Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time

This paper builds a dynamic, non-stochastic model of the “optimal” fiscal control of aggregate demand, deriving the time path of aggregate employment (or “utilization”) that a policymaker who cares about a social utility integral over consumption and leisure should choose, given a mechanism linking inflation, utilization, and the expected rate of inflation. Its key building block is a family of “Quasi-Phillips Curves” relating the actual rate of price inflation to the utilization ratio, which shift vertically one-for-one with the currently expected rate of inflation, together with a Cagan-style adaptive-expectations mechanism by which the expected inflation rate rises whenever actual inflation exceeds it and falls whenever actual inflation falls short. Phelps argues the conventional, static approach to the unemployment-inflation choice – which picks a single unemployment rate by the tangency of a (zero-expected-inflation) Phillips curve with social indifference curves – is wrong because it implicitly assumes infinitely heavy discounting of future utility: holding utilization above the equilibrium ratio y* (where actual and expected inflation coincide) forever causes the Phillips curve to keep shifting upward as expectations catch up, so the same “optimal” unemployment target produces ever-higher inflation, with a steady state eventually reached only at a very high inflation rate. In the dynamic optimum, by contrast, utilization must approach y* asymptotically regardless of the initial conditions; the real policy choice is only the transitional path, since preferences depend jointly on utilization (the consumption-versus-leisure trade-off) and on the money interest rate through a demand to hold enough real balances for “full liquidity.” When future utility is not discounted at all, the paper shows that under-utilization is optimal whenever the inherited expected deflation rate is below the rate needed for full liquidity at equilibrium utilization, that equilibrium utilization is immediately optimal if that rate is already inherited, and that sustained over-utilization is never part of an optimal path in this case. When future utility is discounted at a positive rate, over-utilization can become optimal, and the long-run (asymptotic) equilibrium expected inflation rate rises with the discount rate – so, on Phelps’s reading, what actually separates “inflationist” from “deflationist” policy prescriptions in this model is not a differing view of the employment-inflation trade-off itself but a differing implicit weight placed on the present relative to the future. Phelps is explicit that the model rests on strong simplifications – a closed, non-stochastic economy, an exogenously accommodating monetary policy that keeps a “virtual golden-age” investment path, and inflation depending only on the level (not the rate of change) of utilization – and flags these as priorities for extension rather than as settled features of the analysis.

Edmund S. Phelps | Macro Paper Warehouse

Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time