Barro–Gordon Monetary Policy Model

The Barro–Gordon monetary policy model is a game-theoretic framework for the behavior of a central bank facing rational, forward-looking wage setters. Robert Barro and David Gordon presented it in two 1983 papers: "A Positive Theory of Monetary Policy in a Natural Rate Model" in the Journal of Political Economy and "Rules, Discretion and Reputation in a Model of Monetary Policy" in the Journal of Monetary Economics. The model applies the Kydland–Prescott time inconsistency argument to monetary policy and explains why economies can experience persistently high inflation with no benefit in employment. It became the reference model for the modern theory of central bank credibility.

The economy has two ingredients. The first is an expectations-augmented Phillips curve, in which output y exceeds its natural level y* only when inflation π exceeds the inflation rate that private agents expected, πᵉ:

y = y* + b(π − πᵉ), with b > 0.

The second is a central bank loss function that penalizes both inflation and the gap between output and a target that is above the natural level, which captures distortions such as taxes or monopoly power that make the natural rate inefficiently low:

L = ½(π − π*)² + ½λ(y − y* − k)², with k > 0 and λ > 0.

The timing is crucial. Wage setters choose nominal wages first, forming expectations πᵉ. The central bank then chooses π, observing the wage contracts. This sequence gives the bank an incentive to surprise workers: higher realized inflation than expected temporarily raises output.

Under discretion, the central bank takes πᵉ as given and minimizes L over π. The first-order condition gives π as a weighted combination of the target π* and the expectation πᵉ, with the weight depending on λ and b. Private agents know this reaction function and set πᵉ equal to the inflation rate the bank will choose. In the rational-expectations equilibrium, π = πᵉ, so no output gain materializes, but inflation is above target:

π = π* + λbk.

The term λbk is the inflation bias. It increases when the bank values output more (λ), when output responds strongly to surprises (b), and when the output target is further above the natural rate (k). The outcome is a Nash equilibrium of the one-shot game between the central bank and the public. It is time-consistent, since the bank has no incentive to deviate, but it is inefficient: the same output is obtained with higher inflation.

Under commitment to a rule, the bank announces π = π* and is believed, so the bias disappears and welfare improves. The difficulty is that, once expectations are fixed at π*, the bank gains by inflating, which is why a one-time announcement is not credible. This is the central idea inherited from the broader literature on game theory.

Barro and Gordon's second paper treats the interaction as a repeated game. If the bank cares about the future, the public may adopt a trigger strategy: expect low inflation as long as the bank has delivered low inflation, and revert to the high discretionary rate for some period after a deviation. The bank then compares the one-period gain from surprise inflation with the future cost of lost credibility. If the discount factor is high enough, low inflation can be sustained as an equilibrium, as in the repeated-game cooperation results of game theory. Multiple equilibria exist, with inflation anywhere between the rule outcome and the discretionary outcome, so the model does not pin down a unique level. The reputational equilibrium also depends on the bank's horizon and on how clearly the public can observe deviations, which relates the model to information asymmetry: the public cannot directly observe the bank's intentions, only realized inflation, which is noisy.

Because reputation is fragile, researchers sought institutional fixes.

1. Conservative central banker. Rogoff (1985) showed that society can improve outcomes by appointing a central banker with a higher weight on inflation stabilization than society has. The lower inflation bias outweighs the loss of flexibility in responding to supply shocks, so there is an optimal degree of conservatism. This is a form of delegation that trades off credibility and stabilization.
2. Performance contracts. Walsh (1995) and Persson and Tabellini proposed incentive contracts in which the central banker's pay or tenure depends on inflation outcomes. With a linear penalty equal to the marginal inflation bias, the discretionary equilibrium coincides with the commitment solution, making the bias disappear. This approach uses ideas from mechanism design and the principal–agent problem.
3. Inflation targeting. Svensson (1997) argued that an explicit numerical inflation target, with accountability for missing it, partly replicates the conservative-banker solution while retaining flexibility. Adoption of inflation targets in New Zealand, Canada, and the United Kingdom from the early 1990s followed this logic.
4. Central bank independence. Cross-country evidence from the 1980s and 1990s, such as Alesina and Summers, found that more independent central banks were associated with lower average inflation without lower growth, which is consistent with the model's predictions.

The framework generalizes in several ways. Adding supply shocks creates a tradeoff between rules and discretion: a rule that cannot react to shocks loses stabilization, whereas discretion permits it but at the cost of the bias. Canzoneri (1985) examined the role of private information about the bank's forecasts, in which the central bank's inability to prove that inflation resulted from a shock rather than from opportunism limits reputation. Models with uncertainty about the central banker's type, in the style of reputation models, generate gradual learning. Others link the framework to fiscal policy, where the interaction between fiscal and monetary authorities may exacerbate inflation bias.

Critics note that the model rests on an assumption that the central bank targets output above the natural rate, which does not match the stated goals of most central banks and arguably does not describe their behavior. Blinder (1998), drawing on his experience as a central banker, argued that policymakers do not try to push output above potential. Alternative explanations of 1970s inflation emphasize mistaken estimates of the natural rate and an evolving understanding of the Phillips curve, as in Orphanides and Sargent's work. The model also predicts a pervasive inflation bias in economies without credible institutions, yet inflation has been low in many economies, including those with discretionary regimes. Even so, the Barro–Gordon structure remains the standard way to explain why credibility, transparency, and institutional design matter in modern central banking, and its logic permeates the New Keynesian analysis of optimal policy under discretion, in which the Calvo staggered pricing model supplies the supply-side block.

1. Barro, R. J., & Gordon, D. B. (1983). A Positive Theory of Monetary Policy in a Natural Rate Model. Journal of Political Economy, 91(4), 589–610. https://doi.org/10.1086/261167
2. Barro, R. J., & Gordon, D. B. (1983). Rules, Discretion and Reputation in a Model of Monetary Policy. Journal of Monetary Economics, 12(1), 101–121. https://doi.org/10.1016/0304-3932(83)90051-X90051-X)
3. Kydland, F. E., & Prescott, E. C. (1977). Rules Rather than Discretion: The Inconsistency of Optimal Plans. Journal of Political Economy, 85(3), 473–491. https://doi.org/10.1086/260580
4. Rogoff, K. (1985). The Optimal Degree of Commitment to an Intermediate Monetary Target. The Quarterly Journal of Economics, 100(4), 1169–1189. https://doi.org/10.2307/1885679
5. Walsh, C. E. (1995). Optimal Contracts for Central Bankers. American Economic Review, 85(1), 150–167. https://www.jstor.org/stable/2118158