Age Cohort Analysis and the S&P500[1] Dividend Yield – the Pig in the Python in a Bear Market

Summary and Conclusions

Conclusions are drawn from a partial equilibrium econometric model of capital market supply and demand. Most important is that the S&P500 will very likely trade in the 750 to 1500 range for most of the next 10 years even given a strong economy. The S&P500 dividend yield should increase about one-third by 2013 as foreign capital inflows become a fading memory, government surpluses disappear and the baby boom generation approaches old age. Yields on long term bonds will likely tend to drift upward along with increases in the S&P500 dividend yield.  A secondary conclusion is that investment and consumer durable goods industries will grow much faster than the economy as a whole through the year 2011.

More Detailed Exposition and Conclusions


Currently, the S&P500 dividend yield represents an extreme historic anomaly, one that evolved abruptly over the past eight years. As one sees in Graph I below, no remotely comparable situation existed during the preceding 120 years. Largely as a consequence of this unprecedented decline in the dividend yield, the S&P500 index rose from 336.3 in the first quarter of 1990 to 1115.4 in the fourth quarter of 2001, an increase of 232%.

What Caused the Record Low Dividend Yields?

Table I below uses the model developed in this paper to decompose the impact of different factors causing the 1990 to 2001 increase in the S&P500.  One-third can be attributed directly to dividend growth.  Changes in the age structure of the population contributed 40%, increased foreign capital inflows contributed 7%, and the change in government financing needs added 11%.  The remaining 7% can be attributed to a combination of other variables contained in the model.

 Age Cohort Effect: Baby Boom Generation - the Pig in the Python

Authors writing as demographers, economists and sociologists have commented on the unique impact of the baby boom (Boomer) generation on various aspects of U.S. society.[2]  These arise because of its disproportionate large size [3] and the contrasting small size of the Depression born Silent generation. In 2001 Boomers outnumbered their predecessor Silent generation by two to one and were slightly more numerous than their successor, Gen X. The next generation, Gen Y, will be about the same size as Gen X.[4]

The critical age cohorts for capital markets were found to be:

·         0 to 4 age group – an increase causes greater demand for investment and consumer durable goods, tending to increase market rates of return including the dividend yield on the S&P500

·         15 to 34 age group – the most important age cohort. An increase causes a decrease in the supply of savings and large extra demand for investment and consumer durable goods, both cause an increase in market rates of return including the S&P500 dividend yield

·         35 to 44 age group – an increase causes a small decrease in the demand for investment and capital goods which in turn tends to decrease market rates of return including the dividend yield on the S&P500.

·         55 to 64 age group – an increase causes extra demand for investment and consumer durable goods which tends to increase market rates of return including the dividend yield on the S&P500

·         the 65+ age group – an increase causes a large decrease in the supply of savings and a small increase in demand both of which tend to raise market rates of return including the dividend yield on the S&P500


In 1980 the entire Boomer generation was in the critical 15 to 34 age group. The analysis developed in this paper indicates this was the major factor in pushing the S&P500 dividend yield over five percent for the entire period between 1978 and 1982.  This tight capital market evidently created a certain economic vulnerability.  Inflation and interest rates, both long and short-term, rose steadily in the late 1970’s.  Then in 1979 an oil price shock triggered the most severe economic downturn since the 1930’s, one that had a far worse impact than the preceding 1973 oil shock or the subsequent one in 1990.

Monetary policy changes initiated in the last year of the Carter administration managed to control a potential runaway inflation, and the general economic situation began to show improvement during 1982.  A ‘virtuous cycle’ of a rising stock market, lower inflation and interest rates and higher productivity gains got underway and continued for the next 18 years. Much of this can be attributed to the impact of the Boomer generation.  As the Boomer bulge passed out of the 15 to 34 year age group and was replaced by the slightly smaller Gen X, the dividend yield on the S&P500 began to decline, and interest rates began a decline as well. Enhancing this tendency was the fact that the unusually small Silent generation was entering the 55 to 64 and 65 plus age groups whose numbers tend to increase the market rate of return and the S&P500 dividend yield.

Foreign Capital Inflows- the Globalization of Financial Markets since the mid-1980’s

The current environment, where private international capital flows are relatively unthreatened by the prospect of adverse government meddling, dates only from the mid-1980’s. The preceding period back as far as 1919 was replete with serious event risks associated with potential government actions. This began with the British and French devaluations after WWI, and U.S. devaluation during the depression of the 1930’s. After WWII, the Bretton Woods regime facilitated both trade and government sponsored international capital flows, but private capital flows were often viewed as a nuisance and sometimes actively discouraged.  The decade of the 1970’s after the breakdown of Bretton Woods continued to present serious, long-term, international private investors like pension funds with serious event risk possibilities (e.g. the U.S. interest equalization tax). 

As a consequence, massive international capital flows were seen only during the political upheaval years associated with WWI and WWII.  Until the mid-1980’s, foreign capital inflow/outflow never exceeded 1.5% of GDP during normal times and averaged only 0.5% in absolute value over the period.   Subsequently, from the beginning of 1984 through the first quarter of 2002 (excluding 10 consecutive quarters beginning with 1990-IV that encompass the Gulf War, German reunification and a recession) foreign capital inflows averaged 2.4% of U.S. GDP.

Common sense tells us that this has been a contributor to the post-1982 bull market, and model simulations attribute 7% of the post-1990 increase in the market to this factor.  Recent data show no signs that the inflow is starting to diminish, but eventually the rest of the world will cease accumulating financial claims against the U.S. and begin a net repatriation of the claims they already hold.[5]

Government Deficits

The effect of government borrowings on the S&P500 yield seems rather straightforward as all financial claims, including S&P500 stocks, government paper and bonds, are relatively close substitutes for one another.  According to the analysis, the change in the government surplus from –2.9% of GDP in 1990 to +1.2% in 2001 accounted for 11% of the increase in the S&P500 over that period.

Looking Forward:  the Python and the Bear Market -  2002 through 2020

 The certain shift in U.S. age demographics between now and 2020 should, by itself, be enough to create a significant long term bear market for the next 10 years. Graph II below shows the python.  One sees the Boomer bulge passing through the 55 to 64 age category and then swelling the 65+ age group by the year 2020.  Both changes should tend to increase the dividend yield on the S&P500 (i.e. depress stock prices).


First, the leading edge of the Boomer generation will begin to swell the ranks of the 55 to 64 cohort as it replaces the smaller Silent generation thereby creating an increase the demand for investment goods and consumer durables. By 2010 the Boomer leading edge will reach age 65. Over 65’s cause the supply of savings to decrease and demand to increase so the negative impact on market yields becomes even greater. By 2020 the 0 to 4 age group is larger than in 2002, the high impact 15 to 34 group is about the same size, and the 55 to 64 and 65+ age groups are much larger.  Quantitatively, the calculated effect of all of these age demographic shifts is that the dividend yield on the S&P500 will continually tend to increase over the next 25 years, reaching a level 67% above where it is now by 2026. 

To create the base case forecast for the S&P500 in Graph III, assumptions were made about dividend growth, foreign capital inflows and government surpluses.  Dividend growth was projected at 4% per year, in line with its long-term trend. The latter two items were projected to trend toward zero over the rest of the current decade and remain there.  The resulting forecast is not what the typical long-term, invest and forget, 401 K investor wants to see.  The market remains flat for the next decade, and a legitimate bull market doesn’t get going until 12 years out.  A confidence band of 1.96 standard deviations around this forecast is also shown.[6]  The interpretation is that to the extent that historic experience provides a guide, the odds are 95 out of 100 that the quarterly average of the S&P500 will not fall outside of the range of 850 to 1500 for the next decade.

 

 


Outlook is for an Investment and Consumer Durables Boom over the Next Decade

One additional conclusion is that over the next ten years industries producing investment and consumer durable goods should grow considerably faster than the economy as a whole.  At the peak of the last business cycle in 2000, investment plus consumer durables accounted for just over 26% of GDP. According to the model-derived forecast shown in Graph IV, a level of nearly 29% of GDP should occur by the year 2011. 


The story is that the Boomer generation, by then in the 55 to 64 age group, will be inflating the demand side of the equation while the supply of funds will remain relatively adequate because the undersized Silent generation will be occupying most of the supply-killing over 65 age category. The average-sized Gen Y will occupy the demand enhancing 15 to 34 age group.  The anticipated net effect is a well-funded investment and consumer durable goods boom beginning at the end of the current recession and peaking in 2011.

Development of a Model – the Theory

“When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”  Arthur Conan Doyle, The Sign of Four [1890] Ch. 6

As shown in Graph I, S&P500 dividend yields reached an all-time low in recent years. Sherlock Holmes might have concluded that, by deduction, one of two things must have occurred.  Either the product[7] got much better, or the price[8] changed.  A changed product looks unlikely as according to the capital asset pricing model that would imply one of two things. 

1.        buyers’ expectations of future dividend growth for the S&P500 increased considerably, or

2.        buyers’ view of the risk premium associated with S&P500 shares changed dramatically for the better.

 


There is no evidence of either. Since the 19th century dividend growth over the long term has averaged just over 1.4% per annum in real terms.  Graph V above plots S&P500 dividends[9] since 1871.  The trend line that measures the average annual growth rate is also shown.  Note that the data points for the past several decades do not stray far from the trend.  In short, nothing exceptional seems to have happened to dividend growth recently. So, while possibly a factor, a change in dividend growth expectations is an unlikely driver of the recent bull market.

What about the market risk premium? Can one accept the idea that it has decreased enough to create the S&P500 bull market?  Looking at the market as a whole, it is true examining Graph V that the variability in the growth of real dividends has decreased in recent decades.  Certainly, this could be an element, but it seems unlikely to be the only or even the major factor behind the bull market. Also, at the micro level it’s hard to argue convincingly that individual common shares have become inherently less risky during an era when corporate accounting results have become a less and less reliable guide for investors

Evidently the Market Price Must Have Changed

This leaves us with the proposition that the market price shifted in a way that reduced the premium accorded current income as compared to future income.  In other words, in terms of the capital asset pricing model, the market discount rate must have gone down.

The Analytical Framework: Supply and Demand


This paper’s analysis uses age cohort data to help model both supply and demand according to Professor Irving Fisher’s early 20th century  ‘loanable funds market’ paradigm which sees things in Marshallian comparative statics terms.[10] Just as economics professors teach in first year price theory, there is a demand curve and a supply curve.  Graph VI below illustrates using some results from the model developed in this paper.  Notice that the rather large decrease in demand for investment and consumer durable goods after 1990 was accompanied by an even larger increase in the supply of savings.  As a result investment plus consumer durables actually increased as a percent of GDP despite a clear-cut inward shift in the demand curve.

The notion that population characteristics might affect the supply and/or demand for saving and investment has been put forth by many, including two of the history’s best economists.  In 1937, shortly after his General Theory of Employment, Interest and Money first appeared, John Maynard Keynes spoke to the Royal Eugenics Society.  Discussing  savings and investment, his thesis was directed toward the demand for capital goods:

“ In assessing the causes of the enormous increase in capital in the nineteenth century and since, too little importance, I think, has been given to the influence of an increasing population as distinct from other influences.”

Eminent financial theorist Franco Modigliani, proposed a life cycle theory of savings and investment during the 1960’s. He and his followers subsequently applied it mostly to the then popular Keynesian model of the macro economy as opposed to the Fisher model of a ‘loanable funds’ market.

Despite a beginning sporting distinguished pedigrees, during the past 40 years very little of value has come out of economic studies using age demographics.  Analysis based on macroeconomic data ran into problems that stem from three sources:

1.     The age demographic variables are not properly defined.  Looking back at Table I and Graph II one sees how a study that focuses on one single age group, say the 65+ cohort, will miss much of a complex dynamic involving five separate age cohorts on both the demand and the supply side of the market.  Similarly, transforming the age structure into a single number (e.g. the average age) creates a variable too simple to be very useful

2.     Graph VI illustrates the problem with studies that model only the demand (or supply) side of the market and leave out a price variable (e.g. the market discount rate).  For example, a purely demand side model using a 1990 versus 2001 comparison would see an increase in investment plus consumer durable goods as a percent of GDP, conclude from this that demand increased, and likely attribute this ‘increase’ with a contemporaneous demographic change. In fact, demand actually declined due to demographic changes, but this was more than offset by an increase in supply.    

3.     Lastly, there are single equation models that do include an interest rate or rate of return variable.  Here, the difficulty lies in the econometric problem of simultaneous equation bias.

As far as studies based on microeconomic data go, they have the potential to capture the supply side of the market.  However, unless one uses pure cross sectional data, there is the difficult issue of the effect of differing rates of return at different points in time affecting savings behavior.  Even pure cross section data may be plagued by differing market rates of return in different countries.[11]

Defining Variables in the Model

The real discount rate in the capital asset pricing model is generally thought of as a long term market interest rate ‘adjusted’ to zero risk and for inflationary expectations.  Obviously, these factors are inherently unobservable, so one has great difficulty in trying to use such a variable in quantitative work in any sort of straightforward fashion.  For one thing, there is no way to clarify the distinction between an expectancy that dollars returned in the future will have less purchasing power (purely an expectation of inflation) and the risk element created by the possibility that future hyper-inflation will wipe out the value of a long-term debt instrument altogether.  It is also unclear how to process historic data in order to approximate ‘inflationary expectations’.  Does one use a long historic horizon or a short one?  Does one believe that an acceleration or deceleration in the rate of inflation affects expectations?  If so, how?

In my view, the S&P500 dividend yield offers a better way to attack the same problem.  It is a long-term rate, and it is a real rate of return.  Where it falls short is that future payments are not strictly defined.  This means:

1.        they are less than certain, which implies some degree of risk premium, and

2.        they are expected to increase over time at some unspecified rate.

The dividend yield on the S&P500 plus an expected dividend growth measure was used as a proxy for the market real discount rate. [12]  The thought is that a dividend growth rate expectation is a more tractable concept to work with than that of an inflationary expectation applied to a market long-term interest rate derived from a debt instrument.  In an era of fiat money, there is no inherent tendency for inflation to return to any long-term mean.  Real dividend growth, on the other hand, is tied to real economic growth, and its rate of increase has showed a long-term tendency to return to a long-term mean value. This, in turn, suggests that the historic time horizon people use to reckon such an expectation is likely to be a rather long one.

The expected real growth rate for S&P500 dividends was taken to be the actual growth rate over a historic time horizon.  Horizons between 40 and 57 years were tried, and a 50- year horizon provided the best results when applied to a sample period that began in 1929 and ended in 2001.  This created a data series for an expectations variable that ranged from a low of 0.7% in 1950 to a high of 2.1% in 1969.  Graph VII above shows this data series.

As far as a risk premium goes, factors that affect it doubtless do exist, but they are very difficult to measure.  For better or for worse, they are simply left out of this particular model. As a result of this omitted variable (and others), one can expect a considerable degree of serial correlation.  This does, in fact, exist.


Savings/Investment as a percent of GDP[13] needed to be defined such a way that data were available over a long time period, at least since 1929, so that demographic shifts show enough variation to enable the analysis.  Both the data and the conceptual framework were taken from the national income accounts.  These divide the economy into four sectors, household, business, government and foreign.  Savings is defined to be equal to investment minus net exports.  Savings equals investment and is measured in two ways: on the income side and on the expenditure side.

In this case one only needs to measure it in one way, and this is done on the expenditure side.  Demand for loanable funds in the economy as a whole is built up from four pieces:

1.        demand from the business sector is equal to gross private domestic investment from the NIPA accounts (annual data from 1929 to 1946 and quarterly data from 1947 to 2001), 

2.        government demand is approximately measured by its current account surplus or deficit (defined by NIPA accounts in the same way), 

3.        household demand is equal to purchases of consumer durables plus investment in residences (also from NIPA accounts), and 

4.        the foreign sector is represented by net exports which approximately measures the flow of loanable funds in or out of the economy (also from NIPA accounts).

5.        The only part of this ‘loanable funds’ market left out is the change in household borrowings for current consumption, something which is conceptually similar to the inventory adjustments item in the business sector.  Probably, this has increased as a percent of GDP since 1929, but there seems to be no ready way to address the issue.

The business-oriented reader has to appreciate that these definitions are derived from a national income accounts perspective.  Savings is defined according to academic jargon (in this particular instance) as consumer income not spent on non-durable consumer goods, and business depreciation and retained earnings.  Investment means anyone buying a tangible capital good, structure or consumer durable good.  In some cases the savings decision and the investment decision are made in the mind of the same person and thus do not flow through any recognizable marketplace.  In the national income accounts this phenomenon occurs in the business sector when depreciation allowances and retained earnings are reinvested within the context of a single business organization. In this broadened context, this also happens when a household pays cash for a durable goods purchase.

Indeed, it seems intuitively obvious that a new child creates a demand for schools and additional residential space.  Youth coming of age need workplaces.  Young families need to accumulate household capital.  As persons approach retirement, they tend to make an accumulation of physical capital in addition to increasing their financial claims. [14]

The Age Cohort variables were defined using the available Census Bureau data.  Annual observations were available for age cohorts 0 to 4, 5 to 14, 15 to 24, 25 to 34, 35 to 44, 45 to 54, 55 to 64 and over 65.  

Model Specification

Beginning with Fisher’s 75 year old model of the ‘loanable funds’ market[15] (illustrated above in Graph VI)

1.        Adopted Keynes’ 65 year old notion that demand is partly a matter of population characteristics as measured by age cohorts.

2.        Explained supply, in part, by age cohorts according to Modigliani’s 40 year old concept of  ‘life cycle’ savings, and

3.        Included a GDP growth rate variable in the supply equation as a way to incorporate the ‘permanent income hypothesis’[16], a popular notion of that same era, and

4.        The national income framework of the data means that foreign capital inflows (the current account surplus/deficit is an approximation) adds to the supply of funds, and government surpluses increase the supply.

5.        An unemployment rate variable was introduced to help explain the substantial reduction in investment and consumer durable demand during recessions/depressions.

6.        A trend variable was introduced in the supply equation.[17] It appears to have measured a gradual improvement over the decades in availability of capital markets to the public.

The best functional form turned out to be an equation that was linear in all variables except that of the market discount rate which was introduced in a log-linear form.  The model equations are of the form:

Equation 1: Savings Supply = b0+b1log(S&P500 yield +expected dividend growth rate)                                +b2(current account deficit/surplus) +b3(government deficit/surplus)+b4(recent rate of economic growth)+b 5(age cohort 14 to 34)+b 6(age cohort over 65)+ b7(trend variable)

Equation 2: Investment Demand = a0 +a1log(S&P500 yield +expected dividend growth rate) + a2(age cohort 0 to 4) + a3(age cohort 14 to 34) + a4(age cohort 35 to 44) + a5(age cohort 55 to 64) + a6(age cohort over 65) + a7(unemployment rate)

Equation 3: Investment Demand = Savings Supply

A Priori Expectations for the Model Parameters

The most obvious expectation is that the parameters for both the foreign current account deficit/surplus and the government deficit variables should be close to one. The precise data needed were not available before 1959 so the  current account deficit was used as an approximation for foreign capital inflow, and the current account government deficit as an approximation for the government sector borrowing requirement. Supply elasticity is expected to be positive, and demand elasticity negative. High economic growth rates should cause an increase in supply.  Youthful age cohorts should be associated with lower levels of savings and greater levels of demand. The post-65 cohort should be associated with reduced savings.

The Statistical Results

The demand and supply elasticity estimates are the results from the regression of the natural logarithm of the real discount rate variable on ‘investment’.  ‘Investment’ was defined as the sum of business sector investment from the Commerce Department’s National Income and Product Accounts (NIPA), investment in residential structures and household purchases of consumer durables taken from the same source.[18]  The ‘real discount rate’ was defined as the sum of the S&P500 dividend yield and the long-term (50 year) growth rate in real dividends.[19]

The parameter estimates in Table II evoke little surprise. 

1.     Supply and demand elasticity have the correct sign and are of what seem to be a reasonable magnitude.

2.     A high unemployment rate reduces investment and consumer durable goods demand. 

3.     Rapid GDP growth stimulates saving. 

4.     The trade deficit and government surplus parameters are near their expected values of one.

5.     Newborns and infants (0 to 4 age group) stimulate demand.

6.     Young adults (age 14 to 34) stimulate demand considerably and reduce saving a little.

7.     Early middle aged adults (age 35 to 44) – slightly reduce demand.

8.     Elderly (age 65 and over) substantially reduce the supply of savings and slightly increase demand.

9.     The near retirement age cohort (age 55 to 64) increases demand.


The impact on demand of the 0 to 4 cohort is no surprise to anyone who has brought home a new baby.  The effect of the 14 to 34 age cohort is also intuitively appealing.  Young adults are notoriously poor savers, and they need everything in the way of investment goods and consumer durables.  That the effect of the over 65 cohort reduces savings and only slightly increases the demand side[20] is most a most heartening result, one that would be expected a priori. 

That the 55 to 64 age cohort stimulates demand was a mild surprise. This may be because this cohort frequently receives inheritances, and in addition, there is a well-known tendency for persons approaching retirement to stock up on certain durable goods – e.g. buying a new luxury car for cash and putting a new roof on their house.

That the 35 to 44 cohort reduces demand is understandable.  Early middle-aged adults have already accumulated a stock of housing and household goods, and their employers have already built their workplaces.  Also, families with growing children have pressure on their household budgets that probably leads to more spending on non-durable consumer goods.

 

Appendix A
Technical Evaluation of the Model Parameter Estimates


The most important econometric consideration was related to the fact that both 2SLS and LISE produce consistent as opposed to unbiased estimates.  Consistent and unbiased estimates converge toward the same values if one has enough sample observations.  One would normally expect that 237 observations would be enough, but there is only one way to evaluate this situation.  When both 2SLS and LISE estimators produce similar parameter estimates, concerns about using a consistent (as compared to an unbiased) estimator are considerably reduced.  Since both 2SLS and LISE are k class estimators, one can compare them by comparing their k values.  2SLS has, by definition, a k value of one.  The k value of the LISE estimator is calculated from the data.  When the LISE estimator yields a k value close to one, the parameter estimates of the two methods will be close to the same.  The results shown in Table III below indicates that the two estimators do, in fact, produce near-identical results.

Superficially, the ‘t-ratios’ of the model’s parameter estimates, shown in Table II above, look very good – the smallest one is 3.4.  However, the statistical properties of the model suggest that these estimates are biased and are probably too large.  Autocorrelation is a major problem; the low Durbin-Watson statistics indicate its presence.  In addition, there is likely an unquantifiable ‘errors in variable problem’ arising from both the real discount rate variable and the government and current account surplus/deficit variables.

Fortunately, there are some other criteria one can use to evaluate the results.  The most unique one is that the parameter estimates for both the government and current account surplus/deficit variables ought to be close to one. This is because both are by definition very close to the data one would have ideally liked to have used, variables which would have justified the a priori use of a coefficient value of one.  The 2SLS estimator these parameter estimates were close to one: 0.99 and 0.87.

Evidence from Out-of-Sample Simulations

Lastly, a good model ought to produce reasonably accurate out-of-sample forecasts when the values of the exogenous variables are known.[21]  In this particular case, the parsimonious use of exogenous variables other than age cohorts means that simulations that go out very far in time are not likely to be very accurate.  This is because some variable not in the model may shift and drive the observed value away from that of the model forecast.  The results of two out-of-sample forecasts, one four quarters out and another eight quarters out are shown in Table IV below.

The average error for the one year out-of-sample forecasts was 0.017%, an error in percentage terms of less than one percent. The average absolute error was only 74 one-thousandth of one percent for a variable that had a value of around 1.2%, an error in percentage terms of six percent.



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Keynes, J.M. 1937. “Economic Consequences of a Declining Population”, The Eugenics Review. Vol.XXIX, No.  1, April. Pp. 13-17.

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Lindh, Thomas and Malmberg, Bo. 1999.  “Age Distributions and the Current Account”,  Department of Economics, Uppsala University. Pp. 1-33

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[1] S&P500 is the Standard and Poors index of 500 common stocks. It is the third most commonly followed U.S. stock price index after the Dow Jones Industrial Average and the NASDAQ index.

[2] See Coleman (1999), Cork (1998), Krugman (2000), Bakshi (1994)

[3] The pig in the python analogy is used to describe the movement of this oversized generation through time as it uniquely shapes U.S. society.

[4] For purposes of this discussion the Boomer generation is defined as persons born during the 20 year time span 1945 to 1964, the Silent Generation between 1925 to 1944, Gen X between 1965 and 1984, and Gen Y between 1985 and 2004.

[5] Recent declines in the stock market averages combined with weakness in the dollar versus the Euro and Pound may be a sign that inflows are diminishing or reversing.

[6] Data for the period 1929 to 2001 were used.  The WWII years 1942–46 were excluded.

[7] In this case, S&P 500 stocks.

[8] The market discount rate

[9] Dividends are expressed in ‘real’ (i.e. inflation-adjusted) terms and plotted as their natural (to the base e) logrithm.

[10] See, for example, Fisher’s Theory of Interest

[11] Risk factors associated with inter-country capital flows often lead to market return differentials between countries.

[12] See Gordon, Myron “Dividends, Earnings and Stock Prices,” [dividend yield = r-g, where r is the real discount rate and g is the expected growth rate in dividends].

[13] Non-economists need to be aware that specialized professional jargon is being employed when using the term ‘investment’.  Investment in the sense that it is used here describes only the purchase of durable goods, not investment in financial instruments.

[14] See, Higgins, M.: and Lindh, Thomas and Malmberg, Bo:

[15] Defining a market in this way means that the resultant model is a structural one as opposed to a reduced form.  This allows one to make legitimate a priori assumptions about the signs of the model’s parameters.

[16] Friedman, M., A Theory of the Consumption Function, Princeton University Press, 1949

[17] At the suggestion of SMU professor Tom Fomby in order to capture autocorrelation effects.

[18] To forestall hetroskedasticity problems all NIPA variables were transformed into a percentage of GDP.

[19] A transformation of some sort was essential to make the model tractable.  The 50 year horizon was used because it seemed reasonable and did seem result in a better fitting model than those using shorter periods. Reliable historic data were not available to utilize for time horizons longer than 50 years.

[20] This may be partly a reflection of the need to build additional medical facilities

[21] This does not necessarily mean a model is any good for forecasting because it may be hard to accurately forecast the exogenous variables.  It does indicate a model is good for ‘what if’ simulations.

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