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Endogenous growth theory
II. The empirics of GDP growth
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
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”
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
A distribution of estimators across models:
The most robust variables:
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
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
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
Example 1
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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
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
Looking at convergence allows us to
• Test the relevance of endogenous growth models
• Assess the magnitude of the returns to accumulable factors
)1( gv
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
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:
The BSM Universal Law of Convergence:
The speed of convergence is 2 % per year
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
How universal is the law?
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
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?
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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?
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
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) = 1-0.02/0.08 = 0.75
• To reconcile these two facts, they introduce another form of capital: Human capital
The Augmented Solow model
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The balanced-growth path
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:
Measuring sH
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?
Recomputing the speed of convergence
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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
Old Solow does not work…
…but new does.
Does it add up?
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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