Public sector corruption has been linked to resource dependency and environmental degradation in the developing world. Herein, we examine the persistence of public sector corruption by modeling an elected public official with the power to set agricultural/resource input-subsidization policy in a developing economy. Through common agency, firms offer bribes to influence policy. A more corrupt official extracts a greater bribe. This implies in a political contest between two candidates with different propensities for corruption, the corrupt incumbent, having the greater prize at stake, always expends greater effort and is the contest favorite. The less corrupt 'green' challenger is always the contest underdog. Our results suggest that i) corruption is politically advantageous; and ii) corruption and political instability are mutually reinforcing, leading to over-harvesting and too much pollution.
Introduction
Economists know at least two things about how corruption affects natural resources and the environment. First, corruption leads to too much harvesting and too much pollution, and second, this corruption is persistent.1 The first makes sense — if a local bureaucrat uses his public office to secure private rents through bribes and kickbacks, he will look the other way as developers convert too many acres of forestland to agriculture, or when a firm dumps too many chemicals into a river.2 The second is harder to explain when the country has electoral competition and contestable political markets (Persson and Tabellini, 2002).3 If corruption of the incumbent leadership implies inefficient natural resource use and lower social welfare, an opposing political force should emerge as a viable ‘green’ challenger. The green challenger would work to right this social wrong.
Herein we combine contest theory with a common agency lobbying model to show (a) the more corrupt the elected incumbent, the larger the bribes he extracts from self-interested constituents; (b) the larger the bribe, the more effort the incumbent expends to stay in power against a green challenger; and (c) the more effort expended, the more likely he stays in power — the incumbent is the contest favorite (odds of victory exceed 50 percent).4 The key to this vicious cycle is that the green challenger will — by definition — always be less corrupt than the incumbent. She is honest, and she will always be the contest underdog. She will, if elected, seek to correct the inefficient use of the environment facilitated by corruption. As a consequence, she captures fewer rents from business (e.g., through contributions, bribes, or kickbacks) and no rents from the environmental groups since the efficiency gains are all public goods. It is the classic case in which the general public gains all the benefits, and she pays most of the private cost.
The Model
We demonstrate our main results using a two-stage game (see Figure 1, variable definitions explained below). Beginning with Stage 2, we use a common agency model (Bulte et al., 2007; Grossman and Helpman, 1994) in which a political official maximizes a weighted sum of direct personal utility and social welfare. In Stage 1, we use Dixit’s (1987) contest theory to capture how a corrupt incumbent remains the political favorite — the odds of victory are greater than 50% at the Nash equilibrium.5 Note that effort (x) is expended in Stage 1 (the contest). Compensation (S) occurs in Stage 2 (the lobbying game). Here S is not compensation for x, rather it is compensation for the subsidy package (g) offered by the elected official in Stage 2. Given backward induction, each candidate takes S as given in the Stage 1 contest, and expends an effort level based on the compensation available in Stage 2 for provision of the subsidy. Given this timing, it is unnecessary for the candidate “convince” the firm that he or she has expended effort on being elected in Stage 1. Ex post (i.e., in Stage 2), the effort expended in the contest is sunk, and is inconsequential — what matters is the corruption level of the candidate who has won and now sets subsidization policy. Consider each stage in turn.
Stage 2: Lobbying
First, we consider the Stage 2 lobbying game between an elected official and a representative agricultural or resource firm, fashioning our model after Bulte et al. (2007).6 We formalize a key result: a more corrupt official extracts a greater bribe. The firm credibly signals its willingness to pay a bribe for a favorable subsidy package by committing to a level of resource conversion and ‘semi-fixed’ inputs.7 The firm’s production function is
where total output, Q, is a function of a variable input (i.e., labor), y, resource conversion, A, privately purchased semi-fixed inputs, h, and a government supplied semi-fixed input, g.8 Assume the production function to be (i) strictly increasing and concave in its arguments, and (ii) such that the marginal productivity of each input is increasing in the level of other inputs:
The condition implies gross complementarity.
The lobbying game consists of three stages.9
Equilibrium in the lobbying game is found using backward induction, and comparative static analysis shows how the firm’s optimal bribe changes in response to a change in the official’s level of corruption.
In Stage 2.3 the firm’s objective is
The price of output, p, is exogenous, as are w, r, and v, the unit costs of inputs y, A, and h. The profit function, V(?), is homogenous of degree one in p and w, increasing and concave in p, A, h and g, and decreasing in w. Differentiating with respect to y, the necessary first-order condition is
In Stage 2.2, the firm offers a bribe to influence the official’s supply of inputs.10 The input subsidy is an increasing function of the bribe: 11 Assume concavity, with g(0) = 0 and dg/dS approaching infinity as S approaches zero from above. The firm chooses S to maximize the Stage 2.2 objective function,
taking as given its choices of A and h. The first-order condition with respect to S is dn dg . .
By condition (2), V g is strictly positive. By the inverse function rule, following condition holds at the optimal bribe, denoted S* v g=d s d g
Since S can be thought of as the firm’s cost to secure the government input, Equation (6b) shows the firm’s optimal bribe sets the marginal benefit (profit) of the government input, Vg, equal to its marginal cost (the local truthfulness condition as defined by Grossman and Helpman, 1994).12
Concurrently in Stage 2.2, the official maximizes a weighted sum of personal utility and social welfare. Assume his/her utility of income is U(S*) = m + S* where m is the publicly approved salary (assumed constant, normalized to zero), and (s)he derives no direct personal benefit from increased social welfare, as the efficiency gains are by definition public in nature.13 The official’s objective is to
where W is social welfare and a is a corruption parameter. The weight assigned to social welfare, a e (0, to), is inversely related to the official’s propensity to engage in corrupt behavior.14 Social welfare is the firm’s profits, less the cost of government-supplied inputs.15
Assume the per-unit social cost of subsidized inputs, c , includes the shadow cost of using public funds. Taking the derivative of (7) with respect to g and substituting (6b), the official’s optimal choice for the government-supplied input is
The official supplies the input such that its combined marginal benefit, a weighted sum of collected bribes and producer profit, is equal to its weighted marginal social cost. Rearranging this condition, the effect of a on the efficiency of the subsidy is clear:
As a approaches zero, the official is more corrupt, and the ratio of the marginal social cost of the subsidy to the firm’s marginal benefit from the subsidized input approaches infinity. In contrast, as a approaches infinity that ratio approaches 1, the social optimum. The implication of (9b) is that any level of corruption is socially inefficient: for all
In Stage 2.1, the firm chooses A and h, knowing its choices will affect its potential subsidy in Stage 2.2. Here, and The firm’s objective function in Stage 2.1 is
Taking the first-order conditions, the optimal choice of A is given by
By (6b), the last two terms cancel, leaving
In similar fashion, the optimal choice of h is given by
Conditions (11a) and (11b) indicate the firm chooses A and h in Stage 2.1 such that their marginal benefits in terms of Stage 2.3 profits equal their marginal costs in Stage 2.1.
Proposition 1 summarizes the key result that connects the lobbying game to the political contest in Stage 1.
Proposition 1
Assume (2) is satisfied, the more corrupt the public official, the greater the firm’s optimal bribe, .
Proving Proposition 1, we see from Equation (9a) that
Recall c > Vg for all a to, which says the firm’s marginal profit from g is less than the marginal social cost of its provision, and that a higher a represents less corruption. As dS*/dg > 0 by Equation (6), the optimal bribe is increasing in the corruption level of the official:
The rent incentive associated with holding office increases as a decreases. Using this result, it follows that given two political contestants competing for election to a public office, the more corrupt of the two will have more to gain by winning. Because the efforts expended by each contestant are each a function of the prizes at stake, asymmetric prizes imply asymmetric efforts.
Stage 1: Contest
Following Dixit (1987) and Baik (1994), we develop an election contest between incumbent (player a ) and challenger (player b ). Each candidate expends effort xi to receive the direct payoff S* in Stage 2.16 Assume the incumbent is more corrupt than the challenger, which implies by Proposition 1 that 17 Each player has a probability of winning defined by the classic logit function (Tullock, 1980)18:
Incumbent and challenger each select effort to maximize
taking the other’s effort as given.19 The first-order conditions are
Second-order sufficient conditions for maxima are satisfied. Solving the first-order conditions yields the reaction functions
where e represents the case in which a candidate can win the contest with minimum effort due to the other’s effort being zero. Solving the reaction functions for an interior solution yields the unique Nash equilibrium efforts:
Note (see Figure 2). Given asymmetric bribes in Stage 2, the incumbent expends more effort, and has increased probability of retaining office.
Proposition 2.
In a contest between a corrupt incumbent (player a) who will extract a greater bribe than the challenger (player b) such that This implies the incumbent is the contest favorite and the challenger is the contest underdog,
Greater corruption implies greater rents in Stage 2 and induces greater effort in Stage 1. A higher probability arises that the victorious official will be the one who engages in a higher degree of rent-seeking behavior once in office—an incentive that provided a political advantage when competing for office. Proposition 3 summarizes our main result from the two–stage game.
Proposition 3.
In the Stage 1 contest between the incumbent (player a) and challenger (player b) who have Stage 2 corruption parameters the candidates’ prizes from winning the contest, are asymmetric, such that As a result, the Nash equilibrium effort levels are The more corrupt incumbent expends more effort in Stage 1 and is the favorite, while the challenger expends less effort and is the underdog, such that implying the more corrupt incumbent has a greater probability of winning in Stage 1 to collect his bribe in Stage 2.
The corrupt, rent-seeking incumbent has everything to lose by not retaining office. In contrast, the virtuous green challenger who, being less receptive to bribery and political grift, would put social welfare ahead of her own personal gain in Stage 2, lacks the direct individual incentive to expend the effort needed to oust the incumbent. She remains the contest underdog.
Discussion
We first discuss the implicit “green” aspects of our results related to those of Bulte et al. (2007), who find two key environmental impacts based on how corruption affects a firm’s choice of land conversion in the lobbying game.20First, as the level of corruption increases, the ratio of private investment in semi-fixed inputs relative to land declines. More land conversion in Stage 2.1 induces greater provision of the government-supplied input in Stage 2.2. When the public official is more receptive to bribery, the firm commits to more environmentally damaging, extensive production practices to leverage greater support from the government. From this, it follows that the lower the green challenger’s probability of victory in Stage 1, the greater the odds the firm’s Stage 2 production will be more extensive. The result is a greater expected level of land conversion relative to private investment in semi–fixed inputs, yielding excessive depletion of natural resources for any given output level.
Second, greater corruption induces a greater absolute level of land conversion. The higher the subsidy the firm expects to receive in Stage 2.2 for any given level of land conversion in Stage 2.1, the greater its optimal choice of land conversion. An increase in corruption increases — ceteris paribus — the subsidy provided by the official (see Equation 12). This implies an upward shift in g(S) for all S > 0. Combining these two results, it follows that the more corrupt the official, the more land the firm converts to production. The environmental implications are immediate. Given modern production technology, this translates to more rapid deforestation, pollution, or ecological disturbance of a larger geographic area, over-harvesting of a renewable resource, or inefficiently rapid extraction of a depletable resource. Again, given the green challenger’s underdog status in the Stage 1 contest, the probability is low that the challenger will win office and curtail such environmental impacts once the firm commences production in Stage 2.
Our model also has implications on the incidence and persistence of corruption. Damania et al. (2004) develop a similar lobbying model to examine the relationship between political instability, corruption, and regulatory compliance. Political instability occurs via an exogenous probability of regime change, and greater instability stimulates corruption through weak institutional oversight. We have expanded this framework by endogenizing the probability of regime change by way of a contest model, showing that the stability of a regime is inherently related to its corruption level. Our explanation does not contrast with the results of the Damania et al. (2004) model. They model political instability as an exogenous probability that a given regime will be supplanted at the end of a period — as this probability increases, so does the sitting official’s incentive to behave corruptly. We model the probability that a given regime will be supplanted from one period to the next as being endogenously determined by the rents to be collected by the victor once the political outcome has been decided. It follows that if any challenger is to have at least a 50/50 shot at winning the political contest, he or she must be at least as corrupt as the incumbent.
This inherent political disadvantage for less corrupt potential candidates may act as a sorting mechanism that dissuades them from vying for office in the first place. If only those who are more corrupt than the incumbent are likely to take office, it may be the case that only more corrupt candidates have incentive to “put their names in the hat.” Relating this intuition back to the Damania et al. results, it may be the case that political instability stimulates corruption, which further stimulates political instability — a self-reinforcing feedback loop. Consider this result in relation to Tirole (1996) and Dawid and Feichtinger (1996). Each of these theories harmonizes well with the basic intuition of our model. Corrupt behavior by the incumbent deters the less corrupt from challenging for office, both now and in future contests, due to the political advantage that greater corruption carries with it.
An Extension
Better quality institutions make lobbying more costly (Heckelman and Wilson, 2013).21 We now introduce an “institutional quality” parameter, y, that tempers the influence the lobbying firm enjoys over input-subsidization policy by inhibiting the rent-extraction capability of the official. For a given S, the “effective bribe” received by the official is We interpret y as an exogenous measure of government transparency with regard to the internal allocation of political contributions. A higher y implies the public official is less able to “line his own pockets” with the lobby’s contributions.22
Consider the effect of a change in y. The official’s objective in Stage 2.2 is to choose the input subsidy level that maximizes
Optimal provision of the subsidy is defined by:
It follows that
The optimal input subsidy offered by the official is decreasing in institutional quality.23 It is straightforward to show that and, because Z is a linear transformation of We now have
The firm’s optimal bribe decreases as institutional quality improves. Greater institutional quality reduces the resources the firm allocates toward costly political leveraging.
An improvement in government transparency changes the relative effort levels of the two candidates in favor of the less corrupt challenger. Proposition 4 summarizes this result.
Proposition 4.
When institutional quality, y, inhibits the rent-extraction capability of the public official, an increase in y decreases the effort level of the incumbent relative to that of the less corrupt challenger, increasing the probability that the green challenger wins the Stage 1 political contest.
We offer the following proof of Proposition 4. For Equation (18) becomes
It is straightforward to show that
Differentiating with respect to 7 yields the following:
A marginal increase in 7 decreases the ratio of a’s effort level to b’s — implying a reduction in the probability that a wins the contest — if the
ratio of the firm’s optimal Stage 2 contributions to the two candidates is decreasing in 7.
Proposition 4 follows from condition (24). Together, imply that the incumbent has a higher probability of winning the contest. Note that as 7 approaches infinity, the optimal Stage 2 contribution to either candidate approaches zero. Intuitively, when contributions have no effect on policy, the firm’s optimal contribution is zero. By (21), as 7 approaches infinity, approaches zero. As dgi/dY approaches zero, so does dSj,/d7, implying d2Si/dY2 > 0. Taken together, these conditions indicate that Sa and Sb converge as 7 increases, and that (see Figure 3). By condition (24), as institutional quality improves, the incumbent’s effort level declines relative to that of the challenger, and as a result the challenger’s probability of winning the contest increases.24
This extension highlights some distinct benefits associated with advances in institutional quality that reduce the rent-extraction capabilities of a public official. First, stronger institutions “level the playing
field” by reducing the political advantage the incumbent has in retaining office. The incumbent is now less the contest favorite. Second, stronger institutions suppress the firm’s incentive to commit to inefficient levels of resource conversion and semi-fixed inputs as a political signaling device, improving environmental quality. Third, the firm incurs a lower opportunity cost associated with diverting resources toward potentially wasteful political contributions (further reducing the effective bribe extracted by the public official), which is likely to be growth enhancing.
Concluding Remarks and Future Research
This paper has examined one reason why environmentally damaging political corruption in the developing world might persist, trumping the possibility of welfare improving environmental reform. By linking classical contest theory with a lobbying model, we find an incumbent and a “green” challenger will have fixed asymmetric levels of corruption such that the corrupt incumbent is always the contest favorite — that is, better odds of retaining power — and the green challenger is always the contest underdog. The intuitive implication is that corruption itself serves as a form of political advantage. Taken with Damania et al. (2004), our model suggests a possible feedback loop — corruption and political instability are mutually reinforcing because only a challenger who is more corrupt than the incumbent can be the contest favorite. A sorting mechanism emerges to dissuade less corrupt potential candidates from challenging the incumbent. We also show how better “institutional quality” (i.e., transparency in the internal allocation of political contributions) reduces the firm’s optimal bribe and improves the green challenger’s chances of winning the political contest, not to mention the environmental outcome (regardless of the political victor).
One possible extension is to develop a sorting model with multiple potential candidates of varying corruption levels to derive conditions under which potential candidates have a positive expected return from entering the race for office. Another worthy extension is to add social preferences to the green challenger’s benefit function. This would provide a direct motive to expend more effort given a desire to right the social wrongs allowed under the corrupt incumbent’s regime. For example, we might recast Equation (12) such that the sitting official maximizes utility over the weighted average of bribes and social welfare: where U' > 0 and U" 0. The first-order condition is and the solution is the same as expression (9a). Equilibrium in the lobbying sub-game is unaffected. But if each candidate’s prize in Stage 1 is then Equation (18) becomes
and the green challenger is the contest favorite if
We have examined this model using a static framework. A worthy line of inquiry is to explore how repeated play affects equilibrium outcomes. A recent empirical finding by Fredriksson and Neumayer (2014) suggests that even if the green challenger beats the odds to win control of the public office, the effect on environmental outcomes may depend more on the old policies of her corrupt predecessor than on her new level of corruption. Fredriksson and Neumayer develop a measure of “corruption-control capital stock” to show that countries’ historical experiences dealing with corruption matters for understanding current environmental (i.e., climate change) policies. Even more than current corruption levels, the “bad old days” leave a lasting stain on policy. Such dynamic corruption stock effects make the green challenger’s chances of cleaning up the system even more dismal, especially if a corrupt incumbent's policies are not easily dismantled upon his ouster.
Our model could be adapted and applied more generally to account for corruption in developed and developing economies alike, encompassing the lobbying pressure of firms in general. One might expect institutional factors to play a more prominent role in influencing the behavior of lobbies and government officials in developed economies, given the importance of institutions with regard to economic development (Rodrik et al., 2004; Scully, 1988). One could also develop a model that includes (non-firm) constituents’ preferences over and information asymmetries regarding the candidates’ corruption levels, potentially fostering adverse selection and moral hazard in the model’s various stages. If constituents prefer less corruption, candidates might falsely signal less corruption to influence the political outcome, while still engaging in rent-seeking activity once in office.
Finally, testing our model’s predictions empirically seems worthwhile. Bulte et al. (2007) provide empirical support for the predictions of the lobbying sub-game. Damania et al. (2004) also find an empirical relationship between corruption and the probability of regime change. Using similar data, it may be possible to test whether corrupt incumbent regimes do spend more resources on maintaining power than do their less corrupt challengers, as predicted by our theory. But as Dechenaux et al. (2014) point out, empirical tests of contest theory have proven difficult. Statistical measures of ‘effort’ are either elusive or easily conflated with other factors such as ability and luck. As an alternative to econometric analysis, a controlled experimental contest would allow researchers to identify confounding effects while controlling for endogeneity issues.
References
Researchers have studied the general motivations for and consequences of corruption. See, for example, Rose-Ackerman (1975), Andvig and Moene (1990), Banerjee (1997), Ades and Tella (1999), Barbier et al. (2005), Aidt et al. (2008), Aidt (2009), Blackburn et al. (2006, 2010). Jain (2001) provides a useful historical survey of the economic literature on corruption.
Economists offer other explanations, too. First, Tirole’s (1996) ‘theory of collective reputations’ uses an overlapping-generations principal-agent model in which each principal is matched with an agent who may behave dishonestly. Because principals have imperfect information on whether agents are corrupt, earlier generations who behave corruptly only increase the incentive for subsequent generations to do so. Second, Hauk and Saez-Marti (2002) account for the endogenous transmission of ethical values through education, demonstrating that the lack of anti-corruption campaigns allows corruption to increase over time. Third, Dawid and Feichtinger (1996) propose a continuous-time dynamic optimization model, in which a representative bureaucrat (who “likes to be rich and famous”) maximizes his stream of payoffs from engaging in corruption net of the expected costs of a damaged reputation. An increase in the rate of corruption now increases the expected rate of corruption in the future, implying the expected losses of reputation from future corrupt activity are not as costly. Fourth, another theory contends that the pervasiveness of corruption begets its persistence (Mishra, 2005). The more corrupt people in a society, the more it becomes optimal for another member to be corrupt as well, despite anti-corruption campaigns and incentives.
We focus on an “elected” public official rather than an “appointed” bureaucrat.
In a related paper, Wilson and Damania (2005) consider a model in which a firm pays bribes to competing political candidates prior to election in exchange for the adoption of favorable policy platforms. Once the winner’s policy is implemented, the firm can also bribe ‘inspectors’ to avoid compliance. The main difference with our work is that we use contest theory to capture the endogenous effort associated with competing for re-election — that is, the model’s political component.
Bulte et al. (2007) model a large, land-holding farmer in a developing economy. We expand the view to encompass any large agricultural or resource firm, and refer to this entity as the “firm.” The model can be generalized to represent any private firm seeking subsidization packages for otherwise privately purchased inputs. We focus on producers of agricultural and natural resource products, as they make up the majority of output in developing countries (Barbier, 2005, pp. 25-30).
Semi-fixed inputs are inelastic in the short run due to higher transaction costs, and are combined with variable inputs to produce output. In the agricultural or resource setting, these might include heads of cattle or short-lived machinery.
Assume the government-provided inputs are good but imperfect substitutes for privately purchased inputs.
Because games a and b are structurally identical, exposition of the lobbying game does not require the use of a subscript indexing i = a, b.
Wilson and Damania (2005) distinguish between “petty” and “grand” corruption. Petty corruption involves bribery of lower-level administrators to avoid the consequences of a given policy. These are isolated incidents in which a firm might, for example, pay an administrator to underreport a regulatory violation. In contrast, grand corruption is defined as bribes or contributions to political parties intended to influence policy outcomes writ large. Although Bulte et al. (2007) do not make such a distinction, our adaptation more closely resembles grand corruption — the greater the bribe, the more generous the input subsidization policy enacted by the elected official.
Across countries, the relationship between a firm’s optimal bribe and the level of input subsidy it receives might be affected by some vector of institutional and preference variables related to institutional quality, democratic responsiveness, financial accountability, social tolerance of corruption, and bureaucratic oversight. Damania et al. (2004) model what they call “judicial efficiency” in penalizing corruption. As our model is restricted to the behavior of one public official in a single country over a single political cycle, we assume such variables are fixed. In Section 4, we extend our model to show how a change in a generalized “institutional quality” parameter affects the outcome.
In equilibrium, neither the official nor the firm has incentive to alter its behavior — the policy outcomes are locally truthful. Grossman and Helpman describe this condition in the following way: “... each lobby sets its contribution schedule so that the marginal change in the contribution for a small change in policy matches the effect of the policy change on the lobby’s gross welfare.” That is, the contribution schedule is such that marginal benefits equal marginal costs at all points. The lobby minimizes the cost associated with gaining influence, and playing a truthful strategy incurs no additional cost. Since every point on the lobby’s contribution schedule represents a best response to the strategies of all other players, and since this set of equilibria contains truthful strategies, its true preferences over outcomes are revealed. The local truthfulness condition is necessary for stable equilibria in common agency models (Bernheim and Whinston, 1986).
One might also consider a case in which the official’s utility is directly affected by social welfare — for example, by some “warm glow” effect of social justice. In such instance, given two candidates with similar corruption levels, social welfare would be similar irrespective of who is in office. As the difference between the two candidates widened, the welfare effects on each candidate’s utility would become more pronounced, altering incentives and behavior in the model’s various stages.
The corruption parameter, a, is an inverse cardinal measure of corruption levels over the range (0, ᐸx), such that a higher a indicates a less corrupt official who puts social welfare ahead of his/her own personal gain. For simplicity, assume no information asymmetries — a is known and constant for each candidate/official throughout both stages of the game.
This is a limited specification of social welfare, in that it does not include the consumer surplus associated with the firm’s output or any other values (i.e., scarcity or non-use values of the resource stock). We avoid inserting them to maintain parsimony. The desired result — that the optimal bribe is increasing in the official’s corruption level — would not be affected by the inclusion of such terms.
We envision a political contest based on externally oriented vote-getting behavior. This is in contrast to a model with internal strategic behavior within a department or agency to secure appointment to a lower-level position. In an election setting, we interpret “effort” as monetary expenditure on campaigning. In addition, a worthy extension is to explore the idea that the elected official acts as the “hub of corruption.” He collects the bribes and then re-distributes some fraction of the total to the set of appointed lower level officials to “help” them see things his way (read, the firm’s way). This could be done by having two forms of corruption that would influence policy through the elected official — (i) direct; and (ii) indirect, through his use of bribes of the appointed officials. One might relate this to Yandle’s (1983) classic Baptist-Bootleggers story, in which lobbying/corruption of the Bootlegger is more productive if channeled through a secondary source that cloaks the real motive with a halo — that is, the Baptists (Shogren, 1990).
Backward induction implies each candidate takes as given in Stage 1.
In contest theory, the endogenous probability of winning is commonly referred to as the “contest success function” (CSF). The basic “ratio” specification in (14) reflects “ideal combat conditions” (Hershleifer, 1988), although other forms have been examined in the literature. Skaperdas (1996) derives a generalized CSF from several game theoretical axioms, examining the properties of alternative functional forms within the axiomatic boundaries. See also Hershleifer (1989). Our model assumes no randomness or uncertainty about the probabilities of winning — the probabilities depend only on relative effort. Random factors could be added in future extensions. See Gradstein and Konrad (1999) for rent-seeking contests of this type.
Wilson and Damania (2005) model the probability of winning election as a function of (i) the exogenous ideological bias of the electorate, and (ii) the relative social welfare levels that would obtain conditional on either candidate winning. Each candidate chooses the policy platform that maximizes his or her net expected payoff. We could accommodate the Wilson and Damania view of exogenous ideological bias and relative welfare within our contest model by adding two parameters: anability parameter in the contest success function, _ > 0, such that pi(_xi; xj) = _xi=(_xi + xj), and a valuation parameter, _ > 0, that accentuates or attenuates the contest prize, _S_ (see Baik and Shogren, 1992; Dixit, 1987). In both cases, the contest environment defined by the parameters _ and _ would affect the determination of contest favorite and underdog exogenously. In our model, we choose to avoid this extension, so we can focus on how the expected bribe endogenously creates the contest favorite and underdog. A worthy extension would be to compare the push and pull of the exogenous parameters and endogenous bribes in determining favorites and underdogs (see Baik and Shogren, 1994, for an example in an environmental conflict model). Also see Konrad (2009) for a wide-ranging guide to contest models, and how features similar to those of Wilson and Damania can be added in future extensions.
Bulte et al. (2007) provide the formal analytical exposition of both results.
Heckelman andWilson (2013) link institutional quality to a measure of “economic freedom,” as defined by government intervention in otherwise free market activity. Our interpretation is related. Heckelman and Wilson note, “a politician’s desire to retain power may also drive policy choices that affect economic freedom,” implying that “a desire to win votes from a rationally ignorant public may drive market interventions” such as input-subsidization policy.
Alternative specifications for the influence of institutions are possible. For example, Gonzalez (2007), in the context of conflict over the security of property in the developing world, models institutional effects as additional parameters in the contest success functions. Different specifications for institutional effects would, of course, differ in their interpretations depending on how they enter into the model.
Moreover, it is straightforward to show that the firm’s optimal choices of resource conversion and semi-fixed inputs decrease as institutional quality increases, implying reduced environmental disturbance.
In the limit (i.e., as γ ^ to) each candidate has a probability of winning of 0.5 with minimal effort.
This implies each candidate’s probability of winning is partly a function of the welfare levels that would obtain conditional on either candidate’s victory, similar to Wilson and Damania (2005). The difference is that the effect works through the candidates’ preferences over social welfare, as opposed to the electorate’s preferences, which seems to be the implicit assumption in Wilson and Damania.
