May 15, 1999
Professor Martin Feldstein
Dear Professor Feldstein:
Thank you for taking the time to respond to my earlier letters. The procedural point I have been attempting to make in this debate is very simple. A considerable effort goes into producing the economic and demographic assumptions that provide the basis for analyzing the solvency of Social Security. In addition to the work of the actuaries at SSA, at regular intervals, panels of experts evaluate all the assumptions that appear in the Trustees Report and suggest appropriate changes.
Given the care that goes into developing assumptions for the economic and demographic variables that are currently relevant to the program's solvency, it can not make sense to implement a solution based on totally unexamined assumptions about stock returns. If stock investment is to play a role in the financing of the program (whether through individual accounts or investing the trust fund), it seems essential that we should have projections of decade long averages of stock returns, as with other relevant variables. These projections should include breakouts of the two components of stock returns, dividends and capital gains, which have been examined for their consistency with the other projections in the Trustees Report.
I can see no possible justification for failing to subject assumptions on stock returns to the same level of scrutiny as the assumptions concerning other relevant variables. I would hope that you would agree with me on this issue.
In your letter, you asked whether I had my own set of projections on stock returns. I have produced a set below, which I will explain in some detail. This should clarify exactly what it is that I think SSA should be producing, and also point out the basic problem in the assumption of 6.0-7.0 percent real returns given current valuations and projections of profit growth.
Dividend Yield Capital Gain Total Return
The first step in deriving the projections for dividend yields is to start with the current earnings to price ratio. This is assumed to be 0.033 to 1 in this analysis. After the latest market run-up, the earnings to price ratio is probably somewhat lower than this, but the actual number will depend on the stock market aggregate and the period picked to measure earnings. For this analysis, the earnings to price ratio is assumed to remain constant throughout the period. I will discuss alternative assumptions in the treatment of capital gains.
I then calculated how much net investment will have to take place in order to realize the Trustees projection of 1.3 percent annual productivity growth. This projection does not break down productivity growth into its components (labor composition, capital intensity, and multifactor productivity), but I assumed that the contribution of capital intensity will be 0.6 percent annually, the same as its average over the last twenty five years (Bureau of Labor Statistics, Multifactor Productivity Trends). Using a standard Cobb-Douglas production function, with a capital coefficient of 0.3, this implies that the capital labor ratio will have to increase at the rate of approximately 2.0 percent annually. The current ratio of the stock of physical capital held in the corporate sector to equity prices is approximately 0.6 to 1, which implies that firms will on average have to invest an amount equal to 1.2 percent of their share price in order for the economy to realize the rate of productivity growth assumed in the Trustees Report.
In addition to the capital deepening needed to realize the productivity growth projections in the Trustees Report, it is also necessary that the capital stock grow at the same rate as the labor force. These projections therefore assume that net investment is equal to the projected rate of growth of the labor force, multiplied by the capital stock (which is assumed to be 60 percent of the value of corporate equities), plus an amount equal to 1.2 percent of the value of equities, which is needed for the capital deepening implies by the Trustees productivity projections.
After deducting the fraction of earnings needed for investment, it is assumed that all other profits are paid out as dividends. For example, in the decade from 2030 to 2040, the Trustees assume that the labor force will grow at 0.2 percent annual rate. This means that an amount equal to 0.12 percent of equity prices will be needed to keep the capital labor ratio constant, while net investment equal to an additional 1.2 percentage points of equity prices will be needed for capital deepening. This implies that net investment will be equal to 1.32 percent of equity prices, while earnings will be 3.3 percent. This implies a dividend yield of 2.0 percent.
The Trustees assume that the capital share of income remains constant. This means that domestic profits will grow at the same rate as GDP. Profits on foreign investment could allow for the profit growth of domestic corporations to exceed the growth rate of GDP. This analysis assumes that foreign profits allow the growth of domestic profits to exceed the growth rate of GDP by 0.2 percentage points annually. This assumes an extraordinary rate of growth of investment in developing nations. If the rate of return on investment in developing countries is twice the rate of return on investment in the United States, this assumption implies that 20 percent of the profits of U.S. corporations will be coming from developing nations by 2050, and that 30 percent will be attributable to developing nations by 2075. If the return on investment in developing nations is on average 50 percent higher than in the United States, this would imply that 30 percent of the profits of U.S. corporations would be originating in developing nations by 2050, and 45 percent by 2075. This is an extremely rapid rate of internationalization of capital. It is worth noting that the ratio of foreign profits of U.S. corporations to total domestic profits has actually been falling over the current business cycle.
The Trustees assume that the consumer price index will rise by 0.1 percentage points annually relative to the GDP deflator. Since the CPI is the relevant deflator for Social Security (post retirement or disability benefits are indexed to the CPI), it is necessary to deduct 0.1 percentage points from the rate of growth of real GDP to get the rate of growth of real profits, measured against the CPI.
This analysis assumes that the price to earnings ratio remains constant. Alternative assumptions will be considered below. This assumption implies that stock prices will grow at exactly the same rate as corporate profits. These are the numbers that appear in the capital gains column in the table. The total return column sums the dividend yield and the capital gain.
Alternative Assumptions on Capital Gains
It is possible to project higher returns by assuming that the price to earnings ratio will rise through time. The problem with this assumption is that it quickly leads to price to earnings ratios that are almost certainly implausible. For example, assuming that the price to earnings ratio rises enough to allow a 6.0 percent real stock return implies that the price to earnings ratio will be over 50 to 1 by 2020. The price to earnings ratio would be over 160 to 1 by 2050. I doubt that anyone would want to bet Social Security's solvency on the market reaching these levels.
Alternatively, it could be assumed that the price to earnings ratio will fall. This would allow the dividend yield to rise back to its historic levels, and could eventually allow for real returns of 6.0 - 7.0 percent once the market had fallen enough, even in the slow growing economy projected in the Trustees Report. The problem with this scenario is that the returns will be very low, or even negative, during the period when stock prices are falling back to their proper levels.
I assumed that the proper real return on equities was 7.0 percent, and then calculated average stock returns over the next forty years under three alternative assumptions. In the first scenario, I assumed that stock prices fell gradually over forty years, until they reached the reached the level where a 7.0 percent return could be maintained with the Trustees growth projections. In the second scenario, I assumed that the decline was completed after twenty years, and in third scenario, I assumed that the decline took place over ten years. The average forty year returns in these scenarios were, 2.6 percent, 3.5 percent, and 4.0 percent, respectively. The faster the market falls to its "correct" level relative to corporate profits, the higher the average return over the planning horizon.
In short, it is possible to generate considerably higher returns than those I have projected above, if one is prepared to assume that the market will fall rapidly in the near future. While I think this very possible, and even likely, I have not seen any of the advocates of investing Social Security money in the stock market explicitly assume such a decline. In the absence of a plunge in the stock market in the near future, I can see no way that the stock market can yield 6.0-7.0 percent real returns which is consistent with the other projections in the Trustees Report.
I have laid out a set of projections of stock returns which are consistent with the other projections in the Trustees Report. If it is possible to generate a plausible set of numbers that are qualitatively different, I am sure that one of your graduate students would be able to produce these projections in a matter of hours.
In any case, as a procedural matter, I think it is imperative that the numbers at least be laid out, as I have done here, so that they can be debated. It is possible to raise many reasonable objections to the assumptions that I have made to derive these projections, but we can only begin to have this debate once the assumptions have been explicitly stated. If we can use assumptions on stock returns that have not been subject to serious scrutiny, then there is no point in carefully laboring over the other projections in the Trustees Report. Thanks again for taking the time to pursue this issue.
 The market value of the capital stock, net of debt, of non-financial corporations was $7,225.8 billion at the end of 1998, the most recent data available (Federal Reserve Board, Flow of Funds Accounts table B.102 line 31). The Federal Reserve Board has not updated its data on financial corporations for several years, but if we assume that the net worth of financial corporations is 20 percent of the net worth of non-financial corporations, this would add $1,445.2 billion to get a total net worth for corporate capital of $8,671.0 billion. At the end of 1998, the value of corporate equities was $13.927.1 billion (Federal Reserve Board, Flow of Funds Accounts table L.213 line 19). Since the end of 1998, the S&P 500 has risen by approximately 10 percent, if all equities rose at the same rate, it implies a current market value of corporate equities of $15,319.8 billion. If the value of the physical capital stock rose by 2.0 percent over this period, it would currently be $8844.4 billion, which gives a ratio of the value of physical capital to corporate equities of 0.58 to 1.
 The 1.2 percent figure understates the amount of investment that will actually be needed to achieve the Trustees productivity projections, since the ratio of the capital stock to the value of corporate equities will be rising through time under these assumptions.
 Dividend payouts can take the form of share buybacks. This would not change this analysis in any fundamental way. New issues also do not create any serious complications. The assumption that ratio of the price of all existing shares of stock to aggregate corporate profits remains constant, implies that either new issues enter the composite stock portfolio, on average, at the same price to earnings ratios as existing shares, or that insofar as new issues provide better than average returns, it is exactly offset by the under-performance of existing issues. As a practical matter, if new issues did outperform the market aggregates, and there was some lag in including new issues in a market composite, then the market composite held by Social Security would produce somewhat lower yields than the projections presented here.
 In this respect, the Trustees are considerably more optimistic about the near-term profit outlook than the Congressional Budget Office. CBO projects that the profit share of GDP will fall from 9.4 percent in 1999 to 8.2 percent in 2009 (The Economic and Budget Outlook: Fiscal Years 2000-2009, p 21). According to these projections, real corporate profits will be just 4.3 percent higher in 2009 than in 1999.
 There is some room for profits to grow faster than GDP insofar as it comes at the expense of interest, however, this would have to be through lower interest rates on debt, not a reduction in the extent of debt financing, since the latter would require that a larger portion of earnings be re-invested. The current structure of interest rates is slightly higher than the 3.0 percent real interest rate projected by the Trustees (the real yield on ten-year bonds is 3.8 percent, assuming a 2.0 percent inflation rate), but not enough to have much impact on this analysis. The interest share of capital income is already at a relatively low level (approximately 18.0 percent), so there is little room for profits to grow by increasing its share of capital income.
 This foreign investment would have to be in developing nations, since there is no reason to believe that investment in other industrialized nations would offer any higher returns than domestic investment. The list of nations that are still developing, and therefore provide higher rates of return on investment, would presumably change over this period.
Center for Economic and Policy
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