Getting things right: optimal tax policy with labor market duality
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Transcript of Getting things right: optimal tax policy with labor market duality
Getting things right
Getting things rightOptimal tax policy with labor market duality
Gilbert Mbara, Joanna Tyrowicz, Ryszard Kokoszczynski
NBP Macroeconomic Workshop
June 2016
1 / 24
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 average2 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)
Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment
(+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Little theory to explain this dispersion
Standard in the literature: optimal tax rateStarting from Diamond and Mirrlees (1971a,b), Mirrlees (1971) + ...Slemrod and Yitzhaki (2002), Piketty and Saez (2013)Trabandt and Uhlig (2011), Busato and Chiarini (2013), Orsi et al. (2014)get an “optimal” tax rate without evasion ⇒ general equilibrium effects
Avoidable labor taxes vs unavoidable onesEffects of benefits and insurance on registered employment (e.g. Kruegerand 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
Our contribution to the literature
plausible microfoundations for atypical employment (+ estimates of size)
inquire the optimal policy mix: fiscal and welfare
3 / 24
Getting things right
Motivation
Road map
1 Motivation
2 Model and calibration
3 Calibration
4 Results
5 Conclusions
4 / 24
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
5 / 24
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
5 / 24
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
5 / 24
Getting things right
Model and calibration
The model - firms
Many firms, need both capital and labor
y =Akαn1−α,
nt = ((1− ω)nρP + ωnρ
S)1ρ
σ =1
1− ρ and ω =nSn
Hiring labor atypically exposes to risk of fine for tax evasion
πe = pπD + (1− p)πND = y − dk − (1 + τ s)wPnP − (1 + ps̄τ s)wSnS
6 / 24
Getting things right
Model and calibration
The model - firms
Many firms, need both capital and labor
y =Akαn1−α,
nt = ((1− ω)nρP + ωnρ
S)1ρ
σ =1
1− ρ and ω =nSn
Hiring labor atypically exposes to risk of fine for tax evasion
πe = pπD + (1− p)πND = y − dk − (1 + τ s)wPnP − (1 + ps̄τ s)wSnS
6 / 24
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 + τ c)c + b + x = (1− τ n)wPnP + (1− τ n)wSnS ⇐ labor income
+πe + (1− τ k)(d − δ)k + δk ⇐ capital income
+Rbb + s + m ⇐ bond interest, transfers, etc.
7 / 24
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 + τ c)c + b + x = (1− τ n)wPnP + (1− τ n)wSnS ⇐ labor income
+πe + (1− τ k)(d − δ)k + δk ⇐ capital income
+Rbb + s + m ⇐ bond interest, transfers, etc.
7 / 24
Getting things right
Calibration
A whole bunch of easy parameters
Table: Calibration of model parameters
Parameter Value Source
α Capital share in output Country Specific ECψ TFP growth 1.017 ECR̄ Gross interest rate 1.04 Standardη Inverse of IES 2 Standardϕ Frisch’s elasticity 1 Standard
τ c , τn, τ k Taxes on consumption, labor and capital Country Specific OECDτ s Social Security Taxes Country Specific OECDb Public debt (in % of GDP) Country-specific OECD
g and s Gov. cons. and social transfers (in % of GDP) Country Specific OECDm and x Trade balance and other (in % of GDP) Country Specific OECD
8 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)
Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)Yields wage rates ws and wp
⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)Yields wage rates ws and wp ⇒ yields relationship between ω and ρ
⇒ yields φ
9 / 24
Getting things right
Calibration
Four really tough parameters
s̄ – 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
1
φ=
(1− ωω
)ρ1 + pt s̄τs
1 + τs
One variable to identify: share of (labor) tax in GDP
(τ n + τ s)wPnP + (τ n + pt s̄τs)wSnS = (1− α)
(τ n + τ s
1 + τ s(1− ω)1+ρ +
τ n + τ spt1 + pt s̄τ s
ω1+ρ
)Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ
9 / 24
Getting things right
Calibration
Model fits data (fairly) well
Figure: Irregular employment (ESS)
0 0.1 0.2 0.3 0.4 0.5Model Predicted
0
0.1
0.2
0.3
0.4
0.5ESSData
GERFRA
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
Getting things right
Results
Statics
11 / 24
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: τs+τn
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
0.17
Tax
Rev
enue
s
EU-14
Evasion
No Evasion
Steady State
12 / 24
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 τs in Total Labour Income Tax
0.1
0.11
0.12
0.13
0.14
0.15
0.16
Tax
Rev
enue
s
EU-14
Evasion
No Evasion
Steady State
13 / 24
Getting things right
Results
... although Laffer curve is flat, predictions are plausible...
0 0.1 0.2 0.3 0.4 0.5 0.6τs
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
Getting things right
Results
Dynamics
15 / 24
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 ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10
16 / 24
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 ;
ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10
16 / 24
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 ; ω̂=12%;
φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10
16 / 24
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 ; ω̂=12%; φ̂=0.98
Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10
16 / 24
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 ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ;
ω̂=28%; φ̂=1.10
16 / 24
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 ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%;
φ̂=1.10
16 / 24
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 ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10
16 / 24
Getting things right
Results
Fiscal effects (tax revenues / GDP)
0 10 20 30 40 50 600.085
0.09
0.095
0.1
0.105
0.11
T
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
17 / 24
Getting things right
Results
Output effects (output per worker)
0 10 20 30 40 50 601.9
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
18 / 24
Getting things right
Results
Labor supply (total hours)
0 10 20 30 40 50 600.18
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
19 / 24
Getting things right
Results
Labor supply (total hours)
0 10 20 30 40 50 600.15
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 50 600.02
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 50 601
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 50 601
1.05
1.1
1.15
1.2
1.25
1.3
ws
Initial Steady State
Final Steady State: DEN
Final Steady State: FRA
20 / 24
Getting things right
Results
Consumption (share in GDP)
0 10 20 30 40 50 600.48
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
21 / 24
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
22 / 24
Getting things right
Results
Welfare
Consumption equivalent units:
λ = 1− A1
η−1 , where A =1 + (1− β)(1− η)Welfareold1 + (1− β)(1− η)Welfarenew
FRA: λ = 0.07DNK: λ = −0.13
23 / 24
Getting things right
Results
Welfare
Consumption equivalent units:
λ = 1− A1
η−1 , where A =1 + (1− β)(1− η)Welfareold1 + (1− β)(1− η)Welfarenew
FRA: λ = 0.07DNK: λ = −0.13
23 / 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
24 / 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
24 / 24
Getting things right
References
Bergolo, M. and Cruces, G.: 2014, Work and tax evasion incentive effects of social insuranceprograms: Evidence from an employment-based benefit extension, Journal of Public Economics117, 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: Productionefficiency, 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 transportpreferences, Journal of Economic Psychology 42, 17–27.
Krueger, A. B. and Meyer, B. D.: 2002, Labor supply effects of social insurance, Handbook ofpublic economics 4, 2327–2392.
Mirrlees, J. A.: 1971, An exploration in the theory of optimum income taxation, Review ofEconomic Studies 38(2), 175–208.
Orsi, R., Raggi, D. and Turino, F.: 2014, Size, Trend, and Policy Implications of the UndergroundEconomy, Review of Economic Dynamics 17(3), 417–436.
Pickhardt, M. and Prinz, A.: 2014, Behavioral dynamics of tax evasion–a survey, Journal ofEconomic 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 recentdevelopments, IZA Discussion Paper 8278, Institute for the Study of Labor (IZA).
Slemrod, J. and Yitzhaki, S.: 2002, Tax avoidance, evasion, and administration, Handbook ofPublic Economics 3, 1423–1470.
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Getting things right
Conclusions
Stavrunova, O. and Yerokhin, O.: 2014, Tax incentives and the demand for private healthinsurance, Journal of Health Economics 34, 121–130.
Tonin, M.: 2011, Minimum wage and tax evasion: Theory and evidence, Journal of PublicEconomics 95(11), 1635–1651.
Trabandt, M. and Uhlig, H.: 2011, The Laffer curve revisited, Journal of Monetary Economics58(4), 305–327.
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