1. Endogenous growth theory
II. The empirics of GDP growth

2. Questions
What are the variables (institutional, cultural, demographic…) which determine GDP per capita and/or LT growth
Do we expect poor countries close the gap with rich countries?
What are the policies/institutions which allow such convergence to take place

3. An industry developed in the 1990s
Take a cross-section of countries
Regress their growth performance over a given period on a set of explanatory variables:
Investment
Education
Financial development
Corruption
Age
Political variables: coups, etc…
Then write a World Bank report saying that variable X is “good for growth”

4. The findings:
A recent paper by Sala-i-Martin et al. runs a horse-race between a large number of specifications involving more than 67 variables
They rank variables by robustness using Bayesian techniques

12. A distribution of estimators across models:

13. The most robust variables:

14. The shortcomings
Whether we are really talking about growth depends on the specification
The economic interpretation of these regressions is not clear
Many variables are not robust

15. The initial income problem:
If initial income is not included in the regression, we estimate a permanent sustainable growth rate
If it is and has a negative coefficient, we estimate the long-run output level
It can only grow if
One of the explanatory variables grow (but most can’t)
A growth trend affects all countries

16. The interpretation problem
Some variables affect growth because they proxy for the growth in the inputs of the production function: education, investment, etc…
Others matter because they affect human behaviour and therefore how the economy accumulates these inputs
Finally, whether initial income should enter depends on how the input contributions are specified

17. Example 1

18. Example 2

19. Example 3

20. Convergence in neo-classical models
Neo-Classical models: each country converges to its own steady state
All own steady states grow at the same rate
But the level depend on policies, savings rates, etc
Similar countries converge to same GDP per capita

21. Convergence in endogenous growth models
A laggard never closes the gap
Therefore, no convergence in income levels
This because MPK is no higher for the laggard
Furthermore, differences in policies affect the long-run growth rate

22. Looking at convergence allows us to
Test the relevance of endogenous growth models
Assess the magnitude of the returns to accumulable factors

23. Two approaches
Barro and Sala-i-Martin: take a data set of similar economic units and look at convergence between them in pc GDP
Mankiw-Romer-Weil: take a cross-country regression of growth rates on initial income controlling for own long-run steady state

24. Barro and Sala-i-Martin
They use a data-base of U.S. states over a long-run period
They estimate the equivalent of our local speed of convergence regression:

28. The BSM Universal Law of Convergence:
The speed of convergence is 2 % per year

29. What do we expect? The Solow model predicts (δ+g)(1-α)
A reasonable calibration is δ=0.06, g=0.02, α=0.3
This gives v=5.6 % per year

30. How universal is the law?

32. Findings:
The more similar the countries, the more it holds unconditionally
The less similar the countries, the more likely we find divergence
But the law is restored if controls are added, controlling for own steady state

33. How to eradicate poverty?
1. Adopt the policies and institutions of advanced countries
2. Wait!
How long? Suppose I am 10 times poorer than the US. How long does it take to be 2 times poorer?

35. What do we get? With v=0.02, ρ0 = 0.1, ρ1 = 0.5,
 t = 60 years!
With v=0.056, we instead get
t = 21 years
We want to understand why the speed of convergence is so low
Can policy increase the speed of convergence?

36. Gloom?
In principle, the speed of convergence only depends on the deep technological parameters
That it is low tells us that the technology is not what we thought it was
But it does not tell us we can increase v

37. Mankiw-Romer and Weil
National accounts suggest that the elasticity of capital is 0.3
Speed of convergence is more like
1-v/(g+δ) = /0.08 = 0.75
To reconcile these two facts, they introduce another form of capital: Human capital

38. The Augmented Solow model

39. The balanced-growth path

40. Explaining cross-country differenced in pcGDP:
The preceding equations define “own” steady state
They use it to see if it explains cross-country income differences:

41. Measuring sH

43. What have we learned?
We have seen that with α = 0.3, it is difficult to explain X-country income differences
But now what matters is α + β, which acts as α
So with α + β large enough we can explain cross-country differences.
A natural question is: can we also expect slow convergence?

44. Recomputing the speed of convergence

45. Empirical strategy
Investment rates and schooling are kept to proxy for own steady state
Initial output is added
Coefficient in initial output related to SOV as in BSM
No other control variable is added in strict interpretation of Solow model

46. Old Solow does not work…

47. …but new does.

48. Does it add up?

49. Summary
The Solow model predicts too low income disparities and too quick convergence
The AK model predicts zero convergence and widening disparities
The Augmented Solow model does well to predict both the disparities and the speed of convergence