Efficient credit policies in a housing debt crisis.

Eberly, Janice ; Krishnamurthy, Arvind

VI. Housing Market Equilibrium and the Effect of Foreclosures

So far we have allowed uncertainty in home prices but not endogeneity. An additional reason to modify loans and reduce default might be to intervene in the dynamic equilibrium in the housing market from default to home prices and back to default, as documented empirically by John Harding, Eric Rosenblatt, and Vincent Yao (2008); John Campbell, Stefano Giglio, and Parag Pathak (2011); Atif Mian, Amir Sufi, and Francesco Trebbi (2011); and Anenberg and Kung (2014).

We are therefore interested in understanding how defaults and foreclosures at date I and date 2 affect housing prices. In this section we sketch a minimal general equilibrium of the housing market to clarify whether and how such considerations might alter our conclusions regarding modifications.

Denote [p.sub.t] as the price per unit of housing. Earlier, we described a household purchasing [c.sup.h.sub.t] units of housing services at price [p.sub.t] so that the price per unit of housing was [p.sub.t] = [P.sub.t]/[c.sup.h.sub.t]. Equivalently, [p.sub.t] is the price of a normalized quantity of a house of size "one." Then,

(41) [p.sub.0] = E[[r.sub.1] + [r.sub.2] + [p.sub.2]].

Here [r.sub.1] and [r.sub.2] are the date 1 and date 2 user cost of housing, respectively. Next we close the model to specify a housing market equilibrium that determines [p.sub.0]. We follow our initial framework and assume that at a planning stage, households anticipate income of [bar.y] at both dates and choose housing consumption,

(42) [c.sup.h.sub.t] = [alpha][bar.y]/[r.sub.t].

At date 1, the household's income falls to [y.sub.1]. For now, we assume that exogenously a fraction [m.sub.1,L] of the households default on their mortgages and enter the rental market, where L denotes the liquidity-constrained households. We can think of the households subject to the income shock and default as the liquidity-constrained households we modeled earlier.

We depart from our previous assumption and allow for a degree of friction in the rental markets so that owning a home is more efficient than renting a home. (19) To purchase one unit of housing services costs [r.sub.t] in debt service. The same housing services cost, if generated via the rental market, is [fr.sub.t] where f [greater than or equal to] 1, and/parameterizes the rental friction, with f = 1 being the case we have analyzed in the previous section. Thus, the date 1 demand for housing via the rental market from the foreclosed homeowners is

(43) [c.sup.h.sub.1] = [alpha] [y.sub.1]/[fr.sub.1].

We assume that foreclosure keeps the household out of the ownership market for one period. At date 2, the household purchases a home again so that,

(44) [c.sup.h.sub.2] = [alpha] [y.sub.1]/[r.sub.2].

Suppose that at date 1, across the economy there are [m.sub.1,L] agents renting, and 1 - [m1.sub.L] agents owning. Then total demand for housing at date 1 from these agents is

(45) m[alpha][y.sub.1]/[fr.sub.1] + (1 - m) [alpha][bar.y]/[r.sub.1] = [alpha] [bar.y]/[r.sub.1] - [m.sub.1,L] [alpha]/[r.sub.1]([bar.y] - [y.sub.1]/f).

Foreclosures--that is, an increase in [m.sub.1,L]--decrease the net demand for housing at date 1. At date 2, since the date 1 foreclosed homeowners own

homes again, the total demand for housing is [alpha][bar.y]/[r.sub.2] and invariant to [m.sub.1,L].

We assume that there are other unmodeled agents in the economy who also consume housing services. These may include new home buyers, home builders, speculators, and so on. We denote the demand from these agents as [H.sup.D]([r.sub.t]). Our modeling only takes a stand on the functional forms for the households that are subject to foreclosure and that will be affected by modifications.

The market clearing condition at date 1 is

(46) [H.sup.D]([r.sub.1]) + [alpha] [bar.y]/[r.sub.1] - [m.sub.1,L] [alpha]/[r.sub.1]([bar.y] - [y.sub.1]/f) = H,

where the supply of housing is fixed at H. The housing dividend, [r.sub.1] is increasing in the income of homeowners and renters, decreasing in H, and decreasing in [m.sub.1,L].

VI.A. Effect of Foreclosures

Let us now consider a scenario of rising foreclosures, where [m.sub.1,L] increases. If [dm.sub.1,L] agents switch from owning to renting, the effective consumption of housing services in the economy falls and housing prices will also fall. Define

(47) [[eta].sub.1] = 1/[r.sub.1] [dr.sub.1]/dH < 0

as the percentage change in the housing dividend for a unit increase in housing supply. The reciprocal of the semi-price elasticity of demand is [[eta].sub.1]. This derivative should be interpreted as the percentage reduction in price caused by the sale of an additional unit of housing ("price pressure"). Then,

(48) [DELTA][p.sup.1,L] [equivalent to] dp/[dm.sub.1,L] = [[eta].sub.1][alpha] ([bar.y] - [y.sub.1]/f) < 0.

We can also consider a foreclosure scenario for strategic defaulters. These households differ from the constrained households because their income at date 1 is [bar.y], but they nonetheless default on mortgages whose face value is higher than the home price, including default costs. Reviewing the derivation of housing demand for strategic defaulting homeowners who become renters, we find that the net demand for housing as a function of the number of strategically defaulting renters, [m.sub.1,S], is

(49) [alpha] [bar.y]/[r.sub.1] - [m.sub.1,S] [alpha]/[r.sub.1] ([bar.y] - [bar.y]/f),

so that dp/[dm.sub.1,S] is

(50) [DELTA][p.sup.1,S] = [[eta].sub.1] [alpha] ([bar.y] - [bar.y]/f) > [DELTA][p.sup.1,L].

Thus, foreclosures reduce prices more in the case of liquidity constraints than in the case of strategic defaults. This occurs because the liquidity-constrained defaulters experience a larger drop in the net demand for housing services when going from owning to renting. Note also that if f = 1, so that the rental market is frictionless, then [[DELTA]p.sup.1,s] = 0, and [DELTA][p.sup.1,L] < 0.

We can repeat the same exercise at date 2. At date 2, all default is strategic. Thus, the effect of foreclosures at date 2 is

(51) [DELTA][p.sup.2,s] = [[eta].sub.2] [alpha] ([bar.y] - [bar.y]/f).

It is likely that the housing market is more stressed at date 1 in a recession than at date 2, so home sales have a bigger impact on price at date 1 than at date 2 and [[eta].sub.1] > [[eta].sub.2]. In this case, it follows that we can order the effect of foreclosures on home prices as

(52) [absolute value of [DELTA][p.sup.1,L]] > [absolute value of [DELTA][p.sup.1,s]] > [absolute value of [DELTA][p.sup.2,s]].

That is, the effect on home prices is largest from a default induced by liquidity constraint, which in our model occurs during the crisis period (date 1). Strategic defaults also put downward pressure on home prices, but less so, because these homeowners do not bring an income shock and payment distress into the rental market. Both of these effects ease once the economy moves out of the crisis period.

VI.B. Mortgage Modifications and Home Prices

We now revisit the question of how the proposed mortgage modifications, parameterized by [t.sub.1] and [t.sub.2], would affect home prices. We showed earlier that payment reductions (that is, [t.sub.1] > 0) are most efficient in reducing default at date 1, when households are liquidity constrained. Home prices are also most sensitive to defaults of liquidity-constrained agents. Putting these findings together, we conclude that if a planner's objective includes home price stabilization (or if home prices feed back into consumption and utility), payment reductions for liquidity-constrained agents will be a more effective tool than principal reductions. Thus, payment reductions should be optimally targeted at liquidity-constrained agents. This finding reinforces our earlier conclusions on the benefits of payment reductions for liquidity-constrained agents.

Principal reductions (that is, [t.sub.2] > 0) are less effective in reducing default at date 1, but they do help in reducing strategic default at date 2. Reducing strategic default at date 2 also stabilizes home prices, albeit less strongly than at date 1.

Consequently, endogenous home prices reinforce our general finding that policies that transfer resources to households during a crisis period at least weakly dominate policies providing transfers at later dates. Endogenous home prices also suggest that there is value in associating these transfers with housing. That is, our earlier results, which focused on consumption smoothing alone, could have been accomplished with any type of transfer that supported consumption spending. With endogenous home prices, there is additional value to supporting spending on housing, specifically to prevent foreclosures and the negative effect they have on home prices.

VII. Ex Ante Security Design and the Automatic Stabilizer Contract

So far we have focused on policies put in place once a housing crisis is under way. We have considered only the effects of the policies at the time of implementation and not any effect on the cost of credit that might result from changing the terms of a loan after-the-fact. However, if loans are written down ex post, the cost of credit could rise as lenders anticipate and price in the probability of future write-downs. However, if these problems could be anticipated, policies could be put in place ex ante to ease the policy choices faced in the midst of a crisis.

To examine the security design that would result in our framework, we now shift back to a pre-crisis date 0 and examine the optimal state-contingent design of the mortgage loan. Using ex ante policies in principle avoids the moral hazard problems associated with ex post loan modifications, and also avoids the pragmatic problems that would result from swiftly modifying potentially tens of millions of individual contracts in a crisis environment (as emphasized and documented in Agarwal and others 2011).

Our analysis of loan modifications has shown that different types of policies solve distinct problems in the mortgage market: liquidity constraints and strategic default. The former is a cash-flow problem, whereas strategic default results from a high debt-to-value ratio giving the borrower a default incentive even when he is not in payment distress. A robust mortgage security should be able to address both of these issues.

From a security design perspective, the optimal security should eliminate the deadweight costs of default that are due to aggregate events, that is, events not caused by the borrower. Moreover, the optimal contract should adjust payments in a state-contingent way to eliminate (or minimize) the incidence of the binding cash-flow constraint. Hence, liquidity constraints require that payments fall when the constraints tighten or become binding for more homeowners. Relaxing the liquidity constraints allows greater cash flow for nonhousing consumption and also reduces the probability of cash-flow-driven mortgage defaults. Therefore, this aspect of the optimal contract calls for a reduction in payments in states in which liquidity constraints tighten.

The incentive for strategic default, on the other hand, calls for a different policy prescription and in different states. In particular, in states in which the debt-to-value ratio rises, and especially when homeowners are underwater, the robust mortgage contract should reduce the amount of debt owed by the borrower. This reduces the incentive for strategic default and its associated deadweight costs. Indexing debt to macroeconomic outcomes has been proposed elsewhere, chiefly through indexing face value to home values (for example, Mian and Sufi 2014).

An optimal security design should consider these two objectives together. The optimal contract should both reduce payments in liquidity-constrained states and lower debt when the risk of strategic default rises. Put differently, payments should fall during a recession, and debt should fall when home prices decline.

There is a simple contract, which we call an automatic stabilizer mortgage contract, that goes some way toward implementing the optimal state contingency. This is a contract that allows the borrower the right to convert his fixed-rate mortgage to a floating-rate mortgage as long as he is not delinquent on his mortgage. Current mortgage contracts are priced to reflect the possibility that the borrower will prepay his mortgage when market interest rates fall. From a pricing standpoint, prepaying a mortgage when market interest rates fall and converting it to one with a market floating rate have almost the same present value. However, during the financial crisis, the prepayment option was curtailed for underwater loans, since they could not typically be refinanced (a new loan of equivalent amount was not available, since the loan exceeded the collateral value of the home). The main deviation from current practice in our proposed contract is to remove this restriction and always give the borrower the option to convert his mortgage into a floating-rate mortgage.

The proposed contract achieves the two policy objectives: first, payment relief, and second, principal reduction. It achieves the payment relief objective directly, since in a typical state of recession the central bank reduces short-term interest rates. Thus converting to a floating-rate mortgage can substantially reduce current payments.

The second objective calls for a reduction in debt value when debt-to-value ratios rise, likely due to a decline in home prices. A reduction in debt value avoids the deadweight costs of default by strategic defaulters. In the abstract, allowing for this second objective requires a more complex contract, since the payment reduction and the loan write-down need not be coincident. However, as we argue next, resetting the mortgage interest rate can achieve the same loan value as a principal reduction and thus also achieve the second objective.

To see the parallels between reducing principal and lowering the mortgage interest rate, as in a refinancing, note that both methods of restructuring loans reduce the stream of payments on the mortgage over time. For a given fixed-rate, fixed-term loan, any new stream of payments that can be achieved with a reduction in face value can also be achieved by a reduction in the contract interest rate. (20) This parallel between principal reduction and refinancing can be overlooked, because refinancing does not change the face value (principal) of the loan while principal write-downs explicitly reduce the face value. The distinction can be misleading, however, because face value is a poor measure of the value of a loan. On a market-value basis, resetting to a lower interest rate reduces the value of the loan. Mortgage lenders and investors see the effect in market valuations, and borrowers see the effect in their payments. A reduction in the payment stream achieved through a reduction in face value can always be replicated by a change in the contract interest rate. For example--and to get a sense of magnitudes--a resetting of a 30-year $200,000 mortgage from a 6-percent interest rate to a 4-percent rate reduces monthly payments from $ 1,200 to $950 (20 percent), and the present value of the stream of payments from $250,000 to its face value of $200,000. The identical payment stream would result from a reduction in face value or principal write-down from $200,000 to $160,000 (or 20 percent). (21,22)

VII.A. Comments on Contracts and Modifications

We think of our proposed contract as a housing market version of automatic stabilizers, since it provides state-contingent support to both the housing market and the broader economy. This automatic stabilizer contract reduces payments when the economy is cyclically weak and liquidity constraints are likely to bind, and also reduces loan value when home prices fall. The cyclical movement of interest rates is key to the state contingency: It the central bank reduces rates during cyclical downturns and when home prices fall, the reset option allows mortgage borrowers to reduce their payments and the present value of their debt. Various forms of home price insurance or indexation of contracts to home prices have been proposed (for example, Mian and Sufi 2014) to address the problems posed by negative equity. If implemented at date 2, before default, these options also implement the intent to avoid strategic default at date 2. Some contracts of this type have been implemented on a small scale, although they have run into challenges with measuring home prices at the appropriate level of aggregation and allowing for home improvements and maintenance incentives. Indexing to interest rates, as suggested in the stabilizing contract, has the advantage of observability and consistency, preserving monetary policy effectiveness, and the fact that mortgage contracts with this feature already exist and are implemented and priced on a large scale.

As discussed earlier, the parallels between principal reductions and mortgage rate reductions can be overlooked, perhaps because of the focus on face value in principal reductions. However, from the perspectives of both the lender and the borrower, the value or cost of a loan is the present value of payments, which may be equivalently reduced either by changing face value or by changing the contract interest rate. For example, the Home Affordable Refinance Program (HARP), which allowed refinancings of underwater GSE loans, is estimated to have completed 3.1 million HARP refinancings through the first quarter of 2014, out of a total of 19.2 million refinancings completed at the GSEs over the same period. The HARP refinancings include loans with LTV exceeding 80 percent, with about 12 percent of loans exceeding LTV of 125 percent. Interestingly, the GSEs started offering shorter-term (15- to 20-year) refinancing alternatives under HARP, and about 20 percent of underwater borrowers (with LTV greater than 105 percent) have shortened the loan term this way when refinancing. Consistent with our characterization of principal reduction for unconstrained underwater borrowers, this suggests that these borrowers are not liquidity constrained: by taking a shorter-term mortgage, they increased their mortgage payments when they could have chosen lower payments by extending the term of their new mortgages. (23)

To get a sense of magnitudes, the 30-year fixed-rate loan rate hit a trough in November 2012 at 3.35 percent (Freddie Mac PMMS, monthly average). Its peak in 2008 was 6.48 percent. If we use an average decline of 150 basis points due to refinancing on an average loan balance of $150,000, the present value of payments over the life of the loan falls by $28,000. The same payment reduction could have been achieved with a reduction in face value of 16 percent, or $24,000 for this typical loan. This method of achieving debt reduction relies on the sharp reduction in mortgage rates that occurred during the crisis. Empirical work has begun to examine the effectiveness of payment reduction through refinancing, including Fuster and Willen (2013) and Philip Bond and others (2014), who estimate that refinancing reduces the likelihood of mortgage default in the following year by one-third. Studies of other forms of cash transfers, such as that by Joanne Hsu, David Matsa, and Brian Melzer (2014), suggest that they can be effective in avoiding foreclosures. Separately, as emphasized by John Campbell in his presidential address to the American Finance Association (Campbell 2006) and more recently by Benjamin Keys, Devin Pope, and Jaren Pope (2014), even households that are not underwater might fail to refinance when it appears to be available and desirable, so a mechanism to automate refinancing may have other social benefits.

Finally, while our model specified a date 1 reduction in income which then bounces back at date 2, the persistence of the recent housing crisis prompts examination of a case in which there is no recovery at date 2, so that the date 1 shock is permanent. "Date 1" in our model may encompass many years, and we have allowed date 2 income and prices to be uncertain. Nevertheless, the stabilizer contract we propose is robust in this dimension as well. A temporary shock requires temporary payment relief in order to avoid inefficient foreclosures and reductions in consumption; this payment relief occurs when a borrower refinances his loan. A permanent shock--either a reduction in permanent income or a permanently lower level of home prices--requires a different policy. In this case, it is important whether the lasting shock is aggregate or idiosyncratic. If the persistent downturn is a common shock, then the optimal policy is one that keeps people in their homes. That is, even though home prices will fall, homes will not need to be reallocated. Indeed, foreclosures would only result in deadweight costs of foreclosure. In this case, payment relief and debt reduction reduce the incidence of foreclosure, so the stabilizer contract still has the relevant features.

On the other hand, if the date 1 shock is idiosyncratic and long lasting, then in equilibrium there should be turnover in housing and some reallocation of homes will be required. That is, some homeowners will likely become renters, and vice versa. To the extent that reallocation is necessary, foreclosure is still inefficient because of its deadweight costs. In this case, the optimal policy should allow turnover while minimizing the deadweight costs of foreclosure and encouraging efficient reallocation. Policy in this case could take the form of encouraging short sales and lender write-downs. In practice, modifications to keep borrowers in their homes during the crisis could also be useful for avoiding defaults while homeowners weather the crisis and learn about their ultimate economic prospects (formally, whether their shock is temporary or persistent).

VIII. Conclusions

The structure developed in this paper is very simple, as it is intended to provide a conceptual framework for considering policy responses to a housing crisis and recession. Its important features include liquidity constraints, reflecting households that cannot access housing equity or credit markets to smooth consumption, and the possibility of being underwater, reflecting households that not only have no home equity but may find it preferable to default on their mortgage, even when faced with the deadweight costs of default. In this setting, payment reduction during the crisis has favorable properties, both for supporting consumption during the crisis and hence achieving better macroeconomic outcomes and also for reducing default during the crisis.

Principal reduction can be helpful, but it is a less efficient use of government resources, since it back-loads payments to households that cannot borrow against these future resources to support consumption today, and also because it is most helpful in reducing strategic default, rather than payment-distress-induced default. Defaults resulting from payment distress have a greater negative impact on home prices, since distressed borrowers carry their distress into the rental market and reduce housing demand more than defaults resulting from strategic considerations. When addressing strategic default, lender incentives are aligned in the sense that lenders should renegotiate before default in order to avoid credit losses; the loan is worth more to the lender than is the collateral. Nonetheless, under uncertain conditions, it will be privately optimal for lenders to delay renegotiation as long as possible before default.

The government might have a different view from private agents, for various reasons. The government might value consumption and macroeconomic performance more than individual agents do, and it might take foreclosure spillovers into account. These considerations should lead the government in two directions. First, the government should tend to provide more resources during the crisis period as a countercyclical measure--both to support consumption and to avoid defaults. Second, it should support lenders' efforts at renegotiation, either by providing incentives or by providing a standardized way of modifying and writing down loans to avoid strategic default and the associated deadweight costs, since private market efforts may be socially insufficient or may collapse entirely due to adverse selection.

Anticipating these ex post difficulties, an ex ante contract could incorporate a stabilizing contract, through an expanded refinancing option. The standard prepayment option allowed for payment reductions as interest rates dropped substantially during the crisis. In particular, refinancing into a floating-rate ARM would allow for a much lower mortgage payment, easing the consumption constraint. However, when loans are underwater, prepayment is problematic, since borrowers cannot finance the underwater portion of the loan. We therefore propose a reset option to allow a mortgage to be converted into an ARM even when the loan is underwater. Such a contract would implement the optimal contract and fill the role of automatic stabilizers in the housing market. This stabilizing contract would allow a state-contingent modification to reduce payments and would solve the debt write-down problem under those conditions when interest rates fall coincidentally with a drop in home prices.

Our proposed mortgage contract limits consideration to existing policies around housing, and in particular, around mortgages. Other forms of fiscal and monetary policy may be useful in our setting; indeed, the fact that our proposed mortgage contract is indexed to interest rates suggests that monetary policy is powerful in this setting. Similarly, fiscal policy to transfer resources to date 1 and alleviate the liquidity constraint would be effective, and perhaps more so than a housing payment reduction.

However, we focus on housing by design, because we are addressing the implications of a housing crisis, which includes falling home prices. In particular, policies to reduce mortgage default may have outsized effects in a housing crisis, so focusing resources on mortgage borrowers may be unusually relevant. Moreover, targeting homeowners may be an especially effective way of reaching liquidity-constrained households during a housing crisis. This does imply that it is universally more effective than transfers or tax policy to increase liquidity more generally in the crisis period, but as we show, mortgage policies can alleviate the distress induced by a home price collapse.

Finally, we have intended this paper to provide a framework for considering various types of credit policy in a simple setting. As credit policy becomes a common component of both fiscal and monetary policy, such a framework may be useful more broadly. For example, empirical questions have arisen around the use of credit policy to finance human capital acquisition (such as student loans) as well as housing (through the GSEs and FHA), where such a framework could be a valuable tool.

ACKNOWLEDGMENTS We benefited from the helpful comments of Andy Abel, Gene Amromin, Philip Bond, Zhiguo He, and our discussants, Austan Goolsbee and Paul Willen, as well as research assistance from Ryan Shyu. We have no relevant material or financial interests to declare regarding the content of this paper.

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Comments and Discussion

COMMENT BY AUSTAN GOOLSBEE

In the aftermath of the housing and financial crisis, there has been considerable debate and second guessing about a great many things and especially about housing policy. One of the most controversial of those debates has centered on the idea of principal reduction and whether the government's response to the crisis should have included more explicit efforts to write down mortgage debt for consumers.

Some of the advocates of that view come from a perspective of fairness--that the benefits of the bank bailouts were concentrated in the banks themselves and not shared with ordinary homeowners. Others view it as an economic positive, arguing that only reducing the amount of outstanding debt would have allowed the consumer balance sheet to improve sufficiently to induce consumers to begin spending again the way they did before the crisis. By implication, this also argues that the recession has been longer because of the lack of principal reduction.

Most of the arguments about which approach is better, and even about which housing goal we should be targeting, have had only a vague theoretical basis. This paper by Jan Eberly and Arvind Krishnamurthy attempts to rectify that by producing a straightforward, simplified model of optimizing consumers who receive a negative shock and attempt to rebalance their consumption. Their model is able to confront and inform a surprisingly rich set of economic phenomena and behavior. It is enough to make one wish that all public commentators on the topic would be required to write down the model that underlies their own arguments.

From their model, Eberly and Krishnamurthy show several important things. First, when one is faced with a borrower liquidity crisis, mortgage modifications that reduce monthly payments are more effective at helping consumers rebalance their consumption, in a bang-for-the-buck sense, than writing down mortgage principal of the same magnitude. Second, the benefits of principal reduction come from reducing the incentives for strategic defaults, so that even though government policies to support rebalancing consumption are better off modifying payments, the mortgage lenders themselves will have an incentive to reduce mortgage principal to prevent default. Third, in the world described by their model a new type of mortgage becomes quite appealing: basically, it is a one-way ARM--automatically lowering mortgage rates (and thus monthly payments and total debt loads) when rates fall.

I was heavily involved in the housing policy discussion during the 2008-11 period, at least on the White House's side, and I admit that this involvement colors my reaction to the paper's findings. I believe the direct experiences attempting to provide housing relief shed some light on which parts of the theoretical model are most useful and which could use some further examination.

WHY THERE WASN'T MUCH PRINCIPAL REDUCTION IN U.S. HOUSING POLICY. The essence of the housing policy problem in 2009 was that the data suggested that about 25 percent of homeowners were underwater, and the amount of negative equity among those homeowners was on the order of $700-$800 billion (First American CoreLogic 2012; Hubbard and Mayer 2009). These underwater homes were forecast to translate into 8-10 million impending foreclosures, although people debated whether it was to be strategic default or traumatic default that would cause them.

The basic question for policy was very much the question posed in this paper. What is the best thing to do with the limited government resources? The government did not have an additional $800 billion to pay off people's mortgages (and even if it had, it would have had to deal with a major political outcry about rewarding the undeserving who had borrowed beyond their means). The banks, grappling with issues of insolvency, could not recognize an additional $800 billion in losses on their balance sheets. Consumers seemed unlikely to be able to repay the $800 billion themselves in a troubled economy. There would, in the end, be a much smaller amount of government money made available, a subset of the Troubled Asset Relief Program (TARP), that could be used to help fight foreclosures, and the argument centered on the best way to do so.

Some influential economists have argued that we needed principal reduction (including Geanakoplos and Koniak 2009, Stiglitz 2010, Shiller 2012, Mian and Sufi 2014). But in his review of Atif Mian and Amir Sufi (2014), Larry Summers (2014) notes that with a marginal propensity to consume out of housing wealth of about 15 percent, the impact on short-run consumption and output of principal reduction would have been modest compared to other forms of stimulus. That view is fully in keeping with the thinking of Eberly and Krishnamurthy here. With something like $25 billion to spend on housing relief, reducing negative equity by less than 3 percent of the total did not seem like a particularly efficient way to reduce foreclosures or help the economy.

The other problem with principal reduction--one that fits rather less comfortably with the current paper's view that the lenders have strong incentives to reduce on their own--was the basic fact that banks and mortgage holders refused to write down principal. Some argued that the government should either force them to do so as a condition of receiving bailout money or else allow judges to impose cramdowns of mortgages in bankruptcy (in most bankruptcies home mortgages remain exempt from restructuring). In reality, the TARP money had already gone out to the banks before the Obama administration came into office, so there was not much wiggle room to attach conditions on it after the fact. And concerning bankruptcy cramdown--Congress made it quite clear it would prevent that.

The federal government had actually tried a major policy to encourage write-downs earlier, and it formed the backdrop of all the housing policy discussions in 2009. The 2008 Hope for Homeowners program had sought to encourage lenders to write down principal on underwater mortgages by offering the mortgage holders a government guarantee on the new, smaller, over-water mortgage. This policy failed completely. The Congressional Budget Office had estimated that the policy would help 400,000 homeowners. The actual number of homeowners helped, as reported by the Federal Housing Administration in 2011, was 762 (FHA2011).

Why would lenders not write down principal, if as the theory predicts it would be in their own interest to do so in order to prevent strategic default?

One reason is that American homeowners proved to be almost pathologically honest. Default rates were then, and remain today, well below the share of people underwater. Even among people very heavily underwater, the large majority continued making their payments. Banks decided that it did not make sense to give write-downs to people that would keep paying anyway. Basically, the amount of strategic default seemed notably low, so the lenders were, perhaps, not so concerned with the importance of reducing its incidence.

Beyond that, the majority of the mortgages that might benefit from a write-down had been securitized, so the writing down of principal ignited all sorts of so-called "tranche warfare." Without a single owner, the mortgage-backed securities (MBS) investors were often at odds over what they wanted for the mortgages embodied in their securities. Buyers of an AAA rated tranche might have an incentive for the properties to foreclose, while owners of a low-priority BB tranche might strongly prefer a modification that could avoid default. Often the ownership was so diffused that the owners could not be reached at all.

WHY POLICY TURNED TO MORTGAGE MODIFICATION AND THE IMPLEMENTATION ISSUES THAT FOLLOWED. In sum, principal write-down seemed to be a nonstarter in practice, or at least an extraordinarily expensive and hard-to-get-started option. Instead, the White House opted for a mortgage modification program that would subsidize a cut in the interest rate of the borrower without reducing the principal in an effort to get the monthly payment down to 31 percent of income (our "affordability" threshold) as part of the Home Affordable Modification Program (HAMP).

The rationale was fairly simple. The owner-occupier of a house values it more than anyone else in the market does because of the costs of moving, of changing schools, and so on. A policy of affordability-modification-without-principal-reduction could therefore exploit a wedge. It could get people to stay in houses that were underwater using less money than would be necessary to buy down their principal directly. Eberly and Krishnamurthy also add the option-value insight that homeowners may stay in their negative-equity homes just to keep their option open that their home values might go back up in the future.

Essentially, the theoretical model in this paper argues that this modification approach is the most efficient way to help homeowners in a liquidity crisis. The model concentrates the relief in the current period instead of spreading the relief out over the life of the mortgage as would happen in a principal reduction plan. I find the logic persuasive. I would add that the later empirical work of Andreas Fuster and Paul Willen (2013) rather clearly documents that the idea of the paper is spot-on, since they find that even among people who are underwater, once their payments fell to a level they could handle they stayed in their houses and kept paying.

There were some practical problems with implementing HAMP's theoretically sound policy of modification, however, problems that anyone should ruminate on before proposing radical changes to housing finance.

For example, lenders agreed to participate in the HAMP modifications and agreed to give trial modifications to anyone whose stated income would qualify them for the program until their documentation came through (tax return records, pay stubs, and so on). If they did not qualify at that point, they would not continue with the lower payment modification, but it gave a free option to consumers. But some banks themselves lacked internal controls, so that even as one side of the bank gave a reduced payment modification, a different part of the bank counted the lower payment as delinquency and commenced foreclosure proceedings on the homeowner. This was called the "dual-tracking problem." Often the homeowners sued, successfully, to get the houses back, but they won only after a lengthy delay, during which the houses became dilapidated or were ransacked for materials by thieves while they lay dormant. It was an absurd problem, one that did not make theoretical sense, and yet there were thousands of people dealing with it in reality.

Many mortgage servicers lacked the capacity to process modifications at all. This meant that the benefits of mortgage modification to the borrower depended heavily on who happened to have the service contract for their securitized mortgage (a matter that the borrower had very little control over).

On the borrowers' side, many people were afraid of being thrown out of their houses, and having endured collection agencies calling them to get money were trying to avoid any contact with the lenders. This fear extended even to cases where lenders were actually offering them beneficial subsidized modifications that would reduce their payments by thousands of dollars a year at no cost to them. Large numbers of people simply would not respond.

The government also tried to institute an "automatic" refinancing for underwater mortgages backed by the GSEs that had over-market interest rates but could not refinance because the loan-to-value ratios were too high. The government already had the credit risk in these cases. But the market for GSE bonds included attestations that loan-to-value ratios not exceed various cut-offs, which meant that every house required an appraisal and new title insurance, gumming up any chance of defaulting the mortgages into lower rates.

These kinds of impediments to refinancing are largely what motivates Eberly and Krishnamurthy to say that designing a mortgage that could adjust downward without having to get tranche approvals, re-appraisals, and title insurance would be a big improvement in their model. It is easy to see why that is true, but their model is not subtle enough to say anything about the importance of liquidity in housing finance markets. If their proposed new mortgages had only modest take-up, the experience of the crisis makes me think that liquidity for these instruments would be very low and their prices would be too high to get them on a path to wider adoption.

IS THIS THE RIGHT KIND OF MODEL TO UNDERSTAND A HOUSING BUBBLE? As productive as it can be to apply a model like this to comparing different housing policies, one ought to have a nagging fear in the back of one's mind when doing so. The essence of the model is a rational equilibrium--namely, consumers are maximizing consumption in period one, something bad happens, and they try to smooth consumption in period two as best they can. In the housing boom of the 2000s, however, there were millions of people buying homes that were completely out of their league. They qualified for mortgages they had no business taking, which implied a level of housing consumption that could not be sustained. One can debate the question of why rational lenders were willing to make those loans (because of agency problems with the loan originators? mistaken beliefs that house prices could never decline? government encouragement?) and likewise why consumers would want to take them (because people figured the banks would know what consumers could afford? mistaken beliefs that prices could never decline? speculative frenzy?). But lenders made them, and people took them.

So, does it make sense to ask in these cases about rebalancing optimal consumption in response to an income shock? The consumption levels in period one were completely out of equilibrium. The country was in the middle of a bubble. The premise of this model and also of advocates of principal reduction (like Mian and Sufi) is figuring out how to restore consumption in the quickest way possible. But perhaps we should ask whether policy really ought to try to restore consumption to levels that made no sense to begin with. To me, that seems like a question worth answering for anyone looking at how we should direct our housing policy.

REFERENCES TO THE GOOLSBEE COMMENT

Federal Housing Administration (FHA). 2011. "Annual Management Report Fiscal Year 2011." http://portal.hud.gov/hudportal/documents/huddoc?id=fhafy11annualmgmntrpt.pdf

First American CoreLogic. 2012. "Negative Equity Q1 2012." August. http://www. corelogic.com/downloadable-docs/negative_equity_q1_2012.pdf

Fuster, Andreas, and Paul Willen. 2013. "Payment Size, Negative Equity and Mortgage Default." Staff Report no. 582. Federal Reserve Bank of New York.

Geanakoplos, J., and S. Koniak. 2009. "Matters of Principal," New York Times, March 4.

Hubbard. R. Glenn, and Christopher J. Mayer. 2009. "The Mortgage Market Meltdown and House Prices." B.E. Journal of Economic Analysis & Policy 9, no. 3: 1-47, March.

Mian, Atif, and Amir Sufi. 2014. House of Debt: How They (and You) Caused the Great Recession, and How We Can Prevent It from Happening Again. Chicago: University of Chicago Press.

Shiller, R. 2012. "Reviving Real Estate Requires Collective Action." New York Times, June 23.

Stiglitz, J. 2010. "Foreclosures and Banks' Debt to Society." The Guardian, November 5, 2010.

Summers, L. 2014. "Lawrence Summers on 'House of Debt': Did the response to the financial crisis focus too much on banks while neglecting over-indebted homeowners?" Financial Times, June 6.

COMMENT BY PAUL WILLEN

In this paper, Janice Eberly and Arvind Krishnamurthy use a model of an optimizing household to evaluate the claim that compulsory principal reduction was the optimal policy response to the problem of underwater homeowners during the Great Recession. They show that in an economy populated by borrowing-constrained households, principal reduction is rarely the most cost-effective form of relief for borrowers. Reducing the size of monthly payments is a better idea.

To grasp the logic of the model, consider first the claim that reducing principal stimulates consumption. A household facing a binding borrowing constraint has a marginal propensity to consume (MPC) of 1 out of a reduction in the current monthly payment. On the other hand, constrained households have an MPC of 0 out of a reduction in future payments because their consumption is already limited by the constraint. Principal reduction differs from payment reduction solely in its effect on future payments, so it is easy to see that a dollar spent on principal reduction should have a much smaller effect than a dollar spent on payment reduction.

The logic of Eberly and Krishnamurthy was, implicitly, recognized by policymakers during the crisis. My table 1 shows estimates by Mark Zandi of Moody's of the marginal propensity to consume used in a calculation of the effects of the American Recovery and Reinvestment Act of 2009. Zandi assumes that lower-income households are borrowing constrained and thus will consume most of a temporary increase in after-tax income. Even higher-income households will consume a relatively large fraction.

How does principal reduction match up to other forms of stimulus? If we use the estimates of Atif Mian and Amir Sufi, two of the most outspoken advocates of principal reduction, heavily indebted households would have spent 18 cents of every dollar of principal reduction they received. (1) The MPC used by Mark Zandi (2010) for the households with the lowest MPC is twice as large as the MPC claimed by Mian and Sufi for the group with the highest MPC out of principal reduction. If Congress had wanted to spend one more dollar on stimulus in 2009, it is clear that principal reduction would have come at the bottom of the list. (2)

Now consider the second ostensible effect of principal reductions: reducing foreclosures. For this analysis, the Eberly-Krishnamurthy model marries the logic of borrowing constraints to a modern conception of the mortgage default decision. The borrower decides whether to default each month when his monthly payment is due. By defaulting, the borrower can free up money for extra consumption and reduce his future liabilities, but he also forfeits any future price gains that accrue to the house. For a constrained household, the marginal value of consumption today is far higher than both the marginal value of consumption in the future and the riskless interest rate. Consequently, reducing current payments and raising current consumption has a disproportionately strong effect on the default decision. Here again, the data confirm the theory. Andreas Fuster and Paul Willen (2013) show that the effect of a 50-percent temporary reduction in mortgage payments for a household with a loan-to-value ratio of 135 is equivalent to a reduction in loan-to-value of 35 percent.

All in all, the model of Eberly-Krishnamurthy confirms the likely intuition of many policymakers during the housing crisis. Payment reduction frontloads relief in the current period, whereas principal reduction spreads it out over the life of the loan. As a result, payment reductions are likely to be particularly effective both as stimulus and as anti-foreclosure policy if borrowers are liquidity constrained. An important advantage of the Eberly-Krishnamurthy model is that it can be used to lay out ideal policies that take this logic into account.

How closely did the policies that were actually enacted compare to the idealized polices from the model? In the wake of the crisis, three things happened. First, lenders foreclosed on millions of homeowners. Foreclosure is not a pleasant experience but, for most borrowers, it results in the complete elimination of their mortgage obligations. (3) In other words, it is a dramatic form of principal reduction. Second, policymakers made a concerted effort to drive down mortgage interest rates. The Federal Reserve lowered short-term interest rates to zero and then purchased trillions of dollars in various financial assets in hopes of lowering long-term rates further. (4) Economists will debate the quantitative impact of large-scale asset purchases for years, but in the third quarter of 2008, the Freddie Mac Primary Mortgage Market averaged 6.52 percent. In the first quarter of 2009, it averaged 5.16 percent, and by the end of 2012 the average had fallen to 3.36 percent.

To be sure, many borrowers had trouble refinancing, but many did not. My figure 1 shows how powerful the inducements to refinancing were. By the end of 2010, about half the debt outstanding before the crisis had been retired, either by foreclosure or by refinancing into a lower interest rate. The figure shows that this reduction was true for a sample of all loans as well as for a sample of the riskiest loans, that is, loans sold in private-label securities. Indeed, in one of the hardest-hit states, Nevada, only one-third of pre-crisis debt remained outstanding at the end of 2010.

[FIGURE 1 OMITTED]

The third and final policy response to the housing crisis consisted of millions of loan modifications. Both the private loan modification programs and the government-supported ones, like the Home Affordable Modification Program (HAMP), emphasized payment reductions, not principal reductions. From their inception to date, 1.6 million homeowners have received modifications through HAMP with an average 36 percent reduction in their monthly payment (Department of the Treasury 2014).

The cumulative effect of these policies was that debt evolved in much the way that we would hope, given the results of the Eberly-Krishnamurthy model. My figure 2 shows that in 2008, the mortgage debt-service ratio--the amount of personal disposable income diverted to make mortgage payments--equaled more than 7 percent of income, the highest since the Federal Reserve started keeping records of this in 1980. Over the five years following 2008, the mortgage debt-service ratio fell to under 5 percent, the lowest level since the early 1980s. In other words, the combination of private and public efforts in the aftermath of the crisis largely achieved the policy goal of reducing household mortgage payments.

[FIGURE 2 OMITTED]

REFERENCES FOR THE WILLEN COMMENT

Department of the Treasury. 2014. "Making Home Affordable: Program Performance Report through the Third Quarter of 2014." Washington. http://www.treasury. gov/initiatives/financial-stability/reports/Documents/3QMHAReportFinal.pdf

Federal Housing Finance Agency (FHFA), Office of Inspector General. 2012. "FHFA's Oversight of the Enterprises Efforts to Recover Losses from Foreclosure Sales." Audit Report no. 2013-001. http://thfaoig.gov/Content/Files/ AUD-2013-001.pdf

Fuster, Andreas, and Paul S. Willen. 2013. "Payment Size, Negative Equity, and Mortgage Default." Working Paper no. 19345. Cambridge, Mass.: National Bureau of Economic Research.

Zandi, Mark. 2010. "The Economic Impact of Tax Cut Proposals: A Prudent Middle Course." Moody's Analytics Special Report, September. https://www.economy. com/mark-zandi/documents/Tax_Cuts_091510.pdf

(1.) Atif Mian and Amir Sufi, "Why Tim Geithner Is Wrong on Homeowner Debt Relief," Wonkblog (blog), Washington Post, May 14, 2014. http://www.washingtonpost.com/blogs/ wonkblog/wp/2014/05/14/why-tim-geithner-is-wrong-on-homeowner-debt-relief/

(2.) Mass principal reduction would have required taxpayer funds. According to the Flow of Funds, more than half the mortgage debt outstanding in 2009 was directly insured by the federal government and a majority of the rest was held on the balance sheets of depository institutions insured by the federal government. Mortgage-backed securities not insured by the government accounted for less than 20 percent of mortgage debt.

(3.) Lenders can pursue borrowers for the "deficiency," the difference between what the borrower owes and what the lender recovered from the foreclosure, but they rarely do. FHFA data suggest a recovery rate of less than 1/4 percent (see FHFA, Office of the Inspector General 2012).

(4.) In particular, between 2008 and 2014 the Federal Reserve purchased $2.8 trillion of agency MBS.

Table 1. Effect of Infrastructure and Tax
Cuts on Marginal Propensity to Spend

Infrastructure                          $1

Tax cuts (by income quintile)
  1                                  $1.12
  2                                  $0.70
  3-4                                $0.44
  5                                  $0.40
MDR                              $0.05-0.07
"Targeted MDR"                       $0.18

Source: Zandi 2010.

GENERAL DISCUSSION

John Haltiwanger thought the attention that Janice Eberly and Arvind Krishnamurthy paid to the impact of the housing market collapse on consumption was worthwhile, but he suggested that a different mechanism may be equally relevant. In the Great Recession, young and small businesses were hammered in those places where housing prices fell the most, to a degree that had not happened since 1980. The paper's model has households using their balance sheets mainly to consume, but one could also examine a model in which households use their balances to start businesses. The implication is that the decline in household balance sheets may have contributed to the observed decline in the pace of entrepreneurship in the Great Recession. Recent evidence shows that young firms are very important for job creation and productivity growth, so this impact of the housing market collapse is potentially quite important. He believes looking at this alternative mechanism might raise different questions about the kind of policy instruments the authors are thinking about.

Bradford DeLong said he remained mystified that conforming refinancing loans with equity kickers were not offered to all underwater and above-water homeowners alike. Instead, the debt overhang was removed through foreclosures and some case-by-case renegotiations. It was brutal, as discussant Paul Willen had acknowledged, and it is not clear that it is over yet. Even though during the housing bubble a million single-family homes above trend were being built each year, since 2007 the annual total has dropped to half a million, far below the long-run trend of 1.2 million a year. Now the country is 4 million single-family homes short, based on pre-housing-bubble trends, which translates into 4 million families living in makeshift situations, including relatives' basements. Strangely, this enormous overhang is not exerting any pressure for a single-family housing construction recovery. It is clear that both these potential homeowners and the lenders are unwilling to take on the types of risk they routinely took before 2008. Nevertheless, the single-family housing credit channel has not been restored to its old status. Is this a good finance pattern? Was the previous pattern a poor idea in the first place, or is the country now incurring enormous amounts of societal welfare losses?

Commenting on Willen's discussant remarks, Robert Hall said the continuing decline in household debt service that Willen noted has brought with it a negative effect, since the debts are being paid off by forgoing consumption. The resulting consumption squeeze will not end until the debt-income ratio stabilizes. Hall also commented on discussant Austan Goolsbee's remarks about what is preventing mortgage modifications. Two phenomena are preventing it, Hall argued. One is the "sleeping dog"--that is, households unthinkingly continuing to service mortgages that were deeply underwater. Contrary to what the paper predicted, he agreed with Goolsbee that the number of such households was very large, and most of them have recovered as housing prices have recovered. The other barrier to modifications is what Hall called the "ringing phone syndrome": people simply no longer paying attention when lenders call to make a proposal. The very low number of modifications seems to support this and explain why the modification programs failed. Nearly every affected household turned out to have either the sleeping dog or the ringing phone syndrome. Hall agreed with Goolsbee as well that the right approach would have been to set up a matching system to get people out of the houses they could not afford and into the right houses, but this fundamentally necessary approach was never considered.

Benjamin Friedman thought it would be very useful to know why strategic defaults have been as limited as they have been. For years--since the crisis began--economists have predicted that one would see a flood of strategic defaults. And although it happened in a few places, nationwide the rate of strategic defaults has been far lower than expected.

Friedman also echoed what Goolsbee had said about the difference between losing one's house to foreclosure in the recent crisis and what that used to mean in American life. The traditional notion involved losing something a family had put its life savings into, and even though this also has happened recently, many of the people foreclosed on never had any investment in their house to begin with. Many had bought homes with nearly 100 percent loan-to-value ratios. The discussion of this whole problem would be well served if this newer reality were more explicitly addressed.

Christopher Carroll noted that the paper's authors use an elegant model, in the spirit of work by Gauti Eggertsson and Paul Krugman as well as work by Guido Lorenzoni and Ricardo Caballero, among others, in which the Great Recession's big decline in consumption reflected liquidity problems, with the banks cutting back on lending. However, Carroll said that if that had been the only story, now that the debt-to-income ratio has dropped enormously and banks are healthy again one would expect consumption to spring back again--yet it has not done so. In his view, what has happened is that uncertainty remains, and it seems to be even greater than it was before. Before the Great Recession, risk premiums were at their lowest rates in recorded history, and confidence in the future was high.

Carroll argued that the difference in the degree of uncertainty between then and now is mostly responsible for the difference in the consumption and saving behavior. In 2007, the savings rate was 2 percent, according to the revised data, which was an all-time low. Therefore, perhaps one ought not ask why we have not returned to that period's consumption and saving levels. Perhaps those levels were inappropriate. After financial crises, as Carmen Reinhart and Kenneth Rogoff have famously argued, the recoveries tend to be very slow and drawn out. Carroll averred that this may be because after financial crises, uncertainty remains high for a long time, and this, rather than the banking sector's more mechanical difficulties, may be what makes post-crisis recoveries so slow.

Robert Gordon recounted a personal story in which a new mortgage he had gotten in 2011 at a rate of 5.25 percent was offered to be refinanced two years later at just 2 5/8 percent on a 7-year ARM. His question was. Why are banks today so eager to offer windfall refinancing like that and reduce the amount they earn, yet so unwilling to do the same for lower-income homeowners who are underwater? As far as the high foreclosure rates, the damage one must also consider is what large numbers of foreclosures do to entire neighborhoods, where empty homes have to be torn down, as in Detroit. The true cost of foreclosure is that having vacant houses on one's own block creates an externality. There is a loss of asset value in the whole economy that comes from the declining real value of these houses, and that in turn stems from the way the federal government and the banking system have treated so many people over the last seven years.

Responding to DeLong's comments about the steep drop in home building, Gordon suggested that another contributing cause is the trillion dollars in student debt that now burdens consumers. Simply put, many young people have moved back in with parents because of high student debt, which they cannot escape through bankruptcy. When one combines this reality with the country's extremely slow wage growth and rapid growth in income inequality, one can see that the economy today has deep structural problems.

Returning to the conundrum of the very low level of strategic defaults, Frederic Mishkin asked the authors how they built that into their model, given that it was an optimizing model. The gap between what economists expected before the recession regarding strategic defaults and what has actually materialized has been very wide, so understanding why that has been the case may have important implications.

Caroline Hoxby pointed out that the banks must have been able to see what Willen saw in his analysis as well, namely that after 5-year resets people were a lot less likely to default than they were after 7-year resets. She added that the banks must also have been aware that people like to stay in their own houses rather than strategically default, regardless of the reason. It remained difficult for her to understand, then, why the banks would not want to modify the payments in the short-term on their own, rather than worry about writing down the principal one way or the other. It might suggest that the banks felt that households were fundamentally mismatched with the houses they were paying mortgages on--but then, why had the banks lent them the money in the first place?

Wendy Edelberg said that to know whether principal write-downs might have been useful would depend on the timing. The first signs of pain in the housing market came before the persistent bad news that emerged in labor markets and with wages. In her view, if the causality ran from the problems in the housing market to the subsequent problems in the labor market, the right solution would be to stop the foreclosures first. Another point is that people do not default only for strategic reasons, they can also default because life-cycle events occur that make it necessary for them to move.

When the housing crisis first happened, Edelberg related, many thought that if enough principal write-downs were done across the board, troubled homeowners could get out of mortgages without defaulting. But this turned out to be unrealistic. Echoing Goolsbee's comment, Edelberg said it was generally expected that there would be losses and it was just a matter of who was going to take them. A lot of people were in homes they could no longer afford or that were so big they never could afford them in the first place, but now with the price declines perhaps they could afford to buy them. The matching problem that Hall brought up was actually in many ways solved, in the sense that they belonged in the house they were already in, just at the new price.

Matthew Weinzierl picked up on the question of how people end up in bad mortgage debt situations in the first place. One dimension worth examining may be the policy choices buyers have and the incentives different types of borrowers are given to take out loans that are too big. If a market has speculators trying to game the system and myopic buyers with a tendency to get in over their heads, that might reinforce the result that a payment modification is a better strategy, even in a general equilibrium sense, than principal reductions would be.

Looking back at the state of the housing market before the crisis, Jonathan Pingel noted that the misallocation of housing resources was connected with house price expectations. It took a long time before people realized that home purchases were not going to remain a fantastic investment forever. Even as the crisis began, many thought the problem would remain a small one and that price appreciation would resume. Since a lot of the misallocation was a function of erroneous expectations, the important question now is how economists think about building such expectations into their own models.

Paul Willen said there is little evidence that people were diverting money from consumption to pay down debt. The Krugman-Eggertsson story is one in which the contract requires that when a home price goes down, the borrower has to make higher payments to reduce the level of debt, driving down consumption. But in fact, Widen said, U.S. mortgages are specifically designed so that changes in house prices have no effect on the repayment schedule of the mortgage. In other words, fading house prices do not force homeowners to divert money to pay down debt. Widen said he has seen little evidence that people are "curtailing" or voluntarily paying down their mortgages. Flow of Funds data show that considerable mortgage deleveraging has occurred but that it has largely resulted from write-downs by lenders and, to a lesser extent, scheduled amortization.

Arvind Krishnamurthy responded, first, by addressing strategic defaults. It seems to economists that strategic defaults should happen much more often than they do, he said, because they are making the error of treating the default choice as static, one in which the homeowner must decide "today." But once one treats it as a dynamic problem, the intuition changes, because then one sees that the homeowner is weighing the choice of defaulting today against delaying defaulting until the next period. The only cost of that second choice is making another mortgage payment, a flow cost. So for a good portion of the equity space--the "underwaterness" space if you will--what the homeowner will choose is to continue to pay the flow cost, keeping the possibility that home prices rebound and the homeowner avoids default. It only becomes a better choice to default "now" if prices fall sufficiently low. This is why a reduction in the monthly payments can have a huge effect on the probability of default, as compared to a reduction in the principal, because in the former one is affecting the flow cost, and that is the most pertinent part of the choice.

Krishnamurthy acknowledged that Goolsbee's psychological profiles, such as people simply not paying attention, might also help explain why some strategic default options were not taken. Nevertheless, he believed that the dynamics of exercising a "future" default option go quite far in helping one to understand why people often take a long while before defaulting.

Concerning why more modifications did not take place, he noted that in the paper (but not the conference presentation) he and coauthor Janice Eberly actually do examine the question, and based on that they propose that such modifications be built into contracts ex ante. One of their suggestions is to have a mortgage contract where the buyer has the option to automatically refinance into a variable rate. Although that sounds exotic, in fact it is what people already have, inasmuch as they have the right to prepay the mortgage. Indeed, investors' pricing of mortgage-backed securities accounts for this risk of prepayment. Renegotiations have been inefficient, and a way to end that would be to build into the contract ex ante an efficient renegotiation. Giving homeowners the option to reduce their debt burden via an automatic reset into a variable rate achieves this renegotiation.

Responding to Haltiwanger's comments about depressed investment in startups, Krishnamurthy pointed out that in the model, nonhousing consumption, which is C, enters the utility function with some curvature. They can broaden the model to think of C as including investment in startups, and that would not change the way they interpreted the model or any of the findings.

Concerning the irrational assumptions of homebuyers who thought their incomes would be high forever only to discover that was not the case, he noted that he and Eberly analyzed this by looking at both temporary and permanent income shocks. When a shock is permanent, the best thing to do is to sufficiently smooth out the foreclosure. If people had been "misallocated" into houses, the best thing is to get them out of those houses, not all at once but in a smoothed way, over time.

Finally, Krishnamurthy addressed Goolsbee's analysis of auto spending, in which the different spending responses from high-leverage versus low-leverage households might lead one to think the policy solution is to make the differential spending responses the same by reducing the leverage of the high-leverage households. In Krishnamurthy's view, however, the differential spending responses are only an empirical finding, which should be used to identify the underlying problem rather than to engineer a policy solution. In the housing case, the data showed that the underlying problem was liquidity constraints. The right question is, What is the optimal policy to address these liquidity constraints? Here the optimal policy is not to make the leverage levels the same across households, but to reduce current payments.

Janice Eberly made a few additional responses. In the case of a permanent income shock, she said, one still has to address avoidable versus unavoid able foreclosures. The paper addresses avoidable foreclosures, in which intervention should be designed to increase the homeowner's consumption, reducing the probability of foreclosure. If a permanent shock has led to inefficient negotiations, those are the unavoidable foreclosures, and the best approach is simply to try to smooth them out.

One important challenge the paper does not address, she acknowledged, is the allocation of housing across space, something DeLong referred to. There is huge geographic heterogeneity both in where the foreclosures occur and where the housing demand is. The policies under consideration in this discussion do not help to smooth that aspect of the foreclosure problem, which constitutes one of the unresolved human costs in the housing market that remain with us.

JANICE EBERLY

Northwestern University

ARVIND KRISHNAMURTHY

Stanford University

(1.) With linear utility, the consumption allocation is formally indeterminate, but any amount of curvature will produce consumption smoothing in this way.

(2.) In principle, the household could sell the home and buy another to reoptimize consumption. We assume that this is costly or not feasible as a way of smoothing consumption for temporary shocks. We discuss borrowing further below.

(3.) In principle, the household could also sell the home and use the proceeds to buy a new one, reoptimizing over the two types of consumption. This means that the household is effectively not liquidity constrained, since the home becomes a liquid asset. We assume that this option is not available to the household, either because transaction costs are high, the home is underwater and the household has insufficient other assets (so that a home sale--a short sale--would require a loan default), or credit market frictions prevent the homeowner from consuming out of real estate wealth.

(4.) The importance of liquidity constraints during the crisis is emphasized in the empirical results of Dynan (2012) using household consumption data.

(5.) Note that the government's discount rate is also 1, so we do not give the government an advantageous borrowing rate compared to private agents.

(6.) The budget constraint does not require that the program pay for itself unless Z = 0. If Z > 0, the program provides net funds for mortgage modifications, and date 1 payment reductions can be larger to the extent that they are repaid at date 2 with negative transfers, [t.sub.2] < 0.

(7.) We assume that private lenders use the same discount rate as the government, even in the crisis. If the government can access credit markets at a lower rate than private lenders, our results are strengthened.

(8.) In general, principal reduction to reduce the underwater share of mortgages takes borrowers to an LTV (loan to value) of 100 at best, which does not generally create borrowing capacity. Even if it did, as we allow above, our analysis shows that direct transfers at date 1 remain more efficient.

(9.) Note that we have not assumed that the government has a lower cost of capital than private agents. This result relies only on the fact that by transferring resources at date 1, the government directly relaxes the liquidity constraint, whereas date 2 resources require the agent to borrow and transfer them to date 1. With any default risk, the price to agents of doing so will exceed the cost of the direct transfer.

(10.) This is the same intuition as in the Leland (1994) model of dynamic corporate capital structure.

(11.) A mechanism such as this is apparent in the observed response of households to crisis-related cash transfers which, as documented by Hsu, Matsa, and Melzer (2014), had a significant effect in reducing foreclosures. They find that higher unemployment benefits (which are not repaid later) have a large impact in reducing the probability of default across states and over time.

(12.) The latter effect is likely to dominate in fact. Since the household defaults when the home price outlook is particularly bleak, the details of the left tail distribution do not matter for behavior. That is, the details of bad outcomes do not matter to the household since it defaults in those states. However, the borrower does not default when home prices are expected to improve, so the upper tail is relevant for forward-looking decisionmaking. This is a generalization of Bernanke's (1983) "bad news principle" in the two-sided setting of Abel, Dixit, Eberly, and Pindyck (1996). Here, we have a "good news principle" for borrowers because they have a default, or a put, option.

(13.) Our analysis assumes that the income shock is temporary, which is the interesting case for policy analysis to avoid default. If a shock is permanent but not common to all households, then default may be optimal as reallocation is necessary. In that case, optimal policy may still favor delay (if there is still price or other uncertainty to be resolved or the price elasticity of foreclosures declines over time). Government policy may also favor less-disruptive forms of default, such as short sales or rental-in-place arrangements, which can reduce the deadweight cost of default. Policy may also encourage lender renegotiation by giving more bargaining power to borrowers in these instances, through legal procedures such as bankruptcy and cramdown.

(14.) We assume that the lender has the bargaining power in renegotiation. In intermediate cases of shared bargaining power, the results would depend on the allocation of bargaining power, but the general findings would still hold. Furthermore, we have discussed the case when the borrower remains in his home. But as we showed in earlier sections, the loss of borrower wealth due to the decline in [P.sub.2] will generally lead the borrower to consume less housing. Suppose the loan is renegotiated to D' at which point the borrower immediately repays the loan by selling his home, and then rents a smaller home for one period. In this case, the lender's payoff is D' + [rc.sup.h], which is the same as in equation 36; thus our analysis is unaffected by this consideration.

(15.) In this analysis we are ignoring the fact that ex post loan forgiveness implies that lenders will thereafter expect loan forgiveness and price it into subsequent contracts, making credit more expensive. At this point, however, our intention is to examine under what circumstances even ex post loan forgiveness may make sense. We return to this topic later when we discuss ex ante security design.

(16.) Moreover, we have not modeled the payment stream, but in practice, for loans not in distress, the lender continues to collect the interest and principal on the higher loan balance.

(17.) We have kept the government and the lender separate for the sake of clarity. However, in practice the government-sponsored enterprises (GSEs), Fannie Mae and Freddie Mac, are each a hybrid, where a government entity guarantees loans and hence holds credit risk. In this case, there is a direct incentive for these entities to write down principal as a way of avoiding costly defaults. In fact, there was an active debate around the extension of the PRA (principal reduction alternative) loan modification provision to the GSEs, which was ultimately not adopted by the GSE regulator, the Federal Housing Finance Agency (FHFA). The FHFA promoted an expanded refinance option, which we discuss later.

(18.) A perverse example occurred early in the crisis, as pointed out by Mayer and others (2014), when the Countrywide modification program was made available to borrowers who defaulted by a future date, inducing strategic default leading up to the specified time. Such a design increased the cost of the program, whereas our model suggests program features to limit this adverse selection problem for modifications.

(19.) This may capture moral hazard or other information problems associated with the rental market.

(20.) While the present value of the payment streams can be equated, the time path differs. In particular, a written-down loan will have a lower initial payoff value, while a refinanced loan will have a lower payoff value than the original loan, but will amortize the remaining lower payoff value over time. The distinction does not affect the incentive for strategic default (since by definition the payoff value is not paid in case of default). However, it can matter for the incentive or ability to prepay the loan. Hence, face-value write-downs may tend to increase prepays and turnover more than refinancings do.

(21.) Refinancings often further reduce payments by extending the term of the loan, but that would confound the effects of the interest-rate reduction and the term extension in this example, without changing the essential point.

(22.) Interestingly, refinancings generally occurred during the financial crisis in two ways. Either borrowers had positive equity and could refinance in a competitive market; these are unconstrained borrowers in our setting. This would have been possible regardless of the housing collapse. Alternatively, underwater borrowers from the GSEs, Fannie Mae and Freddie Mac, who were current on their loans, could refinance through the HARP program, and a similar option was made available to some non-GSE borrowers under the National Mortgage Servicing Settlement. (The terms of the National Mortgage Servicing Settlement are described here by the settlement monitor: https://www.jasmithmonitoring.com/omso/ reports/final-crediting-report/) These borrowers were also arguably unconstrained, in that they were making their payments on time and were not in payment distress. Such circumstances fit the model's recommendation for implementing principal reduction for unconstrained borrowers to avoid strategic default. (Because the program was made directly available to borrowers by the GSEs, lenders/investors did not have the option to delay.) Through HARP, borrowers received [t.sub.1] > 0 and [t.sub.2] > 0, financed by a reduction in the mortgage value held by lenders/investors.

(23.) FHFA Refinance Report (http://www.fhfa.gov/AboutUs/Reports/ ReportDocuments/1Q2014RefinanceReport.pdf)