The S&P 500 index was 1372.71 on June 30, 1999. Earnings corresponding to this index are 41.10 for the four quarters ending June 30, 1999, which gives a PE ratio of 33.4. (The values for earnings and dividends that correspond to the S&P index were obtained directly from Standard and Poor's.) A PE ratio of 33.4 is historically very high. Robert Shiller's web site, contains monthly estimates of the S&P 500 PE ratio for the period January 1871--December 1998, and these estimates reveal how high the current PE ratio is. The largest PE value over the entire period prior to 1991 is 26.6 in January 1895. For the 1,452 months between January 1871 and December 1990, only 52 months (3.6 percent) have a PE ratio greater than 20. The average PE ratio over the whole period of the Shiller data (through December 1998) is 14.2. The average for the period since January 1952 is 15.1.

In order to examine the implications of the current level of stock prices on the future share of profits in GDP, one first needs an estimate of the future growth rate of earnings that is implicit in a PE ratio of 33.4. This will be done using the following formula:

P = D(1+s)/(1+r) + D(1+s)²/(1+r)² + ... + D(1+s)^T/(1+r)^T + E(1+g)^TZ/(1+r)^T

where P is the S&P 500 stock price, D is the initial level of dividends, s is the growth rate of dividends, r is the discount rate, T is the length of the horizon, E is the initial level of earnings, Z is the PE ratio at end of the horizon, and g is the growth rate of earnings. The aim is to estimate g. The known values in the formula are P (1372.71), E (41.10), and D (16.45). Therefore, to estimate g, assumptions are needed for T, s, r, and Z. Table 1 lists the assumptions that were made here.

                              Table 1

               Assumptions Regarding T, r, s, and Z

   Value                 Comments

T   10  Above normal growth for 10 years; then return to normal.
s  .07  Average dividend growth since 1952 has been .056, so .07
        is above average.  
r  .08  Long term government bond rate is about .06, so .08 assumes   
        a risk premium of about .02.  
Z   17  Historical average PE ratio is about 15, so 17 is about 
        2 points above average.  

The values in Table 1 lead to a computed value of g of .142, i.e., an annual growth rate of earnings of 14.2 percent over the next 10 years. This growth rate is considerably higher than the annual growth rate of S&P 500 earnings since 1952, which is 6.0 percent.

To see what an annual growth rate of earnings of 14.2 percent over the next ten years implies about the ratio of profits to GDP at the end of 10 years, one needs an assumption about the future growth rate of GDP. Implicit in the government bond rate of 6 percent used above is an expected inflation rate of about 2 percent, and so the future inflation rate will be assumed to be 2 percent. An optimistic assumption about the growth rate of real GDP over the next 10 years is that it will be 4 percent. To achieve this, one would need productivity growth to be between about 2.5 and 3.0 percent, depending on the growth of the labor force, which would be a very good performance. Using 2 percent inflation and 4 percent real growth, the growth rate of nominal GDP is 6 percent.

The ratio of after tax corporate profits to nominal GDP in the National Income Accounts is currently .057. Since 1952 this ratio has ranged from .026 in 1986 to .068 in 1979. The largest ratio since the data began (1929) is .089 in 1929. Now, if earnings were to grow at 14.2 percent per year over the next ten years and nominal GDP were to grow at 6 percent, the ratio at the end of 10 years would be .119. (It is implicitly assumed in this analysis that the growth rate of profits in the National Income Accounts is the same as the growth rate of S&P 500 earnings. In practice this is roughly the case because the S&P 500 index includes most U.S. stocks by market value.) This is more than double the current ratio and nearly double the largest ratio since 1952.

A ratio of .119 is so far above what has ever been observed historically that it seems highly unlikely it would occur. Constraints on reaching this ratio would arise from social, political, and economic forces. In short, the macroeconomic implications of the earnings growth rate implicit in the current level of stock prices seem unrealistic.

This argument is, of course, based on the assumptions in Table 1. There are assumptions that do not lead to unrealistically large estimates of g. For example, if the long run PE ratio, Z, is assumed to be 30 rather than 17 and the other assumptions in Table 1 are unchanged, the estimate of g is .078 and the ratio of profits to GDP is .068 after 10 years, which is not unrealistic. On the other hand, if the discount rate, r, is assumed to be .06 rather than .08, which implies a zero risk premium, and the other assumptions in Table 1 are unchanged, the estimate of g is .119 and the ratio of profits to GDP is .098 after 10 years, which is still quite high. If one experiments with alternative assumptions (as on this website), it will become clear that the crucial assumption is about Z. If there has been a sea change in stock market valuation in that the long run PE ratio is now in the mid 30s rather than somewhere below 20, the implied estimate of g does not have unrealistic macroeconomic consequences; otherwise it does.