Bribes, Lobbying and Industrial Structure

Abstract

This paper deals with the relationship between regulatory compliance, bureaucratic corruption, lobbying and the industrial structure of a country. We show that lobbying and bureaucratic corruption can coexist at the macro level when we allow for heterogeneity in firm size. Countries with similar level of development are often characterized by very different industrial structures: we show the implications this has for the level of compliance, corruption and lobbying in that country. Welfare implications of our model point toward encouraging policies that support the small business sector of an economy and toward flexible regulatory policies meant to suppress regulation for small enough firms.

Appendix

1.1 Proof of Proposition 3.1

Let us fix $t=0,1,\dots , T$ and let ${\underline{\phi }}_\Delta (t)=\left( \phi _\Delta ^{(F)}(t),\phi _\Delta ^{(B)}(t)\right)$ be the vector of the differences in the expected payoffs between the case of agreement and disagreement regarding the bribe between the j-th firm and the bureaucrat, i.e.

$$\begin{aligned} \left\{ \begin{array}{l} \phi _\Delta ^{(F)}(t)={\mathbf {E}}[\pi ^{(F)}_C(t)]-{\pi }^{(F)}_2(t),\\ \\ \phi _\Delta ^{(B)}={\mathbf {E}}[\pi ^{(B)}_C(t)]-{\pi }^{(B)}_2(t), \end{array} \right. \end{aligned}$$

where ${\mathbf {E}}$ indicates the expected value operator.

Follow the generalized Nash bargaining theory, the bribe of agreement comes out from:

$$\begin{aligned} \max \limits _{b_t\in (0, +\infty )}\left\{ \phi _\Delta ^{(F)}(t)\right\} ^\beta \cdot \left\{ \phi _\Delta ^{(B)}(t)\right\} ^{1-\beta }, \end{aligned}$$

(20)

i.e.:

$$\begin{aligned} \max \limits _{b\in (0,+\infty )}\left[ (ck_j+mk_j)(1-q)-(1-q)b\right] ^\beta \cdot \left[ -q \lambda ^B+(1-q)b\right] ^{(1-\beta )}. \end{aligned}$$

(21)

The objective function in (20) is a reversed U-shaped function in b. Therefore, the first order condition leads to the bribe of agreement:

$$\begin{aligned} b_j^{NB}=(1-\beta ) (c+m)k_j + \frac{\beta q \lambda ^B}{1-q}, \end{aligned}$$

which is the unique bureaucratic equilibrium bribe in the last subgame.

1.2 Proof of Proposition 3.2

The game is solved by using backward induction, which enables the equilibria to be obtained. Fix a level of time $t=0,1, \dots , T$.

(3):

At stage three, the j-th firm negotiates the bribe if and only if:

$$\begin{aligned} {\mathbf {E}}[\pi ^{(F)}_{C}]-\pi ^{(F)}_{3,RC}>0. \end{aligned}$$

(22)

Condition (22) is verified when:

$$\begin{aligned} k_j>\frac{\lambda ^Bq}{(c+m)(1-q)}=:k^{(1)}. \end{aligned}$$

(23)

(2):

Ascending the decision-making tree, at stage two the bureaucrat decides whether to ask for a bribe or not. The bureaucrat knows that if she/he asks for a bribe, then the bribe will be negotiated when $k_j>k^{(1)}$, and refused otherwise.

• (I) If $k_j>k^{(1)}$, then the bureaucrat asks for a bribe if and only if

  $$\begin{aligned} {\mathbf {E}}[\pi ^{(B)}_{(C)}]-\pi ^{(B)}_{(2,RC)}>0, \end{aligned}$$

  (24)

  which is always verified.

• (II) If $k_j \le k^{(1)}$, then the bureaucrat asks for a bribe if and only if

  $$\begin{aligned} \pi ^{(B)}_{(3,RC)}-\pi ^{(B)}_{(2,RC)}>0, \end{aligned}$$

  (25)

  which is never verified.

(1):

At stage one, the j-th firm must decide whether to comply with regulation or to bend the rule. To proceed, we need to observe the cases occurring in the previous stage.

• (I) If $k_j>k^{(1)}$, then the j-th firm bends the rule if and only if

  $$\begin{aligned} {\mathbf {E}}[\pi ^{(F)}_{(C)}]-\pi ^{(F)}_{(1,H)}>0, \end{aligned}$$

  (26)

  This condition is verified when:

  $$\begin{aligned} k_j>\frac{\beta \lambda ^Bq}{\beta (1-q)c-m[1-\beta (1-q)]}=k^{(2)}. \end{aligned}$$

  (27)

• (II) If $k_j \le k^{(1)}$, then the j-th firm bends the rule if and only if

  $$\begin{aligned} \pi ^{(F)}_{(3,RC)}-\pi ^{(F)}_{(1,H)}>0, \end{aligned}$$

  (28)

  which is never verified.

It is easy to check that $k^{(1)}< k^{(2)}$. This completes the proof.

1.3 Some Remarks on the Presence of Free-Riding Opportunities

This section is devoted to the discussion of the case in which the lobbying activity is not only in favor of the firms implementing it, but it offers also free-riding opportunities to the other firms.

Proposition 3.2 states that each firm j satisfying $k_j\ge k^{(0)}$ engages in lobbying. Now, assume that there exists at least one firm engaging in lobbying – i.e., satisfying the related condition on the capital. Moreover, let us hypothesize that the gains from the lobbying activity are enjoyed also by a generic firm j having $k_j< k^{(0)}$ by adding a free-riding parameter $\gamma \in (0,1)$, so that the variable cost of compliance paid by j is $\gamma ck_j$, instead of $ck_j$.

The presence of the free-riding parameter $\gamma$ does not imply any additional complexity in the mathematical solution of the model. However, the economic content of the obtained outcomes is particularly relevant.

First of all, in the presence of free riding, the threshold $k^{(2)}$ in (16) becomes

$$\begin{aligned} k^{(2)}(\gamma )=\frac{\beta q\lambda ^B}{\beta (1-q)\gamma c-m[1-\beta (1-q)]}. \end{aligned}$$

(29)

According to (29), the threshold $k^{(2)}(\gamma )$ decreases with respect to $\gamma$. Therefore, cases (I.A) and (I.B) in Proposition 3.2 assure that a high value of $\gamma$-which is associated to a small effect of free-riding, with a large part of variable costs paid by the non-lobbying firms -implies that firms are more likely involved in bureaucratic corruption. This outcome is in line with the economic decision to engage in bureaucratic corruption or, alternatively, of not bending the rule.

Interestingly, we notice that the presence of the free-riding parameter leads also to a new formulation of the bribe $b_j^{NB}$ in (11), as follows:

$$\begin{aligned} b_j^{NB}(\gamma )=(1-\beta ) (\gamma c+m)k_j + \frac{\beta q \lambda ^B}{(1-q)}. \end{aligned}$$

(30)

The bribe $b_j^{NB}(\gamma )$ now increases with respect to $\gamma$; thus, we find that has the free-riding become stronger—i.e., as $\gamma$ declines—the equilibrium bribe declines too. Firms are, therefore, less ready to pay bribes for corrupting bureaucrats when there is the interesting alternative of a meaningful free-riding from the lobbying activity.