Edward Renshaw
Professor of Economics
State University of New York at Albany
In 1990 three economists received the Nobel Prize for their contributions to a relatively new branch of the dismal science that can perhaps best be described as financial economics. The contributions of Harry Markowitz, William Sharpe and Merton Miller have revolutionized the teaching of finance in business schools and have helped to crowd the IS-LM framework, which was made famous by another Nobel Laureate, to the back of most text books on money and banking.
The blurry nature of what used to be separate disciplines has led the National Association of Colleges and Employers, which tracks campus recruiting activity, to make no distinction between economics and finance majors when reporting salary offers that are made to college graduates.
The ideas of Markowitz, Sharpe and Miller, in any event, were well received by Nobel Laureates Paul Samuelson, James Tobin and Franco Modigliani, and a wider spectrum of economists who believe that financial markets are relatively efficient. While the efficient market hypothesis has been challenged in recent years, the economics profession has not had a lot of success at developing models that refute the random walk hypothesis and allow one to take advantage of exceptional circumstances.
There is one model, however, which has withstood a test of both time, and a major change in the way GDP and its components are now deflated, that may be of some value in helping one to understand the bull market of 1995- 97.
During the last six recessions the cumulative decline in gross private domestic investment has always been greater than the decline in real GDP. The volatility of investment and its sensitivity to declines in real GDP can be partially explained on the basis of an accelerator principle.
This principle is firmly embedded in pre-Keynesian literature. Michael Evans (1969) has noted that its origins can be traced back to publications of Aftalian, Bickerdike and Hawtrey in the early 1900s. Probably the best-known early study is J. M. Clark's (1917) article on "Business Acceleration and the Law of Demand".
An updated accelerator model which was publicized by Renshaw in (1992, Table 1.32) is illustrated in Table 4.1 where we show that the year-to-year growth in real gross private fixed domestic investment has often been about equal to three times the growth rate for real GDP minus six percentage points. This relationship can be derived from a Cobb Douglas production function if we assume that fixed investment is proportional to the flow of productive services from the capital stock.
Where Q is real GDP, K is the flow of productive services from the capital stock and T is a time trend that represents technology, labor and other resources that have been left out of the production function we have:
2 1/3
Q = T K (1)
Since depreciation charges and the income from capital services are a primary source of funds for investment purposes it is not unreasonable to suppose that the aggregate amount of real fixed investment might be roughly proportional to the flow of services from the capital stock:
I = vK (2)
Substituting equation (2) into (1) and noting that small changes in variables that are related to each other in a multiplicative way are approximately equal to percentage changes we can conclude that: the percentage change in real GDP should be about equal to 2.0 percentage points plus one-third of the percentage change in real fixed private domestic investment. One of the implications of this relationship (when the equation is solved for the growth of fixed investment) is that real GDP must increase by about two percent per year just to keep private investment from falling and having a deleterious feedback effect on the growth of economic activity.
The instability of the GDP growth rate in the zero to two percent range has sometimes made it very difficult for the Federal Reserve to effectively fight inflation without pushing the U.S. economy into a recession.
When the actual growth of real fixed investment expressed in chained 1992 dollars has been at least 2.1 percentage points greater than the expected increase that is predicted by the accelerator model in Table 4.1, optimism on the part of business enterprises and developers has tended to spread to the stock market and produce following year returns for the S&P index (dividends plus price appreciation expressed as a percent of price at the beginning of the year) that have been positive, at least for the years from 1946-96.
The following year financial returns have also been positive after a decline in real GDP expressed in 1992 dollars of minus .4 percentage points or more. Since the stock market crash of 1929 the best years to have owned common stock, on the average, have been years containing a recessionary trough in economic activity. The average financial returns in these years has been over thirty percent compared to a more risky average return of less than ten percent during the first calendar year of recovery from an economic recession (Table 3.2).
It should be emphasized that investment optimism on the part of business enterprises and developers hasn't done a very good job of protecting investors from some nerve racking "corrections" in the midst of more pronounced bull markets. Persons who purchased an index fund tracking the S&P 500 at the end of 1946, 1947, 1969, 1977 and 1993 would have had to wait a full year to be sure of getting their money back. All of these corrections, however, were followed by at least one year of double digit returns before the S&P index crashed for a long enough period of time so that its dividends were unable to compensate for lower prices.
It should also be noted that positive error terms for the accelerator model in column (4) of Table 4.1 have a propensity to flock together or occur in "runs" and can be considered a good example of the Keynesian notion of "animal spirts". The five error terms in excess of three percent from 1992-95 have now tied the most prolonged period of super investment optimism for the U.S. economy which began toward the end of World War II and persisted from 1944-48 before ushering in the great bull market of the 1950s.
The most protracted period of investment optimism, as indicated by a long series of positive error terms for our the accelerator model, occurred over the eight year period from 1977-84 and may have helped to support another great bull market during the 1980s.
The real value of business investment in producer's durable equipment increased by about 58 percent from 1991-96. It will be interesting to see whether such contemporary innovations as the "internet" and the "PC" revolution will continue to provide enough investment enthusiasm to keep stock prices trending upward during the remainder of this decade and perhaps set another new record for consecutive years that are not marred by a negative financial return for the S&P composite stock price index.
Clark, J. M. (1917). "Business Acceleration and the Law of Demand," Journal of Political Economy, Vol. 25, No. 1 (March), 217-235.
Evans, Michael (1969). Macroeconomic Activity: Theory, Forecasting, and Control(New York: Harper & Row),
Year Real Actual Predicted Actual Minus Following Year
GDP Investment Investment Predicted S&P Financial
Investment Return
(1) (2) (3)n (4) (5)
1960 2.2 .8 .6 - .2 26.6
1961 2.1T - .5 .3 - .8 - 8.8
1962 6.0 9.0 12.0 - 3.0 22.5
1963 4.3 7.4 6.9 .5 16.3
1964 5.8 9.6 11.4 - 1.8 12.3
1965 6.4 10.1 13.2 - 3.1 -10.0
1966 6.4 5.4 13.2 - 7.8 23.7
1967 2.6 - 2.0 1.8 - 3.8 10.8
1968 4.7 6.9 8.1 - 1.2 - 8.3
1969 3.0 5.9 3.0 2.9* 3.5
1970 .0T - 2.4 - 6.0 3.6* 14.1
1971 3.3 7.6 3.9 3.7* 18.7
1972 5.4 11.9 10.2 1.7 -14.5
1973 5.7 9.1 11.1 - 2.0 -26.0
1974 - .4 - 6.6 - 7.2 .6 36.9**
1975 - .6T -11.2 - 7.8 - 3.4 23.6**
1976 5.6 9.9 10.8 - .9 - 7.2
1977 4.9 14.7 8.7 6.0* 6.4
1978 5.0 11.3 9.0 2.3* 18.4
1979 2.9 5.3 2.7 2.6* 31.5
1980 - .3T - 6.8 - 6.9 .1 - 4.8
1981 2.5 1.9 1.5 .4 20.4
1982 - 2.1T - 7.6 -12.3 4.7* 22.3**
1983 4.0 7.2 6.0 1.2 6.0
1984 6.8 16.5 14.4 2.1* 31.1
1985 3.7 4.8 5.1 - .3 18.5
1986 3.0 .7 3.0 - 2.3 5.7
1987 2.9 - .7 2.7 - 3.4 16.3
1988 3.8 2.4 5.4 - 3.0 31.2
1989 3.4 1.7 4.2 - 2.5 - 3.1
1990 1.3 - 3.1 - 2.1 - 1.0 30.0
1991 - 1.0T - 8.0 - 9.0 1.0 7.4**
1992 2.7 5.7 2.1 3.6* 9.9
1993 2.2 6.8 .6 6.2* 1.3
1994 3.5 10.1 4.5 5.6* 37.1
1995 2.0 6.2 .0 6.2* 22.3
1996 2.5 6.7 1.5 5.2* ?
Footnotes for Table 4.1
(3)n. The predicted growth rate for fixed investment is equal to three times the growth rate for real GDP in column (1) minus six percentage points.
T denotes years containing a trough in business activity.
* denotes years when the difference between the actual and the predicted growth rate for fixed investment was equal to 2.1 percentage points or more. Since 1946 these years have so far been followed by a positive financial return for the S&P index.
** denotes financial returns following a year to year decline in real GDP in column (1) of minus .4 percentage points or more. All of these financial returns have been positive.
Source: This is a partially up-dated table that was first published in The Practical Forecasters' Almanac(Burr Ridge, Illinois: Irwin Professional Publishing, 1992), Table 1.32, pp. 131-32. The growth rates for real GDP and gross private fixed domestic investment have been revised to correspond with the chain weighted values published in The Survey of Current Business, January/February, 1996.
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