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Organizational form, prosocial motivation and provision of public services Vlassopoulos, Michael 2007

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Organizational Form, Prosocial Motivation and Provision of Public Services by M i c h a e l Vlassopoulos B . A . , A thens Univers i ty of Economics and Business, 1998 M . A . , M c G i l l Univers i ty , 2000 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y i n T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Economics) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A September 2007 © M i c h a e l Vlassopoulos , 2007 Abstract This thesis is a collection of three essays that are concerned with the role of organiza-tional form and intrinsic motivation in the delivery of public services. The first essay revisits one of the most influential among the economic theories of non-profit organizations, the "contractual failures" theory, which argues that consumers perceive nonprofit status - because of the constraint in the distribution of surpluses - as a com-mitment device, which ensures them against opportunistic behaviour in markets that are characterized by contractual incompleteness in the producer/consumer relationship. This paper questions the robustness of this theory by taking into account the role of reputation. The main result is that when reputations can be sustained, then for-profit status is the preferred organizational form and high quality services are ensured. The second essay provides an explanation for the fact that nonprofit employers are uniquely able to attract volunteers with social concerns and career aspirations and for the related observation that nonprofits figure prominently in mission-related activities. Our theory is predicated on that nonprofit incorporation relaxes the incentive constraint that employers face when implicit ly contracting with volunteers. The not-for-profit commitment is shown to be effective only in activities where producers, who can choose to be for-profit or nonprofit, care about the level or quality of the service being provided. Thus, in the equilibrium of the model developed here nonprofit entry in sectors where missions play a defining role and the hiring of volunteers arise endogenously due to economic forces. This equilibrium outcome has some desirable welfare properties. The third essay, co-authored with Patrick Francois, provides a selective overview high-lighting some major themes of the recent literature on the role of intrinsic motivation in the context of the provision of social services. We focus on how the presence of intrinsic motivation affects the design of optimal incentives, the selection of motivated agents, and how prosociality interacts wi th monetary rewards and organizational form. We also discuss some of the recent literature that addresses issues of organizational design for the provision of public services. Table of Contents Abstract i i Table of Contents i i i List of Tables v i Lis t of Figures v i i Acknowledgements v i i i Co-Authorship Statement ix 1 Introduction 1 2 Quality, Reputation and the Choice of Organizational Form 6 2.1 Introduction 6 2.2 The One-Shot Game 9 2.3 The Repeated Game 11 2.3.1 For Profit Status 11 2.3.2 Nonprofit Status 13 2.4 Opt imal Choice of Organizational Form 14 2.4.1 Overview 14 2.4.2 Opt imal Choice when (5 e [Pf(2m*), 1) 17 2.4.3 Opt imal Choice when P G (±,0f (2m*)) 17 2.4.4 Opt imal Choice when f3 6 (0, ^) 18 2.4.5 Discussion 20 2.5 Relating the Model to Empir ica l Evidence and Policy Implications 21 2.6 Conclusion 22 Bibliography 24 3 Volunteer Hiring, Organizational Form and the Provision of Mission-Oriented Goods 26 3.1 Introduction 26 3.2 Related Literature 31 3.3 The Model 32 3.3.1 Primitives 32 i i i 3.3.2 The Employment Relational Contracts 37 3.3.3 Selection of Relational Contract and Organizational Form 44 3.4 Market Equi l ibr ium 48 3.4.1 A 'Sorting' Equi l ibr ium 49 3.4.2 Welfare Analysis 54 3.5 Discussion 57 3.6 Conclusion 58 Bibliography 60 4 Prosocial Motivation and the Delivery of Social Services (with Patrick Francois) 63 4.1 Introduction 63 4.2 Modell ing prosociality 65 4.2.1 Impure or Action-Oriented Al t ru i sm 67 4.2.2 Output-Oriented Al t ru i sm 72 4.3 Implications for Government Provision 78 4.3.1 Insights from Standard Agency Models 78 4.3.2 Contrasting Implications from Prosocial Motivat ion Approaches . . 82 4.3.3 Empir ica l Evidence 83 4.4 Conclusions ^ 85 Bibliography 87 5 Concluding Remarks 92 Appendices 95 A Omitted Proofs: Chapter 2 95 B Equi l ibrium Strategies Supporting the Relational Contracts in Chapter 3 98 B . l Information Sets 98 B.2 Strategy Space 99 B.3 Equi l ibr ium Strategies Supporting the Volunteering Structure 99 B.4 Equi l ibr ium Strategies Supporting the Internship Structure 101 C Omitted Proofs: Chapter 3 103 D A Parametric Example of a 'Sorting' Equil ibrium in Chapter 3 109 D . l Parameter Values 109 D.2 Computing Equi l ibr ium in the Mission Sector 110 D.3 Computing Equi l ibr ium in the Profit Sector I l l iv D.4 Checking the Sorting Constraint for Workers D.5 Checking the Sorting Constraint for Managers v List of Tables Table 2.1: Summary of Opt imal Choice of F i r m Status and Quality by Region . 19 Table D . l : Parameter Values 110 vi List of Figures 2.1 pf{m) (solid) and (3n{m) (dash) 17 2.2 Summary of O p t i m a l Choice of Organizat ional F o r m 19 3.1 T i m i n g of Events 39 3.2 Volunteering E q u i l i b r i u m i n Mis s ion Sector 52 3.3 Volunteering E q u i l i b r i u m (point V) vs Efficiency Wage E q u i l i b r i u m (point B) 54 3.4 Welfare Analys is 55 3.5 Volunteering E q u i l i b r i u m (point V ) vs E q u i l i b r i u m w i t h Internships (point I) 57 4.1 Predict ions of Cont rac tua l Fai lure Approach 80 4.2 A d d i n g "Care" Dimension 83 4.3 Predict ions of Prosocia l Mo t iva t i on Approaches 84 v i i Acknowledgement s Fi r s t and foremost, I would like to thank my supervisor Pa t r i ck Francois. He never failed to astonish me and uplift me w i t h his energy, enthusiasm, patience, generosity and perspective on life. The ideas developed i n this thesis grew out of the numerous discussions we had and bear his intellectual imprint . M y interaction w i t h Pa t r i ck has been the most gratifying experience of my life as a P h . D . student, and I w i l l always be indebted to h i m for a l l his help and guidance. I am also very grateful to the other members of my thesis committee, Mukesh Eswaran and R a l p h Win te r , for encouragement and insightful comments and suggestions that substantially improved this thesis. Thanks also to D a v i d Green for helpful advice throughout my P h . D . studies and for providing me w i t h financial assistance through T A R G E T . Al so . I would like to acknowledge my classmates and officemates for their friendship and for sharing the challenges and anxieties of graduate school. I am very fortunate to have been blessed w i t h the uncondit ional love and unwavering support of my parents throughout my academic career. I would not have embarked on this endeavour - let alone complete it - i f it had not been for them. I also owe a lot to my brothers, Thomas and Costis, who have always been there for me. Last , but certainly not least, I wish to thank my wife, A n n a , for pu t t ing up w i t h me and helping me through the ups and downs of wr i t ing this thesis. v i i i Co-Authorship Statement Chapter 4 (Prosocial Mo t iva t i on and the Provis ion of Social Services) was co-writ ten wi th Professor Pa t r i ck Francois ( U B C ) . M y contr ibut ion to the product ion of this piece of research is outl ined below. • Identification of research program - Shared responsibili ty w i th co-author. • Design of research program - Shared responsibili ty w i t h co-author. • Performing the research - Shared responsibili ty w i t h co-author. • Manuscr ip t preparation - Shared responsibili ty w i t h co-author. ix Chapter 1 Introduction The starting point and overarching mot ivat ion of this thesis emanates from an interest to understand the relative merits of alternative ins t i tu t ional arrangements - government agen-cies, nonprofit organizations, for-profit firms - in the delivery of publ ic goods and services. W i t h i n this broader research agenda, this thesis attempts to contribute to our understand-ing of what determines the scope of nonprofit organizations and the al location of economic act ivi ty between the for-profit and nonprofit sector. The motivat ion for an investigation into the economic forces that account for the existence of nonprofit organizations stems, partly, from the realization that these organizations are a large and growing part of most modern economies and yet they remain relatively under-researched. 1 A s the relative size of the private nonprofit sector increases and its contr ibut ion to G D P and tota l employ-ment rises, it seems increasingly appropriate to seek to understand the factors that shape the dis t r ibut ion of act ivi ty between the two sectors across countries and across t ime, the differences between the quali ty of services provided in commercial firms versus nonprofit organizations, and the social benefits and losses involved i n favouring one ins t i tu t ional form over the other. Even a casual observation of the sectoral concentration of nonprofit organizations in most developed countries suggests a salient pattern according to which this type of organizations tend to engage predominantly i n the provision of healthcare, education, social and other mission-oriented services. Tradi t ional ly, i n many countries, the government has been the key player in these sectors while the boundary line between the nonprofit and the public sector in some cases can be hard to draw, as some nonprofit inst i tutions are strongly influenced by governments. Nevertheless, since the dominant pat tern is for the government involvement as a direct service provider to wane, interest lies in developing a theoretical framework 1 F o r example, in Canada the G D P of the nonprofit sector was estimated at $61.8 billion in 1999, ac-counting for. 6.8% of the total economy. If the contribution of volunteers is also taken into account then the nonprofit sector's share of G D P increases to 8.5%. Equally impressive is the nonprofit sector's role as an employer, representing 13% of the country's nonagricultural employment. 1 that helps us appraise how should the responsibili ty for the ebbing government ac t iv i ty be replaced and divided among private alternatives (for-profit and nonprofit). Though it may be comparat ively easy to explain why some activities are associated w i t h one and only one type of provider, the coexistence of organizations that appear to engage in similar activities yet operate under different ownership form is much harder to explain. For example, i n the U n i t e d States, the ownership of hospitals, schools, day care centres, nursing homes, museums and theatrical companies is shared between the nonprofit and for-profit sector. T h e persistent m i x of ownership types across many industries poses a serious challenge to some of the existing theories of the neoclassical prof i t -maximizing f irm. In part icular, a valuable insight, emphasized by the property rights theory of the firm, is the importance of the residual claimant i n moni tor ing inputs and organizing product ion efficiently. 2 The most distinctive feature of nonprofit organizations, is that they operate under a strict nondis t r ibut ion constraint , 3 which stipulates that though the organization may earn surpluses no person has legal rights over them, instead any residuals have to be used for the advancement of the organization's mission or kept as endowment. W h i l e nonprofits do not have owners w i t h residual rights, they do have boards of trustees or directors, which exercise control rights. Addi t iona l ly , nonprofits face a set of state imposed legal and reporting constraints that main ta in oversight over the nondis t r ibut ion constraint - ensure that its managers and employees are not pa id excessively. 4 Nonprofit firms are often considered to be wasteful because presumably they face no pressure to maximize profits - in view of the lack of an owner wi th residual c la im on profits. They are expected to exhibit higher costs and grant managerial perks. The presence of the nondis t r ibut ion constraint is remarkable, given the importance at t r ibuted to the residual claimant in the literature on the property rights theory of the firm, and prompts the following questions for economic theory: A r e there circumstances where the commitment to not having a residual claimant conveys a comparative inst i tut ional advantage for nonprofit provision of certain goods and services? W h y would an entrepreneur contemplating entry i n one of the mixed sectors, where for-profits can break even, found a nonprofit if the for-profit status were more cost efficient? There have been some attempts to address such questions, i n the economics literature, which have largely focused on justifying the existence of the nonprofit sector by reference to instances of failures of markets and governments. 5 One of the most influential among the economic theories of nonprofit organizations, the "contractual failures" theory, argues 2See Alchian and Demsetz (1972) and Holmstrom and Mi lgrom (1994) for early and more recent state-ments respectively of this theory. 3 T h e first paper to emphasize this aspect of nonprofits is Hansmann (1980). 4 T l i e effectiveness of oversight mechanisms in nonprofits varies. See Glaeser (2003), for a discussion of governance problems in nonprofits and a model of nonprofit capture by its elite workers. 5Hansmann(1987) and Weisbrod (1988) survey early economic theories of nonprofit organizations while the articles in Anheier and Ben-Ner (2003) revisit older theories and introduce some more recent ones. 2 that consumers perceive nonprofit status - because of the constraint i n the appropriat ion of surpluses - as a commitment device, which ensures them against opportunist ic behaviour i n markets that are characterized by contractual incompleteness i n the producer/consumer relationship. In these markets, profit-taking firms have an incentive to skimp on quali ty in order to reduce costs and improve profitability. B y removing or attenuating the profit incentive, nonprofit status is a signal that a firm w i l l provide the non-contractible qual i ty it promises, and thus i n such circumstances consumers perceive them as more trustworthy. The second chapter of this thesis t i t led "Quali ty, Reputa t ion and the Choice of Orga-nizat ional F o r m " , revisits this theory, to question its robustness by taking into account the role of reputation. If for-profit firms can establish a reputation of not exploi t ing consumers -as they do i n many service sectors where quali ty is unverifiable - then it is not clear whether nonprofit status is the most efficient protection mechanism against consumer exploi tat ion. To investigate this possibility, the paper analyzes an entrepreneur's op t imal choice of organi-zational form and service quality, when quali ty is noncontractible, in a repeated interaction framework. Four possible combinations of firm status (for-profit, nonprofit) and service quali ty (one-shot, reputation) can arise i n equi l ibr ium. T h e m a i n result is that when rep-utations can be sustained, then for-profit status is the preferred organizational form and high quali ty services are ensured. T h i s finding challenges the adequacy of the contractual failure hypothesis as an explanation of nonprofit organizations that generate most of their revenue from the sale of goods and services. T h e next chapter of this thesis t i t led "Volunteer H i r i ng , Organizat ional F o r m and the Provis ion of Miss ion-Oriented Goods" , is motivated by the observation that volunteering constitutes a considerably large and increasing share of the nonprofit sector's contr ibut ion to economic activity, i n most advanced economies. For example, i n 1997 the value of volunteer work amounted to roughly one-quarter of the to ta l value of labour services provided to the nonprofit sector in Canada, while in the U . S . it reached one-third of total earnings i n the sector. 6 Besides volunteering for al truist ic reasons - a desire to help others or contribute to an important cause - there is a widespread belief that volunteering can be a stage i n professional development b y \ providing work experience and a chance to develop skills that strengthen employabili ty. Volunteering offers some of the benefits that are often also associated w i t h unpaid internships in for-profit firms or the government: opportunit ies to receive valuable on-the-job t raining, discover hidden talents and interests, learn about possible career tracks, expand networks of contacts, and enrich one's resume. In many cases the potential is high for the t ransi t ion to a paid posit ion, especially in the nonprofit sector where volunteering experience appears to be a prerequisite for any type of career. For those individuals whose mot ivat ion for volunteering includes the desire to acquire 8 T h e estimate for Canada is taken from the Satellite Account of Nonprofit Institutions and Volunteer-ing of Statistics Canada, which is available at http://www.statcan.ca/english/freepub/13-015-XIE/13-015-XIE2004000.htm. For the U.S. , see the New Nonprofit Almanac and Desk Reference, Table 1.7, pg 22-23. 3 professional skills that improve future earning capacity, it is not clear why they do not as-sociate more often w i t h for-profit employers. Th is chapter provides an explanation for the fact that nonprofit employers are uniquely able to attract volunteers w i t h social concerns and career aspirations and for the related observation that nonprofits figure prominent ly i n mission-related activities. Our theory is predicated on that - by commit t ing to not dis-t r ibut ing profits - nonprofit incorporat ion relaxes the incentive constraint that employers face when impl ic i t ly contracting w i t h volunteers, without relying on ex ante differences i n workers' preferences over the employer's identity or inherent asymmetries between nonprofit and for-profit providers. The not-for-profit commitment is shown to be effective only i n ac-tivit ies where producers, who can choose to be for-profit or nonprofit, care about the level or quali ty of the service being provided. Thus , in the equi l ibr ium of the model developed here nonprofit entry in sectors where missions play a defining role and the h i r ing of volunteers arise endogenously due to economic forces. The welfare analysis of the equi l ibr ium suggests that it has some desirable properties. The fourth chapter t i t led "Prosocial Mo t iva t i on and the Del ivery of Social Services", co-authored w i t h Pa t r ick Francois, provides a synthetic overview that highlights the major themes of the recent literature on the role of intrinsic mot ivat ion i n the context of the pro-vis ion of social services. We focus on the insights obtained from the two alternative ways of modell ing pro-social motivat ion, action-oriented and output-oriented al t ruism, concerning the design of op t imal incentives, the selection of motivated agents, and its interaction w i t h monetary rewards and organizational form. We also discuss the implicat ions for govern-ment provision of social services from the perspective of the li terature that emphasizes the noncontractible nature of output and contrast it w i t h the implicat ions derived from the literature that emphasizes the role of intrinsic motivat ion. In addi t ion to taking stock of what has been learnt so far we suggest a few directions for future work. Chapter 5 provides a brief summary and offers some concluding remarks. 4 Bibliography [1] A lch i an , A . A . , and H . Demsetz (1972): "Product ion , Information Costs, and Economic Organizat ion," American Economic Review, 62(5), 777-795. [2] Anheier , H . , and A . Ben-Ner (2003): The Study of the Nonprofit Enterprise. K luwer A c a d e m i c / P l e n u m Publishers, New York . [3] Glaeser, E . (2003): "Introduction," i n The Governance of Not-for-Profit Organizations, ed. by E . Glaeser. The Univers i ty of Chicago Press. [4] H a l l , M . H . , C . Bar r , M . Easwaramoorthy, S. W . Sokolowski, and L . M . Salamon (2005): T h e Canad ian Nonprofit and Voluntary Sector in Comparat ive Perspective, Imagine Canada, Toronto. [5] Hansmann, H . (1980): "The Role of Nonprofit Enterprise," Yale Law Journal, 89, 835-901. [6] Hansmann, H . (1987): "Economic Theories of Nonprofit Organizat ion," i n The Nonprofit Sector: A Research Handbook, ed. by W . Powell . Yale Univers i ty Press, New Haven. [7] Holmst rom, B . , and P. M i l g r o m (1994): "The F i r m as an Incentive System," American Economic Review, 84(4), 972-91. [8] Shleifer, A . (1998): "State versus Pr ivate Ownership," Journal of Economic Perspec-tives, 12(4), 133-150. [9] Weisbrod, B . (1988) The Nonprofit Economy. Harvard Univers i ty Press, Cambridge, M A . [10] Wei tzman , M . C . and Ja landoni , N . T . (2002) The New Nonprofit Almanac and Desk Reference. Independent Sector, Jossey-Bass, New York . 5 Chapter 2 Quality, Reputation and the Choice of Organizational Form* 2.1 Introduction The importance of the provision of h igh qual i ty public services such as health, education, chi ld care and care for the aged cannot be overstated. 1 Clearly, voters and consequently their elected representatives place a h igh value on these and improvements i n these areas are given high pr ior i ty i n the social agenda of any modern society. However, several poten-t ia l pathologies associated w i t h the provision of such services have been recognized i n the economics literature. In part icular, one k ind of market failure that has received consider-able attention is the one induced by the high degree of information asymmetries between providers and consumers over the quali ty of these services. The problem arises when con-sumers are not as well informed about the quali ty of the service or when the qual i ty of the service is difficult to measure and verify by th i rd parties. In such circumstances, it is argued, service providers have an incentive to act opportunis t ical ly and take advantage of the il l- informed consumer. These informational problems are exacerbated by the fact that often the person that is consuming these services is not the person that is choosing them. A n example from education would be that of the parent who chooses and pays for her child's schooling but is not the recipient of the services; moreover, the quali ty of the provided service may be hard to assess immediately because the potential deficiencies may only manifest themselves as the chi ld grows u p . 2 * A version of this chapter has been submitted for publication. 1 These services are often more accurately characterized as quasi-public goods, in that they yield both public and private benefits. Besides, the mere fact that the private sector is partly involved in the provision of these services, indicates that they fail to satisfy (or do not satisfy fully) one or both of the principal properties associated with pure public goods: non-rivalry and non-excludability. 2 T h i s type of goods which are evaluated by experience, are commonly referred to as experience goods (see Nelson 1970). 6 In response to these informational problems, which following the literature we w i l l refer to as "contractual failures", it has been suggested by some authors, start ing w i t h Hansmann (1980), 3 that nonprofit organizations are an effective solution because the low-powered in -centives that permeate the structure of these organizations provide insurance to the con-sumer that she is not going to be exploited. In other words, what this theory argues is that nonprofit organizations act as a commitment mechanism for the provision of qual i ty services in circumstances where quali ty is too costly to monitor. Interestingly, Har t , Shleifer and V i s h n y (1997) use a s imilar rationale in an influential paper that analyzed the choice between in-house government provision of services and con-tract ing out to private suppliers, when the quali ty of service the government requires cannot be fully specified. The conclusion that emerges from their analysis is that private provision is generally more cost efficient but may result i n lower quali ty service because private suppli-ers have a stronger incentive to undertake cost reduction that adversely affects quality. In a recent formalization of the "contractual failure" idea, Glaeser and Shleifer (2001) apply the incomplete contracts framework of Har t et al . (1997) to study the choice of an entrepreneur between setting up a for-profit firm and a nonprofit organization. The predict ion of their model is that when the benefit of commitment is high, that is, when consumers value qual-i ty highly and are wi l l ing to pay higher prices ant icipat ing better quality, then nonprofit status is preferable, despite the fact that the entrepreneur is not the full claimant of profits, because it ensures softer incentives to skimp on quality. Th i s paper is motivated by the fact that in spite of its intui t ive appeal, the contractual failure approach seems to have overlooked a potential ly important issue, namely, that the relationship between purchaser and supplier is, in many cases, an on-going one. T h e on-going aspect of the relationship should allow reputat ion to emerge as another mechanism for maintaining high unverifiable qual i ty . 4 Therefore, a potential l imi ta t ion of the contractual failure argument is that it fails to take into account the interaction between reputations and the choice of organizational form or treats the two as orthogonal. However, markets that involve unverifiable quali ty are exactly the ones that we would expect long-term relationships to predominate and reputation effects to matter. Specifically, the repeated feature of the interaction between producer and consumer seems par t icular ly relevant i n the case of public services, where the arrangement of services is of a continuing nature and it rarely entails a one-time exchange. A related shortcoming of this theory arises when one considers a salient pattern in the sectoral concentration of nonprofits. In particular, contractual failures cannot be reconciled w i t h the observation that nonprofit 3 Other early studies of nonprofit organizations that emphasize the role of asymmetric information be-tween producers and consumers are Easly and O 'Hara (1983) and Weisbrod (1988). 4 W o r d of mouth is also a means of learning about the quality of the services of various providers. Therefore, reputation is not only valuable because of the multiple purchases by the same person, but also through the impact of this person's experience on his friends and family. 7 organizations tend to engage predominantly i n the provision of health, education, social and other mission-oriented services and not other services where qual i ty is equally unobservable and informational problems are acute - for example business, professional, legal services etc. - yet, only for-profit firms appear to have established themselves as quali ty providers of services i n the latter. Thus , two related questions can be raised: (a) Is it possible for reputation mechanisms to work equally well in the provision of public services and ensure the supply of quali ty services by for-profit firms? (b)What factors determine when reputat ion is a sufficient consumer protection mechanism and when not, in which case nonprofit status is necessary to resolve failures associated w i t h informational imperfections? The purpose of this paper is to expl ic i t ly address these questions by s tudying the op t imal choice of organizational status allowing reputat ion to act as an alternative commitment mechanism to nonprofit status for the provision of high quali ty services. 5 Our analysis builds on the Glaeser and Shleifer (2001) model because it captures the essence of the theory i n a concise and formal way. A repeated game is the natural environment to study reputation effects. Therefore, we extend the one-shot framework to a setting of repeated interaction between the consumer and the provider of the service and establish conditions under which reputation is a sufficient mechanism for the provision of quali ty services by for-profit firms. The in tu i t ion is that the loss of reputat ion associated wi th delivering bad quali ty service implies a substantial loss of future profits for the for-profit f irm and therefore when the entrepreneur is sufficiently forward-looking then the fear of foregoing future profits disciplines h i m to deliver high quali ty services. The idea that repeated purchases are a means of discipl ining the producer to deliver high quali ty has been previously explored i n the Industr ial Organizat ion l i terature. 6 The difference i n our approach is that, besides quality, the choice of organizational form is endogenous and the interest is on what combinat ion of type of firm and quali ty level w i l l be op t imal ly chosen in a dynamic set-up. The main finding of this paper is that when reputations can be established, then for-profit status is the opt imal choice of organization form and firms have an incentive to supply high quali ty services. Therefore, we believe that without dismissing the contractual failure hypothesis, the repeated-interaction version of the model restricts its explanatory power. Furthermore, we argue i n section five that the model can be useful in explaining some empir-ical evidence from the U . S . and Canada on the quali ty differences between commercial and nonprofit chi ld care centres. F ina l ly , we believe the paper has some normative implicat ions, in particular, on the debate over the soundness of policies that favour nonprofit organiza-tions on the grounds that commercial firms cannot be trusted to deliver high quali ty service 5 Licensing is an alternative means of controlling the quality of the service which is arguably imperfect, because it sets only a minimum standard on the inputs used to provide the service and does not directly affect quality. For details on the impact of occupational licensing and certification on consumer welfare, see Shapiro (1986). 6See for example Kle in and Leffler (1981), Shapiro (1983), Tirole (1988) and more recently Horner (2002). 8 because of their interest to earn profits. There may be a number of good reasons why governments should subsidize nonprofits but our analysis suggests that, in many sectors, overcoming contractual failures is not one of them. The rest of the paper is organized as follows. T h e next section sets-up the basic one-period model of Glaeser and Shleifer and section three extends it to a mul t i -per iod setting. The fourth section analyzes the opt imal choice of firm status in the repeated game. Section five discusses the predictions of the model and attempts to relate them to empir ical evidence on the quali ty of chi ld care centres across commercial and nonprofit providers in the U . S . and Canada. F ina l ly , section six offers some concluding remarks. 2.2 The One-Shot Game In order to set a benchmark as well as establish some notat ion we introduce here the basic setup of the one-period Glaeser-Shleifer model . The model analyzes the opt imal choice of organization from the perspective of a rat ional entrepreneur who contemplates entering an industry and decides on firm type i n order to maximize ut i l i ty. The t iming of events is as follows: F i r s t , the entrepreneur sells one unit of the good to a competi t ive market of consumers at price P, which is pa id upfront. Consumers are wi l l ing to pay Pe = z — m(q — qe) for one unit of the good of expected unverifiable quali ty qe, where [qe — qj i f the firm is for-profit and qe = qn if nonprofit), m is a parameter captur ing the consumers taste for unverifiable quality, and z, q are constants. Then , the entrepreneur chooses what level of unverifiable quali ty q to produce and delivers i t . T h e to ta l cost of producing one unit of quali ty q is c(q), where c(.) satisfies the standard regularity conditions: it is twice differentiable w i t h c'(q) > 0, c"(q) > 0, c(0) = 0, c'(0) = 0, c'(oo) = oo. T h e key assumption is that while q may be observable by the consumer, the final quali ty of the good cannot be verified by a th i rd party and therefore the transaction is subject to contractual incompleteness. Before any transactions take place, the entrepreneur decides whether to organize the firm as for-profit or nonprofit, denoted by / and n respectively, i n order to maximize ut i l i ty. Specifically, entrepreneurs maximize a quasilinear u t i l i ty function: U% = I — b(q — qi), i € {/, n} where / is income, and b is a parameter measuring entrepreneurs' al truist ic preferences or intrinsic care for quality, which is independent of the firm's legal status. W h e n the entrepreneur is for-profit then income is equal to the profits the firm makes, while when he is nonprofit then he is subject to a nondis t r ibut ion constraint, which implies that he cannot • 7 A m o n g the social benefits of nonprofit provision of public services one can single out the positive externalities associated with the acquisition of services such as education and childcare. Another important reason that a government may want to subsidize nonprofits is that they offer supplemental services to the ones that are publicly provided, which are tailored to the needs of consumers who are not satisfied wi th the quality of service that the government offers. 9 directly draw on the firm's profits. However, a fraction 5, S < 1, of the profits can accrue to the entrepreneur in the form of benefits such as less work hours, better working conditions etc . 8 Entrepreneurs maximize ut i l i ty by choosing quali ty while the price Pi is predeter-mined by consumer's expectation of quality. Thus, i f they choose for-profit status their objective is: max Uf = P f - c{qf) - b(q- qf) (2.1) if while i f they choose nonprofit status: max Un = 5 (Pn - c(qn)) - b(q- qn) (2.2) w i t h 5 < 1. The opt imal quali ty level of a for-profit entrepreneur is given by c!{qs^) = b, while a nonprofit entrepreneur chooses c'(q^) = | . A s an immediate consequence of the convexity of c(.) it follows that q^ > qsj, a nonprofit entrepreneur commits to higher quality, and consumers correctly ant icipat ing this are wi l l ing to pay the associated higher price ( ^n > Pf). Hence, the entrepreneur chooses nonprofit status i f Un > Uj, or: 5 (z - m{q- qsn) - c(qsn)) - b(q - qsn) > z - m{q- qsf) - c(qsf) - b(q- qsf) (2.3) Th i s inequality implies that there exists a cut-off level of consumer taste for non-contractible quali ty m*, w i t h „ _ (1 ~ S)z - (c(gj) - 5c(qsn)) - b(qsn - qj) ( ! - * ) « + 1 ] below which a l l entrepreneurs choose for-profit status and above which they a l l choose nonprofit status. 9 Thus, the one-shot analysis of the game predicts that markets for services where un-verifiable quali ty is not valued by consumers w i l l be dominated by for-profit firms, while nonprofit firms w i l l provide services whose unverifiable quali ty is important for consumers. In what follows we extend the static model to a mul t i -per iod setting where consumers and entrepreneurs interact repeatedly. 8 One can think of the nondistribution constraint as a discount on the cash value of the entrepreneur's profits. That is, from the entrepreneur's perspective the restriction that residual earnings can only be consumed in kind, makes those earnings less valuable under not-for-profit status than they would have been under for-profit status. Moreover, this discount may vary with the constraints that the state imposes on the kind of perks nonprofits can grant to their managers. 9 Note that for m > m = 6<-z~c<-qn>-h(Q-'!n) ^ [s jjn = Q s o the range of m over which nonprofit status is preferable is bounded by m. To rule out the degenerate case where nonprofit status is never optimal, we assume throughout that m* < m. 10 2.3 The Repeated Game Now suppose that there is infinitely repeated interaction between the consumer and the entrepreneur. 1 0 In the dynamic game, the consumer bases her purchasing decision on the firm's past behaviour, that is, based on the firm's "reputation". If the firm has bui l t a reputat ion for producing high quali ty then the consumer w i l l be wi l l ing to pay the associ-ated price as long as the entrepreneur's past actions live up to his reputation. Thus , the entrepreneur can choose quali ty to maximize one-period u t i l i ty internalizing the adverse effect that his choice of quali ty has on the price that the consumer is wi l l ing to pay, namely, he can choose first-best quality. However, the entrepreneur's promise of high quali ty is credible provided it is incentive compatible for h i m to commit to providing better quality. T h a t is, the entrepreneur w i l l choose to bu i ld and mainta in a reputat ion for high quali ty if this strategy generates a discounted stream of payoffs that exceed the one-shot gains of cheating and being punished i n future transactions. A s might be expected, i f entrepreneurs are sufficiently patient then the first-best outcome can be achieved under any ownership. In what follows we focus on (a) establishing and comparing the level of incentive compatible per-period payoffs, that can be supported using punishment strategies that entail reversion to the outcome of the one-shot game, under the two alternative organizational forms, and (b) on examining the possible configurations of firm status (for-profit, nonprofit) and qual-i ty (one-shot, reputation) that can occur i n the infinite repeti t ion of the stage game, for the different values of the discount factor j3 and the consumer taste for quali ty parameter m. 2.3.1 For Profit Status In each period the structure of the interaction is as follows. The entrepreneur chooses organizational form and the consumer pays upfront for the service. T h e n the entrepreneur makes his quali ty choice and delivers the service. The consumer observes the quali ty chosen by the entrepreneur and forms her beliefs about future quality. If the producer deviates from delivering promised qual i ty he is punished i n future interactions by the consumer agreeing to pay upfront only for one-shot quality. A s a first step we must now determine the first-best level of quali ty and the resulting u t i l i ty that can be sustained in the repeated game. Formally, each per iod the for-profit entrepreneur maximizes the following objective: max Uf(qf) = z - m(q- qf) - c(qf) - b(q- qf) (2.5) if 1 0 T h e assumption that the firm is infinitely lived is important here. Behaviour that would be compatible with (ICF) cannot arise if there is a final period to the firm's life because the unique subgame Nash equilibrium of that game would be for the firm to cheat. So, backward induction rules out behaviour that satisfies {ICF) in a finitely repeated version of the game. In other words, {ICF) can only be satisfied if at any period t, there is a positive probability that the game wil l continue into period t + 1. 11 Therefore, the ut i l i ty max imiz ing choice of quali ty q*f{m), satisfies: c'(q*f(m)) = b + m=$> q}(m) = c + m ) 1 1 (2.6) and — c / / ( g »( m ) ) > 0. Moreover, per-period u t i l i ty i n this case is given by: Uf(q}(m)) = z - m(q- q}(m)) - c(q}(m)) - b(q- q}(m)) (2.7) Note that the convexity of c(.) implies that q*f{rn) > qsp that is, the entrepreneur has an incentive to increase the quali ty of the good relative to what he offers in the one-shot game - indeed, qj(m) maximizes to ta l surplus - since he can extract a l l the surplus that is generated. However, the first-best choice of quali ty ^q*f(m)J w i l l be supported i n equi l ibr ium if and only i f the discounted stream ut i l i ty from adhering to honest behaviour exceeds the payoff stream from the deviat ing path. Tha t is, incentive compat ib i l i ty for the for-profit entrepreneur may be wri t ten as: jhpUf(q*f(m)) > Ucf[m) + Usf(m) if 0 < m < m* YrpUfiqjim)) > Ucf{m) + U°(m) i f m* <m<m (ICF) (2.8) where (3 G (0,1) is the discount factor and Uj(m) = z—m(q—qj(m))—c(qsj-)—b(q—qsjr), is the u t i l i ty the entrepreneur can at ta in i f he deviates from offering the anticipated first-best level of quali ty and instead chooses the most profitable deviation which is to produce the one-shot u t i l i ty maximiz ing choice of quali ty qj (i.e. qj satisfies c'(qj) = b). Moreover, when the entrepreneur deviates he loses reputation, so in subsequent periods the consumer punishes h i m by reverting to the Nash equi l ibr ium of the stage game. G i v e n the strategy adopted by consumers, the entrepreneur's best-response after a deviat ion i n which he cheated by providing one-shot level of quali ty is to continue providing low quali ty from then on. In particular, for m higher than the cut-off level m*, the entrepreneur chooses to come back as a nonprofit firm and make one-shot level of u t i l i ty : U^(m) = 5 (z — m(q — q^) — c(q^)) — b(q — q^), every period thereafter. If, instead, m is less than ra*, then it is more profitable for the entrepreneur to mainta in her for-profit legal status but is punished for having sk imped on quali ty and therefore his u t i l i ty is reduced to the one-shot level of profit: Uj(m) — z — m{q — q^) — c(qj) — b(q — qj), every period after the deviat ion. 1 1 c' is continuous and strictly increasing as a consequence of the continuity of c'(.) and that it is strictly increasing. 12 2.3.2 Nonprofit Status If the entrepreneur is nonprofit, then his problem is to choose qn to maximize one-period ut i l i ty Un(qn): max Un(qn) = 5 {z - m(q- qn) - c(qn)) - b(q- qn) (2.9) The u t i l i ty maximiz ing choice of quali ty ^ ( m ) satisfies: S M = b + S m ~ ^ = c - > [ — ) (2.10) w i t h = _ L _ > o, and q*(m) > qsn. U t i l i t y is given by Un(q*(m)) =5{z- m(q- q*(m)) - c(q*n(m))) - b(q- q*n(m)) (2.11) Notice that (2.6) and (2.10) imp ly that q£ (m) > q*f{m), first-best quali ty under nonprofit status is greater than under for-profit status. L e m m a 1 There exists m G (0, m*), such that Un(q^(m)) is = L7|(m) / o r m = m . Proof. In the Append ix . • L e m m a 1 suggests that for low m, m 6 (0 ,m) , nonprofit status is not desirable even if a reputation for quali ty can be established. The in tu i t ion is that when m is small , the price premium that the consumer is wi l l ing to pay a nonprofit firm for higher quali ty is not enough to compensate the entrepreneur for the loss of income due to the l imi ted access to profits. A s i n the case of a for-profit entrepreneur, the first-best choice of quali ty (q*(m)) w i l l be supported in equi l ibr ium if and only if the discounted stream of u t i l i ty from adhering to honest behaviour exceeds the payoff stream from the deviat ing path. Tha t is, incentive compat ibi l i ty for a nonprofit entrepreneur may be wri t ten as: f T^Un(q*(m*))>U^m) + j ^ Uf(m) if m < m < m* { ^Un(q*(m*)) > Ucn{m) + ^ U^m) if m* < m < m N > where U^(m) = 5 (z — m(q — g*(m)) — c(q£)) — b(q — q^) is the u t i l i ty the entrepreneur can at tain i f he deviates from offering the anticipated first-best level of quali ty and instead produces the one-shot u t i l i ty max imiz ing choice of quali ty q^, i.e. q^ satisfies Sc'(q^) — b. The arguments regarding the choice of legal status and the corresponding payoff after the deviat ion are analogous to the ones we made above for the for-profit case. The difference here is that, as L e m m a 1 suggests, for m < m , it is Uj(m) > Un(q^(m*)), so ( / C A T ) cannot 13 be satisfied, which implies that a nonprofit entrepreneur cannot commit to providing first-best quali ty (g*(m)) to the low m segment of the market. 2.4 Optimal Choice of Organizational Form 2.4.1 Overview In the mult i -per iod formulation, the entrepreneur has two dist inct decisions to make: what organizational type to choose and whether to establish reputat ion for quali ty or not. C o n -sequently, four possible combinations of firm-status (for-profit, nonprofit) and qual i ty (first-best, one-shot) may arise. The opt imal choice of firm status and quali ty can be analyzed wi th reference to the two cr i t ical exogenous parameters: the firm's discount factor (5 and consumer's sensitivity to unverifiable quali ty m. To this end, it is useful to rearrange {ICF) and (ICN) as follows: uW-UfWm)) 0<m<m* p > T T C , — \ „ . — \ it m < m < m (2.13) P > U ^ ^ U i q ^ ) } ^ m<m<m* %{m)-utlrn) l f rn*<m<m The right-hand-side of (2.13) and (2.14) define cr i t ical values for the discount factor /?, which we shall denote f3f(m) and /3 n (m) , respectively, above which delivery of first-best quali ty can be sustained. Tha t is, for m such that j3 > Pj(m), {ICF) is satisfied and the for-profit entrepreneur delivers first-best quali ty qj{m). Likewise, for m such that fi > /3 n (m) , (ICN) is satisfied and the nonprofit entrepreneur chooses the first-best level quali ty g*(m). Our a im is to establish, first, which organizational form is preferable when reputations can be established, and second, which organizational form can support first best quali ty for the widest range of discount factors, namely, we shall be interested i n comparing Pf(m) to Pn(m). To compare u t i l i ty across organizational forms, note that the relative benefit of being for-profit when {ICF) and {ICN) are slack is given by: G{m) = [{m + b)q}{m) - c{q}{m))} - [{5m + b)q*{m) - 5c{q}{m))]+{l-5){z-mq) (2.15) The following lemma applies: L e m m a 2 When the entrepreneur can commit to the first-best level of quality q^{m) and g*(m), then for-profit status is more attractive at any level of m, i.e. G{m) > 0 V m G 14 (0 ,m) . 12 Proof. In the Append ix . • T h i s result suggests that reputat ion forces favour for-profit status. The in tu i t ion for this is that as m increases the for-profit firm can now anticipate the price reduction that w i l l occur if it does not offer better quality, and adjusts the op t imal quali ty offered q*f{m) upwards, thus remaining more attractive than the nonprofit firm for any m. T h i s is the power of the reputation mechanism, it allows for-profit firms to credibly commit to delivering the high quali ty service because it is more valuable to them to do so. Next , i n order to compare (3f(m) to dn{m), notice that, after subst i tut ion and the appropriate simplifications, (2.13) and (2.14) imp ly that: (bqj-c(qj)) - {bq*f (m)-c{q* (m)) ) £ / ( m ) H {bq} - c(^T) - ( m f - c f a (m))) . . . ( 2 - 1 6 ) (l-6)(z~mq)+mq*f(m)-c{qsf)+bqsf-6viq?,+5c(q?l)-bq?, i f 0 < m < m* if m* < m <m and (bq°-Sc(q°))-(bq*(m)-c(q*(m))) i f m < m < m* 0 (m)= ) -a-S)(z-™fi+trnq^m)-6c(q^)+bq^-mq}+c(q})-bq} " i i i »* ~-n K ' | (ftqg-fe(g|))-(6<?n(m)-c(g»(m))) i f 7 B * < TO < m A n a l y z i n g the monotonici ty and the relative posi t ion of Pf(m) and f3n(m) is very subtle. To gain some in tu i t ion for this, notice that (3f(m) and /3n(m) can be rewrit ten as follows: ft("i)=B,(mHt(m)f0read"£t/.»} (2.18) where Bi{m) = Uf{m) — Ui{q*{m)) denotes the one-time benefit from cheating, and L j ( m ) = Ui(q*(m)) — Uf(m) denotes the absolute value of the future loss induced by the punishment. F r o m (2.18), it follows that: < w i w ™ > ~ f ^ i £ $ <»»> This last condi t ion suggests that comparing Pf{m) to (5n{m) amounts to comparing the ratio of benefits and losses associated wi th a deviation, across organizational forms and for different values of m. Intuitively, one might th ink that under nonprofit status the manager's incentive to cheat is attenuated, because he can only par t ia l ly enjoy the ext ra profits generated due to cheating, so we might expect Bn(m) to be smaller than Bf(m). 1 2 I t follows, a fortiori, that for profit status is more attractive when the entrepreneur can choose first-best quality q}{m) when for-profit, but {ICN) is not satisfied. That is, Uf{q}{m)) > Un{qn{m)) implies that Uf{q}{m)) > Un{m) V m 6 (0,m). . 15 O n the other hand, though, the value of the punishment inflicted in the event of cheating is also smaller - the expression in the denominator, so it is not immediately clear how (3f(m) compares to (3n(m). In particular, closer inspection of (2.16) and (2.17) suggests that the value and the monotonici ty of these expressions depend on relative changes of terms involving c(.), which renders the problem intractable. Therefore, i n order to proceed to a full characterization of the properties of Pf(m) and Pn{m) and therefore of the op t imal choice of f irm, we need to place some structure on the cost function c(q). After performing the analysis posi t ing a specific cost function, we return to discuss what part of the results obtained we th ink would hold under more general conditions. Assumpt ion 1 c(q) = \q2-Vi The following lemma describes the properties of [if (m) and f3n ( T O ) . L e m m a 3 (i) (3f(m) — \ for m G (0,m*], and Pn{m) = ^ for m G [TO*, TO). (ii) Pn(m) > (3f(m) form G (0,m*), and Pf(m) > Pn[m) form G ( T O * , T O ) . (Hi) Pn(m) is decreasing, form G ( 0 , T O * ) . (iv) j3f{m) reaches a maximum at m — 2m*. Proof. In the Append ix . • The analysis is significantly aided by reference to Figure 2.1, which L e m m a 3 helps us construct, and which illustrates Pf(m) and Pn(m) i n (m,P) space. Note that for TO such that the punishment path after cheating does not include conversion of legal status, Pf(m) and Pn(m) remain flat and equal. This , however, is not true i n the subintervals of (TO, m) where the punishment phase entails change of the firm's legal status prescribed by entrepreneur's op t imal behaviour i n the one-shot game. In this case, there are two opposite effects governing the monotonici ty of Pf{m) and Pn(m). O n one hand, the first per iod benefit of cheating increases w i t h m, which implies that incentive compat ibi l i ty becomes stricter. O n the other hand, the benefit of commit t ing to high quality, relative to being a one-shot firm, increases w i t h m for periods two onwards as the reputation firm adjusts op t imal quali ty upwards while the one-shot firm adheres to the stage game quality. For m G (0, m*\, the second effect dominates the first effect we described above so the overall tendency is for (ICjv) to become increasingly easier to satisfy and hence Pn{m) is decreasing. For m G (m*, TO), Pj (TO) is nonmonotonic because in i t ia l ly the first effect dominates while for higher m the second effect takes over. We can now determine the entrepreneur's choice of firm status for P ly ing i n three different subintervals of (0,1) by referring to figure 1. 1 3 N o t e that this specification satisfies the regularity conditions imposed on c(.). 16 3/M Figure 2.1: Pj(m) (solid) and Pn(m) (dash) 2.4.2 Optimal Choice when /5 e [/? / (2m*), 1) The following proposi t ion applies: Proposit ion 1 / / the entrepreneur is sufficiently patient (i.e. (3 > (3f(2m*)), then the (ICF) never binds and for-profit status is the preferred choice of organization, for any level of m. Furthermore, the first-best level of quality (q*j(m)) can be sustained. Proof. Follows directly from L e m m a 2 and the fact that (3f(2m*) is the m a x i m u m value that (3j(m) takes in (0 ,m) . Therefore, for f3 > Pj(2m*), (ICF) is always satisfied, so it follows from L e m m a 2 that for-profit status is the op t imal choice of legal status and that first best quali ty (qj(m)) is provided. • 2.4.3 Optimal Choice when )3 e (\,p}(2m*)) To analyze the opt imal choice of organizational form when /? lies i n the interval (\, f3f(2m*)), it is useful to divide the relevant (/?, m) space into the following two mutual ly exclusive and exhaustive regions, also i l lustrated i n Figure 2.2: Definition 1 a) Region A consists of (3 6 {(3j(m), (3j(2m*)) and m £ (0 ,m) such that (3 > f3f(m). 17 b) Region B consists of (3 G (\,(3j(m)) and m G (m*,m) such that Pn(m) < f3f(m). The following proposi t ion summarizes the opt imal choice of organizational form and quali ty for j3 G (\, p f(2m*)): Proposit ion 2 a) In Region A the entrepreneur chooses for-profit status and delivers first-best quality qj(m). b) In Region B the entrepreneur chooses nonprofit status and delivers first-best quality Proof, a) Note that i n region A it is /3 > Pf(m) so (ICF) is satisfied, thus it follows from L e m m a 2 that for-profit status is the opt imal choice of legal status and that first best quali ty (qj(m)) is provided. b) In region B it is Pn(m) < P < Pf(m), imp ly ing that only (ICN) is satisfied which means that nonprofit status offering first best quali ty (g*(m)) w i l l be chosen. • Moreover, whether (ICF) is satisfied or not, for m G (m*,fn) depends on parameters such as the consumer's willingness to pay for the service (z) and the entrepreneur's al truist ic taste b. R e m a r k 1 Differentiation of f3f(m) form G (m*,m) yields: Thus, the higher the profi tabil i ty of the industry or the firm the larger area A becomes, which implies that the greater is the l ikel ihood that (ICF) w i l l be satisfied and entrepreneurs are going to choose for-profit status as the preferred form of organization. O n the other hand, the more an entrepreneur is intr insical ly concerned about quality, the larger area B becomes, which means that it is harder to mainta in first-best qual i ty under for-profit status. 2.4.4 Optimal Choice when j3 e (0, \ ) The following proposi t ion applies: Proposit ion 3 If P < \ , then (ICF) and (ICN) are never satisfied for any level of m and reputations cannot be sustained regardless of what legal status the entrepreneur chooses. The optimal choice of organizational type is the one described in the one-shot game. Proof. It is immediately clear from L e m m a 3 and figure 2.1 that for (3 < \ . (3 < /3f(m) and f3 < Pn(m), so both (ICF) and (ICN) fail. • For reference, the various possible outcomes of the repeated game are also i l lustrated i n Figure 2.2 and summarized i n Table 2.1. 18 0/(277.') • For Profit, first-best quality \ \ \ Area A \ \ \ fi/im) 1 - " Area B One-Shot Analysis 2m* m Figure 2.2: Summary of O p t i m a l Choice of Organizat ional F o r m Table 1.1 Summary of Optimal Choice of Firm Status and Quality by Region Region F i r m Status Qual i ty (0 ,m) x [8f(2m*),l) A: (0 ,m) x (8f(m), 8f(2m*)) B : (rn*,m) x (\,3f(m)) (0,m) x (0,1) The foregoing analysis suggests that i f we imagine that there is a dis t r ibut ion of 8's in the populat ion of entrepreneurs, then those that have sufficiently high 0 w i l l choose for-profit status and w i l l deliver high quali ty service. There is an intermediate range of 8's where the choice of firm status varies w i t h m. F ina l ly , for very low 8, reputations are not going to be established and the one-shot analysis of Glaeser and Shleifer w i l l a p p l y . 1 4 The value of 8 need not be interpreted l i teral ly as a discount factor. There are plenty of reasons that one would expect variat ion in managerial outlook of future profi tabil i ty that are not directly related to one's personal rate of t ime preference. For example, some markets 1 4 There may also be ideological or religious motivations that make nonprofit status attractive for some people and therefore affect the supply of nonprofit activity. Much like most of the literature that relies on contractual failures, we have abstracted from these considerations here. FP q*f FP q} NFP q*n One — Shot Analysis 19 may have higher demand growth than others which means that the potential future losses from shirking on quali ty and losing reputat ion i n these markets are higher. Th i s k ind of differences i n market-specific or sector-specific conditions can be regarded as determinants of the effective discount factors that have to be applied by potential entrants when deciding which firm status to choose and what level of quali ty to offer. It is noteworthy that i f we were to adopt the view that the op t imal organizational form is the one that minimizes the discount factor that is necessary to sustain first-best quality, then the outcome of the repeated game matches w i t h that of the static game. T h a t is, there exists a threshold value for consumer preference for quali ty m*, above which nonprofit status is opt imal and below which for-profit status dominates. Th i s way of ranking organizations may be relevant if, for instance, we believe that free-entry compet i t ion among firms w i l l ensure that the incentive compatible constraints (ICF) and (ICN) b ind . Then , we should expect the organizational form w i t h the lower cr i t ica l value for the discount factor to drive the other one out of the market. 2.4.5 Discussion The analysis of the op t imal choice of firm status was considerably simplified by introducing an explici t functional form for the cost function, since a general characterization is not pos-sible. Here we point out where the difficulties in obtaining general results lie and elaborate on what parts of the analysis are l ikely to generalize under more general conditions. F i r s t , we examine whether the result that for profit status is opt imal for m £ (m,m*}, i.e. Pf(m) < Pn(m), is general. Us ing (2.19) and simplifying one can obtain the following necessary and sufficient condit ion for this to be true: Uf(q}(m)) (Ucn(m) - Usf(m))-Usf(m) (Ucn(m) - Un(ql(m))) > Uf(m) (Un(q*n(m)) - Uf(m)) (2.20) where the left-hand-side is positive because Uf(qj(m)) > Uj(m) and Un(q^(m)) > Usj(m). In addit ion, recall that L e m m a 1 suggests that the term on the right-hand-side is zero, for m in the v ic in i ty of m, and increasing i n m. Th i s suggests that inequality (2.20) holds for m = m; whether it becomes easier or harder to satisfy as m increases depends on the relative changes of the terms on the left and right-hand-side of the inequality, which cannot be assessed generally. Next , we examine whether the predict ion that nonprofit status is op t imal for m > m*, i.e. (3f(m) > (3n(m). We use (2.19) again to derive the following necessary and sufficient condit ion for this to be generally true: Ucf(m) (Un(q*n(m)) - Usn(m))+U^(m) (U^m) + Uf(q}(m)) - Un(q*n(m))) > Uf(q}(m))Ucn(m) (2.21) 20 where a l l of the above terms are positive. Thus, whether inequality (2.21) holds or not depends on the relative magnitude of these terms, which cannot be ascertained unless some structure is imposed on the cost function. The part icular formulation we used is convenient for deriving simple analyt ical results but numerical examples using higher-order power functions suggest that the insights obtained are robust to alternative specifications of the cost function. 2.5 Relating the Model to Empirical Evidence and Policy Implications We believe that the predictions obtained from the dynamic framework can help us under-stand some facts concerning quali ty differentials in mixed sectors which the one-shot model falls short of explaining. For instance, consider the market for chi ld care, which features a considerable nonprofit presence, making it appropriate for drawing comparisons between the quali ty offered by for-profit and nonprofit p roviders . 1 5 Furthermore, the quali ty d i -mension i n child care is arguably hard to measure and verify, which makes it amenable to the incomplete contracts framework we have la id out above. Our reading of the empir ica l evidence on the between-sector differences in quali ty from the U . S . and C a n a d a , 1 6 is that although most studies find that nonprofit centres as a group obtain higher scores on obser-vational measures of overall quali ty developed by chi ld development exper t s , 1 7 this finding cannot be interpreted as a direct confirmation of the contractual failure theory. F i r s t , the differences on average quali ty between the two groups are not overwhelming, and there is variat ion i n quali ty w i th in each category of auspice. T h a t is, there are commercial centres that offer high quali ty and nonprofit centres that offer low quality. T h i s possibil i ty though is in contradiction w i t h the strong form of the contractual failure view of the world which predicts that only nonprofits w i l l occupy the upper part of the quali ty dis t r ibut ion. Second, it seems very l ikely that the greater access to government funding and subsidies nonprofits enjoy in certain jurisdictions, could at least par t ly account for the reported difference i n average quali ty between the nonprofit and commercial chi ld care sectors. F ina l ly , it is possi-ble that the variat ion in quali ty may s imply reflect choice of market niche and be unrelated to informational asymmetries of any sort. For example, for-profit chi ld care centres may choose to substitute lower quali ty care, for more convenient arrangements offered to the parents (convenient location, longer hours etc.). 1 5 Studies that examine the relative performance of nonprofits are too many to list here, see Rose-Ackerman (1996) for a comprehensive review of the literature. Ortmann and Schlesinger (2003) review the empirical work on ownership-related differences in quality from various mixed industries. 1 6 F o r evidence from the U.S . child care sector, see the survey by Blau and Currie (2005) and the references therein. For evidence from Canada, see Krashinsky (1998) and Doherty et al (2002). 1 7 I t is important that these instruments of child care quality refer to non-contractible quality, and is distinct from structural measures of quality, such as the child-teacher ratio, which are contractible. 21 Yet another explanation of the apparent between-sector quali ty differential, and indeed one that the analysis of the repeated version of the model points to, is that because for-profit status dominates the lower part of the quali ty d is t r ibut ion (m < m*), even though there are some high quali ty for-profit centres (in area A and for 0 E [0f(2m*), 1), on average the quali ty provided by the commercial sector is lower than the nonprofit which has a higher quali ty th reshold . 1 8 Furthermore, in markets where nonprofits have lower costs (c(g)), because of access to free space and util i t ies, the model suggests that more entrepreneurs w i l l choose nonprofit status, which would increase the average quali ty care i n the nonprofit sector and lower that one i n the commercial sector. In light of this interpretation of the quali ty differential, it is interesting to revisit the ongoing debate over the effectiveness of subsidy policies that discriminate against for-profit chi ld care centres, on the basis that they are untrustworthy to provide high qual i ty care. We argued above that the existing empir ical evidence on the impact of centre ownership on care quali ty is scant and does not allow for sweeping conclusions, while the model considered here demonstrates that reputations can provide enough incentives for prof i t -maximizing entrepreneurs to offer high quali ty services when the playing field is levelled. Perhaps future empir ical work may be able to settle the debate by identifying the extent to which qual i ty differences between sectors echo contractual failures or unequal funding opportunities. 2.6 Conclusion The idea that nonprofit organizations can solve market imperfections at tr ibutable to asym-metric information between consumers and producers, regarding hard to verify qual i ty of certain services, has been a par t icular ly influential explanation of the emergence and ex-pansion of the nonprofit sector. Our task in this paper has been to perform a robustness check of this theory by allowing reputations to serve as a competing mechanism that can ensure quality. The analysis of the model of repeated interaction between consumers and firms yields some interesting new outcomes while it encompasses the one-shot case original ly examined by Glaeser and Shleifer. In this sense, it may be argued that the predictions of the contractual failure hypothesis apply i n the special case where the long-run reputat ion mechanism cannot be sustained because interaction is not repeated or because of frictions i n the flow of information. In more general circumstances, nonprofit status does not appear to be a necessary mechanism to overcome opportunist ic behaviour that arises because qual i ty is unverifiable. Also , the mul t i -per iod version considered in this paper provides an expla-nation for the differences and var iabi l i ty i n non-contractible quali ty across organizational types that have been identified in empir ical studies of the chi ld care sector. The goal of this paper has not been to ut ter ly dismiss the contractual failure hypothesis, 1 8 R e c a l l that nonprofit status is chosen only for m > m*. 22 only to challenge its scope as an explanation for the widespread presence of nonprofit organizations. The key impl ica t ion of our analysis is that, i n many sectors, the existence of a large number of nonprofit firms cannot be explained wi th reference to their unique abi l i ty to mitigate problems of asymmetric information. In part icular, we shouldn't expect it to be an important factor i n industries where income from sales of services constitutes the largest source of revenue and where there is repeated interaction between consumers and providers - such as the chi ld care sector discussed i n the previous section and other social services. Th i s does not preclude the theory to play an important role in charitable services where donations are a significant source of revenues. A l so , our analysis does not rule out the expropriat ion problem having significant implicat ions on the relationship between the organization and various other economic actors such as its employees, volunteers, donors and the different government agencies. Further research i n these areas may prove fruitful i n advancing our understanding of the role, advantages and evolution of the nonprofit sector. 23 Bibliography [1] B l a u , D . , and J . Cur r ie (2006): "Who 's M i n d i n g the K i d s ? : Preschool, D a y Care, and After School Care," i n The Handbook of the Economics of Education, ed. by E . Hanushek and F . Welch. N o r t h Hol land , New York . [2] Doherty, G . , M . Friendly, and B . Forer (2002): " C h i l d Care by Default or Design? A n Exp lo ra t ion of Differences Between Non-profit and For-profit Canadian C h i l d Care Centres Us ing the You Bet I Care! D a t a Sets," Chi ldcare Resource and Research U n i t , Occasional paper #18. [3] Easley, D . , and M . O ' H a r a (1983): "The Economic Role of the Nonprofit F i r m , " Bell Journal of Economics, 14(2), 531-538. [4] Glaeser, E . , and A . Shleifer (2001): "Not-for-profit Entrepreneurs," Journal of Public Economics, 81(1), 99-115. [5] Halonen, M . (2002): "Reputa t ion and the A l loca t i on of Ownership," Economic Jour-nal, 112(481), 539-558. [6] Hansmann, H . (1980): "The Role of Nonprofit Enterprise," Yale Law Journal, 89, 835-901. [7] Har t , O. , A . Shleifer, and R . V i s h n y (1997): "The Proper Scope of Government: Theory and an App l i ca t i on to Prisons," Quarterly Journal of Economics, 112(4), 1127-61. [8] Horner, J . (2002): "Reputat ion and Compet i t ion ," American Economic Review, 92(3), 644-663. [9] K l e i n , B . , and K . Leffier (1981): "The Role of Marke t Forces i n Assur ing Cont rac tua l Performance," Journal of Political Economy, 89(4), 615-641. [10] Krashinsky, M . (1998): "Does Auspice Mat te r? The Case of Day Care for Ch i ld ren i n Canada," in Private Action and the Public Good, ed. by W . Powell and E . Clemens. Yale Univers i ty Press, New Haven. 24 [11] Nelson, P. (1970): "Information and Consumer Behavior ," Journal of Political Econ-omy, 78(2), 311-329. [12] Or tmann , A . and M . Schlesinger (2003): "Trust, Repute, and the Role of Nonprofit Enterprise ' , i n The Study of the Nonprofit Enterprise: Theories and Approaches, ed. by H . Anheier and A . Ben-Ner . K luwer A c a d e m i c / P l e n u m Publishers, New York . [13] Rose-Ackerman, S. (1996): " A l t r u i s m , Nonprofits and Economic Theory," Journal of Economic Literature, 34(4), 701-28. [14] Shapiro, C . (1983): "Premiums for H i g h Qual i ty Products as Rents to Reputa t ion ," Quarterly Journal of Economics, 98(4), 659-680. [15] Shapiro, C . (1986): "Investment, M o r a l Hazard , and Occupat ional Licensing," Review of Economic Studies, 53(5), 843-862. [16] Tiro le , J . (1988): The Theory of Industrial Organization. M I T Press, Cambridge, M A . [17] Weisbrod, B . (1988): The Nonprofit Economy. Harvard Univers i ty Press, Cambridge, M A . 25 Chapter 3 Volunteer Hiring, Organizational Form and the Provision of Mission-Oriented Goods* 3.1 Introduction Volunteering constitutes a considerably large and increasing share of the nonprofit sector's contr ibut ion to economic activity, i n most advanced economies. So much so, that in fact i t is not uncommon for nonprofit organizations to be referred to as "voluntary organizations" to emphasize their reliance on voluntary employment. For example, in 1997 the value of volunteer work amounted to roughly one-quarter of the to ta l value of labour services provided to the nonprofit sector in Canada, while i n the U . S . i t reached one-third of to ta l earnings i n the sector. 1 Besides volunteering for al truist ic reasons - a desire to help others or contribute to an important cause - there is a widespread belief that volunteering can be a stage i n professional development by providing work experience and a chance to develop skills that strengthen employ ability. Volunteering offers some of the benefits that are often also associated wi th unpaid internships i n for-profit firms or the government: opportunities to receive valuable on-the-job t raining, discover hidden talents and interests, learn about possible career tracks, expand networks of contacts, and enrich one's resume. In many cases the potential is high for the transi t ion to a pa id posit ion, especially in the nonprofit sector where volunteering experience appears to be a prerequisite for any type of career. Previous research which studied factors that determine the decision to supply volunteer t ime, such as Menchik and Weisbrod (1987), Day and D e v l i n (1998), Segal and Weisbrod * A version of this chapter wi l l be submitted for publication. 1The estimate for Canada is taken from the Satellite Account of Nonprofit Institutions and Volunteer-ing of Statistics Canada, which is available at http://www.statcan.ca/english/freepub/13-015-XIE/13-015-XIE2004000.htm. For the U.S. , see the New Nonprofit Almanac and Desk Reference, Table 1.7, pg 22-23. 26 (2002), Gunderson and Gomez (2003) has found evidence suggesting that besides purely altruist ic motives people may engage i n volunteering activities to improve their employment opportunities. For instance, Day and D e v l i n (1998) report evidence of a 6-7% return of volunteering i n annual earnings for Canad ian workers. Surveys also support this. For example, the Nat iona l Survey of G i v i n g , Volunteering, and Par t ic ipa t ing (2000), which provides a snapshot of the state of voluntary and civic action i n Canada, reveals that almost a quarter (23%) of volunteers agreed that improving job opportunities was a reason for volunteering, w i t h younger volunteers more l ikely (55%) to indicate this as a reason. Furthermore, 14% of volunteers reported that volunteering had at some point helped them to obtain employment, w i t h again a greater proport ion of younger volunteers (24%) c la iming l ikewise. 2 These findings confirm the common wisdom that volunteering for some individuals is viewed as a means to help others while at the same t ime increase the chances of success in the labour market, and in part icular in the nonprofit sector. Th i s paper takes the altruist ic motivations and the career concerns of volunteers as a point of departure and provides an explanation for the following salient patterns (1) nonprofit organizations attract the overwhelming share of volunteers 3 that meet this pro-file and (2) volunteer-hiring nonprofits are concentrated i n mission-oriented sectors, where the goods and services produced can be conceived as having a public (or collective) good component 4 - commonly thought to lead to the market underproviding them - and which generate nonpeeuniary benefits to those involved i n their delivery. Educa t ion , healthcare, childcare, international aid, the arts, religious and philanthropic foundations, and the vast social services are examples of mission-oriented fields. 5 These contrast w i t h most other activities, regularly provided by profit taking firms, where non-pecuniary motivations are less of a consideration. The challenge we pose i n this paper is to explain the above set of observations as an equi l ibr ium outcome without posi t ing that workers motivated by concerns for social outcomes have an exogenous disposit ion for working at nonprofit establishments or assuming that nonprofit and for-profit producers have respective ex ante advantages in the delivery of goods and services of different character. We expound our theory by developing a model w i t h two sectors (a mission sector and a non-mission sector), where heterogeneous (some mission motivated and some not) managers (principals) and workers (agents) are matched, choosing organizational form (for-profit, nonprofit), employment contract and sector. To 2See Hal l et al. (2001), figure 2.2, pg 35. 3 I n 1998, the distribution of full-time volunteers by sector in the U.S . was 68.5 percent nonprofit, 26 percent; government and 5.5 percent; for-profit; sector. See the New Nonprofit Almanac and Desk Reference, Figure 1.7, pg 24. 4 E v e n though these goods do not necessarily feature both properties shared by public goods - nonrivalry and nonexcludability - they are associated with external benefits. For example, a person may benefit from high quality healthcare coverage of others, not only because it reduces the chances that she may be infected by a contagious disease, but also because of ethical concerns for the standards of human well-being in society. 5See Rose-Ackerman (1996) for cross-country documentation of the composition of the nonprofit sector. 27 address the previously mentioned challenge we start from a posi t ion of ex-ante symmetry: (a) the intrinsic benefit that caring managers and workers derive in the mission sector is attached to the job that they do, not the identity of the organization (nonprofit or for-profit) in which they do i t ; 6 (b) workers are equally productive working for either type of employer; and (c) managers have access to a common product ion technology regardless of the organizational form they select. Therefore, besides the restrict ion i n the appropria t ion of profits there are no ex ante s tructural differences between for-profit and nonprofit status. We then proceed to demonstrate how the observed configuration (nonprofit firms h i r ing volunteers in the mission sector) arises endogenously i n the equi l ibr ium of the model , among the host of ex ante possible (firm-type/employment structure/sector) combinations, and that this part icular equi l ibr ium has some desirable welfare properties. A n example from healthcare illustrates the reasons why. Consider the case of a hospital or a long-term care facility, which recruits volunteers to support direct patient care. T h e given hospital can benefit by refusing to recognize the volunteering experience of individuals at other firms while at the same t ime taking advantage of the fact that its volunteers w i l l be acknowledged elsewhere. Such a deviat ing firm w i l l like to perpetually fill positions w i t h unpaid volunteers who are denied promotion to paid positions and are replaced by new volunteers, when they turnover to seek employment at another employer. Such behaviour w i l l eventually be detected and punished by future workers who w i l l pass up volunteer opportunities at a hospital which had previously cheated on its volunteers. For nonprofit organizations, the incentive to exploit volunteers is weaker, because of the weaker incentives to pursue profits and the greater concern about the social mission, which allows them to mainta in an incentive compatible scheme. Thei r commitment to not d is t r ibut ing profits conveys a comparative advantage i n mission-oriented sectors by giving them exclusive access to the volunteer pool . A n important feature of the analysis is that workers' effort and output are unverifiable by th i rd parties and as a result performance-contingent remuneration is infeasible; 7 this element is present in both sectors and for a l l types of firm. One standard solution to this incentive problem is the use of impl ic i t contracts that are self-enforcing and that take advantage of the long-term aspect of the employment relationship: a worker receives a fixed payment that exceeds opportuni ty costs as long as performance has been satisfactory and is dismissed otherwise. 8 Th i s type of compensation, namely a wage set above the market clearing rate (efficiency wage), is known to induce important labour market inefficiencies 6 T h i s is not to deny that individuals might receive direct benefits from founding or working for a nonprofit firm. Here we wish to explore whether we can explain the observed patterns of nonprofit activity without assuming such direct rewards. 7 T h e notion that workers' performance is observed by the firm but cannot be verified in court is borrowed from the incomplete contracts literature and has been widely applied to agency models of employment, see Malcomson (1999). 8 I n the context of the provision of public services, this avenue has been pursued in Francois (2003). 28 - sub-optimal employment levels. Here, motivated by the observation that some workers (interns and volunteers) are induced to undertake unpaid or very low pay work by the possibil i ty of rewards in the form of future employment by the same or some other employer, we recognize that this two-tier employment structure provides a more efficient solution to the problem of incomplete employment contracts: it allows firms to extract some of the rents that workers have to be offered later on as pa id workers i n order to supply effort, thus dampening the distort ing effect arising from providing incentives wi th payments above opportuni ty cost. 9 We consider two alternative incentive structures, which i n the interest of facil i tat ing exposit ion we refer to as: - Volunteering: A worker is hired as an unpaid volunteer and is subsequently transferred to a paid posit ion not necessarily at the firm where he has volunteered (incentives are sector-wide). - Internship: A worker is hired as an unpaid intern and is subsequently promoted w i t h i n the firm he has interned, when a vacancy is created (incentives are firm-specific). The key difference between volunteering and internship is that t ime spent volunteering elsewhere is treated "as i f it were volunteered at the firm - much like actual volunteering occurs in reali ty - whereas interns are promoted at the firm where they intern. In bo th structures a worker is wi l l ing to work for a period wi th no pay i f he anticipates that he w i l l be subsequently promoted to a wage posit ion, yie lding an expected lifetime ut i l i ty no less than his outside option. B u t notice that the h i r ing of volunteers (or interns) intro-duces a two-sided moral hazard problem, as firms have incentive to recruit unpaid workers, promising them promotion to pa id positions, and then renege on the promise. It is well known from the theory of repeated games that repeated interaction can help overcome these problems (reputation mechanism), i f the discounted stream of payoffs associated w i t h h i r ing volunteers exceeds the payoffs from cheating and then being punished by having to resort to h i r ing only pa id workers. The dynamic interaction between mult iple firms and workers is formally studied as a repeated game and a characterization of the equi l ibr ium strategies support ing 'volunteering' and the ' internship' structure is provided. A n addi t ional component of the present setting is that managers and workers can be intr insical ly motivated and derive nonpeeuniary benefits from contr ibut ing to the produc-t ion of mission goods (e.g. nurses, teachers, aid workers). Mot iva ted agents are typical ly heterogeneous i n terms of mission preferences - what act ivi ty to pursue and how to pur-sue it - and usually some hands-on experience is required before an ind iv idua l can learn enough about the different causes to be able to identify a preferred mission. For example, 9 T h e possibility that employers use deferred payments as a means of providing incentives has been studied, in a different context, by Lazear (1981) and by Akerlof and Ka t z (1989). 29 the manager of an international a id agency or an aid worker may prefer working for an organization w i t h a part icular religious outlook, or they may develop through experience a preference over the targeted group of beneficiaries (which group is more needy). Because the main parties involved may have different views about how the project should be car-ried out, preference alignment is an important determinant of the quali ty of the mission g o o d . 1 0 Volunteering facilitates the matching of l ike-minded organizations and workers, which improves the qua l i ty / impac t of the mission act ivi ty as well-matched pairs are more productive: a volunteer works for a per iod of 'explorat ion' , then as his mission preferences become known he can transfer to a matching firm, when a vacancy is created. B y contrast, internships match workers and organizations randomly, as when an intern joins the firm his mission preferences have not been determined. Therefore, from employers' perspective volunteer hir ing is the preferred h i r ing practice in the mission sector because it can generate more efficient matching. The workings of the matching process we envisage between mission-motivated principals and agents resemble that of the entry-level medical labour market. There it was recognized that mismatches occurred because compet i t ion led hospitals to sign up interns early on, years ahead of graduation, before their skills and interests were developed. The problem was that when a hospital and an intern reached an early deal they d id not take into account the externality imposed on other hospitals and interns (Ro th 1984). Some rules were eventually designed to move the dates of appointment later into the senior year of medical school when more information about students' abilities and preferences was available and as a result more efficient matches between interns and hospitals were identified. We believe that the process of volunteer h i r ing we described above alleviates a s imilar problem - albeit i n a less structured fashion than the labour market for medical residents - that would arise if mission-oriented organizations hired workers too soon (as would be the case w i t h internships), before their mission preferences have been revealed. No th ing i n the structure of the model we have sketched suggests that a rat ional manager would choose nonprofit over for-profit status, since the only effect of this choice is that the manager's pecuniary payoff from operating the firm is reduced. A possible reason would be that nonprofits are at an advantage in terms of being able to sustain volunteer hi r ing. B u t does the nonprofit incorporat ion relax the incentive compat ib i l i ty constraint that makes commitment to hir ing volunteers credible? Our analysis suggests that the answer to this hinges on the type of act ivi ty (mission-oriented or not) that is undertaken. In part icular, i f volunteering only raises profits then a nonprofit firm does not have a part icular advantage 1 0 T h e role of matching in principal-agent pairs with heterogeneous preferences is explored in Besley and Ghatak (2005), who show that better matching leads to higher effort and productivity. Here we take as given the proposition that better matched pairs are more productive in order to focus on how the interaction between the choice of organizational form (for profit or nonprofit) and incentive structure (volunteering or internship) can lead to more efficient matching. 30 over for-profit firms (true in the non-mission sector). T h i s is because while for a nonprofit manager the benefit from cheating is weaker - under nonprofit status profits are less valuable for managers because they can only be enjoyed as perks - so is the reward for honest behaviour. Therefore, i n this case a nonprofit manager's promise of honest behaviour is not more credible than the one of a for-profit manager. O n the other hand, i f volunteering also enhances the quali ty of the service provided - because of better matching - and managers care about quality, then nonprofit status is helpful in solving employers' moral hazard problem (true in the mission sector). The in tui t ion is that a nonprofit manager w i l l discount more heavily the fact that i f she cheats on volunteers quali ty w i l l suffer and hence a smaller profit (reputational rent) is needed to mainta in incentive compatibi l i ty. W i t h free-entry the incentive compat ibi l i ty constraint for nonprofit firms binds, which means that the one for for-profit firms fails, so they cannot use the volunteer h i r ing structure. Thus, the model accounts for the observed patterns of entry by sector: nonprofits en-gage in the provision of goods and services where better matching on mission preferences improves quality, while in sectors where missions play no role, nonprofit incorporat ion is not essential and for-profit status w i l l be preferred. In addit ion, our analysis explains why oth-erwise similar nonprofit and for-profit organizations w i l l select different incentive structures to motivate their workers. In equi l ibr ium, nonprofit organizations select the volunteering organizational structure while for-profit organizations uti l ize the internship. These features are in tune wi th the patterns of employment structure, work force characteristics and firm-type entry across sectors that we observe i n many modern economies. F ina l ly , we show that this equi l ibr ium has some desirable welfare properties as it generates more employment and output than a benchmark equi l ibr ium where only paid workers are employed, or one where firms hire interns. The rest of the paper is organized as follows. The next section briefly discusses strands of the literature that are relevant to this paper. Section 3 introduces the environment of the model , characterizes the two types of relational employment contract for an exoge-nously matched organization-worker pair, and analyzes the choice of organizational form and employment relational contract i n each sector. Section 4 turns to market equi l ibr ium, characterizing a steady-state 'sort ing' equi l ibr ium in the two sectors and presents a welfare analysis of the equi l ibr ium. Section 5 contains a brief discussion of some anecdotal accounts and case studies that lend support to some of the arguments made i n this paper and Section 6 concludes. 3.2 Related Literature This paper is related to the literature that has identified circumstances where nonprofit status may be a valuable commitment against opportunist ic behaviour that arises because 31 of various forms of contractual incompleteness. For instance, Glaeser and Shleifer (2001) argue that nonprofit incorporat ion is a valuable mechanism for an entrepreneur because, by weakening incentives to maximize profits, i t credibly commits to customers that non-contractible quali ty w i l l be higher, while in Rowat and Seabright (2006), nonprofit status is a valuable signal for aid agencies because it reassures donors that their funds w i l l be indeed directed to unverifiable development projects and not be sk immed off. Francois (2001) establishes conditions under which a nonprofit entrepreneur, by relinquishing residual claims to profits, faces weaker incentives to adjust product ion after a worker has shirked. W h e n workers care about the level of the public good produced this commitment is shown to be valuable i n that it reduces the wage that has to be offered to induce workers' non-contractible effort. Th i s paper is also related to a literature (Weisbrod (1988), T i ro le (1994), Rose-Ackerman (1996), Francois (2000, 2001, 2003), D i x i t (2002)) which emphasizes the notion that organi-zations producing public goods and services pursue missions that depart from strict profit-maximiza t ion , and underlines the significance of the fact that workers in these sectors are intr insical ly motivated by the act ion of par t ic ipat ing i n the provision of these collective goods. Several recent papers study the provision of incentives and the screening of intr insi-cally motivated workers, among others Handy and K a t z (1998), M u r d o c k (2002), Francois (2007), Delfgaauw and D u r (2007). Our paper builds on the contributions by Besley and Ghatak (2005, 2006a), who study incentive design issues in an environment w i t h mission-motivated principals and agents. The i r emphasis is on the role of matching of principals and agents on mission preferences and the effects of competi t ion on product iv i ty and the power of incentives, but they abstract from issues concerning organizational form which are central in our model . Specifically, the contr ibution of the present paper is that it presents a plausible avenue (volunteer h i r ing and sorting) which interacting w i t h the endogenously chosen organizational status allows mission-driven entrepreneurs to match w i t h l ike-minded workers and therefore play the efficiency enhancing role emphasized by Besley and Gha tak (2005). Also , one of our aims (and indeed the one that might be relevant for policy-makers) is to compare welfare outcomes between an equi l ibr ium where the volunteering structure is sustained, and hence the matching is facilitated, to one where it fails. 3.3 The Model 3.3.1 Primitives We consider an economy w i t h discrete t ime and infinite t ime horizon consisting of two sectors: a mission-oriented and a non-mission-oriented sector which serves as a bench-mark, denoted by m and b respectively. T w o groups of agents exist i n the economy: man-32 agers/entrepreneurs and workers . 1 1 Agents remain alive for another per iod w i t h probabi l i ty 0 G (0,1), while w i t h the complementary probabili ty, (1 — 0), they die and are replaced by identical agents. 1 2 There is heterogeneity in mission preferences in both groups. Specifi-cally, we consider three types of workers, indexed by i, and managers, indexed by j, w i t h h 3 £ {u, m i i m2}- T y p e u managers and workers are motivated exclusively by monetary rewards. We refer to type u agents as unmotivated. Types m i and m,2 are referred to as mission-motivated in light of the fact that, besides the usual pecuniary motivations, they are driven by a concern about the missions pursued by the organizations they jo in . We allow for a dis t inct ion between m i and mi which has one of two possible interpretations. It can either reflect the differences in focus among the variety of subfields of public good act ivi ty (e.g. advocacy/act ivis t versus direct care provider), or it can reflect differences i n some attr ibute (e.g. religious affiliation versus secular) w i th in some specific subfield (e.g. education) of the mission sector. We assume that the supply of managers is infinitely elastic. A measure Lu of unmot i -vated workers and a measure Lm of mission-motivated workers are alive every period, half of which are of type mi and half of type m.2, that is (Lmi = Lm2 — % 1 ) . T h e fraction 0 of workers that dies every per iod is immediately replaced by identical workers, who enter the labour market as unemployed, so that the size and the composi t ion of the workforce remain intact and stationary. There are three goods i n the model: two produced goods gm and corresponding to the mission and the non-mission sector respectively, and a non-produced numeraire good y. P roduc t ion of gm and g^ is undertaken by organizations - established as either for-profit or nonprofit - which consist of a manager (founder) employing two workers. Details about the differences between the two types of insti tutions are provided further on. Workers do not care directly about the type of organization they work for and are equally productive working for either type of provider. A l l organizations i n each sector, have access to a common sector-specific product ion technology, gs(e\,e2), where s G {m, b} and G {el,eh}, which describes how the combined effort choices of the two workers and the entrepreneurial input of the manager translate into the product ion of the organization's service, gm or gf,.13 We assume that each worker can choose between two effort levels: high effort (e = eh) w i t h corresponding output gs(e\, e\) — g%, and low effort (e — el — 0) which yields a normalized output gs(e[,el2) — 0. W h e n only one of the workers shirks product ion level falls but not a l l the way to zero: ^ ( e ^ e ^ ) = ^ ( e ^ e ^ ) = 7, where 0 < 7 < g%. Workers ' effort, e, need not admit a one-dimensional interpretation; one can imagine that workers' effort is applied 1 1 For clarity, we shall refer to managers using feminine pronouns and to workers using masculine. 1 2 F o r convenience, we subsume the discounting factor of agents in (3. 1 3 F o r simplicity, we abstract from non-labour inputs. One possible interpretation of the difference between a manager and a worker is that performing the entrepreneurial and supervisory duties of a manager requires an investment in human capital. Thus, a wealthy fraction of workers who have incurred the fixed cost of acquiring the human capital have become managers. We do not model this investment decision here. 33 along a vector of qualitative and/or quantitative dimensions of output that managers care about. In the mission sector, if, in addi t ion to high effort, workers' type matches the type of the organization we assume that preference congruence has a beneficial impact on product ivi ty . W h e n workers' are called to carry out a mission w i t h which they identify, they are more motivated, and hence provision of gm is increased to gm > g^.14 To be concrete, we imagine that there are two sets of actions that workers can take: one set is costly to them to provide, and shirking on this dimension w i l l eventually be detected by the manager of the organization. These actions, denoted by (e) i n the model , are responsible for the organization delivering g!^ when effort is high. In addit ion, there is another unobservable set of actions, not expl ic i t ly modeled, that workers w i l l only undertake i f they buy into the mission of the organization. It is this set of actions that we view as accounting for the higher level of mission good provision, gm, that the organization can achieve w i t h better ma tch ing . 1 5 In order to focus on incentive issues we assume that workers are risk neutral and have a w i th in per iod u t i l i ty function, separable i n income (y) and effort (e). We summarize the per-period uti l i ty, (y, 6ij, e), at tained by worker of type i when working for employer of type j as follows: The parameter 9{j represents the intrinsic payoff of a mission-motivated worker, which accrues to the worker independently of the legal status of the organization (for-profit or nonprof i t ) . 1 6 If employed by one of the organizations, a worker receives an endogenous wage w, while i f not employed workers are able to find work elsewhere at an exogenously given reservation wage w, which does not require high effort . 1 7 To rule out t r i v i a l outcomes, we assume that p s ^ e ^ , e^) — 2eh > 2w, where ps is the market price for good gs, so it is 1 4 Tn reality, the difference between and gm would most likely correspond to differences in the quality of the service being produced. Our model is consistent with this view, if we interpret output as being weighted by quality. 1 5 O u r logic is similar to that in Akerlof and Kranton (2005), who emphasize the notion of workers' identity and argue that when workers identify with the goals of the organizations they are employed they might be will ing to put in high effort with little wage variation. Here we take the view that workers' sense of identity stems from the particular mission the organization is committed to. 1 6 T h e way we specified preferences implies that workers receive a "warm glow" effect; that is, the benefit they receive is action-determined not output-determined, as in Besley and Ghatak (2005). If instead we allowed workers to be motivated by the effects of their actions on the quantity of output, then the benefit generated would entail a public good component and hence a standard free-riding problem would ensue. The implications of this type of preferences on organizational incentives are pursued in Francois (2003, 2006). ^Alternat ively, w may be thought of as the value of home production. (3.1) 34 productively efficient for workers to be employed by a firm and to choose high effort. Unmot iva ted managers, type u, care only about personal consumption of the numeraire good y. O n the other hand, mission-motivated managers have preferences given by Uj4 (y, gm), for j £ {mi ,7712} . Tha t is, we allow mission-motivated managers, as we d id above w i t h mission-motivated workers, to derive personal nonpecuniary benefits from being involved i n the delivery of collective goods. Note, however, that managers' al truist ic motivations are outcome-oriented as they care about the scale of the mission good (gm) produced by the organization they set up and not merely about their par t ic ipat ion i n the product ion of the collective good. A s in the case of workers, intrinsic motivations are present whether the manager sets up a nonprofit or a for-profit organization. We identify the mission of the organization w i t h the manager's type. Furthermore, we assume that the manager's type and the organization's form are common knowledge and so is the worker's type - whether he is mission-motivated or not; however, if he is, his precise mission type ( m i or m^) is revealed to h i m and becomes public information only after working for one period. Before entering a sector, a manager can choose whether to establish the organization as for-profit or nonprofit. Thus, a brief description of the differences between the two organizational forms is i n order. T h e objective of the manager (residual claimant) of a private enterprise is pr imar i ly to maximize profits (n) for the organization. Th i s assumption is standard i n neoclassical economic analysis and does not warrant further justif ication. O n the other hand, when an organization is nonprofit, it is not obvious what the objective of its manager is. Nevertheless, a defining characteristic of nonprofits is that they are subject to a nondistribution constraint, which stipulates that the manager of a nonprofit is banned from appropriat ing any net earnings from the organization's operat ions . 1 8 We follow Glaeser and Shleifer (2001) i n assuming that the effect of this is that a fraction of the firm's profits can indirect ly accrue to her in the form of perquisites such as less work hours, better working conditions e t c . 1 9 Th is way of model ing the objectives of nonprofit managers makes operational the not ion that these organizations can be inst i tuted to have weaker incentives to pursue prof i t s . 2 0 Though it is true that for-profit firms may also be motivated to serve other goals, we mainta in that they must be consistent w i t h their pr imary responsibili ty which is to generate sufficient rewards to shareholders. 2 1 Thus , we take the view that, as a 1 8 I t is important to note that such a constraint does not preclude the possibility that a nonprofit orga-nization may be actually earning positive profits. 1 9 I n addition to the nondistribution constraint, nonprofit, organizations do not have access to the equity capital market and may be also subject to regulations requiring that they engage in specific charitable, religious, educational or scientific activities in order to receive preferential tax treatment. We abstract from these issues here. 2 0 Tt is beyond the scope of this paper to model explicitly the objectives and constraints of nonprofit managers. The approach taken here serves the purpose of focusing attention on whether volunteer hiring can be consistent with a firm objective that departs from strict profit-maximization. 2 1 I n a recent paper, Besley and Ghatak (2006b) show that the pursuit of socially responsible practices by profit-maximizing firms is possible in a competitive environment. They develop a model in which some firms commit to producing a public good along with a private good and are able to finance its production 35 first approximation, for-profit managers w i l l face more high-powered incentives to maximize to ta l firm value than their nonprofit counterparts. In keeping w i t h this discussion, we assume that the decision making process w i t h i n nonprofit organizations - represented by the actions of the manager (founder) i n our analysis - balances the goals of maximiz ing profits and furthering the mission of the organization. We posit that the outcome of this can be represented by an induced per-period quasi-linear u t i l i ty function for a manager of type j who chooses organizational form k, where k — f denotes a for-profit organization and k = n indicates a nonprofit organization, given by: v*(7r,gs) = tfn + 5jsb(gs) (3.2) where n stands for profits and &(.) is a s t r ic t ly increasing and concave function. T h e binary variable 5js G {0,1} captures managers' "care intensity" or al t ruism, which is only present for mission-motivated managers when producing a mission-oriented good (i.e. Sjm = 1 for j G { m i , m 2 } , while 5^ — 0 for j G {u,m\,m.2}). The parameter ^ G [0,1] reflects the extent to which the organization's profits can be enjoyed as income by the manager — so the nondis t r ibut ion constraint implies that <pf > We assume that differences i n mission preferences ( m i or mj ) are orthogonal to the degree to which the nondis t r ibut ion constraint is enforced, and that a for-profit manager is the sole residual claimant, thus a l l profits TT accrue to he r . 2 2 F r o m now on we let 4>mi — ^ m 2 = ^ a n c - ^ 1 = 4>L2 = $1 = 1-Note that when product ion is of the good without the mission component then 5jb = 0, so setting up a nonprofit f irm i n the non-mission sector only corresponds w i t h reducing the u t i l i ty a manager obtains from profit. Equa t ion (3.2) captures, i n a reduced-form, the fundamental trade-off that the manager faces in making the incorporat ing decision, highlighted by Glaeser and Shleifer (2001): commitment to nonprofit status signals greater care for the 'qual i ty ' of the public good, which, however, comes at the cost of restricted access to pecuniary rewards. A n important feature of the environment i n which product ion is undertaken is that though the ind iv idua l performance of the worker can be potential ly assessed by the man-ager or supervisor, it is unverifiable by th i rd parties, and as a result, no standard contractual instruments can be used to induce workers' effort. For example, an aid worker's job de-script ion typical ly involves a variety of complex tasks: from direct care provision to drafting reports, fund-raising and lobbying. Performance related compensation i n this context is rare because (a) The moni tor ing and measurement of a worker's contr ibut ion to these tasks is very costly (and certainly difficult to verify by a th i rd party, such as the courts) or (b) it by charging caring consumers a premium for the private good. These firms can be viewed as exercising corporate socially responsibility (CSR) . 2 2 F o r simplicity, we make no distinction between the owner and the manager of the firm, so that agency problems between ownership and control are assumed away. 36 may be difficult to ascertain an ind iv idua l worker's contr ibut ion (due to the team character of production) or (c) it may induce effort distortions (due to mult i - tasking considerat ions) . 2 3 We abstract from the underlying details regarding the incentive provision problem and sim-ply assume that workers' input and the intrinsic reward they receive, though potential ly observable by the firm and the agent, are noncontractible. A t the heart of the problem is not asymmetric information between pr inc ipal and agent but th i rd party nonverifiabili ty of the ind iv idua l worker's effort and output. W h e n an employer and a worker are engaged in a repeated, on-going relationship, they may be able to sustain informal long-term relational contracts as a means to overcome the noncontract ibi l i ty of worker's performance. Specifically, M a c L e o d and Malcomson (1989) (under symmetric information) and L e v i n (2003) (under adverse selection and mora l haz-ard) have shown, i n a repeated game framework, the existence of an equi l ibr ium outcome where firms can use impl ic i t self-enforcing contracts to motivate workers, provided there is sufficient rent for both parties from the continuation of employment. O p t i m a l self-enforcing contracts can take the form of efficiency wages or performance bonuses depending on market condi t ions . 2 4 We proceed to characterize first, the nature of the internship and volunteering relational contract between an exogenously given single manager-worker pair, and, subse-quently, the market equi l ibr ium i n section 3. 3.3.2 The Employment Relational Contracts The two alternative relational contracts that we consider here are (a) The internship con-tract, which entails the vert ical promot ion of interns within an organization. Under this incentive structure, workers and managers are randomly matched, (b) The volunteering contract, which involves the horizontal sorting of workers to managers w i t h s imilar mis-sion preferences, after the unpaid stage. In the mission sector, this incentive structure w i l l be shown to generate assortative matching of organization-worker pairs. B o t h sorts of self-enforcing contracts give rise to actions that could not be supported i n a one-shot interaction, but which can be sustained when agents have a sufficiently high valuat ion of the future. In the present model, a worker faces the following career choices: what sector to seek employment (m or b), what type of employer (u, mi, 1712) to be matched w i t h and how much effort to exert (eh or el). To fix ideas, we describe briefly the successive stages in the career path of a typica l worker who w i l l enter into an impl ic i t contract w i t h a manager i n a certain sector, assuming that such contracts exist i n equi l ibr ium, abstracting momentari ly from 2 3 T h i s insight is emphasized in the multi-tasking literature, see for example Holmstrom and Mi lgrom (1991). 2 4 I n particular, MacLeod and Malcomson (1998) have shown that efficiency wages are likely to arise in markets where there is excess supply of workers, while performance-related bonus payments in markets with excess demand for workers. 37 issues of sector selection and matching which are considered subsequently. The given worker moves sequentially through three states: the general pool of workers, unpaid employment and paid employment (i.e. deferred wage posit ion). In part icular, the worker is born into the general pool where he receives an exogenous compensation w every period. A t the end of each period there is an endogenous probabi l i ty p that the worker w i l l exit the general pool and w i l l find an unpaid employment posi t ion. Suppose that this occurs in per iod t — 1; then the worker works for no pay dur ing period t and at the end of the per iod he transitions to a wage posit ion w i t h probabi l i ty (1 — 0); otherwise, he remains an unpaid worker for another p e r i o d . 2 5 If the worker is hired into a paid posi t ion he continues to work there un t i l he dies. We model the self-enforcing contracts as equi l ibr ium strategies of a dynamic game be-tween managers and workers. The first step of the analysis is to specify precisely the incom-plete contract environment in which the repeated game is conducted. Information Structure and W i t h i n Per iod T i m i n g Our specification of the information structure of the repeated game between workers and organizations, at any t ime t, can be summarized as fo l lows: 2 6 Publ ic Information. The identity of a l l previous employment pairs and the wage payment histories are common knowledge since they are verifiable pieces of information. In part icular , a l l workers and managers know whether a separation has occurred but do not know whether the worker quit or was fired, since this information is unverifiable. A separation that has taken place because of a death of one of the parties is distinguishable from separations due to the other causes involving one of the parties v iola t ing a promise. A l so , i f a separation occurs because a volunteer transfers to a pa id posit ion wi th a different employer this is also distinguishable from a separation due to malfeasance. 2 7 Note that a manager's publ ic history includes the event of mistreatment of volunteers. B y this we refer to the event where an organization which has been h i r ing volunteers into unpaid positions refuses to reciprocate by promoting workers from the volunteering pool into its own paid work vacancies. We assume that such practice becomes public in fo rma t ion . 2 8 2 5 A t this point the employer must decide whether to honour the promise to promote the worker or cheat by hiring another intern to fill the vacancy. We examine the conditions that ensure employers' incentive compatible behaviour in the next section. 2 6 F o r a similar treatment of the information structure in a dynamic game between workers and firms, see MacLeod and Malcomson (1989). 2 7 F o r example, a letter of confirmation/recommendation from the employer outlining a volunteer's expe-rience may be provided at the end of the assignment. 2 8 W h e n an organization cheats on the promise to promote a volunteer into its paid position, it hires instead an unpaid intern directly from the general pool and therefore ceases to employ a paid worker. We assume that this practice can be detected by labour market participants by observing the composition of the organization's workforce. Essentially what we assume is that whether the organization is employing paid 38 Worker's Private Information. A worker knows his own performance and whether the organization where he was employed i n previous periods honoured any promises made to h im. Manager's Private Information. A manager knows the history of effort contributions of a l l her workers up to t ime t and whether she has delivered on promises made to her workers. The sequencing of decisions within a period i n the contract ing game between a matched manager and worker is: • The manager makes the hi r ing decision (if there is a vacancy). • The manager decides whether to make a payment or not. • The worker makes the effort decision. • The manager observes imperfectly worker's effort contr ibution. • The worker observes manager's h i r ing decision. • B o t h parties decide whether to continue the employment relationship or not. • The period ends and bo th players continue to the next period w i t h probabi l i ty /3. Period Starts Manager makes payment (if any) Manager observes (imperfectly) worker's effort Manager and Worker make separation decisions Period Ends Manager makes promotion decision (if any) Worker chooses effort Worker observes Manager's promotion decision Figure 3.1: T i m i n g of Events T h e 'Internship' Incentive Compat ib le Wage We now focus on the determination of the incentive compatible wage that induces an intern's effort. We consider a stat ionary environment, w i th employers offering the same wage w1 every per iod and the expected u t i l i ty a worker gains from remaining in the general pool workers or not is public information, which is verifiable information since wage payments are verifiable. 39 being constant. Le t t ing V/jt represent the expected lifetime u t i l i ty of a worker of type i who accepts an unpaid posi t ion (internship) at an organization of type j at t ime t, and suppressing the t ime subscripts we write: Vi = - e h + p[(l-P)Vrj+/3Vi\ (3.3) In this expression, (1 — /3) denotes the probabi l i ty that there w i l l be a pa id posi t ion vacancy and thus that the intern w i l l be hired into a pa id job. V[- designates the expected lifetime ut i l i ty of a paid worker who decides to deliver high effort. A n intern receives no compen-sation and provides high effort i n the current period but expects to be hired into a pa id job w i t h probabi l i ty (1 — (3). Thus, (1 — 0) acts as a quasi-discount factor on the value of becoming a pa id worker. Similar ly, V[- is defined below: V? = w1 + dij - e h + P m a x ( V ^ , V$) (3.4) where Vfj represents the expected u t i l i ty of a worker who decides to shirk. If a worker supplies high effort then he attains u t i l i ty w1 + 9{j — eh dur ing the course of the current period, where w1 is the wage associated w i t h the posi t ion i n an organization of type j and 9{j is the intrinsic reward for ind iv idua l of type i associated w i t h a posi t ion i n an organization of type j . If the job is continued, then the worker decides whether to furnish high effort next period or not, if doing so yields greater u t i l i ty to h i m than shirking. W h e n a worker shirks, he receives the wage w1 and the nonpecuniary benefit 9ij but does not undergo the disut i l i ty of supplying effort. A shirking worker is detected w i t h a constant exogenous probabi l i ty / J , E (0,1), i n which case he loses the job at the end of the period, and goes undetected w i t h probabi l i ty (1 — fi) i n which case he makes the effort decision again next p e r i o d . 2 9 We write the value function of a shirker as: V$ =w' + On + {3 [IJLV* + (1 - n) m a x ( V £ , ^ ) ] (3.5) F ina l ly , the value function of being in the outside general pool is: V9 = w + 0[pVl + (l-p)V°] (3.6) where w is the general pool compensation and p is the endogenous, i n equi l ibr ium, job acquisit ion rate. Let us now consider the incentives that employers face in designing the relational con-2 9 T h e assumption of a less than perfect monitoring technology can be justified by the costs associated with supervision. Tn addition, we assume that inference of effort v ia observing output is impossible because of noise and the difficulties of identifying individual contributions due to the team character of production. 40 tract. The i r strategy is to minimize labour costs subject to being able to attract interns and induce them to provide high effort. Consequently, they w i l l choose w1 such that the prospective worker is no worse-off from becoming an intern and not remaining i n the general pool , i.e. the following par t ic ipat ion constraint must be satisfied: vi > V9 ( P C ) If V/j > Vg, then it is in the firm's best interest to adjust the features of the package and transfer the surplus from the worker to itself such that internships are no more attractive than the outside option. The only means of adjusting the package, since the probabi l i ty of t ransi t ioning from unpaid to paid work (1 — (3) is exogenous, is to reduce the wage associated w i t h a pa id posit ion. Let the wage solving ( P C ) w i t h equality be w P C . Subst i tu t ing from (3.3), (3.6) and (3.4) it can be shown that: w PC _ l + 0 , „ h , -0 (e  + w)-9r (3.7) where 6r is the expected intrinsic payoff when workers and firms are randomly matched. (6l < 0r < 0h). A l so , to deter shirking by the worker, the wage offered to the worker must satisfy the following incentive compat ib i l i ty (no-shirking) constraint: Vfj > V* (3.8) this condit ion implies: L e m m a 4 If the probability of detection of a shirking worker is sufficiently low, p < ^\ ^ e , w+eh then the relational contract (w1,eh) between an intern/worker and a firm, consists of a, wage satisfying: = + + ( i - * 8 ) a _ r (ici) 0p(l+0P-82) (l + 0P-02) with > 0. dp Proof. P roo f is in A p p e n d i x B . Note that the assumption on the primit ives I p, < ^_ ^ e ) is needed to ensure that \ w+eh J the wage i n (ICI) is at least as high as the wage i n (3.7), which is necessary to induce par t ic ipat ion by workers i n the general pool . The incentive compatible wage i n (ICI) admits a standard efficiency wage type of interpretation. T h a t is, to induce effort the organization has to pay the worker a p remium over his market alternative. Intuitively, the relational contract defined above allows the organization to elicit effort from the worker 41 while l imi t ing the rent offered to h im . T h i s is accomplished because while the worker gets a wage premium while occupying an efficiency wage posit ion, the rent is par t ia l ly taxed back by making the worker pay an "entrance fee" in the form of the uncompensated effort he has to supply as an i n t e r n . 3 0 Th i s arrangement encourages interns to stay w i t h the firm and supply high effort throughout their career in order to benefit from the higher wages that come w i t h seniority. For the relational contract i n (ICI) to be supported i n equi l ibr ium, a sufficient rent has to be generated from employment. The rent is the difference between the returns to the current arrangement and those that the two parties could achieve i n their outside options. In this model, the surplus is d iv ided between employers and workers. To see this note that an intern prefers his current status than staying in the outside pool (V/j > V9). For employers, profits from hir ing interns are t r iv ia l ly greater than profits from hi r ing straight from the outside pool , which would be the alternative way of fi l l ing a vacancy, because an intern generates as much lifetime expected profits as an outside worker when i n a pa id posit ion, but also makes an uncompensated contr ibut ion to the firm's profits as an intern. Note that we have ruled out the possibil i ty that workers can post a performance bond (in the form of a negative hi r ing wage) dur ing the internship stage of employment. If this were possible, then firms could use this instrument to b ind the par t ic ipat ion constraint of workers (V/j = V9), thereby extract ing the entire surplus from the employment relationship and clearing the labour market. In reality, however, performance bonds are rarely observed. One possible explanation for this absence is credit market imperfections that make it impossible for workers to raise the money for the bond. M o r e generally, the possibil i ty of post ing performance bonds raises a host of issues, as it induces employers to cheat workers i n various ways, so we proceed by assuming that firms leave some rents to workers. T h e 'Volunteering' Incentive Compat ib le Wage The volunteering employment structure resembles the internship structure except that vol-unteering is an impl ic i t contract offered jo in t ly by a l l par t ic ipat ing organizations and not by one specific employer. In part icular, the volunteer is in i t i a l ly randomly matched w i t h an organization and supplies high effort for that employer w i th no compensation; subse-quently, the volunteer learns his type and when a pa id posi t ion i n an organization of the same type is vacated he transitions to that posi t ion even if this means transferring to a different organization. We examine managers' incentives to sustain this structure i n the next subsection. In addi t ion to providing incentives, since volunteering is recognized by other firms, it 3 0 Essential ly, our version of the shirking model allows an entrance fee to emerge which reduces the rent that the employer needs to concede in order to motivate the worker. The suppression of this mechanism in the original Shapiro and Stiglitz (1984) formulation-by assuming that the principal pays the same wage at every period-was considered a theoretical weakness of the efficiency wage theory (see Carmichael 1989). 42 plays the role of facil i tat ing matching between mission-motivated workers and organiza-t i ons . 3 1 We posit a frictionless matching process: the matching is instantaneous and cost-less. We look for allocations of workers to organizations that are voluntary and stable, i n the sense that there is no pair that could negotiate an agreement that would make bo th parties better off than they are in their current matches. The following lemma characterizes the nature of stable matching i n the mission sector. L e m m a 5 Any stable matching equilibrium must have organizations and workers assorta-tively matched. Proof. P roo f is i n A p p e n d i x B . • We now turn to the determination of the incentive compatible wage for an organization hi r ing volunteers. The value functions of being in any of the three possible states, employed and paid, employed and unpaid (volunteer) and unemployed are identical to the ones i n (3.3), (3.6), (3.4) and (3.5). Therefore, maintaining the notat ion we established i n the previous section, incentive compatible wages that support assortative matching have to satisfy the following two conditions: V[3 > V* (3.9) and ivY + 6h > wYj + 0r (3.10) The first condit ion is standard and ensures that the worker supplies high effort. The second condit ion ensures that the payoff to a worker when working for an organization of the same type is at least as high as when working for an organization of a different type. L e m m a 6 The relational contract (wv,eh) between a volunteer/worker and a firm consists of a wage satisfying: W*IP) = fi-m+pp-w-M* + <±z£) w _ * ( I C v ) Pn{i + pP-P2) [i + pP-p2) y 1 with > o. Proof. P roo f is i n A p p e n d i x B . • The interpretation of the incentive compat ib i l i ty wage for volunteering is analogous to that offered above for internship: a worker receives a p remium for . The analysis of the two alternative self-enforcing mechanisms can be summarized in the following proposit ion: 3 1 I n equilibrium, volunteering only occurs in the mission sector, this wi l l be proved later, but for now we take it as given. 43 Proposition 4 Conditional on a common job acquisition rate (p), binding incentive com-patible wages in the mission sector are higher under an 'Internship' relational contract than a 'Volunteering' relational contract (w1(p) > wv(p)). Proof. Follows direct ly from (ICI), (ICV) and noting that 6h > 6r. m The role that mission heterogeneity plays i n the model now becomes clear. A s i n Besley and Ghatak (2005), selecting workers w i t h congruent preferences can be cost saving for organizations, as this allows them to induce high effort at a lower wage. In addit ion, there are product iv i ty gains to be made since volunteering ensures the better matching which raises workers' output. Consequently, those firms that can attract volunteers w i l l be at an advantage. T h i s feature is absent i n the non-care sectors of the economy, so for employers a volunteering contract in those sectors is not preferred to the internship contract we discussed above. It now remains to establish that the wages and employment patterns which have been computed for a single worker can constitute an equi l ibr ium of the multi-player game. 3.3.3 Selection of Relational Contract and Organizational Form Mission Sector The purpose of this sub-section is to explore the role of the interaction between the choice of organizational form and the presence of mission preferences for the type of impl ic i t con-tract that managers w i l l use, in equi l ibr ium, to overcome the non-contract ibi l i ty problem of workers' effort. In what follows, we analyze whether it is incentive compatible for managers to implement volunteer hi r ing. In part icular , we shall show that under the stated assump-tions on the preferences of the managers who control the organizations, a deviat ion from a volunteer structure is more valuable for for-profit firms, which i n equi l ibr ium is going to lead to volunteering being only available to nonprofit organizations. For an organization that implements a volunteer h i r ing structure the composi t ion of its workforce, at any t ime t, is one wage worker plus one volunteer who awaits promot ion to a paid posit ion next period and is going to be replaced by a new volunteer. Profits equal irv = pmgm— w v , where pm is the price of the final product which the firm takes as given. Similar ly, for an organization which uses an internship structure, its workforce consists of one wage worker plus one intern who w i l l be promoted i f a wage posi t ion is vacated next period and wi l l be replaced by a new intern. Profits equal ir1 = pm9m ~ w I •> where gm > g^, reflecting the fact that interns are randomly matched wi th organizations. Note that the volunteer relational contract described above creates mora l hazard on the part of the employer. Organizations have an incentive not to promote current volunteers to wage positions and to replace them w i t h new volunteers from the general pool , thus appropriat ing the unpaid labour contr ibut ion made by volunteers. Workers ant icipat ing that they w i l l not receive the high future payments have no incentive to work and thus 44 incentives are destroyed. Thus, for volunteer h i r ing to be sustainable it has to satisfy the manager's incentive compat ib i l i ty condit ion. Consider what constitutes a deviat ion from the volunteering structure. Suppose that a paid posit ion vacancy is created. The organization deviates by reneging on the promise to hire an ind iv idua l from the volunteering pool to fill its vacancy and instead hires an unpaid intern straight from the general pool to fill this posi t ion. B y doing this, the manager makes a one-period gain from not having to pay the wage she would otherwise have to, if she continued to hire volunteers to paid positions, but has to resort to an internship structure to get around workers' moral hazard i n future periods since workers w i l l refuse to volunteer for her anymore. Tha t is, organizations that cheat lose their reputations and are punished i n future labour market dealings by the workers' equi l ibr ium strategies. Punishment here consists of future workers refusing to volunteer for organizations who have previously chosen not to promote volunteers into paid positions and to instead only accept internship contracts from such organizat ions . 3 2 Th i s k ind of g r im trigger strategy requires that labour market participants can observe whether an organization is employing a pa id worker or not. In part icular, when a manager breaches the impl ic i t agreement to promote a volunteer into a pa id posit ion and hires another unpaid worker then dur ing the deviat ion she employs only unpaid workers; other potential workers can detect this - because wage payments are verifiable information - and so they rat ional ly avoid volunteering for the organization i n the future. E q u i l i b r i u m strategies support ing the volunteer-hiring relational contract are expl ic i t ly defined in A p p e n d i x A . Specifically, i n the first period of deviation the manager hires two interns to fill bo th the vacant pa id posit ion and the unpaid posit ion. Profits are itVd — Pmg^. The opportunist ic manager then loses the goodwil l of being an honest employer so i n future periods workers only accept internship positions that are more costly for the firm because w1 > wv - that is, the wage pa id to interns is greater than the wage pa id to volunteers. A l so the mismatch induced because interns are randomly matched w i t h organizations w i l l also have an impact on the abi l i ty of the organization to successfully fulfill its mission. Tha t is, following a deviation, the organization's mission good product ion is compromised {gm). Hence, volunteering is self-enforcing i f the present value of honouring is greater than the present value of reneging. T h e manager's incentive compat ibi l i ty condi t ion may be wri t ten as: Y=0*fr*V>9m) * ^ V d M + Y ^ j t f M ( 3 -H) for each j E { m i , TO2}, and k E {/, n} 3 2 G i v e n this strategy of workers, the best response for managers who have reneged in the past is to continue cheating on the promise to promote volunteers, so that workers' strategies are a best response. 45 where irvd > n v > n1 and the last inequali ty follows from the fact that w1 > w v . T h e left-hand side of (3.11) is a manager's discounted payoff from not cheating. T h e first term on the right-hand side of (3.11) represents the u t i l i ty the manager can a t ta in i f she cheats. Note that this would raise profits but hurt the quali ty of the mission g o o d . 3 3 The second term captures the expected present value payoff from hir ing interns, which is the h i r ing practice the manager implements along the punishment path. Our goal now is to determine for which organizational form incentive compat ib i l i ty is easier to satisfy. Subst i tu t ing from (3.2) into (3.11) yields: 1 - 0 Lk„V 7T + b(gm) > jk Vd t> 7T + 1 - 0 L k ^ + b{ghm which upon rearrangement and simplif icat ion implies that: / > ( i 0)7rVd + PIT1 K9m) - Kghm) ( I C M ) Define the right-hand side of (ICM) as 6(</>fc). The following result holds: Proposit ion 5 In the mission sector, equilibrium level profits required to satisfy incentive compatibility of managers under a for-profit status is higher than that under a nonprofit status. Proof. Because Q ( < p k ) is increasing m (pk, and <f)f > <f)n it follows that 0 ( ^ ) > Q ( ( j ) n ) . To gain some in tu i t ion for this result notice that the way i n which the reputation mech-anism informally enforces managers' incentive compatible behaviour is by offering to the potential cheater a "premium": a stream of payoffs that exceed the potential gain from cheating. Th i s premium is given in both monetary (i.e. higher profits) and intrinsic (i.e. better quality) terms. Under nonprofit status profits are less valuable for a manager - be-cause they can only be enjoyed as perks - so a nonprofit manager places relatively more weight on the fact that i f she cheats on volunteers quali ty w i l l suffer, and hence a smaller monetary p remium is needed to mainta in incentive compatibi l i ty. Th i s is further i l l u m i -nated by inspecting (ICM): the te rm that is subtracted from the right-hand side captures how heavily the loss of quali ty - due to cheating - is discounted. Thus , i f cheating d id not affect quali ty then this term would be zero so the right-hand side of the inequality would be the same across firm types, and no organizational form would find it easier to attract vol -unteers. But, to the extent that volunteering does affect the qual i ty of the service provided, the term is positive, so nonprofit incorporat ion relaxes the incentive compat ibi l i ty condi t ion 3 3 N o t e that for cheating to be worthwhile it has to be that 4>k (T\VD — TXv) > b(gm) — b(g^). That is, the monetary benefit from cheating (due to higher profits) has to be greater than the intrinsic loss a manager suffers (due to quality degradation). In what follows we assume that this is always true. 46 that makes commitment to h i r ing volunteers credible. T h i s suggests that volunteer h i r ing by nonprofits should occur only i n fields where matching on mission heterogeneity has a noticeable effect on quality. Propos i t ion 5 has the following important impl ica t ion . Corol lary 2 For-profit firms will not be able to participate in a volunteer hiring structure that is just incentive compatible for nonprofit firms. Free entry in the mission sector w i l l ensure that the incentive compat ib i l i ty condi t ion of the nonprofit firm {ICM) binds. However, when this is the case, incentive compat ib i l -i ty for for-profit firms w i l l be violated which means that they cannot credibly commit to h i r ing volunteers. Furthermore, if a mission-motivated manager were to enter the mission sector establishing a for-profit firm and implement an internship structure she would be outcompeted by existing not-for-profit firms recruit ing volunteers because of their lower labour costs. Thus, incorporat ion as nonprofit is valuable for managers because it serves as a commitment device that signals potential volunteers that they w i l l be fairly treated. The very factor that is usually thought of as accounting for the efficiency supremacy of for-profit governance - high-powered incentives - can rule out par t ic ipat ion in the volunteering incentive structure i n mission-oriented sectors. The model's predict ion that only nonprofit firms w i l l part icipate in a volunteering struc-ture and that this w i l l occur i n mission-related activities is consistent w i t h even a casual observation of the pattern of sectoral d is t r ibut ion of volunteer activity, according to which nonprofit agencies are the overwhelming recipients of volunteering services. Th i s is even true in mixed ownership industries (childcare, nursing homes etc) where for-profit coexist and compete against nonprofits in both the service and labour markets. For a different perspective on the difficulties associated w i t h sustaining the volunteer-hir ing structure notice that, because incentives are sector-wide and not employer-specific, their provision has the character of a public good and is susceptible to a form of free-riding. Tha t is, each ind iv idua l employer would like to obtain labour donations from volunteers but refrain from reciprocating by subsequently h i r ing them into paid positions, thereby free-riding on other organizations' h i r ing of volunteers. W h e n the free r id ing is severe -i.e. when condi t ion (3.11) fails - it leads to the unraveling of the volunteering structure. The impl ica t ion of Proposition 5 is that organizing the product ion of collective goods by nonprofit organizations is a less costly way to overcome this k ind of free-riding problem. Non-mission Sector In the non-mission sector mission matching plays no role. The following result holds: L e m m a 7 In the non-mission sector managers choose for-profit status. 47 Proof. P roo f is i n A p p e n d i x B • Th i s prediction of the model is also consistent w i t h the observation that nonprofit firms are absent from sectors of the economy which do not involve mission-oriented product ion. Furthermore, since there is no issue of matching managers and workers i n this sec-tor internships is the preferable h i r ing policy. However, when an internship structure is implemented there is s t i l l scope for opportunist ic behaviour on the part of managers. In particular, when a pa id posi t ion vacancy is created i n an organization which has been h i r ing interns then its manager has an incentive not to honour the promise to hire the exist ing intern into the pa id posit ion, but to fill the posi t ion w i t h an unpaid worker from the gen-eral pool . Such behaviour once detected by labour market participants results i n loss of reputat ion and is punished i n future labour market interactions by the workers' equi l ibr ium strategies. Tha t is, in future periods workers w i l l not be wi l l ing to be recruited as unpaid interns and the manager would have to resort to paying both of its workers an up-front wage w1 satisfying (ICI). E q u i l i b r i u m strategies support ing the internship h i r ing structure are defined in Append ix A . The incentive compat ibi l i ty condi t ion of the manager may be wr i t ten as follows: or equivalently TV**"+TV (3-12) where ir1, irId and 7re denote per-period profits under an internship structure, the deviation, and i n the periods after the deviat ion respectively, and 7rd > irId > 7re. For future reference, it is useful to rewrite (3.12) as: TT' > (1 - 0) n I d + 0ire ~ K (3.13) Th i s incentive constraint must be satisfied for the internship structure to be a credible recruitment strategy. W i t h free entry into the non-mission sector, the level of profits that a manager can enjoy i n equi l ibr ium w i l l satisfy (3.13) as equality. Notice that adding heterogeneity among unmotivated agents would not lead to the impl ica t ion that there is a nonprofit advantage in the non-mission sector as well because of the absence of the non-pecuniary component in managers' payoff. 3.4 Market Equilibrium U p to this point we have discussed the design of incentive schemes between a given exoge-nously formed manager/worker pair. We now tu rn attention to the steady-state analysis of 48 a market equi l ibr ium where mult iple managers and workers interact, and consider the choice of organizational form (by managers) as well as the type of incentive relational contract that w i l l be implemented by organizations i n the two sectors. We characterize an equi l ibr ium wi th sorting of agents into sectors by type. In part icular , mission-motivated managers and workers seek entrepreneurial and employment opportuni-ties only i n the mission sector and the same is true for their unmotivated counterparts i n the non-mission sector. In addit ion, it w i l l be shown that product ion i n the mission-oriented sector w i l l only be undertaken by nonprofit organizations, and the employment structure w i l l take the form of the volunteering contracts derived above. Conversely, i n the non-mission-oriented sector, organizations w i l l only be for-profit, and employment contracts w i l l take the form of internships. 3.4.1 A 'Sorting' Equi l ibrium To close the model, since we d id not expl ic i t ly include i n workers' preferences (3.1) the u t i l i ty benefits derived from consumption of the services (gm,9b) produced, we assume that the demand side of the m a r k e t 3 4 is described by a downward sloping demand schedule for the total services produced in the mission sector and the non-mission sector respectively: Gm = Dm(pm) and Gb = Db(pb) where d D ^ P m ^ < 0 and d D ^ h ^ < 0, and aggregate service provision is given by s imply adding up the ind iv idua l output of a l l producing organizations: Gm — ^2 gm and Gb = Y19b-In the steady-state equi l ibr ium, the same endogenous to ta l number of jobs Em and Eb, i n the mission and the non-mission sector respectively, are created i n every p e r i o d . 3 5 We assume that at full employment (Em + Eb = Lu + Lm) the revenue product of labour covers the opportuni ty cost of labour, that is, full employment is efficient. A t the beginning of each period, workers in the general pool are randomly assigned to the unfilled vacancies created as some existing matches are dissolved w i t h exogenous probabi l i ty 1 — 0. Workers must be wi l l ing to accept positions and supply high effort at the going wage, and managers must be wi l l ing to create enough jobs to replace the workers who turnover because they die and must have an incentive not to renege on the promise to promote unpaid workers into pa id positions. Formally, a steady-state equi l ibr ium is defined as follows: Definition 2 Given the aggregate demand functions Dm(pm) and Db(pb), a steady-state equilibrium consists of a set of wages, prices and allocations of final services (w^, p^, G^, wl, pj^, G£) along with a stationary allocation of workers across sectors (mission, non-mission) and states (paid employment, unpaid employment, general pool), such that 3 4 I n the case of mission goods, both the government and individual agents may be purchasers. 35E encompasses both paid workers (P) and unpaid workers (volunteers or interns) (U), i.e. E = P + U. 49 incentive compatibility is satisfied for both managers and workers. In addition, no new entry, under any choice of organizational form, must be attractive. We now focus on identifying the conditions under which a steady-state 'Sor t ing ' equilib-r ium, that is consistent w i t h the above definition, exists. The equi l ibr ium we are interested i n has the following characteristics: the mission sector attracts mission-motivated man-agers who establish nonprofit organizations that compete w i th each other and hire mission-motivated workers offering them the volunteering relational contract derived above. In the non-mission sector, unmotivated managers establish for-profit organizations that compete w i t h each other and offer unmotivated workers the internship relat ional contract. To establish conditions under which this type of 'Sor t ing ' equi l ibr ium we hypothesize exists, we check whether the prescribed self-selecting behaviour is incentive compatible once we take into account that workers are freely mobile between the two sectors, and that managers are free to enter either sector. T h a t is, for the sorting equi l ibr ium to exist we need to confirm that in equi l ibr ium the entry of mission-motivated workers into the mission sector and of unmotivated workers into the non-mission sector is opt imal . Le t t ing Vf(s) denote the discounted lifetime u t i l i ty of a worker i n the general pool of type i who wishes to enter sector s, the sorting constraint for mission-motivated workers may be wr i t ten as: Vf(rn) >Vf(b) for i e { m i , m 2 } (SW1) while the one for unmotivated workers is: V°(b) > V°(m) (SW2) Similar ly, the sorting constraint for mission-motivated managers is: v?(nV,gm) > I>/(TF£) for j E { m i , m 2 } ( S M I ) and the one for unmotivated managers: 4(H) > KA^m) (SM2) where (~) denotes that the objects i n question are evaluated i n the sorting equi l ibr ium. Also , note that in the equi l ibr ium we are interested in , the probabi l i ty of finding a volunteering posit ion in the mission sector (pm) for a mission-motivated worker in the general pool and for an unmotivated worker in the general pool the probabi l i ty of finding an internship posit ion i n the non-mission sector (pb) is given respectively by: Pm(Em) = and p\Eb) = (3.14) 50 where pm{Em) and pb(Eb) are increasing functions. We make the following assumptions on the parameters of the inverse demand functions: Assumpt ion 2. {pm{Gm(Em))gm — 6(</>n)} takes at least one value i n the interval (wv(0),wv(Lm)). Assumpt ion 3. [pb(Gb(Eb))g^ — Kj takes at least one value i n the interval (K / (0) , w1 (Lb Because wv(Em) and w1 (Eb) are continuous and increasing i n Em and Eb respectively, the above restrictions on the parameters of p m ( G m ) and pb(Gb) ensure that the managers' downward sloping incentive compat ibi l i ty conditions cross the workers' upward sloping incentive compat ibi l i ty conditions i n the relevant region, that is, for Em G (0, Lm) and Eb G ( 0 , L 6 ) . We have: Proposit ion 6 / / the conditions for self-selection of workers (C.4) and managers (C.5) hold, there exists a steady-state 'Sorting' equilibrium (wv, pm, Gm (Em ), w1, pb, Gb(Eb)) with the following properties: a) The mission sector features a 'Volunteering' equilibrium: type m\ and mi managers sort into the mission sector and establish nonprofit organizations hiring type m\ and m^ workers, respectively. The employment structure takes the form of volunteering. There are workers of each type: ^ volunteers and -^p wage workers and ^ organizations of each type (m\ andm^). b) The non-mission sector features an 'Internship' equilibrium: type u managers sort into the non-mission sector and establish for-profit firms hiring type u workers. The em-ployment structure takes the form of internships. There are ^ workers of each type: interns and ^ wage workers and ^ organizations. Proof. P roof is i n A p p e n d i x B . • Condi t ions (C.4) and (C.5) i n the proposit ion, which are derived i n A p p e n d i x B , ensure that i n the 'Sor t ing ' equi l ibr ium no mission-motivated worker or manager has an incentive to deviate from sorting into their designated sector. In part icular, the condi t ion for self-selection of workers (C.4) is not transparent and does not y ie ld a straightforward economic in terpre ta t ion . 3 6 Nevertheless, what this condi t ion suggests is that the higher 6h the more attractive employment i n the mission sector becomes for motivated workers, which makes the self-selection condi t ion easier to satisfy. The sorting condi t ion for managers (C.5) sug-gests that motivated managers w i l l find entry into the mission sector preferable provided that they can extract sufficient economic rents (high cpn) from the operation of the nonprofit 3 8 Ideal ly we would like to recast condition (C.4) in terms of only the exogenous parameters of the model, namely, /3, 0, e, w, fi, Lm, Lf etc. This is possible if we postulate specific functional forms for the inverse demand functions pm(Gm(Em)) and p!(Gf(Ef)), in order to explicitly solve (C.7) and (C.9) for Em and Ef. Because this does not yield any additional economic insight we chose to leave Em implici t ly defined in condition (C.4) and demonstrate existence with a worked example in Appendix C. 51 organization and/or they derive sufficiently strong intrinsic benefits (high b(gm)) from con-t r ibut ing to the product ion of mission goods. In A p p e n d i x C we numerically compute a simple parametric example which illustrates that the sorting constraints for workers and managers i n the 'Sor t ing ' equi l ibr ium can hold i n non- t r iv ia l environments. O n the managers' side, free-entry ensures that incentive compat ib i l i ty (ICM) binds. O n the workers' side, incentive compat ib i l i ty requires that condi t ion (ICV) is satisfied. The two constraints are i l lustrated i n figure 2. Note that (ICM) is downward sloping because the inverse demand function pm(Gm) is decreasing i n the level of employment Em. Workers ' incentive compat ibi l i ty implies that equi l ibr ium must lie on the upward sloping curve defined by (ICV), which is increasing because dWQpP^ > 0 and p is increasing i n E. E q u i l i b r i u m occurs at the intersection of the two conditions. Figure 3.2: Volunteering E q u i l i b r i u m i n Miss ion Sector The comparative statics of the 'Sor t ing ' equi l ibr ium are as follows: Corol lary 3 A rise in the probability of detection (p) or in the intensity of workers' intrin-sic motivation (6h) reduces the equilibrium wage and increases the employment level. The opposite is true when the benefits of being in the general pool (w) rise. On the other hand, positive demand shocks for the service produced Gm, Gb lead to more entry of organizations and higher equilibrium wage and employment level. Proof. P roo f is i n A p p e n d i x B . • It is noteworthy, that i n bo th sectors, workers i n the general pool would be wi l l ing to work for less than the wage received by an identical pa id worker, yet, organizations are not 52 wil l ing to hire them knowing that if hired these workers would have incentive to shirk. In this sense, unemployment i n the 'Sor t ing ' equi l ibr ium can be characterized as involuntary -the k ind commonly associated wi th efficiency wage models, for example Shapiro and St igl i tz (1984). However, compared to a benchmark equi l ibr ium where a l l workers are hired direct ly into efficiency wage positions we have the following result: Proposit ion 7 Ifpm(Gm) > e ^ I , for Em £ ( 0 , L m ) , then in any 'Sorting' equilibrium, n — 9 r n employment and output in both sectors are higher than those that would occur if organiza-tions employed only paid workers and paid them efficiency wages. Proof. P roo f is i n A p p e n d i x B . • The restriction on the parameters of the inverse demand function pm(Gm) is a sufficient but not necessary condi t ion for this to be true. The in tu i t ion for the result i n the proposi t ion is simple. T h e model predicts that workers' incentive compatible wages, when volunteer hir ing is implemented, are less sensitive to employment rates than those when workers are hired direct ly into pa id positions. Hav ing to go through an unpaid stage before hired into a paid posit ion, if they are caught shirking, induces a harsher punishment so it reduces the wage premium needed to motivate volunteers or interns, from that i n the benchmark case where workers i n the general pool are direct ly hired into paid positions. A l so , organizations' demand for labour is lower when at any point i n t ime bo th workers need to be compensated, so managers' incentive compat ib i l i ty constraint is shifted down and t i l t e d . 3 7 B o t h effects result in the employment level at the sorting equi l ibr ium to be higher than the benchmark case. Th is is i l lustrated i n figure 3, which depicts the equi l ibr ium w i t h volunteer h i r ing (point V) and the equi l ibr ium w i t h only paid workers (point B). To summarize the key points made so far, s tart ing from the premise that some ind iv id -uals view volunteer experience as a stepping stone for a professional career, the 'Sor t ing ' equi l ibr ium described provides a plausible explanation for why voluntary effort is almost ex-clusively elicited by not-for-profit organizations and why competing for-profit corporations cannot duplicate the incentives needed to support a sector-wide volunteer-hiring structure. Furthermore, by relaxing the incentive compat ibi l i ty constraint of workers, employment and service provision i n the 'Sor t ing ' equi l ibr ium move closer to the full employment levels. A l imi ta t ion of the 'Sor t ing ' equi l ibr ium is the counterfactual predict ion that a l l h i r ing by nonprofit organizations in the mission sector is done from the volunteer pool . However, we believe that this shortcoming arises because of our stylized assumption of a homogeneous (in abil i ty) workforce. In other words, what the model predicts is that if two otherwise identical workers apply for a paid posit ion, then the organization w i l l always choose the worker who has some volunteering experience over a person who has none, which seems to be a plausible description of the way nonprofit employers screen applicants. 3 7 T h e condition in the proposition ensures that this is true. 53 Eb Ev L E Figure 3.3: Volunteering E q u i l i b r i u m (point V") vs Efficiency Wage E q u i l i b r i u m (point B) 3.4.2 Welfare Analysis Our task i n this sub-section is to assess some welfare properties of the two-sector 'sort ing' equi l ibr ium. In particular, we are interested in gauging its performance against the efficient benchmark set by a social planner. It w i l l be demonstrated that the 'Sor t ing ' equi l ibr ium is constrained Pareto efficient, as a planner, max imiz ing a representative worker's expected u t i l i ty subject to the same informational constraints faced by agents, would not be able to improve worker's welfare. In addit ion, we w i l l show that the 'Sor t ing ' equi l ibr ium has some desirable welfare properties as it generates more employment and output than a benchmark equi l ibr ium where only paid workers are employed, or one where firms hire interns. To begin notice that al though both the volunteering and the internship structures par t ly overcome workers' moral hazard, they introduce another source of inefficiency because pro-ducing organizations must earn a rent i n order to be deterred from behaving opportunist i -cally. A s a result, a wedge between marginal product ion cost and price is created, and the socially opt imal amount of service is not produced. To il lustrate the welfare losses induced by these two frictions, we decompose the departure from the first best al location into two parts: one due to workers' moral hazard and one due to firms' moral hazard. The analysis is significantly aided by reference to figure (4). F i r s t , note that i n the absence of any infor-mat ional constraints the first best al location would correspond to full employment, point FB in figure (4). Let us now introduce the two frictions successively: first, we seek the point that maximizes a representative worker's expected u t i l i ty subject to worker's incen-54 tive compat ibi l i ty constraint (3.16) and the feasibility constraint (3.17) assuming away the commitment problem of firms: max (w + Bh - eh)f + (-eh)^ + w(Lm-E) (3.15) w.E 2 2 subject to: ( l - / ? 2 ) ( l + / 5 f e ^ - / ? d - ^ ) ) h ( 1 - / 3 2 ) _ h , ^ w > \ , , r J-eh + -. \ w - eh (3.16) and w < Pm(Gm)gm (3.17) T h e solution to this problem would be given by the intersection of the workers' incentive compat ib i l i ty condi t ion (3.16) and the b inding feasibility condi t ion (3.17), point P i n figure (4). Figure 3.4: Welfare Analys is The planner would increase wages un t i l there are zero profits. Note the first departure from first best: point P implies lower employment level and therefore service provision than 55 the first best, point FB. Next we add firms' b inding incentive compat ib i l i ty constraint: Trv(pm(Gm), Em) = pm(Gm)gm -w = 0 ( 0 " ) (3.18) and let the planner choose the al locat ion that would maximize a representative worker's welfare. The planner would now choose point V, the volunteering equi l ibr ium, which occurs at the intersection of (3.16) and (3.18). The fact that (3.16) is upward sloping and (3.18) is a parallel inward shift of the planner's feasibility condit ion by the vert ical distance Q(<fin) implies that point V in figure (4) w i l l occur at an even lower employment level in t roducing a second departure from first best. Therefore, the volunteering equi l ibr ium is constrained Pareto efficient, since a social planner subject to the two informational constraints could not increase the welfare of workers, but does not produce the first best amount of service gm. The same logic applies to the internship equi l ibr ium in the non-mission sector so we do not repeat it here. The above argumentation is summarized in the following proposit ion: Proposit ion 8 a) In the mission sector, the 'Volunteering' equilibrium is constrained Pareto efficient but fails to produce the optimal amount of gm. b) In the non-mission sector, the 'Internship' equilibrium is constrained Pareto efficient but fails to produce the optimal amount of gb. We next compare worker's welfare i n the mission sector when the two alternative em-ployment practices are implemented, that is, we compare the volunteering equi l ibr ium to the equi l ibr ium that would occur in the same market i f organizations instead of horizontal ly sorting workers were using the next best alternative hi r ing practice, the internal promot ion of in te rns . 3 8 Proposit ion 9 In the mission sector, if pm(Gm) > &^}~hK, for Em G (0,Lm), then an equilibrium with a volunteer-hiring structure always generates more employment and service provision than an equilibrium with interns. Moreover, workers' welfare is enhanced. Proof. P roof is i n A p p e n d i x B • In the Volunteering equi l ibr ium, higher intrinsic mot ivat ion par t ly substitutes the mon-etary compensation needed at each level of employment to sustain incentive compatible behaviour of workers. Consequently, in this s i tuat ion more matches can be supported and therefore employment and product ion i n the mission sector is enhanced. The two types of equi l ibr ia are depicted i n figure 5. Though the model presented here is too stylized to be taken as a l i teral account of the functioning of the labour market for volunteers, we believe 3 8 T h i s thought experiment would make no sense in the profit sector as in that sector workers and orga-nizations are homogeneous so the two hiring practices would yield identical equilibrium outcomes. 56 Ei Ev L Figure 3.5: Volunteering E q u i l i b r i u m (point V ) vs E q u i l i b r i u m w i t h Internships (point I) it is suggestive of the welfare benefits that the interaction between volunteering act iv i ty and nonprofit organizations can achieve. 3.5 Discussion There is ample anecdotal evidence i n the literature of the selection and sorting of managers and workers across nonprofit organizations and proprietary firms modeled i n this paper. Hansmann (1980) mentions the possibi l i ty that the nondis t r ibut ion constraint may act as a screening device that selects the type of entrepreneurs (managers) and workers who are more concerned about the quali ty of the service being provided and less interested in monetary rewards than other individuals . Weisbrod (1988) suggests that this process is indeed taking place: 'Managers, will, therefore, sort themselves, each gravitating to the types of organizations that he or she finds least restrictive-most compatible with his or her preferences. As a result, nonprofit and proprietary organizations, having different legal regulations, will attract managers with systematically different goals.' (pg 32) He also reports case studies which find that business school and law school students who subsequently enter the nonprofit sector vary substantially in terms of personality traits, values and behaviour from their colleagues preferring to pursue a career i n the for-profit sector. 57 Moreover, our model suggests that those individuals who gravitate toward the mission sector are better-off than i f they sought employment i n the non-mission sector — even i f they may have to suffer a wage penalty - because they derive intrinsic satisfaction from their work. In contrast, individuals w i t h strong monetary motivations are deterred from seeking employment in the mission sector and opt for positions i n the non-mission sector. T h i s may explain the general perception that nonprofit workers, despite being relatively poor ly compensated, enjoy high levels of job satisfaction. M i r v i s and Hackett (1983), analyzing the Qual i ty of Employment Survey report that nonprofit workers may receive lower wages and benefits than their for-profit counterparts, but are more l ikely to find the orientation of their work more important than the money they earn and to receive intrinsic rewards from doing their jobs. In a similar vein, Frank (1996) using a dataset of Corne l l graduates finds sizeable salary differentials between graduates employed i n the profit sector and the nonprofit sector, after controll ing for a r ich set of job and ind iv idua l characteristics. Though these differences admit other interpretations, they can be at t r ibuted to the self-selection of intr insical ly motivated individuals - who are wi l l ing to accept a lower wage (compensating differential) for the possibil i ty to contribute to a goal in which they find intrinsic value — into the nonprofit sector. 3.6 Conclusion This paper helps us understand a number of related observations regarding volunteer ac-t iv i ty and the sectoral concentration of nonprofit firms. B y commit t ing not to distr ibute surpluses, the nonprofit status ensures that the social mission takes precedence over the fi-nancial remuneration of any interested parties. We have shown how this commitment allows nonprofit firms alone to sustain a sector-wide incentive structure - volunteer h i r ing - which is capable of in i t ia l ly extract ing labour donations from volunteers and subsequently com-pensates them w i t h higher wages as they transi t ion to paid positions. In addit ion, we argued that volunteering facilitates the matching of workers and organizations w i t h similar mission preferences. The tighter congruence of organizations' and workers' goals i n nonprofit organi-zations offers them a competit ive advantage in mission-oriented sectors. In the non-mission oriented sector of the economy there is no scope for nonprofit organizations to be founded since the for-profit structure is preferable in that it allows the manager\owner to fully appropriate profits, whereas the nonprofit status rules out this possibility. Consequently, the simple framework developed here explains endogenously the observed dichotomy that the mission-oriented sector is associated wi th nonprofit organizations, which hire volun-teers and sort them into paid positions based on their intrinsic preferences, whereas the non-mission sector is occupied by profit taking firms which hire interns. In addit ion, our analysis suggests that this arrangement improves the provision of public goods and ser-58 vices and therefore highlights a welfare-enhancing impl ica t ion of the interaction between volunteer act ivi ty and the nonprofit ins t i tut ional form. Fina l ly , we should add that both the view that volunteering acts s imply as a screening device and/or as a form of investment in human capital , and the incentive provision (rent extraction) and matching theory we propose here lead to s imilar predictions regarding the process of volunteer engagement, which makes them empir ical ly indistinguishable. There is, however, a crucial piece of evidence which the volunteering as screening and human capital investment views cannot be reconciled wi th . 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Independent Sector, Jossey-Bass, New York . 62 Chapter 4 Prosocial Motivation and the Delivery of Social Services (with Patrick Francois)* 4.1 Introduction W h i l e the presence of nonpeeuniary motivations is considered to be an important component of human behaviour in other social sciences, the use of models i n which agents display some type of other-regarding preferences is only recently becoming common i n the economics literature. Th i s development is, at least i n part, spurred by the mount ing experimental evi-dence attesting to the usefulness of this approach i n rat ional izing many social and economic interactions such as donations of t ime and money, private provision of public goods, voting, intergenerational bequests and so on. To be sure, i n their recent and comprehensive survey of the experimental evidence, Fehr and Schmidt (2006) conclude that: 'Given this evidence the real question is no longer whether many people have other-regarding preferences, but under which conditions these preferences have important economic and social effects and what the best way to describe and model these preferences is'. Here we w i l l argue that one area they do have important economic effects is in the provision of social services, such as health care, education and research, chi ld care, care for the elderly, community development, and international aid. M a n y of these have been seen as part of the t radi t ional role of government, but this view has been increasingly challenged. Governments in many countries have moved from provider to purchaser, and have sought out greater involvement i n direct provision from the private sector. T h e arguments under lying * A version of this chapter wi l l be submitted for publication. 63 this involvement are generally sound. T h e power of incentives created by residual c la imancy in private firms creates a better environment for timely, efficient and innovative service provision. However, it w i l l be argued here that when prosocial mot ivat ion is taken into account, the recent literature looking at its effect on private provision w i l l suggest that governments (or more generally insti tutions without residual claimants, like nonprofit firms) continue to have an important role i n providing such services. In such environments, these may be the unique form of ins t i tu t ion capable of el ici t ing donations of effort that are engendered by prosocial motivations. To provide a bit of background on the motivations behind prosocial behaviour we draw on Benabou and Tiro le (2006). They argue that prosocial behaviour reflects the m i x of three underlying motivations: extrinsic, intrinsic and reputational. Ex t r ins i c mot ivat ion stems from the standard pecuniary or other mater ial rewards that an ind iv idua l may receive from outside. Broad ly speaking intrinsic mot ivat ion refers to the case where an ind iv idua l pursues actions not because of external rewards but because the act ivi ty is valuable i n its own r ight . 1 Different conceptualizations of intrinsic mot ivat ion are possible. In part icular , a dis t inct ion can be made between (a) Impure or Act ion-Or ien ted A l t r u i s m : the ind iv idua l receives a 'warm glow' from the actual act of contr ibut ing to a public good and (b) Pure or Output-Oriented A l t r u i s m : the ind iv idua l cares about the overall value of the publ ic good to which he contributes. In reality, it is l ikely that a combinat ion of these two sources of intrinsic mot ivat ion is at play. F ina l ly , intrinsic mot ivat ion should be differentiated from an instrumental a l t ruism that arises because of the concern about developing a valuable reputation i n repeated interaction settings. We focus on the manifestation of prosocial behaviour in workplace contexts that involve the provision of social services, like those above. G iven the nature of these services, workers engaged in providing them often derive direct nonpecuniary benefits because they have a genuine concern, or care, about the recipients of the service - for example the welfare of the sick, the poor, or underprivileged children - and/or by virtue of the social recognition they might receive for contr ibut ing to an important miss ion . 2 Since such intrinsic motivations seem relevant i n organizations that provide social services, it is important to understand their interaction w i t h monetary incentives and what the implicat ions are for the provision of incentives and opt imal organizational design. The classic agency-theoretic approach to addressing questions i n public sector contract-ing and procurement is p r imar i ly concerned w i t h adverse selection and moral hazard prob-lems that arise when the government wants to procure a public good or service from a 1 Accord ing to Deci (1971), cited by Frey (1997), "one is said to be intrinsically motivated to perform an activity when one receives no apparent reward except the activity i t se l f . 2 Note that besides this kind of prosocial behaviour a worker may exhibit a whole class of other-regarding behaviour, such as altruistic feelings towards his employers or co-workers. For an excellent survey of the literature concerned with such motivations, see Rotemberg (2006). 64 private firm, or regulate a private firm that directly supplies a publ ic service to consumers on behalf of the government (see for example Laffont and Ti ro le 1993). The basic problem is that the firm may have private information regarding the costs of product ion and\or its cost reducing efforts, and so the government i n its attempt to elicit t ruthful revelation of private information is faced w i t h a trade-off between provision of incentives and rent extraction. F r o m the perspective of t radi t ional agency theory, providing incentives for a public agency or a privately regulated firm to deliver a service presents the government w i t h gen-erally similar challenges. M o r e recently, attention has shifted from the distortions associated w i t h asymmetric information towards the effects of alternative ownership and organizational structures. The core problem inhib i t ing private provision here is the non-contract ibi l i ty of the output, in this case the service provided by the publ ic provider. In an environment where the quali ty of the service provided cannot be contracted upon, Har t et al . (1997) have offered insights into the specific trade-offs between government ownership and pr ivat i -zation. Our focus i n the second part of this paper is on the lessons derived from this second wave of the literature on the ins t i tu t ional structure of publ ic services delivery. We w i l l argue, i n our very selective review of this literature, that this work suggests prosociali ty of employees has important implicat ions for the delivery of public services. Prosocial i ty amounts to a statement of what enters into agents' u t i l i ty functions, and it w i l l be seen that the implicat ions for publ ic service delivery hinge on a subtle difference i n the way prosociality is modelled. Importantly, these implicat ions w i l l contrast markedly w i t h those derived from the literature that has examined the effects of ownership in environments where the contract ibi l i ty of output is the core problem. The rest of this paper is organized as follows. T h e next section introduces and discusses the two alternative ways of model l ing prosocial motivat ion: action-oriented and output-oriented al t ruism. Section 3 is concerned w i t h the implicat ions for government provision of social services from the perspective of the literature that emphasizes the noncontractible nature of output and contrasts it w i t h the implicat ions derived from the literature that emphasizes the role of intrinsic motivat ion. The last section offers some concluding remarks. 4.2 Modelling prosociality A t least implic i t ly , recent models emphasizing agent prosociali ty start from a product ion function which converts inputs of either t ime, effort, or other resources into the product ion of a good, service or ac t iv i ty about which some agents care. Something of the form: g = k(e.i....e-i,c) 65 where A; is an increasing function of efforts, ej is the effort of agent i, and also a function of c a vector of other potential inputs into this process. There are smal l differences i n how this product ion process may work that have been the focus of some papers. Outpu t may be mult i-dimensional , i.e. depend on quali ty which can be adversely affected by poor input choice, kc < 0, or multi- task a (e j , e 2 ) where e 2 , for example, does not affect g. B u t these w i l l not be the focus of this survey. The following quasi-linear u t i l i ty function for an agent i embeds, what we w i l l argue, are the main contrasting ways in which prosociali ty has been modelled to affect service provision in the literature. Agent i's ut i l i ty, U~i, is increasing in his own consumption c(yi) and decreasing in the amount of effort he expends at work, ej. Some variant of this is common to a l l papers in this literature. Authors , however, differ i n their inclusion of a possible th i rd and fourth term in this expression below. Papers that have emphasized impurely altruistic, or action-oriented, mot ivat ion include a term like the th i rd one: XJ% = c (yi) - <f> (ei) + In (e*) + 7 i (g) (4.1) If the firm is producing a good or service that the agent considers meritorious, then it is possible for the agent to obtain a benefit from effort expended at the task. Th i s is represented by the term h (ej) w i th h! > 0, over some or a l l of the range. In effect, workers contr ibut ing effort at such firms may actually enjoy contr ibut ing some of that effort, or dislike it less than i f the same efforts were expended elsewhere. A recent example of such an approach is Besley and Ghatak (2005), where the agent's identification w i t h a firm or principal 's "mission", lowers the cost of agent effort. Al ternat ive approaches have started from the assumption that a term like the fourth one i n (4.1) plays a role. Accord ing to these papers, a recent example of which is Francois (2007), agents derive a benefit directly when what they consider a socially worthwhile good or service, g, is provided. Thei r u t i l i ty is thus increasing i n the level of that good, 7^  > 0. Note that this benefit is independent of whether agent i has a hand i n producing the good or service or not; something which does not occur w i t h act ion oriented motivations. Some of the implicat ions of the two alternative conceptual views of intrinsic mot ivat ion are not hard to see. Firs t ly , free-riding. W h e n al t ruism is impure, no free-riding problem ensues as the ind iv idua l worker's intrinsic reward hinges exclusively on his own contr ibut ion to a project that has a social impact . T h i s can be conveniently used as a shortcut to study the structure of op t imal incentive contracts. O n the other hand, when a worker is purely altruistic she derives an intr insic benefit from the project being successful regardless of whether she has been actively involved in delivering it , and therefore the setting has an endemic free-riding problem. Secondly, an addi t ional moral-hazard problem may arise in purely altruist ic settings. W h e n workers care about the level of service provided, they w i l l want to ensure that their 66 efforts are contr ibut ing to that service. The provider of the service, their pr incipal , boss, owner, manager, or employer w i l l thus be able to elicit this effort that is based on care, only when they can ensure that such efforts w i l l contribute to the service of concern. M o r a l hazard problems can arise when the agent is unsure about how much extra effort contributed goes towards provision of their socially desired good. N o such problem arises i n the case of impure al t ruism. The worker knows the effort she provides, and is directly, intrinsically, rewarded for i t . 4.2.1 Impure or Action-Oriented Al truism We first consider impure al t ruism. In this case, the agent derives direct benefit from per-forming what he or she considers to be the meritorious task. Though it is presumably the effects of such actions that the agent u l t imate ly cares about, in this type of modell ing, this is assumed to affect the agent directly by lowering the cost of performing the task. T h e agent does not deliberate regarding the impact of his actions, nor does he wonder what would happen i f he were to act differently. Accord ing to this approach, the u t i l i ty function is of the following form: Ui = c(yi) - 4>{ei) + hi (e,) Besley and Gha tak (2005) are concerned wi th the implicat ions of impure a l t ru ism on the op t imal incentive contract i n a moral hazard setting. Th i s paper studies the provision of opt imal incentives i n a principal-agent model when some agents are driven by intrinsic motivations while others have conventional pecuniary motivations. In particular, the two key implicat ions of this framework are that (1) A n altruist ic worker w i l l provide more effort and (2) A n altruist ic worker requires less monetary compensation. Thus , intrinsic mot iva t ion in this case is akin to a compensating differential. Th is framework also emphasizes the role of endogenous matching of principals and agents w i t h s imilar al truist ic preferences as this can raise product iv i ty and affect the structure of compensation. Another paper i n this strand is the one by D i x i t (2005). T h i s paper features a mult iple-task environment i n which product ion entails two outcomes - a pr imary and a by-product -both of which generate nonpeeuniary rewards to the worker. T h e pr inc ipal can only reward the agent for the pr imary output since the secondary product might even be undesirable to her (for instance, the by-product might be promotion of a part icular faith). The paper provides the properties of the op t imal incentive scheme. In addi t ion to finding that the agent's intrinsic mot ivat ion substitutes for pecuniary compensation that would have to be offered in order to induce part ic ipat ion, it is shown that when the pr incipal exhibits aversion to the by-product she offers weaker marginal incentives. Tha t is, while worker's intr insic mot ivat ion may relax his par t ic ipat ion decision it does not affect the power of incentives. Corneo and R o b (2003) consider a setting where workers engage i n two tasks: an ind i -67 vidual task and a cooperative task which furnishes personal benefits but which is difficult for the pr incipal to reward because of the collective nature of the output workers contribute to. Th i s formulation is used to compare opt imal incentives i n a publ ic firm that maximizes social welfare (including workers' u t i l i ty) and a prof i t -maximizing private f irm. The analysis suggests that incentives in the private firms are stronger, but workers i n the publ ic firm provide more cooperative effort. Can ton (2005) presents a two-task two-output pr inc ipal agent model i n which one output is observable while the other is not. Some agents are intr insical ly motivated and some are not and the type is not observable by the pr incipal , so the model features an element of adverse selection. In common w i t h the two other papers above, intrinsic mot ivat ion reduces the fixed cost of meeting the agent's par t ic ipat ion constraint. In addit ion, this paper finds that i n order for the intr insical ly motivated workers to be induced to provide effort along the unobserved dimension, the power of incentives has to be moderate, a result which he interprets as high-powered incentives crowding-out intrinsic motivat ion. A related paper that focuses on issues of worker selection and screening is Delfgaauw and D u r (2007). Th is paper addresses the question of how should a firm facing a pool of workers that are heterogeneous i n terms of their intrinsic mot ivat ion opt imal ly set its compensation policy. In common w i t h the papers mentioned above, i n their formulation intrinsic mot ivat ion is also of the impurely altruist ic form as the way it enters is by affecting the cost of a worker's effort. Th is allows them to abstract from the free-riding problem that would arise i f workers were purely al truist ic. W h e n the level of intrinsic mot ivat ion is private information of the worker, then the employer faces the following trade-off i n designing the opt imal wage scheme: by increasing the wage she raises the probabi l i ty of filling the posi t ion but attracts workers w i th lower intr insic motivat ion. Th i s trade-off appears to be similar to the one in Francois (2007) but i n the latter there is also moral hazard i n product ion and this serves as an addi t ional inducement for motivated types to apply for the job i n order to deter a shirker from filling the posi t ion. In Francois (2007) a marginal increase i n the wage induces more applications from bo th shirkers and non-shirkers and whether output increases or declines depends on the relative density of the two types of workers. 3 M u r d o c k (2002) studies the role of the agent's intrinsic mot ivat ion for the investment decisions made by the firm. In this paper, the agent's effort contributes to a project that generates a financial return valuable to the firm, and a nonpecuniary return valuable to the agent. Star t ing from a posit ion where the expected intrinsic return that the agent receives is zero, the author shows that the intr insic mot ivat ion affects incentive contracts only by inducing firms to undertake investment projects w i th higher intrinsic payoffs. In part icular, the firm may impl ic i t ly agree to implement projects that have negative financial return but generate positive intrinsic value to the worker, and i n exchange the worker provides higher 3 T h i s paper is covered in the next section. 68 ex-ante effort, thus increasing the firm's expected profits. Moreover, the firm's gains from implementing such an impl ic i t contract are increasing i n the intensity of the agent's intrinsic motivat ion. The common impl ica t ion of a l l of these treatments of impure a l t ru ism is to lower the need for "power" in incentives. Th i s is akin to a compensating differential, and though it does suggest that such services may be cheaper to deliver when people have prosocial motivations, this has relatively l i t t le impact for the delivery of social services. Crowding O u t The other impl ica t ion that arises occurs when service delivery happens i n mult i task envi-ronments. The usual model l ing here treats one good as socially meritorious, and another not, w i t h the socially meritorious one more difficult to contract over. The ma in insight of these is that paying too much for the good that can be direct ly rewarded may crowd out efforts devoted to the socially meritorious good. Th i s crowding out of a l t ruism can also occur when the use of external incentives reduces or eliminates the effects of intr insic motivations. There is a large recent experimental literature documenting this phenomenon in different contexts. Th i s literature is thoroughly surveyed by Frey (1997), and Frey and Jegen (2001). Since these surveys there has been some interesting work by Benabou and Ti ro le on providing an information-based framework to formally th ink about the interplay between extrinsic and intrinsic motivations and the mechanism behind the notions of 'crowding out ' and 'crowding i n ' . 4 In Benabou and Tiro le (2003) they consider an informed pr inc ipal setting where the pr incipal has private information over the characteristics of a task and/or the agent's abi l -4 M a k r i s (2006) analyzes a principal-agent set-up that departs from the canonical adverse selection model in that the agent, besides the monetary payoff, derives direct util i ty from higher output and he is subject to an administrative constraint which gives rise to a limited liability condition. He finds that the agent's intrinsic motivation reduces the power of incentives, and that under certain conditions the principal may decide to distort the output of both the high and low-cost types, unlike the canonical model where only the high-cost's output is reduced from the efficient level. Huck et al. (2006) is concerned with the interaction between economic incentives and social norms and show that the choice of incentive structure can affect the impact that social norms have on team production. Tn this framework, social norms may be beneficial or detrimental to output depending on whether the type of compensation implemented induces positive externalities among workers (team-based incentives) or negative externalities (relative performance-based compensation), and it is possible that higher monetary incentives may reduce workers' effort. Vyrastekova et al. (2006) investigate the effect of power of incentives experimentally. In their experi-mental design, subjects repeatedly perform two tasks: one which improves their own output and another which increases the output of a teammate. Subjects are compensated based on both individual and team performance, and the power of incentives reflects the weight that the payment scheme puts on individual output. Subjects choose to join either a 'private' firm, which has a payment scheme with high weight on individual performance, or a 'public' firm which has a more low-powered incentive scheme. The experimental findings suggest that increasing the power of incentives has a negative effect on effort if the interdependency between workers is high. 69 i ty to perform it, whereas the agent cares about the outcome of the task but has imperfect self-knowledge. The pr inc ipal strategically chooses actions, rewards and punishments, i n order to incentivize the agent and to enhance his self-confidence. The agent on his part, tries to extract information from the principal 's actions about himself and about the task. They show that in situations where the asymmetry of information is important , and under certain condit ions, 5 extrinsic rewards may be detr imental to the agent's intrinsic motiva-t ion, i n that they convey bad news to the agent about the attractiveness of the task or about his own type. In a companion paper, Benabou and Ti ro le (2006) describe a different mech-anism through which crowding out may occur. They argue that the presence of extrinsic incentives crowds out reputat ional mot ivat ion by creating doubt about the extent to which a person is undertaking an action for the monetary rewards rather than for themselves. A n argument in the same vein can be found in Seabright (2005); he develops a two-period model where agents undertake an altruist ic action in the first period and are i n a second per iod assortatively matched i n a matching market. It is shown that the signall ing aspect that ensures an ind iv idua l a more desirable match may induce a higher proport ion of individuals par t ic ipat ing when rewards are zero than when rewards are positive but small . In workplace settings, the informed pr incipal mechanism of intrinsic mot ivat ion crowding out may be the most relevant. Tha t framework has a natural manager-worker interpretation: the manager may be in a better posi t ion to judge the worker's abi l i ty to perform well i n a certain task, or may be a better informed about how difficult a certain task w i l l t u rn out to be. The reputational crowding out, seems to apply to activities such as donating b lood and volunteering where the social aspect is more pronounced, but may be also suitable here, since it is plausible that workers may undertake activities in the workplace to gain social approval. In reality of course both considerations may be relevant. One of the defining characteristics of agencies producing publ ic services is the mul t i -pl ic i ty of bo th the tasks agents have to perform and the principals to which agents have to answer to (Burgess and R a t t o 2003, D i x i t 2002, W i l s o n 1989). A n interesting, i f challeng-ing, extension would be to see whether the information-related crowding-out mechanisms work i n multiple-task and mult iple-principle settings. The insights offered by the literature on crowding out of intrinsic mot ivat ion have impor-tant implicat ions for the on-going debate regarding publ ic service reform, as they indicate that the uncr i t ical in t roduct ion of high-powered incentives, which have been proven to be effective in the private sector, may backfire when workers are altruist ic. 5 T h e key condition is a 'sorting condition', which suggests that a principal must be more will ing to offer an agent rewards when he is less able or the task is more costly. 70 Motivated Bureaucracies and the Del ivery of Social Services A recent paper by Prendergast (2007) argues that the fact of members of bureaucracies and government agencies being public-spir i ted has to be taken into account when considering the various agency problems that arise i n such organizations.. Tha t paper takes the view that bureaucrats act as intermediaries between their principals and their clients. T h e issue that then arises is how to select bureaucrats such that an efficient outcome is generated. In particular, when the objectives of the pr inc ipal and the client are aligned, as is the case for example in healthcare, then efficiency requires that an altruist ic bureaucrat is chosen, that is, one who cares about the welfare of the client. O n the other hand, i n bureaucratic settings where the principal 's interests are in conflict w i th the client's, for instance i n tax authorities, then the op t imal policy is to hire a bureaucrat who is biased against the client. Th is explains why workers w i t h different attitudes are attracted to hospitals (client-friendly) than tax agencies (client-hostile). T h e next question that is addressed is whether, when a bureaucrat 's intrinsic motivat ion is not observable, self-selection w i l l lead to the efficient outcome. The analysis then suggests that this is not necessarily true, as both the most preferred and the least preferred types self-select, the latter attracted by the possibil i ty to undermine the principal 's goals. F ina l ly , another interesting impl ica t ion i n this model is a crowding out effect that emerges due to selection: higher wages induce more workers w i t h no intrinsic motivat ion to apply, which adversely affects efficiency. Leaver (2004) is also concerned w i t h bureaucratic mot ivat ion and behaviour. The paper draws attention to the fact that strong reputat ional concerns i n the presence of informed interest groups may distort bureaucratic behaviour. Another paper that is concerned w i t h the issue of worker selection i n the public sector is Delfgaauw and D u r (2006). Th i s paper assumes that the presence of workers inst i l led w i t h a publ ic service mot ivat ion gives monop-sony power to public sector employers. W h e n workers' effort is unverifiable the paper shows that unmotivated workers may be attracted and crowd-out the dedicated ones. 6 This type of treatment of prosocial mot ivat ion has profound implicat ions for the design of op t imal contracts, but says relatively l i t t le about what sort of organization should be providing the social service - a feature that w i l l be the focus of the next type of a l t ruism that we consider. 6 Another paper on public organizations is Dewatripont et al. (1999). Motivated by a number of obser-vations regarding government agencies made in Wilson (1989), they introduce multiple tasks in a standard career concerns model. This extension generates a set of interesting implications that are consistent with the motivating facts in Wilson: increasing the number of tasks reduces effort because it hinders the market's ability to draw inferences about the agent's ability, while effort is also reduced when the market is uncertain about the nature of tasks undertaken. These results suggest that hiring specialists, and setting a well defined mission enhance the productivity of the organization. 71 4.2.2 Output-Oriented Al tru i sm Output oriented (or pure) a l t ru ism has profound implicat ions for organizational design. Papers that take a purely al truist ic s tart ing point are set up something like: Ui = c{yi) - 4> (e;) + 7 i (g) g = k{ei....e-i,c) (4.2) The implicat ions for organization design were analyzed by Francois (2000). Suppose that a worker is motivated by a desire to advance a cause about which he is concerned, g, the function 7 i capturing the impact of that. However, ind iv idua l is not the only contributor to product ion of the good. The key element here is that the firm manager also controls other inputs that contribute to product ion of the social good, as per equation (4.2). These could be the hir ing of other workers, the e_i , or some other inputs like equipment or facilities. The manager observes the worker's effort before having to decide on the final level of these other inputs. T h a t paper compares the behaviour of managers who are residual claimants i n the neo-classical firm a l a A l c h i a n and Demsetz (1972), and those managers working for a government. In the private firm, the manager owns any accumulated surplus (negative or positive) from product ion. In the government, the manager has to respect a zero budget condi t ion i n planning his inputs, but has no claims on accumulated surpluses. The question it asks is which type of organization has an advantage i n el ici t ing the worker's a l t ruis t ical ly motivated contributions to the organization's output. The answer is that there exist conditions under which the worker is motivated to con-tr ibute effort because of its effect on the social good only when working for the government. Tha t is, the worker paid as a government employee can be pa id less than would have been required to compensate h i m for the disut i l i ty of effort. Or , i n other words, the worker con-tributes more effort than he would contribute i f he d id not care about the good at a l l , i.e., i f 7j (•) = 0. The reason is that he knows that by contr ibut ing this effort he is advancing the cause which he cares about, raising g: and he takes account of this when deciding on his effort level. W h y does this not happen when the same worker works for a private firm? Pure ly altruist ic people care about the output of the good they produce. They are not interested in contr ibut ing effort to such tasks only to see that their efforts imp ly that someone else who should, or could, be contr ibut ing takes the opportuni ty to do less. T h i s is the essence of the moral hazard problem that arises when the firm is run by a residual claimant. The residual claimant may care as strongly about the output of the organization as does the worker, but he also gains financially i f resources can be saved. Consequently, i f he knows he has a worker working for h i m who is wi l l ing to contribute extra effort out 72 of a direct concern for the organization's mission, he can reduce the level of some other inputs that he controls. H i s incentive to do this w i l l be greater the higher the degree of subst i tutabi l i ty between the inputs he controls and the efforts of the worker. In terms of the product ion function above, facing a higher level of ej reflecting the donation of a motivated worker, the marginal contr ibut ion of the inputs that he controls, for example the c, w i l l be lower and the residual claimant w i l l op t imal ly choose to lower these and pocket the savings provided that keiC < 0. K n o w i n g this, the intr insical ly motivated and purely altruist ic worker w i l l rat ional ly choose not to contribute extra effort in pursuit of the organization's mission. He knows that doing this merely crowds out the principal 's contr ibut ion and therefore does not affect (or affects only weakly) the organization's output. The manager in a government bureaucracy, i n contrast, has much weaker incentive to reduce his inputs when faced w i t h extra contributions from a motivated worker. He does not c la im any of the outstanding residual from the department's operations. Consequently, when faced wi th the labour donation of a motivated worker, even though the marginal contr ibut ion of the inputs he controls is reduced, he s t i l l has incentive to use these i n product ion of the good about which he cares. Importantly, his level of direct concern for the firm's output need be no different than that of a for-profit owner. It is s imply that, due to the nature of government provision through bureaucracies, he is directly divorced from a c la im on the operating profits of the product ion unit . He thus can credibly commit to having much weaker incentives to reduce his own inputs ex post. So, the upshot of this story is that a government bureaucracy, which, i n contrast to the high powered incentives buil t in by residual c laimancy in a private firm, has lower powered incentives for operating managers, can obtain labour donations due to the service mot ivat ion of their employees in some situations where a private firm could not. However, as always, this simple story becomes more complicated when we consider its details more deeply. Specifically, we have assumed i n the discussion above that only the relationship between the agent (worker i n the organization) and his boss, who is either the manager in a government bureaucracy, or the residual claimant i n a private firm, is what matters. It has been impl ic i t ly assumed that the organization is rewarded for changes in output by some sort of price for the service. B u t overseeing this whole process is a government, who chooses whether to contract this process of service provision out to the private firm, or to produce it i n house wi th a bureaucracy. It is not clear whether a government purchasing the service could alter the price schedule faced by the private firm so as to help it overcome the credibi l i ty problem that it faces w i t h its employees. Francois (2000) shows that even al lowing for the government to use any sort of unrestricted non-linear pr ic ing schedule it wants, it w i l l not generally be able to undo the problem of credibi l i ty faced by the residual claimant in the private firm. The opt imal pr ic ing schedule for the service w i l l always allow greater potential for labour donations by the motivated bureaucratic worker 73 than it does by the worker in a private for-profit enterprise providing the same service. Another potential way for private firms to overcome this problem is for them to develop a reputation for al lowing their own workers' extra contributions to have an impact . If the problem that private firm owners face is that they have an incentive to distort downwards their input contributions in light of extra effort from their motivated workers, then a firm would have a financial incentive to develop a reputat ion for not doing this. Th i s is explored in Francois (2001). Such a reputat ion would work as follows. The firm is known to not reduce inputs when workers contribute extra to the firm's tasks. Consequently, workers know that when doing so, they w i l l not be expropriated ex post by the firm reducing other inputs and thus keeping the service unadjusted. If the firm were to deviate from doing this, its reputation would be tarnished, and future workers would not donate effort to its service. Consequently, the quali ty of its output would fall, and it would suffer a loss i n value. W i t h such a reputat ion of non-interference i n place, the private firm would be able to elicit labour donations from workers, as the workers would not fear being expropriated ex post. T h i s should imp ly that any worker who was wi l l ing to contribute extra effort to the government bureaucracy should also be able to do the same to the private firm. Though the reasoning here is sound, this means of solving the credibi l i ty problem re-quires some operating profit to accrue to the private firm. In a repeated game context, it is the operating profit that provides the private firm wi th the incentive to not deviate and expropriate the workers' labour donations ex post. These profits must be positive for it to remain worthwhile for the firm to mainta in their reputat ion of non-expropriation. In contrast, the government bureaucracy can obtain labour donations even when its operating surplus is zero. Opera t ing surpluses play no role in discipl ining the government bureaucrat. Consequently, in this repeated game setting where reputations can be developed to mit igate moral hazard problems, though both a government bureaucracy and a private firm can op-erate i n a way that allows bo th to equally obtain labour donations due to purely motivated workers, the private firm has to also obtain positive profit from per period operations. The bureaucracy does not require this, and consequently, should be able to produce at a cost which is lower than the private firm. A g a i n , the bureaucracy, or equivalently a nonprofit entity w i l l perform better than an organization wi th a residual claimant, i.e., the private firm. F ina l ly , there is a free-riding problem impl ic i t i n this discussion that has been skir ted so far. If workers are concerned about the actual output of an organization - irrespective of their own efforts - then the labour donation game resembles a standard private provision of public good problem, w i t h free-riding a key characterist ic. 7 The worker benefits by donat ing labour to a task about which she cares, however she would benefit s t i l l more if someone else 7 Labour donations in this context refer to the circumstance where the worker contributes effort that is not fully compensated by the wage payments he receives. 74 were to undertake the donation for her. A first possibil i ty of solving this problem, identified by Francois (2000, 2003), is when rents accrue to workers so that par t ic ipat ion constraints are not binding. Such a s i tuat ion occurs in the standard agency problem wi th private information. It also occurs when firms use relational contracts to solve moral hazard problems. In that case, the firm implements an efficiency wage type of incentive structure that is able to both overcome moral hazard i n product ion as well as elicit labour donations. B y offering the worker a payment above oppor-tuni ty costs i n order to induce incentive compatible effort provision, workers' par t ic ipat ion is ensured and hence the free-riding problem does not arise. T h i s way of overcoming the free-riding problem applies whenever informational rents imply non-binding par t ic ipat ion constraints; as often arise i n more standard agency problems w i t h heterogeneous types. A second way to overcome the free-riding problem i n the labour donations game is ex-plored i n Francois (2007). Th i s paper is concerned w i t h the par t ic ipat ion decision - not the incentive problem - and so heterogeneity i n workers' evaluation of the publ ic good is intro-duced. In part icular, it is demonstrated that when firms do not use performance-contingent compensation, and the possibil i ty of workers' shirking looms, those workers w i t h high valu-ation of the publ ic good may be motivated to donate labour effort to obviate the outcome where a low valuat ion type takes the job and shirks thereby adversely affecting output. Moreover, the elasticity of output w i t h respect to wages may be negative. T h i s result may be given a crowding out of intrinsic mot ivat ion interpretation: the use of monetary rewards contingent on performance accompanied by the use of direct supervision at the workplace may lead to crowding out of labour donations. The logic of this argument is s imilar to the one made i n Engers and Gans (1998), who also examine a purely altruist ic setting where there are incentives to provide effort when care for output is a central consideration. The outcome of interest in their context is the quali ty of academic journals and their paper provides an explanation for why not paying referees may be editors' op t imal response. W h e n deciding whether to agree to review a paper a referee compares the private cost that he would incur if he decided to referee the paper to the expected delay imposed on the journa l i f he refused. W h i l e adding a monetary payoff would increase a referee's private gain from refereeing a paper it also reduces the cost of refusing because the monetary payoff would increase the acceptance rate. Note, however, that in this setting the free-riding problem is par t ly overcome by the editor sequentially solici t ing referees' services whereas i n the context of labour markets workers usually apply for positions voluntarily, so there is an addi t ional layer to the free-riding problem. In other words, in labour markets the pool of applicants is endogenous, whereas in the context of the refereeing process the pool of referees is fixed and the editor chooses sequentially among them. M a n y other papers have considered purely altruist ic agents i n this context. Grou t and 75 Schnedler (2006) extend the analysis i n Francois (2000) by introducing a th i rd party - be-sides the worker and the manager - who has an interest i n the service being produced and who is wi l l ing to contribute something (money or some other input) toward its provision. They show that the worker's labour donation is sensitive to the other contributor 's nego-t ia t ing power and that this effect may be discontinuous - a slight increase in power may crowd-out donated labour dramatically. Th is suggests that i f the purchaser of the final service is for example a monopsonist, this may adversely affect the workers' willingness to donate labour as they recognize that were they to donate labour the monopsonist would adjust downward its own contr ibut ion, in a s imilar way as a for-profit employer adjusts i n Francois (2000). Other papers that are concerned w i t h the role of firm commitment in inducing donations are Bi lodeau and Sl iv insk i (1998) and Glazer (1998) - monetary donations i n the first case and labour donations in the second. The first paper presents a multistage game i n which an entrepreneur first decides whether to set up a for-profit or nonprofit firm in order to produce a public good and subsequently solicits voluntary contributions by others. It is shown that by commit t ing not to appropriate the funds donated by the community, the nonprofit entrepreneur attracts more contributions, and so the value of the public good is enhanced. Glazer (2004) analyzes a setting i n which a good is produced using a technology that combines capi tal provided by an employer and a worker's labour effort. Importantly, the good being produced is of intrinsic value for the worker. It is shown that if the employer can commit to a level of capi tal and not adjust after observing worker's effort she can induce the worker to increase effort. T h i s result is given the interpretation that government provision of certain goods may be socially preferable because the public sector is slower to react than the private sector. The paper by Rowat and Seabright (2006) is concerned w i t h a id agencies and addresses the question of whether intr insical ly motivated workers, wi l l ing to take wage discounts i n order to contribute to a cause they care about, act as a signal to donors that their funds w i l l be devoted to the cause and not be appropriated. In part icular, the employment of al truist ic workers is viewed as a commitment device against opportunist ic behaviour by the managers of development agencies, because a motivated aid worker would only accept a wage cut i f the organization were indeed undertaking the promised a id projects. Vlassopoulos (2006b) provides an explanation for the observation that nonprofit em-ployers are uniquely able to attract volunteer workers who are bo th intr insical ly motivated and have career aspirations, and also accounts for the fact that nonprofits are concen-trated in mission-oriented sectors. T h a t paper shows that the choice of organizational form (for-profit or nonprofit) and sector (mission sector or non-mission sector) jo in t ly impinge on the credibi l i ty of the promises that managers make when impl ic i t ly contracting w i t h workers\volunteers. To gain some in tu i t ion for this, consider the form that the relational 76 contract between employers and volunteers takes: a volunteer agrees to donate labour i n return for a promise of future compensation that comes i n the form of pa id employment - not necessarily at the employer where volunteering took place. So a firm that wants to participate i n the volunteer-hiring structure has to credibly commit to having bo th pa id work and unpaid work positions and to fil l pa id work vacancies drawing from the pool of workers w i t h volunteer experience - much like actual volunteering occurs i n the real world . Notice, that this structure induces a moral hazard problem on the part of employers, as they have an incentive to recruit unpaid workers, promising them promotion to pa id positions, and then renege on the promise. The analysis suggests that whether nonprofit employers are at an advantage in terms of being able to sustain volunteer h i r ing hinges on the type of act ivi ty (mission-oriented or not) that is undertaken. In particular, if volunteering enhances the quali ty of the service provided and managers care about quali ty - which can only be true in care-related activities, then nonprofit status is helpful in solving employers' moral hazard problem. The in tu i t ion is that a nonprofit manager w i l l put relatively more weight on the fact that i f she cheats on volunteers quali ty w i l l suffer and hence a smaller profit (reputational rent) is needed to mainta in incentive compatibi l i ty. T h i s is true even though the nonpeeuniary payoff a manager receives is the same regardless of firm type. Delfgaauw (2007) is a fascinating exploration of the implicat ions of pure a l t ru ism on the delivery of medical services. He starts from the assumption that some physicians care to deliver medical quali ty provision to patients. They can choose between working in the publ ic health providing service, or private practice. In private practice quali ty can be contracted over and paid for. Patients differ in their demand for quality, w i th the r ich, having higher demand for quality, but due to quasi-concavity of preferences, lower valuat ion of marginal increases i n quality. In public health provision, there is a lower level of quali ty which must be provided, and for which physicians w i l l be paid. A n y extra provision of quali ty above that is unpaid. There are two sorts of physicians - the pure altruists, who care about patient quali ty of service as well as their own income and effort, and purely selfish doctors who only care about income and effort. Since purely altruistic, the physicians care not just about delivering services, but about what their efforts do to raise the level of provision above what a patient would otherwise obtain. In general they would voluntar i ly provide more than the non-altruistic physicians. He assumes that the number of places available i n the publ ic service exceeds the number of al truist ic physicians. Consequently, i n equi l ibr ium, altruist ic physicians correctly conjecture that i f they tu rn away a public patient, or if they work i n the private sector, then one less patient w i l l receive the extra treatment that an altruist provides. Consequently, the altruist 's actions have impact , and this leads them to want to work i n the public sector. Th i s ends up leading to selection of the altruist ic physicians into the public sector as well as the poor patients there. The richer ones select into the private sector and are treated by the doctors who only care about money. Interestingly the 77 mixed equi l ibr ium w i t h some publ ic and private provision Pareto dominates either a fully privatized or fully public provision. 4.3 Implications for Government Provision M a n y papers have explored implicat ions for the op t imal inst i tut ional arrangement for the provision of public goods and services, without any reference to intrinsic motivat ion. We briefly survey that work highl ight ing its main conclusions, and then contrast it w i t h the implicat ions derived from the recent work emphasizing prosocial motivat ion. M u c h of this recent work covers topics such as in-house government provision versus pr ivat izat ion or outsourcing, public versus private ownership of public goods, and comparative ins t i tu t ional analysis (for-profit vs. nonprofit, public-private partnerships, corporate social responsibil-i ty) . 4.3.1 Insights from Standard Agency Models A natural point to start an overview of this growing literature on these issues is the seminal paper by Har t , Shleifer and V i s h n y (1997) (henceforth, H S V ) , which has spawned a lot of the recent research into this area. T h i s paper analyzes the relative merits of providing a public service in-house versus contracting out to the private sector, adopting an incomplete contracts approach, following the earlier work by Grossman and Har t (1986) and Har t and Moore (1990) on the property rights theory of the firm. T h e incomplete contracts framework seems appropriate i n the context of publ ic goods and services that the government either produces or procures, since not a l l aspects of such services that a benevolent government may care about seem to be codifiable into a contract. In such an environment, the residual rights of control are crucial i n determining agents' investment incentives, i n particular, their decisions to improve quali ty and reduce costs. The upshot of the analysis of the model is that private ownership leads to excessive investment in cost reduction and insufficient i n -vestment in quali ty improvement, whereas, government provision leads to less than efficient cost reduction and quali ty improvement. The in tu i t ion for this is that a private manager w i t h residuals rights has stronger incentives to reduce costs and improve quality, while a government employee faces weaker incentives as he benefits less from these improvements. Thus, private provision is preferable the more important cost reduction is and the less important are the adverse effects on quality. O n the other hand, publ ic provision dominates when qual i ty is a more important aspect than cost considerations. Th i s insight is then used to guide a discussion of the wisdom of the pr ivat izat ion of various activities such as pris-ons, garbage collection, education and health. In some cases, the authors are unequivocal about the superiority of the private sector (garbage collection, weapons procurement), or the government (foreign pol icy) , whereas for a whole range of other activities (education, 78 healthcare) things are less clear-cut so they admit that a more detailed cost-benefit analysis is required. Har t (2003) uses the H S V framework to understand the benefits and costs of public-private partnerships ( P P P s ) , that have been widely used for publ ic service provision. T h e key characteristic of P P P s that this paper focuses on is the bundl ing of the bui ld ing and the running of the facility, as opposed to conventional procurement where the builder and the party who operates the facility are two separate entities. T w o kinds of investment can be undertaken both of which reduce operating costs but only one of which generates social benefits. The trade-off between unbundl ing and bundl ing is the following: under unbundling, the builder does not undertake either type of investment, since he does not benefit from improvements that take effect at the operation stage. In contrast, under bundl ing or P P P , the builder does some of the productive investment, al though s t i l l less than the efficient level, but also more of the unproductive investment. T h e impl ica t ion of this is that bundl ing of bui ld ing and management is preferable when investment in the productive component is a serious issue, or in different terms, when it is easier to write contracts on service provision than on bui ld ing provision. T h e same question is also addressed by Bennett and Iossa (2006) who extend the analysis i n Har t (2003) assuming that there is renegotiation after investment decisions are sunk, so that ownership matters because it affects the disagreement payoffs of the parties and hence their shares of the surplus and investment incentives, and that there may be externalities, positive or negative, between the cost reducing activities undertaken at the bui ld ing stage and those at the adminis t ra t ion stage. Natural ly , when there is a positive externality bundl ing of the two activities is preferred since it allows for the internalizat ion of the externality. W i t h respect to ownership, Bennett and Iossa (2006) find that private ownership by a consort ium may or may not be opt imal , for reasons similar to those identified in H S V . In a related paper, Bennett and Iossa (2005) study the desirabil i ty of for-profit versus nonprofit firms as contractors of public services both under P P P s and standard procurement. Besley and Ghatak (2001) extend H S V into a setting where the service being produced has the features of a public good. The i r analysis applies to the question of who should be the owner of joint publ ic projects that require investment contributions from both the government and private organizations, such as N G O s . T h e y show that ownership should reside w i t h the party that cares the most about the public good, which is i n contrast w i t h the result i n H S V where the op t imal ownership is driven by technological factors. Glaeser and Shleifer (2001) apply the H S V framework to understand the entrepreneurial choice between setting up a proprietary firm or a nonprofit organization. The approach is motivated by the contractual failures theory of Hansmann (1980), who had earlier suggested that nonprofit organizations emerge as a remedy to informational problems that pervade markets where quali ty is hard to measure, so that consumers are subject to producers ' 79 moral ly hazardous behaviour, as the commitment not to pursue profits signals greater con-cern over quality. In Glaeser and Shleifer's formalizat ion of this idea, an entrepreneur chooses organizational form (for-profit or nonprofit) to deliver a unit of a good whose quali ty is not contractible. B y choosing to incorporate as a nonprofit the entrepreneur's incentives are blunted - because the nondis t r ibut ion constraint permits only in -k ind con-sumpt ion of residual earnings, making those earnings less valuable to the entrepreneur than they would be under for-profit status - and hence he commands a higher price i n the marketplace. Thus, the trade-off associated wi th the choice of organizational form is that choosing to organize as nonprofit implies that the entrepreneur can charge a higher price but on the other hand it gives h i m only restricted access to the firm's profits. T h e model thus predicts that nonprofits w i l l dominate markets where the costs of moni tor ing quali ty are high, which seems consistent, as nonprofits and governments are heavily involved i n the provision of services - and services are difficult to contract over. These models also predict government and nonprofit provision where consumers' taste for noncontractible quali ty is high, so that the first effect w i l l dominate. Thus, along the "Contrac t ib i l i ty" dimension the predictions of contracting-based expla-nations do quite well as the figure below illustrates. Location of Non-profits And Govt. Provision According to Contractual Failure Hypothesis Low Contractability High e-g. Services Figure 4.1: Predict ions of Contrac tual Failure Approach 80 B u t having a firm without residual claimant is not the only way to solve such problems. Reputa t ion is an alternative mechanism that can deter opportunist ic behaviour that arises because quali ty is not-contractible. Vlassopoulos (2006a) asks the question of whether the predictions of the contractual failures hypothesis are robust in a setting where firms and consumers interact repeatedly, in order to study the effect of reputat ional concerns. T h e analysis suggests that when the manager can establish a credible reputat ion for high quali ty then for-profit status is preferable for a l l levels of consumer sensitivity to quality, which may explain why so many fields that are subject to contractual difficulties (e.g. business consulting, insurance, professional services etc.) are dominated by for-profit firms which have created and maintained valuable reputations for high qual i ty services. Thus, this paper points to a potential shortcoming of a rat ional izat ion of nonprofit organizations based on contractual failures i n the output market - it does not take into account the interaction between organizational form and reputations. O f independent interest is the paper by Acemoglu et al . (2006), which provides a different, incentive-based perspective on the op t imal al location of economic act ivi ty between markets, firms and governments. T h e y present a mult i task career concerns model where a worker can choose two types of effort: one which is socially productive and one which is not. Thus, in this setting high-powered incentives have both benefits and costs, and the relative importance of the two types of effort determines what is the op t imal power of incentives and whether markets, firms or the government are the best way to organize the product ion of a given activity. In part icular, the analysis suggests that activities where productive effort is important should be left for market environments which breed high-powered incentives, whereas as the negative impact of the unproductive action becomes more severe, the act ivi ty should gradually shift toward firms, and the government, which entail progressively du l l the power of incentives provided to workers. F ina l ly , Besley and Ghatak (2006) study the feasibility of corporate social responsibili ty ( C S R ) as a mechanism to deliver public goods that are bundled w i t h product ion of private goods - for example, fairtrade, i.e. goods that meet certain environmental or ethical stan-dards. The economy consists of two sets of consumers: those who care about the public good and those who do not. In the equi l ibr ium characterized, consumers sort according to their preferences: the caring ones choose to patronage firms that promise to deliver a certain level of public good alongside the private good - and pay a price premium, while the non-caring ones purchase the private good from firms producing at marginal cost. In this framework, firms serving the caring consumers are interpreted as exercising C S R . The analysis then suggests that C S R can sustain a level of public good provision that is equivalent to the private contributions game. Moreover, comparing public good provision delivered through this mechanism w i t h that provided by nonprofit organizations reveals that C S R may be superior in activities where the public good is technologically bundled w i t h the product ion 81 of a private good, but not more generally. 4.3.2 Contrasting Implications from Prosocial Motivation Approaches The contract ibi l i ty of output, which, we argued above, plays a key role i n the more standard agency based approaches to the issue of government provision, is not of direct importance i n the literature that has emphasized prosocial motivations. To be sure, non-contract ibi l i ty does play some role, but it is not over output as much as it is over agents' actions. Specifi-cally, i f it is the case that a worker w i l l only contribute effort to a service when they are sure that their efforts direct ly impact that service, then the worker effectively wants a guarantee that some other actions which the principle controls w i l l not be adjusted downwards i n the light of her extra contributions. Th i s sort of guarantee w i l l be impossible for the principle to provide whenever it is not possible to contract over inputs directly. B u t difficulty in contracting over inputs is l ikely to be ubiquitous in most product ion pro-cesses, and so does not suggest where nonprofit or government provision should dominate. In understanding the dis t inct ion between explanations based on prosocial mot ivat ion and those based on t radi t ional agency theory, it is useful to consider the differences suggested by the theories. A s explained above, t radi t ional agency theory suggests that nonprofits and governments should have an advantage in areas where output is difficult to contract over. It is the case that these organizations typical ly provide services, which are difficult to contract over. However, there are many services where provision is entirely by private firms: for example, management consultancy, cleaning, accounting, marketing. Pr ivate firms and markets are somehow able to adequately provide these. A n d , as Vlassopoulos (2006a) has argued, there is no reason that standard reputation based solutions cannot allow for-profit firms to dominate these sectors. So, standard agency based explanations based on the non-contract ibi l i ty of output have trouble explaining why non-contract ibi l i ty can be overcome for some services but not for those provided by governments and nonprofits. Secondly, when one considers the types of services that nonprofits do provide, a definite pattern emerges. Nonprofit firms are heavily over-represented i n sectors where th i rd parties are l ikely to have some interest or concern over the qual i ty of service provided. Chi ldcare , for example, is typical ly a transaction between childcare provider and parent, but even disinterested th i rd parties who do not have direct acquaintance w i t h the chi ld , may have a civic minded interest i n seeing that the care is properly provided. It is unlikely that th i rd parties w i l l take a similar interest in the provision of services that are typical ly transacted between firms and private providers — like, for example, management consultancy. Th i s reasoning suggests that there is another important dimension along which there seems to be a marked separation between for-profit firms on one hand and government and nonprofit providers on the other: the "care" dimension, that is, the degree to which 82 the provision of the service is associated w i t h external benefits to non-purchasers (workers, managers, donors, community) . A t the low-care end we find services such as business consultancy, which do not generate external rewards to non-recipients of the service. A t the high-care end we find social and personal services such as chi ld care, which do. W i t h respect to the "care" dimension then, the contractual failure approach does less well . Nonprofit firms and the goverment seem to be concentrated at the high-care end while for-profit firms dominate the low-care end, a fact which this theory cannot explain. Location of Non-profits And Govt. Provision According to Contractual Failure Hypothesis Low Contractability High e.g. Services Figure 4.2: A d d i n g "Care" Dimension O n the contrary, the predictions of prosocial mot ivat ion approaches seem to do better along this dimension, since they emphasize the care of a not direct ly concerned part icipant, i.e., the provider, who w i l l most generally be a nonprofit or government employee, and therefore predict that governments and nonprofits should be over-represented i n care-based sectors, as the figure below illustrates. 4.3.3 E m p i r i c a l E v i d e n c e There is a relatively large body of li terature on P u b l i c Service M o t i v a t i o n - its prevalence and effect - in the public sector. The first study emphasizing this seems to be Per ry and Wise (1990), and a number of authors have tested the implicat ions of such a mot ivat ion for performance i n the public sector, see for example Alonso and Lewis (2001) and the references therein. Murn ighan and K i m (1993) for a specific focus on non-economic factors mot ivat ing High e.g. Health, Childcare, aged care Care Related Low e-g-Accounting, consulting, managerial 83 High e.g. Health, Childcare, aged care Location of N P O and Govt. Provision according to labour donations hypothesis Care Related Low e-g-Accounting, consulting, managerial Low e-g-Services Contractability High Figure 4.3: Predict ions of Prosocia l M o t i v a t i o n Approaches people to volunteer, and Mench ik and Weisbrod (1987) for an early economic analysis of voluntarism. Segal and Weisbrod (2002) provide a recent investigation of volunteer contributions and their variat ion w i t h observable ind iv idua l characteristics. Some suggestive evidence of the higher civic-mindness of nonprofit employees can be found in Roto lo and W i l s o n (2004). Us ing data from the Current Popula t ion Survey, they report significant differences in workers' propensity to undertake volunteer work across sectors, w i t h workers i n the private sector being less l ikely to volunteer, and those who do volunteer contribute less hours than workers in the nonprofit sector and the government. M i r v i s and Hackett (1983), analyzing the U S Qual i ty of Employment Survey find that nonprofit workers report higher levels of intrinsic motivat ion, feelings of accomplishment, and importance of work relative to money i n their occupations. A l so , a Brookings Inst i tut ion Survey of over 1200 childcare, chi ld welfare, youth services, juvenile justice, and employment and t ra ining workers found that the surveyed workers report that they took the work because they are driven by the desire to help the people i n need and serve the community, though they are not satisfied w i t h the monetary rewards. 8 There is also some empir ical evidence in support of the idea that workers in nonprofit firms should be wi l l ing to donate effort while their for-profit counterparts should not. M o -can and Tek in (2000) provide a direct test of the labour donations hypothesis. Us ing an 8See Table 4, pg 17 in Light (2003). 84 unusually detailed worker / f i rm matched data set for the U S childcare sector and control-l ing for the endogenous selection into sectors, found a significant nonprofit wage premium. Workers were asked what the ma in reason to choose employment i n chi ld care was. One of the options was "this is an important job that someone needs to do", which is an indicator of the intrinsic value the worker derives from working i n the sector. To be consistent w i t h labour donations workers who chose this option should receive lower wages. T h e authors report that this variable had a significant downward effect on wages i f working for a non-profit firm. In contrast, workers i n for-profit firms who chose this opt ion had either no, or a positive wage premium, suggesting no labour donations. There is also some evidence that incentives in nonprofit organizations and the govern-ment are weak relative to those in the private sector and that in sectors where for-profit and nonprofit establishments co-exist the former tend to use more performance related compen-sation. Burgess and Metcalfe (1999) using B r i t i s h cross-sectional establishment data from 1990 find that establishments in the publ ic sector are less l ikely to operate an incentive scheme than comparable ones i n the private sector, and that this difference arises only amongst non-manual workers (workers more l ikely to be involved i n discretionary prac-tices). R o o m k i n and Weisbrod (1999) find greater use of performance related compensation in for-profit than nonprofit hospitals amongst top managerial positions. F ina l ly , DeVaro and Brookshire (2007) using a U S cross-sectional employer telephone survey (1992-1995) find evidence that, relative to for-profit employers, nonprofit employers are less l ikely to use promot ion as incentive device, that promotions are less l ikely to be based on merit and job performance, and that nonprofits are less l ikely to use incentive contracting - output contingent payment or bonuses. These differences are most pronounced amongst the high skil led workers who are most l ikely to have significant effects on firms' missions. 4.4 Conclusions This survey has argued that prosocial motivat ion has effects on the delivery of publ ic ser-vices. A slight difference i n the way the mot ivat ion is modelled, whether as impurely, or purely altruistic, has large implicat ions for service delivery. Mos t of the literature has mod-elled a type of impure a l t ruism which is action, not output, oriented. W h e n this is present, workers w i l l work for less than otherwise, and when workers have mult iple tasks, the pres-ence of such motivations can make it better for firms to use low powered incentives. There are no implicat ions for the type of organization that should be delivering the service. W h e n workers are motivated by pure al t ruism, or direct output considerations, things are very different. The main impl ica t ion is that it may be better to have the actual ser-vice delivery undertaken by an organization that does not have a residual claimant. A government bureaucracy, or a nonprofit firm, can have a distinct advantage i n delivering 85 the service. Such an organization may be uniquely placed to obtain donations of labour effort from output oriented employees because these employees w i l l not fear that their effort donations are expropriated by a residual claimant. Th i s literature would seem part icular ly important i n informing governments as to presently poorly understood benefits of service provision by governments in-house. In many countries, governments have moved away from their t radi t ional ly direct role of providers of public and socially meritorious services, to purchasing them. Some have suggested handing over, en masse, bureaucratic service provision to contractors from the private sector i n a wide va-riety of sectors. Th i s is for the well known incentive reasons that such contractors have as residual claimants. The present survey argues that the government as a provider may s t i l l have an important role. Th i s w i l l be especially the case where the choice is between government bureaucratic provision and for-profit firms, i.e., where nonprofit firms are not able to play a part. B u t we are far from a good understanding of the empir ical significance of these consid-erations. A s this survey has argued, subtle differences i n the way that prosocial mot ivat ion arises can have profound implicat ions for who should be providing social services. D a t a are needed to direct ly test this. A t a theoretical level, the difference between government and nonprofits as providers of services is not well understood. The present survey has treated them much the same, as both do not have residual claimants but there are clearly other differences which need to be better understood. 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T h i s thesis takes a few steps towards a better understanding of what ins t i tut ional arrangements have a compara-tive advantage i n the provision of these services. Our start ing point is the realization that recent years have witnessed an expansion in the involvement of the private nonprofit sector in the delivery of public services, i n bo th advanced and developing countries. In part icular , nonprofit organizations are playing an important role i n delivering public services - often in partnership w i t h the government - i n developed countries, whereas i n the developing world the recent trend is for the state to delegate a large responsibili ty of carrying out social and development projects to non-governmental organizations ( N G O s ) . Despite these developments, the economics literature has not devoted enough attention i n identifying the relevant tradeoffs associated w i t h delegating responsibili ty for the delivery of publ ic services to alternative private providers (for-profit, nonprofit), and this thesis attempts to make a contr ibut ion towards this end. The approach in the first two substantive chapters is p r imar i ly positive: we are con-cerned w i t h the fundamental question of what are the economic mechanisms that lead to the emergence of nonprofit firms and the a im is to identify conditions under which this organizational form is more l ikely to prevail . These chapters share a common perspec-tive: the choice of organizational form is made by rat ional entrepreneurs who take into account the benefits and costs associated w i t h this choice. Chapter 2, investigates whether entrepreneurs choose nonprofit status as a commitment device in those markets that are characterized by contractual failures i n the producer\consumer relationship, a hypothesis which has been rather influential in the economics literature. T h e answer that emerges from the analysis i n that chapter is that when a reputat ion for honest behaviour can be sustained then nonprofit status is not necessary nor opt imal , which suggests that explanations based on contractual failures i n the product market have less explanatory power than previously 92 thought. In chapter 3, the nonprofit commitment was shown to be valuable i n terms of giving those entrepreneurs who choose this form unique access to the pool of volunteer labour. Importantly, this commitment was shown to be effective only in sectors producing goods and services that entrepreneurs consider meritorious. Thus, this chapter provides a the-ory that is able to simultaneously explain two key features of the nonprofit sector: the reliance on volunteers, and the focus i n the delivery of care-related activities. A l so , this chapter highlighted the welfare gains that are achieved when nonprofit organizations use a hir ing structure which allows them to hire volunteers and subsequently sort them into pa id positions across firms i n the sector, based on their mission preferences. Though the models developed in these two chapters are too simple and abstract to pro-vide detailed policy recommendations, they could cast some light on the ongoing pol icy debate as to whether the government should subsidize only nonprofit providers i n mixed sectors, such as chi ld care. In light of chapter 2, the effectiveness of subsidy policies that discriminate against for-profit providers, on the basis that they are untrustworthy to pro-vide high quali ty care, seems questionable. The model considered there demonstrates that reputations can provide enough incentives for prof i t -maximizing entrepreneurs to offer h igh quali ty services when the playing field is leveled. There may be a number of good rea-sons why governments should subsidize nonprofits but our analysis suggests that, in many sectors, overcoming contractual failures is not one of them. O n the other hand, chapter 3 points to the desirabil i ty of subsidizing volunteer h i r ing nonprofits, as a mechanism to enhance employment and service provision. In future work, the framework developed i n this chapter could be used to investigate i n greater detail what tax-subsidy policy would improve employment and welfare. Another theme of this thesis is that understanding the workings of public goods produc-ing organizations requires the recognition that the broader group of stakeholders involved - donors, workers, volunteers, managers - are not s t r ic t ly self-interested, but may have other-regarding preferences. Recognizing this possibility, opens the door to a whole range of interesting issues regarding the selection of intr insical ly motivated managers and work-ers and of the provision of incentives i n organizations employing al truist ic agents that are surveyed in chapter 4 of this thesis. In part icular, the ma in message of this chapter is that prosociali ty of employees has important implicat ions for the delivery of public services, as it not only affects the structure of op t imal incentives but it also provides an efficiency ra-tionale for why publ ic service delivery should be undertaken by organizations that do not have a residual claimant - a government bureaucracy or a non-profit firm - by vir tue of their unique abi l i ty to harness workers' intr insical ly motivated efforts. Crucia l ly , this last impl ica t ion is shown to hinge on a subtle dis t inct ion i n the source of prosocial mot ivat ion -whether it is action or output-oriented. The more systematic collection of micro-based data 93 on organizations delivering publ ic services w i l l be very valuable i n der iving further insights as to the relative roles of the alternative views of prosocial motivat ion. M u c h more remains to be done i n developing theoretical and empir ical implicat ions of alternative inst i tut ional arrangements for the provision of publ ic goods and services. For instance, this thesis has drawn a strict line between for-profits and nonprofits, whereas i n reality this dichotomy is becoming less stark as hybr id organizations that combine resources from the two sectors are engaging i n mission-related activities. The potential merits and pitfalls of these partnerships have not been scrutinized yet. A l so , there are various issues of pol i t ica l economy and accountabil i ty that this thesis has not touched, which are important i n understanding the nature of the interaction between the government and nonprofit orga-nizations. F ina l ly , it remains to be seen whether and how addit ional behavioural elements, such as concerns w i t h fairness and identity, which are being integrated into economic anal-ysis, w i l l interact w i t h the issue of organizational form, which has been the focus of this thesis. We regard a l l of these areas as important ones for future research. 94 Appendix A Omitted Proofs: Chapter 2 P r o o f of L e m m a 1: F i r s t we establish that Uj(0) > C/ n(g*(0)). To see this, note that Un(q*(0)) =S(z- c(g*(0))) - b(q- q*(0)), while Uf(0) = z - c(qf) - b(q- q°f), so U}(0) > Un(q*n(0)) iff z - c(qf) - b(q- qj) > 5 (z - c(g*(0))) - b(q- q*n(0)) ^ bqj - c(qf) + (1 -5)z > bq*(0) - c(q*(0)). The last inequality is true because bqj — c(qsf) > bq*(0) — c(g*(0)) since: i^qj = argmax[bq — c(q)]| . A l so , C/ n(g*(m*)) > Uj(m*). To see this, recall that Uf(m*) = U°{m*), and that <7n(<?;(m)) > U*(m) V m 6 [0,m]. Note that which implies that and that d P - ( f m , ) ) = - i ( ? - t f ( m ) ) ^ , ( < ( m - ) ) | 0 t t | dm < n < d2£/n(C(™*)) = 5dq*(m) > Q d m 2 d m that is, C/ n(g*(m)) is continuous, and U-shaped (it is decreasing, for m such that q^Jjn) < q, and increasing for m such that q*n(m) > q) and Uj(m) is continuous, s t r ic t ly decreasing and linear for m G [0,m], there exists a unique m € (0,m*) such that Un(q*(m)) = Uj(m), and therefore Un(q^(m)) is = Uj(m) for m = m . P r o o f of L e m m a 2: We want to show that Uf(q*j{m)) > C/ n(g*(m)) , or equivalently that z-m{q-q*f(m))-c(qj(m))-b(q-q*f(m)) > <J(z - m ( § " - g * ( m ) ) - c(q*{m)))-b(q-q^(m)) ( A . l ) 95 To show that (A.l) holds note that z - m(q- q}(m)) - c(q}(m)) - b{q- q}(m)) > z - m(q- g*(m)) - c(q*(m)) - b(q- q*(m)) since q*j (TO) = arg max[(6 + m)q — c(q)\ which implies that z-m(q-q*f(m))-c(q}(m))-b(q-q*f(m)) > 6 (z - m(q - q*{m)) - c(q^(m)))-b(q~ql(m) for 5 G (0,1), which establishes (-4.1). P r o o f of L e m m a 3: F i r s t note that when c(q) — \ q l t h e marginal cost is c'(q) = q, which implies that qj — b and = while c(qj) = \b2 and c(q^) — \{jb)2. A l so , subst i tut ion into (2.6) and (2.10) implies that qj(m) — b + m and q£(ra) — \{b + Sm), so c(q*f(m)) = ±(6 +TO)2 and c{q*n(m)) = ±(\(b + 5m))2. We show part (i) by inserting the values for qj,q^,c(qj),c(q^),q^(m),q^(m),c(qj(m)) and c(g*(m)) into (2.16) and (2.17), and simplifying to obtain: \ i f 0 < m < m * 8Am) = { m 2/2 .f * . . _ (A.2) ' J\ > 1 T — ^ , if m <m < m v ' (l-6)(z-£-qm)+m* and 5m2/2 if m < m < m* i 7 72 r n ±n ^ in ^ in 0n(m)={ - ( l -*)^- | j -5-mj+6m2 ( A - 3 j ^ if m* < TO < TO which establishes part (i) of the lemma. For part (ii), it is useful to first compute m*. F r o m (2.4), we have m (1 - S)z - (c(gsf) - 5c(q°n)) - b(qsn - qj) (l-5)q-qsf + 5q^ {l-8)z-(\b2-5\(\b?)-b{)b-b) = z - g (l-5)q-b + 5]b q We need to show that first, for m G (0, m*), 8n(m) > Bf(m), or equivalently that 8m2/2 — (1 — 5) (z — |T — qm j + dm 1 z - b -> - TO < — ^ = m* (A.4) 96 so the inequality holds. Second, we want to show that for m G (m*,m) , j3f(m) > (3n(m), or equivalently that 1 2 < m 2 / 2 (1 - 5) (z - ^ - qm) + mz O m > 26 m (A.5) so the second inequality is also established. For part (hi), differentiating f3n(m) w i t h respect to m yields: dPn(m) dm imp ly ing that d(3n(m 8m - ( 1 - 5) (z - & - qm) + 5m2 - \5m2 (25m + q(l - 5)) dm | 0 5m m = 2Z J 5 -(1 - <5) (z - g - gm) + 5m2 2 -(1-5) ^z - ^ - qm ) + 5m2 62 -5m2 (25rn + q{l-5)) = Q 2m* So for m G (0, m*), d 0 g ^ < 0, that is, f3n(m) is decreasing. For part (iv), differentiating (3f(m) w i t h respect to m: dj3f(m) m (1 — 5) (z — g - qm) + m2 k 2 (2m - q(l - 5)) dm imply ing that —J. - 0 4* m dm > (1 - 5) ( j 2d gm) + mz b2 [1 — 5) I z — — — qm \ + m 2 2o - ^ m 2 (25m + q(l - 5)) = 0 ( z - h -& m = 2[ — ^ 2m* so Pf(m) is flat in (0, m*) increasing in (m*,2m*) , and decreasing i n (2m*, m ) , which implies that it reaches a m a x i m u m at 2m*. 97 Appendix B Equilibrium Strategies Supporting the Relational Contracts in Chapter 3 B . l Information Sets We let hf(t) denote worker i's public history up to t ime t, w i t h hf(t) — 1 i f the worker has not been involved i n a separation due to cheating, and hf(t) = 0, otherwise. Similar ly , a manager j's public history is denoted hj1^), w i t h h™(t) = 1 i f the manager has not been involved in a separation due to cheating, and h™{t) — 0, otherwise. We let qi{t) denote worker i's effort contr ibut ion up to t ime t, w i t h = 1 i f the worker has delivered promised effort and = 0, otherwise. A l so , we let fj(t) denote whether manager j has honoured al l previous promises made to workers, w i t h fj(t) — 1 i f she has and fj(t) — 0 otherwise. Furthermore, if worker i has provided promised effort when working for j or has shirked but has not been caught (an event which occurs w i t h probabi l i ty 1—/z) then we let qij(t) = 1, whereas if the worker has been caught shirking (an event which occurs w i t h probabi l i ty /x) it is qij(t) = 0. Similar ly , let fij(t) denote whether manager j has honoured al l previous promises made to worker i, w i t h fij(t) = 1 i f a l l promises were honoured and fij(t) — 0, otherwise. Agents know al l previous wage payments made since this is verifiable information. We let H(t) = {wo,w\, ...Wt-i} denote the history of wage payments made up to t ime t. Let W denote the set of a l l workers and M. the set of a l l managers, then worker i's information set in period t, is given by the collection of the publ ic histories of a l l workers and managers up to t ime t — 1, hw(t — 1)U hM(t — 1) U H(t — 1), as well as the private information he has from his own employment history qi{t — 1) and his interactions w i t h 98 employers U fij(t — 1), where Mi is the set of managers for w hom worker i has worked. jeMi Similar ly, manager j's information set i n per iod t comprises the collection of the public histories of a l l workers and managers up to t ime t — 1, hw(t — 1 )U hM(t — 1)U H(t — 1), as well as the private information she has from her own history as employer fj(t — 1) and her interactions w i t h her workers U quit — 1), where W,- is the set of workers that manager j has employed. B.2 Strategy Space Strategies consist of rules that specify a worker's and a manager's set of actions at each information set and t ime t. • Worker: A strategy <Jw{t) for the worker specifies two sorts of actions. F i r s t , it specifies whether to accept an employment offer (volunteering or internship) from every manager. A n offer consists of an unpaid posit ion along w i t h a promise of promotion to a wage posit ion (within the organization in the case of an internship, i n an organization of matching type i n the case of volunteering), when a vacancy is created, as well as a wage offer (w). In the second stage, for a worker who has accepted the offer from a given employer, and is either in the unpaid or the pa id posit ion, the strategy specifies whether to provide high effort (qi = 1) or not (qi — 0) and whether to continue i n the employment relationship or quit. • Manager: A strategy am(t) for a manager specifies the following set of actions. Fi rs t ly , it specifies what type of employment offer to make to workers: volunteering or internship, and the accompanying wages. Secondly, i f a volunteering structure is implemented, it specifies whether to honour the promise to promote a worker from the pool of volunteers when a paid posit ion opening has occurred (fj = 1) or to renege on the promise (fj = 0) by fil l ing the vacancy w i t h an intern hired from the general pool . F ina l ly , it specifies whether to continue an employment relationship or not. B.3 Equilibrium Strategies Supporting the Volunteering Struc-ture In what follows we describe the actions that the equi l ibr ium strategies (a*w(t), a*m(t) j support ing the volunteering structure prescribe i n every possible information set. Worker's strategy a*w(t): 1. If manager j's incentive compat ib i l i ty constraint, as defined i n (3.11), is satisfied, and h™(t — l) = 1 and hf(t — 1) = 1, and qi(t — l)fij(t — l) — 1, then accept a volunteering 99 posit ion promising promotion to a wage posi t ion of wv, satisfying (ICV), and set qij — 1. Otherwise, do not accept a volunteering posit ion. If the worker is already i n a paid posit ion then accept any wage offer. If — 1) = 1 and hf(t — 1) = 1, and qi(t — l)fij(t — 1) = 1, and the up-front wage wv satisfies (ICV), then set q^ — 1, otherwise set q^ — 0. 2. If hf(t — 1) = 1, and qi(t — l)fij(t — 1) = 1, then accept an internship posi t ion i n organization j promising a wage of w1, satisfying (ICI), and set q^ — 1. Otherwise, do not accept an internship posit ion. If the worker is already i n a paid posi t ion then accept any wage offer. If hf(t — 1) = 1, and qi(t — l)fij(t — 1) = 1, and the up-front wage offer w1 satisfies (ICI), then set qij — 1, otherwise set qij = 0. 3. Terminate a relationship wi th a manager i f promised promotion or promised wage offer have not been met. Manager's strategy a*m(t): 1. If the manager's incentive compat ib i l i ty constraint (3.11) is satisfied, and /i™(£—1) = 1 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) = 1, then: a) Offer worker i a volunteering posit ion, b) Honour the promise to promote a worker i from the volunteer pool into a pa id posi t ion (fj — 1) whether i has volunteered for j or not, when there is a pa id work vacancy, c) If a worker i is an existing paid worker w i t h /i™(£ — 1) = 1 and hf(t — 1) = 1, and qi(t — l)fij(t — 1) = 1, who has received previous payment of w > wv, make h i m an up-front wage offer of wv satisfying (ICV). 2. If the manager's incentive compat ibi l i ty constraint (3.11) is satisfied, and hj1^—!) = 0 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) — 1, then: a) Offer worker i an internship posit ion, b) Honour the promise to promote a worker i who has interned for you into a pa id posi t ion (fj — 1), when there is a pa id work vacancy, c) If a worker i is an existing pa id worker w i t h an internship history w i t h you and hj1^ — 1) = 1 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) = 1, then make h i m an up-front wage offer of w1. 3. If (3.11) is satisfied, and hf(t - 1) = 1, hf(t - 1) = 1 and q^t - l)fj(t - 1) = 0, then make no offer to worker i. 4. If (3.11) is satisfied, and hf(t - 1) = 1 and hf(t - 1) = 0, then make no offer to worker i. 5. If (3.11) is violated, and hf(t - 1) = 0, hf(t - 1) = 1 and qij(t - l)fj(t - 1) = 1, then: a) Offer worker i an internship posit ion b) Honour the promise to promote 100 worker i into a pa id posit ion (fj = 1), when there is a pa id work vacancy, c) If worker i is an existing paid worker w i t h an internship history and hf (t — 1) = 1, and qij(t — \)fj(t — 1) = 1, then make worker i a wage offer of w1. 6. If (3.11) is violated, and either hf(t-l) = 0, or hf(t-l) = 1, or q^t-l)fj(t-1) = 1 does not hold, then make no offer to worker i. The above strategies induce a perfect equi l ibr ium of the repeated game, i n which man-agers choose to set up a volunteering structure. Workers accept volunteering positions w i t h a promise of promotion to a pa id posi t ion paying wv and choose not to shirk, while managers honour their promises to promote only workers w i t h volunteering experience and rehire workers who have provided the promised effort. Note that the above strategies describe behavior both on and off the equi l ibr ium path, for instance, after one of the parties reneges on a promise. To see this, note that under the equi l ibr ium strategy o-*m(t) a manager who has cheated on a promise to promote volunteers and has therefore lost reputation, w i l l con-tinue to exploit future volunteers, and this would be a best response to workers' equi l ibr ium strategy er*w(t) of not accepting volunteer positions i n organizations w i th stained reputa-tions. In turn, a worker's best response facing a manager who has lost reputat ion is to only accept internship positions paying w1 > w v , which is what the equi l ibr ium strategy cr*™(£) prescribes. Also , this is the best the manager can do since under <J*w(t) workers offered a lower up-front wage w i l l shirk. O r suppose that a worker shirks. T h e n the equi l ibr ium strategy of the manager states that the worker should not be hired again. Th i s is op t imal given that the worker's equi l ibr ium strategy says that a shirking worker w i l l shirk again even i f the wage offer is w v . Furthermore, this is the op t imal th ing for the worker to do, since the equi l ibr ium strategy of the manager calls for a shirking worker not to be hired again. B.4 Equilibrium Strategies Supporting the Internship Struc-ture Worker's strategy <Tj (£): 1. If manager j's incentive compat ib i l i ty constraint, as defined in (3.12) below, is satis-fied, and h™(t — 1) = 1 and hf(t — 1) = 1, and qi(t — l)fj(t — 1) — 1, then accept an internship posi t ion promising promotion to a wage posi t ion of w1, satisfying (ICI), and set qij — 1. Otherwise, do not accept an internship posi t ion. If the worker is a l -ready in a pa id posit ion then accept any wage offer. If hJfft — 1) = 1 and hf(t — 1) = 1, and qi(t — l)fj(t — 1) — 1, and the up-front wage w1 satisfies (ICI), then set q\j = 1, otherwise set qij = 0. 101 2. Accept any non-negative up-front wage offer. If h™(t — 1) — 1, and qi(t — l)fij(t — 1) = 1, and the up-front wage offer satisfies w1 satisfies (ICI), then set qij = 1, otherwise set qij — 0. 3. Terminate a relationship w i t h an organization i f promised promotion or promised wage offer have not been met. Manager's strategy <r- (t): 1. If the manager's incentive compat ib i l i ty constraint (3.12) is satisfied, and 1) = 1 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) = 1, then: a) Offer worker i an internship posit ion, b) Honour the promise to promote a worker i who has interned for you into a paid posi t ion (fj — 1), when there is a paid work vacancy, c) If a worker i is an existing paid worker w i t h an internship history w i t h you and /i™(i — 1) — 1 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) = 1, then make h i m an up-front wage offer of w1. 2. If the manager's incentive compat ib i l i ty constraint (3.12) is satisfied, and h™(t— 1) = 0 and hf(t — 1) = 1, and qij(t — l)fj(t — 1) = 1, then offer an up-front wage offer w1 satisfying (ICI). 3. If (3.12) is satisfied, and h^ifb - 1) = 1, hf(t - 1) = 1 and q^t - l)fj(t - 1) = 0, then make no offer to worker i. 4. If (3.12) is satisfied, and hf(t - 1) = 1 and hf(t - 1) = 0, then make no offer to worker i. 5. If (3.12) is violated, and hf(t - 1) = 0, h™(t - 1) = 1 and q^(t - l)fj(t - 1) = 1, then make worker i a wage offer of w1. 6. If (3.12) is violated, and either hf{t-l) = 0, or hf(t-l) = 1, or qij{t-l)fj(t-l) = 1 does not hold, then make no offer to worker i. The above strategies give rise to a perfect equi l ibr ium of the repeated game, i n which workers accept internship positions w i t h a promise of promotion to a paid posi t ion paying w1 and choose not to shirk, while managers honour their promises to promote interns into paid positions and rehire workers who have provided the promised effort. 102 Appendix C Omitted Proofs: Chapter 3 P r o o f of L e m m a 4: It is and while and Vf = w + p[pVi + (l-p)Vf} Vf = w + 0pV-l - 0 ( l - p ) ( C . l ) V g = - e h + / ? [ ( l - / 3 ) V £ + /3Vg v.'.= - e h + 0(A-0)Vf3 1 - 0 2 (C.2) p = w1 + Ojj - eh i j 1 - 0 (C.3) V*=w Vs = %3 1 + 6lj+0[pVV + (l-p)V°j\ w1 + 6ij + 0pVa l-(3{l-p) 103 So, incentive compat ibi l i ty implies: yp > ys = WI + 8lJ+0pV° = 7// + % I ™ + PPV/J 13 - 13 1-0(1-P) l - m - r i 1-0(1-P) y i - p ( i - P ) p W1 + Ojj 0JMV H - i _ 0(1 — /i) (1 — /3(1 - (1 - / J ( l - p)) 02PP ( - e h + 0(1 - 0)V?\ + (l-P(l-rf)(l-P(l-p))[ i _ ^ 2 J Subst i tut ing from (C.3) and rearranging yields the incentive compatible wage i n (ICI) . A l so note that straightforward computat ion yields: d w a ^ — (1 — 0) eh — p (w + eh^j, which is positive under the condi t ion stated i n the lemma. P r o o f of L e m m a 5: A n assortatively matched pair generates s t r ic t ly more surplus than one where types differ. W h e n workers' type matches the type of the organization, provision of the mission good (gm) is enhanced (gm = gm > g^). Consider a matching-equi l ibr ium without assortatively matched pairs. A n organization employing a worker of a different type would have an incentive to attract a worker of the same type by offering h i m some share of the higher surplus. T h i s would also be preferred by the worker thus undoing the stabil i ty of the equi l ibr ium. P r o o f of L e m m a 6: Similar to that of L e m m a 4, so omit ted. P r o o f of L e m m a 7: Follows from the fact that i n the non-miss ion sector there is no com-mitment benefit to being nonprofit. Thus, managers w i l l find it op t imal to set up for-profit firms since the for-profit status makes them full residual claimants of the organization's net earnings. Derivation of the Sorting conditions (C.4) and (C.5): We derive the sorting condi-tions of workers by comput ing direct ly Vu(m), Vy,(b) and Vf (m),Vf (b) for i € {7711,7712}. Subst i tut ing recursively (C.3) into (C.2) and then into ( C . l ) gives: v » ( r o ) = ^ ^ & * ) * , l - 0 + 0p™(Em) ( l - 0 2 ) ( l - 0 + 0p™(Em)) ( l - / 3 2 ) ( l - / ? + / 3 p ™ ( £ m ) ) 104 w 0pb(Eb)eh l - 0 + 0pb(Eb) (1 - 02)(1 - 0 + 0pb(Eb)) + 02pb(Eb ( l - 0 2 ) ( l - 0 + 0pb(Eb)) (w1 — eh) for i 6 {u,mi, 1712} mm) w 0pm(Em)eh l - 0 + Pp™(Em) (l-02)(l^-0 + 0p™(Em)) 02pm(Em) + (wv + 6h - eh) for i € { m i , m 2 } ( l - 0 2 ) ( l - 0 + 0p™(Em)) where Em and Eb are impl i c i t ly defined below by (C.7) and (C.9) respectively. Subst i tu t ing these expressions into (SW1) and (SW2) and rearranging yields: pb(Eb)(l - 0) 0wI{Eb) - (1 + 0){w + eh) 0 ( l - 0 + 0pb{Eb)) (wv(Eb) + 9h) - (1 - 02)(w + - 02pb(Eb)wI(Eb) pb(Eb)(l - 0) \0w\E,) - (1 + 0){w + eh) < pm(Em) < 0 ( l - 0 + 0Pb{Eb)) (wv{Em)) - (1 - 02)(w + e h ) - 02pb{Eb)wI{Eb (C.4) For mission-motivated managers the sorting constraint ( S M I ) implies that: , h ( 7 ; w - / . ,n . Pb(Gb(Eb))g£ - wf(Eb) - b(gm) Pm(Gm(Em))gm - wv(Em) and the one for unmotivated managers (SM2) implies that: pm(Gm(Em))gm - wv(Em) so combining these two, one obtains pb{Gb{Eb))gj-w\Eb)-b{gm) < ^ < pb(Gb(Eb))g£ - wJ(Eb) pm(Gm(Em))gm - wv(Em) Pm(Gm(Em))gm - wv(Em) (C.5) P r o o f of Proposi t ion 6: Par t (a). The choice of nonprofit organizational form follows from Corol la ry 2. The equi l ibr ium strategies support ing the volunteer structure are de-scribed in A p p e n d i x A . To prove the rest of the proposit ion we analyze the interaction of incentive compat ibi l i ty conditions for workers and managers. O n the managers' side, 105 free-entry ensures that incentive compat ibi l i ty (ICM) binds: KV(Pm(Gm),Em) = Pm(Gm)9m -w = 6 ( 0 n ) (C.6) O n the workers' side, incentive compat ib i l i ty requires that condi t ion (ICV) is satisfied. Combin ing (C.6) and (ICV) yields: (l-P2)(l + P { j ^ - P ( l - p ) ) h _ V L m ~ E m J-eh+— i tLl - w - 6 h (C.7) - Pm(Gm(Em))gm + S(4>n) = 0 Assumpt ion 1 ensures that the two conditions cross i n the relevant region, that is, (C.7) has a solution i n the interval (0, Lm). Par t (b). The choice of for-profit status follows from lemma 7. The equi l ibr ium strategies support ing the internship structure are described i n A p p e n d i x A . O n the managers' side, free-entry implies that incentive compat ibi l i ty (3.13) binds: 7rI(pb(Gb),Eb) = pb(Gb)g1i -w = K (C.8) O n the workers' side, incentive compat ib i l i ty requires that condi t ion (ICI) is satisfied. Note that (C.8) is downward sloping because the inverse demand function pb(Gb) is decreasing i n the level of employment T h e free-entry-condition requires that equi l ibr ium must lie on the downward sloping curve defined by: w1 = Pb(Gb)glbl ~ K, while the workers' incentive compat ibi l i ty implies that equi l ibr ium must lie on the upward sloping curve defined by: [ l - ? ) ( l + P ^ - , 8 ( l - , ) ) ( l — P2) - „ wHE ) = v ^b-^b - 1 c h + A ' ( i + / ^ - / 3 2 ) (i+0<&£-i? E q u i l i b r i u m occurs at the intersection of these two. Assumpt ion 2 ensures that the two conditions cross i n the relevant region, that is, (l-P2)(l+P{-^f-P(l-p)) f1_02) _ _ - - ± r J-eh + - ^ U -w-er-pb(Gb(Eb))g^+K = 0 to ( i + p ^ m - p2) (i + P ^ - P2) (C.9) has a solution i n the interval (0, Lb)-P r o o f of Corol lary 3: Follows from observing that increasing (p) or (9) shifts workers' incentive compat ibi l i ty condi t ion downwards so the equi l ibr ium point moves along the down-ward sloping managers' incentive compat ib i l i ty constraint. Similar ly , increasing pm(Gm), 106 Pb(Gb), shifts up managers' incentive compat ib i l i ty constraint, which causes the equi l ibr ium to occur at a higher point along workers' upward sloping incentive compat ib i l i ty constraint. P r o o f of Proposi t ion 7: F i r s t , let us define workers' value functions associated w i t h the benchmark scheme of h i r ing workers direct ly into paid positions. We denote the expected lifetime value of being i n a paid posi t ion and not-shirking (Up), being i n a pa id posi t ion and shirking (IIs) and being i n the general pool (U9). It is JJP = WBM + e , . _£h + pjjp ^ U P = ™—+y e ( a i o ) while U9 = w + p[pUp + (1 - p)Up] U9 and w + PpUP 1 - 0(1 - P) Us = w a M + % + Q [pUg + (l-p)Us w B M + dlJ + 0pU9 1-p + pp Incentive compat ibi l i ty requires that: ^ -t r\ . r\ i r\ r\ <^ i - p + pp i - p + pp l - p +pp yi-p(i-p)J Subst i tut ing from (C.10) and rearranging implies: w™ > l + ^ - W - / * ) ^ _ ^ + - ( C . n ) pp where 6y = 0r because of random matching. Therefore, ( C . l l ) is workers' incentive compat-ible wage in the benchmark case. Recal l that wv = ^ ^ | i + ^ p _ ^ ^ eh+ ^ w ~ ^ h is the incentive compatible wage under the volunteering structure. Because 6r < dh and (i+pp /g2) < ^' w B M w u l ^ a v e a h i g n e r intercept and increase more steeply i n p than w v . Also , note that the free-entry condi t ion i n the benchmark case becomes: Pm{Gm)gm ~ 2W = 0 W = 107 Recal l that the free-entry condi t ion for the volunteering structure is w = Pm(Gm)9m~Q(4>n)-Therefore, the benchmark free-entry condi t ion is shifted inwards. For this to be true, it has to be that: Pm(Gm)gm - 6(<T) > Pm{G™)d™ Pm(Gm) [2gm - <&] > 26(<T) which is the condi t ion i n the proposit ion. Consequently, equi l ibr ium i n the benchmark case w i l l occur at a lower employment level as figure 3 illustrates. P r o o f of Proposi t ion 9: F i r s t note that workers' incentive compat ib i l i ty constraint w i t h internships (ICI) is shifted up by the difference (8h — 6r) relative to workers' incentive com-pat ib i l i ty constraint w i t h volunteers (ICV). In addit ion, managers' incentive compat ib i l i ty constraint is shifted down. To see this, note that the managers' b inding incentive compati -bi l i ty constraint for internships is wr i t ten as: Pm(Gm)gm — w — K' vo = Pm(Grn)g^n — K, where K is the level of profits that would make the incentive compat ibi l i ty constraint for managers b ind . Therefore, the free-entry condi t ion for internships is shifted inwards i f Pm(Gm)gm - &(4>n) > Pm(Gm)gm ~K=> Pm(Gm) [dm ~ 9m) > 0(0") - K which is the condi t ion i n the proposit ion. B o t h of these effects imp ly that the two constraints that define equi l ibr ium w i l l always cross at a point w i t h more employment (Ey > E{) i n the case where volunteer h i r ing is supported, as i l lustrated i n figure 5. Note also that, as long as (3.15) gives rise to indifference curves that are steeper than the managers' incentive compat ibi l i ty constraint (i.e. ^+sh-w-2eh > dpro(Gn,)g* ^ t h e n t h e v o i u n t e e r i n g equi l ibr ium (point V) w i l l be welfare improving for workers relative to the internship equi l ibr ium (point / ) . 108 Appendix D A Parametric Example of a 'Sorting' Equilibrium in Chapter 3 In this Append ix we provide a parametric example which demonstrates the existence of the Sort ing equi l ibr ium, by checking that it satisfies the existence conditions (C.7) , (C.9), (C.4) and (C.5) . D . l Parameter Values We make the following assumptions on the functional forms of the inverse demand functions Pm{Gm) and Pb{Gb) and on the parameters of the model . Let Pm(Gm(Em)) = 5 - 5 ( £ m / 2 ) 1 / 2 Pb(Gb(Eb)) = 6.5 - 2 . 5 ( £ f e / 2 ) 1 / 2 and 109 Table D . l : Parameter values Parameter Value 4 2 e m 2.5 K 2 p 0.7 1 Lb 3 eh 2 eh 2 w 0.5 0.2 0.5 Note that the values of the parameters are chosen such that the condi t ion /j. < v _ ; — w+eh is satisfied, that is, {1Zf]t = ^ = 0-24 > 0.2 Also , note that the condit ion i n Propos i t ion 4 is satisfied, s i n c e p m ( G m ( E m ) ) ( g m — gb) = [5 - 5 ( x / 2 ) 1 / 2 ] * 2 > 2.5 = 6 0 n ) for x G (0,1). To see this, note that the solution to [5 - 5 ( z / 2 ) 1 / 2 ] * 2 - 2.5 = 0 is (x = 1.125) D.2 Computing Equilibrium in the Mission Sector Recal l that equi l ibr ium in the mission sector is defined by the following two conditions: WV =pm{Gm)gm-Q{4>n) ( D . l ) (i-/? 2) (i + p i ^ m ^ - p i i - , , ) ) , 1 _ 0 2 ) wv(Em) = - \ r \ ; e f e + 7 L E l W - B h (D.2) Subst i tut ing yields (1 - 02) (1 + 3%^§± - (3 (1 - »j) ( l _ 02) 1—'}\ ^^'f- ^\ w V+ 7 ^,-eh+e{(pn)-pm{Gm)gm = (D.3) 110 T h e n (D.3) implies that (1 - 0.7 2)(1 + 0 . 7 £ 3 f £ - 0.7 * (1 - 0.2)) (1 _ Q . 7 2 ) - 0 . 5 - 2 - ( 1 7 . 5 - 2 0 ( E m / 2 ) 1 / 2 ) 0.7 * 0.2(1 + 0 . 7 ^ f | ^ - 0.7 2) (1 + 0 . 7 ^ | ^ - 0.7 2) Th i s equation has two solutions, we pick the one i n the relevant region, that is, for Em G (0,1). The solution is (jEm = 0.771 which implies that: pm(Em) = 1.014 while wv = 5.076 D.3 Computing Equilibrium in the Profit Sector Recal l that the equations that determine the equi l ibr ium are: Pt,(Gt)gt-w'= K _ ( 1 - ^ ( 1 + ^ - ^ ( 1 - , ) ) ( 1 - ^ ) -E q u i l i b r i u m point is solution to ( 1 - 0 . 7 2 ) ( 1 + 0 . 7 ^ - 0 . 7 * ( 1 - 0 . 2 ) ) (1 - 0 7 2 ) " n . F - 2 + 1 n " ' 0 . 5 - ( l l - 5 ( E 6 / 2 ) 1 / 2 ) = 0 0.7* 0.2(1 + 0 . 7 | 2 g - 0.7 2) (1 + 0 . 7 ^ g - 0.7 2) V V ' 1 1 This equation has two solutions. We pick the one i n the relevant region, for Eb G (0,3). The solution is: J £ f c = 1.338}, which implies that pb{Eb) = 0.241 and w1 = 6.910 D.4 Checking the Sorting Constraint for Workers We verify that the sorting conditions of workers hold by comput ing direct ly Vjf (m), vf (b) and Vf(m). Us ing the parametric values from the table and the equi l ibr ium values we obtained above it is ~ 0 / , 0.5 0 . 7 * 1 . 0 1 4 * 2 1/f (m) = 1 - 0.7 + 0.7 * 1.014 (1 - 0.7 2)(1 - 0.7 + 0.7 * 1.014) + ( 1 - 0 . 7 » ) ( 1 - 0.7 + 0.7. 1.014) < 5 - 0 7 6 ~ 2> = ° ' 7 0 6 111 ~ a n , 0.5 0.7*0.241 * 2 1 - 0.7 + 0.7 * 0.241 (1 - 0.7 2)(1 - 0.7 + 0.7 * 0.241) 0.7 2 * 0.241 + ( 1 - 0 . 7 » ) ( 1 - 0 . 7 + 0 . 7 , 0.24!) ' 6 - 9 ' ° " 2 » = 2 0 8 1 f O T ' € * " ' ™ " ' " 2 > ~ Q / , 0.5 0 . 7 * 1 . 0 1 4 * 2 V- (m) — 1 - 0.7 + 0.7 * 1.014 (1 - 0.7 2)(1 - 0.7 + 0.7 * 1.014) + ( 1 - 0 . 7 2 ) ( 0 1 - 0.7 + 0 . 7 . 1.014) < 5 ' ° 7 6 + 2 " 2> = 2 ' 6 3 6 ta ' 6 <"* • •"»> Therefore, V?(m) = 2.636 > Vf(b) = 2.081 for i 6 { m 1 , m 2 } and y » ( 6 ) = 2.081 > "\/n9(m) = 0.706 which implies that workers' sorting constraints are satisfied. D.5 Checking the Sorting Constraint for Managers Recal l that the sorting condi t ion for managers is ph{Gb{Eb))ghb - wJ(Eb) - b{gm) < pb{Gb{Eb))ghb ~ w 1 ^ ) B u t and pm(Gm(Em))gm - wv(Em) Pm(Gm(Em))gm - wv(E, pb{Gb{Eb))gj; - w'jEb) -b{gm) = 13 - 5 (1 .338 /2 ) 1 / 2 - 6.91 - 1 pm{Gm(Em))gm - WV(Em) 20 - 20(0.771/2)1/2 _ 5 . 0 7 6 Pb{Gb{Eb))ghb ~ w^Eb) _ 13 - 5 (1 .338/2) 1 / 2 - 6.910 = 0.4 pm(Gm(Em))gm - wv(Em) 15 - 15(0.446/2)1/2 - 4.910 so for (j/1 € (0.4,0.66) managers' sorting conditions are met. = 0.66 112 

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