Models of Growth (1).


  1. Have full understanding of the characteristics of various theories/models of development.
  2. Their implications to policy making and criticisms.
  3. IB syllabus: Harrod-Domar Growth Model and Structural Change/Dual Sector Model. ♣

  1. An Overview:
    1. Linear Stages Growth Model:
      1. Rostow's Stages of Growth.
      2. Harrod-Domar Growth Model.
    2. Structural Change/Dual Sector Model.
    3. The International Dependence Revolution.
    4. Neoclassical Model
    5. Endogenous Growth Model.
    6. Alternative model to sustainable development.
  2. Recall the distinction between economic growth and economic development. We should remember that economic growth does not automatically lead to an overall improvement in well beings that characterizes economic development. It is possible that economic growth comes at the expense of environmental degradation that actually reduces economic development.
  3. In this chapter, we consider potential economic growth that happens when he PPF shifts outward and the LRAS shifts to the right. Growth models are constructed to describe actual historical growth rates. These models attempt to identify factors that are responsible for historically observed growth and suggest that growth can be replicated by manipulating these factors. In the IB syllabus, we will have to study Harrod-Domar Growth Model and Structural Change/Dual Sector Model. In this note, however, I included other models for reference.
  4. Rostow: Stages of Economic Growth.
    1. Walt Whitman Rostow (1916-2003) published Stages of Economic Growth in 1960 and used insights provided by the Harrod-Domar Model below. This is a historical study and postulates a linear stages of economic growth. There are five common stages that an economy will experience.
      1. Traditional society where batter is common and there is a heavy dependence on agriculture.
      2. Precondition for Take-Off. Usually needs injection from abroad. Extractive industries like mining develop and agriculture becomes more commercialized and mechanized. Some technological improvement and growth in infrastructure that facilitate trade. A single industry (historically this had been textile) dominate the economy. About 5% of GNP is invested.
      3. Take-Off. The economy begins to grow at a positive rate. Infrastructure increases, manufacturing grows rapidly, and both political and social adjustments take place in the economy. Agriculture as a sector declines and growth benefits concentrate in certain limited areas. 10 to 15% of GDP (Todaro put this figure at 15% to 20% of GDP) is invested or capital is borrowed from abroad.
      4. Drive to Maturity. Moving towards a developed nation status. Growth should be self-sustaining and multiplier effect of manufacturing expands as technology improves. The earlier industries that contribute to take-off declines. Rapid urbanization occurs.
      5. High Mass Consumption. Citizens can now enjoy high consumption levels. Rapid expansion of service industries and welfare facilities. Employment in manufacturing declines and industry shifts to the production of durable consumer goods.
    2. Implications:
      1. There is a linear PATH to economic growth.
      2. A right mix of savings, investment level, technology, work ethics and entrepreneurship is required to move from stage 2 to the take-off stage. Injection from abroad may be required to bridge the saving gap (the difference between savings and investment) to finance capital investment that should be around 15% to 20% of GDP.
      3. Mobilizing foreign and domestic savings to generate sufficient investment to accelerate growth is crucial to move from the take-off stage to stage 4 (maturity).
    3. Criticisms:
      1. Injection of aid into stage 2 (precondition for take-off) without utilizing appropriate technology or proper monitoring is not helpful for growth.
      2. Injection from abroad could be lost through corruption and capital flight. In the end the country is left with only Debt Burden.
      3. Aid could be diverted into buying arms rather than paying for productive investments.
      4. This historical "path" is based on experiences of western developed economies. This path is not universal. Recall the diversity found among developing countries and the limited values of observations from historical growth.
      5. Investment alone cannot explain growth. South Asia grew at a rate exceeding 5.5% from 1980-1990 and 1990-1998. In both periods, Sub-Saharan Africa only managed a rate about 2% yet the gross domestic investment as a percentage of GDP (roughly 20%) for both regions were very similar in both periods (World Bank).

      6. Up.
  5. Harrod-Domar Growth Model.
    1. The model was named after works produced by Sir Roy Harrod (in 1939) and Evsey Domar (in 1946).
    2. This model was initially developed to study business cycles and then adapted to "explain" economic development/growth. In this model, investment, saving and implicitly technological change are the key variables that determine economic growth. Technological change is represented by the capital-output ratio (K/Y), that is how much physical capital is needed to produce one unit of output. Of course, better production technology would means a smaller capital-output ratio. .
    3. Basically, this is a Keynesian model.
    4. The model suggests that to obtain growth, the economy needs to increase investment thus pushing out the Production Possibility Frontier (PPF) of the economy. The model implies a higher saving rate can increase the amount of investment. Growth could also be achieved if the capital-output ratio is reduced, that is less capital is required to produced a unit of output. This can be achieved by an improvement in production technology. (See Box 1.)
    5. Implications to growth:
      1. High saving rate is desirable.
      2. High rate of investment in capital goods is desirable.
      3. Improvement in production technology is desirable which leads to a lower capital to output ratio.
      4. If the country cannot meet any of the three desirable factors above then the country can be given a "jump-start" by borrowing from abroad (commercial banks, foreign governments, or multilateral organizations like the World Bank) or/and by receiving aid from abroad (the aid could be monetary, machineries or technical know-how).
    6. Criticisms:
      1. It is difficult to stimulate the desirable saving rate. Historical data suggests that for an economy to take-off it need to save 15% to 20% of GDP.
      2. If saving gap is to be borrowed from abroad then the economy is subjected to the burden of loan repayments. Some developing countries that borrowed heavily from abroad are still experiencing the effects of Debt Burden.
      3. A lot of emphasis on physical capitals. In some cases, these capitals may not be appropriate technology to the economy. The country may not have the expertise to maintain the capital goods or their maintenance requires expensive replacement parts from abroad. Thus,some of these imported capitals will be out of repair in a few years.
      4. Capital goods also experience diminishing marginal returns. This rate increases if the local workers have no expertise to maintain these capital goods. Thus, these capital goods will give only short run returns to the economy.
      5. Technological change in this model is implicitly assumed in the capital-output ratio. There is no room for the economy to develop its human capital (education, training, skills, creativity and experience) or make advances in local technology.
      6. The "jump-start" approach of providing machineries and money is not sustainable. Local workers need to be empower to shape and control their production techniques. Without local empowerment, any imported technique or aid cannot lead to sustainable growth.
      7. Economic growth does not necessary mean development. Economic growth may lead to uncontrolled pollution problems, deforestation, break-down of traditional values, and other problems associated with modernization.
    7. Box 1. An algebraic approach to Harrod-Domar Model.

      1. Savings (S) is a (s) proportion of national income (Y): S = sY.
      2. s can be seen as the Average Propensity to Save (APS) also called savings ratio when expressed as S/Y.
      3. Investment (I) is the change in capital stocks (ΔK): I = ΔK.
      4. Let k represents capital-output ratio: k = K/Y.
      5. In the original Harrod-Domar Model, both Average Propensity to Save (s) and capital-output ratio (k) are held constant, that is they are determined by the structural of the economy which does not change in the short run. Thus, we will also assume that both s and k are constant.
      6. If k is constant then ΔK/ΔY is also constant, and more precisely k = ΔK/ΔY.
      7. Thus, I = ΔK becomes I = k ΔY. And for simplicity sake, let us assume that it is a close economy and when equilibrium level of national income is achieved:

        S = I
        sY = k ΔY. (by replacing I with k ΔY)
        s/k = ΔY/ Y (rearranging from above) or
        ΔY/Y = s/k
        that is the rate of economic (national income) growth is the savings ratio (S/Y) over capital-output ratio (K/Y).

      More growth if the economy has higher saving rate or lower capital-output ratio, that is a unit of output can be produced with less amount of capital. The latter can be achieved by improvement in production technology.

  6. Structural Change/ Dual Sector Model.
    1. By the 1970s, economists used modern economic theory and statistical analysis in an attempt to portray the internal process of structural change that a "typical"developing country must undergo.
    2. The focus is the mechanism of transformation from a traditional society with subsistence agriculture to a modern industrialized economy.
    3. Sir W. Arthur Lewis (Nobel Prize winner of 1979 for economic development research) focused on the role of migration. He argued that growth can be sustained by the gradual movement of workers from low productivity agricultural sector in rural areas to higher productivity industries like manufacturing and services in the urban area.
    4. An illustration of Lewis model. The model assumes two sectors, traditional and modern sectors.
      Let the traditional sector be agriculture. The agricultural sector is assumed to have marginal productivity of labor equals to zero. This model implicitly assumes full employment in the traditional sector and in fact there is surplus labor in the traditional sector. That is, surplus laborers in the rural farms are either not working or contribute nothing even though they work in the farms.
      The modern sector (say manufacturing) has high productivity and offers a fixed wage rate that is higher that the wage rate in the traditional sector.
      The rate of transfer from agriculture to manufacturing is proportional to the rate of capital accumulation in the modern sector. The modern sector does not have to raise its wage rate because there are surplus labor in the traditional sector who are always willing to work at the prevailing fixed wage rate that is higher than that in traditional sector. Entrepreneurs in the modern sector gain profits as prices of products are above fixed wage rate. The model assumes that profits are reinvested to increase capital stock and the static production technology requires a fixed capital-labor ratio. An increase in capital stock will require more laborers to maintain the fixed capital-labor ratio. In another word, the modern sector does not invest in labor saving technology as their business expands. In maintaining the fixed capital-labor ratio, the surplus labor in the traditional sector is reduced and the modern sector is expanded. The process will continue until all surplus labor in the traditional sector are moved to the modern sector which in the end of the process is larger then the traditional sector and the economy is now industrialized. Since the modern sector is usually based in urban areas with better infrastructure then this model also explains the process of urbanization as an economy develops.
    5. Implications for economic growth:
      1. There is a need to invest in modern sector that has high productivity. Modern sector is usually taken to be manufacturing industry and in turn this industry will serve as engine for economic growth. Industrialization is taken as synonymous to economic growth.
      2. High rate of capital investment is desirable as it speeds up the process of industrialization and economic growth.
    6. Criticisms:
      1. The model is too simplistic to assume MPL to be zero in the traditional sector. It is more likely that workers in urban slum to have MPL=0. Stiglitz and Charlton in Fair Trade for All point out that unemployment in most developing countries are persistently high and models that implicitly or otherwise assume that resources are fully employed are unrealistic for the experience of developing countries (pg 25).
      2. There is also an implicit assumption that there will be full employment in urban area where modern sector is located. In fact, unemployment in urban areas (slums) can be high in many developing countries.
      3. There other assumption is that wage rate in the modern sector is fixed as long as the MPL=0 in the traditional sector. Since MPL is assumed to 0 in the traditional sector, wage rate in the modern sector is fixed. This does not fit the experience of economic development. This ignores the bargaining power of labor union, imposed wage increased by the government, and more competitive wage rates from foreign multinationals.
      4. The model assumes that all profits are reinvested in the modern sector but this is unrealistic. Some profits can be repatriated abroad, subject to capital flights, consumed or reinvested in rural areas. All these reduce the need to hire more labor in the modern sector.
      5. The assumption that the rate of labor transfer is proportional to the rate of capital accumulation ignore the possibility that modern sector invests in labor-saving technology.
      6. The model also implicitly assumes that all laborers are equally productive in the use of machineries. However, this is not likely to be true. Farmers cannot be equally skillful in using machineries that they might have never seen before. If training is required, the model has left this out and its costs.
      7. Industrialization does not means economic growth. What is more important is the accumulation of appropriate technology that creates job for the locals.
      8. According to Alan Anderson in Economics 3rd edition, small scale investment in rural area often yields a higher rate of return than urban factory investment.
      9. Moreover, all regions in the developing world have very similar rate of migration to urban area but they have different rates of growth.
      10. Urbanization is not synonymous to development. Urbanization could lead to environmental degradation.

Box 2. Be An Inquirer

Are the Harrod-Domar growth model and the structural change model relevant to the growth model as described in Chapter 3 of The End of Poverty by Jeffrey Sachs? Explain your reasoning.


  1. With the help of the Harrod-Domar growth model, explain the negligible economic growth in Sub-Saharan African countries in recent decades.
  2. With the help of the Structural Change Model, explain the process of industrialization for a developing country that was originally an agrarian economy.
  3. Both Harrod-Domar growth model and the Structural Change Model have heavy emphasis on physical capital accumulation. Evaluate the importance of physical capital accumulation in economic growth.

Models of Growth (2)