Credit policy as fiscal policy.

Lucas, Deborah

ABSTRACT The $1.6 trillion that U.S. households borrowed in 2010 through government-backed direct loan and loan guarantee programs--most notably from Fannie Mae and Freddie Mac, the student loan programs, and the Federal Housing Administration, but also more than 100 smaller programs--provided credit subsidies and relaxed credit-rationing constraints that caused both borrowing and spending that year to be higher than they would otherwise have been. A simple theoretical model illustrates these channels. Estimates of the increases in borrowing, scaled by multipliers similar to those applied to traditional government spending and tax policies, suggest that the programs provided a fiscal stimulus of roughly $344 billion, similar to what was provided by the American Recovery and Reinvestment Act of 2009. Although there is considerable uncertainty about this point estimate, its size suggests the importance of taking the stimulus and automatic stabilizer effects of federal credit programs into account, particularly during economic downturns that are accompanied by severe financial market distress. However, though credit programs are shown to be a relatively low-cost source of fiscal stimulus, to assess their overall welfare implications, these benefits must be weighed against the significant costs of the programs during more normal times, including the likelihood that lax federal credit policies were an exacerbating cause of the 2007 financial crisis.

**********

With the notable exception of William Gale (1991), federal credit policies have been largely overlooked in analyses of the macroeconomic effects of fiscal policies. In this paper, I make the case that because of this omission, the amount of these policies' fiscal stimulus to the U.S. economy has in recent times been seriously underestimated. In general, this error is likely to be particularly severe during downturns that are accompanied by major disruptions in private credit markets, as occurred during the Great Recession of 2007-09 and in its aftermath. The estimates here for 2010 suggest that the stimulus effects of federal credit programs were likely to have been similar in magnitude to those of the American Recovery and Reinvestment Act of 2009 (ARRA), which provided about $392 billion of additional spending and tax cuts that year (CBO 2011b). I also find that federal credit subsidies had a big "bang for the buck"--a large amount of stimulus per $ 1 in taxpayer cost. Furthermore, government credit programs acted as automatic stabilizers because their participation rates and loan amounts could increase during the downturn without legislative action.

The finding of large stimulus effects in 2010 reflects the size and reach of U.S. federal credit support activities, along with the apparent unwillingness of private lenders to extend credit to certain borrowers and market segments during that year. Through its traditional credit programs, the U.S. government routinely provides direct loans and loan guarantees for housing, education, agriculture, small businesses, energy, trade, and other private activities via more than 150 separate programs that appear in the federal budget. New loans originated under these programs totaled $584 billion in 2010. (1) Federal credit-related activities also include implicitly or explicitly guaranteeing the obligations of government-sponsored enterprises such as Fannie Mae and Freddie Mac, the Federal Home Loan Banks, and the Farm Credit System; and insuring bank deposits and defined-benefit pension plans. Notably, Fannie Mae and Freddie Mac, which had received explicit government backing by that time, guaranteed more than $1 trillion in newly originated mortgages in 2010.

To understand how, in principle, such a surprisingly large stimulus could be attributed to incremental loan volume arising from federal credit programs, it is necessary to first consider the ways in which government credit subsidies can affect lending volumes. There are two distinct channels: (i) a traditional elasticity channel (the intensive margin), whereby the demand for loans increases when the costs of borrowing fall; and (ii) a credit-rationing channel (the extensive margin), whereby individuals who are unable to obtain the desired amount of credit at any rate from fully private lenders (for instance, because of asymmetric information about borrower quality) are able to borrow when a direct government loan or a government loan guarantee is made available. A simple model, in the spirit of Michael Rothschild and Joseph Stiglitz (1976), and related analyses shows that the second channel can be highly nonlinear, and that it can be the more important of the two when both are operative. The model also shows why credit rationing can, in some instances, be alleviated with quite small credit subsidies.

Having established that, in principle, credit subsidies can generate large increases in loan volume, the next step in making the case for a potentially large stimulus effect is to link increased loan volumes to increased aggregate output. This connection is made using a fiscal multiplier approach, following a large body of literature that includes Alan Auerbach and Yuriy Gorodnichenko (2012), Charles Whalen and Felix Reichling (2015), and the Congressional Budget Office (CBO 2011b, as well as the references therein). A multiplier approach has the strengths of simplicity and empirical grounding, but there is significant uncertainty associated with point estimates. Because traditional multiplier analysis focuses on tax and expenditure policies, adjustments are required in order to apply existing estimates of fiscal multipliers to credit subsidies. A key adaptation made here is that the multipliers suggested by the literature for various categories of government spending are applied to the estimates of incremental borrowing rather than directly to the credit subsidy amounts. The idea is that because taking out a loan generally involves significant effort and cost, people tend to spend the borrowed funds quickly. When borrowed funds are spent on goods and services, the effects on aggregate output should be similar (or perhaps stronger, because the funds are unlikely to be saved) to those arising from traditional fiscal tax and spending policies directed at similar activities. However, when the borrowed funds are used to refinance existing debt, as when mortgages are refinanced, little money is freed up for new spending and the multiplier effect is assumed to be much smaller. Similarly, on a per-dollar basis, mortgages used to purchase existing houses are unlikely to contribute as much to aggregate demand as loans for education or for investment by small businesses. In principle, the multiplier effects of credit could also be reduced by the fact that the loans need to be repaid. However, because most federally backed loans have a long maturity, the effects of repayments are largely outside the horizon of interest.

Estimates of the subsidies associated with the government's major credit programs are needed to do bang-for-the-buck calculations and to predict increases in borrowing along the intensive margin for each program. For most noncredit fiscal policies, the standard way to assess subsidy cost is as the net cash outflow in a given year, which corresponds to the budgetary cost. Credit subsidies are more complicated because loans and loan guarantees involve uncertain cash flows that extend over many years. For traditional credit programs, federal budgetary estimates of credit subsidies are on an accrual rather than a cash basis. Calculating subsidy cost involves projecting cash flows over the life of the loan and discounting them to the date of origination at Treasury rates to produce a lifetime or accrual cost of the loan. Most administrative costs are omitted from these subsidy estimates (but accounted for elsewhere in the budget, on a cash basis). The legislatively mandated practice of discounting at Treasury rates and omitting administrative costs causes budgetary estimates of credit subsidies to understate the full economic cost to taxpayers of credit assistance (Lucas and Phaup 2010; CBO 2012, 2014). To provide a more accurate cost measure that is conceptually the most comparable to the cash cost of other types of stimuli, the cost estimates used here are fair-value estimates derived from pricing models that my colleagues at the CBO and I have developed to provide fair-value estimates for most major federal credit programs. Conceptually, the fair-value subsidy cost is the lump-sum cash payment at origination that the government would need to make to private lenders in a well-functioning market to induce them to extend credit at the same terms to the same people as under the government program. These fair-value estimates often significantly exceed reported budgetary costs, but for most programs they nevertheless represent a modest fraction of the loan principal.

Extensions in loan volume at the extensive margin are a quantitatively important driver of the stimulus effects of credit programs. Unfortunately, the estimates of increased borrowing along the extensive margin are by necessity subjective because data are not available to rigorously measure these effects. However, the estimates are informed by the programs' histories and by the observed market behavior of private lenders, and the conclusion of a large stimulus effect is robust to fairly conservative assumptions about the size of these margins.

Federal credit support has many other important economic consequences, and it is beyond the scope of this analysis to attempt to quantify its net effect on social welfare. To undertake a welfare analysis, the salutary effects of credit programs during severe downturns that are highlighted here would need to be weighed against the inefficiencies that government credit policies tend to cause during more normal times. These issues have been written about extensively (Gale 1991; Lucas 2012, 2014; La Porta, Lopez-de-Silanes, and Shleifer 2002): Credit subsidies tend to be target-inefficient; they are opaque; they can distort the allocation of capital and crowd out more productive private investment; they encourage excessive levels ot household and business debt; and they create incentives for excessive risk taking that have systemic consequences. Furthermore, some observers have suggested that the overly liberal credit policies of Fannie Mae and Freddie Mac were an underlying cause of the 2007 financial crisis. A further caveat to this analysis is that credit policy includes a panoply of regulations that are likely to have fiscal effects not considered here.

The remainder of this paper is organized as follows. Section I lays out a model that illustrates the channels through which federal credit programs can provide an economic stimulus. Section II provides a context for the analysis by giving an overview of federal credit support activities. Section III explains the calibration of inputs into the model, including subsidy rates for each major program, elasticities, extensive margin effects, and multipliers. Section IV presents estimates of the stimulus provided by federal credit assistance in 2010 under the base case assumptions and for a range of alternative assumptions. Section V concludes.

I. Theoretical Underpinnings

To understand how government credit programs might be expected to affect aggregate borrowing and ultimately aggregate demand, this section lays out a stylized model of credit markets that illustrates the channels through which federal credit subsidies affect loan volumes and pricing. The model is in the spirit of Rothschild and Stiglitz (1976) and other analyses that emphasize the effects of asymmetric information or costly state verification on insurance or credit market outcomes and the potential effects of government intervention. (2) The conceptual linkages between incremental loan demand and aggregate demand are then quantified in section II to estimate the stimulus effects of federal credit programs in 2010.

1. A. Government Credit as a Fiscal Policy Tool

We assume that the credit market consists of large numbers of two types of borrowers, Type A and Type B, and a large number of competitive lenders. Loans last one period, and utility is realized at time 1 when the loan is repaid. (3) The population share of Type A borrowers is [[mu].sub.A]. Type A borrowers always repay their loans in full. Type B borrowers default and repay a fraction, [[rho].sub.B], of the promised amount. Both know their own types, and have the same utility function that depends on fixed parameters v and [gamma], and on the amount borrowed, L, net of the expected amount repaid inclusive of interest, RL:

(1) U(L) = [v[L.sup.(1-[gamma])]/(1 - [gamma])] - RL for L [greater than or equal to] 1 or L = 0.

Setting a minimum loan size reflects the possibility that the activities financed may have a minimum required investment amount, and also the presence of fixed costs in loan origination. The desired amount of borrowing is found from rearranging the first-order condition that results from maximizing equation 1 with respect to the choice of L:

(2) [L.sup.*.sub.i] = [([R.sub.i]/v).sup.1/[gamma] for i = A,B.

Competitive lenders offer borrowers a contractual interest rate and loan size that satisfy a zero-profit condition. The supply of loans is assumed to be infinitely elastic at these equilibrium rates. Lenders cannot identify the type of an individual borrower directly, but they know the population shares and can infer whether a borrower of each type will accept the loan terms [L([theta]), r([theta])] offered, where r([theta]) is the contractual interest rate on the loan, and [theta] is the lender's information set. Thus the lender anticipates whether there is a pooling equilibrium or a separating equilibrium and will choose an offer consistent with that inference and with the zero-profit condition. The offered rate, r([theta]), reflects the fact that the gross expected return to lenders, 1 + [r.sub.m]([theta]), includes a premium for the systematic risk in risky loan returns and any other priced risks. This market rate schedule is an equilibrium outcome that is taken as known and as exogenously given for this partial equilibrium analysis.

The model admits both pooling and separating equilibria (and possibly both), depending on the selected parameter values. In a separating equilibrium, Type A borrowers are offered the risk-free rate, [r.sub.f], and a loan amount that is the lesser of the optimal loan amount implied by equation 2, with [R.sub.A] = 1 + [r.sub.f], and a loan amount that is the maximum size that is small enough to deter Type B borrowers from mimicking Type A borrowers. Type B borrowers are offered a contract with a gross promised return (1 + [r.sub.m]([theta]))/[[rho].sub.B], an expected gross repayment [R.sub.B] = 1 + [r.sub.m]([theta]), and a loan amount that satisfies equation 2. Because the minimum loan size is 1, it is possible that depending on parameter values, one or both types will not borrow anything.

In a pooling equilibrium where the offered rate is a population-weighted average of the two separating rates, Type Bs would like to borrow more than Type As. However, to maintain pooling, Type Bs can only borrow [L.sup.*.sub.A], the optimal level of borrowing for Type As at the offered rate. The offered rate, r([theta]), solves the zero-profit condition:

(3) 1 + [r.sub.m]([theta]) = [[mu].sub.A] (1 + r(theta])) + (1 - [[mu].sub.A]) [[rho].sub.B] (1 + r([theta])).

Rearranging implies that

(4) 1 + r([theta]) = 1 + [r.sub.m](theta])/[[mu].sub.A] + (1 - [[mu].sub.A])[[rho].sub.B].

It follows immediately that as the proportion of Type Bs becomes large, and as their expected repayment becomes small, there will be no pooling equilibrium because the required return goes to infinity. There may be a separating equilibrium in which only Type Bs borrow.

This model can be easily extended to include government credit guarantees. We shall see that the introduction of guarantees can significantly change equilibrium quantities and the rates offered by private lenders, and that large increases in borrowing may be achieved at a low subsidy cost to the government. The government guarantees a portion, g, of the promised repayment, R. For the guarantee to affect outcomes, g > [[rho].sub.B]. With the guarantee, the offered rate in the pooling equilibrium falls to

(5) 1 + r(theta]) = 1 + [r.sub.m]([theta])/[[mu].sub.A] + (1 - [[mu].sub.A])g.

The offered rate in a separating equilibrium where only Type Bs borrow is also given by equation 5, with [[mu].sub.A] = 0. Note that in all cases, g is in the information set [theta] and affects the equilibrium expected return (for example, with a 100 percent credit guarantee, the expected return is the risk-free rate).

The subsidy rate, s, is defined as the cost to the government of providing the guarantee per $1 of loan principal:

(6) s = [pi](g - [[rho].sub.B])(1 - [[mu].sub.B]),

where [pi] incorporates the market risk premium associated with these losses.

Result 1: If there is a pooling equilibrium in the private market, the introduction of a guarantee lowers the offered rate and increases loan demand through an elasticity effect. The elasticity effect operates at the intensive margin.

Result 2: If there is an equilibrium in the private market with no borrowing or with only Type Bs borrowing, then there exists a g [less than or equal to] 1 such that a pooling equilibrium exists. This creates an expansion of lending along both the extensive and intensive margins.

The potential for large increases along the extensive margin induced by the availability of government guarantees is the mechanism whereby federal credit programs can have large stimulus effects. The link between borrowing and stimulus also involves an assumption about how the borrowed funds are used, as discussed in the next section. Clearly, similar conclusions about the stimulus effects of government credit follow from direct lending programs. A more general specification--for example, as given by Stiglitz and Andrew Weiss (1981)--would allow for the probability of default and for the expected recovery rate to also depend on the interest rate for Type B borrowers. This possibility was not incorporated for simplicity, but results 1 and 2 would still be expected to obtain in that more general setting. In that case, the introduction of a government guarantee would have the additional effect of mitigating default losses by making the loans more affordable.

[FIGURE 1 OMITTED]

Simulation of a parameterized version of the model illustrates the possibility of generating large increases in lending volume at a modest subsidy cost, primarily through the extensive margin. It also highlights the potentially high costs for government credit programs that fail to impose lending limits that prevent excessive borrowing by risky borrowers. This is the narrative that motivates the main calibration exercise in section IV.

Figure 1 shows the equilibrium lending volume, the full-information loan volume, and the cost to the government as a function of the government guarantee rate. The guarantee rate is varied between 0 and 1, but the guarantee only affects outcomes when g > [[rho].sub.B]. In this example, parameters are fixed at v = 1.1, [r.sub.f] = 0.01, [r.sub.m] = 0.04 [for Type Bs only], [[mu].sub.A] = 0.75, [[rho].sub.B] = 0.6, and [gamma] = 2.

Figure 1 shows that for guarantee levels below about 70 percent, the pooling interest rate is too high for Type As to participate. Hence, there is a separating equilibrium in which Type Bs borrow at a fair rate and Type As do not borrow. When the guarantee is sufficiently high, the offered rate under the pooling equilibrium falls to a level at which both types borrow. Total loan volume roughly quadruples because of the entry of the safe borrowers. For guarantee rates in excess of the entry level for Type As, aggregate borrowing increases in the guarantee rate through the extensive margin. However, these extensive margin increases are relatively small. Notice also that the subsidy rate, which is the cost to the government per $1 of loan guaranteed, is only 2 percent at the guarantee level that causes loan demand to quadruple. This demonstrates that credit subsidies can have a large bang for the buck because of the nonlinear effects of the subsidies. Increasing the guarantee to 100 percent has a small incremental volume effect, but increases the subsidy rate to 10 percent.

The model also has lessons for the efficient structuring of federal credit programs. The upward blip observed in the subsidy rate at g = 0.65 is a reminder that if the guarantee protects lenders against some of the risk of bad borrowers but is insufficiently high to attract good borrowers into the market, it will provide an inefficient subsidy to low-quality borrowers who would have borrowed anyway. In such cases, setting a high enough guarantee rate to attract new good borrowers lowers the subsidy rate by increasing the average pool quality. The model further suggests that it is important for the government to impose quantity limits in its direct loan programs or in guarantee programs where the government fixes the borrowing rate, in order to avoid excessive borrowing by bad borrowers. (4) Recall that in the pooling equilibrium with private lenders making rate and quantity offers, both types are limited to loan amounts that maximize Type As' utility at a zero-profit interest rate. If there were no constraint on quantities, Type Bs would borrow more than Type As and the subsidy rate would increase. For example, for the figure 1 parameters, faced with the pooling equilibrium interest rates, unconstrained Type Bs would borrow about 30 percent more. That would increase the average subsidy rate by degrading the quality of the borrower pool, and the total subsidy cost would increase by a corresponding 30 percent.

A natural question is whether the large discrete changes in loan volume induced by modest credit subsidies could occur in a setting with a large number of borrower types or under other information structures. I believe that the basic intuition is robust and that similar results would be found in more general settings, but it remains for future research to establish more general conditions under which these effects are present.

I.B. From Loan Demand to Aggregate Output

To translate estimates of the increase in the availability of credit and reductions in its cost into an estimate of increased aggregate output requires several steps. The first is to calculate how much incremental borrowing is induced by the credit programs through both the intensive and extensive margins, adjusting for the offsetting effect of any crowding out of existing private sector loan supply. The second step is to take into account multiplier effects that could cause the amount of incremental borrowing to differ from its ultimate effect on aggregate output.

Incremental aggregate borrowing, [DELTA]B, attributable to federal credit assistance net of crowding out, can be written as

(7) [DELTA]B = dA + S(dB/dS)-C,

where dA is incremental borrowing along the extensive margin, S(dB/dS) is incremental borrowing along the intensive margin induced by the subsidy S, and C is the amount by which private lending is crowded out in aggregate.

This reduced form represents the net effect of supply and demand factors on volume. No distinction is made between guaranteed and direct lending because, as discussed below, in both cases the subsidy mechanisms that induce incremental demand--reduced interest rates and fees, and a decrease in credit rationing--are the same. This incremental demand puts upward pressure on interest rates that may crowd out other lending. The size of the crowding-out effect depends on the elasticity of credit supply.

Incremental borrowing along the intensive margin, S(dB/dS), represents the sum of subsidy effects across individual credit programs. It can be approximated using estimates of the demand elasticities and estimated subsidies for each type of credit program. Specifically, the present value of subsidies associated with all new loans made in a given year, S, is multiplied by the corresponding demand elasticity, dB/dS. Hence, both previously constrained and unconstrained borrowers contribute to increased demand at the intensive margin.

Similarly, total borrowing along the extensive margin, dA, is a sum across individual program effects. As in Gale (1991), and fundamentally by necessity, these estimates are largely judgmental, although they are informed by observations about credit programs and markets. Note also that the ex post observed amount of federally backed borrowing includes the incremental borrowing induced by the credit programs.

A fiscal multiplier approach is used to translate the incremental amounts borrowed into changes in aggregate output. Let [DELTA][b.sub.i], denote total incremental loan volume in program i (the sum of the intensive and extensive margin effects) and [[mu].sub.i], denote the corresponding output multiplier. Then the net stimulus effect of federal credit programs, [DELTA]Y, is

(8) [DELTA]Y = ([summation over (i)] [DELTA] [b.sub.i][[mu].sub.i]) - C[[mu].sub.c].

Although traditional multiplier analyses focus on tax and expenditure policies, there are additional considerations in applying them to credit policies. Perhaps most important, although existing multiplier estimates can provide guidance on the relationship between the incremental amounts borrowed and increases in output, it does not make sense to apply them directly to credit subsidies. To the extent that traditional stimulus policies influence aggregate demand primarily because they provide additional spending capacity to hand-to-mouth or liquidity-constrained consumers, access to $1 in additional borrowing can be expected to have similar effects to $1 received from a grant program. However, the relationship between the cost of a credit subsidy and its effect on aggregate demand would be poorly measured if the multiplier estimates in the literature were to be directly applied. One source of this problem is that credit subsidies are measured on an accrual basis, and from the perspective of the borrower have a wealth effect rather than an income effect. (5) Furthermore, the value of credit subsidies cannot be converted to cash, and therefore the subsidies in themselves do not relax liquidity constraints. Nevertheless, an important question is how much stimulus is generated for each $1 in cost to taxpayers. To provide an answer, multipliers are applied to the incremental borrowing amount and the resulting increase in output is divided by the subsidy cost.

Other attributes of credit are also relevant in assessing the appropriate mapping to existing multiplier estimates for different types of policies. Because borrowers incur significant costs to take out and carry a loan, borrowed funds are likely to be disbursed fairly quickly. However, not all the money will be used for consumption or new investment. Particularly with mortgages, a large fraction of new borrowing goes toward refinancing existing debt or buying a home that is part of the existing housing stock. Another consideration with credit is that, over longer horizons, its stimulus effects could be reversed as the loans come due. However, because most federal loans have long initial maturities, the short-term effects of repayment, which are of interest here, are likely to be minimal.

II. Background on Federal Credit Programs

This section provides background information on the size and nature of federal credit activities in order to give a broader context for the analysis of their fiscal stimulus effects and for the assumptions made in calibrating the model. Federal credit activities can be subdivided between programs classified in the budget as credit programs, which are referred to here as "traditional credit programs," and other programs that provide credit support but are not classified in the budget as credit programs, such as Fannie Mae and Freddie Mac, bank deposit insurance, private pension guarantees, and certain tax credits and exemptions. For the purposes of estimating stimulus effects in 2010, the main focus here is on the traditional credit programs plus Fannie Mae and Freddie Mac.

II.A. Stock Measures of Federally Backed Credit

The large footprint of federally backed credit in the U.S. financial markets can be clearly seen by comparing the stock of government-backed credit balances with those of different types of private credit outstanding. (However, the flow measures presented later on are more directly related to the potential size of the stimulus that these activities provide in a given year.)

The outstanding balances of federal direct loan and loan guarantee programs for the period 1970-2015 are given in figure 2, which shows the historically unprecedented expansion in these programs in the aftermath of the 2007 financial crisis. In reporting on traditional federal credit programs, it is standard to combine direct loans (loans originated and funded by the government) and government loan guarantees because, all else being equal, these two forms of assistance are economically equivalent in the credit support provided and the subsidy cost to the government and ultimately to taxpayers.

[FIGURE 2 OMITTED]

The 2010 credit supplement to the federal budget (OMB 2010) lists more than 150 credit programs that are administered by various federal agencies and bureaus. Figure 3 groups the outstanding balances of federal direct loans and loan guarantees into major loan types--housing, education, farming, business, or other--for the period 1998-2010.6 Housing is the single largest category in all years, though federal student loans underwent the most rapid growth. The total amount of federal guaranteed and direct loans outstanding roughly doubled during the period, reaching about $2.3 trillion in 2010.

The volume of explicitly government-backed credit increased dramatically with the 2008 federal takeover of Fannie Mae and Freddie Mac. That action converted those two government-sponsored enterprises (GSEs) from private companies with implicit government guarantees into entities that are fully owned by the government and whose losses the government has a legal obligation to absorb. Figure 4 shows the totals for federal credit programs that include the credit obligations of Fannie Mae and Freddie Mac. Including these activities plus some of the emergency programs of the Federal Deposit Insurance Corporation (FDIC) and the Federal Reserve brought total outstanding federally backed credit to more than $8 trillion in 2010.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The programs included in figures 3 and 4 are ones in which the federal government has a fairly direct role in determining eligibility and underwriting standards for the credit it backs, and these are the focus of the stimulus estimates here.

The government provides credit subsidies through other programs as well, and some of these may also provide fiscal stimulus under certain market conditions. These credit-related activities include (i) federal deposit insurance, through the FDIC, which in 2010 covered $6.2 trillion in bank deposits; (ii) pension guarantees of private defined-benefit pension plans, through the government's Pension Benefit Guarantee Corporation, which in 2007 had an estimated $2.8 trillion in covered liabilities, according to Alicia Munnell, Jean-Pierre Aubry, and Dan Muldoon (2008); (iii) implicit guarantees to the Federal Home Loan Banks (FHLBs) and the Farm Credit System (FCS), which lower these institutions' funding costs (in 2010 the liabilities of the FHLBs totaled more than $800 billion, and those of the FCS totaled about $200 billion); (iv) support for financial institutions through the Troubled Asset Relief Program (TARP), including purchases of preferred stock that peaked at about $540 billion in 2009 but subsequently declined; and (v) the Federal Reserve System, which is a large participant in debt markets and whose actions affect market prices, but most of whose activities do not involve direct subsidies (the portion of the Federal Reserve's assets that are potentially relevant for subsidy calculations here are its loans to financial institutions and Maiden Lane holdings, which stood at $140 billion in 2010).

In sum, the outstanding balances in the government's traditional direct loan and loan guarantee programs plus the mortgages held or guaranteed by Fannie Mae and Freddie Mac totaled about $8 trillion in 2010. Including credit-related activities--such as bank deposit insurance, private defined-benefit pension insurance, implicit guarantees to the FHLBs and FCS, TARP, and the Federal Reserve's nontraditional programs--increases the sum of federally backed obligations to about $18 trillion.

By comparison, flow-of-funds data for 2010 indicate that there was outstanding home mortgage debt of $10 trillion, other consumer credit of $2.4 trillion, and business (corporate and noncorporate) debt of $10.8 trillion. These aggregates suggest that a large fraction of mortgages and consumer credit in the United States is federally backed, whereas most business debt is not. Governments are also large borrowers; in 2010 state and local government debt stood at $2.8 trillion, and federal debt held by the public totaled nearly $9.4 trillion. (7) As noted by Gale (1991), spending by users of state and local debt is also affected by the associated federal credit subsidies.

[FIGURE 5 OMITTED]

II.B. The Extension of Federal Credit over Time and over the Business Cycle

The pattern of disbursements (that is, new loans originated) of federally backed credit over time via the government's traditional credit programs as a share of GDP from 1992 to 2011 is shown in figure 5. Until 2009, disbursement volumes were fairly steady as a share of economic activity, fluctuating between about 2 and 3 percent of GDP. Disbursement activity peaked in 2009, at 10.8 percent of GDP; and in 2010 it stood at 4.9 percent, still about twice as high as the historical average. The time series is not long enough to discern whether disbursements were countercyclical in the past, but demand for federally backed credit clearly increased dramatically in response to the financial crisis and recession that began in late 2007. Data from Gale (1991) for the 1980-87 period suggest little cyclical variation during that time frame, although disbursements from traditional credit programs were somewhat higher in the recessionary period of the early 1980s than later that decade.

III. Calibration of the Model

The inputs used to calibrate the model include estimates of subsidy rates for each major credit program, demand and supply elasticities, program disbursements, expansions on the extensive margin, and multipliers.

III.A. Program-Specific Subsidy Rates and Disbursement Amounts

Estimates of the credit subsidies received by borrowers in 2010 are important inputs into the calculations of incremental borrowing along the intensive margin and of the bang for the buck of credit programs stimulus. Most noncredit federal subsidies are measured on a cash basis; and for the purposes of measuring stimulus, their sizes and costs are generally equated to the annual cash outflows that are reported in the federal budget. Measuring and interpreting credit subsidy costs is more complicated because credit involves risky cash flows over long horizons. To capture the effects of time and risk, the credit subsidy calculations used in this paper are computed on a fair-value accrual basis. Taking a fair-value approach arguably provides the best measure of the economic cost to taxpayers of credit support extended in a given year, and hence it is the logical basis for fiscal multiplier calculations. However, the fair-value estimates differ from the credit subsidy estimates that are reported in the federal budget. Those budgetary costs are also calculated on an accrual basis; but under the rules of the Federal Credit Reform Act of 1990 (FCRA), they do not recognize the cost of market risk. (See the online appendix for additional discussion of methods and issues. (8)) The fair-value estimates of subsidy costs used here are based on a series of analyses undertaken at the CBO and on a number of academic studies that were aimed at improving cost measurement for selected programs, and on extrapolations from those analyses to cover the larger set of programs considered here. (9) It is convenient to refer to subsidy costs in terms of a "subsidy rate," which is defined as the fair-value subsidy per $1 of loan principal.

MORTGAGE PROGRAMS Since the 2007 financial crisis, the federal government has absorbed the credit risk on most new home mortgages. In 2010, Fannie Mae and Freddie Mac provided financing for 63 percent of new mortgages. (10) Adding to that the 23 percent of home loans insured by federal agencies such as the Federal Housing Administration (FHA), the Department of Veterans Affairs (VA), and the Rural Housing Service (RHS) (all of which are securitized by Ginnie Mae), about 86 percent of new mortgages originated that year carried a federal guarantee.

Fannie Mae and Freddie Mac. In 2010, the principal value of mortgages purchased by Fannie Mae and Freddie Mac was $1,011 billion ($625 billion by Fannie and $386 billion by Freddie). Most of these purchases were of fixed-rate, conforming mortgages on single-family homes. Based on estimates reported by the CBO (2010c), the subsidy rate on the guarantee of these mortgages is taken to be 4.05 percent.

The CBO provides an estimate of the annual fair-value subsidy on new mortgages guaranteed by Fannie Mae and Freddie Mac in its baseline estimates of federal spending. These estimates correspond to the concept of subsidy value used here: The annual estimate covers only the current year's new book of business; it does not reflect losses on mortgages guaranteed or purchased in the past, nor on expected future guarantees. The reported 2010 fair-value subsidy cost was $41 billion, which represents about a 4 percent subsidy rate dividing by the principal amount of originations.

The CBO (2010c) explains that its subsidy estimates are based on a model of expected future loss and prepayment rates, and a cost of capital based on the interest rate spread between jumbo and conforming mortgages. This interest rate spread is often taken as an indicator of the difference between the private cost of insuring mortgage credit risk and what the government charges for it. The spread also reflects other differences between jumbo and conforming mortgages. The CBO does not state the precise portion of the jumbo-conforming spread that it attributes to other factors, but other studies have suggested it was approximately half the spread in the precrisis period. Figure 6 shows that the spread had fallen from its peak levels by 2010, but it still remained substantially elevated above precrisis levels, at about 80 basis points at the beginning of 2010. The 4 percent subsidy rate reported by the CBO and used here can be understood as being roughly consistent with an annual subsidy of 40 basis points over the 10-year average life of a mortgage.

The Federal Housing Administration. In 2010, the FHA guaranteed about $319 billion in new mortgage loans, which represents about 10 17 percent of single-family mortgages originated that year (see figure 7). The fair-value subsidy rate assumed here of 2.25 percent is based on the rate reported by the CBO (2011a) for 2012, adjusted upward to account for the higher credit spreads and lower fees prevailing in 2010.

[FIGURE 6 OMITTED]

The FHA's largest program is its single-family guarantee program, which was designed to provide access to homeownership to people who lack the savings, credit history, or income to qualify for a conventional (that is, GSE-eligible) mortgage. Guarantees are available to qualifying borrowers with down payments as low as 3.5 percent of a property's appraised value. The maximum amounts that can be borrowed are the same as on conforming mortgages insured by the GSEs. The FHA charges borrowers an upfront fee and annual premiums.

Valuing FHA guarantees made in the wake of the financial crisis is complicated by the lack of private subprime mortgage originations that would normally provide reference prices. However, the key insight from the analysis in CBO (2011a) is that information about the market price of mortgage credit risk was available at that time from the private mortgage insurance (PMI) market. Fannie and Freddie require borrowers with less than a 20 percent down payment to purchase PMI. Controlling for borrower and other loan characteristics, the present value of fees charged for PMI plus the fair value of a GSE guarantee approximates the fair value of the guarantee provided by the FHA. The difference between this imputed value of the guarantee and the fees that the FHA is expected to collect approximates the FHA's subsidy at fair value. (11)

[FIGURE 7 OMITTED]

The CBO's analysis yielded a projected subsidy rate of 1.5 percent for FHA guarantees expected to be made in 2012. Two factors suggest assigning a higher subsidy rate to 2010 originations: The FHA's upfront fees were 50 basis points lower before April 2010, and credit spreads were wider in 2010 than in 2012. The 2.5 percent subsidy rate used here for 2010 is lower than the 4 percent rate used for Fannie Mae and Freddie Mac. Although it may seem surprising that the subsidy rate on much riskier FHA loans is lower than for loans purchased by the GSEs, the difference can be explained by higher FHA fees, which more than offset the higher default losses. It appears that most borrowers who qualify for GSE financing choose it over the FHA, which is consistent with the finding of a higher subsidy rate on GSE-backed mortgages.

The Department of Veterans Affairs and the Rural Housing Service. Like the FHA, the VA and RHS offer mortgage guarantees at more favorable terms to borrowers than are available privately. For example, the VA offers guarantees on mortgages, usually with no down payment, to active duty military personnel and veterans. RHS loans are means-tested and offered to relatively low-income rural residents. The subsidy rates for those programs are likely to differ from the FHA's because of differences in fee structures, product mix, and the borrower populations. The subsidy rates used here are 3.2 percent for the VA, which insured $63 billion in mortgage principal in 2010, and 4.4 percent for the RHS, which insured $17 billion.

Detailed estimates of fair-value subsidies have not been published for the VA or RHS, or for other, smaller housing programs. Rough estimates can be constructed by starting with the official subsidy rates published in the federal budget, and adjusting them for a market risk charge based on the risk charge inferred for the FHA. That is, the budgetary subsidy estimates give the present value of projected losses discounted at Treasury rates. The budget calculations take into account differences in expected default and recovery rates across programs. The difference between the fair-value subsidy and the FCRA subsidy is the market risk charge for a program (see the online appendix). For the FHA, the subsidy rate reported in the budget for 2010 was -0.84 percent, whereas the fair-value rate is estimated, as described above, to be 2.5 percent. (12) The fair-value subsidy rate is therefore 3.34 percentage points higher than the FCRA subsidy rate. The assumption that the capitalized market risk charge is similar for all these mortgage guarantee programs can be justified by the many similarities between them--most of the loans are long-term, fixed-rate, and highly leveraged; and they are exposed to aggregate risk primarily through shocks to the housing market. In 2010, the FCRA subsidy rates for the VA and RHS were -0.16 percent and 1.21 percent, respectively. Adding a 3.34 percent risk charge implies a fair-value subsidy rate of 3.2 percent for the VA and 4.4 percent for the RHS.

STUDENT LOANS The federal government makes financing for higher education widely available through its student loan programs. Since July 2010, all new student loans have been made through the direct loan program administered by the Department of Education, but before that time the majority of federal student loans were made through the department's guaranteed loan program. (13) The programs offer long-term, fixed-rate loans with a variety of terms.

The subsidy rates used for loans originated in 2010 were 13 percent for direct loans and 16 percent for guaranteed loans, following Lucas and Damien Moore (2010) and CBO (2010d). The higher subsidy cost of the guaranteed program can be attributed to the statutory fees paid to private lenders, which exceed the government's cost of administering the direct loan program. Collectively, the student loan programs disbursed $105 billion in new student loans in 2010.

Lucas and Moore (2010) and the CBO (2010d) develop fair-value subsidy estimates for the direct and guaranteed student loan programs at that time. The subsidies reported here are based on the subsidy rates reported in table 3 of CBO (2010d). (14) Cash flows on student loans are modeled using historical loan-level data from the Department of Education on performance, and risk-adjusted discount rates are derived from the spreads over Treasury rates charged on private student loans before the financial crisis. (During the crisis, the spreads widened enormously and private lending volumes fell sharply.) The loans have multiple embedded options, including prepayment and deferral options, which were also taken into account in the pricing model. Because the interest rates on the private student loans are primary rather than secondary market rates, adjustments had to be made to subtract an estimate of the fees that were included in the quoted rates. (15)

The subsidy rates used for student loans are much higher than for the mortgage guarantee programs. The higher rates reflect the fact that student loans are long-term, unsecured consumer debt, which is considerably riskier than even highly leveraged mortgages, which are protected by the collateral value of the house.

THE SMALL business administration The Small Business Administration (SBA) assists qualifying small businesses in obtaining access to bank credit by guaranteeing a portion of their loans through its largest program, the 7(a) loan guarantee program. This program had modest default rates in the years leading up to the 2007 financial crisis, but postcrisis loss rates increased dramatically (and in earlier years loss rates had also been high). Based on the analysis by the CBO (2007), the fair-value subsidy rate used here is 6.5 percent for the $17 billion in small business loans guaranteed in 2010.

The CBO estimated the market value of the SBA's subsidy on guaranteed loans originated in 2006 using an options pricing model, which is described in CBO (2007). (16) The CBO reports a market-value subsidy rate for 2006 of 1 percent, versus an FCRA subsidy estimate of 0 percent. The report also concludes that under less benign market conditions (with 20 percent higher default rates and 50 percent lower recovery rates), the market-value subsidy would increase to 2.7 percent for 2006. For 2010, the Office of Management and Budget (OMB 2011) reports an FCRA subsidy rate for the SBA of 3.53 percent. The subsidy for 2010 is approximated by adding a market risk charge of 3 percent to the 2010 FCRA subsidy rate, which roughly corresponds to assuming a market risk premium of 50 basis points annually over an average 7-year loan life.

OTHER TRADITIONAL CREDIT PROGRAMS The programs discussed above account for more than 88 percent of the traditional credit program disbursement volume in 2010. The fair-value subsidy rate used for the $64 billion in loans covered by these other programs is 6 percent.

The larger programs in the "other" category provide credit assistance for agriculture and international trade. Although a few of these larger programs exceeded $5 billion in 2010 lending volume, most were much smaller. Fair-value subsidy estimates have not been published for these programs. However, the OMB (2011) provides summary data that include interest rates and fees, lifetime default and recovery rates, loans originated, and the FCRA subsidy rates. (17) From this information, it is possible to make estimates of a risk charge using a simple model of the annual expected cash flows on the underlying loans. That is, given an assumed prepayment rate, the lifetime default rate is converted into an annual default rate. The cash flows on the underlying loan are based on the borrower rate, the annual default rate, the prepayment rate, and the recovery rate conditional on default. (18) Discounting expected cash flows for each program at a risk-adjusted rate yields an estimate of their fair value. Then the subsidy (either for a direct loan or a loan guarantee) is the difference between the loan principal and the present value of loan payments and fees. FCRA values are approximated the same way, except that Treasury rates are used for discounting. (19) The difference between the fair-value and FCRA estimates is the market risk charge, which is added to the official FCRA estimate for each program to produce a fair-value subsidy estimate. (20)

To risk-adjust the discount rates, the spread over Treasury rates is set at 1.15 percent, which corresponds to the historical risk premium on bonds rated Baa by Moody's Investors Service (Hull, Predescu, and White 2005). The weighted average risk charge is 6 percent, and the weighted average official FCRA subsidy rate is close to 0. Hence, the fair-value subsidy rate for the $64 billion in loans covered by other programs in 2010 is taken to be 6 percent.

III.B. Credit Supply and Demand Elasticities

The elasticity of credit supply affects the extent to which additional borrowing in government credit programs is offset by reductions in private borrowing. For the 1980s, Gale (1991) considers supply elasticities of 0.5 and 5.0 to span the range of plausible values. The high levels of reserves in the banking system and loose monetary policy in 2010 suggest a high elasticity of supply in 2010. Therefore, I do not include an aggregate crowding-out effect. However, in assessing the increase on the extensive margin attributable to credit programs below, I take into account the likely share of borrowers who could have obtained credit for the same purpose from the private sector but chose not to do so because of the more favorable terms offered by the government.

Demand elasticities are an input to the estimated expansion of borrowing at the intensive margin. For the main results reported, I follow Gale (1991) by using elasticities with respect to the dollar subsidy amounts of 1.8 for housing, 0.65 for student loans, and 0.8 for business and other. A more recent estimate of mortgage demand elasticity, from Anthony DeFusco and Andrew Paciorek (2014), finds a reduction in total mortgage debt of between 1.5 and 2 percent per each increase in the interest rate of 1 percentage point. To compare this flow estimate with the stock elasticity of 1.8 requires an assumption about the life of a mortgage and the appropriate discount rate. Very roughly, assuming a 1 percent rate reduction over 7 years provides about 5 percent of the principal value in reduced cost, and the implied elasticity is 0.5. More generally, the literature is inconclusive on demand elasticities for credit, with more recent studies finding a mix of large and small values in different instances. This motivates using a fairly wide elasticity band for all types of borrowing in a sensitivity analysis.

III.C. Increases in Borrowing along the Extensive Margin

As the model in section I illustrates, if credit-rationing effects are important, then the increased availability of credit to previously constrained households from federal credit programs could significantly increase borrowing volumes. The size of these volume increases may be largely unrelated to the cost of the associated credit subsidies; in some instances, a small subsidy may lower the equilibrium interest rate enough to attract both low- and high-risk borrowers in situations where no private loans could be offered without lenders taking a loss. However, in other circumstances, large subsidies may have little incremental effect on loan volume.

The evaluation of extensive margin effects for each program is informed by observations about the programs and related markets, but by necessity is largely judgmental because the counterfactuals would be extremely difficult to estimate. (21) Nevertheless, to the extent that the assumptions are plausible, they are worth taking seriously, precisely because the implied stimulus effects are so large. Alternative assumptions considered in the sensitivity analysis provide some assurance that the effects are large, although they cannot be precisely measured.

The approach used here broadly follows Gale (1991). However, the goals of the two analyses are different, and hence different choices are made. Gale (1991) considers two scenarios for the world without credit subsidies in order to provide upper and lower bounds for his calculations of the effects of policy on the allocation and quantity of credit under normal market conditions. The first is that all markets would clear. The second is that tax-exempt and mortgage markets would clear, but farmers, students, and small businesses would be "redlined," meaning that credit would not be available, even at very high interest rates.

Here I consider two different scenarios for the effects of federal credit assistance on the expansion of credit along the extensive margin and on the multipliers. The first scenario is for normal economic conditions; the second is for periods of recession and financial market distress. In calibrating the model for 2010, the question is: Which scenario more closely reflects conditions at that time, or did they lie somewhere in between? Financial markets had begun to normalize by 2010, and the recovery had officially started; but credit was still tight and unemployment remained elevated. Reflecting the fact that the economy was neither normal nor highly distressed, the reported stimulus effects are based on an equally weighted average of the outcomes in each of these scenarios.

The other two components of the calculation--estimates of credit expansion along the intensive margin, and crowding out--are directly calibrated to the conditions of 2010. The intensive margin effects depend on 2010 credit subsidies, and there is no basis in the literature for cyclically varying credit demand elasticities. Crowding out in 2010 is taken to be minimal because of the accommodative stance of monetary policy and the slack in the financial system.

HOUSING Real estate serves as high-quality collateral, making it relatively easy for firms and households to borrow against it. Perhaps for this reason, Gale (1991) assumes that the mortgage market would clear in the absence of federal housing programs. However, because house prices are volatile, there are limits to leverage. Government programs can increase the availability of mortgage credit by permitting higher loan-to-value ratios than a private financial institution would accept. The FHA, VA, and RHS all allow borrowers to make very small or no down payments. A larger down payment requirement would discourage some people from purchasing a home at all and cause others to buy a less expensive home. To take into account that these programs loosen collateral constraints even during normal times, the constrained share of borrowing for the FHA, VA, and RHS is set to 10 percent (that is, 10 percent of the funds borrowed through these programs would not be available at any price without government assistance). By contrast, the GSEs require a 20 percent down payment or PMI and also impose payment-to-income limits. These requirements appear to be at least as rigorous as those on nonconforming mortgages from private lenders. Hence, it seems unlikely that the GSEs have much effect on the availability of mortgage credit in normal times, and I assume they have no impact. (22)

Federal backing is likely to have a much larger effect on the availability of mortgage credit during periods of severe financial stress. However, the shift from private-label mortgages to government-backed mortgages following the 2007 financial crisis is not necessarily indicative of the size of that effect because the government also attracts additional borrowers at such times with its particularly favorable pricing. I assume that 90 percent of FHA borrowing is incremental during distressed periods because the program is specifically designed for borrowers with no credit history, low savings, and low incomes, and because the down payments allowed are so low. (23) For the VA and RHS, I set the constrained share to 50 percent because some VA borrowers are more likely to be in a position to obtain some credit privately than are FHA borrowers. For the GSEs, even during periods of stress, most conforming borrowers probably would be able to obtain credit from private lenders, albeit at higher interest rates. I assume that 25 percent of the volume of GSE credit is incremental during distressed periods. (24)

STUDENT LOANS The federal student loan programs make unsecured, long-term credit available to borrowers, most of whom have no credit history and little in the way of income or assets. Such loans are generally not offered by private financial institutions. For these reasons, the student loan program is thought to greatly increase the availability of funds for higher education.

I assume that during normal times, 75 percent of observed student loan volume would not have been available without federal support. The presumption that a quarter of the loans could have been obtained anyway is supported by the fairly sizable private student loan market that had emerged before the financial crisis. Also, some student loans are made to parents of students who are more likely to be able to obtain credit privately.

During the financial crisis, many private lenders withdrew from the student loan market, and the ones that remained sharply raised their underwriting standards and rates. I assume that during times of market stress, 95 percent of federal student loans represent incremental borrowing volume. This estimate may be on the high side if some families could use home equity or other forms of collateral to borrow funds to finance education when student loans are not available, or if they would have relied more on savings to cover educational expenses had government loans not been available. However, also contributing to incremental borrowing was the fact that some students probably took out loans that were used by their families for other purposes because of the unusual difficulty of obtaining credit elsewhere.

SMALL BUSINESSES AND OTHER TRADITIONAL CREDIT PROGRAMS The SBA 7(a) program is explicitly aimed at increasing access to credit by businesses that would be unable to obtain loans on their own. The pricing that small businesses obtain through this program does not appear to be particularly favorable, and the volume of SBA loans did not increase much following the onset of the financial crisis. (25) I assume that the constrained share of these loans is 75 percent in normal times and 85 percent in stress periods. The relatively small difference between the normal and distressed share of constrained borrowers reflects the view that the program is relatively unattractive in good times for unconstrained borrowers. As a result, the level of constrained borrowers in good times is assumed to be higher than for most other federal credit programs.

Other traditional credit programs include a mix of support for agriculture, trade, energy, and other activities. The constrained share is set to 50 percent in normal times and 75 percent in periods of stress.