1. Serge Coulombe, ECO 6120 –Convergence and growth regressions

2. Conditional convergence

3. The rate of convergence to the steady state

4. The speed of convergence β is the speed at which economies approach their steady state A positive β implies that the growth rate of an economy decreases as the economy approaches its steady state With α = 1/3, n = 2 %, δ = 5 %, x = 2 %, β is around 6 %

5. In practice, log-linear estimation on the growth rate of y:

6. Investment per unit of effective worker (n+x+δ)k sf(k) k k*k(1)k(0) Time series considerations Cross-section considerations: absolute convergence

7. n+x+δ sf(k)/k k k* k(rich) k(poor) γ(poor) γ(rich) Absolute convergence

8. n(p)+x+δ sf(k)/k k k(p)* k(r) k(p) γ(poor) γ(rich) conditional convergence n(r)+x+δ k(r)*

9. Testing the convergence hypothesis and growth regressions Absolute convergence hypothesis: Barro and Sala-i-Martin (1992) U.S. states 1880-1990 (B&siM2004, section 11.2.) Point estimate of 0.02 for β Coulombe and Lee (CJE, 1995), panel data approach to Canadian provinces, 1961-1991

10. Conditional convergence The underlying framework is the relationship between the growth rate and the gap between the actual level of Y versus the steady-state level (here assume y = log(y): Proxy variables are used for Y*: The long-run equilibrium is:

11. A wave of growth empirics study Absolute convergence hypothesis not rejected for developed countries But was rejected for a broad set of countries when less- developed countries were included using new Heston and Summers data bank But conditional convergence not rejected (Mankiw, Romer and Veil (1992) and Barro and Sala-i-Martin (1995)