Academic journal article Federal Reserve Bank of St. Louis Review

# Demographics, Redistribution, and Optimal Inflation

Academic journal article Federal Reserve Bank of St. Louis Review

# Demographics, Redistribution, and Optimal Inflation

## Article excerpt

The authors study the interaction among population demographics, the desire for intergenerational redistribution of resources in the economy, and the optimal inflation rate in a deterministic life cycle economy with capital. Young cohorts initially have no assets and wages are the main source of income; these cohorts prefer relatively low real interest rates, relatively high wages, and relatively high rates of inflation. Older cohorts work less and prefer higher rates of return from their savings, relatively low wages, and relatively low inflation. In the absence of intergenerational redistribution through lump-sum taxes and transfers, the constrained efficient competitive equilibrium requires optimal distortions on relative prices. The authors' model allows the social planner to use inflation/deflation to try to achieve the optimal distortions. In the model economy, changes in the population structure are interpreted as the ability of a particular cohort to influence the redistributive policy. When older cohorts have more influence on the redistributive policy, the economy has a relatively low steady-state level of capital and a relatively low steady-state rate of inflation. The opposite happens when young cohorts have more control of policy. These results suggest that aging population structures, such as those in Japan, may contribute to observed low rates of inflation or even deflation. (JEL E4, E5, D7)

Federal Reserve Bank of St. Louis Review, November/December 2012, 94(6), pp. 419-39.

OVERVIEW

Can observed low inflation outcomes be related to demographic factors such as an aging population? A calculation that we label as "back of the envelope" (BOTE) based on some basic economic theory might suggest that the answer is no. Suppose we think of the net real interest rate r in a model with capital. We might guess that in steady state r = [delta] + n, where [delta] is the net depreciation rate and n is the net population growth rate. Suppose we also assume that (i) money and capital pay either the same real rate of return or closely related real rates of return (1) and (ii) the real return on money is the negative of the net inflation rate [pi]. Now suppose the rate of population growth increases to n', creating a new steady state with a more youthful population. By itself, this must mean that the real return to capital increases to r' and that the inflation rate decreases to [pi]'. This fact would seem to suggest that, all else equal, countries with relatively young populations would have relatively low inflation rates and, conversely, countries with relatively old populations would have relatively high inflation rates.

However, the BOTE calculation does not seem to square with some of the facts. Figures 1 and 2 show two time series for two countries, the United States and Japan, respectively, for 1960 to 2010. A moving average (MA) of the consumer price index (CPI) inflation rate is plotted on the left scale. A measure of the youthfulness of the population--the percentage of the population 15 to 40 years of age--is plotted on the right scale. In each case, roughly speaking, economies with a higher share of a younger population are associated with higher inflation, whereas economies with a higher share of an older population are associated with lower inflation. (2) This evidence, while far from definitive, is at least suggestive and does run counter to the BOTE standard theory calculation.

In this article, we provide one reconciliation of the BOTE calculation with the suggestion that aging populations are associated with lower levels of inflation (see Figures 1 and 2). The theory we study has all the elements of the BOTE calculation but also considers the desire for redistribution of resources within society. We model this desire as a social planner's problem in which the planner has access to only inflation or deflation as tools to achieve redistribution. We show that the solution to the social planner's problem associates relatively older populations with relatively low inflation. …

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