C Sfienti

M De Napoli

S Bianchin

A S Botvina

J Brzychczyk

A Le Fèvre

J Lukasik

P Pawlowski

W Trautmann

P Adrich

T Aumann

C O Bacri

T Barczyk

R Bassini

E Ducret

H Emling

J Frankland

M Hellström

D Henzlova

K Kezzar

G Immè

I Iori

H Johansson

A Lafriakh

E Le Gentil

Y Leifels

W G Lynch

J Lühning

U Lynen

Z Majka

M Mocko

W F J Müller

A Mykulyak

H Orth

A N Otte

R Palit

A Pullia

G Raciti

E Rapisarda

H Sann

C Schwarz

H Simon

K Sümmerer

C Volant

M Wallace

H Weick

ISOTOPIC EFFECTS IN NUCLEAR REACTIONS AT RELATIVISTIC ENERGIES

A systematic study of isotopic effects in the break-up of projectile spectators at relativistic energies has been performed at the GSI laboratory with the ALADiN spectrometer coupled to the LAND neutron detector. Besides a primary beam of 124 Sn, also secondary beams of 124 La and 107 Sn produced at the FRS fragment separator have been used in order to extend the range of isotopic compositions. The gross properties of projectile fragmentation are very similar for all the studied systems but specific isotopic effects have been observed in both neutron and charged particle production. The breakup temperatures obtained from the double ratios of isotopic yields have been extracted and compared with the limiting-temperature expectation.

Introduction

Challenging motivations for isotopic studies in nuclear multifragmentation are derived from the importance of the density dependence of the symmetry-energy term of the nuclear equation of state for astrophysical applications and for effects linked to the manifestation of the nuclear liquid-gas phase transition. Müller and Serot, in their seminal paper [1], have demonstrated that the two-fluid nature of nuclear matter has very specific consequences for the phase behavior in the coexistence region. Different isotopic compositions are predicted for the coexisting liquid and gas phases, with the gas being more neutron rich than the liquid in asymmetric (N ≠ Z) matter. This difference stems from the decrease in the symmetry energy in nuclear matter as the density is decreased. The expected magnitude of this density dependence, however, is model dependent and very poorly constrained by existing data [2]. The calculations of Müller and Serot are restricted to infinite matter with no Coulomb force included. In addition, the isotopic composition, in the calculations, is typically varied within a range of proton fractions ρ p /ρ = 0.3 to 0.5 whose limits are not easily accessible in experiments with heavy nuclei. Theoretical studies for finite systems also indicate that the sequential decay of excited reaction products has a tendency to reduce some of the expected effects [3].

If the phase transition for asymmetric nuclei still manifests itself as a plateau in the caloric curve [5] (i.e. the correlation between the temperature of the system and its excitation energy), this could be influenced by the degree of asymmetry as well as by the mass of the system undergoing the fragmentation. It has been shown [4] that, due to the Coulomb pressure, there exists a limiting temperature which represents the maximum temperature at which nuclei are found to exist as self-bound objects in Hartree-Fock calculations. The dependence of the breakup temperature on the excitation energy could therefore be governed by the limiting temperature. Figure 1 shows the calculated limiting temperature as a function of the neutron and proton number [4]. As it is possible to see from the picture, in case of protonrich nuclei, the phenomenon of vanishing limiting temperature is predicted, the limiting temperature decreasing with increasing proton fraction. Clearly, new experiments exploring such phenomena are mandatory for having a better knowledge of the thermodynamics of a finite nucleus and its decay. Recently a systematic investigation of projectile-spectator fragmentation has been undertaken at the ALADiN spectrometer at the GSI [6,[START_REF] Bianchin | Contribution to this proceedings[END_REF]: four different projectiles, 124 Sn, 197 Au, 124 La and 107 Sn, all with an incident energy of 600 AMeV on 116 Sn and 197 Au targets, have been studied. The two latter beams have been delivered by the FRagment Separator (FRS) of the GSI as products of the fragmentation of a primary 142 Nd beam at 890 AMeV on a 9 Be production target [START_REF] Bianchin | Contribution to this proceedings[END_REF]. The necessity of low beam intensities for the best operational condition of the ALADiN setup (≅2000 particles/sec), and the possibility of using a thick target in order to achieve high interaction rates are indeed conditions compatible with radioactive-ion-beam experiments. Moreover, the inverse kinematics offers the possibility of a threshold-free detection of all heavy fragments and residues and thus gives a unique access to the breakup dynamics. The measurement of the charge and the momentum vector of all projectile fragments with Z≥2 has been performed, with high efficiency and high resolution, with the TP-MUSIC IV detector [START_REF] Sfienti | Proceeding of the XLI International Winter Meeting on Nuclear Physics[END_REF]. Using the reconstructed values for the rigidity and pathlength, the charge of the particle measured by the TP-MUSIC IV, and the time-of-flight given by the TOF-Wall, the velocity and the momentum vector can be calculated for each detected charged particle. The knowledge of velocity and momentum allows then the calculation of the particle's mass. Neutrons emitted in directions close to θ lab = 0 o , are detected with the Large-Area Neutron Detector (LAND) which covers about half of the solid angle required for neutrons from the spectator decay.

Gross Properties of multifragment decay

The gross properties of projectile fragmentation are very similar for all the studied systems. The fragments emerging from the decay of the projectile spectators are well localised in rapidity. The distributions are peaked around a rapidity value very close to be beam rapidity and become narrower with increasing mass of the fragment. The observed independence of the Rise and Fall, i.e. of the correlation between the multplicity of intermediate mass fragments with Z bound , also for the unstable systems [6], confirms the hypothesis of equilibrium at freeze-out.

The shape of the charge distributions are as well similar for all the systems. For larger values of Z bound , the charge distribution exhibits a U-shape. The heavy fragments are the residues of the lowly-excited projectile-spectators after the evaporation of light fragments and nucleons. In semi-central reactions, i.e. smaller values of Z bound , the distribution broadens and flattens over nearly the full charge distribution. For still lower values of Z bound , the charge distribution becomes steep. This is consistent with the system disassembling into predominantly lighter fragments.

The charge distributions have been fitted with a power-law parameterization, σ(Z) ∝ Z -τ , in the charge range 3≤Z≤15. The power-law parameters τ (Figure 2 -left panel) allow to follow the transition from the U-shape to a pure exponential spectrum and reach the minimum value in the Z bound range which corresponds to the maximum production of IMF, i.e. in the multifragmentation region. They follow a nearly universal curve almost independent of the isotopic composition of the original spectator system. Specific isotopic effects, even though small, can nevertheless be observed: in particular, the hierarchy of τ for the neutron-poor 124 La and 107 Sn and neutron-rich 124 Sn and 197 Au systems for Z bound /Z proj >0.5 is opposite to the standard predictions of the Statistical Multifragmentation Model SMM [9]. It can, however, be explained with a weak isotopic dependence of the surface-term coefficient in the liquid-drop description of the fragment masses at low excitation energy which gradually disappears with increasing excitation of the fragmenting system [10]. Specific isotopic effects are as well found in the reconstructed neutron multiplicities measured with the LAND detector [11] (Figure 2 -right panel). For peripheral collisions the values of the multiplicity depend on the number of available neutrons in the entrance channel. Going towards central collisions the number of emitted neutrons is progressively determined by the N/Z in the entrance channel. In a preliminary comparison with SMM calculation (colored points in Figure 2) a promising agreement has been observed. Neutrons will be important for establishing the mass and energy balance and in particular for calorimetry. In this respect it is crucial to identify the spectator neutrons and to distinguish them from the fireball ones. From a preliminary analysis of their rapidity distributions, the corresponding spectator sources have been identified. They are characterized by temperatures up to 4 MeV, possibly caused by large contributions from evaporation.

Structure and Memory Effects in particle production

The mass resolution obtained for projectile fragments entering into the acceptance of the ALADiN spectrometer is about 3% for fragments with Z=3 and decreases to 1.5% for Z≥6 [START_REF] Bianchin | Contribution to this proceedings[END_REF]. Masses are thus individually resolved for fragments with atomic number Z≤10. The elements are resolved over the full range of atomic numbers up to the projectile Z with a resolution of ΔZ≤0.2 obtained with the TP-MUSIC IV detector. The mean N/Z of the mass distributions of light fragments in the range 3 ≤Z ≤ 13 for two different Z bound cuts is presented in Figure 3. The values obtained for 124 Sn are larger than those for 124 La or 107 Sn (not shown) as expected from the different N/Z of the original projectiles. Their odd-even variation is, however, much more strongly pronounced for the neutron-poor cases. The strongly bound α-type nuclei (even-even N=Z) attract a large fraction of the product yields during the secondary evaporation stage. This effect is, apparently, larger if already the hot fragments are close to N=Z symmetry, as it is expected for the fragmentation of 124 La and 107 Sn [12]. Inclusive data obtained with the FRS fragment separator at GSI for 238 U [13] and 56 Fe [14] fragmentations on titanium targets at 1 A GeV bombarding energy confirm that the observed patterns are very systematic, exhibiting at the same time nuclear structure effects characteristic for the isotopes produced and significant memory effects of the isotopic composition of the excited system by which they are emitted. This has the consequence that, because of its strong variation with Z, the neutron-to-proton ratio <N>/Z is not a useful observable for studying nuclear matter properties. For this purpose, techniques, such as the isoscaling [START_REF] Bianchin | Contribution to this proceedings[END_REF], will have to be used which cause the nuclear structure effects to cancel out. A precise modeling of these secondary processes is, therefore, necessary for quantitative analyses.

Another interesting feature of the mass distributions predicted by SMM is their dependence, in the case of the proton-rich systems, on the excitation energy of the system [10]. This difference arises from the dependence of the number of neutrons in light fragments on the Z spectrum. For the neutron-rich 124 Sn system, on the other hand, the distributions should be independent of the excitation energy. From a first qualitative comparison with the model prediction of the mass distributions for different Z bound cuts, however, we have not observed any noticeable variation in the mean N/Zs for the 124 La system (Figure 3). Also in this case it will be crucial to precisely model the sequential decay in order to clarify whether it has washed out the expected effect.

Limiting temperature

As previously mentioned, for proton-rich systems a rapid drop of the limiting temperature has been theoretically predicted (Figure 1) because of the increasing Coulomb pressure [4]. On the other hand, SMM calculations predict nearly isospin-invariant temperatures for the coexistence region [10]. Therefore, in order to distinguish whether the breakup temperature is determined by the binding properties of the excited hot nuclear system or by the phase space accessible to it by fragmentation we have analyzed the temperature for the studied neutron-poor and neutron-rich systems. The temperatures used in the caloric curve studies [5,15] were deduced from a double ratio of isotopic yields. Under the assumptions of low density and chemical equilibrium a grand canonical treatment [16] yields for the double ratio:

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Δ = T B a Y Y Y Y Z A Z A Z A Z A exp / / ) , ( ) , ( ) , ( ) , ( 4 4 3 3 2 2 1 1
with ΔB being the double difference of the binding energies of the chosen isotopes and a a statistical factor containing spin and mass terms. Furthermore, for best sensitivity the binding energy difference ΔB should be comparable or larger than the temperatures to be measured [17]. The thermometry with the 3,4 He isotope pairs used in the nuclear caloric curve [5] benefits from the large difference ∆B = 20.6 MeV of the binding energies of these two nuclei but it is not the only choice. There are also other combinations of isotopes which can be expected to provide the necessary sensitivity for the measurement of temperatures in the MeV range. In a recent systematic study of different isotopic thermometers for spectator fragmentation [18] T BeLi , T CLi , and T CC have been analyzed in detail. In particular, it has been found that the rise at small Z bound , i.e. high excitation energy, previously observed with T HeLi is well reproduced by most thermometers, including T BeLi which is derived from the 7,9 Be and 6,8 Li isotope ratios. This is an indication that the rise is not necessarily related to a particular behavior of either 3 He or 4 He. An overall good agreement between the different temperature observables has been obtained with the exception of those containing carbon isotopes. In the latter cases, the apparent temperature values remain approximately constant with values between 4 and 5 MeV.

Measured isotope ratios as a function of Z bound for the124 Sn, 124 La and 107 Sn systems are shown in Figure 4. A very interesting dependence on the isotopic composition of the spectator is observed for all analyzed ratios with the exception of the 3 He/ 4 He ratio, exhibiting a reduced difference between the neutron-rich and neutron-poor systems. The strong sequential decay into α particles could explain the difference between these two behaviors. Therefore, also in this case, the structure effects responsible for the observed odd-even variation in the N/Z/s of intermediate-mass fragments (Figure 3) play the major role. For the 124 Sn projectile spectator, moreover, the ratios, with the exception of 3 He/ 4 He, are almost independent of Z bound . For the mentioned ratio the decrease between the most central and the most peripheral collisions is about a factor 4 whereas for example, for the 9 Be/ 8 Li ratio the total variation amounts hardly to a factor of 2. There seems to be a clear correlation between the difference of the binding energies of the involved isotopes and Z bound , i.e. excitation energy of the system [18]: the higher the first the stronger the variation of the corresponding ratio with Z bound . On the other hand, in the case of the proton-rich systems all ratios exhibit a strong dependence on the excitation energy deposited in the system. From the measured ratios the isotopic temperatures have been extracted and an overall agreement with the previous systematics [18] have been obtained for the T HeLi , T BeLi , T CLi , and T CC thermometers. In Figure 5 in particular, the apparent T HeLi and T BeLi temperatures for the 124 Sn and 124 La, Sn spectator systems are reported. By comparing the two systems with the same mass but different isospin-content, the average difference of the obtained T HeLi temperatures is 0.7±0.1 MeV whereas almost no difference (hardly 0.1 MeV in average) between the two systems is observed in the case of the T BeLi thermometer. The small difference observed in the case of T HeLi is caused by the fact that the dependence of the 6 Li/ 7 Li ratio (Figure 4) on the isotopic composition of the system is not compensated by the weak dependence of the 3 He/ 4 He ratio. In the case of T BeLi both isotopic ratios 7,9 Be and 6,8 Li exhibit a dependence on the N/Z of the original projectiles, which cancels out in the double ratio. The invariance of the isotopic temperature with the isotopic composition of the system is inconsistent with the limiting temperature predictions [4] of 2 MeV for the 124 Sn and 124 La systems (Figure 1) and seems to favor a statistical interpretation [10].

Conclusions

Isotopic effects in the break-up of projectile spectators at relativistic energies have been reported. The gross properties of projectile fragmentation are very similar for all the studied systems. Specific isotopic effects, even though small, can nevertheless be observed: in particular, the inversion in the hierarchy of the τ exponential parameter of the charge distribution can be explained with a weak isotopic dependence of the surfaceterm coefficient of the nuclear equation of state [10]. The mean N/Zs of the isotope distributions of light fragments exhibit as well specific isotopic effects. In particular, the observed odd-even variation is much more strongly pronounced for the neutron-poor cases and could be explained in terms of a simultaneous concurrence of both structure effects characteristic for the isotopes produced and memory effects of the isotopic composition of the excited system from which they are emitted. From the double ratios of Z≤4 isotopes, the isotopic temperatures have been determined. The small dependence (of about 0.7 MeV) observed in the T HeLi thermometer could be due to the influence of structure effects in the sequential decay. The invariance with the isotopic composition in the entrance channel is inconsistent with the limiting-temperature predictions and seems to favors the statistical interpretation. On the other hand, the limiting-temperature concept reproduces nicely the mass dependence of the caloric curves [15] and only seems to fail when applied to the isospin degree of freedom. It should be noted that most of the limiting-temperature calculations are made for beta stable nuclei [19] while it was not explicitly tested whether the studied systems are still near the stability at breakup. The weak N/Z dependence of the breakup temperatures measured in this experiment shows that this is not a major point of concern. The same observation, on the other hand, is not compatible with the strong Coulomb effect predicted by Besprosvany and Levit [4]. This open point in the connection between limiting temperatures for heavy nuclei and breakup temperatures of fragmenting nuclear systems will require an improved understanding.

Figure 1 .

 1 Figure 1. Location of the four studied projectiles in the plane of atomic number Z versus neutron number N. The contour lines represent the limiting temperatures according to [4] , the dashed line gives the valley of stability, and the full line corresponds to the N/Z = 1.49 of 197 Au.

Figure 2 .

 2 Figure 2. (Left Panel) The extracted τ parameters as a function of normalized Z bound for 124 La, 124 Sn and 107 Sn at 600 AMeV, compared with earlier data for 197 Au obtained at the same energy. (Right Panel) Neutron multiplicities as obtained from the LAND detector for all the studied systems (colored symbols are SMM predictions).

Figure 3 .

 3 Figure 3. Mean values <N>/Z of light fragments with 3 ≤ Z ≤ 13 produced in the fragmentation of 124 Sn and 124 La at 600 A MeV for two different bins in Z bound.

Figure 4 .

 4 Figure 4. Measured isotopic yield ratios as a function of Z bound /Z proj for the neutron-rich

Figure 5 .

 5 Figure 5. Isotopic temperatures T HeLi and T BeLi as a function of Z bound /Z proj for 124 Sn and 124 La, 107 Sn projectile spectators.

Sn and the neutron-poor 124 La and 107 Sn systems.

C.Sf. acknowledges the receipt of an Alexander-von-Humboldt fellowship. This work was supported by the European Community under contract No. RII3-CT-2004-506078 and HPRI-CT-1999-00001 and by the Polish Scientific Research Committee under contract

No. 2P03B11023.

Bibliography


Emma Tominey
email: emma.tominey@york.ac.uk

Incentives in the Public Sector: Evidence from a Government Agency *

Keywords: JEL Classification: J33, J45, D23 incentives, public sector, teams, performance, personnel economics

This paper addresses a lack of evidence on the impact of performance pay in the public sector by evaluating a pilot scheme of incentives in a major government agency. The incentive scheme was based on teams and covered quantity and quality targets, measured with varying degrees of precision. We use data from the agency's performance management system and personnel records plus matched labour market data. We focus on three main issues: whether performance pay matters for public service worker productivity, what the team basis of the scheme implies, and the impact of the differential measurement precision. We show that the use of performance pay had no impact at the mean, but that there was significant heterogeneity of response. This heterogeneity was patterned as one would expect from a free rider versus peer monitoring perspective. We found that the incentive scheme had a substantial positive effect in small teams, and a negative response in large teams. We found little impact of the scheme on quality measures, which we interpret as due to the differential measurement technology. We show that the scheme in small teams had nontrivial effects on output, and our estimates suggest that the use of incentive pay is much more cost effective than a general pay rise.

Governments employ a lot of people. The productivity of these workers, forming such a substantial fraction of the labour force (15% in the US, more than are employed in manufacturing at 13%) is therefore a major issue and many governments have an explicit agenda of improving the efficiency of public service delivery. 1 One method which has received considerable attention is the use of explicit financial incentives. Early examples include Osborne and Gaebler (1993) "Reinventing Government", promoted by Vice-President Gore in the USA and the Job Partnership Agency Scheme in the USA in the 1980s (Barnow 2000, Heckman et al. 1996). More lately, there has been considerable interest in performance related pay for teachers and public sector doctors (e.g. Muralidharan and Sundararaman 2011, Lavy 2009, Gravelle et al. 2010).

Theorists have addressed the role of such incentives in the public sector, drawing attention to a set of features such as multiple tasks, multiple principals and missions, all of which suggest that even if there is no difference in the inputs of the production process between the private and public sector, there are some specific features related to outputs and to the way public sector agencies are structured which mean that incentives might be expected to have different consequences in public organisations (e.g. Dixit 2002, Prendergast 1999, Baker 2002, Francois 2000, Besley and Ghatak 2005). However, despite the interest (Burgess and Ratto 2003), the empirical evidence on the use of incentives in the public sector is still quite scant and a recent review concluded that there are relatively few estimates from which causal inferences can be made (Bloom and Van Reenen 2010).

This paper aims to fill this gap. In a search for greater public sector productivity, the government of the UK in the late 1990s piloted the use of financial incentives for lower level bureaucrats. As part of this programme they introduced a pilot programme of the use of teambased financial incentives in a large UK public agency. The agency, Jobcentre Plus, was one of the main government agencies dealing with the public: its role was to place the unemployed into jobs and administer welfare benefits. In contrast with many schemes in the private sector, the incentive scheme we analyse was exogenously imposed on the organisation, as it was part of a wider government experiment with incentive pay (Makinson 2000). In addition, it was a team based performance pay scheme: workers were rewarded on the basis of team rather than individual production.

The specific nature of the incentive scheme allows us to investigate three key issues. First, what is the impact of an explicit financial incentive scheme on public sector workers? Dixit's (2002) review of theoretical contributions suggests that such incentives may be counterproductive. Evidence on the effectiveness of incentive schemes in the public sector is mixed. Kahn, Silva and Ziliak (2001) examine a reform to the Brazilian tax collection authority which paid financial incentives based on individual and team performance in detecting and fining tax evaders. Amounts involved were substantial, frequently providing bonuses over twice mean annual salary. Authors find a dramatic effect, with fine collections per inspection 75% higher than in the counter-factual. Lavy (2009) found that teacher incentives to improve pupil performance in maths and English significantly raised student outcomes. Baiker and Jacobson (2007) in a study of the police where participants were able to keep a proportion of the value of drug-related asset seizes found significant effect of the incentives, documenting an increase in heroin related drug offenses and even a rise in the price of heroin. But counterexamples exist -for example Mullen et al. (2010) found little effect of pay for performance on the quality of medical care.

Second, what is the impact of a team-based incentive scheme? Economists have typically been skeptical of a team basis for obvious free-rider problems and free rider effects have been found (e.g. Gaynor and Pauly 1990, Gaynor et al. 2004, Bhattacherjee 2005). 2 On the other hand, Burgess et al. (2010) find that even in quite large teams, a team-based incentive scheme in the UK Customs and Excise raised the productivity of agency workers. Knez and Simester (2001) argue that peer monitoring outweighed free riding effects in a scheme in Continental Airlines which had large teams and Hamilton, Nickerson and Owan (2003) conclude similarly for a garment factory in California. The incentive scheme we analyze was introduced across teams of very different structures, so allowing us to quantify the effect of team size.

Third, how do workers respond to relative task measurement precision in an explicitly multitasking environment? Although the implications of multi-tasking for scheme design are a major part of the literature on incentives, there is very little empirical evidence on the importance of the precision with which targeted outcomes are measured. Gaynor and Pauly (1990) investigate the productive efficiency of physicians practicing in groups of medical partnerships, with differing compensation structures. They showed that output was greater where compensation was more directly related to productivity. The incentive scheme we study here incorporated five targets covering most of the tasks of the agency. In practice, only 4 of these were measured. Of these, one was defined in terms of quantity of output, three were defined in terms of quality. The quantity target was measured with considerable precision as it was a weighted count of every client placed in a job, while the quality targets were measured with considerably less precision. We can therefore evaluate the impact of measurement precision.

The scheme was designed to be a randomised control trial. However, we only observe data for the year that the scheme was in operation, so we compare the treated and controls during that year. Given our communication with the agency, we have access to data that contains the variables arguably determining treatment status and therefore use the Propensity Score Matching method. For internal validity we assume that conditional upon the set of observable variables, the potential outcomes for treated and control come from the same distribution.

Our results suggest that the overall impact of the scheme was zero. However, we also find significant heterogeneity of response that fits with important free rider effects in production.

The impact of the incentive scheme was greatest in small offices and in districts composed of fewer offices. Thus while some mechanism such as peer monitoring does overcome the freeriding problem in small teams, it appears not to do so in large teams. Finally, whilst quantity increased, the scheme had little effect on the quality of service. This suggests that relative measurement precision in a multi-tasking context is important. Overall, the scheme design was not optimal in a number of ways which we briefly discuss in our conclusions.

Section 1 describes the nature of the organisation and the incentive scheme. Section 2 introduces the data and sets out our modelling framework and identification strategy. Section 3 presents our estimation results and robustness checks. In section 4 we use these to evaluate the scheme. Section 5 concludes.

The Incentive Scheme

The Nature of the Incentive Scheme

The initial drive for the introduction of financial incentives was political, originating in the White Paper "Modernising Government" (1999). This was followed up in the Makinson report (2000) for the Public Sector Productivity Panel, advocating incentive schemes for front line government workers. This study evaluates one of these schemes. 3 The pilot incentive scheme at Jobcentre Plus (JP) ran from April 2002 to March 2003. The main relevant features of the scheme are as follows.

Teams

Performance targets and rewards were assessed at the level of a district, comprising different offices. As typical in the public sector, the design of the incentive scheme was constrained by some practical issues relating to output measurement in a complex organization. The official rationale for designing a team-based rather than an individual-based incentive scheme was to promote cooperation among workers, although discussions with the scheme designers revealed that another reason was that some of the output measures relating to the quality of the service provided by the agency are only available at the aggregate level of districts (see also below) 4 .

All workers in the incentivized district got the bonus if the target was hit, and the district manager was responsible for achieving the target. We should note that the boundaries of the team were defined on the basis of administrative reasons rather than on the basis of a production function. 5 These teams were large -there were only 90 districts covering the whole of the country, varying in size from 5 to 39 offices in the team, and from 264 and 1535 people within a team. 6 Only 17 out of the 90 districts were incentivized: these were districts containing at least one new type of office -a 'Pathfinder' office. 7 These districts were designated as Pathfinder districts and contained both Pathfinder and non Pathfinder offices.

Non incentivized districts only contained non Pathfinder offices. The work of non-Pathfinder offices was largely unaffected by the presence of Pathfinder offices in the district. For identification we exclude Pathfinder offices from our analysis, as we discuss in more detail in section 2.2.

Threshold incentive payment

In common with many schemes, the form adopted was a step function, based on a threshold level of performance. Workers were paid a straight salary up to the threshold, the bonus was paid for hitting the threshold, and then there was no further increase in remuneration for further output. The bonus was based around standard rates, which varied with the job grade per target hit. If all five targets were achieved there was an extra 50% of the standard rate. This means that if all five targets were hit, a band A worker would earn an extra £750, whereas a band G job would get £3,750 more. This represents around 7.5 and 8.5 percent of average pay respectively. The targets for the incentivised districts were set as percentage increases on the previous year's achievements. 8

Multiple targets

One central issue in the design of incentive structures is the importance of multi-tasking. In particular, a trade-off between quantity produced and quality is often crucial. 9 This incentive scheme recognized that and included targets for five different functions, which together measure both quantity and quality. Discussed in detail below these are job placements (quantity), customer service, employer service, other business delivery functions, and reducing benefit calculation error and fraud (all quality). The specific activities involved, and the ease with which each target was measured differ widely across these five targets. For workers choosing how to allocate effort, the definition and measurement of the target variables will be important. benefits offices and employment offices. This process of change was slow, and most offices at the time of our study -there were 1464 in total -remained single service providers as ex-BA or ex-ES offices. More Pathfinder offices were created through the year of the pilot scheme. 8 All districts have clear targets set for all functions, but in the control districts these were not incentivised. The terminology of JP describes these base goals as targets and the higher levels as 'stretch'. In this paper we keep to the standard economics terminology and describe the higher levels of output required to win the bonus as the targets. 9 See Paarsch and Shearer (2000) for an analysis of this issue.

Job placements (job entries in the scheme terminology) were measured as weighted numbers of clients who were found work by the office. The weight per placement varied with the priority of the clients and reflected government targets (see table A3 for details). Our main quantity output measure was job entry point productivity, defined as job entry points per member of staff.

A second measure, the quality of service to job seekers (denoted JSQ, also referred to as "customer service") captured aspects of quality -speed, accuracy, pro-activity of service, and the nature of the office environment. It was measured by independent analysis of questionnaires to employers and 'mystery shopping' techniques. 10 The employer quality target (EMQ) was the flip side of job placements, a measure of whether and how quickly vacancies were filled. This was measured (again independently) by a survey of employers.

The business delivery target (BDT) covered a wide range of other functions, and appeared to be an attempt to measure everything else that the offices did. It included two targets for benefit calculation accuracy, appropriate labour market interventions, and basic skills and incapacity screening. It was measured by checking samples of cases. The overall score on this performance measure was simply the average over the five categories. The final target, the monetary value of fraud and error, focused on two particular benefits -Income Support and Jobseeker's Allowance. This was measured by specialist teams visiting each district and examining samples of cases but the measurement and tracking of this particular target was obscure and all 17 Pathfinder districts were treated as a single virtual region and consequently the target provided no scope for policy evaluation. Reporting of the progress on achieving the target was very delayed.

Hierarchy: measurement, reward and production.

A final relevant characteristic of the scheme was that targets were measured at different levels of the JP hierarchy. Job entries were measured monthly at office level and the three quality measures we examine, JSQ, EMQ and BDT, were measured quarterly at district level. This produces quite a complex hierarchical structure. The district was imposed as the decision-making unit in terms of reward and the measurement structure works off the office for some targets and the district for others. This measurement structure has implications for the likely behavioural response of workers in JP.

Theoretical Issues

The nature of the organisation, the size of the team, the measurability of output, the multidimensionality and the nature of tasks are all elements to be considered in the design of team-based incentives and in any evaluation of a scheme. Here we consider the implications for worker behaviour of the way the JP scheme was designed. Note that incentive schemes also impact on selection of workers into organisations (for example, Lazear 2001, Dixit 2002, Besley and Ghatak 2003, 2005, Bandiera et al. 2011), but the timescale of the pilot and the relatively low staff turnover suggest that in our context the main effects will come through changes in the behaviour of incumbent workers.

Structure and size of teams

An important characteristic of the scheme was the structure of the teams. These were defined at the level of a district and were made up of a number of offices with no operational link with each other. In our context, a classic Holmström (1982) team would be at the office level where workers depend on each other to produce output. But teams were defined by administrative boundaries (the districts), chosen as the units of measurement for targets and performance. This created interdependencies among the offices in a district. The expected reward for effort in an incentivised office depended on performance at district level and this was determined by the output of all offices belonging to the same district. However, production occurred at office level, where members of staff interacted with each other.

Hence the structure of the team as designed in the JP incentive scheme was quite complex and resulted in a two-level team: "natural" teams (offices) within reward teams (districts).

At the level of an office, the fact that individual contributions to office output were not separately observable (as only a measure of the office output was available) creates a negative externality, similar to that of Holmström (1982) when output is fully shared among team members whose contributions are not separately observable. In particular, agents will choose an inefficiently low level of effort, as they do not pay in full for the consequences of slacking effort. As predicted in Holmström (1982), if final output depends on a state of nature and not only on workers' effort, the number of team members becomes crucial to deliver optimal incentives. In big teams (where each worker has a trivial impact on the probability distribution of final output) the free-riding problem is more complicated to tackle with the use of group penalties/bonuses only and monitoring performance is also required. We could also argue that peer pressure within an office -where colleagues are able to observe each othercould alleviate free rider problems.11

In our context we have possible free-riding within an office and within a district12 . In terms of the latter, as performance was assessed at district level, offices in large districts (districts which have many offices within them) may have a lower expected return to effort. An office would have the same bonus as one in a small district but each office would have a smaller impact on the probability of reaching the target. Hence the office managers in a large district would face a stronger incentive to free ride. We do not know if offices were communicating with each other or coordinating on the achievement of targets. We were informed that only districts managers were responsible for the achievement of targets. Hence we can assume that it was the role of the district manager to coordinate and monitor the contribution of each office to overall performance. This job was made more difficult the greater the number of offices within a district.

Given these separate issues of effort enforceability at office and district level, when looking at team size we distinguish between office size (staff per office) and district size (number of offices per district). We expect that offices (districts) with relatively fewer staff (offices) should perform better, as the free riding issue is easier to tackle and peer pressure may be stronger.

Multi-tasking and the Measurement Technology

JP staff are required to deliver a range of services. Theory suggests that this matters for the outcome of the scheme. A crucial aspect in a multi-tasking context is how precisely the different dimensions of output are measured. If each outcome could be rewarded in isolation, the optimal scheme would set higher incentives on the better measured outcomes. 13 However, in a context with multiple dimensions of output, this would lead to a misallocation of effort by the agent. Therefore the principal has to weaken the incentives on the more accurately measured tasks. The prediction of the standard models on moral hazard when output is measured with error is that low powered incentive schemes should be used when the different outcomes are measured with differential precision (Holmstrom and Milgrom 1991 for a seminal paper, and Dixit 2002 for an overview).

The five targets in the JP scheme involved very different measurement precision. The main quantity target, job entry productivity, was measured most precisely and directly from the management information database, at office level, monthly. By contrast, the quality of service to job-seekers and employers and business delivery were measured through a sample survey and a sample of cases, only at district level and on a quarterly basis. This greater level of aggregation over both time and space gives a noisier measure of how a worker's effort maps into output on these tasks. The enforcement of effort levels is also more difficult for the tasks measured at district level. When performance outcomes are low the district manager does not know which office is under-performing, making the coordination and monitoring more difficult and therefore free-riding across offices harder to tackle.

What is the optimal response of an employee given this reward structure and measurement technology? The rewards for hitting each target were the same. The cost of employee effort on quantity and quality and the relative effort required to hit the targets is unknown to us. It may be that these were known to the senior management of JP and were factored into the design of the scheme. In this case, workers would have allocated their effort in line with the principal's optimum -possibly equally across tasks. If this assumes too high a degree of sophistication in setting the parameters of the incentive scheme, absent substantial differences in effort costs across targets, we expect a worker to have focused more effort on the quantity target because of the lower noise and less aggregated measure.

Data and Methodology

Data

We use data from JP's management information system and from their personnel database. These data were available for the period of operation of the incentive scheme only (we did not have access to data before or after operation of the scheme). Management information recorded performance against the five targets. Job entry productivity (JEP) achieved for each office on a monthly basis was the measure of quantity. 14 The three quality outcomes (JSQ, EMQ and BDT) were reported for each district on a quarterly basis. A basic description of the data is in Table A1 in the Appendix. It shows wide variation in JEP across offices and time, but much less variation (and fewer observations) for the sample-based measures of quality.

JP was a predominantly a human capital intensive organisation. We obtained, from personnel records, the number of staff in each grade for each office per month. The numbers in different grades appeared in more-or-less fixed proportions. For example, there was about one Executive Officer (EO) to two Administrative Officers (AO). Consequently, including numbers of each grade in the analysis leads to severe multicollinearity. We therefore defined a measure of front-line staff which was the office total of all numbers in EO and AO grades. 15 We merged unemployment and vacancy data from the local labour market, as a control for the difficulty of placing individuals in the labour market. Using the postcode (zip code) for each JP office, we located each office in a Travel To Work Area (TTWA). 16 We then extracted claimant inflow and vacancy inflow data for each TTWA and for each month. 17 We cannot take the unemployment and vacancy stocks as exogenous as they are influenced by the outflow rate, our dependent variable. So we use the inflow, both of unemployed claimants and of vacancies, and take the latter divided by the former. Note that the state of the labour market plays two roles -first it provides the 'raw material' necessary for the office to produce job entries. Second, it proxies labour market tightness and hence the ease of placing claimants in jobs.

Clearly the quality of the workers is an important consideration and there is no reason to expect it to be constant across the country. Traditionally, public sector jobs pay less than private sector jobs but variation in the differences between public and private sector wages across the country will feed into quality variation. To adjust for quality we merge data on the local public/private sector wage differential as a proxy for the different quality of staff (see Nickell and Quintini 2002, Propper and Van Reenen 2010). From the Labour Force Survey Small Areas dataset we constructed the wage gap between the private sector and the public sector for each local authority using the relative hourly wage of full-time workers. This was matched to the office postcode.

We know which offices were Pathfinder (PF) offices. It is important to identify these for three reasons. First, they had newer technology and generally refurbished premises. Second, they were also subject to restructuring in which the managers had to oversee the convergence of two kinds offices (Employment Services (ES) and Benefit Agency (BA)) offices. JP estimated that Pathfinder offices took at least five months to adjust. Third, even beyond the adjustment period, Pathfinder offices fulfilled more roles than an ex-ES or ex-BA office.

Consequently we would expect their productivity as measured on any one task to be lower.

Figure 1 shows the distribution of the annual job entry productivity across different office and district types. Comparing offices in non-incentivised districts with non-PF offices in incentivised districts is closest to a like-with-like comparison and the distributions are fairly similar. PF offices, on the other hand, are clearly associated with lower mean job entry figures. We exclude PF offices from our main analysis but test for the robustness of this choice in Section 3.4. We do include another kind of office that during the scheme also were designated as pathfinder offices, Job Centre Plus Offices. These became pathfinder offices late in the scheme, for example 82% in the final two months, hence little disruption was expected. We again test the robustness of this choice.

The incentive scheme ran from April 2002 to March 2003, and this is the period of our data.

Note that although Jobcentre Plus employees were informed about the incentive scheme in April 2002, they did not know the specific targets until June 2002. It would obviously be very desirable to have data before the scheme was implemented to allow a difference-in-difference technique. Unfortunately this is simply not possible as the district boundaries (that defined the scheme) were re-drawn in 2002, and different PSA targets were in operation before April 2002, implying a different set of output measures.

Empirical Specification

We aim to answer three questions. First, is the productivity of public sector workers influenced by financial incentives? Second, does free-riding matter in a team-based incentive scheme? We sub-divide this into the free-riding deriving from many workers in an office, and into that arising from many offices in a district. Third, does the differential measurement precision of the different targets influence behaviour?

The outcomes we focus on are log job entry productivity as the quantity measure and the quality of service to job seekers (denoted JSQ), the quality of service to firms (denoted EMQ) and the business delivery target (denoted BDT) as the three quality measures.

As already mentioned above, the pilot scheme introduced the incentive structure in the 17 Pathfinder (PF) districts, leaving 73 districts as controls. The way incentivized districts were selected raises two issues for identification: how districts were chosen as PF districts, and how we can distinguish between the effects of the incentive scheme and the effects of the introduction of PF offices.

Identification of this model comes from random treatment of non-PF offices within PF districts. Assignment to the pilot scheme was at district level and was based on a district being designated a PF district (defined as a district containing at least one PF office). PF offices were to be spread across all 11 Jobcentre Plus regions. The specific sites in each region were chosen by Field Directors and their District Managers on the grounds that their management would be able to cope well with the demands of the new structure. Clearly PF status is likely to be correlated with other outcomes. But PF offices were located across the regions, and the selected offices were to reflect a "cross-section of different communities and customer bases, i.e. from large inner-city offices to those in smaller towns, suburbs and rural areas." 18 The consequence of classification of an office to PF status was that all other offices within this district became PF district. This suggests that assignment at district level to the treatment category is stratified random. Assignment of offices other than the PF office itself to the pilot is random. Those offices are in the pilot on grounds entirely unrelated to their own performance and characteristics. 19 The two mechanisms together imply that for offices other than the PF office itself, assignment to the scheme is random and this is what we exploit here to give us internal validity of the impact of the scheme. As selection of PF offices is not random, they are excluded from all analysis. For the remaining offices, given random assignment, we can identify the incentive scheme effect from regression analysis.

We estimate the quantity measures at office level

od od d od βX IS y ν γ α + + + = ( 1
)
where y is log total job entry productivity in office o in district d, X is a set of covariates and ν is random noise. γ denotes the effect of incentivisation status (IS), our parameter of interest. To test for the presence of free riding within teams of the incentive scheme we interact IS with the number of workers within an office and the number of offices within a district. Office level regressions cluster at the district level, given the importance of the district manager to coordinate the activity of the offices in their district.

We estimate the quality measures at district level:

d d d d u Z IS y + + + ∂ = η λ
(2) y={JSQ, EMQ, BDT}, λ denotes the effect of incentivisation and u the error term. To test for free riding at the district level we interact IS with the number district staff and with the number of offices at district level. The controls (Z) are aggregated to a district level. We control additionally for the size of the districts through the total number of staff in the district as, unlike the quantity equation, quality does not measure productivity but rather the level of the outcome 20 .

Our identification assumption for the office level analysis is:

E(y od |IS d =1,PF od =0,X od )=E(y od |IS d =0,X od ); E(v od |IS d ,X od ,PF od =0)=0
and is the same for district level analysis, with the office subscript omitted.

Table A2 shows that incentivised districts are larger, both with more staff per office (485 compared to 268 on average), and more offices (15 compared to 11). They appear to face very similar labour market conditions. Incentivised offices have slightly more staff (32 20 Quality measures were recorded as percentages, making it impossible to normalise by office size.

compared to 27) but similar labour market tightness. To further ensure that our comparison of incentivised offices with non-incentivised offices compares like-with-like we use Propensity Score Matching to select our control offices.

We undertake the matching as follows. Even though districts are the basis for assignment into the treated category, we compute propensity scores at office level because offices are the unit of analysis. We include all non-PF offices in incentivised districts and all offices in nonincentivised districts. We exclude PF offices from our analysis on the grounds they are different from the other offices. This leaves 912 offices. We estimate the conditional probability of assignment to incentivisation status based on a set of observable variables.

These variables might influence choice of pilot areas and/or the outcome variables. 21 We employ a nonparametric regression method with kernel weights proportional to an Epanechnikov kernel and bootstrap to calculate the standard errors using 100 replications with replacement. Common support is imposed on the match following Heckman, Ichimura and Todd (1997). This excludes 71 treated offices.

Results

We present results first for the main quantity variable, testing to see whether the incentive scheme had any effect on productivity and for evidence of free-riding. Next, the effect of the scheme on quality measures is assessed, to examine whether the effect of the scheme changes across outcomes measured with different precision. Finally, we estimate quantity and quality jointly, allowing for production interdependencies.

Quantity -Job Entry Productivity

Descriptive Analysis

The first row of Table 1 shows a simple comparison of the mean job entry productivity difference for the matched sample of treated and non-treated offices. The results indicate a negligible and insignificant effect of the incentive scheme. Those offices subject to treatment had slightly higher job entry productivity than non-treated offices. Specifically, the 21 The propensity score estimator (probit) is shown in Table A4 and the quality of the matching in Table A5.

The latter shows significant differences in the pre-matched sample for variables including the propensity score, standard deviation of labour market conditions and number of offices per district. However post matching, there the significant difference was only an interaction between staff and offices per district. coefficient 0.002 translates into an average treatment of the treated (ATT) of 0.67 job entry points per person. This is a very small effect, equivalent to finding employment for less than one employed individual. 22 We look for evidence of heterogeneity in this effect linked to the free-rider/co-ordination issues discussed above. In rows 2-5 and rows 6-9 of Table 1 we split the matched sample by number of offices within the district (district size) and the staff per office (office size) respectively. Small treated districts have significantly higher productivity than non-treated.

As district size increases, the effect of the incentive scheme on job entry productivity tends to decline such that there is a significant and negative effect of the incentive scheme for districts in the highest size quartile. This translates on average into 118 job entry points per person, which is nearly 10 unemployed lone parents or 118 employed job searchers. The exception is for districts in the third quartile, where there is a more positive effect than the second quartile, but results are not statistically significant. Similarly, splitting the sample by quartile of office size, the ATT declines across office quartile, although these estimates are insignificant.

Despite an insignificant total effect of the incentive scheme, these results are suggestive of free riding both within and between offices and of coordination issues. 23 The mean productivity difference between treated and control districts (offices) declines in the district (office) size. To explore this further, we move to a conditional regression analysis.

Regression Analysis

Table 2 presents the results for the log annual job entry productivity. This is for the sample in We present a number of different specifications for the effects of the incentive scheme along with the office characteristics. We start with the effect of basic office characteristics in column 1. District Offices (which have central administrative functions) are equally productive as other offices. A Job Centre Plus office (one which became a PF office within the year) has no different job entry productivity from other offices, whilst the gap between wages in the private and public sector has a negative productivity effect as expected, as a higher wage gap implies lower quality workers in the public sector. Finally, the state of demand in the labour market has a positive and significant influence on job entry productivity. 24 Similar to the propensity score matching descriptives, column 2 shows an insignificant treatment effect on average. In an incentive scheme where performance is measured at a team level, the marginal return to individual effort decreases in the team size, which raises the incentive to free ride. Column 3 tests for the presence of free riding within offices, including an interaction between treatment status and the office size. Column 4 adds the number of offices per district effect. Column 5 explores free riding across offices by adding an interaction between treatment status and the number of offices per district to this specification.

Allowing for heterogeneity in the effect by the team size in columns 3-5 shows a large positive mean incentive effect, equivalent to 467 job entry points per staff member. But this positive treatment effect falls significantly with both the office size (column 3) and district size (column 5). Increasing office size by one frontline worker and increasing district size by one office lowers job entry productivity by 5 and 18 job entry points, respectively. Thus the average incentivisation effect of zero masks a positive mean effect in small offices and small districts and a negative effect in large offices and large districts.

Our finding of a negative impact of office and district size is consistent with the discussion above that bigger offices and offices in bigger districts face a greater free riding and coordination problem. This echoes Gaynor et al. ( 2004) but is inconsistent for example, with Knez & Simester (2001). Knez and Simester argue that peer monitoring worked in Continental because employees worked in relatively small autonomous groups, within which monitoring and enforcement of group norms were sustainable. In our setting the sub-teams sizes above the median. For small districts, there was no evidence of an effect as office size changed. However, with such small sample sizes, no estimates were significant.

were offices, some of which had over 200 staff members. The consequence of this was that the free riding effect dominated.

Quality -Job-Seeker, Employer Service and Business Delivery

We adopt a similar approach to modelling quality outcomes. We model the quality of service to job-seekers JSQ and to employers EMQ and a measure of quality of business service, BDT. These outcomes are only measured quarterly and at district level, compared to the quantity analysis at a monthly office level. This has implications for behaviour as set out above, but also for our estimation, reducing sample size from around 900 offices to just 90 districts.

Table A1 gives the (log) mean response on these three quality measures, which translate into an 88.2% success rating for EMQ, 84.3% for JSQ and 96.3% for BDT. The table also shows little variation in these scores across districts for JSQ and BDT, but more for EMQ. All districts hit their targets for JSQ, whilst only 64% and 51% did for EMQ and BDT, respectively.

Table 3 shows the results for the district annual averages for JSQ, EMQ and BDT. Few variables are estimated to have a significant effect, due in part to the small number of observations and a lack of variation in the outcomes and in the case of JSQ the targets possibly having been set too low. For JSQ and EMQ, the number of staff in the office has a negative effect. This may arise from a more personal service in smaller offices. The tightness of the labour market has a negative impact, the magnitude of which is largest for EMQ. This is intuitive, as a tight labour market means a difficult time for employers to fill vacancies.

There is no significant impact of any term involving incentivisation status on either of the three quality outcomes.

The lack of significant effect of incentivisation on quality outcomes can be taken in two different ways. First, it could be argued that the scheme failed to elicit any increase. This is not surprising in that the precision of the monitoring technology for quality was low, measured infrequently at a high level of aggregation. This implied a lower marginal return to effort and consequently low optimal effort allocation to this component of the job. Second, it section variation work in the opposite direction, thereby cancelling out the total labour market effect seen in could be viewed more positively as showing that despite the greater effort on quantity, quality did not actually fall, a standard failing of many incentive schemes. Whether this is due to the incentive scheme explicitly targeting quality, or whether due to the existence of sufficient slack to permit the increase in quantity, is difficult to say.

Quantity and Quality Together

The contrast between the significant effect of the scheme on quantity and lack of effect on quality is interesting. It may be that this arose from the differing measurement precision for the three aspects of the job, or it may simply be statistical -90 observations in one case compared to over 800 in the other. Since this matters for incentive scheme design, we get at this by re-running the quantity regression at district level. To do this, we used as the dependent variable log district annual job entry productivity. The results are in Table 4. We run two samples to calculate the productivity effect. In column 1 we use the full sample as used in the quality analyses of Table 3 and in column 2 we use the common support sample used in the quantity analyses of Table 2.

Table 4 shows that for both samples there is a positive impact of incentivisation, which declines with office and district size, although the latter interaction is significant only for the full sample of 90 districts. This suggests that the differences between Tables 2 and3 are not due to size of the sample, but there is something different about the behavioural response to the quantity and quality targets. This could be explicable in terms of the differences in the precision of the monitoring technology. This arises in part from the differences in the nature of quantity and quality measurement (one is based on easily countable job placements at monthly intervals, the other on the views from surveys at quarterly intervals) and in part from the much greater degree of aggregation of the quality measure used in the incentive scheme (district compared to office for the quantity measure).

It could be argued that since time allocated to quantity or to quality is determined jointly, we need to take account of that in estimation. The first step is simply to establish whether good performance on one dimension is positively or negatively correlated with good performance on the other. In fact, there is little correlation between quantity and quality and a positive Table 2.

correlation between quality measures except EMQ and BDT25 . If we take EMQ as more useful a measure given the low variation in JSQ and BDT, there is a very low association26 .

Therefore we do not think that the results arise because time spent on quantity reduces the amount of time to achieve quality, but instead arises because of differences in measurement precision which means that output is much less related to individual productivity. These findings also have support from Gaynor and Pauly (1990) who showed that output was significantly higher in medical practices in which compensation was more directly related to productivity.

Robustness tests

We examine whether the results of the treatment effect on job entry productivity from column 5 of Table 2 are sensitive to various specification choices in the main regression analysis.

These are presented in Table 5. In column 1 the dependent variable is changed to log job entry productivity, standardised so that the coefficients represent standard deviations in productivity and column 2 changes the dependent variable to be the level of standardised productivity. In both cases, while the magnitudes of the coefficients change, the positive incentive effect remains and is decreasing in office size. It is also decreasing in district size, though this interaction is no longer significant. In column 3, we move away from an analysis of the productivity effects and instead regress on the log job entry points per office, controlling for office level frontline staff as a regressor. We find again a positive treatment effect, declining in team size, and while the interaction between treatment status and office size is no longer significant the interaction with district size is.

Table 2 excluded PF offices from the analysis and included the JP offices as these tended to be introduced quite late in the incentive scheme. In column 4 and 5 of Table 5 we include the PF offices and exclude the JP offices respectively. Our results prove robust to both of these changes and both sets of interactions and the main effects are significant. In summary, the quantity effects are broadly robust to various specification change.

Interpreting our results

We have interpreted the lack of significant effect of incentivisation on quality as being due to the low precision of the outcome measures and of the monitoring technology. Poor outcome measures could lead workers to choose not to exert extra effort on these tasks as mapping their effort on getting a reward is more difficult than in the case of the quantity outcome.

Poor monitoring might make workers expect that any slack on effort would not be detected. It is not possible to isolate these two channels. Another possible explanation could be that workers may have a lower chance of success on the quality measures. However, information ex-post on which incentivised districts met the targets does not seem to support this view. In fact, all incentivised districts met two of the quality targets (JSQ and MVFE), which could imply that the targets set on these two outcomes were too low and hence the probability of success was certain. Our results show that there is no difference for the outcome JSQ between incentivised and non incentivised districts, despite the fact that the chance of success on this task was high. One may also wonder if the money at stake was sufficiently high to motivate workers to improve their effort on all targets. We know that only 4 districts of the 17 incentivised met all 5 targets. In these districts the reward varied from £750 for a Band A job to £3,750 for a Band G job. As already noted this represented around 7.5% and 8.5% of average pay respectively. 4 districts met 4 targets and the reward ranged from £400 to £2,000.

The remaining 9 district met 3 targets. For these, the reward ranged from £300 to £1,500. So hitting 5 targets rather than 3 meant more than doubling the reward. Hence the argument that the money at stake was not enough is not very convincing.

Valuing the impact of the incentive scheme

The mean effect of the scheme is zero. So across all offices in the scheme there were no gains. However, our estimates show that for small offices and small districts there were increases in quantity following the scheme. In this section, we ask the question if there scheme were to be introduced in the appropriate settings i.e. in small offices and districts, what value might it have?

We can evaluate the quantitative importance of the change in the quantity outcome in three ways. First we compare the number of people placed into jobs with the monetary cost of the scheme, thereby calculating the cost per placement. Second, we compare the benefits of the incentive scheme to a general pay rise in the government agency.

The cost per placement

Given the estimates in Table 2, column 5, we can straightforwardly calculate the distribution of change in job entry productivity associated with the incentive scheme. The fitted value from the regression is calculated using only variables related to treatment (the treatment effect itself plus any interactions), translated into job entry points then converted into a proportion of total job entry points for the treated office. Since the impact varies according to office and district size, we report this percentage change across the distribution as well as the mean in Table 6. As would be expected from Table 2 column 2, the overall effect of incentivisation is small and negative, at nearly -1%. There is a substantial positive effect in small offices in small districts and this effect falls across both dimensions of office and district size.

The mean percentage increases in small offices (in any district) and the mean in small districts (across all offices) are 39% and 25% respectively. A 39% and 25% change in job entry productivity translates to 6,000 and 2,030 job entry points respectively, or approximately 1,200 and 400 extra people. The ex post cost of the job entry component of the scheme was around £272,100, 0.21% of the salary bill for the 17 incentivised districts. We estimate this from the payments made for 5 of the 17 districts hitting their job entry target and earning 1% of salary (allowing for different numbers of staff). All 5 who hit were small districts. Consequently, in the best case scenario of targeting the incentive scheme towards small districts, the scheme cost £226.75 per job placement.

Incentive Scheme, a General Pay Rise or More Staff

This can be compared to raising the quality of staff through a general pay rise. We can do this straightforwardly through the estimated production function. Using column 5 of table 2, we compute the change in the private-public pay differential (£ per hour) required to produce a 25% and 39% increase in job entry productivity. This is given by ln(1.25)/(-0.03), which equals -7.44 and -10.98. Thus a £7.44 and £10.95 an hour pay increase in the public sector would, through recruitment of higher quality staff, on average elicit the same output improvement as this scheme did in small districts and small offices respectively. Given that the average hourly pay in the organisation was £8.70 at the time, a £7.75 or £10.95 per hour increase would be extremely expensive, and way above the cost of the incentive scheme.

In conclusion had the scheme been applied only in small offices and small districts, it would have been cost effective.

Conclusions

There is a lack of robust evidence on the role and impact of performance pay in the public sector, even though this is a sector that employs as many people in the UK and US as manufacturing does. This paper helps to fill that gap by providing an evaluation of a pilot scheme of financial incentives in a major UK government agency, Jobcentre Plus. The incentive scheme was based on team performance rather than individual and covered five different targets, measured with varying degrees of precision. We focus on three main issues:

whether performance pay matters for public service workers, what the team basis of the scheme implies, and the impact of the differential measurement precision.

We show that the use of performance pay had no effect on the main quantity measure (job placement productivity) at the mean, but that there was important heterogeneity of response.

The heterogeneity was patterned as one might expect from a free rider versus peer monitoring perspective. We found that the incentives had a substantial positive effect in small offices and in offices in small districts. In districts with many offices and in large offices, there was a negative effect. Our interpretation of this is that peer monitoring and better information flows can overcome free rider problems in small units, but that it fails in teams made up of many people, or dispersed across many offices.

The impact of performance pay on quantity was not matched by any impact on different quality measures. One key difference between the quantity and quality targets is the precision of measurement. Quantity in this scheme was measured monthly at office level, with a clear, direct effect of an individual's effort to the target measure. Quality measures were based on samples of different clients' experiences, and were only measured quarterly at district level.

In this case, an individual's effort is only measured probabilistically, and is in any case submerged in a much broader total. Our interpretation of this finding is that individuals responded to this by focussing their effort on quantity rather than quality (see Gaynor and Pauly, 1990).

Could such a scheme be cost effective? Given the heterogeneity of response the overall mean impact is close to zero. But if we examine the size of the positive effect in the small districts where the scheme did work our estimates suggest that if the scheme was well targeted, the use of incentive pay could deliver equivalent output increases to a rise in the quality of recruited staff through a pay rise, at very significantly lower cost. Given that the scheme was not particularly high powered (in contrast, for example, to Kahn et al. 2001), this suggests that incentive schemes -if properly designed -can be useful in the public sector as a means of increasing output without needing very large incentive payments.

There are a number of caveats. First, the scheme only operated for one year, and so the results may include a "first year" novelty effect in addition to the pure incentive effect. Furthermore, if a 'ratchet' design of continual percentage improvements were repeated in a dynamic setting, the optimal response would be different to the response we have measured to a possibly once-only pilot. Second, the outcome could be the result of performance management per se, rather than the financial reward attached. But this is unlikely in that the same performance management system was in place everywhere, across the control offices as well as the pilot offices. It may be that the financial incentives led managers to take the existing framework more seriously but that is surely part of the aim of performance pay.

Third, Jobcentre Plus may have been an organisation with a lot of slack in it. Unemployment and job-seeking had fallen considerably since the peaks of the 1980s up to the start of the scheme, and it may be that staff were less hard-pressed than before. Fourth, it may be that the assignment to the pilot was not completely random and differentially included highperforming offices. Whilst possible, this seems to be unlikely given the nature of the assignment process. Districts were included in the pilot if one office in that district had been selected to be a PF office. Given the few operational links between offices, this is essentially random assignment for other offices in that district. Finally, given the specific structure of the agency and the incentive scheme, it is possible to question the external validity of this study.

Unfortunately there is too little evidence on the use of incentive schemes in the public sector to compare results. There is more evidence for the private sector, but a comparison with the public sector is problematic and usually schemes are of very different nature 27 . More empirical evidence on the public sector is needed before being able to extend our results to the public sector in general. However, we believe we provide an important contribution to the literature, in particular on the issues of team structure and rewards and on the precision of outcome measures, that could be extended to other settings where teamwork is a crucial feature of job design.

We draw some tentative conclusions for the design of team level performance pay schemes in the public sector. There are some obvious conclusions -team size needs to be small and preferably not dispersed over many sites. The connection between effort and output needs to be as clear and well-measured as possible. There are trade-offs here: precise measurement may be very expensive if conducted for many small teams. Finally, there are lessons for the structure of organisations as well as for the nature of optimal incentive schemes.

Dewatripont, Jewitt and Tirole (1999) make this point in the context of mission definition, but it also applies here to team size and task measurement. If incentives are indeed a very cost-effective way of inducing greater output given the right team size, then organisations could be re-structured to create natural teams of the appropriate size. Such re-structuring could also allow for relative performance evaluation to filter away common uncertainty.

These points also fit well with the general ethos of devolved agency inherent in many current public service reforms.

other, would have not been considered. It is also more likely that in a public organisation there is more pressure from unions to use group performance evaluation rather than individual performance evaluation. Note: Standard errors in parentheses. * significant at 10%; ** significant at 5%; ** significant at 1%. Office Productivity is defined as log of the ratio of total JE points to total frontline staff. PF denotes the Pathfinder Office created prior to the incentive scheme. JP status is a dummy variable which equals one if the offices within incentivised districts were given the new JP status during the incentive scheme and 0 otherwise. The private public wage gap is defined as the relative hourly wage differential within Local Authorities. Frontline staff defined as the sum of Executive Officer and Administrative Officer. Labour market is defined as the ratio of the inflow of unemployment claimants to the inflow of vacancies, by TTWA. 5) excludes JP offices. PF denotes the Pathfinder Office created prior to the incentive scheme. JP status is a dummy variable which equals one if the offices within incentivised districts were given the new JP status during the incentive scheme and 0 otherwise. The private public wage gap is defined as the relative hourly wage differential within Local Authorities. Frontline staff defined as the sum of Executive Officer and Administrative Officer. Labour market is defined as the ratio of the inflow of unemployment claimants to the inflow of vacancies, by TTWA. Note: The incentivisation effect for incentivised offices was calculated using the fitted value from Table 2, column 5, using the variables incentivisation status and an interaction of this with office size and district size. Notes: Standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%. Note: the predicted value forms the propensity score used for the office level quantity analysis. Offices included in analysis contributed towards job entry outcome, but were non Pathfinder offices. Labour market is defined as the ratio of the inflow of unemployment claimants to the inflow of vacancies, by TTWA. Frontline staff defined as the sum of Executive Officer and Administrative Officer.

Table 1 :

 1

only offices producing job entries are included in the analysis, PF offices are excluded and we include only offices on common support in the matching. Standard errors are clustered at district level.

Table 1 : Matched sample differences in Job Entry Productivity across offices and districts

 1 Outcome is log job entry productivity per office. This is calculated as the log of total office job entry points per staff. Pathfinder offices are omitted from analysis. Kernel weighted propensity score matching with an Epanechnikov kernel. Bootstrapped standard error in parentheses, with 100 replications. Frontline staff defined as the sum of Executive Officer and Administrative Officer. Number of offices per district for 1 st , 2 nd , 3 rd and 4 th quartile: 0-10, 11-13, 14-17, 18+ front line staff. Number of frontline staff per office for 1 st , 2 nd , 3 rd and 4 th quartiles: 0-11.70, 11.71-22.65, 22.66-37.30, 37.31+ staff.

	Figure 1: Distribution of Annual Log Job Entry Productivity
				PF Offices				Non PF Offices
	Frequency	1 2 3 4 5 6					Frequency	0 60 20 40
		-2	0	2	4	6	8	0	2	4	6	8	10
			Office Annual Job Entry Productivity			Office Annual Job Entry Productivity
		Non PF Offices, Incentivised Districts	Offices in Non Incentivised Districts
	5 10 15 20 Frequency					60 20 40 Frequency
	0					0
		-2	0	2	4	6	8	0	2	4	6	8	10
			Office Annual Job Entry Productivity		Office Annual Job Entry Productivity

Note:

Table 2 : Office Annual Job Entry Productivity

 2 LogOffice Productivity. Office Productivity is defined as log of the ratio of total JE points to total frontline staff. Pathfinder offices were omitted from analysis. The district office indicates the head office. JP status is a dummy variable which equals one if the offices within incentivised districts were given the new JP status during the incentive scheme and 0 otherwise. The private public wage gap is defined as the relative hourly wage differential within Local Authorities. Labour market is defined as the ratio of the inflow of unemployment claimants to the inflow of vacancies, by TTWA. Frontline staff defined as the sum of Executive Officer and Administrative Officer.

	(1)	(2)	(3)	(4)	(5)

Note: standard errors in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%. Dependent variable:

Table 3 : District annual JSQ, EMQ and BDT analysis

 3 JSQ is the job seekers service, EMQ the employer quality outcome and BDT business delivery target. Dependent variables are log annual district average JSQ, log annual district average EMQ and log annual district average BDT. PF denotes the Pathfinder Office created prior to the incentive scheme. JP status is a dummy variable which equals one if the offices within incentivised districts were given the new JP status during the incentive scheme and 0 otherwise. The private public wage gap is defined as the relative hourly wage differential within Local Authorities. Frontline staff defined as the sum of Executive Officer and Administrative Officer. Labour market is defined as the ratio of the inflow of unemployment claimants to the inflow of vacancies, by TTWA.

	(1)	(2)	(3)
	JSQ	EMQ	BDT

Note: Standard errors in parentheses. * significant at 10%; ** significant at 5%; ** significant at 1%.

Table 4 : District Level Job Entry Productivity

 4

	(1)	(2)

Table 5 :

 5 Robustness Checks Standard errors in parentheses. * significant at 10%; ** significant at 5%; ** significant at 1%. Office Productivity is defined as log of the ratio of total JE points to total frontline staff. Column (1) dependent variable is log standardised JE productivity. Column (2) is level of standardised JE productivity. Column (3) dependent variable is log JE points. Column (4) includes PF offices. Column (

	(1)	(2)	(3)	(4)	(5)
	Standardised	Standardised	Log JE	Log JE	Log JE
	Log	JE		Productivity	Productivity
	Productivity	productivity

Note:

Table 6 :

 6 Mean Incentivisation EffectNumber of frontline staff per office quartiles

	First	Second Third	Fourth Mean

Table A4 : Propensity score probit estimates of Incentivisation Status

 A4

	Mean Frontline Staff	-0.035
		(0.013) ***
	Office Frontline Staff Variance	0.035
		(0.021) *
	Office Frontline Staff Squared	0.000
		(0.000)
	Frontline Staff * No. Offices	0.001
		(0.001) *
	Office Mean Labour Market	-0.003
		(0.311)
	Office Labour Market Variance	-0.389
		(0.575)
	Labour Market * Frontline Staff	0.010
		(0.009)
	No. Offices per District	-0.337
		(0.072) ***
	No. Offices per District Squared	0.016
		(0.002) ***
	Regional Variables
	East of England	-0.078
		(0.366)
	London	0.630
		(0.326) *
	North East	0.086
		(0.424)
	North West	0.426
		(0.295)
	Office for Scotland	0.556
		(0.291) *
	Office for Wales	0.131
		(0.324)
	South East	-3.320
		(0.540) ***
	South West	-0.331
		(0.337)
	West Midlands	0.295
		(0.320)
	Yorkshire	-1.227
		(0.407) ***
	Constant	0.484
		(0.627)
	Observations	912
	Psuedo R 2 = 0.2813

The World Development Report (2003) highlights that concern is not limited to developed countries.

[START_REF] Holmström | Moral hazard in teams[END_REF] provides the formalisation.

See Burgess et al. (2010) for the evaluation of another, implemented in the UK HMCE (Her Majesty's Custom and Excise).

It would have also been very hard to get the Unions' consent for the introduction of performance related pay based on individual output.

There were few operational links between offices in a district and different offices were largely self-contained.

[START_REF] Knez | Firm-wide incentives and mutual monitoring at Continental Airlines[END_REF] analyse the impact of incentives within big teams.

These were offices that began to be introduced at the time when JP was launched in 2001, amalgamating the functions of two agencies: the Benefits Agency (BA), responsible for administering benefits to the unemployed, lone parents and others, and the Employment Service (ES), responsible for job placement. New 56 'Pathfinder' offices were initially introduced to provide an integrated service, combining the work of the original, separate,

This consists of a quarterly programme, where the assessors used a variety of techniques to measure the elements of the target. In particular, they went into offices and acted out the role of a customer, checking the environment in which services were delivered and telephoned offices to see how quickly and effectively phone calls were answered.

[START_REF] Kandel | Peer pressure and partnerships[END_REF] show that peer pressure can offset free-riding tendencies, but the strength of this peer pressure varies with unit size, with more effective monitoring in small units.[START_REF] Knez | Firm-wide incentives and mutual monitoring at Continental Airlines[END_REF] find evidence that free riding can be reduced in large teams through team design.

[START_REF] Ratto | Rewarding collective performance to induce cooperation[END_REF] provide a theoretical analysis of the different effects of size of office in the context of subteams operating within a larger team, where the reward is at the larger team level.

 13 The literature often highlights a trade-off between risk and incentives. See[START_REF] Prendergast | The tenuous trade-off between risk and incentives[END_REF],Dixit (2000), for a general discussion.

Note that the incentive scheme had a threshold of job entry points which had to be reached, in order to achieve the bonus. We ran some analysis to determine whether this created behavioural response, such that incentives appeared stronger for districts close to hitting their targets, but found no such effect.

We have no information on the state of the capital (principally computing and communications equipment) in offices.

These are largely self-contained local labour markets, defined by 75% of those living there also working there, and 75% of those working there also living there. There are some 400 covering Britain.

National Online Manpower Information Service, http://www.nomisweb.co.uk/ .

Private communication.

Offices are only linked together in districts through spatial proximity, not through performance levels, for example. In addition, we control for spatial factors such as the local labour market in influencing performance.

See Table A3 for translation of client group categories into points

Note that we tested for interactions across both office and district size in the ATT. For example, the negative ATT in large districts may be strongest in large offices, or vice versa. Estimating the ATT for samples split by both the size of the office and the district shows that for large districts the ATT was more negative for office

Note that in an earlier version of the paper, we conducted a 2-stage approach, firstly calculating an office fixed effect and subsequently regressing office characteristics on this. The time-series variation and cross-

The correlation of average annual job entry productivity with JSQ, EMQ and BDT is 0.20, 0.13 and 0.24, between JSQ and EMQ and BDT is 0.38 and 0.49 and between EMQ and BDT is -0.041.

We also estimate the district level annual quantity and EMQ models jointly using SUR, but as we would expect from the low correlation found above, there is only a small change in the standard errors.

For example,[START_REF] Bandiera | Social Preferences and the Response to Incentives: Evidence from Personnel Data[END_REF], (2007), (2009) run a field experiment in a private firm and consider the impact of relative incentives versus individual incentives on workers' productivity and on managers incentives to select workers. In the public organization we consider, the scheme designers wanted to promote cooperation across workers, so that the use of relative performance evaluation, which puts workers in competition to each

* This work was funded by the Department for Work and Pensions (DWP), the Public Sector Productivity Panel, the Evidence-based Policy Fund and the Leverhulme Trust through CMPO. The views in the paper do not necessarily reflect those of these organisations. Thanks to individuals in the DWP for helping to secure the data for us, particularly Storm Janeway, Stavros Flouris and Phil Parramore. Thanks for comments to seminar participants at Bristol, the Public Economics Working Group Conference at Warwick, the IIES at Stockholm, University of Melbourne, HM Treasury, CPB in The Hague, Tinbergen Institute and Department for Work and Pensions.

Appendix