We develop a dynamic general equilibrium model in which firms evade the employer contribution component of social security taxes by offering some workers non-formal contracts. When calibrated, the model yields estimates of dual labor market participation consistent with empirical evidence for the EU14 countries and the US. We investigate the optimal mix of the avoidable and unavoidable components of labor taxes and analyze the fiscal and macroeconomics effects of bringing the composition to the welfare optimum. We find that partial labor tax evasion makes tax revenues more elastic, but full tax compliance is not necessarily a welfare enhancing policy mix.

1. Getting things right
Getting things right
Optimal tax policy with labor market duality
Gilbert Mbara, Joanna Tyrowicz, Ryszard Kokoszczynski
Warsaw International Economic Meeting
June 2016
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2. Getting things right
Motivation
Remarkable dispersion in how labor is taxed and benefits financed
Figure: Labor taxes and social security contributions in the OECD
Data: OECD, 2014, SINK at 100% of average
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3. Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rate
Trabandt and Uhlig (2011) get an “optimal” tax rate without evasion ⇒
general equilibrium effects
Avoidable taxes (underground economy)
Measuring unregistered employment (predominantly Schneider 2014),
mostly about Latin America, Italy and (some) Germany. Busato and Chiarini
(2013), Orsi et al. (2014) mostly Italy (good data on unregistered work)
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
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4. Getting things right
Motivation
Road map
1 Motivation
2 Model and calibration
3 Calibration
4 Results
5 Conclusions
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5. Getting things right
Model and calibration
Key elements
Two types of labor taxes:
Unavoidable τn paid by workers (e.g. labor income tax)
Avoidable τs paid by employers (e.g. social security contributions)
Labor may be hired with a:
typical contract, both taxes (P=primary)
atypical contract, only labor income tax, τn (S=secondary)
Both types of labor identical in terms of productivity
Houeseholds have preference over types of contracts
Government is not strategic about taxes
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6. Getting things right
Model and calibration
The model - firms
Many firms, need both capital and labor
y =Akα
n1−α
,
n = ((1 − ω)nρ
P + ωnρ
S )
1
ρ
σ =
1
1 − ρ
and ω =
nS
n
Hiring labor atypically exposes to risk of fine for tax evasion
πe
= pπD
+ (1 − p)πND
= y − dk − (1 + τs
)wP nP − (1 + p¯sτs
)wS nS
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7. Getting things right
Model and calibration
The model - households
Representative household with labor endowment
No auditing of households (no tax evasion on labor income tax)
U(c, l(nP , nS )) =
1
1 − η
c1−η
(1 − κ(1 − η)(nP + φnS )
1+ 1
ϕ )η
− 1
With the following budget constraint
(1 + τc
)c + b + x = (1 − τn
)wP nP + (1 − τn
)wS nS ⇐ labor income
+πe
+ (1 − τk
)(d − δ)k + δk ⇐ capital income
+Rb
b + s + m ⇐ bond interest, transfers, etc.
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8. Getting things right
Calibration
Standard parameters
Table: Calibration of model parameters
Parameter Value Source
α Capital share in output Country Specific EC
ψ TFP growth 1.017 EC
¯R Gross interest rate 1.04 Standard
η Inverse of IES 2 Standard
ϕ Frisch’s elasticity 1 Standard
τc
, τn
, τk
Taxes on consumption, labor and capital Country Specific OECD
τs
Social Security Taxes Country Specific OECD
b Public debt (in % of GDP) Country-specific OECD
g and s Gov. cons. and social transfers (in % of GDP) Country Specific OECD
m and x Trade balance and other (in % of GDP) Country Specific OECD
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9. Getting things right
Calibration
Four tough parameters
p¯s – expected penalty for tax evasion.
ω – weight of atypically employed labor ns in labor.
ρ – elasticity of substitution between the two types of labor.
Imposing ω =
nS
n
in n = ((1 − ω)nρ
P + ωnρ
S )
1
ρ =⇒ 1 = (1 − ω)1+ρ
+ ω1+ρ
FSS = τs
wP nP + p¯sτs
wS nS = (1 − α)
τs
(1 − ω)1+ρ
1 + τs
+
τs
p¯sω1+ρ
1 + p¯sτs
LTR = τn
(wP nP + wS nS ) = (1 − α)τn (1 − ω)1+ρ
1 + τs
+
ω1+ρ
1 + p¯sτs
φ – disutility of atypical contract
1
φ
=
wp
ws
=
1 − ω
ω
ρ
1 + p¯sτs
1 + τs
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10. Getting things right
Calibration
Model fits data (fairly) well
Figure: Irregular employment (ESS)
0 0.1 0.2 0.3 0.4 0.5
Model Predicted
0
0.1
0.2
0.3
0.4
0.5ESSData
GER
FRA ITA
GBR
AUT
BELDNK FIN
GRE
IRL
NET
PRT
ESP
SWE
USAEU-14
Pearson’s ρ at 0.6291 (p-value=0.009)
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11. Getting things right
Calibration
Firms SS contributions vs. ω
0 0.1 0.2 0.3 0.4 0.5 0.6
τs
τs+τn
0
0.05
0.1
0.15
0.2
0.25
0.3
ω
GER
FRA
ITA
GBR
AUT
BEL
DNK
FIN
GRE
IRL
NET
PRT
ESP
SWE
USA
EU-14
ω
OLS
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12. Getting things right
Results
Statics
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13. Getting things right
Results
You’d expect tax revenue to be more responsive to taxes ...
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Tax Rate: τ
s
+τ
n
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
TaxRevenues
EU-14
Evasion
No Evasion
Steady State
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14. Getting things right
Results
... we care more about the role of avoidable tax...
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Share of τ
s
in Total Labour Income Tax
0.1
0.11
0.12
0.13
0.14
0.15
0.16
TaxRevenues
EU-14
Evasion
No Evasion
Steady State
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15. Getting things right
Results
Dynamics
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16. Getting things right
Results
Two thought experiments: EU baseline: 37% share of τs; ω=16%; φ=1.07
Scenario 1 (DNK): 0.0% share of τs ; ˆω=12%; ˆφ=0.98
Scenario 2 (FRA): 50% share of τs ; ˆω=28%; ˆφ=1.10
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17. Getting things right
Results
Fiscal effects (tax revenues / GDP)
0 10 20 30 40 50 60
0.085
0.09
0.095
0.1
0.105
0.11
T
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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18. Getting things right
Results
Output effects (output per worker)
0 10 20 30 40 50 60
1.9
1.95
2
2.05
2.1
2.15
2.2
2.25
y
n
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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19. Getting things right
Results
Labor supply (total hours)
0 10 20 30 40 50 60
0.18
0.185
0.19
0.195
0.2
0.205
0.21
0.215
0.22
n
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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20. Getting things right
Results
Labor supply (total hours)
0 10 20 30 40 50 60
0.15
0.155
0.16
0.165
0.17
0.175
0.18
np
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
0 10 20 30 40 50 60
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
0.065
ns
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
0 10 20 30 40 50 60
1
1.05
1.1
1.15
1.2
1.25
1.3
wp
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
0 10 20 30 40 50 60
1
1.05
1.1
1.15
1.2
1.25
1.3
ws
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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21. Getting things right
Results
Consumption (share in GDP)
0 10 20 30 40 50 60
0.48
0.5
0.52
0.54
0.56
0.58
0.6
0.62
c
y
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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22. Getting things right
Results
Welfare
0 10 20 30 40 50 60
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Wel.
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
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23. Getting things right
Results
Welfare
Consumption equivalent units: λ = 1 − A
1
η−1 ,
A =
1 + (1 − β)(1 − η)Welfareold
1 + (1 − β)(1 − η)Welfarenew
FRA: λ = 0.07
DNK: λ = −0.13
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24. Getting things right
Conclusions
Preliminary conclusions and way onwards
What we have so far
A stylized but roughly accurate model
Can talk about optimality
Way to evaluate the welfare and fiscal effects of reforms
Still problem with solving/approximating
What we need / want to do:
Sources of welfare effects: composition vs. general equilibrium
Robustness of solving the model
Possibly other interesting policy experiments
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25. Getting things right
References
Bergolo, M. and Cruces, G.: 2014, Work and tax evasion incentive effects of social insurance
programs: Evidence from an employment-based benefit extension, Journal of Public Economics
117, 211–228.
Busato, F. and Chiarini, B.: 2013, Steady State Laffer Curve with the Underground Economy,
Public Finance Review pp. 109–114.
Diamond, P. A. and Mirrlees, J. A.: 1971a, Optimal taxation and public production i: Production
efficiency, The American Economic Review 61(1), 8–27.
Diamond, P. A. and Mirrlees, J. A.: 1971b, Optimal taxation and public production ii: Tax rules,
The American Economic Review 61(3), 261–278.
Hilton, D., Charalambides, L., Demarque, C., Waroquier, L. and Raux, C.: 2014, A tax can nudge:
The impact of an environmentally motivated bonus/malus fiscal system on transport
preferences, Journal of Economic Psychology 42, 17–27.
Krueger, A. B. and Meyer, B. D.: 2002, Labor supply effects of social insurance, Handbook of
public economics 4, 2327–2392.
Mirrlees, J. A.: 1971, An exploration in the theory of optimum income taxation, Review of
Economic Studies 38(2), 175–208.
Orsi, R., Raggi, D. and Turino, F.: 2014, Size, Trend, and Policy Implications of the Underground
Economy, Review of Economic Dynamics 17(3), 417–436.
Pickhardt, M. and Prinz, A.: 2014, Behavioral dynamics of tax evasion–a survey, Journal of
Economic Psychology 40, 1–19.
Piketty, T. and Saez, E.: 2013, Optimal labor income taxation, Handbook of Public Economics.
Vol. 5 pp. 391–474.
Schneider, F.: 2014, The shadow economy and shadow labor force: A survey of recent
developments, IZA Discussion Paper 8278, Institute for the Study of Labor (IZA).
Slemrod, J. and Yitzhaki, S.: 2002, Tax avoidance, evasion, and administration, Handbook of
Public Economics 3, 1423–1470.
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26. Getting things right
Conclusions
Stavrunova, O. and Yerokhin, O.: 2014, Tax incentives and the demand for private health
insurance, Journal of Health Economics 34, 121–130.
Tonin, M.: 2011, Minimum wage and tax evasion: Theory and evidence, Journal of Public
Economics 95(11), 1635–1651.
Trabandt, M. and Uhlig, H.: 2011, The Laffer curve revisited, Journal of Monetary Economics
58(4), 305–327.
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