Part 3

1. We still have diminishing returns to physical capital (k). But: we have constant returns to h and k combined. ◦ In basic Solow, this resulted in convergence to the same steady state level of k ss & y ss. ◦ Not here: Even if all countries have similar savings rates (q &s), in the long run steady state, these countries will converge to the same long run growth rate  any initial differences in k 0 & y 0 will persist through the long run. ◦ Why? In the basic Solow, k was not a source of growth due to diminishing returns  But after adding human capital h to our k, diminishing returns to both are much less severe! We have constant returns to h and k combined.

2. (q) & (s) have growth effects (not just level effects) as in basic Solow.  When savings rates affect growth rates, models are called endogenous growth models  Growth rates are determined within the model, not exogenously through something like technological change (π)

3. Human capital model may help explain why rates of return to physical capital are low in poor countries. ◦ Intuition from Easterly:  Mankiw noted that human capital (people with skills) could not move across countries, but physical capital could.  Thus if poor countries have low (h), investors do not want to invest there because you need high (h) to get a good return on capital equipment (k).  Thus: countries invested in high skilled countries - - thus capital flows to rich countries.

4. Convergence…do we see it? ◦ Recall first: unconditional convergence ◦ Below is Baumal’s study and De Long’s critique ◦ Point: we know that unconditional convergence does not hold in the basic Solow model

4. Convergence…do we see it? ◦ But…what if we account for ["condition" on] the stock of human capital (h)?? ◦ When estimated with data we find: ◦ If we estimate with data and find:  β1<0: means rich countries grow slowly and poor countries grow fast  conditional convergence: after controlling for (h 1960 ), poor countries can grow faster  β2>0: means countries with high (h) will grow more quickly  conditional divergence: after controlling for (y 1960 ), countries with more human capital grow faster  Putting it all together: Rich countries have more human capital ⇒ model predicts neutrality in growth rates income per capita.

4. Convergence…do we see it? ◦ Intuition from Easterly:  Mankiw finds that once controlling for capital accumulation (k) and education (h), poor countries did tend to grow faster.  But: it is not necessarily true that all countries were moving toward the same destination (as with Solow)  rather countries with different savings rates of capital & human capital accumulation could head to different destinations.  Further, being poor relative to your own steady state destination, did mean that you would grow faster toward that destination ◦ Points:  controlling for (or conditioning on) h, poor countries grow faster but countries with more h also grow faster.  Countries with different savings rates of h accumulation grow differently and grow in different directions.  Countries don't converge to same spot, but converge in growth rates.