Tax evasion, tax progression, and efficiency wages

Tax evasion, tax progression, and efficiency wages

Economics Letters 82 (2004) 35 – 42 Tax evasion, tax progression, and efficiency wages Laszlo Goerke * Department of...

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Economics Letters 82 (2004) 35 – 42

Tax evasion, tax progression, and efficiency wages Laszlo Goerke * Department of Economics (FB 03), Johannes Gutenberg-University Mainz, IZA (Bonn), and CESifo (Mu¨nchen), 55099 Mainz, Germany Received 17 August 2000; received in revised form 02 December 2002; accepted 30 July 2003

Abstract More progressive taxes raise employment in imperfect labour markets. However, this prediction is not robust. For example, any employment effect vanishes in a constant profit efficiency wage economy. It is demonstrated that tax evasion opportunities can re-establish positive employment effects of higher tax progression. D 2003 Elsevier B.V. All rights reserved. Keywords: Efficiency wages; Employment; Income tax; Tax evasion; Tax progression JEL classification: H 24; H 26; J 41

1. Introduction More progressive taxes raise employment in imperfect labour markets. However, if, for example, labour supply is endogenised, workers are heterogeneous or profits cannot vary, this relationship between tax progressivity and labour market performance may not hold.1 In this paper, the consequences of allowing for tax evasion are investigated. The analysis is conducted in a benchmark setting, a constant profit efficiency wage economy with an endogenously determined number of firms. In this benchmark economy, an increase in tax progression has no employment effects in the absence of evasion opportunities. Hence, any positive employment impact is solely due to tax evasion. This paper shows that employment will expand if the penalty for evasion depends at least in part on the undeclared income, rather than solely on the amount of taxes evaded. In this case, more progressive taxes raise the gain from evasion. The worker’s income rises and s/he provides higher effort. Wages can * Tel.: +49-6131-39-20143; fax: +49-6131-39-23827. E-mail address: [email protected] (L. Goerke). 1 For the basic result, see, e.g. Hoel (1990) and Lockwood and Manning (1993). Andersen and Rasmussen (1999), Fuest and Huber (2000), Goerke (2000), Hansen et al. (2000), and Rasmussen (2002) analyse the extensions. 0165-1765/$ - see front matter D 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2003.07.013


L. Goerke / Economics Letters 82 (2004) 35–42

be lowered, new firms enter the market and employment increases. Accordingly, tax evasion can represent a mechanism by which the progressivity of the tax system affects the behaviour of workers and, hence, employment outcomes. Section 2 presents the model, while Section 3 analyses the employment consequences of more progressive taxes. Since these effects depend on the nature of the penalty function, Section 4 looks at real world penalties. Section 5 concludes. Apart from analyses of tax progression in imperfect labour markets, this paper is related to two further strands of literature: tax evasion in efficiency wage models has been looked at by Watanabe (1996), Chang and Lai (1996) and Lai et al. (1999). These authors do not analyse tax progression. The impact of tax progression on evasion has been analysed by Koskela (1983a,b) and Trandel and Snow (1999), inter alia. In those papers, a given wage or a competitive labour market is presumed.

2. Model In the economy, there are a fixed number of workers whose only source of income are wages w and who can evade income taxes. Employed workers maximise their expected utility by choosing tax evasion activities. The (indirect) utility function v is strictly concave in net income, vV> 0, vW< 0. With an exogenous probability 1  p, a worker evades taxes successfully and the net income becomes ye u w  (w  s)t(1  h), where s is the level of tax exemption, 0 < s < w, t the marginal income tax rate, 1 > t > 0, and h the degree of tax evasion, 1 z h z 0. With the probability p, a worker is caught evading taxes, has to pay a penalty F˜(), and obtains an income yc u ye  F˜(). In the economic analysis of tax evasion, two penalty functions have almost exclusively been analysed. Either the penalty is an increasing function of undeclared income (w  s)h (Allingham and Sandmo, 1972) or of evaded taxes (w  s)th (Yitzhaki, 1974). To merge the approaches, a general penalty function F˜() is assumed which depends on a linear combination of evaded taxes and undeclared income, the relative importance of the former being measured by a parameter b, 0 V b V 1, such that F˜() u F [(w  s)h(1  b + bt)]. The expected utility U(h) of an employed worker becomes: UðhÞ ¼ ð1  pÞvðye Þ þ pvðyc Þ


If tax evasion choices are unrestricted, the maximisation of Eq. (1) with respect to h implies: Huðw  sÞðð1  pÞv Vðye Þt þ pv Vðyc Þ½t  Fð1  b þ btÞÞ ¼ 0


An interior solution requires, inter alia, t(1  Fb) < F(1  b), such that the ensuing restriction on F varies with the penalty system, i.e. the value of b, while the second-order condition entails Hh < 0. The variations in the optimal degree of evasion h*, owing to a higher level of tax exemption s or the marginal income tax rate t, are governed by: Ht ¼ ð1  pÞv Wðye Þtðw  sÞð1  hÞ þ ð1  pÞvVðye Þ þ pv Vðyc Þð1  bFÞ  ðw  sÞ ws ð pvWðyc Þ½t  Fð1  b þ btÞ½1  h þ FbhÞ Hs ¼ ð1  pÞvWðye Þt 2 ð1  hÞ þ pv Wðyc Þ½t  Fð1  b þ btÞ½tð1  hÞ þ Fhð1  b þ btÞ ws

ð3Þ ð4Þ

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Given withholding regulations, workers might be unable to choose evasion optimally and may only be able to select a value of h such that h < h*, while they cannot adjust their evasion activities to a change of tax progression. Both cases, an optimally chosen (h = h*) and an exogenously given degree of tax evasion (h < h*) are investigated below. This distinction proves to have an impact on the employment consequences of more progressive taxes. In the framework set out above, a worker’s effort is determined by an exogenously given effort function e. Since the impact of tax evasion on work effort is not well documented, two distinct functions are considered. Effort e is assumed to increase with the unemployment rate u(eu > 0) and to be either a function of the income ye in the case of successful tax evasion, e = e˜( ye, u), or alternatively of the expected utility if employed U, e = eˆ(U, u). The rationale for the effort function e = e˜( ye, u) is that a penalty on which the firm has no (direct) influence does not affect the worker’s performance. The second specification, e = eˆ(U, u), will be more appropriate if expected utility determines effort, irrespective of its source. The effort functions are strictly concave in their first arguments and wages w(ey e, eU, ew > 0, ey ey e, eUU, eww < 0, where subscripts indicate partial derivatives). To make results, furthermore, comparable to those of other studies on the employment consequences of more progressive taxes, which generally assume that the equilibrium wage declines with unemployment u, entailing dw/du = (eu  wewu)/(weww) < 0 (cf. Hoel, 1990), for simplicity the cross-derivatives are assumed to be zero, i.e. e˜yeu = eˆUu = 0 is presumed. In the economy, there are many ex-ante identical firms with a constant capital stock and a production function f which is strictly concave in efficiency units of labour, f V(en) > 0, f W < 0, n being employment per firm. The output price of the homogeneous good is unity. As usual in simple efficiency wage models, firms choose wages and employment optimally (Solow, 1979), such that wages are determined by the Solow-condition, e  wew = 0. In addition, in the present setting the number of firms is endogenous and regulated by a constant or zero profit situation. However, entry and exit decisions are not modelled. Instead, labour demand is determined by the profit constraint p = 0.

3. More progressive income tax system In a setting without tax evasion opportunities, an increase in tax progression, i.e. a combined rise of the marginal income tax rate t and the level of tax exemption s, holding constant taxes at the original wage, will lower unemployment if firms are profitable, while there will not be any employment effect in the case of constant profits (Goerke, 2000). Thus, if a zero profit constraint is combined with a constant level of statutory tax payments (w  s)t at the initial wage, any employment effect of tax progression is attributable entirely to tax evasion opportunities. The economic system which governs the employment effects of higher income tax progression is defined by the Solow-condition e  wew = 0 and the profit constraint p = 0. The level of tax exemption s represents the policy parameter. Total differentiation, taking into account that the marginal income tax rate t varies with the level of tax exemption s to allow for constant statutory tax payments, such that dt/ ds = t/(w  s), while w and u are the endogenous variables, yields: 2 6 4

weww 0

eu f Veu n

32 76 54

dw du



7 6 5¼4

dt es þ wews  ðet  wewt Þ ds

  dt f Vn es þ et ds

3 7 5½ds



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Accordingly, the unemployment effect of a more progressive tax system is given by: du Z ¼ ; where Zues ðw  sÞ þ tet ds ðw  sÞeu


The sign of Z depends, inter alia, on the nature of the effort function. If effort is determined by the income of successful evasion, e = e˜ ( ye, u) will hold, and et and es are found to be: et ¼ eey e ðw  sÞðtht*  ð1  hÞÞ


es ¼ eey e t ðð1  hÞ þ ðw  sÞhs*Þ


In Eqs. (7) and (8), the derivatives of h* represent the adjustment in the optimal degree of tax evasion. For an exogenously given degree of tax evasion (dh = 0), the terms involving these derivatives will drop out if the optimal value of h subsequent to the tax reform is still above the feasible degree of evasion. From Eqs. (6)–(8), it can then be seen by setting h = dh = 0, i.e. by assuming a framework without evasion opportunities, that there is no change in employment due to an increase in tax progression. Hence, the employment effects of higher tax progression in a world with an exogenously given degree of tax evasion (h < h*) are the same as in a setting without tax evasion. The intuition for the equivalence is that the tax reform does not alter effort due to the assumption of a given tax level. Moreover, there is no effect of tax progression on evasion—since dh = 0 by assumption. Hence, effort is unaffected, while profits and employment remain constant. Assuming optimal evasion activities, the unemployment effect of higher tax progression becomes: Z

eeye ððw  sÞHs þ tHt Þðw  sÞt Hh w  s3 teeye ðw  sÞ2 t 2 eeye pvWðyc Þ½t  Fð1  b þ btÞFhð1  bÞ  ¼ Hh Hh e c fð1  pÞvVðy Þ þ pvVðy Þð1  bFÞg > 0; if b < 1

je¼eeðye ;uÞ;h¼h* ¼ eeye ððw  sÞhs* þ tht* Þðw  sÞt ¼ 


If the penalty depends at least in part on undeclared income (b < 1), an interior solution to the evasion problem (cf. Eq. (2)) ensures that the term in square brackets subsequent to the last equality sign in Eq. (9) is negative, while the expression in curly brackets is greater than zero. Accordingly, the optimal degree of tax evasion h* rises because a more progressive income tax reduces the penalty.2 Higher tax evasion increases the income of successful evasion ye and thereby effort, implying Z >0 and du/ds < 0. Greater effort allows firms to reduce the wage and to increase employment. In an efficiency wage economy with variable profits but without tax evasion, higher statutory tax progression at the initial wage reduces the firm’s incentives to raise wages, because the increase in effort 2 This can be seen most clearly by rewriting the penalty as F˜() = F *h[b(w  s)t + (1  b)(w  s)] and is due to the fact that an increase in the level of tax exemption s lowers undeclared income. For a given statutory tax burden (w  s)t and a given degree of evasion h, the penalty declines. See also Koskela (1983b) who shows for a model with exogenous income that tax evasion will rise with an increase in tax progressivity if the fine is a function of undeclared income, and the government’s expected tax revenues or the worker’s expected utility are held constant.

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due to higher wages is mitigated by the higher marginal income tax rate. Lower wages result in a reduction of effort and in lesser profits and greater employment. If firms face a zero profit constraint, the reduction in profits causes some firms to leave the market such that unemployment rises until profits have attained their original level again. A new equilibrium is arrived at the old level of employment, with fewer firms each having more workers (Goerke, 2000). In the presence of tax evasion, the change in statutory tax progression induces workers to provide more effort at a given wage and unemployment level for b < 1, because evasion activities intensify. Thus, profits rise. Employment increases until profits have fallen to the pre-tax reform level of zero. Given these differential effects for a model without evasion and a setting with tax evasion opportunities, the employment expansion is solely due to the existence of tax evasion. Turning to the effort function e = eˆ(U, u), the derivatives with respect to tax rates are given by: et ¼ ˆeU ðw  sÞ½ð1  pÞv Vðye Þð1  hÞ þ pvVðyc Þf1  h þ Fbhg þ eˆ U Hht*


es ¼ eˆ U ½ð1  pÞvVðye Þtð1  hÞ þ pvVðyc Þftð1  hÞ þ Fð1  b þ btÞhg ¼ eˆ U Hhs*


Using Eqs. (6), (10), and (11), the change in unemployment due to higher tax progression is found to be: du eˆ U pvVðyc ÞhFð1  bÞ ¼ < 0; ds je¼ˆeðU;uÞ eˆ u

if b < 1


This result is independent of whether evasion choices are optimal or not, since an optimal selection implies H = 0, while an exogenously determined degree of tax evasion entails dh* = 0. Accordingly, the last terms in Eqs. (10) and (11) drop out, irrespective of whether evasion activities, are optimal (h = h*) or exogenously restricted (h < h*). The reason for the positive impact of higher tax progression on employment is that a greater level of tax exemption s affects all payoffs equally. However, if the penalty also depends on undeclared income, implying b < 1, a higher marginal income tax rate t raising the penalty by less than the increase in the level of tax exemption s will reduce it. This implies a lower penalty. Expected income and effort rise. Higher effort allows for a reduction in wages and induces a fall in unemployment. The findings can be summarised as follows: a more progressive income tax system, holding constant the statutory tax level at the initial wage, will reduce unemployment in a constant profit efficiency wage economy if (a) the penalty for tax evasion depends at least marginally on undeclared income and either (b1) effort is a function of the expected utility of an employed worker, or (b2) effort rises with the income of successful evasion while evasion choices are unrestricted.

4. Penalty Systems In order to evaluate whether the first requirement is fulfilled, a look at penalty systems in OECD countries is instructive. The penalties for tax evasion in many countries are comprised of a monetary component for less severe violations of the tax code and potentially imprisonment in the case of


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criminal offences. Since the costs of a prison term are unlikely to change with tax progression, the subsequent exposition concentrates on the monetary penalty. In most countries, this penalty depends on the level of evaded taxes such that the assumption of b = 1 seems to be justified.3 However, in Belgium, Canada, Finland, the Netherlands, Portugal, Spain, and Sweden, for example, minimum fines or lump-sum penalties (co-)exist with fines which increase with the level of evaded taxes. Given that such penalties are related to taxable income (w  s), the resulting penalty may be expressed as F˜1 = F*( fe1(w  s) + (w  s)th), where f is a measure of the minimum fine and e1 describes the impact of taxable income on this fine. In Germany, furthermore, the penalty is calculated as a function of the product of evaded taxes and a measure of the net income, where this measure is not necessarily equivalent to the net income according to tax law. In particular, the net income for the purpose of the calculation of the fine may not include the entire losses due to personal investments which are, however, tax deductible. The idea being that the penalty should be related to disposable income. If e2 depicts tax deductible losses which are considered not to influence disposable income, evaded taxes will equal ((w  s  e2)th), while disposable income will be given by (w  (w  s)t). The penalty can then be expressed as F˜2 = F*[(w  (w  s)t](w  s  e2)th). Moreover, the costs of a tax adviser or lawyer can reduce the tax burden. Let the costs of legal advice in the case of an evasion charge be C, while its tax deductible fraction is denoted e3. The income of a person who has been detected evading taxes is then given by yc = ye  F˜3  F˜2, where the cost component is, for simplicity, viewed as penalty F˜3 u C(1  te3).4 The positive employment effects of higher tax progression in the presence of evasion hinge on the penalty being not solely a function of evaded taxes but also of undeclared income. In terms of the penalty function F˜, this implies b < 1, which is equivalent to the requirement (BF˜/B(w  s)) (w  s) > (BF˜/Bt)t. For the three set-ups discussed above, this equivalent requirement for b < 1 will be warranted if ei > 0 applies, i = 1, 2, 3. Therefore, the case of b < 1 not only pertains to situations in which the penalty is influenced by the undeclared income but also to cases in which the penalty depends primarily on evaded taxes but in which this relationship is blurred by the institutional details of the penalty system. Accordingly, it seems likely that tax evasion opportunities contribute to positive employment effects of higher tax progression in efficiency wage economies.

5. Discussion The employment effects of more progressive taxes in an efficiency wage economy have been analysed in the presence of tax evasion in a setting in which such policy changes have no employment consequences in the absence of evasion. If the penalty for evasion is influenced by undeclared income and tax evasion choices are unrestricted, then a rise in statutory tax progression increases employment and tax evasion can be argued to re-establish the positive employment impact 3

See OECD (1990, pp. 62 – 66), Bobett (2001, various country chapters), Innes (1987, pp. 211 – 225 on Canada), and Joecks (1998, pp 171 – 174 on Germany) for the subsequent information. 4 In Germany, expenses due to the preparation of a tax declaration reduce taxable income. Recently, the Federal Finance Court has ruled that costs which arise because of a tax evasion charge do not represent deductible expenses. However, according costs which are not unambiguously due to the evasion charge, may still be claimed as tax deductible expenses. Therefore, the tax payer’s costs caused by a tax evasion charge remain to some extent tax deductible.

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of more progressive income taxes. If evasion choices are restricted, for example, due to withholding regulations, the employment effects of higher statutory tax progressivity depend on the nature of the effort function. The analysis has presumed a constant level of statutory tax payments at the initial wage level. However, any employment change due to the penalty also being an increasing function of the undeclared income requires adjustments in evasion behaviour and, therefore, in the efficiency wage. Accordingly, constant statutory tax payments neither guarantee the expected income of workers, nor expected tax payments, nor a balanced budget. If an increase in tax progression is combined with the requirement of either constant tax payments or a balanced-budget, the positive employment effects of higher tax progression can no longer be ascertained, even in the absence of tax evasion (cf. Fuest and Huber, 1998; Rasmussen, 2002). This ambiguity is aggravated in the presence of tax evasion because wage changes affect evasion behaviour which, in turn, alters the level of effort. As the impact of tax variations on effort, taking into account direct tax and indirect wage and evasion effects, cannot be determined unambiguously, the employment consequences of tax reforms become uncertain.

Acknowledgements I am grateful to Wolfgang Eggert, Manfred Holler, Burkhart Heer, an anonymous referee, participants of the annual meetings of the Verein fu¨r Socialpolitik in Innsbruck and the International Institute of Public Finance in Prague, and the CESifo Venice Summer Institute on Tax Policy and Labour Market Performance for the excellent comments. I obviously retain full responsibility for all errors and omissions.

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