This Selected Issues paper on the United States explains the behavior of inflation and unemployment during 1997–98. The paper highlights that a simple Philips curve equation relating inflation to the unemployment gap has overpredicted inflation since 1993. The mean forecast error for 1994–97 is greater than zero by an amount equivalent to two-thirds of the standard deviation of the forecast error. The paper also examines the developments in the U.S. stock prices. Alternative approaches to social security reform are also discussed.


This Selected Issues paper on the United States explains the behavior of inflation and unemployment during 1997–98. The paper highlights that a simple Philips curve equation relating inflation to the unemployment gap has overpredicted inflation since 1993. The mean forecast error for 1994–97 is greater than zero by an amount equivalent to two-thirds of the standard deviation of the forecast error. The paper also examines the developments in the U.S. stock prices. Alternative approaches to social security reform are also discussed.


1. Over the past three years, stock prices in the United States have risen dramatically, with the S&P 500 index of stock prices increasing at an average rate of around 30 percent a year (Chart 1). As a result, a number of traditional indicators of possible future returns on stocks have moved far out of line with their historical averages, raising a question whether stocks have become overvalued and creating doubts about the sustainability of stock prices. Other analysis, however, suggests that to some extent the rise in equity prices may reflect shifts in asset preferences toward stocks. Hence, it is difficult to say with any degree of confidence that stock prices have moved significantly out of line in relation to their fundamental determinants.



Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A002

Sources: The Wall Street Journal, Standard & Poor’s, a division of McGraw-Hill, and staff estimates.1/ The overage P/E ratio for the period is calculated excluding the high-inflation subperiod of 1970–84.

2. Among traditional indicators of stock market performance, price/earnings ratios have recently deviated sharply from their historical averages, suggesting that prices may be overvalued. In particular, the price/earnings ratio for the S&P 500 rose to about 28 in June 1998, compared with an historical average of about 17 (Chart 1).2 The inverse of the price/earnings ratio (the earnings yield) historically has approximated the average annual real rate of return on stocks. Since the end of the Second World War, the average annual real rate of return on stocks has been around 7 percent, while the comparable real return on risk-free (U.S. government) bonds has been about 1 percent.3 This results in a premium on equities of roughly 6 percent, which cannot be explained adequately by reasonable estimates of the riskiness of stocks relative to bonds (which in the economic and finance literature is referred to as the equity premium puzzle). In the period since 1970, the average equity premium has declined to around 4 percent, possibly reflecting changes in perceptions about the riskiness of stocks and in attitudes toward risk, as well as declines in barriers to stock holding (including transactions costs), particularly with the proliferation of mutual funds.

3. The current price/earnings ratio of 28 suggests that the long-run average annual real return on stocks would decline to about 3½ percent. With long-term U.S. government bonds yielding a real return of 3 to 4 percent, this suggests that the equity premium would virtually disappear. While some narrowing of the equity premium would be consistent with anecdotal information that investors have moved to diversify their portfolios, it is difficult to believe that the equity premium would be eliminated. Therefore, on the basis of this indicator, stock prices seem to be overvalued.

4. The price/earnings ratio also reflects investors’ expectations for the growth in company earnings, which can be derived using the capital asset pricing model4 Assuming that the expected nominal return on equity capital is around 9¾ percent (equivalent to the interest rate on long-term government bonds plus an equity premium returning to its average since 1970 of 4 percentage points), the current price/earnings ratio for the S&P 500 of 28 suggests that investors expect that earnings growth would be 8 percent in nominal terms and about 5½ percent in real terms.5 These rates of growth in earnings would substantially exceed their post-Second World War averages of about 6 percent and 3 percent, respectively.6 Alternatively, investors may be willing to accept a lower rate of return on equity capital (i.e., a lower equity premium). If earnings are expected to grow in line with their historical average, the current price/earnings ratio would suggest that investors have reduced their expected nominal return on equity capital to around 6½ percent, which (given a 5½ percent nominal interest rate on ten-year government bonds) implies that the equity premium has declined to 1 percentage point, substantially below its historical average.7

5. Current stock market prices (and the price/earnings ratio) probably reflect some combination of expectations of continued higher than historical growth in earnings and some expected reduction in the equity premium to a level below its historical average. Projected higher earnings growth may reflect expected improvements in productivity, which are anticipated to stem from the adaptation of computer technology and other changes in business practices. Technological innovations might also have reduced the perceived riskiness of stocks and, thereby, reduced the equity premium. However, it is not clear that there has been a marked improvement in productivity, or that the equity premium has declined permanently to a new substantially lower level In sum, combinations of expected earnings and the level of the equity premium that would be consistent with the current price/earnings ratio of 28 imply substantial deviations from historical experience, suggesting that stocks at present may be overvalued.

6. Another traditional approach to evaluating stock prices involves Tobin’s q, the ratio of the market value of firms to the replacement cost of their capital. In 1997, q rose to about 1.2 compared with its historical average of about 0.6 (Chart 2).8 Tobin’s q exhibits a tendency to revert to its mean value, suggesting that stock prices should decline substantially in the period ahead. There are reasons, however, to expect that the equilibrium value of q may have shifted upward in recent years. For example, the value of new technology firms (especially software companies) may depend heavily on the ideas and human capital of their workers and less on their capital stock (hence, their market value would tend to exceed the replacement cost of their fixed capital and q would be greater than 1). Nevertheless, it is difficult to believe that q could be sustained at a level above 1 for an extended period of time.



(In percent)

Citation: IMF Staff Country Reports 1998, 105; 10.5089/9781451839500.002.A002

1/ Based on the balance sheets of the nonfarm nonfinancial corporate business sector as reported by the Federal Reserve’s Flow of Funds.

7. The conclusions from the analysis of the price/earnings ratio and Tobin’s q should not be carried too far. Similar analyses undertaken a year ago would have led to similar conclusions about stock prices potentially being overvalued. Meanwhile, in the past year, stock prices have risen by 27 percent. This development might be interpreted as suggesting that the market has moved significantly out of line with the fundamental determinants of stock prices, or it might suggest that there has been a significant shift in fundamentals that would justify a higher price/earnings ratio on a sustained basis.

8. Alternatively, as a means of trying to capture the influence of multiple factors that help to explain developments in stock prices, Kramer (1996) estimated a simple econometric model relating the dividend yield (the ratio of stock dividends to prices) to fundamental financial variables (real interest rates, the slope of the yield curve, and default premia) and to net purchases of mutual funds. This model does a good job of “forecasting” developments in the dividend yield since 1995 (and in forecasting stock prices because dividends have remained relatively constant in value over time). In recent periods, however, net purchases of mutual funds have explained most of the movement in the dividend yield. It is difficult to discern whether these shifts in the allocation of portfolios toward stocks reflect a fundamental change in asset preferences, or unreasonable expectations of future returns on stocks based on the very high returns of recent years. Evidence presented by Starr-McCluer (1998) supports the view that the shift in portfolio allocations toward stocks reflects a change in preferences. The paper notes that stock ownership by households through mutual funds and retirement accounts has broadened considerably since 1989, and that survey data indicate that stockholders mentioned retirement savings as a key reason behind their decisions to increase their investments in stocks.9

9. The movements in U.S. stock prices can also be tested for evidence of systematic disturbances, which might suggest the presence of a price bubble, by using a simple variance ratio test. If prices in the stock market, as generally is expected, follow a random walk (the current price is the best forecast of future prices), the variance of the rate of return on stocks held for different time periods should increase in proportion to the length of time that the stock is held. Thus, an important condition for the random walk hypothesis to hold is that the ratio of the variances divided by the length of the holding periods should be equal to one.10 If, instead, price increases today lead to further price increases in the future, the variance ratio would be statistically significantly greater than one, suggesting the possibility of a price bubble in the market. Table 1 shows variance ratios for various subperiods of the period 1980–98 based on the Dow-Jones Industrial Average. The variance ratio is statistically signifcantly different from one only in the subperiod prior to the stock market crash in October 1987. In the two subperiods after the 1987 crash (through 1995 and through April 1998), the variance ratio does not differ significantly from one. However, a strong conclusion should not be drawn from these results regarding the absence of a price bubble in the stock market. The variance ratio test, while providing some useful information on the behavior of prices, is not a completely reliable indicator of the existence of a price bubble.

Table 1.

Variance Ratio for the Dow-Jones Industrial Average

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Based on weekly observations, heteroskedasticity consistent test-statistics reported in parenthesis under the null hypothesis of variance ratio equal to one. The statistics have a standard normal distribution asymptotically. An asterisk denoted rejection of the null hypothesis of a random walk at the 5 percent level of significance.

Up to the week of October 16, 1987.

From the week of October 23, 1987.

List of References

  • Campbell, J., Lo, A., MacKinlay, A., 1997, “The Econometrics of Financial Markets,” Princeton University Press.

  • Kennedy, M., et al., 1998, “Asset Prices and Monetary Policy,” OECD, Economics Department, Working Paper No. 188.

  • Kramer, C., 1996, “Stock Market Equilibrium and the Dividend Yield,” International Monetary Fund, WP/96/90.

  • Siegel, J., 1998, “Stocks for the Long Run,” McGraw Hill, second edition.

  • Star-McCluer, M., 1998 “Stock Wealth and Consumer Spending.” Federal Reserve Board of Governors.


Prepared by Martin Cerisola and Steven Dunaway.


This average is calculated for the period 1954–98, excluding the higher-inflation subperiod 1970–84. This subperiod is excluded because the price/earnings ratio was biased downward due to high inflation, as earnings were inflated largely reflecting inventory profits.


The return on a risk-free U.S. government bond has been approximated by the yield on a ten-year Treasury bond. The use of long-term yields, rather than short-term ones, aims to match the implicit time horizon that investors have when purchasing stocks.


The CAPM suggests that for a constant dividend payout rate d and a constant rate of growth in earnings per share g:


where r is the expected return on equity capital.


In the estimates presented here, the dividend payout ratio is assumed to be constant at its post-Second World War average of 0.5.


The average rate of growth of nominal and real earnings per share for the S&P 500 have been comparable to the rates of growth in nominal and real GDP over the post-Second World War period. While earnings per share could grow faster than GDP for some time, they are not likely to do so for an extended period, since this would imply that the capital share of national income would rise (when historically it has been relatively constant over time), unless firms were to continually reduce the number of outstanding shares.


Kennedy et. al. (1998) reaches similar conclusions regarding the possible overvaluation of U.S. stocks based on estimates of implied equity premia and real earnings growth derived from an analysis of the dividend/price ratio (the ratio of per share dividend payments to share prices).


Tobin’s q is calculated using balance sheet data for the nonfarm, nonfinancial corporate business sector, as reported in the U.S. flow of funds accounts.


The share of households owning stocks rose from 31.6 percent in 1989 to 40.3 percent in 1995. At the same time, the percentage of stocks held by households in retirement accounts rose from 20.7 percent to 33.3 percent of total stock holdings in the same period.


The formula for the variance ratio is:


where var(r12) is the variance of the return for a 12-week holding period, and var(r1) is the variance of the return for a 1-week holding period.

United States: Selected Issues
Author: International Monetary Fund