Optimal maturity of government debt without state contingent bonds

Abstract

This paper shows that state contingent debt can be syntethically constructed using non-contingent debt of di¤erent maturities. A main policy implication of this principle is that the Ramsey allocation with complete markets can be sustained with non-contingent debt only by properly managing its maturity structure. The numerical experiments, however, suggest that this policy implication ought to be taken with care. We …nd that the debt positions that sustain the Ramsey allocation are very high (on the order of a few hundred times total GDP for a very simple four state economy) and increasing in the number of states. In addition, they are very sensitive to small variations in the parameters of the model.

In search of a theory of debt management

“…As has already been documented by Buera and Nicolini (2004) the magnitude of the positions derived from this complete market approach are extremely large multiples of GDP, in many cases 3 the government should hold 5 or 6 times GDP in privately issued short bonds and issue similar amounts of long bonds. No government in the real world conducts debt management this way, not even approximately: governments rarely hold private bonds 1 and the positions held at each maturity are substantially smaller.…”

“…This section essentially outlines the model and results of Angeletos (2002) and Buera and Nicolini (2004), henceforth ABN. In later sections we extend and evaluate this model.…”

“…We borrow Chari's et al (1991) calibration of the government spending and the technological processes, which they choose to match the average share of government spending, the variance and serial correlation of consumption growth in the US. Assuming a two state symmetric Markov process for government expenditure 6 . We quote the unconditional average of the ratio of the 5 Assuming utility to be logarithmic helps simplify our analysis when we allow for capital accumulation.…”

“…In this case capital is taxed only in periods 0 and 1 and capital taxes are zero thereafter. 6 Appendix A provides detailed description of the computational methods used to produce the simulations.…”

“…No government in the real world conducts debt management this way, not even approximately: governments rarely hold private bonds 1 and the positions held at each maturity are substantially smaller. Logically this gap between the large positions recommended by the models in Angeletos (2002) and Buera and Nicolini (2004) (henceforth ABN) and those observed in practice could be due to a) preferences and technology in reality being different from the relatively simple endowment model of these papers b) market imperfections matter, especially financial market frictions c) governments do not know exactly the value of some parameters in the economy d) governments may pursue suboptimal policies or be subject to other constraints such as time consistency, etc. Angeletos (2002) suggests that a) is a likely candidate for explaining away the gap 2 but suggests that the qualitative implications of complete markets (to issue long term debt and buy short term bonds) are robust to variations in preferences and technology.…”