏܿܽ ൑

௕ଶܧ ൅ ஻௕ଶܥܵܫܦ ൅ ஻

஻ ൅ ܲଶ௕,ெ஻ௌሾߴଶ௕

ଵܵܤܯ		 ஻

௕ଶߪ	 	 ൅ ஻

஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻሿ

i.e. the commercial bank uses its cash reserves and new capital together with borrowed funds 

from the discount window and revenues from further securitization of retained mortgages and 

from returned MBS that are resold to repay depositors and extend new short-term lending in the 

bad state in the second period 

௕ଶߨ௕ଶܵܶܮ ൑ ஻

஻ ሺ1൅ݎଶ௕

ௌ்ሻ ൅ ܸଶ௕ெைோ் ቀܯܱܴܶ ஻െ ߴଶ௕

ଵܵܤܯ ஻

஻ െ 	ߪଶ௕

஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻቁ ሺ1൅ݎெைோ்ሻ

௕ଶܥܵܫܦ െ

஻ ሺ1 ൅ ݎଶ௕

஼஻ሻ

i.e. the profits in the bad state are equal to the profits on short-term lending plus the repayment 

on the mortgages remaing in the balance sheet less loans that must be repaid to the central bank 

Shadow bank N’s optimization problem 

The non-bank aims at maxizing a concave function of profits made in the second period, since it 

does not make any profits in the initial one. The last term in the payoff function represents the 

reputational loss from default, which is proportional to the loss given default on repo loans. 

max ܲ݋ݎ݂ തതതതതതതே ൌߦ∙߱ଶ௚ܲ݋ݎ݂ே൫ߨଶ௚

ே ൯൅ߦ

∙ ߱ଶ௕ ቂܲ݋ݎ݂ேሺߨଶ௕

ே ሻ െ ߬ଶ௕ே ሾܴܧܱܲேሺ1 ൅ ݎோா௉ைሻെܸଶ௕

ெைோ்ܤܯܵଵ

ேሺ1൅ݎெைோ்ሻሿቃ

where    1

2 2

1

1

N

s

N

N s

N Prof 

 





 

subject to the following budget constraints 

ܲଵ,ெ஻ௌܤܯܵଵ

ே ൑ ܧଵே ൅ ܴܧܱܲே

i.e. the initial purchase of mortgage backed securities is funded by own capital and a repo loan 
29

ܲଶ௦,ெ஻ௌܤܯܵଶ௦

ே ൑ ܧଶ௦ே

i.e. the purchase of mortgage backed securities in the second period is funded out of new capital 

which implies cash-in-market pricing 

௚ଶߨ

ே ൑ ൫ܤܯܵଵ

ே ൅ ܤܯܵଶ௚

ே ൯ሺ1൅ݎெைோ்ሻ െ ܴܧܱܲேሺ1൅ݎோா௉ைሻ

i.e. the profits in the good state are equal to the repayment on the mortgage backed securities 

purchased in both the initial period and the good state minus the repayment of the repo loan 

௕ଶߨ

ே ൑ ܸଶ௕

ெைோ்ܤܯܵଶ௕

ே ሺ1൅ݎெைோ்ሻ

i.e. the profits in the bad state are equal to the repayment of returned mortgages backed 

securities repurchased 

Markets and Equilibrium 

Equilibrium is reached when all agents maximize their payoff functions subject to their budget 

constraints, all markets clear and their expectations are rational. Potatoes prices in equilibrium are 

determined by the clearing of the potatoes market. Supply equals demand in every period and 

state in equilibrium, i.e. ݍଵ,௣

௉ ൌ ܿଵ,௣ோ and ݍଶ௦,௣

௣,ଶ௦ݍ ൅ ௉

ி ൌ ܿଶ௦,௣ோ . Similarly, ݍଵ,௛

ோ ൌ ܿଵ,௛

௛,௚ଶݍ , ௉

ோ ൌ

ܿଶ௚,௛

௉ ൅ ܿଶ௚,௛ி and ݍଶ௕,௛ோ ൅ ܿଵ,௛௉ ൌ ܿଶ௕,௛௉ ൅ ܿଶ௕,௛ி for the housing market in equilibrium. Moreover, 

the loan/deposit markets clear when ܯܱܴܶ ௉ൌ ܯܱܴܶ஻, ܴܧܱܲ ஻ൌ ܴܧܱܲே, ܦோ ൌ ܦ஻, ܮܵܶଵ

஻ ൌ

ଵܵܶܮଵܵܶܮ ൅ ௉

ோ and ܮܵܶଶ௦

஻ ൌ ܮܵܶଶ௦

ଶ௦ܵܶܮ ൅ ௉

ோ ൅ ܮܵܶଶ௦ி . The market clearing for mortgage backed 

securities requires ܤܯܵଵ

஻ ൌ ܤܯܵଵே, 	ߪଶ௚

஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻ ൌ ܤܯܵଶ௚

ே and ߴଶ௕

ଵܵܤܯ		 ஻

஻ ൅

௕ଶߪ		

஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻ ൌ ܤܯܵଶ௕

ே . Finally, the demand from the commercial bank determines 

the equilibrium level of borrowing from the discount window, since there is a perfectly elastic 

supply from the central bank at predetermined interest rates. 

 
30

Appendix III: Definition of Regulatory Ratios 

Loan-to-value regulation on mortgages 

Loan-to-value regulation sets the maximum level of mortgage borrowing for a given value of 

collateral pledged. Given that mortgage extension takes place only in the initial period, this is an 

ex-ante tool. 

௉ܱܴܶܯ

ܲଵ,௛ܿଵ,௛

	݋݅ݐܽݎ	݁ݑ݈ܽݒ	݋ݐ	ܽ݊݋l	permissible	Maximum௉ ൑ 

Haircut regulation on repo loans 

Haircut regulation sets the minimum down-payment for a repo loan used to purchase mortgage 

backed securities. As such, it can be implemented before the resolution of uncertainty and it is an 

ex-ante tool as well. 

ଵܧ

ே

ܲଵ,ெ஻ௌܤܯܵଵ

ݐ݁݉݁݊ݎ݅ݑݍ݁ݎ	݃݅݊ݎܽܯ ൒ ே

Bank capital regulation 

Contrary to the aforementioned regulatory interventions, capital regulation does not attempt to 

regulate specific markets (mortgage or repo loan markets), but rather attempts to affect the 

incentives of the commercial bank to extend credit. Capital requirements are risk weighted in the 

spirit of the Basel accord. Short-term loans are safe and thus should have a zero risk weight, i.e. 

they are not included in the calculation of risk weighted assets. Capital regulation will differ 

depending on the point in time that is implemented. For example, regulating capital requirements 

in the initial period affects the extension of repo loans is different than imposing them once the 

default state has realized. In the former case, repo loans multiplied by their ex-ante risk weight 

counts as part of risk-weighted assets. While, in the latter case, after default they are written off 

and thus generate losses that reduce equity that is in the numerator of the ratio. Thus, capital 

requirements can be both an ex-ante and an ex-post regulatory tool. 

ଵܧଵߨ ൅ ஻

஻

ଵݓݎ

ெைோ் ∙ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻ ൅ ݓݎଵ

݀݋݅ݎ݁݌	݈݅ܽݐ݅݊݅	݅݊	ݐ݁݉݁݊ݎ݅ݑݍܴ݁	݈ܽݐ݅݌ܽܥ ൒ ஻ܱܲܧܴ ∙ ை௉ோா

ଵܧ

௕ଶܧ ൅ ஻

ଵߨ ൅ ஻

௕ௗଶ௠௜ܮ_ܲ ൅ ஻

஻

௕ଶݓݎ

ெைோ் ∙ ሺܯܱܴܶ ஻െ ߴଶ௕

ଵܵܤܯ ஻

݁ݐܽݐݏ	ܾܽ݀	݄݁ݐ	݅݊	ݐ݁݉݁݊ݎ݅ݑݍ݁ݎ	݈ܽݐ݅݌ܽܥ ൒ ሻ஻
31

Bank liquidity regulation 

Like capital regulation, liquidity requirements alter the commercial bank’s incentives offer 

different types of credit But these regulations skew choices based on an asset’s liquidity rather 

than the asset’s credit risk. Short-term loans are considered liquid, while mortgages and repo 

loans, being long-term and partially collateralized, are illiquid. As explained in the text, if 

liquidity requirements are imposed in the bad state they exacerbate fire sales. So we consider 

liquidity regulation only in the initial period. 

ଵܵܶܮ

஻

ଵܵܶܮଵܵܤܯ െ஻ ܱܴܶܯ ൅ ஻ܱܲܧܴ ൅ ஻

݀݋݅ݎ݁݌	݈݅ܽݐ݅݊݅	݅݊	ݐ݁݉݁݊ݎ݅ݑݍ݁ݎ	ݕݐ݅݀݅ݑݍ݅ܮ ൒ ஻

Dynamic provisioning 

Dynamic provisioning is formalized as a requirement for the bank to keep cash on its balance 

sheet throughout the good state of the world when the growth of real estate related credit, g%, 

exceeds a certain threshold x%. Letting the per unit requirement be denoted by ߢ, such regulation 

would imply that the gross dynamic provisioning is ሺ݃% െ ݔ%ሻߢ. 

The budget constraints of the bank is the good state would then become 

௣,௚ଶܵܶܮ

௛,௚ଶܵܶܮ ൅ ஻

௚ଶݒ ൅ ஻

஻ ܦ஻ሺ1൅ݎ஽ሻ ൅ ሺ݃% െ ݔ%ሻߢ

ଵ݄ݏܿܽ 	 ൑

௚ଶܧ ൅ ஻௚ଶܥܵܫܦ ൅ ஻

஻ ൅ ܲଶ௚,ெ஻ௌ	ߪଶ௚஻ ሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻ

and 

௚ଶߨ

஻ ൑ ሺ݃% െ ݔ%ሻߢ ൅ ܮܵܶଶ௚,௣஻ ൫1 ൅ ݎଶ௚,௣

ௌ் ൯ ൅ ܮܵܶଶ௚,௛

஻ ൫1 ൅ ݎଶ௚,௛

ௌ் ൯ ൅ ܴܧܱܲ஻ሺ1൅ݎோா௉ைሻ

																															൅		ሺ1 െ 	ߪଶ௚

஻ ሻሺܯܱܴܶ ஻െ ܤܯܵଵ

஻ሻሺ1൅ݎெைோ்ሻ െ ܫܦܵܥଶ௚

஻ ሺ1 ൅ ݎଶ௚

஼஻ሻ. 

Where the growth rate in real estate related credit is 

݃% ൌ ቆ ܮܵܶଶ௚,௛

஻

௛,ଵܵܶܮ ൅ ஻ܱܴܶܯ

஻ െ 1ቇ %

Note that the short-term real estate related credit in the first period, ܮܵܶଵ,௛

஻ , is equal to the shortterm loan demand of household P, ܮܵܶଵ

௉, while in the good state it is equal to the loan demands 

of both P and F, i.e. ܮܵܶଶ௚,௛

஻ ൌ ܮܵܶଶ௚

௚ଶܵܶܮ ൅ ௉

ி .