- Email: [email protected]
The macroeconomic impact of the baby boom generation
HENRY M. McMlLlAN U.S.
Securities
and
Exchange
Commission
Washington,
D.C.
JEROME B. BAESEL Edward
0.
Thorp
Newport
and Beach,
Associates California
The Macroeconomic Impact of the Baby Boom Generation* This paper analyzes the impact of the Baby Boom generation on macroeconomic relationships in the United States. Using quarterly postwar data, it finds that measures of population age composition influenced real interest rates, income, inflation, and unemployment. The demographic variables complement or dominate other economic variables in reduced-form macroeconomic specifications. The paper also projects how the aging of the generation may influence future macroeconomic activity.
Economic theory predicts that an individual’s age influences many aspects of economic behavior. For example, the life cycle hypothesis of consumption implies that individuals smooth consumption over their lifetime. They borrow when young, save in middle age, and dissave after retirement. Similarly, age affects decisions on labor force participation, education expenditure, and housing purchases. Aggregate behavior is the composite of individual behavior. So, if age influences individual behavior, the age composition of an economy’s population could influence macroeconomic relationships. This need not be true however. For example, suppose there is an increase in the number of middle-aged people in the economy. Middle-aged individuals save a larger fraction of their income, so the national saving rate should increase. But the increase in middleaged workers could also reduce their relative wages. Their wages could fall enough to cause their share of national income to decrease. If so, the aggregate saving rate need not rise and, para-
*We are grateful to Lance Brannman, Robert Connolly, David Lilien and anonymous referees for comments on earlier drafts. We are responsible for any remaining errors. The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication by any of its employees. The views expressed here are those of the authors and do not necessarily reflect the views of the Commission or McMillan’s colleagues on the Staff of the Commission.
of Macroeconomics, Spring 1999, Vol. Journul Copyright 0 1999 by Louisiana State University OR%-0764/99/$1.56
12, No. Press
2, pp.
167-195
167
Henry
M. McMillan
and Jerome B. Baesel
doxically, could fall. Th ese equilibrating reactions, age-specific effects, can offset age-composition effects.’ The age composition of the United States population offers an opportunity to evaluate these issues empirically. The U.S. age composition is unusual, relative to historical standards, due to the Baby Boom that occurred after 1945. Dramatic increases in the United States birth rate from 1946 to 1964 interrupted the long-term trend toward smaller families. After 1964, American birth rates fell below their previous long-term trend rates. These variations in birth rates caused a population bubble, the Baby Boom generation. The effect of the Baby Boom generation on specific markets is well documented.2 Researchers have examined the Baby Boom’s effect on education3 housing,4 labor,5 and social security.6 Less attention has been paid to the Baby Boom’s effect on real interest rates, output growth, and other macroeconomic variables.7 In this paper we systematically evaluate the macroeconomic effects of the Baby Boom generation. We augment reduced-form macroeconomic models with different demographic measures of the We find that a life-cycle-human-capital demoU.S. population. graphic measure helps to explain output growth, unemployment, and the real interest rate. In fact, this demographic measure complements or dominates other economic factors often discussed in the literature. The paper contributes to the literature in two ways. First, it provides empirical support for economic theories in which age is an important factor. In particular, the evidence is consistent with Modigliani’s l&e-cycle hypothesis of saving. Second, the paper shows that demographic variables can aflect the results of tests involving nondemographic economic hypotheses. For example, demographic variables affect the inferences drawn from tests on the neutrality of money.
‘Easterlin (1987) provides a lucid explanation of these age-specific effects and how they depend on generation size. He argues that they are especially important with respect to labor force participation, family formation, and consumption patterns. ‘See Russell (1982) for a summary of this research. ‘Russell (1982, Ch. 3). %raine (1983). Sternlieb and Hughes (1986), Manchester (1988). ‘Berger (1985), Welch (1979), Freeman (1979), Levine and Mitchell (1988). 6Doescher and Turner (1988) and Auerbach and Kotlikoff (1984). ‘Brown (1985), McMillan and Baesel (1988), and Fair and Dominguez (1987) are exceptions.
168
Macroeconomic
Impact
of the Baby Boom Generation
We find demographic effects on interest rates and output growth where other researchers have not. There are at least three reasons for this. First, previous research often used sample periods in which there was little or no variation in the demographic data.’ Second, the demographic measure used here may more closely approximate the theoretical ideal than do dependency ratios or population growth rates used in other studies.’ Third, our empirical specification is motivated by recent research on unit roots and cointegration (Nelson and Plosser 1982; Engle and Granger 1987). The specification links the short-run adjustment process to long-run equilibrium relationships more naturally than do standard time series specifications. Furthermore, it easily distinguishes short-term from long-term effects. The paper is organized as follows. Section 1 discusses how age distribution influences economic activity and describes the empirical method. Section 2 describes the data. Section 3 presents the estimates and analyzes the robustness to specification. Section 4 presents the results of a forecasting exercise using Census Bureau projections of future age distributions. Section 5 summarizes the findings and concludes the paper.
1. Age Distribution and Economic Activity Economic theory suggests that demographic factors can affect output, inflation, unemployment, and real interest rates. We briefly review the theoretical arguments here. An economy’s productivity and thrift determine its real interest rate (Fisher 1930). First, in this context thrift is the propensity to save from current income. According to the life-cycle hypothesis of consumption (Modigliani and Brumberg 1954), this propensity depends on an individual’s age.” The age composition of an econ-
*Fair and age distribution distribution.
Dominguez (1987) also make this have recently exhibited more
point. variation
They note that than measures
measures of of income
‘Heien (1972) uses the median age. Denton and Spencer (1976) use the average age of children. Lieberman and Wachtel (1979) use fractions of the population in several adult age brackets. Ram (1982) uses the ratio of total population to adult population. “‘See Modigliani (1986) for a summary of research on the life-cycle hypothesis. Survey and microeconomic evidence indicates that saving behavior depends on age. The evidence also indicates that the elderly continue to save after retirement, in contrast to the predictions of the life-cycle hypothesis. However, the arguments
169
Henry
M. McMillan
and Jerome B. Baesel
omy’s population can therefore influence the economy’s thrift. Second, the productivity of labor depends on capital stock per labor unit, the quality of labor, and technology. In neoclassical growth theory (Solow 1970), the population growth rate affects the steadystate capital-labor ratio. In human capital models (Becker 1967), a worker’s quality improves as the worker ages due to his investment in human capital. The population growth rate and the age composition of the labor force therefore affect productivity. Unless their respective influences on productivity and thrift are exactly offsetting, a population’s age composition and its growth rate affect the real interest rate. In neoclassical growth theory, output per capita is a function of the capital stock and technology. The capital stock depends on the rate of time preference, the rate of technological innovation, and the population growth rate. The rate of time preference reflects the same factors as thrift in Fisherian models, and so it too depends on age composition. Therefore, output per capita depends on the age composition and population growth rate. and hire rates determine the unParticipation, separation, employment rate. These rates are different for young and old workers in the United States (Flaim 1979). The national unemployment rate is the weighted average of unemployment rates of young and old workers. The age composition of the labor force therefore affects the unemployment rate. Inflation is a function of money growth, output growth, and the transactions technology. While the transactions technology may be independent of demographics, age composition can atfect money demand. An individual’s age influences his risk aversion, financial wealth, and permanent income. These variables, in turn, influence the portfolio choice between money and bonds. Consequently, age composition can influence the velocity of money.‘l We have already discussed how demographic factors affect output growth. In combination, demographic factors are likely to alfect inflation, too. We can summarize the predictions of the primary models as follows: The life-cycle-human-capital model predicts that the higher
(Note cont. from p. 169) presented in this paper only require that the saving rates of the elderly be less than those of middle-aged individuals. The evidence strongly supports this requirement. Bernheim (1987) provides an excellent survey and discussion of this issue. “Mayor and Pearl (1984) and Fair and Dominguez (1987) present evidence on this point.
170
Macroeconomic
Impact
of the Baby Boom Generation
the fraction of middle-aged adults in a population, the lower the real interest rate, the higher the growth rate of per capita output, and the lower the unemployment rate; if the velocity of money is higher, then inflation should be higher, too. Neoclassical growth theory predicts that a higher exogenous population growth rate will raise the real interest rate and lower the growth rate of per capita output; it makes no prediction about inflation or unemployment. In a neoclassical growth model with an endogenous population growth rate, a lower population growth rate occurs when exogenous output growth or real interest rates are high because the opportunity cost of children is higher. Finally, the Easterlin hypothesis predicts that the endogenous population growth rate depends on relative economic status; higher population growth rates would be associated with higher rates of per capita output and with a higher fraction of middle-aged adults in the population. It is difficult to uncover these long-term influences empirically because short-term influences are always present. In the remainder of this section we develop an empirical specification that is capable of distinguishing short-term from long-term effects. Let dy, be the change in an endogenous variable, yt, during quarter t. For example, yt might be the logarithm of real output per capita, and dy, would be the growth rate in per capita output. Let dq be a vector of exogenous variables, such as demand or supply shocks, that affect the economy’s short-term equilibrium. Let w, be a vector of exogenous variables that affect the economy’s longterm equilibrium. These variables might include technology, preferences, and demographic factors. Economic theory often suggests that a macroeconomic variable is stationary or trend-stationary. If the variable is above or below its trend, it tends to grow more slowly or more quickly to return to its trend. An error correction mechanism is an effective way to model this process (Engle and Granger 1987). Let the change in y be a function of (1) the lagged deviation of y from its trend ( y *), (2) exogenous shocks, (3) other dynamic adjustment characteristics, and (4) white noise error:
dyt = Y(yt-1-
Y $1) + %Wyt
+ P’dxt
+ Et .
(1)
In (l), y is the speed of adjustment of the variable y to its longrun trend; we expect -1 < y < 0. The polynomial 8(L) includes enough lagged coefficients to assure that E, is white noise. The vector p determines the initial effect of changes in the exogenous vari171
Henry
M. McMillan
and Jerome
B. Baesel
ables on yt; these effects are by definition temporary. Any permanent or steady-state effects are built into y *, which has the form Yt* = cYrwt .
(2)
The vector w, slowly changes through time and therefore slowly atlects the steady state. It is efficient to estimate all coefficients, o, l3, O(L), and y, simultaneously, as in dy, = y( ytel - a’~,-1)
+ B(L)dy, + P’dx, + E, .
(3)
Alternatively, a macroeconomic variable may be a random walk with drift (Nelson and Plosser 1982). The variable has a trend growth rate, but not a trend level. This specification is dyt = /.L: + e(L)dy, + p’dx, + l t ,
(4)
* = atwt. CLt
(5)
where
Demographic factors could affect the drift term, l~$, and so affect long-term growth rates. Combining (4) and (5), we obtain dyt = cx’wt + e(L)dy, + p’dx, + q .
(6)
The trend-stationary and random walk specifications appear similar, but have very different economic interpretations. Consider a macroeconomic variable, say per capita output. The trend-stationary specification implies that output ultimately returns to its trend level. The associated adjustment process has a traditional business cycle interpretation. In the random walk specification, output returns to its trend growth rate, but not to a trend level. There is no tendency for the economy to make up lost ground. Good times, in the sense of positive shocks E,, permanently raise output in the random walk specification (6). In contrast, good times temporarily raise output in the trend-stationary specification (3) because they do not affect the trend level.”
“Of rates
172
course, through
conditional mean growth rates the polynomial B(L). However,
in (6) can depend on previous growth this influence also exists in (3).
Macroeconomic
2. Data and Variable
Zmpact of the Baby Boom Generation
Definitions
We estimate Equations (3) and (6) for real interest rates, output, inflation, and unemployment using quarterly data for the postWorld War II era (1949:i-1986:iu). The data sources are Citibank Economic Database and Bureau of Census publications. All quarterly data are from national income and product accounts. Let yr be the logarithm of real per capita GNP. Let x, be the logarithm of real per capita exogenous expenditures, which equals total government expenditures and exports. Let ss, (accumulated supply shocks) be the logarithm of the import price deflator divided by the GNP deflator.13 Growth rates for these variables are annualized diiIerences from the previous quarter (for example, dyt = 4[ Yt - Yt-11). Monthly data have been converted to quarterly data by using the last month of the quarter as the quarterly value. Let pt be the logarithm of the revised consumer price index. Inflation is the annualized change in p, from the previous quarter (dp, = 4[p, - p,-J). Let the nominal interest rate i, be the 90-day treasury bill rate.14 The realized real interest rate r, is the difference between the nominal rate and the inflation rate in the next quarter (rt = i, - dp,,,). Let m, be the logarithm of the nominal Ml money supply per capita, and let dm, be the annualized money growth rate during the rate, and let du, be quarter. l5 Let U, be the civilian unemployment the change in the unemployment rate during the quarter. Several demographic variables have been constructed from annual population data. All annual data have been converted to quarterly figures with straight line interpolation. Let AGE = Pop(35-64)/Pop(15-34, DPOP = dPop/dt
65+) ,
,
and
13This measure of the supply shock is common; see Wilcox (1983) and Peek and Wilcox (1987). 14The 90-day treasury bill rate avoids problems with capital gains taxes, holding period yields, and long-term inflationary expectations. In another paper (McMillan and Baesel 1988) we find that the choice of interest rate makes no qualitative difference. 15For years before 1959, money supply figures are from Friedman and Schwartz (1963). All money supply figures are seasonally adjusted.
173
Henry
M. McMillan
and Jerome B. Baesel
DPOP16 = dPop(le+)/dt
.
The variable AGE is the ratio of middle-aged adults to young and old adults; it excludes children. The variables DPOP and DPOP16 are, respectively, the population growth rate and the adult population growth rate. The variable AGE distinguishes between savers and borrowers in common life-cycle models. Its numerator is the number of individuals in common saving age brackets, and its denominator is the number of individuals in borrowing (or dissaving) age brackets.16 This ratio also provides information about the relative fraction of high productivity workers in the economy. The variable AGE is therefore well suited to test the predictions of the life-cycle-human-capital model. It is similar to dependency ratios that compare the total population to the potential workforce (for example, see Ram 1982). Commonly used dependency ratios ignore differences among adults that are important elements of the life-cycle-humancapital model. ” Neoclassical growth theory suggests that population growth rates aifect the steady state. The adult population growth rate (DPOP16) may be closer to the intent of the theory than the total population growth rate (DPOP). These population growth rates were smoothed over four quarters to eliminate seasonal patterns in the original data. is Table 1 presents summary statistics for the demographic variables. They are highly collinear; correlation coefficients are above 0.9 for all pairs. Figure 1 plots the demographic variables. The dependency ratios and AGE are waves of low frequency and different periods. Linear or quadratic time trends can approximate them during short time intervals. Higher order trends are needed for the full sample period. The population growth rates fluctuate much more
l6The variable AGE may be better described as the ratio of individuals in high saving rate age brackets to the individuals in low-saving rate age brackets. Young adults tend to be borrowers; retired adults tend to be dissavers. We shall use the term borrowers for brevity if no ambiguity results. “We considered two dependency ratios (total population to adult population and total population to working age population) in earlier versions of the paper. Neither dependency ratio worked as well as the variable AGE described here. The empirical results are not reported here and are available on request from the authors. “We also considered labor force participation rates and the growth rate of the labor force. The labor force variables performed poorly, perhaps because labor force participation is endogenous and highly procyclical. Estimates are available upon request from the authors.
174
Macroeconomic TABLE
1.
Zmpact of the Baby Boom Generation
Demographic
Variables
Series
Mean
Standard Deviation
Maximum
AGE DPOP DPOP16
0.816 0.013 0.015
0.107 0.003 0.003
0.944 0.020 0.019
NOTES:
The
sample period population = Pop(35-64)/[Pop(l5-34)
Pop = total AGE
DPOP POP16
Summary
Statistics Minimum 0.659 0.009 0.009
is 1948:iu-1986:iii. of the United States, + P&55+)],
= dPop/dt, = dPop(l6+)/dt.
than AGE. The blip in the total population growth rate in 1959 and 1960 is due to the statehood for Alaska and Hawaii. We use dummy variables to account for this fact in the estimates.
3. Empirical Analysis Demographic Factors Table 2 presents estimates of the reduced-form equations, (3) and (6). The dependent variables are the real interest rate in Panel A, output growth in Panel B, inflation in Panel C, and unemployment in Panel D. The basic trend-stationary or random-walk specification is developed in the Appendix. Short-term exogenous shocks and demographic variables supplement this specification. lQ The estimates without demographic variables are largely consistent with traditional macroeconomic theory. Real interest rates increase with fiscal shocks and decrease with monetary shocks, as implied by Keynesian macrotheory (see estimate 2A.l). Output increases with fiscal and monetary shocks (estimate 2B.l). Inflation
19We first determined whether an endogenous variable followed a trend-stationary or a random-walk process. We used the augmented Dickey-Fuller test to do this. Details of this procedure are in the Appendix. We find that the real interest rate is stationary, the unemployment rate is trend-stationary, and the inflation and output growth rates are random walks. Money, government spending, exports, and import prices are assumed to be exogenous. Lagged output growth is included in the inflation and unemployment equations, but excluded from the interest rate equation. Its insignificance in the interest rate equation may be due to financial market efficiency. If the financial market knows dy,-, at time t - 1, then the efficient markets hypothesis implies that dy,-, has no additional effect on i, beyond that in i,-,.
175
Henry
M. McMillan
and Jerome B. Baesel
Dependency
LEMOGRAPHK; Ratios and
MEASURES Population Growth
Rates fO.025 0.025 DPOP16
+ 0.020
,-d-----__
0.6
0.6 0.6 1+ , 1950
I 1955
I 1960
1 1965
I 1970
AGE = Po~t35-64/CPod15-34) DPOP DPGP16
I 1975
I 1985
I
+ Pot1(65+)1
=Growth
Rate
of Total
=Growth
Rate
of AC&H Poputation
Figure
1 1980
Populetion
1
increases with supply shocks and monetary growth but decreases with exogenous spending, perhaps due to countercyclical fiscal policy (estimate 2C. 1). Finally, unemployment decreases with lagged output growth per Okun’s law (estimate 2D.l). The explanatory power of each equation is good, especially given that the dependent variables are differences rather than levels. Also, the various lags of the dependent variables produce white noise error terms; for brevity, diagnostic statistics are suppressed. The remaining equations each include one demographic variable to explain long-run trends.” There is clear support for de-
20All demographic variables are assumed to be exogenous or predetermined. A demographic variable could be endogenous if economic activity contemporaneously affects migration, birth, or mortality rates. Migration was limited during the sample period, and its effect on these demographic variables should be small. Mortality rates in the U.S. are insensitive to economic activity. Birth rates may be endogenous, however (Easterlin 1968; Butz and Ward 1979). Birth rates have no effect
176
Macroeconomic
Zmpact of the Baby Boom Generation
mographic trends in the data. The life-cycle-human-capital variable fits the best across all equations. It is correctly signed and significant in all equations, minimally affects other estimated coefficients, and improves the overall performance of the model. In particular, the time trend in the unemployment equation is insignificant if the estimate includes AGE, but is highly significant if it does not. In contrast, the adult population growth rate (DPOP16) is correctly signed but insignificant in the real interest rate and output growth equations. The total population growth rate (DPOP) significantly increases output and decreases interest rates and inflation. These effects of DPOP are opposite the predictions of neoclassical growth theory. The relation of DPOP to output growth is consistent with Easterlin’s hypothesis of endogenous population growth.‘l To determine the long-run equilibrium relationships, we set the lagged dependent variables equal to zero for trend-stationary variables (dr and du) and equal to the current dependent variable for random-walk variables (dy and dp). We also set exogenous spending growth equal to output growth (dx = dy ) to achieve balanced growth. Then we solved the resulting equation for the steady state, given the coefficient estimates. Using the estimates when AGE is the demographic variable, the steady-state values are=
AGE
on AGE or contemporaneous DPOP16. Changes in the birth rate largely determine changes in the population growth rate, however. So DPOP is endogenous if birth rates are endogenous. While we maintain the hypothesis of birth rate exogeneity throughout this paper, we note when the evidence suggests endogeneity. 2’Seemingly unrelated regression (SUR) estimates differ only slightly from the OLS estimates reported here. Table 2 assumes stationarity for the real interest rate and trend-stationarity for the unemployment rate. As discussed in the Appendix, there is some reason to believe that these time series are random walks instead. We estimated randomwalk specifications for the real interest rate and the unemployment rate with and without the demographic variables. The results are virtually the same as in Table 2 and are omitted. The variable AGE remains significant and continues to provide the best fit of the demographic variables. We also examined other conversions of monthly data to quarterly data. The results are essentially the same using either the second month of the quarter or the quarterly average figures. Roughly speaking, demographic effects are larger, and the overall performance of the model is better for the third-month specification. The model performs poorly with the first month of the quarter data. %For example, to determine the real interest rate from estimate (2A.2), set dr = dr-, = dr-* = 0, and dx = dy*. Then solve for r*. Simplification yields (7). The same procedure applies to the unemployment rate. For inflation and output growth, current and lagged rates of the dependent variable are set equal to each other. Note that dy-, = dy* in the inflation and unemployment equations.
177
2.
Reduced
Form
In(AGE)
DPOP
DPOPIG
(2A.2)
(2‘4.3)
(2A. 4)
-
ln(ACE)
DPOP
DPOPIG
(2B.l)
(2B.2)
(2B.3)
(2B.4)
name
-
-0.462 (04
(2.W
2.618
0.0802 (2.72)
-
coef.
Variable
0.611 (0.92)
-1.846 (2.48)
dy
0.078 (3.24) 0.076 (3.12)
-0.005 (1.45)
0.029
0.142 (3.10) 0.154 (3.33)
0.012 (0.76)
0.139 (3.11)
0.152 (3.36)
dx
(2.90)
-0.031 (1.62)
0.019 (2.93)
0.006 (1.W
c
-0.007 (0.67)
0.074
0.067 (2.76)
0.002 (0.91)
w54)
dx
c
Estimates
dr
coef.
-0.0511 (2.92)
c&??nL-,
Panel B: Dependent
-
(2A.l)
name
Panel A: Dependent Variable denKm,
TABLE
0.035 (0.97)
0.292 (3.24) 0.027 (0.71)
0.037 (1.W
0.340 (3.81)
0.218 (2.83)
0.022 (0.62)
0.191
ass
-0.059 (2.37)
-0.066 (2.71)
-0.065 (2.74)
-0.053 (2.22)
oh
@.fw
dm
-0.080 (1.61)
-0.146 (2.67)
(2.96)
-0.162
-0.065 (1.46)
dm
-
-
4-l
-
-
-
4-l
-
-
-
-
time
-
-
-
-
time
v-1
-0.174 (1.84)
-0.216 (2.46)
-0.207 (2.42)
-0.m (2.30)
0-1
-0.300 (3.48) -0.280 (3.22)
-0.466 (4.71) -0.446 (4.44)
0.091 (1.15) 0.089 (1.10)
0.235 (2.91)
0.230
C-7)
0.082 (1.W
0.235
0.094 (1.17)
dvmo
(2.99)
0.233 (2.91)
do-,
-0.289 (3.21)
-0.273 (3.11)
-0.433 (4.30)
-0.458 (4.35)
doe.p
do-,
-
-
do-,
0.025 (0.W
0.028 (0.38)
0.011 (0.15)
0.035 (0.46)
do-,
-0.253 (3.25)
-0.234 (3.07)
-0.249 (3.30)
-0.242 (3.13)
do-,
-
-
-
-
doe,
0.251
0.273
0.286
0.255
8%
0.341
0.365
0.378
0.346
FP
Reduced
DPOPIG
(2C.4)
DPOP
DPOPIG
(2D.3)
(2D.4)
0.006
-0.0646 F-5)
(0.48)
-0.1219
(2.W
-0.0114
-
coef.
Variable
0.005 (2.40)
(3.81) 0.002 (0.35)
0.004
0.003
(0.W 0.002 (0.42) 0.002 (0.W 0.002 (0.W
0.004
(0.02)
0.001
-0.015 (0.W 0.009 (0.W 0.002 (0.07)
(cont’d)
(3.29)
0.001
(0.38) 0.039 (2.55) -0.014 (1.42)
(2.88) -2.015 (2.22) 1.614 (2.22)
(1.77)
-0.0749
du
dp
Estimates
(4.26) -0.039 (4.40) -0.037 (4.07) -0.039 (4.26)
-0.038
-0.014 (0.31)
-0.066 (1.22)
-0.010 (1.74)
0.003 v-w
(1.13) -0.005 (1.46) -0.003 (1.W -0.003 (0.85)
-0.004
0.061 (2.39)
(2.94)
0.072
0.074 (2.W 0.076 (3.13)
-0.038 (3.82) -0.038 (3.90) -0.036 (3.51) -0.037 (3.62)
0.102 (2.13)
0.102 (2.12)
0.126 (2.67) 0.092 (1.95)
(3.96) -0.105 (4.05)
-0.111
(4.54)
-0.111
-0.102 (4.17)
-
-
-
-
0.00021 (3.98)
(2.~)
0.00023
(1.W
0.00008
(4.40)
o.ooo19
-
-
-
-
0.256 (2.73)
(2.73)
0.256
e-33)
0.240
0.252 (2.74)
0.382 (4.47) 0.329 (3.87) 0.344 (3.99) 0.355 (4.15) 0.110
0.097 w-3) 0.087 (1.08)
(1.01)
0.084 (1.08) 0.077
0.072 (0.88) 0.088 (1.08) 0.092 (1.13)
(1.W
-
-
-
-
(::g 0.316 (3.94) 0.313 (3.90)
0.343 (4.29)
-
-
-
-0.067 (0.80) -0.029 (0.38) -0.031 (0.41)
(0.27)
-0.021
0.416
0.419
0.435
0.422
0.642
0.642
0.652
0.634
NOTES: The sample period is 1949:i-1986:io. t-statistics are in parentheses. In the table, do is the dependent variable, do-l. is the dependent variable lagged k quarters, and o_, is the lagged level of the dependent variable. The dependent variables are tbe following: dr = the change in the ex post real tresury bill rate, dy =, the growth rate of the real GNP per capita, du = the change in the civilian unemployment rate, and dp = the CPI inflation rate. The demographic variables (demo) are defined as follows: AGE = POP(35-64)/[Pop(lS-34) + Pop(65+)], DPOP = dPop/dt, POP16 =dPop(l6+)/dt. The other exogenous variables are the following: dx = the growth rate of exogenous spending, which equals government purchases and exports; dm = the growth rate of the Ml money supply, I&S = the growth rate of the import price deflator minus the growth rate of the GNP deflator, and time = a time trend. Dummy variables for 1960 are included with DPOP and DPOP16; the estimated coefficients of the dummy variables are insignificant and are omitted from the table. All growth rates are annualized.
In(AGE)
-
(2D.2)
(2D.l)
name
h-1
D: Dependent
DPOP
(2C.3)
Panel
In(AGE)
-
(2C.2)
(2C.l)
name
Form
Variable
demo-1
Panel C: Dependent
TABLE 2.
Henry
M. McMillan r* = -0.015
and Jerome B. Baesel - 0.209 ln(AGE)
- 0.621dm
- 0.295&s,
(7)
dy * = 0.024 + 0.101 ln(AGE)
+ 0.429dm
+ O.O47dss ,
(8)
dp* = 0.009 - 0.171 ln(AGE)
+ 0.088dm
+ 0.215d.ss,
(9)
u* = 0.028 - 0.135 ln(AGE) + 0.0007t
- 0.491dm
- 0.06ldss
.
(10)
Figure 2 plots the equilibrium values for the postwar sample period, assuming dm = dss = 0. The figure shows that AGE had a quantitatively large effect on output growth, real interest rates, and unemployment during the sample period. Monetary shocks have larger effects on real variables than on inflation in the long-run equilibrium. This occurs because the model estimates only the shortrun effects of monetary policy. The next section presents model estimates that can better account for long-term effects of monetary and fiscal policy. Other Economic Factors The evidence indicates that the age composition of the U.S. population affected macroeconomic relationships during the postwar era. However, this conclusion is unwarranted if the demographic variables are proxies for other omitted economic factors. To examine this issue, we introduce four economic factors, suggested by the literature, that might affect the long-run equilibrium. The longrun factors are the ratio of exogenous spending to output (Z), the terms of trade (SS), the average growth rate of money (AVEMGR), and the standard deviation of inflation (STDZNF). We briefly review the motivation for each variable. In the steady state, higher levels of government spending relative to potential output increase real interest rates via the crowding-out effect. More government spending decreases output growth and increases inflation if the government sector is less productive than the private sector. The effect on unemployment is ambiguous. To investigate this issue we define Z, = exp(x, - yt) to be the ratio of exogenous spending to output. The higher the terms of trade, the more competitive are U.S.produced goods in world markets and the less competitive are foreign-produced goods in the U.S. Higher terms of trade decrease unemployment and increase output, but have ambiguous effects on 180
Macroeconomic
Zmpact of the Baby Boom Generation
IMPLIED LONG-RUN EOULMUM Rate. Per Capita. Output Growth,
Real Interest
and Unemployment
0.125
0.100
Unempbyment /
Rate / / / /
/-
_/--.--___
0.075
0.050
0.025
0.000 Output -0.025
I
I
I
1950
1955
1
1960
Growth
d;;;;--.--
______
I
I
I
1965
1970
1975
Figure
-__---
1
1990
___---I
1985
2.
inflation and the real interest rate. We measure the terms of trade with the ratio of import prices to the GNP deflator, SS, = exp(ss,). Neutrality propositions from monetary theory imply that the average growth rate of money should affect only the average inflation rate. Money growth should not affect steady-state real output growth, real interest rates, or unemployment. We use AVEMGR, the average monetary growth rate in the previous eight quarters, as the long-run monetary growth rate. This variable should influence only the long-run inflation rate. The current monetary growth rate (dm,) should capture any short-run effects of money on real economic variables. The rational expectations hypothesis implies that the average rate of inflation has no effect on real economic variables. However, the volatility of inflation may affect these real variables by increasing the likelihood of forecast errors. Greater uncertainty about inflation would increase the expected rate of return required by savers, which, in turn, would reduce the desired capital stock and output growth rate. Similarly, the steady-state unemployment rate would increase if firms were less willing to hire workers in an uncertain 181
Henry
M. McMillan
and Jerome B. Baesel
inflationary environment. We use the standard deviation of inflation (STDZNF) in the previous eight quarters to test this issue. We estimated Equations (3) and (6) with AGE and these four long-run economic variables. Table 3 summarizes the results. The estimated coefficients for the short-run adjustment variables are very similar to those in Table 2 and so are not presented in Table 3. The first equation in each panel includes all long-run factors. Collinearity among these variables reduces significance levels of reported coefficients. Subsequent equations in each panel restrict the set of long-run variables to those variable combinations that provide significant coefficient estimates.= The variable AGE is significant in the restricted estimates for all dependent variables. Its coefficient estimates are roughly the same as their respective values in Table 2. The variables AGE, AVEMGR, and TZME are significant in the unemployment equation. The fiscal pressure variable Z and the variable AGE are significant in the interest rate, output growth, and inflation estimates. However, AGE is significant in the inflation estimate only if it replaces STDZNF and AVEMGR. Given the strong theoretical arguments that inflation is primarily a monetary phenomenon, the estimate with AVEMGR and STDZNF may be preferred. Theoretical arguments and the empirical evidence support the conclusion that AGE is a significant determinant of the three real variables.24 To what extent is AGE merely a proxy for a nonlinear time trend in the data? A third-order polynomial in time very closely
=The real interest rate, output growth rate, and inflation equations include the fiscal pressure variable Z. It has the expected sign in the real interest and output equations, but has the wrong sign in the inflation equation. The money growth variable AVEMGR affects the inflation rate, but not the real interest rate or output, as predicted. Thus, money is neutral in the long-run for these variables. However, AVEMGR reduces unemployment, suggesting that it may also be picking up lagged short-run effects of expansionary monetary policy. The terms-of-trade variable SS is never significant. The volatility of inflation STDINF is significant only when combined with AVEMGR in the inflation equation. =The long-run equilibrium estimates are r*
= 0.921
- 0.228
ln(AGE)
+ 0.781
In(Z)
- 0.794dm
- 0.247d.ss,
dy * = 0.152
+ 0.088
ln(AGE)
- 0.147
In(Z)
+ 0.378dm
+ 0.088dss
dp*
+ 0.013
ln(AGE)
- 0.830
In(Z)
= 0.944
+ 1.356AVEMGR
182
- 1.309STDINF
- 0.459dm
+ 0.222dss,
,
Macroeconomic
Zmpact of the Baby Boom Generation
approximates AGE during this sample period.% Estimates similar to those in Table 2 would obtain if time, time squared, and time cubed jointly replaced AGE. Thus, one could say there is a nonlinear time trend in the data during this sample period, and AGE merely proxies this trend. But what would cause the nonlinear trend to be there in the first place? Demographic changes can explain the existence of a nonlinear time trend. The pertinent demographic changes can be parsimoniously modeled with the variable AGE. Other economic factors could explain this nonlinear trend, too. In this respect, Table 3 presents evidence on some plausible variables. Even when the estimates include other plausible economic factors, AGE is a significant explanatory variable of interest rates, output, and unemployment. Note that extrapolating the time trend beyond the sample period soon yields absurd values. Extrapolating the demographic trends does not, as we shall show in the next section.
4. Future Projections Demographic changes can be useful for intermediate and longterm forecasting. The aging of the Baby Boom generation is predictable relative to most economic time series. This provides valuable information for forecasting interest rates, output, and unemployment. Such forecasts would presumably be more sensible than those obtained from extrapolation of time trends, at least in the longer term.
and u* = 0.059
- 0.128
- 0.532AVEMGR
ln(AGE)
+ 0.028
+ 0.0015TIME
In(Z) - 0.264dm
- 0.03ld.w.
These equations are based on the restricted estimates of Table 3. Note that the coefficients for AGE are quite similar to their respective values in (7), (8), and (10). Note too that if dm = AVEMGR, then a 10% money growth rate implies a 9% inflation rate. Similar results obtain if unexpected money growth (udm = dm - AVEMGR-1) replaces dm. Then unexpected money growth is not part of the long-run equilibrium, but AVEMGR is significant in the real interest rate equation. =A regression of AGE on time, time-squared, and time-cubed has an RZ of 0.98. Because AGE and a third-order time trend are highly collinear, their estimated coefficients are insignificant if jointly included in one regression equation.
Alter-native
-0.0559 (3.45)
(3a. 2)
0.0753 (2-W
(3b.2)
(3c. 1)
0.0218 (0.49)
Panel C: Dependent Variable ln(AGE)
0.0581 (0.88)
(3b. 1)
Panel B: Dependent Variable ln(AGE)
-0.0723 (2.14)
(3a. 1)
dp
dy
dr
Economic
Panel A: Dependent Variable ln(AGE)
TABLE 3.
-0.201 (4.04)
in(Z) 0.025 (1.20)
ln(SS)
-
-0.029 (0.79)
-0.118 (1.49) -0.126 (2.05)
ln(SS)
-
0.173 (4.85) in(Z)
0.0117 (0.58)
ln( SS)
Estimated
0.185 (4.24)
in(z)
Trend Variables,
0.372 (2.32)
AVEMGR
-
-0.012 (0.04)
AVEMGR
-
-0.125 (0.86)
AVEMGR
Co&kients
R-2 0.690
-0.464 (2.25)
0.305
0.294
R-2
0.471
0.465
R-2
STDlNF
-
0.121 (0.34)
STDlNF
-
-0.117 (0.60)
STDINF
-0.0193 (3.02)
(3d.4)
where w, is a vector and dzt are short-term
-
0.002 (0.30)
+ -p-l
do, = u’w,
+ p’dz,
+ qL)du,
-0.092 (2.99)
-0.120 (3.52)
-0.056 (1.93)
-0.065 (2.08)
AVEMGR
in parentheses.
are
t-statistics
-
0.003 (0.92)
-
-0.002 (0.43)
ln(SS)
-
-
+ E, ,
-
,Y:Z
-
-0.010 (0.28)
STDlNF
0.308 (3.26)
-
0.00026 (2.95)
0.00051 (3.48)
-
-
TIME
-0.297 (2.01)
-
determining the steady state, du, is the dependent variable, We-, is the lagged level of the dependent shocks. See Tables 1 and 2 for definitions of variables and more detailed specifications of equations.
period is 1949:i-1986:io. a from the equation
of variables economic
The sample coefficients
-0.0057 (0.56)
(3d.3)
NOTES: Estimated
-0.0266 (3.92)
(3d.2)
,~:~
0.010 (1.27)
-0.0296 (3.78)
(3d. 1)
-0.183 (4.68)
du ldz)
-
(3c.3)
-0.103 (2.63)
Panel D: Dependent Variable ln(AGE)
-0.0609 (2.32)
(3~. 2)
variable,
0.462
0.473
0.435
0.430
R-2
0.691
0.672
Henry
M. McMillan
and Jerome B. Baesel
We provide one such forecast here using Bureau of the Census population projections. 26 Figure 3 shows the effect of these population projections on the age distribution of borrowers and savers. According to all three projections, the borrowing population will decline relative to the saving population until 2002 and then increase rapidly in the next century. The change in AGE is dramatic. The middle population projection forecasts AGE to increase from 0.666 in 1980 to 1.013 in 2005 and then to drop rapidly again to 0.796 in 2030. The low population series projects AGE reaching 1.042 in 2005 and declining slowly to 0.862 in 2030. The high series projects AGE to be 0.987 in 2005 and to fall rapidly to 0.733 in 2030. Figure 3 shows that the three AGE series have the same pattern but with different levels. To obtain projections of real interest, output growth, and unemployment rates, we combine the population projections with the steady-state parameter estimates of Table 2 (equilibrium equations [7], [B], and [lo]). Table 4 presents the projections. Using the middle AGE series, output growth per capita is negative through 1990 and then grows rapidly to 2.5% per year in 2010. The steady-state unemployment rate declines from 7.7% in 1985 to 2.7% in 2010 before increasing again. Equilibrium real interest rates decline from 6.1% in 1985 to -1.4% in 2010 before climbing back to 4.2% in 2030. The low AGE series projects higher per capita output growth and lower unemployment and real interest rates. The high AGE series projects smaller swings in these variables than do the middle or low AGE series.27
%We use the three projections (low, middle, and high) developed by the Bureau of the Census (1984). The projections use a smooth transition from 1982 population age distribution to the ultimate projected levels. According to the census bureau’s grows to 261 million in 2010 and “low” assumptions, the United St a t es population declines to 232 million by 2050. With the middle series, population grows to 268 million in 2010 and levels off at 310 million in 2050. The high series shows population growing rapidly to 283 by 2010 and 424 million by 2050. The two extreme series differ by less than 10% in 2000, by 30% in 2025, and by over 60% in 2050. 27Because these low projected interest rates may seem counter-intuitive, it is a useful exercise to consider how and why they occur. The intuition of the overlapping generation models is appropriate here (see especially Cass, Okuno, and Zilcha 1979). Negative real interest rates are plausible in that literature because physical or financial assets are the only way to provide retirement consumption. Even though the rate of time preference is positive (individuals prefer current consumption to future), the marginal rate of substitution of future for current consumption can be greater than one (that is, real interest rates can be negative). The middle AGE series projects 15% more savers than borrowers, according to
186
Macroeconomic
Impact
of the Baby Boom Generation
RATID OF SAVERS TO BORROWERS HISTORICAL AND PROJECTED TIME SERIES. US
DATA
Age 0.8
0.7
0.6 1950
60
70 Age
60
90
= PoH35-64V[
2000 POP( 15-34)
Figure
10
20
+ Pop(65+
30
40
20 80 Year
)I
3.
There are qualifications to these projections, of course. They are point estimates. The 95% confidence intervals for the projected interest rates,include positive real interest rates. These confidence intervals expand with time. Also, the confidence intervals will grow because the projected AGE series has values outside historical experience. The simulation assumes other factors are constant. Fiscal policy, monetary policy, and supply shocks will influence the macroeconomy just as they have in the past. Net migration is fixed by the Census Bureau projections, rather than adjusting to the eco-
our definition, in the year 2000. These people, the Baby Boom generation, will be buying assets with the intent to sell them when they retire. The Baby Boomers will execute this buy-sell strategy at roughly the same time. Other things being equal, the Baby Boomers will be buying assets at high prices and selling assets at low prices. So, the required rate of return on physical and financial assets will be low. Preferences for current consumption notwithstanding, the Baby Boomers will pursue tirement.
this
strategy
if it
is the
only
guaranteed
source
of consumption
during
re-
187
0.696 0.761 0.869 0.974 0.995 0.893 0.796
Mid
Low
Mid
0.061 0.061 0.695 0.042 0.042 0.757 0.013 0.014 0.862 0.961 -0.012 -0.009 0.956 -0.024 -0.014 0.009 0.833 -0.009 0.016 0.033 0.733
High
r*
Low
of U.S.
Census
0.061 -0.013 0.043 -0.003 0.016 0.010 -0.007 0.023 -0.006 0.028 0.023 0.021 0.050 0.009
High
NOTES: Projections of AGE calculated from population projections unemployment based on Equations (7), (8), and (10) of the text.
0.697 0.763 0.874 0.986 1.045 0.972 0.862
1985 1990 1995 2000 2010 2020 2030
and
Low
Year
AGE
TABLE 4. Projected Steady State Values: Real Interest Rate, Output High
Bureau
(1984).
Projected
interest
0.077 0.065 0.046 0.030 0.022 0.032 0.048
Low
and Unemployment
-0.013 -0.013 -0.003 -0.004 0.010 0.009 0.021 0.020 0.023 0.019 0.013 0.006 0.001 -0.007
Mid
&*
Growth,
rate,
output
0.077 0.065 0.047 0.032 0.029 0.043 0.059
Mid
U*
growth,
0.077 0.066 0.048 0.033 0.034 0.053 0.070
High
Macroeconomic
Zmpact of the Baby Boom Generation
nomic conditions that are forecast here.28 Finally, individuals might modify their behavior if they recognize these trends. Some adjustments might amplify rather than dampen the projected swings in output, unemployment, and the real interest rate, however. For example, suppose individuals begin to defer retirement from age 65 to age 70 beginning in the year 2000. Individuals might do this if they see the return on their savings decline or if the minimum eligibility for social security increases.” Surprisingly, this reaction exaggerates the projected changes in output growth, unemployment, and interest rates. We constructed a “deferred retirement” middle AGE series by gradually increasing the retirement age from 65 to 70 during the period 2000-2030. The deferred retirement AGE series is uniformly above the original middle AGE series. This scenario amplifies the swings in the projections. Why? Because under the deferred retirement scenario both the Baby Boom generation and their children are simultaneously in their prime productivity and saving years.
5. Conclusion In summary, this analysis indicates that the age structure of the population influenced macroeconomic relations in the United States during the postwar era. Recent high real interest rates and low output growth may be partially due to the Baby Boom generation being in its prime borrowing and low labor productivity years. As the Baby Boomers age, it is reasonable to expect unemployment rates and real interest rates to be lower and output growth rates to be higher than if no demographic changes occur. The results reported in Section 3 shed light on some important issues in business cycle theory. First, age composition affects macroeconomic behavior. Several demographic variables affect unemployment, real output growth, and real interest rates in reduced
any
?he net meaningful
migration would way. Additionally,
need
to be immigrants
extremely have
large historically
to offset been
the swings predominately
in
prime age adults who save a large fraction of their income. Immigration of this group would tend to amplify the swings in the real interest rate, if not the other variables. Of all migration patterns, emigration of prime age adults would most effectively dampen the projected swings in real interest rates, output growth, and unemployment. =Beginning in 2003, the retirement age for full benefits will gradually increase to 66 in 2009 and to 67 in 2027. The actuarial reduction of benefits for early retirement at age 62 will increase from 20% to 30%.
189
Henry
M. McMillan
and Jerome B. Baesel
form estimates. This evidence supports life-cycle-human-capital models of economic activity. The evidence is inconsistent with the simple neoclassical growth model that implicitly assumes a single representative agent. Also, the Easterlin hypothesis of endogenous fertility dependent on relative income receives support. Second, age composition influences the statistical evidence on other macroeconomic theories. Omitting demographic factors from empirical models biases estimated coefficients of other included variables that are correlated with those demographic factors. The evidence presented in this paper indicates that controls for demographic shifts are necessary for the entire postwar sample period. However, controls can be replaced by time trends for shorter sample periods. Received: July 1987 Final version: July 1989
References Auerbach, Alan, and Laurence Kotlikoff. “Simulating Alternative Social Security Responses to the Demographic Transition.” NBER Working Paper No. 1308, 1984. Becker, Gary. Human Capital and the Personal Distribution of Zncome: An Analytical Approach. Ann Arbor: Institute of Public Administration, Univ. of Michigan, 1967. Berger, Mark. “The Effect of Cohort Size on Earnings Growth: A Reexamination of the Evidence.” Journal of Political Economy 93 (June 1985): 561-73. Bemheim, B. Douglas. “Dissaving after Retirement: Testing the Pure Life Cycle Hypothesis.” In Zssues in Pension Economics, edited by Z. Bodie, J. Shoven, and D. Wise. Chicago: Univ. of Chicago, NBER, 1987. Brown, David. “Age Clienteles, Demographic Shifts, and Equilibrium Security Prices. ” School of Business, Indiana University, 1985. Mimeo. Butz, William, and Michael Ward. “The Emergence of Countercyclical U.S. Fertility.” American Economic Review 69 (May 1979): 318-28. Cass, David, Masahiro Okuno, and Itzhak Zilcha. “The Role of Money in Supporting the Pareto Optimality of Competitive Equilibrium in Consumption-Loan Type Models.” Journal of Economic Theory 20 (March 1979): 41-80. 190
Macroeconomic
Zmpact of the Baby Boom Generation
Craine, Roger. “The Baby Boom, the Housing Market, and the Stock Market.” Federal Reserve Bank of San Francisco Economic Review (Spring 1983): 6-11. Denton, Frank, and Byron Spencer. “Household and Population Effects on Aggregate Consumption.” Review of Economics and Statistics 58 (February 1976): 86-95. Doescher, Tabitha, and John Turner. “Social Security Benefits and the Baby Boom Generation.” American Economic Review 78 (May 1988): 76-80. Easter&, Richard. Population, Labor Force, and Long Swings in Economic Growth. New York: Columbia University Press, 1968. -. Birth and Fortune. 2d ed. Chicago: Univ. of Chicago Press, 1987. Engle, Robert, and Clive Granger. “Co-Integration and Error Correction: Representation, Estimation, and Testing.” Econometrica 55 (March 1987): 251-76. Fair, Ray, and Kathryn Dominguez. “Effects of the Changing U.S. Age Distribution on Macroeconomic Equations.” NBER Working Paper No. 2280, 1987. Fisher, Irving. The Theory of Interest. New York: Macmillan, 1930. Flaim, Paul. “The Effect of Demographic Changes on the Nation’s Unemployment Rate.” Monthly Labor Review 102 (March 1979): 13-23. Freeman, Richard. “The Effect of Demographic Factors on AgeEarnings Profiles.” Journal of Human Resources 14 (Summer 1979): 289-318. Friedman, Milton, and Anna Schwartz. A Monetary History of the United States, 1867-1960. Princeton: Princeton Univ. Press, 1963. Fuller, Wayne. Zntroduction to Statistical Time Series. New York: John Wiley & Sons, 1976. Heien, Dale. Demographic Effects and the Multiperiod Consumption Function. Journal of Political Economy 80 (February 1972): 125-38. Levine, Phillip, and Olivia Mitchell. “The Baby Boom’s Legacy: Relative Wages in the 21st Century.” American Economic Review 78 (May 1988): 66-69. Lieberman, Charles, and Paul Wachtel. “Age Structure and Personal Saving Behavior.” In Social Security versus Private Saving, edited by George von Furstenberg. Cambridge, Mass: Ballinger, 1979. Manchester, Joyce. “The Baby Boom, Housing, and Loanable Funds.” American Economic Review 78 (May 1988): 70-75. 191
Henry
M. McMillan
Mayor, tural
Thomas, Change,
and Jerome B. Baesel
“Life-Cycle Effects, Strucin the Velocity of Money.” Journal of Money, Credit, and Banking 16 (May 1984): 175-84. McMiIlan, Henry, and Jerome Baesel. “The Role of Demographic Factors in Interest Rate Forecasting.” Managerial and Decision Economics 9 (September 1988): 187-95. Modigliani, France. “Life Cycle, Individual Thrift, and the Wealth of Nations.” American Economic Review 76 (June 1986): 297313. Modigliani, France, and Richard Brumberg. “Utility Analysis and the Consumption Function: An Interpretation of Cross-section Data.” In Post-Keynesian Economics, edited by K.E. Kurihara. New Brunswick, NJ: Rutgers University Press, 1954. ’ Nelson, Charles, and Charles Plosser. “Trends and Random Walks in Macroeconomic Time Series.” Journal of Monetary Economics 10 (September 1982): 139-62. Peek, Joe, and James Wilcox. “Monetary Policy Regimes and the Reduced Form for Interest Rates.” Journal of Money, Credit, and Banking 19 (August 1987): 273-91. Ram, Rati. “Dependency Rates and Aggregate Savings: A New International Cross-Section Study.” American Economic Review 72 (June 1982): 537-44. Russell, Louise. The Economics of the Baby Boom Generation. Washington, D. C. : Brookings, 1982. Solow, Robert. Growth Theory. Oxford: Oxford University Press, 1970. Sternlieb, George, and James Hughes. “Demographics and Housing in America. ” Population Bulletin 41 (January 1986): 3-34. U.S. Bureau of the Census. Projections of the Population of the United States by Age, Sex and Race: 1983 to 2050. Washington, D.C.: GPO, 1984. Welch, Finis. “Effects of Cohort Size on Earnings: The Baby Boom Babies’ Financial Bust.” Journal of Political Economy 87 (October 1979): S65-S98. Wilcox, James. “Why Interest Rates Were So Low in the 1970’s.” American Economic Review 73 (March 1983): 44-53.
Appendix:
and Lawrence Pearl. and Long-run Movements
Test for Unit Roots
Economists have long assumed around trend growth (a trend-stationary ser (1982) suggest that the economy 192
that the economy fluctuates process). Nelson and Ploscan be better described by a
Macroeconomic
Impact
of the Baby Boom Generation
random walk with drift. The choice between a trend-stationary and a random-walk process can be made statistically with the Augmented Dickey-Fuller (ADF) test (Engle and Granger 1987). We examine each of the four endogenous variables in this context. The null hypothesis of the ADF test is the random-walk process. The alternative to the null is either a stationary or a trendstationary process. One must specify the alternative to the null because the alternative affects the distribution of the test statistic. Economic theory suggests that the real interest rate is stationary or is a random walk without drift. That is, there should be no time trend. The ADF test requires the estimation of dr, = y,, + ylrtml + O(L)dr, + E,,
(Al)
with enough lags in B(L) to assure that E, is white noise. The crucial statistic is the “t-statistic” of yl. The statistic does not have the tdistribution under the null hypothesis. Instead, the statistic must be compared to a stricter significance requirement found in Fuller (1976, 373, Table 8.5.2). The 5% and 1% significance levels are 2.88 and 3.50 for the 150 observation sample size. Table Al presents the estimates of Equation (Al). Three lags were enough to provide white noise errors. The estimated statistic for y1 is 3.21, which rejects the null at the 5% level, but not at the 1% level.30 However, Nelson and Plosser could not reject the random walk null hypothesis with annual data. The unemployment rate should be stationary around its natural level, but the natural level may have a time trend. The ADF test compares the null hypothesis of a random walk with drift to the alternative of a trend-stationary process. Estimate du, = y. + ylu,-l
+ y2t + e(.L)du, + E,,
642)
where t is a time trend. The “t-statistic” for yi must exceed 3.44 and 4.02 to reject the null hypothesis at the 5% and 1% significance levels. Table Al shows that unemployment was trend stationary at the 1% significance level when using two lags of du,. However, the null could not be rejected when using four lags of du,.
four terly
“The sample period is 1949&1966:iu. measures of the real rate (first, second, average).
The rejection of the null occurs for all or third month of the quarter or quar-
193
-0.114 (4.32)
0.0041 (3.49)
dut
&t
d&t
(3)**
(4.a)**
(4. b)*
0.494 (6.24) -0.312 (3.57)
0.0010 (1.77) -
-0.017 (1.36)
-0.168 (2.90)
0.466 (5.99)
-0.025 (0.26)
0.0011 (2.78)
0.344 (4.26)
-0.374 (3.89)
dvml
0.0055 (3.25)
-
t
Test
-0.181 (2.18)
0.115 (1.35)
0.150 (1.83)
0.151 (1.87)
0.187 (2.31)
-0.218 (2.45)
dv-,
0.105 (1.39)
0.282 (3.48)
-
-0.110 (1.42)
-
-
0.253
0.608
0.299
0.324
0.197
-
0.301
R2
-
dv-,
-
-
0.089 (1.19)
dv-,
NOTES: Numbers in parentheses are t-statistics. The sample period is 1949:i-1986:io. of real per capita GNA; ut = civilian r, = ex post real interest rate; y, = logarithm unemployment rate; p, = logarithm price index; and t = a time trend. dy, = the first difference, and ddy, = the second difference of yr. and so on. *5% and 1% significance levels are 2.88 and 3.30. **5% and 1% significance levels are 3.44 and 4.02. Q(x) is the Box-Pierce Q-statistic for autocorrelation with six lags with r degrees of freedom (dof). Critical values for the = 5.991, Q(3) = 7.815, and Q(4) = 9.837.
0.0070 (2.33)
0.0526 (1.43)
-0.626 (6.24)
0.0116 (3.02)
d&t
(2. b)*
-0.309 (3.37)
0.529 (3.43)
4/t
-0.236 (3.21)
(2.a)**
V-l
c
Dickey-Fuller
0.0021 (1.02)
dv
Augmented
drt
Al.
(I)*
TABLE
are
5% level
Q(2)
consumer
3
2
4
3
4
3
dof
of the
1.209
1.289
9.315
2.633
2.641
1.585
Q
Macroeconomic
Zmpact of the Baby Boom Generation
Output per capita is either a random walk with drift or a trendstationary process. The null hypothesis is not rejected at the 5% level. Furthermore, Nelson and Plosser did not reject the null. The growth rate of output per capita is stationary as indicated by Equation (Lb). Finally, the evidence also indicates that the price level is random walk with a drift, and that the inflation rate is stationary. See Equations (4.a) and (4.b).
195
Securities
and
Exchange
Commission
Washington,
D.C.
JEROME B. BAESEL Edward
0.
Thorp
Newport
and Beach,
Associates California
The Macroeconomic Impact of the Baby Boom Generation* This paper analyzes the impact of the Baby Boom generation on macroeconomic relationships in the United States. Using quarterly postwar data, it finds that measures of population age composition influenced real interest rates, income, inflation, and unemployment. The demographic variables complement or dominate other economic variables in reduced-form macroeconomic specifications. The paper also projects how the aging of the generation may influence future macroeconomic activity.
Economic theory predicts that an individual’s age influences many aspects of economic behavior. For example, the life cycle hypothesis of consumption implies that individuals smooth consumption over their lifetime. They borrow when young, save in middle age, and dissave after retirement. Similarly, age affects decisions on labor force participation, education expenditure, and housing purchases. Aggregate behavior is the composite of individual behavior. So, if age influences individual behavior, the age composition of an economy’s population could influence macroeconomic relationships. This need not be true however. For example, suppose there is an increase in the number of middle-aged people in the economy. Middle-aged individuals save a larger fraction of their income, so the national saving rate should increase. But the increase in middleaged workers could also reduce their relative wages. Their wages could fall enough to cause their share of national income to decrease. If so, the aggregate saving rate need not rise and, para-
*We are grateful to Lance Brannman, Robert Connolly, David Lilien and anonymous referees for comments on earlier drafts. We are responsible for any remaining errors. The Securities and Exchange Commission, as a matter of policy, disclaims responsibility for any private publication by any of its employees. The views expressed here are those of the authors and do not necessarily reflect the views of the Commission or McMillan’s colleagues on the Staff of the Commission.
of Macroeconomics, Spring 1999, Vol. Journul Copyright 0 1999 by Louisiana State University OR%-0764/99/$1.56
12, No. Press
2, pp.
167-195
167
Henry
M. McMillan
and Jerome B. Baesel
doxically, could fall. Th ese equilibrating reactions, age-specific effects, can offset age-composition effects.’ The age composition of the United States population offers an opportunity to evaluate these issues empirically. The U.S. age composition is unusual, relative to historical standards, due to the Baby Boom that occurred after 1945. Dramatic increases in the United States birth rate from 1946 to 1964 interrupted the long-term trend toward smaller families. After 1964, American birth rates fell below their previous long-term trend rates. These variations in birth rates caused a population bubble, the Baby Boom generation. The effect of the Baby Boom generation on specific markets is well documented.2 Researchers have examined the Baby Boom’s effect on education3 housing,4 labor,5 and social security.6 Less attention has been paid to the Baby Boom’s effect on real interest rates, output growth, and other macroeconomic variables.7 In this paper we systematically evaluate the macroeconomic effects of the Baby Boom generation. We augment reduced-form macroeconomic models with different demographic measures of the We find that a life-cycle-human-capital demoU.S. population. graphic measure helps to explain output growth, unemployment, and the real interest rate. In fact, this demographic measure complements or dominates other economic factors often discussed in the literature. The paper contributes to the literature in two ways. First, it provides empirical support for economic theories in which age is an important factor. In particular, the evidence is consistent with Modigliani’s l&e-cycle hypothesis of saving. Second, the paper shows that demographic variables can aflect the results of tests involving nondemographic economic hypotheses. For example, demographic variables affect the inferences drawn from tests on the neutrality of money.
‘Easterlin (1987) provides a lucid explanation of these age-specific effects and how they depend on generation size. He argues that they are especially important with respect to labor force participation, family formation, and consumption patterns. ‘See Russell (1982) for a summary of this research. ‘Russell (1982, Ch. 3). %raine (1983). Sternlieb and Hughes (1986), Manchester (1988). ‘Berger (1985), Welch (1979), Freeman (1979), Levine and Mitchell (1988). 6Doescher and Turner (1988) and Auerbach and Kotlikoff (1984). ‘Brown (1985), McMillan and Baesel (1988), and Fair and Dominguez (1987) are exceptions.
168
Macroeconomic
Impact
of the Baby Boom Generation
We find demographic effects on interest rates and output growth where other researchers have not. There are at least three reasons for this. First, previous research often used sample periods in which there was little or no variation in the demographic data.’ Second, the demographic measure used here may more closely approximate the theoretical ideal than do dependency ratios or population growth rates used in other studies.’ Third, our empirical specification is motivated by recent research on unit roots and cointegration (Nelson and Plosser 1982; Engle and Granger 1987). The specification links the short-run adjustment process to long-run equilibrium relationships more naturally than do standard time series specifications. Furthermore, it easily distinguishes short-term from long-term effects. The paper is organized as follows. Section 1 discusses how age distribution influences economic activity and describes the empirical method. Section 2 describes the data. Section 3 presents the estimates and analyzes the robustness to specification. Section 4 presents the results of a forecasting exercise using Census Bureau projections of future age distributions. Section 5 summarizes the findings and concludes the paper.
1. Age Distribution and Economic Activity Economic theory suggests that demographic factors can affect output, inflation, unemployment, and real interest rates. We briefly review the theoretical arguments here. An economy’s productivity and thrift determine its real interest rate (Fisher 1930). First, in this context thrift is the propensity to save from current income. According to the life-cycle hypothesis of consumption (Modigliani and Brumberg 1954), this propensity depends on an individual’s age.” The age composition of an econ-
*Fair and age distribution distribution.
Dominguez (1987) also make this have recently exhibited more
point. variation
They note that than measures
measures of of income
‘Heien (1972) uses the median age. Denton and Spencer (1976) use the average age of children. Lieberman and Wachtel (1979) use fractions of the population in several adult age brackets. Ram (1982) uses the ratio of total population to adult population. “‘See Modigliani (1986) for a summary of research on the life-cycle hypothesis. Survey and microeconomic evidence indicates that saving behavior depends on age. The evidence also indicates that the elderly continue to save after retirement, in contrast to the predictions of the life-cycle hypothesis. However, the arguments
169
Henry
M. McMillan
and Jerome B. Baesel
omy’s population can therefore influence the economy’s thrift. Second, the productivity of labor depends on capital stock per labor unit, the quality of labor, and technology. In neoclassical growth theory (Solow 1970), the population growth rate affects the steadystate capital-labor ratio. In human capital models (Becker 1967), a worker’s quality improves as the worker ages due to his investment in human capital. The population growth rate and the age composition of the labor force therefore affect productivity. Unless their respective influences on productivity and thrift are exactly offsetting, a population’s age composition and its growth rate affect the real interest rate. In neoclassical growth theory, output per capita is a function of the capital stock and technology. The capital stock depends on the rate of time preference, the rate of technological innovation, and the population growth rate. The rate of time preference reflects the same factors as thrift in Fisherian models, and so it too depends on age composition. Therefore, output per capita depends on the age composition and population growth rate. and hire rates determine the unParticipation, separation, employment rate. These rates are different for young and old workers in the United States (Flaim 1979). The national unemployment rate is the weighted average of unemployment rates of young and old workers. The age composition of the labor force therefore affects the unemployment rate. Inflation is a function of money growth, output growth, and the transactions technology. While the transactions technology may be independent of demographics, age composition can atfect money demand. An individual’s age influences his risk aversion, financial wealth, and permanent income. These variables, in turn, influence the portfolio choice between money and bonds. Consequently, age composition can influence the velocity of money.‘l We have already discussed how demographic factors affect output growth. In combination, demographic factors are likely to alfect inflation, too. We can summarize the predictions of the primary models as follows: The life-cycle-human-capital model predicts that the higher
(Note cont. from p. 169) presented in this paper only require that the saving rates of the elderly be less than those of middle-aged individuals. The evidence strongly supports this requirement. Bernheim (1987) provides an excellent survey and discussion of this issue. “Mayor and Pearl (1984) and Fair and Dominguez (1987) present evidence on this point.
170
Macroeconomic
Impact
of the Baby Boom Generation
the fraction of middle-aged adults in a population, the lower the real interest rate, the higher the growth rate of per capita output, and the lower the unemployment rate; if the velocity of money is higher, then inflation should be higher, too. Neoclassical growth theory predicts that a higher exogenous population growth rate will raise the real interest rate and lower the growth rate of per capita output; it makes no prediction about inflation or unemployment. In a neoclassical growth model with an endogenous population growth rate, a lower population growth rate occurs when exogenous output growth or real interest rates are high because the opportunity cost of children is higher. Finally, the Easterlin hypothesis predicts that the endogenous population growth rate depends on relative economic status; higher population growth rates would be associated with higher rates of per capita output and with a higher fraction of middle-aged adults in the population. It is difficult to uncover these long-term influences empirically because short-term influences are always present. In the remainder of this section we develop an empirical specification that is capable of distinguishing short-term from long-term effects. Let dy, be the change in an endogenous variable, yt, during quarter t. For example, yt might be the logarithm of real output per capita, and dy, would be the growth rate in per capita output. Let dq be a vector of exogenous variables, such as demand or supply shocks, that affect the economy’s short-term equilibrium. Let w, be a vector of exogenous variables that affect the economy’s longterm equilibrium. These variables might include technology, preferences, and demographic factors. Economic theory often suggests that a macroeconomic variable is stationary or trend-stationary. If the variable is above or below its trend, it tends to grow more slowly or more quickly to return to its trend. An error correction mechanism is an effective way to model this process (Engle and Granger 1987). Let the change in y be a function of (1) the lagged deviation of y from its trend ( y *), (2) exogenous shocks, (3) other dynamic adjustment characteristics, and (4) white noise error:
dyt = Y(yt-1-
Y $1) + %Wyt
+ P’dxt
+ Et .
(1)
In (l), y is the speed of adjustment of the variable y to its longrun trend; we expect -1 < y < 0. The polynomial 8(L) includes enough lagged coefficients to assure that E, is white noise. The vector p determines the initial effect of changes in the exogenous vari171
Henry
M. McMillan
and Jerome
B. Baesel
ables on yt; these effects are by definition temporary. Any permanent or steady-state effects are built into y *, which has the form Yt* = cYrwt .
(2)
The vector w, slowly changes through time and therefore slowly atlects the steady state. It is efficient to estimate all coefficients, o, l3, O(L), and y, simultaneously, as in dy, = y( ytel - a’~,-1)
+ B(L)dy, + P’dx, + E, .
(3)
Alternatively, a macroeconomic variable may be a random walk with drift (Nelson and Plosser 1982). The variable has a trend growth rate, but not a trend level. This specification is dyt = /.L: + e(L)dy, + p’dx, + l t ,
(4)
* = atwt. CLt
(5)
where
Demographic factors could affect the drift term, l~$, and so affect long-term growth rates. Combining (4) and (5), we obtain dyt = cx’wt + e(L)dy, + p’dx, + q .
(6)
The trend-stationary and random walk specifications appear similar, but have very different economic interpretations. Consider a macroeconomic variable, say per capita output. The trend-stationary specification implies that output ultimately returns to its trend level. The associated adjustment process has a traditional business cycle interpretation. In the random walk specification, output returns to its trend growth rate, but not to a trend level. There is no tendency for the economy to make up lost ground. Good times, in the sense of positive shocks E,, permanently raise output in the random walk specification (6). In contrast, good times temporarily raise output in the trend-stationary specification (3) because they do not affect the trend level.”
“Of rates
172
course, through
conditional mean growth rates the polynomial B(L). However,
in (6) can depend on previous growth this influence also exists in (3).
Macroeconomic
2. Data and Variable
Zmpact of the Baby Boom Generation
Definitions
We estimate Equations (3) and (6) for real interest rates, output, inflation, and unemployment using quarterly data for the postWorld War II era (1949:i-1986:iu). The data sources are Citibank Economic Database and Bureau of Census publications. All quarterly data are from national income and product accounts. Let yr be the logarithm of real per capita GNP. Let x, be the logarithm of real per capita exogenous expenditures, which equals total government expenditures and exports. Let ss, (accumulated supply shocks) be the logarithm of the import price deflator divided by the GNP deflator.13 Growth rates for these variables are annualized diiIerences from the previous quarter (for example, dyt = 4[ Yt - Yt-11). Monthly data have been converted to quarterly data by using the last month of the quarter as the quarterly value. Let pt be the logarithm of the revised consumer price index. Inflation is the annualized change in p, from the previous quarter (dp, = 4[p, - p,-J). Let the nominal interest rate i, be the 90-day treasury bill rate.14 The realized real interest rate r, is the difference between the nominal rate and the inflation rate in the next quarter (rt = i, - dp,,,). Let m, be the logarithm of the nominal Ml money supply per capita, and let dm, be the annualized money growth rate during the rate, and let du, be quarter. l5 Let U, be the civilian unemployment the change in the unemployment rate during the quarter. Several demographic variables have been constructed from annual population data. All annual data have been converted to quarterly figures with straight line interpolation. Let AGE = Pop(35-64)/Pop(15-34, DPOP = dPop/dt
65+) ,
,
and
13This measure of the supply shock is common; see Wilcox (1983) and Peek and Wilcox (1987). 14The 90-day treasury bill rate avoids problems with capital gains taxes, holding period yields, and long-term inflationary expectations. In another paper (McMillan and Baesel 1988) we find that the choice of interest rate makes no qualitative difference. 15For years before 1959, money supply figures are from Friedman and Schwartz (1963). All money supply figures are seasonally adjusted.
173
Henry
M. McMillan
and Jerome B. Baesel
DPOP16 = dPop(le+)/dt
.
The variable AGE is the ratio of middle-aged adults to young and old adults; it excludes children. The variables DPOP and DPOP16 are, respectively, the population growth rate and the adult population growth rate. The variable AGE distinguishes between savers and borrowers in common life-cycle models. Its numerator is the number of individuals in common saving age brackets, and its denominator is the number of individuals in borrowing (or dissaving) age brackets.16 This ratio also provides information about the relative fraction of high productivity workers in the economy. The variable AGE is therefore well suited to test the predictions of the life-cycle-human-capital model. It is similar to dependency ratios that compare the total population to the potential workforce (for example, see Ram 1982). Commonly used dependency ratios ignore differences among adults that are important elements of the life-cycle-humancapital model. ” Neoclassical growth theory suggests that population growth rates aifect the steady state. The adult population growth rate (DPOP16) may be closer to the intent of the theory than the total population growth rate (DPOP). These population growth rates were smoothed over four quarters to eliminate seasonal patterns in the original data. is Table 1 presents summary statistics for the demographic variables. They are highly collinear; correlation coefficients are above 0.9 for all pairs. Figure 1 plots the demographic variables. The dependency ratios and AGE are waves of low frequency and different periods. Linear or quadratic time trends can approximate them during short time intervals. Higher order trends are needed for the full sample period. The population growth rates fluctuate much more
l6The variable AGE may be better described as the ratio of individuals in high saving rate age brackets to the individuals in low-saving rate age brackets. Young adults tend to be borrowers; retired adults tend to be dissavers. We shall use the term borrowers for brevity if no ambiguity results. “We considered two dependency ratios (total population to adult population and total population to working age population) in earlier versions of the paper. Neither dependency ratio worked as well as the variable AGE described here. The empirical results are not reported here and are available on request from the authors. “We also considered labor force participation rates and the growth rate of the labor force. The labor force variables performed poorly, perhaps because labor force participation is endogenous and highly procyclical. Estimates are available upon request from the authors.
174
Macroeconomic TABLE
1.
Zmpact of the Baby Boom Generation
Demographic
Variables
Series
Mean
Standard Deviation
Maximum
AGE DPOP DPOP16
0.816 0.013 0.015
0.107 0.003 0.003
0.944 0.020 0.019
NOTES:
The
sample period population = Pop(35-64)/[Pop(l5-34)
Pop = total AGE
DPOP POP16
Summary
Statistics Minimum 0.659 0.009 0.009
is 1948:iu-1986:iii. of the United States, + P&55+)],
= dPop/dt, = dPop(l6+)/dt.
than AGE. The blip in the total population growth rate in 1959 and 1960 is due to the statehood for Alaska and Hawaii. We use dummy variables to account for this fact in the estimates.
3. Empirical Analysis Demographic Factors Table 2 presents estimates of the reduced-form equations, (3) and (6). The dependent variables are the real interest rate in Panel A, output growth in Panel B, inflation in Panel C, and unemployment in Panel D. The basic trend-stationary or random-walk specification is developed in the Appendix. Short-term exogenous shocks and demographic variables supplement this specification. lQ The estimates without demographic variables are largely consistent with traditional macroeconomic theory. Real interest rates increase with fiscal shocks and decrease with monetary shocks, as implied by Keynesian macrotheory (see estimate 2A.l). Output increases with fiscal and monetary shocks (estimate 2B.l). Inflation
19We first determined whether an endogenous variable followed a trend-stationary or a random-walk process. We used the augmented Dickey-Fuller test to do this. Details of this procedure are in the Appendix. We find that the real interest rate is stationary, the unemployment rate is trend-stationary, and the inflation and output growth rates are random walks. Money, government spending, exports, and import prices are assumed to be exogenous. Lagged output growth is included in the inflation and unemployment equations, but excluded from the interest rate equation. Its insignificance in the interest rate equation may be due to financial market efficiency. If the financial market knows dy,-, at time t - 1, then the efficient markets hypothesis implies that dy,-, has no additional effect on i, beyond that in i,-,.
175
Henry
M. McMillan
and Jerome B. Baesel
Dependency
LEMOGRAPHK; Ratios and
MEASURES Population Growth
Rates fO.025 0.025 DPOP16
+ 0.020
,-d-----__
0.6
0.6 0.6 1+ , 1950
I 1955
I 1960
1 1965
I 1970
AGE = Po~t35-64/CPod15-34) DPOP DPGP16
I 1975
I 1985
I
+ Pot1(65+)1
=Growth
Rate
of Total
=Growth
Rate
of AC&H Poputation
Figure
1 1980
Populetion
1
increases with supply shocks and monetary growth but decreases with exogenous spending, perhaps due to countercyclical fiscal policy (estimate 2C. 1). Finally, unemployment decreases with lagged output growth per Okun’s law (estimate 2D.l). The explanatory power of each equation is good, especially given that the dependent variables are differences rather than levels. Also, the various lags of the dependent variables produce white noise error terms; for brevity, diagnostic statistics are suppressed. The remaining equations each include one demographic variable to explain long-run trends.” There is clear support for de-
20All demographic variables are assumed to be exogenous or predetermined. A demographic variable could be endogenous if economic activity contemporaneously affects migration, birth, or mortality rates. Migration was limited during the sample period, and its effect on these demographic variables should be small. Mortality rates in the U.S. are insensitive to economic activity. Birth rates may be endogenous, however (Easterlin 1968; Butz and Ward 1979). Birth rates have no effect
176
Macroeconomic
Zmpact of the Baby Boom Generation
mographic trends in the data. The life-cycle-human-capital variable fits the best across all equations. It is correctly signed and significant in all equations, minimally affects other estimated coefficients, and improves the overall performance of the model. In particular, the time trend in the unemployment equation is insignificant if the estimate includes AGE, but is highly significant if it does not. In contrast, the adult population growth rate (DPOP16) is correctly signed but insignificant in the real interest rate and output growth equations. The total population growth rate (DPOP) significantly increases output and decreases interest rates and inflation. These effects of DPOP are opposite the predictions of neoclassical growth theory. The relation of DPOP to output growth is consistent with Easterlin’s hypothesis of endogenous population growth.‘l To determine the long-run equilibrium relationships, we set the lagged dependent variables equal to zero for trend-stationary variables (dr and du) and equal to the current dependent variable for random-walk variables (dy and dp). We also set exogenous spending growth equal to output growth (dx = dy ) to achieve balanced growth. Then we solved the resulting equation for the steady state, given the coefficient estimates. Using the estimates when AGE is the demographic variable, the steady-state values are=
AGE
on AGE or contemporaneous DPOP16. Changes in the birth rate largely determine changes in the population growth rate, however. So DPOP is endogenous if birth rates are endogenous. While we maintain the hypothesis of birth rate exogeneity throughout this paper, we note when the evidence suggests endogeneity. 2’Seemingly unrelated regression (SUR) estimates differ only slightly from the OLS estimates reported here. Table 2 assumes stationarity for the real interest rate and trend-stationarity for the unemployment rate. As discussed in the Appendix, there is some reason to believe that these time series are random walks instead. We estimated randomwalk specifications for the real interest rate and the unemployment rate with and without the demographic variables. The results are virtually the same as in Table 2 and are omitted. The variable AGE remains significant and continues to provide the best fit of the demographic variables. We also examined other conversions of monthly data to quarterly data. The results are essentially the same using either the second month of the quarter or the quarterly average figures. Roughly speaking, demographic effects are larger, and the overall performance of the model is better for the third-month specification. The model performs poorly with the first month of the quarter data. %For example, to determine the real interest rate from estimate (2A.2), set dr = dr-, = dr-* = 0, and dx = dy*. Then solve for r*. Simplification yields (7). The same procedure applies to the unemployment rate. For inflation and output growth, current and lagged rates of the dependent variable are set equal to each other. Note that dy-, = dy* in the inflation and unemployment equations.
177
2.
Reduced
Form
In(AGE)
DPOP
DPOPIG
(2A.2)
(2‘4.3)
(2A. 4)
-
ln(ACE)
DPOP
DPOPIG
(2B.l)
(2B.2)
(2B.3)
(2B.4)
name
-
-0.462 (04
(2.W
2.618
0.0802 (2.72)
-
coef.
Variable
0.611 (0.92)
-1.846 (2.48)
dy
0.078 (3.24) 0.076 (3.12)
-0.005 (1.45)
0.029
0.142 (3.10) 0.154 (3.33)
0.012 (0.76)
0.139 (3.11)
0.152 (3.36)
dx
(2.90)
-0.031 (1.62)
0.019 (2.93)
0.006 (1.W
c
-0.007 (0.67)
0.074
0.067 (2.76)
0.002 (0.91)
w54)
dx
c
Estimates
dr
coef.
-0.0511 (2.92)
c&??nL-,
Panel B: Dependent
-
(2A.l)
name
Panel A: Dependent Variable denKm,
TABLE
0.035 (0.97)
0.292 (3.24) 0.027 (0.71)
0.037 (1.W
0.340 (3.81)
0.218 (2.83)
0.022 (0.62)
0.191
ass
-0.059 (2.37)
-0.066 (2.71)
-0.065 (2.74)
-0.053 (2.22)
oh
@.fw
dm
-0.080 (1.61)
-0.146 (2.67)
(2.96)
-0.162
-0.065 (1.46)
dm
-
-
4-l
-
-
-
4-l
-
-
-
-
time
-
-
-
-
time
v-1
-0.174 (1.84)
-0.216 (2.46)
-0.207 (2.42)
-0.m (2.30)
0-1
-0.300 (3.48) -0.280 (3.22)
-0.466 (4.71) -0.446 (4.44)
0.091 (1.15) 0.089 (1.10)
0.235 (2.91)
0.230
C-7)
0.082 (1.W
0.235
0.094 (1.17)
dvmo
(2.99)
0.233 (2.91)
do-,
-0.289 (3.21)
-0.273 (3.11)
-0.433 (4.30)
-0.458 (4.35)
doe.p
do-,
-
-
do-,
0.025 (0.W
0.028 (0.38)
0.011 (0.15)
0.035 (0.46)
do-,
-0.253 (3.25)
-0.234 (3.07)
-0.249 (3.30)
-0.242 (3.13)
do-,
-
-
-
-
doe,
0.251
0.273
0.286
0.255
8%
0.341
0.365
0.378
0.346
FP
Reduced
DPOPIG
(2C.4)
DPOP
DPOPIG
(2D.3)
(2D.4)
0.006
-0.0646 F-5)
(0.48)
-0.1219
(2.W
-0.0114
-
coef.
Variable
0.005 (2.40)
(3.81) 0.002 (0.35)
0.004
0.003
(0.W 0.002 (0.42) 0.002 (0.W 0.002 (0.W
0.004
(0.02)
0.001
-0.015 (0.W 0.009 (0.W 0.002 (0.07)
(cont’d)
(3.29)
0.001
(0.38) 0.039 (2.55) -0.014 (1.42)
(2.88) -2.015 (2.22) 1.614 (2.22)
(1.77)
-0.0749
du
dp
Estimates
(4.26) -0.039 (4.40) -0.037 (4.07) -0.039 (4.26)
-0.038
-0.014 (0.31)
-0.066 (1.22)
-0.010 (1.74)
0.003 v-w
(1.13) -0.005 (1.46) -0.003 (1.W -0.003 (0.85)
-0.004
0.061 (2.39)
(2.94)
0.072
0.074 (2.W 0.076 (3.13)
-0.038 (3.82) -0.038 (3.90) -0.036 (3.51) -0.037 (3.62)
0.102 (2.13)
0.102 (2.12)
0.126 (2.67) 0.092 (1.95)
(3.96) -0.105 (4.05)
-0.111
(4.54)
-0.111
-0.102 (4.17)
-
-
-
-
0.00021 (3.98)
(2.~)
0.00023
(1.W
0.00008
(4.40)
o.ooo19
-
-
-
-
0.256 (2.73)
(2.73)
0.256
e-33)
0.240
0.252 (2.74)
0.382 (4.47) 0.329 (3.87) 0.344 (3.99) 0.355 (4.15) 0.110
0.097 w-3) 0.087 (1.08)
(1.01)
0.084 (1.08) 0.077
0.072 (0.88) 0.088 (1.08) 0.092 (1.13)
(1.W
-
-
-
-
(::g 0.316 (3.94) 0.313 (3.90)
0.343 (4.29)
-
-
-
-0.067 (0.80) -0.029 (0.38) -0.031 (0.41)
(0.27)
-0.021
0.416
0.419
0.435
0.422
0.642
0.642
0.652
0.634
NOTES: The sample period is 1949:i-1986:io. t-statistics are in parentheses. In the table, do is the dependent variable, do-l. is the dependent variable lagged k quarters, and o_, is the lagged level of the dependent variable. The dependent variables are tbe following: dr = the change in the ex post real tresury bill rate, dy =, the growth rate of the real GNP per capita, du = the change in the civilian unemployment rate, and dp = the CPI inflation rate. The demographic variables (demo) are defined as follows: AGE = POP(35-64)/[Pop(lS-34) + Pop(65+)], DPOP = dPop/dt, POP16 =dPop(l6+)/dt. The other exogenous variables are the following: dx = the growth rate of exogenous spending, which equals government purchases and exports; dm = the growth rate of the Ml money supply, I&S = the growth rate of the import price deflator minus the growth rate of the GNP deflator, and time = a time trend. Dummy variables for 1960 are included with DPOP and DPOP16; the estimated coefficients of the dummy variables are insignificant and are omitted from the table. All growth rates are annualized.
In(AGE)
-
(2D.2)
(2D.l)
name
h-1
D: Dependent
DPOP
(2C.3)
Panel
In(AGE)
-
(2C.2)
(2C.l)
name
Form
Variable
demo-1
Panel C: Dependent
TABLE 2.
Henry
M. McMillan r* = -0.015
and Jerome B. Baesel - 0.209 ln(AGE)
- 0.621dm
- 0.295&s,
(7)
dy * = 0.024 + 0.101 ln(AGE)
+ 0.429dm
+ O.O47dss ,
(8)
dp* = 0.009 - 0.171 ln(AGE)
+ 0.088dm
+ 0.215d.ss,
(9)
u* = 0.028 - 0.135 ln(AGE) + 0.0007t
- 0.491dm
- 0.06ldss
.
(10)
Figure 2 plots the equilibrium values for the postwar sample period, assuming dm = dss = 0. The figure shows that AGE had a quantitatively large effect on output growth, real interest rates, and unemployment during the sample period. Monetary shocks have larger effects on real variables than on inflation in the long-run equilibrium. This occurs because the model estimates only the shortrun effects of monetary policy. The next section presents model estimates that can better account for long-term effects of monetary and fiscal policy. Other Economic Factors The evidence indicates that the age composition of the U.S. population affected macroeconomic relationships during the postwar era. However, this conclusion is unwarranted if the demographic variables are proxies for other omitted economic factors. To examine this issue, we introduce four economic factors, suggested by the literature, that might affect the long-run equilibrium. The longrun factors are the ratio of exogenous spending to output (Z), the terms of trade (SS), the average growth rate of money (AVEMGR), and the standard deviation of inflation (STDZNF). We briefly review the motivation for each variable. In the steady state, higher levels of government spending relative to potential output increase real interest rates via the crowding-out effect. More government spending decreases output growth and increases inflation if the government sector is less productive than the private sector. The effect on unemployment is ambiguous. To investigate this issue we define Z, = exp(x, - yt) to be the ratio of exogenous spending to output. The higher the terms of trade, the more competitive are U.S.produced goods in world markets and the less competitive are foreign-produced goods in the U.S. Higher terms of trade decrease unemployment and increase output, but have ambiguous effects on 180
Macroeconomic
Zmpact of the Baby Boom Generation
IMPLIED LONG-RUN EOULMUM Rate. Per Capita. Output Growth,
Real Interest
and Unemployment
0.125
0.100
Unempbyment /
Rate / / / /
/-
_/--.--___
0.075
0.050
0.025
0.000 Output -0.025
I
I
I
1950
1955
1
1960
Growth
d;;;;--.--
______
I
I
I
1965
1970
1975
Figure
-__---
1
1990
___---I
1985
2.
inflation and the real interest rate. We measure the terms of trade with the ratio of import prices to the GNP deflator, SS, = exp(ss,). Neutrality propositions from monetary theory imply that the average growth rate of money should affect only the average inflation rate. Money growth should not affect steady-state real output growth, real interest rates, or unemployment. We use AVEMGR, the average monetary growth rate in the previous eight quarters, as the long-run monetary growth rate. This variable should influence only the long-run inflation rate. The current monetary growth rate (dm,) should capture any short-run effects of money on real economic variables. The rational expectations hypothesis implies that the average rate of inflation has no effect on real economic variables. However, the volatility of inflation may affect these real variables by increasing the likelihood of forecast errors. Greater uncertainty about inflation would increase the expected rate of return required by savers, which, in turn, would reduce the desired capital stock and output growth rate. Similarly, the steady-state unemployment rate would increase if firms were less willing to hire workers in an uncertain 181
Henry
M. McMillan
and Jerome B. Baesel
inflationary environment. We use the standard deviation of inflation (STDZNF) in the previous eight quarters to test this issue. We estimated Equations (3) and (6) with AGE and these four long-run economic variables. Table 3 summarizes the results. The estimated coefficients for the short-run adjustment variables are very similar to those in Table 2 and so are not presented in Table 3. The first equation in each panel includes all long-run factors. Collinearity among these variables reduces significance levels of reported coefficients. Subsequent equations in each panel restrict the set of long-run variables to those variable combinations that provide significant coefficient estimates.= The variable AGE is significant in the restricted estimates for all dependent variables. Its coefficient estimates are roughly the same as their respective values in Table 2. The variables AGE, AVEMGR, and TZME are significant in the unemployment equation. The fiscal pressure variable Z and the variable AGE are significant in the interest rate, output growth, and inflation estimates. However, AGE is significant in the inflation estimate only if it replaces STDZNF and AVEMGR. Given the strong theoretical arguments that inflation is primarily a monetary phenomenon, the estimate with AVEMGR and STDZNF may be preferred. Theoretical arguments and the empirical evidence support the conclusion that AGE is a significant determinant of the three real variables.24 To what extent is AGE merely a proxy for a nonlinear time trend in the data? A third-order polynomial in time very closely
=The real interest rate, output growth rate, and inflation equations include the fiscal pressure variable Z. It has the expected sign in the real interest and output equations, but has the wrong sign in the inflation equation. The money growth variable AVEMGR affects the inflation rate, but not the real interest rate or output, as predicted. Thus, money is neutral in the long-run for these variables. However, AVEMGR reduces unemployment, suggesting that it may also be picking up lagged short-run effects of expansionary monetary policy. The terms-of-trade variable SS is never significant. The volatility of inflation STDINF is significant only when combined with AVEMGR in the inflation equation. =The long-run equilibrium estimates are r*
= 0.921
- 0.228
ln(AGE)
+ 0.781
In(Z)
- 0.794dm
- 0.247d.ss,
dy * = 0.152
+ 0.088
ln(AGE)
- 0.147
In(Z)
+ 0.378dm
+ 0.088dss
dp*
+ 0.013
ln(AGE)
- 0.830
In(Z)
= 0.944
+ 1.356AVEMGR
182
- 1.309STDINF
- 0.459dm
+ 0.222dss,
,
Macroeconomic
Zmpact of the Baby Boom Generation
approximates AGE during this sample period.% Estimates similar to those in Table 2 would obtain if time, time squared, and time cubed jointly replaced AGE. Thus, one could say there is a nonlinear time trend in the data during this sample period, and AGE merely proxies this trend. But what would cause the nonlinear trend to be there in the first place? Demographic changes can explain the existence of a nonlinear time trend. The pertinent demographic changes can be parsimoniously modeled with the variable AGE. Other economic factors could explain this nonlinear trend, too. In this respect, Table 3 presents evidence on some plausible variables. Even when the estimates include other plausible economic factors, AGE is a significant explanatory variable of interest rates, output, and unemployment. Note that extrapolating the time trend beyond the sample period soon yields absurd values. Extrapolating the demographic trends does not, as we shall show in the next section.
4. Future Projections Demographic changes can be useful for intermediate and longterm forecasting. The aging of the Baby Boom generation is predictable relative to most economic time series. This provides valuable information for forecasting interest rates, output, and unemployment. Such forecasts would presumably be more sensible than those obtained from extrapolation of time trends, at least in the longer term.
and u* = 0.059
- 0.128
- 0.532AVEMGR
ln(AGE)
+ 0.028
+ 0.0015TIME
In(Z) - 0.264dm
- 0.03ld.w.
These equations are based on the restricted estimates of Table 3. Note that the coefficients for AGE are quite similar to their respective values in (7), (8), and (10). Note too that if dm = AVEMGR, then a 10% money growth rate implies a 9% inflation rate. Similar results obtain if unexpected money growth (udm = dm - AVEMGR-1) replaces dm. Then unexpected money growth is not part of the long-run equilibrium, but AVEMGR is significant in the real interest rate equation. =A regression of AGE on time, time-squared, and time-cubed has an RZ of 0.98. Because AGE and a third-order time trend are highly collinear, their estimated coefficients are insignificant if jointly included in one regression equation.
Alter-native
-0.0559 (3.45)
(3a. 2)
0.0753 (2-W
(3b.2)
(3c. 1)
0.0218 (0.49)
Panel C: Dependent Variable ln(AGE)
0.0581 (0.88)
(3b. 1)
Panel B: Dependent Variable ln(AGE)
-0.0723 (2.14)
(3a. 1)
dp
dy
dr
Economic
Panel A: Dependent Variable ln(AGE)
TABLE 3.
-0.201 (4.04)
in(Z) 0.025 (1.20)
ln(SS)
-
-0.029 (0.79)
-0.118 (1.49) -0.126 (2.05)
ln(SS)
-
0.173 (4.85) in(Z)
0.0117 (0.58)
ln( SS)
Estimated
0.185 (4.24)
in(z)
Trend Variables,
0.372 (2.32)
AVEMGR
-
-0.012 (0.04)
AVEMGR
-
-0.125 (0.86)
AVEMGR
Co&kients
R-2 0.690
-0.464 (2.25)
0.305
0.294
R-2
0.471
0.465
R-2
STDlNF
-
0.121 (0.34)
STDlNF
-
-0.117 (0.60)
STDINF
-0.0193 (3.02)
(3d.4)
where w, is a vector and dzt are short-term
-
0.002 (0.30)
+ -p-l
do, = u’w,
+ p’dz,
+ qL)du,
-0.092 (2.99)
-0.120 (3.52)
-0.056 (1.93)
-0.065 (2.08)
AVEMGR
in parentheses.
are
t-statistics
-
0.003 (0.92)
-
-0.002 (0.43)
ln(SS)
-
-
+ E, ,
-
,Y:Z
-
-0.010 (0.28)
STDlNF
0.308 (3.26)
-
0.00026 (2.95)
0.00051 (3.48)
-
-
TIME
-0.297 (2.01)
-
determining the steady state, du, is the dependent variable, We-, is the lagged level of the dependent shocks. See Tables 1 and 2 for definitions of variables and more detailed specifications of equations.
period is 1949:i-1986:io. a from the equation
of variables economic
The sample coefficients
-0.0057 (0.56)
(3d.3)
NOTES: Estimated
-0.0266 (3.92)
(3d.2)
,~:~
0.010 (1.27)
-0.0296 (3.78)
(3d. 1)
-0.183 (4.68)
du ldz)
-
(3c.3)
-0.103 (2.63)
Panel D: Dependent Variable ln(AGE)
-0.0609 (2.32)
(3~. 2)
variable,
0.462
0.473
0.435
0.430
R-2
0.691
0.672
Henry
M. McMillan
and Jerome B. Baesel
We provide one such forecast here using Bureau of the Census population projections. 26 Figure 3 shows the effect of these population projections on the age distribution of borrowers and savers. According to all three projections, the borrowing population will decline relative to the saving population until 2002 and then increase rapidly in the next century. The change in AGE is dramatic. The middle population projection forecasts AGE to increase from 0.666 in 1980 to 1.013 in 2005 and then to drop rapidly again to 0.796 in 2030. The low population series projects AGE reaching 1.042 in 2005 and declining slowly to 0.862 in 2030. The high series projects AGE to be 0.987 in 2005 and to fall rapidly to 0.733 in 2030. Figure 3 shows that the three AGE series have the same pattern but with different levels. To obtain projections of real interest, output growth, and unemployment rates, we combine the population projections with the steady-state parameter estimates of Table 2 (equilibrium equations [7], [B], and [lo]). Table 4 presents the projections. Using the middle AGE series, output growth per capita is negative through 1990 and then grows rapidly to 2.5% per year in 2010. The steady-state unemployment rate declines from 7.7% in 1985 to 2.7% in 2010 before increasing again. Equilibrium real interest rates decline from 6.1% in 1985 to -1.4% in 2010 before climbing back to 4.2% in 2030. The low AGE series projects higher per capita output growth and lower unemployment and real interest rates. The high AGE series projects smaller swings in these variables than do the middle or low AGE series.27
%We use the three projections (low, middle, and high) developed by the Bureau of the Census (1984). The projections use a smooth transition from 1982 population age distribution to the ultimate projected levels. According to the census bureau’s grows to 261 million in 2010 and “low” assumptions, the United St a t es population declines to 232 million by 2050. With the middle series, population grows to 268 million in 2010 and levels off at 310 million in 2050. The high series shows population growing rapidly to 283 by 2010 and 424 million by 2050. The two extreme series differ by less than 10% in 2000, by 30% in 2025, and by over 60% in 2050. 27Because these low projected interest rates may seem counter-intuitive, it is a useful exercise to consider how and why they occur. The intuition of the overlapping generation models is appropriate here (see especially Cass, Okuno, and Zilcha 1979). Negative real interest rates are plausible in that literature because physical or financial assets are the only way to provide retirement consumption. Even though the rate of time preference is positive (individuals prefer current consumption to future), the marginal rate of substitution of future for current consumption can be greater than one (that is, real interest rates can be negative). The middle AGE series projects 15% more savers than borrowers, according to
186
Macroeconomic
Impact
of the Baby Boom Generation
RATID OF SAVERS TO BORROWERS HISTORICAL AND PROJECTED TIME SERIES. US
DATA
Age 0.8
0.7
0.6 1950
60
70 Age
60
90
= PoH35-64V[
2000 POP( 15-34)
Figure
10
20
+ Pop(65+
30
40
20 80 Year
)I
3.
There are qualifications to these projections, of course. They are point estimates. The 95% confidence intervals for the projected interest rates,include positive real interest rates. These confidence intervals expand with time. Also, the confidence intervals will grow because the projected AGE series has values outside historical experience. The simulation assumes other factors are constant. Fiscal policy, monetary policy, and supply shocks will influence the macroeconomy just as they have in the past. Net migration is fixed by the Census Bureau projections, rather than adjusting to the eco-
our definition, in the year 2000. These people, the Baby Boom generation, will be buying assets with the intent to sell them when they retire. The Baby Boomers will execute this buy-sell strategy at roughly the same time. Other things being equal, the Baby Boomers will be buying assets at high prices and selling assets at low prices. So, the required rate of return on physical and financial assets will be low. Preferences for current consumption notwithstanding, the Baby Boomers will pursue tirement.
this
strategy
if it
is the
only
guaranteed
source
of consumption
during
re-
187
0.696 0.761 0.869 0.974 0.995 0.893 0.796
Mid
Low
Mid
0.061 0.061 0.695 0.042 0.042 0.757 0.013 0.014 0.862 0.961 -0.012 -0.009 0.956 -0.024 -0.014 0.009 0.833 -0.009 0.016 0.033 0.733
High
r*
Low
of U.S.
Census
0.061 -0.013 0.043 -0.003 0.016 0.010 -0.007 0.023 -0.006 0.028 0.023 0.021 0.050 0.009
High
NOTES: Projections of AGE calculated from population projections unemployment based on Equations (7), (8), and (10) of the text.
0.697 0.763 0.874 0.986 1.045 0.972 0.862
1985 1990 1995 2000 2010 2020 2030
and
Low
Year
AGE
TABLE 4. Projected Steady State Values: Real Interest Rate, Output High
Bureau
(1984).
Projected
interest
0.077 0.065 0.046 0.030 0.022 0.032 0.048
Low
and Unemployment
-0.013 -0.013 -0.003 -0.004 0.010 0.009 0.021 0.020 0.023 0.019 0.013 0.006 0.001 -0.007
Mid
&*
Growth,
rate,
output
0.077 0.065 0.047 0.032 0.029 0.043 0.059
Mid
U*
growth,
0.077 0.066 0.048 0.033 0.034 0.053 0.070
High
Macroeconomic
Zmpact of the Baby Boom Generation
nomic conditions that are forecast here.28 Finally, individuals might modify their behavior if they recognize these trends. Some adjustments might amplify rather than dampen the projected swings in output, unemployment, and the real interest rate, however. For example, suppose individuals begin to defer retirement from age 65 to age 70 beginning in the year 2000. Individuals might do this if they see the return on their savings decline or if the minimum eligibility for social security increases.” Surprisingly, this reaction exaggerates the projected changes in output growth, unemployment, and interest rates. We constructed a “deferred retirement” middle AGE series by gradually increasing the retirement age from 65 to 70 during the period 2000-2030. The deferred retirement AGE series is uniformly above the original middle AGE series. This scenario amplifies the swings in the projections. Why? Because under the deferred retirement scenario both the Baby Boom generation and their children are simultaneously in their prime productivity and saving years.
5. Conclusion In summary, this analysis indicates that the age structure of the population influenced macroeconomic relations in the United States during the postwar era. Recent high real interest rates and low output growth may be partially due to the Baby Boom generation being in its prime borrowing and low labor productivity years. As the Baby Boomers age, it is reasonable to expect unemployment rates and real interest rates to be lower and output growth rates to be higher than if no demographic changes occur. The results reported in Section 3 shed light on some important issues in business cycle theory. First, age composition affects macroeconomic behavior. Several demographic variables affect unemployment, real output growth, and real interest rates in reduced
any
?he net meaningful
migration would way. Additionally,
need
to be immigrants
extremely have
large historically
to offset been
the swings predominately
in
prime age adults who save a large fraction of their income. Immigration of this group would tend to amplify the swings in the real interest rate, if not the other variables. Of all migration patterns, emigration of prime age adults would most effectively dampen the projected swings in real interest rates, output growth, and unemployment. =Beginning in 2003, the retirement age for full benefits will gradually increase to 66 in 2009 and to 67 in 2027. The actuarial reduction of benefits for early retirement at age 62 will increase from 20% to 30%.
189
Henry
M. McMillan
and Jerome B. Baesel
form estimates. This evidence supports life-cycle-human-capital models of economic activity. The evidence is inconsistent with the simple neoclassical growth model that implicitly assumes a single representative agent. Also, the Easterlin hypothesis of endogenous fertility dependent on relative income receives support. Second, age composition influences the statistical evidence on other macroeconomic theories. Omitting demographic factors from empirical models biases estimated coefficients of other included variables that are correlated with those demographic factors. The evidence presented in this paper indicates that controls for demographic shifts are necessary for the entire postwar sample period. However, controls can be replaced by time trends for shorter sample periods. Received: July 1987 Final version: July 1989
References Auerbach, Alan, and Laurence Kotlikoff. “Simulating Alternative Social Security Responses to the Demographic Transition.” NBER Working Paper No. 1308, 1984. Becker, Gary. Human Capital and the Personal Distribution of Zncome: An Analytical Approach. Ann Arbor: Institute of Public Administration, Univ. of Michigan, 1967. Berger, Mark. “The Effect of Cohort Size on Earnings Growth: A Reexamination of the Evidence.” Journal of Political Economy 93 (June 1985): 561-73. Bemheim, B. Douglas. “Dissaving after Retirement: Testing the Pure Life Cycle Hypothesis.” In Zssues in Pension Economics, edited by Z. Bodie, J. Shoven, and D. Wise. Chicago: Univ. of Chicago, NBER, 1987. Brown, David. “Age Clienteles, Demographic Shifts, and Equilibrium Security Prices. ” School of Business, Indiana University, 1985. Mimeo. Butz, William, and Michael Ward. “The Emergence of Countercyclical U.S. Fertility.” American Economic Review 69 (May 1979): 318-28. Cass, David, Masahiro Okuno, and Itzhak Zilcha. “The Role of Money in Supporting the Pareto Optimality of Competitive Equilibrium in Consumption-Loan Type Models.” Journal of Economic Theory 20 (March 1979): 41-80. 190
Macroeconomic
Zmpact of the Baby Boom Generation
Craine, Roger. “The Baby Boom, the Housing Market, and the Stock Market.” Federal Reserve Bank of San Francisco Economic Review (Spring 1983): 6-11. Denton, Frank, and Byron Spencer. “Household and Population Effects on Aggregate Consumption.” Review of Economics and Statistics 58 (February 1976): 86-95. Doescher, Tabitha, and John Turner. “Social Security Benefits and the Baby Boom Generation.” American Economic Review 78 (May 1988): 76-80. Easter&, Richard. Population, Labor Force, and Long Swings in Economic Growth. New York: Columbia University Press, 1968. -. Birth and Fortune. 2d ed. Chicago: Univ. of Chicago Press, 1987. Engle, Robert, and Clive Granger. “Co-Integration and Error Correction: Representation, Estimation, and Testing.” Econometrica 55 (March 1987): 251-76. Fair, Ray, and Kathryn Dominguez. “Effects of the Changing U.S. Age Distribution on Macroeconomic Equations.” NBER Working Paper No. 2280, 1987. Fisher, Irving. The Theory of Interest. New York: Macmillan, 1930. Flaim, Paul. “The Effect of Demographic Changes on the Nation’s Unemployment Rate.” Monthly Labor Review 102 (March 1979): 13-23. Freeman, Richard. “The Effect of Demographic Factors on AgeEarnings Profiles.” Journal of Human Resources 14 (Summer 1979): 289-318. Friedman, Milton, and Anna Schwartz. A Monetary History of the United States, 1867-1960. Princeton: Princeton Univ. Press, 1963. Fuller, Wayne. Zntroduction to Statistical Time Series. New York: John Wiley & Sons, 1976. Heien, Dale. Demographic Effects and the Multiperiod Consumption Function. Journal of Political Economy 80 (February 1972): 125-38. Levine, Phillip, and Olivia Mitchell. “The Baby Boom’s Legacy: Relative Wages in the 21st Century.” American Economic Review 78 (May 1988): 66-69. Lieberman, Charles, and Paul Wachtel. “Age Structure and Personal Saving Behavior.” In Social Security versus Private Saving, edited by George von Furstenberg. Cambridge, Mass: Ballinger, 1979. Manchester, Joyce. “The Baby Boom, Housing, and Loanable Funds.” American Economic Review 78 (May 1988): 70-75. 191
Henry
M. McMillan
Mayor, tural
Thomas, Change,
and Jerome B. Baesel
“Life-Cycle Effects, Strucin the Velocity of Money.” Journal of Money, Credit, and Banking 16 (May 1984): 175-84. McMiIlan, Henry, and Jerome Baesel. “The Role of Demographic Factors in Interest Rate Forecasting.” Managerial and Decision Economics 9 (September 1988): 187-95. Modigliani, France. “Life Cycle, Individual Thrift, and the Wealth of Nations.” American Economic Review 76 (June 1986): 297313. Modigliani, France, and Richard Brumberg. “Utility Analysis and the Consumption Function: An Interpretation of Cross-section Data.” In Post-Keynesian Economics, edited by K.E. Kurihara. New Brunswick, NJ: Rutgers University Press, 1954. ’ Nelson, Charles, and Charles Plosser. “Trends and Random Walks in Macroeconomic Time Series.” Journal of Monetary Economics 10 (September 1982): 139-62. Peek, Joe, and James Wilcox. “Monetary Policy Regimes and the Reduced Form for Interest Rates.” Journal of Money, Credit, and Banking 19 (August 1987): 273-91. Ram, Rati. “Dependency Rates and Aggregate Savings: A New International Cross-Section Study.” American Economic Review 72 (June 1982): 537-44. Russell, Louise. The Economics of the Baby Boom Generation. Washington, D. C. : Brookings, 1982. Solow, Robert. Growth Theory. Oxford: Oxford University Press, 1970. Sternlieb, George, and James Hughes. “Demographics and Housing in America. ” Population Bulletin 41 (January 1986): 3-34. U.S. Bureau of the Census. Projections of the Population of the United States by Age, Sex and Race: 1983 to 2050. Washington, D.C.: GPO, 1984. Welch, Finis. “Effects of Cohort Size on Earnings: The Baby Boom Babies’ Financial Bust.” Journal of Political Economy 87 (October 1979): S65-S98. Wilcox, James. “Why Interest Rates Were So Low in the 1970’s.” American Economic Review 73 (March 1983): 44-53.
Appendix:
and Lawrence Pearl. and Long-run Movements
Test for Unit Roots
Economists have long assumed around trend growth (a trend-stationary ser (1982) suggest that the economy 192
that the economy fluctuates process). Nelson and Ploscan be better described by a
Macroeconomic
Impact
of the Baby Boom Generation
random walk with drift. The choice between a trend-stationary and a random-walk process can be made statistically with the Augmented Dickey-Fuller (ADF) test (Engle and Granger 1987). We examine each of the four endogenous variables in this context. The null hypothesis of the ADF test is the random-walk process. The alternative to the null is either a stationary or a trendstationary process. One must specify the alternative to the null because the alternative affects the distribution of the test statistic. Economic theory suggests that the real interest rate is stationary or is a random walk without drift. That is, there should be no time trend. The ADF test requires the estimation of dr, = y,, + ylrtml + O(L)dr, + E,,
(Al)
with enough lags in B(L) to assure that E, is white noise. The crucial statistic is the “t-statistic” of yl. The statistic does not have the tdistribution under the null hypothesis. Instead, the statistic must be compared to a stricter significance requirement found in Fuller (1976, 373, Table 8.5.2). The 5% and 1% significance levels are 2.88 and 3.50 for the 150 observation sample size. Table Al presents the estimates of Equation (Al). Three lags were enough to provide white noise errors. The estimated statistic for y1 is 3.21, which rejects the null at the 5% level, but not at the 1% level.30 However, Nelson and Plosser could not reject the random walk null hypothesis with annual data. The unemployment rate should be stationary around its natural level, but the natural level may have a time trend. The ADF test compares the null hypothesis of a random walk with drift to the alternative of a trend-stationary process. Estimate du, = y. + ylu,-l
+ y2t + e(.L)du, + E,,
642)
where t is a time trend. The “t-statistic” for yi must exceed 3.44 and 4.02 to reject the null hypothesis at the 5% and 1% significance levels. Table Al shows that unemployment was trend stationary at the 1% significance level when using two lags of du,. However, the null could not be rejected when using four lags of du,.
four terly
“The sample period is 1949&1966:iu. measures of the real rate (first, second, average).
The rejection of the null occurs for all or third month of the quarter or quar-
193
-0.114 (4.32)
0.0041 (3.49)
dut
&t
d&t
(3)**
(4.a)**
(4. b)*
0.494 (6.24) -0.312 (3.57)
0.0010 (1.77) -
-0.017 (1.36)
-0.168 (2.90)
0.466 (5.99)
-0.025 (0.26)
0.0011 (2.78)
0.344 (4.26)
-0.374 (3.89)
dvml
0.0055 (3.25)
-
t
Test
-0.181 (2.18)
0.115 (1.35)
0.150 (1.83)
0.151 (1.87)
0.187 (2.31)
-0.218 (2.45)
dv-,
0.105 (1.39)
0.282 (3.48)
-
-0.110 (1.42)
-
-
0.253
0.608
0.299
0.324
0.197
-
0.301
R2
-
dv-,
-
-
0.089 (1.19)
dv-,
NOTES: Numbers in parentheses are t-statistics. The sample period is 1949:i-1986:io. of real per capita GNA; ut = civilian r, = ex post real interest rate; y, = logarithm unemployment rate; p, = logarithm price index; and t = a time trend. dy, = the first difference, and ddy, = the second difference of yr. and so on. *5% and 1% significance levels are 2.88 and 3.30. **5% and 1% significance levels are 3.44 and 4.02. Q(x) is the Box-Pierce Q-statistic for autocorrelation with six lags with r degrees of freedom (dof). Critical values for the = 5.991, Q(3) = 7.815, and Q(4) = 9.837.
0.0070 (2.33)
0.0526 (1.43)
-0.626 (6.24)
0.0116 (3.02)
d&t
(2. b)*
-0.309 (3.37)
0.529 (3.43)
4/t
-0.236 (3.21)
(2.a)**
V-l
c
Dickey-Fuller
0.0021 (1.02)
dv
Augmented
drt
Al.
(I)*
TABLE
are
5% level
Q(2)
consumer
3
2
4
3
4
3
dof
of the
1.209
1.289
9.315
2.633
2.641
1.585
Q
Macroeconomic
Zmpact of the Baby Boom Generation
Output per capita is either a random walk with drift or a trendstationary process. The null hypothesis is not rejected at the 5% level. Furthermore, Nelson and Plosser did not reject the null. The growth rate of output per capita is stationary as indicated by Equation (Lb). Finally, the evidence also indicates that the price level is random walk with a drift, and that the inflation rate is stationary. See Equations (4.a) and (4.b).
195