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Abstract

This paper develops a theoretical model of political competition in which a lobby group provides financial support to candidates running for election in return for favorable policy outcomes. The lack of a legally binding contract may lead politicians to use campaign funds for their own personal benefit. However, this expropriation occurs entirely unexpected to the lobby group, which is non-strategic in nature. We find that there is a utility-maximizing fraction based on which politicians should allocate contributions between campaigning and private use. This fraction is increasing in the election winning premium and the proximity of the lobby group’s ideal position. It is less obvious, however, how this fraction relates to the relative importance of money for private consumption in the utility function. This fraction is determined by the comparison between the income effect, which pulls money toward personal consumption, and the substitution effect, which takes money away from personal consumption for campaigning.

JEL Classification: D72, D82.

Plain language summary

A model of non-strategic lobbying with campaign fund misappropriation

We develop a model of political competition in which a lobby group provides financial support to candidates running for election in return for favorable policy outcomes. In the absence of a legally binding contract, politicians may be tempted to use campaign funds for personal purposes. However, this expropriation occurs entirely unexpected to the lobby group that is non-strategic. There is a utility-maximizing fraction based on which politicians should allocate contributions between campaigning and private use. This fraction is increasing in the election winning premium and the proximity of the lobby group’s ideal position. It is less obvious, however, how this fraction relates to the relative importance of money for private consumption in the utility function. This fraction is based on the comparison between the income effect, which pulls money toward personal consumption, and the substitution effect, which takes money away from personal consumption for campaigning.

Keywords

special interest politics non-strategic lobby groups electoral competition expropriation

Introduction

Currently, campaigning for elections is becoming more expensive (see, e.g., Nassmacher, 2019). In the run-up to their next federal election, Australian politicians spent around $3.2 million on YouTube advertisements in 2021, according to a recent report by Google Transparency (https://transparencyreport.google.com/?hl=en). As reported by Harvard Political Review, the amount spent in the 2020 US presidential and congressional elections far surpassed that of the 2016 and 2012 elections. The majority of politicians rely on lobby group contributions to finance their campaign expenditures because of their financial constraints (Hall & Deardorff, 2006). As a result, there is often a deal between a lobby group and a politician. In this arrangement, the lobby group provides a monetary contribution to the politician’s electoral campaign. In exchange, the politician agrees to offer a certain policy concession if they win the election. Throughout history, this has been the most common and most effective means by which lobby groups have influenced policy-making processes (see, for instance, Austen-Smith, 1987; Baron, 1989; Besley & Coate, 2001; Fouirnaies, 2018; Fouirnaies & Hall, 2018; Grossman & Helpman, 1994; Herrnson et al., 2019; Powell & Grimmer, 2016).

Nevertheless, some of the money donated by lobby groups may not be used for campaigning. There have been cases in which politicians are found to misappropriate campaign fund (See Pinto-Duschinsky, 2002 and Senior, 2006 for discussions of publicized cases of malpractice by politicians around the world.). As a donor, do lobby groups always foresee the misappropriation of politicians? And if so, do they stop providing money to politicians? There is no single answer to each of these questions. A different perspective is presented by Acemoglu et al. (2001, 2002) in their studies of the effects of colonial institutions on economic performance in former colonies. They find that economic outcomes are worse in colonies with institutions designed to expropriate wealth. In those countries, a settler’s ability to survive shaped institutional structure. Their research also examine how expropriation strategies lead to institutional stagnation in formerly prosperous regions. Another study was conducted (Caselli & Cunningham, 2009) on how leaders appropriate natural resource revenues for political purposes. They assert that a country with weak institutions is more vulnerable to expropriation, which can lead to lower growth over the long run. In countries where political corruption is rampant, campaign fund misappropriation probably does not come unexpected. According to Solaz et al. (2019), voters, in spite of disliking corruption, may still elect or re-elect corrupt politicians due to the ‘in-group bias’ which makes them prefer supporting their in-group corrupt candidates to those out-group competitors. This means that lobby groups will continue to pay money to politicians to play politics regardless of whether they are able to foresee the corrupt behavior of politicians or not. The difference lies in the presence of strategic calculations of their plan. In fact, there are several situations where a lobby group may not be able to obtain a perfect foresight of the possible misappropriation. For example, the lobby group may be myopic or the lobbied politicians may not be interested in seeking a re-election in the future (If politicians do not seek another term, they may care less about potential consequences of fund misappropriation. As such, they may be more tempted to reward themselves with personal consumption.).

In this paper, we introduce a game theoretic model of menu auction between a lobby group and two politicians. The politicians seek contributions from the lobby group for their campaign funds in exchange for a policy favor. It is assumed that the politicians have a tendency to expropriate part of the contribution for their own use. We consider the situation in which the bad behavior of the politicians is utterly their private information and not at all foreseen by the lobby group. This is a case in which the lobby group is not strategically aligned (i.e., the lobby group is non-strategic). In this framework, we explore how non-strategic lobbying and expropriation of campaign contributions by politicians affect equilibrium policies.

Our model is built on a few existing works dealing with campaign funding expropriation such as those by Le and Yalcin (2018, 2023a, 2023b) and Le et al. (2024) which draw their roots from the menu auction literature (e.g., Austen-Smith, 1987; Baron, 1994; Grossman & Helpman, 1996; Polk et al., 2014). Le and Yalcin (2018, 2023b) are the pioneering research papers that explicitly model politicians’ misappropriation of campaign contributions. In those papers, each politician’s level of misappropriation is assumed to be exogenous but fully observable to lobby groups. Le and Yalcin (2023a) continue to assume that expropriation by politicians is fully observable to the lobby group but make it endogenous in the model instead. By contrast, in this current paper, while the misuse level is endogenously determined by parameters of the model as in Le and Yalcin (2023a), it is a piece of private information and comes entirely unexpected to the lobby group. In other words, the lobby group under consideration is non-strategic. Studies on non-strategic lobbying, which occurs without direct alignment to specific political or economic payoffs, allow us to examine the mechanisms, and contexts. These studies explore how lobbying impacts policy outcomes without providing direct benefits. As a result, the strategy of each politician is to determine the amount of expropriation, the policy platform, and the amount of contributions to maximize their benefit. In contrast, the position of the lobby group is simply to determine the policy platform and contribution amounts in order to maximize its own benefit. Thus, the decision to expropriate funds is revealed at the end of the political game and does not necessarily enter into the lobby groups’ strategic calculations. Across diverse scenarios, a few studies have examined non-strategic lobbying in the existing literature. For example, Grossman and Helpman (2001) analyze how interest groups influence policymakers through non-strategic information provision. They show that it is sometimes possible for interest groups to lobby without having a clear policy target, and instead focus on signaling expertise and legitimacy. In another study, Bertrand et al. (2014) distinguish between informational lobbying and influence peddling in U.S. lobbying. They find that instead of explicitly seeking direct policy favors, firms often lobby to share technical expertise. Lobbying, according to Lohmann (1993), serves as a mechanism of providing credible information for interest groups. He shows that lobbying efforts are non-strategic when they aim to inform policymakers about relevant issues without demanding specific action. Ansolabehere et al. (2003) examine why lobbying expenditures are relatively low in US politics. They claim that rather than influencing immediate policy decisions, lobbying can serve as non-strategic insurance. More recently, de Figueiredo and Richter (2014) emphasize the differences between strategic and non-strategic lobbying efforts as well as empirical methods used to study lobbying. They show that lobbying without a strategic plan is primarily about establishing long-term influence and reputations. In the same vein, Baumgartner et al. (2009) study how lobbying influences policy outcomes over time in the US context. Their findings indicate that lobbying rarely leads to immediate policy changes, suggesting a non-strategic and long-term focus of lobbying activities. In addition, the impact of lobbying depends more on persistence and issue salience than on targeted influence.

Within this theoretical framework, we examine the impact of lobbying on policy-making. Additionally, we analyze how the optimal level of expropriation is determined when the lobby group operates in a non-strategic manner. The lobby group is defined as non-strategic when it does not anticipate any intention on the part of politicians to divert a portion of the contributions for personal purposes. We obtain several interesting results. The lobby group will identify the candidate it wishes to support. It will then reach an agreement with this politician on the policy platform to be implemented and the amount of money to be donated. While the deal maximizes the lobby group’s utility, it leaves the politician at least as well off as in the status quo. However, not all the contribution from the lobby group will be spent on the politician’s campaign. The politician has a proclivity to divert a portion of the funds for personal consumption. Based on our analysis, the politician follows the optimal allocation of funds between campaigning and personal consumption. The optimal level of expropriation is shown to be always increasing in the election winning premium and the lobby group’s ideal policy. It is increasing in the relative importance of expropriated money only when this factor is sufficiently large. In that case, the substitution effect outweighs the income effect. The substitution effect diverts contribution money from personal consumption toward campaigning, while the income effect causes contribution money to be diverted toward personal consumption. The reverse holds true when the utility weight of money for personal consumption is sufficiently small due to the dominance of income effect over its substitution effect counterpart.

While our study is primarily theoretical and contributes to the theoretical literature on lobbying and electoral outcomes, it also aligns with the growing empirical literature examining the impact of campaign contributions on the electoral success of political candidates. As an example, Stratmann (2009) find that campaign spending is productive for both incumbents and challengers in US House of Representatives elections. Similarly, using US county-level data, Bombardini and Trebbi (2011) estimate that each additional vote costs roughly $145 in campaign spending for each political candidate. Similarly, within the context of a developing country, Virananda et al. (2021) observe that campaign money increases the winning probability of political candidates in Indonesia. Specifically, their findings indicate a 5-percentage-point increase in winning probability for every additional IDR 100 million spent on campaign activities. More recently, Wang (2022) and Le et al. (2024) show that campaign contributions exert a positive and significant effect on candidates’ election outcomes in Taiwan and the US, respectively.

The remainder of the paper is organized as follows. Section 2 outlines the basic structure of the model. Section 3 investigates equilibrium policy positions. Section 4 looks into the optimal allocation of contributions between campaigning and personal use. Finally, Section 5 offers some concluding remarks.

The Model

The electorate under consideration has two political parties competing with each other over an election, one lobby group, and a continuum of voters. For simplicity, assume that each party consists of only one politician so party and politician are used interchangeably. The lobby group is assumed to be unsophisticated or non-strategic in the sense that it is unable to foresee all strategic moves of the politicians as described below. Let us consider a political game of multiple stages with the timeline as follows. First, the lobby group reaches out to each politician to negotiate over a menu of policy positions that are linked with monetary contributions, supposed to be used for campaigning purposes. Second, upon observing the menu, each politician chooses the policy position that he or she wishes to pursue. Third, the lobby group pays each politician the corresponding contribution as previously agreed. Fourth, the politicians privately and secretly allocate the received contribution between campaigning and/or personal use. It should be noted that since the lobby group is non-strategic, it has no prediction about the politicians’ expropriation acts when paying the contributions. Fifth, the election takes place with probabilistic voting.

Following Le and Yalcin (2018, 2023a, 2023b), let us begin by defining the two politicians as $X$ and $Y$ , each of which has the following utility function, $V$ :

V_{j} = Ω (S) R + {[(1 - θ_{j}) M_{j}]}^{γ}, for j = (X, Y)

(1)

In this equation, the mathematical notations are as follows:

For the first component, $Ω (s)$ is the probability that party $j$ wins the election. Note that the function $Ω (.)$ has the following properties: $0 \leq Ω (.) \leq 1$ (i.e., bounded between 0 and 1), $Ω' (.) > 0$ and $Ω ″ (.) \leq 0$ (i.e., increasing and concave) while $S \geq 0$ is the proportion of voters supporting party $j$ in the electorate. This means that the probability of winning the election of party $j$ is an increasing and concave function of the proportion its supporting voters and it bounded between 0 and 1. $R > 0$ denotes the election winning premium such as the benefits from holding the office or political reputation once the politician wins the election. Hence, $Ω (S) R$ denotes the expected utility derived from winning an election.

$Mj \geq 0$ is monetary amount that the lobby group contributes to party $j$ ’s election campaign. $θ_{j} \in [0, 1]$ is the fraction of contribution used for campaigning in the election by party $j$ , leaving $(1 - θ_{j})$ as the fraction of fund used for personal use of the politician. $γ \in [0, 1]$ measures how much the politician values personal use of the contribution versus campaigning. Thus, ${[(1 - θ_{j}) M_{j}]}^{γ}$ renders party $j$ ’s utility gain from expropriating the campaign fund.

With $S$ increasing in $θ_{j}$ (to be specified more clearly later), there is a trade-off between spending campaign fund on electoral purposes (to increase $S$ , which in turn increases the utility from winning an election) and spending on personal use. This trade-off triggers the utility maximization for party $j$ .

Assume that expropriation is utterly the politician’s private information so any fund embezzlement can only be revealed at the end of the game.

Remark 1. This assumption is reasonable if the game is only played once. This situation could happen when a politician decides not to run for another election or to retire from his or her political career after the election. As such, the expropriation of campaign money happens as a surprise, rather than an expectation, for the non-strategic lobby group. Therefore, any strategic calculation on expropriation levels will be from the politicians’ viewpoints only. This is the key assumption that marks the substantial departure of the modeling work in this paper from that in existing studies. For the case of fully observable and exogenous expropriation levels, see Le and Yalcin (2018, 2023b) and for the case of strategic lobby groups with endogenous expropriation levels, see Le and Yalcin (2023a).

Note that the representative candidate’s utility defined in Equation 1 is an additive function of two components: winning the election and embezzling money for personal purposes. With $γ$ being the exponent of the monetary component to capture the relative importance of fund embezzlement in the utility function, by assuming γ between 0 and 1, we signal that the candidate values election victory (which has an indirect effect on utility) more than the monetary extraction (which has a direct effect on utility).

Among all voters of mass 1 in the electorate (we normalize the size of all voters to 1 for simplicity), there are $(1 - α)$ voters who fully understand the impact of policies on their welfare (i.e., informed voters). A representative informed voter’s preference is defined as:

u_{i} = - {(P_{i} - P_{j})}^{2}

(2)

where $P_{i}$ is his or her preferred policy and $P_{j}$ is the pliable policy issue conducted by party $j$ . This equation means that any deviation from the preferred policy will result in a utility reduction for the voter. Following Grossman and Helpman (1996), assume that although the parties cannot directly observe $P_{i}$ , they know that the representative informed voter’s relative preference follows a uniform distribution over the range:

u_{i} (P_{X}) - u_{i} (P_{Y}) ~ [- \frac{1}{2 d} - \frac{b}{d}, \frac{1}{2 d} - \frac{b}{d}]

(3)

where $d > 0$ is the measure of the diversity of views about the politicians and $b$ represents informed voters’ inherent ideological bias for party $j$ . The representative informed voter will vote for party $X$ if $u_{i} (P_{X}) - u_{i} (P_{Y}) \geq 0$ . As such, the politicians will perceive $F [u_{i} (P_{X}) - u_{i} (P_{Y})] = \frac{1}{2} + b + d [u_{i} (P_{X}) - u_{i} (P_{Y})]$ as the probability that voter $i$ will vote for party $X$ (in here $F (.)$ is the cumulative distribution function). A similar result can be reached for party $Y$ due to symmetry.

Uninformed voters, with a total number of $α$ in the electorate, have no prior ideological preference. They cast their votes based on the amount of information they receive on each candidate. This means that uninformed voters can be influenced by campaign advertisements (According to Wattenberg, 1991, there may be informed voters who cannot make decisions either. However, to make our model more tractable, we do not consider this case.). Taken together, the share of voters (both informed and uninformed) supporting party $X$ (and with symmetry for party $Y$ ) will be:

S = \frac{1}{2} + b + α h (θ_{X} M_{X} - θ_{Y} M_{Y}) + (1 - α) d [U (P_{X}) - U (P_{Y})]

(4)

where $h > 0$ measures the campaigning efficiency and $U (P_{j}) = \frac{1}{n_{I}} \int_{i \in I} u_{i} (P_{j}) di$ denotes informed voters’ average welfare ( $I$ is the set of informed voters and $n_{I}$ is the total number of them). In the case of no lobbying activity, each party’s optimal policy is to support the policy that best serves the average informed voter. Thus, the expected policy for implementation will be the midpoint of the policy positions by the candidates, or $\frac{P_{X} + P_{Y}}{2}$ . Hence, the share of voters supporting party $X$ in this jurisdiction will be $\hat{S} = \frac{1}{2} + b$ . Assume that within the continuum of policy that spans over [−1, 1], the policy domain for party $X$ is [0, 1] and for party $Y$ is [−1, 0]. This means that an average informed voter expects party $X$ to choose ${\hat{P}}_{X} = 0^{+}$ (on the right side of the median value 0) and party $Y$ to choose ${\hat{P}}_{Y} = 0^{-}$ (on the left side of the median value 0).

Despite being non-strategic, the lobby group has a well-defined preference over the pliable policy issue (i.e., their ideological policy standpoint). To influence the policy outcomes, the lobby group approaches the politicians, offers them monetary contributions toward their election campaigns. In return, the politicians agree to make some concession, particularly in terms of adopting a policy platform that better serves the needs of the lobby group. The lobby group’s expected utility is given by:

U_{L} = - Ω (S) {(P_{X} - P_{L})}^{2} - [1 - Ω (S)] {(P_{Y} - P_{L})}^{2} - M_{X} - M_{Y}

(5)

where $P_{L}$ is the lobby group’s ideal policy.

Political Equilibrium

In an attempt to find a sub-game perfect Nash equilibrium of the above described political game, we put forward the definition below:

Definition 1. An equilibrium is a set of vectors of feasible policy positions $(P_{X}, P_{Y})$ , contribution amounts ${M_{X} (P_{X}), M_{Y} (P_{Y})}$ and fractions of fund spent on campaigning $(θ_{X}, θ_{Y})$ such that:

• $P_{X}$ maximizes $U_{L}$ given $P_{Y}$ , $M_{X} (P_{X})$ and $M_{Y} (P_{Y})$

• $P_{Y}$ maximizes $U_{L}$ given $P_{X}$ , $M_{X} (P_{X})$ and $M_{Y} (P_{Y})$ ;

• Each $M_{j}$ , for $j = {X, Y}$ , is non-negative, continuous and differentiable and satisfies the compatibility constraint $V_{j} \geq \tilde{V_{j}}$ where $\tilde{V_{j}}$ is party $j$ ’s utility in the absence of lobbying;

• Each $θ_{j}$ maximizes $V_{j}$ given $(P_{j}, M_{j})$ , for $j = {X, Y}$ .

Specifically, these conditions define an equilibrium that is reachable in the negotiation process between the parties and the lobby group as well as in the policy announcement phase.

Suppose that the lobby group offers politician $j (j = {X, Y})$ a contribution to his or her electoral campaign. In return, the politician promises to conduct a policy platform $P_{j}$ that is more closely aligned to the lobby group’s own interest if the politician wins the election. Because the lobby group is non-strategic, it does not foresee any intention of politician $j$ in diverting part of the contribution to his or her personal use. As such, it simply offers party $j$ the amount of $M_{j}$ based on the compatibility constraint $S \geq \hat{S}$ . In other words, in doing so, it simply assumes that 100% of the contribution amount will be used for campaigning (i.e., $θ_{j} = 1$ ). This means that any fund embezzlement after the contribution has been paid is totally unexpected to the lobby group (Note that the probability function $Ω (S)$ is increasing in $S$ so an increase in $S$ will improve the probability of winning the election. Hence, the condition $Ω (S) \geq Ω (\hat{S})$ is equivalent to $S \geq \hat{S}$ .). This implies that the minimum amount of contribution is given by:

M_{j} = \frac{(1 - α) {d P}_{j}^{2}}{α h}

(6)

which is tied to policy platforms negotiated (In fact, the contribution takes the form that $M_{j} = \frac{(1 - α) {d P}_{j}^{2}}{α h} + ϵ$ where $ϵ > 0$ . Taking the limit $ϵ \to 0$ gives the result in Equation 6.). In this formulation, $(1 - α) d$ is the expected marginal loss (in terms of informed voter share) due to the deviation from the median policy while $α h$ is the expected marginal gain (in terms of uninformed voter share) due to campaign advertising. It is reasonable to assume that $(1 - α) d \leq α h$ so that lobbying is worth undertaking for the lobby group. Under this assumption, $0 \leq M_{j} \leq 1$ since $0 \leq P_{j}^{2} \leq 1$ by construction. Having obtained the equilibrium level of contributions, we can now solve for the equilibrium policy positions. Here, the lobby group will maximize its utility given in Equation 5 subject to the constraints in Equation 6. This is a standard utility maximization problem with two choice variables, $P_{X}$ and $P_{Y}$ . This problem can be solved by taking derivative of the utility function with respect to each choice variable. However, before proceeding further, we take advantage of the result that has been proved by Le and Yalcin (2018, 2023a) and discussed in Austen-Smith (1987), Baron (1988), and Hall and Deardorff (2006) that the lobby will contribute to at most one candidate to simplify this maximization problem to:

{M a x}_{P_{j}} - Ω (S) {(P_{j} - P_{L})}^{2} - [1 - Ω (S)] P_{L}^{2} - M_{j}

(7)

subject to the constraint on the contribution described in Equation 6. Note that in the lobby group’s view, the share of voters supporting party $j$ in the electorate is given by:

S = \frac{1}{2} + b + α h M_{j} - (1 - α) {d P}_{j}^{2}

(8)

This maximization problem yields the following result:

Lemma 1. Assume that $α hR Ω^{'} (\frac{1}{2} + b) > 1$ . The unique equilibrium policy platform between the lobby group and its allied politician takes the following form:

P_{j}^{*} = \frac{α h Ω (\frac{1}{2} + b) P_{L}}{(1 - α) d + α h Ω (\frac{1}{2} + b)}

(9)

Proof. First, consider the assumption that $α hR Ω^{'} (\frac{1}{2} + b) > 1$ to see why it is needed. Note that $α hR Ω^{'} (\frac{1}{2} + b)$ is the marginal benefit of campaigning and 1 is the marginal cost to the lobby group given that it does not know about the politician’s intention to expropriate a fraction of campaigning fund (i.e., the lobby group is non-strategic in that sense). Hence, the condition $α hR Ω^{'} (\frac{1}{2} + b) > 1$ is required to make sure that campaigning is a worthwhile activity from the politician’s point of view. Otherwise, the politician does not want to launch any election campaign despite taking the contribution from the lobby group. We impose this condition so that the election game can proceed to campaigning and then voting at later stages.

We now turn to the lobby group’s perspective. The first order necessary condition for the lobby group’s utility maximization is:

\begin{matrix} \frac{\partial U_{L}}{\partial P_{j}} = - Ω^{'} (S) \frac{\partial S}{\partial P_{j}} {(P_{j} - P_{L})}^{2} - 2 Ω (S) (P_{j} - P_{L}) \\ + P_{L}^{2} Ω^{'} (S) \frac{\partial S}{\partial P_{j}} - \frac{\partial M_{j}}{\partial P_{j}} = 0 . \end{matrix}

Using Equations 6 and 8 to calculate the partial derivatives for $S$ and $M_{j}$ with respect to $P_{j}$ and inserting the results into the above equation gives:

- Ω (\frac{1}{2} + b) (P_{j} - P_{L}) - \frac{(1 - α) d P_{j}}{α h} = 0 .

Solving this equation for $P_{j}$ yields the equilibrium policy position given in Equation 7. As for the second order sufficient condition, we have:

\frac{\partial^{2} U_{L}}{\partial P_{j}^{2}} = - Ω (\frac{1}{2} + b) - \frac{(1 - α) d}{α h} < 0,

which is satisfied for a maximum.

This lemma indicates that in this equilibrium, the lobby group reaches an agreement with the political party of its choice on an implemented policy, $P_{j}^{*}$ , as expressed in Equation 9. While this policy maximizes the lobby group’s interest, it makes the political party equally well off thanks to the donation made from the lobby group for the party’s campaign funding.

Optimal Allocation of Campaign Contributions

In this section, we examine the politician’s strategy regarding the use of contribution received from the lobby group. As discussed, the politician can spend the money on campaigning and/or other non-campaigning purposes. In making his or her decision, the politician will choose the allocation of funds that maximizes his or her utility. Relevant obtained results are discussed below.

Lemma 2. The optimal fraction of contribution devoted to campaigning, $θ$ , is given by:

θ_{j}^{*} = 1 - {[\frac{γ}{α hR Ω^{'} (\frac{1}{2} + b)}]}^{\frac{1}{1 - γ}} \frac{{[(1 - α) d + α h Ω (\frac{1}{2} + b)]}^{2}}{(1 - α) d α h Ω^{2} (\frac{1}{2} + b) P_{L}^{2}} .

(10)

Proof. The politician’s utility maximization problem will be the one of choosing $θ_{j}$ to maximize $V_{j}$ given in Equation 1. The first order necessary condition is:

\frac{\partial V_{j}}{\partial θ_{j}} = Ω^{'} (S) \frac{\partial S}{\partial θ_{j}} R - γ M_{j}^{γ} {(1 - θ_{j})}^{γ - 1} = 0 .

Using Equation 4 to 8 calculate the partial derivatives of $S$ with respect to $θ_{j}$ before substituting these into the above equation, and then simplifying the obtained results, we have:

θ_{j} = 1 - {[\frac{γ}{α hR Ω^{'} (\frac{1}{2} + b)}]}^{\frac{1}{1 - γ}} . \frac{1}{M_{j}} .

Upon making use of Equations 6 and 9, we get $θ_{j}^{*}$ as specified in Equation 10. It can be verified that the second order sufficient condition with respect to $θ_{j}$ is satisfied for a maximum (For a concise presentation, we do not show the result on the second order sufficient condition here. However, it can be made available from the authors upon request.).

The result in Equation 10 indicates that as soon as $γ \neq 0$ then $θ_{j}^{*} < 1$ . This means that if the lobby group makes a financial contribution to the politician’s electoral fund and if there is no legally binding contract stating that the funds must be used for campaigning only, the politician will have a proclivity to divert some money toward his or her own private use. For a certain set of parameters, Equation 10 specifies the utility maximizing fraction of contributions devoted to campaigning (and, equivalently, the optimal degree of expropriation). Therefore, we can formally state the results obtained above in the following proposition:

Proposition 1. The lobby group and the allied politician will be able to reach an agreement on both policy platform to be conducted and contribution level to be paid. With the contribution received, the allied politician has a proclivity to expropriate some amount for personal purposes. There exists a unique fraction of contribution that the politician should divide between campaigning and personal extraction to maximize his or her utility.

This result is similar to the one obtained in Le and Yalcin (2023a) in which funding expropriation by the allied politician is fully observable by the lobby group. Essentially, in the menu auction game between the lobby group and its allied politician, both sides will be able to negotiate with each other over an agreement. In this agreement, the politician is committed to conduct a policy that is as close to the lobby group’s ideal policy as possible if the politician wins the election (For simplicity, assume that the politician does not renege on the announced policy.). In return, the lobby group makes a monetary payment toward the politician’s campaign fund. In the absence of an effective monitoring mechanism, the politician has an incentive to embezzle some of this contribution. In doing so, the politician privately and secretly splits the money between campaigning (to increase his or her chance of winning the election) and personal consumption in order to maximize his or her utility (Strictly speaking, each politician’s strategy is to maximize the number of votes. Given the context of proportional electoral system that we are considering, maximizing the number of votes is equivalent to maximizing the election winning probability.).

With this establishment on the optimal degree of campaign fund devoted to campaigning, we can now move on to examine the effects of a change in some important parameters on this measure. We summarize the key results in the proposition below:

Proposition 2. The optimal fraction of contribution devoted to campaigning, $θ^{*}$ , is always increasing in the election winning premium, $R$ , and the lobby group’s ideal policy, $P_{L}$ . However, it will be increasing in the relative importance of expropriated contributions, $γ$ , only if $γ$ is sufficiently large.

Proof. Consider Equation 10. It is obvious that the second term on the right hand side (RHS) of this equation is decreasing in either $R$ or $P_{L}$ . This implies that $θ^{*}$ is increasing in those parameters.

To find the impact of a change in $γ$ on $θ^{*}$ , we first identify the relevant component that contains $γ$ in the second term on the RHS of Equation 8 and denote it as:

f (γ) = {[\frac{γ}{α hR Ω^{'} (\frac{1}{2} + b)}]}^{\frac{1}{1 - γ}} .

Taking the natural logarithm of this fraction and differentiating the corresponding logarithmic function with respect to $γ$ , we obtain:

\frac{\partial \ln f (γ)}{\partial γ} = \frac{γ \ln γ + (1 - γ) - γ \ln [α hR Ω^{'} (\frac{1}{2} + b)]}{γ {(1 - γ)}^{2}} .

The sign of this derivative depends on the sign of the numerator of the RHS fraction, which is not immediately clear. To explore this further, we denote the numerator as $g (γ)$ . Differentiating this term with respect to $γ$ yields:

\frac{\partial g (γ)}{\partial γ} = \ln γ - \ln [α hR Ω^{'} (\frac{1}{2} + b)] < 0 .

This derivative is negative because $α hR Ω^{'} (\frac{1}{2} + b) > 1$ by the assumption stated in Lemma 1 and $γ \in [0, 1]$ . This means that $g (γ)$ is decreasing in $γ \in [0, 1]$ . Hence, $\min g (γ) = g (1) = - \ln α hR Ω^{'} (\frac{1}{2} + b) < 0$ and $\max g (γ) = lim_{γ \to 0} g (γ) = 1$ . Thus, there exists a unique $\tilde{γ}$ such that $g (\tilde{γ}$ ) = 0. For $γ \geq \tilde{γ}$ , $g (γ) \leq 0$ so that $f (γ)$ is decreasing in $γ$ . For $γ < \tilde{γ}$ , $g (γ) > 0$ so that $f (γ)$ is increasing in $γ$ . Because $θ^{*}$ is of the opposite sign to $f (γ)$ (i.e., $\frac{\partial θ^{*}}{\partial γ} = - \frac{\partial f (γ)}{\partial γ}), θ^{*}$ will be increasing in $γ$ for $γ \geq \tilde{γ}$ and decreasing in γ for $γ < \tilde{γ}$ .

This proposition deserves some discussion. Similar to Le and Yalcin (2018, 2023a), we find that the optimal fraction of fund devoted to campaigning, $θ^{*}$ , is increasing in the lobby group’s ideal policy, $P_{L}$ . The intuition for this result is as follows. An increase in $P_{L}$ means that the lobby group is more prepared to negotiate with the allied politician over a policy platform that is further away from the median policy (as in Equation 9) and pay a higher level of contribution in return (as in Equation 6). Once receiving this amount in full, the politician will have the freedom to spend more on campaigning while he or she is still able to extract more cash to meet his or her personal consumption demand.

Unlike Le and Yalcin (2023a), we can establish comparative static result for the election winning premium, $R$ , and the relative importance of expropriated contribution, $γ$ . The result that $θ^{*}$ is increasing in $R$ is rather intuitive. An increase in $R$ will make the politician value electoral victory relatively more in comparison to personal use. He or she will, therefore, devote more money toward campaigning.

The impact of an increase in $γ$ on $θ^{*}$ is, however, less straightforward. On the one hand, it creates an incentive for the politician to divert more money toward his or her private use. This is a kind of an income effect. On the other hand, it induces the politician to take money away from personal consumption and direct it toward campaigning. This is a kind of a substitution effect. When $γ$ is sufficiently large, the substitution effect dominates so $θ^{*}$ increases. In other words, the marginal effect of spending on campaigning outweighs that of personal use spending. However, when $γ$ is small, the income effect dominates so the opposite result holds true as the marginal effect of personal spending dominates instead.

To better visualize the relationship between $γ$ and $θ^{*}$ , let us consider the following simple numerical example. Specifically, consider a situation in which an interest group, with an ideal policy of $P_{L} = 0.75$ , is promoting a political party. Let the fraction of uninformed voters be $α = 0.5$ , the measure of diversity of views about parties be $d = 1$ , the inherent ideological bias for party $j$ be $b = 0$ (thus, each party has an equal starting point), and the effectiveness of campaign contribution be $h = 4$ . The election winning premium $R$ is normalized to 1 for simplicity. Assume that the function capturing the probability of winning takes its simple linear form such that $Ω (S) = S$ . Note that these parameter values and functional form are chosen to simplify our calculations while they still satisfy the condition that $α hR Ω^{'} (\frac{1}{2} + b) > 1$ for the existence of an equilibrium.

The response of $θ^{*}$ to a change in $γ$ is illustrated in Figure 1. This figure shows that for $γ \in [0, 1]$ , the function $θ^{*}$ is U-shaped, cutting the horizontal axis at two different points, $γ = 0.5$ and $γ = 0.75$ , respectively. It can be seen that $θ^{*}$ is decreasing in $γ$ with $γ \in [0, 0.5]$ but increasing in $γ$ with $γ \in [0.75, 1]$ . This is in line with the analytical result stated in the proposition above.

Figure 1.

Optimal values of $θ$ .

In summary, the results indicate that political candidates have a strong tendency to expropriate a fraction of campaign funding for their personal use if there is no legally binding contract between the lobby group and its allied party, which specifies that campaign funding can only be used for campaigning. The candidate will use more money for campaigning if the election winning premium is relatively larger and the lobby group has a relatively stronger policy stance point. This will also be the case if, looking that the optimal fraction of campaign spending, the marginal effect of campaign spending outweighs that of the spending on personal use.

Conclusion

In this paper, we have examined how political lobbying influences the policy-making process. We specifically focused on the role of expropriation of campaign contributions by self-interested but financially constrained politicians. Throughout, politicians’ decisions regarding expropriation are assumed to be private information and endogenously determined by parameters of the model. Within this framework, we have shown that in the case of a non-strategic lobby group, the lobby group will be able to reach an agreement on policy platform and associated contributed money with its ideologically aligned party. Since the allied politician tends to divert some part of the contribution for personal use, there is an optimal (i.e., utility-maximizing) allocation of contributions. Beyond this point, monetary contributions can be optimally divided between campaigning and the politician’s personal use. Such an allocation is shown to respond positively to the election winning premium and the lobby group’s ideal policy. However, it is increasing in the relative importance of expropriated money only when this parameter is sufficiently large.

We addressed an important, but largely unexplored, issue in political economy in this paper. Specifically, political corruption in the form of campaign fund expropriation can occur anywhere, even in the world’s finest democracies, provided that politicians can avoid punishment. Due to political sophistication, it is not easy to detect this bad behavior and even more difficult to eradicate it. A strong law and law enforcement system that severely punishes corrupt behavior is necessary to tackle this malpractice.

It seems that the model presented in this paper could be enhanced by the introduction of a legal organization that is capable of detecting and punishing crimes. This extension will affect the strategic behavior of all players in the political game. A number of emerging topics are also being explored in the area of endogenous expropriation. For instance, modern regimes leverage data control to expropriate not just wealth but also information, redefining the concept of traditional expropriation (see, for instance, Zuboff, 2019), or how governments use emergencies (e.g., pandemics, financial crises, conflicts between countries) to justify resource expropriation (see, for instance, Reinhart, 2009). These studies emphasize the relationship between institutions, politicians, and expropriation, showing that strong institutions promote growth and stability by limiting elite exploitation, whereas weak institutions fuel rent-seeking and inequality. These extensions promise to make our future research agenda even more exciting.

Footnotes

ORCID iD

Thanh Le

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research is funded by National Economics University, Vietnam.

Declaration of Conflicting Interests

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

Data Availability Statement

Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Endogenous Expropriation with Non-strategic Lobbying

Abstract

Plain language summary

Keywords

Introduction

The Model

Political Equilibrium

Optimal Allocation of Campaign Contributions

Conclusion

Footnotes

ORCID iD

Funding

Declaration of Conflicting Interests

Data Availability Statement

References