# «Bruno Bosco2 Margherita Savona DEMS DSG University of Milan–Bicocca Piazza Ateneo Nuovo, 1 20127 Milan, Italy Abstract In this paper corruption is ...»

Regulation is costly for the Government. We assume that there are two types of costs.

Implementation costs of the measures are expenditures necessary to prevent the damage (e.g. pollution) from incompliance, call tem D(r ), and assume D(.) is a continuously increasing convex function. A second source of costs is given by the opportunity costs of r itself. Total preventing damage cost evaluated at required full compliance would be D(r)X. Hence, this means that if the government does not invest in regulation/monitoring, people would not comply and society would suffer a loss given by the forgone benefit of X. Hence, the government net utility function at full

**compliance is:**

where the last term indicates the opportunity cost of the resources used in the regulation process.

H2 Privates Private subjects may either completely comply, partially comply or not comply at all.

Hence, we define incompliance as a continuous function x(r ) ∈ [0, X ]. Then, [X – x(r)] is compliance. Since x(r) is the privates’ reaction to regulation we do not say a priori whether it is monotonously increasing or decreasing in r. Hence, dx/dr is the slope of a reaction function to regulation. When it is positive, privates react to regulation by reducing compliance and when it is negative, they increase compliance. Following Mookherjee et al. (1997), we assume that compliance is costly and in order to simplify things we suppose that each private has no other costs but pure compliance costs. Call C the cost per unit of compliance (the cost of each filter). C is assumed to be a random variable realized only after that the government has fixed the norms of conduct. We assume there exists a common knowledge probability distribution F(C) having a density f(C) over a strictly positive support [C, C ]. We assume that h(C) = f(C)/[1–F(C)] is non decreasing in C7. Note that C 0 implies that compliance can never be costless. When privates do not comply and are discovered they will be sentenced to pay a fine whose structure will be specified below. The privates’ utility under full observability (or full compliance) is therefore

**U P = U − E[C ] X**

where U is the value of the regulated project for the privates (the flow of profits of the potentially polluting firm). The latter is supposed to be a constant and therefore the gain from not compliance is the expected cost saving deriving from complete incompliance or partial compliance. With asymmetric information, we will adapt this function to incorporate fines for incompliance as well as the probability of being discovered.

H3 Officers Call S(C) = [1 – F(C)]. Then a non-decreasing hazard rate implies that S(C+z)/S(C) is non-decreasing in C for any non negative z. The higher the cost the higher the probability that your costs will further increase, and vice versa.

The government delegates an agency, the bureaucrats, to monitors privates’ compliance.

To simplify things assume that bureaucracy’s activity has no operating costs but officers’ salary w. Hence, assuming that the working effort is costless, the utility of the officers under fully observability is simply their salary w(r) which is a continuously

**increasing and differentiable function of r:**

**UB = w(r)**

Yet, in an asymmetric information context non-complying privates may try to bribe officials, i.e. they may try to persuade them to misreport about incompliance with the direct consequence that the fine will be greatly reduced or entirely waved. We will call fP and fB the fines for privates and officers if they are discovered giving and accepting a bribe. Hence, UB will be modified to account for bribes, penalties and probability of discovering when asymmetric information is introduced.

**H4 Allocative efficiency**

Finally, corruption will be assumed to be socially costly in terms of allocation of resources. This cost with be treated, in a way that will be discussed below and following an idea of Rose–Ackerman et al. (2012, 6), as a debt-weight loss provoked by a distorsive tax which produces an extra marginal costs of public funds. Therefore, in this paper the total social damage induced by non-compliance and corruption behaviour will be higher than the direct damage from incompliance (however defined) because bribes will not be treated as pure lump-sum inter-individual transfers.

Given H1 – H4 the problem of the government is to determine the optimal r under different assumptions about the distribution of information between government, officers and privates taking into account that, when there is asymmetry of information, corruption may lead private subjects to choose a non-complying behaviour supported by a bribing strategy

** 3.1 A benchmark case: full observability of compliance costs**

We first derive optimal r under the assumption that realized private costs are ex-post perfectly observable and consequently that there cannot be bribes (and fines) because the government can perfectly monitor individuals’ and officers’ behaviour. For simplicity, let us start by setting damage and salaries as constants. The objective function of the government is to maximize welfare at full compliance

**Maxr ( V (r ) − D ) X + U − E[C ] X − r − w**

As one can see the above is a social welfare function similar to the one used by Polinsky et al. (2001, 7) were the government (or the public) gain is given by V(r) – r and the damage plays the same role of their variable h, “the harm from committing the act”. In our case the act is the decision of not complying. Since compliance is assumed to be costly and costs are ex-ante unknown, uncertainty enters the model through the gain privates obtain from their acts, as in Polinsky et al. (2001), i.e. through cost avoidance.

The government, however, has no moralistic views about compliance and requires compliance when the latter is “efficient” from a cost perspective. Hence, considering E[C] we say that efficiency conditions (i.e. an efficient level of regulation) imply (adapting from Shavell, 1980), that it would be preferable to have compliance (state 1) if V(r) – D ≥ C, i.e. when net social wellbeing is greater than or equal to the full compliance cost, and non compliance (state 2) should be seen as efficient when the opposite condition is realized, i.e. when V(r) – D C. We can evaluate F[C] at the cutoff value of C to define the expected value of social wellbeing conditional on costs being lower than the cut-off level. This is simply the government net welfare times the probability of having a cost realization at or below the cut-off level. Accordingly, the probability F[V(r) – D ] is the probability of state 1 whereas the probability of state 2 is [1 – F(V(r) – D )]. Then a pure benevolent welfare maximizing government calculates

**the optimal r by maximizing the net benefit of regulation as follows:**

The participation constraint requires that in State 1 full compliance does not exhaust the private’s utility. It can be easily shown that in State 1 the participation constraint is always satisfied. Maximization of problem (1) gives an optimal regulatory policy when

3.1.1 Regulation when damage and salary depend on r Under realized costs observability and no bribes, the underinvestment result is not necessarily obtained when D and w vary with r. Consider some possibilities.

i) Assume that D = D −ψ (r ) where ψ(.) is a continuous increasing function (the damage can be reduced by r) and that wages are fixed. In this case, the cut-off value of C would be C = [ ( V (r ) − D + ψ (r ) ) ] and problem (1) would rewrite as ɶ

where w is the fixed level of the salary when r = 0. Then, the optimal salary structure is the sum of two components. One is certain and represents the fixed minimum part of the salary. The uncertain component is given by the difference between a quota of the value of the total marginal government’s gain at full compliance generated by investing up to r* and the investment opportunity cost of regulation. Then, under (ex-post) cost observability, the above salary structure links salary to expected net performance (increase in V) as if salaries were directly dependent of the expected benefits of the investment in regulation. Then, even when costs are ex-ante uncertain, a (sub) optimal level of regulation is obtained when compliance costs can be ex-post observed by both government and officers. Officers’ activity can be rewarded in a way that ensures they ɶ receive a fair share – given by F [C ], i.e. by the probability of state 1 – of the government benefit from investment in regulation. However, cost observability implies that incompliance and bribing are impossible. Then, the above results should be contrasted with that emerging from a situation in which cost observability in any state of the world is restricted to officers only, so that an efficient penalty structure should be designed to help achieving a policy of determining the optimal r that induces compliance without bribing.

** 3.2 Compliance and corruption without observability**

When the government cannot observe costs, pure regulation/monitoring does not lead to efficient outcomes, the probabilities of state1 and state 2 cannot be defined and, consequently, the optimal r cannot be derived from the maximization of the benefit of regulation in which a tolerance level of incompliance is defined by efficiency cost conditions. Moreover, recall that under cost observability the very role of bureaucracy may even look somehow superfluous. Officers are simply the longa manus of the government. To give bureaucracy an active and autonomous role, we now assume that compliance costs can be observed only by bureaucracy but not by the government. The latter, fearing that privates and officers may collude can impose pre-determined fines to non complying privates (upon bureaucracy’s report) and to officers when they are discovered to be corrupt, i.e. when they misreport. Hence, the government must determine its optimal measures taking into account not only compliance costs uncertainty but also that privates and officers may bargaining over the officers’ reports, i.e. over the gain generated by avoiding the compliance costs required by regulation. As a result the government must first understand how a Nash equilibrium between privates and officers can be characterized (i.e. what the best decisions about a bribe can be) and then incorporate the results into his maximization problem regarding optimal policy in order to obtain simultaneously conditions for an optimal r and for the fines.

We start with the private-officers bargain problem. Assume that Θ is the probability that a corrupted transaction is discovered when a bribe b changes hands. If an officer is discovered he/she is not fired from the office but his salary is reduced by the amount given by a lump-sum payment b fB w. This means that the bribe is confiscated and the officer pays a positive penalty on top of the bribe confiscation. As a result his expected utility is modified as follows

**E[U B ] = (1 − Θ)[ w + b] + Θ[ w + b − f B ]**

with a status quo (no bargaining) utility of w.

If the private is discovered he/she is compelled to fully comply (then, his/her total cost will be C[X – x(r)] + Cx(r) = CX), and is fined with a penalty fP per unit of incompliance evaluated at C. Then, since the gain of a private is given by the monetary value of his/her regulated activity U (e.g. an house he/she builds) plus the avoided compliance costs (e.g. the unpaid fees)8 net of the bribe, we have, assuming that CX+b+fP U, E[U P ] = (1 − Θ)[U − C ( X − x(r )) − b] + Θ[U − C ( X − x(r )) − b − Cx(r ) f P ] with a status quo (no bargaining and no incompliance) utility of U − CX (the gain net of total compliance cost). X is total required compliance and x is incompliance. The latter We assume that the lump-sum penalty is smaller than U which implies that the government cannot confiscate entirely the gain of the private (an house built “illegally” cannot be demolished).

is assumed to depend on r in two possible different ways: x’(r) 0 (burdensome regulation) or x’(r) 0 (simplifying regulation) and it is observed by both parties (see H2). This allows for bribing over partial compliance. A Nash solution (see Ades et al.