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Distributions in Motion

Growth and the Dynamics of Poverty and Inequality

Frontiers in Practice WorkshopFrancisco H.G. Ferreira

March 23rd, 2006

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Roadmap

1. An integrated framework for growth and distribution dynamics.

2. Understanding changes in distributions: statistical counterfactual decompositions.

3. Understanding changes in distributions: towards economic decompositions?

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1. An integrated framework for growth and distribution dynamics

Growth in Thailand, 1975-1992, seen as rightward shifts in the Cumulative Distribution Function.

Source: Ahuja et al. 1997

Growth (in the mean), poverty dynamics and inequality dynamics are simply different aspect of the same process.

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Growth in mean incomes

Growth in mean incomes is simply a weighted average of income growth along the distribution, with weights given by relative incomes.

This can be written in terms of the growth incidence curve (GIC):

So growth (in the mean) is simply a particular aggregation of the percentile-specific growth rates in the GIC.

ydFy

y

y

dppypg

The Growth Incidence Curve was first formally described by Ravallion and Chen, 2003.

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Changes in Poverty Drawing on Kraay (2003)

1

0

))(( dppyP tt

z

pyzpy t

t

)(,)(

)(ln)(

py

zpy

tt

1

0

)()( dppgpdt

dPtt

t

)()(

))(()( py

pdy

pydp t

t

tt

)p(y

1

dt

)p(dy)p(g

t

tt

gives you the FGT class, for instance, and

Write a general poverty measure formulation as:

where

gives you the Watts index.

Differentiating with respect to time yields

with and

So poverty changes are also simply a particular aggregation of the information in the GIC.

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Changes in inequality

Like poverty measures, most inequality indices can be written as functions of a sum of “individual distance indicators”:

So, gives you the Generalized Entropy Class.

And gives you the Atkinson Class, etc..

1

0

))(( dppyhGI tt

1

1))((

1

02

1

0

dpy

dppyhG t

1

111

0

1

0

1))(( dpy

dppyhG t

Differentiating with respect to time yields 1

0

)()(' dppgpGdt

dItt

t

with )()(

))(()( py

pdy

pydhp t

t

tt and

)p(y

1

dt

)p(dy)p(g

t

tt

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So economic growth, changes in poverty and changes in inequality are

effectively different ways of weighing the income changes along the

distribution which are presented in a growth incidence curve.

Growth Incidence Curve - GIC, Brazil 1989-1981, 2004-1989

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

55%

60%

1 2 3 4 5 6 7 8 9 10

Decil

%

GIC 1989-1981 GIC 2004-1989 Average Growth 1989-1981 Average Growth 2004-1989

∆P0 = +2pp

∆P0 = -9pp

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2. Understanding changes in distributions: statistical counterfactual decompositions. To seek an understanding of changes in the

distribution of incomes is to seek an understanding of why the GIC looks the way it does. To understand the nature and determinants of the incidence

or distribution of economic growth. The first step is statistical:

py

pypy

py

pypypg

t

ts

t

st

1

1

1

)(

Counterfactual GICResidual

Counterfactual income distribution

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Statistical counterfactual decompositions(continued) Of course, this is just another way of describing generalized Oaxaca-

Blinder decompositions such as

Where the counterfactual distribution is constructed from:

By simulating a change in in either the conditional distribution of y on X, or on the joint distribution of X. For example:

yfyfyfyfyfyf stt

stt 11

dXXXygyf ttt ...

dXXXygyf tss ...

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Statistical counterfactual decompositions(continued) There are a number of ways to implement such

simulations in practice. They may be based simply on reweighing the sample, so as to

reproduce the changes in the distribution of some exogenous characteristic, such as the age composition of the labor force, or the number of people receiving the minimum wage. DiNardo, Fortin and Lemieux (1996) Hyslop and Maré (2005)

They may be based in importing parameters from models estimated in one year to the other. Bourguignon, Ferreira and Lustig (2004)

They may be based on aggregating counterfactual transfers (with or without simulated household response Bourguignon, Ferreira and Leite (2003)

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An Example from Brazil, 1976-1996.(Ferreira and Paes de Barros, 1999)

Level 1: g (y | X)  Aggregation rule: 

Earnings: 

Level 2: (X)

Occupational Choice: Education: MLE (EA, R, r, g, nah; )

 Fertility: MLC ( nch E, A, R, r, g, nah; )

 Other Incomes: T ( y0h E, A, R, r, g, nah; ) 

hn

ih

J

j

jhi

jhi

hh yyI

ny

10

1

1

ijhijjhi xy )(log

sj

ZZ

Z

s

i jisi

si

ee

eP

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Comparing g(p) and gs(p) (i): The price effect.

Figure 15a: A Complete Decomposition

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96

Percentiles

Dif

fere

nces

of

log

inco

mes

alphas and betas 1996-1976

Source: "Pesquisa Nacional por Amostra de Domicilios" (PNAD), 1976 and 1996.

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Comparing g(p) and gs(p) (ii): The price effect and the occupational structure effect combined.Figure 15b: A Complete Decomposition

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96

Percentiles

Dif

fere

nces

of

log

inco

mes

alphas and betas alphas, betas, gammas 1996-1976

Source: "Pesquisa Nacional por Amostra de Domicilios" (PNAD), 1976 and 1996.

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Comparing g(p) and gs(p) (i): Price, Occupation, Education and Fertility effects. Figure 15: A Complete Decomposition

-2.0

-1.5

-1.0

-0.5

0.0

0.5

0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96

Percentiles

Dif

fere

nces

of

log

inco

mes

alphas and betas alphas, betas, gammas

mu(d), alphas, betas, gammas mu(d), mu(e), alphas, betas, gammas

1996-1976

Source: "Pesquisa Nacional por Amostra de Domicilios" (PNAD), 1976 and 1996.

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3. Understanding changes in distributions: towards economic decompositions? Generalized Oaxaca-Blinder decompositions such as

those discussed above, whether parametric or semi-parametric, suffer from two shortcomings: Path-dependence

The counterfactuals do not correspond to an economic equilibrium. There is no guarantee that those counterfactual incomes would be sustained after agents were allowed to respond and the economy reached a new equilibrium.

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3.1. Partial Equilibrium Approaches The first step towards economic decompositions, in

which the counterfactual distributions may be interpreted as corresponding to a counterfactual economic equilibrium, are partial in nature.

One example comes from attempts to simulate distributions after some transfer, in which household responses to the transfer (in terms of child schooling and labor supply) are incorporated. Bourguignon, Ferreira and Leite (2003)

Todd and Wolpin (2005)

(These two papers differ considerably in how they model behavior. Todd and Wolpin are much more structural.)

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3.2 General Equilibrium Approaches.

However, a number of changes which are isolated in statistical counterfactuals – such as changes in returns to education, or in the distribution of years of schooling – are likely to have general equilibrium effects.

Similarly, certain policies one might like to simulate may require a general equilibrium setting.

There are two basic approaches to generate GE-compatible counterfactual income distributions (and thus counterfactual GICs): Fully disaggregated CGE models, where each household is individually

linked to the production and consumption modules. E.g. Chen and Ravallion, 2003, for China.

“Leaner” macroeconomic models linked to microsimulation modules on a household survey dataset. E.g. Bourguignon, Robilliard and Robinson, 2005, for Indonesia.

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Distributional Impact of China’s accession to the WTO. (Chen & Ravallion, 2003)

GE-compatible counterfactual GICs corresponding to a specific policy.

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3.2 General Equilibrium Approaches (continued).

Macro model

Linkage AggregatedVariables

(prices, wages, employment levels)

Household income micro-simulation model

In the Macro-Micro approach, some key counterfactual linkage variables are generated in a “leaner” macro model, whose parameters may have been calibrated or estimated from a time-series, and then fed into sector-specific equations estimated in the household survey, to generate a counterfactual GIC.

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The distribution of the impacts of the 1999 Brazilian devaluation (Ferreira, Leite, Pereira and Pichetti, 2004)

Figure 7 - Comparison betweenActual Observed Changes &

Experiment 1 - using Representative Households Groups (RHG)Experiment 2- using Pure Micro Simulation model

Experiment 3 - using Full Macro-Micro Linkage model

-6%

-4%

-2%

0%

2%

4%

6%

8%

0 10 20 30 40 50 60 70 80 90 100

Percentiles

Lo

g d

iffe

ren

ce

Actual Experiment 1 - RHG

Experiment 2 - Pure Micro Simulation Experiment 3 - Full Macro-Micro Linkage

Percent changes between 1999 and 1998 in Nominal Income (in Reais, R$) / Month for each percentile of the distribution in Brazil

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Conclusions1. Growth, changes in poverty and changes in inequality are all

summary measures of changes in the disaggregated distribution of incomes.

2. Understanding these changes requires understanding the determinants of the growth incidence curve.

3. Counterfactual simulations that isolate the individual impacts of changes in prices, in occupational structure, in the distribution of household endowments, or in transfers, are a useful first step.

4. Counterfactual GICs that are consistent with (partial or general) economic equilibria are more difficult to estimate, as they involve modeling behavior. But starts have been made.

Beware of Lucas critique and the ‘black-box’ critique.

5. When thinking about policies, do not think of “growth versus distribution”. Think ‘policy incidence’.