Edward C. Prescott | 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.

The equity premium: A puzzle

This 1985 Journal of Monetary Economics paper by Rajnish Mehra and Edward C. Prescott documents that over the ninety-year period 1889-1978, the average real annual return on the Standard and Poor’s 500 Composite Index was 6.98 percent while the average real return on short-term, virtually default-free securities was only 0.80 percent, an average equity premium of 6.18 percent (standard error 1.76 percent), and asks whether this gap can be accounted for by a class of general-equilibrium pure-exchange models that abstract from transactions costs, liquidity constraints, and other frictions absent from the Arrow-Debreu framework (Sections 1-2, pp. 145-147, 155-156). Using a variant of Lucas’s (1978) exchange-economy model – modified so that the growth RATE, rather than the level, of the (single) representative household’s consumption endowment follows a two-state Markov process, in order to accommodate the sustained, non-stationary growth actually observed in U.S. per capita consumption – the authors calibrate the consumption process to match the historical mean, standard deviation, and first-order serial correlation of U.S. consumption growth, then search over the whole empirically defensible range of risk-aversion (0 to 10) and time-discount parameters to see what combinations of average risk-free rate and average equity premium the model can produce (Sections 3-4, pp. 150-155). They find that the model can generate a maximum average equity premium of only 0.35 percent – compared with the 6.18 percent observed – and that this conclusion is robust to measurement error in inflation, to the level of temporal aggregation, to alternative specifications of the consumption process (including higher moments), and to introducing financial leverage on the modeled firm or extending the model to allow production and capital accumulation (Section 4, pp. 155-158). The intuition, as the authors explain it, is that in a growing economy the levels of risk aversion needed to generate a six-percent premium also imply implausibly high average real interest rates, since sufficiently risk-averse agents discount future (higher) consumption so heavily that the model-implied risk-free rate rises far above the 0.80 percent actually observed (Section 1, pp. 146-147; Section 5, p. 157). The paper concludes that the puzzle can equally well be framed as asking why the risk-free rate was so low rather than why the equity return was so high, and conjectures that resolving it will most likely require an equilibrium model with some friction or market incompleteness – rather than a complete-markets Arrow-Debreu economy – doubting that either investor heterogeneity or non-time-additive preferences alone will suffice (Section 5, pp. 157-159).

Time to Build and Aggregate Fluctuations

This 1982 Econometrica paper by Finn Kydland and Edward Prescott builds an equilibrium growth model, fitted to post-war U.S. quarterly data, in which business-cycle fluctuations arise from technology shocks propagating through two departures from the standard growth model: a time-to-build technology, in which new productive capital requires multiple periods (calibrated to four quarters) of construction and only finished capital counts as productive, and a non-time-separable utility function in which current leisure’s marginal value depends on a distributed lag of past leisure choices, admitting substantially greater intertemporal substitution of leisure than a standard time-separable specification. The technology shock is decomposed into a highly persistent (autoregressive, calibrated at 0.95 per quarter) permanent component and a transitory component, both observed only through a noisy indicator at the time labor-supply and new-investment decisions are made, so the model incorporates a signal-extraction problem alongside its intertemporal optimization. Because there are no externalities, the authors compute the competitive equilibrium as the solution to a representative-household planning problem, approximated by a quadratic objective and linear constraints around the model’s deterministic steady state so that equilibrium decision rules are linear and second moments can be computed analytically; nearly all parameters are calibrated from steady-state national-accounts ratios and evidence from other applied literatures (e.g., surveyed construction lags of about two years) rather than formally estimated, leaving a small number of free parameters chosen to match the model’s simulated second moments to Hodrick-Prescott-filtered U.S. data for 1950:1-1979:2. The fitted model reproduces, surprisingly well given its simplicity, the U.S. economy’s pattern of output autocorrelation over six lags, the relative volatility ranking across output components (investment about three times as volatile as output, consumption about half as volatile), the strong procyclicality of consumption and hours, and the fact that cyclical output variation comes mainly from variation in hours worked rather than in labor productivity. The paper directly tests time-to-build against the leading alternative propagation mechanism, a quadratic adjustment-cost technology, and finds that even a small adjustment cost badly distorts the model’s implied comovements – making output driven mainly by productivity rather than hours, and making consumption too volatile and investment too smooth relative to the data – concluding that adjustment costs “were not a substitute for the time-to-build assumption in explaining the data.”