Planning for the optimal mix of paygo tax and funded savings

We analyze the optimal balance between social security taxation and private saving in the provision of retirement income in dynamically efficient economies, a question at the center of policy debates in Europe and the United States. We consider the relative importance for this question of the return to capital, the internal return of the pay-as-you-go system, and the variabilities and correlation (or independence) of labor earnings and the capital return. We analyse these influences theoretically in the context of a two-period, overlapping generations model with uncertainty. We use a new method to calibrate the model using annual data on GDP per worker and the total real return on equities, from 1950 to 2002, from which we infer the stochastic characteristics of lifetime labor income and the return to lifetime savings in the US, UK, France and Japan. We obtain a range of optimal, steady-state values of the social security tax and the rate of lifetime savings. When the relative rate of risk aversion is assumed to be 2.5, the computed optimal tax varies from 5% in the United States to 22% in Japan. France is similar to Japan, and the UK is in between.