Fiscal Consolidation Programs and Income Inequality - Pedro Brinca

Fiscal Consolidation Programs and Income Inequality
Pedro Brinca1 2 Miguel Ferreira1 Francesco Franco1
Hans Holter 3 Laurence Malafry 4
1Nova SBE
2CEF.UP
3University of Oslo
4Stockholm University
November 17th, 2017, ADEMU @ EUI
Brinca, Ferreira, Franco, Holter, Malafry Fiscal Consolidation Programs November 17th, 2017 1 / 46

Introduction: Motivation
Following the Financial crisis, many European countries implemented
Fiscal Consolidation Programs, aimed at reducing government debt.
Tax increases
Spending cuts
A combination
Seemingly different impacts in different countries.
What determines the quantitative impact of consolidation on the
economy (the fiscal multiplier)?

Introduction: What we do
Study the empirical relationship between the ﬁscal multipliers and
income inequality.
Develop a life-cycle, overlapping generations economy with
uninsurable labor market risk.
Calibrate it to match key characteristics of a number of European
economies, including the distribution of wages and wealth, social
security, taxes and debt.
Study the impact of ﬁscal consolidation programs on the economy.

Introduction: What we ﬁnd
Output in countries with higher income inequality respond more
negatively to ﬁscal consolidation.
A calibrated life-cycle model with incomplete markets can reproduce
this pattern.
Mechanism: With more income risk, agents locate further away from
the borrowing limit. The elasticity of labor supply is particularly low
for credit constrained people and increasing in wealth.
Fiscal consolidation through taxation is more contractionary than
austerity.

Roadmap
Empirical analysis
Blanchard and Leigh (2013)
Alesina et al. (2015)
Ilzetzki et al. (2013)
Model
Calibration
Inspecting the mechanisms
Cross-country analysis
Validating the mechanism
Household debt and consolidation
Income inequality and labor supply response to consolidation
Shutting down risk
Conclusion

Empirical Analysis: rational expectation model
Blanchard and Leigh (2013) find:
IMF under-estimated the recessive effects of fiscal consolidation in
European Countries in 2010-2011 period.
No other variable helps to explain IMF GDP forecast errors.
Method: Cross-section with robust standard errors. here
We find income inequality to amplify IMF GDP forecast errors, as it
amplifies the recessive effects of fiscal consolidation. here

Empirical Analysis: IMF shocks
Alesina et al. (2015) dataset:
Expand Devried et al. (2011) dataset, which consist on fiscal
consolidations motivated by the desire to decrease deficits, identified
using Romer and Romer (2010) narrative approach
Breakdown between unanticipated and announced fiscal consolidations,
as in Alesina et al. (2012)
Method: Panel data OLS fixed effects, with robust standard errors.
We find income inequality amplifies the recessive effects of
unanticipated fiscal consolidations. here

Empirical Analysis: SVAR
Ilzetzki et al (2013) use data for 44 countries over time to explain
differences in fiscal multipliers. They find:
Pooling countries across meaningfull diminsions yields different Fiscal
multipliers.
Method: Blanchard-Perotti (2002) SVAR. here
We use the same data and code but pool countries by income
inequality.
We find that following a decrease in government expenditures, GDP
falls more in countries with larger income inequality. here

Model Environment
Life-cycle economy with heterogeneous agents and incomplete
markets. here
Standard preferences, heterogeneous discount factors and bequest
motive. here
Neoclassical/frictionless on ﬁrm side but income risk and
precautionary savings on household side. here
Wages: permanent ability and transitory shocks, age proﬁle. here
Progressive earnings taxes, proportional consumption and capital
income taxes. Social security system. Government runs balanced
budget. here

Recursive formulation of the Agent’s problem
Agent characterized by (k, β, a, u, j), wealth, discount factor,
persistent and transitory components of income shock and age.
Working-age agent’s problem
V (k, β, a, u, j) = max
c,k ,n
U (c, n) + βEu V (k , β, a, u , j + 1)
s.t.:
c(1 + τc) + k = (k + Γ) (1 + r(1 − τk)) + g + Y L
Y L
=
nw (j, a, u)
1 + ˜τss
1 − τss − τl
nw (j, a, u)
1 + ˜τss
n ∈ [0, 1], k ≥ −b, c > 0 (1)

Recursive formulation of the Agent’s problem
Retired agent’s problem
V (k, β,j) = max
c,k
U (c, n) + β(1 − π(j))V (k , β, j + 1) + π(j)D(k )
s.t.:
c(1 + τc) + k = (k + Γ) (1 + r(1 − τk)) + g + Ψ,
k ≥ −b, c > 0 (2)
Equilibrium deﬁnition:
Consumers’ optimization problem is solved by the value and policy functions;
markets clear; factors prices equal their marginal productivity; government
and social security budgets balance; the assets of the dead are uniformly
distributed among the living.
here

Calibration strategy
Choose ϕ, β1, β2, β3, b, χ and σu in order to minimize the loss
function below:
L(ϕ, β1, β2, β3, b, χ, σu) = ||Mm − Md || (3)
Mm and Md are moments of the model and the data. We match:
- share of wealth of the households in the age cohort 75 to 80 year old
- capital-output ratio and fraction of hours worked
- variance of log wages
- Q1, Q2 and Q3, the three quartiles of the wealth distribution.
We change 7 variables to match 7 moments and thus have an exactly
identified system.
Parameters Calibration fit Age profile of wealth

Fiscal experiment
What is the impact of decreasing public debt by 10% of GDP in 50
periods, ﬁnanced either by an increase in labor taxes or by a decrease
in government spending?
We produce:
I. Responses from a model calibrated to German data vs model calibrated
to German data but decreasing the variance of log wages, by changing:
Variance of ability;
Variance of idiosyncratic shock;

Experiments: τl consolidation
Multiplier not as sensitive to changes in the variance of ability as to
variations in variance of risk.

Experiments: G consolidation
Multiplier not sensitive to changes in the variance of ability. But variations
in variance of risk produce results in accordance with empirical exercise.

Inspecting the mechanism: % constrained
Percentage of agents constrained sensitive to the variance of risk, but not
to the variance of ability.

Inspecting the mechanism: risk
The lower the percentage of agents constrained the larger the output
response.

Inspecting the mechanism: Risk
Credit constrained agents have a more inelastic labor supply response to
the ﬁscal shock.

Calibrated to 13 European countries
Correlation coeﬃcient var log(w) and impact multipliers:
ρG = 0.36 (p − valG = 0.23)
ρtl = −0.60 (p − valtl = 0.03)

Multipliers vs % constrained
Correlation coeﬃcient % agents constrained and impact multipliers:
ρG = −0.69 (p − valG = 0.01)
ρtl = 0.55 (p − valtl = 0.06)

Validating the mechanism in the data
Three test to validate the mechanism:
Household debt diminshes the recessive effects of fiscal consolidation.
here
Labor supply is more responsive in countries with higher inequality.
here
Model data is able to replicate Blanchard and Leigh regression
amplified with income inequality. here

Conclusions
Income inequality is one dimension that helps to explain the fiscal
multipliers during fiscal consolidation episodes in European countries
between 2010 and 2011.
In the data: Higher income inequality is associated with more
recessive impacts from fiscal consolidation.
In the data: Higher income inequality is associated with more
recessive impacts from contractions in government consumption.

Conclusions continued
The amplification effect of income inequality on fiscal multipliers can
be explained through cross-country differences in idiosyncratic risk.
Countries with high income risk will have a smaller share of agents
with credit constraints due to precautionary behavior and therefore
higher labor supply elasticity with respect to fiscal consolidation
shocks.
Consolidation done through increases in labor tax produces deeper
recessions.

Empirical Analysis: Rational Expectation Model
Blanchard & Leigh (2013) found the bigger the fiscal consolidation
the bigger the IMF GDP forecast error. So IMF under-estimated the
fiscal multipliers.
Blanchard & Leigh find no evidence of any variable explaining IMF
GDP forecast errors besides the size of the fiscal consolidation.
They use a standard rational expectation model specification for 26
European countries 1, with ∆Yi,t:t+1 − Ê{∆Yi,t:t+1|Ωt} being the
cummulative GDP forecast errors in 2009 and 2010 and
{∆Fi,t:t+1|t|Ωt} being the planned fiscal consolidation.
∆Yi,t:t+1 − Ê{∆Yi,t:t+1|Ωt} = α + β Ê{∆Fi,t:t+1|t|Ωt} + i,t:t+1 (4)
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1
Countries: Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Germany, Denmark, Finland, France, Greece, Hungary,
Ireland, Iceland, Italy, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden,
Switzerland, and the United Kingdom.

Empirical findings: rational expectation model
Adding as control several earnings inequality measures 2 for 2009 and a
demeaned interaction term between inequality and consolidation, we found
inequality to amplify the fiscal multiplier. Results are robust to using GDP
growth rate instead of forecast error.
(1) (2) (3) (4) (5) (6) (7)
VARIABLES Blanchard-
Leigh
inequality
4/1
inequality
5/1
inequality
10/1
inequality
95/1
inequality
100/2
inequality
gini
β -1.095*** -0.841*** -0.806*** -0.697** -0.759*** -0.750*** -1.267***
(0.255) (0.227) (0.234) (0.252) (0.240) (0.238) (0.275)
γ -0.194 -0.144 -0.065 0.008 0.018 0.273**
(0.385) (0.291) (0.120) (0.036) (0.032) (0.121)
ι -0.251 -0.238 -0.154*** -0.071*** -0.066*** -0.085
(0.208) (0.153) (0.054) (0.021) (0.019) (0.084)
Constant 0.775* 2.150 2.041 1.812 0.805 0.558 -9.344**
(0.383) (2.632) (2.422) (1.758) (0.928) (0.597) (4.463)
Observations 26 26 26 26 26 26 26
R-squared 0.496 0.545 0.559 0.612 0.600 0.610 0.624
Robust standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
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2
25% highest earnings over the bottom 25%, the highest over the lowest 20%, the top over the bottom 10%, top over
bottom 5%, highest 1% over the lowest 2% and the earnings Gini coefficient. Data from European Union Statistics on Income
and Living Conditions (EU-SILC). 1 SD of inequality above the mean in (4) leads to an increase of 66% in the multiplier in the
f.e regression and 76% in the GDP growth rate regression.

Empirical ﬁndings: IMF shocks
∆Yi,t = α+β1eu
i,t+β2ea
i,t+γIi,t−1+ι1eu
i,t(Ii,t−1−µI )+ι2ea
i,t(Ii,t−1−µI )+δi +ωt+
(5)
(1) (2) (3) (4) (5) (6) (7)
VARIABLES Benchmark inequality
4/1
inequality
5/1
inequality
10/1
inequality
95/1
inequality
100/2
inequality
gini
β1 -0.003 0.006 0.004 -0.004 -0.004 -0.004 0.011
(0.005) (0.007) (0.007) (0.006) (0.006) (0.007) (0.007)
β2 -0.002 -0.003 -0.002 -0.000 -0.002 0.001 -0.001
(0.005) (0.007) (0.007) (0.007) (0.006) (0.006) (0.007)
γ -2.294** -1.308* -0.024 0.036 0.009 -1.100***
(1.001) (0.756) (0.344) (0.135) (0.049) (0.380)
ι1 -1.363** -0.882* 0.103 0.069 -0.005 -0.501**
(0.590) (0.501) (0.232) (0.077) (0.030) (0.191)
ι2 -0.357 -0.213 -0.094 -0.017 0.022 -0.112
(0.633) (0.510) (0.245) (0.091) (0.026) (0.173)
Constant 0.014*** 0.171** 0.123* 0.018 0.005 0.012 0.434***
(0.005) (0.069) (0.063) (0.050) (0.034) (0.014) (0.145)
Observations 84 84 84 84 84 84 84
R-squared 0.008 0.132 0.086 0.012 0.030 0.021 0.179
Number of
countries
12 12 12 12 12 12 12
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
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Empirical findings: SVAR
Ilzetzki et al (2013) use data for 44 countries to explain differences in
fiscal multipliers. They assume the following relation between variables
AYnt =
K
k=1
CkYn,t−k + un,t (6)
Ynt is a vector containing government consumption, output, current
account in percentage of GDP and the natural logarithm of the real
effective exchange rate.
Given that A is not observable, we pre-multiply everything by A−1 and
estimate the following equation using OLS
Ynt =
K
k=1
A−1
CkYn,t−k + A−1
un,t (7)

Empirical Analysis: SVAR
Fiscal multipliers may differ for a variety of reasons, and the data
indicates heterogeneity across time and space.
Ilzetzki et al (2013) use data for 44 countries over time to explain
differences in fiscal multipliers.
Use Blanchard-Perotti (2002) approach to VAR heterogeneity.
Countries are pooled by some factors
We use the same data and code but pool countries by income
inequality.
back

Empirical Analysis: SVAR gini
Figure: Impulse response functions of output to a 1% decrease in government
consumption (95% error bands in gray)
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Empirical Analysis: SVAR share ten
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Empirical Analysis: SVAR share twenty
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Model: Demographics
Economy populated by J overlapping generations of ﬁnitely lived
households, born at 20, retire at 65.
Retired agents face age-dependent probability of dying π(j).
Retired agents receive a social security payment, Ψt. Unintended
bequests are redistributed as a lump-sum Γ.
At age 20, agents are assigned an idiosyncratic productivity level
(ability) and then build their age proﬁle of productivity.
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Model: Preferences
Standard additive-separable preferences in consumption and hours:
U(c, n) = c1−1/σ
1−1/σ − χn1+1/ψ
1+1/ψ
Retired households gain utility from the bequest they will leave when
they die: D(k) = ϕ log(k)
Each generation consists of three types of agents with equal mass,
that diﬀer w.r.t. the time preference parameter β. back

Firm’s problem
Representative ﬁrm combines capital and labor in a Cobb-Douglas
production function
Yt(Kt, Lt) = Kα
t [Lt]1−α
Capital evolves as:
Kt+1 = (1 − δ)Kt + It
Firm chooses inputs to maximize proﬁt:
Πt = Yt − wtLt − (rt + δ)Kt
Competitive equilibrium yields factor prices:
wt = ∂Yt/∂Lt = (1 − α) Kt
Lt
α
rt = ∂Yt/∂Kt − δ = α Lt
Kt
1−α
− δ
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Labor income
An agent’s wage depends on the wage per efficiency unit of labor, w,
and the number of efficiency units the agent is endowed with.
This endowment depends on agent i s age (j), the realization of an
idiosyncratic shock (u) and the realization of ability (a) at the
beginning of the life cycle.
wi (j, u, a) = weγ1j+γ2j2+γ3j3+u+a
γ1, γ2 and γ3 capture the age profile of wages.
Shock follows simple AR process: u = ρu + , ∼ N(0, σ2
)
Ability is realized (at age 20) from N(0, σ2
a)
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Government
Government runs a balanced social security system by taxing
employers and employees, τss and ˜τss, and paying benefits, Ψt, to
retired agents:
Ψ( j≥65 Ωj ) = Rss
Government also taxes consumption, labor and capital income to
finance public consumption, Gt, interest on the national debt, rtBt,
and lump sum transfers, gt.
Consumption and capital income are taxed at rates τc , and τk .
Progressive labor income taxes.
Lump-sum transfers financed by government surplus:
g(45 + j≥65 Ωj ) = R − G − rB
back

Stationary Recursive Competitive Equilibrium
Let Φ(k, β, a, u, j) be the measure of households with the
corresponding characteristics.
Equilibrium deﬁnition
1 Value function V (k, β, a, u, j) and policy functions, c(k, β, a, u, j), k (k, β, a, u, j),
and n(k, β, a, u, j), solve the consumers’ optimization problem given the factor
prices and initial conditions.
2 Markets clear:
K + B = kdΦ
L = (n(k, β, a, u, j)) dΦ
cdΦ + δK + G = Kα
L1−α

Equilibrium deﬁnition continued
3 The factor prices satisfy:
w = (1 − α)
K
L
α
r = α
K
L
α−1
− δ
4 The government budget balances:
g dΦ + G + rB = τk r(k + Γ) + τc c + τl
nw(u, ν, j)
1 + ˜τss
dΦ

Equilibrium deﬁnition continued
5 The social security system balances:
Ψ
j≥65
dΦ =
˜τss + τss
1 + ˜τss j<65
nwdΦ
6 The assets of the deceased are uniformly distributed among the living:
Γ ω(j)dΦ = (1 − ω(j)) kdΦ
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Parameters held constant across countries
Parameter Value Description Source
Preferences
η 1 Inverse Frisch Elasticity Trabandt and Uhlig (2011)
σ 1.2 Risk aversion parameter Literature
Technology
α 0.33 Capital share of output Literature
δ 0.06 Capital depreciation rate Literature
ρ 0.335 u = ρu + , ∼ N(0, σ2) PSID 1968-1997
σa 0.423 Variance of ability European economies average from Brinca et al (2016)
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Calibration ﬁt: Benchmark model for Germany
Table: Calibration Fit
Data Moment Description Source Data Value Model Value
75-80/all Share of wealth owned by households aged 75-80 LWS 1.51 1.51
K/Y Capital-output ratio PWT 3.013 3.013
Var(ln w) Variance of log wages LIS 0.354 0.354
¯n Fraction of hours worked OECD 0.189 0.189
Q25, Q50, Q75 Wealth Quartiles LWS -0.004, 0.027, 0.179 -0.005, 0.026, 0.182
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Calibration ﬁt: Agents with negative wealth
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Validating the mechanism: Household debt
The mechanism suggests that the fall in output is larger the lower the
share of constrained agents.
To test this in the data, we run Blanchard & Leigh (2013) regression
with an interaction between household debt (positively correlated with
the % of constrained agents) and planned consolidation.3
(1) (2) (3)
Leigh
Blanchard-Leigh Precrisis household
debt
Precrisis household debt
Consolidation -1.095*** -1.086*** -1.389***
(0.255) (0.262) (0.117)
Household Debt -0.001 -0.004
(0.006) (0.003)
Interaction 0.010***
(0.001)
Constant 0.775* 0.887 1.422***
(0.383) (0.699) (0.420)
Observations 26 25 25
R-squared 0.496 0.489 0.690
*** p<0.01, ** p<0.05, * p<0.1
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3
Household total ﬁnancial liabilities in percent of household disposable income. 1 SD deviation of household debt above
the mean in (3) leads to an decrease of 52% in the multiplier

Validating the mechanism: Labor supply response
Using Alesina et al.(2015) dataset and assuming hours worked per capita
as the dependent variable we see that labor supply is more responsive to
ﬁscal consolidation in countries with larger inequality.
(1) (2) (3) (4) (5) (6) (7)
VARIABLES Benchmark inequality
4/1
inequality
5/1
inequality
10/1
inequality
95/1
inequality
100/2
inequality
gini
β1 -0.004*** -0.003** -0.003* -0.003** -0.003*** -0.007*** -0.004**
(0.001) (0.002) (0.002) (0.001) (0.001) (0.001) (0.002)
β2 -0.004*** -0.001 -0.002 -0.006*** -0.006*** -0.004** 0.000
(0.001) (0.002) (0.002) (0.002) (0.001) (0.001) (0.003)
γ 0.319 0.191 0.100 0.026 0.023** 0.068
(0.232) (0.167) (0.068) (0.027) (0.010) (0.093)
ι1 -0.116 -0.155 -0.134*** -0.045*** -0.014** -0.029
(0.123) (0.103) (0.045) (0.015) (0.006) (0.040)
ι2 -0.266 -0.161 0.091 0.044** 0.005 -0.114
(0.206) (0.171) (0.070) (0.020) (0.006) (0.068)
Constant 0.211*** 0.188*** 0.194*** 0.196*** 0.204*** 0.204*** 0.184***
(0.001) (0.016) (0.014) (0.010) (0.007) (0.003) (0.036)
Observations 55 55 55 55 55 55 55
R-squared 0.502 0.582 0.577 0.601 0.618 0.563 0.567
Number of
countries
11 11 11 11 11 11 11
Standard errors in parentheses
*** p<0.01, ** p<0.05, * p<0.1
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Validating the mechanism: Blanchard and Leigh replication
Forecast error given by the diﬀerence between benchmark model and
model with no risk.
(1) (2) (3) (4) (5) (6) (7)
Leigh
inequality
4/1
inequality
5/1
inequality
10/1
inequality
95/1
inequality
100/2
inequality
gini
G consolidation -0.610*** -0.634*** -0.654*** -0.747*** -0.879*** -0.844*** -0.623***
(0.154) (0.097) (0.095) (0.099) (0.113) (0.129) (0.123)
Inequality -0.064 -0.028 0.010 0.021 0.013 -0.097
(0.155) (0.110) (0.049) (0.027) (0.019) (0.081)
Interaction -0.073 -0.072* -0.068*** -0.063*** -0.040*** 0.002
(0.053) (0.038) (0.019) (0.017) (0.011) (0.027)
Constant -0.652* -0.321 -0.447 -0.640 -0.772 -0.723 2.283
(0.348) (0.803) (0.744) (0.647) (0.613) (0.576) (2.208)
Observations 13 13 13 13 13 13 13
R-squared 0.370 0.444 0.444 0.450 0.456 0.442 0.510
*** p<0.01, ** p<0.05, * p<0.1
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Validating the mechanism: Blanchard and Leigh replication
(1) (2) (3) (4) (5) (6) (7)
Leigh
inequality
4/1
inequality
5/1
inequality
10/1
inequality
95/1
inequality
100/2
inequality
gini
τl consolidation -2.578 -2.321*** -2.662*** -4.134*** -5.987*** -5.603*** -2.475***
(2.143) (0.656) (0.657) (0.691) (0.825) (1.134) (0.656)
Inequality -2.144*** -1.500*** -0.549** -0.189 -0.143 -0.880***
(0.524) (0.377) (0.187) (0.117) (0.089) (0.187)
Interaction -0.006 -0.219 -0.563*** -0.635*** -0.407*** 0.148
(0.341) (0.243) (0.117) (0.099) (0.092) (0.117)
Constant -4.263** 5.694* 4.208 1.389 -0.422 -0.554 22.246***
(1.508) (2.621) (2.443) (2.173) (2.065) (1.989) (5.478)
Observations 13 13 13 13 13 13 13
R-squared 0.129 0.657 0.649 0.646 0.634 0.599 0.784
*** p<0.01, ** p<0.05, * p<0.1
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Fiscal Consolidation Programs and Income Inequality - Pedro Brinca

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