Is the Stock Market Overvalued?

The value of U.S. corporate equity in the first half of 2000 was close to 1.8 times U.S. gross national product (GNP). Some stockmarket analysts have argued that the market is overvalued at this level. We use a growth model with an explicit corporate sector and find that the market is correctly valued. In theory, the market value of equity plus debt liabilities should equal the value of productive assets plus debt assets. Since the net value of debt is currently low, the market value of equity should be approximately equal to the market value of productive assets. We find that the market value of productive assets, including both tangible and intangible assets and assets used outside the country by U.S. subsidiaries, is currently about 1.8 times GNP, the same as the market value of equity. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. As the 20th century drew to a close, the U.S. stock market boomed. Between 1994 and 2000, the value of corporate equity relative to gross national income, or equivalently, gross national product (GNP), nearly doubled. In the first half of 2000, the value of all U.S corporate equity was close to 1.8 times GNP. A ratio of 1.8 is high by historical standards. The previous post–World War II peak was 1.0, which occurred in 1968. Over the 1946–99 period, the value of corporate equity averaged only 0.67 of GNP. (See the accompanying graph.) Thus, at 1.8, the current ratio is two and a half times the ratio’s average in the postwar period. Is the current stock market value too high? Glassman and Hassett (1999) have argued that it is not. In fact, they have said that the market is undervalued by a factor of three. But others have expressed concern that the market is, indeed, overvalued. Federal Reserve Chairman Alan Greenspan (1996), for example, has suggested that the recent high value of the market may reflect “irrational exuberance” among investors. Shiller (2000) has reiterated this concern and said that a 50 percent drop in the value is plausible. General concern about an overvalued market is fueled by the experience of Japan in the 1990s. The value of Japan’s corporate equity fell 60 percent in 1990, and its economy subsequently stagnated. We use standard theory to value U.S. corporate equity and find that the current value of 1.8 times GNP is justified. An implication of the theory is that the value of corporate equity should equal the value of productive assets in the corporate sector, if net indebtedness is small (as it has been recently). Our basic method is to estimate the current value of corporations’ productive assets and compare that value to the current value of corporate equity. This is not as easy as it may seem. Productive assets include tangible assets—like factories, office buildings, and machines—and intangible assets— like patents, brand names, and firm-specific human capital. And a good measure of the value of these assets must include not only those used by U.S. corporations in the United States itself, but also those used outside the country, by U.S. corporations’ foreign subsidiaries. Estimates of the value of some of these assets are reported by the U.S. government. The Commerce Department’s Bureau of Economic Analysis (BEA) estimates the value of tangible corporate assets located in the United States. In the 1990s, the estimate is slightly above 1.0 GNP. However, the BEA does not estimate the value of intangible assets in the corporate sector or the value of assets of U.S. corporate foreign subsidiaries. Therefore, we must construct estimates of these values ourselves. To estimate the value of corporate intangible assets, we use data on corporate profits and tangible assets and an estimate of the return on capital used in the corporate sector. We find that corporate profits are larger than can be justified with tangible assets alone. By redoing the U.S. national income and product accounts (NIPA) with intangible assets included, we can derive formulas that allow us to residually determine the value of these assets. The key assumption is that the after-tax returns on tangible and intangible capital are equal. We find that the value of intangible capital is roughly 0.4 of GNP. That value may seem large. We think it is reasonable in light of direct evidence. The value of high-technology companies, for example, can only be justified by their intangible capital, particularly human capital. A significant fraction of the value of drug companies must be assigned to the value of the patents that they own. And as Bond and Cummins (2000) point out, brand names such as CocaCola account for much of the value of many companies. To estimate the value of assets of U.S. corporations’ foreign subsidiaries, we use profits of these subsidiaries divided by an estimate of the return on tangible capital in the United States. Our estimate of these assets is close to 0.4 of GNP. Summing the values of corporate tangible assets located in the United States, corporate intangible assets, and assets of foreign subsidiaries gives us a total value of productive assets in the U.S. corporate sector of 1.8 times GNP—the same as the current value of corporate equity. This equality is just what economic theory predicts. According to standard economic theory, therefore, the stock market today is correctly valued. Although our focus here is on the value of corporate equity, our work has implications for real returns on debt and equity. With our estimates of productive assets, theory predicts that returns on both debt and equity should average about 4 percent, as long as there are no important policy changes that significantly affect the pricing of financial assets. This prediction appears to be accurate so far: interest rates on U.S. Treasury inflation-protected securities with various maturities are currently around 4 percent. Theory Our method of estimating the value of corporate assets involves constructing a standard growth model and quantifying it. The growth model we use is established aggregate economic theory and is fast becoming the textbook model in intermediate and advanced undergraduate macroeconomic courses. In this section, we derive formulas for the values of corporate equity and asset returns. In the next section, we use data from the Commerce Department and the Federal Reserve Board of Governors to derive estimates of these values for the United States. Our model economy includes two sectors, a corporate sector and a noncorporate sector. Since our focus is on the value of domestic corporations, output from the corporate sector is the gross domestic product of corporations located in the United States. Output of the noncorporate sector of our model is the remaining product of U.S. GNP. Our noncorporate sector thus includes the household business sector, the government sector, the noncorporate business sector, and the rest-of-world sector. Willingness to Substitute Our model economy is inhabited by infinitely lived households with preferences ordered by the expected value of (1) ∞ t=0 β[(ctlt )/(1−σ)]Nt where t indexes time, ct is per capita consumption, lt is the fraction of productive time allocated to nonmarket activities such as leisure, and Nt is the number of household members. The fraction of productive time allocated by households to market activities is denoted by n = 1 − l. The size of a household is assumed to grow at the rate of population growth, η. The curvature parameter on consumption, σ ≥ 0, measures how risk averse a household is. The larger this parameter’s value, the more risk averse is the household. The parameter 0 < β < 1 measures impatience to consume, with a smaller value implying more impatience. The parameter ψ measures the relative importance of leisure and consumption to the household. The larger ψ is, the more important is leisure. Ability to Transform The model economy has two intermediate good sectors— a corporate sector, denoted by 1, and a noncorporate sector, denoted by 2. These provide the inputs to produce the economy’s final good. The noncorporate production technology is simple: (2) y2,t ≤ (k2,t) (ztn2,t) 1−θ. Here y2 is sector output, k2 is capital services, n2 is labor services, z is a stochastic technology parameter, and θ is the capital share parameter, 0 < θ < 1. For our purposes, the corporate sector is the important sector, and it is more complicated. It has both tangible and intangible assets. U.S. corporations make large investments in such things as on-the-job training, research and development (R&D), organization building, advertising, and firm-specific learning by doing. These investments are large, and the stock of intangible assets has important consequences for the pricing of corporate assets. So we assume that production in the corporate sector requires both tangible assets, which are measured, k1m, and intangible assets, which are unmeasured, k1u. In addition to capital, labor services n1 are required. The aggregate production function for the corporate sector is (3) y1,t ≤ (k1m,t) (k1u,t) (ztn1,t) 1−φmt−φut where φmt and φut are the random capital shares for measured and unmeasured capital, respectively. In order to capture variations in profit shares over the business cycle, we make the nonstandard assumption that capital shares vary. Variations in profit shares affect the equity risk premium, which we want to estimate. The three per capita capital stocks in this economy— corporate tangible and intangible capital and noncorporate capital—depreciate geometrically and evolve according to (4) ki,t+1 = [(1−δi)ki,t + xi,t]/(1+η) where i = 1m, 1u, or 2; δi is the rate of depreciation for capital of type i; and xi,t is gross investment of type i in period t. The right side of the capital accumulation equations (4) is divided by the growth in population (1+η) because ki and xi are in per capita units. The model also has a final good sector, which combines the intermediate inputs from the corporate and noncorporate sectors to produce a composite output good that can be used for consumption and investment. This production function is (5) ct + gt + x1m,t + x1u,t + x2,t ≤ yt ≡ A[μ(y1,t) + (1−μ)(y2,t)] 1/ρ where g is government consumption, 0 < μ < 1 is a parameter that determines the relative sizes of the corporate and noncorporate sectors, ρ ≤ 1 is a parameter that governs the substitutability of corporate and noncorporate goods, and A > 0 is a scale parameter. Government production is assumed to be included in noncorporate production. However, the government plays a special role in the economy: it taxes various activities to finance government purchases and transfers. In particular, the government taxes consumption, labor income, property, and profits. Taxes are proportional in our model economy.