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

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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


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


Motivation


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





3 / 24


Motivation







3 / 24


Motivation





plausible microfoundations for atypical employment

(+ estimates of size)


3 / 24


Motivation







3 / 24


Motivation







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)

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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Key elements






5 / 24



Key elements






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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



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

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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.

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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.

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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

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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

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Calibration






1

φ=

(1− ωω

)ρ1 + pt s̄τs

1 + τs



(τ n + τ s

1 + τ s(1− ω)1+ρ +


ω1+ρ


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Calibration






1

φ=

(1− ωω

)ρ1 + pt s̄τs

1 + τs



(τ n + τ s

1 + τ s(1− ω)1+ρ +


ω1+ρ

)

Yields wage rates ws and wp ⇒ yields relationship between ω and ρ ⇒ yields φ

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Calibration






1

φ=

(1− ωω

)ρ1 + pt s̄τs

1 + τs



(τ n + τ s

1 + τ s(1− ω)1+ρ +


ω1+ρ

)Yields wage rates ws and wp

⇒ yields relationship between ω and ρ ⇒ yields φ

9 / 24


Calibration






1

φ=

(1− ωω

)ρ1 + pt s̄τs

1 + τs



(τ n + τ s

1 + τ s(1− ω)1+ρ +


ω1+ρ

)Yields wage rates ws and wp ⇒ yields relationship between ω and ρ

⇒ yields φ

9 / 24


Calibration






1

φ=

(1− ωω

)ρ1 + pt s̄τs

1 + τs



(τ n + τ s

1 + τ s(1− ω)1+ρ +


ω1+ρ


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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)

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Results

Statics

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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

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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

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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

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Results

Dynamics

15 / 24


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

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Results


Scenario 1 (DNK): 0.0% share of τs ;

ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10

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Results


Scenario 1 (DNK): 0.0% share of τs ; ω̂=12%;

φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10

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Results


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

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Results


Scenario 1 (DNK): 0.0% share of τs ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ;

ω̂=28%; φ̂=1.10

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Results


Scenario 1 (DNK): 0.0% share of τs ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%;

φ̂=1.10

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Results


Scenario 1 (DNK): 0.0% share of τs ; ω̂=12%; φ̂=0.98Scenario 2 (FRA): 50% share of τs ; ω̂=28%; φ̂=1.10

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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


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




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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




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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




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




0 10 20 30 40 50 601

1.05

1.1

1.15

1.2

1.25

1.3

wp




0 10 20 30 40 50 601

1.05

1.1

1.15

1.2

1.25

1.3

ws




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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




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Results

Welfare

0 10 20 30 40 50 60-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Wel.




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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

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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


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


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 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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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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Getting things right: optimal tax policy with labor market duality

Economy & Finance