Optimal monetary policy with staggered wage and price contracts

In an optimizing-agent model in which both product and labour markets are monopolistically competitive and both prices and wages are set in Calvo-style staggered nominal contracts, the authors show that monetary policy cannot reach the allocation a frictionless economy would reach. Their argument runs through welfare: approximating average household utility gives an objective that depends on just three unconditional variances – the output gap, price inflation, and wage inflation – and each enters with a strictly negative weight. Price inflation stays constant only if firms are continuously on their labour demand schedules; wage inflation stays constant only if households are continuously on their labour supply schedules; and those two conditions together imply a zero output gap. But holding nominal wages and prices both fixed would pin the real wage at its steady-state value, whereas the Pareto-optimal real wage moves in response to productivity and labour-supply shocks. The contradiction means no more than one of the three variables can have zero variance, so a three-way stabilisation tradeoff is unavoidable, and the Pareto optimum is attainable only in the two special cases where either wages or prices are completely flexible. Solving numerically under a quarterly calibration – discount factor 0.99, Cobb-Douglas capital share 0.3 (labour elasticity of output 0.7), wage and price markup rates of 1/6, and Calvo parameters of 0.75 for both contracts (a mean duration of four quarters) – the authors compute the optimal interest rate rule and find the expected welfare loss relative to the Pareto optimum to be about 0.0024 percent of steady-state consumption, roughly a quarter of Lucas’s (1987) baseline estimate of the gains from eliminating aggregate consumption fluctuations. Two regularities emerge from grids over contract durations: it is optimal, other things equal, for the more flexible nominal variable to absorb a larger share of the required real-wage adjustment, and output-gap volatility is low under the optimal rule for essentially every combination of contract durations. Comparing rules against the optimal benchmark, strict price inflation targeting is clearly suboptimal – at the baseline it produces a welfare loss roughly eight times the optimal rule’s, and when the labour elasticity of output goes to zero the ratio explodes – while strict output-gap targeting does nearly as well as the optimal rule except when the price markup rate is much smaller than the wage markup rate, and two hybrid rules (price inflation plus the output gap, or price inflation plus wage inflation) perform nearly as well as the optimal rule in every case considered.

Andrew T. Levin | Macro Paper Warehouse

Optimal monetary policy with staggered wage and price contracts