Gerhard Illing – Macro 2 Summer 2019

Macro economics II

Gerhard Illing

Summer term 2019

Chapter 4. Growth and Distribution Additional material

1

Gerhard Illing – Macro 2 Summer 2019

Gerhard Illing – Macro 2 Summer 2019

4,02

2,08

3,87

2,35 0

1

2

3

4

5Meritocracy

Principle ofEntitlement

Principle of Need

OutcomeEgalitarianism

What does equity mean ... for students in economics (macro 2) at LMU Munich?

Gerhard Illing – Macro 2 Summer 2019

Gerhard Illing – Macro 2 Summer 2019

Economist April 2014 What explains the surge in self-employment? link

4.1 Functional income distribution

Nt

Kt

KtBGP

wt/rt

● A

NtBGP

B

Kt/Nt

How capital and labor shares react to a change in the capital-labor-ratio

depends on the elasticity of substitution σ.

With a Cobb-Douglas production function (σ=1) capital and labor shares stay constant

●

Gerhard Illing – Macro 2 Summer 2019

4.1 Functional income distribution

More general case than Cobb Douglas : production function with constant elasticity of substitution σ: Relation between w/r ratio and capital intensity: Thus

( ) σσσ αα /11/11/11 )1( −−− ⋅−+⋅= ttt NKY

σ

αα

/11

−=

t

t

t

t

NK

rw

1/11

−

−=

⋅⋅

σ

αα

t

t

tt

tt

NK

KrNw

σ = 1: 𝑌𝑌 = 𝐾𝐾𝛼𝛼𝑁𝑁1−𝛼𝛼

( ) tttttt

t rZKKNKKY

=⋅⋅=⋅−⋅⋅⋅−+⋅−=∂∂ −−−−− σσσσσ ασααασ /1/1/1/11/11 )/11()1()/11(

( ) tttttt

t wZNNNKNY

=⋅⋅−=⋅−⋅−⋅⋅−+⋅−=∂∂ −−−−− σσσσσ ασααασ /1/1/1/11/11 )1()/11()1()1()/11(

( ) 1/11 −−= σ

αα

tt kx( ) 2/1111 −−

−=

∂∂ σ

αα

σ tt

t kkx

Gerhard Illing – Macro 2 Summer 2019

Paul Krugman March 14, 2014, Notes on Piketty (Wonkish)

8

What determines r-g? Piketty stresses the effects of changes in economic growth. I find this easiest to see in terms of a standard Solow model. In the figure below, we assume that s is the aggregate rate of saving; that technological change is labor-augmenting, so that it can be thought of as increasing the number of effective workers faster than the number of actual workers; and that there is an aggregate production function Q/L = f(K/L) where Q/L is output per effective worker and K/L is capital per effective worker. The familiar diagram then looks like this:

Over time, the economy converges to steady-state growth at the rate g, which is the sum of labor force growth and technological progress, and the capital-output ratio converges to s/g.

As the figure shows, a decline in g will lead to a rise in the capital-output ratio and a fall in r. Which falls more? Well, it depends on what happens to the capital share in output, which in turn depends on the elasticity of substitution between capital and labor.

Gerhard Illing – Macro 2 Summer 2019

r- g - Which falls more? I find this easiest to think of in terms of a numerical example. Let’s assume that s = .09 and initially g = .03. Then the capital-output ratio is 3; if the capital share is .3, r=.10.

Paul Krugman March 14, 2014, Notes on Piketty (Wonkish)

9

Now let the steady-state g fall to .015. K/Q rises to 6. If the capital share doesn’t change, r falls to .05 – that is, it falls in proportion to growth. If the elasticity of substitution is less than 1, the higher ratio of capital to effective labor means a fall in the capital share, so the return on capital falls more than the growth rate. However, Piketty asserts that the elasticity of substitution is more than 1, so that the capital share rises, and r falls less than g.

KY

= 𝒔𝒔𝒈𝒈

= 0.090.03

= 3 𝑟𝑟 KY

= 0.3 Capital share of income: 𝑟𝑟 = 0.3/ KY

=0.1

KY

= 𝒔𝒔𝒈𝒈

= 0.090.015

= 6 𝑟𝑟 = 0.3/ KY

=0.05

Gerhard Illing – Macro 2 Summer 2019 10

Thomas Piketty, Capital in the 21. Century, link

Gerhard Illing – Macro 2 Summer 2019 11

Thomas Piketty, Capital in the 21. Century, link

Gerhard Illing – Macro 2 Summer 2019 12

Matt Rognlie: landlords, not corporate overlords, are sucking up the wealth in the economy Deciphering the fall and rise in the net capital share BPEA Conference, March 19–20, 2015 link

Gerhard Illing – Macro 2 Summer 2019

David Autor Work of the Past, Work of the Future, 2019 link

USA

Gerhard Illing – Macro 2 Summer 2019

Thomas Piketty, Emmanuel Saez, and Gabriel Zucman, Distributional National Accounts: Methods and Estimates for the United States, 2018, Quarterly Journal of Economics, vol 133(2), 553-609 link

Annualized growth rate of per-adult national income (pretax and posttax, with income equally split between spouses) for each percentile of the income distribution (with a zoom within the top percentile) over the 1980– 2014 period. Macro growth rate 1.4%

Gerhard Illing – Macro 2 Summer 2019

Thomas Piketty, Emmanuel Saez, and Gabriel Zucman, Distributional National Accounts: Methods and Estimates for the United States, 2018, Quarterly Journal of Economics, vol 133(2), 553-609 link

The top 10% adult income shares pretax and posttax since 1962. The unit is the individual Adult. Incomes within married couples are split equally.

Gerhard Illing – Macro 2 Summer 2019

Thomas Piketty, Emmanuel Saez, and Gabriel Zucman, Distributional National Accounts: Methods and Estimates for the United States, 2018, Quarterly Journal of Economics, vol 133(2), 553-609 link

The bottom 50% adult income shares pretax and posttax since 1962. The unit is the individual Adult. Incomes within married couples are split equally.

Gerhard Illing – Macro 2 Summer 2019

Thomas Piketty, Emmanuel Saez, and Gabriel Zucman, Distributional National Accounts: Methods and Estimates for the United States, 2018, Quarterly Journal of Economics, vol 133(2), 553-609 link

Average pretax national income of the bottom 50% adults from 1962 to 2014 in the US and France. The unit is the individual Adult. Incomes within married couples are split equally.

Gerhard Illing – Macro 2 Summer 2019

Deaton

UK link

Gerhard Illing – Macro 2 Summer 2019

Deaton

the 90:10 ratio measures the household income of the person who is 90% of the way up the distribution – with a higher income than 90% of the population – relative to that of the person 10% of the way up

UK link

Gerhard Illing – Macro 2 Summer 2019

Deaton

Meanwhile, household earnings have stagnated towards the bottom of the distribution. Higher cash transfers from government – in particular the rapid expansion of tax credits from the late 1990s – have plugged this gap, so that overall income inequality remained stable even as household earnings inequality increased. After taxes and benefits, household incomes at the bottom have broadly kept pace with incomes further up the distribution (Figure 4).

UK link