Time-Consistency | Macro Paper Warehouse

Rules Rather than Discretion: The Inconsistency of Optimal Plans

This 1977 Journal of Political Economy paper by Finn Kydland and Edward Prescott argues that optimal control theory – the standard technique proposed for macroeconomic stabilization policy – is not the appropriate tool for economic planning even when policymakers agree on a social objective function and know the timing and magnitude of policy effects, because economic planning is a game against rational economic agents rather than a game against nature. The authors define a policy to be “consistent” if, at every date, the piece selected for that date maximizes the objective function taking past decisions and future policy (similarly selected) as given; a simple two-period example shows the consistent policy is generally not the socially optimal one, because it ignores the effect that today’s policy choice has on agents’ prior expectations and decisions. Applied to a standard expectational Phillips curve under rational expectations (following Muth 1961), this logic implies that discretionary demand management settles at an equilibrium with excessive inflation and no unemployment gain relative to a policy of price stability, because rational agents anticipate the policymaker’s temptation to inflate and build it into their expectations. In a rational-expectations equilibrium model of investment-tax-credit policy (following Lucas & Prescott 1971), the authors show numerically that the iterative process by which policymakers estimate agents’ investment response, apply optimal control to derive a new tax-credit rule, and then re-estimate after the induced structural change typically converges to a consistent-but-inferior policy that is dominated by simple fixed feedback rules – and for some parameterizations fails to converge at all, instead amplifying fluctuations with each iteration. The paper concludes that, absent a tested theory of the business cycle, active discretionary stabilization is hazardous, and that even once such a theory exists, policymakers should be bound by simple, publicly known rules – for example, constitutional or legislative rules with an enactment delay – rather than case-by-case discretion, not because policymakers are inept but because discretion is by definition the selection of what looks best given the current situation, which is exactly the source of the inconsistency.

Rules, discretion and reputation in a model of monetary policy

This 1983 Journal of Monetary Economics paper by Robert Barro and David Gordon shows that a monetary authority acting with full discretion each period will generate more inflation on average than one bound by a fixed rule, because private agents rationally anticipate the policymaker’s temptation to spring inflation surprises and build that expectation into wages and prices, so the surprises never systematically materialize and only the extra average inflation remains. The model gives the policymaker a per-period cost, z = (a/2)π² - b(π - π^e), that is increasing and convex in realized inflation π but falls with a positive inflation shock (π - π^e), where the benefit parameter b (varying randomly with mean b̄) captures gains such as reducing unemployment below a distorted natural rate or extracting revenue by depreciating the real value of nominally denominated money and government debt. Under discretion the policymaker minimizes expected cost taking expectations as given, yielding π̂ = b̄/a and, in rational-expectations equilibrium, π^e = π̂, so inflation shocks average zero but expected cost is strictly higher than under the “ideal rule” of zero inflation, which would eliminate the inflation term entirely; that ideal rule, however, is generally not enforceable, because if people expect zero inflation the policymaker’s one-period temptation to cheat, (1/2)(b̄)²/a, exceeds the enforcement available from the mere threat of losing credibility for one period, (1/2)q(b̄)²/a (with q the discount factor, necessarily less than one). The paper’s central extension is to reputational equilibria: given a postulated expectations mechanism under which the private sector reverts to discretionary expectations for one period after any policy violation and then restores trust, the best rule the policymaker can credibly sustain is the constant-inflation rate π* = (b̄/a)(1-q)/(1+q), which is a weighted average of the ideal rule and the discretionary outcome, moving toward discretion as the discount factor falls (e.g., during wars) and toward the ideal rule as it rises. When the benefit parameter and discount factor are instead observed before inflation is set, the best enforceable contingent rule has the policymaker “bite the bullet” with surprisingly low (even negative) inflation when the benefit parameter is low, investing in credibility that is cashed in as surprisingly high, welfare-improving inflation when the benefit parameter is high (e.g., during a war or recession). The authors note their results depend on assuming a fixed one-period punishment interval and flag that varying this interval generates a family of reputational equilibria among which the model, as developed, cannot select.

Self-Fulfilling Debt Crises

The paper builds a dynamic, stochastic general equilibrium model in which a government that cannot commit to repay must roll one-period debt over each period, and uses it to answer two questions: when is a purely belief-driven default possible, and what should a government do about the risk. The mechanism is a liquidity crunch: because the government issues new debt before retiring the old, “the liquidity crunch induced by the inability to sell new debt can lead to a self-fulfilling default,” so if lenders refuse to buy at any positive price the government may find default optimal, confirming their refusal. The answer to the first question is the paper’s central object, the crisis zone: if fundamentals – “the level of the government’s debt, its maturity structure, and the private capital stock” – lie in a particular range, “the probability of default is determined by the beliefs of market participants.” The zone is bounded below by the largest debt the government would still repay even with no access to new borrowing (the no-lending condition) and above by the largest debt consistent with repayment when it can borrow (the participation constraint). Crises are coordinated by a sunspot uniform on [0,1], whose cutoff is simultaneously the crisis probability, and the consequences inside the zone are real rather than merely financial: consumers, anticipating a crisis with probability π, set a capital stock satisfying β(1−π)+παf′(k^π) = 1, so “the country’s economic activity is depressed in proportion to the probability that a crisis will take place,” while bankers pay only β(1−π) per unit of debt. The answer to the second question is that only preemptive policy works. Reacting once a crisis has begun is useless: pegging the interest rate on government debt, as Calvo (1988) suggested, “simply results in a refusal of the private agents to buy government debt,” and lengthening the maturity of the debt being issued is irrelevant to a crisis today because “it is the maturity structure of the prevailing debt, and not that of the debt being issued, that determines whether or not a crisis is possible.” What does work is reducing the debt below the crisis-zone floor – which triggers “an investment boom in period T−1” and, in period T, rising consumption and government spending – or lengthening maturity in advance, for which Proposition 4 shows that for any debt level in the zone there is a maturity long enough to preclude crises. Two results cut against intuition. Making default costlier raises both bounds of the zone without necessarily closing it, so “the consequences of the acquisition of some additional credibility can be to make the effects of a crisis much worse.” And the governments most exposed are the well-behaved ones: “a government that cares sufficiently more about private than government consumption or is sufficiently farsighted is guaranteed to have a crisis zone.” The model is motivated by Mexico in 1994-95, where the debt/GDP ratio looked responsible but average maturity had become very short, and where the government could sell neither dollar-indexed tesobonos nor peso debt – a pattern “hard to explain on the basis of currency risk, but easy to explain on the basis of default risk.”