Demographic Dynamics and the Empirics of Economic Growth

This paper examines the effects of demographic dynamics on the measured rates of economic growth. It develops a model of production with labor productivity that varies with age. Macroeconomic and demographic data are used to estimate the relative productivity of different age groups. A panel database of effective labor supply is constructed in order to reflect the changing age structure of the population. The historical measured growth rates are then deconstructed into effects of demographic dynamics and into “real” growth rates, net of demographic effects.

Abstract

This paper examines the effects of demographic dynamics on the measured rates of economic growth. It develops a model of production with labor productivity that varies with age. Macroeconomic and demographic data are used to estimate the relative productivity of different age groups. A panel database of effective labor supply is constructed in order to reflect the changing age structure of the population. The historical measured growth rates are then deconstructed into effects of demographic dynamics and into “real” growth rates, net of demographic effects.

THE PRESENCE of strong demographic dynamics affects measurements of the differences in economic performance both across countries and over time. The main aim of this paper is to estimate the magnitude of this effect, in order to construct measures of economic growth that are free of demographic effects. In order to do so, we also need to estimate the relative productivity of different age groups. But before doing this, we must develop a model of production with labor productivity that varies with age.

To estimate this age–related labor productivity function, the paper uses macro data, in the form of two international panel databases—a macroeconomic database and a demographic database—rather than micro data. Based on these data, the paper produces the following databases, all of which are available upon request from the author: an estimated function describing how labor productivity varies with age; estimated labor productivity for each country in the database during 1950–1985; forecasts of labor productivity for each country in the database for 1990–2025; and a new panel database for 1960–1985, including measures of output that are adjusted so as to be free of demographic effects.

The paper is organized as follows: Section I discusses the problem of measuring the rates of economic growth using data affected by demographic dynamics. Section II develops a model of production with age– related productivity and derives a method to measure the effects of demographic dynamics on economic growth. Section III presents the empirical data that are used in the paper. Section IV uses these data to estimate the model developed in Section II and to determine the exact way in which productivity varies with age. Section V constructs two panel databases—one that measures effective labor supply, and one that adjusts measured GDP data to eliminate demographic effects. Finally, Section VI presents concluding remarks.

I. The Demographic Factor in Empirical Studies of Growth

There has been much empirical research on economic growth in recent years. A common feature of this work is its reliance on databases that contain GDP per capita measures over a period of 25–40 years, such as Summers and Heston’s 1991 database. A significant problem associated with this type of data is that the period covered is short in terms of demographic dynamics. For example, suppose a strong baby boom occurs in some countries at a time that closely precedes the beginning of the sample. Then, in the base period of the sample, a large fraction of the population in these countries consists of young children, who are less productive than average or even have a net negative effect on total production. In this situation, even if GDP per capita is measured accurately, it cannot be a good proxy for the real strength of the economy. Furthermore, at the end of the sample, the baby boom generation will be mature and fully productive, and the whole demographic structure will be much more favorable. Then. the economic growth measured by the growth of GDP per capita in the period covered by the sample will be biased significantly upward.

The problem is that the measured growth is a combination of two factors: “real” growth, as usually defined by economists and other observers and by policymakers; and demographic dynamics. In the short period covered by most databases used in the empirical research of economic growth, the effect of the demographic dynamics on measured growth may be quite strong. Therefore, any comparison of growth rates across countries or across periods should take demographic effects into account.

Some studies have tried to do this by looking at measures of GDP per worker (or per potential worker), instead of GDP per capita.1 The first flaw in this approach is that the definition of a worker or a potential worker is arbitrary and the results are sensitive to the specific choice of the age at which one starts to work and the retirement age. The second problem is the unrealistic assumption of flat productivity over the work period. A third flaw is the assumption of zero net contribution to production by young children or elderly persons; there is no a priori reason to believe that the net contribution of these groups is zero rather than positive or negative.

II. The Age–Related Productivity Model

This section develops a model of production that assumes different productivity levels for different age groups. The model yields a simple reduced form that can easily be estimated to determine the relative productivity of the different age groups.

We assume a Cobb–Douglas production function

Yit=AitKitαLit1α,(1)

where i is the country index, t is the period index, Y is the output, A is a technology (or knowledge) parameter, K is the amount of capital, and L is the amount of labor supplied.

Dividing production function (1) by the population size yields

Yit=AitKitαlit1α,(2)

where y is the output per person, k is capital per person, and lis the amount of labor supplied by the average person.

Taking logs results in

log(yit)=log(Ait)+αlog((ky)it)+αlog(yit)+(1α)log(lit).(3)

Isolating y and dividing both sides by (1 — α) yields

log(yit)=log(Ait)1α+α1αlog((ky)it)+log(lit).(4)

Taking the first differences of equation (4) yields an expression that describes the growth rate of output per person:

log(yi(t+1)yi(t))=11αlog(Ai(t+1)Ai(t))+α1αlog((k/y)i(t+1)(k/y)i(t))+log(li(t+1)li(t)).(5)

A normalization of the rate of technological progress, g, can be defined as

git=11αlog(Ai(t+1)Ai(t)).(6)

Following the conditional convergence literature, we assume that the rate of growth of the capital/output ratio diminishes as the economy grows richer.2 This rate of growth can be expressed as a linear function in the log of output per person:

α1αlog((k/y)i(t+1)(k/y)i(t))=θ0θ1log(yi(t)),(7)

resulting in the growth equation

log(yi(t+1)yi(t))=gi(t)+θ0θ1log(yi(t))+log(li(t+1)li(t)).(8)

At this stage, we make the crucial assumption that the average labor supply per person, 1, is a function of demographics. Specifically, we assume that lis a function of the demographic structure of the population, which can be summarized by n age groups; that each age group provides a different intensity of labor proportional to its relative productivity: and that the type of labor supplied by one age group is a perfect substitute for the type of labor supplied by another age group. Then, omitting thei and tsubscripts:

l=β1b1++βnbn,(9)

where the βs are the coefficients of relative productivity and the bs are the shares of each age group in the total population (b1 + … + bn= 1).

We define the mean demographic distribution of all the bundles (b1, …, bn) in the sample (for each age group j, mj is the mean value of bj in the sample) as (m 1, … , m n). The mean labor supply, which corresponds to the mean demographic distribution, is defined as l mand we define its value as equal to 1:

lm=β1m1++βnmn,(10)

For each age group j, we define the deviation of bj from the mean as dj:

d1=b1m1,...,dn=bnmn.(11)

Finally, we define

γ=β1d1+...+βndn.(12)

Using all these definitions, we can write the labor supply as:

l=1+γ.(13)

Because the demographic distribution (b1, … , bn) cannot be very different from its mean (m1,…mn), γ is a small number (close to 0) and I (the labor supply) is close to 1 (the mean labor supply). Therefore, we can use the first order approximation log (1 + γ)= γ to obtain:

log(l)=β1d1++βndn.(14)

We take first differences to obtain the growth rate of the average labor per person:

log(li(t+1))(li(t))=β1(d1i(t+1)d1i(t))+...+βn(dni(t+1)dni(t)).(15)

This expression can also be written as

log(li(t+1)li(t))=β1(b1i(t+1)b1i(t))+...+βn(bni(t+1)bni(t)).(16)

If we substitute this last expression into the expression for the growth rate of output, we get:

log(yi(t+1)yi(t))=gi(t)+θ0θ1log(yi(t))+β1(b1i(t+1)b1i(t))+...+βn(bni(t+1)bni(t)).(17)

We can use the definition of the mean labor supply (equation (10)) to express βn, as a function of the other coefficients of relative productivity:

βn=1(β1m1+...+βn1mn1)mn(18)

Define:

qi(t)=bni(t+1)bni(t)mn(19)
pj[i(t)]=bji(t+1)bji(t)mjqi(t)(20)
yyi(t)=log(yi(t+1))log(yi(t))qi(t).(21)

Finally, we can obtain a reduced form that can be used to estimate the coefficients of relative productivity (β1,…,βn-1):

yyi(t)=gi(t)+θ0θ1log(yi(t))+β1p1[i(t)]+...+βn1pn1[i(t)].(22)

III. The Data

The data used in this paper come from two databases. The Penn World Table (PWT)–5.5 database3 contains data on GDP for 150 countries in the period 1950–1990, but we restrict our attention to the 121 countries that have continuous observations every five years during 1960–1985.4 The second database is the United Nations (1990) database on the distribution of the population among different age groups for each country at five–year intervals. The ages also are divided into five–year groups, and the period covered is 1950–1985, with forecasts for the period 1990–2025. All of the countries covered by the first database except Seychelles and the Taiwan Province of China are also covered by the United Nations data. Therefore, we restrict our observations to the 119 countries for which we have continuous macroeconomic and demographic information for 1960–1985.

IV. Estimation of the Age–Related Productivity Structure

This section estimates the relative productivity of each age group and the effects of demographic dynamics on economic growth. We use the reduced form we obtained from the model presented in Section II (equation (22)). The dependent variable, yyi(t), is constructed using data on growth rates of income per person from time r to time t +1; data on the change in the fraction of population of one of the age groups (bni(t+1)bni(t));and data on the average fraction of population at this age group in the sample. The right–hand side of equation (22) comprises a constant; a term linear in the log of output per person; and a group of n — 1 other variables, each corresponding to one of the other n — 1 age groups. Our purpose is to estimate the vector of productivity coefficients (β1,…,βn‐1).

The GDP series is constructed from the PWT–5.5 database, which contains information on output per person and on population size. The GDP per person series is constructed by dividing the GDP series by the total population data from the United Nations’ database.5

The United Nations data divide the age structure into 17 age groups, each covering a five–year interval (0–4, 5–9, 75–79, 80+). For symmetry reasons, we define age group n, the one that is used as numeraire, to be the middle group (40–44). Therefore, we need to estimate the coefficients for the other 16 groups. An estimated coefficient greater than 1 means that the productivity of the respective age group is above average. An estimated coefficient less than I means that the productivity of the respective age group is below average. Finally, a negative coefficient indicates that the net contribution of the respective age group is negative, meaning that not only do people at this age not increase total production, but they actually decrease it.6

One necessary assumption is the direction of causality. We assume that income responds immediately to changes in the age distribution, but that the age distribution is “sticky” in the short run (a five–year period) and cannot respond immediately to differences in growth rates. Of course, over longer periods, the demographic distribution may respond to differences in growth rates through changes in fertility and in life expectancy. By restricting the period to five years only, it is safe to assume that this reversed causality is nonexistent or negligible.7

The essence of the econometric problem is to find a reasonable way to estimate the 16 productivity coefficients. The difficulty is not only the large number of explanatory variables, but also the high degree of multicollinearity among them. Therefore, we define a polynomial transformation of the age groups and then estimate the coefficients of this polynomial function. The values of the 16 productivity coefficients can then be recovered from the estimated coefficients of the polynomial function by using the inverse of the polynomial transformation.

The prior expectation about the function that relates productivity to age is that it is continuous and has an inverse–U shape (a parabola). Therefore, it is natural to choose a second degree polynomial function to represent the productivity coefficients of the age groups. We define for each age group j an age–distance, ad, which represents the group’s position in the age structure relative to group n, the middle group 40–44. Table 1. describes the construction of this measure.

In order to construct the second degree polynomial function, we define:

xi(t)0=(p1i(t))+...+(p16i(t))23
xi(t)1=(ad1)(p1i(t))+...+(ad16)(p16i(t))24
xi(t)2=(ad1)2(p1i(t))+...+(ad16)2(p16i(t))(24)

Now, instead of having to estimate 16 coefficients (one for each age group), it is enough to estimate only the 3 coefficients (an, al, and a:) for the polynomial function

x=a0x0+a1x1+a2x2.(26)

The results of the regression

yyi(t)=[constant]ilog(yi(t))+a0x0+a1x1+a2x2+ϵ(27)
Table 1.

Construction of the Age–Distance Measure

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Table 2.

Regression Results

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Notes: Dependent variable: yy. Number of observations: 595. Adjusted R2: 0.408.

are presented in Table 2 In order to control for country–specific effects, we include in the regression 118 country dummies (for all countries, except United States). The estimated values of these dummies are not reported in Table 2.

Using the estimated values of the 3 polynomial coefficients, we can construct the 16 productivity coefficients (β1,…β16).Even better, we can construct the general function that relates productivity to age. In order to do this, each age group is assumed to represent the age at its middle and the age group 80+ is assumed to represent the age 82.5. In addition, we calculate an interval of one standard error, using the variance–covariance matrix of the estimated coefficients a0, al, and a2. The results of this construction are presented in Figure 1. The solid line describes the estimated relative productivity at each age, in the age range 2–82. The dashed lines represent a standard error deviation of 1.

Figure 1.
Figure 1.

Productivity by Age

Citation: IMF Staff Papers 1995, 002; 10.5089/9781451947205.024.A007

The estimated productivity coefficients confirm the expected “inverse–U” shape. The peak in productivity is achieved at age 55. The productivity at this age is 2.48, compared with an average productivity of 1. The net productivity becomes positive at age 8. Children at age 7 and below have a negative net productivity. While the decline in productivity at old age is not significant, the difference in productivity levels between childhood and middle age is extremely strong and significant.8

V. Creating Two New Panel Databases

Using the estimated coefficients for each of the age groups and the demographic database, we construct a new panel database, describing the effective labor supply in each of the countries for each of the periods covered by the demographic sample. Many countries in the sample had a pattern of demographic dynamics in which the effective labor supply first decreased and later increased.9

For example, the effective labor supply in the United States decreased from 1.39 in 1950 to 1.32 in 1965. After 1965 it started to increase, reaching 1.48 in 1985. These demographic dynamics are described in Figure 2. They correspond, of course, to the dynamics of the baby boom generation. From 1950 to 1965 the proportion of young children in the population increased, having a negative effect on average labor productivity. After 1965, as the baby boom generation advanced into the more productive ages, the demographic dynamics had a positive effect on growth.

For comparison, Figure 3 presents the demographic dynamics that took place in Japan during the same period. Comparing Figure 3 to Figure 2 demonstrates that the Japanese advantage in terms of demographic dynamics in the 1950s can partly explain the difference in growth performance between Japan and the United States during that period.

Figure 2.
Figure 2.

Demographic Dynamics in the united States

Citation: IMF Staff Papers 1995, 002; 10.5089/9781451947205.024.A007

Figure 3.
Figure 3.

Demographic Dynamics in Japan

Citation: IMF Staff Papers 1995, 002; 10.5089/9781451947205.024.A007

After 1965, however, there was no significant difference in demographic dynamics between the two countries.

According to the effective labor supply database, some of the countries in the sample had demographic dynamics with particularly strong effects on output. For example, the effective labor supply in Puerto Rico, Japan, Singapore, and Mauritius increased dramatically during the period 1950–1985, while in Kenya, Benin, Cape Verde, and Bangladesh it decreased significantly during the same period. In all these cases, the absolute value of the rate of change in the effective labor supply was close to 1 percent a year. Adjusting for demographic effects (assuming that the share of labor in income is two thirds). the estimated growth rate of output per person changes (in absolute value) by about 0.6 percent a year for each of these countries. This is an extremely significant correction, given the 35–year period considered. The cross–section results are equally interesting. In 1985, for example, the most favorable demographic situation was in West Germany (1.65), while the most unfavorable was in Kenya (0.77).

The “effective labor supply” database is used to update the conventional PWT database. The result is the “adjusted for demographic dynamics” database, which includes 119 countries at six points in time (from 1960 to 1985, every five years). For each observation the database includes three variables: population size; measured GDP per person; and adjusted GDP per person, a measure of output that is free of demographic dynamics.10 An obvious use of this database is to correct the measured growth rates for demographic effects.

VI. Conclusions

Demographic dynamics and their relations to the dynamics of economic growth are little understood by growth economists. From a theoretical perspective, the convenient assumptions of constant population or constant population growth in models of economic growth are unrealistic and misleading. From an empirical perspective, the effects of demographic dynamics can have dramatic effects on measured growth rates. Having better measures of economic growth is obviously extremely important for improving our understanding in this area, as well as for direct policy applications.

This paper attempts to improve the empirics of economic growth by taking full account of the effect that demographic dynamics have on economic growth. The methodology used in this paper is unique, in the sense that it relies on macro, rather than micro, data.

One of the intermediate results of the study presented in this paper, which is also important in its own right, is a function that describes how productivity of labor varies with age. Another important result is a panel database of effective labor supply per person. This database is obtained by estimating the effects of demographic dynamics on economic growth.It contains estimates of average labor productivity for a large set of countries in the past, as well as forecasts for future periods, up to the year 2025. This database may prove especially useful for long‐run economic policy and social planning. The final outcome of this paper is a panel database that includes, for each observation, the measured output per person, as well as its corresponding value when adjusted for demographic dynamics. This might be used for direct policy applications, as well as in future empirical studies of economic growth. An obvious use of this database is to calculate growth rates that are free of demographic effects.

REFERENCES

  • Mankiw, N. Gregory, David Romer, and David N. Weil, “A Contribution to the Empirics of Economic Growth,” Quarterly Journal of Economics, Vol. 107 (May 1992), pp. 407 -37.

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    • Export Citation
  • Sarel, Michael (1994a). “On the Dynamics of Economic Growth” (Ph.D. dissertation; Cambridge, Massachusetts: Harvard University, 1994).

    • Search Google Scholar
    • Export Citation
  • Sarel, Michael, (1994b), “On the Dynamics of Economic Growth,” IMF Working Paper 94/138 (Washington: International Monetary Fund, November 1994).

    • Search Google Scholar
    • Export Citation
  • Summers.Robert, and Alan Heston, “The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950–1988.” Quarterly Journal of Economics, Vol. 106 (May 1991), pp. 32768.

    • Search Google Scholar
    • Export Citation
  • United Nations, Sex and Age (computer disk; New York: United Nations, 1990).

*

Michael Sarel is an Economist in the Research Department. He graduated from the Hebrew University of Jerusalem and received a Ph.D. from Harvard University. This paper draws on the author’s Ph.D. dissertation (Sarel (1994a, Chapter 3)). The author thanks Robert Barro and the participants in the Macro– Growth Seminar at Harvard for helpful comments on an earlier draft.

1

This approach was taken, for example, by Mankiw, Romer, and Weil (1992).

2

Sarel (1994b), for example, discusses at length the dynamics of the output/ capital ratio.

3

The PWT–5.5 database is an updated version of the PWT–5.0 database, published by Summers and Heston (1991).

4

The set of countries for which we have information before 1960 is much smaller. It does not include many less developed countries, and in particular many African countries.

5

Alternatively, we could use directly the GDP per person data from the PWT–5.5 database. The two measures are almost identical. For consistency, we decided to use the United Nations’ database for all demographic data.

6

This may happen if these people require the time resources or the physical resources of people in other age groups. These resources could otherwise be used in production.

7

Another way to look at this problem is the following: The three factors that affect population dynamics are fertility, mortality, and migration. We assume that these three factors respond only to income per person and not to the rate of growth. A 5–year period is short enough to assume that changes in income per capita caused by differences in growth rates are small enough and recent enough to affect any one of these three factors. If there is reverse causality, the estimated productivity of the different age groups will be affected. For example, if life expectancy responds immediately to changes in income, the model will overestimate productivity at old age.

8

This significant difference is evident in Figure 1. It is important to note that the relevant source for this conclusion is Figure 1. and the standard error that it calculates using the variance–covariance matrix, and not the estimated coefficients in Table 2 The estimated coefficients of al and a2 in Table 2 have low r–statistics because of the negative correlation between the two coefficients. The magnitude of this correlation depends on the particular choice of the reference age group we previously made.

9

The effective labor supply is a relative measure and should be compared with the value 1, which is the effective labor supply that corresponds to the average demographic distribution in the sample.

10

Both databases described in this section. the “effective labor supply” (ELS) database and the “adjusted for demographic dynamics” (ADD) database, are in ASCII IBM format and are available upon request.