Is GDP/cap a representative welfare measure? An alternative - - PowerPoint PPT Presentation
Motivation Discussion Proposal Final Discussion Is GDP/cap a representative welfare measure? An alternative proposal, accounting for level and distribution Lorenzo Cerda Planas PhD Seminar of the Inequality research group INEQUO December 13
Motivation Discussion Proposal Final Discussion
Lorenzo Cerda Planas PhD Seminar of the Inequality research group INEQUO December 13th, 2013
Motivation Discussion Proposal Final Discussion
Some (important) disclaimers: The idea is to present you some thoughts and results, in order to discuss them (at the end!) I am (definitely) not an expert in the subject. Work in progress...
Motivation Discussion Proposal Final Discussion
’Triggering’ question: After so much economic development, why it seems that people are not doing well? (or not being happy or pleased) Maybe we are not measuring or focusing on the right index? Not a new problem → Stiglitz-Sen-Fitoussi commission: Recommendation 4: Give more prominence to the distribution of income, consumption and wealth. It looks that the rich are much better off than the poor. That
GDP/cap definitely doesn’t show this. Inequality indexes might not tell too much either.
Lets see the following...
Motivation Discussion Proposal Final Discussion
First video: Think Reality - USA
Video 1
Second video: Fundaci´
Video 2
Motivation Discussion Proposal Final Discussion
We want to measure how we are doing (as societies). And the GDP/cap was a (fairly) good index, back then. Why?
Maybe before inequality was lower. Maybe because at those levels of income, it better measured welfare.
Motivation Discussion Proposal Final Discussion
Concerning inequality...
Motivation Discussion Proposal Final Discussion
But what is the aftermath of a growing economy with a growing inequality?
Motivation Discussion Proposal Final Discussion
But what is the aftermath of a growing economy with a growing inequality?
Motivation Discussion Proposal Final Discussion
But what is the aftermath of a growing economy with a growing inequality?
Motivation Discussion Proposal Final Discussion
Motivation Discussion Proposal Final Discussion
Motivation Discussion Proposal Final Discussion
IDEA: Instead of having two indexes (level and inequality), lets have
We can measure the Social Welfare: W = W (y1, y2, . . . , yN)
where yi is the income of the i-th individual.
We can use an additive Social Welfare Function (SWF): W = 1 N
N
U(yi) This expression says that the social welfare is represented by average utility, being agent’s i utility: U(yi) With U(yi) = 1 1 − ǫy 1−ǫ
i
ǫ = 1 U(yi) = ln(yi) ǫ = 1
where ǫ is the parameter of inequality aversion.
Motivation Discussion Proposal Final Discussion
Lets use U(yi) = ln(yi/ymin) Maslow’s Hierarchy of Needs
where ymin is the subsistence income level.
Motivation Discussion Proposal Final Discussion
In order to have a number that tells us something, lets: ˜ Y = U−1(W (y))
with y = (y1, y2, . . . , yN)
in other words, ˜ Y is a ’representative’ income level. Some (cool?) properties of ˜ Y :
˜ Y is independent of the chosen value of ymin. ˜ Y (A · y) = A · ˜ Y (y) for A > 0. If we use U(yi) = ln(yi) then: ˜ Y (y) =
n
√y1 · y2 · · · yn ← geometric mean.
˜ Y is increasing in individual income levels (sometimes called Paretian principle) If ǫ = 0, then it is inequality averse.
Motivation Discussion Proposal Final Discussion
A simple example: two agents, y1 the poor one and y2 the rich one:
A transfer from the rich to the poor moves X to the right. Meaning same GDP/cap and higher ˜ Y . ˜ Y attains its maximum when there is perfect equality. This is a general result: the AM-GM inequality.
Motivation Discussion Proposal Final Discussion
For the general case (ǫ = 1):
Actually, the ˜ Y function used so far, is the Equally Distributed Equivalent Income YEDE used by Atkinson in his index of inequality.
Motivation Discussion Proposal Final Discussion
(2006 data)
1 2 3 4 5 6 7 8 9 10
0.000 0.500 1.000 1.500 2.000 2.500 3.000 $0 $200,000 $400,000 $600,000 $800,000 $1,000,000 $1,200,000 $1,400,000 $1,600,000 $31,229 $79,064 $108,663 $134,197 $161,375 $198,473 $252,989 $337,196 $513,404 $1,470,620 Ingreso por Persona ln(ing/ingMin)
$328.720 $193.680
Motivation Discussion Proposal Final Discussion
1967 1969 1971 1973 1975 1977 1979 1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 30,000 35,000 40,000 45,000 50,000 55,000 60,000 65,000 70,000 75,000 80,000 0.20 0.25 0.30 0.35 0.40 0.45 0.50
USA
Mean Yede(e=1) Gini
Gini (Inequality) Source: US Census Bureau
Motivation Discussion Proposal Final Discussion
1990 1992 1993 1994 1995 1996 1997 1998 2001 500 1,000 1,500 2,000 2,500 3,000 30 32 34 36 38 40 42 44
China
GDP/capita Yede (e=1) GINI index
GDP (PPP, current international $) Gini (Inequality) Source: World Bank
Motivation Discussion Proposal Final Discussion
Motivation Discussion Proposal Final Discussion
Motivation Discussion Proposal Final Discussion
Is it that we are not able to agree on an inequality aversion parameter ǫ? But actually the difference is not that big:
Source: Atkinson (1970): On the Measurement of Inequality.
And knowing that YEDE = (1 − I)Y
with I the Atkinson’s Inequality Index and Y the mean, or just GDP/cap.
We can see that the change in YEDE with ǫ = 1 or ǫ = 1.5 is not that big, even for the USA (which was unequal already that that time). But recall that GDP/cap is just saying that ǫ = 0 (an implicit agreement?) Or it is that...
Motivation Discussion Proposal Final Discussion