Annexes—Rational Expectations and the New Classical Macroeconomics

foundational article of NMC published by Robert Lucas in the Journal of Economic Theory (vol. 4, no. 2, April 1972, pp. 103-124), which provides the first rigorous microfoundation of monetary neutrality under rational expectations.

Model framework

the economy is represented by a continuum of geographically isolated islands. Each agent observes only the price on his island and must decide, each period, how to adjust his labor supply.

Signal extraction problem

the agent does not know whether a local price change reflects (a) a relative shock specific to his island that warrants a real labor-supply adjustment or (b) an aggregate monetary shock affecting all islands uniformly that should not alter real supply. Under rational expectations, the agent applies optimal Bayesian reasoning, weighting the two possibilities according to the relative variances of the shocks.

Neutrality result

anticipated monetary policy has no real effects because agents correctly deduce it and adjust their behavior without extraction error. Only unanticipated monetary shocks (the surprises) generate a temporary employment and output response.

Methodological contribution

Lucas replaces the Friedman-Phelps expectations-augmented Phillips curve (adaptive expectations, see previous vocab entry) with a fully microfounded formulation consistent with agent optimization and rational expectations. It is this microfoundation that satisfies the Lucas critique (1976) which Lucas himself would formulate four years later.

Empirical test

Lucas tests this prediction in "Some International Evidence on Output-Inflation Tradeoffs" (American Economic Review, vol. 63, no. 3, June 1973, pp. 326-334), showing that the slope of the short-run Phillips curve is inversely related to the inflation variance, consistent with the prediction of the islands model.

Nobel

Robert Lucas received the 1995 Nobel Prize "for having developed and applied the hypothesis of rational expectations, and thereby having transformed macroeconomic analysis and deepened our understanding of economic policy".

set of contributions that preceded Lucas's NMC by formulating the natural rate of unemployment hypothesis under adaptive expectations.

Friedman (1968)

Milton Friedman, "The Role of Monetary Policy" (American Economic Review, vol. 58, no. 1, March 1968, pp. 1-17), presidential address delivered at the December 1967 American Economic Association meeting. Friedman formulates the informal critique of the original Phillips curve (1958), showing that the stable inflation-unemployment tradeoff exists only in the short run and disappears in the long run as expectations adjust. He introduces the concept of the natural rate of unemployment, defined as the labor-market equilibrium rate consistent with stable expected inflation. Friedman received the 1976 Nobel Prize "for his achievements in the fields of consumption analysis, monetary history and theory and for his demonstration of the complexity of stabilization policy".

Phelps (1967, 1968)

Edmund Phelps independently publishes two complementary articles. "Phillips Curves, Expectations of Inflation, and Optimal Unemployment over Time" (Economica, vol. 34, no. 135, August 1967, pp. 254-281) proposes a normative analysis of the inflation-unemployment tradeoff under adaptive expectations. "Money-Wage Dynamics and Labor-Market Equilibrium" (Journal of Political Economy, vol. 76, no. 4 part 2, July-August 1968, pp. 678-711) develops the microfoundation via search frictions and natural rate. Phelps received the 2006 Nobel Prize "for his analysis of intertemporal tradeoffs in macroeconomic policy".

Phelps volume 1970

Edmund Phelps edits "Microeconomic Foundations of Employment and Inflation Theory" (W.W. Norton, 1970), a collective volume gathering contributions on labor-market microfoundations (search, mismatch, embryonic efficiency wages) and inflation. This volume marks the systematic effort to give macroeconomics microeconomic consistency, independently and in parallel with the NMC initiated by Lucas (1972, previous entry).

Synthesis

the Friedman-Phelps convergence establishes that the long-run Phillips curve is vertical at the natural rate. The initial disagreement of Samuelson-Solow (1960), who saw the Phillips curve as an exploitable policy tradeoff, is definitively set aside. Lucas (1972) inherits this conceptual framework and radicalizes it by replacing adaptive expectations with rational expectations, which eliminates even the short-run stabilizing role granted by Friedman-Phelps to systematic monetary policy.

foundational chapter by Phillip Cagan, "The Monetary Dynamics of Hyperinflation", published in Milton Friedman (ed.), "Studies in the Quantity Theory of Money" (University of Chicago Press, 1956, pp. 25-117), which introduces the first rigorous formalization of adaptive expectations applied to empirical data.

Formalization of adaptive expectations

Cagan proposes the specification πᵉₜ − πᵉₜ₋₁ = λ × (πₜ₋₁ − πᵉₜ₋₁), where λ is the speed of adjustment (0 < λ ≤ 1). Agents revise their inflation expectations based on their past forecast error, weighted by λ. This specification will become the standard reference used by Friedman and Phelps in their work of the 1960s.

Application to hyperinflations

Cagan estimates money-demand functions over seven 20th-century hyperinflation episodes, namely Austria 1921-1922, Germany 1922-1923 (Weimar Republic), Greece 1943-1944, Hungary 1923-1924, Hungary 1945-1946 (absolute hyperinflation record with a monthly rate reaching 4.19 × 10¹⁶ %), Poland 1923-1924 and Russia 1921-1924.

Empirical result

even in the most extreme hyperinflations, agents' real money demand remains predictable and inversely related to expected inflation. The speed of adjustment λ varies across episodes but remains measurable.

Historical position

Cagan's article is the methodological bridge between the classical quantity theory of money (Fisher, Friedman) and the expectations macroeconomics that will rise with Muth (1961), Friedman (1968), Phelps (1967-1968) and Lucas (1972). It is also the first major empirical work to impose a formal expectations structure within an econometric macro model.

Identified limits

the adaptive specification is backward-looking because agents use only past inflation to anticipate the future. If the monetary policy regime changes (for example stabilization after hyperinflation), adaptive expectations overestimate persistent inflation. This is precisely the limit that Muth (1961) and then Lucas (1972) will attack with rational expectations.

Finn Kydland and Edward Prescott, "Rules Rather than Discretion — The Inconsistency of Optimal Plans" (Journal of Political Economy, vol. 85, no. 3, June 1977, pp. 473-492), article that formally introduces the concept of time inconsistency in economic theory.

Core problem

a plan of action can be optimal at the initial date t = 0, but the decision-maker nonetheless has an incentive to deviate from this plan at a later date t > 0, even if no new information has appeared in the meantime. Inconsistency is not due to a change in preferences or information, but to the very structure of the intertemporal problem under rational expectations.

Monetary application

the central bank announces at t = 0 a low inflation target. If agents believe it and set their wages accordingly, the central bank then has an incentive to deviate at t = 1 and create an inflation surprise to exploit the short-run Phillips curve tradeoff and stimulate employment. Anticipating this temptation, rational agents do not believe the initial announcement and set their wages incorporating the likely effective inflation.

Result

inflationary bias, a high-inflation equilibrium without output gain, strictly inferior to the initial optimal plan that would have been obtained with credible commitment.

Conceptual solution

Kydland and Prescott advocate rules against discretion. The central bank must irrevocably commit to a simple and observable rule, abandoning ex post flexibility in favor of ex ante credibility.

Institutional legacy

the article justified the independence of central banks adopted in a worldwide wave in the 1990s-2000s (ECB 1998, Bank of England 1997, Bank of Japan 1998, etc.) as well as the adoption of explicit inflation targets (New Zealand 1990, Canada 1991, United Kingdom 1992, Sweden 1993, etc.).

Theoretical extensions

the article generated a considerable literature, notably Barro-Gordon ("A Positive Theory of Monetary Policy in a Natural Rate Model", Journal of Political Economy, vol. 91, no. 4, August 1983, pp. 589-610) which formalizes the central-bank-public game, Rogoff ("The Optimal Degree of Commitment to an Intermediate Monetary Target", Quarterly Journal of Economics, vol. 100, no. 4, November 1985, pp. 1169-1189) which proposes the conservative central banker solution, and Walsh ("Optimal Contracts for Central Bankers", American Economic Review, vol. 85, no. 1, March 1995, pp. 150-167) which proposes incentive contracts.

Nobel

Kydland and Prescott jointly received the 2004 Nobel Prize "for their contributions to dynamic macroeconomics — the time consistency of economic policy and the driving forces behind business cycles". The Nobel rewards both the 1977 article on time inconsistency and their later work on Real Business Cycle theory (RBC, "Time to Build and Aggregate Fluctuations", Econometrica, vol. 50, no. 6, November 1982, pp. 1345-1370, see entry 7 below).

Robert Barro and David Gordon publish in 1983 two complementary articles that rigorously formalize Kydland-Prescott's (1977, previous entry) time inconsistency within a repeated game between the central bank and the private sector.

Formalization of the inflationary bias

"A Positive Theory of Monetary Policy in a Natural-Rate Model" (Journal of Political Economy, vol. 91, no. 4, August 1983, pp. 589-610) constructs the static version of the game in which the central bank trades off inflation cost against anticipated employment benefit. The discretionary equilibrium leads to a strictly positive inflation bias, formally proving the Kydland-Prescott intuition.

Institutional response (rules, reputation)

"Rules, Discretion and Reputation in a Model of Monetary Policy" (Journal of Monetary Economics, vol. 12, no. 1, July 1983, pp. 101-121) proposes the dynamic extension that introduces reputation as an endogenous solution. If the central bank plays over an infinite horizon, it can sustain a low-inflation equilibrium out of fear of losing its reputation should it cheat. The game then admits a continuum of equilibria between the pure-rule solution and the pure-discretion solution.

Central contribution

Barro-Gordon transform Kydland-Prescott's informal argument into a formal game-theoretic framework and make explicit the existence conditions for reputational equilibria (discount rate, horizon, observability of actions).

Legacy

the Barro-Gordon analysis becomes the canonical framework of monetary-policy theory and inspires the later institutional solutions, notably Rogoff (1985) on the conservative central banker, Walsh (1995) on incentive contracts and Lockwood (1997) on market sanctions. Modern central banks explicitly cite this framework in their justifications of independence and inflation targets.

article co-authored by Robert Lucas and Thomas Sargent presented at the Federal Reserve Bank of Boston conference in June 1978 and published in the proceedings ("After the Phillips Curve: Persistence of High Inflation and High Unemployment", Conference Series no. 19, Federal Reserve Bank of Boston, June 1978, pp. 49-72), reprinted in 1981 in Robert Lucas and Thomas Sargent (eds.), "Rational Expectations and Econometric Practice", University of Minnesota Press, pp. 295-319.

Central thesis

the Keynesian macroeconometric models in use in the 1970s are fundamentally flawed. They incorporate behavioral relationships estimated under a specific monetary and fiscal policy and therefore cannot serve to evaluate the effect of a policy change (direct application of the Lucas critique 1976).

Polemical tone

the article is famous for its frontal tone and its uncompromising rejection of the Keynesian tradition dominant since the 1940s. Lucas and Sargent argue that the inability of Keynesian models to explain the stagflation of the 1970s is not a calibration problem but a deep conceptual failure.

Research programme

the article explicitly proposes to rebuild macroeconomics on three pillars, namely (1) microfoundations from agent optimization, (2) rational expectations, (3) Walrasian equilibrium discipline. This programme will become effective with the RBC models (Kydland-Prescott 1982, next entry) then DSGE (entry 9).

Reception and counter-attack

the Boston 1978 conference remained famous for Robert Solow's biting reply qualifying the Lucas-Sargent position as arrogant and premature. Solow and Tobin defend the pedagogical and operational relevance of Keynesian models despite their theoretical limits. Mankiw (1985) on menu costs (see entry 8 below) constitutes the formal New Keynesian technical response to this manifesto, demonstrating that nominal rigidities preserve the effectiveness of monetary policy even under rational expectations.

Historical status

the article is unanimously regarded as the theoretical and programmatic manifesto of NMC, the ideological counterpart of the Lucas critique 1976 on the methodological plane. It marks the definitive rupture between orthodox Keynesians and the new classical school of Chicago-Minnesota.

article by Finn Kydland and Edward Prescott (Econometrica, vol. 50, no. 6, November 1982, pp. 1345-1370) founding Real Business Cycle (RBC) theory, the most radical extension of the NMC programme in the analysis of economic fluctuations.

Model framework

Solow-type neoclassical growth economy augmented with random technology shocks (stochastic variations of total factor productivity) and the time-to-build friction (installed capital takes several periods to become productive after investment, typically four quarters for structures and one quarter for equipment).

Evaluation method

Kydland and Prescott calibrate the model with preference and technology parameters measured on micro data rather than estimating parameters by maximum likelihood as in the Keynesian tradition. They then simulate the stochastic model and compare simulated moments (variances, correlations, autocorrelations) to the empirical moments of US macro series (GDP, consumption, investment, hours worked). This is the origin of the calibration methodology.

Results

the pure RBC model, without any nominal rigidity, without any expectational error and without monetary policy, reproduces approximately 70% of the variance of US GDP and most observed cyclical correlations. The empirical conclusion is that technology shocks explain the bulk of macroeconomic fluctuations.

Strong implication

the conclusion radicalizes the NMC programme. If fluctuations are the expression of technology shocks on permanently clearing markets, then there is no coordination failure to correct, and stabilization policy is not only ineffective (PIP of Sargent-Wallace 1975) but useless, or even harmful if it disturbs the optimal allocation.

Legacy and critiques

RBC theory dominates academic macroeconomics in the 1980s-1990s (King-Plosser-Rebelo 1988, Cooley 1995 "Frontiers of Business Cycle Research", Princeton University Press).

Main critiques

(a) measured technology shocks (Solow residual) partly reflect non-technological effects (variations in factor utilization, frictions, etc.), (b) the model fails to reproduce employment dynamics (excessive hours variance relative to the real wage), (c) the model says nothing about severe recessions of the 2008-2009 type.

Contemporary synthesis

current DSGE models (entry 9 below) integrate the RBC skeleton (microfoundations, technology shocks, rational expectations) with New Keynesian nominal rigidities (Calvo prices, Calvo wages). This New Keynesian DSGE synthesis is the contemporary methodological standard.

Nobel

Kydland and Prescott jointly received the 2004 Nobel Prize (see entry 4 on Kydland-Prescott 1977). The Nobel rewards both the 1977 time inconsistency and the 1982 RBC theory.

this is where Gregory Mankiw, the author of the textbook from which this explanation is drawn, intervenes himself as a protagonist of the debate rather than as a neutral expositor (see the reformulated anecdote). Two articles published in the same volume of the Quarterly Journal of Economics in 1985 found the technical rebuttal of the New Keynesian Economics (NKE) to Lucas-Sargent's NMC and to the manifesto "After Keynesian Macroeconomics" (entry 6 above).

Mankiw (1985)

"Small Menu Costs and Large Business Cycles: A Macroeconomic Model of Monopoly" (Quarterly Journal of Economics, vol. 100, no. 2, May 1985, pp. 529-538). Mankiw demonstrates that within a framework of monopolistic competition, very small price-adjustment costs (menu costs of a few cents per product) suffice for it to be privately rational for firms not to adjust their nominal prices in response to a monetary shock. Yet socially, this rigidity has a first-order effect on output and employment.

Order asymmetry

the private loss from a failure to adjust is second-order (envelope effect around the optimum), whereas the social loss is first-order (linear effect). This result is a direct rebuttal of the Sargent-Wallace Policy Ineffectiveness Proposition (1975) because systematic monetary policy does have real effects even under rational expectations as soon as one admits even microscopic rigidities.

Akerlof-Yellen (1985)

George Akerlof and Janet Yellen, "A Near-Rational Model of the Business Cycle, with Wage and Price Inertia" (Quarterly Journal of Economics, vol. 100, Supplement, 1985, pp. 823-838) propose a complementary approach based on near-rationality. If agents deviate slightly from perfectly optimizing behavior by following simple rules, the private utility loss is second-order but the macroeconomic effect of their inertia on prices and wages is first-order. George Akerlof received the 2001 Nobel Prize (shared with Michael Spence and Joseph Stiglitz) for his work on asymmetric information. Janet Yellen chaired the Federal Reserve from 2014 to 2018 and then served as US Treasury Secretary from 2021 to 2025.

NKE synthesis

these two articles found the New Keynesian research programme which accepts the methodological tools of NMC (microfoundations, rational expectations, general equilibrium) but recovers the Keynesian policy conclusions through the introduction of microeconomic frictions (menu costs, efficiency wages, nominal contracts à la Taylor 1980, Calvo pricing 1983). This is the synthesis that Mankiw presents in his textbook chapter 14, where he falsely poses as a neutral expositor when he is precisely one of the co-founders of this current.

Contemporary position

the NKE synthesis is today dominant in central-bank practice through the New Keynesian DSGE models (next entry).

Frank Smets and Raf Wouters publish "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area" (Journal of the European Economic Association, vol. 1, no. 5, September 2003, pp. 1123-1175) then "Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach" (American Economic Review, vol. 97, no. 3, June 2007, pp. 586-606). These two articles become the reference DSGE models at the ECB and the Fed respectively.

Architecture

New Keynesian dynamic model with microfoundations from optimization, rational expectations, seven structural shocks (productivity, risk premium, investment, monetary, price-push, wage-push, government) and New Keynesian frictions (Calvo prices, Calvo wages, habit formation in consumption, investment adjustment costs, past-price indexation).

Programmatic realization of NMC

Smets-Wouters concretizes the Lucas-Sargent (1979, entry 6) agenda by building a fully microfounded model under rational expectations, in line with the manifesto "After Keynesian Macroeconomics". The model is estimated by Bayesian methods over long series, satisfying the econometric discipline demanded by Lucas-Sargent. But it is also deeply New Keynesian in its conclusions because nominal rigidities preserve the effectiveness of monetary policy (Mankiw 1985 and Akerlof-Yellen 1985, entry 8) and the central bank can stabilize fluctuations by following an optimized Taylor rule.

NMC-NKE synthesis

Smets-Wouters illustrates the final methodological convergence. NKE adopts the technical tools of NMC (microfoundations, rational expectations, dynamic general equilibrium). NMC accepts in return the nominal frictions (Calvo rigidities) and the Kydland-Prescott time inconsistency. The result is a unified frontier-macro framework used in all major central banks (ECB NAWM as direct heir, Fed FRB/US complemented by EDO and SIGMA, Bank of England COMPASS, Bank of Japan Q-JEM, Banque de France FR-BDF, IMF GIMF and GEM).

Position within the explanation

this is the contemporary terminus of the rational expectations genealogy that starts with Muth (1961), passes through Cagan (1956, entry 3), Friedman-Phelps (1967-1968, entry 2), Lucas (1972, entry 1), Lucas-Sargent (1979, entry 6), Kydland-Prescott (1977 and 1982, entries 4 and 7), Barro-Gordon (1983, entry 5), Mankiw and Akerlof-Yellen (1985, entry 8), and culminates in Clarida-Galí-Gertler (1999) then Smets-Wouters (2003, 2007). Mankiw's chapter 14 is only a pedagogical entry point into this complete genealogy.

foundational article by Christopher Sims (Econometrica, vol. 48, no. 1, January 1980, pp. 1-48) that introduces the Vector Autoregression (VAR) methodology as an alternative to the structural approach of Cowles Commission macroeconometric models.

Critique of structural identification

Sims demonstrates that the identification restrictions imposed by Klein-Goldberger or Wharton-type Keynesian models are "incredible identification" because they rest on arbitrary a priori assumptions (variable exclusions, simultaneity restrictions, shock contemporaneity) that are not testable and that are contradicted by the theoretical analysis of agent optimization. This critique shares the target of Keynesian models with Lucas-Sargent (1979, entry 6) but on a different methodological basis, since Sims attacks identification whereas Lucas-Sargent attack parameter stability.

VAR approach

Sims proposes an empirical model without a priori structural identification, where each macro variable is regressed on its own lags and on the lags of the other variables without exclusion restrictions. The system is estimated in reduced form, and dynamic effects are characterized by impulse response functions and variance decompositions.

Minimal identification

to move from the reduced form to structural shocks, Sims initially proposes a Cholesky decomposition (recursive ordering of shocks), interpreted as a minimal and transparent identification restriction.

Research programme

the article founds an empirical school distinct from NMC and New Keynesians, which becomes dominant for analyzing monetary transmission from the 1990s onward. Later structural extensions by Bernanke (1986), Blanchard-Quah (1989), Galí (1992) introduce more sophisticated identification schemes (long-run restrictions, sign restrictions).

Nobel 2011

Christopher Sims receives the 2011 Nobel Prize (shared with Thomas Sargent, see entry 11 below) "for their empirical research on cause and effect in the macroeconomy". The Nobel motivation explicitly recognizes Sims's VAR contribution as "new methods of analyzing how the economy is affected by temporary changes in economic policy and other factors".

Methodological tension with NMC

the 1980 article proposes an atheoretical approach that opposes the theoretical radicalization of NMC. For NMC, only microfounded equilibrium models are valid. For Sims, these models impose untestable restrictions, and VARs offer a more honest method of empirical analysis. The contemporary synthesis accommodates both approaches by having DSGE serve theoretical analysis and calibration, while VARs serve empirical validation and shock analysis (Christiano-Eichenbaum-Evans 2005, Boivin-Giannoni 2006).

Thomas Sargent receives in 2011 the Nobel Prize in Economics (shared with Christopher Sims, see entry 10 above) "for their empirical research on cause and effect in the macroeconomy". The Nobel motivation rewards the full intellectual trajectory of Sargent, from the Sargent-Wallace Policy Ineffectiveness Proposition of 1975 (see PIP vocab entry), through his empirical work on structural VAR identification in the 1980s-1990s, to the later contributions on learning and bounded rationality.

Methodological evolution

Sargent's intellectual trajectory is interesting because it shows the maturation of NMC. The young Sargent of the 1970s defends perfect rationality and dogmatic rational expectations alongside Lucas. The mature Sargent of the 1990s-2000s acknowledges the empirical limits of this assumption and develops alternative frameworks in which agents progressively learn the structure of the economy.

Adaptive learning

Sargent and his collaborators (notably Albert Marcet, George Evans, Seppo Honkapohja) develop in the 1990s-2000s the theory of recursive least-squares learning, in which agents estimate the parameters of the economy in real time instead of knowing them by assumption. The central reference is Albert Marcet and Thomas Sargent, "Convergence of Least-Squares Learning Mechanisms in Self-Referential Linear Stochastic Models" (Journal of Economic Theory, vol. 48, no. 2, August 1989, pp. 337-368). The framework extends rational expectations toward sophisticated adaptive expectations, and demonstrates that under certain conditions, learning converges to rational expectations in the long run.

Application to US inflation

Thomas Sargent, "The Conquest of American Inflation" (Princeton University Press, 1999) applies the adaptive learning framework to explain the great inflation of the 1970s and its resorption under Volcker. Sargent defends the thesis that the Federal Reserve progressively learned the structure of the Phillips curve, explaining the persistence of inflation in the 1970s and then its rapid disinflation after 1979. This analysis breaks with the radical conclusion of pure NMC according to which agents perfectly know the structure, and reintroduces an institutional-evolution dimension into macroeconomic analysis.

Robustness and Knightian uncertainty

Lars Hansen and Thomas Sargent ("Robustness", Princeton University Press, 2008) develop the theory of robust control applied to macroeconomics, where agents face not only risk (known probability distributions) but Knightian uncertainty (unknown distributions). This framework generalizes rational expectations by allowing agents to hedge against the worst-case model specification (max-min).

Intellectual synthesis

the Sargent trajectory illustrates the maturation of the NMC programme. The perfect rationality postulated in the 1970s gradually gives way to softer assumptions (learning, robustness, ambiguity) that remain faithful to the microfounded and optimizing spirit without imposing complete clairvoyance. This evolution is consistent with that of Lucas himself, who worked in the 1980s-2000s on endogenous growth (Lucas 1988 "On the Mechanics of Economic Development", Journal of Monetary Economics, vol. 22, no. 1, July 1988, pp. 3-42) and on departures from perfect rationality.

Position within the explanation

Sargent illustrates the intellectual evolution of NMC from the revolutionary dogmatism of the 1970s to a mature research programme that dialogues with New Keynesians (entry 8) and accepts departures from perfect rationality without renouncing fundamental methodological requirements (microfoundations, equilibrium, optimization).