Rules, discretion and reputation in a model of monetary policy

The policymaker’s per-period cost is z_t = (a/2)(π_t)² - b_t(π_t - π_t^e), with a, b_t > 0 (eq. 1, p. 6). The first term captures a cost of inflation that rises at an increasing rate with the realized inflation rate π_t; the second is a linear benefit from positive inflation shocks (unexpected inflation, π_t - π_t^e). The authors ground the benefit parameter b_t in two channels discussed at length in the introduction (pp. 3-5): (1) the expectational Phillips curve, where unanticipated monetary expansion raises output/lowers unemployment below a “natural rate” that the policymaker views as excessive because of preexisting distortions (income taxation, unemployment compensation, etc.); and (2) governmental revenue from surprise inflation, which depreciates the real value of existing money holdings and nominally denominated public debt – a channel the authors argue is quantitatively larger than ordinary seigniorage, illustrating that a 1-percentage-point surprise in 1981 would have transferred roughly $10 billion via public debt versus about $8-13 billion in annual seigniorage revenue (pp. 4-5). Benefits require existing distortions; without them, the argument for surprise inflation collapses, following Calvo (1978).

Under discretion the policymaker treats current and future expectations as fixed and minimizes E z_t, yielding π̂ = b̄/a; rational private agents, knowing this optimization problem, set π^e = π̂ exactly, so realized inflation shocks are zero in expectation and the expected cost is Ez̄ = (1/2)(b̄)²/a (eqs. 3-5, pp. 7-8). Under a rule prescribing π = 0 (the “ideal rule”), the inflation-shock term drops out entirely and expected cost is zero – strictly lower than under discretion, even though neither regime delivers any systematic inflation surprises. The reason discretion is worse is that it delivers the costs of positive average inflation (from the convex cost term) without any of the benefits that would come from an actual, unanticipated inflation shock: “inflation ends up being excessive… but no benefits from higher inflation result” (p. 9-10). This restates and extends the time-consistency logic of Kydland and Prescott (1977), whom the authors cite explicitly (p. 3), in a fully rational-expectations game-theoretic setting.

If people expect π^e = 0, the policymaker’s best response is to renege and set inflation at the discretionary level, π̃ = b̄/a, capturing an expected-cost saving (the “temptation”) of E(z_rule - z_cheat) = (1/2)(b̄)²/a relative to sticking with the rule (eqs. 8-10, pp. 9-10). Absent any cost to reneging, “zero inflation is not an equilibrium in our model” (p. 14) – the ideal rule is simply not incentive-compatible, regardless of how much better it would perform if honored.

The authors postulate an expectations rule (eq. 11, pp. 11-12): if the policymaker validated expectations last period, people expect the announced rule this period; if the policymaker cheated last period, people expect the discretionary (noncooperative) outcome this period, after which trust is restored the following period. This defines a one-period “punishment” for any deviation. A proposed rule is sustainable only where enforcement – the discounted expected cost of one period of reverting to discretion, q·(1/2)(b̄)²/a – is at least as large as the temptation to cheat (eq. 13, p. 14); since the discount factor q is strictly less than one, this condition fails for the zero-inflation rule but can hold for a positive constant-inflation rule.

Graphing temptation and enforcement against the announced inflation rate π̄ (Fig. 1, pp. 15-17), both curves decline as π̄ rises (temptation because cheating gains less when the rule already prescribes more inflation; enforcement because the punishment itself becomes less costly to bear), intersecting at π̄ = 0 and again at the discretionary rate b̄/a. The best enforceable rule is the interior intersection point, π* = (b̄/a)·(1-q)/(1+q) (eq. 17, p. 17), which is a weighted average of the ideal rule (0) and discretion (b̄/a), with the weight on discretion rising as the mean discount factor q falls – e.g., during a war, when q is plausibly low, the model predicts higher sustainable inflation via exactly this channel, in addition to any direct effect of wartime spending on b̄ (pp. 17-18). Expected cost at π* is likewise strictly between the ideal-rule cost (zero) and the discretionary cost, so reputation is shown to be an imperfect substitute for a genuine binding commitment: “the attraction of the first best [cheating] makes the second best [the ideal rule] unattainable” (p. 18).

Because π* rises with the ratio b̄/a, anything that raises the average benefit from an inflation shock relative to its cost – a higher natural unemployment rate, a recession, wartime government spending, larger deadweight losses from ordinary taxation, or a larger real stock of nominally denominated public debt – predicts higher sustainable monetary growth and inflation (pp. 18-19). The authors list five such episodes their framework rationalizes: the joint rise in mean inflation and the natural unemployment rate in the U.S. over the prior 10-15 years, countercyclical monetary policy, high wartime monetary expansion, high monetary growth in some developing countries, and an inflationary effect of the outstanding real stock of public debt (p. 19).

When bₜ is known at the time of choosing inflation, the ideal contingent rule is no longer constant: π = (1/a)(bₜ - b̄) (eq. 22, p. 22), so mean inflation is still zero but realized inflation moves one-for-one with departures of bₜ from its mean – rising above expectation when bₜ is high (an emergency where the benefits of a surprise are large) and falling below expectation (i.e., surprisingly low or negative inflation, a contractionary surprise) when bₜ is low. The authors argue this apparently perverse behavior is optimal: “the policymaker invests in credibility when it is relatively cheap to do so – namely, when b is low – in order to cash in on this investment when it is most important – that is, when bₜ is high” (p. 23). The best enforceable version of this contingent rule (eq. 27, p. 25) again equates temptation and enforcement state-by-state, so that low realizations of bₜ or high realizations of the discount factor imply the policymaker again “bites the bullet” with contractionary surprises to sustain low prior expectations, reserving the payoff for genuine emergencies (pp. 25-26).

The baseline results fix the punishment interval at exactly one period, but the authors show this is not pinned down by the model: since discretionary outcomes never actually occur along a reputational equilibrium path, expected costs are (weakly) improved by lengthening the punishment interval, so within this stylized setup an infinite punishment interval (“capital punishment”) is in fact preferred (Sec. “The Length of the Punishment Interval,” pp. 26-27). The authors sketch two extensions that could pin down a finite, more realistic interval: (i) allowing inflation to be partly non-controllable so that punishments are occasionally triggered by bad luck rather than deliberate cheating, trading off enforcement strength against the cost of erroneous punishments; and (ii) introducing policymaker-type uncertainty in the spirit of Kreps-Wilson (1980) and Milgrom-Roberts (1980) reputation models, which the authors note “sometimes” yields unique equilibria but which they had “not yet pursued” (pp. 27-28). The paper explicitly flags multiplicity of reputational equilibria as an open problem it does not resolve.

The paper is explicitly presented as extending “the positive theory of monetary policy from our previous paper (Barro and Gordon, 1983 [in the Journal of Political Economy]) to allow for reputational forces” (Abstract, p. i; References, p. 32), which had analyzed discretion and the ideal rule as the only two possible regimes. Kydland and Prescott (1977) is cited as the source of the time-inconsistency logic underlying the benefits of surprise inflation via the expectational Phillips curve (p. 3, footnote), and as itself a source (p. 3) for one of the two channels generating a positive b_t. This paper’s distinct contribution is showing how repeated interaction and reputational concerns can partially, though not fully, substitute for the kind of external legal commitment that Kydland-Prescott’s “rules” required.

The concluding observations frame reputation as delivering “a combination of the outcomes from discretion with those from the ideal rule,” with the relative weight on each determined by the policymaker’s discount rate and the state of the economy, rather than treating discretion and rules as the only two possible regimes (Concluding Observations, pp. 28-29). This establishes an early formal argument for why institutional and reputational features that raise the effective cost of reneging – which later literature would connect to central bank independence and transparent inflation targets – can lower average inflation even without a literal binding rule, while also showing why reputation alone typically cannot achieve the fully optimal (zero-inflation) outcome.