FAJ Jan Feb 2012 Demographic Changes Financial Markets and the Economy

January/February 2012 www.cfapubs.org 23

Financial Analysts JournalVolume 68 Number 1

©2012 CFA Institute

Demographic Changes, Financial Markets, and the Economy

Robert D. Arnott and Denis B. Chaves

Using a large sample of countries and 60 years of data, the authors found a strong and intuitivelink between demographic transitions and both GDP growth and capital market returns. Unlikeprevious researchers, who used ad hoc and restrictive demographic variables, the authors imposeda smooth and parsimonious polynomial curve across all age groups. They also performed robustnesschecks and produced forecasts for the coming decade, with all the necessary caveats.

Demography is destiny.—Auguste Comte (1798–1857)

emography is one of the rare social sci-ences in which forecasts—at least for theshort run—have startlingly little uncer-tainty. Today’s 40-year-olds are next

year’s 41-year-olds. We can count them; we knowthe likely mortality for 40-year-olds and the likelyrate of immigration and emigration for this agecadre. Looking 10 years into the future, we can seesome uncertainty in the number of people under 10and in the number of people over 70 (depending onthe progress of medical science), but surprisinglylittle uncertainty in the number of people aged 10–70—barring war, pestilence, or other catastrophes.As the Baby Boomers have aged, many researchershave studied past demographic data in an effort toextract indications of the future influence of Boom-ers on various aspects of the economy, from housingprices to consumer preferences to retirement plans.

Although the genesis of our study has the sameroots—curiosity about the potential impact ofaging Baby Boomers—we decided to pursue abroader course of study that spans decades of dataand dozens of countries. We concentrated on threeareas in which demographic shifts might influencethe economy: real per capita GDP growth, stockmarket returns, and bond market returns.

We strove not to extend the theoretical rela-tionships between demographic changes andfinancial markets or the economy but, rather, toapply new empirical techniques. First, we soughtto extract more statistical significance by looking at

data from many countries over many years. Sec-ond, instead of fitting regressions against broadand ad hoc demographic cohorts, we fit polynomi-als to the regression coefficients between demo-graphic age groups and both GDP growth andstock and bond returns. The use of polynomials isintuitive because it satisfies two important criteria:parsimony (only a small number of parameters arerequired) and continuity across age groups (behav-ior should change reasonably smoothly from oneage cadre to the next).

Two core principles influenced our researchdesign. First, we deemed models for GDP growthless interesting than models for real per capita PPP-adjusted GDP growth.1 All three of these modifiersof GDP growth are important. After all, in a countrywith 3 percent population growth, 3 percent GDPgrowth means no growth at all for the averagecitizen—hence, our reliance on per capita data. Thesame logic holds for 10 percent per capita GDPgrowth in a country with 10 percent inflation—thus, our focus on real per capita GDP growth. ThePPP adjustment creates a fairer global comparisonby emphasizing the domestic purchasing power ofthe average citizen for the consumption basket thatmatters for each country.2

Second, we measured stock and bond returns asexcess returns relative to domestic cash returns ratherthan as simple annualized returns. We did so for twosimple reasons. Stock and bond excess returns overcash can fairly be compared around the worldbecause arbitrage equalizes the returns for domesticcash within relatively narrow bounds for the cur-rency-hedged investor. In addition, by looking atexcess returns over domestic cash, we crudely butreasonably effectively stripped out inflation differ-ences: Cash yields rarely differ from domestic rates ofinflation by more than a couple of percentage points.

Robert D. Arnott is CEO and chairman of ResearchAffiliates, LLC, Newport Beach, California. Denis B.Chaves is a senior researcher at Research Affiliates, LLC,Newport Beach, California.

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24 www.cfapubs.org ©2012 CFA Institute

Financial Analysts Journal

Effects of Demographic Changes on Financial Markets and the EconomyThe relationship between per capita GDP growthand demographic changes can be motivated by adecomposition of per capita total output of goodsand services in an economy into age groups andthen into a product of per worker productivity andper capita number of workers:

That a growing workforce—or even a growingpopulation, for that matter—should be better forGDP growth than a shrinking workforce seemstautological. To isolate these effects, we can focuson per capita GDP growth. In this construct, therelevant measure becomes the size of the working-age cadre (generally, people aged 20–60) as a per-centage of the total population: If the working-agecadre is growing faster than the broad population,that should provide a tailwind to real per capitaPPP-adjusted GDP; if slower, then our GDP mea-sure should face a headwind.3

This simple equation allows us to identify twochannels through which demographic changes caninfluence a country’s GDP. First, let us assume thatproductivity varies significantly across age groups.As a large age group makes its way into the work-force, then into the more productive stage of its life,and subsequently into retirement, total per capitaoutput should first increase and then decrease. Inthe demography literature, this effect is known asa demographic dividend: Imagine the waves createdby a rock thrown into a lake and their paths as theymove away from the point of contact.

Second, anecdotal evidence tells us that mostentrepreneurs, inventors, and innovators areyoung adults. For instance, Nobel Prizes are usu-ally awarded to older scientists and researchers forcontributions made years earlier, when they weremuch younger. Kanazawa (2003) found that theproductivity of scientists, musicians, and painterspeaks between 30 and 40—the only exception isauthors, whose productivity tends to peakbetween 40 and 50. Therefore, we would alsoexpect to identify a higher increase in productivityacross all age groups—and thus in total per capitaoutput—in countries with a relatively higher shareof younger cadres.

Another reason that young adults have moreimpact on GDP growth than do middle-aged and

older adults is even simpler. Because we are usinggrowth rates in output as opposed to merely out-put, the effects that we identify should peak at agesconsiderably earlier than pre-retirement. Aworker’s contribution to total output likely peakswhen she has more experience, but her contribu-tion to growth in total output is highest when she isin the process of acquiring that experience.4 Foreach of us, the biggest jump in our contribution toGDP occurs as we transition from nonworking ado-lescents into gainfully employed 20-somethings.Another, often smaller, jump in our contribution toGDP occurs as we mature into our 30s. By our 40s,the evidence of real wages would suggest that mostof us are at or approaching our peak contributionto GDP, with a falling contribution to GDP in our50s and 60s.

Either way, we would expect per capita GDPgrowth to be strongest in populations dominatedby young adults and in populations in which theyoung-adult population is growing quickly. Thiscircumstance is indeed the case for most emergingeconomies and is assuredly not the case for mostdeveloped economies.

Establishing a theoretical link between finan-cial markets and demographic changes is a com-plex task and would require more space than isavailable here, not to mention that many excellentpapers on this topic already exist. Moreover, thefocus of our study was on trying to advance theempirical side of the literature. Therefore, as amotivation for our empirical analysis, we offer asummary of the intuition and findings in the the-oretical literature.

Brooks (2000), for instance, solved anoverlapping-generations model with forward-look-ing agents, a risky asset, and a riskless one-periodbond. Various age cohorts trade with each other.During baby booms, consumption is relativelyhigher and savings relatively lower, effectivelypushing up returns on both stocks and bonds; dur-ing population busts, the opposite effect dominates.Moreover, agents shift their investments fromstocks to bonds as they approach retirement.5

In contrast, the main argument made by skep-tics of the demographic effects on financial marketsis that rational and forward-looking agents wouldincorporate any slow-moving and predictablechanges in age distributions into their informationset and act accordingly. Thus, age effects would beinsignificant and, in practice, unobservable. Toaddress and dismantle this criticism, someresearchers (see, e.g., Abel 2003; Geanakoplos,Magill, and Quinzii 2004) developed models toexplain how demography can affect stock and bondreturns even in the face of fully informed, rational

Total output

Population

Productivity per worker in age gr j

ooup

Number of workers in age group

Population

j

j

.



agents. The intuition is simple, as explained by theInternational Monetary Fund (2004) in its WorldEconomic Outlook:

This is because only living generations trade infinancial markets at a point in time, meaningthat differences in the demand and supply offinancial assets—a reflection of differences insize across generations—cannot be arbitragedaway ahead of time. (p. 151)

To summarize, the findings of most of thesemodels reflect common wisdom. Young adults,often in the process of starting a family, will rarelybe major contributors to the quest for savings,investments, and capital accumulation.6 As theylook past their own and their children’s immediateneeds to their eventual retirements, they begin toinvest—first in stocks, then in bonds. As they slideinto retirement, they begin to sell assets in order tobuy goods and services that they no longerproduce—either directly, through their owninvestments, or indirectly, through their pensionbenefits. They tend to liquidate their riskiest assets(stocks) before their less risky assets (bonds).

Review of the Empirical LiteratureAnalyzing the relationship between demographicchanges and the economy, whether qualitatively orquantitatively, has been a topic of interest for cen-turies.7 Accordingly, summarizing all the relevantresearch would be an impossible task. In this shortreview, we focus on the recent literature, with anemphasis on empirical tests, comparing it with ourown application of new methods to the data.

Mankiw and Weil (1989) conducted one of thefirst studies to link demography and financialassets. They showed a strong relationship betweenthe U.S. Baby Boom, the subsequent increase inhousing demand in the early 1970s, and a substan-tial impact on housing prices over the next 20 years.Their forecast that housing prices would declinesharply after 1990, following the Baby Bust, did notmaterialize on schedule, although demographiceffects may have magnified the recent collapse ofthe housing bubble.8

Arnott and Casscells (2003, 2004) discussed thedemographic changes that will likely occur in theUnited States in the coming decades, explored theirimplications for capital markets, and examinedpossible solutions. Their important finding wasthat the entitlements problem is not a financialproblem exacerbated by a failure to prefund theseobligations but, rather, is a support ratio problemtied to demography, pure and simple: Prefundingdoes not create—in advance—the goods and ser-vices that will change hands. Regardless of pre-funding, goods and services must still change

hands, from those who produce the goods andservices to those who no longer do so. Arnott andCasscells also speculated on the likely implicationsfor capital market returns, consistent with theresults that have subsequently been seen in theUnited States, Japan, and parts of western Europe.Finally, they examined and largely dismissed thecommon arguments that immigration or produc-tivity gains can offset the pressures associated withpending demographic shifts.

Bosworth, Bryant, and Burtless (2004) surveyedthe literature on analyzing and forecasting prices(returns) of financial assets and identified twoapproaches. The first approach uses microeconomicdata on goods or asset holdings,9 together withforecasts of age distributions, to predict how futuredemand and prices (returns) will evolve (seePoterba 2001). For example, DellaVigna and Pollet(2007, p. 1667) defined what they called “age-sensitive sectors, such as toys, bicycles, beer, lifeinsurance, and nursing homes,” and estimated howthe demand for products or services in those sectorswill decrease or increase. They found that theirdemand forecasts predict both profitability andstock returns by industry 5–10 years in the future.The second approach—followed in our study andsurveyed by Davis and Li (2003)—estimates thedirect time-series relationship between prices(returns) and demographic variables. Notable stud-ies in this strand include, but are not limited to, Yoo(1994), Bakshi and Chen (1994), Lindh and Malm-berg (1999), Ang and Maddaloni (2003), Goyal(2004), and DellaVigna and Pollet (2007).

Yoo (1994) estimated multivariate time-seriesregressions of annual U.S. stock, corporate bond,and government bond returns on shares of totalpopulation for the 25–34, 35–44, 45–54, 55–64, and65+ age groups. His strongest results were a nega-tive relationship between short- and medium-termgovernment bonds and the 45–54 age group. Thestatistical significance, however, was weak foralmost all coefficients in all five age groups. Healso estimated the regressions with three- and five-year centered moving averages and found a signif-icant increase in terms of both statistical signifi-cance and fit, which supports our claim that longhorizons provide a better test for low-frequencypopulation changes.

Bakshi and Chen (1994) hypothesized that rel-ative risk aversion is positively correlated with ageand modeled the utility function of the representa-tive consumer as a function of aggregate consump-tion and average age of the population. In theirtests, they used Euler equations and a two-factormodel based on consumption growth and percent-age change in average age.10 They found strong



support for their life-cycle risk aversion hypothesisand a positive and statistically significant relation-ship between U.S. stock excess returns and growthin the average age of the U.S. population.

Using both a long sample (1900–2001; 5 coun-tries) and a short sample (1970–2000; 15 countries),Ang and Maddaloni (2003) studied the relationshipbetween excess stock returns (at one-, two-, andfive-year horizons) and log changes in three demo-graphic variables: average age of the populationover 20, fraction of adults over 65, and percentageof people in the 20–64 age group. In pooled regres-sions, their results displayed a strong and negativeeffect for the fraction of retirees in the population(65+). Interestingly, they found an opposite andpositive result in isolated regressions for the UnitedStates and the United Kingdom. To explain thisdifference in results, they conducted additionaltests and found that the effect for the 65+ age groupis stronger in countries with well-developed socialsecurity systems and less developed financial mar-kets. Finally, and most important for our study,they also found that “pooling data from five coun-tries gives almost the same power as increasing thesample size of the United States by five times” (p.10), which validates the strong results that wefound by using an extended sample of countries.

Using a sample of countries in the Organisationfor Economic Co-Operation and Development(1950–1990), Lindh and Malmberg (1999) studiedthe effects of log age group shares (15–29, 30–49, 50–64, and 65+) on five-year growth rates in GDP perworker. They found significant and positive coeffi-cients for the 50–64 age group and significant andnegative coefficients for retirees (65+). With respectto their choice of age groups, they commented that“the youngest age group, children aged 0–14, hadto be dropped in order to avoid high degrees oflinear dependency among the age variables. Somearbitrariness in the definition of the age group vari-ables cannot be avoided” (p. 435). These concernsraised by Lindh and Malmberg highlight the needfor an approach that uses all available informationand that defines the demographic variables lessarbitrarily and more systematically. Indeed, givenour findings, we wonder whether any study thatignores young people could be important.

Our most important means of identification—and most significant improvement over priorresearch—is our use of the econometric methodol-ogy pioneered by Fair and Dominguez (1991).They used a polynomial to analyze the relationshipbetween a changing U.S. age distribution and sucheconomic variables as consumption, housinginvestment, money demand, and labor force par-ticipation. This methodology, which forces the

regression coefficients on age groups into a poly-nomial, has at least two advantages: (1) It permitsthe inclusion of all age groups in the regressionwhile avoiding the statistical issues created by thehigh correlation between them, and (2) the inter-pretation of the results is more intuitive. In thatregard, we closely followed Higgins (1998), whostudied the effect of demographic changes on sav-ings, investment, and the current account balance,but we analyzed the implications for financial mar-kets and economic growth.

In the empirical arena, Poterba (2001, p. 565)lodged one of the strongest criticisms, maintainingthat “statistical tests based on the few ‘effectivedegrees of freedom’” lack the power “to find robustevidence of such relationships in the time seriesdata.” Because we agree with this statement andrecognize that demographic variables are both per-sistent and slow moving, we took a number of stepsto increase the power of our tests:1. Relied on five-year rates of GDP growth and

capital market returns instead of annual data2. Controlled for starting valuation levels, GDP

levels, and business cycle measures so that thedemographic effects could be viewed in isola-tion from these other powerful effects

3. Used a large cross section of countries4. Included the information from all age groups

in the regressions, as previously mentionedThe result is a substantial improvement in the

statistical significance of our findings as comparedwith those of prior studies of demographic effectson the capital markets and GDP growth.

Data and VariablesWe drew our data from many sources. The demo-graphic and GDP data are deepest, with demo-graphic age profiles and GDP on well over 200countries from the UN and the Penn World Table,typically well documented back to 1950.11 Thestock and bond data are solid for only the devel-oped economies and the largest emerging econo-mies, with comparatively thin data before 1970.Using nonoverlapping five-year returns or growthrates, we were able to extract more than 200 obser-vations in 22 countries for our main regressions andmore than 1,600 observations in 176 countries forour extended group of countries.

We obtained population data by five-year agecadres with a half-decade frequency from the UNPopulation Division.12 For most countries, the datastart in 1950 and include projections through 2050in five-year intervals. For future years, eight differ-ent variants are available to forecast combinationsof trends in fertility, mortality, and internationalmigration. For our forecasts for future GDP growth



and capital market excess returns, we chose themedium variant available online, which assumes amidrange expectation for fertility and normaltrends in mortality and migration.13

We obtained our financial variables from vari-ous sources, primarily Global Financial Data. Wecomplemented total return indices for stocks withdata from Claus Parum14 (Denmark), the CentralStatistics Office15 (Ireland), and Daniel Wydler(1989; Switzerland). We proxied any missing 10-year yields with 5- or 7-year yields and any missingthree-month yields with central bank discount rates.

We used measures of real per capita GDP fromVersion 6.3 of the Penn World Table (see Heston,Summers, and Aten 2009). This version includesannual observations over 1950–2007 and assigns aquality grade ranging from A (best) to D (worst) toeach country “to signal the relative reliability of theestimates” (p. 18 of the Data Appendix).16 Dataavailability and reliability—missing observationsare mainly an issue with the financial variables—restricted our main sample to 22 developed coun-tries,17 of which 16 had a quality grade of A and 6a B. Given the broad coverage of the population andGDP data, however, we were able to conductrobustness tests—with respect to GDP growthonly, not stock or bond excess returns—for a sam-ple of 176 additional countries.

Our dependent variables are annualized, five-year, nonoverlapping growth rates, denoted by ri,tand identified individually when necessary. Stockand bond returns are in excess of the domestic(same-country) bill return. Real per capita GDPgrowth measures economic activity as the averagecitizen might perceive it. Unlike most previousresearchers, we chose five-year returns, chiefly fortwo reasons: (1) Demographic data are morewidely available in five-year intervals, and (2)demographic changes occur slowly, giving low-frequency data a better shot at identifying theeffects of interest in our study. The intersection ofdata sources left us with approximately 200–250nonoverlapping observations in our main tests andmore than 1,600 in our robustness tests. This broaddatabase provided ample degrees of freedom anddelivered surprisingly strong statistical signifi-cance for our results.

Our explanatory variables are the percentage

of total population by age group, , and changes

therein, 18 Our age groups range from 0–4,

, through 70+, , yielding a total of 15 five-year demographic variables. We used dividendyields (DYi,t), three-month yields (3Mi,t), and 10-year yields (10Yi,t) as control variables in our

regressions. Taking into account the initial valua-tion (or stage of the business cycle) in our regres-sions was vital, given that temporary swings inprices or economic activity might affect the estima-tion. For example, if stock market returns werehigh following a high initial dividend yield, wecould not be confident that we were properly sep-arating the demographic effects from well-knownvaluation effects. Our demographic results, how-ever, are relatively robust with regard to the choiceof the valuation measure. For instance, in one ofour robustness tests, we were forced to use the logof the ratio of consumption to GDP, log(Ci,t/GDPi,t), given that interest rates for most countriesare unavailable.

In our view, these data are deep enough todraw some important conclusions about past linksbetween demography, on the one hand, and GDPgrowth and the capital markets, on the other.Applying our results to predict the prospectiveinfluence of demography on the economy or on thecapital markets is a bit riskier: Past is not prologue.Nonetheless, although our confidence in the for-ward links is weaker than our confidence in thepast links, the potential implications of our resultsare sobering.

Results and DiscussionIdeally, one would like to estimate the joint effect of

all 15 age groups— , j(0–4, . . . , 70+)—or their

changes, , on stock and bond excess returns (oron per capita GDP growth):

(1)

where Xi,t–1 represents such control variables asinterest rates and valuation ratios. The problemwith this approach is that the demographic vari-ables are highly correlated and would generate theusual multicollinearity problems.19 Moreover, inour case, the estimation of Equation 1 is impossible!Because the maximum number of nonoverlappingfive-year observations for each country (12 in 60years) is less than the number of demographicregressors (15 age groups), the covariance matrix of

is singular.20 In the literature, the usual solutionis to include only a limited number of broad agegroups or to combine them in some ad hoc way—introducing a risk of data mining—or to pool mul-tiple countries with far too many independent vari-ables, which still leads to unwieldy regressions.

We chose a different approach. Following Fairand Dominguez (1991) and Higgins (1998), weforced the demographic coefficients, bj, to satisfy a

si tj

,

si tj

, .

si t,0 4 si t,

70

si tj

,

si tj

,

r a X b s b si t i t i t N i tN

i t, , , , , , 1 11

si tj

,



polynomial of order k, allowing us to incorporatethe information in the entire demographic profile.See Appendix A for details of the methodology.After imposing this restriction, we obtain k trans-

formed demographic variables, , whose coeffi-

cients, Dj, can be estimated with21

(2)

Because k ranges between 2 and 4 (discussedlater), this approach reduces the number of demo-graphic variables. Equation 2 and its k polynomialcoefficients provide the ingredients for regressiondiagnosis. The 15 implied coefficients by age groupin Equation 1 convey all the economic intuition.

Note that unlike the control variables, Xi,t–1,the

age group shares, , and their changes, , areconcurrent with the dependent variables. Thistiming is important because we are exploringdemographic effects on financial assets, which pre-sumably occur primarily via shifts in the demand forfinancial assets. The same logic applies to our con-current timing on GDP and demographic variablesbecause any demographic effects on GDP will pre-sumably occur mainly via changes in the active pop-ulation and their relative contributions to GDP.Moreover, these data can be concurrent because weknow the demographic profile for each country overthe next 5–10 years with some precision, especiallyfor the future working-age and retirement-agecadres, which we can simply count today.

In each case, the choice of polynomial degreefor the demographic variables strikes a compro-mise between parsimony and statistical power.Searching a large number of options is meaninglessbecause larger values of k provide no reduction indimensionality and also create a concern aboutdata mining. For these reasons, we entertained onlythree options: polynomials of order k equal to 2, 3,or 4. In other words, we limited our tests to qua-dratic, cubic, and quartic polynomials. Becausemodels with lower degrees are special cases of theirhigh-degree counterparts, we relied on Wald testsfor nested models to gauge which order of polyno-mial was most appropriate.

For simplicity and parsimony, in each regres-sion we included only one control variable, Xi,t–1,out of these three: dividend yield, 10-year yield, andthree-month yield. These variables play a centralrole in the literature as forecasters of stock and bondreturns and of economic growth (see, e.g., Keim andStambaugh 1986; Campbell 1987; Ang, Piazzesi,and Wei 2006). Demographic coefficients—the

main point of interest in our study—are relativelyinvariant to the choice of controls. Other alterna-tives, such as yield spreads, produce very similarresults because demographic effects are low fre-quency by nature and any variables that reflectmedium-term movements in prices or economiccycles were effective in our study, wholly consistentwith prior research.

Some skeptics might argue that other factorsnot included in the regressions could contribute togrowth in per capita GDP or stock and bondreturns. Our first response is that comprehensivedata for other variables—both over time and acrosscountries—practically do not exist. Second, thefinancial yields that we included in the regressionsserved as controls or proxies for some of thesevariables because lower initial prices reflect higherrisk aversion or higher risk premiums, among otherthings. Third, the effects that we captured have alow frequency by construction, making the argu-ment for high-frequency variables, such as liquid-ity, less plausible. Finally, we note that missingvariables always have the potential to alter theresults of any regression, but the various robust-ness tests that we ran make us confident that ourresults are not spurious.

We report a total of six sets of results for com-binations of the three dependent variables (excessstock and bond returns and growth in per capitaGDP) and the two demographic regressors (sharesof total population and their changes).

Demographic Shares. For the first set ofresults, we used shares of total population by age

group, , as the regressors. Table 1 reports theresults from Equation 2, and Figure 1 plots theimplied polynomial coefficients for each of the agecadres relative to Equation 1. The three columns ofTable 1 under “Demographic Shares” show coeffi-cients and t-statistics for regressions using each ofour three dependent variables: five-year stock andbond excess returns and five-year growth in percapita GDP. We estimated all regressions by usingpooled ordinary least-squares (OLS) analysis andincluded country dummies (or fixed effects) to con-trol for any unobserved characteristics peculiar toeach country. We corrected standard errors for het-eroscedasticity and cross-sectional correlation(time clusters).22

The coefficients of the dividend yield and the10-year yield in the first two regressions are positiveand statistically significant, as is the case in most ofthe literature: Higher yields signal high risk aver-sion, depressed prices, and higher expected returnsfor stocks and bonds. In the third regression, we

i tj,

r a X D D

D

i t i t i t i t

k i tk

i t

, , , ,

, , .

1 11

22

si tj

, si t

j,

si tj

,



found a negative and statistically significant rela-tionship between GDP growth and the three-monthyield. The intuition for this relationship is simple:The Fed keeps the short yield at lower levels duringrecessions, which are inevitably followed by peri-ods of faster growth in GDP.

We begin the discussion of the demographicresults with the choice of k, the polynomial degree.The last two rows of Table 1 present the p-values ofWald test comparisons between cubic and qua-dratic polynomials (k = 3 k = 2) and betweenquartic and cubic versions (k = 4 k = 3). In theregression for bonds, we can see that a polynomialof the fourth degree is the best choice because bothtests strongly reject the null of statistical equiva-lence between the nested models. In the case ofstocks, the choice is a cubic polynomial because thetests cannot reject a difference between k = 3 and k= 4 (a p-value of 28 percent). In the case of GDPgrowth, a parabola is the best choice because bothp-values are above 10 percent.

The fit of all three regressions is relativelystrong, with R2s on the order of 30 percent. Thestatistical significance of the demographic polyno-mial coefficients is usually not as high as that of thefinancial variables, yet most of the t-statistics areclose to or above 3. This outcome is expectedbecause most of the variation in prices and eco-nomic activity occurs at a medium frequency andis captured by the yields. Given the difficulty inevaluating the economic significance and intuitionof the demographic effects in Table 1, we plottedthe implied coefficients for each age group in Fig-ure 1, together with 90 percent two-sided confi-dence intervals (shaded areas).

The graphs in Figure 1 and Figure 2 deservesome explanation. Consider Panel A in Figure 1. Thesolid line shows the implied coefficient that links thesize of each five-year demographic age cadre in thepopulation, as an independent variable, with thecorresponding stock market excess return for theconcurrent five-year span in the same country, as adependent variable. We can see a negative link for

Table 1. Regression Results, 1950–2010Demographic Shares Change in Demographic Shares

Stocks Bonds GDP Stocks Bonds GDP

Dividend yield 3.39 3.38(6.23) (6.30)

10-Year yield 0.66 0.62(4.98) (4.07)

3-Month yield –0.15 –0.19(2.97) (4.14)

D1 (1) –0.81 –1.56 0.09 3.09 –0.02 0.21(1.63) (3.33) (3.77) (2.90) (0.04) (3.56)

D2 (10) 1.69 3.47 –0.07 –10.27 –1.83 –0.14(2.47) (3.10) (4.39) (3.57) (1.42) (3.51)

D3 (100) –0.83 –2.72 11.81 2.96(3.05) (2.74) (4.25) (2.58)

D4 (1,000) 0.69 –4.22 –1.17(2.37) (4.77) (3.32)

R2 28% 34% 30% 31% 30% 17%

Observations 203 241 255 203 241 255

Countries 22 22 22 22 22 22

k = 3 k = 2 0.3% 0.0% 25.7% 7.7% 3.4% 13.4%k = 4 k = 3 28.4% 1.8% 12.4% 0.0% 0.1% 53.6%

Notes: This table reports coefficients and t-statistics (in parentheses) for six separate panel regressions,one in each column. Standard errors are corrected for heteroscedasticity and cross-sectional correlation(time clusters). The dependent variables are annualized five-year growth rates of per capita GDP, excess

stock returns, and excess bond returns. The demographic regressors are shares of total population, ,

in the first three columns, and changes therein, , in the last three columns. D1–D4 are the coefficientsof the polynomials that approximate the demographic coefficients. All regressions include country fixedeffects. The last two rows report the p-values of Wald tests for comparisons between nested models,opposing a parabola and a cubic polynomial, and cubic and quartic polynomials.

si tj

,

si tj

,



Figure 1. Effect of Demographic Shares

0

Equal-Weighted Regression GDP-Weighted Regression

Implied Regression CoefficientA. Stock Returns and Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

90 Percent Confidence Intervals

0

Implied Regression CoefficientB. Bond Returns and Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

0

Implied Regression CoefficientC. GDP Growth and Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

1

–1

–2

0.5

–0.5

–1.0

0.1

0.2

–0.2

–0.1

–0.4

–0.3



Figure 2. Effect of Changes in Demographic Shares

0

0

Implied Regression CoefficientA. Stock Returns and Changes in Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

Implied Regression CoefficientB. Bond Returns and Changes in Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

0

Implied Regression CoefficientC. GDP Growth and Changes in Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

4

2

–2

–4

–6

1.0

0.5

1.5

–1.0

–0.5

–1.5

0.5

–0.5

–1.0

Equal-Weighted Regression GDP-Weighted Regression




the first six age cadres (0–29), with statistical signif-icance at the 90 percent level for the three age cadresfrom 5 to 19. This finding means that, excluding anyvaluation effects based on the starting dividendyields, a larger share of the population in these agecadres historically conforms to lower stock marketreturns (excess returns over cash). Note that thispolynomial hits a trough for the 10–14 age cadre,with a coefficient of –0.7, which means that a 1percent higher concentration in this age cadreresults in 0.7 percent lower annual stock returns.That is a big number for a 1 percent change in thesize of one five-year age cadre. These effects areeconomically meaningful, especially consideringhow fast the age structure is changing in most devel-oped countries and that these results reflect annualreturns over five years. Note also that the coefficientfor the 70+ age cohort is slightly less than –1.5, whichis important in some of the faster-aging countries.

The OLS estimation implicitly assigned thesame weight to all countries in our sample. Toensure that our conclusions held unaltered in largercountries (e.g., the United States has a PPP-adjusted GDP that is roughly 100 times that of NewZealand), we estimated the same regressions byusing pooled weighted least-squares (WLS) analy-sis. Weighting by GDP (the natural choice), how-ever, would create the opposite imbalance.

Using the reciprocal of the Herfindahl Index(HI) as a measure of the “effective” number of obser-vations in a dataset, we found that our sampleshrank from 22 equally weighted countries to onlyabout 5 GDP-weighted countries.23 Thus, we choseto weight the regressions by the square root of PPP-adjusted GDP, measured in 2005 international dol-lars. This choice represented a balance and still leftus with 14 “effective” countries. The dotted linesshow the results for these regressions. That everyone of these lines in Figures 1 and 2 lies well withinthe confidence bands for the equal-weight regres-sions is reassuring. Thus, our first important robust-ness test has helped confirm the merits of our results.

Comparing the three panels in Figure 1, we cansee that the most striking fact about the polynomi-als is the similarity between the demographiceffects on stocks and bonds and, at the same time,how different they are from the demographiceffects on real per capita GDP growth. Althoughlarger age groups in the early 20s clearly benefiteconomic growth, they hurt the performance ofstocks and bonds. This effect may be due to therelatively lower savings and higher debt levels ofyoung adults, perhaps in an attempt to smoothconsumption over their lifetimes (young adultsmay be more rational than the older generationthinks!). The opposite holds for the middle-aged

groups in their 50s, which affect GDP growth neg-atively (already, even before they stop working!)and financial assets positively: Apparently, pro-ductivity starts to decline and savings to acceleratelong before retirement.24

One common theme emerges from all threepanels in Figure 1: Large populations of retirees(65+) seem to erode the performance of financialmarkets as well as economic growth. This findingmakes perfect sense; retirees are disinvesting inorder to buy goods and services that they no longerproduce, and they are no longer contributing goodsand services into the macroeconomy. This effect isless pronounced for bonds, presumably becausethey are sold later in retirement than stocks, inconformity with widespread financial advice.

Using the age group polynomials to estimatedemographic effects has several benefits. The firstbenefit, as mentioned earlier, is the possibility ofestimating the joint effect of all demographic vari-ables in the regressions, which allows us to use allthe available information in the age distributions,even after imposing a (possibly) restrictive polyno-mial structure on the coefficients. Second, insteadof using ad hoc age group selections as others havedone (e.g., 35–45), we can use the resulting polyno-mials to tell us exactly how to select and weight theage groups in order to obtain the most powerfulexplanatory variables.

One concern that afflicts other demographicstudies is the persistence of—some might even sug-

gest a risk of nonstationarity in— , the size ofeach age cadre as a percentage of the population.One answer is that these variables are limited to theinterval (0,1), but we also note the following:1. We used 60 years of data for most countries.

Although this horizon might seem unimportantin terms of demography, significant changes inpopulation structure occurred in most coun-tries over 1950–2010. Indeed, Japan went frombeing the youngest country in the developedworld to being the oldest, with its median agedoubling, from 22 to 44, in just 60 years.

2. With a large cross section of countries, weincreased the power of our tests by exploringthe varying stages in the demographic transi-tion process experienced by various nations.25

3. The polynomial curves show very significantdifferences among the implied coefficients forthe various age groups (e.g., the coefficients ofyounger and older cohorts have opposite signs).This finding is a strong indication that theempirical methodology also explores variations

across the age groups— versus —whichare arguably less persistent and more volatile.

si tj

,

si tm,

si tn,



Changes in Demographic Shares. We repeatedthe same analysis on changes in the demographic

shares of each age group, , which exhibit more

independence than the demographic shares, , bothrelative to neighboring five-year age cadres and rela-tive to prior and subsequent five-year spans.26 Usingthese alternative regressors, which largely avoid anyrisk of nonstationarity, we found similar results, whichwe hope will answer any remaining criticisms.

The last three columns in Table 1, under“Change in Demographic Shares,” together withthe graphs in Figure 2, present the results for therates of change in each demographic variable, The regressions for stocks and bonds have R2s thatare similar to those reported earlier, but we can seea decrease to 17 percent in the case of GDP growth.The degree of the polynomial is the same for bothbond returns and GDP growth; for stock returns,however, the Wald test strongly favors a quarticover a cubic curve (a p-value of zero). The magni-tude and statistical significance of the financial vari-ables are almost the same as in the previous tests.

Comparing the demographic coefficients withthose from the previous tests (the first three col-umns in Table 1) reveals some interesting facts. Thedemographic coefficients are similar in proportionacross the two regressions for GDP growth but arenoticeably different in the case of stock and bondreturns. To understand whether these changesaffect our intuition about the demographic effects,we need to look at the implied coefficients in Figure2. The magnitudes of the coefficients haveincreased, roughly by a factor of 2, reflecting the

lower volatility of when compared with The polynomials for stocks and bonds have thesame pattern as before but seem to shift to the right.This finding makes intuitive sense because the peakrate of change in the size of a given age cadre will

lead the peak size of that cadre— leads —

in most cases by as much as a decade or more.27

Thus, the polynomial curves should exhibit peaks

at later ages for than for

Out-of-Sample Robustness Tests. We con-ducted a third and more conventional series ofrobustness tests by checking our hypothesis on anew set of different countries. Unfortunately, apartfrom the developed markets, there is a dearth ofreliable financial data beyond the data we used inthe previous tests. Nevertheless, the two main data-sets in our GDP tests—the UN (population) and thePenn World Table (national income accounts)—

span about 200 countries. Thus, our robustnesstests were restricted to economic activity only;stock and bond market data are simply unavailableor too sparse to be useful.

To get around the lack of financial yields ascontrol variables, we used the log of the ratio ofconsumption to GDP, log(Ci,t–1/GDPi,t–1), as a proxyfor business cycles. Cochrane (1994) showed that thisratio forecasts GDP growth because consumption isnearly a random walk. Finally, there is also theimportant issue regarding the quality of the data forthe remaining countries not used in our main tests.Johnson, Larson, Papageorgiou, and Subramanian(2009) showed that the vast majority of these coun-tries have a quality grade of C or D (worst), asassigned by the authors of the Penn World Table,and that the standard errors of the estimates and thelikelihood of revisions are much larger for thesmaller countries and economies. Therefore, weshould expect wider confidence bands.

Many of these countries are very small, withunreliable data and undiversified economies. Wethus followed our earlier approach and estimatedthe regressions by using pooled WLS analysis,whereby each country is weighted by the squareroot of its 2005 GDP, measured in PPP-adjustedinternational dollars. This approach assigns moreweight to larger economies and provides moreaccurate estimates, without reducing the smallcountries to irrelevance.28

Table 2 shows that this sample includes 176new countries and 1,640 observations. The depen-dent variable (nonoverlapping five-year growth

si tj

,

si tj

,

si tj

, .

si tj

, si t

j, .

si tj

, si t

j,

si tj

, si t

j, .

Table 2. GDP Growth Regression Results (Robustness Tests), 1950–2010

DemographicShares

Change in Demographic Shares

log(C/GDP) 1.67 2.02(1.25) (1.58)

D1 (1) 0.09 –0.09(4.29) (1.19)

D2 (10) –0.07 0.31(4.76) (2.15)

D3 (100) –0.18(2.49)

R2 4% 3%

Observations 1,640 1,640

Countries 176 176

k = 3 k = 2 17.9% 1.3%k = 4 k = 3 40.6% 40.3%

Note: This table repeats the per capita GDP growth tests in Table1 with a different set of countries (see Table 1 for details).



rate in real per capita GDP) and the demographic

variables—either or —are the same asbefore, but we add log(Ci,t–1/GDPi,t–1) as a substi-tute for 3Mi,t, which is unavailable in most of thesesmaller economies. The statistical fit, as expected,is much lower, with R2s at 4 and 3 percent. TheWald tests recommend a parabola and a cubic poly-

nomial for and , respectively.In the regression for (first column of Table

2), the demographic coefficients D1 and D2 are thesame as their counterparts in Table 1, up to twodecimal places. This finding is also confirmed byFigure 3, which plots the corresponding GDP poly-nomials from our primary tests (Panel C in Figures1 and 2) as a dotted line. Panel A in Figure 3 depicts

a remarkable similarity between the two parabolas,showing that our results with demographic sharesas forecasters also hold in a much larger sample.

The second regression has demographic coef-ficients that differ from our main results, and so werely on the implied-coefficient profile in Figure 3 tovisually confirm a connection with the earlierresults. The general curve is broadly similar,although less statistically significant. In Figure 3,the comparison in Panel B is less precise than thatin Panel A—the dotted line for the primary GDPmodel in Figure 2 falls mostly outside the 90 per-cent confidence range for the polynomials in thetest depicted in Figure 3 (though largely within thejoint 90 percent confidence range on differences,which is not shown).

si tj

, si t

j,

si tj

, si t

j,

si tj

,

Figure 3. Robustness Tests

0

Developing Countries Developed Countries

Implied Regression CoefficientA. GDP Growth and Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group


0

Implied Regression CoefficientB. GDP Growth and Changes in Demographic Shares

0–4 70+20–2410–14 40–44 50–5430–34 60–64

Age Group

0.1

0.2

–0.2

–0.1

–0.3

–0.4

0.5

–0.5

–1.0



Figure 3 reveals the same positive relation-ship between GDP growth and middle-agedgroups and the same negative relationshipbetween GDP growth and children and retirees.In addition, the transition ages, or roots of thepolynomials, are only 10 years apart. One possibleinterpretation of this result is simple: Most of thesecountries are very poor and very young. Perhapsa few additional oldsters might add stability andpatience to a demography that might otherwise befairly volatile!29

Forecasts and ImplicationsWhat does the future hold? To state the obvious,past is not prologue. Indeed, the assumption thatpast statistical significance implies prospectiveforecasting accuracy has been the downfall of manyquantitative models. So, we must share these indic-ative results with this very important caveat: Highin-sample statistical significance does not guaran-tee that these models can be trusted to predict thefuture accurately. In these “forecasts,” we tacitlyassume that past relationships between demogra-phy and GDP growth, or between demography andcapital market returns, will hold unaltered in thefuture. The prospective scenarios that flow fromthis work are entirely possible, but we dare notassume that they are highly likely. Accordingly, weshould not view these daunting results as anythingmore than a cautionary tale.

The number of factors that could affect theoutcomes of individual countries is too large toeven try to enumerate here, so our predictionsshould be taken not with a grain but with a shaker-ful of salt. Still, the combination of the thoroughlyresearched projections by the UN Population Divi-sion for the years ahead and the statistical signifi-cance of our estimated relationships creates anopportunity that is too tempting to resist. To thebest of our knowledge, our study is the first to makesystematic projections for GDP growth and finan-cial markets on the basis of demographic changesfor practically every country in the world.30

Our forecasts are based on Equation 2. Becausethe regressions include country dummies, or fixedeffects, we can rewrite them as

(3)

Further, we used only the demographic variablesto construct our predictions:

(4)

where, for example, represents the time-seriesaverage of ri,t for country i. These forecasts focussingularly on the demographic component, settingaside all starting valuation effects. Unlike yieldsand interest rates, the population variables are pro-jected by the UN far into the future, allowing us tomake extended forecasts.

All our predictions should be seen as abnormalGDP growth or abnormal stock and bond returns.These are deviations from long-term means relativeto past individual country performance. We chosenot to include in our forecasts for two reasons.First, we could include them for only a small num-ber of countries owing to data availability. Second,the statistical precision around these historicalmeans is small, introducing even more uncertaintyinto our figures. This decision means that compar-isons across countries should be made carefullyand under the perhaps reasonable assumption thatnations have relatively similar long-term expecta-tions for

Because the population data are in five-yearintervals, we calculated decade-long forecasts for2011–2020 as the geometric average between theforecasts for two periods: 2011–2015 and 2016–2020. For all our forecasts, we used the coefficientsin Table 1. In Figure 4 (GDP), Figure 5 (stocks),and Figure 6 (bonds), Panel A depicts projected

demographic shares, , and Panel B

depicts changes in projected demographic shares,

Each figure contains two types of

graphs: color-coded maps showing results for allcountries and bar charts for the 22 developedeconomies in our main tests. The bar charts alsoprovide a sense of scale for the color-coded maps.The countries are first divided into positive (blue)and negative (red) groups and then into threesubgroups, with approximately the same numberof countries in each subgroup.

We see two common themes in the developedcountries: negative values for GDP growth andpositive values for abnormal excess bond returns.This finding is intuitive given their current demo-graphic stage: A rising number of retirees com-bined with low birth rates creates significantpressure on output (negatively) and savings (posi-tively). The net effect on excess stock returns varies

r r X X D

D

i t i i t i i t i

i t i

, , ,

,

1 11 1

22 2

Dk i t

kik

i t , , .

E E

E

t t

t

r r D

D

i t j i i t j i

i t j i

, ,

,

11 1

22 2

Dk i t jk

ik

Et , ,

ri

ri

ri .

E st i t jn,

E st i t jn , .



Figure 4. Annualized GDP Growth Forecasts, 2011–2020

(continued)

> 0.9% GDP Growth0.4% to 0.9% GDP Growth

0% to 0.4% GDP Growth

< –1.8% GDP Growth–1.0% to –1.8% GDP Growth

0% to –1.0% GDP Growth

–5 –2 –1–4 –3 0

Abnormal GDP Growth (%)

A. Forecasts Using Demographic Shares

Norway

United Kingdom

Ireland

United States

New Zealand

Austria

Sweden

Belgium

Australia

France

Spain

Denmark

Switzerland

Canada

Portugal

Greece

Netherlands

Germany

Italy

Singapore

Finland

Japan



Figure 4. Annualized GDP Growth Forecasts, 2011–2020 (continued)

–2.0 –1.0 –0.5–1.5 0

Abnormal GDP Growth (%)

B. Forecasts Using Changes in Demographic Shares

Greece

Norway

United Kingdom

Sweden

Italy

Portugal

Spain

Belgium

United States

Denmark

France

Germany

Switzerland

Australia

New Zealand

Finland

Austria

Japan

Ireland

Netherlands

Canada

Singapore

> 0.5% GDP Growth0.3% to 0.5% GDP Growth

0% to 0.3% GDP Growth

< –0.9% GDP Growth–0.5% to –0.9% GDP Growth

0% to –0.5% GDP Growth



Figure 5. Annualized Stock Market Forecasts, 2011–2020

(continued)

–8 4 8–4 0

Abnormal Stock Market Return (%)


Ireland

Spain

Singapore

Canada

New Zealand

Portugal

Greece

Austria

United States

Norway

Netherlands

Australia

United Kingdom

Switzerland

Italy

Belgium

France

Germany

Denmark

Sweden

Finland

Japan

> 9% Stock Market Return4% to 9% Stock Market Return

0% to 4% Stock Market Return

< –2% Stock Market Return–1% to –2% Stock Market Return

0% to –1% Stock Market Return



Figure 5. Annualized Stock Market Forecasts, 2011–2020 (continued)

> 4.0% Stock Market Return1.7% to 4.0% Stock Market Return

0% to 1.7% Stock Market Return

< –1.6% Stock Market Return–0.6% to –1.6% Stock Market Return

0% to –0.6% Stock Market Return

–5 3 5 7–3–7 –1 10

Abnormal Stock Market Return (%)


Greece

Italy

Spain

Portugal

Ireland

Germany

Belgium

Austria

France

United Kingdom

New Zealand

Switzerland

United States

Singapore

Australia

Norway

Canada

Netherlands

Sweden

Denmark

Finland

Japan



Figure 6. Annualized Bond Market Forecasts, 2011–2020

(continued)

0 3 4 5 61 2

Abnormal Bond Market Return (%)


Spain

Ireland

Singapore

Portugal

Greece

Canada

Italy

Austria

Netherlands

New Zealand

Germany

Australia

Japan

Switzerland

United States

Norway

Belgium

United Kingdom

France

Finland

Denmark

Sweden

> 4% Bond Market Return2% to 4% Bond Market Return

0% to 2% Bond Market Return

< –2% Bond Market Return–1% to –2% Bond Market Return

0% to –1% Bond Market Return



Figure 6. Annualized Bond Market Forecasts, 2011–2020 (continued)

0 3 41 2

Abnormal Bond Market Return (%)


Spain

Ireland

Singapore

Austria

Germany

Greece

Portugal

Belgium

Italy

Canada

New Zealand

France

Switzerland

Australia

Netherlands

United States

United Kingdom

Norway

Finland

Denmark

Sweden

Japan

> 3.3% Bond Market Return1.7% to 3.3% Bond Market Return

0% to 1.7% Bond Market Return

< –1.2% Bond Market Return–0.6% to –1.2% Bond Market Return

0% to –0.6% Bond Market Return



across countries; in a handful of cases, we alsofound divergence between the two graphs in thesame figure, most dramatically for Singapore andGermany. This divergence between the forecastswith demographic shares and those with changesin demographic shares is mainly due to unusuallyrapid variations in some age groups, creating

extreme values for or , rela-

tive to their historical means.31 These effects areamplified in the case of stocks, given their highervolatility and the relatively larger differencesbetween the coefficient profiles in Figures 1 and 2.We do not favor one set of results over the other.

Not surprisingly, there is a much wider rangein the global forecasts. In the case of GDP growth,the implied forecasts are bleak, with rare excep-tions that include India and most African countries,given their large working-age cohorts and verysmall number of senior citizens. Bonds exhibit theopposite results: Most of the aging world has a fast-rising roster of middle-aged potential savers, lead-ing to positive predictions for bonds, whereasAfrica presents mostly negative forecasts owing toa large number of younger borrowers relative toolder savers.

We recognize that many of the emerging-market results, for both stock and bond markets,are hypothetical because many of these countriesdo not have well-developed stock or bond mar-kets. Still, these results are ever more relevant andinteresting as capital markets begin to take shapein many of these countries.

The most interesting and extreme cases concernstocks. Japan, Finland, and Sweden have a danger-ous combination of very low birth rates and anexploding number of retirees, giving them a strongdemographic headwind, which has been much inthe news lately. Our findings may add scientificrigor to those discussions. The results for Canada,the United States, and central Europe are mixed,with slightly negative or positive projections,depending on the measure used. The Europeanperiphery—including Ireland, Portugal, Spain, andGreece—has slightly better forecasts for stock andbond returns, showing that there is hope for thosecountries despite their recent troubles. Again, theemerging economies present mixed results. LatinAmerica (including Mexico) and Asia fare relativelywell, with mostly positive returns. Much of sub-Saharan Africa has too many young people and toofew savings-age adults for stock markets in theregion to fare well. Finally, the BRIC countries (Bra-zil, Russia, India, and China) seem to have a brightfuture ahead of them, at least for the next 10 years.

ConclusionWe studied the effect of demographic changes onthree measures of great importance for countries allover the world: real per capita PPP-adjusted GDPgrowth, stock market excess returns, and bondmarket excess returns. We used an econometrictechnique that had never been used for this pur-pose; it allowed us to use all the available informa-tion in population profiles by fitting a polynomialcurve on the regression coefficients of demographicage groups. For our main regressions, we used alarge panel spanning more than 60 years and 22countries (and 176 countries in some special cases).

By force-fitting a polynomial to our demo-graphic variables, we extracted surprisingly strongstatistical significance, with implications that alignnicely with intuition. Children are not immediatelyhelpful to GDP. They do not contribute to it, nor dothey help stock and bond market returns in anymeaningful way; their parents are likely disinvestingto pay their support. Young adults are the drivingforce in GDP growth; they are the sources of innova-tion and entrepreneurial spirit. But they are not yetinvesting; they are overspending against their futurehuman capital. Middle-aged adults are the engine forcapital market returns; they are in their prime forincome, savings, and investments. And senior citi-zens contribute to neither GDP growth nor stock andbond market returns; they disinvest to buy goodsand services that they no longer produce.

We offered “forecasts” of GDP growth and ofabnormal stock and bond market excess returns foralmost every country in the world. With respect toGDP growth, our projections are bleak for most ofthe developed world. The developed countries—Japan, in particular—have alarmingly low birthrates and high numbers of retirees. But the pictureis relatively bright for bonds and mixed for stocks,especially for the younger of the developed econo-mies. These forecasts must be seen for what theyare—namely, out-of-sample extrapolations ofsome reasonably powerful in-sample relationships,to be viewed as more cautionary than predictive.

Finally, we again stress that these are long-termtrends only, estimated by assuming past relationshipsbetween demographic structures and measures ofeconomic growth and capital markets. Populationprofiles change very slowly, and these forecasts are byno means immutably bleak scenarios. The time torespond gets shorter every year, but countries havemany tools to use in acting on these forecasts in orderto position themselves for more benign circumstances.This topic is outside the scope of our article but couldcertainly be the subject of many future studies.

This article qualifies for 1 CE credit.

E st i t jn,

E st i t jn ,



Appendix A. Construction of the Demographic PolynomialThe effect of each age group, , or changes

therein, , can be estimated with the followingregression:

(A1)

where rt is the rate of return on stocks or bonds, orthe growth rate in GDP, and Xt–1 represents anycontrol variables, such as interest rates or valuationratios. We constrain the demographic coefficients,bi, to satisfy a polynomial of order k:

(A2)

where i = 1, . . . , N. Substituting these coefficientsback into Equation A1 gives us

which we can rearrange as

(A3)

Note that the demographic shares add up to a

constant, or , at all points intime. To avoid multicollinearity with the intercept

a, we impose the restriction on the demo-graphic coefficients. Translating this restrictioninto the polynomial coefficients, we obtain

Finally, substituting D0 back into EquationA3 shows us how to obtain the restricted coeffi-cients of the demographic polynomial, Dj , witha regression:

We use Equation A2 to reconstruct the originaldemographic coefficients.

Notes1. Purchasing power parity (PPP) adjusts income or GDP to

reflect the cost of goods and services in an economy. If a high-quality hotel room and an excellent dinner for four each costs$30 in Urumqi, China, and a similar room and dinner eachcosts $300 in Chicago, then a smaller GDP will buy moreconsumer goods and services in Urumqi than in Chicago.

2. In other recent research, the suggestion has even been madethat GDP is a poor measure of prosperity. Arnott (2011)spotlighted GDP net of deficit spending as a measure of“structural GDP” and GDP net of all government spending asa measure of “private sector GDP.” Both seem much morerelevant than traditional, debt-laden GDP. Although wethink it is a purer measure of national prosperity andgrowth, we chose not to add this complication to our GDPmeasure because it is not yet accepted by the broad main-stream and would thus trigger controversy that woulddistract from the main implications of our study.

3. This observation has direct relevance for the developedworld today. For roughly the last 50 years, the working-agecadre has been growing faster than the overall populationby a quarter to a half percentage point a year. For most ofthe developed world, this dynamic will be reversed for thenext 30 years. Should not this fact alone reduce the natural

per capita real GDP growth by about a half to a wholepercentage point a year relative to what we have learned toexpect? This simple fact has been overlooked by much ofthe media and academia in their ruminations on our recentinability to match the growth rates of past decades.

4. This observation is a sad acknowledgment for one of theauthors of this article as he endures his relentless decline inhis late 50s and relies increasingly on the innovative spiritof younger adults like his coauthor, who is in his early 30s.Our results might suggest that one of the authors is savingand investing on the basis of the surging GDP contributionof the other author. Neither author would entirely reject thisinterpretation!

5. Brooks’s simulations show effects of around 14–39 bps ayear, materially weaker than our empirical estimates andforecasts. Nonetheless, the extensive literature on the equitypremium puzzle, summarized by Mehra (2008), shows thatmarket frictions—especially borrowing constraints (seeConstantinides, Donaldson, and Mehra 2002)—can exacer-bate returns on risky and long-term securities.

6. Nor should they be. They will typically have far morehuman capital than investment capital. Why invest at ayoung age? Or, more provocatively, why not borrow

sti

sti

r a X b s b st t t N tN

t 1 11( ) ( ) ,

b D D i D i D ii kk 0 1 2

2 ,

r a X D s

D N s

t t jj

j

k

t

jj

j

k

tN

t

10

1

0

1

,

r a X D D is

D i s D i s

t t ti

i

N

ti

i

N

kk

ti

i

N

1 0 11

22

1 1

( )

( ) ( ) t .

sti

iN 11 st

iiN 01

biiN 1 0

DN

D i D i D ii

N

i

N

kk

i

N

0 11

22

1 1

1

.

r a X D isi

N

D i si

N

t t ti

i

N

ti

i

1 11

22

2

1

NN

kk

ti

k

i

N

tD i si

N

1

.



against the future human capital in order to smooth out thelifetime consumption expectations? Sadly, we seem not toshake this pattern as we age, continuing to borrow andspend even as our human capital dwindles.

7. In 1798, Thomas Malthus published the first of six editionsof his famous treatise An Essay on the Principle of Population.He argued that the combination of linear growth in foodproduction and geometrical growth in population wouldresult in famine. Given the intervening two centuries ofrising population and rising per capita longevity and livingstandards, his work is seen by many as discredited. Still, weshould acknowledge that his study was the first seriousexamination of the connections between demography andhealth or wealth. And some view him as merely beingearly—very early—in his prognostications.

8. Green and Hendershott (1996) objected to Mankiw andWeil’s finding that housing demand begins to decline afterthe age of 35. Researchers and commentators have alsopointed to a variety of possible causes for the surge inhousing prices in the last few decades before the recentcrisis: the Fed’s loose monetary policy, government housingpolicy, lack of proper screening by lenders, and the mis-management of financial risks spread by the use of deriva-tives (collateralized debt obligations, credit default swaps,etc.). We also note that among our friends, the demand forimproved housing often continues well into the 50s.

9. The U.S. Federal Reserve Board’s Survey of ConsumerFinances is a good example of a source of such data.

10. See Cochrane (2005) for an introduction to consumption-based asset pricing, Euler equations, and factor models.

11. See http://pwt.econ.upenn.edu/.12. See www.un.org/esa/population/unpop.htm.13. Other possible variants include low- or high-fertility trends,

mortality rates constant at 2005–10 levels, and zero migra-tion as of 2005–2010.

14. See http://staff.cbs.dk/parum/.15. See www.cso.ie/.16. For a discussion of problems and concerns with this dataset,

see Johnson, Larson, Papageorgiou, and Subramanian(2009).

17. Australia, Austria, Belgium, Canada, Denmark, Finland,France, Germany, Greece, Ireland, Italy, Japan, the Neth-erlands, New Zealand, Norway, Portugal, Singapore,Spain, Sweden, Switzerland, the United Kingdom, and theUnited States.

18. By looking at shares of the population, which must alwayssum to 1.0, and changes in shares, which must always sumto 0.0, we tacitly chose to ignore overall growth rates. Thus,we assumed that although overall population growth maymaterially affect overall real GDP growth, it will not affectper capita real GDP growth. This untested hypothesis isworth exploring in future research.

19. For a detailed discussion of multicollinearity problems, seeGreene (2008).

20. Many of our readers are probably familiar with this issuein the context of portfolio optimization. The availability ofdata relative to the sheer number of assets in the investmentuniverse renders the estimation and inversion of covariancematrices a challenge. A common solution is to adopt a factorstructure for the asset returns or their covariance matrix,which is akin in spirit to the solution we used in that bothimpose a limit on the number of parameters to be estimated.

21. A polynomial of order k is completely specified with k + 1parameters, but because the demographic shares add up to

a constant, or , the methodology

imposes the extra restriction to avoid the perfectcorrelation with the constant term in the regression. SeeAppendix A for details.

22. Because the dependent variables are nonoverlappingreturns and growth rates, we believe that cross-sectionalcorrelation is the most important deviation from traditionalOLS assumptions. We also corrected for time-series corre-lation (country clusters) and for both time and countryclusters, which resulted in small and occasional differences,but our qualitative conclusions remained unchanged.

23. The Herfindahl Index is calculated as the weighted averageof individual weights, or It is widely used as ameasure of competition among companies in a country,market, or industry and ranges between 1/N (perfect com-petition) and 1 (monopoly). The reciprocal of this index,ranging between N and 1, serves as an indicator of thehypothetical number of equally powerful companies in acountry, market, or industry. If two countries have equalweight, HI = 0.5, and so 1/HI = 2; with equal weighting, theeffective number of countries matches the actual number.If two countries are weighted 90/10, the former utterlydominates the regression and HI = 0.82; so, we effectivelyhave only 1.2 (1/HI) countries in our regression.

24. A controversial paradox in the field of demography stemsfrom the fact that economic growth seems to be unrelatedto the performance of financial markets (see, among manyothers, Dimson, Marsh, and Staunton 2002). Our study mayhelp resolve this paradox. The age cadres that are mostassociated with GDP growth are young adults; the agecadres that are most associated with stock and bond excessreturns are middle-aged adults. The young adults help GDPleap forward but are not yet serious about investing. Themiddle-aged, aware of their approaching retirements, arebidding stocks and bonds higher, but most are no longeradvancing rapidly in their careers, whereby they oncehelped facilitate rapid GDP growth. Therefore, to the extentthat demography drives GDP growth or capital markets,the impact is decidedly asynchronous, with about a 20-yearspread between peak impact on GDP and peak impact onstock or bond excess returns.

25. Skeptics might argue that because most of the countries inour sample are developed and thus highly correlated, wewere unable to conduct independent tests. We address thispoint in two ways. First, we refer the reader to Ang andMaddaloni (2003), who showed that using a sample of fivecountries increased the power of their tests by almost thesame amount as augmenting their 20th century U.S. sampleby a factor of 5. Second, in checking for robustness (dis-cussed later in the article), we extended our test for GDPgrowth to other, less developed countries and found rela-tively similar but noisier results (unsurprising, given thelower quality of the data).

26. Note that a large age cadre— larger than average—can

be associated with positive change if it is rising

to its peak or with negative change if it is fallingfrom its peak.

27. The rate of change of an age cadre must be positive beforethat age cadre can have above-average weight in thepopulation.

28. If we used equal weighting, China would have the sameweight as Kiribati. So, even though we would have 176countries, we would have no confidence that our modelswere relevant to the major markets. If we used GDP weight-ing, then Brazil, Russia, India, and China (BRIC) wouldcompose almost half the sample. The “effective” number ofst

ii 115 1 st

ii 115 0

biiN 1 0

HI wiiN 2

1 .

si tj

,

si tj

,

0

si tj

,

0



countries is about 16 because of our heavy reliance on thebiggest countries. An inviting compromise is to split thedifference, using the square-root-of-GDP weighting:China’s GDP is 100 times that of Haiti, so it gets 10 timesthe weight. The effective number of countries is about 75because we rely on the smaller countries only lightly, andyet BRIC still get a 14 percent weight vis-à-vis the 176countries. With this compromise, we can have some confi-dence that our models are useful for the major markets.

29. We acknowledge that this interpretation may be an ex postrationalization of the modest differences between theseresults and our core results.

30. Although we recognize that most countries do not havewell-established and well-functioning financial markets,

the questions posed here are still interesting because theanswers to them inform us about deeper aspects of thepopulation structure of various countries. For instance, onecan learn a lot about the demographic pressures on nationalsavings, investments, and productivity.

31. A plot of the population distribution for these two countries(not reported here) reveals some very interesting proper-ties. Germany was more affected by World War II than anyof its neighbors. Thus, although it will experience similardevelopments in the 0–39 age group, the structural changesin ages 40+ will be significantly different. Singapore hasexperienced very intense migration, which gives it one ofthe fastest-changing demographic structures in the worldacross all age groups.

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