Research and the Approval Process

Transcription

1 Reseach and the Appoval Pocess Emeic Heny y Maco Ottaviani z Febuay 2014 Abstact An agent sequentially collects infomation to obtain a pincipal s appoval, such as a phamaceutical company seeking FDA appoval to intoduce a new dug. To captue such envionments, we study stategic vesions of the optimal stopping time poblem st poposed by Wald (1945). Ou exible model allows us to conside di eent types of ules and commitments by the pincipal as well as stategic withholding of infomation by the agent. We shed light on cuent egulation and poposed efoms of the dug appoval pocess. The model also captues situations such as a m seeking antitust appoval to mege with a competito, a manage poposing a poject to the m s headquates o an autho submitting a pape to an edito. Keywods: Reseach, oganization, appoval, egulation. JEL Classi cation: D83 (Seach; Leaning; Infomation and Knowledge; Communication; Belief), M38 (Govenment Policy and Regulation). Ottaviani acknowledges nancial suppot fom the Euopean Reseach Council though ERC Advanced Gant We thank Umbeto Sagliaschi fo excellent eseach assitance. y Sciences Po and CEPR z Bocconi and CEPR

2 1 Intoduction Phamaceutical companies un costly clinical tials on new dugs to demonstate the safety and e ectiveness necessay to obtain egulatoy appoval. Similaly, a m intending to take ove a competito seaches fo evidence of synegies to convince the antitust authoity to appove the tansaction. A manage collects infomation to push the m headquates to validate his poject. And an autho submitting a pape conducts eseach and obustness checks to convince the edito to accept. In tun, the egulato, the headquates o the edito can can also conduct additional independent eseach on these issues. In all these situations an agent seaches sequentially fo evidence to convince a pincipal, with a pioi di eent pefeences, of the desiability of an activity with uncetain pivate and social payo s; the pincipal, in tun, also conducts some eseach. How does the oganization of the appoval pocess a ect the infomation that gets poduced and the quality of the nal decision? How does the possibility fo the agent to withhold infomation a ect the pocess? Conside ou leading application to the dug appoval pocess. Afte identifying a pomising compound, phamaceutical companies conduct an extensive and well de ned seies of clinical tials to obtain the appoval of the egulato in chage of dug safety. 1 Phamaceutical eseach is conducted sequentially, so that at each point in time one of thee decisions is made: continue eseach by acquiing additional infomation, abandon the poject altogethe, o ask fo appoval fo intoducing the dug to maket. 2 This coesponds to the cuent oganization of the dug appoval pocess, in paticula in the US. This pocess has evolved geatly ove time and new issues ae cuently emeging (as descibed in detail in section 2). The histoical evolution of legislation on dug appoval has tended to stengthen the powes of the FDA to mandate eseach and ceated oppotunities fo the agency to commit to standads and to a pecise pocess of appoval. In this pape, we will study the bene ts fom these di eent types of commitment. Cuently the attention has tuned to both the issue of withholding of infomation, following some heavily publicized scandals, 3 and 1 In the US the Food and Dugs Administation (FDA) egulates the appoval of new dugs. In the Euopean Union, phamaceutical companies can choose between applying to a EU-wide authoity, the Euopean Medicines Agency (EMA), o to one of the national authoities, such as the Medicines and Healthcae poducts Regulatoy Agency (MHRA) in the UK o the Agenzia Italiana del Famaco (AIFA) in Italy. 2 Obtaining additional evidence can mean conducting additional clinical tials o adding patients to a tial. As epoted in Nundy and Gulhati (2005), inceasingly Westen dug companies conduct tials in India to decease costs and bene t fom easie egulatoy appoval. Moeove, seveal scandals involve illegal tials not appoved by the Indian authoities. 3 Scandals include the allegation that fo seveal yeas Meck withheld evidence on advese e ects of its blockbuste dug Vioxx. Thee has been a ecent push to impose stonge disclosue equiements. Fo example, 2

3 the question of post-appoval egulation. Ou theoetical analysis will shed light on these new concens and on the necessay egulatoy steps. Ou model captues these types of envionments in a simple, tactable and exible way. A choice needs to be made between ejection and appoval. Rejection yields a zeo payo while the bene ts fom appoval depend on a binay state of natue; they ae positive if the state is high and negative if it is low. Reseach can be conducted to obtain additional infomation about the state. It is costly on two accounts: thee is a diect nancial cost and, in addition, eseach delays decision making with an associated oppotunity cost. The aival of new infomation is conveniently modeled in continuous time as a Wiene pocess with a dift that depends on the state. If the same playe wee in full contol of both eseach and appoval, the model would boil down to a vesion of the classic single-agent optimal stopping poblem that has been widely analyzed in the statistical decision theoy liteatue on sequential analysis pioneeed by Wald (1945). The well-known solution involves two theshold values (o standads) fo the belief, such that it is optimal to abandon the poject when the belief that the state is high is su ciently low (below the ejection standad) and such that it is optimal to adopt the poject when the belief is su ciently high (above the appoval standad). When the belief lies within these thesholds, it is optimal to continue eseaching this is Wald s celebated sequential pobability atio test. The payo s of agent and pincipal ae typically misaligned. Fo instance, because the phamaceutical m does not intenalize all extenalities, it typically gets a highe payo than the egulato in the bad state. In most of the pape we thus focus on situations whee, fo the stand-alone Wald Poblem, the agent seaches moe than the pincipal at the lowe end, when the state is bad, and less at the uppe end, when the state is good. It is the case most people have in mind fo dug appoval: phamaceutical companies ae eage to stop eseaching, obtain appoval, and adopt the dug ealie than the egulato when infomation is good and moe eluctant to abandon the poject when the state is bad. In pactice, the eseach and appoval pocesses ae not single agent poblems; intuitively the agent contols the eseach decision, at least initially, while the pincipal has the hold on the appoval decision. The baseline situation we thus study is one whee the agent chooses the lowe benchmak of seach and the pincipal simultaneously chooses the uppe benchmak (the Nash medical jounals and egulatoy authoities have pushed fo ealy egistation of tials and fo disclosue of the esults obtained in the tials. 3

4 Equilibium). 4 In equilibium, we show that the pincipal will compomise at a lowe standad fo appoval compaed to the pincipal s non-stategic standad. Intuitively, given that the agent now chooses when to abandon eseach, the pincipal s value of infomation is educed thus the pincipal becomes moe eage to appove. Two popeties of this Nash equilibium solution stand out. Fist, the pincipal can obtain a negative payo in equilibium. Indeed he contols the uppe benchmak, and can foce immediate appoval but cannot foce ejection. If the agent has su ciently misaligned pefeences and seaches too much at the lowe end, the pincipal at the uppe benchmak gets a negative expected bene t. The goal of eseach in such situations is that it will povide su ciently bad news that the lowe benchmak will be eached and the agent can be convinced to abandon. Second, moe eseach is conducted in the Nash equilibium solution than in eithe stand-alone poblems. INTUITION The pincipal thus has an inteest to commit to a couse of action that discouages eseach by the agent at the lowe end. We st conside commitments ex ante to an appoval standad, what we call the Stackelbeg outcome. The pincipal chooses his pefeed point on the agent s best esponse cuve. Depending on the value of the initial belief, di eent types of commitments ae optimal. When the belief is low, a high blocking commitment that discouages eseach by the agent is pefeed: this allows the pincipal to avoid the negative payo that sometimes chaacteizes the nash outcome. Fo intemediate values of the belief, the pincipal will commit to an inteio commitment, allowing fo some eseach by the agent. Finally, when the initial belief is vey favoable, the pincipal will commit to immediate appoval. In pactice, this type of commitment is not easy to achieve and futhemoe, as suggested by the above discussion, cannot be unifom and independent of the cuent state of knowledge. In fact, as descibed in section 2, this is not the appoach chosen fo dug egulation. Rathe, thee is a commitment to a well de ned sequential pocedue fo appoval. We thus study a model whee the inteaction occus in two stages as follows: 1. In the st stage the agent conducts eseach, and then decides when to tansfe the decisionmaking powe to the pincipal. 2. Once that happen, in the second stage, the pincipal conducts eseach and eventually 4 This is in fact the outcome of a game whee the pincipal can mandate eseach: in each peiod the agent chooses between thee actions, eseach, submit o wait and if the agent chooses submit, the pincipal chooses between eseach, appove and wait. 4

5 decides whethe to appove. Clealy, the solution in the second stage coesponds to the non-stategic solution fo the pincipal. Expecting that outcome, in the st stage the agent has less incentive to undetake eseach at the bottom because of the exta eseach conducted at the top in compaison to the baseline Nash equilibium. Ou analysis shows that this type of commitment is not necessaily optimal fom the point of view of the pincipal. Wheeas in the Nash Equilibium outcome, the issue was excessive eseach by the agent at the bottom, the issue is hee one of excessive eseach at the top. This suggests that egulation of dug appoval should be eoiented towads a commitment to standads. 5 Recent egulation of the dug appoval pocess has focused on the issue of withholding of infomation. As ecent scandals suggest, the agent can withhold some of the evidence, but this is nevetheless costly; Meck fo instance in the Vioxx case has paid ove 4.8 billion dollas fo settling complaints. We enich the model and suppose that the agent can epot any belief, but is then subject to an expected penalty when the state tuns out to be low. The expected penalty inceases in the distance between the actual state of knowledge and the epot (the case is hade to defend in cout when the lie is big). Even though the agent will always lie in equilibium, by exploiting the knowledge of the bounds of the agent s eseach inteval, the pincipal is able to pefectly invet the infomation and not be deceived. In fact, we demonstate that the pincipal will actually bene t fom the agent s ability to costly misepot infomation. The eason is that the cost of lying deceases the value of infomation fo the agent, leading to a eduction of eseach at the lowe end, something that is bene cial fo the pincipal. We show that it is optimal fo the pincipal to choose a penalty fo misepesentation that is not in nite so that the agent caies out some costly misepesentation in equilibium. As initially suggested, ou model is ich enough to cove othe cases of eseach and appoval than ou main application to the phamaceutical maket. this case, vaying some assumptions to bette t the applications. We deive some futhe esults in We st depat fom the assumption that the agent caes about the cost of the pincipal s eseach (i.e.. has to pay fo eseach) and evisit the two stage commitment game. We show that even though this intoduces 5 Thee is some discussion of elevant standads in the liteatue. Fo instance, Ocana and Tannock (2011) ague that, even though the FDA has tended to accept any tial showing statistically signi cant esults, they should become sticte and equest clinically impotant di eences, i.e., statistical di eences lage enough to make it woth unning the isk of intoducing a new dug. 5

6 a fee iding incentive, the agent still has incentive to do eseach to move the pincipal away fom his ejection theshold which is ine ciently high fom the agent s point of view. Related Liteatue. The oiginal poblem of sequential eseach, examining the tadeo between the cost of an exta signal and the bene t of a moe infomed decision, was intoduced by Wald (1945, 1947) and Wald and Wolfowitz (1948). 6 The ensuing applied pobability liteatue of this non-stategic poblem has a lage impact on the actual design of clinical tials. Closely building on Wald s decision-theoetic foundational famewok, we focus on the stategic issues that aise when the decisions to collect infomation and to make the nal decision ae made by two di eent playes. Ou pape thus elates to the liteatue on stategic expeimentation (see Bolton and Hais 1999) and especially to Stulovici (2010), who highlights how the loss of contol of decision making (detemined though voting in his model) educes the incentives to acquie infomation and thus induces a status quo bias; see also Fenandez and Rodik (1991). Ou model is closest to Gul and Pesendofe (2012), Lizzei and Yaiv (2011), and Chan and Suen (2012) who conside stategic settings in which public infomation aives ove time to votes. In Gul and Pesendofe s (2012) model infomation is povided by the paty that leads, wheeas in Lizzei and Yaiv (2011) and Chan and Suen (2012) votes decide collectively themselves when to stop acquiing public infomation and each a decision. In thei setting infomation is evealed publicly to all votes, while we focus on the sequential inteaction between an agent who collects pivate infomation and then epots (o possibly misepots) it to a pincipal who makes the appoval decision. We also analyze the commitment solution in which the pincipal moves st by setting the appoval standad, and then extend the model to analyze appoval in multiple stages. Fo ou baseline analysis we constain epoting of the belief (coesponding to the nal esults) to be tuthful at the moment of application, fo example because misepesentation is in nitely costly as in the disclosue models of Gossman (1981) and Milgom (1981). We also conside the possibility of costly misepoting. While Katik, Ottaviani and Squintani (2007) and Katik (2009) chaacteize the amount of equilibium costly lying in static models of stategic communication, in ou dynamic model we show that ex post lying costs educe the ex ante incentives fo infomation collection. See also Shavell (1994), Heny (2009), and Dahma, González, 6 Moscaini and Smith (2001) ecently advanced this liteatue on non-stategic sequential analysis by analyzing a continuous-time model in which the decision make can the vay numbe of expeiments in each peiod. Ou fomulation is also in continuous time, but we focus on the simple case with one expeiment pe peiod. 6

7 and Poteio (2009) fo stategic analysis of patial disclosue of eseach esults. In Heny (2009), phamaceutical ms ae wose o when thei eseach e ots ae not obseved by the egulato as they ae foced to do additional tests to convince him they ae not hiding any evidence. Ou setup is di eent in the sense that infomation is not vei able: in fact the possibility of hiding infomation hee educes eseach because of the cost of lying. This tuns out to be bene cial fo the egulato who wants to limit eseach at the lowe end. Finally, we do not allow ou pincipal to use monetay tansfes, in line with the liteatue on mechanism design without tansfeable utility; see Holmstöm (1977) and Alonso and Matouschek (2008), Amstong and Vickes (2010), and Taylo and Yildiim (2011). This appoach delives a numbe of impotant insights on the functioning of appoval pocesses that we obseve in a numbe of pactical settings whee, by and lage, tansfes ae actually not used. A complementay liteatue analyzes the poblem of optimal incentive povision fo innovation, seach, and expeimentation whee tansfes ae allowed; ecent papes in this aea ae Manso (2011), Lewis and Ottaviani (2008), Lewis (2012), Geadi and Maesti (2012), Höne and Samuelson (2012), and Halac, Katik, and Liu (2012). 2 Dug Appoval Pocess We pesent a bief oveview of the dug appoval pocess, past and pesent, in the US. This execise will guide ou theoetical analysis: we will both analyze the possible e ects of past egulations and conside potential consequences of cuent egulatoy e ots. The evolution of the legislation on dug appoval was a seies of eactions to esounding scandals. Pio to 1938, the ole of the US Food and Dug Administation (FDA) was mostly limited to peventing misleading statements on dug labeling. In 1937, a dug company developed a liquid pepaation that was not tested pio to maketing and contained a poisonous solvent. The dug killed ove a 100 people. In eaction, the 1938 Food, Dug and Cosmetic Act was swiftly passed. The main featue of this law is that it equied that eseach esults be submitted to obtain appoval fo the dugs, although the FDA had little powe to mandate futhe eseach if the initial evidence was unsatisfactoy. It was an impotant step: it intoduced the New Dug Application (NDA) necessay to obtain appoval, a pocedue that still exists today. 7 Howeve, the powe of the FDA still emained 7 The NDA had to include all clinical investigations, a full list of the dug s components and copies of both the packaging and labelling of the new dug" 7

8 limited. Fo instance it had only 60 days to examine the evidence and thee was no speci cation of the ules fo testing. A new scandal in 1962 highlighted the need fo egulation of the pocess of testing. A hypnotic known as thalidiomide was discoveed in Euope to lead to bith defects. It was not allowed the US, but seveal thousands of samples had been sent to US doctos who gave them to patients without mentioning it was expeimental, leading to a numbe of cases of a ected babies. In eaction, the 1962 Dug Amendments intoduced the pocess of dug testing as we know it. The main featues of the amendments can be summaized as follows: It put in place a system of pe-clinical testing noti cation so that egulatos could judge whethe it was safe to stat testing on humans It gave moe powe to the egulato to mandate eseach. As explained by Junod (2008), FDA was given the authoity to set standads fo evey stage of dug testing fom laboatoy to clinic. Howeve the law did not set vey stict legal standads fo appoval. The law equied that thee be substantial evidence that the dug be e ective. As pointed out in Junod (2008), altenative stonge language such as pepondeance of evidence o evidence beyond any easonable doubt could have been used. The cuent phase of egulation is anothe example of a eaction to a scandal, this time involving misepoting of evidence by ms, in paticula infomation on side e ects of dugs. A case in paticula, the allegation that fo seveal yeas Meck withheld evidence on advese e ects of its blockbuste dug Vioxx, has led to a ecent push to impose stonge disclosue equiements. The FDA Modenization Act of 1997 ceated the clinical tial egisty ClinicalTials.gov. The FDA Amendments Act of 2007 expanded the types of clinical tials needed to be egisteed and the amount of details that should be included. Some legislatos ae tying to push fo futhe expansions. 8 8 Fo example, medical jounals and egulatoy authoities have pushed fo ealy egistation of tials and fo disclosue of the esults obtained in the tials. 8

9 3 Model and Best Responses 3.1 Model To captue most of the featues of the inteactions between an agent and a pincipal, such as a phama m and the FDA, we conside the following model. A choice needs to be made between two altenatives, adoption A o ejection R. The bene ts deived fom these altenatives depend on the state of the wold! that can be eithe high H o low L. The payo fo playe i in state j if the choice is k is given by v i jk. We assume that the payo fom ejection is zeo fo all playes, egadless of the state. Futhemoe we assume that, fo any playe i, accepting a good poject povides positive payo s while accepting a bad one povides a negative one: v i HA > 0 and v i LA < 0. Fo convenience, we use the following log-likelihood paametization of beliefs = log P (! = H) P (! = L) ; so that the pobability that the state is high is given by e = (1 + e ). All playes shae a common pio 0. Given the estictions we imposed on the payo s, if playe i is foced to make a decision at belief, thee exists a theshold value (o standad) of the belief ^, such that A is chosen if > ^ and R is chosen if < ^. That value ^ solves e^ 1 + e^ v HA e^ v LA = 0 Reseach can be conducted to lean the value of the state. The aival of new infomation is modeled as a Wiene pocess d. The dift is detemined by the state. Speci cally, the pocess has positive dift and vaiance 2 if the state is H o dift and vaiance 2 if the state is L. Accumulating infomation ove a peiod of time dt costs c i dt, whee the cost of collecting infomation can vay acoss individuals. Finally, payo s ae discounted, so that if an altenative is chosen at date t it is discounted at ate i. Thee ae theefoe two costs associated with seaching fo moe infomation: the diect nancial cost and the oppotunity cost associated to the delay in the accual of the decision payo s. Suppose playe i undetakes eseach until time t. The accumulated infomation at date t is given by t. The log-likelihood atio of obseving t = in the two states is given by h log = 2 h 2 ; (1) + 9

10 whee h is the density of a standad nomal distibution. Accoding to Bayes ule, the log posteio pobability atio is equal to the sum of the log pio pobability atio and the loglikelihood atio. Thus, the posteio belief at time t is given by t = t (2) whee d 0 is a Wiene pocess with dift 2 2 = 2 if the state is H and and instantaneous vaiance 4 2 = = 2 if the state is L When the same playe i makes both the seach and appoval decisions, fo a belief that is close to i, thee may be a bene t of seaching fo moe infomation to make a moe infomed decision. This is a standad stopping time poblem: thee exists two values of, s and S (s S) such that: if < s the playe stops eseaching and ejects; if s < < S the playe conducts eseach; if > S the playe stops eseaching and appoves. It is immediate to chaacteize the utility function of the playe when 2 (s; S) whee u() = e dt E[u( + d 0 )] cdt: Following Stokey (2009, Chapte 5), stating in the intemediate egion, we let T be the st time the belief hits eithe s o S. The diect monetay cost of seaching is given by R T 0 ce t dt = c c e T. Once we de ne, as in Stokey (2009): (;!) = E[e T j(t ) = S;!] P [(T ) = Sj!] (;!) = E[e T j(t ) = s;!] P [(T ) = sj!]; the utility fo 2 (s; S) is given by c u() = v + P [! = H] HA + c + P [! = L] v LA + c (; L) c + P [! = H] (; H) c + P [! = L] (; L): (; H) The st line coesponds to the case whee the state is high and the uppe benchmak S is eached st. The second line is the case whee the state is low but the uppe benchmak is eached st, and so on. 10

11 3.2 Best Response Analysis We stat by chaacteizing the best esponses of the eseach poblem. Speci cally, fo a given value of the lowe standad s (esp. uppe standad S) we chaacteize the optimal choice of the uppe standad S = BR(s) (esp. lowe benchmak s = b(s)). This best esponse analysis allows fo a bette undestanding of ou poblem and will seve as a building block fo the next sections. We stat by chaacteizing b(s). Fo the moment we dop the subscipt i. Poposition 1 Fo a given uppe benchmak S: 1. The best esponse b(s) is independent of the cuent belief and is such that b(s) = S if S < ^. 2. The best esponse b(s) is deceasing in v HA, v LA and inceasing in c. 3. The length of the eseach inteval l(s) = S b(s) is inceasing in S and conveges to a nite value l when S conveges to +1, whee l is solution to v HA = (e g(l) 1) c. The st esult states that thee is dynamic consistency in the sense that the best esponse is independent of the cuent belief. It also states that b(s) = S fo values S < ^. This esult is natual, since when S < ^, appoval at S gives a negative value and the playe can guaantee himself a zeo payo, when S, by choosing s = S and imposing ejection. Fo S ^, the st-ode condition chaacteizing the best esponse (deived in the appendix) is given by: with 1 (s; S) > 0 and whee: V A (S) {z } = 1 (s; S) c= {z } bene t of gaining moe infomation nancial cost of eseach (3) V A (S) = es 1 + e S v HA e S v LA is the expected bene t fom appoval when the belief is = S (with V A (S) 0 if and only if S ^). 11

12 At the lowe benchmak s, the tadeo expessed by (3) is clea. Thee ae typically two costs associated with eseach: st the diect nancial cost, popotional to c= and second the cost of delaying the decision. At the lowe benchmak of eseach ejection yields a zeo payo. Thus thee is no cost of delay and the only cost is the nancial one. This expected cost has to be equal to the expected value of infomation which is popotional to V A (S), i.e., the value if the uppe standad is eached. Oveall this gives condition 3. The compaative statics then natually follow. Inceasing the cost c natually deceases eseach. On the othe hand inceasing v HA o v LA has the e ect of inceasing the value of infomation without a ecting the cost and thus deceases the lowe benchmak. Inteestingly, esult 1.3 indicates that the length of the eseach inteval, measued by S b(s) (an indiect measue of the quantity of eseach), is inceasing in S. The intuition is the following: fo a given length l between s and S, the expected bene t V A (S) is highe fo lage values of S and the expected cost of moving fom s to S is lowe since thee is a highe pobability that the dift will be positive. Thus, if fo a cetain value of S, the optimal choice is a length l(s) = S b(s) of the eseach inteval, fo highe values of S, the inteval will be lage. This popety is visible in Figue 1 whee we plot both b(s) and BR(S). As indicated in esult 1.3, at the limit, when S goes to in nity, the value of l(s) conveges to l such that v HA = (e g(l) 1) c. This limit value depends only on c= and v HA : when S goes to in nity, the playe is sue the state is good and at the lowe benchmak b(s) he is indi eent between stopping immediately and getting a zeo payo o incuing the cost of eseach and obtaining v HA when the uppe benchmak is eached. At the uppe benchmak, the tadeo is moe inticate since the cost of eseach now has the two components mentioned above: the diect cost and the cost of delaying the decision. Oveall 12

13 we nd: Poposition 2 Fo a given lowe benchmak s 1. the best esponse BR(s) is independent of the cuent belief 2. the best esponse BR(s) is deceasing in v HA, v LA and c. 3. the length of the eseach inteval l(s) = BR(s) s is deceasing in s and conveges to a nite value l when s conveges to 1, whee l is solution to v LA = (e g(l) + 1) c The st ode condition chaacteizing the best esponse to a given value of s can be expessed in the following way (whee (s; S) > 0, 2 (s; S) > 0 and (s; S) > 0). (s; S) v {z LA } = (s; S) V A (S) {z } + 2 (s; S) c= {z } bene t of infomation cost / bene t of delaying decision nancial cost of eseach (4) Fo the intepetation of these conditions we distinguish between the case whee V A (S) 0 (i.e S > ^) and the case V A (S) < 0. Conside the st case, that occus when s is not too low. At the uppe benchmak S the cost of eseach is composed of the diect nancial cost and of the cost of delaying the decision, which is popotional to V A (S). Infomation has value since it can lead to avoiding the negative payo v LA if the state is in fact low. Condition (4) e ects this tadeo between cost and value of infomation. In the second case, when s is vey low, the tadeo is di eent: fo these values, it will be too costly in tems of expected cost of eseach, to choose a value of S > ^ p. At the uppe benchmak S, the playe will thus incu a loss V A (S) < 0. Reseach then has value to ty since it can allow to each the lowe benchmak whee a zeo payo can be obtained. Thus, in these cases, at the uppe benchmak S the loss V A (S) has to be equal to the expected cost of eseach needed to each the lowe benchmak. Finally, esult 2.3 indicates that the length of the eseach inteval deceases with s. As stated above, when s is small, the pupose of eseach at the uppe benchmak S is to avoid incuing the loss V A (S) by pefoming eseach to each s and get a zeo payo. When s is small, the loss is paticulaly lage and futhemoe, the expected time cost to each s will be smalle, since thee ae moe chances that the dift is negative. This popety is epesented in Figue 1. At the limit, l conveges to a value l that depends only on v LA and c=. The intuition is simila 13

14 to that of 2.3. The playe is sue that the state is bad and at BR(s), he is indi eent between getting the sue loss cost popotional to c=. v LA and seaching in the hope of eaching the lowe benchmak, with a These best esponses ae a natual building block fo the est of ou agument. If the same playe was making both the eseach and appoval decisions, his optimal choice (s i ; S i ) would be chaacteized by the intesection of the best esponse cuves. Howeve in pactice these decisions ae typically made by di eent agents and these stategic inteactions ae the focus of ou pape. To claify the exposition of the est of the pape, we add moe stuctue on how the pefeences of agent and pincipal ae misaligned. We will focus on the leading case whee the agent does not bea the entie social cost of a wongful adoption, so that the payo s of adoption in the low state satisfy vla a > vp LA. Fo instance, in the application to dug appoval the key concen is that the phamaceutical company does not fully compensate patients who su e fom taking an unsafe dug because of the di culty in identifying these individuals and the company s ability to shelte fom liability (the judgement poofness poblem). Accoding to the pevious compaative statics, this implies that the agent pefes to stop ealie at the uppe end but to conduct moe eseach at the lowe end. The compaison in the high state is less obvious. It seems easonable to think that v a HA > vp HA, i.e.., that the submitte has moe at stake than society at lage. Fo instance an autho that has a pape accepted gets the full pivate bene ts fom that decision, but does not take into account the negative extenality he imposes on othe authos. In the case of a pivate m conducting eseach, this can be less obvious. Indeed, it is often thought that a m cannot captue the full social bene t fom an innovation; see fo instance Bloom, Schankeman, and Van Reenen (2012). Of couse the facto mentioned above, that goes in the othe diection, is still pesent: the m that innovates, in the case of non adical innovations, takes some po ts away fom the cuent maket leade, an e ect typically not intenalized. Ou esults fo the leading case hold povided the extenality associated to adoption in the high state is eithe negative o positive but lowe than the negative extenality associated to adoption in the low state: v a HA + va LA > vp HA + vp LA.9 Given this type of con ict in pefeence, the bliss point of the pincipal (s p; S p) and of the agent (s a; S a) ae such that the agent conducts moe seach at the lowe end s a < s p and less seach at the uppe end S a < S p as epesented in Figue 2. One popety is notable and will 9 Thee is an additional facto speci c to the phamaceutical industy that can push v a HA above v p HA. Given dug uses typically do not pay diectly but ae eimbused, phamaceutical companies might be able to obtain pivate bene ts highe than social bene ts. 14

15 pove useful in the est of the pape: the bliss point coesponds to the maximum of the uppe best esponse and the minimum of the lowe best esponse. 4 Appoval Regulation In pactice, in all the applications we have in mind, the same playe does not contol the full eseach pocess and at the same time make the appoval decision. As descibed in section 2, in the case of dug egulation, sepaating these oles was pecisely the pupose of the 1938 law, that intoduced an appoval equiement befoe maketing. A natual way of thinking of the e ects of such a elatively weak egulation is that the m conducts eseach and, at some point submits the evidence to the pincipal who, based on the evidence, makes a decision to appove o wait. The 1938 law did not give the pincipal powe to mandate futhe eseach. Thus, in a subgame pefect equilibium, the pincipal appoves any dug when the evidence is above p (i.e. any evidence that gives the pincipal a positive expected bene t). With small con icts of inteest (vla a = v p LA ), the eseach inteval is then the st best of the agent, (s a; S a). With intemediate con ict of inteest s.t. B a (b a (^ p )) < ^ p, the agent seaches in (b a (^ p ) ; ^ p ). While with lage con ict of inteest such that ^ p > S de ned as the lowest S above ^ p such that S = b a (S), agent does not do any eseach. The 1962 Amendments gave the futhe powe to the pincipal to mandate eseach. examine in Section 4.1, how this exta powe a ects the outcome of the game. We then show in Section 4.2 that committing ex ante to an appoval standad can impove the payo of the designe. This was not the path chosen by the lawmakes, who instead chose to oganize the egulation as a sequential pocess that we examine in Section 4.3. Thoughout this section we will maintain the assumption that the egulato cannot misepot the infomation he obtains, an assumption we elax in Section Nash Equilibium The e ect of ganting the pincipal the powe to mandate eseach (as in the 1962 Amendments) in he inteaction with an agent who initiated the eseach pocess, is natually captued by the following baseline model. In each peiod t, agent and pincipal move sequentially. Fist, the agent chooses between thee actions eseach R a, submit S a o wait/withdaw W a. Second, if the agent submits S a, the pincipal chooses between eseach R p, appove A p o wait W p. Reseach is the peiod s outcome if eithe the agents chooses eseach R a o the agent chooses submit S a and the We 15

16 pincipal chooses eseach R p (in that sense the pincipal can mandate eseach). Appoval A is the peiod s outcome if the agent chooses S a and the pincipal A p. Finally withdawal W is the peiod s outcome if the agent chooses W a o the agent chooses to submit S a and the pincipal chooses W. We assume that the cost of eseach entes symmetically in the agent s and pincipal s utilities egadless of who conducts the eseach. In the case of the FDA, the pincipal can mandate eseach but integates this eseach cost in he welfae function, since these costs e ect the costs to patients. We show in the appendix that the outcome of all Makov Pefect Equilibia of the game above, with as the state vaiable, coespond to what we call the Nash equilibium solution and denote (s N ; S N ). This equilibium is at the intesection of the best esponse cuve of the agent to the uppe benchmak b a (S) and the best esponse cuve of the pincipal to the lowe one BR p (s). In othe wods, in this setting, the pincipal contols the uppe standad S while the agent contols the lowe standad s. We have: Poposition 3 Thee exists a unique Nash equilibium such that: 1. the pincipal conducts less seach at the uppe end and the agent less seach at the lowe end: Sa < S N < Sp and s p > s N > s a; 2. the length of the eseach inteval is lage than fo the stand-alone poblems: S N s N > max(sp s p; Sa s a). The stategic inteaction between the agent and the pincipal of couse a ects the eseach decision compaed to the non stategic benchmak. These changes can be decomposed in two e ects. Fist, thee is an e ect on the extensive magin: the ange of values of fo which eseach is conducted changes. Second, thee is an e ect on the intensive magin: the length of the eseach inteval is a ected. Result 3.1 above efes to the extensive magin. Compaed to the pincipal s st best, in the Nash solution, moe eseach is conducted at the lowe end and less at the uppe end. The logic of the esult is clea. Since both the agent and the pincipal now contol only one benchmak, the value of infomation is deceased: the pincipal conducts less eseach at the uppe end and the agent less eseach at the lowe end then in thei espective stand-alone poblems. These ideas ae illustated in Figue 1. The solid lines coespond to the best esponse S to a given s and the dotted ones to the best esponse s to a given S. The equilibium (s N ; S N ) is at the 16

17 Figue 1: Best eplies, the Nash equilibium, the commitment solution, and compaison with the pincipal s and the agent s unconstained solutions. intesection of the lowe best esponse cuve b a (S) of the agent and the uppe best esponse cuve of the pincipal BR p (s). The gue illustates the fact that S N < Sp and s N > s a. Indeed, as the lowe benchmak s moves away fom s p, the pincipal s best esponse deceases (Sp being the maximal value), since the value of infomation is deceasing. Result 3.2 above efes to the intensive magin. Supisingly, intoducing stategic inteactions inceases the intensity of eseach (the length of the eseach inteval is inceased). This uns contay to the classical intuition that tends to nd the opposite e ect (fo instance Stulovici 2010). To undestand this esult, conside the agent s poblem. The pincipal conducts moe eseach at the uppe end than the agent would like him to do (S N > Sa). Thus, when the agent consides the choice of the lowe benchmak, expessed in equation (3), his incentives to seach ae highe: if he eaches the uppe benchmak, he gets a highe value (V A (S N ) > V A (Sa)) and moeove he eaches it faste in expectation since the belief that the state is H is highe fo lage values of S. These two e ects (undelying the esult of Poposition 1.3) imply that the seach inteval is lage S N s N > Sa s a. 10. We now discuss the payo of the pincipal and the agent in the Nash Equilibium solution. These values ae plotted as a function of in Figue 1. The key message is that the utility of the pincipal can be negative at the Nash equilibium solution. Conside a belief s N < < s p: if the 10 A simila logic leads to the esult S N s N > Sp s p. 17

18 pincipal was picking both benchmaks alone, he would not be able to obtain a positive utility and he would thus choose s p >, in othe wods immediate ejection, to guaantee himself a zeo payo. In the Nash equilibium solution, this is not an option since the agent contols the lowe payo and actually sets it below. Poposition 4 At the unique Nash equilibium: the agent gets a positive payo fo all values of the pincipal gets a negative payo fo 2 [s N ; b p (S N )], In pactice, it seems natual that the pincipal would ty to achieve a highe payo by committing ex ante to a cetain behavio. The most natual fom of commitment, that we conside in the next section, would be to commit ex ante to a cetain standad of appoval. As highlighted in section 2, this was not the appoach chosen in the 1962 Amendments, who chose athe weak legal language in tems of standads. The legislato chose athe to commit to pefom the evaluation in a pede ned numbe of ounds, something we conside in section Commitment: Stackelbeg Solution We study in this section the case whee the pincipal has the ability to commit to an appoval standad that depends only on the cuent state of knowledge (and not on the path o time taken to get thee). Clealy, if the pincipal could commit to an appoval ule that could be conditioned on the entie path, the pincipal would be able to obtain the unconstained optimal solution s p; S p. Such commitment, howeve, might be di cult to achieve in pactice so we conside a simple and moe ealistic commitment to appoval ules that depend only on the cuent state of knowledge with the following cuto fom: appove if and only if S C. This is the type of commitment, although weak, that was intoduced in the 1962 law with the tems signi cant evidence. We now chaacteize the path of the commitment solution; see Figue fo an illustation. Dynamic consistency no longe applies: the optimal choice of commitment by the pincipal depends on the initial belief as descibed in the following esult. We use the notation b 1 a the uppe invese function constucted by inveting b a fo S > S a. fo Poposition 5 In the Stackelbeg equilibium with commitment by the pincipal, thee exist beliefs ~ 2 (s p; b p (S N )) and 2 (S N ; S p) such that: 18

19 1. If the initial belief is such that < ~, the pincipal chooses a blocking commitment inducing no eseach: If s a, any commitment above is pat of an equilibium: S c () 2 (; +1); If s a < < ~, any commitment above b 1 a () is pat of an equilibium: S c () 2 (b 1 a (); +1). 2. If 2 (~; S N ), the pincipal chooses an inteio commitment S c () deceasing in. Thee is a discontinuity in commitment at ~: S c (~) < b 1 a (~). 3. If > S N, the pincipal chooses an appoval commitment S c (). Fo low values of the initial belief, the optimal commitment is what we call a blocking commitment: the pincipal commits to an uppe benchmak that induces the agent to do no eseach. If s a, the initial belief is so low that even the agent would not want to do any eseach, egadless of the commitment. Fo slightly highe, the commitment to be blocking, i.e induce the agent to do no eseach, needs to be above b 1 a () (by de nition of b a (S)). Note that this minimum blocking commitment is an inceasing function of. When the initial belief, stats to be su ciently favoable, blocking eseach by the agent by committing to ejection becomes too costly and thee is a pefeable inteio commitment. This happens at belief ~, which is the belief at which the zeo iso-utility cuve of the pincipal is tangent to the lowe best esponse cuve of the agent: if the pincipal chose his pefeed 19

20 point on the best esponse cuve of the agent b 1 a (~), he would get a zeo utility and he is thus indi eent. If the belief is above that value, an inteio commitment is stictly pefeable. At this point thee is a discontinuity in the commitment: thee is a discete downwads jump fom a blocking commitment to the optimal inteio commitment. Poposition 5, indicates that the value ~ is necessaily in the inteval (s p; b p (S N )). obvious that it has to be above s p, since fo beliefs lowe than s p, even when the pincipal has full contol, he cannot obtain a positive utility. On the contay, at = b p (S N ), the pincipal obtains a zeo payo at the Nash equilibium solution and could do stictly bette by committing to a di eent point on the agent s lowe best esponse cuve. The belief fo which the pincipal is indi eent between inteio commitment and the blocking commitment (yielding zeo payo ) thus has to occu ealie. When the initial belief is vey high, the optimal choice fo the pincipal is to chose immediate appoval, what we call an appoval commitment. This occus fo beliefs below S p (the point whee the pincipal would chose immediate appoval if in full contol), since the pincipal cannot contol the uppe benchmak. In fact, as indicated in Poposition 5, fo beliefs above S N immediate appoval is optimal. In tems of welfae, it is clea that the pincipal can always do weakly bette by committing. In fact, the following poposition indicates that she does stictly bette wheneve the initial belief is in (s a; S N ). This esult natually follows fom the pevious discussion. Fist, the blocking commitment is chosen fo beliefs whee the Nash equilibium gives negative utility to the pincipal, so that commitment is stictly pefeable. Second, when an inteio commitment is chosen, the pincipal s optimal commitment is stictly above S N indicating that a bette commitment exists. It is Poposition 6 In the Stackelbeg equilibium, the pincipal s payo is: weakly highe than the payo in the Nash equilibium fo all values of ; stictly highe fo 2 (s a; S N ). The fact that the inteio commitment is stictly above S N fo S N e ects the tadeo between two e ects: A second-ode negative diect e ect: Holding xed the agent s stategy s, an excessive amount of eseach is induced at the uppe end, which induces a loss fo the pincipal. This 20

21 loss is clealy second ode by the envelope theoem because we stat fom the pincipal s optimal choice of S holding xed the agent s choice of s. A st-ode positive stategic e ect: The agent s stategic esponse of the incease in S is to incease s given that the agent s best eply is upwad sloping in the elevant ange stategies ae stategic complements in the teminology of Bulow, Geanakoplos, and Klempee (1985). Intuitively, the inceased loss of contol at the uppe end futhe educes the agent s value of infomation at the lowe end. Given that the agent s choice of s at the lowe end was oiginally lowe than the pincipal would have liked, this incease in s bene ts the pincipal. This is st-ode e ect because the envelope theoem does not apply given that the agent, not the pincipal, chooses s. The nal essential consideation is the e ect of commitment on both the extensive and intensive magins of eseach discussed in the pevious sections. Poposition 7 In the Stackelbeg equilibium : the extensive magin of eseach is deceased compaed to the stand-alone pincipal outcomes: (~; ) (s p; Sp) the intensive magin of eseach is inceased compaed to both the nash equilibium and the stand-alone pincipal outcomes: fo 2 (~; ), S c b a (S c ) > max(s N b a (S N ); Sp s p) Poposition 7 suggests that, in the Stackelbeg solution, thee ae less instances whee some eseach is conducted, but fo the values whee this is the case, moe eseach will be pefomed. Thee ae two instances whee no eseach is pefomed in the Stackelbeg solution: fo low values of, the pincipal chooses a blocking commitment and fo high values he induces immediate appoval. The st esult is then due to the fact that the pincipal, since he does not contol the lowe benchmak, wants to pevent eseach fo moe values of. The second esult echoes the esult on the extensive magin fo the Nash outcome: fo beliefs such that eseach is conducted, moe eseach will be pefomed. 4.3 Commitment: Sequential Reseach In pactice a commitment is not always easy to achieve. In fact, as stated ealie, the 1962 law explicitly chose not to commit to a stict standad. As suggested in the pevious section, one of 21

22 the main eason could be that the optimal level of commitment is speci c to the baseline state of knowledge, which can vay acoss types of dugs, and thus thee is no unifom standad that can be applied. Of couse, the close inteaction between the m and the egulato could allow fo individualized commitments, but even those ae not easy to cedibly make. A di eent way of committing is in the way eseach is oganized. Often the communication between the agent and the pincipal is oganized in a numbe of ounds. This was the appoach chosen by the 1962 law that oganized the inteaction between the m and the egulato in a well de ned seies of clinical tials. We conside in this section a model whee the inteaction is oganized in two ounds of inde nite length. Fist the agent conducts eseach and at some point decides to tansfe this infomation to the pincipal. The pincipal then decides how much additional eseach to pefom befoe making the appoval decision. 11 We maintain the assumption that the agent caes about the eseach cost of the pincipal. This assumption is sensible in the application to the FDA that can mandate eseach. It is less so fo othe applications and we conside those in section 7. We denote (s seq ; S seq ) the choice of the agent, whee seq stands fo sequential. When the agent submits the infomation to the pincipal, the pincipal pefoms eseach and makes the appoval decision as in the stand-alone case since thee will be no moe inteaction with the agent: the pincipal will then pefom eseach if 2 (s p; Sp). Thus the agent will neve want submit befoe Sp is eached because the agent beas the full eseach cost egadless of who pefoms the eseach but would lose fom submitting to the pincipal befoe Sp is eached because then pincipal would cay too little eseach at the lowe end in the eyes of the agent. Futhemoe, at the lowe end the agent chooses the best esponse to Sp: s seq = b a (Sp). These esults ae summaized in the following poposition: Poposition 8 In the sequential poblem: 1. In equilibium the agent conducts eseach wheneve is in (b a (Sp); Sp), abandons fo lowe values and submits the evidence fo highe ones 2. If 2 (s N ; ~), the pincipal obtains a highe payo in the sequential than in the Nash equlibium 11 In most applications, thee could be additional ound but we will focus on the one ound case without loss of geneality of the message. 22

23 3. If 2 (^; Sp), the pincipal obtains a highe payo in the Nash equlibium than in the sequential 4. The length of the eseach inteval is lage in the sequential than in the Nash o in the stand-alone poblems The Nash equilibium, the Stackelbeg commitment solution consideed in section 4.2 and the sequential eseach pocedue coespond each to a di eent point on the best esponse cuve of the agent, b a (S). Clealy, the Stackelbeg point esults in highest expected payo fo the pincipal. Results 8.2 and 8.3, indicate that the compaison between the Nash and sequential outcomes is potentially ambiguous. This suggests that the type of commitment put in place though the 1962 law was not necessaily welfae enhancing, in paticula in cases whee the initial belief is quite favoable as in 8.3. Does the pincipal pefe the Nash equilibium outcome o the sequential eseach outcome? Compaed to the Nash equilibium, the sequential pocedue esults in moe eseach at the top and less eseach at the bottom. The pincipal is not necessaily bette o, as illustated in Figue 2. On the one hand, the pincipal bene ts fom eduction of s and incease in S along p s BR p (s); the movement towad Noth-East along BR p (s) fom (s N ; S N ) to (b a (S p ) ; BR p (b a (S p ))) inceases the pincipal s expected payo. On the othe hand, the pincipal loses fo additional incease in S; the upwad movement fom (b a (S p ) ; BR p (b a (S p ))) to (b a (S p ) ; S p ) esults in a eduction in the pincipal s expected payo. The dashed indi eence cuve coesponds to a setting in which the pincipal pefes the sequential solution to the Nash equilibium; the opposite anking holds with the continuous indi eence cuve. As can be seen gaphically, a su cient condition fo the pincipal to pefe the sequential solution to be Nash equilibium is that S C > Sp = S seq ; othewise the anking is ambiguous. In the egion whee the blocking commitment is the optimal Stackelbeg commitment ( 2 (s N ; ~)), the pincipal pefes sequential commitment to the Nash outcome because sequential commitment esults in the same outcome as the Stackelbeg commitment in some cases and limits the amount of eseach pefomed in othes. When instead 2 (; Sp), the optimal commitment is to appove immediately and this is also the outcome with the Nash solution, wheeas additional eseach is pefomed unde the sequential commitment thus leading to a lowe payo fo the pincipal. 23

24 Figue 2: Welfae compaison between the Nash solution and sequential eseach. 5 Misepesentation of Infomation The new phase of egulation has stated focusing on the egulation of the disclosue of clinical tial esults. The alleged withholding of negative esults by phamaceutical companies in the ecent cases of Vioxx (an anti-in ammatoy dug poven to incease the isk of cadiovascula events) o Paxil (an anti-depessant that could incease the suicide ates among childen) geneated majo upoa and lage demands fo compensation. Withholding infomation has a potential cost fo the m itself: in the case of Vioxx, Meck paid ove 4.85 billion dollas fo settling individual complaints fom patients. In 2011, it ageed to plead guilty and pay 950 million to the fedeal govenment to settle the ciminal and civil chages led against it. These costs seem to be an inceasing function of the size of the misepesentation. It is because Meck was shown to have withheld evidence that the penalties wee of that magnitude. A lage lie makes it easie fo the plainti s to win thei case in cout. To captue such situations, we enich the model and assume that the agent who collects the evidence can misepot it at no cost. 12 Howeve, if the state tuns out to be low the agent expects a ne F. The pobability of obtaining this sentence depends on the size of the misepoting. If the agent has collected evidence showing that the state is and conveys infomation 0 the pobability of being convicted is given by P ( 0 ) and we denote the oveall expected sentence C( 0 ) = F P ( 0 ) whee C (i.e.., P ) is inceasing and C(0) = C 0 (0) = 0. We concentate on the commitment case as in Section 4.2 whee the pincipal can commit to an appoval standad, that we denote S M (M stands fo withholding). The ule is thus: appove 12 In ou model, evidence comes in in nitesimal amounts so that the agent can fo any state, always hide a su cient quantity of negative esults to be able to pesent vei able evidence consistent with that state. 24