Optimal fiscal and monetary policy under sticky prices
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
Should a government use surprise inflation as a hidden tax to cover budget shocks, or keep prices stable no matter what? Two strands of theory gave opposite answers. Schmitt-Grohé and Uribe combine them in one model, where the government can only tax income, at a real cost, and firms find it costly to change prices. They find that even a tiny amount of price stickiness, far less than real economies show, is enough to make price stability optimal -- inflation volatility collapses to near zero, and the government smooths shocks through tax rates and debt instead. This helps explain why real-world central banks prize price stability so highly.
What this paper finds — and why it matters
This paper resolves a contradiction between two branches of optimal monetary policy theory. Ramsey models with flexible prices (Calvo and Guidotti; Chari, Christiano, and Kehoe) find that an optimizing government, restricted to distortionary income taxation and nominal non-state-contingent debt, should make inflation highly volatile and serially uncorrelated, using unanticipated price-level changes as a non-distorting, state-contingent tax on nominal wealth so that regular tax rates can stay smooth; New Keynesian models with sticky prices, by contrast, typically find optimal inflation should be zero or near-zero at all times – but usually by assuming the government can also rely on lump-sum taxes, eliminating any need for inflation to double as a fiscal instrument. Schmitt-Grohé and Uribe build a single model that combines the empirically relevant assumptions of both literatures – only distortionary income taxation and nominal non-state-contingent debt available to the fiscal authority, plus monopolistic competition and Rotemberg-style costly price adjustment on the supply side – and solve for the Ramsey-optimal fiscal and monetary policy under full commitment. Their central finding is that the tradeoff between using inflation as a shock absorber and avoiding the real costs of price adjustment is overwhelmingly resolved in favor of price stability: calibrating price stickiness to even one-tenth of available U.S. estimates already reduces the optimal standard deviation of inflation from about 7% per year under full price flexibility to well under 1%, and at their full baseline calibration it falls to just 0.17% per year. They trace this fragility to Aiyagari et al.’s result that the welfare gain from being able to issue real state-contingent debt (which flexible-price surprise inflation effectively replicates) is itself small, so even minor price-adjustment costs are enough to make the Ramsey planner abandon front-loading altogether. In its place, the government relies on ordinary tax-rate and debt adjustments, smoothed over time to minimize distortion – which induces near-random-walk behavior in both taxes and public debt, reproducing the Barro (1979)/Aiyagari et al. finding usually derived by assuming the government can issue only real (not nominal) non-state-contingent debt, but here obtained instead from a purely nominal, non-state-contingent debt structure plus even minimal price rigidity. The paper further shows that price stickiness induces a systematic, quantitatively significant deviation from the Friedman rule (roughly half of it attributable to stickiness itself, the rest to an existing monopoly-profit-taxation channel), and that a regression of the Ramsey-optimal nominal interest rate on inflation and output, estimated on simulated data, produces an inflation coefficient statistically indistinguishable from zero (and negative in point estimate) – the opposite of what an actual Taylor rule requires – a result the authors present as a cautionary finding about inferring policy rules from optimal-policy time series, not as a claim that a passive rule can implement the Ramsey outcome.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What contradiction in the optimal-monetary-policy literature is this paper trying to resolve?
One branch of the literature, following Lucas and Stokey’s flexible-price framework, finds that an optimizing (“Ramsey”) government restricted to distortionary taxes and nominal non-state-contingent debt should make inflation “highly volatile and serially uncorrelated,” using unanticipated inflation as a lump-sum tax on financial wealth; a more recent, sticky-price New Keynesian branch finds the optimal inflation rate should be “zero or close to zero at all dates and all states” (Section 1, pp. 198-199). The authors note the second branch’s price-stability result rests on assuming away the first branch’s fiscal motive: New Keynesian models typically assume “the government has access to (endogenous) lump-sum taxes to finance its budget,” so there is no need to use unanticipated inflation as a tax at all – “Taken together, these two strands of research on optimal monetary policy leave the monetary authority without a clear policy recommendation” (Section 1, p. 199).
Q2. How does the paper’s model combine the key assumptions of both literatures?
The model keeps three empirically realistic features from the flexible-price fiscal literature – only distortionary income taxation is available (no lump-sum taxes), the government cannot subsidize away monopolistic distortions, and it issues only nominal, non-state-contingent one-period bonds – while adding two features from the New Keynesian literature: monopolistically competitive firms and Rotemberg-style costly price adjustment, in which “the firm faces a resource cost that is quadratic in the inflation rate of the good it produces” (Section 1, pp. 199-200; Section 2.1, eq. following (3)). This combination puts a genuine tradeoff in front of the Ramsey planner: use surprise inflation to minimize the need for distortionary tax variation, or minimize inflation to avoid firms’ price-adjustment costs – a tradeoff neither literature’s simplified assumptions allows the planner to actually weigh.
Q3. What does the Ramsey planner choose to do under full price flexibility, as a baseline?
Under flexible prices and perfect competition, the Friedman rule is exactly optimal (a constant zero nominal interest rate), the average labor income tax rate is 18.7% and extremely smooth (standard deviation 0.04 percentage points), and inflation is highly volatile – a mean of -3.7% per year with a standard deviation such that “a two-standard deviation band on each side of the mean features a deflation rate of 15.7 percent at the lower end and inflation of 8.3 percent at the upper end” – and has near-zero serial correlation (Section 4.2.1, pp. 212-213). This confirms and quantifies the flexible-price “front-loading” result: inflation is used almost entirely to absorb unanticipated shocks to the fiscal position, not to serve any systematic role, which is precisely why it shows so little persistence.
Q4. What is the paper’s central quantitative finding once price stickiness is introduced?
Even a minuscule degree of price stickiness – ten times smaller than available U.S. empirical estimates – reduces the optimal standard deviation of inflation to “below 0.52 percent per year, 13 times smaller than under full price flexibility,” and at the paper’s full baseline calibration (matched to Sbordone’s estimated New Keynesian Phillips curve, implying firms reprice roughly every 9 months) it falls to just “0.17 percent per year,” a roughly 40-fold decline from the 7% flexible-price figure (Section 4.2.2, pp. 213-215). The authors describe the tradeoff as “overwhelmingly resolved in favor of price stability” even at empirically modest degrees of rigidity, bringing the sticky-price Ramsey outcome much closer to the near-zero-inflation prescriptions of the fiscally-simplified New Keynesian literature it set out to reconcile with the fiscal-theory literature.
Q5. Why does even a small amount of price stickiness have such an outsized effect on optimal inflation volatility?
The authors interpret price-level volatility as the government’s way of making nominally non-state-contingent debt effectively state-contingent in real terms, and argue – drawing on Aiyagari et al.’s finding that Ramsey welfare is nearly identical whether or not the government can issue truly state-contingent real debt – that the welfare gain from this “front-loading” channel is inherently small, so it takes very little price-adjustment cost to tip the balance against it (Section 4.2.2, pp. 215-216). Mechanically, because the Ramsey planner keeps the nominal interest rate roughly constant under flexible prices, “large surprise inflations must be as likely as large deflations… inflation must have a near-i.i.d. behavior,” so high inflation volatility cannot reduce the average resources collected via distortionary taxes (a first-order benefit) – it can only smooth the timing of tax distortions (a second-order benefit) – “without affecting their average level,” making the whole channel fragile to even modest price-adjustment costs.
Q6. What happens to tax rates and public debt once price stickiness makes surprise inflation too costly to use?
Following an unanticipated government-spending shock, the flexible-price Ramsey planner inflates away the resulting fiscal pressure and returns taxes and debt to their pre-shock levels within a single period, whereas the sticky-price planner instead “finances the increase in government spending partly by increasing public debt and partly by increasing taxes,” smoothing the tax increase over time to minimize distortion, so that “the stock of public debt displays a persistent increase” (Section 5, pp. 216-217). The result reproduces the Barro (1979)/Aiyagari et al. finding that optimal tax rates and debt behave like a near-random walk – a result usually derived from the stark assumption that the government can issue only real, non-state-contingent debt – but here obtained with purely nominal non-state-contingent debt, given only “a minimal degree of nominal rigidities”: the authors show the near-random-walk pattern survives even reducing their price-stickiness parameter by a factor of ten (Section 5, p. 217).
Q7. Does price stickiness affect the desirability of the Friedman rule, and if so, by how much?
Yes – in the paper’s baseline sticky-price economy the average nominal interest rate is 3.8% per year rather than zero, a deviation the authors decompose into two roughly equal parts: about 1.8 percentage points from monopolistic competition alone (the government uses inflation as an indirect tax on otherwise untaxed monopoly profits, a channel present even under flexible prices), and the remaining roughly half of the 3.8-point gap attributable specifically to price stickiness itself (Section 6, p. 218). They show the relationship is monotonic: “there exists a strong increasing relationship between the degree of price stickiness and the average nominal interest rate associated with the Ramsey allocation” – the costlier it is for firms to adjust prices, the more the benevolent planner is willing to accept a positive average nominal rate (moving away from the Friedman rule) in exchange for a lower, steadier inflation rate.
Q8. Does the Ramsey-optimal interest-rate process look like an empirically estimated Taylor rule?
No – regressing the simulated Ramsey-optimal nominal interest rate on contemporaneous inflation and output yields “Rt = 0.04 - 0.14pi_t - 0.16y_t + u_t, R^2 = 0.92,” an inflation coefficient that is “insignificantly different from zero with a negative point estimate,” and a negative output coefficient, both opposite in sign to what an actual Taylor rule (inflation coefficient above one, positive output response) requires (Section 8, pp. 220-221). The regression fits well statistically (R^2 above 90%) but not structurally: “an econometrician working with data sampled from the Ramsey economy would conclude that monetary policy is passive, in the sense that the interest rate does not seem to react to changes in the rate of inflation,” a result that is robust to interest-rate smoothing terms and to using lagged rather than contemporaneous inflation. The authors are explicit this is a cautionary, positive-economics finding about the risk of misreading optimal-policy time series through the lens of a reduced-form feedback rule, not a claim that such a rule could itself implement the Ramsey allocation as a competitive equilibrium.
Q9. What broader interpretation do the authors offer for why real-world central banks appear to prize price stability so strongly?
They conjecture that the mechanism is not specific to price-adjustment costs per se, but to any friction that ties the equilibrium real allocation to innovations in the price level: “Any friction that causes changes in the equilibrium real allocation in response to innovations in the price level is likely to induce the Ramsey planner to refrain from using the price level as an instrument to front-load taxation” (Section 9, p. 222), citing informational rigidities and limited asset-market participation as other candidate frictions with potentially the same qualitative effect. Under this reading, “our sticky-price model is simply a metaphor to illustrate a deeper mechanism at work in the macroeconomy that leads central banks all over the world to favor price stability above any other goal of monetary policy” (Section 9, p. 222) – a conjecture the authors explicitly flag as a direction for future research rather than something demonstrated within this paper.
Key terms in this paper
Definitions below follow the paper's own usage.
- The Ramsey problem under sticky prices and distortionary taxation
- the paper's central policy exercise: a benevolent government that finances an exogenous stream of purchases only by levying distortionary income taxes, printing money, and issuing one-period nominal, non-state-contingent bonds, choosing fiscal and monetary policy under full commitment to maximize household welfare in a monopolistically competitive, Rotemberg-sticky-price production economy. The authors build this problem specifically to bridge two literatures that "deliver diametrically opposed policy recommendations": flexible-price Ramsey models, which call for highly volatile inflation used as a lump-sum tax, and sticky-price New Keynesian models (which typically assume lump-sum taxation is available), which call for near-zero inflation.
- Inflation as a lump-sum tax ("front-loading") under flexible prices
- the mechanism, central to the flexible-price branch of the literature (Calvo and Guidotti; Chari, Christiano, and Kehoe), by which an optimizing government facing only distortionary taxes uses unanticipated inflation to erode the real value of its outstanding nominal debt in bad states, "front-loading" fiscal adjustment instead of raising future tax rates. The paper's calibrated flexible-price Ramsey economy exhibits a standard deviation of inflation of about 7% per year with near-zero serial correlation, while the income tax rate stays essentially flat -- "inflation displays a near zero serial correlation" precisely because it is used to absorb unanticipated shocks rather than serving any systematic role.
- The "near-zero optimal inflation volatility" result
- the paper's headline quantitative result: introducing price stickiness at a degree ten times smaller than available US estimates is enough to push the optimal standard deviation of inflation from about 7% per year (flexible prices) to well under 1% per year, and the paper's baseline calibration (matching Sbordone's estimated New Keynesian Phillips curve slope) reduces it to a mere 0.17% per year. The authors attribute this fragility to Aiyagari et al.'s finding that welfare under Ramsey policy is nearly identical whether or not the government can issue real state-contingent debt -- so the welfare gain from using inflation as an implicit state-contingent tax is small enough that even minor price stickiness costs make abandoning it worthwhile.
- Near-random-walk taxes and debt (the Barro-Aiyagari result reproduced)
- the paper's reconciliation of its sticky-price findings with the Barro (1979) and Aiyagari et al. tax-smoothing literature, which derives near-random-walk tax rates and debt from the assumption that government debt is restricted to be real and non-state-contingent. Here, with debt restricted only to be nominal and non-state-contingent (the empirically realistic case) plus "a minimum amount of price rigidity," the same near-random-walk dynamics emerge endogenously: following an i.i.d. government-spending shock, sticky-price public debt and tax rates jump and then persist near their new, permanently higher level, whereas under flexible prices both return to their pre-shock values within a single period because the Ramsey planner instead inflates the shock away immediately.
- The Ramsey-optimal interest-rate process does not look like a Taylor rule
- the paper's finding that a regression of the Ramsey-optimal nominal interest rate on contemporaneous inflation and the output gap, run on simulated data from the baseline sticky-price economy, yields an inflation coefficient that is "insignificantly different from zero with a negative point estimate" and a negative output coefficient -- the opposite sign pattern from an actual Taylor rule's greater-than-one, positive inflation response. The authors caution this is a positive, not normative, finding about how an econometrician would misread the Ramsey-optimal policy process, not a claim that a passive interest-rate rule can by itself implement the Ramsey allocation.