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Lecture 6: Conditional Convergence and Growth L11200 Introduction to Macroeconomics 2009/10 Reading: Barro Ch.4 : p February 2010

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Introduction Last time: – Solow model with no variation in s, n, δ, A between nations implies all countries (eventually) move to same GDP per capita and low GDP per capita nations grow faster: absolute convergence – Data appears to reject this Today – Allow these factors to vary and introduce idea of conditional convergence

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Conditional Convergence How do the models predictions for growth change when we allow the factors to vary – E.g. economies have different saving rates – The economy with the lower saving rate will have lower steady state k*, y* compared to an economy with a higher saving rate – At any level of K(0), the economy with a higher saving rate will be growing faster

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Other factors The same is true for n, δ and A – Higher n implies lower k*, y* – Higher δ implies lower k*, y* – Higher A implies higher k*, y* And at any K(0), the economy with higher technology or lower depreciation / population growth will grow faster.

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Implications for growth rates This gives to implications – For a given K(0), the economy with the higher k* will have a faster growth rate – For a given k*, a decrease in K(0) raises the growth rate We can write this as:

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Implications for Convergence This may explain the lack of absolute convergence – Economies dont converge to the same GDP per capita levels, so growth rate doesnt depend on level of GDP per capita – Maybe the economies with lower growth rates also have lower k*, y* steady states, so they are on a growth path to a different steady state.

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Conditional Convergence This is the idea of conditional convergence: each economy is converging to its own steady state k*, y* determined by it own s, n, δ, A – This can be tested if we have data on each of these factors – Data is available on each: so can plot relationship between per capita GDP and per capita GDP growth conditional on these covariates

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Conditioning Variables Graph actually hold more than just s, n, δ and A constant. It also controls for other factors which affect k*, y* not in our model: – Measures of extent of rule of law and democracy – Extent of openness to trade – Investment in health and education – Measure of inflation

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Example I Europe after World War II: – Previously strong characteristics, but capital and labour had been destroyed by war – So steady state k*, y* are high, current k low due to effects of war – Post WWII fast growth in European economies – consistent with conditional convergence

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Example II Sub-Saharan African nations are very poor – Absolute convergence predicts they should grow rapidly – But they dont: because they have poor levels of saving and technological growth – Also (maybe more importantly) they have poor rule of law, governments, education programmes and health systems. All factors which influence k* and y*.

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Summary of Progress We began with some questions: – Why are some economies more developed than other? – Why do GDP growth rates vary across nations? – What is the relationship between the level of GDP and the growth rate of GDP

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Explaining the patterns Absolute convergence: all economies have the same steady state. Smaller economies should grow faster, all should converge to same per capita GDP. – Limited evidence for this Conditional Convergence: economies converge to own steady-state, conditional on structural factors – Much stronger empirical evidence

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Long-Run Growth Question still remains: why do we observe long-run persistent growth rates for U.K. and U.S.? – Conditional convergence predict economy moves towards steady state – So expect growth rate would slow over time – But growth rate is steady over time: continual, or long-run growth.

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Summary Conditional convergence more plausible model than absolute convergence – Better supported by the data – Explains lack of growth in poorly developed nations through structural factors How to explain long-run growth? – Need a model in which economy can maintain high growth rate continually.

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