Fiscal hedging with nominal assets

The paper asks how a government should manage the maturity structure of its nominal liabilities when it must finance shocks entirely with ordinary, non-contingent nominal bonds, solving this “in a fully specified general equilibrium model” rather than treating inflation and the yield curve as given (Introduction, p. 1-2). It contrasts itself with Campbell (1995), who argues a cost-minimizing government should shorten maturity when the yield curve steepens because high spreads predict high future bond returns, and Barro (1997), who argues shortening maturity better smooths taxes when inflation becomes more volatile and persistent, and who reads the falling average maturity of U.S. federal debt from 1946-1976 as an optimal response to changing inflation. The authors note that “both lines of argument treat the processes for inflation and nominal interest rates exogenously” (p. 1) – their contribution is to instead derive optimal debt policy, and the resulting behavior of inflation and yields, jointly and endogenously.

The model combines sticky prices (a fraction ρ of firms set prices before the period’s shock is realized) with a cash-in-advance constraint applied only to “cash goods” and not “credit goods,” following Siu (2004) (Section II, pp. 3-4). Both frictions are needed because, absent them, the government could achieve any hedging it wanted through purely contemporaneous adjustments to inflation, and nominal debt “would effectively function as a real contingent claim” (footnote 2, p. 3) – i.e., the maturity-structure question the paper wants to study would not exist. With the frictions in place, inflation surprises are costly (they misallocate production between sticky- and flexible-price firms) and positive short-term nominal rates are costly (they misallocate consumption between cash and credit goods), so the government’s inflation and interest-rate choices carry a genuine tradeoff between hedging benefits and real distortions.

The paper’s “measurability constraint” (equation 8) is a genuinely restrictive, cross-state condition – unlike the analogous condition in Lucas and Stokey (1983), where the government trades real state-contingent debt and the constraint (equation 9) is essentially redundant after date 0 (Section III.B, pp. 9-10). Restricting to nominal debt of only a single maturity, as in Siu (2004), collapses the constraint to a form (equation 10) in which liability values can be varied across states only through contemporaneous inflation shocks. Restricting to single-maturity real debt, as in Aiyagari, Marcet, Sargent and Seppälä (2002), removes even that channel (equation 11), so debt values cannot be altered contemporaneously at all. The present paper’s contribution, relative to Siu specifically, is to let the government trade nominal debt of more than one maturity, opening a second hedging channel – influencing the price of already-outstanding bonds through current and future nominal-interest-rate policy – that is absent when only one maturity is traded (p. 2, Section III.B).

Under complete markets, optimal policy (Proposition 3) sets the Friedman rule (equating the marginal utilities of cash and credit goods, so nominal rates are zero at every maturity) and eliminates inflation surprises entirely (Nt = 1 always), meaning “nominal yields equal to zero at all maturities and an absence of inflation surprises” (Section IV, p. 11-12). But this complete-markets allocation typically requires that liability values ξt(st)/U1t(st) vary across states – exactly what hedging fiscal shocks requires – while simultaneously requiring zero state-contingent variation in interest rates and inflation, which are the only channels available for hedging once debt is restricted to non-contingent nominal bonds. The paper shows that although allocations arbitrarily close to the complete-markets one can technically satisfy the measurability constraints via small cash-credit substitutions, implementing them “usually requires very large negative (and positive) asset positions at some maturities” that the no-lending (no-short-selling) constraint rules out (Section IV, p. 12) – so in practice the government cannot get close to the complete-markets allocation, and non-trivial inflation and interest-rate variation is unavoidable.

In a tractable example with a single shock at date 1, the paper shows it is strictly optimal to use only the longest available maturity of debt, because using longer debt lets the government obtain the same hedging benefit from a given nominal-interest-rate increase while delaying, and hence discounting, the transaction-cost distortion it causes (Section V, pp. 13-16, esp. equation 20 and Lemma 4). Mechanically, the first-order condition for a k-maturity bond (equation 20) shows the hedging benefit term is increasing in k, so “it is strictly optimal to use only the longest term debt” (p. 16). Lemma 5’s “postponement effect” further shows that in the high-funding-need state the government sets the near-term bond price Q¹ₜ = 1 (i.e., zero short rates) for a while and only raises nominal rates later, at longer effective maturities within the outstanding debt’s term – because “a perturbation to the cash-credit allocation at date t+k… confers a hedging benefit at t,” but “the utility cost of the former perturbation is not born for k periods and is correspondingly discounted” (p. 15), which favors both delaying the rate increase and using the longest bond available to maximize the room for delay.

A transition from low to high government spending triggers a gradual accumulation of nominal interest rates that peaks either when the high-spending spell ends or when the debt outstanding at the shock’s onset matures, and this response is quantitatively much larger at longer maximum maturities (Section VII.B.2, pp. 19-21, Figure 1). In a baseline calibration (K = 7 maximum maturity), a 10-period high-spending spell drives the one-period nominal rate up to about 0.83%, versus only about 0.3% when the maximum maturity is shortened to K = 3 (p. 20). Inflation follows a matching pattern: a small positive inflation innovation (~0.2%) at the onset of a short shock spell is followed by a symmetric negative innovation when it ends, while a long spell produces a sustained rise in realized and expected inflation over several periods, tracking the buildup in nominal rates (p. 20, Figure 2). The yield curve itself becomes hump-shaped upon the shock’s arrival, rising and steepening out to the longest outstanding maturity (K-1) and falling at maturities beyond that, with the hump migrating to progressively shorter maturities as the initially outstanding debt matures, before the curve flattens again once all of it has rolled off (Section VII.B.2, p. 21, Figure 4).

Long simulations show that the average variation in the real value of the government’s debt portfolio in response to shocks (ΔVB/Y) rises roughly five-fold, from about 0.4% of GDP when the maximum maturity K = 1 to about 2.1% of GDP when K = 7, and the composition of that hedging shifts from being entirely inflation-driven to mostly price-of-debt-driven (Section VII.B.3, Table 1, p. 23). At K = 1, all hedging necessarily comes from contemporaneous inflation surprises (since there is no term structure to move); at K = 7, over 80% of the variation in portfolio value instead comes from changes in bond prices. Measured relative to the amount of hedging attainable under complete markets, the nominal-debt economy achieves only 4.7% of the complete-markets hedging benchmark at K = 1 but 24.4% at K = 7 (Table 1). Table 2 shows the standard deviation, autocorrelation, and correlation with spending shocks of both inflation and short-term nominal rates all rise monotonically with the maximum maturity K (from K = 1 to K = 3 to K = 7) – longer permissible maturities make policy do quantitatively more hedging work, at the cost of more volatile and more persistent inflation and interest rates.

The welfare gain from raising the maximum maturity from K = 1 to K = 7 is positive but small: the consumption-equivalent gain Δ ranges “between 0.02% and 0.1%, with larger values at higher initial debt values” (Section VII.B.3, p. 24). This is computed as the proportional increase in the K = 1 economy’s consumption allocation needed to match the expected lifetime utility attained in the K = 7 economy, holding the underlying shock process fixed – so while the paper’s main results establish that long-term debt is strongly preferred conditional on being available, the aggregate stakes of the maturity-structure choice, at least under this baseline calibration, are modest.

The paper argues that the higher volatility of long-term nominal debt returns found in the model is deliberately engineered by the government to hedge fiscal risk, so that “the risk premium on this debt resembles an insurance premium paid by the government; it does not provide a motive for shortening the maturity structure” (Introduction, p. 2). This directly reverses the logic of prior arguments (the paper cites Campbell 1995 and Barro 1997 in this connection) that treat observed yield-curve risk premia and volatility as costs of long debt that argue for a shorter maturity structure; because in this model inflation and the whole term structure are themselves optimally chosen instruments for hedging, higher long-bond volatility is a symptom of successful hedging, not a financing cost to be minimized away.