Rules Rather than Discretion: The Inconsistency of Optimal Plans

The paper’s thesis is that optimal control theory is not the appropriate tool for dynamic economic planning even when there is “a well-defined and agreed-upon, fixed social objective function” and policymakers correctly know the timing and magnitude of their policies’ effects, because economic planning is “not a game against nature but, rather, a game against rational economic agents” (Introduction, pp. 473-474). Control theory presumes that current outcomes and the system’s evolution depend only on current and past policy and the current state; but current decisions of economic agents depend in part on their expectations of future policy, and those expectations are not invariant to the policy plan actually selected. In situations where the economic structure is well understood, agents will “surmise the way policy will be selected in the future,” so a change in administration or objective changes expectations immediately – a channel optimal control theory omits (pp. 474-475). The authors stress this does not require perfect forecasting by agents, only that policy be partially predictable.

A policy is defined as consistent if, for each time period t, the policy chosen for t maximizes the objective function taking as given previous decisions and that future policy will be similarly (i.e., myopically) selected (Sec. II, p. 476, Definition). In the two-period illustration, period-2 policy π₂ is chosen to maximize the objective given period-1 outcomes, ignoring the effect π₁ had on period-1 agents’ decisions x₁; but the optimal first-order condition for π₁ requires accounting for how π₁ affects x₁ and, through x₁, later outcomes. The consistent policy equals the optimal one only in the knife-edge case where either policy has no effect on prior decisions or those prior decisions have no bearing on the objective function (pp. 476-477). Kydland and Prescott credit Pollak’s (1968) resolution of an analogous intergenerational-preference inconsistency, adapting his feedback-solution approach to the case where the policymaker, unlike a sequence of generations, is the single dominant player each period.

These two well-known public-policy cases are offered as intuition pumps showing that nobody actually applies the “control-theory” consistent solution in practice, even though it seems locally reasonable. If government policy on flood control were only ever to be decided ex post – i.e., not to build levees given that houses already exist in a flood plain – rational agents, anticipating that levees would in fact be built if they settled there, would build houses in the flood plain anyway, and the government would end up building the levees (Sec. II, p. 477). Likewise, the ex post efficient patent policy is to grant no protection once an invention already exists, but nobody seriously proposes this: the sensible question is the optimal patent life, i.e., a rule fixed in advance that trades off innovation incentives against the deadweight loss of monopoly rents (p. 478). Both examples show a policy that is optimal considered only from today onward can be a poor rule once its effect on ex ante behavior is included.

Assuming a linear expectational Phillips curve, u_t = -k(π_t - π_t^e) + u, with rational expectations (π_t^e = Eπ_t) and a social objective function S(π_t, u_t) that the policymaker maximizes period-by-period subject to the Phillips-curve constraint, the consistent equilibrium occurs where an indifference curve is tangent to a Phillips curve along the vertical (zero-inflation-surprise) axis – point C in the paper’s Figure 1 – which the authors argue implies a positive, generally excessive, socially undesired inflation rate* (Sec. III, pp. 478-480). Crucially, unemployment at this consistent equilibrium is no lower than it would be under a rule of price stability, since the optimal equilibrium, point O, lies on a higher indifference curve at the same (natural) rate of unemployment. If policymakers were bound to price stability and had no discretion, the resulting equilibrium would have unemployment no higher than under discretion, and higher welfare. The authors relate this to Taylor’s (1975) finding that the optimal rational-expectations monetary policy is random, noting that in both cases the optimal policy is inconsistent, so it is not optimal for a policymaker to continue with an initially announced policy.

For infinite-horizon recursive structures, backward induction cannot pin down consistency (there is no terminal period to start from), so the authors instead define consistency in terms of policy rules**: a stationary feedback policy rule Π is consistent if it is a fixed point of the mapping from an assumed future rule to the best current-period rule given that future rule** (Sec. IV, pp. 480-482). Because changes in the future policy rule change the functional form of agents’ equilibrium decision rules – “a point convincingly made by Lucas (1976) in his critique of current econometric policy-evaluation procedures” – the best current policy is a function of the future rule actually expected to be used. The authors also note that even when policymakers and agents lack a clear understanding of the economy’s structure, both are likely to grope toward and converge on the (suboptimal) consistent rule over time, since policymakers naturally trade off current outcomes against an (approximately correct) valuation of the end-of-period state, which is exactly the consistent procedure.

The authors build a rational-expectations competitive equilibrium model (following Lucas & Prescott 1971, and building on Muth 1961’s rational-expectations concept) of a constant-returns industry choosing investment subject to adjustment costs, in which firms’ investment demand depends on the expected future path of the investment-tax-credit rate as well as its current level (Sec. V, pp. 482-484). The policymaker chooses a sequence of tax-credit rates each period to minimize a quadratic loss function in output, investment, and the tax credit itself, relative to target levels (p. 484). The exercise is explicitly designed to mimic actual policy practice: “econometricians are continually revising their estimates of the structure on the basis of which new policies are devised and are continually surprised to find that the structure has changed” (p. 484) – i.e., a passive stabilization policy is estimated, optimal control is applied to derive a new rule under the (mistaken) assumption that the estimated investment function is invariant to the policy rule, the economy moves to a new equilibrium investment function once the new rule is implemented, econometricians re-estimate, and the cycle repeats.

In the example with weights (ω₁,…,ω₆) = (2,4,1,10,20,10) and autoregressive parameter ρ = 0.6, the iterative process converged, but the resulting consistent policy was “decidedly inferior” to a passive policy of never varying the investment tax credit – with variables averaging about 10 percent away from their targets – after initially appearing to improve performance over the first two iterations before deteriorating (Sec. V, pp. 484-485). In every case where the process converged, the authors found linear feedback rules that outperformed the consistent rule, typically by a substantial margin. In a second example with weights (1,2,1,10,3,20) and ρ = -0.6, the iterative process did not converge at all: successive policy-rule revisions induced ever-larger changes in the investment function, and the variables fluctuated with increasing amplitude at each iteration – a result the authors call “very disturbing,” since it suggests that continuing the standard practice of re-optimizing policy after each econometric re-estimation could, in principle, make an economy less stable than it already is (p. 485).

Beyond monetary/fiscal stabilization, patents, and flood control, the authors sketch three further applications (Sec. VI, pp. 485-486). In dynamic oligopoly with a dominant firm (Kydland 1975a), the dominant firm faces “precisely the same paradox” in taking into account how other firms will react to its planned decisions. In constitutional law, a majority group (e.g., workers) that controls policy might rationally choose a constitution limiting its own future power to expropriate capitalists’ wealth, since agents with low discount rates will save more – raising the capital stock and wages and lowering capital’s rental price – once they know their wealth will not be expropriated. And in energy policy, the authors suggest rational firms may underinvest in new oil sources in anticipation that windfall-profit taxes or price controls will later be imposed on any resulting profits, so that policies presented as merely redistributing past gains can reduce future supply through their effect on current expectations.

The paper’s conclusion is that policymakers should follow rules rather than have discretion – not because policymakers are “stupid or evil,” but because discretion is definitionally the selection of the decision that is best given the current situation, and such behavior results either in a consistent-but-suboptimal outcome or in economic instability (Sec. VII, pp. 486-487). Until economists possess a tested theory of business cycle fluctuations, the authors argue active stabilization “may very well be dangerous,” and reliance on simple rules – a constant money-supply growth rate, constant tax rates – constitutes “a safer course of action.” Once such a theory exists, the recommended procedure, following Lucas (1976), is to use economic theory to evaluate the operating characteristics of alternative policy rules rather than to optimize policy period-by-period; in a democratic society, the authors add, selected rules should preferably be simple and easily monitored so that deviations by a policymaker are obvious, and they float the idea of legislated rules taking effect only after a multi-year delay to make discretionary reversal difficult (p. 487).

The paper explicitly builds on and cites Lucas (1976): “since optimal decision rules vary systematically with changes in the structure of series relevant to the decision maker, any change in policy will alter the structure of these rules” (Introduction, p. 474), and Kydland and Prescott’s investment-tax-credit example operationalizes exactly this mechanism – a change in the tax-credit rule changes the equilibrium investment function, invalidating forecasts based on the old function. Where Lucas’s critique is chiefly a methodological argument against using estimated reduced-form relationships to simulate the effects of new policy regimes, Kydland and Prescott’s distinct contribution is a game-theoretic point that survives even if the “true” structural model is known with certainty: optimizing “given the current situation” each period is, by construction, time-inconsistent whenever current agents’ decisions depend on expectations of future policy – a logically separate reason, beyond parameter drift, for control theory’s inapplicability to policy design (pp. 480-481, 486-487).