August 2005

The Polish economist Michal Kalecki - pronounced "Kaletski" - (1971)

gives an analysis of an obscure economic debate between Rosa Luxemburg and Tugan Baranovsky called the underconsumptionist debate. We begin this chapter with an oversimplication of the Kalecki's analysis of this underconsumptionist debate.

This debate went as follows: As labor saving automation replaces labor, will not unemployment eventually become so acute and downward pressure on wages so intense that business activity will falter for lack of a market? No, according to Tugan Baranovsky. As long as businesses keep investing flat out, they will always constitute a market for each other's products until, ultimately, the economy consists of "machines producing machines for the sake of producing more machines"as in the science fiction movie "Terminator".

Quote taken from M. Kalecki 1971.

Not a desirable outcome perhaps, but a possible one. According to Rosa Luxemburg, however, Tugan Baranovsky's outcome was not possible. Eventually the "chain letter effect" of "investment for investment's sake" would be broken as some businesses slacked off in their investment and the whole process imploded.

Rosa Luxemburg, maintained that the only way for economic growth to continue was for more and more geographical areas, formerly outside the market economy, to be brought into it by Western colonization of non-Western countries

For those who are interested, J. Robinson in the introduction to R. Luxemburg (1968) describes Luxemburg's growth model as follows:

"As soon as a primitive (pre-industrial) closed economy has been broken into, by force or guile, cheap mass-produced consumption goods displace the old hand production of the family or village communities, so thata market is provided for the ever increasing output from theindustries of the (consumer goods sector) in the old centresof capitalism, without the standard of living of the workers who consume these commodities being raised. The ever growing capacity of the export industries requires the products of the (capital goods) sector thus maintaining investment at home. At the same time, great new works such as railways are undertaken in the new territories." Though this pattern certainly represented the dreams of many Western businessmen ("If every Chinaman added an inch to his coattails, the mills of Lancashire could be kept running forever"), few economists would say that demand from the European colonies was an indispensible factor in early 20th century global economic growth.

This process would come to a halt when all countries were colonized or, more likely, when it precipitated a period of calamitous global upheavals, as the colonizers fought over colonies, and as the colonized rebelled. On this latter point, at least, Rosa Luxemburg was indeed right, although, today, her economic growth theory would be viewed as farfetched (as would Tugan Baranovsky's) and not an explanation for the catastrophes of the 20th century.

Economic growth theory has become far more sophisticated since Rosa Luxemburg's day. We bring up this archaic argument between Rosa Luxemburg and Tugan Baranovsky to illustrate the kinds questions we want to ask about future global economic growth.

Namely, where and how is it likely to occur? Will it involve the inclusion of more and more people into the world market economy? Perhaps the hundreds of millions of people in the former centralized economies?

Or the billions of people in the less developed economies? Or will it involve more and more growth in the already developed industrialized economies, and more and more stagnation in the rest of the world, leading to what Z. Brzezinski (1993) calls a global clash between "insatiable consumers and starving spectators"? Will it be blocked by environmental constraints or propelled forward by constantly evolving new technologies?

Here's a simple growth model. Businesses hire workers to produce economic output. Part of this output is consumed by the workforce and part is invested by businesses in order to create more economic capacity. This greater capacity is, in turn, used to hire more workers, which are used to produce an expanded amount of output, part of which is consumed by the expanded workforce and part of which is invested to create still more economic capacity to hire still more workers, and so on, the only limiting constraint being the size of the potential workforce.

Given the billions of people outside the industrial market economies, such a growth model would certainly seem to have a lot of potential. The Malthusians often look at the burgeoning populations of the underdeveloped world as an unmitigated disaster.

But to many investors, the enormous amount of talent, resourcefulness, ingenuity and drive for material betterment that must be present among so large a number of people, is often seen as an opportunity for unbounded economic expansion. The economist Milton Freedman (1992) has compared it to "the equivalent of a second industrial revolution". A good idea of how some investors look at this model of "economic growth through geographical expansion" is given by an interview between Barron's magazine and Barton Biggs, manager of Morgan Stanley Asset Management:

"Barton Biggs: The domestic demand in these (large Latin American) countries is so big, and they are not like the Asian Tigers - Singapore, Taiwan, Korea, etc. - who had to rely on export demand. I mean their domestic demand is big enough so that they can bootstrap themselves by that. They can't grow 8% or 10% a year, the way the Tigers did in their prime, but they can grow 5% or 6% a year....

Barron's: ..What we're asking is not so much whether latent demand exists as whether there realistically is any way of satisfying it? Barton Biggs: But you see, that's the magic- when you start opening these economies up to foreign capital and equity capital, that's the spark that gets them going, and you start creating virtuous circles. You get people to work, you pay them wages, so they can buy washing machines and all that stuff.

Barron's: Well, I think it's much more complex than you suggest.

Barton Biggs: "Gotta dream! Gotta dream!" Barron's International Roundtable, September 16, 1991.

In what way is it "much more complex" as Barron's suggests. As we shall see, the exact nature of these "complexities" embody some of the most important issues of present day history.

Here's another simple model of economic growth, this time with a fixed number of workers. Businesses produce economic output. Part of this output is consumed by the workforce and part is invested in industrial innovations which yield productivity improvements. Let's say (for the sake of argument) that these productivity improvements are labor enhancing rather than labor replacing so that nobody gets fired, and the workforce remains the same.

Part of the increased output goes into wage rises for the workforce (as opposed to hiring more workers) and part goes into investment in yet more industrial innovations which yield still more productivity improvements (which are labor enhancing as opposed to labor replacing). This is followed by more wages rises and more productivity improvements, and so on. This is growth with a fixed labor force and a constantly rising level of consumption per capita (a rising standard of living). This is the type of economic growth that the U.S. experienced from 1945-1973 and the alleged end of which was the main issue in the 1992 presidential elections. ("Will your children have a higher standard of living than you" and so on).

Can such a model of economic growth continue indefinitely? Can it continue indefinitely in the absence of revolutionary technical innovations (something along the lines of "cold fusion" say)?

This is another important question of present day history.

So the main question we address is this: will future economic growth consist of more and more economic activity in the same geographical areas, or will it consist of the spread of economic activity to more and more geographical areas?

By indefinitely, we mean within a very long-term planning horizon.

Let us now briefly examine some of the old and new economic growth theories. First, we will describe the so called Harrod-Domar growth model which was developed in the late 40's. This model says, basically, that in order to achieve a desired increase in economic output, the economy needs a proportionate increase in the amount of capital stock, (so many railroads, so many roads, so many bridges, so many machine tools, etc. are needed in order to achieve a unit of output increase).

In other words, the ratio of incremental economic output to incremental increase in capital stock is fixed, the so called incremental capital output ratio (ICOR).

Suppose, for example, that the incremental capital-output ratio for a particular economy is 2. Then, in order for the economy to increase its output by 1 unit, it needs to acquire 2 units of additional capital. Of course, once it has acquired 2 units of additional capital, it also needs to acquire additional workers to operate this capital (to drive the trucks, operate the machines, etc.) However, if it has acquired less than 2 units of additional capital, then, no matter how many additional workers it acquires, it's output will increase by less than 1 unit. This is because, in the Harrod-Domar model, labor can operate capital, but it cannot substitute for it. No amount of runners, for example, carrying packages, can substitute for even an infinitesimal proportion of the economy-wide stock of locomotives.

In other words, in the Harrod-Domar model, the economy needs capital and labor in fixed proportions. For this reason, it can be shown that, in the Harrod-Domar model, in order for an economy to achieve long term balanced growth, the capital stock has to grow at the same rate as the labor force, otherwise unemployment or shortages will result. Actually, the situtation is even worse than this. In the Harrod-Domar model, the amount of economic output saved is assumed to be a fixed percentage of total output, the so called savings rate.

Thus, in order for balanced growth to be achieved, the savings rate, the amount of output invested and the rate of population growth all have to be in balance, otherwise gluts, shortages, unemployment or labor scarcity will develop.

The Harrod-Domar economic is very much in the tradition of the Keynesian revolution with its concern for economic stability and unemployment and also for the rigid assumptions useful primarily for short-term economic analysis. The Harrod-Domar model neglected the effects of relative prices on factor proportions, such as capital and labor, implying that they were in fixed ratio. Thus, the Harrod-Domar model is generally thought to be more applicable to a developing country with a capital constraint on growth.

The World Bank uses a Harrod-Domar type model, a "two-gap model", called the "Revised Minimum Standard Model (RMSM)" in its evaluations of LDC structural adjustment programs. The "Shimomura strategy" for doubling Japan's national income in the 60's was based on a Harrod-Domar growth model.

This strategy, devised by Dr. Osamu Shimomura, said that if firms invested flat out and consumers save the maximum amount that they could, then Japan's GNP would double in the 60's. The basis behind this reasoning was the low capital/output ratio made possible by investing in thelatest, most productive technology. This enabled the instability inherent in the Harrod-Domar model to be circumvented. (See H. Takenaka, 1991).

Thus, the Harrod-Domar model suggests that balanced economic growth in the absence of central planning is a highly unlikely occurrence. This is clearly not an accurate description of reality, since there have been long periods in history when balanced economic growth has been propelled largely by private decentralized investment decisions.

"This sort of growth theory is essentially uninteresting because no economy could function if it did not contain definite stabilizing features that the permitted the system to absorb the shocks that it regularly receives froms outside. What we want to know is how much we can rely on these stabiliy properties and for that purpose we need more flexible growth models. This explains why recent developments in growth theory have gone far beyond Harrod's original formulations." M. Blaug (1962)

To address the flaw described above, the economist Robert Solow developed the so called neo-classical model of economic growth (R. Solow, 1956)

We concentrate on the neoclassical growth theory and its variants in this chapter, as opposed to the structuralist growth theories of N. Kaldor, N. Kalecki, L. Pasinetti, and J.Robinson, not because we wish to slight these other growth theories, but because we're not writing an encyclopedia, and the neoclassical growth theory is better known and has attracted a larger body of empirical research.

For those interested in other growth theories, see H. Wan, 1971.

According to the neo-classical model of economic growth, the assumptions of the Harrod-Domar model are highly unrealistic. In a modern economy, according to the neo-classical model, there are many different kinds of techniques, some more capital intensive, some less capital intensive, for performing the same economic functions. This means that capital and labor are partially substitutable, one for the other, and different combinations of capital and labor can yield the same amount of total economic output. It is this partial substitutability of capital and labor, one for the other, that ensures balanced long term economic growth. (As we shall see below.)

A simple formulation of neo-classical growth model can be stated as follows:

Y = F(K,L),

where Y is total economic output, L is total labor, K is the total capital stock, and where F is a production function. What is a production function? To explain this, (for those unfamiliar with functional notation) imagine that the entire economy consists of a single factory. The production function, F(K,L), of this factory, then, is a sort of schedule (or computer program), which, given inputs of labor (L) and capital (K), tells you how much output (Y) the factory can produce

Equivalently one can regard the economy as consisting of a large number, M, of identical firms each of which has theproduction function F(K/M,L/M). The total economy then has the production function MF(K/M,L/M) which, by constant returns to scale, is F(K,L).

For the purposes of this discussion, labor (L) is taken to be the number of people in the workforce. The measurement of total capital stock (K), on the other hand, is much more complex. There are many different kinds of capital stock (inventories, durable equipment of various kinds, structures, land and so on).

For purposes of simplification, capital stock (K), in the Solow growth model, is assumed to be a uniform homogeneous substance, which is measurable in some sort of unit, a "unit of capital".

Obviously that is a drastic oversimplification of a real economy. After all, "what does it mean to say that the capital stock was (say) twenty times larger in 1980 than 1880?

How many spinning jennies equal a personal computer?"

(B Bernanke, 1987).

In fact, the aggregation (lumping together) of all the different kinds of capital stock into a single homogenous substance was probably the most controversial aspect of the Solow growth model. It started a long theoretical debate, called the "battle of the Cambridge's", between the economists of Cambridge Massachusetts and the economists of Cambridge England . The details of this debate are far beyond the scope of this book.

Those interested in this arcane debate, see R. Solow, 1960.

For our purposes, we will simply accept the this simplification.

The production function, F(K,L) above, is assumed to exhibit constant returns to scale, by which we mean that, if both K and L are multiplied by a factor, then F(K,L) will be multiplied by the same factor. For example, doubling both K and L will double F(K,L), tripling both K and L with triple F(K,L), increasing both K and L by 5% will increase F(K,L) by 5%, and so on.

In other words, for any constant z, F(zK, zL) = zF(K,L).

One of the consequences of constant returns to scale is that output per worker (Y/L) is solely a function of capital per worker (K/L). (For a proof of this, see the notes at the end of this chapter)

If Y = F(K,L), where Y is economic output, K is the totalcapital stock, and L is the total labor force labor used, then dividing both sides of the above equation by L yields Y/L =1/L * F(K,L). Because F(K,L) has constant returns to scale,1/L * F(K,L) = F(K/L,1). Thus, Y/L = F(K/L,1). Defining y asY/L, k as K/L and f(k) as F(k,1), we have y = f(k). In otherwords, output per capita is a function of capital stock percapita. If an increase in K and L were to cause a larger thanproportionate increase in economic output Y, the economy is said to have increasing returns to scale The standard Solow economic growth model postulates that increasing returns to scale are not an important factor in a large economy. New variants of the Solow growth model, the so called "new growth theories" study the role of increasing returns to scale on an economy-wide level.

If one makes the not unreasonable assumption that adding more and more capital to a single worker will cause output of this worker to increase very rapidly at first and then at a slower and slower rate as more and more capital is added (the Inada conditions)

For those familiar with elementary calculus, the Inada conditions can be stated as follows; (letting k = K/L, y = Y/Land f(k) = F(k,1)), df/dk > 0, d²f/dk² < 0 and df/dk increases without bound as k goes to 0.

For those familiar with elementary microeconomics, the Inada conditions state that themarginal product of capital is always positive, the marginalproduct of capital always diminishes as capital per capitaincrease, the marginal product of capital is infinite when there is no capital at all in the economy. In other words, adding on more and more capital to a single worker yields diminishing returns.

And, if one makes the additional three assumptions that the savings rate is constant over a long period of time, that all savings are invested, and that the work force is growing at a constant rate, then it is possible to show, using calculus, that economic growth will converge towards a stable path, where the capital per worker (K/L) is constant, and where output (Y), and capital stock (K), are all growing at the same rate as the labor force.

Although, it can take a fairly long time for an economy to converge to its "stable growth path." (K. Sato, 1966)

Let's explain (not prove) why this is so in English. At low levels of capital per worker, the gain in output from adding on additional capital is large (the Inada conditions); hence, at low levels of capital per worker, additional capital is being added to each worker, and the amount of capita per worker is increasing. At high levels of capital per worker, on the other hand, the gain in output from adding on additional capital is small. Thus, at high levels of capital per worker, it pays to simply let the workforce grow and not to add on capital, and the amount of capital per worker is decreasing. This provides a "thermostatic mechanism" which, in the "long run", causes the amount of capital per worker to even out at a constant level

A level which depends on the savings rate, the proportion of total economic output which is saved.

Suppose that, "in the long run", the rate of growth of the labor force is 5% per annum. Since, in the long run, the amount of capital per worker, is constant, the rate of growth of the capital stock is also 5% per annum. Because of constant returns to scale, the rate of growth of economic output is likewise 5% per annum.

This is a very incomplete, oversimplified explanation, nota proof. For those familiar with elementary calculus, let the proportion of output saved be designated by s. The amount invested in a unit of time is the rate of change of total capital stock per unit time, which is dK/dt. The amount saved is then sY.

Since what is saved is invested, dK/dt = sY.Defining, k, f, and y as above, setting the rate of growth ofthe workforce dL/dt to be a constant n, and differenting both sides of dK/dt = sY logarithmically, yields the equation dk/dt= sf(k) - nk. Let k^* be the value for k^* at which dk/dt = 0;i.e. sf(k^*) = nk^*. A simple version of the 'phase diagram' technique, shows when k is less than k^*, dk/dt is positive (k is increasing), and when k is greater than k^*, dk/dt is negative (is decreasing) and, therefore, k will converge to k^*as time goes to infinity. k^* is the capital per worker which the economy will converge to as it grows. It depends on the savings rate and the rate of growth of the workforce, n.

Output per capita (or standard of living) will also depend on the savings rate. However, the rate of growth of output isequal to the rate of growth of the workforce, and does not depend on the savings rate, a result which has seemed counterintuitive to many economists, and which is addressed inthe newer variants of the Solow model, the so called "new growth theories".

Thus, the Solow model removes the instability inherent in the Harrod-Domar model.

The Solow model also shows that, in the absence of technological change, the economic growth rate will be determined by the rate of growth in the labor force, a fact which would seem to make a stable population a potential impediment to growth

This is not strictly true of the model presented here, but is true in a more complex version of the Solow neoclassical growth model called the optimizing version which takes long term consumer demand into account. For another model (using different methods) of the drag that a finite population puts on economic growth, see P. Samuelson, 1988.

However, technological change does occur so that the same amounts of labor and capital yield more and more output as time goes on. In a simple version of the Solow model this fact is dealt with as follows:

Y = F(K,L,t),

where K is the capital stock, L is labor and t is time.

If the above equation is converted into rates,

This is done by means of logarithmic differentiation.

It can be shown that the overall economic growth

rate can be decomposed into the following three constituents:

- growth in the capital stock;

- growth in the labor force;

- another factor called total factor productivity, tfp.

Growth accounting studies have shown that economic growth in most of the developed countries has largely consisted of growth in total factor productivity.

"The developed economies are characterized by

little growth in labor inputs (1.1%), moderate

growth in capital stock (5.4%) and a relatively large

contribution of tfp to economic growth (50%)."

From H. Chenery, 1986.

Tfp has been described as "technological change", "growth in productive skills", "human capital" and "everything we don't know about growth". Thus, essentially, in the Solow growth model, technological advance is considered to be something arising from "outside" the workings of the economy ("manna from heaven"), something determined, say, by the general state of scientific knowledge and which interacts with capital (K) and labor (L) to make them more productive. In his work on economic growth theory, Solow demonstrates that assuming a "constant rate of technological progress", economic growth will converge towards a rate which is the sum of the rate of growth in the labor force plus the "rate of technical progress".

More precisely, the technical progress has to be of the type known as "labor augmenting" i.e. where output, Y =F(K,e^btL), where t = time and b is a constant which is the"rate of technological change". In other words, the technicalprogress should be labor enhancing not labor replacing.

From the point of view of the present discussion, the important factor about the Solow neo-classical growth model is that it would seem to imply optimism about the growth prospects for the underdeveloped economies.

"It would seem to follow that all national economies with access to the same changing technology should have converging growth rates. There might be temporary or even prolonged differences in growth rates because countries that are still fairly close to their initial conditions having started with lower ratios of capital to labor than they will eventually achieve in the steady state, will be growing faster than countries that are further along in that process."

(R. Solow 1989)

"If a technology is 10 times more advanced in one country than another, there should be large returns to anyone who can cause the advanced technology to be used in the less advanced country. If technology has the kind of public good character attributed to it in the neoclassical world, it should not be hard to put it to use somewhere else in the world".

(P. Romer, 1991)

Indeed, the 50's and 60's were times of optimism about prospects for economic growth in the less developed areas of the world. In fact, the only obstacle to capitalist growth in the less developed world was seen to be the threat of Communist takeovers which American foreign policy in the Third World was largely dedicated to preventing.

However, in the 70's and 80's a series of economic upheavals and "growth failures"

began to take place in large parts of the less developed world,

(the Iranian upheaval, the oil shocks, the Latin debt crisis,

the unraveling of the African economies),

upheavals which also had profound repercussions on the economies of the developed world.

So that even as the economic, social, political and cultural linkages between the developed and the underdeveloped world continued to rapidly increase, doubts and confusion began to arise in the West about the prospects for economic growth in the latter.

In addition, in the late 80's, fears began to arise about environmental constraints to economic growth,

(the thinning of the Ozone layer, the projected Greenhouse effect).

It was at this point that the so-called "new growth theories" began to emerge to replace the "neo-classical growth theory". Two of the main originators of these new growth theories were the economists Paul Romer and Robert Lucas.

From our point of view two of the most important features of these "new growth theories" are (1) attempts to construct plausible models of perpetual growth in the presence of "fixed factors" such as a fixed population base or a rigid environmental constraint, (2) attempts to model technological advance as a predictable function of economic activity rather than as "manna from heaven" which arrives from outside the economy and then interacts with it.

In our opinion, the motivations behind these "new growth theories" are: (1) a desire to find a model in which economic growth is free from the necessity of having to wait for the next big "breakthrough" in human scientific knowledge (i.e. superconductivity, nuclear fusion, artificial intelligence) and in which technical progress is controllable by economic agents, (2) a desire to find a model in which growth is not hampered by environmental constraints, and (3) a desire to find a model which explains the growing gap between the West and the underdeveloped world, and does so in a way that avoids the controversy and facile argumentation that always swirls around this topic.

"Economic growth being a summary measure of all of the activities of an entire society, necessarily depends, in some way, on everything that goes on in a society. Societies differ in many easily observed ways, and it is easy to identify various economic and cultural peculiarities and imagine that they are the keys to growth performance.

For this as Jacobs (1984) rightly observes, we do not need economic theory. 'Perceptive tourists will do as well'. The role of theory is not to catalog the obvious, but to help us sort out effects that are crucial quantitatively from those that can be set aside.", R. Lucas, 1988.

In order to do this, it is necessary to construct "a mechanical artificial world, populated by the interacting robots that economics typically studies, that is capable of exhibiting behavior the gross features of which resemble those of the actual world."

(R. Lucas, 1988).

In other words, the idea is to find the economic equivalent of "cosmological equations", equations which describe how the "economic cosmos" coalesces into "stars and galaxies" of development and vast empty voids of underdevelopment (empty, that is, of commercial prospects). This is accomplished by the addition of two new factors of production. knowledge and human capital.

What is human capital? To answer that questions, let's ask another one. In 1946, after a large part of its physical capital stock was destroyed, was Germany an underdeveloped country? The answer is obviously no. The wars which shattered Europe in the twentieth century did not render it underdeveloped. In other words, there must be some factor other than the size of the capital stock in a country which makes a country "developed".

It must be something to do with the people of the country, both individually and as a social aggregate.

This "something" is called human capital.

To take another example (in discussing the 19th century classical economist,

John Stuart Mill) M. Blaug (1962) writes:

"Mill notes..that the average durability of capital goods is only about ten years. This accounts for the fact that countries recover so quickly after destructive wars; skills, technical knowledge and the more durable buildings ususally remain umipaired and make possible a rapid recovery. This obviously valid argument has never received the attention it deserves; it could be elaborated into a complete theory of the causes of economic growth."

Using human capital as a factor of production is an attempt to do that.

For those who are familiar with the so called Cobb-Douglas production function, and the concept of 'marginal product', R. Lucas (1990) is a simple, readable introduction to human capital calculations. We'll give a brief summary of this paper. Recall that in the neoclassical growth model above, because of contant returns to scale, economic output per worker is solely a function of capital stock per worker.

It is also a feature of this model that the smaller the amount of capital stock per worker the greater the gain in output from increasing the amount of capital stock per worker (the Inada conditions). In other words, capital investment should yield much greater returns in a capital poor country like India than a capital rich one like the United States.

So Lucas (1990) asks the question, "why doesn't capital flow from rich to poor countries?". Given India's large population and low average wage, the flow of capital from the United States to India, should be enormous, in fact all new investment capital should flow to the poorer countries. This is obviously not the case in fact. The reason why this is not the case in theory, is because there is another factor of production called human capital. A high level of human capital per worker makes physical capital more productive and a low level makes physical capital less productive. Poor countries have a low level of human capital, and this counteracts the low amount of capital per worker. Suppose that India has a human capital per worker of 1, and suppose that the United States has a human capital per worker of h, (which means that a worker in the U.S. would be, on the average, 'h' times more productive than a worker in India, even if India were to be given the same physical capital per worker endowment as the United States

Note that this refers to the average productivity of the population as a whole not whether an Indian fork lift operator, say, is more or less productive than an American forklift operator.

Lucas (1990) postulates a simple production function of the form:

Y = F(K,hL,h) = A K^b (hL)^1-b h^c,

which applies to production in both countries, where K = capital, h = human capital per worker

In the discussion of the Lucas article, "per worker" should actually read "per capita" because that is how the statistics were compiled.

h = 1 in India, L = labor and A is independent of K, L and h. Those who are familiar with college level economics, will recognize the above equation, A K^b (hL)^1-b, as an extension of the so-called Cobb-Douglas function, a production function often used in economic models because it is easy to work with. However, the exact form of this equation need not concern us here. For our purposes, there are two important things to stress. First of all, the term (hL) above implies that a worker in the U.S. would be, on the average, 'h' times more productive than a worker in India even if India were to be given the same physical capital per worker endowment as the United States. Secondly, the term 'h^c' above is called an external effect and expresses the fact that workers in the U.S. are collectively more productive, more productive as a society, as well as being individually more productive. A migrant from India , whatever his or her skill level, can have his or her 'productiveness' multiplied by this external effect simply by being in the United States. Hence the incentive for migration from poor countries to rich.

Lucas (1990) uses the results of three economic surveys to calculate b, h, and c. A study by A. Krueger (1969) of labor efficiency in the U.S. and India allows h to be calculated as 5. On the average one American worker is the equivalent of 5 Indian workers, even if India were to be given the same amount of capital per worker as America. A study by E. Dennison (1962) of the sources of economic growth in the United States from 1909-1959 shows that output per worker has grown at a rate 1% faster than would be explained by growth in capital per worker. Attributing this difference to growth of "human capital" allows c to be calculated as .36. From other economic data b is estimated at .4.

A survey by R. Summers and A. Heston (1988) of real economic output and price levels in 130 countries is used (together with the above equation) to calculate the difference between gains from capital investment in India and gains from capital investment in the United States. This difference is shown to be approximately 4%. The proofs use elementary algebra, elementary microeconomics, and elementary calculus

For those who are familiar with college level calculusand college level economics, the "gain from capitalinvestment" is the marginal product of capital which, ofcourse, is the partial derivative of the production function with respect to K. Thus, the proofs of assertions above are partial differentiation and the chain rule.

Thus, human capital is the "missing ingredient" or, at least, a "missing ingredient" which shows why returns to capital invested are not an order of magnitude greater in capital-poor countries than capital-rich ones.

What then is human capital? It has been attributed to skills, training, experience, literacy, schooling etc. Denison (1962) attibutes unexplained growth in per capita output as due to schooling. Does this mean that, if every middle class person in India gets a Ph.D. in Hindi love poetry, Indian economic output will double? Obviously such a thesis would be preposterous.

Human capital must consist of more than schooling. It must consist of skills at economic, industrial, commercial, manufacturing and entrepreneurial activity, both on an individual basis and collectively as a society.

K. Arrow (1962) attributes it to experience gained by cumulative capital investment of a continually new and improved capital stock. Newer theories of human capital formation have stressed manufacturing, industrial and commercial skills acquired while going up against the world market.

Defining human capital as knowledge, the Economist survey of Asia, entitled A Billion Consumers (Economist, 10/20/93,page 9), denies that human capital is the source of total factor productivity, since the Soviet Union slid into economiccollapse despite an impressive accumulation of human capital.

One of the inspirations for the concept of human capital comes from the concept of learning by doing:

"The role of experience in increasing productivity has not gone unobserved though the relation has yet to be absorbed in the main corpus of economic theory. It was early observed by aeronautical engineers..that the number of labor hours expended in the production of an airframe..is a decreasing function of the total number of airframes of the same type produced... (another example) The Horndal iron works in Sweden had no new investment (and therfore presumably no significant change in methods of production) for a period of 15 years, yet productivity rose on the average close to 2% per annum ...which can only be imputed to learning from experience."

K. Arrow (1962)

The term human capital is not used in K. Arrow's formulation. Instead, cumulative production of capital goods is used an an index of experience or learning by doing:

"Each new machine produced and put to use is capable of changing the environment in which production takes place. so that learning is taking place with continually new stimuli. This at least makes plausible the possibility of continued learning in the sense, here, of a steady rate of growth in productivity"

K. Arrow, (1962)

In Arrow's formulation, capital investment increases economic output directly, because it is a factor of production. It also increases economic output by generating experience and learning by doing which increase economic productivity.

In 1967, E. Sheshinski developed a simpler version of the Arrow model. In his formulation the economy consists of N identical firms and the production, function for each individual firm is written:

y = F(k,(Nk)^cw), where k is capital per firm, w is labor per firm and c is an exponent less than 1, and y is output per firm,

In the equation above, labor w is augmented or scaled up by the factor (Nk)^c where (Nk) is the total economy-wide capital investment. The greater the total amount of capital investment, the more effective is labor. The process by which this happens is learning by doing.

As we mentioned above, in the recently developed new growth theories, human capital is a separate factor of production. Such growth theories have mathematical formulae which describe how economic activity generates human capital, i.e. production functions for human capital.

For example, in Lucas (1988), an invididual's human capital is simply his or her general skill level, so that a worker with human capital h is the productive equivalent of two workers with human capital h/2. The percentage growth of human capital per annum is proportional to the percentage of non-leisure time devoted to human capital accumulation (schooling, training, on-the-job learning, etc).

If all workers have human capital h and devote fraction u of their non-leisure time to productive work, and fraction 1-u of their non-leisure time to human capital accumulation then:

percentage increase in h per annum = c(1-u) where c is a constant

The production function for the economy is similar to Lucas (1990) above. The mathematics in Lucas (1988) is well beyond the scope of this book, but the significant feature of the human capital equation above is that, since there are no diminishing returns to the production of human capital, human capital can act as an "engine of growth" in the presence of a fixed population. Thus, human capital allows long-term growth in the demographically stable developed countries, and explains the differences between the developed and underdeveloped countries.

R Lucas (1988) also postulates that 'external human capital' (h^c above) could be an explanation for why economic development tends to cluster in certain geographical areas

i.e. such as cities for example.

R. Barro once said,

"I never knew what geographical region the Solow growth model was supposed to refer to.

A city? A state? A country? The world?"

"But we know from ordinary experience that there are group interactions that are central to individual productivity and that involve groups larger than the immediate family and smaller than the human race. Most of what we know we learn from other people."

This is an explanation for the economic role of cities.

"The theory of production contains nothing to hold a city together. A city is simply a collection of factors of production-capital, people and land. Why don't people and capital move outside, combining themselves with cheaper land and thereby increasing profits? ....It seems to me that the 'force' we need to postulate to account for the central role of cities in economic life is of exactly the same character as 'external human capital' I have postulated to account for certain features of aggregative development. If so, then land rents should provide an indirect measure of this force....What can people be paying Manhattan or downtown Chicago rents for, if not for being near other people."

Another factor of production in the new growth theories is knowledge. Knowledge consists of ideas, designs, scientific theories, technology etc.

Unlike skills, knowledge is independent of the people possessing the knowledge. Sometimes it can take the form of private property through the use of patents or trade secrets, etc. Sometimes is is freely available to everyone. In the new growth theories, in contrast to the neoclassical growth theory, knowledge is generated by economic activity, for example, industrial research. The more resources directed to research, the more knowledge. Sometimes knowledge is regarded as a homogeneous mass (P. Romer 1986) like capital in the neon-classical model above. At other times, capital is regarded as a list of different types of capital equipment and "knowledge" is postulated to be the length of that list (P. Romer 1990) so that the economy grows by generating a greater and greater variety of products rather than more and more of a homogeneous mass.

These models often have a "production function" for the generation of knowledge such as "capital invested in research in, knowledge out" or "knowledge and human capital in, more knowledge out". A sample "production function" for knowledge might look like: "The amount of increase in knowledge per unit time is proportional to the currently existing stock of knowledge multiplied by the amount of human capital allocated to research."

(P. Romer 1990)

However, from our point of view, the most interesting thing about these growth models is what they have to say about the patterns of future global economic development. First of all, unlike technology in the Solow growth models, "human capital" is not freely transferable across national boundaries. Since human capital is a critical determinate of the growth rate, in many of these models, growth in the developed and undeveloped economies need never converge, and it is entirely possible for an economy to permanently experience a greater rate of growth the greater its level of development.

Furthermore, it can do this in the presence of a "fixed factor" such as a fixed population or an environmental constraint. On the other hand, it will often benefit an underdeveloped country, even one with a large population, such as China or India to seek external trade with a developed one because "what is important for growth is integration not into an economy with a large number of people, but rather into one with a large amount of human capital" (R. Romer 1990).

How well have the new growth theories stood up to empirical tests? Obviously, the new growth theories have not had the same amount of time to attract empirical research as has the Solow growth model, which has inspired an enormous number of growth accounting studies. None the less, there have been an increasing number of empirical studies of the new growth theories.

In the October 1992 edition of the Economic Review of the Federal Reserve Bank of Atlanta, E. W. Tallman and P. Wang discuss the empirical evidence on the relationship between human capital, and economic growth. First of all, there is the question of how one goes about measuring human capital. This is done by means of proxies (substitutes). Some of these proxies are literacy rates and enrollment in primary and secondary schools.

Secondly, there is the question of the reliability and consistancy of the data from different countries. Thirdly, "human capital proxies are necessarily crude. For instance, although the literacy rate may be a fairly consistently measured variable, it may only tangentially measure the human capital concept of interest (that is, a measure of knowledge or achievement)." Thus, the empirical evidence regarding the controversial new growth theories is itself controversial.

Paul Romer (1990) investigates whether the 1960 literacy rate, affects the economic growth of a cross-section of countries in the subsequent 25 years. Romer finds that the initial level of human capital and the change in literacy has a significant effect on the rate of investment, and, thus, on economic output growth as a whole. Robert J. Barro (1991) studies the relationship, for many different countries, of the 1960 enrollment rates in primary and secondary schools (human capital) and the average economic output growth for the period 1960 - 1985. He finds that the 1960 human capital level, has, on average, a positive impact on subsequent economic growth. C Azariadis and A. Drazen (1990) find that possessing a literacy rate of 40% or greater has a positive effect on economic output growth for the sample of countries that they study. R. Levine and D. Renelt critize the above studies from a statistical point of view. See D. Renelt (1991) for a more detailed review of the empirical work on the new growth theories.

The new growth theories are a very rapidly expanding field. We have touched on only a very small fraction of the questions that are being currently investigated by these theories. There have been studies on growth and inflation (N. Roubini), growth and government macroeconomic policies (G. Saint-Paul), growth and international trade (E. Helpman, G. Grossman), growth and international capital flows (S. Rebelo), and growth and individual decision making under uncertainty (R. Lucas, N. Stokey, 1989).

One of the problems in writing about the new growth theories is that these theories make heavy use of advanced mathematical concepts, such as the "Kuhn-Tucker theorem" and "dynamic equilibrium theory". Some of their most interesting results, concern the extent to which individual, decentralized decisions lead to "optimal" or "suboptimal" outcomes.

Thus providing a theoretical justification of government intervention in the economic growth process through"industrial policies" or the promotion of education and research a la Clintonomics.

Results, or the extent to which government policy changes have permanent as opposed to one-shot economic effects, cannot even be adequately described in English. For those who are familiar with college level microeconomics, (and those who aren't can skip this paragraph) some other highly technical issues that the new growth theories are forced to deal with are the issues of "externalities", "non-convexities" and "economies of scale". Such concepts are difficult to model using the assumptions of "perfect competition" and "marginal cost pricing".

For example, perfectly plausible production functions using human capital and knowledge as factor inputs can be shown by elementary calculus to contradict the assumptions of "marginal cost pricing", something which would seem to render the generation of new technologies incomprehensible under a regime of perfect competition and profit maximization.

Let A be technological knowledge say in the form ofindustrial designs and let X be other inputs say raw materials. Then a plausible production function might have the form F(A,X) where F(A,QX) = Q . F(A,X). In other words, you only need the design once, but if you multiply the inputs X bya constant Q then the output is also multiplied by Q. Assuming A is "productive", then increasing A should also increase output, so that F(QA,QX) > F(A,QX) = Q.

F(A,X).

Differentiating both sides of this inequality by Q, using thechain rule, and then setting Q equal to 1, one can show that producers with the above production function must always losemoney if they pay for their inputs at their "value marginalproducts". In this case, how can private, profit maximizingbehavior generate new technologies? See P. Romer, 1990 for details of this argument.

Some of the new growth theories address this dilemma by constructing mathematical models which use "Marshallian external increasing returns" to make human capital and technology compatible with perfect competition and "price taking" (P. Romer 1986). Others abandon perfect competition altogether and construct growth theories with "monopolistic competition" (P. Romer 1990). For those who are familiar with advanced college calculus, and who are willing to take a great deal on faith, P. Romer (1989) is a readable, heuristic overview of the new growth theories.

There are two widespread points of view concerning long term economic growth. The first point of view is that economic growth ultimately needs more and more participants in order to sustain itself, because, without them, it will end up producing only labor shortages or gluts. The second point of view is that economic growth does not need more and more participants in order to sustain itself

In fact, P. Romer (1987) implies that a large populationmay inhibit economic growth because an important part of thegrowth process may be labor-saving technical innovations induced by shortages of labor.

The populations of the already developed economies are quite sufficient.

"The developed countries no longer need (the LDC's) as they did during the nineteenth century. It may be hyperbole to say, as Japan's leading management consultant Kenichi Ohmae, has said that Japan, North America and Western Europe can exist by themselves with out the two-thirds of humanity who live in developing countries. But it is a fact that during the last 40 years the countries of this so-called triad have become essentially self-sufficient except for petroleum. They produce more food than they can consume in glaring contrast to the 19th century. They produce something like three fourths of all the world's manufactured goods and services. And they provide the markets for an equal proportion." P. F. Drucker (1988)

To state Ohmae's point of view above in its most extreme form, one could say that, even in a stable population, human wants and desires are infinite, human inventiveness equally infinite. Therefore, no matter how advanced technology becomes, people will always be able to find ways to occupy their time in the production of commercially viable goods and services. In other words, technological advance will not make people redundant, but will, on the contrary, make them more and more able to interact commercially in a way that magnifies their capabilities and satisfactions.

Before writing off such visions of perpetual economic growth on a fixed population as "too good to be true", one should note that there have been many such prognoses of limits to economic growth on a fixed population.

Some of the prognosticators have included Malthus, Ricardo, Marx, Luxemberg, and Schumpeter. During the depression of the 30's, there were predictions that growth in the West had reached a stage of "maturity", and that further economic growth would be confined to the European colonies.

All these predictions were invalidated by technological innovations that the prognosticators had no way of forecasting. Therefore, forecasters have become very leery about predicting that the West "needs" the Third World for future economic growth.

As R.Heilbroner (1990) puts it:

"Fears that capitalism will run out of things to doappear much less plausible than they did in the past.There's no doubt that important markets may become saturated...but the long term process of expansion hasbypassed saturation by discovering or creating new commodities, and that process does not suffer from the same fixed capacities for absorption that limit the demand for specific goods."

To be sure, this type of intensive economic growth might be possible only for the minority of the world's population in the already developed economies, but it is possible nonetheless. Indeed, it is the type of growth that has actually taken place in the West since 1945.

That is, since 1945, much of the economic growth in the West has not consisted of increases in the aggregate mass of capital stock (a la Tugan Baranovsky) nor of increases in the number of participants (a la Rosa Luxemburg), but rather in the increased ability of the same number of participants to generate more and more economic output, and to consume a greater and greater variety of goods and services. The standard Solow growth model has no economic explanation for the latter type of growth, and, indeed, maintains that no such economic explantion exists.

After all, "can one really explain by economic models, the discovery of the transistor, or the laser, or the host of other breakthroughs of the last century?" (J. Stiglitz, 1990). And yet, according to the new growth theories, technology, knowledge and skills are themselves economic commodities, which are "produced" by economic activity, and which should, therefore, obey economic laws.

The new growth theories investigate these economic laws. They do so in order to explain the phenomenon of long term growth on a stable population, and also to explain the widening gap between the developed and underdeveloped parts of the globe.

The new growth theories have generated an enormous amount of excitement both in the economics profession and, increasingly, in the business press as well. Part of this excitement is due to the fact that these theories have had to overcome formidable theoretical difficulties in order to model the economics of technology and human capital.

The new growth theories, (which project perpetual growth on a stable population), satisfy this desire, because, in these models, the participation of people outside the West, either as producers or consumers, is not needed to ensure economic growth in the West.

To sum up, the new growth theories purport to demonstrate the possibility of perpetual economic growth on a stable population. In addition, these growth theories, according to some economists, have been remarkably successful in explaining economic growth from 1945 to the present.

What about the future?

To address this question, let's examine some of the assumptions behind the new growth theories

Or rather the assumptions behind some of the new growth theories.

First, there is the assumption that the payoff to commercial and non-commercial research, in the form of growth-inducing technologies, will be the same or greater in the future than it was in the past.

"Assuming that the increasing returns arise because of increasing marginal productivity of knowledge accords with the plausible conjecture that, even with fixed population and fixed physical capital, knowledge will never reach a level where its marginal product is so low that it is no longer worth the trouble it takes to do research.

If the marginal product of knowledge were truly diminishing, this would imply that Newton and Darwin and their contemporaries mined the richest veins of ideas and that scientists must sift through its tailings and extract ideas from low grade ore."

P. Romer, 1986

This point of view certainly coincides with the commonly held belief that

"the future = now + new technology".

However, there is a sense in which the technologies that are now being investigated, (high temperature superconductivity, fusion, artificial intelligence, climatic and global environmental modeling, genetic engineering, etc.) are fundamentally different from the technologies which propelled global economic growth up until now.

The latter technologies were "reductivist technologies" which employed isolated chemical, electro-magnetic, physical and quantum reactions which were controlled by "clockwork mechanisms", such as gears, levers, pipes, circuits, hydraulics, etc. The new technologies being looked at now are far more complex, involving intricate "non-linear" systems, plasma control, complex molecular systems, "holistic" pattern recognition, etc.

Is it really so obvious when these technologies will yield commercial applications whose growth inducing effects are so powerful as to constitute a "technological fix" for the current global economic crisis? Will it be months, years, decades, centuries? Will an ad hoc "production function" for technological development really predict this? In other words, isn't it true that revolutionary new technologies are, to some extent, "manna from heaven" and outside the realm of purely economic analysis?

"There is something not quite right with the idea that an increasing allocation of labor-time (or just output) to research activity can buy increases in the rate of growth of knowledge. If anything like that were true, then R&D outlays equal to 2% of the GNP would be unaccountably small. The numbers get much larger when the activity in question is understood to include all education and training. It still seems to me to play fast and loose with the rates of growth. .....Fundamental technological change probably is more nearly exogenous. Anyone who has ever done research knows that. Given a functioning research activity, a lot depends on chance and erratic insight."

R. Solow, 1990

Of course, this doesn't mean that perpetual economic growth on a stable population is impossible. It only means that such growth cannot be predicted using economic arguments alone. Will such economic growth in fact occur?

Our own opinion is that, barring some completely revolutionary technological development such as, for example, "cold fusion", it's hard to imagine perpetual economic growth in the West that does not also involve the participation of large numbers of people outside the West.

In other words, to paraphrase Paul Romer, a great deal of future economic growth will, inevitably, consist of "causing advanced technologies to be used in the less advanced countries" whether this be easy or hard.

Everyone agrees that the new growth theories provide valuable insights into the economic growth process. However, they remain controversial. They have been criticized for being too ambitious, for attempting to explain too much by means of mathematical formulae.

J. Stiglitz (1990), for example, describes them as being characterized by "a certain amount of chutzpah combined with a high level of technical ingenuity". In the same way that the new growth theories attempt to model the generation of new technologies some of which will inevitably involve "facts of nature" which are not as yet known and could be quite surprising when they are discovered, so to do these new growth theories propose to explain institutional, historical, social, cultural and political change as well:

"Changes in institutions can solve the problem of explaining the time trend in growth rates but they do so by exchanging exogenous technological change for exogenous institutional change. Making institutional change exogenous allows economists to conduct a provisional analysis that focuses on issues that they understand relatively well and sets aside ones that they do not. But ultimately, one would like to be able to explain the evolution of institutions as well. It seems quite plausible that increasing rates of return and increasing opportunities for private investment caused the evolution of institutions that supported these activities." (P. Romer, 1991)

Many historians think the important chain of historical causality went in the reverse direction:

"In Europe, .....the private trade sector had evolved from the wreckage of central authority during the Dark Ages. The small scale of early government attached itself to trade---for the sake of the revenues that sector could quickly provide. In China and Asia generally the private sector emerged only after government on sufferance. No independent laws arose to shield it. Contractual legalism never replaced statist morality. The Chinese (in particular) showed signs of development nevertheless but was turned aside by the dead-end opportunity of internal colonization." E.L. Jones (1981)

During the early feudal ages in Europe. a pattern of development began in which technology (the water mill (Roman), the heavy plough (Slavic), the three field system, the horseshoe (Celtic), and a new method of harnessing draught animals (China)) began to be assimilated and applied to agricultural production at a very rapid rate promoting a growth in output which, over the long term, exceeded demographic growth, something not true in the classical civilizations. Furthermore, the institutions to block these activities had not had time to arise (the Carolingian empire fell apart, the Mongol invasion of the 13th century stopped short of Western Europe, etc.)

It was at this time, in Western Europe, that a new type of society emerged in which productive growth in advance of population growth emerged as a "social organizing principle" involving the formation of decentralized stocks of capital and decentralized political power centers. It involved the growth of feudal society, the growth of contractual relations, the dependence of the monarchs on the merchant classes in the towns, the rapid expansion of trade and ultimately the "scientific" and "industrial" revolutions.

Why, after so many thousands of years of agricultural civilization, such an unprecented and unique form of social and historical evolution should have occured in the small Western promontory of Eurasia is ultimately a mystery.

It had something to do with Christianity, something to do with the prior Celtic and Germano-Roman cultures, something to do with the nature of decaying Western Roman society, something to do with the geographic, climatic, environmental and epidemiological nature of Europe. Its eastward spread was hampered by the nomadic invasions of the 13th century, which, in turn, determined the centralized shape of the Russian political economy.

The "South" was formed by 500 years of colonization, by the West, of what is now the "underdeveloped world"(South America, Africa, the Ottoman Empire, Mughal India, Safavid Persia, the Ching Dynasty and East Asia).

All of this greatly influenced the differing amounts of "human capital" in different sectors of the world. It's no accident, for example, that Japan, the only non-Western country to fully join the developed world, was spared both the Mongol invasion and European colonization, and had a feudal social structure closer to that of pre-industrial Europe than to the centralized political structure of the "classical civilizations" of antiquity.

Can the results of such long term historical evolution really be described by means of mathematical equations? If not, it certainly won't be for lack of trying. Some new growth theorists are attempting to do just that (M. Kremer, 1992, A, Ades and T Verdier, 1993).

However, for the purposes of this book, we will stick to purely qualitative exposition when we discuss very long term economic development in the next chapter.

ECONOMIC GROWTH AND HUMAN CAPITAL