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

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

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

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

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

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

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:

resulting in the growth equation

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:

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

We define the mean demographic distribution of all the bundles (b₁, …, b_n) in the sample (for each age group j, m_j is the mean value of b_j 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:

For each age group j, we define the deviation of b_j from the mean as d_j:

Finally, we define

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

Because the demographic distribution (b₁, … , b_n) cannot be very different from its mean (m₁,…m_n), 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:

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

This expression can also be written as

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

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

Define:

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

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, ${yy}_{i\left(t\right)},$ 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 $(b_{ni(t+1)}-b_{ni\left(t\right)});$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,…,β_n‐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:

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

The results of the regression

Table 1.

Construction of the Age–Distance Measure

Table 1.

Construction of the Age–Distance Measure

	age	ad
1	0–4	–8
2	5–9	–7
3	10–14	–6
4	15–19	–5
5	20–24	–4
6	25–29	–3
7	30–34	–2
8	35–39	–1
9	45–49	+1
10	50–54	+2
11	55–59	+3
12	60–64	+4
13	65–69	+5
14	70–74	+6
15	75–79	+7
16	80+	+8

View Table

Table 1.

Construction of the Age–Distance Measure

	age	ad
1	0–4	–8
2	5–9	–7
3	10–14	–6
4	15–19	–5
5	20–24	–4
6	25–29	–3
7	30–34	–2
8	35–39	–1
9	45–49	+1
10	50–54	+2
11	55–59	+3
12	60–64	+4
13	65–69	+5
14	70–74	+6
15	75–79	+7
16	80+	+8

Table 2.

Regression Results

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

Table 2.

Regression Results

	Coefficient	t–statistic
constant	3.1331	11.9139
log (y)	–0.3248	–11.8168
a0	2.2974	5.8780
a1	0.1411	1.1548
a2	–0.0275	–1.3852

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

View Table

Table 2.

Regression Results

	Coefficient	t–statistic
constant	3.1331	11.9139
log (y)	–0.3248	–11.8168
a0	2.2974	5.8780
a1	0.1411	1.1548
a2	–0.0275	–1.3852

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, a_l, 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.

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Productivity by Age

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

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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.

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Demographic Dynamics in the united States

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

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Demographic Dynamics in Japan

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

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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.