Unexpectedly Intriguing!
11 May 2005

Update (17 May 2005): I've changed my thinking regarding whether the CEPR calculator should be used. My reasons are at the bottom of the post....

With the President having recently refined his proposal for reforming Social Security, the second generation of web-based calculators that purport to model the President's proposal are just now coming online. While I have not yet finished detailed reviews of the Version 2.0 efforts, I have seen enough of the "Accurate Benefits Calculator" developed by the Washington D.C. based Center for Economic Policy Research to conclude that it's a wasted effort whose primary purpose is to misdirect its users into accepting its unfounded underlying assumptions.

Which is a shame, because it otherwise has a relatively clean interface, some really neat features (the graphing function is truly cool), and it does its math correctly. If it were not fundamentally flawed in its methodology, it would be a real contender for Political Calculations' Gold Standard. But it is, and it no more deserves the award than the highly flawed first generation effort put forward by the Senate Democrats.

The key element of CEPR's effort at misdirection revolves around the calculator's assumption that the rate of return in the stock market may be directly related to the rate of growth in the United States' Gross Domestic Product (GDP). This assumption is detailed in CEPR's accompanying methodology (available as a 23KB PDF document), which shows the derivation of a mathematical formula linking growth in GDP to the stock market returns. The formula, when fully derived, links the stock market's rate of return to it's Price-to-Earnings (P/E) ratio, it's Dividends-to-Earnings (D/E) ratio and the rate of growth in GDP (G). I'll account for the math, as it's nearly perfect - if I were grading it, it would receive 9 out of 10 points (not all work was shown, but it was possible to figure out the missing steps). A much larger version of the miniaturized image at the right detailing CEPR's math is available.

By linking growth in GDP to the rate of return one may expect from the stock market, the effect of CEPR's assumption is to reduce the stock market rate of return well below its long term inflation-adjusted average of 6.5 to 7.0% given what would otherwise be reasonable P/E and D/E ratios. The value identified as being a "stable" rate of return from equities by CEPR is 4.35%, more than 2.0% too low when compared to the stock market's long term averages. Users of the CEPR calculator are warned against increasing the "premium" on stock market returns, since this action may produce P/E and D/E ratios that represent "implausible levels." It would take a very knowledgable user to recognize that the "implausible levels" in the Price to Earnings ratio and the Dividends to Earnings ratio are the result of an assumption that is, in itself, utterly unrealistic.

### Correlating GDP Growth and the Stock Market

When I say there's a mountain of data to test the assumption, I mean it. Perhaps the most comprehensive example of this data is represented in the most recent release of the Global Investment Returns Yearbook, which provides a comprehensive analysis of the long-term record of investment options (including stocks, bonds, etc.) around the world since 1900. The yearbook is the result of the work of the London Business School's Professors of Finance Elroy Dimson and Paul Marsh, and the school's Director of the London Share Price Database Mike Staunton. The Ireland-based business and personal finance portal finfacts.com notes:

The core of the Yearbook is provided by a long-run study covering 105 years of investment since 1900 in all the main asset categories in Australia, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, the Netherlands, Norway, South Africa, Spain, Sweden, Switzerland, the United Kingdom, and the United States. These markets today make up over 92% of world equity market capitalisation. With the unrivalled quality and breadth of its database, the Yearbook has established itself as the global authority on long-run stock, bond, bill and foreign exchange performance.

The authors of the Yearbook examine all this data, considering whether or not there is a real correlation between the growth in a nation's Gross Domestic Product (GDP) and the real rates of return provided by their stock markets. They find that:

• Using data for all 17 countries, including that for the rapid post-war expansion period in the German and Japanese economies, the authors demonstrate that there is no apparent relationship between equity returns and GDP growth.
• The study also analyses additional countries where data is available, but for fewer than 105 years. Using this extended group of 53 countries, the authors again find no relationship between economic growth and stock returns.

- Excerpted from finfacts.com

The following chart illustrates the inflation adjusted rates of GDP growth per capita and the rates of return in the stock markets of the seventeen countries with data extending back to 1900:

Click for a larger image.
Source: ABN AMRO/LBS Global Investment Returns Yearbook 2005 (Chart 28), via finfacts.com.

The lack of consistent proportionality between each country's rate of GDP growth and the rate of return in its stock market across the board shown in the chart illustrates the lack of correlation between the two figures. For reference, the data from the chart is presented in the dynamic table below. Click any of the column headings to rank the countries according to their respective performance:

Real GDP Growth per Capita and Real Equity Returns, 1900-2004
Country Real GDP Growth per Capita (%) Real Equity Returns (%)
Australia 1.9 7.8
Belgium 1.8 2.2
Denmark 2.1 5.0
France 2.2 3.4
Germany 1.5 2.9
Ireland 2.4 4.7
Italy 2.7 2.3
Japan 3.6 4.2
Netherlands 1.9 5.1
Norway 2.6 3.5
South Africa 1.2 7.0
Spain 2.6 3.6
Sweden 2.6 7.8
Switzerland 1.8 4.2
UK 1.8 5.4
USA 2.0 6.8

### A Sad Conclusion

The problem with the assumption advanced by CEPR, which I should note has also been advanced by economist Paul Krugman, is that it does not agree with historic data. At all. If the assumption that the nominal return on stocks is tied to nominal growth in the economy is going to be considered to be valid, it has to be able to demonstrate that the correlation exists in the mountain of data available to test the hypothesis. This is the test the CEPR calculator fails. Worse, it demonstrates a lack of critical thinking and understanding of scientific method on the part of those who developed and advanced this key assumption behind the calculator's math. At the very worst, it suggests either that those advancing the assumption do not understand basic economic principles or are all too willing to resort to dishonesty for the sake of making a partisan argument.

Sadly, much of the calculator's user interface is devoted to convincing its users to not adjust the rate of return from the stock market to a more realistic, higher figure. As such, the calculator becomes little else than an exercise in misdirection, whose results must default to a lack of trustworthiness as its assumed links between the stock market's price to earnings ratio, dividend to earnings ratio and GDP growth are wholly without merit. In the final measure, it's just not worth the disturbing the flow of otherwise happy electrons to download the CEPR's calculator onto your personal computer.

Update: The Heritage Foundation has noted the contributions of this "Scrappy Little Blog"(TM) to the Social Security debate, and has also noted additional deficiencies in the CEPR's tool.

P.S.: Changed "and have noted" to "and has also noted" in the previous update. Also, here's a link to a better description of the London Business School study.

Update (17 May 2005): As I hinted at the top of the page, I've changed my thinking as to whether or not the "otherwise happy flow of electrons" should be redirected to bring CEPR's calculator to your personal computer. While the calculator's interface may overemphasize an assumption that I believe lacks sufficient evidence to accept without clearly reinforcing studies to support its central premise, its creators truly did build a good tool - one that allows the user to disregard CEPR's assumption and adjust the calculator's default values to values they believe more appropriate. I believe a good tool will let you play "what-if" and the CEPR tool's flexibility delivers in this regard.

If you use the CEPR tool, I strongly encourage you to adjust the "premium" in the advanced user portion of the interface. You may increase the value by as much as 2.45%, which brings the total inflation-adjusted return from the modeled PRA to 6.8%, which agrees with the long-term historic average for returns on equities. You may also enter negative values, say -1.35%, which would represent a portfolio made up of government bonds earning 3.0% returns.

Also, in looking at the table of results, while your eye may be drawn to the "Scheduled" benefits, make sure you look at the "Payable" benefits immediately below it - for those retiring after 2052, this is the value you need to compare your "Bush" plan against, since this is the year the CBO projects Social Security's trust fund will be depleted. For those retiring before 2052, and who will be receiving benefits after 2052, multiply the payable benefits number by 78% to get your post-trust fund depletion benefit level, since your current law benefits, regardless of their level, will be cut by 22% at that point.

The truth is that while I have reservations about CEPR's assumption, I do recognize that the tool itself has real value and represents an honest effort - the more so since it effectively models the Congressional Budget Office's (CBO) projections for Social Security. As such, it makes for an excellent counterpoint for the Heritage's Foundation's calculator which is based upon the Social Security Administration's own projections. Go use both.

Update 10 October 2009: We should also have pointed out a major deficiency in the CEPR's math. The formula they use to replace earnings growth with GDP growth is fundamentally flawed in that they've mistaken earnings per share for earnings. While aggregate earnings for publicly traded companies are indeed proportional to GDP, the same cannot be said of earnings per share. Since it is changes in the "per share" aspect that distinguishes stock prices, one cannot substitute GDP for it. This is a primary reason why changes in stock prices are not correlated with changes in national GDP.

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