Journal of Economic Theory | Macro Paper Warehouse

Expectations and the Neutrality of Money

This 1972 Journal of Economic Theory paper by Robert Lucas constructs an overlapping-generations general equilibrium model — young and old traders exchanging in two physically separated, non-communicating markets — to show how a Phillips-curve-like relationship between money and real output can emerge as an equilibrium property of a fully rational, market-clearing economy, without contradicting the classical long-run neutrality of money. The key mechanism is imperfect information: traders in each market observe only the local price, which reflects the ratio of a monetary shock (a random change in the money supply, x) to a real shock (a random reallocation of traders across markets, θ), so they cannot fully distinguish a price increase caused by “more money” from one caused by “more real demand for my goods specifically” — and this confusion causes traders to raise output in response to nominal (monetary) shocks. Lucas proves that when only monetary disturbances are present (no real shocks), money is perfectly neutral in the classical sense (Theorem 2); when only real disturbances are present, real magnitudes vary but money’s neutrality doesn’t apply since there’s no money-supply variation at all (Theorem 3); and in the general case with both shocks present, an unanticipated monetary shock has genuine real effects because it cannot be fully separated from the real shock via the observed price (Theorem 4), while a fully anticipated, proportional (scale) change in monetary policy has no real effects at all (Corollary). He also shows that a constant “k-percent” money growth rule (per Milton Friedman) yields a Pareto-optimal competitive equilibrium allocation (Theorem 5), and that fitting an econometric Phillips-curve regression to data simulated from this model produces a strong positive, but entirely spurious and non-exploitable, inflation-output correlation — “much more convincing” than the corresponding real-world evidence — even though no genuine policy trade-off exists in the model.

Optimal fiscal and monetary policy under sticky prices

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.

The Ramsey steady-state conundrum in heterogeneous-agent economies

When macroeconomists solve for optimal capital and labor taxation in Aiyagari-style heterogeneous-agent, incomplete-markets economies, they routinely assume – without proving it – that the long-run “Ramsey steady state” exists and is well-behaved (interior), a step Aiyagari (1995) himself admitted was hard to justify. This paper proves that assumption is generally false in the standard Aiyagari model with constant-relative-risk-aversion preferences: for the empirically normal case of risk aversion sigma >= 1, no interior Ramsey steady state exists at all, and the only steady state the Ramsey planner can reach has aggregate consumption collapsing to zero and the labor tax rising to 100%, because the planner has a permanent incentive to borrow cheaply against a market interest rate that sits below the household discount rate, front-loading consumption until public debt becomes unsustainable. Using a modified, analytically tractable version of the Aiyagari model that nests the standard model as a limiting case, the authors then show that when an interior steady state does exist (under a feasibility condition on public debt capacity), it features a zero long-run capital tax – the opposite of Aiyagari’s celebrated positive-capital-tax result – with the modified golden rule instead satisfied purely through a high steady-state labor tax and public debt; for the alternative low-risk-aversion case (sigma < 1), an interior steady state can exist but only with a divergent Ramsey multiplier and a violation of the modified golden rule. The paper’s conclusions rest on a standard incomplete-markets model with CRRA power utility, ad hoc borrowing constraints, and a Ramsey planner maximizing time-zero discounted welfare; the authors are explicit that their results do not apply to Ramsey plans that instead maximize only steady-state welfare, where the incentive to front-load consumption disappears.