The Impacts of Price Controls on the Performance of the Pharmaceutical Industry

Transcription

1 The Impacts of Prce Controls on the Performance of the Pharmaceutcal Industry Darren Flson * Claremont Graduate Unversty February 27, 2007 * Send correspondence to Darren Flson, Assocate Professor of Economcs, Claremont Graduate Unversty, 160 E. Tenth St., Claremont, CA Phone: (909) Fax: (909) Emal: Darren.Flson@cgu.edu.

2 The Impacts of Prce Controls on the Performance of the Pharmaceutcal Industry Abstract: Ths paper ntroduces a dynamc equlbrum model of the research-based pharmaceutcal ndustry and parameterzes t usng ndustry facts. In the model, mposng prce controls n the U.S. reduces frm value, R&D, the flow of new drugs, and the net present value of consumer welfare n the U.S. and globally. Removng prce controls n one or more non-u.s. countres ncreases frm value, R&D, the flow of new drugs, and consumer welfare globally, but reduces consumer welfare n the countres changng ther polces. The results explan why the U.S. ressts adoptng prce controls even whle non-u.s. countres resst abandonng prce controls. JEL Codes: C61: Dynamc Computatonal Models; C73: Dynamc Games; D61: Welfare Analyss; I18: Health Polces; L65: Pharmaceutcal Industry; O38: Innovaton Polces Keywords: nnovaton, prce caps, technologcal change, nnovaton polcy 1

3 Most countres mpose some form of prce controls on prescrpton drugs. To date, the U.S. has ressted polces that explctly nterfere wth market prcng, but there s ongong debate about whether U.S. polcymakers should take steps to reduce prces, ether through drect prce controls or ndrect means such as permttng consumer mports. Many commentators have argued that prce controls affect ncentves for R&D and ultmately the flow of new drugs, but to date there s lttle formal analyss that quantfes the expected effects of alternatve polces. Quantfcaton s necessary to assess whether the benefts of lower prces outwegh ther costs. Would the U.S. beneft by adoptng prce controls? Would other countres beneft by abandonng controls? Ths paper uses a statonary nfnte-horzon dynamc equlbrum model of the research-based pharmaceutcal ndustry to quantfy the benefts and costs of prce controls. The structural model facltates an economc welfare analyss. Prevous efforts to analyze the mpacts of nternatonal prce controls have employed rch data sets but have not used behavoral models to gude the analyss (Danzon and Furukawa, 2003; Brouwers, Slversten, and Wolff, 2004; U.S. Department of Commerce, 2004; Danzon, Wang, and Wang, 2005; Gaccotto, Santerre, and Vernon, 2005, Vernon, 2005). I estmate the mpacts of prce controls on the flow of new drugs, consumer welfare, frm value, and other ndustry performance measures. The model s parameterzed to match exstng emprcal estmates of R&D costs, attrton rates, the dstrbuton of product values, ndustry sales n the U.S. vs. the rest of the world (lmtng attenton to major markets), the trend n sales over a product s lfe cycle, the annual flow of new molecular enttes, and other ndustry facts. Thus, the model yelds a realstc depcton of the current envronment, and ts behavoral assumptons make t sutable for polcy analyss. Consumers maxmze utlty. Frms are forward-lookng value-maxmzng agents that respond optmally to polcy changes. Prces each perod are determned by Nash equlbrum 2

4 (subject to prce caps where caps are mposed), and decsons to begn research programs or abandon canddates n development are Markov-perfect Nash equlbrum choces. These features dffer from prevous dynamc models of the research-based pharmaceutcal ndustry that rely heavly on reduced forms for consumer demand (such as smple lnear demand functons, as n Hughes et al. 2002), assume varous ad hoc behavoral rules that may not persst after substantal polcy changes (such as the assumpton that frms determne R&D polces usng R&D-to-sales targets rather than forward-lookng value-maxmzaton rules, as n Grabowsk and Vernon, 1987), and do not emphasze equlbratng forces that nfluence behavor n the short and long runs (as n Flson and Masa, forthcomng). The model bulds on the semnal approaches of Hopenhayn (1992) and Ercson and Pakes (1995). What happens f the U.S. adopts prce controls lke those n the rest of the world? Frms reduce research substantally, and n the long run, the flow of new drugs falls by approxmately 75%. Industry frm value falls approxmately 80%. The full mpact takes over a decade to occur, because most late-stage canddates n the ppelne reman proftable under the polcy change. The opton to pursue a late-stage canddate s usually well n the money because many hurdles have been overcome, many R&D costs are sunk, and the prospect of obtanng profts s more near. Consumer welfare n the U.S. rses for the frst twelve years and falls thereafter. Lower prces yeld short run benefts, but the harmful effect of the reduced flow of new drugs outweghs the prce effect n the long run. The net present value (NPV) of consumer welfare falls n the U.S. and n the rest of the world by over $13 trllon year 2000 dollars. In the current envronment, the prospect of hgh U.S. profts encourages nnovaton that consumers everywhere beneft from. The model explans why non-u.s. countres resst abandonng prce controls even though t s optmal for the U.S. to resst adoptng prce controls. I show that f one or more non-u.s. 3

5 countres abandon prce controls, R&D, the flow of new products, frm value, and consumer welfare n the world as a whole all rse. However, consumer welfare falls n the countres that abandon controls. Ths last result helps explan why non-u.s. countres resst abandonng prce controls. The result mght also explan why partcular U.S. states have attempted to crcumvent U.S. federal government polces on prcng and mportaton, whle the federal government has tended to be more of a supporter of market-based prces. Essentally, small subgroups n the populaton can beneft by free rdng on the U.S. states wllng to support market prces, but the U.S. as a whole benefts from mantanng market prcng everywhere. Interestngly, the result that global consumer welfare rses when non-u.s. countres adopt market prcng suggests that, n prncple, other countres could compensate ther consumers for the welfare losses they would ncur from market prces. The lack of global nsttutons to accomplsh such transfers, along wth the ntrnsc dffcultes assocated wth commttng to polces and wealth transfers that nvolve generatons of consumers far n the future, ensure that countres other than the U.S. beneft by mantanng ther nterventonst polces. Thus, the world as a whole remans n a poltcal equlbrum n whch non-u.s. countres free rde on the U.S. II. The Model The model has several therapeutc classes and dfferent regons wth dfferent polcy regmes. Tme s dscrete, and there s an nfnte horzon. Each perod, opportuntes for ntatng new research programs arse, and frms choose whether to pursue these opportuntes or not. Some programs yeld canddates for development, and some canddates eventually yeld new products. New products have patent protecton, but patent protecton eventually expres and genercs enter the product market. In equlbrum, generc versons of older products typcally co-exst wth newer branded products, as n realty. 4

6 The unt of tme s a sx-year perod. As Flson and Masa (forthcomng) show, even extremely severe reductons n ndustry proftablty do not mpact the flow of new drugs for over fve years, because frms optmally keep ther canddates n late stages of development. Gven ths, a sx-year perod does not dmnsh the model s ablty to capture the mpacts of the polcy changes I consder. DMas, Hansen, and Grabowsk (2003) show that t takes 142 months to develop a new drug, whch I approxmate wth two sx-year perods; the frst perod focuses on research and the second on development. Hughes et al. (2002) show that new drugs typcally experence patent expraton and generc entry by year twelve of market lfe and then co-exst wth the generc for a tme. I approxmate ths by assumng that new drugs lve for three sx-year perods; n the thrd of these they co-exst wth a generc. The generc potentally outlasts the branded drug, and t exts only f another superor generc replaces t. Therapeutc Classes, Regons, Consumer Choce, and Demand The model s therapeutc classes dffer by R&D costs, the growth rate n opportuntes for mprovng qualty, consumer prce senstvtes, and sze of the patent populaton. In equlbrum, dfferent classes have dfferent R&D portfolos, products, genercs, prces, levels of sales, and profts. For smplcty, events n one class have no effects on events n other classes; therapeutc classes are dstnct submarkets n consumpton, producton, and R&D. For most realworld classes, ths s reasonable (the market for cholesterol-lowerng drugs, for example, s ndependent of the market for cancer-related drugs and drugs n other classes). The number of patents requrng medcne each perod s constant over tme wthn each class. Denote the number of patents n class k each perod by n. Patents are dspersed k geographcally nto four regons: n k 4 = nkr r= 1. Regons vary by ncome and by prcng polces. Regons 1 and 2 have hgh mean ncome and regons 3 and 4 have low mean ncome. Regons 1 5

7 and 3 have market-based prcng and regons 2 and 4 have prce caps (polcy makers mpose an upper bound on prces). The regons dffer only n these ways; all products are assumed to be avalable everywhere. 1 In the base case, regon 1 s the U.S., regon 4 s the rest of the world (ROW), and regons 2 and 3 have no one n them. Other polcy regmes nvolve reassgnng populaton from one regon to another. Each therapeutc class can have zero or more branded drugs n each age category: 1, 2, and 3. There s also always a generc prced at margnal cost. For smplcty, margnal cost s assumed to be constant across products, classes, and tme. The generc plays the role of the outsde opton n the demand model. If a consumer needng treatment does not buy one of the branded drugs, the consumer buys the generc. Demand s derved from a dscrete choce model. Each patent n a class n a perod chooses one of the branded drugs or the generc and buys one unt of the chosen product. Insttutonal features of the market for prescrpton drugs are suppressed, and I mplctly assume that, through ther separate actons, ntermedares such as physcans, employers, health mantenance organzatons, nsurance companes, pharmaceutcal beneft managers, and pharmacsts collectvely help consumers maxmze ther utltes and consder both the qualty and prce of the drugs consumed. Gven that the analyss focuses on ndustry aggregates, not on ndvdual choces per se, ths s a reasonable smplfcaton. Detalng and other promotonal actvtes are also suppressed. The model smplfes prcng and packagng, too. Each drug n the model has a standard unt and a prce for that unt, and dfferences between hosptal and drugstore prcng and prce heterogenety wthn a regon are suppressed. 1 In realty, prce controls may also contrbute to launch delays (Danzon, Wang, and Wang, 2005), but the sx-year perod of the model cannot easly accommodate the emprcal dfferences n launch tmes across regons, whch, condtonal on launch occurrng at all, are typcally around one year. 6

8 For now, focus on a sngle perod; I develop the dynamc aspects of the model below. Branded drugs n a gven class dffer by ther qualty, how recently they have been ntroduced, and ther prce. Consder consumer n regon r. Consumer s utlty for drug j n class k s U = β θ γ A α p + ε (1) j j j jr j where θ j s the qualty of drug j, A j s a postve dsutlty of newness term that allows for resstance n adoptng new drugs 2 (ts level s determned by the age of the drug), and p jr s the prce of drug j n regon r. 3 The parameters β, γ, and α are ndvdual-specfc taste parameters. Thus, the model allows for ndvdual taste heterogenety that has been shown to be mportant n recent econometrc studes of demand (Berry, Levnsohn and Pakes, 1995; Petrn, 2002). Fnally, ε j s an dosyncratc taste shock that allows for the fact that dfferent ndvduals react dfferently to dfferent drugs n terms of therapeutc benefts and sde effects. Consumer s utlty for the generc n class k s U0 βθ0 αc ε 0 = + (2) where θ 0 s the qualty of the generc and c s the margnal cost of producton. Under the standard assumpton that the taste shocks are type 1 extreme value, the probablty that consumer n regon r chooses drug j n class k s: 2 Several studes establsh that sales of new pharmaceutcals begn low and grow over many years (Lu and Comanor, 1998). Ths pattern n sales occurs even though manufacturers often employ penetraton prcng prces rse over many years so the pattern n sales s not due to prce skmmng. The leadng theoretcal explanatons for the patterns n sales and prces emphasze consumer and physcan resstance to adoptng new drugs because of rsk averson and the lack of knowledge about the new products. Informaton provson and learnng that occurs over tme causes the trends n sales and prces (Bhattacharya and Vogt, 2003; Crawford and Shum, 2005). To ease the computatonal burden, I do not explctly model learnng. Instead, I smply assume that consumers resst adoptng new drugs. In the absence of such resstance, sales and prces of new drugs n the model typcally peak n the perod of ntroducton and then fall over tme as hgher-qualty competng drugs are subsequently ntroduced. Y Y 3 An equvalent formulaton s U = β θ γ A + α ( Y p ) + ε, where s consumer s ncome, but j j j jr j drops out of the choce probabltes and the comparsons of consumer welfare, so for smplcty I exclude t here. As I dscuss below, I assume that prce senstvtes (the α s) depend on ncome, so ncome stll affects choces. 7

9 µ jr exp[ βθ j γaj αpjr] = exp[ βθ αc] + exp[ βθ γ A α p r] 0 j j j j J k (3) where J k s the set of branded drugs avalable n therapeutc class k. Smplfy ths expresson by dvdng top and bottom by exp[ β θ 0 α ] to obtan c µ jr = exp[ β( θ j θ0) γaj α( pjr c)] 1 + exp[ β ( θ θ ) γ A α ( p c)] j J k j 0 j jr (4) Note that the choce probabltes are now expressed as functons of the qualty of the branded drugs relatve to the qualty of the generc, the dsutlty of newness terms, and the markups m jr = p c. The expected demand for drug j n regon r s gven by q jr = µ jr. To help jr structure the results, I assume that n each therapeutc class and regon there are fve possble values of each of the consumer taste parameters β, γ, and α, and that each of these values s equally lkely to occur. Under ths assumpton, consumers n each class/regon are dvded nto 3 5 = 125 subcategores, and the expected demand for drug j n regon r s gven by 125 nkr q jr = µ jr, where now ndexes the subgroup rather than the ndvdual consumer. 125 = 1 Proft Maxmzaton and Prcng Contnue to focus on a sngle perod and a sngle therapeutc class. For smplcty, assume that each frm has at most one product n each class. Gven that demands, costs, and R&D n dfferent classes are ndependent, all frms behave lke sngle-product frms n each class. For convenence, I wll dentfy a product wth the frm that produces t and use the notaton descrbe the frm or the product. Frm j chooses ts regon-specfc prces to maxmze ts proft n each regon: j to 8

10 pj1 pj2 pj3 pj4 j jr jr r 4 max,,, π = ( p cq ) (5) = 1 subject to p p and p j2 j4 p, where p s the polcy-nduced upper bound on prces n regons 2 and 4. The frm s proft maxmzaton problem can be expressed as one of choosng approprate markups n each regon: max π = n m µ mj1, mj2, mj3, mj4 j kr jr jr 125 r= 1 = 1 (6) subject to mj2 m and mj4 m, where m= p c. Note that multple products typcally co-exst n a class. In ths case, all frms choose ther markups smultaneously takng the other frms markups as gven. Markups are determned n Nash equlbrum to solve all frms proft maxmzaton problems subject to the markup constrants. If no constrant bnds, the markup s determned by the frm s frst-order condton. In the computer algorthm, a nonlnear equaton solver computes equlbrum markups by solvng the system of frst-order condtons. If any markups n regons 2 or 4 exceed the cap, the hghest markup s set at the cap and the solver computes the rest. Ths process s repeated untl all constraned markups are at or below the cap. Technologcal Progress Technologcal opportuntes n dfferent therapeutc classes advance at dfferent rates, but the rate wthn each class s assumed to be constant over tme. Ths s the smplest way to compare classes wth hgh opportuntes to those wth low opportuntes. To understand how progress works n a gven class, envson a lnear ncreasng functon of tme. Each pont on the lne represents the qualty of products ntroduced at that pont n tme. Thus, the qualty of a product, θ j, s determned by ts perod of ntroducton. If multple products are ntroduced n the same 9

11 perod n a class, they all have the same qualty, and n equlbrum they all have the same prce. If no products are ntroduced n a perod, technologcal opportuntes contnue to advance; I assume that scentfc progress n unverstes and elsewhere that provdes the bass for mprovements n a class contnues whether any frm explots the resultng opportuntes or not. Recall that a product lves for three perods. The product s patent expres at the end of ts second perod, and n ts thrd perod t co-exsts wth a generc equvalent. The generc has the same qualty as the product but s prced at margnal cost. For smplcty, one and only one generc exsts n each class at each pont n tme; ts qualty s gven by the qualty of the most recent product to undergo patent expraton. Conceptually, ths s the same as havng many dentcal genercs wth perfectly correlated dosyncratc taste shocks (the ε terms n the utlty functons) and free entry; dentcal genercs enter untl the prce of a generc falls to margnal cost, and consumers do not dfferentate between genercs. Ths s a reasonable smplfyng assumpton gven that my focus s on ncentves for nnovaton and not the generc market per se. R&D n the model conssts of two stages: research and development. Research, f successful, yelds a canddate for development the followng perod, and development, f successful, yelds a marketable product the followng perod. Research programs and canddates belong to a specfc therapeutc class. I assume that each frm has at most one research program or canddate n each class. Each perod, each frm wth a canddate decdes whether to shut down development or not. The frm earns 0 f t exts, so n equlbrum a canddate remans n development as long as ts value s non-negatve. Each frm wth a potental research program n a class decdes whether to enter or not. I assume there s an unlmted supply of potental entrants and that frms earn 0 outsde the market, so n equlbrum research programs enter untl the value of the next program s negatve. All entry and ext decsons are made smultaneously. 10

12 The dynamc game focuses on research program entry decsons and canddate ext decsons. In general, there may be multple equlbra n entry-ext games. It mght be possble, for example, that 2 programs and 1 canddate n a class permts no further postve-value entry, and that no programs and 2 canddates also permts no further postve-value entry. Both confguratons could be equlbra f there are 2 canddates at the begnnng of the perod. Gven that canddate ext and research-program entry requres acton, nerta favors the equlbrum where both canddates reman n the market, and ths s the equlbrum selecton rule I employ: research programs enter only f all canddates reman n development. The rule s sensble even wthout nerta. Emprcally, the value of a canddate typcally exceeds that of a research program because the probablty of obtanng fnal approval s hgher (more hurdles havng already been overcome), expected future profts are dscounted less, and there are fewer future costs to bear. Thus, canddates are n a stronger poston than research programs. The State of a Class A class dffers over tme only because the followng varables evolve: the tme perod, the number of canddates n development, the number of age1, age2, and age3 products, and the qualty of the generc. To compute the equlbrum, I elmnate the tme perod to create an envronment that s statonary wth one qualfcaton that I dscuss presently. Recall from equaton (4) that consumer behavor, and hence frm behavor, depends on the dfference between branded qualty and generc qualty, not on the absolute levels of these qualtes. I keep track of the ntroducton date of the product that yelded the generc relatve to the ntroducton date of the age3 product, f any. For example, suppose there are 5 canddates, 4 age1 products, and 3 age2 products. If there are 2 age3 products, then the state s {5,4,3,2,0}, where the 0 ndcates that the generc has the same qualty as the age3 products. If there are no age3 products, 11

13 and the last tme a patent expred was two perods before, then the state s {5,4,3,0,-2}. The only qualfcaton s that f no products are ever ntroduced, then the value of the generc age ndcator can decrease wthout bound. Such an event occurs wth an extremely small probablty, and I mpose a bound on the generc age ndcator to construct a fnte state space. The other elements of the state space have natural upper bounds because n equlbrum, the number of research programs that enter s always fnte. Ths mposes upper bounds on the number of canddates and products that are observed n equlbrum. 4 The net present values of all products, canddates, and research programs depend on the current and expected future states of the class. An age3 product s value s gven by ts current proft; t exts the followng perod. An age2 product s value s gven by ts current proft, whch n equlbrum depends on the current number of products n each age category and the relatve age of the generc, plus ts dscounted expected next-perod proft, when t s an age3 product. The future proft t earns as an age3 product depends on the number of age1 products next perod, whch depends on how many canddates reman n development n the current perod: e c ' ' 2 c = π δ π ψc 1 ' m1 = 0 V ( m, m, m, m, a) ( m, m, m, a) ( m, m, m, a') ( m e ) c (7) where V s the value of an age2 product, m s the number of canddates enterng the perod 2 c (whch s gven by the number of research programs that generated canddates the prevous perod),,, and m are the number of age1, age2, and age3 products n the current perod, m1 m2 3 ndexes the age of the generc relatve to an age3 product, π s the maxmzed proft of a frm a 2 4 The grd I use to compute the model mposes a maxmum generc age of 12 perods relatve to an age3 good. Ths generc age would be realzed f the branded good that yelded the most current generc was ntroduced 84 years ago. The probablty that ths generc age s realzed n the base case statonary equlbrum I compute (dscussed below) s approxmately 5e-6. The fnte grd I use also mposes upper bounds on the number of canddates (30) and products n each age category (5); these bounds are also rarely reached. 12

14 wth an age2 product facng m1, m2 1, and m 3 age1, age2, and age3 products and a generc wth an age of a relatve to an age3 product, δ s the ndustry dscount factor, π 3 s the ' maxmzed proft of a frm wth an age3 product facng, m, and m2 1 age1, age2, and age3 m1 1 products and a generc wth an age of a ' relatve to an age3 product next perod, and ψ (..) s a c functon that gves the probablty of havng ' m1 new products next perod gven that canddates reman n development n the current perod. Note that the number of new products ec next perod s the only source of uncertanty about the future state: the future values of m 2 and m3 m1 2 are gven by the current values of and m because age1 and age2 products today become age2 and age3 products next perod, and a ' s zero f m 2 > 0 and s a 1 otherwse. The value of an age1 product depends on ts current proft plus ts dscounted expected future value as an age2 product: V ( m, m, m, m, a) = π ( m, m, m, a) + 1 c δ e e c ' ' c m 1 m = 0 = 0 V ( m, m, m, m, a') ψ ( m e ) ψ( m e) ' ' ' ' 2 c c 1 c c (8) where V1 and π 1 are defned smlarly to V2 and π 2, s the number of canddates at the begnnng of next perod, and ψ (..) s a functon that gves the probablty of enterng next perod wth ' m c canddates gven that e research programs enter n the current perod. As I dscuss n the next secton, the emprcal dstrbuton of new product values s hghly skewed. A small percentage of new products accounts for the overwhelmng majorty of product value, and the least popular drugs are not effectve substtutes for the most popular drugs. I focus on the top decles by assumng that a canddate generates a new product on the qualty ladder wth probablty λcλ v, generates a margnal new product not on the qualty ladder wth ' m c 13

15 probablty λ (1 λ ), and generates no product otherwse. For smplcty, I assume that a new c v product that s not on the qualty ladder gets an exogenous expected value V x and contrbutes nothng to consumer welfare. The value of a canddate that remans n development n class k s W ( e, e m, m, m, m, a) = x + c c c ck e ec ' ' ' ' c v V mc m1 m1 m2 a c m1 ec mc e + v Vx m = 0 = 0 λδ[ λ (,,,, ') ψ ( 1 1) ψ( ) (1 λ ) ] ' ' c m 1 (9) where x s the cost of developng a canddate n class k. The value of a canddate on enterng ck the perod s gven by W c tmes the probablty the canddate s one of the ones that remans n development, whch s gven by e c m. Thus, c e V ( m, m, m, m, a) = W ( e, e m, m, m, m, a) (10) c c c c c c mc As dscussed n the prevous subsecton, n equlbrum, f e > 0 then ec = mc. Research programs cost xk and yeld canddates wth probablty λ. The value of a research program n class k s V( m, m, m, m, a) = x + c e e c ' ' c m 1 λδ V ( m, m, m, m, a') ψ ( m e ) ψ ( m 1 e 1) m = 0 = 0 k ' ' ' ' c c c 1 c c (11) Note that R&D costs xk and xck dffer by class. For smplcty, λ, λ c, λ v, δ, and V x are constant across classes, products, and tme; all R&D efforts have the same probabltes of success and all frms have the same dscount factor. The values ψ (..) c takes are determned by a bnomal dstrbuton where the probablty of success s λcλ v and the number of trals s gven by the number of canddates consdered. The values ψ (..) takes are determned by a bnomal 14

16 dstrbuton where the probablty of success s λ and the number of trals s determned by the number of research programs consdered. Total frm value n a state s 5 : 3 ev + m V + mv (12) c c = 1 The statonary structure permts computatonal technques that have been developed for computng ndustry equlbra n statonary dynamc games. Pakes and McGure (1994) and Ercson and Pakes (1995) descrbe how standard technques for computng dynamc programmng problems can be adapted to ndustry equlbrum models. I compute the Markov- Perfect Nash Equlbrum of the model. In each state, consumers make choces to maxmze ther utltes, and frms choose markups optmally subject to caps mposed by polcymakers (f any are mposed). Frms make canddate-ext and research-program-entry decsons to maxmze ther values, and equlbrum choces are functons of the current state. The computaton method s teraton on the value functons. The Statonary Equlbrum The equlbrum research program entry and canddate ext decsons that frms make n each state of the game determne the probablty of beng n each state n the future. Workng wth a fnte grd of possble states, t s possble to construct a statonary equlbrum dstrbuton of states. Ths s a vector of probabltes, one probablty for each state on the grd, such that f the current state s to be randomly drawn from the dstrbuton, then the equlbrum dstrbuton of future states s gven by the orgnal vector. The statonary equlbrum s analogous to the steady state n determnstc dynamc models; t provdes the long-run probablty of beng n each state. 5 Expresson (12) does not consder the value of new goods that are not on the qualty ladder, but the average ndustry value calculatons I report below nclude such goods usng the followng calculatons: Compute the average usng the statonary equlbrum dscussed below, then compute the average number of low-value new products m 1 by scalng the average m by (1 λ ) / λ, and then multply ths average by. 1 v v V x 15

17 Hopenhayn (1992) ntroduces the concept of a long-run statonary equlbrum. I prove exstence of the statonary equlbrum and dscuss how to compute t n Appendx A. The statonary equlbrum facltates parameterzaton, because the long run average values of varables can be computed and matched to ther emprcal counterparts. The analyss of transtons due to polcy changes s also facltated. Each class begns from ts ntal statonary equlbrum, and the dstrbuton of future states s determned usng the entry and ext rules under the polcy change. Each perod the dstrbuton of states s updated, and eventually a new statonary equlbrum s reached. The results provde the expected mpacts of the polcy change on each therapeutc class wthout condtonng on the partcular ntal state of each class. If the ntal states were known, the analyss of the transton could be based on partcular ntal states. The one output of the model that cannot be summarzed wth a statonary equlbrum average s consumer welfare, because consumer welfare grows as the qualty of the avalable products and the generc mproves. However, average expected consumer welfare can be computed n such a way that t depends only on a tme trend and statonary equlbrum averages. Usng results from Cameron and Trved (2005), the expected consumer welfare of group regon r and class k, expressed n dollar terms, s gven by n nkr ln(exp[ βθ 0 αc] + exp[ βθ j γaj αp jr]) (13) 125α j Jk The frst term n the logarthm can be factored out to obtan nkr {[ βθ 0 αc] + ln(1 + exp[ β( θj θ0) γaj α( pjr c )])} (14) 125α j Jk The statonary equlbrum average generc age can be computed usng the generc age state varable. Subtractng the average generc age from the tme trend assocated wth a zero generc age and notng the correspondng pont on the qualty ladder yelds the expected θ 0 at every 16

18 pont n tme. The statonary equlbrum and the equlbrum markups can be used to compute the long run average value of the last term n equaton (14). III. Parameterzaton Parameters are determned usng three methods, two of whch approxmate method-of-moments estmaton (MM) and use ndustry facts. Frst, some parameters are assgned ther emprcal average values. Second, several parameters have mplcatons for endogenous moments. The model takes too long to run to mplement conventonal MM, because MM requres computng the statonary equlbrum many tmes just to evaluate potental adjustments of the parameters. Instead, I begn wth a grd of possble parameter values and then refne the parameter values to match ndustry facts. Fnally, some of the parameters pertanng to consumer and class heterogenety cannot be dentfed usng ndustry-level data, and n these cases I mpose parameter values n a structured way to facltate the subsequent analyss. In the followng paragraphs, I summarze how each parameter value was obtaned. Table 1 lsts parameter values, and Table 2 shows that the model s endogenous moments match the data well. Classes dffer n four ways: R&D costs, opportuntes for mprovng qualty, prce senstvtes, and sze. I allow each factor to be ether hgh or low, whch requres computng 16 dstngushable classes. To obtan ndustry-level results, I aggregate the 16 classes and then scale up to the ndustry level by multplyng by a factor of 146/16. Where useful, I also dvde by 6 to convert from the model s sx-year perod to an annual average. Scalng by 146/16 s based on the recently establshed Medcare Prescrpton Drug Beneft Program, whch adopted 146 categores and classes for the entre ndustry (McCutcheon, 2004). The number of therapeutc classes n the ndustry s mportant for relatng class-level outcomes to ndustry-level facts. The number of Medcare classes provdes a reasonable benchmark. 17

19 R&D Costs, Probabltes of Success, the Industry Dscount Factor, and Producton Costs R&D costs, probabltes of success, and the ndustry opportunty cost of captal are parameterzed usng the emprcal estmates of DMas, Hansen, and Grabowsk (2003) (DHG). 6 DHG estmate that the annual real opportunty cost of captal n the research-based pharmaceutcal ndustry s I convert ths to a sx-year rate to parameterze δ. DHG s estmates mply that, on average,.215($121 mllon) of dscovery expendture yelds a canddate that enters Phase 1 of human clncal trals. Dscovery typcally takes 52 months, but a perod n the model s 72 months, so I nclude the frst 20 months of clncal trals n the model s research stage. DHG s data on costs and probabltes of success by phase of clncal trals s reported n Table 3. In the frst 20 months, all phase 1 costs are ncurred, and wth probablty.71, 8 months of the phase 2 costs are ncurred (anmal test costs may also be ncurred). DHG assume that all phase costs are evenly dstrbuted across months wthn the phase. Gven ths, on average, x k = (.215) (23.5)8/ (3.14)16/36 = I assume that 8 months n phase 2 s too lttle to update the lkelhood of success, so λ =.71. Smlar calculatons establsh that development costs, whch consst of the remanng phase 2 costs, phase 3 costs that are ncurred wth probablty.314/.71 condtonal on enterng the model s development stage, and anmal costs are 23.5(18/26) + (.314/.71) (.314)20/(36(.71)) = 55.71; x = on ck average. The probablty that a phase 1 canddate becomes a product s.215, so λλ =.215, whch mples that λ c =.303. DMas, Grabowsk, and Vernon (2004) examne how clncal tral costs vary across classes. Ther results mply that the standard devaton of clncal tral costs c 6 DHG s analyss, and most of the lterature on the research-based pharmaceutcal ndustry, focuses on new chemcal enttes (NCEs). As DHG dscuss, not all new drugs are NCEs; some use exstng chemcal enttes. NCEs are the most nnovatve new drugs. The proft estmates dscussed below (from Grabowsk, Vernon, and DMas 2002) are also for NCEs, and they take nto account the addtonal costs and profts of products derved from NCEs. 18

20 across classes s approxmately 13% of the mean. 7 Gven ths, x and x are 13% and 6% above the mean n hgh-r&d-cost classes and the same amount below the mean n low-cost classes. Grabowsk, Vernon, and DMas (2002) (GVD) estmate NPV decles, n mllons of year 2000 dollars, for NCEs ntroduced between 1990 and The dstrbuton s very skewed: {2,722, 1,015, 629, 433, 235, 126, 56, 30, 9, 0}. Only 30% of new drugs cover ther accumulated after-tax captalzed costs of R&D; most fall far short of ths mark. Gven the parameterzaton of technologcal progress and taste parameters dscussed below, the model produces a skewed dstrbuton of value smlar to GVD s. I use GVD s estmates to set λ V =.45 and equal to the mean of the bottom 5.5 decles after rescalng to match DHG s cost fgures. Because DHG s cost estmates are for drugs frst tested n humans between 1983 and 1994, the NPV data must be rescaled to reflect ntroducton dates well after I do not deduct taxes because my goal s to dentfy the total resource benefts and costs assocated wth prcng polces. I compute the margnal cost of producton c usng the results of Grabowsk and Vernon (1992, 1996) as dscussed by Hughes et al. (2002) on the extent to whch prces fall after generc entry. The emprcal average branded prce mmedately pror to patent expraton s sx tmes the generc prce after genercs have dffused, whch mples that the average markup s 5 tmes c. ck k V x As shown n equatons (4) and (6), choces n the model do not depend at all on c. I compute the statonary equlbrum of the model wthout assgnng a value of c and then choose c to be 1/5 of the average markup of age2 goods (goods mmedately pror to patent expraton). Class Characterstcs Food and Drug Admnstraton statstcs show that n the perod , the average number of new molecular enttes (whch are smlar to NCEs) ntroduced annually was 27 (PAREXEL, 7 The emprcal SD/mean based on out-of-pocket costs s slghtly hgher than the rato based on captalzed costs; 19

21 2005). The man parameters that affect the number of new drugs are the class szes. To facltate comparsons, I set class sze to be ether above or below the average sze by 10%. Table 1 reports the average class sze that generates an ndustry average annual flow of 27 new drugs. To parameterze the rate of qualty mprovement, data on long-run qualty mprovements n several classes would be deal. Lackng such data, I attempt to match two sets of facts. Frst, the rate of qualty mprovement affects the dstrbuton of new product values dscussed above. Second, I use data on cholesterol-reducng drugs. In the 1950s, drugs could lower LDL cholesterol approxmately 15% (Expert Panel, 2001). By 1997, drugs could lower LDL cholesterol up to 50%. In the model, technologcal opportuntes mprove as a lnear functon of tme; a gan of 35 percentage ponts n 42 years mples an mprovement of 5 percentage ponts every 6-year perod. I assume that technologcal opportuntes advance at an average rate of 5. To facltate comparsons, I set the rate to be ether above or below the average rate by 10%. To parameterze A j for each age category (1,2, and 3), I attempt to match three sets of facts. Frst, data on the evoluton of sales of an average product provded by GVD as reported by Berndt et al. (2005) establshes that the average rato of year 7-12 sales to year 1-6 sales (age2 to age1 n the model) s Data on top decle products yelds a rato of Both sets of facts mply that consumers resst age1 products substantally more than age2 products. Second, Hughes et al. (2002) report that the average market share of unts sold of a branded product relatve to ts generc after patent expraton s 20%. In order for the model to match ths fact, consumers must resst even age3 goods to a small extent. Fnally, the Generc Pharmaceutcals Assocaton reports that n 2004, genercs accounted for 53% of prescrptons dspensed n the U.S. (based on IMS data). Ths last fact determnes the overall scale of the vector of resstance to 13% s n between the two. 20

22 newness parameters. The resultng vector s reported n Table 1. Consumers manly resst adoptng age1 products, but there s some resstance to older drugs as well. Consumer Characterstcs There are enough moment condtons to pn down the man parameters of the model, but the dstrbutons of taste heterogenety for qualty and averson to newness n each therapeutc class ( β, γ ) cannot be dentfed usng ndustry-level aggregates. I assume that both dstrbutons can be approxmated by a normal dstrbuton dvded nto quntles, where the standard devaton s 10% of the mean. The mean of β cannot be dentfed separately from the mean rate of growth n opportuntes for mprovng qualty, because β and θ j enter the utlty functon as a product. Smlarly, the overall mean of γ cannot be dentfed separately from the scale of the Gven ths, I set both means equal to 1. A j vector. I assume that prce senstvty ( α ) s determned by ncome. De Navas-Walt, Proctor, and Lee (2005) provde ncome quntles for the U.S.; I assume that ncome dstrbutons n the major economes n the ROW have smlar shapes. Phelps (2003, pg. 148) estmates that the ncome elastcty of demand for medcal care s 0.2. Appendx B shows that the ncome elastcty of demand s gven by the negatve of the ncome elastcty of α. Gven ths, I compute the percentage changes n ncome from quntle to quntle and multply by -.2 to determne how vares by quntle. Ths determnes the relatve values of α but t does not pn down the mean level of α. Appendx B establshes that the model s results do not depend on the mean α ; approprate adjustments to szes and markups can offset any change n the mean α and yeld exactly the same results. Gven ths, I set the mean α to be 1 n the U.S.. I use the CIA World FactBook ( to compare 2005 estmates of α 21

23 purchasng-power-party-adjusted gross domestc product per capta across the U.S., Canada, E.U., and Japan. These economes account for almost 90% of ndustry sales and vrtually all of ndustry profts (PAREXEL, 2005). Incomes n the ROW are approxmately 30% less than ncomes n the U.S.. I multply -30% by -.2 to compute the vector of α s n the ROW. To evaluate the net present value of consumer welfare n alternatve polcy regmes, I need a consumer dscount factor. The health economcs lterature typcally uses an annual dscount rate of 3%. I apply ths rate to a sx-year perod to construct a consumer dscount factor. Polcy Varables To parameterze m, the markup cap n the ROW, I note that m affects the percentage of ndustry sales that occur n the U.S. market n the statonary equlbrum. I set the level of m so that 53% of ndustry sales occur n the U.S. market. To arrve at 53%, I use the 2004 relatve share of the North Amercan market n the world defned as North Amerca, the European Unon, and Japan (the major markets for prescrpton drugs), and the 2003 relatve share of the U.S. market n North Amerca. These fgures are provded by PAREXEL (2005). Consderng alternatve prcng polces n dfferent countres smply nvolves adjustng the relatve values of the n s holdng n constant. Every other parameter remans the same. To kr k n k1 n k 4 parameterze the base case levels of and, I use the relatve populaton szes n 2005 from the CIA World FactBook for the U.S., Canada, Japan, and the European Unon. The U.S. accounts for 32% of the populaton of ths group, so n the base case, nk1 =.32n. Canada k accounts for 3.6% of the populaton of ths group, so when I consder the scenaro where Canada adopts market prcng, n k3 =.036n. If the U.S. adopts prce controls, n 1= 0 and n 2 =.32n. k k k k IV. Results 22

24 For the base case, where the U.S. has no prce caps and the ROW does, I compute statonary equlbrum average levels of the varables of nterest. For the comparson cases, I re-compute the model usng the approprate values of the n kr s. Then I begn from the base-case statonary equlbrum and update the dstrbuton of states usng the choces agents make n the comparson case. The dstrbuton of states evolves and eventually reaches a new statonary equlbrum. Some of the results compare statonary equlbrum average levels of varables, but most consder the transton over tme. The mplct assumpton underlyng the transton s that frms do not antcpate the change n polcy before t occurs. The base-case statonary equlbrum average levels are mantaned as long as frms foresee no changes n the envronment. Fgures 1-6 llustrate the effects of polcy changes. Fgure 1 compares the base-case statonary equlbrum average number of research programs per class to how research programs evolve n response to polcy changes. If the U.S. mposes prce caps, the number of research programs ntally falls to vrtually nothng and then recovers somewhat to hover around 20% of ts base-case level. I use Canada as an example to llustrate what happens f an ndvdual country abandons prce controls, but the basc conclusons are the same for other countres or groups of countres. If Canada adopts market prcng, the average number of research programs ntally jumps by about 10% and then falls, but t remans above ts base-case level. If all regons abandon prce controls, the average number of research programs over doubles ntally but then settles down to hover around 50% above ts base-case level. The reason why research frms appear to over-react to polcy changes early on s that they are confronted wth the base-case levels of canddates and exstng products. In the case where U.S. prce caps are mposed, these base-case levels exceed the new equlbrum average levels substantally, and the prospects for obtanng future profts are very poor. Research frms respond by stayng out of the market. 23

25 Eventually, the number of canddates and products falls to a level more consstent wth coverng the captalzed costs of R&D n the new polcy regme, and the number of research programs rses somewhat. In the case where one or more non-u.s. countres adopt market prcng, the opposte patterns occur; ntally the prospects for obtanng profts are unusually good, entry occurs n response, and eventually the market settles on a new equlbrum average level. Fgure 2 shows the mpacts of polcy changes on the flow of canddates. Note that polcy changes take a perod to have an mpact. In most states, late-stage canddates reman vable even when expected prces fall, and the number of canddates cannot be ncreased wthout watng for research programs to be completed. Thus, frms do not shut down ther canddates mmedately n response to prce caps n the U.S., and they cannot mmedately ncrease the number of canddates n response to non-u.s. countres abandonng prce caps. The changes n canddates that eventually occur happen because of the precedng changes n research programs. Fgure 3 shows how polcy changes eventually mpact the flow of new products. The changes n the number of research programs that occur at the tme of the polcy change take two perods to affect the flow of new products. After that, the ndustry agan appears to over-react ntally, but ths just reflects the earler adjustment n the number of research programs. In the long run, the flow of new products under U.S. prce controls s less than 25% of the flow under the current polcy regme. On the whole, the long run adverse mpacts of U.S. prce caps are substantal, but t takes many years for the adverse mpacts to be notced by patents. Fgure 4 shows how the flow of new products eventually mpacts the average age (and hence the average qualty) of generc products. The flow of new products changes two perods after the polcy change, and n the thrd perod of a product s lfe a generc equvalent enters the market. Thus, the mpacts on generc qualty do not begn untl four perods after the polcy 24

26 change. Although t takes tme to occur, ths mpact on average generc qualty has mportant welfare mplcatons n the long run, because many patents are treated wth genercs. Although polcy analyses nvolvng pharmaceutcals typcally focus on consumers as patents, many consumers are also affected as shareholders of pharmaceutcal frms. Whle the results on the flow of new drugs suggest that the most substantal effects of polcy changes occur n the future, the model also suggests some mmedate fnancal mplcatons for frms. Fgure 5 shows that the base-case average level of annual ndustry R&D expendture s over four tmes the long run level wth U.S. prce caps mposed. Fgure 6 shows that the long run mpact on frm value s even more dramatc. In the long run, average frm value under U.S. prce caps s less than 20% of ts base-case average level. Part of the shareholder wealth loss s a transfer of wealth to patents who obtan lower prces for branded drugs, but part s a real welfare loss to socety, because the future flow of new drugs s dmnshed. Even f polcymakers want to provde a transfer to patents, reducng pharmaceutcal ndustry value s not the best way to accomplsh such a transfer, because there are other ways to provde transfers that do not have the welfarereducng effect of slowng the flow of new drugs. The results also confrm that nnovatonpromotng polcy changes n non-u.s. countres mprove shareholder value. It s worth notng that the base-case statonary equlbrum level of annual ndustry R&D expendture n Fgure 5 s substantally below the emprcal annual ndustry R&D, whch exceeds $40 bllon (PAREXEL 2005). Two factors account for the dscrepancy. Frst, although estmates suggest that the substantal majorty of pharmaceutcal R&D s for NCEs, some R&D s assocated wth exstng NCEs. More mportantly, DHG s estmates of R&D costs are based on drugs that entered development years ago, and, as DHG dscuss, R&D costs have rsen substantally over tme. The scale of costs s not crtcal for matchng percentage changes or the 25

27 flows of real (non-monetary) varables such as the flow of new drugs, because all dollar values n the model can be rescaled by a common factor wthout changng any of the percentage changes or real varables. Put dfferently, monetary unts are arbtrary. However, the monetary values of consumer welfare reported below would also be scaled by the same common factor, so f one decdes, for example, that the true R&D costs are double the DHG fgures, then all of the consumer welfare effects reported below should be doubled. Precse estmates of R&D costs more up-to-date than DHG s are not avalable. Consumer Welfare Table 4 reports the dfference between the annual consumer welfare under U.S. prce caps and n the base case. Intally, U.S. consumers beneft from U.S. prce caps because exstng branded products have lower prces. By the md 2020s, U.S. consumers begn to suffer from the reduced flow of new drugs and the resultng mpacts on average generc qualty dscussed above. After that pont, the negatve mpact of the prce-controlled envronment worsens steadly over tme. Consumers outsde the U.S. also suffer from U.S. prce caps, but ther sufferng begns sooner. Consumers outsde the U.S. are affected by the reduced flow of new drugs but have no offsettng beneft because they already face capped prces n the base case. The last column of Table 4 shows that total consumer welfare worldwde ntally rses because U.S. consumers beneft, but by 2018, global consumer welfare s lower under U.S. prce caps than n the base case. The standard approach for evaluatng the net mpact of a polcy change that benefts consumers today but costs consumers tomorrow s to dscount the future costs to make them comparable to the current benefts. The bottom of Table 5 reports the mpacts of U.S. prce controls on the net present value of consumer welfare n the U.S., the rest of the world, and globally usng an annual dscount rate of 3% converted to a sx-year dscount factor. The full- 26

28 foresght net present value, approxmated wth a 30-perod tme horzon, s substantally negatve. The last row adds the effects on consumer welfare to the effects on frm value to compute the effects on total welfare. Frms n the model have no locaton, but I assume that shareholders are dstrbuted across regons accordng to relatve gross domestc products. 8 Tables 5 s smlar to Table 4; t evaluates the mpact of Canada market prcng and all non-u.s. market prcng on consumer welfare n Canada, the U.S., and the rest of the world. Consumers outsde Canada beneft f Canada adopts market prcng, but consumers n Canada suffer. Table 5 shows that the sufferng of Canadan consumers outweghs the benefts obtaned outsde Canada ntally. The results favor Canada s prce controls unless Canadan polcy makers consder the long term mpacts of ther polces on global welfare. Canada s consumers do not prvately beneft from abandonng prce controls regardless of the tme horzon. Conclusons for the scenaro where all non-u.s. countres abandon prce controls are smlar, although, as I dscuss further below, non-u.s. consumers eventually beneft from global nonnterventon. The non-u.s. countres do not prvately beneft n NPV terms, but global consumer welfare rses. The postve global NPVs n Table 5 suggest that consumer groups outsde Canada would be wllng to compensate Canada for abandonng prce controls. Further, U.S. consumers would be wllng to compensate all non-u.s. countres to encourage them to abandon controls. The dffculty of establshng contracts that could enforce non-nterventon polces and compensate non-u.s. consumers n the future for gvng up lower prces they could have had suggests that the prospects for accomplshng a global-welfare-mprovng polcy change are slm. Consumers far n the future outsde Canada would reap most of the benefts from Canada abandonng prce 8 The market for pharmaceutcals s global, and R&D locatons are not dependent on the prce control regme. Research typcally locates close to major unverstes or other research nsttutons. Development actvtes typcally 27