Hanging off a cliff: fiscal consolidations and default risk
1. Hanging off a cliff: fiscal consolidations and default risk
Francesco Pappadà (BdF) Yanos Zylberberg (Bristol)
Ademu Conference
Toulouse School of Economics
April 5-6, 2018
The views expressed in this presentation are those of the author and do not necessarily represent those of the
Banque de France or of the Eurosystem.
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3. Motivation
Do fiscal consolidations always reduce default risk?
1. If the government has an imperfect ability to raise revenues, fiscal
consolidations induce distortions that may affect the price of debt.
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4. Motivation
Do fiscal consolidations always reduce default risk?
1. If the government has an imperfect ability to raise revenues, fiscal
consolidations induce distortions that may affect the price of debt.
2. The distortions induced by tax reforms impact default risk:
in the literature, the price of debt is q(bt+1, zt),
in this paper, the price of debt will be q(bt+1, τt, zt),
where bt+1: debt, τt: tax rate, zt: shocks.
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5. Fiscal consolidations and default risk
When the ability to raise revenues is imperfect, fiscal consolidations may only
reduce marginally default risk (bt+1-effect versus τt-effect).
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6. Fiscal consolidations and default risk
When the ability to raise revenues is imperfect, fiscal consolidations may only
reduce marginally default risk (bt+1-effect versus τt-effect).
The distortions induced by a fiscal consolidation may affect the future
incentives to default and therefore have a muted effect on the price of debt.
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7. Fiscal consolidations and default risk
When the ability to raise revenues is imperfect, fiscal consolidations may only
reduce marginally default risk (bt+1-effect versus τt-effect).
The distortions induced by a fiscal consolidation may affect the future
incentives to default and therefore have a muted effect on the price of debt.
∆ Spread (10 yrs) (1) (2)
∆ Primary Balance -0.120 -0.118
(.031) (.032)
∆ Primary Balance × High-volatilityTC 0.084 0.075
(.034) (.036)
Observations 433 326
Country fixed-effects Yes Yes
Year fixed-effects Yes Yes
Basic controls Yes Yes
Extended controls No Yes
where the ability to raise revenues is captured by the volatility of tax compliance
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8. Plan
We proceed in three steps:
1. We provide stylized facts about fluctuations in tax compliance (TC) and the
ability of governments to raise revenues—dynamic distortions.
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9. Plan
We proceed in three steps:
1. We provide stylized facts about fluctuations in tax compliance (TC) and the
ability of governments to raise revenues—dynamic distortions.
2. We embed the distortions arising from the imperfect ability to raise
revenues in a plain-vanilla Eaton and Gersovitz [1981] sovereign debt model
with:
an internal constraint arising from imperfect tax enforcement,
an external constraint related to limited commitment.
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10. Plan
We proceed in three steps:
1. We provide stylized facts about fluctuations in tax compliance (TC) and the
ability of governments to raise revenues—dynamic distortions.
2. We embed the distortions arising from the imperfect ability to raise
revenues in a plain-vanilla Eaton and Gersovitz [1981] sovereign debt model
with:
an internal constraint arising from imperfect tax enforcement,
an external constraint related to limited commitment.
3. We calibrate the model using empirical estimates for the elasticity of tax
compliance and we assess its ability to reproduce:
(i) the sensitivity of debt prices to policy shocks,
(ii) the dynamics of fiscal policies for high-debt levels, and the occurrences
of periods of high tax rates, high tax evasion and high default risk
(austerity trap or tax evasion overhang),
(iii) the cyclical property of fiscal policies across different environments.
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11. Related literature
Sovereign default and fiscal policy: Eaton and Gersovitz [1981]; Aguiar
et al. [2005]; Aguiar and Gopinath [2006]; Arellano [2008]; Cuadra et al.
[2010]; Bi [2012]; D’Erasmo and Mendoza [2013]; Arellano and Bai [2016];
Dovis et al. [2015].
Cyclicality of fiscal policies: von Hagen and Harden [1995]; Aaron Tornell
[1999]; Kaminsky et al. [2004]; Ilzetski and Vegh [2008]; Cuadra et al. [2010];
Frankel et al. [2013]; Vegh and Vuletin [2015].
Tax evasion in the recent crisis: Pappa et al. [2015]; Pappadà and
Zylberberg [2017].
Fiscal fatigue: Ghosh et al. [2013]; Dovis et al. [2015].
Defaults and distortions: Mendoza and Yue [2012]; Bocola [2016].
Fiscal multiplier: Alesina and Ardagna [2009]; Romer and Romer [2010];
Favero et al. [2011]; Auerbach and Gorodnichenko [2012]; Ilzetzki et al.
[2013]; Alesina et al. [2015].
Informal sector: Rauch [1991]; Enste and Schneider [2000]; Straub [2005];
Pomeranz [2015].
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13. A measure of tax compliance
ti,t,c denote VAT revenues collected on good i in year t and country c,
τi,t,c the VAT rate,
ci,t,c the reported consumption.
Our measure γt,c of VAT compliance is defined as:
γt,c = i ti,t,c
i τi,t,cci,t,c
γt,c measures discrepancies between two different sources of
declaration—VAT revenues and consumption.
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14. Data description
Data sources:
1. VAT revenues as declared by the National Tax Authorities,
2. household consumption collected by National Statistics (Income,
Expenditure and Wealth questionnaires),
3. a catalogue of VAT rates.
Coverage: 35 (mostly European) countries, unbalanced panel between 1990
and 2014, 48 good sub-categories.
Adjustments (VAT rates):
we smooth the “high-frequency” measurement error, i.e., reforms during
the year and seasonal adjustments,
some tax reforms do not modify rates but also modify the category of
goods that are subject to the different tax regimes,
some reforms modify the tax environment without modifying the tax rates
per se.
Sources , VAT rates
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18. Empirical strategy
We estimate the following baseline specification:
∆ ln γtc = εzytc + βXtc + δt + µc + εtc,
where t indexes the period (year) and c stands for the country.
ytc captures economic conditions, i.e., the HP-filtered growth of GDP per
capita, or the change in standard/effective VAT tax rate,
the vector X includes some time-varying controls, such as the existence
of concurrent tax reforms, the lagged measures of tax compliance and
lagged GDP per capita,
νt captures time fixed-effects,
γc captures country fixed-effects,
εtc is the error term with standard errors clustered at the country level.
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19. 1. Tax compliance and the business cycle
Tax compliance fluctuates markedly with the cycle, especially among the
group of high-volatility countries.
Tax compliance (1) (2) (3) (4)
GDP growth .392 .395 .408 .401
(.108) (.124) (.124) (.139)
Observations 602 524 524 419
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Tax compliance (1) (2) (3) (4)
GDP growth .018 .060 .083 .022
(.146) (.157) (.159) (.167)
GDP growth × High-volatility .582 .565 .545 .637
(.157) (.167) (.168) (.171)
Observations 602 524 524 419
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
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20. 2. Tax compliance and tax rates
Tax compliance decreases in response to tax hikes, especially among the
group of high-volatility countries.
VAT compliance (1) (2) (3) (4)
VAT rate -.368 -.385 -.379 -.371
(.055) (.057) (.057) (.081)
Observations 539 477 477 385
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Tax compliance (1) (2) (3) (4)
VAT rate -.110 -.115 -.104 -.053
(.116) (.121) (.121) (.136)
VAT rate × High-volatility -.327 -.341 -.347 -.477
(.130) (.137) (.137) (.165)
Observations 539 477 477 385
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Effective rate , Developed
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23. Summary
VAT compliance responds to economic conditions, and these fluctuations
are persistent.
We can identify two types of economies:
low-volatility with stable tax compliance,
and high-volatility with responsive tax compliance.
The model describes the implications of such dynamic distortions on
default risk.
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25. Environment
Two frictions:
imperfect commitment from the government to reimburse its debt
which limits the government capacity to transfer consumption,
imperfect tax enforcement, i.e., the government cannot implement
non-distortive payments from/to the household.
The framework is otherwise standard:
small open economy,
representative household,
and a government financing an exogenous public good, and issuing debt
on the household behalf.
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26. Preferences
The economy is populated by a continuum of infinite-lived households of
measure one.
Letting ct denote her consumption at time t, the representative household
maximizes:
Et
∞
s=0
βs
u(ct+s),
where β < 1 denotes the discount factor and u(·) represents the utility
function, which satisfies u (·) > 0 and u (·) < 0.
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27. Technology
There is one consumption good, which can be produced with two
technologies:
1. it can be assembled by final good producers using investment goods,
y = z
1
0
yφ
i di
1
φ
,
where φ < 1 captures production complementarity and z is an
aggregate technology shock.
This technology represents the formal sector (fully transparent).
2. the final good can be directly produced by entrepreneurs transforming
their product variety yi into the final good using a private technology with
unobservable return R and distributed along H(.).
This technology is not taxed and represents the informal sector.
In each period, with probability 1 − θ, the entrepreneur can freely decide to
sell her unit to the final good producer or use her private technology. more
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28. Government
There is a benevolent government whose objective is twofold:
finance a public good whose cost g is exogenous and subject to shocks,
maximizes the welfare of the representative household by issuing debt
and purchasing assets on its behalf.
There is imperfect tax enforcement:
the government levies indirect taxes τ on final output,
the government is not able to collect taxes on the goods directly
produced by entrepreneurs (informal sector).
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29. Financial markets
Financial markets: the government can issue and trade one-period bonds,
and the international financial market is willing and able to purchase any
asset that yields an expected return at least as high as ρ = 1/β.
Let bt+1 and qt+1 respectively denote the amount and price of debt issued by
the government at time t. The resource constraint for the government is:
(1 − Dt)bt − qt+1bt+1 = tt − gt.
Default: the government has imperfect commitment. We assume that there
are two defaults costs,
as in Arellano [2008], there is credit exclusion from markets after default
with a reintegration probability ν,
an exogenous default cost δ is incurred by the household during market
exclusion.
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30. Timing
At the beginning of each period, the government starts the period with
assets bt and the aggregate shock zt is revealed and perfectly observed
by all agents. For excluded governments, there is a reintegration draw.
The government decides to repay or default, and commits to an indirect
taxation rate τt. Production takes place and taxes are paid by agents.
International financial markets open and sovereign bonds are traded.
The government finances the public investment and households
consume.
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31. The government program
v(ht, st) = 1ht=AvA(st) + 1ht=EvE(st),
where st = (ht, bt, γt−1, Rt−1, zt, gt)
vA(st) = max
Dt,bt+1,γt,Rt
{u (wt − Dtδ) + β(1 − Dt)EtvA(st+1) + βDtEtvE(st+1)} ,
vE(st) = (1 − ν) (u(wt − δ) + βEtvE(st+1)) + ν max
bt+1,γt,Rt
{u (wt) + βEtvA(st+1)} ,
subject to
(1 − Dt)bt − qt+1bt+1 = tt − gt budget
qt+1 = βEt [1 − Dt+1|bt+1, γt, zt, gt] debt price
Rt = (1 − θβ)rt + θβEtRt+1 transparency
where Rt = H−1 γt − θγt−1
1 − θ
, and rt = ztγ
1
φ
−1
t − tt/γt.
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32. Fiscal policy and default risk
1. An increase in tax rates leads to higher fiscal surplus (bt+1-effect).
2. An increase in tax rates also
lowers the contemporary return rt to the formal sector,
affects the indifference threshold between the formal and the informal
sector,
with staggered technological choices, this reponse is persistent and
increases the future costs of raising tax revenues,
investors incorporate this risk in debt prices.
The last effect (γt-effect) reduces the returns to fiscal consolidations.
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33. Fiscal policy and default risk
1. An increase in tax rates leads to higher fiscal surplus (bt+1-effect).
2. An increase in tax rates also
lowers the contemporary return rt to the formal sector,
affects the indifference threshold between the formal and the informal
sector,
with staggered technological choices, this reponse is persistent and
increases the future costs of raising tax revenues,
investors incorporate this risk in debt prices.
The last effect (γt-effect) reduces the returns to fiscal consolidations.
Both the bt+1 and γt-effects play a role and this has three implications:
1. default risk is less sensitive to fiscal policy,
2. optimal fiscal policy may be (weakly) pro-cyclical,
3. the dynamics of the system is stable.
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34. Fiscal multiplier
We can derive a simple formula for the fiscal multiplier:
∂ct
∂tt
= −1 +
rt
φ
− Rt
∂γt
∂tt
when taxes are distortive and entrepreneurs respond (∂γt/∂tt < 0),
consumption drops even further
when complementarities are high in the formal sector (φ is low), there
are large differences between the social returns in the formal and
informal sectors at equilibrium and transparency sharply responds to
changes in fiscal surplus.
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36. Calibration and solution method
Calibration:
We set all parameters (but the technological ones) as is standard in
models of sovereign defaults [Aguiar and Gopinath, 2006; Arellano,
2008].
We estimate the production parameters by matching: (a) the tax
compliance level, (b) the elasticity of tax compliance to tax rate, and (c)
the auto-correlation of tax compliance Moments .
Discretization: We create grids for each of the state variables. AR(1)
processes are discretized using Tauchen [1986].
Solution method: We solve numerically the model as a fixed point problem,
we set two policy functions s → γ(s) (future transparency) and s → q(s)
(future expected default),
given s → γ(s) and s → q(s), we solve the dynamic problem of the
government through value function iteration,
we update the policy functions and we iterate until convergence.
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37. Parameters
Parameter Value Rationale
Preferences
Discount factor β 0.90 Aguiar and Gopinath [2006]
Risk-aversion (CRRA) s 2 Arellano [2008]
Production
Risk-free interest rate ρ 0.015 Arellano [2008]
Distribution (informal) a1 -0.12 steady-state tax compliance
Distribution (informal) a2 0.91 steady-state tax compliance
Complementarities φ 0.9 elasticity of tax compliance
Probability to set technology θ 0.45 persistence of tax compliance
Default
Probability of reintegration ν 0.04 Arellano [2008]
Output cost δ 0.02 Arellano [2008]
Shocks
TFP z, autocorrelation ρz 0.8 GDP autocorrelation
TFP z, standard deviation σz 0.03 GDP volatility
Expenditures g, autocorrelation ρg 0.8 Spending autocorrelation
Expenditures g, standard deviation σg 0.03 Spending volatility
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40. Simulated and empirical moments (in progress)
Our objective is to explore how fluctuations in tax compliance
(i) affect the impact of fiscal consolidations on default risk and debt prices,
(ii) contribute to the existence of an austerity trap or tax evasion overhang,
(iii) rationalize the differences in dynamics of (optimal) fiscal policies across
countries?
Along with the baseline economy, we run three different counterfactuals:
Experiment I refers to a low-type economy
Experiment II shuts down the tax compliance channel by keeping fixed
the transparency choice
Exp. III shuts down the default channel by decreasing the probability of
reintegration
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41. Simulated moments under different scenarios (in progress)
Description Benchmark Exp. I Exp. II Exp. III
Elasticity of tax compliance to tax rates -0.30 -0.40 0 -0.30
Average default 0.027 0.272 0.123 0.013
Average default (high debt) 0.029 0.978 0.215 0.020
i) Austerity trap
Occurrences 0.232 0.200 0 0.207
Average length AT episodes (years) 1.215 1 – 1.174
Exit AT is a default 0.026 0.990 – 0.039
ii) Fiscal policy
Corr. tax rate/output -0.482 -0.139 0.075 -0.327
Corr. tax rate/output (high debt) -0.553 -0.149 0 -0.627
iii) Primary Balance and spread
Corr. PB/spread 0.033 0.032 -0.169 -0.048
Corr. PB/spread in FC -0.018 0.049 -0.253 -0.123
Corr. PB/spread in FC and high debt -0.010 0.077 -0.218 -0.185
Exp. I refers to a low-type economy
Exp. II shuts down the tax compliance channel
Exp. III shuts down the default channel
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42. Concluding remarks
The fluctuations of tax compliance generate distortions in the collection of
tax revenues:
tax compliance fluctuates markedly with tax reforms, especially among
a group of high-elasticity countries
The distortions generated by elastic tax compliance:
increase the probability to default on sovereign debt
and therefore decrease fiscal space
High-elasticity countries face:
an internal constraint: increasing taxes reduces tax compliance and this
has persistent effects on the economy (dynamic effect on future output)
an external constraint: imperfect tax compliance increases the interest
rates on sovereign debt
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44. An example of VAT reforms : Greece (2010-2011)
Source : Pappadà and Zylberberg [2017]
back
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45. Data description : 1. VAT revenues
For European Union countries, data on tax revenues are collected centrally by
Eurostat under the European system of national and regional accounts (ESA
2010) transmission programme.
European Union member states are legally obliged to transmit this information for
each individual tax (we focus on category D.211: Value added type taxes (VAT))
For non-EU/OECD members, we take advantage of the OECD Model Tax
Convention to collect revenues from the category Value added type taxes (VAT).
back
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46. Data description : 2. Household consumption
In countries complying with the ICLS Resolution on household income and
expenditure statistics (2003), household consumption is collected by statistical
office using integrated surveys including Income, Expenditure and Wealth
questionnaires.
There are several measurement issues arising with these surveys:
1. there may exist a difference between the time of acquisition and the time of
use / some statistical offices may use fixed reference periods, others moving
reference periods
2. expenditure may be computed as an accounting variable, i.e., a purchase
value or a payment approach, or a consumption costs approach estimating
the service flow from the good acquisition. In most cases, statistical offices
use the payment approach which fits our purposes
3. goods may be consumed gradually and be durable or semi-durable.
The scope of the survey and the sampling design are less problematic : sample
size and questions are designed such as to provide precise estimates for the
baskets of goods and services, which is also our variable of interest.
back
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47. Data description : 3. Value-added tax rates
We collect VAT rates and we reference the types of goods (at the 2 digit level) that
are subject to these rates for each country/year, taking into account goods subject
to reduced rates or exemptions.
For European Union members, we use two administrative sources, i.e., the
European Commission and Eurostat, to construct the monthly VAT rates for about
80 expenditure categories since 2005. We complete this dataset for European
Union members before 2005 and all countries by using national sources. This
exercise requires some harmonization across expenditure categories in different
accounting systems.
Among the sample of 35 countries, we can identify 65 major VAT reforms implying
changes in VAT rates larger than 5%:
45 of these reforms are associated with an increase in the effective VAT rate
20 reforms imply lower effective rates
back
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48. Robustness 1
VAT compliance (1) (2) (3) (4)
VAT rate -.442 -.442 -.437 -.412
(.046) (.050) (.050) (.069)
Observations 539 477 477 385
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Tax compliance (1) (2) (3) (4)
VAT rate -.380 -.288 -.279 -.190
(.086) (.105) (.121) (.127)
VAT rate × High-volatility -.084 -.195 -.201 -.307
(.097) (.118) (.118) (.147)
Observations 539 477 477 385
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Back
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49. Robustness 2
VAT compliance (1) (2) (3) (4)
GDP growth -.006 .069 .092 .063
(.160) (.174) (.175) (.188)
GDP growth × High-volatility .657 .611 .589 .753
(.160) (.171) (.172) (.181)
GDP growth × Industrial .008 -.017 -.012 -.114
(.168) (.183) (.182) (.191)
Observations 558 485 485 392
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Tax compliance (1) (2) (3) (4)
VAT rate -.089 -.154 -.136 -.374
(.151) (.168) (.168) (.229)
VAT rate × High-volatility -.334 -.311 -.319 -.225
(.134) (.143) (.143) (.209)
VAT rate × Industrial -.044 .034 .023 .318
(.112) (.122) (.123) (.199)
Observations 558 485 485 392
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
Back
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50. Tax policy
Tax policy is pro-cyclical in high-elasticity countries
VAT effective rate (1) (2) (3) (4)
Cycle -.335 -.292 -.285 -.292
(.081) (.096) (.103) (.103)
Observations 603 476 421 421
Fixed effects Yes Yes Yes Yes
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
VAT effective rate (1) (2) (3) (4)
Cycle -.338 -.346 -.316 -.326
(.133) (.138) (.127) (.145)
Cycle × High-elasticity -.201 -.174 -.255 -.245
(.133) (.137) (.133) (.144)
Observations 603 476 421 421
Fixed effects Yes Yes Yes Yes
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
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51. Tax policy
In developed countries, it is acyclical back
Correlation with cycle (1) (2) (3) (4)
A: VAT rate -.059 -.161 -.130 .010
(.112) (.139) (.143) (.099)
[613] [371] [371] [228]
B: Corporate rate .155 -.014 -.007 .118
(.108) (.184) (.191) (.245)
[504] [328] [328] [200]
C: Individual rate .184 .003 -.050 -.122
(.154) (.203) (.211) (.147)
[447] [318] [318] [199]
Fixed effects Yes Yes Yes Yes
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
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52. Tax policy
In developing/peripheral countries, it is pro-cyclical back
Correlation with cycle (1) (2) (3) (4)
A: VAT rate -.296∗∗∗
-.352∗∗∗
-.353∗∗∗
-.255∗∗∗
(.049) (.058) (.058) (.068)
[1386] [1092] [1091] [601]
B: Corporate rate -.097 -.024 -.025 -.228∗∗
(.075) (.082) (.082) (.103)
[920] [770] [769] [422]
C: Individual rate -.171∗∗
-.113 -.105 -.084
(.083) (.091) (.090) (.152)
[876] [710] [709] [383]
Fixed effects Yes Yes Yes Yes
Sectoral composition No Yes Yes Yes
Trade No No Yes Yes
Government expenditures No No No Yes
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53. Final good producers and entrepreneurs
Program of final good producers:
max
yi
z(1 − τ)
1
0
yφ
i di
1
φ
−
1
0
piyidi .
The resulting demand is characterized by the following equation:
z(1 − τ)yφ−1
i
1
0
yφ
i di
1
φ
−1
= pi.
The aggregate transparency γt, i.e. the share of entrepreneurs operating in
the formal sector, verifies the following dynamics:
γt = (1 − θ)γ∗
t + θγt−1
where γ∗
t is the share of entrepreneurs deciding to operate in the formal
sector among entrepreneurs with the opportunity to modify their technology.
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54. Technological choice
Entrepreneurs compare the returns in the formal sector to the returns in the
informal sector and are indifferent when:
∞
k=0
δt+krt+k =
∞
k=0
δt+kR
where:
rt+k = (1 − τt+k)zt+kγ
1
φ
−1
t+k is the expected price for one unit of variety i in
the formal sector in period t + k
δt+k = βk
θk
Et
u (ct+k)
u (ct)
is the (effective) discount factor between period t
and t + k
R is the unobserved individual return to the private technology
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55. The dynamics of aggregate transparency
The share of entrepreneurs adopting the formal technology is equal to the
ones with sufficiently high returns in the formal sector:
γ∗
t = H
∞
k=0 Etδt+krt+k
∞
k=0 Etδt+k
.
We can then replace γ∗
t and γ∗
t+1 and obtain an equation describing the
(sluggish) dynamics for aggregate transparency and distortions in the
production side of the economy :
γt − θγt−1
1 − θ
= H (1 − θβ)rt + θβEtH−1 γt+1 − θγt
1 − θ
.
back
48/ 35
56. Matched moments
We calibrate the three parameters θ, φ, λ in order to match at the steady-state:
1. the aggregate tax compliance:
γ = H (1 − τ)γ
1
φ
−1
,
2. the elasticity of tax compliance:
∂γ
∂τ
= −
(1 − θ)(1 − θβ)γ
1
φ
−1
h[H−1(γ)]
1 + θ2β − (1 − θ)(1 − θβ)(1 − τ)γ
1
φ
−2 1
φ
− 1 h[H−1(γ)]
,
3. the persistence of tax compliance:
∂γ
∂γ
=
θ
1 + θ2β − (1 − θ)(1 − θβ)(1 − τ)γ
1
φ
−2 1
φ
− 1 h[H−1(γ)]
,
The distribution of returns in the informal sector is set to be equal to H(x) = 1 − e−λx.
back
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57. Extreme cases
When the government has perfect commitment, the solution verifies a slightly
modified Euler equation λt = Etλt+1 where:
λt = −
∂wt/∂γt
∂tt/∂γt
u (wt) − β
1
∂tt/∂γt
Et
∂vA(st+1)
∂γt
.
The first term is the marginal utility of consumption weighted by a discount factor
accounting for leakages.
The second term captures the expected future gains of a marginal increase in tax
compliance.
The leakages implied by taxes depend on the elasticity εγ < 0 of the formal sector size
γ to taxes as follows:
−
∂wt/∂γt
∂tt/∂γt
=
1 − 1−τt
τt
1−φ
φ
εγ
1 + 1
φ
εγ
.
Optimal fiscal policy is counter-cyclical.
When the government has zero commitment, then it needs to satisfy in each period a
balanced budget and
tt = gt,
which implies a pro-cyclical fiscal policy.
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58. Episodes of fiscal consolidation and default risk
Episodes of fiscal consolidation are associated with high default risk in
high-elasticity countries.
high elasticity low elasticity
Fiscal consolidation Yes No Yes No
Default episodes .084 .026 .000 .000
[.050] [.000]
Average interest rate (%) 7.96 5.58 5.03 4.58
[6.74] [4.79]
Average debt/GDP 67.97 49.19 53.93 53.23
[57.04] [53.58]
51/ 35
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