The Services Growth Engine
Perspectives on World Growth
Lesson 3 Productivity: Not Such a Mystery


Most of the above discussion focuses on using AS policy in the short-run. Now we turn to long-run economics. Probably all nations share the goal of wanting to have a decent level and growth in their standard of living.

If one could put into a big pile all the goods and services they purchased this year, including everything from food and beverages to healthcare, this pile might be a visual image of what we mean by the standard of living. We can compare our pile to last year’s to see how much it improved. We can compare our pile to those of other countries, to see whose is the biggest. Most people in most countries like to see their standard of living improve.

This visual image probably wouldn’t be very helpful for these kinds of comparisons and we find that most countries use numbers instead. The most popular approach is to use real GDP per capita – or real consumer spending per person. In the U.S. real GDP and real consumer spending per person in 2003 were about $36,000 and $25,000 respectively. Since 1980 real GDP per capita increased by about 60%. Real consumer spending per person increased by about 66%. So try to imagine a pile of goods and services that was about 66% larger than in 1980.

Doing international comparisons of real GDP per capita involves converting each country’s real GDPs into one currency – usually to U.S. dollars. Thus the exchange rate used for these comparisons is critical to the results. Results can differ depending on the precise value of the exchange rate used. Furthermore, cultural practices and values can differ so much that such comparisons are fraught with technical and interpretation issues. Nevertheless, we make these comparisons anyway. In 1999, according to the CIA Factbook, the following countries real per capita GDP as a percent of the U.S. were (the average real GDP per capita of the world was about 21% of the U.S. level):

Luxembourg 103%

Hong Kong  80

Japan  73

Canada  71

Ireland  59

S. Korea  40

Venezuela  27

Poland  22

China  11

India    5

Let’s look, too, at nominal GDP worldwide :

Using the IMF listing the top countries in 2010 were Luxembourg ($108,952), Norway ($84,144), Qatar ($74,901), and Switzerland ($67,779).  Rounding out the top 10 were UAE, Denmark, Australia, Sweden, USA and Netherlands. Of the 183 countries listed the median country was Angola ($4,329 per person). Korea was listed as 33rd with  nominal GDP of $20,756 per person. China #91 at $4,382 per person. India #133 was $1,371 per person. Vietnam #141 with $1,174 per person.

Why make these comparisons? For one purpose – to illustrate there are differences and to show – whether these data are perfectly accurate or not – what many of these countries are striving for. Some of these countries had already come a long way by 1999. Others have made great progress since then. But the crucial issue is that most of them want to raise their standard of living and close the gap on the U.S. Meanwhile the U.S. wants its own standard of living to grow at a good rate.

How can these countries accomplish these goals? The answer is to increase their AS sector – to increase productive capacity. But how do they do that?

To answer that question we discuss the key determinants of capacity and then we discuss how they can be used to accomplish the task.

Economic Growth and the Economics of Growth

Economics Nobel Laureate Robert Lucas of the University of Chicago once said that economists should stop worrying about business cycles and think about economic growth instead, because this is what really matters for a nation’s well being. In this chapter, we consider the record of economic growth. We then turn to the sources and determinants of growth, beginning with the traditional framework that explains growth on the basis of capital accumulation and demographics. This serves mainly to see that these two factors are not enough to explain the enormous growth of the world’s major economies in the past. Capital and labor have become increasingly productive over time, i.e., the same amounts of capital and labor produce more output today than in the past. Thus, productivity growth is the main driver of economic growth. Productivity growth in turn is explained by “human capital” formation and technological progress. We end this chapter with an outlook on the future: Are there limits to economic growth and, if so, how far or close are they?

The Record of Economic Growth

The figure below shows the development of real GDP of the European economy in millions of USD and prices of 1990 (in terms of its 16 main countries) from 1830 to 2000. The figure is in logarithmic scale. During this time, the European economy increased 37 fold. From 1830 to the beginning of World War I in 1914, the growth path has a constant trend and shows very little variation around that. The two World Wars (1914-18 and 1939-45) and the Great Depression (1929-35) are major interruptions in that secular growth path. After World War 2 growth accelerated for two decades and then returned to the previous trend in the 1970s.

Some of that spectacular growth is due to population growth during the same period – an increasing number of people produce an increasing amount of stuff. To account for population growth, the second figure shows the development of real GDP per capita in the same countries over the same period. In per-capita terms, real GDP increased approximately 14fold. A typical European person has 14 times the resources to live on today compared to a typical European person in 1830. In other words, he or she is incredibly rich compared to his or her ancestors. Again, we see a pretty much constant trend until 1914 and three major breaks connected to the two World Wars and the Great Depression. The picture demonstrates what Robert Lucas had in mind: Over time, economic growth is the dominant force that matters for the economy. Business cycles are mere wiggles around the growth path. Government policies should care about long-term growth rather than managing the business cycle.

Real GDP in 16 West European Countries 1830-2000  – (Mill. Of $, in prices of 1990)

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Source: A. Carreras and X. Tafunell, “Western European Long Term Growth, 1830–2000: Facts and Issues“, Opuscles del CREI, num. 20, June 2008, p. 7

Real GDP per capita in 16 West European Countries 1830-2000

(Mill. Of US$, in prices of 1990)

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Quelle: A. Carreras and X. Tafunell, “Western European Long Term Growth, 1830–2000: Facts and Issues“, Opuscles del CREI, num. 20, June 2008, p. 18

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Source: Angus Deaton, Historical Statistics of the World Economy, 1-2008

The figures above take a broader and longer perspective. Note that the time axes are shortened at the left end. The figures show the development of the global economy in terms of estimated populations and real GDP per capital over the past 2000 years. World population was roughly constant for the first 1200 years. It began to grow significantly in Asia in the first part of the 2nd millennium and in Africa in the middle of the 20th century. Compared to Asia, population growth in Europe and the US was very modest.

Real GDP per capita was roughly constant and equal throughout the world until about 1700. The average person on this globe in 1700 was about as well off economically as the average person in 1000 and in year 1. In the first millennium, per capita incomes ranged between $400 and $450 (in 1990 prices) in Europe, Asia, Africa, and Latin America with practically no growth in per capita terms everywhere2. In other words, economic growth in per capita terms is a relatively recent phenomenon in world history. For the longest part of that history, each generation was about as well off as the previous one. This does not, of course, exclude the possibility that individual groups of society and even individual regions saw increases in their prosperity. On average, however, the world seemed to be the same forever. Only with the onset of the “industrial revolution,” i.e., the turn from a predominantly agrarian economy with small manufacturing to an industrial economy, in the 18th century, economic growth in per-capita terms became a significant fact of the world economy. It started in Western Europe and in the US. In Asia, per-capita GDP began to grow in the late 19th century, mainly driven by Japan. Africa remains the continent with the slowest economic growth and the lowest level of per-capita GDP.

The figure below gives more detail and precision to these trends. It shows the development of world population and world production of output over one thousand years beginning in the year 1000. The scale is logarithmic.

World Population and Production, 1000-2000

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Quelle: Robert Lucas “The Industrial Revolution: Past and Future”, Federal Reserve Bank of Minneapolis, Annual Report Essay 2003 (

The figure shows that for about 700 years, from 1000 to 1700, the world’s population grew very slowly. More importantly from our perspective, world production grew at the same pace as world population, i.e., world output per capita was roughly constant. The figure below looks more deeply behind that average for the past 250 years. It shows real per-capita GDP in five major regions of the world. They are defined in terms of economic similarities. The figure shows that per-capita real GDP growth first set off in the Anglo-Saxon world (region 1). The main Western European and Scandinavian economies (group III) lagged behind that group for a long time and began to grow only in the mid-19th century. The Japanese economy started growing in per-capita terms only around the beginning of the 20th century and set off to much more rapid growth after 1950. Significant growth in the rest of Asia is a story that begins only in the late 1970s. Thus, we see important differences in the growth performance of different groups of nations around the world.

Per-capita real GDP in 5 Regions of the World, 1750-2000 (USD of 1985)

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Source: Robert Lucas “The Industrial Revolution: Past and Future”, Federal Reserve Bank of Minneapolis, Annual Report Essay 2003 (

The figure below shows that this conclusion holds even among the countries that do not belong to the industrialized world. Since the 1960s, the so-called Asian Tigers have seen spectacular economic growth bringing their per-capita GDP from levels close to those of African and Latin-American countries to four times the level of Latin America and 10 times the level of Africa in 2000. Growth in China started to set off around 1980. African countries saw almost no growth during the half century covered in the figure.

Economic Growth in Asia, Latin America and Africa

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Source: Angus Maddison, „Contours of the World Economy”, 2007

The large differences in economic growth have had large differences in the world income distribution. The next figure shows the distribution of world income per capita. Note that this is the distribution of average incomes per person in each country. The length of the segment of the x-axis a country occupies indicates the relative share of its population. This distribution is extremely uneven: A small part of the world’s population has very high income per capita, while the large majority has low income. Holding this figure against the previous ones demonstrates that where a country is on the global income distribution depends primarily on its growth performance, not on the size of its territory, nor on its natural resources.  In fact, Japan and Germany, which are both relatively far right on that distribution stand out as countries with very poor endowments of natural resources and poor conditions for agriculture.

World Distribution of Income Per Capita

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Quelle: Economist Intelligence Unit

Economic Growth: Intensive versus Extensive

What is the nature of economic growth? Economists distinguish between intensive and extensive growth. Intensive growth means producing ever more of the same stuff. Early industrial development was marked primarily by intensive growth. Production methods were improved, economies of scale were realized, ever larger firms could produce ever more output at falling costs3. Henry Ford’s invention of mass production of automobiles is a good example: Ford was able to produce large quantities of Model T’s – which all looked the same – making automobiles affordable for a much larger number of consumers.

Extensive growth means producing a growing variety of goods and producing goods of increasing quality. Because consumers value variety, the value added produced by an economy (its real GDP) increases, when it produces goods in greater variety. As the economies of scale in producing Model T’s were exhausted, car makers realized that their consumers wanted cars in different shapes, colors, etc. Extensive growth includes the development of new products which did not exist before, such as PCs, mobile telephones etc. Because the developed economy is very much a service-oriented economy, extensive growth also includes the production of new services for markets, services that perhaps were previously provided by the larger family in home rather than market production, e.g., child care or care for the elderly.

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Source: „Time well spent“, 1997 Annual Report, Federal Reserve Bank of Dallas, S. 6 (

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Source: „Time well spent“, 1997 Annual Report, Federal Reserve Bank of Dallas, S. 11 (

The figures above illustrate the concept of extensive growth by showing the features of new homes and new automobiles over a time span of 25 years. They remind us of the fact that many features we take for granted today did not exist or were available only in luxury homes and cars 40 years ago. That fact that the construction industry and the car industry grew over this period does not simply mean that they produced ever more homes and cars of the same type. Homes and cars became more valuable, because they were of better quality and had more differentiated features.

If a country’s economy grows faster than its population and, therefore, its labor force, this must mean that the average worker can produce more than before, i.e. his or her productivity has increased. In terms of work time (not necessarily individual incomes), this must imply that he or she can afford more goods and services. The table below illustrates the point. It shows that an average worker in the US had to work 463 hours to buy a dishwasher in 1913. In 1997, he had to work 28 hours to afford (a much improved) dishwasher. In 1916, an average worker in the US had to work 3162 hours to buy a refrigerator, almost a year at 10 hours work days. In 1997, he or she worked 68 hours to buy a (much better) refrigerator, a week and a half at eight hours a day.

The cost of home appliances in US$ and average hours worked

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Source: „Time well spent“, 1997 Annual Report, Federal Reserve Bank of Dallas, S. 8 (

Economic Growth: Capital and Labor

The preceding discussion shows that, indeed, long-term economic growth is the dominant source of well being and much more important to worry about than managing the business cycle. How then can we explain economic growth and what can we do to promote it?

Traditional analysis of economic growth focuses on population growth and capital accumulation as the two main drivers of economic growth. Generally speaking, capital includes all durable inputs which are used in the process of production, such as tools, machinery, buildings and structures etc. The use of capital in production increases the productivity of human labor. Thus, by accumulating more and more capital per worker, output per worker can be increased and the economy can grow in per-capita terms. An important question is, can such growth continue forever?

Economic analysis of this question is due mainly to Nobel laureate Robert Solow of MIT4. Accordingly, the level of production depends on the volume of the factors of production the economy has. We distinguish between two main factors of production: labor and capital. In doing so, we treat all labor the same, i.e., we assume that all differences between individual workers and their qualifications, which of course do exist, are relatively unimportant to explain what we want to explain. Similarly, we treat all capital the same. Population growth increases the size of the labor force allowing more production. Investment increases the capital stock, allowing more production.

We describe the relationship between the economy’s level of output (real GDP) and the labor force and the capital stock employed by means of a production function. A production function, F(K,L) indicates the maximum amount of output, Y, that can be produced with a given stock of capital, K, a given labor force, L, and a given technology.

Y = AF(K,L)

The word “maximum” in this definition indicates that we are only interested in efficient production; producing less than the maximum possible would amount to wasting valuable resources of labor and capital. The parameter A is a number which indicates the level of technological progress: The larger A, the more output can be produced with given amounts of capital and labor. We return to that point later. We focus on the per-capita production function f(k), which indicates the maximum amount of output per-capita, y, that can be produced by a given level stock of capital per person, k.

y = af(k).

By focusing on per-capita magnitudes, we already account for population growth in the analysis.

It is reasonable to assume that the production function has positive and declining marginal products of capital and labor. This means that, for a given labor force, increasing the size of the capital stock increases the amount of output, but the increase is the smaller, the larger the amount of capital that is already being used. Similarly, for a given capital stock, adding a person to the labor force increases output, but the increase is the smaller, the larger the labor force that is already employed. The reason why it is reasonable to assume this is this: If firms wish to maximize their profits, positive marginal products of labor and capital imply that they are willing to pay positive prices for the capital and labor they imply. Declining marginal products of capital and labor imply that firms will want to employ less capital, if the cost of capital goes up, and less labor, if wages go up. This is confirmed by empirical observations.

In formal terms, this implies for the per-capita production function:

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The first derivative is positive while the second derivative is negative.

A host of empirical literature in economics over the past century has shown that the concept of a production function works well to describe the relationship between a country’s real GNP and the production factors, capital and labor, it has available. Much of this research goes back to Chicago economist Paul Douglas. The figure below illustrates a production function of this kind with a=1.

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Production Function

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Every period, the value of the output produced is paid out to workers and capital owners as labor income and capital income, respectively. These incomes can be used in two ways: They can be consumed or saved. To keep things simple, we assume that workers and capital owners save a fixed portion, s, out of every income, so that savings per capita equals sy. These savings are made available to the firms in the economy for investment. If i denotes investment per capita, and savings are equal to investment, this means that i = sy. Every period, per-capita investment is a fixed part of total output. Since per-capita output is a function of the capital stock per capita, so is investment, i = saf(k).

Every period, investment can serve two different purposes. It either replaces that part of the capital stock which is worn out in production, i.e., depreciation, or it serves as new capital. Assuming that depreciation is proportional to the capital stock at a rate δ, i = Δk + δk, where Δk is net investment, or the increase in the capital stock per person over time.


Δk = i – δk = saf(k) – δk.

The increase in the capital stock over time is itself a function of the capital stock, because it depends on the level of output produced less what is consumed every period.

We are now interested in the question whether the economy grows up to a point from which on all per-capita magnitudes are constant. We call such a point a steady state. The answer is: yes, necessarily so! First, if Δk = 0, the capital stock per capita is constant and, therefore, output per capita is constant. Second, Δk = 0 at the point where all investment is used to replace depreciation, i = δk. Third, because of declining marginal productivity of capital, output, and hence savings and investment, increases with increasing capital per person, but at a declining rate. In contrast, depreciation grows linearly, with a constant rate. Therefore, there must be a point where the two are just equal. The next figure illustrates this point. There is exactly one steady state at k*. The corresponding output per capita is y*

Steady State

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Suppose that we begin at a level of capital k < k*. Investment exceeds depreciation every period and the capital stock grows until we reach k*. Conversely, if we begin a k > k*, investment is smaller that depreciation and the capital stock falls until we reach k*.

Simple as it, this framework has a number of important implications. The first is that capital accumulation does not lead to economic growth forever. Because of the declining marginal productivity of capital, the contribution of capital to economic growth will eventually be exhausted. From that point on, if nothing else occurs, the economy will not grow any further in per-capita terms, i.e., any economic growth in its absolute size will be due to population growth.

Second, if technology is the same in different countries, all countries will converge to the same level of per-capital income eventually. Countries with less capital per person than k* will accumulate more capital, countries with more than k* will decumulate capital.

Third, the level of per-capita income depends critically on the nation’s savings rate. With a higher savings rate, a country can finance more investment and sustain the depreciation on a larger capital stock. Recall that this is a closed economy, i.e., we abstract from the role of international trade and finance. In an open economy context, countries can invest more than they save, if their investment is financed through foreign savings, i.e., if they run current account deficits. In such a context, and with free and undistorted international financial markets, the tendency for per-capita GDP to converge internationally would be reinforced.

Is there economic convergence over time? At a first glance, statistics such as figure 7 above seem to suggest that the answer is unambiguously no. But we must not forget that the framework depicted here is a very simple one, i.e., it leaves out many factors explaining the specific circumstances and histories of individual countries. Natural conditions such as climate and access to maritime waterways, but also cultural and legal traditions and histories may play a role, as do regimes of market regulation. To test for convergence internationally, economists have considered the relationship between the per-capita GDP growth rate of countries over long time periods and the initial level of per capita GDP,

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Here, T is the length of the period considered, a and b are parameters, i=1,…N is the group of countries. Regression analysis of this type typically finds that “other variables” are needed to detect the parameter b, which is the one we are interested in. If b< 0, countries with a higher per-capita real GDP initially grow less fast than countries with initially lower per-capita real GDP. The implication is that countries converge.

A host of empirical studies of this kind have been done. The general conclusion is that, statistically, b<0. Taking into account the impact of “other variables”, convergence is a fact of the world economy. What is amazing is that the literature finds that b is approximately (-2%) for different groups of countries and economies around the world. Whether the economies considered are the different states of the US, different countries in Europe, or industrialized and developing countries, the estimated b always seems to be of that order. What differs is the kind and impact of the “other variables.” With b = -0.02, it takes about 34 years for a given gap between the per-capita incomes of two countries to shrink by one half. If nothing else happens, i.e., the “other variables” do not push the gap up in the meantime. Of course, in real life other things happen all the time. But that’s a different story…

Economic Growth: Saving and Investment

The previous section has shown that there is a level of capital per capita of the population at which the economy settles down. Per capita output remains constant from this point on, although total output and the total capital stock may grow at the rate of population growth. An obvious question is, what happens if workers and capital owners save more?

Consider the next figure. Starting from a steady state at k1*, an increase in the savings rate increases the amount of investment. This causes the capital stock per capita to grow. Output per capita grows and savings with it. This fuels further growth in the capital stock etc. Eventually, the economy settles at a new steady state, k2.

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An increase in the savings rate

This suggests that the government can stimulate growth by stimulating savings. Tax policies, for example, that give households the incentive to save more, would lead to an increase in the savings rate. Such policies could exempts interest income from income tax, for example.

It is not clear, however, that this is always desirable. The goal of government policy should not be to maximize capital per capita but consumption per capita, since consumption is what people care about. Why this makes a difference is easy to see: A higher savings rate means that a lower share of real GDP is available for consumption. Thus, a higher savings rate leads to two countervailing forces: On the one hand, real GDP increases and this increases the potential for more consumption. On the other hand, the capital stock increases and needs higher savings to be sustained. Unless the former effect is larger than the latter, a higher savings rate leads to a reduction in consumption per capita.

These considerations lead us to ask, is there a level of the capital stock per capita that maximizes economic welfare in the sense that it leads to the largest possible level of consumption per capital? The following section, which is a bit technical, shows that the answer is yes. Those who like a little math will enjoy it, those who don’t can skip it. The answer is in the Golden Rule of Economic Growth: The economy reaches its maximum consumption per capita, if all capital incomes are saved and invested and all labor incomes are used for consumption. Empirically, this would imply an investment rate of about one third for the US economy.   

The Golden Rule of Economic Growth

In the steady state, the equality of savings and depreciation implies that

saf(k*) =δk *

and consumption is

c* = y* – i* = af(k*) – saf(k*) = af(k*) – δk *.

We wish to maximize per-capita consumption, c*, with respect to the per-capita capital stock, k*. Taking first derivatives, this requires that

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It is optimal to choose the per-capita capital stock for which the marginal product of capital just equals the rate of depreciation.

The figure below illustrates the point. Per capita consumption equals the distance between total output per capita, f(k), and total savings, sf(k). The optimal capital stock is kGR, which maximizes the distance between the two curves.

Thus, it is best to choose the savings rate which makes kGR the steady state capital stock.

In a competitive market economy, the real rate of interest, r, equals the marginal product of capital and the real wage, w, equals the marginal product of capital. Thus,

Y = rK + wL.

The Golden Rule then says that, at the optimal capital stock k*, the real interest rate equals the rate of depreciation, r = δ. Since total capital income in the economy is rK, it follows that total investment, δK = rK. Thus, at the optimal capital stock, all capital income is invested and finances depreciation, while all labor income is consumed.

Golden Rule of Growth

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Economic Growth: Technological Progress

The framework due to Robert Solow has two weaknesses. The first is the prediction that per-capita GDP converges to a constant level over time. As we have seen above, the industrialized world has seen positive growth for more than 200 years now. The second is that the long-lasting process of economic growth we have observed above cannot be explained on the basis of capital accumulation and population growth alone, if we assume a production function with declining marginal products.

This second point can be demonstrated based on growth accounting. For this purpose, we assume a Cobb-Douglas production function

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Empirically, production functions of this kind have proven very successful and robust. Typical values of the parameter α are between 0.25 and 1/3. The parameter A is called “Total Factor Productivity, TFP. In per-capita terms,

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Given a production function of this kind, the relative change in real GDP over time can be separated into two parts:

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The first term is the growth rate of TFP, the second is the effect of “capital deepening,” i.e., the increase in the per-capita capital stock of the economy. TFP growth is also sometimes called the “Solow residual”, indicating more clearly that, relative to the Solow framework, it is the unexplained part of economic growth. This table shows the results of growth accounting for the OECD countries.

Growth accounting in OECD countries 1960-2000

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Source: P. Aghion and P. Howitt, „Capital, innovation, and growth accounting“, Oxford Review of Economic Policy, Volume 23, Number 1, 2007, pp.79–93, S. 83

The table  shows the embarrassment of the Solow framework to explain economic growth: TFP growth accounts for the largest part of economic growth in the industrialized world. For the most part, more is needed to explain long-term economic growth. This “more” is productivity growth beyond capital accumulation. At the same time, the table indicates that productivity growth is really what a nation needs to worry about. In the long run, the wellbeing of a modern economy depends primarily on achieving sufficient TFP growth. The question is, what is behind TFP growth?

The Contribution of Human Capital

A first extension of the Solow framework takes into account that labor is more than pure manual work and simple operation of machinery. Workers acquire specialized knowledge which they bring to fruition in the process of production and which increases their productivity. Economists talk about human capital in this context, a concept developed by economics Nobel Laureates Theodore Schultz and Gary Becker, both from the University of Chicago5. It is human, because it is connected to the human mind and personality; it is capital, because knowledge has the properties of an asset stock. Like capital, it can be accumulated. Like capital, it loses value over time.

Denoting the stock of human capital per worker by h, we extend the production function as follows:

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Empirical studies measure the human capital stock per worker by variables such as the average number of years of schooling, perhaps distinguishing between primary and secondary schooling. This table shows how differences human capital can explain differences in the level of real GDP per worker.   

The Impact of Human Capital

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For example, Germany’s real GDP per worker was 82 percent of that in the US in 1988. Germany’s capital stock per worker was two percent larger than in the US, while its human capital was 80 percent of that in the US. Total factor productivity – after accounting for human capital, was 94 percent of US TFP. Thus, with the same amounts of capital and human capital per worker, Germany would have had 94 percent of US real GDP per worker. Thus, while intuitively attractive, the contribution of human capital to the explanation of cross-country differences in real GDP per worker is limited.

The concept of human capital can contribute to understanding economic growth. If the level of output depends on the stock of human capital available in the economy, output can grow over time through the accumulation of more human capital. This is an attractive idea, because the stock of human capital does not consist of physical resources and is, therefore, not constrained by the scarcity of physical resources. The stock of human capital grows through learning: Learning based on education in schools and colleges and learning on the work place, i.e., learning by doing. Both can be considered as factors contributing to economic growth6.

The concept of human capital moves learning and education into the focus of the economics of growth. Time spent in education is time not spent working and earning wages. Hence, the decision to get education is an investment decision, in which current cost must be weighed against future pay-offs. Government can improve long-term economic growth by subsidizing education and training of the work force. Note, however, that human capital empirically exposes declining marginal products, similar to physical capital. If so, the effect on human capital on growth and the desired stock of human capital will be limited. Empirical studies suggest that the growth of human capital explains at best 12-14 percent of long-term economic growth7.

Technological Progress and “Endogenous” Growth

Recent extensions of the Solow framework due to Paul Romer8 ascribe the Solow residual and TFP growth to technological progress, i.e., the accumulation of technological knowledge in an economy. This knowledge serves to increase the productivity of the economy‘s capital and labor. In technical terms, the level of productivity captured in the parameter A in the production function is allowed to grow over time. This alone, of course, does not explain anything. What makes the extension interesting is the idea that new technological knowledge is produced according to principles similar to the production of output. Specifically, producing new technological knowledge requires the investment of capital (building labs, computing equipment etc) and to hire workers who work in this area.

This idea yields a number of interesting ideas about economic growth in the long run. We now think about the economy as consisting of two sectors, one producing output – real GDP – and one producing new technological ideas. We call the latter the “research and development” (R&D) sector. In both sectors, production is described by a production function, relating production output to the inputs of capital and labor. Since the economy has a given stock of capital and a given labor force, it must divide both between the two sectors. Thus we have

Production of goods and services

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research and development:

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Here, Ky and KA are the amounts of capital employed in output production and in R&D, and similarly for Ly and LA. Given the economy’s total resources, K and L, it must be true that KA + Ky = K and LA + Ly =L. In the R&D sector, we allow for the possibility that the stock of technological knowledge already available, A, affects the production of new knowledge. For example, the more ideas are already around, the harder it is no develop new ones. In that case, 0 < θ < 1, which is what we assume.

In every period, both sectors compete for capital and labor. Assuming that both are fully mobile between the two sectors (since we consider long time periods), wages and the return to capital must be the same in both sectors. Here, again, we abstract from differences in the qualification of workers between sectors to illustrate the basic argument in the simplest possible way. Consider the allocation of capital between the two sectors. In a competitive market economy, the return on capital equals the marginal product of capital. For the production of goods and services, this is

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The R&D sector, however, cannot function like a competitive market. This is because of the special nature of what is produced in this sector: knowledge. Like all information, it has the characteristic that it is freely and universally available once it is “out.” If a firm’s competitor can get the information about its rival’s latest innovation for free and use this information, it will simply copy the innovation and save the cost of its development.

Hence the return on the development will be lower for the firm that came up with the new information than the true value of this information for the economy. We capture this idea by saying that the marginal product of capital in the R&D sector is γ > 0 times rate of return on investment in that sector. Governments can influence γ e.g. though patent protection. The better patens are enforced, the larger the return on investment in R&D.

Thus, we have

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Allocation of Capital

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We can now use a simple diagram to show the allocation of capital between the two sectors. Consider the figure above. On the horizontal axis, we plot the total capital stock of the economy. The amount of capital invested in the goods sector is measured from point Y to point A: At A, all capital is invested in output production. The opposite holds for output invested in the R&D sector. On the vertical axes we measure the rates of return on. The left axes starting in point Y measures the rate of return in the goods sector. The right-hand-side axis measures the rate of return in the R&D sector. Both are falling as capital in the sector increases.

From the point of view of the investor, the two rates of return must be equal. Thus the allocation of capital is the one where the two lines intersect. Of the economy’s total capital stock the amount (Q-Y) goes to the goods and services sector, while the amount (A-Q) goes into R&D.

Now consider an improvement of patent protection in the economy. As γ rises to γ’, the curve showing the rate of return in the R&D sector shifts upwards. More capital is attracted into this sector. A new allocation is found where the new curve intersects with the curve showing the rate of return on investment in the goods sector, i., point Q’. As more capital is now used in the R&D sector, more technological knowledge is produced. The level of technology, A, begins to grow faster. Generally, this will also increase wages in this sector at least temporarily, leading to further economic growth.

A similar analysis can be done for the allocation of labor between the two sectors.

An interesting question for such a framework is whether it generates the possibility of economic growth going on forever. The answer is yes, but showing it formally requires more technical analysis, which we skip at this point9. This will depend on the parameter values, i.e., it is logically possible and, therefore, ultimately an empirical question.

This analysis bears a number of interesting insights and implications. First, economic growth can continue for very long time periods at least, fuelled by technological progress. Second, in the long run, what matters for the wellbeing of a nation is its ability to keep improving the productivity of its labor force and capital endowment. Unless the US maintains a satisfactory rate of productivity growth, it will not be able to achieve high standards of living for ever larger parts of society.

Third, the growth rate of the economy depends primarily on the productivity of its R&D sector. To raise the growth rate of the economy for long periods of time requires to increase the rate of return on investing in R&D. This point is not always sufficiently appreciated. Government can subsidize the cost of R&D, e.g., by paying subsidies to the training of highly skilled workers in that sector. This will have a level effect, i.e., it will induce more workers to work in the R&D sector which may increase the growth rate for a while. In order to keep the growth rate up, government will have to raise the rate of return, e.g. by better patent protection. It is, therefore, important to look at individual policies and see whether they have level or growth rate effects.

At the same time, it is important to realize that policies attracting resources into the R&D sector will, at the same time, reduce the resources available in the goods and services sector. Thus, it is possible that per-capita consumption falls as a result of such policies. In other words, increasing the growth rate of the economy can generate a fall in the wellbeing of the current generation of consumers, from which future consumers, of course, will benefit.

Limits to Economic Growth?10

In 1972, a book presented by the Club of Rome shocked economists and politicians around the world. The Club of Rome ( is a global think tank, which, at the time, had asked a team of economists to study the question whether or not the world economy could go on growing as it had done in the previous century or so, using the world’s resources and polluting the world’s air and water reserves. The report presented to the Club of Rome, entitled “The Limits to Grow” presented a dramatic forecast, concluding that, without major changes in the patterns of production and consumption around the globe, the world economy would sooner or later reach a point of collapse11. Depending on the scenario analyzed, “sooner” would mean by the turn of the century, “later” would mean well before the year 2100. For example, at the then prevailing growth rate of oil consumption, technologies, and known oil reserves, the world would run out of oil by 1992. Increasing the reserves by a factor of five would push this event to 2020.

The main points of the book are summarized as follows12:   

Our world model was built specifically to investigate five major trends of global concern – accelerating industrialization, rapid population growth, widespread malnutrition, depletion of nonrenewable resources, and a deteriorating environment.

The model we have constructed is, like every model, imperfect, oversimplified, and unfinished.

In spite of the preliminary state of our work, we believe it is important to publish the model and our findings now. (…) We feel that the model described here is already sufficiently developed to be of some use to decision-makers. Furthermore, the basic behavior modes we have already observed in this model appear to be so fundamental and general that we do not expect our broad conclusions to be substantially altered by further revisions.

Our conclusions are:

1. If the present growth trends in world population, industrialization, pollution, food production, and resource depletion continue unchanged, the limits to growth on this planet will be reached sometime within the next one hundred years. The most probable result will be a rather sudden and uncontrollable decline in both population and industrial capacity.

2. It is possible to alter these growth trends and to establish a condition of ecological and economic stability that is sustainable far into the future. The state of global equilibrium could be designed so that the basic material needs of each person on earth are satisfied and each person has an equal opportunity to realize his individual human potential.

If the world’s people decide to strive for this second outcome rather than the first, the sooner they begin working to attain it, the greater will be their chances of success.

The behavior mode of the system is that of overshoot and collapse. In this run the collapse occurs because of nonrenewable resource depletion. The industrial capital stock grows to a level that requires an enormous input of resources. In the very process of that growth it depletes a large fraction of the resource reserves available. As resource prices rise and mines are depleted, more and more capital must be used for obtaining resources, leaving less to be invested for future growth. Finally investment cannot keep up with depreciation, and the industrial base collapses, taking with it the service and agricultural systems, which have become dependent on industrial inputs (such as fertilizers, pesticides, hospital laboratories, computers, and especially energy for mechanization). For a short time the situation is especially serious because population, with the delays inherent in the age structure and the process of social adjustment, keeps rising. Population finally decreases when the death rate is driven upward by lack of food and health services. The exact timing of these events is not meaningful, given the great aggregation and many uncertainties in the model. It is significant however, that growth is stopped well before the year 2100.

… We can thus say with some confidence that, under the assumption of no major change in the present system, population and industrial growth will certainly stop within the next century, at the latest.

The authors conclude that, in order to survive, mankind must achieve two things:

  • To stop population growth and
  • To stop the accumulation of capital per worker.

The world economy would then converge to a steady state of the kind discussed above, where all per-capita variables are constant.

The book caught a lot of attention around the world and fuelled the then fledgling ecological movement. It provided the impetus for regulation protecting the environment and saving resources such as recycling. In that it was very useful. Nevertheless, it contained a number of severe methodological flaws. The main one was to neglect the role of market prices in guiding economic decisions. For example, as oil became much more expensive in the 1970s, new technologies were invented that reduced the amount of oil needed in industrial production.

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Source: OECD

This figure illustrates that point. It shows the development of energy efficiency, measured as the number of tons of crude oil used per USD 1000 real GDP from 1971 to 2005. On average for the OECD, this number has fallen by 38 percent, on average in the European Union by 47 percent. For China, which started at a much higher level, the reduction is even 75 percent. Technological developments allow the world economy to use its resources much more efficiently, and the development of such technologies is driven by price developments.

A second, important price mechanism neglected in the Report concerns the technological progress in resource extraction. Here it is useful to distinguish between the following concepts. For an exhaustible resource such as oil or iron ore,

Proven reserves are known deposits which are economically recoverable with given technologies. For oil, these would be oil fields that are known and can be exploited with current drilling techniques.

Unproven reserves are known deposits which are not economically recoverable with given technologies. For oil, these would be oil fields which are currently not accessible, e.g., because they are offshore and in currently inaccessible depth.

Unconventional reserves are deposits which occur in forms other than those which are economically recoverable with given technologies. For oil, these could be oil sands as opposed to oil fields.

Technological progress moves unproven reserves into proven reserves and unconventional reserves into conventional reserves. Thus, it increases the reserves available to the global economy. The implication is that the point of exhaustion at given rates of production and usage is pushed out in time. For oil, the current rate of proven reserves over annual production stands at 40 years, while the rate of unproven reserves stands at 23 years and the rate of unconventional reserves at 202 years13.

With this in mind, the conclusion that world population growth has to be stopped quickly is difficult to maintain. It is an ethically difficult conclusion, anyway, because stopping global population growth needs an immediate answer to the question, which and where new human beings are allowed to be born? Giving development aid to poor countries in return for (forced) birth control, a policy approach promoted, among others, by the United Nations, certainly is no good answer.

The next figure shows the development of world population as predicted by current trends. It suggests that world population will keep rising from about seven billion people today to over nine billion in 2050. Figure 16 shows that the population growth rate has fallen steadily since the 1960s. Population growth is driven by two forces, increasing life expectancy and, at the same time, falling birth rates. Birth rates have generally fallen in countries after economic growth took off and incomes increased. In the now industrialized countries, this is a tendency that began already in the 19th century.

World Population 1950-2050

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Source: U.S. Census Bureau, International Data Base, World Population: 1950-2050 (

World Population Growth Rates 1950-2050

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Source: U.S. Census Bureau, International Data Base, World Population Growth Rates: 1950-2050 (

The combination of increasing life expectancy and falling birth rates implies that, at some point, populations will begin to shrink. Germany’s population, for example, is projected to decline from 80 million today to below 70 million by 2050. At the same time, the share of old people in the population will steadily increase.

While the size of markets around the world can be expected to keep growing, these demographic trends will certainly impact the structure of markets as well. Increasing the share of the elderly in the population means that demands for services and goods consumed by older people will increase – fewer sportsy cars and more cars designed for safety and convenience.

It will also put an increasing burden on the average young person, who has to work not only for his or her own family but increasingly to feed people beyond working age. This will put stress on retirement and health care systems around the world, which must be designed to be sustainable under such circumstances. Finally, it will create competition for young especially young and skilled people, as countries around the world will try to attract them to work. As in the 19th century, large-scale migration could, once again, become a major force of the global economy, driving the distribution of economic activity, growth, and wellbeing around the world.   

2Oded Galor, Unified Growth Theory. Princeton: Princeton University Press 2011

3Economies of scale“ occur when the average cost of producing a good falls as the quantity produced increases.

4M. Solow, „A Contribution to the Theory of Economic Growth.” Quarterly Journal of Economics 70(1), 65-94

5Gary S. Becker, Human Capital. New York: Columbia University Press 1964; Theodore W. Schultz, The Economic Value of Education. New York: Columbia University Press 1963, Investment in Human Capital: The Role of Education and Research, New York: Free Press 1971

6Although the idea of learning as a factor of growth had been around for a while, it was first formally presented by Robert E. Lucas Jr., “On the mechanics of economic development.” Journal of Monetary Economics 22, 1988, 3-42.

7 Bas van Leeuwen, Human Capital and Economic Growth in India, Indonesia, and Japan, A quantitative analysis 1890-2000, Diss. Utrecht Universität, 2007, google-books, Tabelle 2.1  

8Paul Romer, „Endogenous Technological Change“, Journal of Political Economy 98, October, Part 2, 71-103, and “Increasing Returns and Long Run Growth”, Journal of Political Economy 94, 1986, 1002-1037.

9For a good exposition, see Philippe Aghion and Peter Howitt, Endogenous Growth Theory. Cambridge, MIT Press, 1998, chapter 3.

10The idea that the potential for economic growth was limited, because continued population growth would at some point lead to general famine was first proposed by the English economist Rev. Thomas R. Malthus (1766-1834).  

11Donella and Dennis L. Meadows, Jay W. Forrester, Jorgen Randers, and William W. Behrens III, The Limits to Growth – Report to the Club of Rome. New York: Universe Books, 1972.

12The Limits to Growth“. Abstract established by E. Pestel.

13Martin Stuermer and Gregor Schwerhoff, „Non-renewable but Inexhaustible – Resources in an Endogenous Growth Model.” Working paper, University of Bonn.