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**Lecture 6: Conditional Convergence and Growth**

L11200 Introduction to Macroeconomics 2009/10 Lecture 6: Conditional Convergence and Growth Reading: Barro Ch.4 : p83-94 4 February 2010

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**Introduction Last time: Today**

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 model’s 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 don’t converge to the same GDP per capita levels, so growth rate doesn’t 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 it’s 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 don’t: 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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The Solow Model When 1st introduced, it was treated as more than a good attempt to have a model that allowed the K/Y=θ to vary as thus avoid the linear.

The Solow Model When 1st introduced, it was treated as more than a good attempt to have a model that allowed the K/Y=θ to vary as thus avoid the linear.

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