The Funding Deal That Makes Risky Loans Tempting
The bank balance sheet in Canzoneri, Diba, Guerrieri, and Mishin's model is where the paper's abstract policy problem becomes concrete. This chapter follows the funding and payoff chain that makes a socially inefficient risky loan attractive to a bank, then shows how a capital requirement changes both the bank's incentives and the household's access to deposits. The goal is to understand why capital regulation has two effects at once: it can make banks bear more of the losses they create, but it can also displace a safe, liquid asset that households value.
The key distinction is between a project's average return and the payoff received by a bank that can walk away from losses. A risky project may be worse for the economy on average and still be appealing to the bank financing it. To see why, start with the two kinds of firms in the model and follow their outcomes through the bank's balance sheet.
Two projects, one distorted choice
The model contains competitive safe and risky firms. Both need bank financing to acquire capital and both are exposed to aggregate shocks, so neither is a guaranteed source of income. The risky firm faces an additional idiosyncratic shock. That shock has a negative mean but positive variance: on average it subtracts from the project's return, yet it also creates a wider range of outcomes than the safe project.
This is not the familiar case of a risky asset offering a higher expected return as compensation for volatility. In the model, the expected return on a loan to a risky firm is lower than the expected return on a loan to a safe firm. If a social planner could compare the projects without financial distortions, the additional risky exposure would be inefficient. The risky firm is producing with an extra source of uncertainty whose average contribution is negative.
A bank does not, however, receive the project's social payoff directly. It assembles a portfolio of loans using two sources of funding: deposits from households and equity supplied by households. The bank receives the returns on its loans, pays depositors what they are owed, and passes any remaining value to its equity holders. The order of payment matters. Depositors have a prior claim, while equity holders receive the residual only when the bank's assets are worth enough to cover its deposits.
Suppose the bank directs a share of its portfolio toward the risky firm. Its next-period net worth is the return on the loan portfolio minus the interest it owes on deposits. The risky firm's idiosyncratic shock enters that net worth directly. A sufficiently bad realization makes net worth negative. At that point the bank declares bankruptcy: depositors are protected by deposit insurance, while the equity holders receive nothing.
Limited liability changes the meaning of that last outcome. The equity holders lose their initial stake, but they do not make an additional payment to cover the shortfall. Their payoff is effectively bounded below at zero. On the upside, they participate in the bank's residual earnings when risky lending pays off. The bank therefore evaluates the risky loan through a truncated payoff: bad outcomes beyond the failure point no longer reduce the equity holders' return, while favorable outcomes can still raise it.
Government deposit insurance completes the distortion. Depositors regard their claims as safe because the government promises to protect them if the bank fails. They therefore do not demand a higher interest rate from a bank merely because it has chosen a riskier portfolio. In the model, the government later collects lump-sum taxes from households to cover the losses incurred when it bails out depositors. But the bank's decision is made before that social cost is fully charged to the bank's own equity holders. Deposit insurance has made the bank's funding source safer and cheaper than it would be if depositors bore default risk.
The result is an incentive wedge with a clear transmission path:
- The risky firm has a lower expected loan return because its additional shock has a negative mean.
- Greater volatility creates more upside states for the bank's residual claim.
- Limited liability removes the equity holders' exposure to losses below the failure point.
- Deposit insurance keeps deposits cheap and prevents depositors from disciplining the bank through a risk-sensitive funding price.
- The bank may choose risky exposure even though the project is socially inefficient on average.
The third step is the decisive one. If equity holders had to absorb every loss, the negative expected return on the risky loan would weigh heavily against it. Limited liability turns some of the downside into a cost borne outside the equity contract. The bank is not being irrational when it takes the risk; it is responding rationally to a payoff structure that does not make it bear the full social cost.
That is why simply describing risky lending as “high risk” is inadequate. The important question is who receives the upside and who absorbs the downside. In this model, the upside accrues to the bank's residual claimants, while deposit insurance protects the bank's main creditors and households ultimately finance the insurance losses through taxes. The policy problem concerns that allocation of risk, not an abstract dislike of uncertainty.
The bank's choice is also state-dependent. A change in aggregate conditions can depress the expected return on safe lending enough to make the protected upside of risky lending look attractive. The model does not require risky firms to become better projects in social terms. It requires only that safe lending become relatively less appealing to the bank's equity holders. This relative comparison will later explain why the appropriate capital response does not always line up with the direction of GDP or credit.
The sequence also shows why the bank's private calculation and the household's social calculation diverge. The bank compares the return left for equity after deposit payments. Households care about consumption, the liquidity services of deposits, and the taxes needed to repair the insurance fund. Those are not the same objective, even though households own the banks in the representative-household construction.
Why capital changes the price of funding
The paper represents capital regulation as a requirement that bank equity cannot fall below a fraction of the bank's loans. If loans are denoted by the bank's total assets, the balance sheet can be written simply as loans equal to equity plus deposits, with equity required to be at least gamma sub t times loans. The exact notation matters less than the relationship: a higher requirement means that more of every loan portfolio must be financed by the bank's own loss-absorbing stake and less can be financed by deposits.
Why does the bank not voluntarily use more equity? Because deposits are valuable to households as a liquid, safe asset. Households hold deposits not only for the interest they pay but also for the services of having a readily usable claim whose nominal safety is protected by insurance. That liquidity value lowers the deposit rate relative to the return households require on uncertain bank equity. From the bank's perspective, deposits are consequently the cheaper source of funding.
The model's equilibrium makes this preference operational. Since debt is cheaper than equity, banks fund as much of their loans with deposits as the capital rule allows. The requirement binds: at the margin, the bank uses the minimum equity share permitted and fills the rest of the balance sheet with deposits. This is not a claim about every bank's legal capital ratio. It is a proposition about the paper's funding market under its assumptions, where deposit liquidity is in household utility and equity is risky.
The regulatory ratio therefore changes more than a solvency statistic. It changes the price and quantity of the bank's funding. Consider a tightening. The bank must replace some deposit funding with equity to support a given loan portfolio. Equity is more expensive because it does not provide household liquidity and because its payoff is uncertain. The cost of making loans rises, and the bank's demand for deposits falls. Households may still want to save, so the deposit rate can fall from both sides: banks issue fewer deposits while households continue supplying them.
The result is a real welfare effect even if the bank remains safely in the same lending regime. In a model without a special value for deposits, replacing debt with equity might look like a neutral rearrangement of claims. Here it is not. Deposits enter household utility directly. Removing them takes away liquidity services, so Modigliani–Miller neutrality does not apply to this funding change.
A one-percentage-point capital-requirement shock in the paper illustrates the scale of the two sides of the trade-off. Under the calibration, deposits make up roughly 90 percent of bank funding. A tightening shifts funding toward equity and produces a sizable movement in deposits and the deposit rate, while the effects on consumption, investment, and output are tiny. The real economy may therefore look almost unchanged even as household welfare falls because a valued liquid asset has become scarcer.
This does not mean that a tightening is harmless. It means that its first-order cost in this experiment is concentrated in the financial side of the household's problem. The bank has more skin in the game, but households receive fewer deposit services. A regulator who looked only at GDP might miss the welfare cost of the intervention; a regulator who looked only at deposit growth might miss the safety benefit.
The reverse movement is more dangerous. Lowering the capital requirement allows the bank to fund more loans with cheap deposits and leaves less equity exposed to losses. That can expand the bank's portfolio and make risky exposure more attractive. As long as the bank remains on the safe side of the incentive boundary, the immediate effect may look like more liquidity and cheaper credit. But once the lower requirement makes risky lending the better private choice, the bank's payoff changes discontinuously. Some loans can fail, equity is destroyed, and the government must raise taxes to honor deposit insurance.
The distinction between these two movements is important. A one-percentage-point tightening and a one-percentage-point loosening are symmetric as policy shocks only in the arithmetic sense. They are not symmetric in their economic consequences because the loosening may cross an endogenous boundary. The tightening can mainly rearrange funding within a safe equilibrium. The loosening can activate the limited-liability subsidy, produce risky lending, and reduce output through failures.
Capital also affects the bank's incentive through the amount of loss it must bear, not just through the amount of lending it can support. If equity finances a larger fraction of loans, a bad loan return destroys more of the bank's own capital before deposit insurance becomes relevant. The value of walking away from the downside is smaller. If equity finances a smaller fraction, the bank can use more protected deposits to expand the portfolio while keeping less of its own stake exposed. Capital is therefore a way of changing the payoff geometry of risk-taking.
At this stage, it would be tempting to conclude that the regulator should simply set the highest feasible equity requirement. That would confuse one side of the objective with the whole objective. Higher capital can reduce the incentive to exploit limited liability, but it also eliminates deposits whose liquidity households value. The relevant question is how much capital is enough to prevent the damaging incentive from taking over, not how much capital can be imposed without regard to funding costs.
The paper's model makes that question especially sharp because the bank has only two broad project categories and a transparent insurance mechanism. In a richer real banking system, the supervisor would face many forms of credit quality, interconnected exposures, and difficult judgments about how to assign capital to them. Yet the basic tension would remain recognizable: safe regulation can be expensive when it replaces a useful funding instrument, while cheap funding can be dangerous when it shields the bank from losses.
The funding deal therefore supplies the foundation for the paper's broader policy result. Risky lending is not driven solely by a bank's forecast of project returns. It is shaped by the contract that allocates losses, by the insurance that protects depositors, and by the liquidity value that makes deposits cheap. A capital requirement pushes against that structure by forcing more equity into the deal. But the requirement itself has a price, paid partly in lost deposits. The next question is why the bank's response to this price can jump from safe lending to a crisis rather than adjust gradually.