Munich Personal RePEc Archive
Tournaments in religious organizations with investment in religious human
capital: choosing the pope
Oliveira, Livio Luiz Soares de and Netto, Giácomo Balbinotto
Fundação de Economia e Estatística, Post-Graduate Program in Applied Economics (PGPAE) of the Federal University of Rio Grande do Sul (UFRGS)
21 February 2013
Online at https://mpra.ub.uni-muenchen.de/44606/
MPRA Paper No. 44606, posted 27 Feb 2013 14:27 UTC
1. I NTRODUCTI O N
All reli gious organization, as an y other fi rm, have thei r obj ect ives, among which are wa ys to att ract new convert s. To att ain thei r ai ms, each rel i gious organi zation is endowed wi th a di versit y of opti ons am ong several organiz ational strat egi es. To be successful in achi evi ng t hese obj ecti ves will be conditioned, in great m easure, to the skill s and perform ance of t hose who are responsible for t he l eadership of t he organiz ati on, regardi ng the commitm ent of t hese persons wit h what has been planned. It is of t he utmost import ance for t he reli gious fi rm that its cl erics, in t heir several hi erarchi cal levels, superi ors and subordi nates, exerci se a l evel of effort suitabl e with the result s expect ed from each one of them.
The cont racts establ ished bet ween reli gi ous organiz ations and its cl eri cs (workers) may be insert ed in the approach of the pri ncipal -agent problem. Withi n thi s context, t he fi rm woul d be the princi pal and its cl eri cs, the agent s. Therefore, accordi ng to Zech (2001, p.328) th is rel ati onship princi pal -agent woul d not be immune t o probl ems such as moral hazard – in the case of shi rki ng behavior on the part of the workers – adverse sel ection – with hidden i nfor mat i on – and dislodgement of obj ectives – where the workers mi ght exer t an effort , but i n act iviti es which are not t hose having priorit y for the fi rm.
The cl eri cs, in t he lack of appropriate incent ives, would rather reduce thei r efforts to a minimum, acting in thei r own benefit. These problems tend to becom e worse when th e monitoring cost s are hi gh.
Evident l y, t he more det ail ed and complet e the contract bet ween t he agent and the princi pal, t he nearer the y wi ll be to the optim um relat ivit y of the equati oning of t he i nterest of both parti es i nvol ved in the contractual rel ati onship, thi s m eans, a “first-best” contract. However, t his contract woul d be conditioned to the nonexist ence of hi dden inf or mation, to measurability and to the observability of the agent’s behavior, the absence of ri sk or of reduced ri sk, as well as the possibilit y of the princi pal i mposing severe penalti es on the agent, in t he case of the agent not compl yi ng wit h the contract. W hen t his i s not possibl e, t he alternative is to create a “s econd-best” contract.
Aft er this int roducti on , we discuss, in next section , the model of Câm ara (2002 ) modi fied to reli gi ous organiz ations , t hrough t he i ncl usion of non -monet ar y income or ps ychi c income , with t wo cl erics skills and a homogeneous phase. The objecti ve of thi s procedure is t he m odificati on, for the purpose of t his work, that consi ders a Tournam ent between t wo cl eri cs, who possess homogeneous skills and abiliti es, t o be applied to the case of a reli gious organization, especi all y, t he Rom an C athol ic Church and reli gious fi rms wit h sim ilar hierarchi cal st ructures.
2. Tourn amen ts I n Reli gious O rganizations With In ves tmen t In Rel igiou s Hu man Capital .
In t his secti on, we will present a version, modi fied, of C âmara´s Tournament s model (2002), whi ch i ncludes t he possi bil it y of the parti cipant s in the prom otion tournam ent to invest in hum an capital.
However, here we will consider an adapt ation of the model for the purpose of this work, specificall y for rel i gi ous organiz ations. In stead of the wider concept of human capital, considered b y C âm ara i n his work, the concept of reli gious hum an capit al will be considered. The main modi ficati on is the incl usion of ps ychic i ncome or non -monet ar y i ncom e in the m odel.
The m odel has one stag e and two com pet ing cl erics, and , who present a di fferenti at ed producti on functi on given b y ( ), where µ represent s the effort , is the religious capital of the cleric, ( ) and ⁄ ⁄ ⁄ , ⁄ . The cost function is given by ( ) ( ) ( ) in which ( ) ( )=0, ( ) ( ) ( ) ( ) . The cl eri cs have identical functions, both in terms of production an d cost, presenti ng in t his wa y, homogeneous abili ties. Besides, the y present neut ralit y to risk.
The reli gi ous organi zation will observe the production of each cl eri c parti cipating in the tournament, whi ch will be a functi on of ( ), multi pli ed b y a random error common to bot h clerics parti cipating in the tournament. Here, we consider the common error and not i ndividual and independent errors, since the heavi er the wei ght of the com mon error the hi gher the effi ci enc y of the tournament. In this wa y, cl erics and , wi ll present the followi ng indivi dual productions:
( )
(1) ( )
The probabili t y ( ) of cl eri c overcoming cleri c will be gi ven b y:
( ) ( ( ) ( ) ) (2)
Where t he random factor , that i s common to bot h cleri cs and has the propriet y of bei ng multi pli abl e, i s annull ed, and does not affect the probabilit y of t he two cleri cs t o win the disput e.
For t he problem of maximizati on of each one of the cl eri cs, an alteration of Câmara’s (2002) model will be made, which is the inclusion of non-m onetar y differenti al bet ween cl erics. This non-m onet ar y incom e is also known as psychic i ncom e according to Thurow (1978) and Zech (2001, p.331; 2007, p.738), ori ginating i n st atus, pri vil eges, use of tit les and insi gni as, sati sfaction in pl easi ng and serving God and fellow men,
testim on y of eternal salvation through a fait hfull y professed priesthood, et c1.
Therefore, we have that:
( )( ) [ ( )]( ) ( ) (3)
Here, and represent, respecti vel y, the monet ar y and non - monetar y i ncom e of the cleri c who obt ains t he fi rst pl ace i n the Tournam ent (t hat of Bishop or Supervisor); and represent the sam e thing for the cl eri c classi fi ed in second place (assist ant ) . Wit h that, the rem unerati on of the Supervi sor or Bishop wi ll be and the rem unerati on of the assist ant will be . Besi des, as in t he previous case, havi ng and consequent l y , for the margi nal effort t o be positi ve. S ubst i tuting (2) int o (3) we have that:
( )
( ) ( )( ) [ ( )
( ) ( )] ( ) ( ) ( )
The first order condi tions will be given by:
( )
( )
[ ( ) ( )] ( ) ( )
( )
( )
( )
[ ( ) ( )] ( ) ( )
( )
Where:
( ) ( ) ( ) ( )
( ) ( )
Rewriti ng equations (5) and (6), the resul t is:
1 S e e a l s o S a v yc h, 2 0 0 5 , p . 5 5 -6 3 .
( )( ) [ ( ) ( )]
( ) ( )
( )
( )( ) [ ( ) ( )]
( ) ( )
( )
In t his m anner, the first order c onditi ons (F.O.C) wi ll be respected when:
( ) ( )
( ) ( )
( )( )
[ ( ) ( )] ( )
Where ( ) ( ) ( ) ( ) , ( ) ( ) and ( ) ( )
The condi tions of t he second order require that t he one derived from t he cleri cs maximization function , gi ven b y equati on (4), be a negati ve semi defined Hessian m at rix.
In t his wa y, we have that:
( ) {
( ) ( )
( )
[ ( ) ( )]} ( )
(10) ( ) { ( )
( )
( )
[ ( ) ( )]} ( )
The sam e reasoni ng is appl ied for cleri c . R ewriti ng equat ion (9) we have t hat:
( ) ( )
( ) ( )
( )( )
[ ( ) ( )] ( )
The equation above indicat es t hat , in a situation of bal ance, the marginal substi tution rate (MSR ) between and , this is t o sa y, bet ween the effort of cl eri c and his reli gi ous capital, m ust be equal to his margi nal substi tution cost (MSC ). It also informs that those vari abl es depend upon the spread bet ween prizes, whet her monetar y or non-monet ar y.
Equation (11) indi cat es t hat the values rel at ed to effort an d rel i gious hum an capi tal chosen b y cl eri c , given respectivel y b y and
, will depend on t he spread between monet ar y income and non - monetar y incom e (psychic incom e), given, respecti vel y, b y and . Here, di fferentl y from the C âm ara (2002) model, where should be positi ve, due t o the incl usion of the non -m onet ar y incom e, ma y assume a null val ue, but onl y i f is positi ve for the cl erics who parti cipat e in the t ournam ent to have incenti ves to do their best and invest i n rel i gious human capit al. Thi s is: .
Besides, it can be observed i n (9 ) and (11) that a lower spread in monetar y i ncom e can be compensat ed by hi gher spread in non -m onet ar y income and vi ce -versa. Even i f , t his is, spread in m onet ar y income is null, when the candidat es recei ve equal monet ar y incom e, or if this is, even if t he candidates do not receive an y m onet ar y income, t he spread i n ps ychi c income m ight be suffi cient as a stim ulus for the effort of the cleri cs partici pating i n the promotion tournament.
Such is the case of catholi c cl erics who bel ong t o Institut es of Consecrat ed Li fe (C ode of C anon Law ), of the R oman C athol ic Church, who must take a vow of povert y (toget her with t hose of obed i ence and chastit y) and do not receive a monetar y sal ar y. This i s not a reason, for a novi ce who ent ers an order or a Cat holi c Instit ut e of Consecrat ed Li fe, for example, not to seek becom ing a hi gh -ranking abbot withi n this organiz ati on , for example .
In other words, when deal ing wit h prom otion tournam ents appli ed to cl eri cs, the spread in monet ar y incom e mi ght be of littl e im port ance or even, not m ake an y difference at all in stimul ating t he cl erics to the effort. This is because, according to the exi g enci es made t o those who wish t o dedi cat e t hemsel ves tot all y t o a reli gious life, the most si gni fi cant factor, in order to extract the maximum perform ance from the parti cipant s of the t ournam ent, mi ght be the expansi on in spread of the ps ychi c income and n ot an increase i n monetar y remuneration, as i t happens in secul ar organizati ons.
In these, t he stimul us to increase the effort of t he workers ma y com e not onl y from the spread of t he monetar y i ncome but also from non-monet ar y incom e, in forms such as pre sti ge, influence, hierarchi cal power and status of the job, pl aced as priz es for the promot ion tournament, for exampl e. This i ndi cat es t hat, both in t he case of rel i gious organiz ati ons, t he t ournam ent model would need to be onl y minim all y adapted, i n order t o incl ude the ps ychi c income as well, as i t is bei ng done here and, in t his wa y, becoming closer to si tuations as the one being dealt wit h in this paper. Besi des, it is necessar y t o take i nto account that, in sit uations where the cl eric does not receive a m onet ar y income, the import ance of i ncl ude the ps ychi c incom e is cruci al, in order to satisf y (9) and (11 ). Otherwise, the marginal cost exercise i ncurred i n b y t he cl eri c woul d be equal to zero, in whi ch case a promot ion tournament woul d be nonexist en t.
Still observing equation (9) and (11), it can be percei ved that an increase either in and/or in , increases the ratio on the ri ght hand side of t he equat ion. With the obj ective of m aint aining t he equalit y, t he rat io bet ween the m arginal cost and t he m arginal product of and , on the l eft hand side, should also increase correspondingl y. This means that an increase in and/ or in gives rise to an increase of t he effort
and of the investment in reli gious capit al of cl eri c . Identical reasoning i s appli ed to cleri c .
In equations (9) and (11) the effect s of the variat ions of the production functi on of cl eric are not const ant , si nce ( ) is present both in the num erator as in t he denominat or of t he equations. Therefore, increases in ( ) when its value is suffi ci entl y sm all, will i mpl y in corresponding increases in ( ), until there is a balance in ( ). Be yo nd that point, i ncreases in ( ) will impl y correspond ing decreases i n ( ). This means that cleric will respond to the increase of effort and of rel i gious capital i nvestm ent of cleri c equival ent l y, with the objective of winni ng the t ournament , according to the descri ption i n equation (9) until there i s a bal ance. Be yond that point, it will not compensate, in terms of benefit, for cl eri c to increase and , where t he cost ( ) will be so hi gh that the cl eri c prefers not to continue di sputing the tournam ent .
Equatio n (11) informs the enti re range of optim um choices in terms of and , in order to satisf y t he F.O.C. so to m aximize the indivi dual utilit y of t he cl eri c. In this way, with the aim of obtaini ng the best response functi on, each opti mal bundl e must be substit uted, in (4), b y a feasibl e equi val ent vari abl e ( ) . With this, t he functi on t o be maxi mized would be the following:
( )
( ) ( )( ) [ ( )
( ) ( )] ( )
( ) ( )
The F.O.C. conditions wil l be given b y:
( ) ( )
[ ( ) ( )] ( )
( ) ( ) The second order conditions will be gi ven b y:
( ) { ( ) ( )
( )
[ ( ) ( )] } ( ) ( )
The reaction function of cl eri c will be gi ven b y:
[ ( ) ( )]
[ ( ) ( )][ ( ) ( )] ( )
The reaction functi on of cl eri c will be s ymm et ri cal . Bot h reactions funct ions are represent ed in t he foll owi ng fi gure:
Fi gure I, as well as the reacti on functi on in (15), indi cat es that , considering the existence of a Nash bal ance in pure st rategies, it will result in
, whi ch derives in and This is, in the bal ance, both cleri cs will present the sam e level of effort and investm ent of reli gi ous hum an capit al, where the probabi liti es of each one of them winni ng the tournam ent will be equal to ( )
F i n a l c o n s i d e r a t i o n s
Remuneration per product is not a rul e among organizati ons to stimul at e the effort of thei r workers, and this is parti cularl y t rue for rel i gious organizati ons, considering the i ntri nsi c di fficult y in measuring and moni toring the performance of their cl eri cs (Zech, 2001, p.331).
Therefore, in t his work, we consider promot ions as an i ncentive rem unerati on mechanism, that is to say, the T our naments Prom otion Model, as an expl anat or y and pl ausi bl e theoretical fram ework for t he rem unerati on rul e s of the workers in reli gi ous organizati ons.
Tournam ents are commonl y used b y reli gi ous organiz ati ons, even if t he y are not aware of it, in order to st imul at e their workers, who act in the scenario of an organiz ational i nternal market , where asym m et ri cal inform ation and rel ativel y hi gh moni toring costs are hi ghl ight ed, and where promoti ons are t he main form of incentive.
R e f e r e n c e s
Câm ar a , O d i l on R o b er to V. G . de Ar r ud a . 20 02 . O s Ef e i tos do T or n e io So br e o In v es t im en to em Cap i ta l H um an o n as Em pr es as . M es tr a d o em E c on om ia de Em pr es as , U n i v er s i d a de C a tó l ic a de Br as í l i a.
𝑦𝑗
𝑦𝑗
𝑦𝑘 𝑦𝑘
𝑀𝐶𝑅𝐾
𝑦𝑗 𝑦𝑘
𝑀𝐶𝑅𝐽
F i g u r e I - B e s t r e p l y c u r v e s o f t h e c l e r i c s
__ _ __ _ . C od e of Can o n L a w . ht tp :/ / www. v a t ic an . va / ar c h i v e/ E N G 11 0 4/ _I N D EX .HT M . Ac es s in 1 9/ 0 1/ 20 1 1.
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