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  • 1. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola Universidad de Guadalajara leonardo.gatic@gmail.comClientelism as a political strategy has been used in a wide variety of societies across time.The last democratization wave brought high expectations for the new democracies.Economic development, efficient governments and the decline of corrupt politicalbehavior were some of the expected results in the new democratic regimes.Unfortunately, in many cases these promises have panned out. What we have learnedfrom these experiences is that these outcomes are not necessarily inherent of politicalsystems where individual rights of free speech and association are constitutionallyenshrined and open and free competitions for elected offices takes place regularly. Onecharacteristic that has prevailed in the new democracies is political competition based onpatron-client relations. However, this result should not be surprising since politicalclientelism has been a practice in many developed democracies as well as in authoritarianregimes. This phenomenon has been extensible studied from different theoreticalperspectives and in particular from culturalist and developmentalist approaches.However, there is still a lack of an approach capable to explain the resilience andexistence of this strategy in so many different contexts as well as the theoretical andempirical contradictions that this implies. The classical literature on clientelism characterizes the patron-client relation in away that is usually attached to traditional groups and societies. There is no doubt that insuch traditional societies, and also authoritarian regimes and dictatorships, patronage andclientelism have been used to gain support within the citizenry. However this practice canalso be found in some developed democracies and prosperous economies (see Blakeley
  • 2. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola2001, Krisinsson 1996 and 2001, and Warner 1997 and 1998 for an analysis of someEuropean countries; for the United States and Canada, see Clark 1994, Alesina, Baquirand Easterly 1998, and Fletcher 1994). These approaches also argue that dyadicity,personalism and inequality of power and resources, are important determinants ofclientelist relations (Silverman 1977; Einsestand and Lemarchand 1981; Einsestand andRoniger 1984; Graziano 1976; Schmidt et al. ed. 1977; Brusco, Nazareno and Stokes2002; Medina and Stokes 2002; Robinson and Verdier 2000). This perspective underliesanalyses that consider clientelism a coercive and exploitative practice (Graziano 1976;Mouzelis 1985; Li Causi 1981). Nonetheless, in contemporary clientelism, themonopolistic position of the patron over the means of livelihood of her clients is lesscommon; therefore, clients can enter the relation voluntarily and in many cases they areable to abandon it without jeopardizing their survival. Moreover, although in many casesa personal relationship between the patron and the client does exist, clientelism hasevolved into a massive and anonymous strategy, involving groups like unions orcorporations (Silverman 1977; Mavrogordatos 1997; Collier and Collier 1991; Heredia1994), where personalism and, to some degree, the coercive power are diluted. The idea of traditional societies is always linked with developing economies, whichtend to have unequal wealth distributions and significant poverty problems. Thus,clientelism has been positively related with inequality and poverty and it has beenconsidered an endemic problem of developing countries as Robinson and Verdier (2002)observed. Political clientelism, however, is not an uncommon practice in developedeconomies; moreover, it is not also uncommon to find wealthy and powerful clients orbrokers such as entrepreneurs and union leaders (Verdier 1995; Roniger 1990; Loweryand Brasher 2004). Clientelism is neither absent in low inequality economies like Icelandor Canada (see Kristinsson 2001 and Fletcher 1994). There is an important literature thatexamines and reports the use of patronage and clientelism in developed economies andthe existence of clients within wealthy social groups, however there is no analyticalframework that can consistently solve this contradiction. Clientelism is also associated with corruption and inefficiencies within a democraticpolitical system since it threatens the freedom of choice, including the free formation andexpression of political preferences. Therefore it is considered a typical problem of less 2
  • 3. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreoladeveloped democracies. Rational choice analyses of democracy and political competitionargue that, even if the political market is not perfect, the rise of party competition willweaken this and other non optimal and inefficient political behaviors (Becker 1983, 1985;Stigler 1971, 1972; Wittman 1989). Some scholars argue that under a more competitiveparty system, the median voter acquires significant importance and encourages the use ofprogrammatic policies as a mean of gaining political support (Verdier 1995). However,clientelism has survived the development of competitive party systems, and is used as apolitical strategy in some developed democracies. Furthermore, in some cases the use ofpatronage increased when the party system becomes more competitive (Villarreal 2002;Moreno 2005). Within this literature there is no consensus about a single definition of clientelismand patronage. These two concepts are sometimes used indistinctly while other times theyare considered different phenomena (see Medina and Stokes 2002 and Piattoni 2001). Inthis essay both concepts are considered the same type of political strategy based on theirgeneral features. An increasing number of scholars acknowledge that a generalcharacteristic of the patron-client relationship is the logic of exchange (Roniger 1994;Piattoni 2001). Following this idea I consider that clientelism is an exchange relationwhere political rulers seek to increase and maintain their power by trading publicdecisions that produce private benefits in exchange of citizens’ support. In this relationthe means used to buy political support are called patronage. The formal analysispresented in this essay is based on these concepts. This essay presents a formal theory that seeks to clarify these contradictions. It triesto advance in the search of the conditions for the existence of patron-client relations; inanalyzing the effects of structural issues such as income distribution, poverty, socialcleavages and ideological preferences of the citizens on patronage as well as inexplaining how patronage and clientelism are affected by institutional variables like theinternal organization and composition of parties and the level of freedom and fairness tocompete within the political arena. In the next section I present a simple probabilistic spatial model where anincumbent party and an opposition party compete to gain political support within a set ofcitizens which ideological and programmatic policy preferences are private information. I 3
  • 4. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolaanalyze how a given amount of public resources is allocated in the provision of patronageand public goods. Parties compete programmatically by assuming an ideological positionobserved by the citizens and, in the case of the incumbent, by making public decisionsabout the allocation of the public expenditure. Patronage would only be used to co-optcitizens who programmatically oppose the incumbent, but since the ideological andprogrammatic policy preferences of the citizens are not observed by the parties, theincumbent faces an agency problem. Citizens however, have other observablecharacteristics that can signal their preferences. Thus, the incumbent can separate thepopulation into different clusters according to these characteristics and link them withtheir possible ideological positions by a set of subjective probability functions. Bothparties then choose their political platforms according to their competitive strengths, andthe party in office decides how to allocate the public resources. The different political-economic equilibria are characterized by a set of party decisions, containing theprogrammatic positions of the parties, the amount of public resources used to providepublic goods and the level of patronage invested in each group within the economy. In this setting patronage and the way it is allocated within the citizenry is not justdriven by the cost of co-optation determined by the political preferences of the citizens,their private consumption utility function, and their capacity to generate wealth.Patronage is instead determined by the programmatic competitiveness of the parties andthe relative political relevance that each group of citizens has as a support provider in thepolitical competition process. AN ECONOMY WITH CLIENTELISM AND POLITICAL COMPETITIONConsider an economy with the following characteristics. There are two political partiesthat compete to gain as much support as possible within the citizenry which consists in alarge number I of agents. Both parties are predators in the sense that their main objectiveis to maximize the political revenue given their resources and institutional constraints. Incontrast with other models, this is not a case of electoral competition where parties seek 4
  • 5. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolato win an election. Instead, parties seek to gain the support of each citizen which isconsidered a political asset that can be used in different ways within the political arena. One of the two parties is an incumbent and the other one is an opposition partydenoted by A and B respectively. Both parties compete programmatically by assuming apolitical platform which is publicly known. The incumbent party, however, has somefixed amount of public resources, G, that can be used either to provide public goods or tocreate clientelist relations by patronage. Incumbent parties have the advantage of usingpublic resources to favor individuals and buy their political support with a threat ofwithdrawing the favor if the support is not given to them. Thus, the model assumes thatthe incumbent has a fixed amount of public resources G that can be invested to produceand provide a public good or to establish a clientele-patron relationship. The budgetconstraint for the incumbent is: g  p G, (0.1)where g is the amount of public resources invested in public goods and p are thoseresources utilized for patronage. To simplify the analysis, I will assume that the opposition does not have anyresources to use them as patronage. Thus the incumbent does not just compete bypresenting a political platform but also by distributing the available public resources aspublic goods and patronage. Following Hinich and Munger (1994) and Enelow and Hinich (1990), the modelassumes ideology is used by agents as a mechanism to link the perception they have ofpolitical competitors and the way their rule may affect them. Preferences over the policyand political program space have a correspondence over the one dimensional ideologicalspace. Political programs embraced buy the parties Even though parties are assumed to be predators, they have preferences over thepolitical program space, and therefore over the ideological single space. Then, parties Aand B have different ideal ideological positions upon by their members agree. To simplifyand without lose of generality in our results, the model assumes that these ideal positionsare located on the extreme points of the ideological line which is normalized around theincumbent position. Thus the incumbent ideal position is located on 0 and the rival issituated some point L, with L  0 . These positions are common knowledge for both 5
  • 6. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolaparties. When the parties compete programmatically they may embrace a politicalprogram other than their ideal one. Let a and b denote the position of these programs ovrthe ideological line. Any deviation from its ideal point implies a cost for the party. It isassumed that deviating costs may be different for each party and respond both to thecharacteristics of the party itself and to the structure of the political system. Costs forparties A and B are represented by functions C A  and CB  respectively with thefollowing characteristics: C A   0 , C A   0 , C A  0   0 , (0.2) CB   0 , CB   0 and CB  0   0 . (0.3) Each citizen i has symmetric single peaked preferences over the ideological line andis indexed according the location of her ideal position over this space. These preferencesare private and they reflect different individual characteristics; it is assumed that politicalplatforms cannot credibly modify these preferences; therefore they are fixed parametersin the model. Citizens, however, have other observable characteristics that can beprobabilistically liked with ideological preferences. Citizenry can be divided in a finite number J of disjoint groups. The size of group j Jis given by I j with  j 1 j  1 . The members of each group share the same observableindividual characteristics given by a vector with q j  R n for j  1, 2,..., J . The partiescan observe these vectors and use them to infer the ideological preferences within thedifferent social groups. The incumbent party uses this information to conform efficientclient patron relations within the citizenry. One element in every vector q j is the individual income level for the members ofthe social group j. To simplify, assume that there are J different income levels and y j isan element of vector q j . It is assumed that there is a unique consumption good in the economy which price isequal to one. Citizen i has an exogenous income yi  y1 , y 2 ,..., y J  which is totallyexpended in the consumption good. When any citizen becomes a client, she is paid a 6
  • 7. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolapatronage transfer ti . Then consumption level for citizen i is yi  ti if i is a client and y iif not. Thus, the allocation of public resources in patronage can be used to gain thepolitical support of groups of citizens. Public resources, however, can be used to providea pure public good and the provision of this public good favors the position of theincumbent relative to the opposition party within the citizenry. Citizens select the party which they support in view of the parties’ politicalplatforms, their provision of public goods and the clientelist relations established by theincumbent. The preferences of citizen i over the two parties are represented by thecomparison of the following utility functions: V  A i     a  i   g  u  yi  ti   u  yi  2   (0.4) V  B i    b  i  2 (0.5) Then, functions V  A i  and V  B i  represent the level of citizen i’s “empathy” forthe government party and the opposition respectively. The difference u  yi  ti   u  yi  is the utility gain of becoming a client. Functionu   is assumed to be the same for every citizen, to be continuous, differentiable andstrictly concave: u  0  0, u   0, u   0, u  0   . (0.6) Each citizen gives her support just to one party. Thus, citizen i supports theincumbent party if V  A i   V  B i  ; if V  A i   V  B i  , she gives her support to theopposition and if she is indifferent between both parties, she supports each of them with aprobability of 0.5. POLITICAL COMPETITION Both parties compete programmatically to maximize the number of supporterswithin the polity taking into account the costs of embracing an ideological position otherthan their ideal one. The incumbent can also use public resources in patronage to gain the 7
  • 8. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolasupport of programmatic opponents. However, the incumbent faces an agency problemwhen she allocates public resources in the supply of public goods and patronage sinceideological preferences are not publicly observed and citizens act strategically to increasetheir private consumption. Thus, the allocation of patronage is based on the possibility ofseparate the society in ideologically oriented groups, according with some observablecharacteristics, including income. In order to maximize the support within the citizenry, the political parties need toinfer the ideological distribution of the citizens. They consider a set of group-specific probability functions F j  x   J , which are assumed to be continuous, with probability j 1  1 1 density function f j  x over  j  j , j  j  , where  j   0,   , and which are  2 2 common knowledge for the political parties. To simplify, every f j  x is assumed to be  1 1 single picked with a unique maximum at m j   j  j , j  j  .  2 2  The members of each group have some inherently ideological bias given by  j andthe ideological volatility of the group is represented by the parameter  j . The singlepicked assumption can be interpreted as if there exists some predominant ideologicalposition in any group and that predominance is unique.  Thus, F j  x   prob i  x qi  q j  and it is a mapping function that goes from thespace of observable characteristics to a segment of the ideological line. Since individualideological positions are not observable, political parties decide their strategiesconsidering an ideological space given by the union of the supports of the group-specific J  j 1 1    2 j ,  2 j  which jdensity functions. Then the ideological space is given by j 1  is assumed to be continuous. The space is normalized around the incumbent positionlocated on 0 and the rival is situated on point L. Each party tries to obtain as many supporters as possible by considering thecost of embracing a particular ideological platform. The incumbent also allocates thepublic resources to maximize her revenue by investing in public goods and in patronage. 8
  • 9. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola In this setting the incumbent party will allocate a patronage transfer t j  0 for eachmember of group j. Then the total amount of patronage is distributed in individual Jtransfers and t  j 1 j j I  P with 0  t j  P for every j. Then, given platforms a and b, the investment in public goods g and the set of t  J jpatronage transfers , the expected share of the population that supports the j 1incumbent, is J u y j t j u y j S   F  j j   g  b2  a 2  .    Note that if the  2 b  a  2 b  a   j 1  probability of support the incumbent for any member of group j  is one, then there is no 1patron-client relation between this group and the incumbent. That is, if    j  , 2 j g  b2  a 2then F j    1 and t j  0 , with   . For the rest of the paper I will call  2 b  a the pivotal point. Thus the goal for the parties is to maximize their expected revenue in a one shotgame by setting their platforms, the investment in public goods and the allocation ofpatronage, which is define by the following two problems: maxJ IS  C A  a  (0.7)   a, g , t j j 1 s.t. IS  CA  a   0 J I  jt j  g  G j 1 g 0 tj 0 La0and max I 1  S   CB  L  b  (0.8) b s.t. I 1  S   CB  L  b   0 9
  • 10. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola L  b  0. In any equilibrium with positive patronage, some groups become clientelist and theincumbent party offers an individual patronage transfer to the members of these groups.Each member of a clientelist group collects the same amount of patronage, but individualtransfers may differ along the different clientelist groups. Thus, not all the members of aclienteist group would necessarily support the incumbent. Within each clientelist groupexists a point over the ideological line that determines the expected share of its membersthat support the incumbent; to differentiate this from the pivotal location, I will call it thej swing member point. In this context political competition may drive to the creation of patron-clientrelations; however this is not a necessary result. When for any combination of ideological platforms, it is not possible to find aclientelist structure where the marginal effect of patronage would be greater than theeffect of the provision of public goods over the expected political support, no clientelismoccurs. This type of political-economic equilibrium is given by a set a , b , t j    , such J 1  G  b2  a2   G  b2  a2 that t j  0 and f j     u  y j  I  j   I   h f h   (0.9) for    2 b  a      j   2 b  a     every j . The left side of (0.9) is the net marginal political revenue that the incumbentobtain from group j. For any group j to be prone of becoming a client this net marginalrevenue must be positive. In that case the gain of patronage investment in group j wouldbe greater than the marginal benefit obtained in that same group of providing publicgoods. This implies that if any of the following: i) the individual income level for group j given the size of the group and the incumbent’s efficiency, is such that u  y j   I j ;  J   TK   h f h  xm   J ii) if y j  u1  h 1  (0.10), where xm  arg min   h f h  x  ;  f j m j   x h 1     10
  • 11. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola     f x  , ˆ h u y j j m iii) the population share is such that   j where I f j m j xm  arg min   h f h  x  ; ˆ x j iv) the population size is such that I  u y j f   m  ; j j  f x  J h m h 1  f x  J  , h m u y j v) or the relative density is such that h 1  f j m  j Ithen group j is never targeted as a clientelist one. This is consistent with the intuitive idea that high income agents are difficult to co-opt. However, the possibility of co-opting high income clients is not ruled out. If themembers of some group have high income, but the number of members is small, it maybe considered a possible client since the total amount of patronage would be not so higheven though it is more costly to obtain the support of these citizens. Moreover, if a highincome group has a low ideological dispersion it may be an important source ofclientelistal political support in comparison with other groups. When a group is lessidentified with an ideological or programmatic position, its variance will be high andtherefore the density in every point would be low. Then, the expected support given somelevel of patronage will be low compared to what would be expected from other groupwith less ideological volatility. Patronage is therefore allocated within the groups withgreater ideological identification. When political competition results in an equilibrium with patronage and provisionof public goods, the marginal political revenue of patronage in each clientelist group isequal to the marginal political revenue of the public good provision. It may happen thatsome number of groups could be completely co-opted, in which case the marginalrevenue of patronage within that group would be greater than the marginal revenue of thepublic good. To simplify the exposition I withdraw this last case. 11
  • 12. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola Thus, from the Kuhn Tucker conditions of the problem, the characterization of anequilibrium with patronage and public goods is given by a set a , b , t j    J 1 such that JG  T   j t j , where for every clientelist group k 1, 2,..., J  , j 1      u y k  t k   u y k  g   b2  a2 f  k  u y k  t k       2 b  a      J I  f  h h      u y j  t j  u y j  g   b2  a2  , (0.11) j 1   2 b  a     and for every non clientelist group h it is the case that  g   b2  a2       u y j  t j  u y j  g   b2  a2    Jf  h  u y h  I   j f j  ,  2 b  a     j 1      2 b  a    Jwhere g   G  T   j t j , t k  0 and t h  0 . j 1 Neither the left nor the right side of condition (0.11) is linear on t  and anequilibrium of this type may arise or not. Moreover, if an equilibria of this type existscondition (0.11) may have multiple solutions, however not all of them are equilibriapoints. The next lemma shows this.Lemma 1: If in an equilibrium a , b , t j     condition (0.11) holds with equality for any J 1clientelist group k then the following must holds:  u y k  t k   I k        u y k  t k   u y k  g   b2  a2  2 b  a      k  u y  t  I f  k k k    2 b  a             u y k  t k   u y k  g   b2  a2  u y  t k k  f  k 0,    2 b  a    otherwise group k is totally co-opted and condition (0.11) holds with inequality. 12
  • 13. A Formal Analysis of Patronage Politics Leonardo A. Gatica ArreolaProof: See Appendix A1. This lemma implies that the expected marginal revenue in every not totally co-optedclientelist group is decreasing on patronage. Otherwise, since there are available publicresources, it would be possible either increase or reduce the investment in patronagewithin that group and gain a greater political revenue. Thus if an equilibrium of this type exists, the patronage each member of the  I clientelist group k receives is given by t k   u1  I k  k   y k (0.12), where    f  k      u y k  t k   u y k  g   b2  a2       2 b  a    , which is the relative density of  k  j     u y  t  u y  g  b  a 2  j j  2  f  j j  k     2 b  a   group j with respect to the weighted average density of all the clientelist groups and thenon clientelist groups containing a pivotal point member. DETRMINANTS OF PATRONAGE; A PARTIAL EQUILIBRIUM ANALYSISIn this section I analyze the effect that the parameters in the model have over patronageconsidering as given the ideological positions of both parties. This partial equilibriumanalysis provides us with important insights and will be useful for the general equilibriumanalysis presented in the next section. The final effect that different variables andparameters have over patronage depends on how the relative average density is affected.According to equation (0.12), the patronage transfers for any clientelist group depend onits relative average density. The greater the relative density of group j, the grater is itspolitical relevance as a source of clientelist support; therefore patronage within this groupis higher. The clearest result is that from the ideological dispersion of the clientelistgroups. However, the effects of other parameters depend on the specific forms of thedensity functions therefore in this section I will introduce some assumptions about thedensity functions to clarify the causal mechanisms in the model.Ideological Dispersion 13
  • 14. A Formal Analysis of Patronage Politics Leonardo A. Gatica ArreolaIf some group has a low ideological dispersion it would be easier to co-opt some of itsmembers. The political return of patronage and the expected political revenue of group jincrease when the ideological dispersion decreases. Therefore when the swinger memberdensity of some clientelist group increases, it is always the case that optimal patronagealso increases.Income EffectAs in the case where all the public resources are used in patronage, it is expected thatricher groups would be more expensive to co-opt than the poor. That implies that themarginal revenue of patronage is greater within poor groups and therefore the incumbentwould target these groups as clients in the first place. But the negative relationshipbetween income and patronage is less clear when there is private information andmembers are not distributed uniformly within some group. This is due to the effects onthe expected support within each group which depends on the change of the swingermembers’ densities. If income grows for the members of some clientelist group, given theamount of the patronage transfers, fewer members can be co-opted. This implies that theswinger member shifts towards the incumbent location. When this shift affects thedensity of the swinger member, the relative marginal revenue of patronage changes butnot necessarily decreases and then it is possible a relocation of resources with graterpatronage transfers. Obviously if the relative density is constant, then the transfers arealways decreasing on income level and therefore patronage and clientelism within agroup always decline when its members’ income level grows. That is for example thecase in which every group has a uniform distribution. Then equation (0.12) becomes  J j j   I    1  j 1   yk , t k  u (0.13)  k     where the relative density just depends on constant parameters and then the transferdecreases if income grows. But if the relative density is affected by changes in incomelevel, the story can be different. 14
  • 15. A Formal Analysis of Patronage Politics Leonardo A. Gatica ArreolaIf an increase on income reduces the marginal revenue of patronage within a particulargroup, its relative density declines and the individual transfer for that group decreases justas in the uniform distribution case. An increase on income within some group alwaysshifts the swinger member reducing the expected support within that group. However, themarginal change of the swinger member’s density may be high enough to more thancompensate the loss of individual marginal utility of the transfer caused by the rise ofincome. If when public resources are reallocated the final relative average density isgreater than the initial one, then even though the members become more expensive to co-opt, the group is relatively more profitable than the others and therefore the incumbentallocates more patronage within that group. (See Appendix A2 for the general formalstatement) To clarify this mechanism, consider the following simple case.Assumption 1: Every group has a uniform distribution except group k which is aclientelist group with a continuously differentiable p.d.f., f k   , and  1 1  a , b    j  j , j  j  for j  1, 2,..., J .   2 2  This assumption implies that any change on the relative density of any group is dueto movements of group k’s density. Thus, if the swinger member’s density within group kis steep enough it will have an important change if income within that group grows. Ifthis change is sufficiently high, it would imply a loss of support within the group but themarginal revenue of patronage would increase and therefore more resources would beallocated to maintain the existing client-patron relations. The next result shows this.Result 1: Under Assumption 1, t k  i) If f k     0 , then 0, y k t k  ii) If y k  u1  I k   t k  , then 0, y k 15
  • 16. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola t k  iii) When f k     0 , then     0 if y k  f k          2 b  a u y k  t k   , f k    u  y k  t k   u  y    u  y  t   I  k k k k t k  iv) When f k     0 , then 0, y kwhere       u y k  t k   u y k  g   b2  a2 . 2 b  a   Proof: See Appendix A3. The result characterizes the profitability of the clientelist groups. A change of themembers income can lead to lower or higher amount of patronage invested in that group.What determines this is the net expected rate of return of public resources when they areinvested in patronage instead of public goods. Intuitively when the expected political rateof return of patronage of some clientelist group is greater than the one obtained byinvestment of public goods within whole polity, that group would be such an importantsource of revenue that the incumbent will always try to co-opt it. Then, even if anincrease of income within the group rises the co-optation cost of each member, moreresources are allocated in patronage to maintain the client-patron relation. Thus patronagetransfers not necessarily have a negative relation with individual income levels in everycase. The second part of the result implies, however, that if income rise enough,patronage always decreases until the group becomes non clientelist.Ideological Distance and Ideological BiasWhen the political parties assume similar ideological platforms, the use of policies andstrategies to differentiate themselves from their rivals become more important. It is alsothe case that the relative position of both platforms over the ideological line, changes theeffectiveness of the parties’ strategies. This means that given the ideological distance ofthe platforms, if the population preferences increase their ideological bias towards some 16
  • 17. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolaparty the political return of the strategies change. Assumption 1 is once more a usefulsetup to show this. Changes in both the ideological bias and the ideological distance of the programsaffect the relative average density of every group around the pivotal point. For example,under Assumption 1 the relative average density of the clientelist group k becomes 1   j j k  k . k f  k  k k     u y  t  u y k  g  b  a         2 b  a  2   ba If the ideological distance b  a is constant but the midpoint between the 2political platforms increases, the swinger members deviate toward the opposition. Thismeans that, given the investment on patronage, the expected support within each groupincreases. The effect on patronage depends once more on the change of the swingerdensity. A similar effect occurs when the ideological distance change. Given the ideologicalbias, if the distance is reduced the political parties become more alike and therefore theutility differences of supporting one or the other are reduced. This implies that themarginal revenue of both, patronage and public goods, increases. The final result dependson the magnitude of both marginal effects. This is shown in the next result.Result 2: Under Assumption 1, b  a  i) If f k      0 , then the political bias to the incumbent, , has a positive 2 effect on patronage transfers and the ideological distance, b  a , has a negative effect on patronage transfers for the clientelist group. b  a  ii) if f k      0 , then the political bias to the incumbent, , has a negative 2 effect on patronage transfers and the ideological distance, b  a , has a positive effect on patronage transfers for the clientelist group. 17
  • 18. A Formal Analysis of Patronage Politics Leonardo A. Gatica ArreolaProof: See Appendix A4. COMPETITIVNESS AND PATRONAGE; A GENERAL EQUILIBRIUM APPROACHEIn this section the essay analyzes the effect of an increase in the competitiveness withinthe political system over the allocation of patronage. In contrast with the idea thatcompetitiveness drives to more efficient outcomes, the model shows how this relation canbe reversed. In the previous section I show the circumstances where a stronger opposition, whichcan modify the swinger point by changing the ideological distance or the mid pointbetween the competitors, leads to an increase in patronage investment. That analysis,whoever, does not consider the secondary effects of the patronage investment over theideological positions of the parties. An increase in patronage discourage the opposition tocompete and can reverse the initial effect. As equation (0.12) suggests, the final effectdepends on the sensitivity of the relative density of each clientelist group. To clarify thismechanism here I will focus on a simple case where every group has a uniformdistribution except group j which is the only clientelist group with a continuouslydifferentiable p.d.f., f j  , over 0, L . The competitiveness issue in the model is reflected by the cost structure ofprogrammatic competition. When the costs for both parties are similar, competitivenesswithin the political arena is higher. To simplify the discussion, assume that the costs forthe parties are such that C A  a   C for any a, and CB  L  b    C for any b, where C isa positive constant and  is a positive parameter which determines the competitiveadvantage of the incumbent. When parameter  is close to one, competitiveness is high.On the contrary the greater is  , the less competitive is the party system. Note that these assumptions do not place further restrictions either on the clientelistgroup’s density function or on the rest of the agents’ characteristics. Thus any adjustmentof the relative density does just depend on the changes of the clientelist group’s density. 18
  • 19. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola I will depart from an interior equilibrium where political parties compete bysignaling a pair of political platforms other than their ideal positions and where theincumbent invests in both patronage and public goods. Then, according with ourassumptions, the Kuhn-Tucker conditions for an interior solution are: 1 jC   T     hKg  h    T j f j         1 u y j  t j  u y j  Kg  , (0.14)  2 2 b  a   2 2 2 b  a  2  h     1j C   T      Kg  h h    T j f j         1 u y j  t j  u y j  Kg   , (0.15)  2 2  b  a 2  2 2 b  a  2  h     j f j     u  y j  t j   KT j   KT  h h , (0.16) hwhere        u y j  t j  u y j  (0.17). b  a    Since with the exception of group j the rest of the groups have a uniformdistribution, the right sides of conditions (0.14) and (0.15) are not necessarily continuousnor monotone on a and b respectively. Then it is convenient then to make a lastassumption.  1 1   h 1 1  Assume that  i  i , i  i    2 h ,  2 h    for any two groups h  2 2     1 1 h, i 1, 2,..., J  ,  j  j , j  j   o, L  and 0, L   ,     where  is the  2 2  J  1 maximum element of the sequence  h  h  and  is the minimum element of the  2 1 J  1 sequence  h  h  .  2 1 19
  • 20. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola This assumption implies that   h h is constant over the interval  0, L  then there jare no jumps of this weighted average density when the swinger point change and themarginal revenue of political competition for each party is continuously differentiable onthe ideological position of its platform. Moreover, the assumptions guarantee that thechanges in the relative density are smooth; this simplifies the static comparative analysis. In this case, then it is the case that an interior equilibria implies (0.14), (0.15),   g   f j     4 j b  a  u y j  t j     1 j u y  j      T   (0.18), where  is(0.16) and  f j      uy   2 2 b  a   u y j  t j  j  Kg defined by (0.17). Our assumptions guaranty continuity and differentiability of the marginal revenue,but it does not implies monotonicity. Thus, and since marginal cost is constant, there existmultiple solutions for conditions (0.14) and (0.15), but not all of them can be sustained asan equilibrium. This implies that there can be different ideological platform combinationsthat equalize the marginal revenue of political competition and the marginal cost, but notall of them are profitable for the parties and won’t be sustained as equilibria. This is consistent with the partial equilibrium results which show that if theclientelist group is an important supporter for the incumbent, this last would try tomaintain its support when the system becomes more competitive by increasing patronage. For our simple case, the following result holds.Result 3: When the political system becomes more competitive patronage increases if inthe equilibrium the clientelist group’s density, f j    , is such that f j     1 . Patronagedecreases when the political system becomes more competitive if f j      1 , 2  ,where 1 and  2 are defined by the following:   u  y j  t j    j KT    2 u   y j  t j    j KT  2 4    4 j f j    u  y j  t j  2  b  a   4 b  a  2  1  2 j  20
  • 21. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola 2   j        1 u y  t  u y  Kg 2   j  j j , 2  2    2  2 b  a     j u  y j  t j   u  y j   kg  f  j     Kg   h h jwhere   and   3   b a         2 2  u y j  t j  u y j  kg    u y j  t j   u y j  kg   1  1  . 2    2    2 2      b a   b a Proof: See Appendix A12. Note that 1  2  0 . What this formal statement says is that when the swingermember of the clientelist group is around the mode or on a broader interval of thedecreasing part of the density function near the mode, an increase on the competitivenessof the system leads to a greater investment in clientelism. In an equilibrium where theswinger member is in such location, the incumbent invest in patronage in such a waybecause the group is an important revenue source and therefore the incumbent will try tokeep the support of this group. Concluding RemarksSummarizing, this essay presents a formal model of political competition and clientelismwhich leading idea is that patronage is determined by the relative political relevance thatdifferent social groups have. This contrast with other analytical theories that focus on theplain co-optation cost driven by the private consumption utility function of the citizens,their productivity or wealth, and their political preferences (Robinson and Verdier 2002;Estevez, et al. 2002; Medina and Stokes 2002). The argument is similar to Shefter’s (1994) since it is based on a supply-demandrelation; however, the mechanisms of the two theories are different. Since this modelconsiders that personalism and dyadicity are not necessary characteristics of patron-client 21
  • 22. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolarelations, it suggests that political parties recognize potential clients within the whole setof citizens who demand patronage. I argue then that the supply of patronage match thepotential demand depending on three main issues: the ideological bias of the group, itsideological volatility and the relative value citizens give to private consumption andpublic goods which depends on their income level. The model assumes that any citizen would be better off if her income risesindependently of her initial wealth, therefore any citizen is prone to sell her politicalsupport at some price. This price depends not just on a demand of consumption goods buton a subjective valuation of the political activity. Ideology is then an important issue inthe dynamics of patronage. The more bias toward the opposition, the greater will be thecost of co-optation. Therefore, clientelism would be less costly within groups around thepivotal position. However, it is not uncommon that parties try to use patronage to co-optopposition groups even though this could be more expensive than co-opting those groupsaround the pivotal point. The model shows that if opposition groups are consideredrelatively important supporters, the incumbent will target them as clients. Manyopposition groups are organizations of citizens that have an active political life, they areeasily monitored and their ideological dispersion is low. These groups are generally animportant source of political revenue since they can be organized and can act as activists.Other opposition groups are not necessarily organized but can be monitored, likeintellectuals and artists, and they have a relevant role within the public opinion. Thusthese groups are in many cases strategically more relevant than other groups within thepolitical arena and therefore they are targeted as clients even though their co-optation canbe expensive because their ideological bias. Ideological dispersion also has an important role The less the ideological dispersionwithin a social group the greater its clientelist relevance. Thus organized ideologicalgroups become attractive clientelist targets. The model argues that the possibility ofdivide the society in ideological groups is one of the most important sources ofclientelism. If society can not be divided in ideological groups the cost of patron-clientrelations will be too high unless they are established in a personal way with thepossibility of monitor the client’s behavior. Under this logic, it is expected that politicalparties and governments take advantage of social cleavages or implement strategies to 22
  • 23. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreoladivide the citizenry in groups minimizing the ideological variance. This provides anexplanation to the positive relationship between clientelism and ethnic cleavages andcorporative states that has been observed (see Fearon 2002). Contrary to most theories and analysis of clientelist relations that associate it withpoverty and therefore with developing economies, I argue that low income is neither anecessary nor a sufficient condition for clientelism. The model is consistent with theintuitive idea that less wealthy groups are easier to co-opt. However, the model suggeststhat there is not necessarily a unidirectional causal relation between wealth andclientelism. The fact is that low income groups are not necessarily clients even when theirvaluation of private consumption would be high, and it’s also common to find wealthyclients. This is possible since an individual or group with low income is not necessarily apotential client and it won’t be considered strategically relevant. On the contrary, sincethe relative relevance depends not just on income level, wealthy groups may beconsidered important sources of clientelist revenue. Moreover, when the incumbent setsher strategy, she also takes into account the negative externalities that patronage produceswithin the citizenry and other clientelist groups; a greater amount of patronage withinsome group may imply less provision of public goods and less patronage for othergroups. Due to these effects there is not necessarily an income level or a distributionalpattern that explain clientelism. The comparative static results also show that an increaseon income levels does not necessarily reduces the investment in patronage since anincumbent will find important to maintain the control over strategically groups. Thus themodel is consistent with the fact that clientelism is neither a general practice in lesseconomically developed societies nor an absent practice in rich economies. It alsocontrasts with the culturalist approaches and may contribute to the explanation of thepresence of clientelist practices in a broad number of different cultural groups andcountries. Finally, an important feature of the model is that it can address some insights aboutthe relation between the level of competitiveness within the parties and the use ofpatronage. Despite the expected social and political benefits of democratization, and theidea that patronage and clientelism will diminish under the competitive political marketthat liberal democracy implies, this strategies are present in modern democracies and 23
  • 24. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreolahave survived even after different democratization processes. More over, some analysessuggest that the use of patronage may increase when the political the arena becomes morecompetitive (Moreno, 2005). This behavior is explained by the model when clientelistgroups are an important source of political support and therefore the incumbent willprefer to maintain their control instead of trying to compete programmatically and bysupplying public goods. In conclusion, the model developed in this essay formalizes the main characteristicsthat the informal literature attaches to the patron-client relation providing explanationsnot just for developing and poor democracies, but also for developed ones. It can help toexplain a number of paradoxes that other theories have failed to clarify, particularly fordeveloped democracies, by analyzing clientelism and patronage as a pure relation ofexchange of political support for public excludable decisions. It also helps to understandwhy democratization as a purely process of development of a competitive politicalmarket, does not necessarily provide the incentives to diminish the use of clientelism as apolitical strategy. 24
  • 25. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola APENDIXA1 Proof of Lemma 1.  Suppose a , b , t j    is an equilibrium where: J 1  u y k  t k    k        u y k  t k   u y k  g   b2  a2  2 b  a       k k  u y  t  I f  k k   2 b  a              u y k  t k   u y k  g   b2  a2   u y  t k k  f  k   0 . (0.19)    2 b  a   If (0.19) holds with inequality, then there exist some x, t k   x  0 , such that for anyt    x, t k   ,      u y k  t   u y k  g   b2  a2 f k  u  y k  t   I  k        2 b a       I  f  j j      u y j  t j  u y j  g   b2  a2  , k   2 b  a     and therefore total political revenue is greater with t  than with t j , therefore it can notbe an equilibrium. If equation (0.19) holds with strict equality, then      u y k  t   u y k  g   b2  a2 f   j  2 b a     u y k  t   I k      is either a maximum or a  minimum. If it is a maximum then the previous part of the proof applies. If it is aminimum then there exist some x  t j such that for any t   t j , x        u y k  t   u y k  g   b2  a2 f k  u  y j  t   I  k        2 b a       25
  • 26. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola I  f  j j      u y j  t j  u y j  g   b2  a2   , and therefore total political k   2 b  a     revenue is greater with t than with t j , therefore it can not be an equilibrium. A2 Income Effect over Patronage Transfers   1   y j   2u  u1    j dt     Differentiating equation (0.12) we get  , where dy j  1  1    t j   u  u    2    x   x . If       2u y j  t j  min  y j , t j , max  y j , t j   , then income haspositive effect over the individual transfer. This is possible just if at least one of  y j and t j is positive and high enough, where as the other effect over the relative density is lowenough. In all other cases income and individual transfers have a negative relationship.A3 Proof of Result 1 According with Assumption 1 and differentiating (0.12) the following isobtained,     u y k  t k   I k 2     f k   u y k  t k  f k       t k     2 b a        ,y k     u y k  t k   u y k       2 b  a        u y k  t k   I k f k     u y k  t k  f k        with       u y k  t k   u y k  g   b2  a2 . From (0.6) and Lemma 1 the result follows 2 b  a   straightforward. A4 Proof of Result 2. b  a  Let   , then under Assumption 1, from (0.12), 2 26
  • 27. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreoladt k    u  y k   t k   I k f k      .      Id  u y  t k k k fk 2 b  a     f k    u y k  t k    According to Lemma 1, the denominator is always negative for any clientelist dt k group, therefore if f k         0 , then   0 . d       u yk  t k  u yk  g     f k        2   dt k   b a In the same way,  ,  d b  a        u y  t   I  k k k 2 fk  f    u  y k k  t k  2 b  a    dt k therefore if f         0 , then k    0 .   d b  a  A Proof of Result 3. Differentiating the equation system (0.14), (0.15) and (0.16), and after somealgebra it followst j      u y j  t j   j KT  C T   u  y  t    KT    2 j   j j j     f            j  f j    2   u y j  t j j f j 2 b  a            (0.20)where:   j u  y j  t j   u  y j   kg  f  j     Kg   h h j , b  3   a         2 2  u y j  t j  u y j  kg    u y j  t j   u y j  kg   1  1  , 2   2   2 2      b a   b a       u y j  t j  u y j  . b  a    27
  • 28. A Formal Analysis of Patronage Politics Leonardo A. Gatica Arreola Thus it follows that if:  u  y    2  t j   j KT       0 (0.21), j u y j  t j f f         j  f j      2 j    j  2 b  a      t then   0 .  Note that given the characteristics of the utility function (0.6), the right side ofequation (0.21), is a strictly convex function on f j    with two real roots:   u  y j  t j    j KT    2 u  y j  t j    j KT  2 4    4 j f j    u  y j  t j  2 b  a    4 b  a  2  r1  0 2  jand   u  y j  t j    j KT    2 u  y j  t j    j KT  2 4    4 j f j    u  y j  t j  2 b  a    4 b  a  2  r2  0 2  j     2  u y j  t j   jTKwith r2  r1 and with a minimum at  . 4 b  a    j  t  Therefore, if f j      r1 , r2  , then  0 . Nevertheless Lemma 2 states that  2in any equilibrium f      j j   j j j     1 u y  t  u y  Kg  . Therefore, since      2    2  2 b  a   2r1   j   j j j     1 u y  t  u y  Kg       0 , in an equilibrium t   0 if f j     r1  2     2  2 b  a   2and t   0 if f      r1 ,   , where    j j   j j     1 u y  t  u y  Kg  j .        2    2  2 b  a   28
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