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Open access to research data: Strategic delay and the ambiguous welfare effects of mandatory data disclosure
Accepted Manuscript
Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure Frank Mueller-Langer, Patrick Andreoli-Versbach PII: DOI: Reference:
S0167-6245(16)30114-7 10.1016/j.infoecopol.2017.05.004 IEPOL 786
To appear in:
Information Economics and Policy
Received date: Revised date: Accepted date:
6 October 2016 23 May 2017 29 May 2017
Please cite this article as: Frank Mueller-Langer, Patrick Andreoli-Versbach, Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure, Information Economics and Policy (2017), doi: 10.1016/j.infoecopol.2017.05.004
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Highlights • Data disclosure is an essential feature for credible empirical work • However, universal mandatory data disclosure may have two unintended effects
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• It decreases a researchers effort to generate data
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• It decreases overall welfare if it induces strategic delay of paper submission
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Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure Frank Mueller-Langera,b∗ , Patrick Andreoli-Versbacha,c Planck Institute for Innovation and Competition, Marstallplatz 1, 80539 Munich, Germany
b European
Commission, Joint Research Center, Edificio Expo, Calle Inca Garcilaso, 3, 41092 Seville, Spain
c Ludwig
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a Max
Maximilian University of Munich, Department of Economics, Schackstraße 4, 80539 Munich, Germany
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Abstract
Mandatory disclosure of research data is an essential feature for credible empirical work but comes at a cost: First, authors might invest less in data generation if they are not the full residual claimants of their data after the first journal publication. Second, authors might ”strategically delay” the time of submission of papers in order to fully exploit their data in subsequent research.
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We analyze a three-stage model of publication and data disclosure. We find that the welfare effects of universal mandatory data disclosure are ambiguous. The mere implementation of
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mandatory data disclosure policies may be welfare-reducing, unless accompanied by appropriate
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incentives which deter strategic delay.
Keywords: Data disclosure policy; strategic delay; welfare effects
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JEL classification: B40, C80, L59 ∗ Corresponding author at Max Planck Institute for Innovation and Competition: Tel.: +49 177 3163096;
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E-mail: [email protected]; Andreoli-Versbach: Tel.: +44 7586312838; E-mail: [email protected] We gratefully acknowledge financial support from the German Research Foundation (DFG) under the European Data Watch Extended Project (DFG-Grant Number WA 547/6-2). The funders had no role in study design; in the writing of the manuscript; and in the decision to submit the article for publication. We thank Linda Gratz, Dietmar Harhoff, Fabian Herweg, Mark Schankerman, Olaf Siegert, Ralf Toepfer, Sven Vlaeminck, Gert G. Wagner and Joachim Wagner for their helpful comments and suggestions. We also thank participants of the Conference on ”Academia & Publishing” at the Universit` a del Piemonte Orientale
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in Turin and seminar participants at the INNO-tec in Munich for their valuable comments. Philippe van der Beck, Michael Khotyakov and Stefan Suttner provided excellent research assistance. The views and opinions expressed in this paper are the authors’ and do not necessarily represent those of the Joint Research Center or the European Commission.
Introduction
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Data sharing is an essential feature for the scientific principle of credibility, replication and further research. It guarantees that research methods used to produce the results are known and that incorrect results can be withdrawn from the cumulative body of knowledge (Anderson, 2006; An-
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derson et al., 2008; Dewald et al., 1986; Hamermesh, 1997; Vlaeminck and Wagner, 2014).1 Also, replicable research fosters learning and thus facilitates the development of subsequent research, which boosts scientific advancement. However, whereas a large majority of researchers seems to recognize the importance of data sharing, they are reluctant to apply this principle in practice (Nelson, 2009; Andreoli-Versbach and Mueller-Langer, 2014). In the status-quo, the researchers’
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costs of disclosing data seem to be higher than their benefits associated with data-sharing, which leads to an equilibrium with minimal sharing.2 In order to overcome the gap between the large
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demand for replicable results and the low supply of data, some of the major economics journals have introduced mandatory data disclosure policies, which require authors to share their data prior
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to publication. While the aim of these policies is to increase credibility and replicability, they may lead to welfare-decreasing behaviour.
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The introduction of mandatory data disclosure distorts the incentives of researchers in several ways and may ultimately have detrimental effects. Authors who invest in costly data generation,
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e.g., collecting data and programming, are not the full residual claimants of their data after the first publication, as they have to disclose it. This might lead to two negative effects: first, a decrease in researchers’ initial effort to generate data (”underinvestment”) and second, it may induce researchers to strategically delay the submission of papers in order to fully exploit their 1
Studies aiming at replicating published economic articles often fail (Camerer et al., 2016; Dewald et al., 1986; McCullough et al., 2006 and 2008; Lacetera and Zirulia, 2011). Similar results are found in other disciplines, e.g., psychology (Bohannon, 2015), political science (King, 1995) or physics (Grant, 2002). 2 The private benefits to share data include, for example, higher citations and a positive signal on the quality of the research.
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data (”strategic delay”). In this paper, we investigate the effects of mandatory disclosure policies by analysing the decision of a researcher under different policies. We derive effort choices to show the presence of underinvestment effects. We compare optimal effort choices to show that there is a strategic delay effect. In a simple model of publication and data disclosure we analyze the interaction between a
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data-creating researcher and a competing researcher and study the incentive and welfare effects of data disclosure.
Our motivating example is a researcher who exerts effort to generate a novel data set, e.g., via laboratory or field experiments, surveys or interviews, in order to pursue a research agenda consisting of a set of subsequent papers. This researcher chooses the effort to create data in the
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initial stage of the model, the number of papers written based on the data and whether and when to share the data with the research community. These decisions depend on the data disclosure policy of journals. Under No Policy, i.e., the status quo of most journals in economics, the creator of data can freely choose whether and when to share the data and whether to write one or two
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papers using the data. Following Dasgupta and David (1994), who emphasize that an institutional response is necessary to overcome the gap between researchers’ demand for data sharing and its
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voluntary provision, we consider a second policy type, the First Paper Policy. The leading example is the data availability policy of the American Economic Association, which requires the creator of data to share the data after the first publication so that the data is available to other researchers.
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The creator of the data has a strong incentive to protect the competitive advantage associated with her data, as she might benefit from using the data for subsequent research and keep the data
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secret until their private value is fully exploited (Anderson et al., 2008; Haeussler, 2011; Haeussler et al., 2014; Stephan, 1996). If the data is kept private, another researcher cannot use it for
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replication or for subsequent research and thus self-induced competition associated with disclosed data is avoided. The model endogenizes the decision to strategically delay the time of publication and thus the disclosure of data under the First Paper Policy. We derive exact conditions for positive welfare effects of mandatory data disclosure and discuss the conditions under which the transition to mandatory data disclosure has negative welfare properties. The general tension in our model is between the private incentives of a researcher to exert effort to create a novel dataset and exploit it in subsequent papers against the public benefit of 4
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having replicable results and using available data to generate new research. Ultimately, the welfare effects depend on the cost to generate data, the impatience of a researcher to publish (discount factor) and the additional value created by sharing data both for the data-creating researcher and
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A Simple Model of Data Disclosure
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the competing researcher.
We analyze the optimal effort choices of a researcher, R, to generate novel data and to share the data produced with the scientific community, which is represented by a second researcher, C, who may use the data for subsequent research. The fundamental difference between the two researchers
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is that R has a data set which would be valuable for C, but C cannot influence R’s decision when to share the data as there is no market for the exchange of data.3
We consider a three-stage model, t = 0, 1, 2, where the incentives to share depend on two factors. First, data disclosure may increase the value of a published article for R, e.g., it may increase the credibility of the article as well as the number of citations.4 Second, disclosure may change R’s
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personal value of the data after the last publication. For instance, the loss of control of disclosed data reduces R’s competitive advantage over C and R’s returns from the data.
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We study two data availability policies of journals. Under No Policy (henceforth N P ), R can freely choose whether and when to share the data and whether to write one or two papers using
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the data. In contrast, the First Paper Policy (F P P ) forces R to share the data after the first publication so that the data is available to C. For simplicity, we consider a maximum number
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of two journal publications that a single researcher can achieve by using the same data set. We assume that the marginal benefit from the re-use of the data is decreasing and that the returns
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to publication are diminishing with increased output (Tuckman and Leahey, 1973). Under both policies, R chooses effort e0 to create a data set in the initial stage. The quality and the value of the data set and the publication increase in this initial effort. Thereby, it also affects R’s decision to disclose the data and the quality of published articles which are derived from the data. R’s effort to publish is given by e1 in the first stage and by e2 in the second stage. As Figure 1 illustrates, 3 The assumption that there is no market for data is very plausible in economics. The only market for data in economics is between institutions and researchers but not between researchers. Thus there is no monetary incentive to share the data and an efficient allocation of efforts not achievable (Coase, 1960). 4 This might also occur through more data citations.
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there are six possibilities, four under N P and two under F P P . FIGURE 1 HERE Under N P , R may choose to (1) publish one paper and share in t = 1 (1-Share), (2) publish two subsequent papers in t = 1 and t = 2 and share in t = 2 (2-Share), (3) write one paper in t = 1 and
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never share (1-Never ) and (4) publish two subsequent papers and never share (2-Never ). Under F P P , R may (5) choose to publish the first paper in t = 1 while being forced to share the data. In stage 2, C will then choose effort x2 and publish a paper using R’s data (No Strategic Delay). (6) R may strategically delay the first publication in order to evade the forced disclosure of data and publish two papers in t = 2 (Strategic Delay). By ”strategic delay” we mean that a researcher
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does not submit her papers one after another but all at the same time after the completion of the second paper in order to maintain the exclusive use of the data. This is detrimental for welfare in several aspects: The research community would neither enjoy the benefits of publicly available data, nor have the confidence that the results have undergone the peer-review process and thus are
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more reliable than the unpublished version. Finally, not all papers are available before publication.5 Hence, strategic delay would lead to a delay in the accumulation of knowledge.
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Figure 1 illustrates a set of six reasonable publication strategies for R under the two data policies under study. For instance, R’s decision to write one or two papers depends on the value of the data for subsequent use. In addition, R’s decision to disclose or withhold data depends on her
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personal value of the data after the last publication. On the one hand, data disclosure may increase R’s personal value of the data, e.g., due to subsequent use in data journals. On the other hand, it
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may also be the case that the data has a higher value for R if it remains her private information. For example, loss of control associated with data sharing can result in data falsification or flawed
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interpretation that may negatively affect R’s reputation (Costello, 2009; Perrino et al., 2013). Thus, even though we assume that data disclosure always has a positive effect on the value of the published article that is based on this data, withholding the data after the final publication may be the optimal strategy for R in our model. Note that R still works on a second paper after the data is disclosed. However, she is now part of the scientific community C as the only differentiating 5
For instance, recent evidence suggests that open access (OA) pre-prints are uncommon in fields such as biology, life science and health science (Eger et al., 2015). Mueller-Langer and Watt (2014) find that OA pre-prints are available for 36% of published journal articles in economics.
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factor between R and C - the data - is now publicly available. Thus, the scenario can be simplified by saying that only a member of the scientific community C continues to work with the disclosed data set. Let v be the value of a research idea that is generated by the scientific community based on R’s data. Let α > 1 be a creativity coefficient that measures the superior creativity of the scientific
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community as compared to the single researcher R. This is an important assumption as it implicitly states that the social optimum could be reached if the research was done by C. The intuition for this assumption is that C would achieve the highest value of research when he initially creates the data and writes both articles.6 In our model, however, R initially produces the data and writes (at least) the first paper. For instance, we assume that R has the initial research idea together
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with exclusive access to data sources that give him a head start in the creation of data. Following Fudenberg et al. (1983), we argue that this head start enables R to preempt C from generating data (as well as publication as long as the data are private information). A time coefficient, c > 1, indicates that the value of the second idea based on the data is lower v α
and
v c·α
be the value of the idea for R based on the data in stage 1
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than that of the first idea. Let
and 2, respectively. Henceforth, we normalize v to one. The higher c is, the stronger does the value 1 c
be the value of the idea based on the data for C in
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of the idea based on the data devaluate. Let the second stage. As α > 1,
1 c
>
1 c·α .
Thus, data availability creates positive spillovers as it enables
C to publish an article of higher value as compared to R’s second article under non-disclosure. To
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illustrate, the higher α the larger is the difference between the value of C’s article and R’s second article. For very large values of α, the value of R’s second article tends towards zero. This is the
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case when R fails to publish a second article because she has no ideas to test. Hence, the second paper can only be published if the data is disclosed. In this case, the total volume of publications
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is reduced when R keeps her data secret. The cost functions are given by c (et ) =
1 2 2 et
for R and c (x2 ) =
1 2 2 x2
for C, i.e., we assume
increasing marginal costs of both data and article creation. Without data no research occurs and players get Ui,kjm = 0 with players i = R, C , policies k = N P, F P P , number of papers published j = 1, 2 and (in case that k = N P ) R’s sharing decision m = share, never. Welfare is given by 6
The reason behind this simplification is that there will be a member or a combination of members within C that will have a more valuable idea than R.
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Wkjm = UR,kjm + UC,kjm .
2.1
No Policy
Researcher publishes one paper and shares at t = 1 (1-Share): R’s optimization problem 1 1 2 1 δ e0 e1 (1 + κ) − e1 + δ 2 γ D e0 − e20 −→ max, α 2 2
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under 1-Share is
(1)
where δ t is the discount factor at time t which measures R’s impatience to publish.7 For instance, this impatience arises from the researcher’s ambition to push her academic career by obtaining tenure through publication (Dasgupta and David, 1994; Gans and Stern, 2010). For
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δ = 1, R is indifferent between a publication today and a publication tomorrow. κ represents the change of the value of an article due to the disclosure of the data. We assume that κ is positive and not too large, 0 < κ ≤ 12 .8 For instance, suppose that the availability of the data used in an article is perceived by peers as a signal of quality (Dasgupta and David, 1994). In that sense, data sharing may be seen as a means to disclose R’s private information on the quality of her empirical article.
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Thus, researchers of higher quality may be more likely to share their data voluntarily in order to signal the robustness of their results (Andreoli-Versbach and Mueller-Langer, 2014; Feigenbaum
generate more citations.
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and Levy, 1993). In addition, empirical articles for which the applied data is publicly available may
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Let γ D (γ N D ) measure the value of the data for R after the last publication if R discloses (does not disclose) the data and define ξ =
γD γN D .
For example, the data set might contain information
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that is valuable for non- or semi-academic projects, such as expert or policy advice, that do not necessarily lead to further scientific publications. Second, the data set itself might be cited in
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subsequent literature as it provides, for instance, a widely applicable index. In addition, a data set could become valuable if data journals are later established in economics. In these cases, the remaining personal value of the data after the last publication depends on whether the data are public or private information. The lower ξ the lower are ceteris paribus R’s incentives to share data. The higher the scope for individual use of the data, the higher will be R’s incentives to keep 7
The solutions of all optimization problems presented in this paper are based on straightforward calculations which are therefore omitted here. They are available from the authors upon request. 8 We discuss the main assumptions of our model in Section 5.1.
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the data. The first term in (1) is R’s discounted net value from publishing in t = 1. The second term is R’s discounted value of the disclosed data set, which depends positively on the effort to create it. The third term describes the effort cost to create the data. C’s optimization problem under 1-Share depends on R’s optimal effort to create data, e∗0,N P share : 1
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1 1 δ 2 e∗0,N P share x2 − x22 −→ max . 1 c 2
(2)
C maximizes his discounted net value from publishing in t = 2. Table 1 summarizes R’s optimal effort to create data, R’s utility and overall welfare under the six publication and data disclosure
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scenarios under study. TABLE 1 HERE
Under 1-Share, optimal efforts in all stages are increasing in γ D and κ.9 The higher the value of the article and the data due to data disclosure, the higher is R’s initial effort to create the data, e∗0,N P share . Optimal efforts to publish chosen by C and R in stages 1 and 2 then depend on R’s 1
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initial effort of data creation. The higher the quality of the data, the higher is the benefit from an article and thus the higher are the efforts to publish it. R’s utility depends positively on the
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remaining personal value of the data after the last publication. It also increases if the positive κ-effect on the value of the article due to the disclosure of the data is more pronounced. C’s utility
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(see welfare under 1-Share in Table 1) increases if, at optimum, R increases her effort to create the data. It decreases if the devaluation of the value of the research idea based on R’s data over time
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is more pronounced. Under 1-Share, overall welfare is increasing in γ D and κ and decreasing in c. Researcher publishes two subsequent papers and shares at t = 2 (2-Share): R’s
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optimization problem under 2-Share is 1 1 1 1 1 (1 + κ) − e22 + δ 3 γ D e0 − e20 −→ max . δ e0 e1 (1 + δ · κ) − e21 + δ 2 e0 e2 α 2 c·α 2 2
(3)
The first term in (3) is the discounted net value of publishing in t = 1. Note that in contrast to 1-Share, the positive κ-effect is discounted under 2-Share as data availability develops its positive 9
See also Proposition 0 in the appendix where we derive the exact condition for positive optimal efforts to create data.
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effect on the value of the first article at a later stage. The second term in (3) is the discounted net value of publishing in t = 2. It accounts for the devaluation of the research idea over time. The third term is R’s discounted value of the disclosed data set. The last term describes the effort cost to create the data. Under 2-Share, overall welfare increases in γ D and κ and decreases in c and α (see Table 1).
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Researcher publishes one paper in t = 1 and never shares (1-Never): The optimization problem of R is given by
1 1 2 1 δ e0 e1 − e1 + δ 2 γ N D e0 − e20 −→ max . α 2 2
(4)
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In contrast to 1-Share, there is no positive κ-effect in the first term of (4). The second term is R’s discounted value of the undisclosed data set. Note that C does not generate any utility in this case. Overall welfare increases in γ N D and decreases in α (see Table 1). Researcher publishes two subsequent papers and never shares (2-Never): R’s optimiza-
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tion problem under N P if she never shares10 is
(5)
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1 2 1 1 2 1 1 2 − e2 + δ 3 γ N D e0 − e20 −→ max . δ e0 e1 − e1 + δ e0 e2 α 2 c·α 2 2 Note that C does not generate any utility in this case.
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Finally, consider the four N P scenarios summarized in Table 1. In optimum, R’s utility is a function of R’s effort to create data, her patience and the value of the disclosed (non-disclosed)
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data. R’s effort to create data and thus her utility under 1-Share and 2-Share increase if κ increases. Hence, R’s incentive to create and share data increases if κ increases. In contrast, R’s incentive to
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share data decreases if γ N D increases while her effort to create data increases in γ N D . The question of which of these countervailing effects on the incentive to share data dominates depends on R’s patience.
We now analyze the conditions under which R does not share her data. All proofs are provided in the appendix. 10
Note that if R does not share the data immediately after her last publication, she will never share.
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Proposition 1: Never Share Under N P the Researcher can decide not to share only if γ D < γ N D , i.e., if ξ =
γD γN D
< 1. (i) She will always choose not to share if ξ is sufficiently small, i.e.
ξ ≤ ξ l , where ξ l (κ) negatively depends on κ. (ii) For ξ l < ξ < 1 she will choose not to share if she is impatient enough, i.e. δ ≤ δ h , where δ h (κ, ξ) depends nonpositively on both κ and ξ. (i) Intuitively, R does not have an incentive to share data if the remaining personal value of the
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undisclosed data after the last publication by far exceeds the personal value of the disclosed data. In this case, the disclosure-driven decrease in the remaining value of the data more than outweighs the positive ”κ-effect” associated with the increase in the value of an article due to data disclosure. Note that (i) illustrates the status quo in economics as only very few economists voluntarily share their data with the scientific community (Andreoli-Versbach and Mueller-Langer, 2014).
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(ii) However, this result does not hold true in general if the above-stated decrease in the remaining value of the data is sufficiently low, i.e. ξ > ξ l . Then, the level of patience comes into play and only a sufficiently impatient researcher will keep the data private information. In this case, the (strongly) discounted ”κ-effect” does not outweigh the disclosure-driven decrease in the remaining
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value of the data. Figure 2 illustrates the utility under 1-Never and 1-Share as a function of R’s patience, δ, and the value of the non-disclosed data, γ N D , for (a) κ = 0.05 and (b) κ = 0.45. Other
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model parameters are kept constant (c = α = 1.5 and γ D = 1). In Figures 2a) and 2b), the blue plane represents R’s utility if she writes one paper and shares the data. Her utility if she writes one paper and never shares the data is given by the red plane. We can see that if the value of
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non-disclosed data is relatively large, i.e. greater than about 1.4, non-disclosure is always better for R, i.e. the red plane lies above the blue one in Figures 2a) and 2b). In contrast, if the value
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of the non-disclosed data tends towards one (with γ D = 1), non-disclosure might be detrimental to R. However, this is only the case if R is very patient, i.e. the blue plane lies above the red one
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for sufficiently high values of δ. This is due to the fact that disclosing or non-disclosing implies different effort levels (see Table 1). A comparison of Figures 2a) and b) also suggests that data disclosure is beneficial for R for a larger set of parameter constellations if k increases from 0.05 to
0.45, as illustrated by the larger visible section of the blue plane in b). FIGURE 2 HERE
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2.2
First Paper Policy
To simplify matters we omit labels for the obvious number of papers published, j = 1, 2, and R’s sharing decision, m = share, never, in efforts, utilities and welfare under F P P . First Paper Policy without Strategic Delay: Under F P P without strategic delay (N SD), R
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publishes the first paper in t = 1. She is required to share the data and does not compete with C in t = 2 (due to the competitive advantage that is captured in C’s superior creativity). R’s optimization problem is
1 2 1 1 (1 + κ) − e1 + δ 2 γ D e0 − e20 −→ max . δ e0 e1 α 2 2
(6)
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R’s maximization problem under N SD is the same as under 1-Share. The main difference, however, is that she is forced to make the data available under F P P upon publication of the first paper. F P P is detrimental to R as it reduces her set of possible publication strategies. The competitor C uses the data and publishes a paper in t = 2. C’s optimization problem is
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1 1 2 ∗ δ e0,F P PN SD · x2 − x2 −→ max . c 2 2
(7)
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The outcomes under N SD and 1-Share are identical for i = R, C (see Table 1). First Paper Policy with Strategic Delay: R may choose to delay her publications in order
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to fully exploit her data under F P P . In this case, she will incur the costs of completing the first and second paper in the first and second period, respectively. However, she will realize the total
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benefits associated with the publication of two papers in the second period, as she strategically delays publication in order to keep the data private. Under F P P with strategic delay (henceforth,
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SD), R does not publish in t = 1 but publishes the first and the second paper together in t = 2. R’s optimization problem is
1 1 δ δe0 e1 (1 + κ) − e21 α 2
1 1 2 1 + δ e0 e2 (1 + κ) − e2 + δ 3 γ D e0 − e20 −→ max . c·α 2 2 2
(8)
To understand R’s optimization problem under SD, it is constructive to compare it with R’s optimization problem under 2-Share as given by (3). The second, third and fourth terms are
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identical under both scenarios. The first term, however, is different if R is not perfectly patient, i.e., δ < 1. In contrast to 2-Share, R realizes the net value of the publication of the first paper at a later stage under SD. Under 2-Share, the first paper is published right after completion in the first stage whereas its publication is postponed to the second stage under SD. Note that C does
α (see Table 1).
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Analysis and Comparison of Policies
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not generate any utility in this case. Overall welfare increases in γ D and κ and decreases in c and
We first examine the conditions under which R finds it optimal to delay submission strategically
3.1
Conditions for Strategic Delay
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under F P P . Then, we analyze the effect of the transition from N P to F P P on R’s efforts.
We provide the conditions for strategic delay under F P P in the following proposition. The Researcher will delay strategically under F P P if and only
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Proposition 2: Strategic Delay
if she is sufficiently patient, i.e. δ ≥ δ hSD , where δ hSD = δ hSD (κ) depends negatively on κ.
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The depreciation of the value of the first article under strategic delay depends on R´s impatience. Intuitively, if R is sufficiently patient, the additional benefits from the second publication more than
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outweigh the delayed realization of the benefits from the first paper inducing her to choose strategic delay under F P P . Regarding the interpretation of this proposition, note that junior researchers
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are typically less patient than senior researchers because they are in need of a good publication soon in order to obtain a tenured position (Dasgupta and David, 1994; Gans and Stern, 2010).
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Hence, one may interpret Proposition 2 in the sense that junior researchers are ceteris paribus less likely to strategically delay their submission than senior (tenured) researchers. Finally, note that strategic delay is ceteris paribus more likely to occur if the positive effect of data disclosure on the value of an article is higher, i.e. κ increases. In this case, R’s benefits from the second paper are
higher.
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3.2
Efforts to Create Data
We analyze the effect of the transition from N P to F P P on R’s efforts to create data. We obtain: Proposition 3: Change in efforts under F P P
Transition to F P P (i) does not influence
efforts to create data if the Researcher chooses to share after one publication, which is the case
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when ξ ≥ 1 and the Researcher is not very patient, i.e. δ ≤ δ h1 , or when ξ h ≤ ξ ≤ 1 and δ h ≤ δ ≤ δ h1 . (ii) reduces efforts to create data, (1) if ξ is sufficiently small, i.e. ξ < ξ le < 1, or (2) if ξ le < ξ < 1 and the Researcher is impatient enough, i.e. δ < δ he , or (3) if ξ > ξ h and the Researcher is very patient, i.e. δ > δ he1 := max{δ h1 , δ hSD }. (iii) increases efforts to create data (1) if ξ le < ξ < 1 and δ he < δ < min {δ h , δ hSD }, or (2) if ξ ule (δ) < ξ < ξ h1 and
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δ > max {δ 01 , δ hSD , δ h1 }.
The economic intuition behind these results is the following. Under the conditions specified in (i), sharing after one publication is optimal for R under N P whereas no strategic delay is optimal under F P P . The transition to F P P does not influence R’s effort to create data as she is indifferent
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between voluntarily sharing after one publication and being forced to do so. (ii)(1) and (2) Intuitively, if sharing the data harms R significantly, the transition to F P P
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reduces her incentives to create the data in the first place independently of her publication choice under N P . (3) Whenever R chooses to delay submission strategically under F P P and to share after two publications under N P , transition to F P P reduces her efforts to create the data. Intuitively,
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both scenarios lead to the same outcome in the sense that data are available after two publications. However, R generates a lower (discounted) utility from the first publication under F P P with
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strategic delay as compared to publishing it right away under N P . (iii) Intuitively, under these conditions, R chooses higher efforts to create data under SD than
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under 2-Never because she can benefit from the positive κ-effect under SD but not under 2-Never.
More specifically, the optimal effort to create data under SD increases in κ while the effort to create data under 2-Never is independent of κ (see also Table 1). In addition, R can never achieve the
higher γ N D under F P P . Under these conditions, F P P forces R to adjust her optimal effort choice, which ceteris paribus turns out to be effort-increasing under the conditions specified in Proposition 3(iii) since, in this specific case, she takes advantage of the barely discounted κ-effect.11 11
The discrepancy between higher overall incentives to not disclose data under N P (i.e., R prefers 2-Never over
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Figure 3 illustrates the effort to create data under 2-Never under N P and SD under F P P as a function of R’s patience, δ, and the value of the non-disclosed data, γ N D , for (a) κ = 0.05 and (b) κ = 0.2. Other model parameters are kept constant (c = α = 1.5 and γ D = 1). In Figure 3, the blue plane represents R’s effort if she delays strategically under F P P . Her effort if she writes two papers and never shares under N P is given by the red plane. We can see that for very low
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values of κ the transition to F P P never increases R’s effort to create data, i.e. the blue plane lies below the red one. In contrast, if κ increases, the transition to F P P increases R’s effort to create data for sufficiently high levels of patience and sufficiently low values of the non-disclosed data, i.e. the blue plane lies above the red one. This is due to the fact that the optimal effort to create data
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under SD increases in κ while it is independent of κ under 2-Never. FIGURE 3 HERE
4
Welfare Analysis
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We analyze the welfare properties of the transition to F P P . The conditions under which this transition has neutral, negative or positive welfare properties are given in the following proposition.
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Proposition 4: Welfare effects Transition to F P P (i) does not influence welfare if the Researcher chooses to share after one publication, which is the case when ξ ≥ 1 and the Researcher
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is not very patient, i.e. δ ≤ δ h1 , or when ξ h ≤ ξ ≤ 1 and δ h ≤ δ ≤ δ h1 . (ii) (1) It increases welfare if ξ lw < ξ ≤ 1 and δ l < δ < δ h0 := min{δ h , δ hSD }, or (2) if ξ l3 < ξ < ξ h1 and
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δ 01 < δ < min{δ hSD , δ 00 }. (iii) It reduces welfare when ξ is sufficiently small, i.e. ξ < ξ l1 , or if the Researcher is very patient, i.e. δ > δ hSD .
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The economic intuition behind these results is the following. (i) Voluntary data sharing after one publication under N P and no strategic delay under F P P
lead to the same outcome from a social welfare perspective. Both researchers are indifferent between N P and F P P .
2-Share) but higher incentives to exert effort to generate data if disclosure is mandatory is driven by the following factors: First, as R chooses 2-Never under N P we know from Proposition 1 that γ D < γ N D in this case. Second, κ is sufficiently low in this case to not make sharing beneficial under N P . Third, as R prefers strategic delay over no strategic delay under F P P , we know from Proposition 2 that R is sufficiently patient.
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(ii) (1) Under these conditions, R publishes one article and never shares her data under N P and chooses not to strategically delay her first article under F P P . The welfare gain due to the additional paper published by C under F P P more than outweighs the potentially negative impact of forced data sharing on R. (2) Even if R finds it optimal to publish two articles and never share data under N P , the transition to F P P increases welfare. The quality difference between C´s
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paper and the paper R would have published under N P more than outweighs the negative impact of forced data sharing on R.
(iii) These results specify two sets of conditions under which the transition to F P P has negative welfare properties.
First, the transition to F P P always reduces welfare if it induces R to delay submission strate-
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gically. If R delays strategically, two negative effects emerge: There will be a delay in the time the scientific knowledge is made public and C cannot use the data to publish his (higher value) paper. Moreover, it is straightforward to show that there is always at least one strategy option under N P that dominates strategic delay under F P P . Consequently, whenever a policy change induces R to
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delay her submissions strategically R’s utility and thus overall welfare decreases. Second, for sufficiently low ξ, the transition to F P P reduces welfare if it forces R to switch from
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never sharing after the first or second publication under N P to not delaying strategically under F P P . This serves as a counterpart to (ii)(1)and (2) discussed above: The welfare gain due to the additional paper published by C does no longer outweigh the negative effect of forced data sharing
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on R.
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Graphical Example
Figure 4 illustrates R’s choices and the effects of the transition from N P
to F P P depending on the impatience rate, δ (vertical axis), and the ratio of data values after all
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publications in case of disclosure/nondisclosure, ξ =
γD γN D
(horizontal axis). Other model parameters
are kept constant (c = α = 1.5 and κ = 0.2). The black lines divide the whole area into 4 zones, indicating R’s choices under N P : R chooses
to publish one paper and never share data (1-Never ) in the bottom left zone, publish two papers and never share data (2-Never ) in the top left zone (see Proposition 1), publish two papers and share data (2-Share) in the top right zone and publish one paper and share data (1-Share) in the bottom right zone. The horizontal blue line denotes the border for R’s choice under F P P : 16
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she chooses to delay strategically (SD) above the blue line and not to delay (N SD) below it. It represents δ hSD from Proposition 2. FIGURE 4 HERE The light blue area indicates those combinations of δ and ξ for which the transition from N P
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to F P P is welfare reducing. The light yellow area indicates combinations for which the transition to F P P increases welfare. As for the white zone, which is exactly the zone where R chooses the publish one paper and share data under N P , the transition to F P P does not change welfare. Finally, the checked areas (always bordered by red lines on one side) indicate where the transition to F P P increases efforts to create the data. Most notably, Figure 4 suggests that there is scope
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for a socially beneficial transition to F P P that increases the effort to create data, as indicated by the overlapping checked and light yellow areas. Efforts do not change after transition to F P P in the white zone and decrease everywhere else (Proposition 3). Strategic delay under F P P is
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unambiguously welfare reducing.
Discussion and Policy Recommendations
5.1
Discussion
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5
Assumptions: Our model relies on the assumption that a single set of data can produce more
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than one paper. Recent empirical evidence from a survey among the members of the German Economic Association (VfS)12 and the German Academic Association for Business Research (VHB)13
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- conducted under the European Data Extended (EDaWaX) Project - provides support for this assumption (Mueller-Langer and Winter, 2017). It suggests that overall 40% of the 340 respondents
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(VfS: 40.9%, 225 respondents; VHB: 38.3%, 115 respondents) have already published more than one paper with the same dataset. On average, they spent 38% of the total time spent on their last empirical paper on the creation of data and published 4.3 journal articles using self-created datasets (e.g., obtained from own experiments, surveys or interviews) within the last five years. 12
VfS is the largest association of German-speaking economists in the world and was founded in 1872. VHB is closely linked to the most influential German-speaking researchers in business administration and was founded in 1921. 13
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Another important assumption is that the value of an article moderately increases if the respective data is disclosed, 0 < κ ≤ 12 . Evidence from the EDaWaX survey among the members of VfS and VHB supports the assumption of a positive but moderate effect of data disclosure. Overall, 90% of the respondents (VfS: 93.8%; VHB: 81.8%) support the hypothesis that empirical articles subject to data disclosure gain credibility. However, evidence from the same survey also suggests
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that data disclosure only has a rather moderate effect on the academic reputation of authors. When asked about the importance of data disclosure for their own academic reputation on a five-point Likert scale, 88.3% of the respondents (265 of 300) replied that data disclosure was not important at all (79), rather not important (117) or neither important nor unimportant (69); rather important: 31; very important: 4.
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However, while evidence from the EDaWaX survey supports our assumptions on κ, it is important to clarify that R’s incentives to disclose data will ceteris paribus decrease if the benefits of disclosing data are actually negative. For instance, this might be the case when R judges the risk that she made an inadvertent error higher than the benefits from the increased credibility from data
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disclosure.14 As we can see from Table 1, R’s utility under 1-Never and 2-Never is independent of κ. In contrast, however, R’s incentives to create data and thus R’s utility under 1-Share and
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2-Share are ceteris paribus lower if −1 < κ < 0.15 Hence, if κ is negative, R’s incentives to disclose data would decrease as compared to a situation where data disclosure has a positive κ-effect on the value of an article.
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Possible extensions: There are at least two ways to relate data creation to publications. First, one may consider uncertainty to publish in combination with the fixed costs connected to
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data creation. In this case, the expected value of a publication would depend on the probability to publish. However, the value of a publication would not be a function of the quality of the data
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in this set-up. Second, one may consider certainty to publish in combination with variable cost of data creation. Here, we opted for the latter approach due to the specific nature of the data under study. Arguably, papers that use novel self-created (experimental) data have ceteris paribus a higher probability to get published than papers that reanalyze archived data. Second, for this type of data it is particularly important to relate its quality (as a function of effort) to the value of 14
We thank an anonymous referee for this suggestion. We make this assumption because R would not have an incentive to publish under 1-Share as the discounted net value of publishing would be negative if κ < −1, see (1). 15
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the publication. Finally, the prospects of a high probability of publication might be an important ex ante incentive to incur the relatively high costs of creating novel data in the first place. Another interesting extension would be to incorporate endogenous belief formation in the model. In our setting the beliefs of a researcher, concerning her assumptions about the nature of the world and the likely choices of other researchers, are given exogenously and do not form or evolve. Adding
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endogenous beliefs might facilitate the transaction towards more sharing, while at the same time minimizing strategic delay and under-investment. One expansion of this setting might concern the signalling effect of sharing data.16 If sharing data is perceived as an important signal of ”quality”,17 researchers might incorporate this into their preferences and share more irrespectively of the data disclosure policy. In such a framework, editors and referees would be more willing to publish papers
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of data-sharing researchers as non-disclosure of data would be interpreted as a signal of low quality or non-replicability.18
An additional extension might be to incorporate social beliefs about the normative standpoint of academia. If researchers perceived data-sharing as a necessary step to publish, because of the
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ideal standards and norms in the research community, this would increase voluntary sharing. For the scope of this paper, we focus on a profit-maximizing researcher with exogenous preferences.
5.2
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Future research might shed light on incorporating endogenous beliefs in this setting.
Policy recommendations
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The public availability of research data is an important issue from a research policy perspective (Burgelman et al., 2010; European Commission, 2012 and 2016; OECD, 2007; US House of Repre-
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sentatives, 2007). Several journals and research-funding organizations have recently introduced data availability policies (Andreoli-Versbach and Mueller-Langer, 2014; Doldirina et al., 2015; ESRC,
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2010; McCullough, 2009; NIH, 2003; NSF, 2011; Wellcome Trust, 2007). However, compiling and documenting data and code for subsequent use is costly and the data creator’s benefits of shared data in the form of recognition or citations to the data are relatively low (Anderson et al., 2008; Costello, 2009). On the basis of our findings and the fact that an institutional response is highly 16
Intuitively, this could work in a similar way as a second-hand car dealer who adds a warranty to his cars, see for example Grossman (1981). See also Milgrom (1981). 17 For example, because it diminishes the information asymmetry between the reader and the author. 18 For a review of the theoretical and empirical literature on quality disclosure see Dranove and Jin (2010).
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needed to increase data sharing (Dasgupta and David, 1994) we argue that mandatory data disclosure policies are necessary. However, our results also show that the implementation of universal mandatory data disclosure can have unintended negative effects. In the following we discuss policy options that may incentivize data sharing and deter welfare-reducing strategic delay. Possible actions for universities: The transition to mandatory data disclosure reduces
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welfare if it induces researchers to delay their submissions strategically (see Proposition 4). Strategic delay depends on a researcher’s patience to publish which in turn may depend on factors such as research experience or tenure. Early-stage researchers are ceteris paribus less likely to delay their submissions strategically as they are in need of a publication soon to get tenure. In this case, the transition to mandatory data disclosure is less likely to have negative welfare properties. In contrast,
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more experienced (tenured) researchers may have a higher incentive to delay the submission of their papers strategically as they are more patient. In this case, forced data sharing associated with the transition to mandatory data disclosure is not a recommendable policy option unless accompanied by appropriate incentives and data support to deter strategic delay. For example, universities could
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incentivize immediate data disclosure through priority-based rewards, e.g. research grants or prizes (Dasgupta and David, 1994; Fienberg et al., 1985; Gans and Stern, 2010; Mukherjee and Stern,
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2009). Universities could also promote immediate data disclosure through institutional assistance. According to Kim and Stanton (2012), the compilation, preparation and sharing of research data are perceived as costly, thereby preventing researchers from sharing their data. Reducing these
PT
obstacles could result in a higher net benefit of sharing data and help to generate a pro-datasharing attitude. Some universities have recently taken the lead in this respect by developing data
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repositories and structured guidance for the creation of data management plans (Andreoli-Versbach and Mueller-Langer, 2014).
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Data journals and citations: As the social value of knowledge increases by sharing the data
one variable which can be changed by policy makers is the value of the data for their creator after the last publication if she discloses the data, γ D (see Proposition 1). In particular, γ D could be the increasing value of data citations on academic reputation.19 In this respect, policy-makers and research funding agencies might incentivize and support the establishment of data journals. The 19
For example, information http://thedata.org/citation.
about
the
newly
implemented
20
data
citation
standard
is
available
at
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establishment of data journals in economics together with the obligation to cite the author of the data collection may create a market for the exchange of data and increase the value of a data set for its creator and the availability of data.20 This would increase the incentives to disclose data (Candela et al., 2015). It may also increase the quality of available data if data publications are subject to a peer-review process. Lessons could be learned from other disciplines. For instance,
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Nature (2013) has announced the launch of the online data journal Scientific Data. Moreover, the online-only Geoscience Data Journal has recently been launched (Allan, 2012). In addition, incentive schemes rewarding the production and documentation of data (Fienberg et al., 1985), such as a new standard of data citation (Altman and King, 2007), should be implemented so that sharing becomes more valuable to the original creator of data. Examples of recently established
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tools for data retention and citation are, among others, Dryad, Figshare and Zenodo. In general, if the individual academic value of data increases, i.e. due to data journals and increased and more valuable data citations, some researchers may have an incentive to specialize in the creation of data if they expect to have a competitive advantage, i.e. they have the necessary (financial) resources,
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knowledge and experience in the creation of data. This may have a positive effect on the overall quality of available data.
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Finally, this paper considered two policies, N P and F P P . Other policies trying to mitigate the negative effects of F P P while at the same time promoting sharing might be implemented as well. For example, one could think of a policy that delays a researcher’s data submission, e.g.
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for two years, which gives her enough time to start working on follow-up projects. Such policies however may not fulfil the standards of replicability and credibility. First, it is questionable how
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an enforcement agency would deal with non-compliance.21 Second, if the data is not made public, possible errors are not detected and further research is hindered.22 Third, some papers might be
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of high interest for current matters.23 20 See Gans and Stern (2010) for a similar discussion on the missing market for ideas in research. See also DuchBrown et al. (2017) for an overview of the relatively underdeveloped economics literature on markets for commercial data. 21 If the researcher refuses to supply the data afterwards, or she claims to have lost the data, it would be difficult for the journal to take actions against her. 22 In fact, the policies of government-supported research state that data should be made openly available as early as possible, with the timing of release and the duration of any exclusive-use period explicitly defined. 23 Examples include the debate after 2008 about austerity measures imposed on Greece, or, looking at other disciplines, the release of new drugs.
21
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6
Conclusion
We set up a simple model describing the incentives of a researcher to generate novel data, publish articles and share her data with the research community so that other researchers can use the data for subsequent empirical research. We compare two different scenarios. Under ”no policy”, the cre-
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ator of data has complete freedom as when to share her data voluntarily. Second, under ”mandatory data disclosure”, she is required to share the data immediately after her first publication.
The universal implementation of mandatory data disclosure may distort her incentives in two fundamental ways. First, she might strategically delay her submissions in order to continue publishing with the same data without making it available to others. Second, she might reduce her effort
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to create data as she would not be the full residual claimant of her data after the first publication. Our analysis suggests that universal mandatory data disclosure has ambiguous welfare properties. It reduces welfare if it induces researchers to strategically delay the submission of subsequent papers. Under this scenario the research community would not be in a position to make use of the data when it is still valuable for further research. Mandatory data disclosure may only be welfare
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enhancing if researchers have no incentives to postpone the time of their publication and if the positive effect of data availability outweighs the negative effect associated with reduced efforts to
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create data. We conclude that the implementation of mandatory data disclosure should be complemented by other policies that deter strategic delay, such as career incentives, and increase the
of data journals.
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stand-alone value of academic data, such as new standards for data citation and the establishment
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Finally, as a publication in a top-tier economics journal is highly desired by most researchers and might lead to promotion within a university, the benefits of a publication are likely to outweigh
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the cost of data sharing. It is questionable whether this result holds for medium-ranked journals with a data availability policy, where authors may choose competing journals with similar ranking but without a data availability policy.
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7
Appendix: Proofs
From the optimal efforts under the four N P scenarios (see Table 1), we obtain: Proposition 0: Positive efforts condition All optimal efforts are well-defined and positive for c2 α2 . 1+c2
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all δ ∈ (0, 1] if (1 + κ)2 <
Proof of Proposition 0: Since the denominators of optimal efforts depend negatively on δ, the efforts are positive for all δ ∈ (0, 1] if all of the following conditions hold:
1 1 − >0 α2 c2 α2 1 e∗0,N P1never (δ = 1) > 0 if 1 − 2 > 0 α 2 (1 + κ) (1 + κ)2 e∗0,N P share (δ = 1) > 0 if 1 − − >0 2 α2 c2 α2 (1 + κ)2 e∗0,N P share (δ = 1) > 0 if 1 − >0 1 α2 (1 + κ)2 (1 + κ)2 − >0 e∗0,F P PSD (δ = 1) > 0 if 1 − α2 c2 α2
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e∗0,N P2never (δ = 1) > 0 if 1 −
(1) (2) (3) (4)
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(5)
It is clear that conditions (1), (2) and (4) hold whenever condition (3) or, equivalently, (5) holds.
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We can rewrite (3) as c2 α2 − (1 + c2 )(1 + κ)2 > 0 ⇒ (1 + κ)2 <
U
R,N P1never
We first show that for ξ ≥ 1 it always holds that UR,N P share ≥
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Proof of Proposition 1:
and UR,N P share ≥ U
R,N P2never
2
1
. The first inequality is
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δ 4 γ 2D 1 1 δ 4 γ 2N D ≥ ⇔ 2 2 1 − δ 1 (1 + κ)2 21−δ 1 2 α α
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which holds whenever ξ = 1 21−δ
c2 α2 . 1+c2
γD γN D
γD γN D
2
≥
≥ 1. The second inequality is δ 6 γ 2D
1−δ
1
1 2 (1 + α 2 − δ α1
κ)2
δ 6 γ 2N D 1 ⇔ 1 2 1 − δ 1 2 − δ2 1 2 (1 + δκ)2 − δ 2 cα (1 + κ)2 α α cα 2 1 2 1 − δ α1 (1 + δκ)2 − δ 2 cα (1 + κ)2 γD 2 , ≥1≥ 2 1 2 γN D 1 − δ α1 − δ 2 cα 1 2
which holds whenever ξ =
γD γN D
,
(6)
≥
2
≥ 1, since (1 + κ)2 , (1 + δκ)2 ≥ 1. 23
(7)
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(i) We define v u u1 − t
v u u 1 − δ2 (1 + κ)2 α , ξ l (κ) := min t δ∈(0,1] 1 − δ2 α
δ (1 α2
+ δκ)2 −
1−
δ α2
−
δ2 (1 α2 c2 2 δ α2 c2
+ κ)2 .
(8)
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Obviously, for ξ ≤ ξ l (κ) the Researcher will choose to never share and ξ l (κ) negatively depends on r δ 1− 2 (1+κ)2 (1+κ)2 1 α κ. ξ l (κ) is positive for positive efforts. We now simplify (8). Since α2 > α2 , is 1− δ α2
monotonically decreasing in δ and
δ∈(0,1]
Since
(1+δκ)2 α2
δ and
>
1 α2
and
(1+κ)2
v u u1 − min t
c2 α2
δ (1 α2
1
c2 α2
1−
,
s
+ δκ)2 −
1−
δ α2
−
+
κ)2
δ α2
v u 2 u 1 − (1+κ) t α2 = . 1 − α12
1−
2 δ (1+δκ)2 − δ2 2 (1+κ)2 α2 α c 2 1− δ2 − δ2 2 α α c
δ2 (1 α2 c2 2 δ α2 c2
+ κ)2
is monotonically decreasing in
v u 2 2 u 1 − (1+κ) − (1+κ) α2 α2 c2 =t . 1 − α12 − α21c2
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v v u u 2 2 (1+κ)2 u 1 − (1+κ) u 1 − (1+κ) − α2 c2 t t α2 α2 < 1 − α12 − α21c2 1 − α12
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⇔ α2 − (1 + κ)2 < α2 (1 + κ)2 − (1 + κ)2 ⇔ 1 < (1 + κ)2 ⇔ 0 < κ, so we can state
(9)
(10)
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δ∈(0,1]
Finally,
>
δ (1 α2
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v u u1 − min t
v u 2 2 u 1 − (1+κ) − (1+κ) t α2 α2 c2 ξl = . 1 − α12 − α21c2
(11)
(12)
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(ii) Now we aim to show that for ξ l < ξ < 1 there always exists some δ h (κ, ξ) > 0, such that for every δ ≤ δ h (κ, ξ) it holds UR,N P1never ≥ UR,N P share , UR,N P1never ≥ UR,N P2never and UR,N P1never ≥ 1
UR,N P share . So, the first inequality is equivalent to 2
δ≤
α2 (1 − ξ 2 ) , (1 + κ)2 − ξ 2
(13)
where the expression on the right-hand side (r.h.s.) is always positive for ξ < 1 and κ > 0. Thus,
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there exists some δ 00 (κ, ξ) :=
α2 (1−ξ 2 ) (1+κ)2 −ξ 2
∈ [0, 1] such that UR,N P1never ≥ UR,N P share for all δ ≤ δ 00 . 1
The second inequality is equivalent to c2 δ 3 − (1 + α2 c2 )δ 2 − c2 δ + α2 c2 ≥ 0.
(14)
−1 < 0 and
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Denoting the function on the left-hand side (l.h.s.) lhs(δ), we compute lhs(0) = α2 c2 > 0, lhs(1) = ∂lhs (δ) = 3c2 δ 2 − 2(1 + α2 c2 )δ − c2 < 0 ∂δ
(15)
for all δ ∈ [0, 1]. So there exists some δ 01 = δ 01 (κ, ξ) ∈ [0, 1] such that lhs(δ 01 ) = 0 and lhs(δ) > 0
δ3 2 (ξ − κ2 ) − δ 2 α2
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for all δ < δ 01 . The third inequality is equivalent to 2κ (1 + κ)2 2 + ξ + α2 α2 c2
−
δ + 1 ≥ 0. α2
(16)
Denoting the function on the l.h.s. LHS(δ), we find that LHS(0) = 1 > 0 and
1 LHS(1) = (1 − ξ ) 1 − 2 α
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2
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Further,
for all δ ∈ [0, 1].
−
2κ κ2 (1 + κ)2 − − . α2 α2 α2 c2
2κ (1 + κ)2 2 + ξ + α2 α2 c2
−
1 <0 α2
(17)
(18)
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∂LHS (δ) δ2 = 3 2 (ξ 2 − κ2 ) − 2δ ∂δ α
If LHS(1) < 0, then there exists some δ 02 = δ 02 (κ, ξ) such that LHS(δ 02 ) = 0 and LHS(δ) > 0
CE
for all δ < δ 02 . For completeness, define δ 02 ≡ 1 in case LHS(1) > 0. Combining our considerations,
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we define
δ h (κ, ξ) := min {δ 00 , δ 01 , δ 02 } ,
(19)
which is always positive for 0 ≤ κ ≤ 0.5 and ξ l < ξ < 1. Clearly, for δ < δ h the Researcher will choose not to share. It remains to show that δ h (κ, ξ) depends nonpositively on both κ and ξ. Computing the κ and ξ derivatives of the first term on the r.h.s. of (19), one can see that both of them are negative everywhere. If δ 02 = 1, then the statement is proved, since the first term is the only one that depends on κ and ξ.
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We now consider LHS(δ) for a fixed δ as the function of κ and ξ, denoting it LHS δ (κ, ξ). 2δ 3 ∂LHS δ (κ, ξ) = − 2 κ − δ2 ∂κ α
2 2(1 + κ) + 2 α α2 c2
<0
(20)
<0
(21)
and ∂LHS δ (κ, ξ) 2δ 3 = 2 ξ − 2δ 2 ξ = 2δ 2 ξ ∂ξ α for δ ∈ [0, 1].
δ −1 α2
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Notice that
So the function LHS(δ) is pointwise monotone decreasing separately in κ and ξ. Since LHS(δ) is monotonically decreasing in point δ 02 , it follows that δ 02 (κ, ξ) depends nonpositively on both κ
Proof of Proposition 2:
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and ξ.
We prove the statement generally for all 0 ≤ κ ≤ 0.5 and c, α > 1.
The Researcher chooses to delay strategically under F P P if and only if UR,F P PN SD ≤ UR,F P PSD , i.e.
1
1+
(1+κ)2 c2 α2
M
s
≤ δ,
(22)
where the first step is correct under the assumption of positive efforts. So there is some δ hSD =
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δ hSD (κ) ∈ [0, 1] with UR,F P PN SD ≤ UR,F P PSD for every δ ≥ δ hSD . Note that δ hSD (κ) depends
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negatively on κ.
Proof of Proposition 3: (i) We define δ h1 so that UN P share ≥ UN P share for δ ≤ δ h1 . For this 2
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AC
consider
1
δ 4 γ 2D δ 6 γ 2D 1 1 ≥ ⇔ 2 1 − αδ2 (1 + κ)2 2 1 − δ2 (1 + δκ)2 − 2δ2 2 (1 + κ)2 α c α " # 2 1 + 2κ 2κ (1 + κ) δ δ3 − δ2 1 + 2 + − 2 + 1 ≥ 0. 2 2 2 α α c α α
(23)
Denoting l.h.s. of the last expression LHS(δ) we compute LHS(0) = 1 > 0 and
LHS(1) =
1 + 2κ 2κ (1 + κ)2 1 (1 + κ)2 − 1 − − − + 1 = − < 0. α2 α2 c2 α2 α2 c2 α2
26
(24)
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The first derivative of LHS with respect to δ is LHSδ0
= 3δ
21
2κ (1 + κ)2 1 + 2κ − 2δ 1 + 2 + − 2. 2 2 2 α α c α α
(25)
We compute LHSδ0 (0) = − α12 < 0 and
because positive efforts imply
1+κ α2
2(1 + κ) (1 + κ)2 − 2 − 2 < 0, α2 c2 α2
CR IP T
LHSδ0 (1) =
(26)
< 1 (see (4)). The derivative of LHSδ0 with respect to δ is
monotone as the derivative of any quadratic function and we conclude that LHS(δ) is monotonically
AN US
decreasing for all δ ∈ [0, 1]. Accordingly, δ h1 ∈ (0, 1) is well-defined as the first positive root of LHS(δ) = 0, i.e. for δ ≤ δ h1 it indeed holds UN P share ≥ UN P share . 1
2
Now by the proof of Proposition 1, for ξ ≥ 1 and δ ≤ δ h1 the Researcher will choose to share after one publication under N P . Whenever the Researcher chooses to share after one publication under N P , she also chooses not to delay strategically under F P P . We show this indirectly, proving that
M
sharing after 2 publications strictly dominates strategic delay. This would imply that the Researcher will not choose strategic delay, because she does not choose sharing even after 2 publications. 2
δ 6 γ 2D
δ (1 α2
+ δκ)2 −
2
δ (1 c2 α2
+ κ)2
≥
1 2 1−
δ 6 γ 2D 3
δ (1+κ)2 α2
−
δ 2 (1+κ)2 c2 α2
1 − δ 2 (1 + 2κ) + 2δκ ≥ 0,
⇔
(27)
CE
PT
1 21−
ED
UN P share ≥ UF P PSD is equivalent to
which is true for all δ ∈ (0, 1].
AC
Since sharing after one publication is the same as not delaying strategically, it is clear that for ξ ≥ 1 and δ ≤ δ h1 and, analogously, for those cases where ξ < 1 and the Researcher chooses to
share after one publication under N P , transition to F P P does not influence efforts. We first show the dependence of δ h1 (κ) on κ and then discuss the case ξ < 1. Consider LHS(δ) for a fixed δ as the function of κ and ξ, denoting it LHS δ (κ, ξ). Notice that ∂LHS δ (κ, ξ) 2 2 2κ 3 2 2 =δ 2 −δ + + < 0. ∂κ α α2 c2 α2 c2 α2 27
(28)
ACCEPTED MANUSCRIPT
for δ ∈ [0, 1]. So the function LHS(δ) is pointwise monotone decreasing in κ. Since LHS(δ) is monotonically decreasing in point δ h1 , it follows that δ h1 (κ) depends negatively on κ. For the case ξ < 1 we aim to find conditions on δ and ξ under which the utility of sharing after one publication is higher than other utilities. First, we already know from the beginning of this 1
2
that for ξ ≥ ξ h1
v u u1 − := t
δ (1 α2
+ δκ)2 −
1−
δ α2
−
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proof that UR,N P share ≥ UR,N P share for δ ≤ δ h1 . Second, we know from the proof of Proposition 1 δ2 (1 c2 α2 2 δ c2 α2
+ κ)2
(29)
it holds that UR,N P share ≥ UR,N P2never . So for ξ h1 ≤ ξ < 1 and δ ≤ δ h1 the Researcher chooses 2
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to make one publication and then either to share or not to share. As we know from the proof of Proposition 1(ii), this last choice is met in favour of sharing in case
Now δ 00 (1) = 0 and
α2 (1 − ξ 2 ) . (1 + κ)2 − ξ 2
−2α2 ξ((1 + κ)2 − ξ 2 ) + 2α2 ξ(1 − ξ 2 ) ((1 + κ)2 − ξ 2 )2 2α2 ξ(1 − (1 + κ)2 ) <0 = ((1 + κ)2 − ξ 2 )2
(31)
PT
ED
δ 000 (ξ) =
(30)
M
δ ≥ δ 00 (ξ) :=
for ξ > 0. Since δ h1 does not depend on ξ, there exists some ξ h2 such that δ 00 ≤ δ h1 for every
CE
ξ ≥ ξ h2 . Defining ξ h := max{ξ h1 , ξ h2 } we get that the Researcher chooses to share after one publication if ξ h ≤ ξ ≤ 1 and δ 00 ≤ δ ≤ δ h1 . Under these conditions δ 00 = δ h , since the relevant
AC
term in the definition of δ h is exactly δ 00 . We get the statement. (ii) (1) We know from the proof of Proposition 1 that for ξ < ξ l the Researcher chooses to never
share and decides to publish two papers if and only if δ > δ 01 . From Proposition 2, transition to
F P P urges the Researcher to delay strategically if and only if δ > δ hSD . We now compare the efforts to create a data set for different combinations of Researcher’s decisions.
28
ACCEPTED MANUSCRIPT
e∗0,N P never > e∗0,F P PN SD is equivalent to 1
2
1 − δ(1+κ) δ2ξ δ2 α2 > > ξ. ⇔ 2 δ δ(1+κ) 1 − α2 1 − αδ2 1 − α2
(32)
e∗0,N P never > e∗0,F P PSD is equivalent to δ3 1−
δ α2
−
>
δ2 c2 α2
δ3ξ 1−
δ 3 (1+κ)2 α2
−
1−
⇔
δ 2 (1+κ)2 c2 α2
2 2 δ 3 (1+κ)2 − δ (1+κ) α2 c2 α2 2 1 − αδ2 − c2δα2
We define
min
δ
δ (1 α2
1−
+ κ)2
δ α2
1−
,
min
δ>max{δ 01 ,δ hSD }
1−
δ3 (1 α2
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ξ le0 (κ) := min
(
CR IP T
2
> ξ.
+ κ)2 −
1−
δ α2
−
δ2 (1 α2 c2 δ2 α2 c2
(33)
+ κ)2
)
(34)
and notice that in general ξ le0 < ξ l , since a square root of a number that is smaller than one is bigger than the number itself (there is still a little difference between the second term in the definition of ξ le0 and the term under the second root in the definition of ξ l , so we will not use this fact in e∗0,N P never > e∗0,F P PSD is equivalent to
ED
1
M
the proof). It remains to consider the small interval of δ, with δ 01 > δ > δ hSD or δ 01 < δ < δ hSD .
δ3ξ
δ 3 (1+κ)2 α2
PT
δ2 > 1 − αδ2 1−
−
δ 2 (1+κ)2 c2 α2
⇔
1−
δ 3 (1+κ)2 α2
δ−
−
δ 2 (1+κ)2 c2 α2
δ2 α2
> ξ.
(35)
e∗0,N P never > e∗0,F P PN SD is equivalent to
CE
2
AC
1−
δ3 δ α2
−
δ2 c2 α2
>
δ2ξ 1−
δ(1+κ)2 α2
⇔
δ 2 (1+κ)2 α2 2 δ − c2δα2 α2
δ−
1−
> ξ.
(36)
Combining all these results we get that for (
ξ < ξ le := min ξ l , ξ le0 ,
min
δ 01 >δ>δ hSD
1−
δ 3 (1+κ)2 α2
δ−
−
δ2 α2
δ 2 (1+κ)2 c2 α2
,
min
δ 01 <δ<δ hSD
δ 2 (1+κ)2 α2 2 δ − c2δα2 α2
δ−
1−
)
(37)
transition to F P P reduces efforts to create data set for all δ ∈ [0, 1]. It is easy to see that ξ le (κ) depends negatively on κ.
29
ACCEPTED MANUSCRIPT
(2) When ξ le < ξ < 1, the Researcher chooses to never share after one publication under N P or not to delay strategically under F P P if and only if δ < min{δ h (ξ), δ hSD }, as we know from the proof of Proposition 1 and from Proposition 2. From (32) we can conclude that in this case F P P reduces efforts to create data set if and only if δ α2 (1 − ξ) δ(1 + κ)2 > ξ − ξ ⇔ > δ. α2 α2 (1 + κ)2 − ξ
(38)
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1−
It follows that for ξ le < ξ < 1 and
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α2 (1 − ξ) δ < δ he (κ, ξ) := min δ h (κ, ξ), δ hSD (κ), (1 + κ)2 − ξ
(39)
transition to F P P reduces efforts to create data set. As δ 01 does not depend on κ or ξ, δ h (κ, ξ) depends negatively on both of them and δ hSD (κ) depends negatively on κ and does not depend on ξ, δ he (κ, ξ) obviously depends nonpositively on κ and on ξ as well, since
α2 (1−ξ) (1+κ)2 −ξ
∂ξ
=
−α2 [(1 + κ)2 − ξ] + α2 (1 − ξ) −α2 [(1 + κ)2 − 1] = ≤ 0. 2 2 [(1 + κ) − ξ] [(1 + κ)2 − ξ]2
(40)
M
∂
ED
(3) We want to show that transition to F P P reduces efforts to create data set if ξ > ξ h = max{ξ h1 , ξ h2 } and δ > max{δ h1 , δ hSD }. In this case, the Researcher chooses to delay strategically
PT
under F P P (since δ > δ hSD ) or to share after 2 publications under N P . To prove the last statement recall the arguments from the proof of Proposition 3(i). For ξ > ξ h1 it holds that UR,N P share > UR,N P2never . For δ > δ h1 it holds that UR,N P share > UR,N P share and for
CE
2
δ > δ 00 we have UR,N P share > U 1
2
R,N P1never
1
. Further, δ h1 > δ 00 whenever ξ > ξ h2 , so for ξ > ξ h and
AC
δ > δ h1 the Researcher chooses to share after 2 publications. e∗0,N P share > e∗0,F P PSD is equivalent to 2
1 + 2δκ > δ (δ + 2δκ ) ,
(41)
which is true for all δ ∈ (0, 1]. So whenever the Researcher chooses to delay strategically under F P P and to share after 2 publications under N P , transition to F P P reduces efforts to create data set. (iii)(1) As we know from the proof of Proposition 1 and from Proposition 2, for ξ < 1 and 30
ACCEPTED MANUSCRIPT
δ < min {δ h , δ hSD } the Researcher chooses to never share after one publication under N P or not to delay strategically under F P P . From the definition of δ he (see (39)) it follows that if δ he < δ < min {δ h , δ hSD }, then transition to F P P increases efforts to create data set. We show that for κ > 0 there always exist such δ. Consider ξ < 1 near to 1 and small δ. As was shown in the proof of Proposition 3(i) (see text
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after equation (29)), with these parameters the Researcher chooses to make one publication and then either to share or not to share, so that the relevant condition in min {δ h , δ hSD } is UR,N P1never ≥ UR,N P share , i.e. 1
δ 00 (ξ) =
α2 (1 − ξ 2 ) , (1 + κ)2 − ξ 2
(42)
AN US
since δ 01 and δ hSD are positive and do not depend on ξ, whereas δ 00 (1) = 0.
Notice that for ξ = 1 it holds that δ he = 0. So both δ 00 (ξ) and δ he (ξ) continuously approach 0 as ξ → 1. In the neighborhood of ξ = 1 it holds that δ 00 (ξ) > δ he (ξ), since α2 (1 − ξ 2 ) α2 (1 − ξ) ⇔ > 2 (1 + κ)2 − ξ (1 + κ)2 − ξ
M
(1 + κ)2 > 1,
(43)
ED
which is true for κ > 0. For ξ < ξ le transition to F P P reduces efforts to create data set (see this Proposition, (ii)(1)) and it follows that for ξ le < ξ < 1 and δ he < δ < min {δ h , δ hSD } transition to
PT
F P P increases efforts to create data set.
(2) For ξ < ξ h1 (see (29)) and δ > max {δ 01 , δ hSD , δ h1 } the Researcher chooses to never share
CE
after two publications under N P or to delay strategically under F P P . Further we know from this
AC
proof, (ii)(1), that in this case F P P increases efforts to create data set if and only if
ξ ule (δ) :=
1−
2 2 δ 3 (1+κ)2 − δ (1+κ) α2 c2 α2 2 1 − αδ2 − c2δα2
< ξ.
(44)
Since a square root of a number between 0 and 1 is bigger than the number itself, for δ = 1
and κ > 0 it holds ξ ule < ξ h1 . It follows that F P P increases efforts to create a data set when ξ ule (δ) < ξ < ξ h1 and δ > max {δ 01 , δ hSD , δ h1 }, whereby the set of such (ξ, δ) is always nonempty.
31
ACCEPTED MANUSCRIPT
Proof of Proposition 4: (i) Transition to F P P does not influence welfare whenever R chooses to share after one publication under N P and not delay strategically under F P P [see proposition 3(i)]. (ii) (1) By Proposition 2 and the proof of Proposition 1 (ii), we know, that if ξ l < ξ ≤ 1 and δ < δ h0 := min{δ h , δ hSD }, the Researcher will choose to publish one paper and never share under
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N P or not to delay strategically under F P P . We also already know the dependence of ξ l (κ) and δ h0 (κ, ξ) on κ and ξ. We now show the existence of δ l and ξ lw such that for ξ lw < ξ ≤ 1 and δ l < δ < δ h0 it holds that WF P PN SD > WN P1never . The last expression is equivalent to δ 4 γ 2D
2 1−
+ 2
δ(1+κ) α2
ξ2 >
1
δ 6 γ 2D
2c2 1 −
> 2 2
δ(1+κ) α2
δ 4 γ 2N D ⇔ 2 1 − αδ2 −1
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1 − αδ2 2 − δ(1+κ) α2
2
+
δ c2
1−
1−
δ α2
δ(1+κ)2 α2
2
(45)
(1+κ)2 α2
>
1 , α2
CE
+
−1
1 α2
1− 1 2 2 c (1+κ)2 1 − α2
> 0.
(46)
both
PT
Moreover, since
1
1 − α12 2 − (1+κ) 2 α
ED
RHS(1) =
M
Denoting the r.h.s. of the last expression RHS(δ), we compute RHS(0) = 1 and
δ α2 δ(1+κ)2 α2
1−
1−
and
1− 1−
δ α2
δ(1+κ)2 α2
2
(47)
are monotone increasing and since δ 2 is also monotone increasing, RHS(δ) is monotonically decreas-
AC
ing in δ. We conclude that for all ξ f with RHS(1) < ξ 2f ≤ 1 there exists δ l such that WF P PN SD > p WN P1never holds for every ξ f < ξ < 1 and δ l < δ ≤ 1. Define ξ lw := max{ RHS(1), ξ l }. For ξ = 1 it holds ξ 2 ≥ RHS(δ) for all 0 < δ ≤ 1, so the set of points (ξ, δ) with ξ lw < ξ ≤ 1 and δ l < δ < δ h0
is always nonempty. Finally, from Proposition 1 ξ l (κ) depends negatively on κ and it is easy to see that the same holds for RHS(1). (2) There might be a case where δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 , i.e. the Researcher chooses to never share after two publications under N P or not to delay strategically under F P P . 32
ACCEPTED MANUSCRIPT
Therefore, we consider WF P PN SD > WN P2never . From this, we obtain δ2
1− 1
1−
δ(1+κ)2 α2
2 δ − 2δ 2 α2 c α
+
2
δ 2 δ(1+κ)2 c2 1− 2 α
!.
(48)
CR IP T
v u u u ξ>u u u t
Denoting the term on the r.h.s. ξ l3 (δ, κ), we obtain that F P P increases welfare if δ 01 < δ < min{δ hSD , δ 00 } and ξ l3 < ξ < ξ h1 . It is easy to see that ξ l3 (κ) depends negatively on κ. Finally, we provide a numerical example which suggests that WF P PN SD > WN P share if δ h1 < δ < δ hSD . For 2
c = α = 1.5 and κ = 0.2, it is straightforward to see that WF P PN SD > WN P share if δ h1 = 0.8171 < 2
AN US
δ < δ hSD = 0.8824.
(iii) As we have seen in part (i) of proposition 3, sharing after two publications strictly dominates strategic delay. This means that whenever the Researcher chooses to delay strategically under F P P , she could have been better off under N P (even if she would not choose sharing after two publications in this case, as some other N P option could in its turn dominate sharing after two publications). 2
M
Since WN P share = UN P share and WF P PSD = UF P PSD , this means that F P P reduces welfare if the 2
ED
Researcher chooses to delay strategically under it, i.e. if δ > δ hSD . Now recall from the proof of Proposition 1, (ii), that there exists some δ h such that for δ < δ h 1-Never is the dominant strategy under N P . It follows that for δ < min{δ h , δ hSD } the Researcher chooses to never share after one
PT
publication under N P or not to delay strategically under F P P . From (45) we find out that if
CE
v −1 u u δ δ 2 u 1 − α2 1 − α2 δ + 2 ξ < ξ l0 := u , t 2 2 2 δ(1+κ) c δ(1+κ) 1 − α2 1− 2
(49)
AC
α
then WF P PN SD < WN P1never . That is, for ξ < ξ l0 and δ < min{δ h , δ hSD } transition to F P P reduces welfare. ξ l0 (κ) depends nonpositively on κ. There may remain a case where δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 , i.e. the Researcher chooses to never share after two publications under N P or not to delay strategically under F P P . We consider the inequality WF P PN SD < WN P2never by taking ξ l3 (κ) from (48) into account.
33
ACCEPTED MANUSCRIPT
Together we get that F P P is welfare reducing when
ξ < ξ l1 (δ) :=
ξ l (δ), 0 ξ l (δ), 3
δ < min{δ h , δ hSD }
(50)
δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 .
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Figure 1 | Stages of the model First Paper Policy
Researcher (R) chooses effort e0 to create data
R chooses effort e0 to create data
Status quo in Economics
R publishes her second paper and shares data
1-share
2-share
1-never
AC
CE
PT
ED
Scenario
Competing researcher (C) publishes one paper using R’s data
(3) R publishes one paper and never shares
(4) R publishes her first paper
Strategic Delay
(5) R publishes one paper
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Stage 2
(2) R publishes her first paper
(6) R writes her first paper but strategically delays submission in order to evade disclosure of data
R publishes her second paper and never shares data
C publishes one paper using R‘s data
R publishes her first and second paper at once
2-never
No Strategic Delay
Strategic Delay
M
Stage 1
(1) R publishes one paper and shares data
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Stage 0
No Policy
ACCEPTED MANUSCRIPT
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Figure 2 | Utility of R under 1-Never (red plane) and 1-Share (blue plane) for different levels of patience and values of undisclosed data
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Figure 3 | R’s effort to create data under 2-Never (red plane) and SD (blue plane) for different levels of patience and values of undisclosed data
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Figure 4 | R’s choices and the effect of the transition from NP to FPP
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Table 1 | R’s optimal effort, R’s utility and overall welfare under different regimes
Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure Frank Mueller-Langer, Patrick Andreoli-Versbach PII: DOI: Reference:
S0167-6245(16)30114-7 10.1016/j.infoecopol.2017.05.004 IEPOL 786
To appear in:
Information Economics and Policy
Received date: Revised date: Accepted date:
6 October 2016 23 May 2017 29 May 2017
Please cite this article as: Frank Mueller-Langer, Patrick Andreoli-Versbach, Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure, Information Economics and Policy (2017), doi: 10.1016/j.infoecopol.2017.05.004
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Highlights • Data disclosure is an essential feature for credible empirical work • However, universal mandatory data disclosure may have two unintended effects
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• It decreases a researchers effort to generate data
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• It decreases overall welfare if it induces strategic delay of paper submission
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Open Access to Research Data: Strategic Delay and the Ambiguous Welfare Effects of Mandatory Data Disclosure Frank Mueller-Langera,b∗ , Patrick Andreoli-Versbacha,c Planck Institute for Innovation and Competition, Marstallplatz 1, 80539 Munich, Germany
b European
Commission, Joint Research Center, Edificio Expo, Calle Inca Garcilaso, 3, 41092 Seville, Spain
c Ludwig
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a Max
Maximilian University of Munich, Department of Economics, Schackstraße 4, 80539 Munich, Germany
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Abstract
Mandatory disclosure of research data is an essential feature for credible empirical work but comes at a cost: First, authors might invest less in data generation if they are not the full residual claimants of their data after the first journal publication. Second, authors might ”strategically delay” the time of submission of papers in order to fully exploit their data in subsequent research.
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We analyze a three-stage model of publication and data disclosure. We find that the welfare effects of universal mandatory data disclosure are ambiguous. The mere implementation of
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mandatory data disclosure policies may be welfare-reducing, unless accompanied by appropriate
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incentives which deter strategic delay.
Keywords: Data disclosure policy; strategic delay; welfare effects
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JEL classification: B40, C80, L59 ∗ Corresponding author at Max Planck Institute for Innovation and Competition: Tel.: +49 177 3163096;
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E-mail: [email protected]; Andreoli-Versbach: Tel.: +44 7586312838; E-mail: [email protected] We gratefully acknowledge financial support from the German Research Foundation (DFG) under the European Data Watch Extended Project (DFG-Grant Number WA 547/6-2). The funders had no role in study design; in the writing of the manuscript; and in the decision to submit the article for publication. We thank Linda Gratz, Dietmar Harhoff, Fabian Herweg, Mark Schankerman, Olaf Siegert, Ralf Toepfer, Sven Vlaeminck, Gert G. Wagner and Joachim Wagner for their helpful comments and suggestions. We also thank participants of the Conference on ”Academia & Publishing” at the Universit` a del Piemonte Orientale
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in Turin and seminar participants at the INNO-tec in Munich for their valuable comments. Philippe van der Beck, Michael Khotyakov and Stefan Suttner provided excellent research assistance. The views and opinions expressed in this paper are the authors’ and do not necessarily represent those of the Joint Research Center or the European Commission.
Introduction
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1
Data sharing is an essential feature for the scientific principle of credibility, replication and further research. It guarantees that research methods used to produce the results are known and that incorrect results can be withdrawn from the cumulative body of knowledge (Anderson, 2006; An-
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derson et al., 2008; Dewald et al., 1986; Hamermesh, 1997; Vlaeminck and Wagner, 2014).1 Also, replicable research fosters learning and thus facilitates the development of subsequent research, which boosts scientific advancement. However, whereas a large majority of researchers seems to recognize the importance of data sharing, they are reluctant to apply this principle in practice (Nelson, 2009; Andreoli-Versbach and Mueller-Langer, 2014). In the status-quo, the researchers’
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costs of disclosing data seem to be higher than their benefits associated with data-sharing, which leads to an equilibrium with minimal sharing.2 In order to overcome the gap between the large
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demand for replicable results and the low supply of data, some of the major economics journals have introduced mandatory data disclosure policies, which require authors to share their data prior
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to publication. While the aim of these policies is to increase credibility and replicability, they may lead to welfare-decreasing behaviour.
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The introduction of mandatory data disclosure distorts the incentives of researchers in several ways and may ultimately have detrimental effects. Authors who invest in costly data generation,
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e.g., collecting data and programming, are not the full residual claimants of their data after the first publication, as they have to disclose it. This might lead to two negative effects: first, a decrease in researchers’ initial effort to generate data (”underinvestment”) and second, it may induce researchers to strategically delay the submission of papers in order to fully exploit their 1
Studies aiming at replicating published economic articles often fail (Camerer et al., 2016; Dewald et al., 1986; McCullough et al., 2006 and 2008; Lacetera and Zirulia, 2011). Similar results are found in other disciplines, e.g., psychology (Bohannon, 2015), political science (King, 1995) or physics (Grant, 2002). 2 The private benefits to share data include, for example, higher citations and a positive signal on the quality of the research.
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data (”strategic delay”). In this paper, we investigate the effects of mandatory disclosure policies by analysing the decision of a researcher under different policies. We derive effort choices to show the presence of underinvestment effects. We compare optimal effort choices to show that there is a strategic delay effect. In a simple model of publication and data disclosure we analyze the interaction between a
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data-creating researcher and a competing researcher and study the incentive and welfare effects of data disclosure.
Our motivating example is a researcher who exerts effort to generate a novel data set, e.g., via laboratory or field experiments, surveys or interviews, in order to pursue a research agenda consisting of a set of subsequent papers. This researcher chooses the effort to create data in the
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initial stage of the model, the number of papers written based on the data and whether and when to share the data with the research community. These decisions depend on the data disclosure policy of journals. Under No Policy, i.e., the status quo of most journals in economics, the creator of data can freely choose whether and when to share the data and whether to write one or two
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papers using the data. Following Dasgupta and David (1994), who emphasize that an institutional response is necessary to overcome the gap between researchers’ demand for data sharing and its
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voluntary provision, we consider a second policy type, the First Paper Policy. The leading example is the data availability policy of the American Economic Association, which requires the creator of data to share the data after the first publication so that the data is available to other researchers.
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The creator of the data has a strong incentive to protect the competitive advantage associated with her data, as she might benefit from using the data for subsequent research and keep the data
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secret until their private value is fully exploited (Anderson et al., 2008; Haeussler, 2011; Haeussler et al., 2014; Stephan, 1996). If the data is kept private, another researcher cannot use it for
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replication or for subsequent research and thus self-induced competition associated with disclosed data is avoided. The model endogenizes the decision to strategically delay the time of publication and thus the disclosure of data under the First Paper Policy. We derive exact conditions for positive welfare effects of mandatory data disclosure and discuss the conditions under which the transition to mandatory data disclosure has negative welfare properties. The general tension in our model is between the private incentives of a researcher to exert effort to create a novel dataset and exploit it in subsequent papers against the public benefit of 4
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having replicable results and using available data to generate new research. Ultimately, the welfare effects depend on the cost to generate data, the impatience of a researcher to publish (discount factor) and the additional value created by sharing data both for the data-creating researcher and
2
A Simple Model of Data Disclosure
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the competing researcher.
We analyze the optimal effort choices of a researcher, R, to generate novel data and to share the data produced with the scientific community, which is represented by a second researcher, C, who may use the data for subsequent research. The fundamental difference between the two researchers
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is that R has a data set which would be valuable for C, but C cannot influence R’s decision when to share the data as there is no market for the exchange of data.3
We consider a three-stage model, t = 0, 1, 2, where the incentives to share depend on two factors. First, data disclosure may increase the value of a published article for R, e.g., it may increase the credibility of the article as well as the number of citations.4 Second, disclosure may change R’s
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personal value of the data after the last publication. For instance, the loss of control of disclosed data reduces R’s competitive advantage over C and R’s returns from the data.
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We study two data availability policies of journals. Under No Policy (henceforth N P ), R can freely choose whether and when to share the data and whether to write one or two papers using
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the data. In contrast, the First Paper Policy (F P P ) forces R to share the data after the first publication so that the data is available to C. For simplicity, we consider a maximum number
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of two journal publications that a single researcher can achieve by using the same data set. We assume that the marginal benefit from the re-use of the data is decreasing and that the returns
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to publication are diminishing with increased output (Tuckman and Leahey, 1973). Under both policies, R chooses effort e0 to create a data set in the initial stage. The quality and the value of the data set and the publication increase in this initial effort. Thereby, it also affects R’s decision to disclose the data and the quality of published articles which are derived from the data. R’s effort to publish is given by e1 in the first stage and by e2 in the second stage. As Figure 1 illustrates, 3 The assumption that there is no market for data is very plausible in economics. The only market for data in economics is between institutions and researchers but not between researchers. Thus there is no monetary incentive to share the data and an efficient allocation of efforts not achievable (Coase, 1960). 4 This might also occur through more data citations.
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there are six possibilities, four under N P and two under F P P . FIGURE 1 HERE Under N P , R may choose to (1) publish one paper and share in t = 1 (1-Share), (2) publish two subsequent papers in t = 1 and t = 2 and share in t = 2 (2-Share), (3) write one paper in t = 1 and
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never share (1-Never ) and (4) publish two subsequent papers and never share (2-Never ). Under F P P , R may (5) choose to publish the first paper in t = 1 while being forced to share the data. In stage 2, C will then choose effort x2 and publish a paper using R’s data (No Strategic Delay). (6) R may strategically delay the first publication in order to evade the forced disclosure of data and publish two papers in t = 2 (Strategic Delay). By ”strategic delay” we mean that a researcher
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does not submit her papers one after another but all at the same time after the completion of the second paper in order to maintain the exclusive use of the data. This is detrimental for welfare in several aspects: The research community would neither enjoy the benefits of publicly available data, nor have the confidence that the results have undergone the peer-review process and thus are
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more reliable than the unpublished version. Finally, not all papers are available before publication.5 Hence, strategic delay would lead to a delay in the accumulation of knowledge.
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Figure 1 illustrates a set of six reasonable publication strategies for R under the two data policies under study. For instance, R’s decision to write one or two papers depends on the value of the data for subsequent use. In addition, R’s decision to disclose or withhold data depends on her
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personal value of the data after the last publication. On the one hand, data disclosure may increase R’s personal value of the data, e.g., due to subsequent use in data journals. On the other hand, it
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may also be the case that the data has a higher value for R if it remains her private information. For example, loss of control associated with data sharing can result in data falsification or flawed
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interpretation that may negatively affect R’s reputation (Costello, 2009; Perrino et al., 2013). Thus, even though we assume that data disclosure always has a positive effect on the value of the published article that is based on this data, withholding the data after the final publication may be the optimal strategy for R in our model. Note that R still works on a second paper after the data is disclosed. However, she is now part of the scientific community C as the only differentiating 5
For instance, recent evidence suggests that open access (OA) pre-prints are uncommon in fields such as biology, life science and health science (Eger et al., 2015). Mueller-Langer and Watt (2014) find that OA pre-prints are available for 36% of published journal articles in economics.
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factor between R and C - the data - is now publicly available. Thus, the scenario can be simplified by saying that only a member of the scientific community C continues to work with the disclosed data set. Let v be the value of a research idea that is generated by the scientific community based on R’s data. Let α > 1 be a creativity coefficient that measures the superior creativity of the scientific
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community as compared to the single researcher R. This is an important assumption as it implicitly states that the social optimum could be reached if the research was done by C. The intuition for this assumption is that C would achieve the highest value of research when he initially creates the data and writes both articles.6 In our model, however, R initially produces the data and writes (at least) the first paper. For instance, we assume that R has the initial research idea together
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with exclusive access to data sources that give him a head start in the creation of data. Following Fudenberg et al. (1983), we argue that this head start enables R to preempt C from generating data (as well as publication as long as the data are private information). A time coefficient, c > 1, indicates that the value of the second idea based on the data is lower v α
and
v c·α
be the value of the idea for R based on the data in stage 1
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than that of the first idea. Let
and 2, respectively. Henceforth, we normalize v to one. The higher c is, the stronger does the value 1 c
be the value of the idea based on the data for C in
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of the idea based on the data devaluate. Let the second stage. As α > 1,
1 c
>
1 c·α .
Thus, data availability creates positive spillovers as it enables
C to publish an article of higher value as compared to R’s second article under non-disclosure. To
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illustrate, the higher α the larger is the difference between the value of C’s article and R’s second article. For very large values of α, the value of R’s second article tends towards zero. This is the
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case when R fails to publish a second article because she has no ideas to test. Hence, the second paper can only be published if the data is disclosed. In this case, the total volume of publications
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is reduced when R keeps her data secret. The cost functions are given by c (et ) =
1 2 2 et
for R and c (x2 ) =
1 2 2 x2
for C, i.e., we assume
increasing marginal costs of both data and article creation. Without data no research occurs and players get Ui,kjm = 0 with players i = R, C , policies k = N P, F P P , number of papers published j = 1, 2 and (in case that k = N P ) R’s sharing decision m = share, never. Welfare is given by 6
The reason behind this simplification is that there will be a member or a combination of members within C that will have a more valuable idea than R.
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Wkjm = UR,kjm + UC,kjm .
2.1
No Policy
Researcher publishes one paper and shares at t = 1 (1-Share): R’s optimization problem 1 1 2 1 δ e0 e1 (1 + κ) − e1 + δ 2 γ D e0 − e20 −→ max, α 2 2
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under 1-Share is
(1)
where δ t is the discount factor at time t which measures R’s impatience to publish.7 For instance, this impatience arises from the researcher’s ambition to push her academic career by obtaining tenure through publication (Dasgupta and David, 1994; Gans and Stern, 2010). For
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δ = 1, R is indifferent between a publication today and a publication tomorrow. κ represents the change of the value of an article due to the disclosure of the data. We assume that κ is positive and not too large, 0 < κ ≤ 12 .8 For instance, suppose that the availability of the data used in an article is perceived by peers as a signal of quality (Dasgupta and David, 1994). In that sense, data sharing may be seen as a means to disclose R’s private information on the quality of her empirical article.
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Thus, researchers of higher quality may be more likely to share their data voluntarily in order to signal the robustness of their results (Andreoli-Versbach and Mueller-Langer, 2014; Feigenbaum
generate more citations.
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and Levy, 1993). In addition, empirical articles for which the applied data is publicly available may
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Let γ D (γ N D ) measure the value of the data for R after the last publication if R discloses (does not disclose) the data and define ξ =
γD γN D .
For example, the data set might contain information
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that is valuable for non- or semi-academic projects, such as expert or policy advice, that do not necessarily lead to further scientific publications. Second, the data set itself might be cited in
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subsequent literature as it provides, for instance, a widely applicable index. In addition, a data set could become valuable if data journals are later established in economics. In these cases, the remaining personal value of the data after the last publication depends on whether the data are public or private information. The lower ξ the lower are ceteris paribus R’s incentives to share data. The higher the scope for individual use of the data, the higher will be R’s incentives to keep 7
The solutions of all optimization problems presented in this paper are based on straightforward calculations which are therefore omitted here. They are available from the authors upon request. 8 We discuss the main assumptions of our model in Section 5.1.
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the data. The first term in (1) is R’s discounted net value from publishing in t = 1. The second term is R’s discounted value of the disclosed data set, which depends positively on the effort to create it. The third term describes the effort cost to create the data. C’s optimization problem under 1-Share depends on R’s optimal effort to create data, e∗0,N P share : 1
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1 1 δ 2 e∗0,N P share x2 − x22 −→ max . 1 c 2
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C maximizes his discounted net value from publishing in t = 2. Table 1 summarizes R’s optimal effort to create data, R’s utility and overall welfare under the six publication and data disclosure
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scenarios under study. TABLE 1 HERE
Under 1-Share, optimal efforts in all stages are increasing in γ D and κ.9 The higher the value of the article and the data due to data disclosure, the higher is R’s initial effort to create the data, e∗0,N P share . Optimal efforts to publish chosen by C and R in stages 1 and 2 then depend on R’s 1
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initial effort of data creation. The higher the quality of the data, the higher is the benefit from an article and thus the higher are the efforts to publish it. R’s utility depends positively on the
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remaining personal value of the data after the last publication. It also increases if the positive κ-effect on the value of the article due to the disclosure of the data is more pronounced. C’s utility
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(see welfare under 1-Share in Table 1) increases if, at optimum, R increases her effort to create the data. It decreases if the devaluation of the value of the research idea based on R’s data over time
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is more pronounced. Under 1-Share, overall welfare is increasing in γ D and κ and decreasing in c. Researcher publishes two subsequent papers and shares at t = 2 (2-Share): R’s
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optimization problem under 2-Share is 1 1 1 1 1 (1 + κ) − e22 + δ 3 γ D e0 − e20 −→ max . δ e0 e1 (1 + δ · κ) − e21 + δ 2 e0 e2 α 2 c·α 2 2
(3)
The first term in (3) is the discounted net value of publishing in t = 1. Note that in contrast to 1-Share, the positive κ-effect is discounted under 2-Share as data availability develops its positive 9
See also Proposition 0 in the appendix where we derive the exact condition for positive optimal efforts to create data.
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effect on the value of the first article at a later stage. The second term in (3) is the discounted net value of publishing in t = 2. It accounts for the devaluation of the research idea over time. The third term is R’s discounted value of the disclosed data set. The last term describes the effort cost to create the data. Under 2-Share, overall welfare increases in γ D and κ and decreases in c and α (see Table 1).
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Researcher publishes one paper in t = 1 and never shares (1-Never): The optimization problem of R is given by
1 1 2 1 δ e0 e1 − e1 + δ 2 γ N D e0 − e20 −→ max . α 2 2
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In contrast to 1-Share, there is no positive κ-effect in the first term of (4). The second term is R’s discounted value of the undisclosed data set. Note that C does not generate any utility in this case. Overall welfare increases in γ N D and decreases in α (see Table 1). Researcher publishes two subsequent papers and never shares (2-Never): R’s optimiza-
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tion problem under N P if she never shares10 is
(5)
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1 2 1 1 2 1 1 2 − e2 + δ 3 γ N D e0 − e20 −→ max . δ e0 e1 − e1 + δ e0 e2 α 2 c·α 2 2 Note that C does not generate any utility in this case.
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Finally, consider the four N P scenarios summarized in Table 1. In optimum, R’s utility is a function of R’s effort to create data, her patience and the value of the disclosed (non-disclosed)
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data. R’s effort to create data and thus her utility under 1-Share and 2-Share increase if κ increases. Hence, R’s incentive to create and share data increases if κ increases. In contrast, R’s incentive to
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share data decreases if γ N D increases while her effort to create data increases in γ N D . The question of which of these countervailing effects on the incentive to share data dominates depends on R’s patience.
We now analyze the conditions under which R does not share her data. All proofs are provided in the appendix. 10
Note that if R does not share the data immediately after her last publication, she will never share.
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Proposition 1: Never Share Under N P the Researcher can decide not to share only if γ D < γ N D , i.e., if ξ =
γD γN D
< 1. (i) She will always choose not to share if ξ is sufficiently small, i.e.
ξ ≤ ξ l , where ξ l (κ) negatively depends on κ. (ii) For ξ l < ξ < 1 she will choose not to share if she is impatient enough, i.e. δ ≤ δ h , where δ h (κ, ξ) depends nonpositively on both κ and ξ. (i) Intuitively, R does not have an incentive to share data if the remaining personal value of the
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undisclosed data after the last publication by far exceeds the personal value of the disclosed data. In this case, the disclosure-driven decrease in the remaining value of the data more than outweighs the positive ”κ-effect” associated with the increase in the value of an article due to data disclosure. Note that (i) illustrates the status quo in economics as only very few economists voluntarily share their data with the scientific community (Andreoli-Versbach and Mueller-Langer, 2014).
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(ii) However, this result does not hold true in general if the above-stated decrease in the remaining value of the data is sufficiently low, i.e. ξ > ξ l . Then, the level of patience comes into play and only a sufficiently impatient researcher will keep the data private information. In this case, the (strongly) discounted ”κ-effect” does not outweigh the disclosure-driven decrease in the remaining
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value of the data. Figure 2 illustrates the utility under 1-Never and 1-Share as a function of R’s patience, δ, and the value of the non-disclosed data, γ N D , for (a) κ = 0.05 and (b) κ = 0.45. Other
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model parameters are kept constant (c = α = 1.5 and γ D = 1). In Figures 2a) and 2b), the blue plane represents R’s utility if she writes one paper and shares the data. Her utility if she writes one paper and never shares the data is given by the red plane. We can see that if the value of
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non-disclosed data is relatively large, i.e. greater than about 1.4, non-disclosure is always better for R, i.e. the red plane lies above the blue one in Figures 2a) and 2b). In contrast, if the value
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of the non-disclosed data tends towards one (with γ D = 1), non-disclosure might be detrimental to R. However, this is only the case if R is very patient, i.e. the blue plane lies above the red one
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for sufficiently high values of δ. This is due to the fact that disclosing or non-disclosing implies different effort levels (see Table 1). A comparison of Figures 2a) and b) also suggests that data disclosure is beneficial for R for a larger set of parameter constellations if k increases from 0.05 to
0.45, as illustrated by the larger visible section of the blue plane in b). FIGURE 2 HERE
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2.2
First Paper Policy
To simplify matters we omit labels for the obvious number of papers published, j = 1, 2, and R’s sharing decision, m = share, never, in efforts, utilities and welfare under F P P . First Paper Policy without Strategic Delay: Under F P P without strategic delay (N SD), R
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publishes the first paper in t = 1. She is required to share the data and does not compete with C in t = 2 (due to the competitive advantage that is captured in C’s superior creativity). R’s optimization problem is
1 2 1 1 (1 + κ) − e1 + δ 2 γ D e0 − e20 −→ max . δ e0 e1 α 2 2
(6)
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R’s maximization problem under N SD is the same as under 1-Share. The main difference, however, is that she is forced to make the data available under F P P upon publication of the first paper. F P P is detrimental to R as it reduces her set of possible publication strategies. The competitor C uses the data and publishes a paper in t = 2. C’s optimization problem is
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1 1 2 ∗ δ e0,F P PN SD · x2 − x2 −→ max . c 2 2
(7)
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The outcomes under N SD and 1-Share are identical for i = R, C (see Table 1). First Paper Policy with Strategic Delay: R may choose to delay her publications in order
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to fully exploit her data under F P P . In this case, she will incur the costs of completing the first and second paper in the first and second period, respectively. However, she will realize the total
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benefits associated with the publication of two papers in the second period, as she strategically delays publication in order to keep the data private. Under F P P with strategic delay (henceforth,
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SD), R does not publish in t = 1 but publishes the first and the second paper together in t = 2. R’s optimization problem is
1 1 δ δe0 e1 (1 + κ) − e21 α 2
1 1 2 1 + δ e0 e2 (1 + κ) − e2 + δ 3 γ D e0 − e20 −→ max . c·α 2 2 2
(8)
To understand R’s optimization problem under SD, it is constructive to compare it with R’s optimization problem under 2-Share as given by (3). The second, third and fourth terms are
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identical under both scenarios. The first term, however, is different if R is not perfectly patient, i.e., δ < 1. In contrast to 2-Share, R realizes the net value of the publication of the first paper at a later stage under SD. Under 2-Share, the first paper is published right after completion in the first stage whereas its publication is postponed to the second stage under SD. Note that C does
α (see Table 1).
3
Analysis and Comparison of Policies
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not generate any utility in this case. Overall welfare increases in γ D and κ and decreases in c and
We first examine the conditions under which R finds it optimal to delay submission strategically
3.1
Conditions for Strategic Delay
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under F P P . Then, we analyze the effect of the transition from N P to F P P on R’s efforts.
We provide the conditions for strategic delay under F P P in the following proposition. The Researcher will delay strategically under F P P if and only
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Proposition 2: Strategic Delay
if she is sufficiently patient, i.e. δ ≥ δ hSD , where δ hSD = δ hSD (κ) depends negatively on κ.
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The depreciation of the value of the first article under strategic delay depends on R´s impatience. Intuitively, if R is sufficiently patient, the additional benefits from the second publication more than
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outweigh the delayed realization of the benefits from the first paper inducing her to choose strategic delay under F P P . Regarding the interpretation of this proposition, note that junior researchers
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are typically less patient than senior researchers because they are in need of a good publication soon in order to obtain a tenured position (Dasgupta and David, 1994; Gans and Stern, 2010).
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Hence, one may interpret Proposition 2 in the sense that junior researchers are ceteris paribus less likely to strategically delay their submission than senior (tenured) researchers. Finally, note that strategic delay is ceteris paribus more likely to occur if the positive effect of data disclosure on the value of an article is higher, i.e. κ increases. In this case, R’s benefits from the second paper are
higher.
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3.2
Efforts to Create Data
We analyze the effect of the transition from N P to F P P on R’s efforts to create data. We obtain: Proposition 3: Change in efforts under F P P
Transition to F P P (i) does not influence
efforts to create data if the Researcher chooses to share after one publication, which is the case
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when ξ ≥ 1 and the Researcher is not very patient, i.e. δ ≤ δ h1 , or when ξ h ≤ ξ ≤ 1 and δ h ≤ δ ≤ δ h1 . (ii) reduces efforts to create data, (1) if ξ is sufficiently small, i.e. ξ < ξ le < 1, or (2) if ξ le < ξ < 1 and the Researcher is impatient enough, i.e. δ < δ he , or (3) if ξ > ξ h and the Researcher is very patient, i.e. δ > δ he1 := max{δ h1 , δ hSD }. (iii) increases efforts to create data (1) if ξ le < ξ < 1 and δ he < δ < min {δ h , δ hSD }, or (2) if ξ ule (δ) < ξ < ξ h1 and
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δ > max {δ 01 , δ hSD , δ h1 }.
The economic intuition behind these results is the following. Under the conditions specified in (i), sharing after one publication is optimal for R under N P whereas no strategic delay is optimal under F P P . The transition to F P P does not influence R’s effort to create data as she is indifferent
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between voluntarily sharing after one publication and being forced to do so. (ii)(1) and (2) Intuitively, if sharing the data harms R significantly, the transition to F P P
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reduces her incentives to create the data in the first place independently of her publication choice under N P . (3) Whenever R chooses to delay submission strategically under F P P and to share after two publications under N P , transition to F P P reduces her efforts to create the data. Intuitively,
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both scenarios lead to the same outcome in the sense that data are available after two publications. However, R generates a lower (discounted) utility from the first publication under F P P with
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strategic delay as compared to publishing it right away under N P . (iii) Intuitively, under these conditions, R chooses higher efforts to create data under SD than
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under 2-Never because she can benefit from the positive κ-effect under SD but not under 2-Never.
More specifically, the optimal effort to create data under SD increases in κ while the effort to create data under 2-Never is independent of κ (see also Table 1). In addition, R can never achieve the
higher γ N D under F P P . Under these conditions, F P P forces R to adjust her optimal effort choice, which ceteris paribus turns out to be effort-increasing under the conditions specified in Proposition 3(iii) since, in this specific case, she takes advantage of the barely discounted κ-effect.11 11
The discrepancy between higher overall incentives to not disclose data under N P (i.e., R prefers 2-Never over
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Figure 3 illustrates the effort to create data under 2-Never under N P and SD under F P P as a function of R’s patience, δ, and the value of the non-disclosed data, γ N D , for (a) κ = 0.05 and (b) κ = 0.2. Other model parameters are kept constant (c = α = 1.5 and γ D = 1). In Figure 3, the blue plane represents R’s effort if she delays strategically under F P P . Her effort if she writes two papers and never shares under N P is given by the red plane. We can see that for very low
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values of κ the transition to F P P never increases R’s effort to create data, i.e. the blue plane lies below the red one. In contrast, if κ increases, the transition to F P P increases R’s effort to create data for sufficiently high levels of patience and sufficiently low values of the non-disclosed data, i.e. the blue plane lies above the red one. This is due to the fact that the optimal effort to create data
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under SD increases in κ while it is independent of κ under 2-Never. FIGURE 3 HERE
4
Welfare Analysis
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We analyze the welfare properties of the transition to F P P . The conditions under which this transition has neutral, negative or positive welfare properties are given in the following proposition.
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Proposition 4: Welfare effects Transition to F P P (i) does not influence welfare if the Researcher chooses to share after one publication, which is the case when ξ ≥ 1 and the Researcher
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is not very patient, i.e. δ ≤ δ h1 , or when ξ h ≤ ξ ≤ 1 and δ h ≤ δ ≤ δ h1 . (ii) (1) It increases welfare if ξ lw < ξ ≤ 1 and δ l < δ < δ h0 := min{δ h , δ hSD }, or (2) if ξ l3 < ξ < ξ h1 and
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δ 01 < δ < min{δ hSD , δ 00 }. (iii) It reduces welfare when ξ is sufficiently small, i.e. ξ < ξ l1 , or if the Researcher is very patient, i.e. δ > δ hSD .
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The economic intuition behind these results is the following. (i) Voluntary data sharing after one publication under N P and no strategic delay under F P P
lead to the same outcome from a social welfare perspective. Both researchers are indifferent between N P and F P P .
2-Share) but higher incentives to exert effort to generate data if disclosure is mandatory is driven by the following factors: First, as R chooses 2-Never under N P we know from Proposition 1 that γ D < γ N D in this case. Second, κ is sufficiently low in this case to not make sharing beneficial under N P . Third, as R prefers strategic delay over no strategic delay under F P P , we know from Proposition 2 that R is sufficiently patient.
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(ii) (1) Under these conditions, R publishes one article and never shares her data under N P and chooses not to strategically delay her first article under F P P . The welfare gain due to the additional paper published by C under F P P more than outweighs the potentially negative impact of forced data sharing on R. (2) Even if R finds it optimal to publish two articles and never share data under N P , the transition to F P P increases welfare. The quality difference between C´s
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paper and the paper R would have published under N P more than outweighs the negative impact of forced data sharing on R.
(iii) These results specify two sets of conditions under which the transition to F P P has negative welfare properties.
First, the transition to F P P always reduces welfare if it induces R to delay submission strate-
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gically. If R delays strategically, two negative effects emerge: There will be a delay in the time the scientific knowledge is made public and C cannot use the data to publish his (higher value) paper. Moreover, it is straightforward to show that there is always at least one strategy option under N P that dominates strategic delay under F P P . Consequently, whenever a policy change induces R to
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delay her submissions strategically R’s utility and thus overall welfare decreases. Second, for sufficiently low ξ, the transition to F P P reduces welfare if it forces R to switch from
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never sharing after the first or second publication under N P to not delaying strategically under F P P . This serves as a counterpart to (ii)(1)and (2) discussed above: The welfare gain due to the additional paper published by C does no longer outweigh the negative effect of forced data sharing
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on R.
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Graphical Example
Figure 4 illustrates R’s choices and the effects of the transition from N P
to F P P depending on the impatience rate, δ (vertical axis), and the ratio of data values after all
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publications in case of disclosure/nondisclosure, ξ =
γD γN D
(horizontal axis). Other model parameters
are kept constant (c = α = 1.5 and κ = 0.2). The black lines divide the whole area into 4 zones, indicating R’s choices under N P : R chooses
to publish one paper and never share data (1-Never ) in the bottom left zone, publish two papers and never share data (2-Never ) in the top left zone (see Proposition 1), publish two papers and share data (2-Share) in the top right zone and publish one paper and share data (1-Share) in the bottom right zone. The horizontal blue line denotes the border for R’s choice under F P P : 16
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she chooses to delay strategically (SD) above the blue line and not to delay (N SD) below it. It represents δ hSD from Proposition 2. FIGURE 4 HERE The light blue area indicates those combinations of δ and ξ for which the transition from N P
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to F P P is welfare reducing. The light yellow area indicates combinations for which the transition to F P P increases welfare. As for the white zone, which is exactly the zone where R chooses the publish one paper and share data under N P , the transition to F P P does not change welfare. Finally, the checked areas (always bordered by red lines on one side) indicate where the transition to F P P increases efforts to create the data. Most notably, Figure 4 suggests that there is scope
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for a socially beneficial transition to F P P that increases the effort to create data, as indicated by the overlapping checked and light yellow areas. Efforts do not change after transition to F P P in the white zone and decrease everywhere else (Proposition 3). Strategic delay under F P P is
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unambiguously welfare reducing.
Discussion and Policy Recommendations
5.1
Discussion
ED
5
Assumptions: Our model relies on the assumption that a single set of data can produce more
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than one paper. Recent empirical evidence from a survey among the members of the German Economic Association (VfS)12 and the German Academic Association for Business Research (VHB)13
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- conducted under the European Data Extended (EDaWaX) Project - provides support for this assumption (Mueller-Langer and Winter, 2017). It suggests that overall 40% of the 340 respondents
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(VfS: 40.9%, 225 respondents; VHB: 38.3%, 115 respondents) have already published more than one paper with the same dataset. On average, they spent 38% of the total time spent on their last empirical paper on the creation of data and published 4.3 journal articles using self-created datasets (e.g., obtained from own experiments, surveys or interviews) within the last five years. 12
VfS is the largest association of German-speaking economists in the world and was founded in 1872. VHB is closely linked to the most influential German-speaking researchers in business administration and was founded in 1921. 13
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Another important assumption is that the value of an article moderately increases if the respective data is disclosed, 0 < κ ≤ 12 . Evidence from the EDaWaX survey among the members of VfS and VHB supports the assumption of a positive but moderate effect of data disclosure. Overall, 90% of the respondents (VfS: 93.8%; VHB: 81.8%) support the hypothesis that empirical articles subject to data disclosure gain credibility. However, evidence from the same survey also suggests
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that data disclosure only has a rather moderate effect on the academic reputation of authors. When asked about the importance of data disclosure for their own academic reputation on a five-point Likert scale, 88.3% of the respondents (265 of 300) replied that data disclosure was not important at all (79), rather not important (117) or neither important nor unimportant (69); rather important: 31; very important: 4.
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However, while evidence from the EDaWaX survey supports our assumptions on κ, it is important to clarify that R’s incentives to disclose data will ceteris paribus decrease if the benefits of disclosing data are actually negative. For instance, this might be the case when R judges the risk that she made an inadvertent error higher than the benefits from the increased credibility from data
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disclosure.14 As we can see from Table 1, R’s utility under 1-Never and 2-Never is independent of κ. In contrast, however, R’s incentives to create data and thus R’s utility under 1-Share and
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2-Share are ceteris paribus lower if −1 < κ < 0.15 Hence, if κ is negative, R’s incentives to disclose data would decrease as compared to a situation where data disclosure has a positive κ-effect on the value of an article.
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Possible extensions: There are at least two ways to relate data creation to publications. First, one may consider uncertainty to publish in combination with the fixed costs connected to
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data creation. In this case, the expected value of a publication would depend on the probability to publish. However, the value of a publication would not be a function of the quality of the data
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in this set-up. Second, one may consider certainty to publish in combination with variable cost of data creation. Here, we opted for the latter approach due to the specific nature of the data under study. Arguably, papers that use novel self-created (experimental) data have ceteris paribus a higher probability to get published than papers that reanalyze archived data. Second, for this type of data it is particularly important to relate its quality (as a function of effort) to the value of 14
We thank an anonymous referee for this suggestion. We make this assumption because R would not have an incentive to publish under 1-Share as the discounted net value of publishing would be negative if κ < −1, see (1). 15
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the publication. Finally, the prospects of a high probability of publication might be an important ex ante incentive to incur the relatively high costs of creating novel data in the first place. Another interesting extension would be to incorporate endogenous belief formation in the model. In our setting the beliefs of a researcher, concerning her assumptions about the nature of the world and the likely choices of other researchers, are given exogenously and do not form or evolve. Adding
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endogenous beliefs might facilitate the transaction towards more sharing, while at the same time minimizing strategic delay and under-investment. One expansion of this setting might concern the signalling effect of sharing data.16 If sharing data is perceived as an important signal of ”quality”,17 researchers might incorporate this into their preferences and share more irrespectively of the data disclosure policy. In such a framework, editors and referees would be more willing to publish papers
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of data-sharing researchers as non-disclosure of data would be interpreted as a signal of low quality or non-replicability.18
An additional extension might be to incorporate social beliefs about the normative standpoint of academia. If researchers perceived data-sharing as a necessary step to publish, because of the
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ideal standards and norms in the research community, this would increase voluntary sharing. For the scope of this paper, we focus on a profit-maximizing researcher with exogenous preferences.
5.2
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Future research might shed light on incorporating endogenous beliefs in this setting.
Policy recommendations
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The public availability of research data is an important issue from a research policy perspective (Burgelman et al., 2010; European Commission, 2012 and 2016; OECD, 2007; US House of Repre-
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sentatives, 2007). Several journals and research-funding organizations have recently introduced data availability policies (Andreoli-Versbach and Mueller-Langer, 2014; Doldirina et al., 2015; ESRC,
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2010; McCullough, 2009; NIH, 2003; NSF, 2011; Wellcome Trust, 2007). However, compiling and documenting data and code for subsequent use is costly and the data creator’s benefits of shared data in the form of recognition or citations to the data are relatively low (Anderson et al., 2008; Costello, 2009). On the basis of our findings and the fact that an institutional response is highly 16
Intuitively, this could work in a similar way as a second-hand car dealer who adds a warranty to his cars, see for example Grossman (1981). See also Milgrom (1981). 17 For example, because it diminishes the information asymmetry between the reader and the author. 18 For a review of the theoretical and empirical literature on quality disclosure see Dranove and Jin (2010).
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needed to increase data sharing (Dasgupta and David, 1994) we argue that mandatory data disclosure policies are necessary. However, our results also show that the implementation of universal mandatory data disclosure can have unintended negative effects. In the following we discuss policy options that may incentivize data sharing and deter welfare-reducing strategic delay. Possible actions for universities: The transition to mandatory data disclosure reduces
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welfare if it induces researchers to delay their submissions strategically (see Proposition 4). Strategic delay depends on a researcher’s patience to publish which in turn may depend on factors such as research experience or tenure. Early-stage researchers are ceteris paribus less likely to delay their submissions strategically as they are in need of a publication soon to get tenure. In this case, the transition to mandatory data disclosure is less likely to have negative welfare properties. In contrast,
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more experienced (tenured) researchers may have a higher incentive to delay the submission of their papers strategically as they are more patient. In this case, forced data sharing associated with the transition to mandatory data disclosure is not a recommendable policy option unless accompanied by appropriate incentives and data support to deter strategic delay. For example, universities could
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incentivize immediate data disclosure through priority-based rewards, e.g. research grants or prizes (Dasgupta and David, 1994; Fienberg et al., 1985; Gans and Stern, 2010; Mukherjee and Stern,
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2009). Universities could also promote immediate data disclosure through institutional assistance. According to Kim and Stanton (2012), the compilation, preparation and sharing of research data are perceived as costly, thereby preventing researchers from sharing their data. Reducing these
PT
obstacles could result in a higher net benefit of sharing data and help to generate a pro-datasharing attitude. Some universities have recently taken the lead in this respect by developing data
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repositories and structured guidance for the creation of data management plans (Andreoli-Versbach and Mueller-Langer, 2014).
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Data journals and citations: As the social value of knowledge increases by sharing the data
one variable which can be changed by policy makers is the value of the data for their creator after the last publication if she discloses the data, γ D (see Proposition 1). In particular, γ D could be the increasing value of data citations on academic reputation.19 In this respect, policy-makers and research funding agencies might incentivize and support the establishment of data journals. The 19
For example, information http://thedata.org/citation.
about
the
newly
implemented
20
data
citation
standard
is
available
at
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establishment of data journals in economics together with the obligation to cite the author of the data collection may create a market for the exchange of data and increase the value of a data set for its creator and the availability of data.20 This would increase the incentives to disclose data (Candela et al., 2015). It may also increase the quality of available data if data publications are subject to a peer-review process. Lessons could be learned from other disciplines. For instance,
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Nature (2013) has announced the launch of the online data journal Scientific Data. Moreover, the online-only Geoscience Data Journal has recently been launched (Allan, 2012). In addition, incentive schemes rewarding the production and documentation of data (Fienberg et al., 1985), such as a new standard of data citation (Altman and King, 2007), should be implemented so that sharing becomes more valuable to the original creator of data. Examples of recently established
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tools for data retention and citation are, among others, Dryad, Figshare and Zenodo. In general, if the individual academic value of data increases, i.e. due to data journals and increased and more valuable data citations, some researchers may have an incentive to specialize in the creation of data if they expect to have a competitive advantage, i.e. they have the necessary (financial) resources,
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knowledge and experience in the creation of data. This may have a positive effect on the overall quality of available data.
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Finally, this paper considered two policies, N P and F P P . Other policies trying to mitigate the negative effects of F P P while at the same time promoting sharing might be implemented as well. For example, one could think of a policy that delays a researcher’s data submission, e.g.
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for two years, which gives her enough time to start working on follow-up projects. Such policies however may not fulfil the standards of replicability and credibility. First, it is questionable how
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an enforcement agency would deal with non-compliance.21 Second, if the data is not made public, possible errors are not detected and further research is hindered.22 Third, some papers might be
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of high interest for current matters.23 20 See Gans and Stern (2010) for a similar discussion on the missing market for ideas in research. See also DuchBrown et al. (2017) for an overview of the relatively underdeveloped economics literature on markets for commercial data. 21 If the researcher refuses to supply the data afterwards, or she claims to have lost the data, it would be difficult for the journal to take actions against her. 22 In fact, the policies of government-supported research state that data should be made openly available as early as possible, with the timing of release and the duration of any exclusive-use period explicitly defined. 23 Examples include the debate after 2008 about austerity measures imposed on Greece, or, looking at other disciplines, the release of new drugs.
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6
Conclusion
We set up a simple model describing the incentives of a researcher to generate novel data, publish articles and share her data with the research community so that other researchers can use the data for subsequent empirical research. We compare two different scenarios. Under ”no policy”, the cre-
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ator of data has complete freedom as when to share her data voluntarily. Second, under ”mandatory data disclosure”, she is required to share the data immediately after her first publication.
The universal implementation of mandatory data disclosure may distort her incentives in two fundamental ways. First, she might strategically delay her submissions in order to continue publishing with the same data without making it available to others. Second, she might reduce her effort
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to create data as she would not be the full residual claimant of her data after the first publication. Our analysis suggests that universal mandatory data disclosure has ambiguous welfare properties. It reduces welfare if it induces researchers to strategically delay the submission of subsequent papers. Under this scenario the research community would not be in a position to make use of the data when it is still valuable for further research. Mandatory data disclosure may only be welfare
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enhancing if researchers have no incentives to postpone the time of their publication and if the positive effect of data availability outweighs the negative effect associated with reduced efforts to
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create data. We conclude that the implementation of mandatory data disclosure should be complemented by other policies that deter strategic delay, such as career incentives, and increase the
of data journals.
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stand-alone value of academic data, such as new standards for data citation and the establishment
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Finally, as a publication in a top-tier economics journal is highly desired by most researchers and might lead to promotion within a university, the benefits of a publication are likely to outweigh
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the cost of data sharing. It is questionable whether this result holds for medium-ranked journals with a data availability policy, where authors may choose competing journals with similar ranking but without a data availability policy.
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7
Appendix: Proofs
From the optimal efforts under the four N P scenarios (see Table 1), we obtain: Proposition 0: Positive efforts condition All optimal efforts are well-defined and positive for c2 α2 . 1+c2
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all δ ∈ (0, 1] if (1 + κ)2 <
Proof of Proposition 0: Since the denominators of optimal efforts depend negatively on δ, the efforts are positive for all δ ∈ (0, 1] if all of the following conditions hold:
1 1 − >0 α2 c2 α2 1 e∗0,N P1never (δ = 1) > 0 if 1 − 2 > 0 α 2 (1 + κ) (1 + κ)2 e∗0,N P share (δ = 1) > 0 if 1 − − >0 2 α2 c2 α2 (1 + κ)2 e∗0,N P share (δ = 1) > 0 if 1 − >0 1 α2 (1 + κ)2 (1 + κ)2 − >0 e∗0,F P PSD (δ = 1) > 0 if 1 − α2 c2 α2
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e∗0,N P2never (δ = 1) > 0 if 1 −
(1) (2) (3) (4)
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(5)
It is clear that conditions (1), (2) and (4) hold whenever condition (3) or, equivalently, (5) holds.
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We can rewrite (3) as c2 α2 − (1 + c2 )(1 + κ)2 > 0 ⇒ (1 + κ)2 <
U
R,N P1never
We first show that for ξ ≥ 1 it always holds that UR,N P share ≥
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Proof of Proposition 1:
and UR,N P share ≥ U
R,N P2never
2
1
. The first inequality is
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δ 4 γ 2D 1 1 δ 4 γ 2N D ≥ ⇔ 2 2 1 − δ 1 (1 + κ)2 21−δ 1 2 α α
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which holds whenever ξ = 1 21−δ
c2 α2 . 1+c2
γD γN D
γD γN D
2
≥
≥ 1. The second inequality is δ 6 γ 2D
1−δ
1
1 2 (1 + α 2 − δ α1
κ)2
δ 6 γ 2N D 1 ⇔ 1 2 1 − δ 1 2 − δ2 1 2 (1 + δκ)2 − δ 2 cα (1 + κ)2 α α cα 2 1 2 1 − δ α1 (1 + δκ)2 − δ 2 cα (1 + κ)2 γD 2 , ≥1≥ 2 1 2 γN D 1 − δ α1 − δ 2 cα 1 2
which holds whenever ξ =
γD γN D
,
(6)
≥
2
≥ 1, since (1 + κ)2 , (1 + δκ)2 ≥ 1. 23
(7)
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(i) We define v u u1 − t
v u u 1 − δ2 (1 + κ)2 α , ξ l (κ) := min t δ∈(0,1] 1 − δ2 α
δ (1 α2
+ δκ)2 −
1−
δ α2
−
δ2 (1 α2 c2 2 δ α2 c2
+ κ)2 .
(8)
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Obviously, for ξ ≤ ξ l (κ) the Researcher will choose to never share and ξ l (κ) negatively depends on r δ 1− 2 (1+κ)2 (1+κ)2 1 α κ. ξ l (κ) is positive for positive efforts. We now simplify (8). Since α2 > α2 , is 1− δ α2
monotonically decreasing in δ and
δ∈(0,1]
Since
(1+δκ)2 α2
δ and
>
1 α2
and
(1+κ)2
v u u1 − min t
c2 α2
δ (1 α2
1
c2 α2
1−
,
s
+ δκ)2 −
1−
δ α2
−
+
κ)2
δ α2
v u 2 u 1 − (1+κ) t α2 = . 1 − α12
1−
2 δ (1+δκ)2 − δ2 2 (1+κ)2 α2 α c 2 1− δ2 − δ2 2 α α c
δ2 (1 α2 c2 2 δ α2 c2
+ κ)2
is monotonically decreasing in
v u 2 2 u 1 − (1+κ) − (1+κ) α2 α2 c2 =t . 1 − α12 − α21c2
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v v u u 2 2 (1+κ)2 u 1 − (1+κ) u 1 − (1+κ) − α2 c2 t t α2 α2 < 1 − α12 − α21c2 1 − α12
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⇔ α2 − (1 + κ)2 < α2 (1 + κ)2 − (1 + κ)2 ⇔ 1 < (1 + κ)2 ⇔ 0 < κ, so we can state
(9)
(10)
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δ∈(0,1]
Finally,
>
δ (1 α2
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v u u1 − min t
v u 2 2 u 1 − (1+κ) − (1+κ) t α2 α2 c2 ξl = . 1 − α12 − α21c2
(11)
(12)
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(ii) Now we aim to show that for ξ l < ξ < 1 there always exists some δ h (κ, ξ) > 0, such that for every δ ≤ δ h (κ, ξ) it holds UR,N P1never ≥ UR,N P share , UR,N P1never ≥ UR,N P2never and UR,N P1never ≥ 1
UR,N P share . So, the first inequality is equivalent to 2
δ≤
α2 (1 − ξ 2 ) , (1 + κ)2 − ξ 2
(13)
where the expression on the right-hand side (r.h.s.) is always positive for ξ < 1 and κ > 0. Thus,
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there exists some δ 00 (κ, ξ) :=
α2 (1−ξ 2 ) (1+κ)2 −ξ 2
∈ [0, 1] such that UR,N P1never ≥ UR,N P share for all δ ≤ δ 00 . 1
The second inequality is equivalent to c2 δ 3 − (1 + α2 c2 )δ 2 − c2 δ + α2 c2 ≥ 0.
(14)
−1 < 0 and
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Denoting the function on the left-hand side (l.h.s.) lhs(δ), we compute lhs(0) = α2 c2 > 0, lhs(1) = ∂lhs (δ) = 3c2 δ 2 − 2(1 + α2 c2 )δ − c2 < 0 ∂δ
(15)
for all δ ∈ [0, 1]. So there exists some δ 01 = δ 01 (κ, ξ) ∈ [0, 1] such that lhs(δ 01 ) = 0 and lhs(δ) > 0
δ3 2 (ξ − κ2 ) − δ 2 α2
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for all δ < δ 01 . The third inequality is equivalent to 2κ (1 + κ)2 2 + ξ + α2 α2 c2
−
δ + 1 ≥ 0. α2
(16)
Denoting the function on the l.h.s. LHS(δ), we find that LHS(0) = 1 > 0 and
1 LHS(1) = (1 − ξ ) 1 − 2 α
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2
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Further,
for all δ ∈ [0, 1].
−
2κ κ2 (1 + κ)2 − − . α2 α2 α2 c2
2κ (1 + κ)2 2 + ξ + α2 α2 c2
−
1 <0 α2
(17)
(18)
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∂LHS (δ) δ2 = 3 2 (ξ 2 − κ2 ) − 2δ ∂δ α
If LHS(1) < 0, then there exists some δ 02 = δ 02 (κ, ξ) such that LHS(δ 02 ) = 0 and LHS(δ) > 0
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for all δ < δ 02 . For completeness, define δ 02 ≡ 1 in case LHS(1) > 0. Combining our considerations,
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we define
δ h (κ, ξ) := min {δ 00 , δ 01 , δ 02 } ,
(19)
which is always positive for 0 ≤ κ ≤ 0.5 and ξ l < ξ < 1. Clearly, for δ < δ h the Researcher will choose not to share. It remains to show that δ h (κ, ξ) depends nonpositively on both κ and ξ. Computing the κ and ξ derivatives of the first term on the r.h.s. of (19), one can see that both of them are negative everywhere. If δ 02 = 1, then the statement is proved, since the first term is the only one that depends on κ and ξ.
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We now consider LHS(δ) for a fixed δ as the function of κ and ξ, denoting it LHS δ (κ, ξ). 2δ 3 ∂LHS δ (κ, ξ) = − 2 κ − δ2 ∂κ α
2 2(1 + κ) + 2 α α2 c2
<0
(20)
<0
(21)
and ∂LHS δ (κ, ξ) 2δ 3 = 2 ξ − 2δ 2 ξ = 2δ 2 ξ ∂ξ α for δ ∈ [0, 1].
δ −1 α2
CR IP T
Notice that
So the function LHS(δ) is pointwise monotone decreasing separately in κ and ξ. Since LHS(δ) is monotonically decreasing in point δ 02 , it follows that δ 02 (κ, ξ) depends nonpositively on both κ
Proof of Proposition 2:
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and ξ.
We prove the statement generally for all 0 ≤ κ ≤ 0.5 and c, α > 1.
The Researcher chooses to delay strategically under F P P if and only if UR,F P PN SD ≤ UR,F P PSD , i.e.
1
1+
(1+κ)2 c2 α2
M
s
≤ δ,
(22)
where the first step is correct under the assumption of positive efforts. So there is some δ hSD =
ED
δ hSD (κ) ∈ [0, 1] with UR,F P PN SD ≤ UR,F P PSD for every δ ≥ δ hSD . Note that δ hSD (κ) depends
PT
negatively on κ.
Proof of Proposition 3: (i) We define δ h1 so that UN P share ≥ UN P share for δ ≤ δ h1 . For this 2
CE
AC
consider
1
δ 4 γ 2D δ 6 γ 2D 1 1 ≥ ⇔ 2 1 − αδ2 (1 + κ)2 2 1 − δ2 (1 + δκ)2 − 2δ2 2 (1 + κ)2 α c α " # 2 1 + 2κ 2κ (1 + κ) δ δ3 − δ2 1 + 2 + − 2 + 1 ≥ 0. 2 2 2 α α c α α
(23)
Denoting l.h.s. of the last expression LHS(δ) we compute LHS(0) = 1 > 0 and
LHS(1) =
1 + 2κ 2κ (1 + κ)2 1 (1 + κ)2 − 1 − − − + 1 = − < 0. α2 α2 c2 α2 α2 c2 α2
26
(24)
ACCEPTED MANUSCRIPT
The first derivative of LHS with respect to δ is LHSδ0
= 3δ
21
2κ (1 + κ)2 1 + 2κ − 2δ 1 + 2 + − 2. 2 2 2 α α c α α
(25)
We compute LHSδ0 (0) = − α12 < 0 and
because positive efforts imply
1+κ α2
2(1 + κ) (1 + κ)2 − 2 − 2 < 0, α2 c2 α2
CR IP T
LHSδ0 (1) =
(26)
< 1 (see (4)). The derivative of LHSδ0 with respect to δ is
monotone as the derivative of any quadratic function and we conclude that LHS(δ) is monotonically
AN US
decreasing for all δ ∈ [0, 1]. Accordingly, δ h1 ∈ (0, 1) is well-defined as the first positive root of LHS(δ) = 0, i.e. for δ ≤ δ h1 it indeed holds UN P share ≥ UN P share . 1
2
Now by the proof of Proposition 1, for ξ ≥ 1 and δ ≤ δ h1 the Researcher will choose to share after one publication under N P . Whenever the Researcher chooses to share after one publication under N P , she also chooses not to delay strategically under F P P . We show this indirectly, proving that
M
sharing after 2 publications strictly dominates strategic delay. This would imply that the Researcher will not choose strategic delay, because she does not choose sharing even after 2 publications. 2
δ 6 γ 2D
δ (1 α2
+ δκ)2 −
2
δ (1 c2 α2
+ κ)2
≥
1 2 1−
δ 6 γ 2D 3
δ (1+κ)2 α2
−
δ 2 (1+κ)2 c2 α2
1 − δ 2 (1 + 2κ) + 2δκ ≥ 0,
⇔
(27)
CE
PT
1 21−
ED
UN P share ≥ UF P PSD is equivalent to
which is true for all δ ∈ (0, 1].
AC
Since sharing after one publication is the same as not delaying strategically, it is clear that for ξ ≥ 1 and δ ≤ δ h1 and, analogously, for those cases where ξ < 1 and the Researcher chooses to
share after one publication under N P , transition to F P P does not influence efforts. We first show the dependence of δ h1 (κ) on κ and then discuss the case ξ < 1. Consider LHS(δ) for a fixed δ as the function of κ and ξ, denoting it LHS δ (κ, ξ). Notice that ∂LHS δ (κ, ξ) 2 2 2κ 3 2 2 =δ 2 −δ + + < 0. ∂κ α α2 c2 α2 c2 α2 27
(28)
ACCEPTED MANUSCRIPT
for δ ∈ [0, 1]. So the function LHS(δ) is pointwise monotone decreasing in κ. Since LHS(δ) is monotonically decreasing in point δ h1 , it follows that δ h1 (κ) depends negatively on κ. For the case ξ < 1 we aim to find conditions on δ and ξ under which the utility of sharing after one publication is higher than other utilities. First, we already know from the beginning of this 1
2
that for ξ ≥ ξ h1
v u u1 − := t
δ (1 α2
+ δκ)2 −
1−
δ α2
−
CR IP T
proof that UR,N P share ≥ UR,N P share for δ ≤ δ h1 . Second, we know from the proof of Proposition 1 δ2 (1 c2 α2 2 δ c2 α2
+ κ)2
(29)
it holds that UR,N P share ≥ UR,N P2never . So for ξ h1 ≤ ξ < 1 and δ ≤ δ h1 the Researcher chooses 2
AN US
to make one publication and then either to share or not to share. As we know from the proof of Proposition 1(ii), this last choice is met in favour of sharing in case
Now δ 00 (1) = 0 and
α2 (1 − ξ 2 ) . (1 + κ)2 − ξ 2
−2α2 ξ((1 + κ)2 − ξ 2 ) + 2α2 ξ(1 − ξ 2 ) ((1 + κ)2 − ξ 2 )2 2α2 ξ(1 − (1 + κ)2 ) <0 = ((1 + κ)2 − ξ 2 )2
(31)
PT
ED
δ 000 (ξ) =
(30)
M
δ ≥ δ 00 (ξ) :=
for ξ > 0. Since δ h1 does not depend on ξ, there exists some ξ h2 such that δ 00 ≤ δ h1 for every
CE
ξ ≥ ξ h2 . Defining ξ h := max{ξ h1 , ξ h2 } we get that the Researcher chooses to share after one publication if ξ h ≤ ξ ≤ 1 and δ 00 ≤ δ ≤ δ h1 . Under these conditions δ 00 = δ h , since the relevant
AC
term in the definition of δ h is exactly δ 00 . We get the statement. (ii) (1) We know from the proof of Proposition 1 that for ξ < ξ l the Researcher chooses to never
share and decides to publish two papers if and only if δ > δ 01 . From Proposition 2, transition to
F P P urges the Researcher to delay strategically if and only if δ > δ hSD . We now compare the efforts to create a data set for different combinations of Researcher’s decisions.
28
ACCEPTED MANUSCRIPT
e∗0,N P never > e∗0,F P PN SD is equivalent to 1
2
1 − δ(1+κ) δ2ξ δ2 α2 > > ξ. ⇔ 2 δ δ(1+κ) 1 − α2 1 − αδ2 1 − α2
(32)
e∗0,N P never > e∗0,F P PSD is equivalent to δ3 1−
δ α2
−
>
δ2 c2 α2
δ3ξ 1−
δ 3 (1+κ)2 α2
−
1−
⇔
δ 2 (1+κ)2 c2 α2
2 2 δ 3 (1+κ)2 − δ (1+κ) α2 c2 α2 2 1 − αδ2 − c2δα2
We define
min
δ
δ (1 α2
1−
+ κ)2
δ α2
1−
,
min
δ>max{δ 01 ,δ hSD }
1−
δ3 (1 α2
AN US
ξ le0 (κ) := min
(
CR IP T
2
> ξ.
+ κ)2 −
1−
δ α2
−
δ2 (1 α2 c2 δ2 α2 c2
(33)
+ κ)2
)
(34)
and notice that in general ξ le0 < ξ l , since a square root of a number that is smaller than one is bigger than the number itself (there is still a little difference between the second term in the definition of ξ le0 and the term under the second root in the definition of ξ l , so we will not use this fact in e∗0,N P never > e∗0,F P PSD is equivalent to
ED
1
M
the proof). It remains to consider the small interval of δ, with δ 01 > δ > δ hSD or δ 01 < δ < δ hSD .
δ3ξ
δ 3 (1+κ)2 α2
PT
δ2 > 1 − αδ2 1−
−
δ 2 (1+κ)2 c2 α2
⇔
1−
δ 3 (1+κ)2 α2
δ−
−
δ 2 (1+κ)2 c2 α2
δ2 α2
> ξ.
(35)
e∗0,N P never > e∗0,F P PN SD is equivalent to
CE
2
AC
1−
δ3 δ α2
−
δ2 c2 α2
>
δ2ξ 1−
δ(1+κ)2 α2
⇔
δ 2 (1+κ)2 α2 2 δ − c2δα2 α2
δ−
1−
> ξ.
(36)
Combining all these results we get that for (
ξ < ξ le := min ξ l , ξ le0 ,
min
δ 01 >δ>δ hSD
1−
δ 3 (1+κ)2 α2
δ−
−
δ2 α2
δ 2 (1+κ)2 c2 α2
,
min
δ 01 <δ<δ hSD
δ 2 (1+κ)2 α2 2 δ − c2δα2 α2
δ−
1−
)
(37)
transition to F P P reduces efforts to create data set for all δ ∈ [0, 1]. It is easy to see that ξ le (κ) depends negatively on κ.
29
ACCEPTED MANUSCRIPT
(2) When ξ le < ξ < 1, the Researcher chooses to never share after one publication under N P or not to delay strategically under F P P if and only if δ < min{δ h (ξ), δ hSD }, as we know from the proof of Proposition 1 and from Proposition 2. From (32) we can conclude that in this case F P P reduces efforts to create data set if and only if δ α2 (1 − ξ) δ(1 + κ)2 > ξ − ξ ⇔ > δ. α2 α2 (1 + κ)2 − ξ
(38)
CR IP T
1−
It follows that for ξ le < ξ < 1 and
AN US
α2 (1 − ξ) δ < δ he (κ, ξ) := min δ h (κ, ξ), δ hSD (κ), (1 + κ)2 − ξ
(39)
transition to F P P reduces efforts to create data set. As δ 01 does not depend on κ or ξ, δ h (κ, ξ) depends negatively on both of them and δ hSD (κ) depends negatively on κ and does not depend on ξ, δ he (κ, ξ) obviously depends nonpositively on κ and on ξ as well, since
α2 (1−ξ) (1+κ)2 −ξ
∂ξ
=
−α2 [(1 + κ)2 − ξ] + α2 (1 − ξ) −α2 [(1 + κ)2 − 1] = ≤ 0. 2 2 [(1 + κ) − ξ] [(1 + κ)2 − ξ]2
(40)
M
∂
ED
(3) We want to show that transition to F P P reduces efforts to create data set if ξ > ξ h = max{ξ h1 , ξ h2 } and δ > max{δ h1 , δ hSD }. In this case, the Researcher chooses to delay strategically
PT
under F P P (since δ > δ hSD ) or to share after 2 publications under N P . To prove the last statement recall the arguments from the proof of Proposition 3(i). For ξ > ξ h1 it holds that UR,N P share > UR,N P2never . For δ > δ h1 it holds that UR,N P share > UR,N P share and for
CE
2
δ > δ 00 we have UR,N P share > U 1
2
R,N P1never
1
. Further, δ h1 > δ 00 whenever ξ > ξ h2 , so for ξ > ξ h and
AC
δ > δ h1 the Researcher chooses to share after 2 publications. e∗0,N P share > e∗0,F P PSD is equivalent to 2
1 + 2δκ > δ (δ + 2δκ ) ,
(41)
which is true for all δ ∈ (0, 1]. So whenever the Researcher chooses to delay strategically under F P P and to share after 2 publications under N P , transition to F P P reduces efforts to create data set. (iii)(1) As we know from the proof of Proposition 1 and from Proposition 2, for ξ < 1 and 30
ACCEPTED MANUSCRIPT
δ < min {δ h , δ hSD } the Researcher chooses to never share after one publication under N P or not to delay strategically under F P P . From the definition of δ he (see (39)) it follows that if δ he < δ < min {δ h , δ hSD }, then transition to F P P increases efforts to create data set. We show that for κ > 0 there always exist such δ. Consider ξ < 1 near to 1 and small δ. As was shown in the proof of Proposition 3(i) (see text
CR IP T
after equation (29)), with these parameters the Researcher chooses to make one publication and then either to share or not to share, so that the relevant condition in min {δ h , δ hSD } is UR,N P1never ≥ UR,N P share , i.e. 1
δ 00 (ξ) =
α2 (1 − ξ 2 ) , (1 + κ)2 − ξ 2
(42)
AN US
since δ 01 and δ hSD are positive and do not depend on ξ, whereas δ 00 (1) = 0.
Notice that for ξ = 1 it holds that δ he = 0. So both δ 00 (ξ) and δ he (ξ) continuously approach 0 as ξ → 1. In the neighborhood of ξ = 1 it holds that δ 00 (ξ) > δ he (ξ), since α2 (1 − ξ 2 ) α2 (1 − ξ) ⇔ > 2 (1 + κ)2 − ξ (1 + κ)2 − ξ
M
(1 + κ)2 > 1,
(43)
ED
which is true for κ > 0. For ξ < ξ le transition to F P P reduces efforts to create data set (see this Proposition, (ii)(1)) and it follows that for ξ le < ξ < 1 and δ he < δ < min {δ h , δ hSD } transition to
PT
F P P increases efforts to create data set.
(2) For ξ < ξ h1 (see (29)) and δ > max {δ 01 , δ hSD , δ h1 } the Researcher chooses to never share
CE
after two publications under N P or to delay strategically under F P P . Further we know from this
AC
proof, (ii)(1), that in this case F P P increases efforts to create data set if and only if
ξ ule (δ) :=
1−
2 2 δ 3 (1+κ)2 − δ (1+κ) α2 c2 α2 2 1 − αδ2 − c2δα2
< ξ.
(44)
Since a square root of a number between 0 and 1 is bigger than the number itself, for δ = 1
and κ > 0 it holds ξ ule < ξ h1 . It follows that F P P increases efforts to create a data set when ξ ule (δ) < ξ < ξ h1 and δ > max {δ 01 , δ hSD , δ h1 }, whereby the set of such (ξ, δ) is always nonempty.
31
ACCEPTED MANUSCRIPT
Proof of Proposition 4: (i) Transition to F P P does not influence welfare whenever R chooses to share after one publication under N P and not delay strategically under F P P [see proposition 3(i)]. (ii) (1) By Proposition 2 and the proof of Proposition 1 (ii), we know, that if ξ l < ξ ≤ 1 and δ < δ h0 := min{δ h , δ hSD }, the Researcher will choose to publish one paper and never share under
CR IP T
N P or not to delay strategically under F P P . We also already know the dependence of ξ l (κ) and δ h0 (κ, ξ) on κ and ξ. We now show the existence of δ l and ξ lw such that for ξ lw < ξ ≤ 1 and δ l < δ < δ h0 it holds that WF P PN SD > WN P1never . The last expression is equivalent to δ 4 γ 2D
2 1−
+ 2
δ(1+κ) α2
ξ2 >
1
δ 6 γ 2D
2c2 1 −
> 2 2
δ(1+κ) α2
δ 4 γ 2N D ⇔ 2 1 − αδ2 −1
AN US
1 − αδ2 2 − δ(1+κ) α2
2
+
δ c2
1−
1−
δ α2
δ(1+κ)2 α2
2
(45)
(1+κ)2 α2
>
1 , α2
CE
+
−1
1 α2
1− 1 2 2 c (1+κ)2 1 − α2
> 0.
(46)
both
PT
Moreover, since
1
1 − α12 2 − (1+κ) 2 α
ED
RHS(1) =
M
Denoting the r.h.s. of the last expression RHS(δ), we compute RHS(0) = 1 and
δ α2 δ(1+κ)2 α2
1−
1−
and
1− 1−
δ α2
δ(1+κ)2 α2
2
(47)
are monotone increasing and since δ 2 is also monotone increasing, RHS(δ) is monotonically decreas-
AC
ing in δ. We conclude that for all ξ f with RHS(1) < ξ 2f ≤ 1 there exists δ l such that WF P PN SD > p WN P1never holds for every ξ f < ξ < 1 and δ l < δ ≤ 1. Define ξ lw := max{ RHS(1), ξ l }. For ξ = 1 it holds ξ 2 ≥ RHS(δ) for all 0 < δ ≤ 1, so the set of points (ξ, δ) with ξ lw < ξ ≤ 1 and δ l < δ < δ h0
is always nonempty. Finally, from Proposition 1 ξ l (κ) depends negatively on κ and it is easy to see that the same holds for RHS(1). (2) There might be a case where δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 , i.e. the Researcher chooses to never share after two publications under N P or not to delay strategically under F P P . 32
ACCEPTED MANUSCRIPT
Therefore, we consider WF P PN SD > WN P2never . From this, we obtain δ2
1− 1
1−
δ(1+κ)2 α2
2 δ − 2δ 2 α2 c α
+
2
δ 2 δ(1+κ)2 c2 1− 2 α
!.
(48)
CR IP T
v u u u ξ>u u u t
Denoting the term on the r.h.s. ξ l3 (δ, κ), we obtain that F P P increases welfare if δ 01 < δ < min{δ hSD , δ 00 } and ξ l3 < ξ < ξ h1 . It is easy to see that ξ l3 (κ) depends negatively on κ. Finally, we provide a numerical example which suggests that WF P PN SD > WN P share if δ h1 < δ < δ hSD . For 2
c = α = 1.5 and κ = 0.2, it is straightforward to see that WF P PN SD > WN P share if δ h1 = 0.8171 < 2
AN US
δ < δ hSD = 0.8824.
(iii) As we have seen in part (i) of proposition 3, sharing after two publications strictly dominates strategic delay. This means that whenever the Researcher chooses to delay strategically under F P P , she could have been better off under N P (even if she would not choose sharing after two publications in this case, as some other N P option could in its turn dominate sharing after two publications). 2
M
Since WN P share = UN P share and WF P PSD = UF P PSD , this means that F P P reduces welfare if the 2
ED
Researcher chooses to delay strategically under it, i.e. if δ > δ hSD . Now recall from the proof of Proposition 1, (ii), that there exists some δ h such that for δ < δ h 1-Never is the dominant strategy under N P . It follows that for δ < min{δ h , δ hSD } the Researcher chooses to never share after one
PT
publication under N P or not to delay strategically under F P P . From (45) we find out that if
CE
v −1 u u δ δ 2 u 1 − α2 1 − α2 δ + 2 ξ < ξ l0 := u , t 2 2 2 δ(1+κ) c δ(1+κ) 1 − α2 1− 2
(49)
AC
α
then WF P PN SD < WN P1never . That is, for ξ < ξ l0 and δ < min{δ h , δ hSD } transition to F P P reduces welfare. ξ l0 (κ) depends nonpositively on κ. There may remain a case where δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 , i.e. the Researcher chooses to never share after two publications under N P or not to delay strategically under F P P . We consider the inequality WF P PN SD < WN P2never by taking ξ l3 (κ) from (48) into account.
33
ACCEPTED MANUSCRIPT
Together we get that F P P is welfare reducing when
ξ < ξ l1 (δ) :=
ξ l (δ), 0 ξ l (δ), 3
δ < min{δ h , δ hSD }
(50)
δ 01 < δ < min{δ hSD , δ 00 } and ξ < ξ h1 .
CR IP T
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[48] Perrino, T. et al. (2013), Advancing science through collaborative data sharing and synthesis, Perspectives on Psychological Science, 8, 433-444.
AC
[49] Stephan, P.E. (1996), The economics of science, Journal of Economic Literature, 34(3), 1199-1235. [50] US House of Representatives (2007), America Creating Opportunities to Meaningfully Promote Excellence in Technology, Education, and Science Act, 110th Congress, 1st Session. H.R. 2272, Section 1009, Release of scientific research results, Government Printing Office: Washington.
[51] Vlaeminck, S. and G.G. Wagner (2014), On the role of research data centres in the management of publication-related research data, LIBER Quarterly, 23(4), 336-357.
[52]
Wellcome Trust (2007), Policy on data management and sharing. Retrieved from http://www.wellcome.ac.uk/About-us/Policy/Policy-and-position-statements/WTX035043.htm (5 March 2014).
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Figure 1 | Stages of the model First Paper Policy
Researcher (R) chooses effort e0 to create data
R chooses effort e0 to create data
Status quo in Economics
R publishes her second paper and shares data
1-share
2-share
1-never
AC
CE
PT
ED
Scenario
Competing researcher (C) publishes one paper using R’s data
(3) R publishes one paper and never shares
(4) R publishes her first paper
Strategic Delay
(5) R publishes one paper
AN US
Stage 2
(2) R publishes her first paper
(6) R writes her first paper but strategically delays submission in order to evade disclosure of data
R publishes her second paper and never shares data
C publishes one paper using R‘s data
R publishes her first and second paper at once
2-never
No Strategic Delay
Strategic Delay
M
Stage 1
(1) R publishes one paper and shares data
CR IP T
Stage 0
No Policy
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CR IP T
Figure 2 | Utility of R under 1-Never (red plane) and 1-Share (blue plane) for different levels of patience and values of undisclosed data
0.3
0.2
0.1
1.4
0.0
AN US
Utility
1.2
0.5
Patience
0.0
Data value
1.0
PT
ED
M
a) R’s utility, κ=0.05
CE
0.3
AC
0.2
Utility
0.1
1.4
0.0 1.2 0.5
Patience 0.0
1.0
b) R’s utility, κ=0.45
Data value
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CR IP T
Figure 3 | R’s effort to create data under 2-Never (red plane) and SD (blue plane) for different levels of patience and values of undisclosed data
2.0
1.5
Effort 1.0
AN US
2.0
1.8
0.5
1.6
1.4
0.0 1.0 0.8 0.6
0.4
0.2
0.0 1.0
M
Patience
Data value
1.2
PT
ED
a) R’s effort, κ=0.05
AC
CE
2.0
1.5
Effort 1.0 2.0 0.5
1.8 1.6
0.0 1.0
1.4 0.8 0.6
Patience
1.2
0.4 0.2 0.0
1.0
b) R’s effort, κ=0.2
Data value
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AC
CE
PT
ED
M
AN US
CR IP T
Figure 4 | R’s choices and the effect of the transition from NP to FPP
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AC
CE
PT
ED
M
AN US
CR IP T
Table 1 | R’s optimal effort, R’s utility and overall welfare under different regimes