D
epartment of
E
conomic
S
tudies
University of Naples “Parthenope”
Discussion Paper
No.6/2007
Title: Effect of social contribution evasion on working time allocation: theoretical contribution in a two sector model
Author: *Marco Di Domizio
Affiliation: * Faculty of Political Sciences, University of Teramo
Effect of social contribution evasion on working time allocation:
theoretical contribution in a two sector model
Marco Di Domizio∗+
Faculty of Political Sciences, University of Teramo, Campus of Coste S.Agostino, 64100 Teramo, Italy.
∗ Tel.: +39 0861266783, fax +39 0861266033. E-mail address [email protected].
+ I’m grateful to all participants at the DSE seminar, organized by University “Parthenope” of Naples on
6th November 2006, for helpful comments and suggestions, to Elisabetta Marzano of the University of Naples, to Simone Valente of the University of Zurich and to Prof. Piersanti of the University of Teramo.
1. Introduction
Since the seminal contribution of Allingham-Sandmo (1972) and Yithzaki (1973), the tax evasion has been examined in the literature from different perspectives during the last forty years. The 70s followed prevalently microeconomic approach finding exhaustive answers on the relationship between tax policy and tax evasion. The 80s, using simple macroeconomic models, focused on the relation between tax evasion and tax revenue loss or gain of fiscal authority [Peacock-Shaw (1982), Ricketts (1984), Lai-Chang (1988), Von Zameck (1989)]. The 90's, following tax compliance approach, examined tax behaviour as a result of a “game” played by the taxpayers and the fiscal agency [Andreoni-Erard-Feinstein (1998), Franzoni (1998)]. More recently, the attention moved toward the analysis of the impact of the tax evasion on economic growth. Since the contributions of Braun-Loayza (1994), Roubini-Sala-i-Martin (1995) and Loayza (1996) several papers suggested that the increase of tax evasion (i.e. informal economy) is detrimental to the economic growth, inducing public authority and fiscal agencies to increase the effort in fighting this phenomena. The key role in these models is played by the link between tax revenue loss and public expenditure. For example Caballé-Panades (1997) introducing public expenditure as a productivity inputs in the production function show that an increase of the enforcement policy could have ambiguous effects on growth, which depends on the ability of the enforcement policy to generate resources that can be used to finance public capital formation. Alternatively, entering public goods in the utility function, it can be shown within a dynamic optimizing problem of resources allocation, that the relationship between tax evasion and growth is U-shaped and that the sign depends on the way by which the resources
are reallocated from non-productive public sector to the productive private one [Lin-Yang (2001)].
The paper aims to test the impact of tax evasion on income level and economic growth abstracting from government spending, fiscal revenues and/or public goods arguments. This allows us to neglect relationships between costs of enforcement policy and public collection. This approach follows recent studies on shadow economy focused on the relationships between human capital contribution and long run growth [Carillo-Papagni (2002), Carillo-Pugno (2004)].
In this model we examined tax evasion on paying wages. The main innovation of the paper is the contrast of the prevailing idea that tax evasion and/or shadow economy is the source of opportunities for firms to subtract themselves from competitive regime rules. We adopt, on the contrary, the idea that is the presence of non competitive markets, due to asymmetric information about technology of firms, that creates the opportunity to evade taxes, or in our model, social contributions. The inverse direction of the cause-effect relationship between competitive market regimes and social contribution evasion is the “core” idea from which to start in order to introduce monopolistic bias.
We use a multi-sector supply side model to show that including public expenditure in the production function is not vital to disclose a negative influence of tax evasion on growth since changing the enforcement policy does not influence output through tax revenues. The income level and economic growth are only affected by the re-allocation of working time in the two sectors, following changes in the enforcement parameters of each sectors.
Three results are obtained. First, the enforcement policy results crucial to preserve optimal allocation of working time and the ex-ante horizontal equity of fiscal laws in order to maximize income level. Second, the growth rate can be directly related to the enforcement policy conduced in the non competitive sector if workers use the same learning by doing processes. Third, a non-monotonic function between ex-post tax rate and growth could also be generated.
The paper is organized as follows: section 2 presents the model analysing the long run effect of tax evasion. Section 3 extends the analysis of the impact of tax evasion to the long run taking into account factors influencing economic growth. Section 4 concludes the paper.
2. The standard multi-sector model 2.1 Evading social contributions
The demand side of the economy is modelled in the simplest way: each agent has linear instantaneous utility which depends on consumption, and maximizes the integral of instantaneous payoffs discounted at a constant rate of time preference rate. As in Aghion and Howitt (1992), this assumption aims at isolating demand-side effects in order to concentrate on supply-side determinants of growth process. In this model we focus on the role of labor allocation among different sectors, and analyse the macroeconomic phenomena resulting from the presence of shadow economies that distort inter-sectoral allocation of working time.
The structure of the economy is as follows. The consumption good (taken as numeraire) is produced by the final sector which consists of N firms
(
n=1,2,...,N)
sharing the same constant-returns-to-scale technology. As in Spence (1976) and Dixit and Stiglitz (1977), the final good is produced using labor and J varieties of intermediate goods denoted by K j
(
j =1,2,...,J)
. Intermediate goods are fully consumed in the production process, so that K can be interpreted as a variety of jperishable capital produced using labor. Labor quality is homogeneous, so that workers mobility between sectors occurs without frictions. On the labor demand side, unemployment is ruled out by assuming that population equals total labor force and that labor services are supplied inelastically by each worker. Assuming also zero population growth and normalizing total labor supply to unity, yields
y t k
t L
L = 1− , (1)
where L and y L represent total labor units employed in final and intermediate sector, k
respectively, and subscripts t denotes time. We assume that in the final sector firms act competitively, while in the intermediate one each firm acts as a monopolist. Every final- good producer uses a positive amount of each intermediate goods, so that
∑
= = nN jnt tj k
K , 1 , is the total amount of the j− capital good, where th kjn,t is the
amount of the j− capital good used by the th n−th firm at time t .
We assume that in each sector i
(
i= y,k)
the productivity index A is given at ithe firm’s level and that the production function shows non-decreasing returns in
aggregate input. We denote by
(
)
it i t y t k t i L L t A A
f , , = +1/ the gross growth rate of productivity index A . We than use the function i f to extend the basic framework in a i
variety of directions, so as to model the process of growth in terms of learning-by-doing, human capital accumulation, and knowledge spillovers. Following Ethier (1982)
we also allow for expanding variety due to horizontal innovation treating J as time varying.
2.1.1 Ex-ante tax rates and ex-post wedges
The government levies proportional taxes on labor gross wage paid by each producer. This form of taxation, which is sometimes referred to as “social security contribution”, represents an important share of fiscal revenues in many European Countries, where labor-tax fiscal wedge - i.e. the difference between the unit labor cost and the net wage paid - is non negligible. Modelling this form of taxation in the present model is justified by empirical evidence, which suggests that tax evasion on social contributions, usually associated with the so called “black labor” phenomenon, is huge even in most advanced economies [Schneider-Enste (2000), Schneider (2002)].
Let us denote by τ and y τ the ex-ante tax rate on final and intermediate k
production respectively, and assume that τ is independent from k t
J for simplicity, so
that we do not require necessarily equality between the tax rates in the two sectors < > k y τ
τ . What is crucial is the possibility of inter-sectorsl differences in ex-post tax
wedges coming from the possibility to evade a fraction of the social contributions
burden. 1 Behind that is the assumption of asymmetric information between individual firms and fiscal authorities on the number of employed workers, technological parameters and the effective market size of firm. We assume that the fiscal authorities in each period inspect a sample of firm chosen randomly. As a result each firm in sector i
1 The prevailing idea underlying the paper is to avoid arguments related to the costs of the enforcement
policy affecting the public revenues. To preserve this goal we restrict the fiscal authority to modify the rules in fighting tax evasion with no-cost strategies, as the increase in the penalty rate, or with rationalisation of enforcement activities.
faces a non zero probability of being caught evading i t
µ ∈
( )
0 . We define ,1 i tµ the ratio between the number of inspections and the number of firms in sector i . In addition, following Yithzaki (1974), we introduce a proportional fine on evaded taxes denoted by
1 >
i
ε . The expected profit in period t for firm in sector i can thus be written as
(
i)
t i t i t i t i t t i t r wl τ µ ε π − − 1+ ,where π are revenues from output sales, r are rents paid on no-labor inputs, w is the net wage rate, and l are total labor units employed by the firm in sector i . In each i
sector ex-post tax wedges τ can be defined as
y y y y τ µ ε
τ = , τ =k τkµkεk, (2)
and tax evasion requires τ < . Equation (2) shows that the inter-sectoral allocation of i τi
labor can be distorted by each of the three factors determining the tax wedge, namely
i
τ , µ , and i ε . No inter-sectoral distortions would arise if i τ =y τ k, because in this
case the ratio between unit labor costs in the two sectors would be the same as with no taxes.
2.1.2 Static equilibrium, inter-sectoral labor allocation and the monopolistic bias
Output of the n−th firm in the final sector in period t equals
( )
∑
( )
= − = Jt j t jn y t n y t t n A l k y 1 , 1 , , α α , n=1,2,...,N (3) where y nl indicates labor units employed by the n−th firm and A is external to the y
degree one with respect to private inputs, the final sector may be represented as a single competitive firm (Romer, 1990) and aggregate output equals
( )
∑
= − = Jt j t j y t y t t A L K Y 1 , 1 α α (4) where =∑
n y n y lL . Denoting by w the net wage rate, and by y j
P the unit price of the th
j− capital good, standard profit maximization yields
(
)
(
)
y t t y y t L Y w 1+τ = 1−α ⋅ (5) α α − ⋅ = 1 , , t j y t y t t j K L A P , (6)where the left hand side of (5) is the marginal cost of employed labor in the competitive firm, and (6) represents the demand schedule for each capital good j . Each variety of the intermediate good is produced by a single monopolist: each of the J firms produces t
its variety of capital good using l units of labor according to the linear technology Kj [see Aghion-Howitt (1992)] j K t k t t j A l K , = ⋅ (7)
where A is beyond the firm's control. Denoting by k w the net wage rate, the problem Kj faced by the j− monopolist in each period t is that of maximizing th
(
)
jj k K
K j
jK w l
P − 1+τ taking the demand schedule for K as given. Substituting the j
demand schedule (6) for P and (7) for j l , this problem can be rewritten as Kj
{ }
(
)
j k k K j y y K A K w K L A j j + − − τ α α 1 max 1 (8)The first order conditions are
(
)
( )
α α α τ − = + 1 2 1 j j K y k y k K l L A A w . (9)Perfect competition on labor markets implies that wages are equalized among each intermediate firm, so that we can set K k
w
w j ≡ , and from (9) lKj ≡ for each lk monopolist. Therefore k
t t k t J l
L = and equation (9) becomes
(
τ)
α( )
α α α − − = + 1 1 2 1 k y k y k k L L J A A w . (10)Using equation (7) and denoting by K ≡Kj for each intermediate firms, yields
∑
= =J
j 1Kj JK α
α . Equilibrium aggregate output may thus be rewritten as
( ) ( )
α −α ⋅ ⋅ = y 1 t t k t k t y t t A A L J L Y . (11)Combining (5) and (10) and equating net wage rates wk =wy we have
+ + − = ky y k L L τ τ α α 1 1 1 2 , (12) or, setting k t y t L L = 1− ,
(
)
(
)
(
) (
y)
t k t y t k t L τ α τ α τ α + + + − + = 1 1 1 1 2 2 . (13)From (13) we can see that:
(a) if τ and y τ are constant over time, k Lk Ly is also constant.
(b) if τ =y τ k the inter-sectoral allocation of labor would coincide with that obtained
(c) if τ =y τk the level of aggregate income in the equation (11) is fully determined by
the productivity parameter α , except for the number of intermediates goods J . t
In the previous case the working time allocation in the two sectors is only determined by productivity parameter α . As represented in figure 1, note that working time allocation in the intermediate sector is above the final sector one for a large range of α , even for α =0.5. This means that a fraction of working time allocated in the intermediate sector is more productive than the one spent in the final sector. It depends on the “chain” effect from intermediate sector to the final one due to the assumption of a linear technology in the former.
Figure 1
In general, however, there are at least four reasons to hypothesize the appearance of
asymmetric wedges, when τ ≠y τk:
(i) Discriminatory tax regimes prevailing when ex ante tax rate and/or fines differ
among sectors
[
τ ≠y τk and/or ε ≠y εk]
. This regime may be the result, for instance, ofa different tax policy applied to firms operating in the competitive sector and in the monopolistic sector.
(ii) Aggregate random sampling implying µ ≠y µk. This may happen because the
number of inspections is chosen at the aggregate level, so that the ratio between inspections and the number of firms (per unit of time) in the final sector might be different from the ratio between inspections and the number of firms in the intermediate sector.
(iii) Ability to hide. In this case µ has a different interpretation. If firms can hide a i
caught
( )
µ is lower than i µ~ . Measuring the ability to hide social contributions during ian inspection by an index qi∈
[
0,1)
, we can define the probability of being caught asµi =µ~i(
1−qi)
; so that ex-post tax wedges in the two sectors may differ because ofthe ability of monopolists to hide taxes.
(iv) Government optimizing behaviour. Abstracting from productivity factors and the
number of intermediate goods, the current income level is maximized at Lk =α. To reach this goal the tax burden on final sector must be heavier than the one in the intermediate sector, namely
(
1+τk) (
=α1+τ y)
.Since the government has to respect the horizontal equity of fiscal law, by setting ex-ante tax regimes τ = , enforcement policy (e.g. y τk µ ≠y µk and/or ε ≠ ) y εk
in the two sectors could be a way to preserve the (ex-ante) “ethical” prescription of equal tax rate, allowing the income to be at its maximum level.
Points (i) and (ii) do not suggest a particular bias for wedge asymmetries, since discriminatory regimes and aggregate random sampling may determine either τ >y τk
or τ <y τk. Points (iii) and (iv), on the other hand, can be used to introduce a
monopolistic bias, that is a situation of asymmetric tax wedges where τ >y τk. Notice
that point (iii) arises because fiscal inspections often consist of calculations carried over by fiscal authorities, where the amount of tax evasion is evaluated on the basis of estimated technological parameters. This can also explain why for monopolists hide social contributions is easier, since their private knowledge over employed technologies due, e.g. to patent rights. On the contrary in the final sector hiding social contributions
may be more difficult, since perfect competition generally implies a shared common-knowledge technology.
3 Tax evasion, monopolistic bias and growth 3.1 Intra-sectorial spillovers: learning by doing
Turning to economic growth, we can see from (11) that
α α φ − + + + ⋅ ⋅ = 1 1 1 1 t y t t k t k t k t y t t t L L L L f f Y Y , (14)
In order to study the effects of sectoral distortions on the growth rate, we simplify the analysis setting tax wedges constant: i.e. y y
t τ τ = and k k t τ τ = . This implies k t L and y t L
constant as well. To avoid expanding varieties in order to concentrate on learning by doing processes (Lucas, 1988), let us set ≡ +1 =1
t t t
J J
φ for each t and assume that intra-sectoral spillovers take the following form
(
y)
ζ t y t y t y t A A L f = +1 = 1+ , (15)(
k)
σ t k t k t k t A A L f = +1 = 1+ . (16)We can now state proposition 1:
A ceteris paribus increase in Lk Ly reduces the growth rate if
σα ζ ζ σα α α τ τ − − ⋅ − > + + 2 2 1 1 1 2 k y . (17) Proof. Since y y t τ τ = and k k t τ
τ = implies that Lk Ly is constant we can rewrite
(
k) (
ζ k)
ασ t t L L Y Y + − = +1 2 1 , (18)Differentiating (18) with respect to L yields k
(
)
(
) (
)
− − + + − = + k k k k k t t L L L L dL Y Y d 2 1 1 2 1 ζ ασ ασ ζ ,which implies that
(
+1)
<0 k t t dL Y Y d iff ζ σα ζ σα + − > 2 k L . (19) Substituting (13) in (19) yields (17).Proposition 1 defines a necessary and sufficient condition for
(
)
[
d Yt+1 Yt dLk]
<0. Inequality (17) can be met for a wide range of parameters values. Notice that condition (17) holds for any α <0.5 if the learning processes (15)-(16) are identical(
σ = . Condition (17) is also satisfied for a wide range of values within the ζ)
interval ∈ ,1 2 1
α (see Figure 2)2. The restriction σ = may be labelled as a “pure ζ knowledge” assumption, since the learning by doing process takes place at the same rate among homogeneous workers in both sectors.
[Figure 2]
Notice, however, that σ = is not a necessary condition for (17) to be satisfied. Even ζ when σ ≠ , the effect on growth of an increasing number of workers in the ζ intermediate sector is negative. The reason is that y
t
A affects final output linearly,
whereas k t
A affects the growth rate with decreasing returns, since setting labor units
2 Setting σ = (19) is satisfied for about 86.3% of relevant cases. This percentage is obtained solving ζ
the following integral:
∫
+ − − 1 5 . 0 1 1 2 1 α α α d .constant in (14) yields
( )
k α t y t t t Y f fY+1 = ⋅ . This implies that condition (17) is fulfilled for a wide range of elasticity parameters, even if σ > . ζ
An interesting implication of Proposition 1 is that in the presence of the monopolistic bias, fighting tax evasion in the intermediate sector reduces inter-sectoral distortions and is also growth-improving. Under a monopolistic bias τ >y τk, so that if
fiscal authorities modify one (or more) of the three variables τ , k µ , k ε in order to k
raise τ , the ratio k y k L
L decreases and the growth rate increases provided (17) is fulfilled. The growth-enhancing effect of fighting tax evasion in our model relies entirely on inter-sectoral reallocation effects. This explanation is quite different from the “public-budget arguments” put forward by Braun-Loayza (1994) and Loayza (1996). In these contributions, public expenditures are assumed to affect aggregate productivity, and tax evasion is growth-reducing because lower tax revenues reduce public spending. From this perspective our result brings additional support to the idea that fighting tax evasion may be growth-enhancing, and do not require productive public spending and congestion effects.
This result is interesting because it implies a possible trade-off between short and long run objectives. Since in this economy the government sets τ at a level such k
that
(
1+τk) (
<α1+τ y)
(i.e. at high values of monopolistic productivity parameterand/or high values of ex post tax rate on competitive sector) an increase in the enforcement policy rising the ex-post tax rate in the monopolistic sector augments both income equilibrium level and growth rate. On the other hand, if the government has already set the optimal value of τ , being k Lk =α, an increase in the enforcement
4 Summary and conclusion
In this paper we used a standard multi-sector model in which the presence of an intermediate sector, that produces intermediate capital goods exclusively, generates tax evasion taking the form of social contributions evasion on wages. In this model tax burden on monopolistic sector should be lesser than the one set in the final competitive sector, in order to maximize income level. If so, public authorities aiming to preserve the horizontal equity of fiscal law could adapt the enforcement policy in order to reach
ex-post optimal tax burden starting from equals ex-ante tax rates.
From the economic growth point of view it has been shown that when workers in both sectors share the same learning by doing processes there is a high probability (about 86,3%) that an increase in enforcement policy in the monopolistic sector that reduces tax evasion is growth enhancing. Finally it should be noted that there are some parametric range on productivity, spillovers, tax rate, probability of being caught and on penalty rate in which the growth rate is not a monotonic function of ex-post tax rate, disclosing the growth being ambiguously affected by enforcement policy.
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