A Frictionless View of U.S. Inflation

“More and more transactions are handled electronically or via credit and debit cards, while ATMs, sweep accounts, and banking by computer have a major influence on cash management… leaving the supply of transaction-facilitating assets beyond the Fed’s control,” while “the quantity theory has also not had much success in describing the history of postwar U.S. inflation: inflation seems to have very little to do with the history of monetary aggregates or interest rates” (Introduction, p. 323). Cochrane asks: “Can we understand the history of U.S. inflation using a framework that ignores monetary frictions?” – a question he says only became coherent to ask once Leeper (1991), Sims (1994, 1997), and Woodford (1995, 1996, 1997) developed the fiscal theory of the price level, since “some friction seemed necessary to determine any value for unbacked fiat money” before that work.

"[Nominal debt / price level] = present value of real surpluses" (equation 1) “determines the price level in much the same way that Mv = py determines the price level in the quantity theory. However, since total government debt rather than the supply of transactions-facilitating assets appears on the left, fiscal price-level determination is immune to financial innovation, including elastically provided private media of exchange, and even a cashless or frictionless economy” (Introduction, p. 324). Cochrane frames this as providing “an implicit backing or commodity standard for even apparently unbacked fiat money,” equivalent to treating money and nominal debt together “as a (non-voting) equity claim on the flow of surpluses.”

In a terminal period (no new debt sold), the government’s flow budget constraint reduces to B_{t-1}(t)/p_t = s_t: “nominal debt B_{t-1}(t) is predetermined, so the price level must adjust to equate the real value of the debt to the real value of surpluses that will retire the debt” (Section 2.1, equation 3). Iterating this logic forward using the ex post real return on bonds and imposing a transversality condition yields the multiperiod present-value budget constraint (equation 7): “the price level adjusts to equate the real value of nominal debt to the present value of the surpluses that will retire it” – the frictionless analogue of equation (1) stated formally.

“A Ricardian regime is any policy rule [B_t(t+j), s_t] in which the sequence of government budget constraints holds for any sequence of price levels” – geometrically, the case where the two sides of the present-value budget constraint, viewed as curves in the price level, “happen to fall right on top of each other” (Section 2.3.2). Cochrane argues the quantity theory is “a particularly important case of a Ricardian regime”: once M, v, and y jointly pin down p_t via Mv = py, the budget constraint “is still part of the system,” but is reinterpreted “as a constraint on fiscal policy” – if surpluses are insufficient given the money-determined real debt value, “the government must raise future surpluses, by seignorage if explicit taxation is insufficient.” Models that “explicitly rebate seignorage revenues” (following Lucas 1980) are Ricardian “by choice, so that the budget constraint will not fight with the quantity theory for price-level determination” (Section 2.3.3).

Cochrane imagines a “100%-backed commodity standard”: one dollar equals one bushel of wheat, with a government warehouse holding enough wheat to back the entire nominal debt, and institutional guarantees so strong “the government can never raid the warehouse” – an arrangement that “would seem to decisively nail the price level at $1/bushel” (Section 2.3.4, pp. 335-336). He notes that “a Ricardian regime advocate would argue that it does nothing to determine the price level,” reasoning that an off-equilibrium price announcement of $0.50/bushel would simply force the government to raise taxes, buy more wheat, and “validat[e] the lower price.” Cochrane uses this example to press on the equilibrium-versus-off-equilibrium distinction at the heart of the “long and rather confusing debate” over whether governments “must” follow Ricardian regimes – a debate he says hinges on whether the government commits to validate literally any announced price, or instead follows a rule (like the wheat-warehouse commitment) that responds to the equilibrium price while “refus[ing] to validate out-of-equilibrium price levels” (p. 336).

“The fiscal theory per se has no testable implications for the joint time series of prices, debt, and surpluses. Briefly, the identity (1) holds, in equilibrium, whether fiscal or monetary considerations determine the price level. Therefore, one can always rationalize the price level by reference to debt and subsequent surpluses” (Introduction, p. 325). He demonstrates this concretely under “Testing Feedback Rules?” (Section 2.3.4, pp. 340-341): regressing surpluses on the real value of debt cannot distinguish a Ricardian regime (where surpluses are estimated to respond because the price level actually did the adjusting) from a genuinely fiscal regime (where the same equilibrium relationship holds because debt levels are simply forecasting future surpluses) – “this coefficient again tells us nothing about the regime.” He gives an explicit example in which a purely exogenous surplus process, run through the accounting identity, generates a VAR in which debt appears (misleadingly) to forecast future surpluses in a Ricardian-looking way.

“The fiscal theory does predict that open market operations should have little effect on the price level, and this implication is fairly easy to see in the data” (Introduction, p. 325). Because a pure open-market swap of money for bonds at market prices leaves the total nominal value of government liabilities and the present value of surpluses backing them unchanged, the fiscal theory implies such operations should not move the price level – a prediction Cochrane treats as distinct from, and more empirically tractable than, the theory’s general (and untestable, per Q6) present-value claims about the joint behavior of debt and surpluses.

Constructing a maturity-structure dataset of total outstanding federal debt and inferring the surplus from debt transactions rather than accounting data, Cochrane finds “the biggest primary deficit occurs in 1975, along with the onset of serious inflation,” while “the primary ‘Reagan deficits’ are surprisingly small, and even those are largely accounted for by the dramatic recessions of 1980-1982” (Introduction, p. 326). He also documents that “fluctuations in the rate of return of government bonds are as large as fluctuations in surpluses,” so discount-rate variation may matter as much as surplus expectations for the present value of debt, and that debt maturities were “very short in the 1970s” but lengthened after 1975, a structural change that “allow[s] debt sales to immediately affect the price level.”

“The central puzzles are that the level of the real value of the debt seems to have very little to do with surpluses, and, worse, high surpluses are associated with declines in the value of the debt” – a pattern that fits a naive, backward-looking monetary story (high deficits mechanically raise real debt through accumulation) far better than a naive forward-looking fiscal one (Section 3.3, pp. 366-367). Cochrane shows that if the surplus follows a simple AR(1) process, the fiscal theory predicts “a perfect positive correlation between surpluses and debt” – “completely counterfactual,” and “the basic idea of Canzoneri, Cumby, and Diba’s (1997) rejection” of the fiscal theory.

He argues the AR(1) specification is “obvious but perhaps too simple”: if the surplus instead follows an AR(2) or higher-order process, “low current surpluses can come with news of higher future surpluses, so that the value of the debt rises” – and this is, “on second thought,” the natural specification, because “deficits go up…when taxes decrease and spending increases in a recession,” and “the only way extra nominal debt sales can raise revenue is if they come with a promise to raise surpluses in the future” (Section 3.3, pp. 367-368). If low current surpluses did not come with such promises, extra nominal debt sales would raise no revenue at all; Cochrane further argues that this policy – selling debt in recessions against promised future surpluses, rather than inflating away existing debt to cover shortfalls – is precisely what “smooths inflation and the value of government bonds, at least to some extent,” relative to the alternative.

“First, one can use the fiscal theory to understand why money is valued in modern economies with apparently unbacked fiat money…When money is valued because it is backed, the fact that certain assets have a liquidity value in exchange has at best second-order effects on the price level, and the value of money will therefore not be affected by financial innovation” (Conclusion, p. 382). “Second, in order to understand U.S. data from this fiscal perspective, we must view the primary surplus as following a process in which a negative shock today induces a positive change in the long run” – not an ad hoc fix, but the natural implication of a government that “is faced with cyclical surplus shocks about which it can do little, yet…does not want wildly fluctuating and countercyclical inflation,” and so “sells extra debt in recessions, raising revenue by so doing because it implicitly promises to raise subsequent surpluses” (p. 382).