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2 HUMAN CAPITAL AND CORRUPTION: A MICROECONOMIC MODEL OF THE BRIBES MARKET WITH DEMOCRATIC CONTESTABILITY Pedro Cosme Costa Vieira pcosme@ep.up.pt Faculdade de Economia Universidade do Porto Aurora A. C. Teixeira ateixeira@ep.up.pt CEMPRE Faculdade de Economia Universidade do Porto Abstract To overcome market ailures society creates common laws that stimulate or penalize individual actions the enorcement o which depends on the actions o public authorities who may be susceptible to corruption. Thus a new market emerges where inluences are traded. Legislators have incentives to deviate rom the goal o eiciency and produce laws that maximize the gains that can be expected rom bribes. We model this behaviour or an autocracy versus a democracy using a microeconomic ramework. We assume that in an autocracy rulers have a monopoly over the bribes market whereas in a democracy conlicting groups compete in the bribes market. In order to bring about the downall o the incumbent rulers these groups inorm voters o the rulers'deviant actions so that by a stochastic process they convince voters o the existence o bribes and thereore gain their votes. The models constructed produce results that are compatible with the well-known stylized acts namely that in a democracy the level o corruption is lower than in an autocracy although still positive that 2 in environments where the level o human capital is higher the proxy or the voters receptivity to the eorts o the opposition regimes are closer to democracies and the level o corruption is lower and that 3 the level o corruption is higher in more regulated economies. Keywords: Human capital; corruption; democracy; computational models JEL-Codes: J24; D73; C63

3 . Introduction Researchers have been interested in the determinants and eects o corruption or quite some time - Aidt 23 Jain 2 Rose-Ackerman 999 Bardhan 997 and Ades and Di Tella 997 provide excellent and comprehensive surveys on the subject. Recently the availability o adequate data corruption especially indices o corruption perceptions or dierent countries boosted new and interesting studies Goel and Nelson 25; Xin and Rudel 24; Fisman and Svensson 22. Corruption although unethical may be perectly rational rom an individual rame o reerence Barreto 2. Corruption can thereore take place in any economic transaction involving the public sector since any economic transaction brings mutual beneits to both parties. Given that natural resources are a actor in production by imposing restrictions on their use governments create economic incentives or producers to overcome these restrictions. In addition economic incentives also exist or producers to adjust the production process or example through the division o labour and the level o output. The producers thereore have an incentive or attempting to corrupt the government agents who control the consumption rate or natural resources and the level o competition. A government strategy which maximizes the potential or corruption involves imposing very strict limits on the use o natural resources and in addition a concentrated market. In this way the value o a natural resource its shadow price is enhanced and comes to represent a greater gain when the imposed limits are overcome. It is easy or governments to justiy such policies. In the irst place it is easy to convince the public that they should economize on natural resources and that policies should thereore be restrictive. Secondly it is also easy to convince the public that the existence o economies o scale means that production is more eicient i it is in the hands o one sole producer. We assume that government controls the use o natural resources but this concept can be conceptually extended to accommodate any market regulation policy. Despite having imposed tight restrictions on the use o the natural resource government oicials can organize ways o selling permission to overstep these limits. For example the measurements o the natural resource used are not directly observed by the public and inspectors can alter the igures. 2

4 Thus the enorcement o law depends on the actions o public authorities who could be corrupted. A new market emerges where inluences are traded. Legislators have incentives to deviate rom the goal o eiciency and produce laws that maximize the gains that can be expected rom bribes. We model this behaviour or an autocracy versus a democracy using a microeconomic ramework. We assume that in an autocracy rulers have a monopoly over the bribes market whereas in a democracy conlicting groups compete in the bribes market. The present paper is structured as ollow. In the next section we ormalize the model. In the Section 3 using simulation techniques we analyse the level o social welare that occurs when a government imposes a maximum level o use or a natural resource which is distributed amongst various producers. The Section 4 details a reduced model o interaction between government oicials and the opposition and Section 5 concludes the paper. 2. Formalization o the model In our economy there is a natural resource and decisions on how it is assigned are the responsibility o the government. The use o this natural resource has on the one hand a positive eect in terms o company output and on the other hand a negative externality or people. The government thereore has to make a ruling on the use o this natural resource that takes both the positive and the negative eects into account. In abstract terms the production o goods and services requires capital labour and the natural resource whose use causes environmental damage e.g. air pollution that has a negative eect on the welare o agents. Since environmental damage is not taken into account in the producers'decisions there is a need or the government to intervene. Let us suppose that technology allows or the partial substitution o actors that may be condensed into a Cobb-Douglas production unction and that there are increasing returns to scale. The act that increased production implies greater use o the natural resource and the production technology involves economies o scale enables corrupt government oicials to convince the electorate to adopt policies that are not the best in terms o social welare even though they increase the potential gains or these individuals. One o these policies concerns the level o market concentration. The existence o economies o scale introduces the oicials'argument or the existence o a natural monopoly" which avours market concentration. I we observe the situation in various dierent countries it can 3

5 be seen that this justiication has been used requently by governments together with the Schumpeterian issue o appropriate investment in innovation and development to justiy awarding concessions to just a ew companies. In Portugal or example this argument is used to justiy the existence o monopolies in water supply reuse collection rail transport urban public transport and port authorities amongst others. A second policy is associated with the natural resource s consumption rate. The act that there is a positive relationship between consumption o the natural resource and output emerges here as a justiication on the part o governments or allowing a level o use o the natural resource that is beyond that which is socially beneicial causing environmental damage. Both o these policies avour the producers who are already operating in the market and who thereore push or the situation to be maintained by paying bribes. In ormal terms let us assume that a producer using a level o capital k labour supply l and amount m o the natural resource has the output level y: α γ y k l m A k l m α γ > As there are economies o scale this implies α γ >. Assuming that the market rate or capital is rate r which includes depreciation and risk that the hourly-paid market wage is w and that the private sector price o the natural resource is zero the proits o a producer whose production unction is represented by the expression will be: π k l m y k l m p k r l w 2 Concentrating on market structure let us assume still in general terms that the aggregate market demand is known and decreases linearly according to price: D D b p p D D / b 3 Thus the selling price o the product depends on aggregate output. Assuming additionally that the producers compete according to Cournot it ollows that the proits o a producer who assumes D as a reerence this being the level o output o the other producers will be expressed as ollows: π y D D y / b k r l w 4 4

6 The level o activity o each producer will depend on the price o the actors they use the level o aggregate production amongst the other producers D which is assumed to be exogenous and the total amount o the natural resource that the government allows them to use. Presuming that each unit o the natural resource consumed causes the environmental damage Pa that the wages received by employees is equal to the eort expended i.e. working does not lead to a direct increase in employee welare only in the consumption o goods and services and that the capital is oreign taxes do not lead to any increase in social welare because they represent remuneration or the sacriice o saving in overall social terms welare is expressed by the sum o the producer's proit added to the consumer gains rom which the environmental damage is subtracted: i i n n F y ki li di 5 D / b p D di Pa 5 I we take into consideration the act o the market economy and the act that producers even in a monopoly have little inluence on the labour and capital market we can assume that capital remuneration r the hourly-paid wages w and the unitary environmental damage Pa are exogenous actors. Note that any discussion on the level o eiciency/ineiciency o public planning in terms o the production o goods and services lies beyond the scope o this study. In this context the agents aspire to a government which imposes the simplest possible laws in order to allow producers to maximize the aggregate beneits deined in equation 5. As scale economies operate in the production process i the size o a producer increases ewer resources will be needed or each output unit produced. Thereore i concessions or the use o the natural resource are granted to various producers with the eventual possibility o mergers or the acquisition o rights to the natural resource the market will tend towards a monopoly structure. Government oicials take advantage o this situation to justiy the existence o one sole producer in the market an argument that is easily accepted by the electorate. However the lack o competition in the market is socially harmul since the monopolist will set a level o output whose marginal production costs are higher than the market price. Regulation apparently allows this problem to be overcome but on the one hand it attracts 5

7 corruption and on the other hand it requires the regulator to have previous knowledge o the most socially beneicial perormance. 3. Simulation o market behaviour In this section using simulation techniques we will analyse the level o social welare that occurs when a government imposes a maximum level o use or a natural resource which is distributed amongst various producers. These compete but cannot merge i.e. the government controls the level o market concentration. Starting with equations -5 and setting the model toα γ 5 D b r 5% e w we see a rise in social welare when the situation changes rom a monopoly to a duopoly n para n2. As can be seen in Figure this is accompanied by the use o larger amounts o the natural resource m: 3 Welare 25 n n m Figure : Relationship between the level o social welare number o producers and use o the natural resource However it is possible to see rom the same igure that even i the consumption level or the natural resource remains steady i.e. veers rom the vertical the transition rom monopoly to duopoly increases social welare. This is due to the act that even though there is no increase in the consumption o the natural resource there will be an increase in production through the greater use o labour and capital as the next igure shows. 6

8 9Labour 5 Capital 6 3 n n m n n m Figure 2: Relationship between the use o labour and capital number o producers and use o the natural resource It is possible to observe rom Figure that with a given number o producers in the market there is an optimum level or consumption o the natural resource. Restricting ourselves to these optimum points in Figure 3 we can see the evolution o social welare according to the number o producers operating in the market. In concrete terms the existence o a certain amount o competition avours social welare. In our simulation the evolution o the level o welare together with the number o producers reaches a maximum at n 2. At up to n social welare is higher than in a monopoly n. However the existence o economies o scale in the production process means that the number o competitors has to be limited n so that technological ineiciency is not superimposed on the gains created by the existence o competition. 3 Welare n Figure 3: Relationship between social welare and number o producers Another important issue that our model enables us to analyse is whether as an alternative to maintaining a ixed level or the use o the natural resource it would be in society's interests or the government to set a price or the use o the natural resource internalise the impact 7

9 and to use this money to compensate or the environmental damage caused whilst making the agents responsible or setting the criteria or the amount used. In this case the cost o the natural actor has to be added to the proit unction: π y D D y / b k r l w m pa 6 In the simulation it can be seen that when social damage is incorporated into the optimization model or agents consumption o the natural resource alls slightly and is partially replaced by labour and capital. However in terms o social welare the policies are identical. To conclude the best policy or a government is to set reasonable limits on the levels o use o the natural resource and to distribute the rights to more than one producer at least two but less than ten in the case o our settings or else to set the price o the natural resource as environmental damage and let the producers decide on the best ratios or labour capital and natural resource. However the producers must not be allowed to merge towards monopoly or create a cartel. Given the theoretical equivalence o the two policies imposing either a maximum level o use or a price in empirical terms it is to be expected that approximately 5% o governments would opt or each o them. However the vast majority o governments and in the case o some resources all o them opt to limit use. In our opinion this is due to the act that putting a price on use reduces the potential gains or corrupt government oicials. From this micro-oundation model we illustrate how a policy which avours the existence o corruption is unavourable to social welare. This being the case in a second step we may in abstract terms condense possible government policies into the variable which has the value o i the policy is optimum and i it promotes the highest possible levels o corruption and lower levels o social welare. 4. Reduced model o interaction between government oicials and the opposition In this reduced model the gains o government oicials during the present period B are shown as a decreasing unction o government policy when social welare WF rises: B B ' < WF WF ' > 7 8

10 I the government policy veers away rom the optimum i.e. i the value o veers rom the likelihood o the government being replaced by the opposition increases. This happens because the public reacts to the reduced level o welare in relation to its optimum level WF* increasing the probability o the government alling as the distance between WF* WF increases. As the optimum value is diicult to observe the inormation is not ully accurate the likelihood o a government deeat also increases in line with the level o political activity on the part o the opposition measured by the parameter and the receptivity o the public to opposition activities measured by the parameter ξ. This receptivity in empirical terms may be measured by the average level o education o the electorate since a more educated electorate tends to be able to understand and discern the relevant inormation better than a less educated one Gibbons and Johnston 974. As Welch 97: 42 argues increased education may enhance a [person] s ability to acquire and decode inormation about costs and characteristics o other inputs. The opposition incurs costs in inorming the electorate e.g. pamphlets announcements and speeches which are derived rom the unit price o creating opposition po multiplied by the amount o opposition realized po. The government determines the value o which maximizes its expected gains with ξ and po given whilst the opposition determines the level o political activity which maximizes its expected gains with ξ and po given assuming that the government does not inluence po. In this way the expected gains rom being in power and rom being in opposition are shown in the resolution o the ollowing dynamic optimization problem: P Gov out ξ max max [ B { }] [ po { }] 8 < ξ ξ > ξ > ξ ξ 9 9

11 This represents a symmetry in which all the agents government and opposition adopt the same strategy or the government the policy is represented by and or the opposition. Thereore the level o good governance as opposed to the level o corruption will result rom the interaction between the government and the opposition in a similar way to the competition that takes place between companies to win market leadership. From the results shown below the model demonstrates that the level o corruption in a democracy is lower than in an autocracy and is very much dependent on the ability o the opposition groups to captivate the electorate. { } { } po B ξ In an analysis o comparative statics : { } { } po B [ ] [ ] po B [ ] [ ] [ ] [ ] po B / / the irst optimization condition can be derived: [ ] [ ] [ ] [ ] / / po B [ ] [ ] po B : : 2

12 This demonstrates that when the price o creating opposition po is ininite we are aced with a strong dictatorship and when po is reduced the level o democracy rises. When po is ininite the government adopts the most corrupt policy possible. In the second equation the level o opposition activity is zero: [ ] [ ] 3 meaning that the government remains in power regardless o its politics and government oicials adopt whatever maximizes their level o corruption: [ ] B 4 When the price o creating opposition po is zero we are aced with a "perect" democracy and the government adopts a orm o politics that only contains a certain level o corruption no government is incorruptible. In the second equation there is a positive level o opposition which makes it likely that the government will change and that it is worth creating an opposition. [ ] [ > * > ; > * > ; * > ] 5 Note that i taken to absurd lengths the level o opposition would be ininite and the government would all immediately thus implying that there are no gains or government oicials. Thereore it would not be worth orming an opposition since there would be no gains to be had rom orming a government. I the government implements optimum policies the government oicials remain in power but still gain nothing as there are no incentives to orm any opposition. However i the opposition is inite the likelihood o the government oicials who have maintained a certain level o corruption losing oice is lower when the units representing the gains to be had rom remaining in oice and the gains to be had rom creating an opposition are positive. From these two limited cases it may be concluded that when the cost o orming an opposition is lower the level o opposition is greater as are the chances o government oicials being removed rom oice and their level o corruption being reduced. [ ] p [ < *; < *; < * ] [ > *; > * ] p > 6

13 Note that i the costs o creating an opposition are subsidized there are no longer any incentives to orm a government and government oicials no longer concern themselves with re-election thus increasing the level o corruption. In addition it may also be concluded that when the level o education o a population as relected in the parameter ξ is higher the level o opposition and o government corruption will be lower. In this sense ormal education may be seen here as a means o tempering the discrepancy between the actual levels o corruption in particular countries in relation to the optimum levels Dewey 985 [96]; Parker 23. Perversely it may also justiy a lack o investment on the part o dictatorships in policies to promote levels o human capital in their respective populations as was the case with the Salazar regime in Portugal Carreira Conclusion Corruption tends to be a actor in economic ineiciency since the economic incentives or corruption only exist when governments do not commit themselves to optimum policies. In our work we have aimed to study in theoretical terms the implications o the existence o opposition to a government i.e. a democracy in relation to the corruption o government oicials and the social welare o a nation. To this end we have constructed a dynamic theoretical model in which two groups alternate between the positions o government/opposition with probability. We assume that the probability o the government becoming the opposition rises in line with the level o ineiciency corruption the level o opposition activity and the level o education o the electorate. Using computational methods and algebraic manipulation on a reduced model we concluded that the reedom to create opposition leads to a all in the level o corruption amongst government oicials and a rise in eiciency without however totally eliminating it. In addition the level o education the human capital o the electorate equates with a all in the cost o creating opposition thus contributing towards a reduction in the level o corruption and consequently a all in the rate o economic ineiciency. Our results thereore appear to accord with the empirical stylized acts namely that in less democratic countries people tend to be less educated Parker 23 governments only loose power when there are very high levels o opposition and the level o development and economic growth tends to be lower than in more "democratic" countries Barro 99; Repkine 23 even though as a rule the respective government oicials beneit rom 2

14 obviously higher levels o welare and wealth than the majority o the rest o the population as well as oicials in the more democratic countries Barro 994. Reerences Ades A. and R. Di Tella 997 The New Economics o Corruption: A Survey and Some New Results Political Studies vol. 45 pp Aidt T.S. 23 Economic Analysis o Corruption: A Survey Economic Journal vol. 3 pp. F632 F652. Bardhan P. 997 Corruption and Development: A Review o Issues Journal o Economic Literature vol. 35 pp Barreto R.A. 2 Endogenous corruption in a neoclassical growth model European Economic Review vol. 44 pp Barro R.J. 99 Economic Growth in a Cross Section o Countries NBER Working Papers 32 National Bureau o Economic Research Inc. Barro R.J. 994 Democracy & Growth NBER Working Papers 499 National Bureau o Economic Research Inc. Carreira H. M. 996 As políticas sociais em Portugal in Barreto António org. 996 A Situação Social em Portugal pp Lisboa: ICS-UL. Dewey J. 985 [96] Democracy and education vol. 9 Carbondale: Southern Illinois University Press original work published in 96. Fisman R. and R. Gatti 22 Decentralization and Corruption: Evidence Across Countries Journal o Public Economics vol. 83 pp Fisman. R. and J. Svensson 22 Are Corruption and Taxation Really Harmul to Growth? Firm Level Evidence working paper Columbia University. Gibbons M. and Johnston R. 974 The roles o science in technological innovation Research Policy vol. 3 pp Goel. R.K. and M.A. Nelson 25 Economic reedom versus political reedom: crosscountry inluences on corruption Australian Economic Papers June pp Jain A.K. 2 Corruption: A Review Journal o Economic Surveys vol. 5 pp

15 Parker W.C. 23 Schools Are Not Private Places Like Our Homes: Diversity Democracy and Education New Horizons or Learning in Repkine A. 23 Turkmenistan: economic autocracy and recent growth perormance Economic Education and Research Consortium EERC Russian Federation. Rose-Ackerman S. 22 Grand Corruption and the Ethics o Global Business Journal o Banking and Finance vol. 26 pp Welch F. 97 Education in production Journal o Political Economy vol. 78 pp Xin X. and T. Rudel 24 The Context or Political Corruption: A Cross-National Analysis Social Science Quarterly vol. 85 nº 2 pp

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