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 th , 2013

Motivation Discussion Proposal Final Discussion Before Starting 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 Motivation ’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 overwhelming difference is not reflected in the indicators. GDP/cap definitely doesn’t show this. Inequality indexes might not tell too much either. Lets see the following...

Motivation Discussion Proposal Final Discussion Motivation VIDEOS First video: Think Reality - USA Video 1 Second video: Fundaci´ on Sol - Chile Video 2

Motivation Discussion Proposal Final Discussion 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 Proposal IDEA: Instead of having two indexes (level and inequality), lets have one that accounts for both dimensions. We can measure the Social Welfare: W = W ( y 1 , y 2 , . . . , y N ) where y i is the income of the i -th individual. We can use an additive Social Welfare Function (SWF): N W = 1 � U ( y i ) N i =1 This expression says that the social welfare is represented by average utility, being agent’s i utility: U ( y i ) 1 With 1 − ǫ y 1 − ǫ U ( y i ) = ǫ � = 1 i U ( y i ) = ln( y i ) ǫ = 1 where ǫ is the parameter of inequality aversion .

Motivation Discussion Proposal Final Discussion Proposal Lets use U ( y i ) = ln( y i / y min ) Maslow’s Hierarchy of Needs where y min is the subsistence income level.

Motivation Discussion Proposal Final Discussion Proposal In order to have a number that tells us something, lets: ˜ Y = U − 1 ( W ( y )) with y = ( y 1 , y 2 , . . . , y N ) in other words, ˜ Y is a ’representative’ income level. Some (cool?) properties of ˜ Y : ˜ Y is independent of the chosen value of y min . Y ( A · y ) = A · ˜ ˜ Y ( y ) for A > 0. If we use U ( y i ) = ln( y i ) then: √ y 1 · y 2 · · · y n ← geometric mean. ˜ Y ( y ) = n ˜ 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, y 1 the poor one and y 2 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 Y EDE used by Atkinson in his index of inequality.

Motivation Discussion Proposal Final Discussion Some results: Chilean example (2006 data) 3.000 $1,600,000 $1,470,620 2.500 $1,400,000 2.000 $1,200,000 1.500 $1,000,000 1.000 $800,000 0.500 $600,000 $513,404 0.000 $400,000 $337,196 $328.720 $252,989 $198,473 -0.500 $161,375 $200,000 $134,197 $193.680 $108,663 $79,064 $31,229 -1.000 $0 1 2 3 4 5 6 7 8 9 10 Ingreso por Persona ln(ing/ingMin)

Motivation Discussion Proposal Final Discussion Some results Mean USA Yede(e=1) Gini 80,000 0.50 75,000 0.45 70,000 65,000 0.40 60,000 Gini (Inequality) 55,000 0.35 50,000 0.30 45,000 40,000 0.25 35,000 30,000 0.20 1969 1973 1977 1981 1985 1989 1993 1997 2001 2005 2009 1967 1971 1975 1979 1983 1987 1991 1995 1999 2003 2007 2011 Source: US Census Bureau

Motivation Discussion Proposal Final Discussion Some results GDP/capita China Yede (e=1) GINI index 3,000 44 42 2,500 GDP (PPP, current international $) 40 2,000 Gini (Inequality) 38 1,500 36 1,000 34 500 32 0 30 1990 1992 1993 1994 1995 1996 1997 1998 2001 Source: World Bank

Motivation Discussion Proposal Final Discussion Final Discussion

Motivation Discussion Proposal Final Discussion Final Discussion

Motivation Discussion Proposal Final Discussion 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 Y EDE = (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 Y EDE 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 Final Discussion Or it is just that we don’t want to ’see’ this reality? THANK YOU For your attention