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Targeting the Poor: A Macroeconomic Analysis

of Cash Transfer Programs

Tiago Berriel

EPGE, FGV - Rio Eduardo Zilberman

PUC-Rio

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Preview Literature Model Quantitative Exercise Conclusion Motivation

What are the effects of transfers targeting the poor on income inequality, wealth inequality, poverty, employment, and welfare?

• two policy views:

1. enhance human capital formation among poor children

• focus on the conditions (schooling and health) 2. improve the social safety net

• focus on the scope of transfers

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Motivation

What are the effects of transfers targeting the poor on income inequality, wealth inequality, poverty, employment, and welfare?

• two policy views:

1. enhance human capital formation among poor children

• focus on the conditions (schooling and health) 2. improve the social safety net

• focus on the scope of transfers

• vast implementation in emerging countries

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Motivation

What are the effects of transfers targeting the poor on income inequality, wealth inequality, poverty, employment, and welfare?

• two policy views:

1. enhance human capital formation among poor children

• focus on the conditions (schooling and health)

2. improve the social safety net

• focus on the scope of transfers

• vast implementation in emerging countries

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Setup

• Imrohoroglu-Huggett-Aiyagari model:

• heterogeneous agents

• idiosyncratic labor income risk • indivisible labor supply

• savings through risk-free bonds and money

• costly access to financial services

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Intuition

Why can transfers targeting the poor increase poverty and inequality?

1. leisure is a normal good, so transfers reduce labor supply

2. in order to be eligible for the program, households can

• reduce labor supply (labor is indivisible) • allocate savings from risk-free bonds to money

3. transfers targeting the poor is also a source of insurance

• valuable for those at risk of being borrowing constrained • it weakens precautionary motives asymmetrically

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Application Results

Model calibrated to Brazil

1. no change in income inequality; 2. wealth inequality increases; 3. poverty decreases;

4. employment slightly decreases.

5. welfare increases: equivalent to an increase of 1.2% in consumption of all households.

6. imperfect financial system amplifies welfare gains from CTPs. Lesson: when do CTPs matter?

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Related Literature

• Oh and Reis (2011): positive implications of the increase in transfers after the crisis as a stabilization policy;

• Floden and Linde (2001): focus on optimal taxes scheme given income process for US and Sweden;

• Alonso-Ortiz and Rogerson (2011): effects of tax-transfers on labor supply;

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Demographics, endowment, preferences, and technology

• Demographics: continuum of infinitely lived, ex-ante identical households.

• Endowment: ε units of efficient labor.

• ε follows a Markov process i.i.d. across households.

• Preferences: E0P∞t=0[log ct− θnt]. • indivisible labor: nt∈ {0, 1}.

• Production technology: Yt= KtαH 1−α

t (representative firm).

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Market arrangements • no insurance market for the idiosyncratic risk

• savings:

• bonds, bt≥ 0: interest r.

• money, mt≥ 0: depreciates at rate π.

• pecuniary cost ξ to access financial markets (bt> 0).

• interest rate r is fixed (small open economy).

• wage rate wt clears labor market (no migration).

• timing of decisions:

1. savings decision, at≥ 0, takes place;

2. idiosyncratic risk εtis realized;

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Government

• CTP: threshold income ¯y and a fixed transfer T .

• household is eligible if rbt+ ntεtwt≤ ¯y.

• total transfers are equal to a fixed, exogenous budget, B.

• Brazilian experience: B is a tiny fraction of total income. • results are robust to funding B with lump-sum taxes. • not concerned with the efficiency-equity trade-off

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Agents’ Problem V (a, ε) = max c,n,m,b,a0 ( log c − θn + β X ε0∈E V (a0, ε0)π(ε0, ε) ) s. t. c + a0 = (1 + r)b + (1 − π)m + wεn + I{y≤y}T − I{b>0}ξ a = b + m y = rb + wεn c ≥ 0; n ∈ {0, 1}; b ≥ 0; m ≥ 0; a0 ≥ 0. • 3 possible portfolio allocations

1. b = 0 and m = a

2. b = a and m = 0

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Equilibrium

• Stationary Recursive Equilibrium: a value function V ; policies for the household a0, c, n, b and m; policies for the firm K and H; prices r and w; government policies T and ¯y; and a measure λ:

1. Given r, w, T and ¯y, the households solve their problems and V is the associated value function;

2. Given r, w, T and ¯y, the firm solves its problem – that is,

maxK,H{KαHα− (r + δ)K − wH};

3. Labor market clears – that is,R

A×En(a, ε)εdλ(a, ε) = H;

4. Government budget balances – that is,

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Welfare

• Social Welfare:

W (¯y) = Z

A×E

V (a, ε; ¯y)dλ(a, ε; ¯y). • ∆: corresponding change in consumption to keep same

welfare when moving from ¯y to ¯y0.

1 1 − β

Z

A×E

[log(c(a, ε; ¯y)) − θn(a, ε; ¯y)] dλ(a, ε; ¯y) =

= 1

1 − β Z

A×E

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Application to Brazil around 2006 • eligibility:

• if below extreme poverty line (USD$36 PPP per capita):

• fixed transfer (USD$36 PPP)

• variable transfer per child (USD$11 PPP), up to three children

• if below poverty line (USD$72 PPP per capita):

• no fixed transfer

• variable transfer per child (USD$11 PPP), up to three children

• poverty line is16.7%of the average income per capita

• fixed budget: 0.69%of total income.

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Calibration

Idiosyncratic risk follows an AR(1) process:

log(ε0) = ρ log(ε) + u, u ∼ N (0, σ2)

No PSID equivalent in Brazil:

• set ρ = 0.96 (similar to the U.S.)

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Calibration

parameter target model data

ρ = 0.96 persistence of shocks 0.96 0.96 σ2= 0.074 Gini coefficient 0.560 0.560 α = 0.4 capital share 0.4 0.4 δ = 0.093 capital/GDP 3 3 β = 0.94 consumption/GDP 0.79 0.78 θ = 0.62 % households employed 0.81 0.82 ξ = 0.046 % households connected 0.54 0.55 r = 0.04 rate savings 0.04 0.04 π = 0.04 inflation rate 0.04 0.04 T = 0.093 program budget (% income) 0.0069 0.0069

¯

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External Validation

• Does the model replicate other dimensions of poverty and inequality in Brazil?

Earnings quintile earnings share earnings share

data (PNAD) model

First 0.4% 0.0%

Second 4.6% 4.3%

Third 10.0% 10.7%

Fourth 19.0% 21.8%

Fifth 66.0% 63.2%

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External Validation

• Does this model replicate wealth distribution?

• Davies et al (2008), Gini coefficient for wealth was 0.783 in 2000.

• In our benchmark model, Gini coefficient for wealth is 0.763.

Wealth quintile earnings share wealth share

model model First 8.9% 0.0% Second 9.0% 0.0% Third 16.3% 3.2% Fourth 24.9% 18.0% Fifth 41.0% 78.7%

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External Validation

• Does the model replicate the number of poor agents?

model data

(PNAD) % households in extreme poverty 1.9% 3.9%

% households in poverty 12.4% 11.4%

% threshold of the program 16.2% 16.7%

(as % of avg. income)

members per family 2.5 3.2

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Results

Does the CTP reduce inequality?

benchmark no program no program

coverage 18.4% 100% 0%

% households employed 80.7% 81.3% 81.3% % households connected 53.5% 54.6% 55.9% Gini coefficient 0.560 0.560 0.563

Gini coefficient for wealth 0.763 0.753 0.749

% households in extreme poverty 1.9% 4.3% 4.4% % households in poverty 12.4% 16.5% 16.5%

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Results

Does the CTP reduce poverty?

benchmark no program no program

coverage 18.4% 100% 0%

% households employed 80.7% 81.3% 81.3% % households connected 53.5% 54.6% 55.9% Gini coefficient 0.560 0.560 0.563 Gini coefficient for wealth 0.763 0.753 0.749 % households in extreme poverty 1.9% 4.3% 4.4%

% households in poverty 12.4% 16.5% 16.5%

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Results

Does the CTP reduce employment?

benchmark no program no program

coverage 18.4% 100% 0%

% households employed 80.7% 81.3% 81.3%

% households connected 53.5% 54.6% 55.9% Gini coefficient 0.560 0.560 0.563 Gini coefficient for wealth 0.763 0.753 0.749 % households in extreme poverty 1.9% 4.3% 4.4% % households in poverty 12.4% 16.5% 16.5%

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Results

Does the CTP increase social welfare?

benchmark no program no program

coverage 18.4% 100% 0%

% households employed 80.7% 81.3% 81.3% % households connected 53.5% 54.6% 55.9% Gini coefficient 0.560 0.560 0.563 Gini coefficient for wealth 0.763 0.753 0.749 % households in extreme poverty 1.9% 4.3% 4.4% % households in poverty 12.4% 16.5% 16.5%

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Results

The role of costly access to financial services. Budget is funded with lump-sum-taxes.

program no program program no program ξ = 0 ξ = 0

coverage 18.3% 100% 19.2% 100%

% households employed 80.8% 81.3% 78.6% 79.8%

Gini coefficient 0.563 0.563 0.564 0.561 Gini coefficient for wealth 0.761 0.749 0.728 0.713 % households in extreme poverty 3.0% 4.4% 3.5% 4.7% % households in poverty 12.5% 16.5% 13.6% 16.0%

Welfare ∆ 1.1% 0.6%

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Alternative Policy

• Complements income up to ¯y, only for those working:

c + a0 = b + (1 − π)m + max {rb + wεn, n¯y} − I{b>0}ξ. • y chosen such that total transfers equals B, CTP budget¯

Z

A×E

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Alternative Policy

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Alternative Policy

program alt. policy program alt. policy benchmark (ξ = 0) (ξ = 0)

coverage: 18.4% 13.4% 19.4% 12.9%

% households employed 80.7% 82.8% 78.3% 81.3% % households connected 53.5% 51.1% 100% 100% Gini coefficient 0.560 0.556 0.561 0.554 Gini coefficient for wealth 0.763 0.770 0.730 0.740 % households in extreme poverty 1.9% 1.6% 2.5% 2.1% % households in poverty 12.4% 3.5% 13.4% 4.3%

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Conclusion

• CTPs decrease poverty, small effect on income inequality and increases wealth inequality.

• Positive effect on welfare. • Financial frictions are relevant.

Referências

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