18 l Existence of a debt overhang creates disincentives for domestic investment in the debtor country. l Debt forgiveness can è stimulate domestic investment; è increase the actual payments received by creditors. l Sachs (1989b): two-period model. l Debtor government maximizes the discounted utility U( ) derived from domestic consumption in each period: U(c 1, c 2 ) = u(c 1 ) + u(c 2 ), u( ): standard concave utility function; c t : domestic consumption in period t, 0 < < 1: discount factor.
19 l Country enters the first period with an existing stock of debt, which gives rise to a contractual payment obligation of D 0 during the second period. l No debt service payments are due in the first period. l Actual payments to the original creditors in the second period are given by R, where R < D 0. l Actual amount to be paid emerges from negotiations that take place between the government and its original creditors. l In the second period the government pays R to its original creditors, plus it services any additional debt it incurs from new creditors in the first period. l However, the government cannot agree to pay more than a fraction 0 < < 1 of the country's second-period income in total debt service.
20 l If this constraint becomes binding, all creditors are paid in proportion to their exposure, the implication being that no creditor class has seniority. l Government has to decide how much to invest and borrow during the first period, subject to the constraints: c 1 = f(k 0 ) + D 1 - I 1, c 2 = f(k 0 + I 1 ) - (1+r*)D 1 - R, k 0 : initial capital stock at the beginning of period 1, I 1 : investment during period 1, D 1 : new borrowing during period 1, r*: world risk-free interest rate, f( ): standard neoclassical production function.
21 l Credit supply constraint also needs to be satisfied by the government, because new loans will be available only if new creditors expect to be fully repaid. l Given the existing obligations to the original creditors, this requires (1+r*)D 1 < f(k 0 + I 1 ) - R. l As long as condition (A4) holds, new borrowing D 1 is a choice variable for the government, because funds are available in infinitely elastic supply at the interest rate r*. l If it does not hold, country is unable to borrow at all because new creditors would be unable to receive the market rate of return from lending to this country. (A4)
22 l If (A4) holds, first-order conditions for a maximum -u (c 1 ) + u (c 2 )f (k 0 + I 1 ) = 0, u (c 1 ) - (1+r*)u (c 2 ) = 0. l To solve for I 1, substitute (A5) in (A6) and simplify. l Domestic investment is given implicitly by f (k 0 + I 1 ) = 1+r*. l Substituting (A7) in (A6) defines first-period borrowing implicitly as a function of R. l Increase in R reduces c 2, because it reduces the resources available for consumption in that period. (A5) (A6) (A7)
23 l This raises the marginal utility of c 2 and thus increases the incentive to postpone consumption. l This can be done by reducing D 1. l Formally, D 1 = d(R), < 0. - f u (c 2 ) u (c 1 ) + (1+r*)f u (c 2 ) -1 < d =
24 l Note that -1 < (1+r*)D 1 < 0. l Thus, while (A4) may hold for low values of R, an increase in R reduces the right-hand side of (A4) more than the left-hand side. l There will thus be some critical value of R, say R*, at which (A4) will hold as an equality. l For R > R*, (A4) will be violated. l Suppose that R = D 0 > R*. l Since all creditors would experience a shortfall, new creditors will not enter.
25 l Constraints (A2) and (A3) become c 1 = f(k 0 ) - I 1, c 2 = (1- )f(k 0 + I 1 ). l In this credit-rationed regime, the government's only choice is over the level of first-period investment. l First-order condition in this case is given by -u[f(k 0 +I 1 )] + (1- )u[(1- ) f(k 0 +I 1 )]f (k 0 +I 1 ) = 0. l To show that debt forgiveness can increase investment and make both parties better off, let I 1 denote the solution to (A10). (A10) ~
26 l Total debt service to the original creditors in this case is R = f(k 0 +I 1 ), which is less than D 0 by assumption. l If the original creditors had written down the country's debt obligation to this amount initially, (A10) would become c 2 = f(k 0 +I 1 ) - R, with the first-order condition: -u[f(k 0 +I 1 )] + (1- )u[f(k 0 +I 1 ) - R]f (k 0 +I 1 ) = 0. ~~ ~ ~ (A12) (A13)
27 l By substituting R= f(k 0 +I 1 ) in (A13) and calculating dI 1 /d < 0, it is easy to show that investment increases when the contractual debt obligation is reduced from D 0 to R. Reason: l When contractual debt is not fully serviced, external creditors claim a share of any additional output forthcoming from new investment. l This is like imposing a distortionary tax in the form of the fraction in (A10), which reduces the incentive for the government to invest. l Additional investment increases domestic welfare since, by (A11), -u(c 1 ) + u(c 2 )f ( ) > 0 when this expression is evaluated at I and R, implying that additional investment is welfare enhancing. ~~ ~ ~ ~
28 l Result: debt forgiveness increases domestic welfare without harming the original creditors; that is, debt forgiveness is Pareto-improving. l With an increase in R to above R (but below D 0 ), debtor country could remain better off than in the no- forgiveness condition. l Value of debt service to original creditors increases over what they would have received without debt forgiveness. l Result: removing distortionary effect of the debt overhang can make both parties better off. ~