Poverty, Inequality and Growth: Empirical Issues

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Damian Casey
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1 Poverty, Inequality and Growth: Empirical Issues Start with a SWF V (x 1,x 2,...,x N ). Axiomatic approaches are commen, and axioms often include 1. V is non-decreasing 2. V is symmetric (anonymous) 3. a transfer axiom a small transfer from i to j increases V iff x i >x j 3 is implied by quasi-concavity (but not the reverse)

2 You can maintain these properties and also let V be homogeneous of degree 1, so we can let social welfare be measured in terms of mean x and proportional deviations of each i from that mean: W = µv ( x 1 µ,...x N µ ) and define units such that V (1,...1) = 1. Then we can develop an inequality measure from V as I( x 1 µ,..., x N µ )= 1 V (). So total welfare is W = µ(1 I). [do graph]

3 For example (Atkinson) W = 1 N NX i=1 x 1 ε i 1 ε Make this function homogeneous of degree 1 by the monotone transformation z 1/1 ε so that I =1 1 N NX i=1 x 1 ε i 1 ε 1 1 ε Increases in ε increase inequality aversion. Gini coefficient also satisfies transfer principle... interquartile range doesn t. Lorenz curves gini coefficient, rankings of distributions

4 On the other hand, we talk mostly about poverty, ignoring changes in the distribution of income above the poverty line. Poverty lines are arbitrary. They tend to come from notions of the PCE required to achieve a minimally acceptable level of food consumption. But a multitude of obvious problems exist.

5 Standard measures 1. Headcount P 0 = 1 N X 1(xi z) 2. Poverty gap P 1 = 1 N X (1 x i z )1(x i z) 3. Foster, Greer Thorbecke P α = 1 N X (1 x i z )α 1(x i z) [show as SWF]

6 What is x? Consumption, income, education, nutrition, morbidity, mortality, water supply, TVs, an index of well-being? Households or individuals? If households, how do we deal with numbers of people? Demographic structure? How do we deal with distribution within households? If individuals, how do we deal with household public consumption? National, regional price indicies Reference time period

7 Looking Across Countries and Over Time: Growth, Poverty and Inequality Kuznets New conventional wisdom little relationship between growth and distribution. see picture from Dollar and Kraay

8 Figure 1: Incomes of the Poor and Average Incomes Levels 10 9 y = x R 2 = Log(Per Capita Income in Poorest Quintile) Log(Per Capita Income) Growth Rates 0.2 Average Annual Change in log(per Capita Income in Poorest Quintile) y = 1.185x R 2 = Average Annual Change in log(per Capita Income) 42

9 How do they come up with numbers like this? They get the share of income (or consumption) attributable to the poorest 20%, then multiply by per-capita income Now, they see if anything affects this share: y p ct = α 0 + α 1 y ct + α 0 2 X ct + µ c + ε ct Why OLS is going to be wrong

10 country fixed effects nonlinearities simultaneity measurement error omitted variables - especially with fixed effects heterogenous effects

11 Their solution y p ct yp ct k = α 0+α 1 (y ct y ct k )+α 0 2 (X ct X ct k )+ε ct ε ct k Using lags for IV on the two equations. lagged growth in y for y level lagged level of y for growth in y lagged growth of y for growth in y How successful is this strategy for dealing with the problems?

12 Table 3: Basic Specification Estimates of Growth Elasticity (1) (2) (3) (4) (5) Levels Differences System No Inst Inst No Inst Inst Intercept Slope P-Ho: α1= P-OID T-NOSC # Observations Intercept Lagged Growth First-Stage Regressions for System Dependent Variable: ln(income) Growth Lagged Income Twice Lagged Growth P-Zero Slopes Notes: The top panel reports the results of estimating Equation (1) (columns 1 and 2), Equation (3) (columns 3 and 4), and the system estimator combining the two (column 5). OLS and IV refer to ordinary least squares and instrumental variables estimation of Equations (1) and (3). The bottom panel reports the corresponding first-stage regressions for IV estimation of Equations (1) and (3). The row labelled P- Ho: α 1 =1 reports the p-value associated with the test of the null hypothesis that α 1 =1.The row labelled P- OID reports the P-value associated with the test of overidentifying restrictions. The row labelled T-NOSC reports the t-statistic for the test of no second-order serial correlation in the differened residuals. Standard errors are corrected for heteroskedasticity and for the first-order autocorrelation induced by first differencing using a standard Newey-West procedure. * (*) (***) denote significance at the 10 (5) (1) percent levels. 36

13 Chen/Ravallion and Deaton Mystery: If no strong relationship between income distribution and growth in per-capita gdp, and lots of growth in per-capita gdp, should see strong gains at the bottom. This is the point of Dollar and Kraay. But, Chen and Ravallion find very slow movement in poverty rates [chen-ravallion table]

14 Table 2. Population living below $1.08 per day at 1993 PPP Region Headcount index (% living in households that consume less than the poverty line) (prelim.) Number of poor (millions) (prelim.) East Asia (excluding China) Eastern Europe & Central Asia Latin America & Caribbean Middle East & North Africa South Asia Sub-Saharan Africa Total (excluding China)

15 Why? [Deaton graphs]

16 C onsum ption to consum ption ratio Incom e to consum ption ratio Log of real G D P PC 1995 PPP 2 Incom e to G D P ratio Log of real G D P PC 1995 PPP L og of real G D P PC 1995 P PP Figure 2: Ratio of survey estimates of mean income or consumption per capita to comparable national accounts estimates: 498 surveys, 124 countries, years from 1979 to Unweighted. 46

17 8 Consum ption, PW T, m atched to surveys Consum ption, PW T, all survey countries Log consumption or income Survey m eans, incom e whe re possible Survey m eans, consum ption w here possible Figure 3: Logarithms of population weighted averages of consumption or income, household surveys and Penn World Tables, v

18 IN D IA C H IN A 0.8 ratio of survey incom e to nas consum ption 0.7 ratio of survey consum ption to nas consum ption old series new series ratio of survey consum ption to nas consum ption Figure 5: Ratios of survey means to national accounts means of consumption and/or income per head, India and China 49

19 Growth captured by rich non-responders Overstatement of consumption in NA production boundaries mostly match in surveys and NA, except housing home production, officially unrecorded activities better captured in surveys FISM residual method of collecting consumption in NA and double counting of intermediate inputs

Inequality, poverty and redistribution

Inequality, poverty and redistribution EC426 http://darp.lse.ac.uk/ec426 17 February 2014 Issues Key questions about distributional tools Inequality measures what can they tell us about recent within-country