Appendix A Modified SDC
To better understand the properties of the modified SDC contract let the function RB (xt) denote the state-contingent payment of the bank. The following features characterize the modified SDC (also see Longhofer (1997)):
1. There exists a
such that the bankruptcy region is a lower interval, that is, for all the entrepreneur is solvent and for all the entrepreneur declares bankruptcy. For convenience, let’s call the solvency cutoff.
, a non-contingent payment if the entrepreneur is solvent, where is the cutoff return such that .
3. RB(xt+1) = ξ(xt+1) is the maximum (gross) recovery for the bank in bankruptcy states.
To simplify the contracting problem, henceforth I assume that ξ(x) is linear, ξ(x) = ξx with ξ ∈ [0,1]. This payment function is actually a measure of creditor protection. Creditors have no protection if ξ = 0, partial protection if 0 < ξ < 1 and full protection if ξ = 1, in which case the APR is fully met. The transfer to the entrepreneur in bankruptcy states, x ξ(x), can be interpreted in the real world as APR violations, legal concessions by the bankruptcy court, or diversion of resources by insiders.14
The possibility of partial creditor protection substantially changes the properties of the contracting problem. As Figure 3 illustrates, ξ < 1 reduces the slope of the function in all bankruptcy states and increases the bankruptcy region. To see this more clearly, note that the solvency cutoff satisfies
Linearity of the investment technology and the creditor protection function implies that
where the first integral is the expected transfer to the entrepreneur in bankruptcy states and the second is the payment in solvency states, net of loan repayment. For the bank:
where the first integral is the expected transfer to the bank in bankruptcy states, net of bankruptcy costs, and the second is the loan repayment in solvency states.
B Properties of the Loan Contract
To show the relationship between the cutoff value
Totally differentiate this function, substitute
To verify the properties of the leverage ratio and loan demand, first rewrite ψt+1 as a function of the ratio
Second, take the partial derivatives with respect to its two arguments and use the results from (B2) and (B2) to obtain:
The entrepreneurial expected rate of return (11) inherits the properties of
Therefore, if the leverage ratio is large enough, the last term in these sentences will be out-weighted by the others and
To verify the properties of the lending rate (12), first use the definition of
To show that the lending rate is larger than the deposit rate note that:
Also note that the term
However, the impact of the price of capital is unambiguously positive:
C Properties of the Capital Policy Correspondence
To derive the properties of the law of motion of capital, first note that (24) gives an implicit function relating the deposit rate and the price of capital:
Substituting ψ(RD,Q) and sH(RD) into this and rearranging terms I obtain:
Using the implicit function theorem and (A1)-(A2) I find:
Now define the function:
and substitute in (21) to obtain:
The derivative of J with respect to Q is given by:
are related to the elasticity of savings and investment to the interest rate, respectively. Or, alternatively, to the elasticity of loan supply and loan demand curves (see Figure 5). These two terms illustrate that the sign of J′(Q) will ultimately depend on the value of γ. It can be also checked that J is bounded above and below, (1 κ) (1 – τ) ημ < J(Q) < (1 τη])μ. Finally, taking (16) into account, the derivative of next period’s capital Kt is:
This derivative is clearly positive if one of the following three cases hold. The first case (baseline) requires γ < 1 and HJS > |(H – 1)JI|, that is, household savings are increasing in the deposit rate and savings are more sensitive to the interest rate than investment. Although γ < 1 may be seem as a restrictive assumption on preferences, Galor and Ryder (1989) have shown that sH′(RD) > 0 is a necessary condition for uniqueness and stability of the steady state. Second, γ > 1 and |HJS| < (H – 1)JI and investment is more sensitive to the interest rate than savings. Finally, J′ (Q) is negative but J(Q) >|QJ′ (Q)|, i.e., the price elasticity of the capital stock is relatively small.
The numerical simulations in Section 5 illustrate that assuming reasonable values for the key parameters γ, κ, τ and ξ and ruling out solutions where
For instance, in the special case of logarithmic preferences conditions (8) and (24) imply a cutoff productivity that is independent of aggregate prices and a constant
D Alternative Deposit Supply Function
This appendix assesses the responses of the economy to the three distortions when the interest rate-elasticity of the deposit supply is unity (i.e., logarithmic preferences) and 2. If γ = 1, the household savings rate converges to β/(l + β), and the deposit supply becomes perfectly inelastic (Figure 5, third panel). Combining equations (8), (10) and (24) implies that the solvency cutoff
and so does the leverage ratio. This implies that the credit-to-output ratio in (25) converges to a constant that is independent of any distortions:
Hence, the response of output per capita is smaller than under the baseline, but the impact on lending spreads is not neutral as it is still affected by the behavior of the solvency cutoff. In fact, the response of spreads is slightly larger than in the baseline (Figure 11, dashed blue lines).
When γ > 1, savings are decreasing in the deposit rate, and the deposit supply is downward-sloping (Figure 5, first panel). Mechanically, higher costs of doing business and resolving insolvency (lower creditor protection) will reduce (increase) the deposit rate and the price of capital. But the deposit rate will decline (rise) by less than the price of capital, and so the ratio RD/Q will increase (decrease) in equilibrium, thereby boosting corporate leverage and credit (also see Appendix B). This counterintuitive reaction of financial intermediation will mitigate the impact on output or even lead to some output gains relative to the baseline. On the other hand, the solvency cutoff will rise in response of RD/Q so that banks still break even in equilibrium and this will culminate in higher default rate and lending spreads compared to the baseline (Figure 11, dotted red lines).
Beyond the inner workings of the model, this exercise illustrates two important points. First, financial sector outcomes reflect complex interactions between depositors’ behavior, corporate financing structure, and distortions in the financial and real sectors of the economy. Second, correct identification of the underlying distortions and design of appropriate policies to eliminate them would require deep understanding of country-specific circumstances as well as learning from cross-country experiences. Researchers and policy-makers would need to assess a broad range of macro and microeconomic indicators, including measures of financial development and financial stability, legal foundations of debt contracts, and the modus operandi of the bankruptcy and judicial systems.
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I am very grateful to Mark Flanagan for his guidance and significant suggestions. I thank Ali Abbas for his very useful comments. I also thank the participants of a LACEA conference and Central Bank of Brazil seminar for their feedback on an older and preliminary version of the paper. All remaining errors are mine.
This paper does not cover issues pertaining consumer bankruptcy technology (e.g., Chatterjee et al. (2007)), or the resolution of sovereing debt distress. However, some of the principles and results discussed here could be applied to unincorporated business. Formal or statutory mechanisms for resolving sovereign debt distress have been proposed in the past but lacked support from the international comunity (e.g., Krueger (2002)). Gitlin and House (2015) provide an updated account of the ongoing debate on how to improve the resolution of sovereign debt crises.
Under the APR, secured claims must be paid off before unsecured claims, and senior debt should be paid off before junior debt.
This view of creditor rights does not necessarily apply in the context of sovereign. For instance, non-economic considerations also play an important role in sovereign-to-sovereign debt contracts. See, for instance, IMF (2013), IMF (2014), IMF (2015), and IMF (2016)).
See, for instance, Castro et al. (2004), Beck and Levine (2005), Japelli et al. (2005), Djankov et al. (2007), Dabla-Norris et al. (2013), as well as Christiansen et al. (2013) and their literature survey.
See, for instance, http://www.imf.org/external/np/speeches/2015/040915.htm.
To be effective, this would require some sort of capital controls in the case of small open economies.
Under the old law, tax and wage claims had absolute priority, whereas under the new law secured claims are second only to wage claims.The new law also attempts to speed up the resolution of bankruptcy. See Araujo and Funchal (2005) for more details.
Lenders (households) will be effectively risk-neutral for the purpose of the debt contract. Bernanke and Gertler (1989), among other, obtain this condition directly by assuming that lenders have risk-neutral preferences in the second period. Risk neutrality is required for the optimality of the debt contract.
Assuming different marginal impact would not change the results of the paper but would add another layer of complexity.
This type of credit market distortions also affect the equilibrium outcome in Dubey et al. (2005). In their model, the debtor faces a utility punishment for defaulting and is better off not borrowing if the punishment is too harsh, whereas the lender chooses not to lend if the default penalty is too small.
This is close to the average return on assets of publicly traded firms across the world in the 1990s (Claessens et al. (2000)). Evidence also suggests that average returns to private equity in the U.S. are approximately equal to S&P 500 (e.g, Moskowitz (2002) and Kaplan and Schoar (2005)).
Creditor protection below .2 typically violates the bank’s limited liability constraint in the baseline calibration.
For a recent discussion on the impact of corruption on growth see, for instance, the G20 issues paper on the topic: https://www.oecd.org/g20/topics/anti-corruption/Issue-Paper-Corruption-and-Economic-Growth.pdf.