Age Structure and the Personal Savings Rate in the United States, 1956-1995.

• Author: Thornton, John

John Thornton [*]

Cointegration techniques are applied to time series data on the personal savings rate and the age structure of the population in the United States over the period 1956-1995, The personal savings rate is cointegrated with the ratios of minors and of retired persons to the working-age population and both of these ratios had a negative and significant impact on the personal savings rate. The results support the life-cycle hypothesis of savings.

1. Introduction

   In a recent paper Horioka (1997) found that the age structure of the population affected the household savings rate in Japan and interpreted his findings as strong support for the lifecycle model. This note shows that these conclusions also apply to the United States. Specifically, it applies cointegration techniques to annual time series data for the period 1956-1995 and finds that the ratio of minors to the working-age population and that of the aged to the working-age population both had a negative and significant impact on the personal savings rate in the United States.

2. Model and Data

   According to the life-cycle model, individuals work and save when they are young and run down their savings during retirement. [1] Similarly, minors, who have yet to begin work, consume but do not earn income. Accordingly, personal savings will be lower the higher the ratio of the retired population to the working population, and the higher the ratio of minors to the working population. Assume that individuals begin working at D years of age, work for W number of years, retire for R number of years, and die at age L. Also, assume that consumption and growth are independent of age, there is no productivity growth, the interest rate is zero, and there are no intergenerational transfers. Then a simplified version of Modigliani's (1970) life-cycle model for the personal savings rate is given by:

   [S.sup.h] = (D + R)/L - (W/L)*DEP - (W/L)*AGE (1)

   where [S.sup.h] is the personal savings rate, DEP is the ratio of minors to the working population, and AGE is the ratio of retired to the working population. In Equation 1, personal savings are a decreasing function of DEP and AGE, and the coefficients of both variables are the negative of the ratio of the working life to life span. In the empirical analysis, personal savings are specified as a function of DEP and AGE. DEP is proxied by the ratio of the population under 15 years of age to that from 15 to 64 years of age and AGE is proxied by the ratio of the population 65 years of age and over to that from 15 to 64 years of age. [2] The personal savings rate, [S.sup.h] is calculated as personal savings as a percentage of personal disposable income. [3] Annual data on the U.S. personal savings rate and the age structure of the population are published in the U.S. Department of Commerce, Survey of Current Business and the OECD, Labour Force Statistics, respectively.

3. Methodology and Results

   As a first step, the time series properties of the data were examined using the Augmented...