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.

The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957

This paper tests, using nearly a century of British data (1861-1957), the hypothesis that the rate of change of money wage rates can be explained by the level of unemployment and the rate of change of unemployment, except in or immediately after years of a sufficiently rapid rise in import prices. Phillips reasons that when demand for labour is high and unemployment low, employers compete for scarce workers and bid wages up quickly, while when demand for labour is low and unemployment high, workers are reluctant to accept less than prevailing rates so wages fall only slowly – making the relation “highly non-linear” – and that wages also respond to whether unemployment is rising or falling, not just its level, since employers bid more vigorously in a year of improving business activity than in a year with the same average unemployment but no improvement. Fitting a curve of the form y + a = bx^c to a scatter of wage-change against unemployment for 1861-1913 (excluding the war and immediate post-war years), the paper finds this relation holds closely across most individual trade cycles between 1861 and 1913, largely holds up (with some cost-of-living-driven deviations attributable to import price shocks) through the disrupted 1913-1948 period, and – once a roughly seven-month lag between unemployment and wage response is introduced – again holds closely for 1948-1957, including a notable match to the sharp wage deceleration during the 1925-1929 return to the gold standard. Decomposing 1948-1957 wage changes into a “demand pull” component (predicted from the fitted unemployment relation) and a “cost push” component (from contemporaneous retail-price inflation, itself often import-price driven) identifies 1951-52 as a clear case of cost-push inflation following the 1949 sterling devaluation and the Korean War import-price shock, and 1950 and 1953-57 as episodes of “pure demand inflation” matching the fitted curve closely. Phillips concludes that, aside from rare years with a sufficiently sharp rise in import prices, the fitted relation implies unemployment of a little under 2.5 per cent would be consistent with stable product prices (given 2 per cent annual productivity growth), while unemployment of about 5.5 per cent would be consistent with stable wage rates, and that because the curve is strongly convex at low unemployment, holding unemployment constant at a given level yields a lower average rate of wage increase than allowing unemployment to fluctuate around that same level. He explicitly describes these conclusions as “tentative” and calls for further research linking unemployment, wages, prices, and productivity.

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Phillips Curves, Expectations of Inflation and Optimal Unemployment over Time

The Relation Between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861-1957