Robert E. Lucas, Jr. | Macro Paper Warehouse

Inflation and Welfare

Lucas surveys and extends the Bailey (1956)/Friedman (1969) tradition of estimating the welfare cost of inflation, fitting a money-demand curve to U.S. time series on M1, nominal GDP, and short-term nominal interest rates for 1900-1994. Interpreting these two series as points on a demand function for real balances, he finds a “log-log” specification (interest elasticity of demand around 0.5) fits noticeably better than a “semi-log” specification, and uses Bailey’s consumers’-surplus method – the area under the inverse money-demand curve – to translate the fitted demand curve into a welfare cost function. The headline estimate: the gain from reducing the annual inflation rate from 10 percent to zero is equivalent to an increase in real income of slightly less than one percent; using the fitted curves, cutting interest rates from 14 percent to 3 percent (both roughly historically observed extremes) is worth about eight-tenths of one percent of income. The paper then provides two distinct general-equilibrium rationales for this reduced-form calculation. First, a simplified version of Sidrauski’s (1967) model, in which households derive utility directly from real balances, is shown to generate exactly the same steady-state money-demand relation and (to a close approximation) the same welfare-cost formula as the Bailey method, giving the atheoretical curve-fitting exercise an explicit microeconomic foundation; extending this model to allow only distortionary income taxation (rather than lump-sum transfers) to finance government spending is shown to leave the estimated welfare costs essentially unchanged down to extremely low interest rates, though it means the literal Friedman-rule optimum of zero nominal interest is replaced by a strictly positive, but quantitatively trivial, optimal rate. Second, a transactions-technology model adapted from McCallum and Goodfriend (1987), in which money economizes on time spent transacting rather than yielding direct utility, is shown to imply the same log-log demand curve and welfare-cost estimates, and in the specific case that fits the U.S. data (elasticity 0.5) reduces exactly to Baumol’s (1952) classic inventory-theoretic square-root formula for optimal cash management. Lucas argues these convergent, theoretically grounded estimates for moderate inflation levels are reliable, but cautions that behavior at very low interest rates – and hence the size of any further gain from pushing all the way to the deflationary Friedman rule – cannot be reliably extrapolated from aggregate time series alone, citing Mulligan and Sala-i-Martin’s evidence that a large share of U.S. households hold no interest-bearing assets at all, which points to a fixed cost of portfolio management that aggregate data cannot detect but that could be quantitatively important near zero interest rates.

Nobel Lecture: Monetary Neutrality

Lucas’s 1995 Nobel Prize lecture asks why changes in the quantity of money seem, from David Hume’s 1752 essays onward, to be simultaneously “neutral” – mere units changes with no effect on real activity – and yet, in Hume’s own account, a source of short-run stimulus or depression as money works its way through the economy. Lucas argues this tension sat at the center of monetary theory for two centuries because pre-1970s economists lacked the mathematical equipment to model rational, forward-looking behavior during the transition between one quantity-theoretic equilibrium and another; verbal treatments from Hume through Keynes and Patinkin described agents reasoning intertemporally about the adjustment process without ever formally working out what such reasoning implied. Reviewing cross-country evidence (a near-perfect correlation between thirty-year average money growth and inflation, but no such relation between money growth and output growth), Friedman and Schwartz’s account of U.S. depressions, and Sargent’s account of the ends of four European hyperinflations, Lucas shows that money’s long-run neutrality is decisively confirmed while its short-run real effects appear in some data and not others. He then works through a sequence of overlapping-generations examples, building on Samuelson (1958), to show formally how rational expectations resolves the puzzle: a fully anticipated, once-and-for-all or steadily growing money supply is neutral (net of a genuine, non-neutral “inflation tax” effect when transfers are lump-sum rather than proportional to earnings), while an unanticipated monetary transfer can raise output, in Lucas’s own (1972) formulation, because suppliers trading in incomplete markets cannot immediately distinguish a monetary shock from a real, market-specific demand shift and so hedge by producing more. Lucas surveys several alternative rational-expectations mechanisms (staggered price-setting, gradual revelation of shocks) that reach the same anticipated/unanticipated distinction by different routes, and reviews the mixed econometric record – money-shock variance effects on the output-inflation tradeoff are confirmed across countries, but tests requiring the shock to be transmitted via price surprises specifically find only a small role for that channel. He closes by conceding that no single 1970s monetary business-cycle model, including his own, now stands as a satisfactory full theory of the business cycle, and notes that subsequent research shifted toward purely real (technology-driven) accounts of fluctuations before beginning to reintroduce monetary features.

Review of Milton Friedman and Anna J. Schwartz's 'A Monetary History of the United States, 1867-1960'

Writing for the 30th anniversary of Milton Friedman and Anna Schwartz’s A Monetary History of the United States, 1867-1960, Lucas argues that the book’s enduring contribution is not merely its “beautiful time series on the money supply and its components” but a coherent normative narrative: nearly a century of U.S. monetary history, organized around two principles – long-run monetary neutrality and a short-run non-neutrality operating through unexplained but transient price rigidities – in which every major depression is traced to an avoidable policy mistake or an unchecked banking panic, so that the whole period “might have evolved, with stable prices and smoothly growing real output” had the monetary authority acted differently. Lucas states he finds this normative argument “wholly convincing,” particularly for the 1929-33 contraction, but presses on what a model-free narrative history cannot do: answer how much smoother money growth would have helped, since the book’s own conclusions are, in his words, not “a verbal summary of tables describing the results of a numerical simulation” but “the simulation” itself. He then surveys three later research programs against this yardstick – 1970s rational-expectations models that reconciled the book’s two neutrality principles but reached opposite normative conclusions about optimal policy depending on how price rigidity is modeled; Christopher Sims’s atheoretical statistical approach and Romer and Romer’s “natural experiments,” each proposing a different, non-equivalent notion of monetary “independence” from Friedman and Schwartz’s own; and real-business-cycle theory, which Lucas judges incapable of explaining the Depression’s actual magnitude – the Solow residuals for 1928-1933 are far too small to map into a 40% decline in output – while nonetheless reshaping how the discipline reads the comparatively small role of money in accounting for postwar fluctuations, not as evidence money is unimportant but as evidence postwar monetary policy has been close to efficient.

Two Illustrations of the Quantity Theory of Money

This short paper offers empirical “illustrations” – deliberately not a full structural test – of two implications of the quantity theory of money: that a given change in the rate of money growth induces an equal change in the rate of price inflation, and an equal change in nominal interest rates (a Fisherian relationship). Using quarterly U.S. M1, CPI, and 90-day Treasury-bill data for 1953-77, Lucas applies a family of two-sided exponentially weighted moving-average filters, indexed by a smoothing parameter beta, to strip high-frequency “business cycle” variation out of money growth, inflation, and interest rates and isolate a common, slowly moving component. At low smoothing the raw series show no visible relationship, but as beta rises toward 0.9-0.95 the smoothed scatter plots of inflation and of interest rates against money growth both converge onto a near-45-degree line – exactly the unit-elastic relationship the theory predicts – reproducing within a single country’s postwar time series roughly the same clean confirmation that Robert Vogel had found comparing steady-state inflation and money growth across sixteen Latin American economies. Lucas frames the exercise explicitly as a “minimal” use of the quantity theory, since it imposes only the theory’s weak, long-run/steady-state implications rather than embedding it in a full structural macro model, and interprets the resulting low-frequency component as effectively “anticipated” money growth in the Sargent-Barro sense. He also demonstrates, using a parallel filtered plot of unemployment against smoothed money growth, that heavy moving-average filtering of any two series can manufacture a “pattern” with no economic content – so the quantity-theoretic pictures are meaningful only because they are the implication of a coherent theory, not because filtering alone produces order. He concludes that both the inflation and the historically high nominal interest rates of the 1970s are well accounted for on this quantity-theoretic evidence.

Why Doesn't Capital Flow from Rich to Poor Countries?

The simplest neoclassical models of trade and growth make an egalitarian prediction that follows from assumptions about technology alone: if two countries produce the same good with the same constant-returns production function in capital and homogeneous labour, then differences in output per worker must come from differences in capital per worker, diminishing returns put the marginal product of capital higher in the poorer country, and free competitive trade in capital goods sends all new investment to the poorer economy until returns and wages equalise. Lucas puts numbers on it. Taking production per person in the United States as about fifteen times India’s (Summers and Heston, 1988) and a Cobb-Douglas capital share of 0.4 – an average of US and Indian capital shares – the marginal product of capital in India must be about 58 times that in the United States. The point of working the arithmetic is that “there is nothing at all delicate about this standard neoclassical prediction on capital flows”: the observed flows fall so far short that the assumptions must be “drastically wrong,” and the question is which. Four candidates follow. Correcting labour for quality using Anne Krueger’s (1968) estimates – which imply each American or Canadian worker is the productive equivalent of about five Indians or Ghanaians – cuts the US-India income ratio per effective worker from 15 to 3 and the predicted return ratio from 58 to about 5, “a substantial revision” that nonetheless “leaves the original paradox very much alive.” Adding external benefits of human capital, with the spillover exponent estimated at 0.36 from Denison’s US 1909-1959 data, brings the predicted India-US return ratio to 1.04 – eliminating the differential entirely, though Lucas flags as “important and troublesome” that this calculation assumes knowledge spillovers across national borders are exactly zero. The third candidate, political risk, faces a historical objection: contracts in colonial India were enforced as reliably as domestic ones, so why were returns not equalised in the two centuries before 1945? The fourth is a colonial monopoly model in which an imperial power with exclusive control of the colony’s trade and monopsony power over its wages finds it optimal to retard capital flows, implying a colonial return about 2.5 times the European one at a capital share of 0.4 – although Lucas’s own footnote reports contrary evidence from Davis and Huttenback (1989). The conclusion is where the stakes sit: under either human-capital hypothesis, or under the monopoly hypothesis, official capital transfers to poor countries are fully offset by reductions in private investment; only insofar as political risk binds can transfers speed the equalisation of factor prices.