Carroll and Summers “Facts” across countries High output growth  high consumption growth

1. Christopher Carroll and Lawrence Summers, Consumption Growth Parallels Income Growth: Some New Evidence, in B. D. Bernheim and J. Shoven, National Saving and Economic Performance, eds., an NBER Project. University of Chicago Press, 1991. Carroll and Summers “Facts” across countries High output growth  high consumption growth Consumption growth over lifetime is not in line with life-cycle/permanent income theories of consumption Would expect C(old folks)/C(young folks) to fall with output growth (young folks in high growth economies would expect their incomes to grow rapidly and hence would consume more NOW) For individual, consumption growth rate increases with economy’s growth rate (Japan vs. U.S. vs. UK, etc). Consumption growth rates are not correlated with real interest rates across countries Real interest rates are not correlated with growth rates across countries

2. N. Gregory Mankiw’s Comments(How to explain the Carroll-Summers facts) • If Y = A Kα L1-α L = 1, no depreciation and A grows @ rate g and • Young folk consume λof their (labor) income share CY = λ (1-α) Y while • Old folk consume all of their (capital) income share Co = αY then • Economy’s saving rate, where only young save, is s = (1- λ) (1-α) Y/Y = (1- λ) (1-α)

3. N. Gregory Mankiw’s Comments(How to explain the Carroll-Summers facts) • Total consumption by young and old: C = λ (1-α) Y + αY = [λ (1-α) + α] Y i.e, C is proportional to Y and grows in pace (as Carroll-Summers observe) • For an individual CO/CY = αY+/λ(1-α)Y = [α/ λ (1-α)]Y+/Y = [α/ λ (1-α)] g i.e., individual consumption grows more quickly if aggregate income is growing quickly (as Carroll-Summers observe)

4. N. Gregory Mankiw’s Comments(How to explain the Carroll-Summers facts) • But…Solow model predicts real interest rate is proportional to growth rate: Future Capital Income/Present Saving = αY+/[(1- λ) (1-α) Y] = [α/(1- λ) (1-α)] [Y+/Y] = [α/(1- λ) (1-α)] g contrary to Carroll-Summers observation that real rate is independent of growth rate • Mankiw proposes endogenous growth model (a la Paul Romer) A = aKβ where α + β = 1 Then Y = aKL1-α

5. N. Gregory Mankiw’s Comments(How to explain the Carroll-Summers facts) With Y = aKL1-α Steady State Condition (output grows in pace with growth in capital stock  must save and invest enough for capital stock to grow at economy’s rate of growth) sY = gK (1- λ) (1-α) Y = a (1- λ) (1-α) K(1)1-α = g K g = a (1- λ) (1-α) The greater the saving rate, (1- λ ) (1-α), the greater the growth rate ( the stylized fact Modigliani started with)

6. N. Gregory Mankiw’s Comments(How to explain the Carroll-Summers facts) • As before, aggregate consumption is proportional to aggregate output and grows in pace C = λ (1-α) Y + αY = [λ (1-α) + α] Y With g = a (1- λ) (1-α) in endogenous growth model For individual: CO/CY = αY+/λ(1-α)Y = αgY/λ(1-α)Y = αa(1- λ)(1-α)/λ(1-α) CO/CY = αa(1- λ)/λ • Consumption in retirement increases with saving rate, (1-λ), and hence with output growth rate, as observed. • Also, the real interest rate is independent of the growth rate, as Carroll-Summer observe…but should it be? Future Capital Income/Present Saving = αY+/[(1- λ) (1-α) Y] = αgY /[(1- λ) (1-α) Y] = α a (1- λ) (1-α) / [(1- λ) (1-α)] = α a