Profit Tax Evasion under Wage Bargaining Structure

3.1 Characterization of the Solution

As is typical in the right-to-manage approach, ^[12] we assume that the firm and the union bargain over the wage rate w only. The timing of the game is as follows: (i) we set the proportional profit tax rate t and the firm and the union negotiate over the wage rate w; (ii) taking t and w as given, the firm chooses optimal tax evasion S∗ and the employment level L∗. We proceed to solve it by backward induction.

Step 2: Firm’s tax evasion and employment decisions

Taking t and w as given, the firm chooses S and L to solve the following problem:

The first-order conditions of interior solutions are

where ΠS=∂Π/∂Π∂S∂S and ΠL=∂Π/∂Π∂L∂L. We note that the employment level, L, does not enter into eq. [5], which implies the firm’s tax evasion is separable from the employment decision. Equation [6] implies the firm’s employment choice only depends on wage rate if wage bargaining is unavailable (a given wage). This is because (1−t)R′−w can be reduced to R′=w. This is consistent with the findings of Wang and Conant (1988) and Yaniv (1995). From eq. [6], we can derive the following comparative static effects

Equation [7] implies that an increase in the wage rate leads to a decrease in the employment level. In addition, eq. [8] indicates that the change of tax rate has no impact on L∗.

Step 1: Wage bargaining

Anticipating the outcomes from the firm setting labor demand and tax evasion, a trade union and firm solve the following problem:

where Ψ denotes a Nash product of the bargaining, ^[13] and 0≤θ≤1 is the relative bargaining power of the union with a lager value of θ denoting a greater bargaining power. Using V=U−U0, the first-order condition with respect to wage is

where Vw=φ′(w)L+(φ(w)−φ(b))Lw and Πw=−(1−t)L by the envelope theorem. Note that the term Vw can be interpreted as the marginal benefit from a higher wage from the union’s standpoint and Πw can be interpreted as the marginal cost from a higher wage from the firm’s standpoint. We make use of the explicit form of the first-order condition, which can be written as

We assume that the second-order sufficient condition (Ψww<0) is fulfilled and Vw>0 in order to guarantee an interior solution. With regard to Vw, except for θ=1, ^[14] we assume Vw>0 throughout the paper. In eq. [10], θVwΠ and (1−θ)(1−t)LV represent the marginal benefit and the marginal cost in bargain from the increasing w, respectively. The optimal wage rate w∗ is therefore the solution in which the marginal benefit equals to the marginal cost.

In line with most of the literature referred to in the introduction, we address the following two questions: (i) whether profit taxes are neutral, and (ii) whether the firm’s production and tax evasion decisions are separable. The answers to these questions hinge critically on the presence of wage bargaining.

First, if the union has no bargaining power at all (θ=0), then from eq. [9] we would obtain

Equation [11] shows that it is optimal for the firm to set the lowest possible wage rate. Intuitively, the reason for this is that if the union has no bargaining power at all (θ=0), the firm leaves no rent for the union, and the wage rate is cut down by the firm. This result indicates that the firm’s optimal wage level is independent of its optimal choice of tax evasion S∗ and the profit tax t. Thus, tax evasion and profit tax cannot indirectly affect the wage rate and employment level (output). That is, the firm’s production and tax evasion decisions are separable from each other and profit tax is neutral in this case.

Second, if θ=1, i. e., in the presence of a monopoly union, then from eq. [9] we would obtain

Equation [12] shows that the monopoly union’s optimal wage level is independent of the firm’s choice of tax evasion S∗ and the profit tax t. Thus, the neutrality and separability results of the profit taxes are quite robust in a monopoly union model.

The present paper assumes that the firm and the union bargain over the wage only and the firm unilaterally sets the employment level in a profit-maximizing way, it can be obviously seen that eq. [10] could no longer be reduced into eqs [11] and [12] since 0<θ<1. We note that the wage rate w and employment level L do not enter into eq. [5]. That is, the extent of the firm’s tax evasion is decided separately from the wage and employment decisions. However, eqs [6] and [10] simultaneously solve the optimal wage level w∗, and optimal employment level L∗. It is worth noting that w∗ and L∗ are determined by S∗, but S∗ does not depend upon w∗ and L∗. This demonstrates that tax evasion does affect employment when wage bargaining is available, i. e. the separability result and tax neutrality will not hold. Notice that if wage bargaining is unavailable (θ=0 or θ=1), eq. [10] will reduce to eq. [11] or eq. [12]. Thus, tax evasion does not have an effect on employment, i. e. the separability result holds and profit taxes are neutral.

To proceed further with the analysis, we need to answer the connection between tax evasion, wage rate, and output. We do so by comparing the wage rate in the presence of tax evasion with that in the absence of tax evasion. Without tax evasion the terms tS and f(tS)would no longer be present in eqs [1] and [2] respectively, and the first-order condition for eq. [10] would be reduced to

where θVw(1−t)π and (1−θ)(1−t)LV represent respectively the marginal benefit and the marginal cost in bargain from increasing w. Let w˜ satisfy eq. [13].

To compare w∗ in eq. [10] to w˜ in eq. [13], evaluating eq. [10] at w=w˜ and using eq. [13] yield ^[15]

Since Vw>0 and 0<θ<1 by assumption, the sign of eq. [14] depends on the sign of (1−p)tS−pf(tS). If (1−p)tS−pf(tS)>0, then tax evasion takes place and the sign of eq. [14] is positive. Thus, we obtain that w∗ is greater than w˜. This is because the firm is better off from evading taxes (i. e. enjoys a higher rent), the union will receive a share of this improvement of the firm’s rent via higher wages. This result is different from that of Goerke (2003), who has shown that the existence of individual tax evasion opportunities lowers wages. In addition, an increase in wage rate leads to a reduction in employment level. Therefore, tax evasion exerts indirect influence on output level by increasing the wage rate.

We can then summarize the finding into:

3.2 Comparative Statics

In this subsection, assuming a solution exists, the analysis goes on to investigate how the optimal wage rate is affected by changes in various policy parameters. With the implicit function theorem applied to eq. [10], the effect of a change in any parameter β∈{t,p,b,θ} on w∗ is given by

where Ψwβ=∂Ψw/∂Ψw∂β∂β. Differentiating eq. [10] with respect to β yields

The signs of eqs [17], [18] and [19] are easy to obtain clear-cut results. However, eq. [16] needs to be explained more. By using eqs [5] and [10], we obtain respectively (1−p)=pf′(tS) and (1−θ)LV=θVwΠ/θVwΠ(1−t)(1−t). Substituting these terms into eq. [16] yields the positive sign.

From eqs [16]–[19] and Ψww<0, we put forward:

The rationale underlying this result is as follows. First, due to the existence of tax evasion, an increase in the profit tax enhances the marginal benefit of wage rate. This provides the firm with a greater incentive to raise wage rate. Consequently, an increase in the profit tax leads to a positive effect on the wage rate. Note that with the firm’s fallback level set at zero, if the firm tax evasion is absent, our result would be the same as the one presented by Goerke (1996): profit tax has no impact on wage rate.

Secondly, a higher detection probability, threatening to reduce the gain from tax evasion, may also force the firm to secure profits by lowering wage rate. Thirdly, as the unemployment benefit increases, the union has a weaker incentive to bargain with the firm. The firm will push a higher wage to reach agreement with the union if profitable tax evasion is possible. Finally, if the union has larger bargaining power, it can strive for a higher wage rate.

Interestingly, in this paper, firms use lower wages as a substitute for less profitable tax evasion. Similarly in the context of a Cournot oligopoly model with an endogenous number of firms and evasion of indirect taxes, Goerke and Runkel (2011) have show that firms use tax evasion as a substitute for the loss in market power.

4.1 Characterization of the Solution

The assumptions and notations in this section are similar to those in Section 3 except that we assume both wage and employment are the subjects of the bargain. ^[16] Therefore, by differentiating eq. [9] with respect to w and L, we have

where Vw=φ′(w)L>0, ^[17]Πw=−(1−t)L<0, VL=φ(w)−φ(b)>0 and ΠL=(1−t)(R′−w). Let (wˆ,Lˆ) represent the solutions to eqs [20] and [21]. Division of eqs [20] and [21] shows that

or

By using eq. [23], we can rewrite eq. [20] as

According to eq. [24]), we obtain ΠL=(1−t)(R′−w)<0. Equation [23] shows the optimal employment rule for efficient bargain, implying that the marginal product of labor should be less than the per worker wage wˆ. Equation [24] states that the wage in the efficient bargain model is determined by the marginal product of labor (R′), the bargaining power of the union (θ), the profit tax (t), tax evasion (S), and the expected profit of the firm (Π). Notice that, from eq. [5], the optimal tax evasion (S∗) does not depend upon wˆ and Lˆ. However, eqs [23] and [24] are determined simultaneously and depend upon the optimal tax evasion (S∗) and the profit tax t. Thus, both the tax evasion S∗ and the profit tax t can affect the wage rate and employment level. This immediately implies that the neutrality and separability results will not hold.

Notice that if θ=0 or θ=1, we can get the same result as in eqs [11] and [12], i. e., profit taxes are neutral, and the firm’s tax evasion decision and its production decision are separable.

Above results bring us to the following proposition:

It is worthwhile to note that Proposition 1 and 3 are based on profit tax evasion. In addition to profit tax evasion, the conclusions in Proposition 1 and 3 can also apply to payroll or revenue tax evasion as discussed by Yaniv (1995) and Marrelli (1984).

4.2 Comparative Statics

Applying the implicit function theorem to eqs [20] and [21], the effect of a change in any parameter β∈{t,p,b,θ} on wˆ and Lˆ is given by:

where H≡ΨwwΨLL−(ΨwL)2>0, Ψww=∂Ψw/∂Ψw∂w∂w<0, ΨLL=∂ΨL/∂ΨL∂L∂L<0, ΨwL=∂Ψw/=∂Ψw∂L∂L, ΨLβ=∂ΨL/∂ΨL∂β∂β and Ψwβ=∂Ψw/=∂Ψw∂β∂β. Because H is positive, the direction of the effect of a change in any parameter β∈{t,p,b,θ} on wˆ and Lˆ is the same as the sign of the numerators of eqs [25] and [26]. Since ΨwL is a key factor in determining the signs of eqs [25] and [26], we are interested in knowing the sign of ΨwL. To this end, differentiating eq. [20] with respect to L yields

where VwL=φ′(w)>0, ΠwL=−(1−t)<0. By using eq. [20], it will simplify ΨwL and we obtain ΨwL=θVwΠL+(1−θ)ΠwVL. Since Vw>0, ΠL<0, Πw<0 and VL>0, the sign of ΨwL is negative. In addition, differentiating eqs [20] and [21] with respect to β yields

Since Π>0 and ΠL<0, the sign of ΨLb is ambiguous. In addition, by using eq. [21], we obtain ΨLt>0. The eqs [27]–[34] have clear-cut signs except ΨLb.

We find that when ΨwL<0, the comparative static results are uncertain. This is because the numerators of eqs [25] and [26] include two terms. With two decision variables, a parameter change alters the marginal effect for each decision variable, termed the direct effect. There is also an indirect effect, which implies a parameter shift indirectly affects the one decision variable via altering the other decision variable. The first term in the numerators on the right-hand side of eqs [25] and [26] represents the indirect effect, while the second term represents the direct effect. Under ΨwL<0, we find that the direct effect counteracts the indirect effect. Hence, changes in policy parameters have an ambiguous effect on the wage rate and the employment level.

For reasons of concreteness and tractability, we then provide some numerical examples to illustrate the comparative static results. We assume a linear demand function p(L)=a−L, with a>0, and convex penalty functions f(tS)=(tS)2/(tS)222. In addition, we suppose that the worker’s utility functions are φ(w)=lnw and φ(b)=lnb. Also, it is assumed that the baseline parameters are a=5, t=0.1, p=0.1, θ=0.1, and b=0.1. From eq. [5], we then get the equilibrium values S=(1−p)/(1−p)pt2pt2. By using this term and solving the simultaneous eqs [23] and [24], we obtain the equilibrium values wˆ=2.9614 and Lˆ=6.0357. We then present comparative statics by varying t, p, b, and θ as shown in Figures 1–4. Figures 1 and 2 show that higher values of t and p lead to smaller wage rate and employment. Figures 3 and 4 reveal that higher values of b and θ lead to greater wage rate and employment. As a result, we can identify at least one example where the impact of t, p, b or θ has a non-zero impact on the wage and employment level in order to prove non-separability. ^[18]

Figure 1:

Extents of w and L for varying t.

Figure 2:

Extents of w and L for varying p.

Figure 3:

Extents of w and L for varying b.

Figure 4:

Extents of w and L for varying θ.