Lecture 5: Working With The Model

1. Lecture 5: Working With The Model L11200 Introduction to Macroeconomics 2009/10 Reading: Barro Ch.4 : p68-82 4 February 2010

2. Introduction • Where we are so far • Built a model of growth: crucially, output growth determined by growth in capital per worker • Showed what determines growth of capital per worker • This time: reinforce how the model works • Predictions for level and rates of growth in GDP • Aim: to understand what determines economic growth and explain cross-county growth rates

3. Where are we? • Growth in GDP per worker depend on growth in capital per worker • Growth in capital per worker given by • So growth in GDP per worker is:

4. Where are we? • Showed that means that: • At low levels of k output per worker grows faster • But the growth rate falls it nears k* • When it reaches k* growth in output per worker is 0 • Output is growing, but output per worker is 0 because the population is growing at the same rate as output growth.

5. Implications 1 • Implications • Economics with low levels of GDP per capita should grow faster than economies with higher levels of GDP per capita. • For all economies, growth in GDP per capita will fall over time and eventually stop. Economies reach ‘k*’ at which GDP per capita growth = 0.

6. Today: changing s, δ, n or A • So far we have assumed all of these are fixed. • What happens if they change? E.g. • Workers decide to save more, so s increases • Workers decide to reproduce more!, so n increases • Machines wear-out faster, so δ increases • Technology (not considered so far) improves so A increases.

7. Predictions from Solow Model • Increasing the saving rate: raises rate of growth and level of steady state k*, y* • Increasing the technology level: raises rate of growth and level of steady state k*,y* • Increasing population growth rate: lowers rate of growth and level of steady state k*, y*

8. ‘Absolute’ Convergence • Now can begin to use the model to address data. • We will look at two predictions • ‘Absolute convergence’: if s, n, δ, A are the same across all economies, they will all converge to the same level of k*, y*. i.e. the same GDP per capita • ‘Conditional Convergence’

9. ‘Absolute’ Convergence • Absolute convergence: all economies moving towards the same GDP per capita • So counties with lower k*, y* are only the same trajectory for growth as countries with higher k*, y* • economies with lower k, y are further away from k*,y* so should grow faster. • Ccan test this empirically

10. Empirical Evidence • So absolute convergence doesn’t appear to hold internationally: actually, higher GDP per capita economies have higher growth rates • But it does appear to hold within groups of similar nations / within nations • So.. maybe variation in s, n, δ, A across nations, but not within nations (or similar nations) explains the puzzle…

11. Summary • Model predict that economies move to different levels of GDP per capita if key variables vary between economies • No variation in these implies absolute convergence to a level of per capita GDP, but evidence rejects this • Next time: allow these factors to vary and test ‘conditional convergence’