Review of Economic Studies (2010) 77, 417–458 © 2009 The Review of Economic Studies Limited 0034-6527/10/00411011$02.00 doi: 10.1111/j.1467-937X.2009.00574.x Social Incentives in the Workplace London School of Economics IWAN BARANKAY University of Pennsylvania and IMRAN RASUL University College London First version received July 2007; final version accepted May 2009 (Eds.) We present evidence on social incentives in the workplace, namely on whether workers’ behaviour is affected by the presence of those they are socially tied to, even in settings where there are no externalities among workers due to either the production technology or the compensation scheme in place To so, we combine data on individual worker productivity from a firm’s personnel records with information on each worker’s social network of friends in the firm We find that compared to when she has no social ties with her co-workers, a given worker’s productivity is significantly higher when she works alongside friends who are more able than her, and significantly lower when she works with friends who are less able than her As workers are paid piece rates based on individual productivity, social incentives can be quantified in monetary terms and are such that (i) workers who are more able than their friends are willing to exert less effort and forgo 10% of their earnings; (ii) workers who have at least one friend who is more able than themselves are willing to increase their effort and hence productivity by 10% The distribution of worker ability is such that the net effect of social incentives on the firm’s aggregate performance is positive The results suggest that firms can exploit social incentives as an alternative to monetary incentives to motivate workers INTRODUCTION Individuals are embedded in a network of social relationships that shape their incentives and constraints, and ultimately affect their behaviour and outcomes In the labour market, social networks have been shown to play a key role in matching workers to firms, and in determining outcomes for workers once they are within the firm.1 In relation to the first literature, Granovetter’s (1974) seminal study finds that the majority of surveyed residents of a Massachusetts town had obtained their jobs through social contacts There is also evidence on the importance of social networks on the demand side of labour markets such that firms use the social contacts of their workers to fill vacancies (Fernandez and Weinberg, 1997) In relation to the second literature, research in organizational behaviour and sociology has stressed the role of social relations within firms (Rotemberg, 2006) Examples of such work includes that on how social networks within the firm influence within firm promotions (Podolny and Baron, 1997), and on the effect of manager–subordinate similarity on subjective outcomes such as performance evaluations, role ambiguity, and job satisfaction (Wesolowski and Mossholder, 1997) 417 Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 ORIANA BANDIERA 418 REVIEW OF ECONOMIC STUDIES The interplay between social relations and worker behaviour has long been studied in the organizational behaviour and sociology literatures (Mayo, 1933; Barnard, 1938; Roethlisberger and Dickson, 1939; Roy, 1952) Such concerns have been incorporated into economic analysis (Akerlof, 1980; Kandel and Lazear, 1992; Rotemberg, 1994; Bewley, 1999; Rob and Zemsky, 2002) A number of papers have recently exploited natural experiments that lead to the random assignment of peers to address similar econometric concerns This has been done in settings mostly related to education (Angrist and Lavy, 1999; Krueger, 1999; Hoxby, 2000; Sacerdote, 2001) Our analysis therefore complements three strands of the literature The first examines the interplay between workers’ behaviour in the presence of production technologies that cause there to be externalities of worker effort on co-workers’ behaviour (Ichino and Maggi, 2000; Mas and Moretti, 2009) The second explores the interplay between workers’ behaviour within firms when the compensation schemes in place cause there to be an externality of workers’ effort on the pay of their co-workers, such as relative performance evaluation (Ehrenberg and Bognanno, 1990; Bandiera, Barankay and Rasul, 2005) or team pay (Jones and Kato, 1995; Knez and Simester, 2001; Hamilton, Nickerson and Owan, 2003) The third is a literature based on experimental evidence to identify social concerns or peer pressure in workplace environments (Fehr and Falk, 2002; Charness and Kuhn, 2007; Falk and Ichino, 2006) Such concerns have been found to play an important role in shaping behaviour in the field in contexts such as informal insurance agreements in rural economies (Dercon and Krishnan, 2000) or transfers within extended family networks (Cox and Fafchamps, 2008) © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 This paper presents evidence on whether and how workers’ social ties in the workplace affect their individual performance and the performance of the firm as a whole The paper focuses on a prominent form of social ties–friendship To this purpose, we combine a firm’s personnel records on individual worker productivity with a survey we administered to workers to elicit information on the identity of their friends within the firm The firm we study is a leading UK farm producer of soft fruit Each year, the firm hires foreign workers on seasonal contracts The main task of workers is to pick fruit from fields on the farm Worker productivity, defined as the kilograms of fruit picked per hour, is observable, comparable within a worker over time, and comparable across workers at the same moment in time Two features of this setting make it ideal to study social incentives in firms.2 The first is that for any given worker, the identity of co-workers that are physically located in close proximity to her changes on a daily basis for reasons that are shown to be orthogonal to her productivity We therefore observe the same worker on days in which she works with her friends and on days in which she works with people outside of her social network Moreover, for any given worker, we also observe variation in the precise identity of her friends that are present in the field, conditional on at least one friend being present These sources of variation together allow us to make some headway in empirically identifying a causal effect of the behaviour of individuals within the same social network on each other (Manski, 1993; Moffitt, 2001).3 The second feature is that the workers’ compensation scheme and production technology are such that workers’ behaviour places no externalities onto their co-workers This allows us to assess whether workers’ behaviour is shaped by social incentives per se, rather than because social ties facilitate cooperative agreements in the presence of such externalities The question is of interest because the effect of social incentives is a priori theoretically ambiguous.4 On the one hand, the presence of friends might make work more enjoyable, generate contagious enthusiasm, or generate incentives to compete to be the best in the group All these mechanisms cause a worker to be more productive in the presence of friends relative to when she works alongside only non-friends Alternatively, the presence of friends may generate contagious malaise, or the establishment of low effort norms, that cause workers to be less productive in the presence of friends Finally, the productivity effect of the presence of friends might depend on the worker’s characteristics relative to her friends’ For instance, if workers’ preferences are such that, in equilibrium, groups of friends conform to a common productivity norm that is in between the productivity level of the most and least able friend in the network, BANDIERA ET AL SOCIAL INCENTIVES IN THE WORKPLACE 419 © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 then the presence of friends will reduce the productivity of higher ability workers and increase the productivity of lower ability workers Our analysis yields three main findings First, on average, the effect of social incentives is zero Namely, the average worker’s productivity is the same regardless of whether she has social ties with her co-workers or not This, however, masks a considerable degree of heterogeneity, as the effect of social incentives is found to differ in sign and magnitude across workers Using data on workers’ productivity when they work without their friends, we build a measure of individual ability that is unaffected by the presence of friends and we analyse how the effect of social incentives varies as a function of the worker’s ability relative to her friends’ We show that, relative to when they work only with non-friends, workers are on average significantly less productive when they work with friends who are less able than them and are significantly more productive when they work with friends who are more able than them The evidence thus rules out the class of models that predict unambiguously positive or negative effects of social incentives, in favour of models that predict conformity As workers are paid piece rates based on individual productivity, social incentives can be quantified in monetary terms and are such that, other things equal, (i) workers who are more able than their friends are willing to forgo 10% of their earnings; and (ii) workers who have at least one friend who is more able than themselves are willing to increase their effort and hence productivity by 10% To provide some context for these magnitudes, we note that others have previously estimated the incentive effect on individual productivity of moving from lowpowered incentives, such as fixed wages, to high-powered incentives in the form of piece rates, to be in the order of 20% (Lazear, 2000; Shearer, 2004) Second, we explore the empirical relevance of two mechanisms that might drive the observed conformism–the desire to socialize and inequality aversion (Fehr and Schmidt, 1999; Charness and Rabin, 2002) To so, we exploit a feature of the technology that yields different predictions on workers’ behaviour, depending on whether they adjust their productivity levels to be in close physical proximity–as implied by the socialization hypothesis–or whether they adjust their productivity levels to minimize the difference among them–as implied by the inequality aversion model Under some assumptions, we are then able to provide suggestive evidence that workers’ behaviour is consistent with a desire to socialize with their friends rather than them being averse to inequality within their groups of friends Third, we use our estimates of the effect of social incentives on each worker to conduct a simple accounting exercise to measure whether the firm benefits from the existence of social incentives The findings indicate that, although social incentives reduce the productivity of some workers, the distribution of worker ability is such that the net effect is positive Namely, the positive effect on workers who would be less productive without friends dominates the negative effect on workers who would be more productive without their friend However, the firm could have increased productivity by only 2.6% had they kept friends together at all times, relative to the allocation actually observed Whether this would have increased profits ultimately depends on the cost of always assigning friends to work together in terms of reduced flexibility to adjust the workforce within the same day While the form that social incentives take might be specific to this setting, the essence of the results is of general interest The fact that some workers are willing to sacrifice earnings and others are willing to exert more effort in the presence of friends within the firm, indicates social incentives can, more generally, reinforce or countervail monetary incentive schemes in solving agency problems This has important implications for how workers respond to a given set of monetary incentives, and sheds light on the design of optimal compensation schemes The paper is organized as follows Section describes a framework from which to understand how social incentives within the workplace affect individual behaviour Section 420 REVIEW OF ECONOMIC STUDIES describes our empirical context and data Section tests the class of models that predict unambiguously negative or positive effects of social incentives Section tests the class of models that predict the effect of social incentives depends on the characteristics as well as the presence of friends among co-workers Section measures the impact of social incentives on the firm’s overall performance Section concludes Further results and evidence in support of the identifying assumptions are in the Appendix CONCEPTUAL FRAMEWORK max B(ei ) − C(ei , θ i ) ei (1) The goal of this section is to explore whether and how worker behaviour is affected by social incentives, namely by the social relationships with her co-workers in a setting where a worker’s effort does not impose an externality on her co-workers.5 In general, several types of social relationships can be thought to affect individual behaviour To fit the model to our empirical context, we focus on friendship ties because our data allow us to partition the set of co-workers between those who are reported to be friends by worker i and those who are not The majority of these non-friends, as described in detail in Section 3, will be unknown to worker i Hence we will compare worker i’s behaviour in two settings: (i) when she works alongside her reported friends as well as other workers with whom she has no social ties; (ii) when she only works alongside workers with whom she has no social ties To model social incentives, we assume the composition of the group of co-workers enters in the cost of effort function C(.) The simplest case is the one in which the mere presence of friends affects the cost of effort Worker i’s maximization problem in this case is max B(ei ) − C(ei , θ i , fi ), ei (2) This case is therefore complementary to the framework of Kandel and Lazear (1992) who model peer pressure in environments where individual i’s effort imposes an externality on her peers In Kandel and Lazear (1992), the externality creates incentives to exert pressure on co-workers, and leads to the peer pressure that is exerted to be a function of the efforts and actions of peers Rotemberg (2006) reviews the theoretical literature and field evidence from the organizational behaviour literature on the effects within firms of individuals having two specific types of social concern–altruism and reciprocity On the empirical side, Fehr and Falk (2002) review the experimental evidence on the importance of such concerns in laboratory labour market settings, and Levy-Garboua et al (2006) review the literature in biology and psychology that delves deeper into understanding the formation of such social concerns in the first place © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 We present a framework, tailored to our setting, that makes precise how social incentives can influence individual behaviour Worker i chooses the amount of effort ei ≥ to devote to production In our setting, the production technology is such that each worker’s effort places no externalities on co-workers, hence the productivity of a given worker depends on her effort alone In addition, there are no externalities of a worker’s effort on co-workers arising from the compensation scheme either–workers are paid a piece rate per kilogram of fruit picked, and hence the pay of a given worker depends on their own effort We assume that workers derive utility from pay, which depends on productivity and ultimately on effort This is captured by the benefit function B(ei ), which, as standard, we assume to be increasing and concave in ei Workers are assumed to be of heterogeneous ability Denoting worker i’s ability by θ i , we assume effort entails disutility C(ei , θ i ), with Cei > 0, Cei ei > 0, and Cei θ i < Namely, disutility is increasing and convex in effort, and that, other things equal, more able workers face a lower marginal cost of effort In the absence of social incentives, worker i’s maximization problem is BANDIERA ET AL SOCIAL INCENTIVES IN THE WORKPLACE 421 max B(ei ) − C(ei , θ i , fi , θ f ), ei (3) where θ f is a measure of the ability of the friends present In this setting, the sign of Cei fi can depend on the sign of θ i − θ f For instance, conformism to a common norm would imply that sign(Cei fi ) = sign(θ i − θ f ), so that worker i exerts more (less) effort in the presence of friends that are more (less) able than her If such mechanisms are at play, then the effects of social incentives on behaviour are heterogeneous across workers More precisely, the sign of the marginal effect on worker effort from having friends present depends on worker i’s ability relative to her friends’ In the empirical analysis, we will explore such mechanisms in detail CONTEXT AND DATA 3.1 Workplace operations We analyse the behaviour of workers in the fruit picking division of a leading UK farm producer of soft fruit during the 2004 season Workers are hired from eight countries in Eastern Europe on seasonal contracts that last between and months The workers’ primary task is to pick fruit from fields on the farm site They typically pick on two different fields each day, and there are between 40 and 50 workers in each field Within a field, workers are assigned their own row of fruit to pick Workers are present on the field for the number of hours it takes to pick all the available fruit The only choice variable of workers is how much effort to exert into picking As each worker picks on her own row, her productivity is independent of the de Indeed, dfi = Cei fi /(Bei ei − Cei ei ), and the denominator is negative due to the twin assumptions that B(.) i is concave and C(.) is convex © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 where fi is a measure of the physical presence of friends, such as, for instance, the share of co-workers that are friends Differentiating the first-order condition for effort with respect to fi illustrates that whether social incentives lead to higher or lower effort intuitively depends on whether the presence of friends decreases or increases the marginal cost of effort for worker i, namely whether Cei fi < or Cei fi > 0.6 The presence of friends would decrease the marginal cost of effort if, for example, working alongside friends generates contagious enthusiasm, or generates incentives to compete to be the best in the network of friends In contrast, the presence of friends would increase the marginal cost of effort if, for example, working alongside friends creates contagious malaise The framework thus captures in reduced form all models that predict positive or negative effects of social incentives for all workers, regardless of their characteristics or the characteristics of their friends In other words, while the magnitude of the difference in efforts of any given worker with and without her friends may differ, the key prediction of this class of social incentive model is that the sign of the difference is the same for all workers A second class of models suggests that the effect of social incentives might depend on the characteristics as well as the presence of friends among co-workers For instance, a given worker might take a high-ability friend as role model and work harder in her presence, or take a negative example from low-ability friends and slow down in their presence Other causes of such heterogeneous effects are preferences for status (Bernheim, 1994) or aversion to inequality (Fehr and Schmidt, 1999; Charness and Rabin, 2002) that can generate conformism to a common norm In all these models, the effect of social incentives in reduced form depends on the ability of worker i relative to her friends’ Worker i’s maximization problem thus becomes 422 REVIEW OF ECONOMIC STUDIES efforts of other workers on the same field-day, so there are no externalities arising from the production technology.7 Workers are paid a piece rate per kilogram of fruit picked Each worker’s pay is thus related to her own productivity, which is an increasing function of her effort, the quantity of fruit available on the rows of fruit within the field to which she is assigned, and the general conditions in the field in which she works As pay is based on individual performance only, there are no externalities of workers’ effort arising from the compensation scheme either.8 3.2 The assignment of workers to fields 3.3 The assignment of workers to rows within a field Within each field-day, workers are organized and supervised by managers The COO allocates workers and managers to fields, and managers are hired from the same pool of individuals as workers, and like workers, they are hired on seasonal contracts Each manager is responsible for the field logistics of around 20 workers As the fruit plants are organized in rows, managers are responsible for allocating workers to rows at the start of the field-day, and for reallocating workers to new rows once they have finished picking the row they were originally assigned to On any given field-day, managers focus on their assigned group of workers and work independently of each other.9 A key feature of the technology is that there is considerable variation in the quantity of fruit across rows within a field Fields are covered by plastic sheets supported by pillars placed every fifth row On rows close to pillars, air circulation is worse and hence heat tends to To be recruited, individuals must be full-time university students and have at least year remaining before graduation Workers are not typically hired from the local labour market, and few are hired for consecutive seasons There is also the possibility that workers learn from their friends Such knowledge spillovers would imply that workers’ productivity would increase in the presence of their friends, and that such spillovers die out over time As documented later, we not find any evidence of such a pattern of spillovers A separate group of individuals, called field runners, are responsible for physically moving fruit from the field to the packaging plant They neither pick fruit nor manage workers © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Workers are assigned to fields on a daily basis by a permanent employee of the farm, whom we refer to as the Chief Operating Officer (COO) Workers not themselves decide which field they work on, nor they decide whom to work with The quantity of fruit varies across fields on any given day because fields vary in their size and, within a field, over time because plants reach maturity at different times The fruit is planted some years in advance so the total quantity of fruit to be picked is given and the sequence in which fields are picked over time is pre-determined and is not decided by the COO This natural variation implies that the demand for picking labour and hence the number of workers vary across fields at any given moment in time, and within a field over time In addition, there are shocks to the demand for picking labour within a day as fruit orders from supermarkets are received These orders specify a quantity of specific fruit types that need to be picked and delivered by some date These orders further cause some workers to be reassigned across fields within the same day Importantly for our study, these sources of variation cause the group of co-workers to change each field-day and so allow us to observe an individual working alongside her friends on some field-days, and to observe the same individual working in the absence of her friends on other field-days Moreover, these sources of variation also lead to the subset of worker i’s friends that are actually present on the field with her to vary across the field-days on which i picks BANDIERA ET AL SOCIAL INCENTIVES IN THE WORKPLACE 423 3.4 Data sources We use two sources of data for our analysis This first is the firm’s personnel records which contain information on each worker’s productivity on every field-day they pick fruit Productivity is defined as the kilograms of fruit picked per hour and is electronically recorded with little measurement error In this setting, productivity is therefore observable, comparable across workers at any given moment in time, and comparable within the same worker over time Personnel records also allow us to identify all the co-workers and managers present each field-day We focus on fruit picking operations during the peak picking season from May until 30 September 2004 The second data source is a survey we administered to workers This provides information on each worker’s socioeconomic background, characteristics, and self-reported social network of friends on the farm Workers are surveyed once, generally around weeks after their arrival, thus allowing time for new social ties to form and be reported Individuals are asked to name up to seven of their friends on the farm Hence, the peer group of friends of each worker is self-reported and specific to the worker For each named friend, workers report whether the social tie existed prior to the individual’s arriving to the workplace–which would be the case if, for example, the individuals are friends from their home country–or whether the friendship newly formed within the workplace.10 3.5 Sample selection The worker survey is administered on three different dates over the peak picking season It is administered in the evening after workers have returned from the fields We aimed to interview 10 The survey is translated into a number of Eastern European languages, and administered by enumerators from Eastern Europe Note, finally, that the personnel records identify all co-workers and managers present on each field-day, and record all workers’ productivity, including those not interviewed in our survey © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 accumulate, so the quantity of fruit is lower In addition, these rows are harder to pick because of the presence of the supporting pillars Both factors reduce workers’ productivity, other things equal Indeed, since the quantity of fruit per plant is lower, workers need to pick more plants–and hence spend more time moving from one plant to the next–to pick a given quantity Similarly, since the pillars restrict some movements, workers have less discretion on how to approach a plant In summary, for every five rows between pillars, the marginal productivity of workers’ effort is highest in the central row and lowest in the two lateral rows next to the pillars Due to the complementarity between workers’ ability and row quality, managers are required to assign the fastest workers to the most abundant rows It is important to stress that this feature of the technology might bias the estimates of social incentives In particular, if friends are assigned to contiguous rows, these will necessarily have different quantities of fruit in them, hence making the friends’ productivity diverge, other things equal We are thus less likely to find support for models that predict that social incentives make friends conform to a common productivity norm, other things equal This feature also weakens any common productivity shocks among friends that work on contiguous rows on the field If, on the other hand, friends are assigned to similarly plentiful rows, they will necessarily be physically distant in most cases All else equal, this would mitigate against finding evidence of some forms of social concern driving behaviour, such as the benefits of socializing with friends on the field, which are more relevant when friends are in close physical proximity to each other 424 REVIEW OF ECONOMIC STUDIES 3.6 Reported friendships Table shows the pattern of self-reported friendship ties within the workplace The table shows that 70% of surveyed workers report having at least one friend in the workplace, and that 30% of workers report having no friends in the workplace We refer to these as “isolated” workers to distinguish them from those that report at least one friendship tie, whom we refer to as “connected” workers The median worker reports three co-workers as friends, and this rises to four, conditional on reporting at least one friend The last column shows that workers who report having more co-workers as friends are themselves more likely to be named to be a friend of other workers that are surveyed For example, among connected workers, they are on average themselves named as a friend by 2.16 other surveyed workers In contrast, isolated workers are on average themselves named as a friend by only 1.49 other workers Moreover, of the 87 workers that report no friends within the firm, 37% of them are not reported to be a friend of any other surveyed worker.11,12 Taken together, the results highlight that the extent to which workers are socially tied to their co-workers varies considerably This is despite workers being hired from the same pool, having similar observables, and working frequently with each other within the same tier of the firm hierarchy To provide further evidence that workers reliably report the identity of their friends, Table A2 reports survey evidence on the type and frequency of interactions among connected workers and their friends We collected information along four dimensions of social interaction–going to the supermarket together, eating together, lending/borrowing money, and talking about problems Although workers were not asked to rank their friends, the table shows that workers report first the friend with whom they interact most frequently along all dimensions, followed by the second reported friend, and so on The first named friend i is also more likely to be a preexisting friend and to report i as a friend of theirs The high frequency of interaction between 11 The terms “connected” and “isolated” are used only to ease the expositional, and we not mean to imply that workers who name no friends are literally isolated in the workplace in that they have no social interaction with co-workers 12 The majority of friendships are newly formed in the workplace, and pre-existing friendships are more likely to be reciprocal For any given number of friendship ties, the ratio of newly formed ties to pre-existing ties varies considerably across workers On average this ratio is 1.33, although it varies from to across surveyed workers © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 all workers present on the survey date, and obtained a 95% response rate Workers who were not present on the living site on the survey date–around half the total workforce–are not in our sample This may occur if they are engaged in other non-work-related activities away from the farm site at the time of the survey Table A1 presents descriptive evidence on the characteristics of workers who were interviewed and those who were on the farm’s payroll but were not present on survey day Information available on both sets of workers mostly relates to that contained in personnel records Three points are of note First, those surveyed have similar productivity to those not surveyed This is true both for worker productivity on average, and also the entire distribution of worker productivity Second, the gender and nationality composition of the two groups is quite similar Third, surveyed workers are more than four times more likely to name another surveyed worker as their friend as they are to name an individual who was not surveyed This is consistent with non-surveyed workers not being present at the time of the survey due to social engagements away from the workplace, and indicates that the social networks of non-surveyed workers not overlap with those of surveyed workers on which our analysis is based BANDIERA ET AL SOCIAL INCENTIVES IN THE WORKPLACE 425 TABLE Reported friendships Number of self-reported friends Median Mean Standard deviation Conditional on at least one reported friendship Median Mean Standard deviation Number of times mentioned as a friend by another surveyed worker (standard deviation) 87 (30.1) 33 (11.4) 24 (8.30) 29 (10.0) 48 (16.6) 19 (6.57) 16 (5.54) 33 (11.4) 2.71 (2.44) 1.49 (1.59) 1.45 (1.73) 1.58 (1.18) 1.79 (1.24) 2.38 (1.38) 2.68 (1.63) 2.94 (1.29) 2.64 (2.22) 1.96 (1.65) 3.87 (1.99) 2.16 (1.64) Notes: All the information is derived from the worker survey There were 289 individuals interviewed Each individual was asked to list up to seven of their friends on the farm friends outside of the work environment implies friendship networks may be qualitatively more important drivers of behaviour than other networks, say based on similarity in gender or nationality Moreover, although workers may have more than seven friends in the firm, the strength of the social ties between workers–measured by either forms of social interaction or the probability that the relationship is reciprocal–is highest for the friends who are mentioned first This implies that we may well capture the strongest friendship bonds in the workplace, and it is these bonds, if any, that are likely to provide social incentives SOCIAL INCENTIVES AND WORKERS’ PRODUCTIVITY: HOMOGENEOUS EFFECTS 4.1 Identification In this section we present evidence on whether workers’ performance is affected by the presence of their friends among co-workers We begin by scrutinizing the class of models that predict the effect of social incentives to have the same sign on all workers: namely, we test whether workers are always more or less productive in the presence of their friends compared to when friends are absent To identify the effect of the presence of friends, we exploit the fact that the same worker is observed on some field-days in the presence of his friends, and on other © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Number of surveyed workers (percentage) 426 REVIEW OF ECONOMIC STUDIES field-days she is observed working in the absence of her friends We therefore estimate the following panel data specification for the productivity of connected workers: yif t = α i + λf + βFif t + δXif t + ηZf t + λt + uif t , (4) 13 As fields are operated on at different parts of the season, and not all workers pick each day, the effects of the field life cycle and workers’ picking experience can be separately identified from the effect of the time trend 14 These identifying assumptions are analogous to the standard identifying assumptions in the program evaluation literature (Heckman, Lalonde, and Smith, 1999) In this context, the treatment individuals are subject to being assigned to work with their friends on a field-day, and the control group is the same individual on field-days in the absence of her friends We therefore require the treatment to be orthogonal to other determinants of worker productivity, and for there to be no spillover effects from field-days in which friends are present onto behaviour on field-days in the absence of all friends © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 where yif t is worker i’s productivity, measured in kilograms per hour, on field-day f t, α i and λf are worker and field fixed effects that capture time-invariant determinants of productivity at the worker and field level, respectively, Xif t is the worker’s cumulative picking experience to capture the fact that there are positive returns to experience in fruit picking, and Zf t is the field life cycle that captures within field time trends in productivity as plants ripen and field conditions alter, and finally we include a linear time trend to capture learning by farm management and aggregate trends in productivity.13 Our variable of interest is Fif t , which measures the presence of worker i’s friends on fieldday f t The analysis exploits several alternative measures such as an indicator variable for the presence of friends, measures that exploit the different strength of various friendship ties, and measures that exploit the difference in the size of the friends’ group on different field-days All continuous variables are in logarithms, and the error term, uif t , is clustered by worker because the variable of interest–the presence of friends–is correlated within a given worker through time The coefficient of interest is β, which captures the difference between workers’ productivity on days when they work with their friends and on days when they not The interpretation of β depends on the composition of the co-workers’ group when friends are not present We can partition this set into two: (i) individuals with whom worker i has no social ties, namely “strangers”; (ii) individuals with whom worker i has ties other than friendship, such as acquaintances or even enemies Given that a given worker has 40–50 colleagues on the same field, and these are selected from a pool of 300 individuals from eight different countries, the majority of co-workers on any field-days will be strangers to worker i The coefficient of interest β should therefore be interpreted as the difference between workers’ productivity on days when they work with their friends and on days when they work with individuals they are not socially connected to Given that we only collected information on friendship ties, we are unable to compare the estimated effects against those of other types of social tie For example, it is plausible that enemies may also influence each other’s behaviour If so, then our parameter of interest of the difference between workers’ productivity on days when they work with their friends and on days when they work with individuals they are not socially connected to, in part also captures any influence enemies might have The identification strategy relies on the validity of two assumptions: (i) the assignment of worker is orthogonal to unobserved determinants of productivity so cov(Fif t , uif t ) = 0; (ii) there are no intertemporal productivity effects that spillover from field-days when friends are present to field-days when only non-friends are present, and vice versa.14 826 REVIEW OF ECONOMIC STUDIES b (s) = r (s) − maxk∈S θ (k)1/(1−α) g (s) 1−β for r (s) which corresponds to the level of revenue associated with τ (s) Assume that b−1 s ≤ b (s0 ) We can construct an efficient equilibrium in which b s t |s t−1 = b s t−1 = max b(s t−2 ), b (st−1 ) , so that debt is no longer state-contingent and it is increasing along the equilibrium path In such an environment, the government permanently increases taxes and debt whenever the politician requires incentives When incentive constraints on politicians not bind, debt is held constant and rents increase (decrease) when public spending decreases (increases) When incentive constraints on politicians bind, both debt and rents permanently increase into the future.29 This example thus shows that political economy distortions generate endogenous market incompleteness since contingent claims are not used despite their availability 5.4 Long-run dynamics We have shown that taxes in the short run are volatile and persistent To what extent is this true in the long run? The simple example of Section shows that if we ignore the incentive compatibility constraint of the representative citizen, revenues permanently increase following a one-time shock and they not revert back down Analogous reasoning implies that if we ignore the incentive compatibility constraint of the politician We use this observation to explore the long-run properties of the tax rate By Proposition 3, the tax rate converges if the sustainable intervals for the tax rate have an overlapping region A tax rate in this region satisfies all incentive compatibility constraints under all states Theorem (Long Run) ∃ χ c (·) and χ p (·) which are weakly increasing continuous functions s.t τ which solves equation (26) converges almost surely if and only if χ c ≤ χ c (χ p ) and χ p ≥ χ p (χ c ) Theorem states that the tax rate converges if χ c is sufficiently low (i.e the incentive compatibility constraints on the representative citizen are sufficiently slack) and if χ p is 28 Given the assumption of quasi-linearity, there are many sequences of rents and debt which are associated with the unique sequence of labour and public spending which solve the program 29 This follows from the fact that in this environment, the government’s dynamic budget constraint implies that x s t = τ s t n s t − g s t + βb s t − b s t−1 © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 on the politician since taxes must rise into the future to finance this spending In contrast, when θ decreases, public spending decreases, and this tightens the incentive compatibility constraint on the representative citizen since taxes must decrease into the future in order to generate support for the government Given the policy rule (40), this means that the equilibrium tax rate is more likely to increase (decrease) tomorrow if θ increases (decreases) tomorrow While the underlying driver of the persistence of taxes in our economy is the conflict between politicians and citizens, operationally, the persistence emerges because the government in our economy effectively under-insures, and this brings the economy closer to an incomplete market economy in which contingent debt is unavailable An easy way to see this is to construct an example in which the government does not actually use contingent debt, despite its availability.28 Consider the setting in which χ c = 0, and consider the solution described in Proposition for V0 = Define YARED POLITICIANS, TAXES AND DEBT 827 sufficiently high (i.e the incentive compatibility constraints on the politician are sufficiently slack) These conditions guarantee that the sustainable tax rate intervals have an overlapping region Moreover, the theorem states that if χ c decreases (χ p increases), then the tax rate converges for a weakly larger range of χ p (χ c ) In other words, if incentive compatibility constraints are sufficiently slack, then even though tax rates are volatile and persistent along the equilibrium path, they converge to a constant level in the long run If these conditions are not satisfied, then a constant tax rate cannot simultaneously satisfy both the politician and the representative citizen, so that taxes are volatile even in the long run The theorem is displayed in Figure 2, which plots χ c against χ p with the relevant regions of long run tax convergence and long run tax volatility Note that in addition to these regions, we also display the range over which an equilibrium without replacement does not exist.30 Intuitively, incentive provision for the politician puts upward pressure on the tax rate under some shocks and incentive provision for the representative citizen puts downward pressure on the tax rate under some shocks When there is sufficiently little benefit to the representative citizen from throwing out the politician, the representative citizen will tolerate very high tax rates Analogously, when there is sufficiently little benefit to the politician from additional rent-seeking, he will tolerate low tax rates For example, imagine if χ c is low Along the equilibrium path, the government accumulates debt and rents to accommodate the politician’s incentives, and the representative citizen receives sufficiently little benefit from throwing out the incumbent so that he accepts the gradual increase in the tax rate and decrease in public spending which accompany the government’s accumulation of debt and rents In the long run, this economy is qualitatively similar to an economy managed by a benevolent ruler but with more debt net of rents than that associated with a benevolent ruler The long-run behaviour of this economy stands in contrast to that of Aiyagari et al (2002), in which markets are exogenously incomplete They show that in an economy without statecontingent debt, taxes respond persistently to shocks along the equilibrium path, as they 30 In our setting, such an equilibrium involves the tax rate converging to the maximum © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Figure Long run taxes 828 REVIEW OF ECONOMIC STUDIES here However, the benevolent ruler accumulates assets along the equilibrium path until he can finance the entire stream of public spending with zero taxes In our economy, taxes not converge to zero and they can remain volatile even in the long run 5.5 Predicting tax rate movements E (τ t |τ t−1 , , τ , θ t−1 , , θ ) = E (τ t |θ t−1 ) In contrast, according to Barro (1979)’s intuitions, taxes are a random walk, which means that yesterday’s tax rate alone can predict today’s tax rate: E (τ t |τ t−1 , , τ , θ t−1 , , θ ) = E (τ t |τ t−1 ) Our model combines features of both of these statistical processes Given (40), both past tax rates and past shocks are required to forecast tomorrow’s tax rate: E (τ t |τ t−1 , , τ , θ t−1 , , θ ) = E (τ t |τ t−1 , θ t−1 ) This statistical process for the tax rate in our model is qualitatively similar to that of Aiyagari et al (2002), even though there are no exogenous limits on the contingency of government debt in our model The crucial distinction between our model and theirs is in the long-run implications for the tax rate In their model, the tax rate converges to zero and the government holds more assets in the long run than would be implied under a benevolent ruler with complete markets In our model, the tax rate may not converge, and if it converges, it will not generally converge to zero Our model therefore links the existence of politicians to the endogenous incompleteness of markets, and it provides different implications than an economy with exogenous market incompleteness 5.6 Numerical example In this section, we illustrate the mechanics of our model using a numerical simulation Let (η, γ , α, b0 , V0 ) = (0.75, 2, 0.5, 0, 0), β = 0.95, and θ t = {4, 5, 6} Normalize the resource constraint to c + g + x = 10n The transition matrix for θ is ⎡ ⎤ 0.98 0.02 ⎣ 0.01 0.98 0.01 ⎦ , 0.02 0.98 so that each shock is very persistent, and a path between the highest to the lowest shock must pass through the middle shock Let θ = We compare three cases: χ p = ∞ and χ c = (case 1), χ p = 633 and χ c = (case 2), and χ p = 633 and χ c = 1200 (case 3) © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Our model predicts that tax rates should sometimes adjust persistently to shocks, and this is in line with what we observe empirically As mentioned in the introduction, both Barro (1979) and Aiyagari et al (2002) also predict persistent tax rates, and they achieve this by ruling out state-contingent debt A natural question is how the stochastic process of tax rates in our economy compares with theirs To simplify the discussion, let the shock θ map one to one with the state s According to Lucas and Stokey (1983), the tax rate covaries one to one with θ (in the quasi-linear model, the covariance is zero), which means that tax rates tomorrow are best predicted by today’s shock used to forecast tomorrow’s shock: YARED 30 POLITICIANS, TAXES AND DEBT Panel A: Government Purchases 829 Panel B: Tax Rate 0.2 25 20 0.15 15 10 50 100 t 150 200 Panel C: Government Debt Net of Rents 0.1 50 100 t 150 200 150 200 Panel D: Output 120 200 100 115 -100 110 -200 50 100 t 150 200 Case 50 100 t Case Figure Comparing cases and As a reminder, case corresponds to the economy under a benevolent ruler, since the incentive compatibility constraint on neither the politician nor the representative citizen binds Case ignores the incentive compatibility constraint of the representative citizen, and case takes the incentive compatibility constraint of the representative citizen into account In cases and 3, the size of χ p is chosen such that a deviation in period zero yields r max to the politician off the equilibrium path In case 3, χ c is chosen such that the representative citizen’s constraint binds in the low state only Figure compares cases and for a realized sequence of θ shocks In case 1, rents are zero, public spending (Panel A) and government debt (Panel C) vary only with the state, and taxes (Panel B) and output (Panel D) are constant These policies are not incentive-compatible in case since they violate equation (29) In case 2, policies reflect the last binding incentive compatibility constraint on the politician, until the tax rate reaches a maximum and the economy becomes qualitatively the same as in case Since χ c = 0, the representative citizen’s incentive compatibility constraint never binds Figure compares cases and Because χ c is large, the representative citizen’s incentive compatibility constraint binds in the lowest state in a transition path from the high state to the low state In the low state, the government is less productive, and citizens need incentives to © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 830 REVIEW OF ECONOMIC STUDIES 30 Panel A: Government Purchases Panel B: Tax Rate 0.2 25 20 0.15 15 10 50 100 150 200 0.1 50 t Panel C: Government Debt Net of Rents 100 t 150 200 150 200 Panel D: Output 120 200 100 115 -100 110 -200 50 100 t 150 200 50 Case Case 100 t Figure Comparing cases and not throw out the politician, so that the tax rate decreases As a consequence, the tax rate in the middle state depends on whether the highest or the lowest state occurred most recently This means that even in the long run, the tax rate and output continue to be volatile and continue to reflect the history of shocks We compare the period welfare of households in different economies to determine the welfare cost due to the existence of rent-seeking politicians We calculate the fraction of consumption that would be sacrificed in the economy of case to make a household indifferent between living in case (i.e under a benevolent ruler with complete markets) and living in a given economy This welfare cost is 1.94% both in case and in case Since rents represent around 1.6% of case consumption in both cases and 3, this suggests that the welfare cost is primarily due to the transfer of consumption away from households towards politicians, and it is not primarily due to the extra volatility in taxes or reduction in public spending.31 As a comparison, the welfare cost of imposing a balanced budget on a benevolent government is 31 More specifically, if one replaced case with an economy managed by a benevolent government constrained to providing the politician with the same period welfare as under case 2, then the welfare cost under case becomes 0.06% © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 YARED POLITICIANS, TAXES AND DEBT 831 EXTENSIONS Our analysis thus far has ignored two important frictions that could realistically interact with politicians’ rent-seeking incentives: politicians can default on outstanding debt, and politicians can be replaced even after good behaviour In this section, we explore the effect of allowing for these two frictions, and we highlight how our main results are insensitive to allowing for these possibilities For simplicity, we let χ c = so as to ignore the incentives of the representative citizen, we let V0 = 0, and we let citizens to throw a politician out at the end of the period t so that the politician receives −χ p once thrown out.33 6.1 Default Imagine that in addition to its policy choices, the government chooses an indicator Dt = {0, 1} which represents a decision to default on outstanding debt In such a setting, one can define sustainable equilibria, as we in Section 4, and an important implication of this definition is that, in their savings decisions, households will take into account their expectations of future default This is important in characterizing the optimal deviation as well as the optimal punishment for the politician It is obvious that a politician’s best deviation will involve defaulting on outstanding debt in addition to choosing maximal taxes and minimal public spending More subtle, however, is that if the politician attempts to extract the maximal amount of debt b, the optimal punishment strategy will involve households expecting default by future governments, and this induces a market clearing price of zero for this debt Consequently, the politician’s best deviation yields: V b s t |s t−1 = r max − 0, b s t |s t−1 − χ p, 32 Another way to see this is to perform the same exercise as in footnote 31, so that the welfare cost of political economy becomes 2.77% 33 This does not alter the incentive compatibility constraint on the incumbent in our original framework © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 0.07%, and the welfare cost of excluding non-contingent debt for a benevolent government is 0.04% Therefore, the welfare cost due to political economy distortions relative to these constraints is high, though the primary source of this additional cost is a pure transfer of resources to politicians This does not however imply that political economy distortions are small It only means that they are small under the optimal policy For example, consider the solution to equation (26) subject to τ s t = τ s t−1 ∀s t and g s t = g s t−1 ∀s t , which is a policy appropriate for a benevolent government under which there is no volatility in taxes The cost of this suboptimal sustainable policy is very high and equal to 8.77% This cost is high because there is an increase in the transfer of rents from citizens to politicians which equals 5.2% of case consumption Moreover, in addition to this pure transfer, the economy suffers because public spending declines In other words, under the suboptimal sustainable policy, the government provides fewer public goods and wastes more resources on rents than in the best sustainable policy.32 This is because the politician cannot be trusted to pledge accumulated revenues for public use, and this simultaneously limits the size of the government while making the government more wasteful 832 REVIEW OF ECONOMIC STUDIES which implies that the politician’s incentive compatibility constraint is equivalent to the following two constraints for z s t |s t−1 defined in Section 5.2: z s t |s t−1 ≥ r max − χ p ∀s t , and (43) ∞ β k−t π s k |s t x s k ≥ r max − χ p ∀s t (44) k=t s k ∈S k 6.2 Equilibrium replacement Imagine that at the end of every period, the incumbent is exogenously replaced with probability − δ (st ) ∈ (0, 1), and let the realization of replacement be independent of all actions and the identity of the politician The economy we study in the text considers the special case for which δ (st ) = ∀st 34 Note that equation (24) in the presence of replacement can only become tighter at every history since the politician facing potential replacement assigns a weakly lower weight to x s t relative to the politician guaranteed to remain in power forever Nonetheless, despite the tighter constraints, the efficient path of taxes and public spending in our original economy can be sustained in the presence of replacement To see why, choose taxes and public spending as in the original economy, and let x s > and x s t = for all s t for t > so that the entire equilibrium stream of rents is paid to the incumbent in period and so that b s t |s t−1 = z s t |s t−1 for t > For t > 0, equilibrium rents are zero and the replacement probability plays no role in the incumbent’s calculus, and since equation (24) is satisfied in the original economy, the politician has no incentive to deviate If t = 0, the politician facing exogenous replacement assigns the same weight to his assured initial rent x s as the politician permanently in power, so that again the replacement probability plays no role Thus, the presence of replacement does not change the characterization of our results This analysis changes somewhat in the presence of default as in Section 6.1 In this circumstance, equations (43) and (44) must accommodate the survival probability δ (st ) If r max > χ p , it can be shown that in this circumstance, equation (44)—which now includes δ (st )—always binds so that x s t = (r max − χ p ) (1 − δ (st ) β) for all s t Intuitively, the politician is less patient than the representative household, so it is best to front-load rents to the extent allowed by incentive compatibility constraints This requires paying him more when 34 Debt could in principle depend on whether or not a politician was replaced Nonetheless, it can be shown that there is no efficiency gain from letting debt be contingent on replacement since every incumbent receives the lowest continuation value © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Note that equation (43) is analogous to equation (29), though the constraints on the values of z s t |s t−1 are now weaker so that the possibility of default is actually allowing the government to be less constrained in its savings The additional constraint of equation (44) puts discipline on incentive-compatible sequences of x which can be chosen for a given unique optimal sequence of n and g, and such a constraint can be easily satisfied by choosing a constant level of rents Consequently, our analysis of the case without default can be applied to this case with default, and the time path of taxes and public spending is characterized by updating rules analogous to equations (40) and (41) The reason why the possibility of default does not affect our results is that our results are driven in large part by the fact that large government asset positions are costly since they are associated with high rents This fact is unaffected by the government’s ability to renege on its debt YARED POLITICIANS, TAXES AND DEBT 833 his survival probability is low Given this stream of rents, equation (43) can be rewritten as: ∞ β k−t π s k |s t (1 − δ (sk ) β) ∀s t z s t |s t−1 ≥ r max − χ p (45) k=t s k ∈S k CONCLUSION In this paper, we have developed a theoretical framework that studies the optimal management of taxes and debt in an environment with self-interested politicians and citizens In doing this, we have argued that incentive compatibility for the incumbent politician and the representative citizen takes the form of endogenous debt limits on the government, and this creates distortions which generate more macroeconomic persistence and volatility than under a benevolent ruler under optimal policies Our model predicts that taxes respond persistently to shocks even though financial markets are complete, and long-run taxes are non-zero, which is in contrast to an economy with exogenously incomplete financial markets While we have made our arguments in a setting in which households have quasi-linear preferences, many of the insights achieved here transmit to an economy which allows for risk aversion.35 Our analysis leaves some natural directions for future research We have assumed the perfect observability of the politician’s actions, although in practice rent-seeking is a private activity Relaxing this assumption would generate even further distortions in our economy and provide more limits on financial markets It would also potentially generate endogenous political replacement and a political business cycle Second, our model ignores the important interaction between fiscal policy and monetary policy by focusing on the real economy We plan to explore these extensions in future research APPENDIX A DEFINITIONS The following definitions simplify notation: (s, λ) = n − ηnγ − g, and W (s, λ) = ηnγ (1 − 1/γ ) + θ (s) g α /α 35 We have shown this result in previous versions of this paper for a particular class of preferences Intuitively, even if politicians can manipulate the interest rate, it is still the case that taxes respond persistently to shocks since the government cannot save as much to prepare for shocks due to the incentive compatibility constraint of politicians © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 Consequently, our analysis of the case without exogenous replacement and without default can be applied to this case, and the time path of taxes and public spending is characterized by updating rules analogous to equations (40) and (41) Moreover, note that equation (45) is tighter (i.e the upward pressure on taxes and debt rises) whenever survival probabilities going forward are projected to be low We emphasize that this comparative static refers to exogenous changes in the survival probability of the government such as term limits A more detailed model of political cycles should also take into account an additional force embedded in χ c which parameterizes the popularity of the current incumbent One can show, for example, that exogenous fluctuations in χ c will affect the sustainable bounds on taxes and public spending in equations (40) and (41), where a reduction in the popularity of the incumbent pushes the government towards reducing taxes and increasing public spending 834 REVIEW OF ECONOMIC STUDIES for n and g which satisfy equations (36) and (37) given λ By the implicit function theorem, (s, λ) > (k, λ) and W (s, λ) < W (k, λ) if θ (s) < θ (k) λ (s, λ) > and Wλ (s, λ) < if n ≥ nmax Also, APPENDIX B PROOFS OF SECTION B.1 Proof of Proposition Step For necessity, equation (21) follows from equation (19) The intra-temporal and inter-temporal conditions for the household at s t , respectively, are: = ηn s t |s = βπ s q s t+1 t γ −1 t+1 |s t (46) (47) Equation (46) implies the function r (n) For the necessity of equation (22), let q s t |s = q s t |s t−1 × · · · × q s |s By equation (47), q s t |s = β t π s t |s Substitute βπ s t+1 |s t in for q s t+1 |s t and r n s t in for τ s t n s t in equation (17) at s t , multiply both sides of equation (17) at s t by β t π s t |s , and take the sum of all constraints (17) subject to the transversality condition implied by equation (20) lim β t+1 π s t+1 |s b s t+1 |s t = 0, t→∞ (48) for b s t+1 |s t which represents a bond traded at s t with a payment contingent on the realization of s t+1 This yields equation (22) Similar arguments imply equation (23) Step For sufficiency, choose τ s t which satisfies equation (46) Let b s t |s t−1 satisfy equation (23) Equation (17) is satisfied Given equation (21), equation (16) is satisfied by Walras’s law B.2 Proof of Lemma and Proposition Step A sustainable equilibrium must be competitive so as to satisfy equations (21) and (22) Step For the necessity of equation (24), the politician at history s t can choose a deviation to τ s t = τ max , b s t+1 |s t = b ∀s t+1 , g s t = 0, and x s t = r max / (1 − β) − b s t |s t−1 , for x s t derived from equations (17), (46), (47), and the definition of b Since g s k ≥ and x s k ≥ ∀k > t, then τ s k = τ max , b s k+1 |s k = b, g s k = 0, and x s k = ∀k > t Since χ p > 0, the lowest welfare to the politician after the deviation is V b s t |s t−1 Step For the necessity of equation (25), the representative citizen can throw out the current incumbent Following this decision, the current incumbent’s best response sets x s t = r max / (1 − β) − b s t |s t−1 with the same policies as in step No other response can dominate this response since by equations (23) and the definition of r max and b, ∞ β k−t π s k |s t x s k ≤ r max / (1 − β) − b s t |s t−1 , (49) k=t s k ∈S k and x s k ≥ ∀k > t By step 2, all future governments set τ s k = τ max , b s k+1 |s k = b, g s k = 0, and x s k = ∀k > t The best response of all future representative citizens is to throw out future incumbents By equations (21) and (23), the representative citizen receives U b s t |s t−1 after the deviation Step For the sufficiency of equations (24) and (25), consider the following equilibrium Any deviation by the incumbent at s t results in the representative citizen throwing out the incumbent at s t+1 as in step Any deviation by the representative citizen at s t results in the incumbent choosing extractive policies as in step Given this punishment, the best deviation by the incumbent at s t yields the right-hand side of equation (24) This is because the politician’s welfare from rents under the best deviation, x s t + s t+1 ∈S t+1 βπ s t+1 |s t x s t+1 , cannot exceed the right-hand side of equation (49), and the right-hand side of equation (49) can be achieved with the same policies as described in step By equation (24), this deviation is weakly dominated If the representative citizen deviates by throwing out the current incumbent at s t , then he achieves the right-hand side of equation (25) by step 3, but this deviation is weakly dominated by equation (25) © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 − τ st YARED POLITICIANS, TAXES AND DEBT 835 APPENDIX C SUFFICIENT CONDITION FOR ASSUMPTION The required condition is that V0 ≥ and that ∃ λ s t ∞ t=0 with λ s t ≥ ∀s t s.t ∞ β k−t π s k |s t sk , λ s k > r max / (1 − β) − χ p ∀s t , (50) > U AUT + χ c ∀s t , and (51) k=t s k ∈S k ∞ β k−t π s k |s t W sk , λ s k k=t s k ∈S k β k−t π s k |s t sk , λ s k ∀s t (52) k=t s k ∈S k We can show that this condition implies Assumption Step This condition implies that ∃ξ ∈ s.t V {ξ , P } |s > V b−1 s and U {ξ , P } |s > U b−1 s ∞ ∞ starting from any s0 Starting from s0 , choose the sequences n s t t=0 and g s t t=0 to satisfy equations ∞ t t t (36) and (37) for a sequence λ s t=0 satisfying the condition Let P s = ∀s All incentive compatibility constraints are satisfied and V {ξ , P } |s > V b−1 s and U {ξ , P } |s > U b−1 s Finally, given ∞ equation (52), an implied sequence x s t t=0 which satisfies equation (22) is non-negative so that it is feasible s.t V ξ , P |s > V b−1 s and U ξ , P |s > U b−1 s Step Starting from any s0 , ∃ξ ∈ given b−1 s < b−1 s Consider ξ identical to ξ with the exception that x s = x s + b−1 s − b−1 s and c s = c s − x s + x s Then ξ ∈ and U ξ , P |s > and V ξ , P |s > V b−1 s U b−1 s Step The solution to the program admits P s = If instead P s = 0, then V {ξ , P } |s = V b−1 s and U {ξ , P } |s = U b−1 s by steps and of the proof of Proposition 2, and by step there exists an allocation which makes everyone strictly better off Step Imagine that the solution admits P s T = for some s T in which the incumbent in period is thrown out under an optimal sequence ξ Let ξ be identical to ξ with the exception that ∞ x sT = I0 s t β t π s t |s x s t / β T π s T |s t=0 s t ∈S t for I0 s t which is an indicator which equals if the incumbent in period holds power at t Also, let x s t = if I0 s t = and s t = s T , and let c s t = c s t − x s t + x s t It can be verified that ξ ∈ and the perturbation leaves both agents as well off Step Given the perturbation of step 4, incentive compatibility for the politician in period implies that β T π s T |s x s T − χ p ≥ max V0 , r max / (1 − β) − b−1 s − χ p (53) From steps and from the proof of Proposition and from equation (23), x s T = r max / (1 − β) − b s T |s T −1 , so that substitution into equation (53) implies that b s T |s T −1 ≤ b−1 s However, by steps and 3, ∃ξ ∈ which is identical to ξ but which differs from s T onward under which V ξ , P |s T > V b s T |s T −1 and U ξ , P |s T > U b s T |s T −1 Therefore, ξ yields strictly higher welfare for the politician and the households relative to ξ Therefore, P s T = is sub-optimal By forward induction, P s t = ∀s t APPENDIX D PROOFS OF SECTION D.1 Proof of Lemma Step Consider the original solution and perform the same substitutions as in the text © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 ∞ b−1 s < 836 REVIEW OF ECONOMIC STUDIES Step Consider the solution s.t b−1 s = b + V and V {ξ , P } |s = and imagine if {n, g} does not attain the optimum but n , g = {n, g} attains it From equation (31), this implies that ∞ β t π s t |s u n s t − g s t , n s t , g s t , st > t=0 s t ∈S t ∞ β t π s t |s u n s t − g s t , n s t , g s t , st , t=0 s t ∈S t which contradicts the optimality of {n, g} in the original solution Step The solution ξ to equation (26) sets n s t ≥ nmax ∀s t If this is not the case, then ∃ξ ∈ identical to ξ with the exception that n s t > n s t and r n s t = r n s t for all s t s.t n s t < nmax so that c s t = c s t + n s t − n s t , g s t = g s t , and x s t = x s t for all such s t This perturbation strictly increases the welfare of the households and leaves the politician as well off Step Define the sequence program implied by equations (32)–(35) for a given z−1 s in terms of {r, g} so α γ that the instantaneous utility to the household becomes u (r) − g + θ gα for u (r) = n − η nγ s.t r (n) = r u (r) < by the implicit function theorem given step Step Let zs be the set of feasible values of z for our program given s If z , z ∈ zs , then zκ = κz + (1 − κ) z ∈ zs ∀κ ∈ (0, 1) since {r κ , g κ } = κ r , g + (1 − κ) r , g is feasible and satisfies all constraints Moreover, {r κ , g κ } yields strictly greater welfare than κJ s, z + (1 − κ) J s, z , establishing concavity j j Step To show that zs is closed, consider a sequence zs ∈ zs such that limj →∞ zs = zs There is a corresponding stochastic sequence r j , g j which converges to r ∞ , g ∞ since social welfare net of rents and debt net of rents are continuous in r j , g j Since every element of r j , g j at s t is contained in r , r max × 0, g max for some arbitrarily low r and arbitrarily high g max , and since equations (34) and (35) are weak inequalities, then r ∞ , g ∞ is incentive compatible Since β ∈ (0, 1), then by the Dominated Convergence Theorem, r ∞ , g ∞ achieves zs and the household welfare net of rents associated with zs Therefore, zs ∈ zs Step Consider a sequence {r, g} associated with the solution for some z ∈ zs , zs Consider the sequence {r , g } for which the only difference between {r, g} and {r , g } is that r0 = r0 + for arbitrarily low gα Define F (s, z, ) = u r0 − g0 + θ (s) α0 + β π ks J (k, zk ), so that F (s, z, 0) = J (s, z) Optimality implies that F (s, z, ) ≤ J (s, z + ) for F (s, z, ) which is concave and differentiable By Lemma of Benveniste and Scheinkman (1979), J (·) is differentiable D.3 Proof of Proposition Step By equations (36), (39), and step of the proof of Lemma 3, Jz (s, z) = − − ηnγ −1 / γ ηnγ −1 − ≤ 1/γ , which implies that J (s, z) − z is decreasing in z Step Define λ (s) = −Jz (s, r max / (1 − β) − χ p ) and define λ (s) = −Jz (s, z) for z which solves J (s, z) − z = U AUT + χ c Step Suppose that λ s t−1 < λ (st ) Then by the concavity of J (·), for (34) to hold, we require λ s t ≥ λ (st ) > λ s t−1 , so that from equation (38), φ s t > This implies that z s t |s t−1 = r max / (1 − β) − χ p and therefore λ s t = λ (st ) Analogous arguments hold for λ s t−1 > λ (st ) Step Suppose that λ s t−1 ∈ λ (st ) , λ (st ) If φ s t > 0, we have z s t |s t−1 = r max / (1 − β) − χ p and consequently λ s t = λ (st ) But from equation (38), φ s t > implies that λ s t > λ s t−1 which is a contradiction Therefore, φ s t = Analogous arguments hold if ψ s t > Step Therefore λ s t ⎧ ⎨ λ (st ) = λ s t−1 ⎩ λ (st ) if λ s t−1 > λ (st ) if λ s t−1 ∈ λ (st ) , λ (st ) , if λ s t−1 < λ (st ) which implies equations (40) and (41) from equations (36), (37), and (46) © 2009 The Review of Economic Studies Limited (54) Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 D.2 Proof of Lemma YARED POLITICIANS, TAXES AND DEBT 837 D.4 Proof of Corollary Step The solution to the problem which ignores equations (34) and (35) is associated with λ in equations (36) and (37) which solves ∞ β t π s t |s (st , λ) = z−1 s t=0 s t ∈S t for z−1 s = b−1 s + max {0, V0 } Step Choose χ p = ∞ χ c = 0, so that equations (34) and (35) not bind under the implied allocation of step Step Choose V0 = and choose s0 = arg mins θ (s) Choose χ p sufficiently low so that r max / (1 − β) − b−1 s − χ p > and z−1 s = r max / (1 − β) − χ p Since equations (34) binds in period 0, τ s = τ (s0 ) associated with λ (s0 ) Step Since (k, λ) < (s, λ) if θ (s) < θ (k) then necessarily λ (s1 ) > λ (s0 ) and τ (s1 ) > τ (s0 ) for some s1 in order that equation (34) be satisfied for such s1 Step Consider a path s0 , s1 , s0 for s1 for which τ (s1 ) > τ (s0 ) From equation (40), τ s = τ (s1 ) , τ (s0 ) > τ s = τ (s0 ), where we have used Assumption and the definition of τ (s0 ) in Proposition to establish τ (s0 ) > τ (s0 ) Step Choose V0 sufficiently large that z−1 s = z (s0 ) for z (s0 ) associated with λ (s0 ) and choose s0 = arg maxs θ (s) Analogous arguments to steps 1–3 imply that for χ c sufficiently high, there exists a path s0 , s1 , s0 with taxes τ (s0 ), τ (s1 ), max τ (s1 ) , τ (s0 ) < τ (s0 ) D.6 Proof of Proposition Step Given equation (54) and the i.i.d assumption, E {λk |st , λt } for k > t is independent of st and is weakly increasing in λt Step Let k represent the realized value of s k and let Wk represent the realized value of W s k Then ∞ ∞ k−t k−t β |s , λ and E Wk |st , λt weakly decreases in λt , and both are weakly increases in λ E k t t t k=t+1 k=t+1 β independent of st ∞ k−t Step If θ (st ) is increasing in st , then E k |st , λt strictly decreases in st conditional on λt and k=t β ∞ k−t Wk |st , λt strictly increases in st conditional on λt E k=t β Step By the definitions of λ (st ) and λ (st ), these solve ∞ β k−t E k |st , λ (st ) = r max / (1 − β) − χ p and k=t ∞ β k−t Wk |st , λ (st ) E = U AUT + χ c , k=t for a given st , which by step implies that λ (st ) and λ (st ) are increasing in st which implies that τ (st ) and τ (st ) are increasing in st by (54) D.7 Proof of Theorem ∞ Step If ∩s∈S τ (s) , τ (s) is non-empty, then τ s t t=0 converges almost surely Equation (40) implies that τ s t ∈ mins∈S τ (s) , maxs∈S τ (s) so that it is bounded Moreover, since maxs∈S τ (s) ≤ mins∈S τ (s), then τ s t−1 ≤ τ s t ≤ maxs∈S τ (s) or τ s t−1 ≥ τ s t ≥ mins∈S τ (s) Since τ s t is monotone and bounded, then τ s t converges to a limit for every history s ∞ Therefore, it converges almost surely ∞ Step If ∩s∈S τ (s) , τ (s) is empty, then τ s t t=0 converges with probability Consider two state k and l ∞ for which the intervals τ (k) , τ (k) and τ (l) , τ (l) are mutually exclusive with τ (k) < τ (l) Imagine if τ s t t=0 ∞ converges with positive probability for a subset of histories κ ∈ S ∞ For a given history κi ∈ κ in which τ s t t=0 t converges to τ (κi ), ∃T (κi ) s.t for every t > T (κi ), τ (κi ) − τ s < τ (l) − τ (k) /2 Given equation (40) this implies that either st = k ∀t > T (κi ) or st = l ∀t > T (κi ) Let T = minκi ∈κ T (κi ) Since there is full support, Pr {s ∞ ∈ κ} ≤ Pr st = k ∀t > T or st = l ∀t > T ∀sT ∈ S = 0, yielding a contradiction © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 D.5 Proof of Theorem 838 REVIEW OF ECONOMIC STUDIES Step If ∃λ ≥ s.t ∞ β k−t π s k |s t sk , λ ≥ r max / (1 − β) − χ p and (55) k=t s k ∈S k ∞ β k−t π s k |s t W sk , λ ≥ U AUT + χ c , (56) k=t s k ∈S k APPENDIX E EXTENSION OF SECTION 4.1 In this section, we continue the formal definition of the equilibrium We define how strategies induce histories, we define continuation strategies, and we define the problem of each agent Strategies induce histories as follows Given h0t , ϒ induces h1t = h0t , ϒ t h0t , and given h1t , σ induces h2t = h1t , σ t h1t and h0t+1 = h1t , σ t h1t , st+1 , and so on Continuation strategies are generated as follows Given h0t and σ , a continuation of ϒ is ϒ t h0t , ϒ t+1 h0t , ϒ t h0t , σ t h0t , ϒ t h0t , st+1 , Given h1t and ϒ, a continuation of σ is σ t h1t , σ t+1 h1t , st+1 , ϒ t+1 h1t , σ t h1t , st+1 , Given h2t , ϒ, and σ , a continuation of f is ft h2t , ft+1 h2t , st+1 , ϒ t+1 h2t , st+1 , σ t+1 h2t , st+1 , ϒ t+1 h2t , st+1 , Given h2t , ϒ, and σ , a continuation of ζ is defined analogously Consider the private household solving its market problem in period t Given h2t , ϒ, σ , and ζ , a household chooses a continuation of f to maximize: ∞ β k−t u ck h2k , nk h2k , gk h1k , sk + − Pk+1 h0k E χ c (1 − β) |h2t , ϒ, σ , f, ζ k=t s.t h ct h2t + bt−1 (st ) h2t−1 = − τ t h1t nt h2t + qt (st+1 ) h2t bth (st+1 ) h2t , st+1 ∈S h ck h2k + bk−1 (sk ) h2k−1 = − τ k h1k nk h2k + qk (sk+1 ) h2k bkh (sk+1 ) h2k sk+1 ∈S for k > t , and nt h2t , nk h2k ≥ For k > t all future histories are induced by ϒ and σ from h2t Note that we have taken into account that the household achieves χ c (1 − β) from throwing out the current politician Since future histories not depend on f , households are non-strategic in this allocation Let W˜ t h2t ; ϒ, σ , f, ζ represent the welfare of households at h2t implied by f given ϒ, σ , and ζ Consider the politician in power at t Such a politician takes into account whether he will be in power in the future, and we can define It h1t , h1t = and Ik h1t , h1k = kl=t+1 Pl h0l−1 for k ≥ t + 1, an indicator which equals if the politician in power at t is still in power at date k Note that if Ik h1t , h1k = 1, the politician effectively receives flow © 2009 The Review of Economic Studies Limited Downloaded from http://restud.oxfordjournals.org/ at Taylor's University College on December 6, 2012 k−t ∀s t , then ∩s∈S τ (s) , τ (s) is non-empty Starting from initial conditions st and z s t |s t−1 = ∞ π k=t s k ∈S k β s k |s t sk , λ , the unconstrained solution which ignores equation (34) and (35) sets τ s k = τ and g s k = g ∀s k for τ and g associated with λ through equations (36) and (37), respectively Since this solution satisfies equations (34) and (35) ∀s k , it is the constrained solution which by equation (40) implies that τ ∈ ∩s∈S τ (s) , τ (s) = ∅ Step If λ ≥ which satisfies equations (55) and (56), then ∩s∈S τ (s) , τ (s) is empty If ∩s∈S τ (s) , τ (s) were non-empty, then associated with every τ ∈ ∩s∈S τ (s) , τ (s) is a value of λ which satisfies (55) and (56), yielding a contradition ˆ as the state st ∈ S in which the left-hand side of equation (55) is minimized for a given λ, Step Define s p (λ) ˆ as the state st ∈ S in which the left-hand side of equation (56) is minimized for a given λ Since and define s c (λ) ˆ is increasing in λ and the (·) and W (·) are monotonic in λ, the left-hand side of equation (55) evaluated at s p (λ) ˆ is decreasing in λ For a given λ ∈ R+ , there exists a value χˆ p left-hand side of equation (56) evaluated at s c (λ) ˆ Moreover, there exists a value χ c which which is decreasing in λ which sets equation (55) to an equality at s p (λ) ˆ Define χ p (χ c ) as the level of χ p associated with λ for is decreasing in λ which sets (56) to an equality at s c (λ) which χ c = χ c , and define χ c (χ p ) analogously Step By step 5, ∃λ which satisfies equations (55) and (56) if and only if χ c ≤ χ c (χ p ) and χ p ≥ χ p (χ c ) The rest then follows from steps 1–4 YARED POLITICIANS, TAXES AND DEBT 839 utility v x h1k , and if Ik h1t , h1k = 0, the politician effectively receives flow utility −χ p (1 − β) /β 36 Therefore, given h1t , ϒ, f , and ζ , he chooses a continuation of σ to maximize: ∞ β k−t Ik h1t , h1k v x h1k E − − Ik h1t , h1k k=t χp 1−β β2 |h1t , ϒ, σ , f, ζ , s.t gk h1k +x k h1k + g bk−1 (sk ) h1k−1 = τ k h1k g nk h2k + qk (sk+1 ) h2k bk (sk+1 ) h1k , sk+1 ∈S g W˜ t h0t , ϒ t h0t , σ t h0t , ϒ t h0t ; ϒ, σ , f, ζ for future histories which are induced by ϒ and σ from h0t Given h2t , ϒ, σ , and f , ζ must clear the bond market: g bt (st+1 ) h1t + bth (st+1 ) h2t = ∀st+1 ∈ S Acknowledgements I am especially grateful to Daron Acemoglu and Mike Golosov for their support and encouragement I would also like to thank Manuel Amador, Marios Angeletos, Roc Armenter, Abhijit Banerjee, Ricardo Caballero, Larry Christiano, Alexandre Debs, Per Krusell, Roozbeh Hosseini, Dimitris Papanikolaou, Tomasz Piskorski, James Poterba, Catarina Reis, Kjetil Storesletten, Aleh Tsyvinski, Ivan Werning, and three anonymous referees for comments REFERENCES ABREU, D (1988), “On the Theory of Infinitely Repeated Games with Discounting”, Econometrica, 56, 383–397 ACEMOGLU, D., (2003), “Why Not a Political Coase Theorem? 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