On the cohomology of discriminantal arrangements and Orlik-Solomon algebras

We relate the cohomology of the Orlik-Solomon algebra of a discriminantal arrangement to the local system cohomology of the complement. The Orlik-Solomon algebra of such an arrangement (viewed as a complex) is shown to be a linear approximation of a complex arising from the fundamental group of the complement, the cohomology of which is isomorphic to that of the complement with coefficients in an arbitrary complex rank one local system. We also establish the relationship between the cohomology support loci of the complement of a discriminantal arrangement and the resonant varieties of its Orlik-Solomon algebra.Comment: LaTeX2e, 16 pages, to appear in Singularities and Arrangements, Sapporo-Tokyo 1998, Advanced Studies in Pure Mathematic

Resonance of basis-conjugating automorphism groups

We determine the structure of the first resonance variety of the cohomology ring of the group of automorphisms of a finitely generated free group which act by conjugation on a given basis.Comment: 7 page

The sustainability of African debt

The role of debt forgiveness is to alleviate what is known as"debt overhang". This concept is the core idea of the Brady deals, and it now comes to the African debt crisis. How can one gauge the hypothesis of the debt overhang? To what extent can one attribute the growth slowdown of the 1990s to the debt crisis of the 1980s? Using data from the past decade, the author finds that debt variables play a significant role in that slowdown. In one exercise, he finds that more than half the growth slowdown of the large debtor countries in the 1980s could be attributed to the debt crisis. To what reasonable debt ratio should African debt be written down? Most exercises set the threshold of sustainability of debt at about 200 percent. The easiest way to rationalize such a threshold is first to measure the average value of debt-to-export ratios reached at the time of the first rescheduling of debt in a given country. Using Latin America as a benchmark, one finds an average threshold of 248 percent. However short-sighted such a ratio might be, it goes a long way toward rationalizing the view that a debt-to-export ratio between 200 and 300 percent is a strong signal of a forthcoming crisis. This naive approach takes no account of the changing environment (growth and interest rates) a country must confront. A more subtle approach should allow for the prospect of a country's growth to assess the sustainability of the debt it inherits. With the author's formula for so doing, Africa's debt-to-export ratio should be brought to 198 percent. Another way to assess the sustainability of debt is to look at the secondary market, which allows one to estimate the prospect of repayment expected by market participants. Few African debts are actually quoted on secondary markets, but the author presents a formula for reconstructing estimates of repayment prospects econometrically. By that method, Africa's debt-to-export ratio should be 210 percent, suggesting that a threshold between 200 and 250 percent is about right.Environmental Economics&Policies,Payment Systems&Infrastructure,Economic Theory&Research,Strategic Debt Management,Banks&Banking Reform,Economic Theory&Research,Environmental Economics&Policies,Strategic Debt Management,Banks&Banking Reform,Financial Intermediation

A valuation formula for LDC debt

A large gap may lie between the amount of debt relief that is nominally granted to a debtor and that which is actually given up by the creditors. To help put that gap in perspective, the author proposes a valuation formula that provides: (i) the price at which a buy-back of the debt, on the secondary market, is advantageous to the country; (ii) the value to creditors of having the flows of payment guaranteed against factors that hinder a country in servicing its debt; and (iii) the degree of tradeoff between growth of payments and levels of payments. The author argues that it is not good business for a country to announce its intention to buy back debt, because doing so immediately raises the price. The value of guarantees, the author argues, cannot exceed 25 percent of the market price of the debt. Typically they're worth only about 10 percent. As for the degree of tradeoff, the author's formula finds that 1 percent additional growth rate is worth a 15 percent increase in the flows of payments. An assessment of the Mexican debt-relief agreement reached in 1990 is also offered.Economic Theory&Research,Financial Intermediation,Strategic Debt Management,Environmental Economics&Policies,Banks&Banking Reform

Is the discount on the secondary market a case for LDC debt relief?

In 1988, the prices on the secondary market of LDC debt averaged 50 cents per dollar of face value. From the observation of such discount, this paper goes one step further and argues thatthe debt should be written down in order to account for the discrepancy between the face and market value of the debt. The paper is structured as follows. Section 1 spells out the model, section 2 calculates the socially efficient and the post-default growth rates of the economy. Section 3 shows that the lenders, if they were to monitor the investment and the consumption strategy of the borrower, would choose a lower investment strategy than the socially efficient one. Section 4 shows how an optimum rescheduling can achieve the equilibrium described in section 3. Section 5 shows the dynamic inconsistency of the optimal strategy spelled out in section 4, and shows the link with the"debt overhang"literature. Section 6 investigates the empirical relevance of the"debt overhang".Economic Theory&Research,Banks&Banking Reform,Environmental Economics&Policies,Strategic Debt Management,Financial Intermediation

Why are poor countries poor?

We attempt to explain why standard explanations of the poverty of nations are unsatisfactory. We first argue that human capital is low in poor countries because its production has increasing returns with respect to life expectancy. We then show that the reason why capital does not flow to poor countries (the Lucas paradox) can readily be explained once market prices rather than PPP prices are used to assess the return to physical capital: the return to capital in poor countries is not higher than in the rich world in spite of its relative scarcity. We finally argue that PPP calculations bias downwards the measured TFP of poor countries, which may in part explain their lower productivity. The message of hope is that education can shoot up as life expectancy increases. A higher level of human capital would appreciate the real exchange rate through a Balassa-Samuelson effect, thus raising the profitability physical capital. This in turn would encourage foreign capital to flow to developing countriesHuman capital, capital flows, Lucas Paradox