6It does not add up Common estimates suggest α = 1/3 Therefore, to have a 10-fold difference in GDP, we need a 20-fold difference in savings rate (2 % vs. 40 %)More leeway if technology differed across countries, but unlikely if technology is transferableSo what do we do?
7If α were greater? Growth would take more time to fall to zero Convergence would be slowerThe speed of convergence is the coefficient of gdp growth on (local) initial log gdpIncome differences between countries would be magnified
9An extreme case: α = 1,g=0 The speed of convergence goes to zero The convergence path becomes a balanced growth path at a constant rateMRK no longer falling capital accumulation can sustain long-run growthThe growth rate is now endogenous and depends on preferences
10Convergence in neo-classical models Neo-Classical models: each country converges to its own steady stateAll own steady states grow at the same rateBut the level depend on policies, savings rates, etcSimilar countries converge to same GDP per capita
11Convergence in endogenous growth models A laggard never closes the gapTherefore, no convergence in income levelsThis because MPK is no higher for the laggardFurthermore, differences in policies affect the long-run growth rate
12Looking at convergence allows us to Test the relevance of endogenous growth modelsAssess the magnitude of the returns to accumulable factors
13Two approachesBarro and Sala-i-Martin: take a data set of similar economic units and look at convergence between them in pc GDPMankiw-Romer-Weil: take a cross-country regression of growth rates on initial income controlling for own long-run steady state
14Barro and Sala-i-Martin They use a data-base of U.S. states over a long-run periodThey estimate the equivalent of our local speed of convergence regression:
22Findings:The more similar the countries, the more it holds unconditionallyThe less similar the countries, the more likely we find divergenceBut the law is restored if controls are added, controlling for own steady state
23How to eradicate poverty? 1. Adopt the policies and institutions of advanced countries2. Wait!How long? Suppose I am 10 times poorer than the US. How long does it take to be 2 times poorer?
25What do we get? With v=0.02, ρ0 = 0.1, ρ1 = 0.5, t = 60 years!With v=0.056, we instead gett = 21 yearsWe want to understand why the speed of convergence is so lowCan policy increase the speed of convergence?
26Gloom?In principle, the speed of convergence only depends on the deep technological parametersThat it is low tells us that the technology is not what we thought it wasBut it does not tell us we can increase v
27Mankiw-Romer and WeilNational accounts suggest that the elasticity of capital is 0.3Speed of convergence is more like1-v/(g+δ) = /0.08 = 0.75To reconcile these two facts, they introduce another form of capital: Human capital
33What have we learned?We have seen that with α = 0.3, it is difficult to explain X-country income differencesBut now what matters is α + β, which acts as αSo with α + β large enough we can explain cross-country differences.A natural question is: can we also expect slow convergence?
35Empirical strategyInvestment rates and schooling are kept to proxy for own steady stateInitial output is addedCoefficient in initial output related to SOV as in BSMNo other control variable is added in strict interpretation of Solow model
39SummaryThe Solow model predicts too low income disparities and too quick convergenceThe AK model predicts zero convergence and widening disparitiesThe Augmented Solow model does well to predict both the disparities and the speed of convergence