Money as stock

Cochrane’s central claim is that the government-debt valuation equation – “Nominal government debt / Price level = Expected present value of primary surpluses” – is a valuation (market-clearing) equation exactly like the stock-pricing formula “Number of shares / Price level = Expected present value of future dividends,” and valuation equations are not budget constraints (Section 1.1, pp. 501-503). He motivates this with a thought experiment: if Microsoft stock became the unit of account and medium of exchange, “such a monetary system can establish a well-determined price level,” understood through the ordinary frictionless stock-valuation equation. The analogy does real theoretical work throughout the paper: because “if a bubble pushes stock prices up, no budget constraint forces Microsoft to raise subsequent earnings,” Cochrane argues no comparable force need compel the government to raise future taxes if an off-equilibrium deflation raises the real value of its nominal debt (Section 1.2, p. 504).

Critics including Buiter (2002), Kocherlakota and Phelan (1999), Ljungqvist and Sargent (2000), Bohn (1999), and Marimon (2001) argued the fiscal theory requires the government’s intertemporal budget constraint to hold only in equilibrium rather than as an identity at all prices, which they characterized as either an illegitimate large-agent/first-mover advantage for the government or a violation of Walras’s law (Section 1.2, pp. 503-504). Buiter is quoted calling the theory “fatally flawed” because it “denies that government’s intertemporal budget constraint must hold as an identity … [and] requires it to be satisfied only in equilibrium,” concluding the theory “does not constitute a valid starting point for further research in monetary economics.” Cochrane concedes that even his own earlier work, Cochrane (1999, 2001), had loosely called the valuation equation an “intertemporal budget constraint” – “It only seems obvious in retrospect” – and sets out to show the theory can hold in “a perfectly standard and well-specified Walrasian economic model, one in which the government has no special status.”

Cochrane argues that if the valuation equation were truly a constraint linking debt issuance to future surpluses, a pure currency reform – doubling nominal debt with no change in future real surpluses – would be logically impossible, yet currency reforms plainly occur and everyone understands their effect in advance (Section 1.2, p. 504). “The government can double nominal debt (including the monetary base) without changing the corresponding real surplus stream. This is a currency reform. Everyone understands that the price level doubles. If Eq. (2) were a budget constraint … a currency reform would be impossible.” The exact parallel on the corporate side is a stock split: doubling shares outstanding with no change in future earnings simply halves the price per share, and “no budget constraint of the firm is violated” by a split. Cochrane contrasts this deliberately with the far more common case – a debt sale explicitly paired with a promised increase in future surpluses, analogous to a seasoned equity offering – arguing that most real-world debt issuance looks like the latter, but that the mere possibility of the former (a pure reform) is what proves the valuation equation cannot be a constraint (Section 3.1.2, pp. 515-516).

Working through a terminal-period cashless example and then a general recursive one, Cochrane shows the government’s only commitments are to redeem maturing debt for cash, accept cash for tax payments, and auction new debt for cash – commitments it can satisfy at any price level, including ones at which some debt is simply left unredeemed in private hands or, symmetrically, more cash comes in than debt is outstanding (Section 3.1.1 and 3.2, pp. 515, 517-520). If the “auctioneer” calls too low a price, “tax payments would be insufficient to soak up the outstanding debt … Some debt would be left in consumer’s hands … this event does not violate the government budget constraint,” just as no rule of Walrasian equilibrium is violated if my announced demand for two Hope Diamonds at an off-equilibrium price goes untested because only one Hope Diamond exists. He shows the same logic extends to an entire equilibrium price path that violates the transversality condition – the government can, mechanically, keep rolling over an explosively growing real value of debt – “these are market-clearing conditions, not a budget constraint, since they involve consumers.”

Only nominal debt – a state-uncontingent promise denominated in the government’s own unit of account – can behave like equity; real, indexed, or foreign-currency debt genuinely does constrain the government, because its real payment is fixed independently of the price level Cochrane’s own model determines (Section 3.1.3, pp. 516-517). “A real bond is a state-uncontingent promise to pay one unit of the numeraire good. In this case, the government valuation equation (22) does constrain the government … The government cannot ‘split’ its (say) gold-denominated debt, counting on the price of gold to halve.” His summary formulation: “Nominal government debt walks like debt and quacks like debt, but it is really equity.” The same logic explains, in Cochrane’s reading of Sims (2001), why dollarizing (converting nominal debt into effectively foreign-currency debt) removes a government’s equity-like fiscal cushion and forces it toward explicit default when shocks hit, rather than absorbing them through a change in the price level.

No – Cochrane credits Sargent and Wallace as “a pioneering study of fiscal-monetary links” but argues their framework specified indexed (not nominal) debt, so that in their model a fiscal shortfall can only generate inflation through the seigniorage channel, whereas his frictionless model shows a decline in expected future surpluses can raise the price level with “no money demand or seignorage whatsoever” (Section 3.3.4, pp. 522-523). Because Sargent and Wallace’s left-hand side is a real (indexed) quantity unaffected by the price level, only the money-creation term on their right-hand side can adjust; Cochrane’s nominal-debt formulation instead lets the price level itself revalue the debt directly, “deleting” the money-demand equation and setting money to zero entirely – “a possibility not present in Sargent and Wallace’s analysis.” He also notes their setup is inherently a Ricardian regime (surpluses adjust to satisfy the constraint), whereas the fiscal theory’s distinguishing move is to consider non-Ricardian fiscal regimes as well.

Cochrane argues this worry misreads what has been shown: the valuation equation is a pricing relationship, not a permission slip, so cutting surpluses ex post does not create free resources – it devalues the outstanding debt, an act with real costs closely analogous to default, exactly as diluting shares is costly to a firm’s existing shareholders rather than costless to the firm (Section 3.3.2, p. 522). He directly answers Buiter’s (1999) and Christiano and Fitzgerald’s (2000) versions of this worry – that legislators “understanding that tax cuts … do not necessarily have to be paid for with higher taxes later” might be tempted into runaway deficits – by noting that “issuing more debt is no better for the government than diluting (splitting) shares is for Microsoft,” and that questions of time-consistency, contract enforcement, and default remain live and important, but “these issues are not special to the fiscal theory.”

No – Cochrane argues a fiscal regime still contains a money-demand equation, but it determines the quantity of money passively supplied rather than the price level, so a stable empirical link between money and nominal income is uninformative about which regime is operating, and in any case begs a question of causal direction (Section 3.3.3, p. 523). Quoting the claim that “the U.S. Inflation of the 1970s and 1980s can be fully accounted for by the corresponding increase in M2 (or M1) growth rates,” Cochrane responds: “The observation that the quantity of money tracks nominal income is irrelevant to the regime question. The issue is the direction of causality. Rich men drive fancy cars, but will driving a fancy car make you rich?” He adds that most of M2 consists of interest-paying inside assets that would “survive unchanged in a cashless economy,” so such correlations would persist even in an economy with literally no cash.

Cochrane shows the basic existence result is unaffected by long-term debt, but the dynamics change qualitatively: with a perpetuity, the price level at each date is tied directly to that period’s coupon and surplus rather than to the total value of outstanding debt and the whole future surplus stream, and changes in the maturity structure of outstanding debt – “open market operations” – can move the price-level path even with no change in surpluses (Section 2.3.3, pp. 513-514). He attributes this to a numeraire convention: the model treats maturing debt (dollars) as numeraire rather than the long-term bonds themselves, a choice he suggests may not be coincidental given “the volatility of long-term bond prices.” He flags this as the subject of his companion paper, Cochrane (2001) (“Long-Term Debt and Optimal Policy in the Fiscal Theory of the Price Level”), which works out the full dynamic implications.

He closes by cautioning, via the same stock analogy he opened with, that a valuation-based theory of the price level is likely to be just as resistant to decisive short-run empirical testing as stock-price valuation is, since asset prices generally move for reasons well beyond observable news about future cash flows (Section 4.3, pp. 525-526). “Stock prices do typically move as we expect them to when there is earnings or discount rate news. However, they also fluctuate a great deal in ways that are hard to explain by independent news about future earnings or discount rates.” He expects the same for the price level under a fiscal regime – some historical episodes (the end of hyperinflations, prospective-deficit-driven currency crashes) fit the theory well, but much short-run variation in prices and exchange rates is likely to remain “just as difficult to explain from obvious news about surpluses or discount rates as stock prices are difficult to explain from obvious news about earnings.” He also explicitly does not take a stand on whether the U.S. or any other specific economy is actually in a fiscal (non-Ricardian) regime – the paper’s claim is only that such a regime is theoretically coherent within a standard Walrasian model, not that it describes any particular country’s data (Section 1.2, p. 504).