Econ 133 Overheads04-P.1 Human Capital • Extension of the Solow growth model that helps explain cross-country differences in income: Replace raw labor by human capital • Define human capital hLH⋅= as product of labor effort L and the average skill level of workers h. • Assume output is Y = F(K,AH)= Kα(ALh)1−α • Assume skill h depends on workers’ years of education u: each year of education increases skill by ψ percent (greek psi): h=eψu Empirical estimates: ψ is about 10%/year or 0.10. • Assume improvements in technology A at rate g are responsible for output growth that cannot be explained by capital, raw labor, or education • Trick: Re-define the effective labor force as A⋅L⋅h , and interpret all “~” variables as measured per effective labor unit. The the algebra of ratios remains unchanged. For example: ˜ y *=sd + n + g⎛ ⎝ ⎜ ⎞ ⎠ ⎟ α1−α • NEW: Real units are now effective units multiplied by H=L⋅h - For example: income is hAyy⋅⋅=~ at all times. As converges, ˜ y →˜ y *y(t) ≈ y*(t) =˜ y *⋅ A(t)⋅eψu(t) depends on the growth path of A and on the level of education. - Relevance: Education levels differ drastically across countries. - Countries with high education levels should have higher per capita incomes.Econ 133 Overheads04-P.2 Can the model explain income differences? • The model specifies exactly which variables should determine per-capita income. These determinants differ across countries. Does this explain persistent cross-country differences in income? • Call yi the income of country i (yUS, yUK, yFRA,...) Defineˆ y i= yi/yUS as the country’s income as fraction of US income. Defineˆ y i*= yi*/yUS* as steady state income relative to the US. • Apply the theory: - Unless there are recent disturbances, income in each country should have converged to the steady state, . )(*~)(*)( tAhiytiytiy ⋅⋅=≈- Income differences should be due to differences in , in h, or in A. ˜ y i*Recall that ˜ y i*=sid + g+ ni⎛ ⎝ ⎜ ⎞ ⎠ ⎟ α1−αand definexi=ni+d+g. Then obtain: - Summary equation in Jones: yi*=ˆ s iˆ x i⎛ ⎝ ⎜ ⎞ ⎠ ⎟ α1−α⋅ˆ h ⋅ˆ A • Conclude: The sources of income differences are savings (s), population growth (in x), education levels (in h), technology (A). • Empirical questions: - How much can we explain without technological differences? See Fig.3.1. - How much unexplained differences are there that we have to attribute to technology? See Fig.3.2.Econ 133 Overheads04-P.3 Convergence • Are income differences across countries increasing or decreasing over time? Do incomes “converge” over time? • Theory: Solow model assumes exogenous technology growth g. If g is common, all countries’ per-capita income will grow at rate g in the long run. => Solow model can only explain growth rate differences during the transition process to the steady state. • Evidence: See Jones’ Figures 3.3-3.6. • Interpretation: Distinguish conditional & unconditional convergence 1. Unconditional convergence hypothesis: Without caveats, poor countries grow faster and tend to catch up. Clearly rejected for worldwide data. 2. Conditional convergence hypothesis: Countries that are poor as compared to the country’s steady state should grow faster than others. Solow model implies that conditional convergence should hold, but NOT that unconditional convergence