The Convergence Speed in Solow Growth Model

The speed of convergence in Solow growth model is

Δk/k=-λ[ln(k)-ln(k*)],

Δy/y=-λ[ln(y)-ln(y*)],

where λ≡(1-α)(n+g+δ).

"n+g+δ is typically about 6% per year (1-2% population growth, 1-2% growth in output per worker, and 3-4% depreciation). If capital's share is roughly one-third, λ is thus roughly 4%. k and y therefore move 4% of the remaining distance toward k* and y* each year, and take approximately 18 years to get halfway to their balanced-growth path values."

Romer, "Advanced Macroeconomics"

Saving Rate Differenece in Solow Growth Model

The elasticity of output with respect to the saving rate is α/(1-α)
 (Check y*=(k*)^α=(s/[n+g+δ])^(α/[1-α])!)

Thus, " a 10 percent increase in the saving rate raises output per worker in the long run by about 5 percent relative to the path it would have followed."

Romer, "Advanced Macroeconomics"

Two Sources of Variation in Solow Growth Model

1. Capital per worker (K/L)

2. Effectiveness of Labor (A)

Romer, "Advanced Macroeconomics"

Problems in Solow Growth Model

"There are two problems with trying to account for large differences in incomes on the basis of differences in capital."

1.  Required differences in capital are far too large.

10 times difference in output per worker → 1000 times difference in capital per worker! (α=1/3)

"Although capital-output rations vary somewhat across countries, the variation is not great. For example the capital-output ratio appears to be two to three times larger in the United States than in India."

2. Required differences in capital return are far too large.

10 times difference in output per worker → 100 times difference in capital return! (α=1/3, MPK=αy^[(α-1)/α])

"There is no evidence of such differences in rates of return. Direct measurement of returns  on fincancial assets, for example, suggests only moderate variation over time and across countries."

Romer, "Advanced Macroeconomics"