Empirical Applications of Neoclassical Growth Models Chapter 3 Charles I. Jones

Human Capital and Solow Growth Model 1992 Mankiw, Romer, and Weil found a good empirical fit of the Solow growth model to the empirical data. Introducing human capital Empirical fit of the Solow model can be improved by differentiating labor by education. That is, by explicitly recognizing that the same number of working hours or workers can produce more output if labor is educated. Basic setup In essence, we use Solow model of Chapter 2 with technology, but we replace labor L with human capital H defined as follows: Here is a constant, u is the fraction of time devoted to education, L is labor from the Solow model of Chapter 2.

Returns to Education Education increases human capital Interpreting If u increases by 1 unit (i.e. one additional year of schooling) and if , then H rises by 10%. is given exogenously (i.e. we don’t ask how individuals decide on how much to study). Empirical literature finds that one more year of schooling results in wage increases of 10% Capital accumulation and production function These are almost identical to the model of Chapter 2:

Solving the Human Capital Model Define new state variables Production function in terms of new state variables Capital accumulation equation Steady state We find steady state by setting Solving the capital accumulation equation yields

Steady State Solution Steady state level of the output-technology ratio: Steady state level of the output-technology ratio: Countries are rich if They have high investment rates They spend a large fraction of time on education (i.e. u is high) They have low population growth rates Similarly to the Solow model with technology, output per capita grows at the rate of technological progress, g.

Relative Per Capita Income Relative per capita income is a useful tool to test the convergence hypothesis Define a new variable equal to the per capita income in a specific country relative to the United States (or, in fact, any other country we choose). This variable is defined as follows: From the formula for the steady state level we obtain:

Constant Relative Incomes We assume that in the steady state all countries are growing at the same rate of technological progress g We need this assumption because without it, gap in technological development between countries will become infinite at one point. Technological progress g is likely to be roughly the same sooner or later because of the process of technology diffusion Technological levels can be nevertheless different between countries

How Well does the Human Capital Model Fit the Data? Relative income per capita is computed according to is assumed to be equal to 1/3 based on economic studies u is the number of schooling years is assumed to be 0.1, and

How Well does the Human Capital Model Fit the Data? We also assume that A, the technological level, is the same across countries The model still predicts fairly well the steady state income levels However, a lot of countries (e.g. Africa) are above the 45-degree line This failure of the model is due to the assumption of the same level of technological development

Incorporating Differences in the Technological Level We can compute technological level A in each country from the production function formula Given we know data on per capita income, capital stock, and the number of schooling years, we can compute the technological level A as follows:

Empirical Correlation Between Relative Incomes and Relative Level of Technological Development Levels of A are strongly correlated with income per capita (in relative terms) across countries Rich countries not only have higher levels of physical and human capital, they are also more productive However, there are some outliers: Turkey, Guatemala, Syria, Rwanda Also, Turkey has a higher A compared to Korea Computing A from the production function aggregates all differences between countries, not just technology. Quality of education On-the-job training General health The richest countries are TEN times more productive than the poor

How Rich Countries are Different from the Poor Technological level is ten times higher with the rich Output per worker is roughly 40 times higher in the rich countries This gap can be decomposed into differences in investments in physical and human capital, and differences in productivity Investment rates in the rich countries are 25% versus 5% in the poor economies s/x varies by a factor of 5 between the rich and the poor In rich countries, the average number of schooling years is 11, while it’s only 3 years on average in the poor economies Productivity differences are also very large, but we don’t have a theory just yet to explain these

Summary of the Solow Framework What Solow models do not tell us Solow framework explains very well differences in wealth across countries You become rich by: Investing a larger fraction of your resources in physical and human capital Using productive resources (i.e. labor, physical and human capital) more productively What Solow models do not tell us Why do some countries invest more than the others? Why do some countries have a better technology than the others? Why are some countries more productive than the others?

Convergence between Countries Convergence hypothesis Gerschenkron (1952) and Abramovitz (1986) hypothesized that the poor countries will grow faster than the rich so that in the end every country will enjoy the same output per capita. This is the so-called catch-up effect However, we do know that differences in per capita incomes are enormous Do we observe convergence? Are we likely to observe convergence in the future?

Empirical Evidence on Convergence Baumol (1986) documented both convergence, and the lack of it Convergence is obvious Only developed countries are featured in this graph US has been the world leader ever since after the WWII

Fast Growth from the Low Base Richer countries like the UK, Australia, the Netherlands, grew slower Poorer countries like Japan, Finland and Norway, grew faster It is apparently easy to grow fast from a low base Korea started from the low base, too, but it kept on growing fast even after development

Convergence in the OECD Countries Convergence hypothesis works very well for the OECD countries Turkey grows less well than expected

Lack of Convergence in the World African countries grow much slower than predicted Non-OECD countries in general do not conform to the convergence hypothesis Poor countries are not catching up Why do we see convergence among rich countries, but not among the poor ones?

Why Should We Have Convergence? Rewrite the capital accumulation equation: or The right-hand-side will be lower for higher ! Since the growth in is proportional to the growth in , lower per capita capital will be associated with higher growth rates.

When does Convergence Hold? Among countries that have the same steady state, the convergence hypothesis should hold. That is, poor countries should grow faster on average than rich countries. Steady state is defined by . While these parameters are similar for the more developed countries, they are different for the poor economies. The Principle of Transition Dynamics The further an economy is “below” its steady state, the faster the economy will grow. The further an economy is “above” its steady state, the slower the economy should grow.

“Conditional” Convergence for the World Poor countries still don’t grow faster. However, countries that are “poor” relative to their steady state, they do grow more rapidly. Differences in growth rates are explained by the distance from one’s own steady state.

Why Would Countries be Away from their Steady States? Government policies leading to an increase in the savings/investment rate Change in the population growth rate Chinese birth restriction Immigration control Medical care improvement Wars Changes in TFP Lower A results in higher hence slower growth Oil prices changes Mismanagement of the macroeconomy Hyperinflations (Latin America, Zimbabwe)

Factors Affecting Economic Growth Durlauf, Johnson and Temple (2005) find 145 factors affecting economic growth, but there are only about 200 countries in the world Most relevant factors appear to be: Higher rates of primary schooling in 1960 Higher life expectancy in 1960 Higher prices for investment goods in 1960 Prevalence of malaria in 1960 Factors increasing economic growth rates Increases in investment/savings rates Skill accumulation Level of technology increases

Evolution of Income Distribution We say that a country belongs to the 10th percentile if its income is among the 10% world’s poorest incomes. Accordingly, the 90th percentile means the country’s income is among the 10% richest incomes in the world. The income gap has risen a lot over time. However, this might be due to the fact that not every country is on the “escalator” of economic growth yet.

Evolving “Width” of Income Distribution Proportion of world population with 10% of the US income has fallen from 60% in 1960 to 20% in 2008 In both 1960 and 2008 the fraction of population with less than 50% of the US level was about 80% Absolute poverty has been decreasing since 1960.