Measuring the Welfare Costs of Inflation in a Life-cycle Model

In macroeconomics, life-cycle models are typically used to address exclusively life-cycle issues. This paper shows that modeling the life-cycle may be important when addressing public policy issues, in this case the welfare costs of inflation. In the representative agent model, the optimal inflation rate is characterized by the Friedman rule: deflate at the real interest rate. In the corresponding life-cycle model, the optimal inflation rate is quite high: for the benchmark calibration, it is around 95% per annum. Much of the paper is concerned with understanding this result. Briefly, in the life-cycle model there are distributional consequences of injecting money via lump-sum transfers. The net effect is to transfer income from old, rich agents to young, poor ones. These transfers twist the age-utility profile in a way that agents find desirable from a lifetime utility point of view. A second issue concerns how to assess the costs of inflation in a life-cycle model. Metrics that are equivalent in the representative agent model can give very different answers in a life-cycle model.