On the joint production of research and training

On the joint production of research and training∗ António Freitas†and Inés Macho-Stadler‡ Universitat Autònoma de Barcelona February 9, 2011 Abstract Universities and research institutions have the responsibility to produce science and to provide training to new generations of researchers. In this paper, we propose a model to analyze the determinants of a senior scientist’s decisions about allocating time between these tasks. The results of this decision depend upon the characteristics of the research project, the senior scientist’s concern for training and the expected innate ability of the junior scientist involved. We analyze the role that a regulator can play in defining both the value of scientific projects and the future population of independent scientists. Keywords: Allocation of time between tasks; research and training; senior and junior scientists ∗We are grateful to David Pérez-Castrillo, Pau Olivella and Pedro Rey-Biel for their insightful comments. We would also like to thank the participants in the presentations at Jornadas de Economía Industrial (Madrid, 2010), Universitat Autònoma de Barcelona, Universidade do Porto and Universitat Rovira i Virgili. We would like to thank ECO2009-7616, Consolider-Ingenio-CSD2006-16, 2009SGR-169, and Fundação Ciência e Tecnologia (Grant SFRH/BD/40182/2007) for financial support. Inés MachoStadler is a research fellow of MOVE (Markets, Organizations and Votes in Economics) and Barcelona Economics. †Department of Economics. Universitat Autonoma de Barcelona. E-mail: an[email protected] ‡Corresponding author. Department of Economics. Universitat Autonoma de Barcelona. Fac CCEE Edifici B. 08193 Bellaterra (Barcelona). Spain. Phone: 34 93 5811812. Fax: 34 93 5813767. E-mail: ines.mac[email protected] 1 1 Introduction It is widely accepted that universities and research institutions have the responsibility to produce science. However, there is another task of great importance to our society’s advancement of knowledge: training the new generations of researchers. In this paper, we consider senior scientists to be involved both in doing research and in providing training to junior scientists, as in a system of apprenticeship. Understanding the allocation of time among the two activities is of great interest because the training of junior researchers needs to be performed by the people who know how to do research, and this is crucial in assuring a high-quality research workforce for the future. However, there are voices that point out that our research institutions may be failing in this dimension, meaning that there is a shortage of time devoted to training scientists able to perform outstanding independent research in the future.1In this paper, we propose a model to address this problem, to discuss the allocation of time between research and training the next generation of researchers and to discuss the problems that may arise. Our motivation comes from two facts. On the one hand, it is a documented fact that the most prominent candidates who attain an independent research status are PhDs and postdoctoral researchers who, thrive through more experience and skills in science, either in academics or in industry (Cech and Bond, 2004). The literature on higher education, human resource management and mentoring extensively recognizes the effects of training by senior staffin the competence, productivity, career development and independent skills of young professionals, both in industry and academia. The student-supervisor relationship is the most critical issue affecting the quality of the PhD training (which affects both eventual job placement and success in obtaining a degree). In this process, it is natural that doctoral students hold expectations with respect to the role of their supervisors. The most important expectations are guidance in the early days of obtaining a PhD, knowledge about the area they are working in, and most importantly involvement with their work (Pole et al., 1997).2On a postdoctoral level, Vogel (1999) reports the experience 1Obviously, an alternative to training one’s own researchers is to attract researchers trained elsewere. While this is an interesting idea, we choose to ignore this topic in this paper. 2Murray (2004) illustrates this issue on a study on academic scientists working for the industry in the biosciences. The author identifies one of the sources of social capital to be the scientist’s laboratory 2 of a principal investigator (PI) supervising postdocs in an internationally appraised lab.3 She states that the PI’s key to producing successful and high-quality junior scientists is to provide them with original ideas and orientation, to encourage strong participation in the projects, and to listen to them to assess their skills, motivations and ambitions. On the other hand, training problems persist on a global scale. Student doctoral attrition remains a common problem in PhD training, and this is estimated at approximately 50% on the U.S. (Lovitts, 2001). In a case study about former students who spent at least two years in a PhD program Golde (2000) identifies a lack of support and guidance from supervisorsasoneofthecausesofattrition.Theauthorisalsoabletoidentifycharacteristics for good supervision: the amount of time spent, the quality of interactions between student and supervisor, and an interest in the student’s work are important to guarantee training success. Accessibility seems to be an important issue as well.4Training problems also occur at the postdoctoral level. Puljak (2006) reports that the most common complaint in postdoctoral training is ironically, a the lack of postdoctoral training. Postdocs join a research lab and, shortly thereafter, many realize that they are on their own. It has also been identified that some advisors tend to take over the design of experiments, making postdocs feel like they are overeducated technicians.5 We study this issue by building a multitask model that examines the incentives of a senior scientist to provide training to a junior scientist. The senior scientist chooses the time to allocate to her own research and the time to train to the junior scientist under her supervision. We then evaluate the impact of time allocation on the level of research network, which includes his former Ph.D. advisor, post-doctoral mentor, graduate student colleagues and his own graduate student, resident, and fellow advisees. 3A PI is a head researcher and author who supervises doctoral students, conceives ideas and conducts projects that may include collaborating with research assistants (Armbruster, 2008). 4It seems that there can be a mismatch in the perceptions of the supervisor and of doctoral students with respect to accessibility. In a study on the provisions of PhD training in biomedical research PhD programs, virtually all supervisors reported meeting frequently with their students, whereas 1/4 of the students reported problems in accessing their supervisor (Frame and Allen, 2002). 5Nerad and Cerny (1999) also survey the perspective on postdoctoral employment in the U.S. and report that there exists a generalized discontent on behalf of postdoctoral researchers. The length of postdoctoral appointments has increased and these appointments are increasingly being seen as ‘holding base’, rather than being an important step in a young researcher’s career. 3 and the final skills of the junior scientists as a researcher. The junior scientist is not an active player in our model (he does not make any decisions), but has a productive role in the project (he contributes to its final value). In addition, we assume that the junior scientist’s final capabilities are not only affected by the training received from the senior scientist but are also affected by his innate ability. On this respect, we abstract from information features: senior and junior scientists have the same information about the junior scientist innate ability.6 Not surprisingly, when we analyze the senior scientist’s allocation of time between research and training, we find that when she has more time available this results in more time allocated to both tasks. Also, we show that when there is an increase in the innate ability of the junior scientist, an increase in the importance that training has on the senior scientist’s utility function, or a decrease in the productivity of the senior scientist in the project then there is a tendency to increase the time allocated to training. We also discuss the final capability of the junior scientist and the final value of the scientificprojectin different scenarios. Most interestingly, we show that ignorance about the true innate ability of the junior scientist may lead to more training for less able junior scientists, while there is a tendency toward an under-investment in training for the most talented ones. As a robustness check, we consider two extensions. First, we consider the case where the senior scientist can also spend time selecting a better junior scientist. Second we examine the case where the senior scientist chooses the total amount of time she will work (and allocate to research and training), that is, the total amount of time spent on both tasks. We also discuss possible policy instruments for a regulator who is concerned with maximizing the value of projects and attaining highly qualified scientists in a desired proportion. We highlight that the implementation of training programs in earlier education 6This does not mean that the junior scientist’s innate ability is public information. It is ex-ante unknown by both participants. Even though a student is selected to participate in a graduate programme or in a lab according to a GRE score, and other internal admission criteria of a department, significant uncertainty remains in predicting if a student has the potential to become a successful independent researcher (Lovitts, 2005). 4 and tougher selection processes to attract high-ability junior scientists for research under supervision, as well as attractive training conditions, can be effective measures to attain it. Following the work by Holmstrom and Milgrom (1991), where the authors propose a principal-agent model where the principal wants the agent to perform multiple tasks, several papers have considered the incentives for scientists to perform different tasks. For example, Lacetera and Zirulia (2008), in a context of corporate science with a great deal of competition, propose a model to explain the optimal choice of an effort to do applied research and an effort to do basic research. They analyze the strength of incentives in the effort allocation decision of the scientist and the effects of different levels of competition. In Banal-Estañol and Macho-Stadler’s work (2010), the authors present a model of incentives of a researcher who can choose to either allocate time between undertaking a new research idea or developing an existing one that will deliver immediate commercial benefits. In the same branch of the literature, Walckiers (2008) argues about whether it is more attractive for a university to produce both research and teaching. The author conducts his analysis in a contractual setting between the university (principal) and the academic/scientist (agent) and studies the incentives for university scientists to perform either one of the tasks or both of them. In contrast to Walckiers (2008), where the agent does teaching at the undergraduate level, we consider training at the graduate level which implies that there are complementarities among the two tasks. Walckiers (2008) uses an adverse selection framework, where researchers differ on their preference for both tasks7and he shows that it can be optimal to produce research and teaching in the same institution (bundling the two tasks). This paper is organized as follows. Section 2 describes the model and analyzes the equilibrium allocation of time to the two tasks: research and training. It also provides the comparative statics of the equilibrium efforts with respect to the parameters of the model. In Section 3, we evaluate and draw the patterns that the project’s expected value and the junior scientist’s final capability follow. We also present the ex-post ability of the junior scientist and the role of imperfect information in the distortions with respect to 7In our model, we could also discuss the researcher preferences, but this is not the main aspect of the analysis. 5 the full information and efficient outcomes. In Section 4 we perform a robustness check by considering two possibilities. First, we consider that the senior scientist can choose the total amount of time to exert in both tasks. Second, we consider the incentives for a senior scientist to spend time in previous activities that allow her to know more about the innate ability of the junior scientist. In Section 5 we discuss some policy instruments that may change the time allocation. In Section 6 we conclude. All proofs are remitted in the Appendix. 2BasicModel We consider a senior scientist who is in charge of a research project and allocates her time between research and the training of a junior scientist under her supervision. We denote the research effort by and the training (guidance or education) effort by and assume that the senior scientist has limited time to allocate to these tasks. Formally, the senior scientist’s time constraint is written as: += In Section 4.1, we study how the available time that the senior scientist works is determined. For now, we assume that 0is exogenously given. In our model, the junior scientist does not make any decisions. He is endowed with an innate ability ˆ,ex-ante unknown by all the players. We assume that there is a population of junior scientists with different innate abilities. The innate ability of the junior scientist who works with the senior takes a value in the interval [¯],with¯, and the expected innate ability is ()8 The senior scientist’s vector of efforts affects two outcomes: the quality (the value) of the research project and the final capability of the junior she is training. The final capability of the junior scientist depends on his innate ability and on the senior scientist’s educational effort. Our view is that education provided by the senior is 8In our model, there is always symmetric information about the junior scientist’s innate ability. Under complete information senior and junior know that his innate ability is ˆ;under ignorance they expect it to be () 6 a necessary input to develop the junior’s scientific capability. The junior scientist’s final capability, denoted by , is a function of his true innate ability ˆ∈[¯]and the training he receives , and it is defined as follows: =ˆ(1) Without training, even the most gifted junior scientist will not be able to acquire the capability to work on the research project in a profitableway(andmayberunaresearch project in the future). The project’s value depends on the direct research effort exerted by the senior scientist and on the junior scientist’s final capabilities. The scientific value of the senior’s project is given by: =+(2) where is the productivity of the senior’s research time ,andcaptures the synergies of working together with a junior scientist of capability . In this sense, senior and junior scientists provide complementary inputs to the research project. Researchers may have different projects defined by ( )and we will discuss this further on. The level may represent the publications obtained, patents achieved or other results of the discoveries. Note that by following this functional form, no value will be produced from the project if the senior scientist does not provide any research effort. We assume that the senior scientist’s utility function combines the project’s value and the junior’s final capability. Formally, ( )=+ The project’s value is included in the senior’s preferences because it is a verifiable outcome that determines the senior scientist’s payoff. It is also a proxy for the usual argument of peer recognition and the “puzzle joy” (Stephan and Levin, 1992). The junior scientist’s final capability enters the senior’s utility in a proportion , which represents the relative appreciation of the training outcome. We may also interpret this second term of the senior’s utility as a concern with reputation associated to having a network and disciples who excel in the profession.9 9Our model aims to encompass the fact that both senior and junior scientists benefit from the train7 Given the parameters (   )and the ex-ante expectation about the junior scientist’s innate ability with ∈{ˆ ()}, the senior scientist chooses the optimal allocation of time between and that maximizes the ex-ante (expected) value of her utility:10   {++}  += ∈[0] ∈[0] From the solution to this problem we obtain the result that follows. Lemma 1 Given (   )and the innate ability of the junior scientist  with ∈ {ˆ ()}the senior scientist’s allocation of time among the tasks of research and training is: a) When and   − ∗ =0and ∗ = b) When   + ∗ =and ∗ =0 c) Otherwise, ∗ = 2+− 2 and ∗ = 2−− 2 ing relationship. For the senior scientist, training increases visibility and reputation when the young professional is a productive member. Therefore, she earns more respect from the organization by developing the trainee (Kram, 1983). This model also includes the trainer’s inner satisfaction in passing along knowledge (Levinson et al., 1978). For the junior scientist, the benefits include learning technical aspects of the profession, developing writing and critical skills, defining career perspectives, performing research collaborations (Kram, 1983) and receiving an important push toward building networks (Kram and Isabella, 1985). 10Note that is a linear function of that allows us to use a simplification where we write the ex-ante value of the project as a function of ,∈{ˆ ()}. This allows us to consider at the same time the cases where the information about the junior scientist’s innate ability is perfect or imperfect. 8 The senior scientist’s allocation of time for the interior solution depicted in Lemma 1 µ∗ = 2+− 2  ∗ = 2−− 2 ¶ depends on all the relevant parameters. It shows the deviation from the half-half distribution of time as a function of the senior scientist’s effectiveness in the research process (), the complementarity among the senior’s and junior scientist’s participation (), the expected innate ability of the junior () and the senior’s concern about the junior’s training (). Lemma 1 also shows that when the junior has a low expected ability he does not receive any training. It also shows that when the senior scientist’s concern about the junior’s training is high as compared to the time available and the complementarity ()then the possibility exists that she decides ,only to perform training. Note for example, that if =0(and 6= )i.e., there is no effect of the junior scientist toward the result of the research project, then time will only be allocated to training. Corollary 2 For the combination of parameters satisfying ∈[(−)(+)] (region c) in Lemma 1), the static comparative of the efforts is presented in Table 1:      ∗ +− − iff +− ∗ −+ + iff + + Table 1 As expected, the senior scientist’s research effort (resp., training effort) increases (resp., decreases) when increases, decreases or decreases. Both efforts go in different directions when increases, and the direction of the change depends on the sign of − In addition, both efforts increase with the time the senior scientist has to work. The effect of in equilibrium is in accordance with stylized facts. In a 5 1 2year longitudinal investigation with 233 PhD students (Paglis, Green, and Bauer, 2006, which was an extension of a similar study by Green and Bauer, 1995), the effects of supervisory mentoring of advisors on PhD students in the applied sciences were analyzed. The results show that supervisory mentoring increases the productivity and the self-efficacy of PhD students. Most importantly, a positive relationship between student potential (ability, 9 the distortion increases proportionately. The effect of a higher prior ()over the junior scientist’s ability is a higher slope of the "ignorance" ex-post curve, which means that the distortion increases for lower values of ˆand will decrease for higher values. More accurate training is provided to the population of junior scientists with more potential. â q )(aE    t aE )( Case  t  Ignorance Full info    t aE )(   t Figure 4: ∗(ˆ)and (ˆ ()) when  ≥ For   , as illustrated in Figure 5, the distortion and the effects of a higher () are very similar. As in the case with the value of the project, the sign of the distortion may be aligned or not aligned with social interest. We will discuss this aspect in Section 5. Note also that if the interval [¯]is smaller or if, for a given interval the expected innate ability of the junior scientist, ()ishigher,thenitmaybethecasethatmoreeducationisprovided under ignorance and the distortion is not too big. 4Extensions Let us consider two natural questions that may come to mind that we present here in two independent extensions. In the first one, we allow for the senior scientist to choose the amount of time that she will work. In other words, is not exogenous but her choice. In the second extension we assume that the time available is exogenously given, but we 16 â q* )(aE ) Case  t  Ignorance Full info    t aE )(       t aE t)( t aE    )( t      t Figure 5: ∗(ˆ)and (ˆ ()) when    allow the senior scientist to have access to a better pool of junior scientists at the cost of some of her time. Both extensions can be viewed as a sequential decision problem where, once either the time allocated to work or the ability of the junior scientist is determined, the analysis of the previous sections tells us the result in terms of research and training. Hence, it is useful to use the optimal allocation of time as a function of and to write the utility of the senior in terms of these variables. Using Lemma 1 we see that: a) When and   − ∗( )= b) When   + ∗()= c) Otherwise, ∗( )=( +)2−()2 4 +µ 2−− 2¶ 4.1 Total Time Worked Until now we have considered that the time the senior scientist works is fixed. Let us now consider that, as in the line of more traditional moral hazard models, the senior 17 scientist may decide the total amount of time shewilldevotetowork(thetotaleffort). To determine this total working time , the senior scientist maximizes her expected utility netofthecostoftheworkingtime. Wewillassumethatthecostofworkingtimeis high enough. More precisely, we assume ≥ 2.16 Hence, the senior solves  n∗( )− 22o From this problem, we obtain the following result:17 Lemma 3 The senior scientist’s total time as a function of the parameters is a) When − ≥0and ≥ −  ∗=  b) When − ≥0and  2≤ − or −  0and 2 − ∗=+ 2− c) When −  0and  2≤2 − ∗=  Lemma 3 is depicted in Figure 6 in the space ( (−)). From Lemma 3 we conclude that, as expected, the time the senior scientist works ∗ is a non-decreasing function of     and is decreasing in  The comparative statics 16If the cost is smaller that 2the optimal time goes to infinite. In this case it would be natural to include a maximum time limit  We will comment on this assumption later, but we will concentrate on the case where is high for the sake of simplicity. 17Note that for − ≥0we have  2≤ − and for −  0we have  22 −Hence, the regions of Lemma 3 are well defined. 18  a c c t   *   ac a t  2 * c a t   *   a a c     a a c2 Figure 6: Optimal ∗in the space ( (−)) are summarized in Table 3.      ∗= +00−0 ∗=+ 2− +++−+ ∗= 0+0−+ Table 3 Given the optimal ∗we compute the time allocated to each task. As expected, the time allocated to both tasks is decreasing in (that now plays a role similar to a decrease in in the previous sections). Effort is non-increasing and is non-decreasing in the concern for training,  More precisely, for ∗= the optimal allocation of time is ¡=  =0 ¢and research increases with but nothing is affected by or  At the other extreme, for ∗= the optimal allocation of time is ¡=0 = ¢For the case ∗=+ 2− the time allocated to both tasks deserves some attention, and we perform comparative statics given in Corollary 4. Corollary 4 When ∗=+ 2− , region b) in Lemma 3, we have that the allocation of time 19 to the tasks is ∗ =1 2µ+ 2− +−  ¶ ∗ =1 2µ+ 2− −−  ¶ and the comparative statics are presented in Table 4:     ∗ (   ) + +iff  +iff  2 (2+)  +iff  2³(+)12 (−)12−1´ ∗ (   )+iff  + + + Table 4 For completeness let us remark that in a version of the model where is not constrained from below, and there is a maximum amount of time that the senior scientist has available, the results will be similar, except for low costs ¡≤ 2¢and/or small enough ³|−|  ´. In these cases, the senior chooses to work for all the available time and she allocates all the time either to research () or to training () (except if = case where she is indifferent). Changes in or in do not affect the total time allocated to work and only discrete changes may affect to which task this time is allocated. In these cases, only changes of the time available for these activities may have an effect on the senior scientist’s behavior. 4.2 WhenExpectedAbilityandTimeAreRelated In Section 2 we analyzed the decisions of a senior scientist that is (randomly) matched with a junior scientist of innate ability  However, one may wonder about what happens if the junior’s expected innate ability depends on some previous activity that the senior performs and that consumes time. This may correspond to a selection process that tries to identify a better population of junior scientists, an advertising or investment procedure that aims to attract a junior scientist with a higher expected innate ability, or an undergraduate system that provides better skills and better information about the juniors’ 20 abilities. Here, we model the relationship between the time invested in increasing the innate ability of the junior she works with and the remaining time available for research and training. Let us assume that is the maximum amount of time available for the three tasks and the innate ability of the junior scientist if no effort is made to improve it. Let us denote by (−)with 0the improvement of the innate ability of the junior scientist that the senior can obtain by using an amount of time (−)to improve the quality of the junior with whom she works, in such a way that she will have to allocate to the tasks of research and formation. Hence, the ability of the junior scientist with whom the senior will work with is =+(−) In this case, the senior scientist chooses ( )by maximizing her utility function, taking into account the constraints =+(−). To simplify presentation and to avoid cumbersome calculations for different regions of parameters, we just present an example where we assume that the senior has no appreciation of the junior scientist’s final capability (=0) and that the complementarity effect is 1 (=1).Thisimpliesthatwe will be in Region  ≥(that, in this case, is reduced to ≥0)Under this parameter combination, as a function of  the senior’s allocation of time depends on whether ≥  (and her time will be allocated to research and formation) or ≤  (and she will only do research). Lemma 5 Assuming =0,=1and the relation between time and ability given as =+(−), the senior scientist’s decision on the optimal innate ability and on the optimal amount of time spent in previous activities is: a) When ( +)2−12 ≥0 ∗= ++p( +)2−12 6and ∗=5( +)−p( +)2−12 6 b) When ( +)2−12  0 ∗=and ∗= Lemma 5 illustrates that in projects where the productivity of the senior scientist’s direct research () is low enough, the senior is willing to spend time in selection activities 21 that allow to work with a junior scientist of higher expected innate ability. This finding is because being a less productive scientist, the senior will want to increase the prospects of working with a more talented junior scientist. When is high enough, then she will choose not to spend any time in activities to retrieve more information about the junior’s innate ability, leaving it at level . This way, she chooses to allocate all of the time resources to training and research only. Note also that for a given combination of the other parameters ()when or are small it is more often the case that the senior’s optimal decision is not spend time in improving the innate ability of the junior (while this does not mean that she will not allocate some time to formation). 5WelfareAnalysis We would like to consider here a situation with a social planner who is concerned about the level of research that the senior scientist achieves and the final capacity of the junior, that he interprets as a measure of the potential of the next generation of researchers. We consider first that this social planner has the welfare function: =((ˆ ())) + ((ˆ ())) where can be interpreted as the society’s relative concern about the capability of the next generation of researchers. If coincides with  then the decision of the senior and the aims of the society concur. If and do not coincide, the social planner may be tempted to intervene. To discuss this possibility, we take as a starting point our basic model presented in Section 2, where we assume that there is no moral hazard problem, just a decision about the allocation of time. An alternative way of looking at the comparative static in Table 1 (and the discussion after it) is to consider how society may induce changes in some parameters to affect the senior scientist’s allocation of time to research and formation. For this purpose, the social planner must affect the senior’s utility =++possibly using ( )and as instruments.18 18Obviously, the social planner can also change the time available for these tasks (for example, by reducing the senior’s involvement in other time-consuming tasks, such as administrative ones). 22 If the outcome of research and the outcome of training are verifiable, the regulator can manipulate the decision of the senior scientist by changing her awareness about these two variables. The planner can increase the senior scientist’s utility from the project’s value (that is, increasing and in the same proportion or, equivalently decreasing ) or to increase the senior’s payoffas a function of the quality of the junior she mentors (increasing )viathedefinition of a successful career or the allocation of research funds that weight this aspect of the academic career. Note that increasing both perceptions is useless when the aim is to change the allocation of total time, because total time is fixed. Also, if only publications (and other measures of the senior scientist project results) are verifiable, the social planner can only encourage more time to research (through tenure tack rules, opportunities to travel and access to research funds, or peer esteem, which in our model corresponds to decrease )but he cannot increase it above the natural inclination of the senior scientist. Only by discouraging research can the time allocated to training be increased. The social planner can change the junior scientist’s innate quality (for example, by having an attractive and selective program of fellowships) that allows the attraction of better students. Indeed, several European expert institutions (e.g., EURAB, ESF) have given priority to the training of scientists and developed actions so that postdoctoral researchers ascend to PIs in recent years. These actions involve providing access to special grants, as well as promoting free and secure mobility. When total time is fixed, these instruments have a positive effect on one task but anegativeeffect on the other. Both efforts only increase simultaneously by inducing a higher , as already mentioned. If a moral hazard situation exists, and the senior scientist decides how much time to work, the previous discussion of the instruments to use holds partially. In this case, incentivizing the results for both research and training may be optimal because these instruments affect not only time allocation but also how much time the senior decides to work. As shown in Corollary 4, if the cost of the effort or the quality of the junior is high enough, then increases in ( )which correspond to a higher utility associated to the value of the research project, or increases in induce more research and more training (because they induce more incentives to work). If juniors are gifted enough, both instruments (increasing the utility the senior scientist receives from research 23 or from training) have positive effects on the senior scientist’s dedication to both tasks. In a society where the population of juniors is of low expected ability, the instruments have positive effects on one task and negative on the other and encouraging one activity crowds out the effort on the other one. This emphasizes the importance of attracting a good population of junior scientists. This comment connects with the analysis conducted in Section 4.2 where Lemma 5 draws attention to the possibility that the population of juniors can be linked to the time allocated to select them. Note however, that measures that increase ∗will decreases ∗. This may lead to an increase in the senior’s dedication to a task but may trigger a decrease in the time allocate to the other task unless the cost of obtaining better pools of junior scientists,  decreases. Another point of view is to consider that the social planner is not just concerned about the expected level of research and training. His concern may be to reach high enough outcomes in both tasks. In other words, it can be the case that the social planner is only interested in excellence and in achieving the highest innovation level (project quality) and the highest level of ex-post capability.19 Imagine a social planner considers research to be valuable only if ≥and wants junior scientists to be endowed with a minimum final capability ≥to be considered good independent researchers. In this framework, the social planner cares about ˜ , ˜ =≥((ˆ ())) + ≥((ˆ ())) where the minimum requirements ()are given by the social planner a level of exigency. We use now the results presented in Section 3.1 based on the model where time  is given. To have projects and young researchers above the cutoffs()with high probability (or a high proportion) the social planner may use the available instruments  ,. We have seen in Figures 5 and 6 that the level of final capability under ignorance, (ˆ ()), increases with the senior scientist’s priors with respect to the innate ability of the junior. To help the discussion along, in Figure 7 (using the information conveyed in Table 2) 19The reason may be that the society may not consider results below a minimum requirement on both outcomes as an achievement: the society may value only "good enough" discoveries to be patented or to improve knowledge, and only "capable enough" junior scientists may be considered good researchers. 24 we represent in the space ( )the expected value of the project in equilibrium, as well as the iso-project value curves and the iso-final capability curves of the junior scientist, keeping constant other parameters (the dotted lines). This figure shows that a higher total amount of time always induces a higher expected project value as well as a higher junior scientist capability. However, increasing only does not have the same effect. If the social planner wants project values to have at least value 0and the junior capability 0 then it has, on one hand, to procure a higher total time available to the senior scientist, and on the other hand induce as much as possible a selected junior scientist with enough potential. For the social planner, the senior scientist’s priors is a possible instrument to obtain a superior outcome in the training component because a higher prior induces more time allocated to training. Besides the quantity effect, which is the fact that more of the population reaches an independent research status (attains above ), there is a quality effect on junior researchers since they are better prepared. Analyzing here, we conclude that the project value under ignorance increases with the senior scientist’s priors, but only until a certain point. For very high values of the expected ability the equilibrium value of the project starts to decrease. Hence, when fixing the level of ()both effects must be taken into account. Increasing the expected ability of the juniors population, (), can be performed by implementing or increasing subsidies to a tougher selection of scientists eligible to perform research under supervision.20 Implementing good programs in earlier education can also cause this shift. Also, offering more attractive conditions in programs for PhD and postdocs may attract better candidates for the task, who are otherwise drawn to more attractive careers in other sectors. These conditions mean not only better stipends, but also better lab equipment accessible to junior scientists. Implementing such measures will shift the population to higher levels of innate ability, first order stochastically dominating the initial population distribution or even an increase in 20One can assume that the senior sceintist or ither department are in a better position to assess the ability of a junior scientist, but it also seems reasonable to think that higher resources allocated to the selection processes may help. Any selection process would include the past education of the junior sceintist, as well as considering the university of origin and inviting the juniors for an interview. If these resources are not available, their own students may be less risky that outsiders. 25 with respect to the first region:  ½µ−− ¶¾   ≥ ≤ +−p( +)2−4 2 The lagrangian is L=³−− ´+(−)+(+−√(+)2−4 2−).TheFOC is − +−=0 There are two possible cases for the lagrangian multipliers: 1) 0=0=is a candidate. 2) 00.Thisholdswhen=+−√(+)2−4 2⇔ =which is a particular case of 1). Hence =is again a candidate. Formalizing the problem with respect to the second region, the FOC is: − −+=0 One possible case exists for the lagrange multiplier: 1) =00.Inthiscase,=++√(+)2−4 2is a candidate. Since the utility function is decreasing in ,=is a candidate for the optimal ability. Case b)  ≤and ( +)2−4  0 The region to work with is ≤≤ +, since the function always has positive values in this case. Since the utility function of the senior is decreasing in ,=is a candidate for the optimal ability. Case c)    and ( +)2−4 ≥0 This is a particular case of case 1.a), where we only consider the second region, hence =++√(+)2−4 2is a candidate for the optimal ability. We now summarize the candidates for step 1: =if  ≤ = ++p( +)2−4 2if    and ( +)2−4 ≥0 Step 2: 2−( +)+ ≤0 32 The utility function to be considered in this case is ∗( )=(+)2 4 Followingthesamelogicasinstep1,wehave2subcasestosolvethisproblem:2.a) when  ≥and ( +)2−4 ≥0; 2.b) when  ≤and ( +)2−4 ≥0. The other two subcases are impossible, since ( +)2−4  0means the function always has positive values. Hence, in this step we take as given that ( +)2−4 ≥0 Case a)  ≥ There is one region for to work with: ≤≤++2 √(+)2−4 2.Themaximization problem is:   (1 4µ(−− )+¶2)   ≥and ≤ ++p( +)2−4 2 The FOC is: 1 2µ(−− )+¶µ(−3− )−¶+−=0 There are 4 possible cases for the lagrange multipliers: 1) 0=0.LookingattheFOC,itmustbethat(−3− )−0,thatis, ∈(+−√(+)2−12 6++√(+)2−12 6),whichisthecasewhen=. 2) =00In this case, =++2 √(+)2−4 2is a candidate if ∈(+−√(+)2−12 6 ++2 √(+)2−12 6).Wecheckthatindeedbelongs to this interval. This holds only if ( +)2−12 ≥0 3) =0=0=+±2 √(+)2−12 6are candidates, provided ( +)2−12 ≥ 0 4) 0,0. This holds when =+−√(+)2−4 2⇔ =. Hence = is a candidate again. The utility function is decreasing from until +−√(+)2−12 6increasing from then on until ++√(+)2−12 6, and decreasing onwards. Hence, when ( +)2− 12 ≥0=++√(+)2−12 6is candidate for the optimal ability and when ( + )2−12  0=. Case b)  ≤ 33 There is one region for to work with:+−√(+)2−4 2≤≤++√(+)2−4 2. TheFOCisthesameasincasea),hencethepossiblecasesforthelagrangeanmultipliers are: 1) 0=0.=+−√(+)2−4 2anditmustbethat∈(+−√(+)2−12 6 ++√(+)2−12 6).Since+−√(+)2−4 2+−√(+)2−12 6, indeed it is a candidate. 2) =00.=++√(+)2−4 2anditmustbethat∈(+−√(+)2−12 6 ++√(+)2−12 6). It is straightforward to check that indeed belongs to this interval, so it is a candidate, provided that ( +)2−12 ≥0 3) =0=0In this case, =+±√(+)2−12 6provided that (+)2−12 ≥ 0 4) 0,0.Inthiscase,=+ 6, which happens when ( +)2−12 =0,a particular case of 3). Analyzing all the candidates and the behavior of the utility function, =++√(+)2−12 6 is a candidate for the optimal ability when (+)2−12 ≥0and =+−√(+)2−4 2 when ( +)2−12  0 We now summarize all candidates for case 2: = ++p( +)2−12 6if ( +)2−12 ≥0 =if  ≥and ( +)2−12  0 = +−p( +)2−4 2if    and ( +)2−12  0 As function of the parameters, we evaluate and compare the utility of the solutions attained in step 1 and step 2. The final solutions for ∗and ∗(attained recursively) are: ( +)2−12 ≥0∗=++√(+)2−12 6∗=5(+)−√(+)2−12 6 ( +)2−12  0∗= ∗= 34 References [1] Armbruster, L. (2008): "The Rise of The Post-Doc as Principal Investigator? How PHDs May Advance in Their Career and Knowledge Claims in the New Europe of Knowledge", Policy Futures in Education 6(4), 409-423. [2] Banal-Estañol, A. and Macho-Stadler, I. (2010): "Scientific and Commercial Incentives in R&D: Research vs. Development", Journal of Economics and Management Strategy 19(1), 185-221. [3] Cech, T. and Bond, E. (2004): "Managing Your Own Lab", Science June 18, Vol. 304, No. 5678, 1717. [4] European Commission (2004): "Increasing Human Resources for Science and Technology in Europe", Report chaired by J.M. Gago, High Level Group (HLG) Human Resources for Science and Technology in Europe. [5] Frame, I. and Allen, L (2002): "A Flexible Approach to PhD Research Training", Quality Assurance in Education 12(2), 98-103. [6] Golde, C. (2000): "Should I stay or should I go? Student descriptions of the doctoral attrition process", The Review of Higher Education 23(2), 199-227. [7] Green, S. and Bauer, T. (1995): "Supervisory Mentoring by Advisers: Relationships With Doctoral Student Potential, Productivity and Commitment", Personnel Psychology 48(3), 537-561. [8] Kram, K. (1983): "Phases of the Mentor Relationship", Academy of Management Journal 26, 608-625. [9] Kram, K. and Isabella, L. (1985): "Mentoring Alternatives: The Role of Peer Relationships in Career Development", Academy of Management Journal 28(1), 110-132. [10] Holmstrom, B. and Milgrom, P. (1991): "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design", Journal of Law, Economics and Organization 7, 24-51. 35 [11] Levinson, D. (1978): "The season’s of a man’s life ", New York: Knopf. [12] Lacetera, N. and Zirulia, L. (2008): "Knowledge Spillovers, Competition, and Taste for Science in a Model of R&D Incentive Provision", Universita’ di Bologna, Working Paper.. [13] Lovitts, B. E. (2001): "Leaving the ivory tower: the causes and consequences of departure from doctoral study", Lanham, MA, Rowman & Littlefield. [14] Lovitts, B. E. (2005): "Being a good course-taker is not enough: a Theoretical Perspective on the Transition to Independent Research", Studies in Higher Education 30(2), 137-154. [15] Murray, F. (2004), ‘The role of academic inventors in entrepreneurial firms: sharing the laboratory life,’ Research Policy 33(4), 643—659. [16] Nerad, M. and Cerny, J. (1999): "Postdoctoral Patterns, Career Advancement, and Problems", Science September 3, Vol. 285. No. 5433, 1533-1535. [17] Paglis, L., Green, S. and Bauer T. (2006): "Does Advisor Mentoring Add Value? A Longitudinal Study of Mentoring and Doctoral Student Outcomes", Research in Higher Education 47(5), 451-476. [18] Pole, C., Sprokkereef, A., Burgess, Robert G., and Lakin, E. (1997): "Supervision of Doctoral Students in the Natural Sciences: expectations and experiences", Assessment & Evaluation in Higher Education 22(1), 49-63. [19] Puljak, L. (2006): "Career Blocker: Bad Advisors" in http://sciencecareers.sciencemag.org. [20] Stephan, P. E. and S.G. Levin, 1992, Striking the Mother Lode in Science: The Importance of Age, Place, and Time, New York: Oxford University Press. [21] Vogel, G. (1999): "A Day in the Life of a Topflight Lab", Science September 3, Vol. 285, 1531-1532. 36 [22] Walckiers, A. (2008): "Multidimensional Contracts with Task-Specific Productivities: An Application to Universities", International Tax and Public Finance 15, 165-198. 37