Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment

Standard New Keynesian models generate no unemployment, only voluntary movements in hours or employment, which the authors call a surprising basis for the workhorse models used by central banks. They extend the framework with a labour market in which hiring is costly and the cost per hire rises with labour market tightness – defined as the ratio of aggregate hires to the pool of jobless individuals available at the start of the period, which is also the job-finding rate facing an unemployed worker – and they proceed in two steps. With flexible prices and their utility specification (log consumption, power disutility of employment), the constrained-efficient allocation has a constant job-finding rate and hence a constant unemployment rate, invariant to productivity shocks, because income and substitution effects on labour supply exactly offset; the same invariance survives under Nash bargaining, though the bargained unemployment rate generally differs from the efficient one unless a Hosios-like condition holds (no effective market power by final goods firms, and worker bargaining power equal to the elasticity of hiring costs with respect to tightness). The authors are careful to distinguish this invariance from the Shimer puzzle: Shimer derived small unemployment responses assuming a constant marginal rate of substitution, whereas here “our neutrality result follows entirely from movements in the marginal rate of substitution,” which moves one-for-one with productivity so that labour market frictions play no role – and they note that under more general assumptions “the Shimer puzzle will be even stronger than in the original Shimer set-up.” Because the one-for-one wage response looks counterfactual, they impose real wage rigidity through a schedule indexed by a parameter running from Nash bargaining at zero to Hall’s fully rigid wage at one, and add Calvo price staggering. Real marginal cost then depends on tightness and on the rigidity index, which yields a Phillips curve linking inflation to expected inflation and to the current, lagged and expected unemployment rate – with the weights on the level versus the change in unemployment determined by how fluid the labour market is. Since constrained-efficient unemployment is constant, both stabilisation goals are desirable, but with partial wage adjustment neither can be achieved alone: there is no divine coincidence. Calibrating quarterly (discount factor 0.99, unit Frisch elasticity, elasticity of substitution 6 implying a gross markup of 1.2, Calvo slope 1/12, rigidity index 0.5, hiring cost elasticity 1) to a fluid U.S. market (5 percent unemployment, job-finding rate 0.7, separation rate 0.12) and a sclerotic European one (10 percent unemployment, job-finding rate 0.25, separation rate 0.04), with hiring costs set at 1 percent of GDP in the U.S. case, they find that after a persistent (AR(1) coefficient 0.9) one percent fall in productivity, stabilising unemployment requires about a 150 basis point rise in inflation on impact under both calibrations, while strict inflation targeting raises unemployment by about 3 percentage points on impact under both and, in Europe, produces a hump-shaped path peaking near 8 percentage points – a response the authors themselves label possibly unrealistic while noting the policy assumed is also unrealistically extreme. Optimal policy sits between: unemployment rises 50 basis points in the U.S. calibration and about half that in Europe, at the price of persistently higher inflation of roughly 1 and 1.4 percentage points, and the welfare losses under strict inflation targeting are 25 times those under optimal policy in the European calibration.

Real Wage Rigidities and the New Keynesian Model

Most central banks behave as though stabilising inflation and stabilising the gap between output and its desired level are competing goals, yet the standard New Keynesian framework implies no such conflict: because the New Keynesian Phillips curve makes inflation a function of expected inflation and the output gap alone, holding inflation constant delivers a zero output gap, and because the log distance between the efficient (first-best) and natural (second-best) levels of output is a constant in that model, a zero output gap is also a zero welfare-relevant gap. The authors name this property the “divine coincidence” and argue it is an artefact of the absence of non-trivial real imperfections rather than a robust feature. Introducing one such imperfection – real wages that adjust only partially toward the marginal rate of substitution, with the adjustment weight serving as an index of real rigidity – makes the distance between first- and second-best output fluctuate with both supply and preference shocks, so that stabilising inflation, while still equivalent to stabilising the output gap, is no longer equivalent to stabilising the welfare-relevant gap, and the central bank faces a genuine tradeoff. The authors show the tradeoff is quantitatively non-trivial: with a real-rigidity index of 0.9 (a six-quarter half-life for real wage adjustment), an oil share in production of 0.025, an average price duration of six months and the discount factor taken to one, a 10 percent rise in the price of oil requires annualised inflation slightly above 4 percent on impact if the welfare-relevant gap is fully stabilised, or a 1.1 percent first-quarter fall in the welfare-relevant output gap if inflation is fully stabilised – with both magnitudes falling sharply, to roughly 2 percent and 0.5 percent at an index of 0.8 and to below 0.5 percent and 0.1 percent at 0.5, since the expressions are highly non-linear in the rigidity index. The same friction multiplies the short-run output cost of a disinflation by a factor of ten at an index of 0.9, turning a move from 5 percent inflation to zero from a 0.25 percentage point permanent output loss into a 2.5 percentage point short-run loss. On the positive side, real wage rigidities generate inflation inertia – persistence in inflation beyond that inherited from the output gap – and yield an inflation equation in lagged and expected inflation, unemployment and the change in the real price of the non-produced input that is close to traditional Phillips curve specifications; estimated by instrumental variables on annual U.S. data for 1960-2004 (GDP deflator inflation, the civilian unemployment rate, and the PPI raw materials index relative to the GDP deflator, instrumented with four lags of each), all coefficients carry the predicted sign and are statistically significant, and the restriction that the coefficients on lagged and expected inflation sum to one cannot be rejected at the 5 percent level, though the authors note it is not rejected by much.

Olivier Blanchard | Macro Paper Warehouse

Labor Markets and Monetary Policy: A New Keynesian Model with Unemployment

Real Wage Rigidities and the New Keynesian Model