offering TIPS, which have their principal and coupon payments indexed to the CPI. Although TIPS will likely be an important part of Treasury debt management in future years, they currently remain small relative to nominal obligations. In the interest of tractability, I exclude them from my model. Let prinold and coupold be, respectively, the existing principal t t and existing coupon payments due at time t. Although the Treasury occasionally initiates open-market buyback programs to pay down old debt, existing obligations are almost always paid as promised. The total financing needs at t will be new new duet = oldcasht + coupold + prinold + de f t (1) t + coupt t + print
with de f t denoting the government’s primary budget deficit. The primary deficit is revenues minus all expenditures other than net interest. The Treasury’s need for short-term cash is difficult to predict in any given period, so it will occasionally retain cash balances from previous periods which I denote as oldcasht . That is, if duet < 0, then oldcasht+1 = duet and we replace with duet = 0. Without this provision it would be necessary to assume either the Treasury would initiate very short-term buyback programs, or that it could invest cash in the private market, neither of which are practical.
4.1
A Simple Zero Coupon Model
Suppose the Treasury can only auction a single zero-coupon security that pays $1 in k ∈ K. Using the basic discount formula, the principal from each issue will come due at time t + k such that prinnew t+k =
duet (1 + ykt )k
(2)
with ykt being the relevant yield to maturity. Total debt outstanding is simply the sum of existing and new principal payments due. Note that after the Treasury decides which maturity to offer in the first period, it is constrained to offer only that same security in all other periods. however, some debt issued prior to WWI such as the Panama Canal Loans or the Consols of 1900 made quarterly payments.
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