1. Chapter 4

2.  “Second Generation” growth models  The role of human capital in economic growth  Determinants of technological progress  Externalities and growth  Measuring Technological Progress: Total Factor Productivity (TFP)

3.  Basic models of growth assume that production takes place through the use of physical capital and unskilled labor human capital  By investing in education and training, the labor force acquires a set of skills over time. This is the idea of human capital.  Physical capital can then be complemented by human capital (skilled labor) in the process of output creation.

4.  Suppose households have two forms of savings:  Physical capital (buying shares, stocks, bonds, etc)  Investing in education (to acquire skills)  Households decide on the composition of savings between physical and human capital

5.  Production takes place via the use of the stocks of physical capital (k) and human capital (h):  Households invest a fraction s of output to physical capital and a fraction q to human capital:

6.  The rate of growth of physical and human capital can be expressed as:

7.  In the long-run, both human and physical capital must grow at the same rate (balanced growth). Then, we get  The long-run balanced growth rate for the economy is then given by

8. constant returns  There may be diminishing returns to physical and human capital individually, but when combined, there could be constant returns to the two reproducible factors of production  This makes per-capita output grow in a sustained fashion in the long-run endogenous  This growth is endogenous, since it is determined from within the model (by household choices)

9.  Countries that have similar savings and technological parameters can grow at the same rate in the long-run, but there may not be any convergence in their per-capita incomes  Weaker form of convergence: even similar countries can have different levels of per-capita income in the long-run

10.  This model helps explain why rates of return on physical capital may not be high in poor countries  Poor countries have a shortage of skilled labor, which drags down the return to physical capital

11.  Barro (1991) tested for conditional convergence using school enrolment data (primary and secondary levels) as a proxy for human capital. His main findings were:  There is evidence for conditional convergence after controlling for human capital ▪ Poor countries do grow faster once human capital is accounted for ▪ Countries with more human capital grow faster once per-capita income is controlled for

12.  Technical progress is not exogenous as in the Solow model, but an outcome of human behavior:  R&D expenditures by firms  Investment in higher education (research at universities)  Government investment in Science & Technology  “Learning by doing”

13.  Technical progress can be of two types:  Deliberate: new  Deliberate: conscious diversion of current resources to the production of new consumption and investment goods ▪ Benefits are internalized by innovator  Diffusion:  Diffusion: transfer of knowledge across firms or countries ▪ “outsiders” can profit from new technology ▪ Create foundation for future innovations and research ▪ Benefits accrue through “externalities”

14.  Externalities refer to the unintended consequences of actions and decisions taken by individuals, firms, or the government  These consequences can be  Positive  Positive (knowledge creation, government provision of public goods like highways and ports, etc) and enhance productivity of a larger group of economic agents, or  Negative  Negative (pollution or highway congestion), and hurt overall productivity. complementarities  Positive externalities are also sometimes referred to as complementarities: when the actions of one agent prompt others to take similar actions.

15.  Consider an economy with many firms, each equipped with a production function: where, E(t) denotes the overall level of productivity  Assume that E(t) is a positive externality generated by capital accumulation by all firms in the economy  Let

16.  Then, the production function for each firm is given by  How does this externality affect capital accumulation decisions by firms?  An individual firm, being a small player, takes the average stock of capital as exogenously given  The firm then underestimates the true(social) return to capital  private return is less than social return underinvests  Each firm underinvests in capital sub-optimal  Economic growth is sub-optimal

17.  Underinvestment by firms provides a rationale for government intervention social plannerinternalize  To see this, consider the presence of a social planner, who can internalize all externalities  The planner is not concerned with productivity of an individual firm, but with overall (or average) productivity

18.  The planner therefore sets in the production function  The planner’s (social) production function is  The planner sets social return on capital to its private return  Ensures optimal investment in capital  Generates the “first-best” or “Pareto Optimal” growth rate for the economy

19.  Therefore, the existence of externalities provide a rationale for government intervention in the growth process  Subsidize the accumulation of capital to increase the growth rate  Note also that production exhibits increasing returns at the level of society, even though there are diminishing returns for individual firms  Per-capita economic growth tends to accelerate over time in the presence of externalities  This view was proposed by Romer (1990)

20.  How should we measure technical progress?  Consider the production function in functional form:  Totally differentiate both sides, assuming E is constant:  The above can be expressed as:

21.  This leads to where,

22.  The growth rate of output should be explained by the sum of the growth rates of capital and labor, weighted by their income shares does not equal  If we insert actual data and the right-hand side does not equal the left-hand side, what can we infer?  Our assumption of a constant level of productivity, E, was wrong

23.  If, then it must be the case that the difference between the LHS and RHS represents the growth of porductivity total factor productivity (TFP)  Then, we can define total factor productivity (TFP) growth as residual  TFP growth is thus calculated as a residual

24.  To correctly estimate TFP growth we must  Control for all changes in factors of production ▪ Labor force participation, rural-urban migration, sectoral shifts, changes in education, etc  Assume that all factors are paid their marginal products ▪ If industries are not competitive, then we cannot measure TFP growth