Targeting the Poor: A Macroeconomic Analysis
of Cash Transfer Programs
Tiago Berriel
EPGE, FGV - Rio Eduardo Zilberman
PUC-Rio
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
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
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
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
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
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?
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;
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).
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;
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
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
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,
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
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.
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.)
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
¯
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%
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%
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
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%
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%
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%
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%
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%
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
Alternative Policy
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%
Conclusion
• CTPs decrease poverty, small effect on income inequality and increases wealth inequality.
• Positive effect on welfare. • Financial frictions are relevant.