Clientelism and development: Vote-buying meets patronage

Abstract

Offering employment in the public sector in exchange for electoral support (patronage politics) and vote-buying are clientelistic practices frequently used by political machines. In the literature, these practices are typically studied in isolation. In this paper, we study how the interaction between these two practices (as opposed to having just one tool) affects economic development. We present a theoretical model of political competition, where, before the election, the incumbent chooses the level of state investment that can improve productivity in the private sector. This decision affects the income levels of employees in the private sector, and, thereby, the costs and effectiveness of vote-buying and patronage. We show that when the politician can use both clientelistic instruments simultaneously, his opportunity cost for clientelism in terms of foregone future taxes declines. As a result, the equilibrium amount of public investment is typically lower when both tools are available than otherwise.

Keywords

Political clientelism vote-buying patronage economic development

1. Introduction

Political clientelism has received lots of scholarly attention over the past three decades. There is an extensive literature about non-programmatic distributive practices such as vote-buying and patronage that politicians use to try to win and retain office.¹ Clientelistic practices have been a subject of interest in seminal theoretical contributions to redistributive politics (Dixit and Londregan, 1996; Gallego, 2015; Lindbeck and Weibull, 1987; Persson and Tabellini, 2000; Rosas et al., 2014) as well as many empirical studies (Frye et al., 2014; Holland and Palmer-Rubin, 2015; Mares and Zhu, 2015). Yet most of the theoretical work study different clientelistic strategies in isolation (Dekel et al., 2008; Robinson et al., 2014; Robinson et al., 2017; Robinson and Verdier, 2013; Stokes et al., 2013). In practice however, politicians and political parties generally combine several non-programmatic methods. For instance, Bratton (2008) demonstrates the co-existence of vote-buying and threats of violence in the Nigerian elections. Recent work on the use of economic intimidation in the elections in Eastern Europe (e.g. Frye et al., 2019; Mares et al., 2018) show that politicians use a portfolio of clientelistic strategies, including vote-buying and economic threats in the workplace. Why do political machines use several instruments simultaneously? One immediate answer is that different instruments are needed to effectively target different sub-groups of the electorate. Gans-Morse et al. (2014) for example have argued that politicians prefer to use a mix of strategies, including turnout-buying of supporters and vote-buying and abstention-buying of citizens who are closer to opposition candidates because they care about net votes. However, to better understand how patrons choose among the menu of clientelistic tools at their disposal, one may need to move beyond the effect of each instrument in isolation and think about how one instrument complements or undermines the other when used together. Mares and Young (2018) have argued that politicians use both positive and negative inducements because they complement each other. For example, loss-averse voters are more likely to vote for the patron when political brokers first offer them privileged access to some goods or services, like cheap credit, state transfers, and then threaten to take these away if turnout and electoral support are not high enough. Rosas et al. (2014) lay out a theory of clientelism where incumbent politicians use programmatic politics (public good provision) and turnout-buying conjointly because they complement each other. The first policy helps the incumbent increase his popularity, and the second policy raises the probability that people will go to the polls.

This paper offers an alternative reason why political machines can resort to several non-programmatic methods simultaneously and show how the multiplicity of clientelistic tools can have a detrimental effect on private sector productivity. Our departure point is that clientelism not only diverts existing resources away from more productive uses but can also generate perverse incentives such as underinvestment in public goods that benefit large segments of the society without generating much political rent to politicians. We present a model, where an incumbent politician can both allocate public sector jobs as a patronage tool and hire a political broker to buy votes for him. Before the election takes place, the incumbent politician first decides on the level of public investment (e.g. in infrastructure) that increases productivity in the private sector. This raises tax revenues, a source of economic rent for the incumbent if he is reelected. The incumbent values income in the private sector only for the tax revenues it generates. This is because voters cannot commit to rewarding the incumbent for high levels of public investment since the latter is decided before the election in an irreversible way and leads to higher income for workers in the private sector regardless of the electoral outcome. After the public investment is made, both the incumbent and the opposition announce income tax rates on private sector incomes. Unlike the opposition, the incumbent has two additional tools he can use before the election. The first is patronage employment, a wage offer for public sector employees in exchange for their loyalty (electoral support). The second option is to buy the votes of private-sector workers using a broker.

Our model builds upon Robinson and Verdier (2013), where patronage motive is present but vote-buying is not an option. Robinson and Verdier (2013) consider a model, where the incumbent sets the level of productivity-enhancing public investment and faces a tradeoff between the higher amount of collected votes and lower future tax revenues. They show that the incumbent politician underinvests vis-à-vis the socially optimal level because lowering investment renders patronage more effective. A lower level of investment means lower incomes in the private sector, thereby making jobs in the public sector relatively more attractive. In our model, there are two additional mechanisms through which lowering investment raises the electoral support for the incumbent. First, lower incomes in the private sector mean more votes bought for a given transfer per client. This increases the incumbent's winning probability. Second, the higher the chances of electoral victory for the incumbent become, the more effort the broker exerts to allure clients. This is because his rewards —unlike his costs— are conditional on the reelection of his patron. The downside is that the lower incomes in the private sector lead to lower tax revenues. Hence, the potential rents to reelection decrease. Therefore, the incumbent faces a tradeoff between the number of votes collected and the level of future tax revenues. But since both patronage and vote-buying incentives work to reduce investment, having both tools at one's disposal, rather than just one of them, reduces the opportunity cost of clientelism (due to lost taxation rent) per vote.

To see why, first consider the case where patronage, via public sector employment, is the only available tool of clientelism. In the model, patronage employment in public sector is socially inefficient. Yet it generates private rents for employees as well as the politician who gets to win the election. A reduction in investment (i.e. incomes) in the private sector attracts more people into the public sector for a given patronage wage. This leads to a narrowing of the tax base. Suppose that, for each dollar of reduction in investment (in the private sector), tax revenues decrease by x dollars, while votes collected by patronage increase by q votes. Then, the opportunity cost of patronage per vote is $\frac{x}{q}$ dollars. Now, suppose that vote-buying is the only option and there is no patronage (i.e. no public sector employment). Say that a one-dollar reduction in investment leads to a fall in tax revenues by $y$ dollars but increases the number of votes bought by w votes. Thus, the opportunity cost of vote-buying is $\frac{y}{w}$ dollars per vote. Note that $y > x$ because, without patronage, more people are employed in the private sector, and so the tax base is larger. Finally, suppose that both patronage and vote-buying are used together. Then the patron could buy $w + q$ votes with a one-dollar reduction in investment, while the tax revenue foregone would only be x dollars (for the same initial size of the private sector). Therefore, the opportunity cost will be $\frac{x}{w + q}$ dollars per vote, which is less than the opportunity costs of patronage and vote-buying in isolation, that is, $\frac{x}{q}$ and $\frac{y}{w}$ , respectively. Since clientelism becomes cheaper (in terms of lost tax revenues) for the incumbent politician, we get more clientelism and lower investment (hence lower productivity) in the private sector.

Our comparative statics analyses show that higher office rents strengthen the incentives to underinvest in the private sector since stakes in winning the election become larger. This effect is stronger when vote-buying is added to patronage. We also show that when taxation becomes more efficient, the incumbent invests more in the private sector. This is because tax revenues, which depend on public investment, become more attractive in comparison to rents from public sector employment (patronage) and office rents.

We extend the model in various directions. In the baseline model, we assume that voters do not take the winning probabilities of the politicians into account as they vote, although their payoffs may depend on who wins the election. In an extension, we let voting decisions be partly observable to politicians and affect the post-election rewards to individual voters. In this case, voters with perfect foresight behave strategically (i.e. based on the probabilities of electoral victory for each politician), and the underinvestment problem becomes even more severe. When one clientelistic tool raises the winning probability for the incumbent, and voters become more confident about his victory, they have even more incentive to support him. Thus, in this case, vote-buying and patronage complement each other, that is, the use of one clientelistic tool increases the marginal effect of the other tool on the political outcome. This is the second explanation for why the political machine can use several clientelistic tools.

In another extension, we allow for clientelistic competition, in which, not only the incumbent but also the opposition can use patronage and/or vote-buying. We demonstrate that, when political machines compete, the incumbent's incentives to underinvest in the private sector get weaker. When the opposition can also buy votes, underinvestment in the private sector generates a positive externality for the opposition by lowering the cost per vote that the latter faces. Thus, the marginal effect of lowering investment on the incumbent's winning probability decreases. This result hints at one potential upside to clientelistic competition. Allowing for more clientelistic spending would not necessarily be detrimental as long as it levels the playing field in clientelistic competition. Yet, higher competition also intensifies a socially wasteful arms race between political parties, a downside that we abstract from in this model.

As we have mentioned above, in the literature of clientelism there are other clientelistic tools besides patronage and vote-buying, such as turnout buying and abstention buying (rewards to indifferent or opposing individuals for not voting). Although our main results would hold for other combinations of clientelistic tools under certain conditions, patronage is special because it affects the structure of the politician's post-election payoff. It creates additional rents that the politician can receive after winning the election, and these rents do not depend on the level of investment. They depend on how many people are employed in the public sector (tax-free sector). Patronage employment in turn reduces the size of the tax base. Therefore, the cost of patronage for the incumbent depends on income levels in the private sector, and thus on the level of investment. Moreover, because of the diminishing marginal utility of money for the incumbent, patronage rents make additional tax incomes less lucrative. When patronage and any other clientelistic tool are used together, the effect of the other tool becomes more detrimental since there is an additional part of the post-election payoff (rent from the public sector) that does not depend on the level of investment.

Our analysis, first and foremost, contributes to the literature about the connection between political clientelism and economic development.² Existing literature largely agrees that clientelism undermines economic development (Bustikova and Corduneanu-Huci, 2017; Kitschelt and Wilkinson, 2007; Remmer, 2007). But what are the channels through which clientelistic politics may restrain economic development? One way to answer this question is to study how rising incomes change the costs of clientelistic practices. One view is that higher incomes lower the marginal utility of money and, as a consequence, vote-buying becomes costlier for the politicians (Calvo and Murillo, 2004; Dixit and Londregan, 1996). Therefore, in a political environment where parties largely rely on clientelistic networks and vote-buying is rampant, politicians may have less incentive to follow growth-promoting policies. The second reason why clientelistic incentives may harm economic development is the hypothesis that poor voters have lower involvement in the broader national economy, and, due to lower levels of education, they cannot properly assess the indirect effects of macroeconomic policies on their economic well-being while welcoming the direct benefits politicians deliver in exchange for their votes (Kitschelt and Wilkinson, 2007). The third reason is connected with the risk-averse behavior of the poor, who prefer immediate vote-buying benefits to future programmatic policy (Kitschelt, 2000; Kitschelt and Wilkinson, 2007). Finally, economic growth may promote social and residential mobility, making it harder for brokers to maintain their clientelistic networks (Bloom et al., 2001; Kitschelt, 2010; Kitschelt and Wilkinson, 2007).

Our paper adds to this literature by analyzing how the developmental consequences of clientelism change when politicians use two instruments (patronage and vote-buying) simultaneously. We show that public investment and per capita incomes decline further when the incumbent politician has two instruments, instead of a single instrument, at his disposal. The reason is that with two instruments, lowering public investment to buy votes becomes cheaper for the incumbent (in terms of lost tax revenues per vote). In other words, having multiple instruments makes clientelism more efficient from the incumbent's perspective, but less efficient from the society's perspective.

This paper also draws on the literature on patron-broker-client relationships within clientelistic networks. Stokes (2005) studies the relationship between brokers and clients in Argentina. She finds that brokers can infer voters’ choices, and because of repeated interactions with clients in their network, they can credibly commit to rewards and punishments. She argues that vote-buying is an effective tool when political machines can use brokers to overcome informational problems. Another mechanism to discipline voters is described in Gallego (2015), where aggregate electoral results motivate voters to cooperate with clientelistic politicians. In our model, the incumbent relies on a broker to buy votes, and the broker makes transfers to voters before the election. Drawing on the existing justifications in the literature, we assume that recipients fully comply with their commitment to support the incumbent. Stokes et al. (2013) present a formal model of clientelism where the patron chooses a political broker, and the latter engages in vote-buying. In that model, the expected utility of the broker depends on the probability that the patron wins the election. We also model brokers similarly. They anticipate benefits from the patron, only if the latter wins the election. Thus, the broker's effort to reach out to voters does not only affect but also depends on the likelihood of electoral victory. Larreguy et al. (2016) observe that brokers have incentives to shirk, and provide evidence from Mexico that the patron's ability to monitor brokers affects the latter's performance. In line with this observation, in our model, we allow the broker to shirk. Our model also allows us to differentiate between three different channels through which productivity-enhancing public investments influence the electoral fate of the incumbent politician, and thus the latter's incentive to invest. The first channel concerns how public investment affects the brokers’ effort. The second channel concerns how investment reduces the size of the electorate the incumbent can attract via vote-buying, keeping the broker's effort constant. Lastly, we identify by how much the incumbent's winning probability is affected due to the effect of investment on patronage employment.

The paper is organized as follows. Section 2 presents the main model and our comparative statics results. In section 3, we study the case when the voters’ electoral choice is partially observable to the patron. Section 4 presents an extension where both candidates compete in vote-buying and patronage. Section 5 concludes.

2. Model

We present a theoretical model of electoral competition in the shadow of clientelistic politics. There are two politicians: an incumbent political machine (or patron)³ denoted by superscript ‘ $M$ ’ and an opposition denoted by superscript ‘ $O$ ’. First, the incumbent sets the level of public investment I, which determines the productivity and, hence, incomes in the private sector. Then he competes in an election contested by the opposition candidate, where both politicians announce a tax rate on incomes in the private sector. The incumbent has two additional tools at his disposal. He can offer some of the voters employment in the public sector. We call this strategy patronage. He can also buy votes by hiring a broker to attract voters employed in the private sector.

We consider a standard probabilistic voting model. There are two groups of voters: $g = 1, 2$ . As will be clear later on, one of these groups will be targeted via patronage and the other one for vote-buying. The mass of voters in group g is given by $λ_{g}$ such that $\sum_{g} λ_{g} = 1$ . A member i of group g gets a utility equal to $U^{i M} (\cdot) \equiv η H (c^{i M})$ if she votes for the incumbent, and receives $U^{i O} (\cdot) \equiv η H (c^{i O}) + δ_{g}^{i} + θ$ otherwise. We set $H (c^{i j}) = \frac{{(c^{i j})}^{1 - κ}}{1 - κ}$ , where $0 < κ < 1$ . This function reflects the utility from consumption, where $c^{i j}$ is consumption of the voter i under the policy proposed by politician $j \in {M; O}$ . $η > 0$ is a parameter denoting the non-random component in the utility function. $δ_{g}^{i}$ and $θ$ are random variables capturing the political preferences of agents. $δ_{g}^{i}$ captures the ideological proclivity of agent i in group g for the opposition candidate, relative to the incumbent. It measures the net utility of agent i from voting against the patron (incumbent) and is uniformly distributed within each group g. In particular, $δ_{g}^{i} \sim U [- \frac{1}{2 s_{g}}; \frac{1}{2 s_{g}}]$ , and $s_{g} > 0$ differ by group. $θ$ denotes the aggregate preference shock common to all voters. It captures the overall popularity of the opposition politician. It also follows a uniform distribution with $θ \sim U [- \frac{1}{2 h}; \frac{1}{2 h}]$ and $h > 0$ .

There are three potential sectors of employment in the economy: public sector, private formal sector and private informal sector. The mass of agents in group $g,$ who are hired to the public sector by politician $j,$ is denoted by $L_{g}^{j}$ . Each public worker from group g chooses to exert some effort $e_{w}^{g j} \in {0, ξ}$ ⁴ incurring a cost $ψ (e_{w}^{g j})$ with $ψ (ξ) > ψ (0) = 0$ and generating a surplus (public sector rents per worker) of $Q (e_{w}^{g j})$ for politician j such that $Q (ξ) > Q (0) = 0$ . With some probability $q_{g}^{j},$ the politician can observe the effort exerted by a given worker hired from group g.

Each worker in the private sector earns a pre-tax income of $A y (I)$ , where $y (I)$ is a continuously differentiable, strictly concave and strictly increasing function of public investment with $y^{'} (I) > 0, y^{″} (I) < 0, y (0) > 0$ and $A > 0$ denotes the worker productivity that does not depend on public investment. Formal employment in the private sector is taxable, but informal activity is not. If workers choose to move their income to the informal sector, they can only retain $α$ fraction of it, and their net income would be $α A y (I)$ . Taxation is costly so that net tax revenues are given by $τ T^{j}$ for $j \in {M; O}$ . $T^{j}$ is the gross tax revenue, and $τ$ is the fraction retained thereof after costs of taxation are deducted.

Voters, who work in the private sector, can sell their votes in exchange for an individual transfer $b_{i} (e_{b r})$ by the broker (a vote-buying payment). $e_{b r}$ captures the effort the broker spends to deliver benefits to voters. The broker's vote-buying technology is such that $b_{i} (0) = 0;$ $b_{i}^{'} (\cdot) > 0, b_{i}^{″} (\cdot) < 0$ and $lim_{e_{b r} \to 0} b_{i}^{'} (\cdot) = + \infty;$ $lim_{e_{b r} \to + \infty} b_{i}^{'} (\cdot) = 0$ . The broker's payoff is given by $P^{M} (\cdot) R - V C (e_{b r})$ , where $P^{M} (\cdot)$ is the probability that the incumbent gets elected, $R > 0$ is the exogenously given private rents the broker receives if the incumbent wins, and $V C (e_{b r})$ denotes the broker's cost of vote-buying and is equal to $V C (e_{b r}) = F + C (e_{b r})$ , with $F > 0, C (0) = 0 C^{'} (e_{b r}) > 0, C^{″} (e_{b r}) > 0$ . When $e_{b r} = 0$ , broker's payoff is zero. We assume that vote-buying is credible, because the broker provides goods or money to targeted voters before the election. The total utility that worker $i$ in the private sector receives from consumption is given by $H (b_{i} (e_{b r}) + α A y (I)),$ where consumption is the sum of private sector income $α A y (I)$ and the vote-buying transfer $b_{i} (e_{b r})$ .

Politicians’ payoff (conditional on electoral victory) is the utility of net taxes from the private sector $τ T^{j}$ , fixed monetary rents from holding office $V,$ and the net surplus (rents) the politician obtains from the public sector $\sum_{g} (Q (e_{w}^{g j}) - w_{g}^{j}) L_{g}^{j}$ , whereby $Q (e_{w}^{g j})$ and $w_{g}^{j}$ are the per capita output by and the wage offered to public sector workers, respectively. $\sum_{g} L_{g}^{j}$ is the size of public employment. As a result, the politician receives a payoff equal to $η H (τ T^{j} + V + \sum_{g} (Q (e_{w}^{g j}) - w_{g}^{j}) L_{g}^{j})$ if he wins the election; $η H (c^{j}) = η \frac{{(c^{j})}^{1 - κ}}{1 - κ}$ , where $0 < κ ⟨ 1, η ⟩ 0$ . Otherwise, the payoff is zero. Importantly, the incumbent incurs a cost of I that is equal to the level of investment he chooses regardless of the electoral outcome. Thus, the incumbent maximizes the following function: $E U_{V P}^{M} = P^{M} (\cdot) η H (τ T^{M} + V + \sum_{g} (Q (e_{w}^{g M}) - w_{g}^{M}) L_{g}^{M}) - I$ , where subscript $V P$ indicates that the incumbent ( $M$ ) uses both vote-buying and patronage at the same time, and $P^{M} (\cdot)$ is the probability that the incumbent gets elected.

The timing of the game is as follows:

First, the incumbent chooses the level investment I, and incomes in the private sector are realized.

Second, both politicians $j \in {M, O}$ offer a level of taxation on private sector incomes. In addition to that, the incumbent (but not the opposition) hires some of the voters for public employment, and his broker buys votes by offering $b_{i} (e_{b r}$ ) to each voter employed in the private sector.

People vote sincerely, and the candidate who gets the most votes wins the election.

Payoffs to politicians (utility from the sum of tax revenues, office rents and patronage rents) net of investment costs, the broker and voters (after-tax consumption and ideological utility associated with the candidate that is voted for) are realized.

2.1. Credible policies

We solve for the subgame-perfect Nash equilibrium (SPNE) in pure strategies. For this, we use backward induction. First of all, note that, no matter who wins the election, the level of taxation will be set to make voters indifferent between working in the formal private sector and moving to the informal one. So, the unique credible amount of tax each private sector worker is asked to pay is $(1 - α) A y (I)$ . Thus, taking into account the number of workers employed in public and private sectors and the costs of taxation, the total amount of net tax revenues will be $τ T^{j} = (1 - α) τ A y (I) ((λ_{2} + λ_{1} - \sum_{g} L_{g}^{j}), j \in M, O$ .

Now we consider the public sector. Politician j offers the wage in the state sector $w_{g}^{j}$ to voter i from group g. Due to moral-hazard problem in the public sector, the politician must offer at least an efficient wage such that the public worker prefers to exert effort $(e_{w}^{g j} = ξ)$ over shirking $(e_{w}^{g j} = 0) :$

η H (w_{g}^{j} - ψ (ξ)) \geq (1 - q_{g}^{j}) η H (w_{g}^{j})

where

q_{g}^{j}

is the probability that politician j catches a worker from group g when shirking. When worker is caught shirking, then he is fired and gets zero consumption. Since

H (c^{i j}) = \frac{{(c^{i j})}^{1 - κ}}{1 - κ}

, this condition can be rewritten as

w_{g}^{j} \geq \frac{ψ (ξ)}{1 - {(1 - q_{g}^{j})}^{\frac{1}{1 - κ}}} > ψ (ξ) > 0

(1)

We make the following assumption about the monitoring technology in the public sector.

Assumption 1.

$\frac{1}{1 - {(1 - q_{1}^{O})}^{\frac{1}{1 - κ}}} > \frac{Q (ξ)}{ψ (ξ)} > \frac{1}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}}$ and $\frac{1}{1 - {(1 - q_{2}^{j})}^{\frac{1}{1 - κ}}} > \frac{Q (ξ)}{ψ (ξ)}$

This assumption ensures that (i) it does not pay off for the opposition to hire from any group⁵ and (ii) if the incumbent decides to hire anyone, he will only recruit workers from group 1. Interpreted more broadly, this assumption reflects the idea that it may be optimal for the incumbent to target a particular group for patronage due to informational problems or lack of trust in the other groups’ loyalty. Formally, due to Assumption 1, we have $L_{2}^{M} = 0$ and $L_{1}^{O} = L_{2}^{O} = 0$ . Since only people in group 1 will work in the public sector, we can relabel the wage $w_{1}^{M}$ they receive from the patron simply as $w^{M}$ .

If the incumbent wants to offer employment in the public sector, he should offer a wage that also satisfies the participation constraint for the workers:

η H (w^{M} - ψ (ξ)) \geq η H (α A y (I))

The constraint ensures that a worker from group 1 is offered high enough a wage in the public sector that he is better off working as a public employee than in the private sector.⁶ Since

H (\cdot)

is an increasing function, we can rewrite this participation constraint as

w^{M} - ψ (ξ) \geq α A y (I)

(2)

So we can rewrite conditions (1) and (2) as

w^{M} \geq max {α A y (I) + ψ (ξ); \frac{ψ (ξ)}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}}}

(3)

This condition gives the lower-bound for wages that ensures that workers find public sector employment desirable and spend effort rather than shirking. Patronage takes place only when it is attractive for the incumbent to hire people at this lower-bound of efficiency wages. There is a tradeoff for the incumbent: hiring a worker for the public sector implies lower employment in the private sector and leads to a loss in future tax revenues. So, patronage employment exists when it is better, ex post, for the incumbent to have worker i work in the public sector instead of the private sector⁷:

Q (ξ) - w^{M} \geq (1 - α) τ A y (I)

(4)

When conditions (3) and (4) are both satisfied, the incumbent can credibly transfer part of his patronage rents to his clients. We impose two conditions given the following assumption

Assumption 2.

$\frac{(1 - α) τ}{α} > \frac{Q (ξ) (1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}) - ψ (ξ)}{ψ (ξ) {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}}; A y (0) > Q (ξ) - ψ (ξ)$

Firstly, Assumption 2 allows us to focus on the case where $w^{M} = \frac{ψ (ξ)}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}}$ ; and the inequality in (2) is always slack, whenever the condition in (4) is slack. Secondly, it implies that the socially efficient level of patronage employment is zero. We follow Robinson and Verdier (2013) and concentrate on the case, where the incumbent offers the efficiency wage, that is, $w^{M} = \frac{ψ (ξ)}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}}$ .

Assumption 3.

$η (A y (0))^{- κ} A y^{'} (0) > 1; lim_{I \to + \infty} {η {(A y (I))}^{- κ} A y^{'} (I)} < 1$ .

Assumption 3 guarantees that socially efficient level of the public investment is positive.⁸

Assumption 4.

Fixed costs of vote-buying F is sufficiently large such that vote-buying is socially inefficient.⁹

Assumption 4 means that creation of clientelistic networks involves high fixed costs so that it is inefficient to have vote-buying in the society.

Let us denote by $I_{0}$ the level of public investment, such do that $Q (ξ) - w^{M} = Q (ξ) - \frac{ψ (ξ)}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}} = (1 - α) τ A y (I_{0})$ . Then, if $I \leq I_{0},$ patronage takes place – in this case public employment is more attractive than taxes from the private sector, and thus, all members of group 1 will be hired for public employment, that is, $L_{1}^{M} = λ_{1}$ . Otherwise, that is, when $I > I_{0},$ we have the non-patronage case where $L_{1}^{M} = 0$ .

In the private sector, we assume that the vote-buying arrangement is fully credible for brokers as well as clients. This would be the case because the broker provides goods or money to voters before the election, and he interacts with his clients repeatedly (Gallego, 2015; Nichter, 2008; Stokes, 2005) so that non-compliant clients can be identified and excluded from future benefits. Another explanation why credible arrangement takes place can be reciprocity (Finan and Schechter, 2012), that is, the feeling of obligation to vote for the politician who provides vote-buying benefits. Each voter in the broker's network is offered a benefit of $b_{i} (e_{b r})$ . Then, including the private sector income $α A y (I)$ , the total utility a client within the broker's network obtains from consumption is $H (b_{i} (e_{b r}) + α A y (I))$ .

2.2. Behavior of voters

Now, let's turn to the voters’ decision. Constituents from the first group know that public employment with wage $w^{M}$ is credible only when offered by the incumbent political machine, because the latter can extract rents while the opposition cannot. Therefore, an agent from the first group supports the incumbent if

η H (w^{M} - ψ (ξ)) - η H (α A y (I)) - θ \geq δ^{i}

(5)

Let

N_{g}^{M} \in [0, λ_{g}]

be the total number of people in group

g,

who support the incumbent. For a given level of investment I, the total number of voters in the first group, who support the incumbent is

N_{1}^{M} = N_{1}^{M} (I) = λ_{1} Prob (δ^{i} \leq η H (w^{M} - ψ (ξ)) - η H (α A y (I)) - θ) = λ_{1} {\frac{1}{2} + s_{1} [η H (w^{M} - ψ (ξ)) - η H (α A y (I)) - θ]}

Voter i from group 2 has a private income of

α A y (I)

and can also get an individual vote-buying payment. Constituent

i,

who is offered a vote-buying payment from the incumbent supports the incumbent if

η H (b_{i} (e_{b r}) + α A y (I)) - η H (α A y (I)) - θ \geq δ^{i}

(6)

Let us denote

b (e_{b r})

as the benefit of the marginal voter (i.e. the voter for whom condition (6) holds as equality and, therefore, who is offered the largest vote-buying payment). The total number of people from the second group, who vote for the incumbent, is the sum of the mass of core supporters of the incumbent

S_{2}^{M}

, who vote for the incumbent even in the absence of vote-buying payments, and the mass of agents

V B (I, b)

who agree to sell their votes for a payment of

b_{i}

\begin{aligned} N_{2}^{M} = N_{2}^{M} (I, b) = S_{2}^{M} + V B (I, b) = λ_{2} {\int_{- \frac{1}{2 s_{2}}}^{0} s_{2} d i + \int_{0}^{η H (b (e_{b r}) + α A y (I)) - η H (α A y (I)) - θ} s_{2} d i} \\ = λ_{2} {\frac{1}{2} + s_{2} [η H (b (e_{b r}) + α A y (I)) - η H (α A y (I)) - θ]} \end{aligned}

Clearly, the number of votes for the political machine from the second group increases with vote-buying payment

b (e_{b r})

Now we can determine the probability that the political machine wins the election:

Prob {\sum_{g} N_{g}^{M} \geq \frac{1}{2} \sum_{g} λ_{g}} \equiv P^{M} (I, b) \equiv P^{M}

This condition is equivalent to the probability that the aggregate ideology shock

θ

is sufficiently small:

\begin{aligned} P^{M} (I, b) = & Prob {θ \leq η λ_{1} s_{1} [H (w^{M} - ψ (ξ)) - H (α A y (I))] \\ + η λ_{2} s_{2} [H (b (e_{b r}) + α A y (I)) - H (α A y (I))]} \\ = \frac{1}{2} + h η λ_{1} s_{1} [H (w^{M} - ψ (ξ)) - H (α A y (I))] \\ + h η λ_{2} s_{2} [H (b (e_{b r}) + α A y (I)) - H (α A y (I))] \end{aligned}

(7)

For simplicity, we have normalized the sum

\sum_{g} λ_{g} s_{g}

so that

\sum_{g} λ_{g} s_{g} = 1

Equation (7) reflects the fact that when the incumbent does not use vote-buying and patronage, elections are fair. Indeed, if $b (e_{b r}) = 0$ and $w^{M} = α A y (I) + ψ (ξ)$ , then $P^{M} = \frac{1}{2}$ , that is, the opposition and the incumbent candidates have equal chances to win.

2.3. Broker's optimization problem

A hired broker has the following optimization problem:

max_{e_{b r} \geq 0} E U^{B R} = P^{M} (I, b (e_{b r})) R - V C (e_{b r})

The broker's payoff is the difference between the expected rents from the incumbent's victory

P^{M} (I, b (e_{b r})) R

and the vote-buying costs for the broker

V C (e_{b r}) = F + C (e_{b r})

. The first-order condition for the broker's problem is

\frac{\partial E U^{B R}}{\partial e_{b r}} = \frac{\partial P^{M}}{\partial e_{b r}} R - C^{'} (e_{b r}) = 0

(8)

We assume that the rents R is sufficiently large so that equilibrium broker's expected utility is positive and, as a consequence, we have an interior solution to the broker's problem.

On the one hand, additional effort by the broker increases the incumbent's winning probability, that is, $\frac{\partial P^{M}}{\partial e_{b r}} > 0$ , and thus, raising the broker's expected rents. On the other hand, additional effort is costly for the broker and thus diminishes his utility. The influence of public investment on the broker's effort is negative, that is, $\frac{d e_{b r}}{d I} < 0$ . This is because a higher level of I reduces the marginal utility of money, that is, the vote-buying effect on elections decreases. As a result, expected rents from the incumbent's victory become lower, and, thus, the broker prefers to exert less efforts.

2.4. Incumbent patron's problem

Now let us turn our attention to the incumbent's choice. He maximizes his expected utility from consumption, which depends on fixed office rent V, tax revenues $τ T^{M}$ , and rents he extracts from the public sector $\sum_{g} (Q (e_{w}^{g M}) - w_{g}^{M}) L_{g}^{M}$ . When $I \leq I_{0}$ , all agents from the first group have patronage employment, $L_{1}^{M} = λ_{1}$ . Since it is not optimal to target group 2 via patronage, we also have $L_{2}^{M} = 0$ . Thus, public sector rents for a reelected incumbent are equal to $(Q (ξ) - w^{M}) λ_{1}$ . At the same time, only the second group of voters, who work in the private sector, generates tax revenues: $τ T^{M} = (1 - α) τ A y (I) λ_{2}$ . The incumbent obtains a payoff of $η H (V + (1 - α) τ A y (I) λ_{2} + (Q (ξ) - w^{M}) λ_{1})$ only in the case of victory, that is, with probability $P^{M} (I, b (e_{b r} (I)))$ . The incumbent's cost is equal to public investment, $I,$ that he chooses before the elections. Thus, the incumbent politician's problem is

max_{0 \leq I \leq I_{0}} E U_{V P}^{M} = P^{M} (I, b (e_{b r} (I))) η H (V + (1 - α) τ A y (I) λ_{2} + (Q (ξ) - w^{M}) λ_{1}) - I

We assume that the second-order condition for the incumbent's problem is satisfied on the interval

[0; I_{0}]

. The first-order condition for the patron's problem is given by

\frac{\partial P^{M}}{\partial I} η H (X^{M}) + P^{M} η H^{'} (X^{M}) (1 - α) τ A y^{'} (I) λ_{2} - 1 = 0

(9)

where

X^{M} = V + (1 - α) τ A y (I) λ_{2} + (Q (ξ) - w^{M}) λ_{1}

\begin{aligned} \frac{\partial P^{M}}{\partial I} = \underset{p a t r o n a g e e f f e c t}{\underset{⏟}{- h λ_{1} s_{1} η H^{'} (α A y (I)) α A y^{'} (I)}} \\ + \underset{d i r e c t v o t e - b u y i n g e f f e c t}{\underset{⏟}{h λ_{2} s_{2} η [H^{'} (b (e_{b r}) + α A y (I)) - H^{'} (α A y (I))] α A y^{'} (I)}} \\ + \underset{n e g a t i v e e f f e c t o n p o l i t i c a l b r o k e r}{\underset{⏟}{h λ_{2} s_{2} η H^{'} (b (e_{b r}) + α A y (I)) b^{'} (e_{b r}) e_{b r}^{'} (I)}} < 0 \end{aligned}

Equation (9) shows the tradeoff between a higher amount of collected votes, on the one hand, and a lower level of tax revenues, on the other hand. A smaller level of I increases the probability of winning for the incumbent, that is,

\frac{\partial P^{M}}{\partial I} < 0

. This is partly due to the existence of patronage employment (Robinson and Verdier, 2013). However, as we can see, vote-buying gives additional incentive to the incumbent to reduce public investment. A higher amount of investment I, reduces the difference between the utilities that the incumbent and the opposition offer to the constituents:

[H^{'} (b (e_{b r}) + α A y (I)) - H^{'} (α A y (I))] < 0

. This is the direct vote-buying effect. A smaller amount of public investment gives comparative advantage to the political machine. Finally, the last term in the above inequality quantifies the reduction in the winning probability that is due to the negative effect of public investment on the broker's vote-buying effort, A higher public investment reduces the voters’ desire to sell their votes, which, in turn, reduces the marginal return (in terms of votes) to the broker's effort and hence the expected benefit from his effort.

Let's denote $(I_{V P}^{*}, e_{V P}^{*})$ ¹⁰ as an equilibrium values, for the levels of investment chosen by the incumbent, and the broker's vote-buying effort, when both patronage in the public sector and vote-buying are used together (the problem described above). Let's denote $(I_{V}^{*}, e_{V}^{*})$ as the corresponding equilibrium values, when only vote-buying is used. Finally, let us denote the equilibrium level of investment, when only patronage is used by $I_{P}^{*}$ .¹¹ The following proposition compares levels of investment, I, when the incumbent combines the two clientelistic tools to the levels when he uses only one of them.

Proposition 1 (Public investment under different clientelistic configurations).

Equilibrium public investment is lower than the socially efficient level when both vote-buying and patronage are used together, that is, $I_{V P}^{*} < I_{e}^{*},$ where $I_{e}^{*}$ is determined by the following condition $\frac{d (η H (A y (I_{e}^{*})))}{d I} = 1.$

If $V (o r Q (ξ))$ is sufficiently large, then $I_{V P}^{*} < I_{P}^{*}$ ,that is, public investment is lower when the incumbent uses both clientelistic tools instead of just patronage.

If $V (o r Q (ξ))$ is sufficiently large, then $I_{V P}^{*} < I_{V}^{*}$ , that is, public investment is lower when the incumbent uses both clientelistic tools instead of just vote-buying.

Proof

See the Appendix.

The incumbent invests in the private sector just because higher I boosts tax revenues he will collect if he wins the election. However, there are several reasons, why $I_{V P}^{*} < I_{e}^{*}$ . First, since $P^{M} < 1,$ the political machine may lose the election and lose access to future tax income. Unlike the social planner who does not care about the elections, the incumbent internalizes this effect by lowering investment. Second, the existence of an informal sector and tax administration costs $τ$ reduces the net amount of collected taxes, thereby lowering the incumbent's incentive to enhance private sector productivity. Third, although public sector rents for the incumbent go up when the incumbent hires more people to work in the public sector, at the same time, taxable income base (total private sector output) goes down. Finally, the incumbent underinvests in the private sector also due to a desire to amplify the effects of both patronage and vote-buying as clientelistic tools: First, smaller incomes in the private sector make public employment more attractive, thereby increasing the effect of patronage on political outcome. Second, when incomes are low the marginal utility of money is high. Thus, marginal electoral return to vote-buying payments is higher. Finally, when I is lower, the likelihood of victory for the incumbent is higher, and therefore the political broker exerts higher effort.

To compare the levels of public investment when the incumbent uses both clientelistic tools instead of only patronage, we should determine the role of vote-buying. Vote-buying has two effects on public investment. On the one hand, it gives an incentive to the incumbent for investing less so as to attract more votes from constituents who are employed in the private sector. On the other hand, a higher number of purchased votes means a higher probability of winning, and as a consequence, a higher chance of collecting tax incomes after the election. Thus, a higher chance of winning incentivizes investment. When V (fixed office rent) or $Q (ξ)$ (rents from public sector) is large, the first effect dominates, and we have $I_{V P}^{*} < I_{P}^{*}$ .

Similarly, patronage has also two opposing effects on public investment. However, unlike vote-buying, patronage employment changes the allocation of workers across sectors. Higher employment in the public sector reduces the amount of tax income because only $λ_{2}$ agents (workers in the private sector) pay taxes. This, in turn, diminishes the incentive to invest in the private sector. Moreover, because of diminishing marginal utility of money, the marginal value of tax revenues for the politician is lower in the presence of patronage rents. Finally, when both instruments are used together, the negative effect of vote-buying on I gets stronger, because, now, in addition to tax revenue, the incumbent can capture patronage rents from the public sector $(Q (ξ) - w^{M}) λ_{1}$ . This, other things being equal, makes electoral victory more lucrative. On the other hand, since the winning probability goes up (because of using two instruments instead of one), other things being equal, the incumbent has more incentive to increase tax income by providing more public investment. However, with V $(o r Q (ξ))$ being large, the negative effect dominates.

2.5. Opportunity cost of clientelism

We have shown that vote-buying and patronage affect I in the same direction. One way to understand this result is to analyze how the incumbent's opportunity cost (in terms of utility from lost taxes) per vote change when he uses two instead of one clientelistic tool. Let's define the opportunity costs of getting one additional vote, as

O C = - \frac{\frac{\partial (η H (X^{M}))}{\partial I}}{\frac{\partial P^{M}}{\partial I}}

where

\frac{\partial (η H (X^{M}))}{\partial I}

reflects the change in the patron's utility from the net tax revenues, and

\frac{\partial P^{M}}{\partial I}

is the change in the probability of winning.

Proposition 2.
For any given level of $I \in [0; I_{0}]$ , when the incumbent uses both patronage and vote-buying simultaneously, his opportunity cost (in the form of lost taxes) per vote in this situation

is lower than in the case where he only uses patronage, that is, $O C_{V P} < O C_{P}$ ;

is lower than in the case where he only uses vote-buying, that is, $O C_{V P} < O C_{V}$ .

Proof
The first-order condition in (9) states that the incumbent needs to sacrifice part of the tax revenue (by reducing $I)$ to increase his probability of winning the election, that is, for each lost dollar of tax revenue, the incumbent receives some additional votes. Since vote-buying and patronage both lower I, the use of both clientelistic tools, simultaneously, allows the incumbent to reduce the opportunity cost per vote. When investment is reduced by a given amount, this not only allows the incumbent to buy more votes, but it also amplifies the effect of patronage. Thus, when the political machine uses both patronage and vote-buying, for each lost dollar of tax revenue, he gets a higher number of votes than if he had used only one tool. In addition, it should be stressed that $O C_{V P} < O C_{V}$ , not only because of a higher probability of winning, but also due to two additional reasons. First, in the absence of patronage, there is no inefficient public employment, and tax revenues are higher for any $I,$ that is, the losses from economic underdevelopment are higher. Second, the existence of patronage rents decreases the value of tax revenues for the incumbent due to diminishing marginal utility of money.
Proposition 3.
When the political machine uses both patronage and vote-buying, simultaneously, the equilibrium level of opportunity cost per vote

is lower than in the case where only patronage is used, that is, $O C_{V P} (I_{V P}^{}, e_{V P}^{}) < O C_{P} (I_{P}^{}),$ if $V$ $(o r Q (ξ))$ is sufficiently large and* $O C$ is an increasing function of $I .$ ¹²

is lower than in the case where only vote-buying is used, that is, $O C_{V P} (I_{V P}^{}, e_{V P}^{}) < O C_{V} (I_{V}^{}, e_{V}^{}),$ if V $(o r Q (ξ))$ is sufficiently large and $O C$ is an increasing function of $I .$

Proof
See the Appendix.
2.6 Comparative statics

The following propositions present the comparative statics results for the solution $(I_{V P}^{*}, e_{V P}^{*})$ to our baseline model.

Proposition 4.

An increase in fixed office rent, $V,$ leads to a decline in incomes in the private sector and raises vote-buying benefits
$\frac{d b (e_{b r}^{} (I^{}))}{d V} > 0, \frac{d (α A y (I^{}))}{d V} < 0.$

When* $O C$ is an increasing function of $I,$ a rise in fixed office rent, $V,$ leads to a decrease in the equilibrium level of opportunity cost of clientelism
$\frac{d O C_{V P} (I^{})}{d V} < 0.$

Proof
See the Appendix.

A higher value of fixed office rent makes clientelism more attractive for the incumbent. Moreover, utility from tax incomes becomes lower when V is high because of diminishing marginal utility of money for the incumbent. It leads to a decrease in investment which, in turn, reduces incomes in the private sector, that is, $\frac{d (α A y (I^{}))}{d V} < 0$ . A lower level of $I^{}$ raises the expected rents for the broker, and thus, he exerts higher effort. $\frac{\partial (Δ_{3} (I))}{\partial I} > | \frac{κ (1 - α) τ λ_{2} \frac{\partial P^{M}}{\partial I}}{X^{M}} |$ ensures that the opportunity cost of clientelism increases with I . This lowers the equilibrium level of $O C_{V P} (I^{})$ as fixed office rent V increase.
Proposition 5.

When taxation becomes more efficient, that is, $τ$ rises, incomes in the private sector increase and the amount of vote-buying diminishes
$\frac{d b (e_{b r}^{} (I^{}))}{d τ} ⟨ 0, \frac{d (α A y (I^{}))}{d τ} ⟩ 0.$

When,* $O C$ is an increasing function of $I,$ an increase in the efficiency of taxation (higher $τ$ ) raises the opportunity cost of clientelism
$\frac{d O C_{V P} (I^{})}{d τ} > 0$

Proof
See the Appendix.

A change in administrative costs of taxation has three effects on public investment. First, when the costs decrease (i.e. higher $τ$ ), post-election tax revenues increase. This makes clientelism more attractive and in response, the incumbent wants to lower public investment so as to increase his probability of winning the election. Second, since the incumbent's utility is concave in consumption, an increase in post-election tax revenues lowers the marginal return to public investment as a second tool for the incumbent to raise revenues. On the other hand, when the administrative costs of taxation decline (i.e. higher $τ$ ), for each additional dollar of taxable income the marginal gain for the incumbent in terms of net tax revenues goes up. Thus, raising incomes in private sector via public investment becomes more attractive in comparison to getting rents from public sector employment or private rents from holding office. In the Appendix, we show that, in equilibrium, the latter positive effect of $τ$ on $I^{}$ dominates the negative effects. At the same time, when $I^{*}$ increases, the expected rents for the broker go down, and the latter exerts less effort. Hence, vote-buying payments and the number of votes bought go down. Thus, equilibrium opportunity cost of clientelism increases in this case.
3. Observable voting

In the main model, we have assumed that constituents vote sincerely, and voting is not observable. In this section, we relax both of these assumptions. Now let's suppose that voters know the probability of winning for the incumbent $P^{M} (I, b (e_{b r} (I)))$ and that this is common knowledge. Suppose that, with probability $p \in (0; 1],$ the incumbent can observe how his constituent has voted. In this case, a citizen from the first group votes for the incumbent if

p P^{M} η (H (w^{M} - ψ (ξ)) - H (α A y (I))) - θ \geq δ^{i}

Since the relationships between the political broker and his clients are long-term, clients often expect getting vote-buying payment, not only before elections, but also after political competition in the case of patron's victory. For simplicity, we consider the situation, when clients get benefits only after elections. Constituent i from the second group supports the political machine if

p P^{M} η (H (b^{i} (e_{b r}) + α A y (I)) - H (α A y (I))) - θ \geq δ^{i}

Again, we can calculate the probability of winning for the incumbent as

P^{M} = \frac{1}{2 (1 - h λ_{1} s_{1} p η (H (w^{M} - ψ (ξ)) - H (α A y (I))) - h λ_{2} s_{2} p η (H (b (e_{b r}) + α A y (I)) - H (α A y (I))))}

Like in the main setup, the impact of public investment on the probability of winning the election consists of three effects: (i) the effect through patronage, (ii) the direct effect through vote-buying and (iii) the indirect effect on vote-buying through changing the incentives of the broker

\frac{\partial P^{M}}{\partial I} = \frac{P^{M}}{D} (\begin{matrix} \underset{p a t r o n a g e e f f e c t}{\underset{⏟}{- h λ_{1} s_{1} p η H^{'} (α A y (I)) α A y^{'} (I)}} + \underset{d i r e c t v o t e - b u y i n g e f f e c t}{\underset{⏟}{h λ_{2} s_{2} p η (H^{'} (b (e_{b r}) + α A y (I)) - H^{'} (α A y (I))) α A y^{'} (I)}} \\ + \underset{n e g a t i v e e f f e c t o n p o l i t i c a l b r o k e r}{\underset{⏟}{h λ_{2} s_{2} p η H^{'} (b (e_{b r}) + α A y (I)) b^{'} (e_{b r}) e_{b r}^{'} (I)}} \end{matrix}),

where

D = 1 - h λ_{1} s_{1} p η (H (w^{M} - ψ (ξ)) - H (α A y (I))) - h λ_{2} s_{2} p η (H (b (e_{b r}) + α A y (I)) - H (α A y (I)))

Now that voters anticipate the winning probability that would result for a given set of policies, politicians pursue, and have an incentive to respond to it. The optimal behavior for the incumbent needs to internalize, not only the effects of relative monetary rewards, offered to voters in case of victory, but also how patronage, and vote-buying decisions, shape voters’ expectations, regarding the outcome of the election. Therefore, one should, intuitively, expect patronage and vote-buying to further reinforce each other. If the constituent knows that the political machine uses patronage and vote-buying, he understands that the patron will win the election with a higher probability. Since, in that case, the post-election rewards to supporters accrue with higher probability, voters become uniformly more likely to vote for the incumbent. Moreover, since the broker's effort has a greater impact on election outcomes now, he exerts more effort in this case. Accordingly, we can see the complementarity of two clientelistic tools, since the using of one of them increases marginal effect of other on the political outcome.

In this section, we assume that the incumbent has an alternative technology, in the public sector, which allows him to generate a personal rent of $(Q (ξ) - \frac{ψ (ξ)}{1 - {(1 - q_{1}^{M})}^{\frac{1}{1 - κ}}})$ and allows him to punish deviating voters.¹³ As a result, ex post, not all voters from the first group get the job in the public sector. Thus, the incumbent's problem becomes

max_{0 \leq I \leq I_{0}} E U_{V P}^{M} = P^{M} (\cdot) η H (V + (1 - α) τ A y (I) (λ_{2} + λ_{1} - L_{1}^{M}) + (Q (ξ) - w^{M}) L_{1}^{M}) - I

where

L_{1}^{M} = E [N_{1}^{M}]

is the expected number of voters from the first group who support the incumbent.

\frac{\partial E U_{V P}^{M}}{\partial I} = \frac{\partial P^{M}}{\partial I} η H (X^{M}) + P^{M} η H^{'} (X^{M}) (1 - α) τ A y^{'} (I) (λ_{2} + λ_{1} - L_{1}^{M}) + P^{M} η H^{'} (X^{M}) ((Q (ξ) - w^{M}) - (1 - α) τ A y (I)) \frac{\partial L_{1}^{M}}{\partial I} - 1 = 0

(10)

where

X^{M} = V + (1 - α) τ A y (I) (λ_{2} + λ_{1} - L_{1}^{M}) + (Q (ξ) - w^{M}) L_{1}^{M}

The first-order condition in (10) is similar to the condition in (9), but there is an additional term

{P^{M} η H^{'} (X^{M}) ((Q (ξ) - w^{M}) - (1 - α) τ A y (I)) \frac{\partial L_{1}^{M}}{\partial I}} < 0, where \frac{\partial L_{1}^{M}}{\partial I} < 0

. This term reflects the effect of the change in the number of taxpayers. For low levels of

I,

fewer voters from the first group will deviate. Thus, in equilibrium there will be fewer taxpayers from the first group. In general, all the main insights which we derive from our main model carry through for this extension.

4. Dueling machines

Although monopolistic clientelism is more common, there are cases where clientelism is competitive. For instance, it is not uncommon that different parties target different constituencies via clientelistic tools. Now we extend our main model to consider two competing machines, namely that both the incumbent and the opposition can use both clientelistic tools (patronage and vote-buying). For this purpose, we introduce two more groups in the model: group 3 and group 4, with population mass of $λ_{3}$ and $λ_{4},$ respectively. We assume that group 3 is the (only) constituency that the opposition candidate can target via patronage. That is, the public rents to the opposition from patronage satisfies: $\frac{1}{1 - {(1 - q_{3}^{M})}^{\frac{1}{1 - κ}}} > \frac{Q (ξ)}{ψ (ξ)} > \frac{1}{1 - {(1 - q_{3}^{O})}^{\frac{1}{1 - κ}}}$ . For simplicity, we consider the case when $q_{3}^{O} = q_{1}^{M}$ and, as a consequence, $w^{M} = w^{O},$ where $w^{O} -$ efficiency wage paid by the opposition. Suppose that the opposition hires his own broker, who can offer vote-buying payments only to clients in group 4. This broker's problem is given by $max_{e^{O} \geq 0} E U_{O}^{B R} = (1 - P^{M}) R^{O} - V C^{O}$ .

We assume that the incumbent cannot target group 3 or group 4 via any clientelistic tool. Thus, he receives the following number of votes from the third and fourth groups, respectively

N_{3}^{M} = λ_{3} {\frac{1}{2} + s_{3} [η H (α A y (I)) - η H (w^{O} - ψ (ξ)) - θ]}

N_{4}^{M} = λ_{4} {\frac{1}{2} + s_{4} [η H (α A y (I)) - η H (b^{O} (e^{O}) + α A y (I)) - θ]}

Unlike the first and second groups, the mass of supporters

N_{3}^{M}

and

N_{4}^{M}

increases with the level of public investment I. The probability that the incumbent wins the election is

P^{M} (I, e^{M} (I), e^{O} (I)) = \frac{1}{2} + h λ_{1} s_{1} η [H (w^{M} - ψ (ξ)) - H (α A y (I))] + h λ_{2} s_{2} η [H (b^{M} (e^{M}) + α A y (I)) - H (α A y (I))] + h λ_{3} s_{3} η [H (α A y (I)) - H (w^{O} - ψ (ξ))] + h λ_{4} s_{4} η [H (α A y (I)) - H (b^{O} (e^{O}) + α A y (I))]

P^{M} (I, e^{M} (I), e^{O} (I)) = \frac{1}{2} + h λ_{1} s_{1} η Δ U_{P}^{M} + h λ_{2} s_{2} η Δ U_{V}^{M} + h λ_{3} s_{3} η Δ U_{P}^{O} + h λ_{4} s_{4} η Δ U_{V}^{O}

where

Δ U_{P}^{M} = [H (w^{M} - ψ (ξ)) - H (α A y (I))]

Δ U_{V}^{M} = [H (b^{M} (e^{M}) + α A y (I)) - H (α A y (I))]

Δ U_{P}^{O} = [H (α A y (I)) - H (w^{O} - ψ (ξ))]

Δ U_{V}^{O} = [H (α A y (I)) - H (b^{O} (e^{O}) + α A y (I))]

Now, this probability does not necessarily decrease with public investment anymore, because of clientelistic competition. The direction of the effect depends on the number of groups

λ_{i},

their ideological homogeneity

s_{i}

and the difference between brokers’ offers to clients. As in the main model, we can define the opportunity costs of acquiring an additional vote (i.e. clientelism) for both politicians as

O C^{M} = - \frac{\frac{\partial (η H (X^{M}))}{\partial I}}{\frac{\partial (h η (λ_{1} s_{1} Δ U_{P}^{M} + λ_{2} s_{2} Δ U_{V}^{M}))}{\partial I}}; O C^{O} = - \frac{\frac{\partial (η H (X^{O}))}{\partial I}}{\frac{\partial (h η (λ_{3} s_{3} Δ U_{P}^{O} + λ_{4} s_{4} Δ U_{V}^{O}))}{\partial I}} .

Utilities from consumption for the incumbent and the opposition are given by

η H (X^{M}) = η H (V + (1 - α) τ A y (I) (λ_{2} + λ_{3} + λ_{4}) + (Q (ξ) - w^{M}) λ_{1})

and

η H (X^{O}) = η H (V + (1 - α) τ A y (I) (λ_{1} + λ_{2} + λ_{4}) + (Q (ξ) - w^{O}) λ_{3}),

respectively. We can see that for any given level of investment

I,

\frac{\partial (η H (X^{M}))}{\partial I} \leq \frac{\partial (η H (X^{O}))}{\partial I},

when

λ_{1} \geq λ_{3} .

Then, if

| \frac{\partial (h η (λ_{1} s_{1} Δ U_{P}^{M} + λ_{2} s_{2} Δ U_{V}^{M}))}{\partial I} | > | \frac{\partial (h η (λ_{3} s_{3} Δ U_{P}^{O} + λ_{4} s_{4} Δ U_{V}^{O}))}{\partial I} |

and

λ_{1} \geq λ_{3},

that is, when the incumbent has less tax-payers in the private sector and his clientelistic networks allow him to produce more votes, the opportunity cost of clientelism, for the incumbent, is lower than the cost for the opposition. Therefore, we can say that, in this case, he has a comparative advantage in clientelistic competition.

Proposition 6.
When $\frac{\partial P^{M}}{\partial I} < 0$ and $λ_{1} \geq λ_{3},$ if the incumbent politician uses both patronage and vote-buying, for any given $I \in [0; I_{0}]$ , then

his opportunity cost is less than the opposition's opportunity cost, when the latter uses both patronage and vote-buying, $O C_{V P}^{M} < O C_{V P}^{O} .$

his opportunity cost is less than the opposition's opportunity costs, when the latter uses only vote-buying, $O C_{V P}^{M} < O C_{V}^{O} .$

his opportunity cost is less than the opposition's opportunity costs, when the latter uses only patronage, $O C_{V P}^{M} < O C_{P}^{O} .$

Proof
Condition $\frac{\partial P^{M}}{\partial I} < 0$ guarantees that the incumbent is more efficient in clientelistic networks, that is, vote-buying and patronage generate more votes for him in all three cases. $λ_{1} \geq λ_{3}$ means that in any of the scenarios (i) to (iii), the utility from lost taxes for the incumbent are not higher than those for the opposition for any given $I \in [0; I_{0}]$ .

Finally, note that the net effect of investments for the incumbent, (in terms of the opportunity cost defined in the basic model) ${- \frac{\frac{\partial (η H (X^{M}))}{\partial I}}{\frac{\partial P^{M}}{\partial I}}},$ will be higher than in the main model, because the decline in the level of public investment also benefits the opposition and, thus, generates a smaller share of votes.
5. Conclusion

Previous studies consider patronage and vote-buying in isolation. Building on Robinson and Verdier (2013), we have presented a formal model, in which we consider the interaction between two main types of clientelistic practices –patronage via public employment and vote-buying. A political machine chooses the level of public investment which improves productivity in the private sector before the election takes place and faces a tradeoff between getting more votes today and obtaining a lower amount of tax revenue from the private sector if elected.

Similar to some of the previous literature, in our model costs of vote-buying for the politicians rise with the income of individuals due to diminishing marginal utility of money (Calvo and Murillo, 2004; Dixit and Londregan, 1996). However, our work shows that vote-buying and patronage interact in non-trivial ways. Combining both tools makes clientelism cheaper by reducing the opportunity costs of clientelism in the form of lost taxes. This does not necessarily mitigate the economic inefficiency associated with clientelism. In particular, when personal rents from holding office or rents from patronage employment is sufficiently high, using vote-buying and patronage conjointly is more detrimental for economic development than using each in isolation. This problem is exacerbated when the political choice of constituents is observable, and voters’ post-election benefits depend on the likelihood the incumbent wins the election. These predictions are new contributions to the literature on the developmental consequences of clientelism.

Our paper also contributes to the patron-client relationship literature by showing that a high level of public investment has a negative effect on the political broker's efforts. To overcome this effect, the incumbent decreases the amount of public investment. In the case when both politicians use clientelistic strategies, the opportunity cost for the incumbent becomes larger and the latter has less incentive to underinvest While we have abstracted from the agency problems between the patron and the broker, studying these problems within the same framework may be a fruitful direction for future research.

Footnotes

Acknowledgements

We thank the editor, the three anonymous referees and Kemal Kıvanç Aköz for valuable comments. The article was prepared within the framework of the Basic Research Program at the National Research University Higher School of Economics (HSE). Vladimir Shchukin also acknowledges institutional support RVO 67985998 from the Czech Academy of Sciences.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship and/or publication of this article.

Appendix

ORCID iD

Vladimir Shchukin

Notes

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