Notes on Mankiw, Romer, Weil Simon Gilchrist EC 502

1

Introduction: • To a first approximation, predictions of the Solow Growth Model are correct: – Savings and population growth affect GDP per capita in directions predicted by the Solow model. – 50% of variation in GDP per capita can be predicted by the Solow model. • While qualitative predictions are confirmed, quantitative effects of savings and population growth are too large to be consistent with standard Solow growth theory.

1

•

An augmented version of the Solow growth model that allows for human capital accumulation can explain the data however. – Adding human capital explains why coefficients on savings and population growth are upward biased – human capital is an omitted variable which is positively correlated with savings. – When schooling is included in the regression as a measure of human capital, MRW find that ∗ Coefficient on savings and population growth are now of the correct magnitude for the augmented model. ∗ The augmented Solow model now explains 80% of the variation in cross-country living standards.

2

2
•

Model: Population and technology grow at constant exogenous rates: L(t) = L(0) exp(nt) A(t) = A(0) exp(gt) Cobb-Douglas production Y (t) = K(t)α (A(t)L(t))1−α Constant savings rate: I(t) = S(t) = sY (t) Capital accumulation dk = sy(t) − (n + g + δ)k(t) dt where k(t) = K(t) A(t)L(t) Y (t) y(t) = = k(t)α A(t)L(t)

•

which implies that dk = s (k(t))α − (n + g + δ)k(t) dt

3

3
•

Steady-state: In steady state dk =0 dt which implies
1/(1−α) s ∗   k = n+g+δ
 

•

Labor productivity: Y (t) = A(t) (k ∗)α L(t)

•

Taking logs we have log(Y (t)/L(t)) = log(A(0))+gt+ α α log(s)− log(n+g+δ) 1−α 1−α

•

Model predictions: if α = 1/3 then α/(1 − α) = 1/2, implying that a 10% increase in savings should lead to a 5% increase in GDP per capita.

4

4
•