Anti-mafia policies and public goods in Italy

Abstract

This paper aims to evaluate the impact of a policy that targets criminal infiltration in local governments on the provision of local public goods in Italian municipalities. Building on the theoretical framework proposed by Dal Bò (American Political Science Review 100:41–53, 2006), we use a sufficient statistic approach to describe the dynamic behaviour of local public goods when stricter law enforcement weakens criminal pressure groups. Utilizing data on the local public finances of Italian municipalities spanning from 2004 to 2015, our findings reveal that, after the dismissal of infiltrated governments, the targeted municipalities devote a larger share of resources to public goods, with an estimated increase of approximately 3.9 percentage points. Notably, this effect seems to be driven by an increase in investment of approximately 3 percentage points. Overall, our results suggest that policies targeting the problem of criminal infiltration in local governments can improve socioeconomic conditions and the well-being of local communities, by increasing investments in economically and socially relevant public goods.

Appendices

Appendix A: Mathematical appendix

The model has two stages. In the first stage, citizens with different abilities choose whether to run for office in the public sector or work in the private sector, depending on the payoff they expect from each. In the second stage, a pressure group tries to influence politicians to obtain a given resource.

1.1 A.1 First stage

1.1.1 A.1.1 Comparison of private and public sector payoffs

Each citizen chooses whether to enter the public office by comparing the wage they can earn in the private sector and the expected payoff of the public sector. Private sector wage reflects individual ability $a_i \epsilon [0,\infty )$. The public sector wage is w. Denote V as the expected payoff of the public sector. Without pressure groups, $V=w$.

1.1.2 A.1.2 Quality of politicians without the pressure group

all citizens of type $a \leqslant w$ will run for office (they can earn as much or more in the public sector than they would in the private sector). By assumption, those of type $a=w$ will be elected.

1.2 A.2 Second stage: interaction between the pressure group and politicians

1.2.1 A.2.1 Instruments of political pressure

The pressure group has two tools to influence policy choices: bribes b and punishment p. The cost of delivering a bribe is $\beta \phi (b)$; the cost of delivering a punishment is $\rho \psi (p)$. $\beta >0$ and $\rho >0$ are exogenous parameters representing institutional and technological factors that affect the cost of delivering a bribe or a punishment. By assumption, $\phi (.)$ and $\psi (.)$ are both twice continuously differentiable, and the marginal cost of starting to use these tools is 0.

$$\begin{aligned} \phi (0)=0\qquad \phi '(0)=0\qquad \phi '>0\qquad \phi ''>0 \end{aligned}$$

$$\begin{aligned} \psi (0)=0\qquad \psi '(0)=0\qquad \psi '>0\qquad \psi ''>0 \end{aligned}$$

1.2.2 A.2.2 Profit maximization of the pressure group

The pressure group chooses $b^{*}$ and $p^{*}$ to solve the following maximization problem:

$$\begin{aligned} Max_{b,p}\left\{ \prod (b,p)=\gamma [\pi -\beta \phi (b)-(1-\gamma )\rho \psi (p)\right\} \end{aligned}$$

under the constraint $b\ge c-p$, where $\pi$ is the amount of resources subject to political discretion; $\gamma$ is the probability that the policymaker will accept the bribe; $(1-\gamma )$ is the probability that it is impossible for the policymaker to accept the bribe and that he/she has no other choice than refuse it and receive the punishment.

The maximization is constrained in that the politician will accept the bribe as long as it provides him with a payoff greater than or equal to the payoff he would have had by refusing it:

$w+b-c\ge w-p$

$b\ge c-p$

where c is the cost for the politician to get involved in a corruption deal.

Once the optimal values $b^{*}$ and $p^{*}$ have been identified, there will be two possible cases:

$\prod (b^{*},p^{*})\ge 0\quad$: the profit the group can make is non-negative and the group decides to bribe because the expected profit covers the expected costs.

$\prod (b^{*},p^{*})<0\quad$: the profit the group can make is negative and the group decides not to bribe because the expected profit does not cover the expected costs.

Given the parameters $\gamma ,\beta ,\rho$, we denote as ${\widetilde{\pi }}(\gamma ,\beta ,\rho )$ the number of resources such that $\prod (b*,p*)=0$. Below this threshold, the group remains inactive and decides not to bribe. ${{\widetilde{\pi }}}$ is interpreted as an inverse measure of the level of state capture. It denotes the size of the set of possible values of ${\pi }$ for which the group does not engage in influence activities. The smaller this set, the higher the level of state capture, and vice versa.

1.2.3 A.2.3 Results with bribes only

Lemma 1a

An active group offers a bribe equal to the cost the corrupt action has for the official $b^\circ =c$.

Given, $p=0$ the only means of political influence is the bribe. The pressure group chooses optimal $b^\circ$ which solves:

$Max_{b}\left\{ \prod (b,0)=\gamma [\pi -\beta \phi (b)]\right\}$

s.t. $b\ge c$

Since all bargaining power lies with the pressure group, there is no reason why $b>c$ should be offered. For the politician to accept the bribe, it is enough that it covers the cost of c, so an active group will choose an optimal bribe $b^\circ =c$.

Lemma 1b

The group only becomes active if $\pi$ is larger than the cost of the bribe $({\widetilde{\pi }}^\circ \equiv \beta \phi (b^\circ )=\beta \phi (c))$.

The pressure group will be active if the expected profit makes it possible to cover the expected cost: $\prod (b^\circ ,0)\ge 0$, or equivalently $\pi \ge \beta \phi (b^\circ )$.

Given, $\prod (b^\circ ,0)=0$ we find the threshold value for $\pi$: ${\widetilde{\pi }}^\circ \equiv \beta \phi (b^\circ )=\beta \phi (c)$.

Lemma 2

In a world with bribes and no punishment, the quality of politicians is w, regardless of whether the pressure group is active or not.

If $\pi \ge {\widetilde{\pi }}^\circ$ the group is active and the public sector payoff is $w+{b^\circ }-{c}=w$.

If $\pi <{\widetilde{\pi }}^\circ$ the group is not active and the public sector payoff is w.

Proposition 1

More room for influence through bribes (a lower $\beta$) implies a higher degree of state capture, but it does not decrease the quality of politicians.

From lemma 1b, ${\widetilde{\pi }}^\circ =\beta \phi (b^\circ )$ implies $\tfrac{d{\widetilde{\pi }}^\circ }{d\beta }=\phi (b^\circ )>0$.

The group still pays the same $b^\circ =c$ but at a lower cost $\beta \phi (b^\circ )$, given that $\beta$ has decreased. The expected costs are lower, so the threshold ${\widetilde{\pi }}^\circ$ sufficient to cover the costs of political influence activity is also lowered.

From lemma 2, the payoff of politicians and hence their equilibrium quality is still w.

1.2.4 A.2.4 Results with bribes and punishment

Lemma 3a

An active group uses both bribes and punishment ($b*>0;p*>0)$ and the total amount of pressure is such that ($b^{*}+p^{*}=c$).

The politician will accept the bribe as long as $w+b-c\ge w-p$. Since all bargaining power lies with the pressure group, it will be sufficient that $b=c-p$. By substituting the constraint in the objective function, the maximization problem becomes:

$max_{p}\prod (b(p),p)=\gamma [\pi -\beta \phi (c-p)]-(1-\gamma )\rho \psi (p)$

F.o.c. $\gamma \beta \phi '(c-p)]-(1-\gamma )\rho \psi '(p)=0$

We restate the f.o.c. as $f(p)=0$. Given that:

• (1) f(p) is continuous ($\phi$ and $\psi$ are both continuous)

• (2) For $p=c$, $f(p)<0$: $\gamma \beta \underbrace{\phi '(0)}_{=0}-(1-\gamma )\rho \underbrace{\psi '(c)}_{>0} <0$

• (3) For $p=0$, $f(p)>0$: $\gamma \beta \underbrace{\phi '(c)}_{>0}-(1-\gamma )\rho \underbrace{\psi '(0)}_{=0}>0$

By the intermediate value theorem there exists a $p^{*}\,\epsilon \,(0,c)\,|\,f(p^{*})=0$ (the f.o.c. is satisfied) and $p^{*}>0.$

S.o.c. $(-1)[\gamma \beta \underbrace{\phi ''(c-p)}_{>0}]-\underbrace{(1-\gamma )}_{>0}\rho \underbrace{\psi ''(p)}_{ >0}<0$

Since the s.o.c. is also satisfied, there exists a maximizing $p*$.

Moreover, since $b=c-p$, also $b^{*}\,\epsilon \;(0,c)$, both ${p^{*}}$ and ${b^{*}}$ are strictly positive, and $b^{*}+p^{*}=c$.

Lemma 3b

The group only becomes active if $\pi \ge {\widetilde{\pi }}\equiv \frac{(1-\gamma )}{\gamma }\rho \psi (p^{*})+\beta \phi (c-p^{*})$.

The total cost of the exerted pressure is $\gamma \beta \phi (c-p^{*})+(1-\gamma )\rho \psi (p^{*})$. The pressure group becomes active if the expected benefit covers this cost: $\prod (b^{*},p^{*})\ge 0$, or equivalently $\gamma \pi \ge \gamma \beta \phi (c-p^{*})+(1-\gamma )\rho \psi (p^{*})$.

Given $\prod (b^{*},p^{*})=0$ we find the threshold value for $\pi$, below which the group is not active:

$\prod (b^{*},p^{*})=\gamma [\pi -\beta \phi (b^{*})]-(1-\gamma )\rho \psi (p^{*})=0$

$\gamma [\pi -\beta \phi (b^{*})]=(1-\gamma )\rho \psi (p^{*})$

${\widetilde{\pi }}=\frac{(1-\gamma )}{\gamma }\rho \psi (p^{*})+\beta \phi (b^{*})=\frac{(1-\gamma )}{\gamma }\rho \psi (p^{*})+\beta \phi (c-p^{*})$

Lemma 4

In a world with bribes and punishment, the quality of politicians is $w-p*$ if the group is active, and w if the group is not active.

If $\pi \ge {\widetilde{\pi }}$ the group is active. Accepting the bribe yields a payoff of $w+b^{*}-c=w+c-p^{*}-c=w-p^{*}$. Refusing the bribe and receiving the punishment also yields a payoff of $w-p^{*}$.

If $\pi <{\widetilde{\pi }}\quad \rightarrow \quad$ the group is not active and the public sector payoff is simply w.

1.2.5 A.2.5 Further results

Proposition 2

From lemma 1a and 3a, bribe offers are lower in a world with bribe and punishment.

Proposition 3

From lemma 2 and 4, if the pressure group is active, the quality of politicians is lower in a world with bribe and punishment.

Proposition 4

The degree of state capture is higher in a world with bribe and punishment $({\widetilde{\pi }}<{\widetilde{\pi }}^\circ )$

By lemma 3a, $p^* > 0$. Therefore, putting $p=0$ (as in the world without punishment) means putting a binding restriction (the unbounded maximum lies outside the set of values allowed by the constraint), and $\prod (b^{*},p^{*})>\prod (b^\circ ,p=0)$

As a result:

$\gamma \pi -\gamma \beta \phi (c-p^{*})-(1-\gamma )\rho \phi (p^{*})>\gamma \pi -\gamma \beta \phi (c)$

$\beta \phi (c)>\frac{(1-\gamma )}{\gamma }\rho \psi (p^{*})+\beta \phi (c-p^{*})$

${\widetilde{\pi }}^\circ >{\widetilde{\pi }}$

Lemma 5a

More room for influence through bribes (a lower $\beta$) implies higher bribes and lower punishment $(\frac{dp^{*}}{d\beta }>0\qquad ;\frac{db^{*}}{d\beta }<0)$.

Proof:

$max_{p}\prod (b(p),p)=\gamma [\pi -\beta \phi (c-p)]-(1-\gamma )\rho \psi (p)$

F.o.c. $\gamma \beta \phi '(c-p)]-(1-\gamma )\rho \psi '(p)=0$

Take p as a function of $\beta$ and differentiate with respect to $\beta$:

$\gamma \beta \phi '[c-p^{*}(\beta )]-(1-\gamma )\rho \psi '[p^{*}(\beta )]=0$

$\gamma \phi '[c-p^{*}(\beta )]-\frac{dp^{*}}{d\beta }[\phi ''(c-p^{*}(\beta )]-\frac{dp^{*}}{d\beta }(1-\gamma )\rho \psi ''[p^{*}(\beta )]=0$

$\frac{dp^{*}}{d\beta }\left\{ [\phi ''(c-p^{*}(\beta )]+(1-\gamma )\rho \psi ''[p^{*}(\beta )]\right\} =\gamma \phi '[c-p^{*}(\beta )]$

$\frac{dp^{*}}{d\beta }=\frac{\gamma \phi '[c-p^{*}(\beta )]}{[\phi ''(c-p^{*}(\beta )]+(1-\gamma )\rho \psi ''[p^{*}(\beta )]}>0$

$\frac{dp^{*}}{d\beta }>0$

Furthermore, since $b^{*}=c-p^{*}$, $\frac{dp^{*}}{d\beta }>0$ implies $\frac{db^{*}}{d\beta }<0$.

Lemma 5b

More room for influence though punishment (a lower $\rho$) implies higher punishment and lower bribes $(\frac{dp^{*}}{d\rho }<0\qquad ;\frac{db^{*}}{d\rho }>0)$.

Proof:

$max_{p}\prod (b(p),p)=\gamma [\pi -\beta \phi (c-p)]-(1-\gamma )\rho \psi (p)$

F.o.c. $\gamma \beta \phi '(c-p)]-(1-\gamma )\rho \psi '(p)=0$

Take p as a function of $\rho$ and differentiate with respect to $\rho$:

$\gamma \beta \phi '[c-p^{*}(\rho )]-(1-\gamma )\rho \psi '[p^{*}(\rho )]=0$

$-\frac{dp^{*}}{d\rho }\gamma \beta \phi ''[c-p^{*}(\rho )]-\frac{dp^{*}}{d\rho }(1-\gamma )\rho \psi ''[p^{*}(\rho )]-(1-\gamma )\psi '[p^{*}(\rho )]=0$

- $\frac{dp^{*}}{d\rho }\left\{ \gamma \beta \phi ''[c-p^{*}(\rho )]+(1-\gamma )\rho \psi ''[p^{*}(\rho )]\right\} =(1-\gamma )\psi '[p^{*}(\rho )]$

$\frac{dp^{*}}{d\rho }=-\frac{(1-\gamma )\psi '[p^{*}(\rho )]}{\gamma \beta \phi ''[c-p^{*}(\rho )]+(1-\gamma )\rho \psi ''[p^{*}(\rho )]}<0$

$\frac{dp^{*}}{d\rho }<0$

Furthermore, since $b^{*}=c-p^{*}$, $\frac{dp^{*}}{d\rho }<0$ implies $\frac{db^{*}}{d\rho }>0$.

Proposition 5

More room for influence through bribes (a lower $\beta$) or punishment (a lower $\rho$) increases the degree of state capture (a lower ${\widetilde{\pi }}$).

Proof:

${\widetilde{\pi }}=\frac{(1-\gamma )}{\gamma }\rho \psi (p^{*})+\beta \phi (c-p^{*})$

Take $p^{*}$ as a function of $\beta$ and $\rho$:

$\frac{d{\widetilde{\pi }}}{d\beta }=\frac{dp^{*}}{d\beta }\frac{(1-\gamma )}{\gamma }\rho \psi '(p^{*})-\frac{dp^{*}}{d\beta }\beta \phi '(c-p^{*})+\phi (c-p^{*})$

$=\frac{dp^{*}}{d\beta }\underbrace{\left[ \frac{(1-\gamma )}{\gamma }\rho \psi '(p^{*})-\beta \phi '(c-p^{*})\right] }_{\text {=0 from f.o.c.}}+\phi (c-p^{*})=\phi (c-p^{*})>0$

$\Rightarrow \frac{d{\widetilde{\pi }}}{d\beta }>0$

$\frac{d{\widetilde{\pi }}}{d\rho }=\frac{(1-\gamma )}{\gamma }\psi (p^{*})+\frac{dp^{*}}{d\rho }\frac{(1-\gamma )}{\gamma }\rho \psi '(p^{*})-\frac{dp^{*}}{d\rho }\beta \phi '(c-p^{*})$

$=\frac{(1-\gamma )}{\gamma }\psi (p^{*})+\frac{dp^{*}}{d\rho }\underbrace{\left[ \frac{(1-\gamma )}{\gamma }\rho \psi '(p^{*})-\beta \phi '(c-p^{*})\right] }_{\text {=0 from f.o.c.}}=\frac{(1-\gamma )}{\gamma }\psi (p^{*})>0$

$\Rightarrow \frac{d{\widetilde{\pi }}}{d\rho }>0$

Proposition 6a

More room for influence through bribes (a lower $\beta$) has an ambiguous effect on the payoff of politicians and their quality.

Assume $\beta '<\beta$. From lemma 5a and proposition 5:

${b}^{*\prime }>{b}^{*}$

${p}^{*\prime }<{p}^{*}$

${\widetilde{\pi }}^{\prime } < {\widetilde{\pi }}$

Depending on the activity/inactivity of the pressure group, there will be three possible cases:

• 1. $\pi \ge {\widetilde{\pi }}$ and $\pi \ge {\widetilde{\pi }}'$ The group was also active before the lowering of the threshold. In this case, since the payoff $w-p^{*}$ (lemma 4) and since $\frac{dp^{*}}{d\beta }>0$ (lemma 5 a), if $\beta \downarrow$, $p\downarrow$, the payoff and the quality of the politicians increase: $V(\beta ')>V(\beta )$

• 2. $\pi <{\widetilde{\pi }}$ and $\pi <{\widetilde{\pi }}'$ The group is inactive both before and after the lowering of the threshold. The minimum threshold, although lowered, is still too high and the pressure group would not be able to gain from the influencing activity, thus remaining inactive. The payoff w (lemma 4) remains unchanged, as does the quality of the politicians: $V(\beta ')=V(\beta )$.

• 3. $\pi <{\widetilde{\pi }}$ and $\pi \ge {\widetilde{\pi }}'$ The group was inactive before and becomes active after the threshold is lowered. The payoff goes from w to $w-p^{*}$ (lemma 4), with $p^{*}>0$ (lemma 3). The payoff decreases and so does the quality of politicians: $V(\beta ')<V(\beta )$.

Proposition 6b

More room for influence though punishment (a lower $\rho$) decreases the payoff of politicians and their quality.

Assume $\rho '<\rho$. From lemma 5b and proposition 5:

$b^{*'}<b^{*}$

$p^{*'}>p^{*}$

${\widetilde{\pi }}'<{\widetilde{\pi }}$

Depending on the activity/inactivity of the pressure group, there will be three possible cases:

• 1. $\pi \ge {\widetilde{\pi }}$ and $\pi \ge {\widetilde{\pi }}'$ The group was also active before the lowering of the threshold. In this case, since the payoff $w-p^{*}$ (lemma 4) and since $\frac{dp^{*}}{d\rho }<0$ (lemma 5b, if $\rho \downarrow$, $p\uparrow$, the payoff and the quality of politicians decrease: $V(\rho ')<V(\rho )$.

• 2. $\pi <{\widetilde{\pi }}$ and $\pi <{\widetilde{\pi }}'$ The group is inactive both before and after the lowering of the threshold. The payoff w (lemma 4) remains unchanged, as does the quality of the politicians: $V(\rho ')=V(\rho )$.

• 3. $\pi <{\widetilde{\pi }}$ and $\pi \ge {\widetilde{\pi }}'$ The group was inactive before and becomes active after the threshold is lowered. The payoff goes from w to $w-p^{*}$ (lemma 4), with $p^{*}>0$ (lemma 3). The payoff decreases and so does the quality of politicians: $V(\rho ')<V(\rho )$.

1.3 A.3 Public goods and endogenous punishment

We now assume that $\rho$ is an increasing function of the level of public services: $\frac{d\rho _{t}}{dg_{t}}>0$. From lemma 5b, we have that $\frac{dp_{t}}{dg_{t}}<0$.

As a result, the public sector payoff increases as g (and $\rho$) increase:

$V_{t}=w_{t}-p_{t}^{*}(\rho _{t}(g_{t}))$

$\frac{dV_{t}}{dg_{t}}=\frac{d\rho _{t}}{dg_{t}}\left( -\frac{dp_{t}^{*}}{d\rho _{t}}\right) =-\frac{dp_{t}^{*}}{dg_{t}}>0$

And by assumption: $\frac{d^{2}V_{t}}{d^{2}g_{t}}<0$.

Consider an increase in public goods such that $\rho '>\rho$. From proposition 5, $\frac{d{\widetilde{\pi }}}{d\rho }>0$, and ${\widetilde{\pi }}(\rho ')>{\widetilde{\pi }}(\rho )\quad$. Now, depending on whether the increase in ${\widetilde{\pi }}$ is such that $\pi$ is exceeded or not, two cases can occur:

• 1. ${\widetilde{\pi }} > \pi$. The group switches to inactivity, and the public sector payoff increases discretely from $w-p*$ to w.

• 2. ${\widetilde{\pi }} < \pi$. The group remains active and the public sector payoff increases continuously because $p^{*}(\rho ')<p^{*}(\rho )$.

Appendix B: Descriptive statistics

Table 6 Descriptive Statistics

Table 7 Local public spending components (2004–2015)

Table 7 presents detailed summary statistics of each local public spending component. These include: administrative expenses (spending on municipal administrative structures); roads and transport (spending on local public transportation, public lighting, road construction, and maintenance); education (spending on school services, infrastructure, building maintenance, canteen service, and local school transportation); social services (spending on the provision of social services and the construction and maintenance of facilities such as childcare centers and elderly residences); environment, a function divided into several sub-items, including expenditures on waste management (service delivery, construction, and maintenance of facilities), expenditures on social housing and urban planning, and expenditures on water service delivery. The municipal budgets also include spending for municipal police, culture (promotion of cultural activities, maintenance and construction of theatres, libraries, and museums), sport (maintenance and construction of municipal sports facilities, organization of local events), tourism, justice (expenditures for the maintenance and management of judicial offices), productive services and expenditure for local economic development (classified as “Other” in the table).

Table 8 Total per-capita spending before, during, and after commissioner administration

Table 9 T-test on differences in average total per-capita spending

Appendix C: Southern Italian regions

See Table 10

Table 10 Southern Italian regions

Appendix D: Larger set of control variables

See Table 11

Table 11 Descriptive statistics for the larger set of control variables

Appendix E: Covariate balance before and after refinement

See Figs. 3 and 4

Fig. 3

Covariate Balance Before and After Refinement. Notes: Each scatter plot compares the absolute value of standardized mean difference for each covariate before and after refinement using propensity score weighting. Each row represents the results using different lag lenghts, whereas each column represents results related to different outcome variables. Dots below the 45-degree line indicate that the standardized mean balance improves after refinement

Fig. 4

Covariate Balance Over the Pre-treatment Time Period. Notes: Each plot shows the standardized mean difference over the pre-treatment period of three years. The solid black line represents the balance of the lagged outcome variable, whereas the grey lines represent that of other time varying covariates. The first row shows the balance before refinement (that is, after matching only on treatment history). The second row shows the balance after refining on past outcomes and past punishment activities from the mafia group, as suggested by the sufficient statistic approach. Finally, the third row presents covariate balance after refining for the full set of controls. Due to low variation within each municipality, corruption indices and the number of confiscations per capita are not plotted.

Appendix F: Randomly assigned placebo treatment

See Table 12

Table 12 Randomly assigned placebo treatment