Getting things right: optimal tax policy with labor market duality

Getting things right
Optimal tax policy with labor market duality
Gilbert Mbara, Joanna Tyrowicz, Ryszard Kokoszczynski
NBP Macroeconomic Workshop
June 2016
1 / 24

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
2 / 24

Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rate
Starting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...
Slemrod and Yitzhaki (2002), Piketty and Saez (2013)
3 / 24

Motivation
Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)
get an “optimal” tax rate without evasion ⇒ general equilibrium eﬀects
3 / 24

Motivation
Avoidable labor taxes vs unavoidable ones
Eﬀects of beneﬁts and insurance on registered employment (e.g. Krueger
and Meyer 2002, Bergolo and Cruces 2014), reported earned income (e.g.
Stavrunova and Yerokhin 2014) or other work incentives (e.g. Tonin 2011,
Pickhardt and Prinz 2014, Hilton et al. 2014)
Measuring unregistered employment (predominantly Schneider 2014),
mostly about Latin America, Italy and (some) Germany
3 / 24

Motivation
Our contribution to the literature
plausible microfoundations for atypical employment
3 / 24

Motivation
plausible microfoundations for atypical employment (+ estimates of size)
3 / 24

Motivation
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: ﬁscal and welfare
3 / 24

Motivation
Road map
1 Motivation
2 Model and calibration
3 Calibration
4 Results
5 Conclusions
4 / 24

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)
5 / 24

Key elements
Both types of labor identical in terms of productivity
Houeseholds have preference over types of contracts
5 / 24

Key elements
Both types of labor identical in terms of productivity
Houeseholds have preference over types of contracts
Government is not strategic about taxes
5 / 24

The model - ﬁrms
Many ﬁrms, need both capital and labor
y =Akα
n1−α
,
nt = ((1 − ω)nρ
P + ωnρ
S )
1
ρ
σ =
1
1 − ρ
and ω =
nS
n
6 / 24

The model - firms
Many firms, need both capital and labor
y =Akα
n1−α
,
nt = ((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
6 / 24

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
7 / 24

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.
7 / 24

Calibration
A whole bunch of easy 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
8 / 24

Calibration
Four really tough parameters
¯s – penalty for tax evasion
ω – share of atypically employed labor (evasion on τs )
ρ – elasticity of substitution between the two types of labor
φ – disutility of atypical contract
9 / 24

Calibration
1
φ
=
1 − ω
ω
ρ
1 + pt ¯sτs
1 + τs
9 / 24

Calibration
1
φ
=
1 − ω
ω
ρ
1 + pt ¯sτs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τn
+ τs
)wP nP + (τn
+ pt ¯sτs
)wS nS = (1 − α)
τn
+ τs
1 + τs
(1 − ω)1+ρ
+
τn
+ τs
pt
1 + pt ¯sτs
ω1+ρ
9 / 24

Calibration
1
φ
=
1 − ω
ω
ρ
1 + pt ¯sτs
1 + τs
(τn
+ τs
)wP nP + (τn
+ pt ¯sτs
)wS nS = (1 − α)
τn
+ τs
1 + τs
(1 − ω)1+ρ
+
τn
+ τs
pt
1 + pt ¯sτs
ω1+ρ
Yields wage rates ws and wp
9 / 24

Calibration
1
φ
=
1 − ω
ω
ρ
1 + pt ¯sτs
1 + τs
(τn
+ τs
)wP nP + (τn
+ pt ¯sτs
)wS nS = (1 − α)
τn
+ τs
1 + τs
(1 − ω)1+ρ
+
τn
+ τs
pt
1 + pt ¯sτs
ω1+ρ
Yields wage rates ws and wp ⇒ yields relationship between ω and ρ
9 / 24

Calibration
1
φ
=
1 − ω
ω
ρ
1 + pt ¯sτs
1 + τs
(τn
+ τs
)wP nP + (τn
+ pt ¯sτs
)wS nS = (1 − α)
τn
+ τs
1 + τs
(1 − ω)1+ρ
+
τn
+ τs
pt
1 + pt ¯sτs
ω1+ρ
Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24

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)
10 / 24

Results
Statics
11 / 24

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
12 / 24

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
13 / 24

Results
... although Laﬀer curve is ﬂat, predictions are plausible...
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
14 / 24

Results
Dynamics
15 / 24

Results
Two thought experiments: EU baseline: 37% share of τs; ω=16%; φ=1.07
16 / 24

Results
Scenario 1 (DNK): 0.0% share of τs ;
16 / 24

Results
Scenario 1 (DNK): 0.0% share of τs ; ˆω=12%;
16 / 24

Results
Scenario 1 (DNK): 0.0% share of τs ; ˆω=12%; ˆφ=0.98
16 / 24

Results
Scenario 2 (FRA): 50% share of τs ;
16 / 24

Results
Scenario 2 (FRA): 50% share of τs ; ˆω=28%;
16 / 24

Results
Scenario 2 (FRA): 50% share of τs ; ˆω=28%; ˆφ=1.10
16 / 24

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
17 / 24

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
18 / 24

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
19 / 24

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
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
0 10 20 30 40 50 60
1
1.05
1.1
1.15
1.2
1.25
1.3
wp
0 10 20 30 40 50 60
1
1.05
1.1
1.15
1.2
1.25
1.3
ws
20 / 24

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
21 / 24

Results
Welfare
0 10 20 30 40 50 60
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
Wel.
22 / 24

Results
Welfare
Consumption equivalent units:
λ = 1 − A
1
η−1 , where A =
1 + (1 − β)(1 − η)Welfareold
1 + (1 − β)(1 − η)Welfarenew
23 / 24

Results
Welfare
Consumption equivalent units:
λ = 1 − A
1
η−1 , where A =
1 + (1 − β)(1 − η)Welfareold
1 + (1 − β)(1 − η)Welfarenew
FRA: λ = 0.07
DNK: λ = −0.13
23 / 24

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
24 / 24

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
24 / 24

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.
24 / 24

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.
24 / 24

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