Underdevelopment and Serial Industrialization in a Ricardian Trade Model with Learning­by­Doing
Paul Friesen
Draft 2
May, 2009
Abstract: This trade and development paper presents a Ricardian trade model of the world economy with two goods – manufacturing and agriculture, and many countries. Each good has its own type of human capital, which is accumulated through producing that good. Most countries specialize in one good or the other. Preferences are such that the share of world spending on manufacturing grows with the world economy. This forces manufacturing to expand into countries with low manufacturing human capital, driving up the price of manufacturing and making established manufacturing countries rich.
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Underdevelopment and Serial Industrialization in a Ricardian
Trade Model with Learning-by-Doing*
1. INTRODUCTION
The industrial revolution which began in Britain in the mid 1700's was, in many ways, the beginning of the world we know today. Before it, the world economy was overwhelmingly agricultural. Most people could afford little beyond the basic necessities of food, shelter, and clothing. The world also seems to have been much more uniform than what we see today. The vast gap which we have between rich and poor countries did not exist. There is little reason to think that a European peasant was typically better off than an African or native American farmer.
Since that time, the world has changed radically and, on a historical time scale, incredibly quickly. The population has exploded. And many parts of the world are far wealthier than before. Our knowledge of science has been put to use in our service, and has itself grown rapidly.
Yet there are many countries which have been left behind. They remain largely agricultural, or are a source of other raw materials. In many, life is very poor and precarious.
Since the industrial revolution, industrialization has been spreading. From England, it spread to other European countries, then to North America and other areas from which the original inhabitants had been displaced by European settlement. From there, after some delay, it spread to Japan, and from there to Hong Kong, Taiwan, South Korea, and South­East Asia. Now, China and India are beginning the process. At any given time, the number of countries that are industrializing seems to be quite limited. As countries industrialize, they become rapidly wealthier.
There are models in the new economic geography literature that produce industrialization patterns suggestive of this. In Puga and Venables (1999), or Fujita, Krugman, and Venables (1999), there are models of international agglomeration involving agriculture and manufacturing. Because manufacturing firms use each others' outputs as inputs, they tend to cluster together to reduce transportation costs. At first, therefore, manufacturing is confined to a single country.
Another ingredient of these models is consumer preferences that simulate Engel's law. As world output grows, demand for manufacturing grows more quickly than that for agriculture. Therefore, the price of manufacturing and the wage in the industrialized country rise due to rising relative demand. Eventually, the wage gap between industrialized and unindustrialized countries * I would like to acknowledge the input of Stephen Kosempel and Clive Southey of the University of Guelph, who have been of great help in developing these ideas. However, any errors are strictly my own fault.
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becomes large enough that manufacturing becomes profitable in one of the latter despite the transportation costs. This country therefore industrializes quickly and its wage converges with that of the original industrialized country. This pattern repeats until all countries are industrialized. Puga and Venables describe the pattern: “...development takes the form of countries being drawn in turn out of the poor group, and taken through a process of rapid development into the rich group.” This is what I call serial industrialization. It seems to capture the real­world pattern rather well.
These models can be understood as cases where factor price equalization for labour does not occur because all of the mechanisms which might lead to it are blocked or restricted. Labour cannot move between countries by assumption. Manufacturing firms, also, are reluctant to move because of transportation costs. It is only when the pressure to move, in the form of the wage differential, becomes sufficient, that they do move. It is these two things – the pressure for firms to move which is ultimately caused by the expanding relative demand for manufacturing – and the resistance to movement caused by the transportation costs – that generate the wage differential between rich and poor countries.
Transportation costs are surely one reason for the reluctance of real world firms to move production to poor countries, but there are others. One such reason is the lack of many specific skills in the people of poor countries. These people do have skills, but they may not be the skills such firms need. Detailed, sophisticated knowledge about things like how to grow and process cocoa or how to build a good thatched roof is not of interest to firms needing welders and bookkeepers. This suggests that serial industrialization could also occur in a learning­by­doing model. Agents in industrialized countries learn manufacturing skills, while those in unindustrialized countries learn agricultural skills. As the world, on average, becomes richer, the share of spending devoted to manufacturing rises, while that devoted to agriculture falls. This creates pressure for manufacturing production to spread to unindustrialized countries. But these countries have the “wrong” kind of knowledge for manufacturing firms. These firms will only move when the wage differential between industrialized and unindustrialized countries becomes great enough to overcome this problem.
This paper shows that this can be modelled easily. I would certainly not suggest this as an alternative to the new economic geography model, but as a compliment to it. It contains many of the same elements – international trade, labour immobility, and the rising share of manufacturing in spending as the world becomes richer. The only important difference is the type of barrier firms face if they are considering moving production to a poor country to take advantage of cheap labour. In new economic geography models, the barrier is increased transportation costs. In this model, it is lack of the right kind of knowledge. In the real world, I would suggest that both are important, and also that there are other barriers, as discussed below.
Growth models in which learning by doing occurs in various sectors are fairly common. The production side of my model is almost identical to one in Lucas (1988). But Lucas avoids the case where countries switch from producing one good to the other by assuming that the goods are good 3
substitutes – not at all what I want to do. Krugman (1987) also has a similar model, which he uses to investigate ways in which activities might be made to move from country to country, but he does not consider the effects of a long­term shift in demand composition.
A number of papers consider learning by doing in various sectors, and explain low growth in poor countries using mechanisms by which these countries wind up producing goods which are, in various ways, unsophisticated or low technology. For example, see Boldrin and Scheinkman (1988), Young (1991), Nakajima(2003). In this model I steer away from labeling either of the two goods as less sophisticated. A wage differential in favour of industrialized countries develops for any positive rates of learning in the two goods. This is governed by the relative prices of the goods, which are poor substitutes. The only sense in which agriculture is “inferior” to manufacturing is that its share of spending falls over time, while that of manufacturing rises.
This model produces rapid growth in newly industrialized countries. There are also other papers which produce, in various ways, this phenomenon. See Matsuyama (1991), Lucas (1993), Nakajima (2003). Part 2 of this paper presents the model. Part 3 discusses the results. Part 4 is conclusions.
2. THE MODEL
2.1 General Description
The model is simply a two­good, multi­country Ricardian trade model in which the productivity of each country's labour in producing each good is human capital acquired during production. I call the two goods manufacturing and agriculture and give them properties intended to capture in a simple way certain real­world characteristics of these goods. With suitable assumptions, I show that this can lead to a pattern in which countries industrialize one after the other. After countries industrialize, they grow rapidly, until their growth slows as they converge with the richest country, which was the first to industrialize.
The model contains many countries, and each country has an index number j  (0,J) . We consider J to be large, so that j can be treated as a continuous variable. Each country has a constant population of 1 unit. Agents cannot move between countries.
Both goods are traded costlessly between countries. Human capital accumulation is external to firms. All markets are perfectly competitive, so firm profits are zero. There is no borrowing, lending, or saving, so all income is spent when earned and all goods are consumed as soon as they are produced.
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2.2 Consumption
If agents are very poor, they consume no manufacturing at all, but spend all income on agriculture. However, agents become satiated with agriculture when they consume co units per population unit. All income in excess of that required to buy co units of agriculture is spent on manufacturing. We take agriculture as the numeraire. Thus,
cA(j,t) and cM(j,t) are consumptions of agriculture and manufacturing respectively, per population unit, in country j at time t. w(j,t) is the wage.
This simple way of capturing Engel's law follows Eswaran and Kotwal (1994).
2.3 Production
The agriculture production function is
Where yA(j,t) is agricultural output of country j at time t, hA(j,t) is per capita agricultural human capital, and lA(j,t) is labour in agriculture. Similarly, for manufacturing,
where variable definitions are analogous. Note that the knowledge used in manufacturing is assumed to be different from that used in agriculture.
Since agriculture is the numeraire good, if agriculture is produced in country j at time t, the wage in j must be
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If manufacturing is produced, the wage is
where PM(t) is the price of manufacturing at time t. I assume no trade costs, so this price is common to all countries.
If both goods are produced in j, both (4) and (5) must be true. Define r(j,t) as follows:
Thus, r(j,t)is the value that PM(t) would have if both goods were produced in j at t. If r(j,t) is less than PM(t), country j specializes in manufacturing. If r(j,t) is greater than PM(t), it specializes in agriculture. If the two quantities are equal, both goods are produced. As the r(j,t)'s are real numbers, we can assume that no two are ever exactly equal, so at most one country can be producing both goods at any time. All others must be specialized in one good or the other.
Because the total number of countries is large, any single country makes a negligible contribution to production of either good. For the purpose of calculating outputs, we can neglect any country producing both goods and consider the world to contain only countries specialized in producing one good or the other.
2.4 Equilibrium
In each time period, total world production of each good equals total world consumption. All agents in all countries are employed making one good or the other. They are paid according to (4) or (5), depending on their industry, and spend all of their income from each period on goods produced in that period. Wages are the same within countries, but differ from country to country. Agents cannot move between countries.
The competitive general equilibrium consists of allocations for each industry {yA(j,t), lA(j,t)} and {yM(j,t), lM(j,t)}; an allocation for the consumers of each country {cA(j,t), cM(j,t)}; and a set of prices {PM(t), w(j,t)}; such that, at any time t and for all j:
(i) the allocations of the industries satisfy (2) and (3), given human capital levels;
(ii) the consumer allocations satisfy (1) given the wage and price functions; and
(iii)all markets clear. Market clearing requires that the world supply of each good equals world demand and that the total labour in each country equals 1:
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2.5 Dynamics of Human Capital
We assume a simple rule of human capital accumulation similar to Lucas (1988). Per capita human capital for agriculture in a country accumulates at a rate proportional to the fraction of labour employed in agriculture in that country. Except for a negligibly brief time when a country produces both goods, this fraction is always 0 or 1.
If a country specializes in agriculture, human capital in agriculture evolves according to
where gA is a constant.
We assume a similar rule for human capital accumulation in manufacturing, but add another wrinkle. Per capita human capital accumulates at a rate proportional to the fraction of the labour force in manufacturing, but which varies with the distance a country is behind the knowledge frontier. If country j specializes in manufacturing,
gM is also a constant, and hM(0,t) is the manufacturing human capital level of country 0. Obviously, this can be simplified because the denominators are the same on both sides. I write it this way to make the logic clear.
As will be seen later, we will set the model up in such a way that country 0 will always have the highest level of manufacturing human capital. Its level will grow at constant rate gM while it is specialized in manufacturing. Other countries' human capital levels grow at rates that are not constant. The farther a country's level is behind that of country 0, the faster it will grow. This is to capture the fact that agents can learn from technology already produced. As the level of manufacturing human capital approaches that of the leader, the growth rate will slow, approaching that of country 0. We 7
could assume that agriculture also has this feature of learning from the leader – in other words that (7) has the same form as (8). In this particular model, however, it would make no difference as all countries that produce agriculture turn out to always have the same level of agricultural human capital. We therefore use the simpler formulation in (7).
If a country specializes in manufacturing, its agricultural human capital does not grow. If it specializes in agriculture, its manufacturing human capital does not grow. At any time, there may be a country which is producing both goods, but, because of the large number of countries, the time any individual country does this is negligible. We neglect what happens to human capital in this case.
We start the model out in a state where all countries have a common level of agricultural human capital hA(j,t), which is too low for agents to be satiated with agriculture. No manufacturing is consumed or produced. World agricultural output is JhA(j,t) and consumption of each unit of labour (i.e. each country) is just hA(j,t). hA(j,t) grows according to (7) in all countries until it reaches co. At this point, all agents become satiated with agriculture at the same time. We will call this time 0.
Agents now want to start consuming manufacturing. We assume that all countries start with levels of manufacturing human capital that are essentially equal at hMo, but we also assume that there are infinitesimal differences between countries. Country 0 has the highest level and levels decrease monotonically with j to country J, but the differences are so small that all initial levels can be considered the same for production. What these differences do is give different countries very slightly different levels of r(j,0). At time 0, it is just a tiny bit cheaper for manufacturing to be produced in country 0 than in any other country, so it starts being produced there. hM(0,t) then starts growing, reinforcing the tiny initial advantage. These differences simply serve to break what would be an unstable equilibrium if all countries were exactly identical.
After time 0, world demand for agriculture is constant at coJ. In the countries still producing agriculture, agricultural human capital continues to grow. This means that fewer and fewer countries can supply the world demand. By Walras' law, the other countries produce manufacturing, producing enough to clear the market. Every time manufacturing spreads to a new country, it moves to the agricultural country with the lowest r(j,t), which is determined by the infinitesimal differences in initial value of manufacturing human capital. Therefore, manufacturing starts at country 0 and spreads to countries in ascending order of j. We call the j value of the country which is just undergoing industrialization at time t k(t). All countries with a j value less than k(t) are specialized in manufacturing. All with j greater than k(t) are specialized in agriculture. Country k(t) itself is assumed to be so negligibly small that we can ignore its output, some of which will be agriculture and some manufacturing.
In the rest of the discussion, time will be assumed to be always greater than 0.
All countries with j greater than k(t) have always been specialized in agriculture, so they have a common value of agricultural human capital. Thus,
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This has the solution
Total agricultural output must equal consumption. Agricultural output is just the common agricultural human capital level times the number of agricultural countries (each with population 1). With all agents satiated with agriculture, consumption is just the satiation consumption level times the world population:
Using (10) in this, we can find k(t):
In any country j, manufacturing human capital starts to grow according to (8) when the country becomes specialized in manufacturing. This happens at the time when j=k(t). Call this time tM(j). It can be found by setting k(t) equal to j in (12) and solving for t:
Country 0 industrializes at time 0. In this case, (8) reduces to
and the initial value of hM(0,t) is hMo. This has the solution
Using this in (8),
At time tM(j) , hM(j,t) is hMo. It grows according to (16). The path of hM(j,t) is then
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Figure 1: Human capital levels at one point in time
Figure 1 shows how the relevant levels of human capital vary with country at a point in time. Countries to the left of the k(t) line are specialized in manufacturing. Country 0 has been in manufacturing the longest, so has the highest manufacturing human capital. Countries near the k(t) line are newly industrialized, so their levels are low. These countries also have varying levels of agricultural human capital, but they are irrelevant because the countries will never produce agriculture again. Countries to the right of the k(t) line produce agriculture. They all have the same level of agricultural human capital. They also have the same level of manufacturing human capital, hMo, except for the infinitesimal differences. Here, hMo is 1.
For this and later graphs, other parameters are as follows: co=1, gA=.01, gM=.01, J=100. In this graph, t=100.
In country k, wages in agriculture must equal wages in manufacturing, because both activities exist there. Agents are switching from agriculture to manufacturing. Manufacturing human capital is hMo, because manufacturing is just starting up. Agricultural human capital is given by (10). Using these facts and equating wages from equations (4) and (5), we can find the price of manufacturing:
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We are now in a position to find the wage in any country. In the agricultural countries, the wage is just the agricultural human capital level. Thus,
In the industrialized countries, (17) and (18) in (5) give
We can now see how this model generates income disparity between industrialized and unindustrialized countries. We can calculate, for example, the wage ratio between the richest country, country 0, and the unindustrialized countries, which all have the same wage.
Thus, the income ratio between the richest and poorest countries grows exponentially with time. The income difference is due to the fact that manufacturing is expanding into countries which have a low level of manufacturing human capital and a high level of agricultural human capital. Agents in those countries will only switch to manufacturing if the price of manufacturing is high. The high price then makes agents in countries with high levels of manufacturing human capital rich.
Before agents become satiated with agriculture, the wage in terms of units of agriculture, calculated above, is very relevant. As the model proceeds, however, spending on agriculture becomes small relative to that on manufacturing. The wage in terms of units of manufacturing then becomes more relevant. Call this v(j,t) = w(j,t)/PM(t) . After industrialization,
We can calculate the growth rate of v(j,t)
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This is higher than gM at first, but approaches it as time becomes large. We can also calculate the growth rate immediately after industrialization:
There is a spike in the growth rate of each country after industrialization. As time goes on, the j value of the industrializing country rises, so the height of the spike is rising. This is because the manufacturing human capital level of county 0 is rising, so the gap in manufacturing knowledge between it and unindustrialized countries is rising. This leads to faster learning in a newly industrialized country.
As countries approach the leader in terms of manufacturing human capital, their growth rate slows, so we tend to get a group of rich countries with a similar level of wealth. (As evident from equation 22, they actually maintain the same absolute difference from each other. However, this constant difference becomes a smaller and smaller fraction of their income.)
Figure 2: Wage in units of manufacturing
It may seem as if world inequality just keeps increasing in this model forever (equation 21). However, remember that the number of unindustrialized countries is falling, and more and more countries are approaching the level of country 0. Also, if we imagine this as an approximation of a situation in which countries do have a finite size, eventually the last country will also start industrializing. We can thus expect that, eventually, inequality will fade away.
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Figure 3: Growth rates
3. RESULTS
The behaviour of the model can be seen more clearly graphically. The figures are for a model run with 100 countries. Figure 2 shows the evolution of v(j,t) for a number of representative countries. Figure 3 shows growth rates for the same run. Note the rising growth rate spikes following industrialization. In units of manufacturing, unindustrialized countries always have a wage equal to hMo, so there is no growth. Actually, though, welfare is improving because the price of agriculture is falling in manufacturing units. As each country industrializes, its growth rate jumps discontinuously to the level found in equation (24). Growth then slows gradually as the manufacturing human capital level approaches that of country 0. Countries which industrialize later show higher growth rate spikes because their initial manufacturing human capital levels are farther behind those of country 0, leading to faster learning.
Figure 4 shows the same run, but for a longer time. This is the ratio between each of our representative countries' wages and the average wage for all countries. It shows clearly how wages first diverge and then re­converge (at a much higher average level). Note the resemblance between this figure and, for example, figure 15.3 in Fujita, Krugman, and Venables (1999).
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Figure 4: Relative wages
4. CONCLUSIONS
The main conclusion of this model is that it is, in fact, possible to produce a serial industrialization pattern in a learning­by­doing model, which is similar to and compatible with the patterns produced in the new economic geography literature. This pattern is also suggestive of the real world industrialization pattern since the industrial revolution.
Another conclusion is rather discouraging. Taken literally, this model suggests that only one country at a time can industrialize – that the population of unindustrialized, poor countries at any time is predetermined and unchangeable. It is easy to imagine that a poor country in this model could use education to raise its manufacturing human capital level a bit, and so put itself “at the front of the line” for industrialization. But that would push other countries back, and delay their industrialization.
I would not suggest that we take the model too literally. More complex and realistic models may well suggest ways in which the world is less fatalistic. But this feature of the model does bear thinking about. If, somehow, we can successfully foster industrialization in a country and put it on the road to “development”, would we also necessarily delay the industrialization of other countries?
What drives the division of the world into rich and poor countries in this model? It is evident that rich countries are the ones producing the good labeled “manufacturing”, while poor ones produce the good labeled “agriculture”. But what is the key difference between these goods? It is not differences in growth rates. We get such differences for any positive values of gM and gA. Rather, the key difference is the assumption about the consumption pattern. The share of manufacturing in consumption increases with income, while that of agriculture falls. This causes manufacturing to keep expanding into new countries which lack the human capital type required to produce it effectively, pushing up its price and making those able to produce it more effectively rich.
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In many growth models, poor countries are the ones with low human capital. Here, poor countries actually have far higher levels of agricultural human capital than rich ones. It is only in manufacturing human capital that they are behind. They are poor because the good they are skilled at producing commands a low price relative to the labour required, not because they are unskilled at anything.
Is this realistic? I would argue that it is. Poor country economies may look “primitive” to a casual observer from a rich country, but many observations support the view that they are actually complex, sophisticated, and highly optimized. (see Sanwal, 1964; Tax, 1963; Hopper, 1965; Welsch, 1965). The labour­intensive production methods used are not used because of lack of knowledge or resistance to change. Rather, they are simply cost­effective methods of production in an environment where the prices of manufactured inputs are high relative to the cost of labour. Development workers from rich countries do not often find it easy to come up with improvements on local methods. It is all too common for fancy new “appropriate” technologies to get rave reviews in development agency literature, but not to be actually used by the people due to some fatal flaw. If there are actual improvements to be had from the adoption or development of new technology, it is common for poor country people to discover that for themselves, without outside help.
A great deal of knowledge is involved in poor country economies. This is not the knowledge to be gained by formal education, which is developed by and suitable for industrialized countries. Rather, it is knowledge gained by experience and handed down through the generations. I would therefore argue that it is very realistic to consider these countries to have “different” human capital rather than “low” human capital.
Possibly the most unrealistic feature of this model is the way in which all agriculture is eliminated from rich countries. This feature could be changed just by giving agriculture a decreasing returns to scale production function. For more realism, we would need to allow it to use manufacturing as an input, so that equipment and chemicals could be substituted for some of the labour. (Rich country human capital in agriculture would continue to grow, but at a low rate because of the low fraction of the population involved.)
Another feature which may be unrealistic is the exponential growth in the gap between richest and poorest countries. Chari, Kehoe, and McGrattan (1996) graph the ratio between the incomes of the richest 6 countries and the poorest 6 out of a sample of 125 countries for the years 1960­1985. The result seems fairly constant, not growing exponentially as in equation 21. But it has clearly grown in the past, since pre­industrial revolution differences in the wealth of various regions seem to have been small. Lomborg (2001) shows the ratio of per capita income in the “developed” world to that in the “developing” world as rising from 1820 to about 1960, then starting to decline.
In the sense that the number of poor countries eventually becomes very small, while the others converge in wealth, this model does predict an eventual decline in inequality. But it does not predict the leveling off of the difference between the very richest and very poorest countries suggested by the 15
Chari, Kehoe, and McGrattan data. It seems very likely, however, that small changes in the assumptions could produce such a result.
Despite these shortcomings, this simple model produces behaviour that seems very suggestive of world economic history since the industrial revolution. I hope that it can also serve as a bridge between the growth model literature and that of the new economic geography.
I certainly do not believe that this model captures all the factors causing the division of the world into rich and poor countries. Rather, I suggest that it is part of the story, and that it and other models can be combined to provide a more complete picture. In this section, I suggest how such an integration could be achieved.
It is very evident that, in the case of labour, in the real world, factor price equalization does not occur. I find it useful to look at the situation as one in which all of the mechanisms which might lead to this equalization are blocked. One such mechanism is the movement of labour from poor countries to rich ones in search of higher wages. It is obvious that this mechanism is heavily restricted by the immigration controls of rich countries.
Another mechanism which would lead to factor price equalization if it were not blocked or heavily restricted is the movement of firms from rich countries to poor ones in search of cheap labour. What restricts such a movement? I suggest that there are many answers to this question, and that these answers should be seen as working together, reinforcing each other. One such answer is that modelled by Krugman, Venables, and others in their new economic geography. Firms do not move to poor countries because their customers and suppliers are concentrated in rich countries, and shipping and other transaction costs would offset the reductions in their labour costs. Thus, the concentration of firms in rich countries is self­reinforcing.
Another such reason is the one modelled in this paper. Firms are reluctant to move to poor countries because, while they might be able to obtain cheap labour there, that labour would not have all the skills they need. The concentration of manufacturing human capital in rich countries is also self­
reinforcing. The concentration of manufacturing firms causes the concentration of manufacturing human capital, and this human capital concentration makes the rich countries more attractive to firms than the poor countries, despite the high wages.
There are other reasons for the reluctance of firms to take advantage of the cheap labour in poor countries. Government corruption and political instability in poor countries make the investment climate uncertain. I would argue that these things are also self­reinforcing, because they help to cause poverty, and are, in turn, caused by poverty. People who are poor are more likely to be tempted by bribery opportunities, often out of desperation. This can lead to a culture in which corruption is relatively acceptable and practiced also by higher officials who may not be poor at all. People who are poor are also likely to blame other countries, other ethnic groups, other classes, or their own government for their misery, leading to conflict.
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Poor countries also often lack good government services and good infrastructure. They suffer from brain drains. These things are also self­reinforcing because they help to cause the poverty, and are caused by it.
We thus have many different reasons for industries to remain in rich countries instead of seeking low wage labour in poor countries. New economic geography models include one such reason. This model incorporates another. Presumably, other similar models of international inequality could be built on others of these reasons. In the real world, I suggest that all of them are significant. Together, they act to keep manufacturing and other growing, wealth­producing sectors of our modern world economy largely confined to certain countries. I submit that this provides a realistic framework in which factor price equalization for labour would not be expected to occur, and which can thus explain the great wealth divide between nations in a realistic way.
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