Reference Pricing with Endogenous Generic Entry

Transcription

1 Reference Pricing with Endogenous Generic Entry Kurt R. Brekke, Chiara Canta, Odd Rune Straume Aril 18, 2016 Abstract Reference ricing intends to reduce harmaceutical exenditures by increasing demand elasticity and stimulating generic cometition. We develo a novel model where a brandname roducer cometes in rices with several generics roducers in a market with brandbiased and brand-neutral consumers. Comaring with coinsurance, we show that reference ricing, contrary to olicy makers intentions, discourages generic entry, as it induces the brand-name roducer to rice more aggressively. Thus, the net effect of reference ricing on drug rices is ambiguous, imlying that reference ricing can be counterroductive in reducing exenditures. However, under rice regulation, we show that reference ricing may stimulate generic entry, since a binding rice ca weakens the aggressive rice resonse by the brand-name roducer. This may exlain mixed emirical results on the cometitive effects of reference ricing. Finally, we show that reference ricing may be welfare imroving when accounting for brand references desite its adverse effects on entry and rices. Keywords: Pharmaceuticals; Reimbursement schemes; Generic entry JEL Classification: I11; I18; L13; L51 We are grateful for comments from Paolo Pertile, three anonymous referees, and articiants at the 16th Euroean Health Economics Worksho in Toulouse Deartment of Economics, Norwegian School of Economics NHH), Helleveien 30, N-5045 Bergen, Norway. kurt.brekke@nhh.no Corresonding author. Deartment of Economics, Norwegian School of Economics NHH), Helleveien 30, N-5045 Bergen, Norway. chiara.canta@nhh.no Deartment of Economics/NIPE, University of Minho, Camus de Gualtar, Braga, Portugal; and Deartment of Economics, University of Bergen, Norway. o.r.straume@eeg.uminho.t. 1

2 1 Introduction The design of reimbursement schemes for rescrition drugs is a key issue for olicy makers around the world. To contain the growth in harmaceutical exenditures, almost every health insurance scheme includes cost sharing on the demand side. One of the most oular cost sharing instruments recently is reference ricing, which is now adoted by most Euroean countries for reimbursement of drug exenditures, esecially for theraeutically equivalent branded and generic) drug versions. 1 Outside Euroe, countries such as Canada and New Zealand have introduced some form of reference ricing. 2 In the US, reference ricing is a well-established ractice through the Maximum Allowable Cost MAC) rogrammes used by Medicaid and some managed-care rogrammes for multisource comounds. 3 Under reference ricing, the ayer limits the insurance coverage by defining a maximum rice that will be reimbursed for a category of drugs with theraeutically similar effects. 4 Consumers demanding a branded) drug version riced higher than the reference rice will not receive reimbursement for the additional costs and have to ay the difference between the actual rice of the branded) drug and the reference rice out-of-ocket. 5 The intention of reference ricing is not rimarily to shift costs from the ayer to the consumers, but rather to reduce total both ayer and consumer) exenditures by making demand more rice elastic and romoting cometition between branded and generic) drug roducers. In this aer, we will show that these conjectures are not necessarily true. In fact, we find that reference ricing can be anticometitive when accounting for the entry decision by generics roducers and counter-roductive in reducing harmaceutical exenditures. 6 To study the cometitive effects of reference ricing, we develo a novel Salo-tye model 1 See, for instance, Carone et al. 2012) for a review of harmaceutical regulation and cost containment olicies in the Euroean Union. A few countries, such as Germany and the Netherlands, also aly reference ricing to theraeutically related drug categories, otentially including drugs with different substances. 2 See Lee et al. 2012). 3 See, for instance, Danzon and Ketcham 2004) or a recent study by Kelton et al. 2014). 4 Sulementary health insurance is not very common in Euroe excet for in France, the Netherlands, and Belgium), and will usually not cover out-of-ocket exenses related to rescrition drugs see OECD, 2015). 5 The reference ricing schemes may vary across countries according to the formula for fixing the reference rice and the wideness of the theraeutic categories that are included. See, for instance, Danzon and Ketcham 2004) and Carone et al. 2012). 6 Generics roducers can enter the market after the atent has exired. The entry rocedures are much less restrictive than for the original brand-name drug. In the US, there is an abrreviated new drug alication rocess ANDA) in lace that exedites generic entry. In Euroe, a similar rocedure is imlemented by the Euroean Medicine Agency and the national authorities in most countries. 2

3 where a brand-name roducer cometes in rices with several generics roducers. In the market there are two tyes of consumers; brand biased and brand neutral. Brand-biased consumers have a reference for the brand-name drug and only buy a generic alternative if the coayment outof-ocket ayment) is sufficiently lower. 7 Brand-neutral consumers, on the other hand, always refer a generic drug if it is cheaer than the brand-name drug. Thus, as long as the rice of the brand-name drug is higher than the rice of generic drugs, these consumers only choose between different generic alternatives. Based on this modeling aroach, we derive the equilibrium under reference ricing both exogenous the reference rice does not deend on current rices) and endogenous the reference rice deends on current rices) and comare with the equilibrium under coinsurance, where the consumer ays a fixed ercentage of the medical cost. 8 We reort four key findings. First, for a given number of firms, reference ricing triggers rice cometition. The brand-name roducer resonds aggressively to reference ricing by cutting rices more than the generic roducers, resulting in higher brand-name market shares. This result holds irresective of whether the reference rice is exogenous or endogenous. The strong rice resonse by the brand-name roducer is due to the increased demand elasticity induced by reference ricing. The weaker rice resonse by the generics roducers is due to two counteracting forces. For a given brand-name rice, reference ricing shifts demand towards generic drugs and thus rovides an incentive for generics roducers to increase rices. However, the rice reduction by the brand-name roducer gives an incentive for generics roducers to also reduce rices, which is due to the fact that rices are strategic comlements. Second, reference ricing limits generic entry. Desite the extra coayments on brand-name drugs, we show that, in a free entry equilibrium, the number of generic entrants are weakly) lower than with ure coinsurance. The reason is the aggressive rice resonse by the brandname roducer induced by reference ricing, which reduces the exected rofits for the generic roducers from entering the market. This result also holds for both endogenous and exogenous reference ricing. Thus, the net effect of reference ricing on drug rices and exenditures 7 Coayments refer to the out-of-ocket ayments made by a consumer when demanding a given drug. It should not be confused with co-ay, which in the US refers to a fixed ayment deductible) that is usually just a art of the total out-of-ocket ayments. 8 Coinsurance is highly common for reimbursement of drug costs and thus a natural benchmark. In Euroe almost every country uses coinsurance; see Carone et al. 2012). In the US, The Medicare Modernization Act in 2003 established a standard drug benefit that all Medicare Part D lans must offer, which basically is a coinsurance scheme with a deductible). For exact details, see 3

4 are in general ambiguous when accounting for the entry decision by generics roducers. Using numerical simulations, we illustrate that reference ricing can reduce generic entry, lead to higher rices, and result in increased harmaceutical exenditures mainly for the consumers). Third, other forms of rice regulation may reverse the adverse effects of reference ricing on generic entry. We consider the case where drugs are subject to rice cas, which are a very common regulatory tool in Euroe and often coexist with reference ricing. 9 Assuming a rice ca that is binding for the brand-name drug under ure coinsurance, we show that reference ricing may increase the number of generic entrants if the rice ca is sufficiently strict. The reason is that rice ca regulation weakens the rice resonse by the brand-name roducer, imlying that generics roducers may obtain higher market shares under reference ricing. In this case, reference ricing can actually stimulate generic entry and result in lower rices and cost-savings mainly for the third arty ayer). Thus, erhas somewhat counterintuitively, reference ricing tends to erform better in the resence of rice regulation than under unconstrained ricing. Finally, reference ricing can increase both total welfare and consumer welfare desite the adverse effects on generic entry and rices. There are two effects that contribute to these results. First, there is excessive generic entry under ure coinsurance, a market failure that is artly corrected by reference ricing. Second, reference ricing may reduce the coayment difference between brand-name and generic drugs, inducing a larger share of brand-biased consumers to urchase the brand-name drug and leading to lower mismatch costs in this consumer segment. Our aer contributes to the existing literature along several dimensions. First, our model builds on the seminal work by Frank and Salkever 1992) who roosed a model with two consumer segments a rice insensitive and a rice sensitive segment in order to exlain the generic cometition aradox, i.e., brand-name roducers resond to generic entry by increasing their rices. Their model rovides a very aealing exlanation for the generic cometition aradox, namely market segmentation: the brand-name roducer serves only the rice insensitive consumers, leaving the rice sensitive consumers to the generics roducers. 10 To arrive at this 9 Carone et al. reorts that, in 2012, 24 EU members alied rice cas also called external reference ricing since cas deend on rices abroad), and 20 alied reference ricing. 10 Frank and Salkever 1992) and Grabowski and Vernon 1992) also confirm the generic aradox emirically. However, Wiggins and Maness 2004) find that the brand roducers tend to reduce their rice due to generic entry. 4

5 result, the model involved three key assumtions; i) the demand from the rice insensitive consumers deends only on the rice of the brand-name drug, ii) the game is Stackelberg where the brand-name roducer commits to a rice; iii) generics roducers comete in quantities à la Cournot with a market-clearing rice of generic drugs. Later studies by Kong and Seldon 2004) and Regan 2008) generalise the model by Frank and Salkever 1992) by allowing demand from rice insensitive consumers to deend on both the brand-name and the generic drug rices, but they maintain the other two assumtions. 11 The contribution of our aer is to build on the market segmentation model by Frank and Salkever 1992), but roose a model that relaxes all the three above-mentioned assumtions. More recisely, we allow for i) the demand from brand biased or rice insensitive) consumers to deend on rices of generic drugs; ii) brand-name and generics roducers to simultaneously set rices; and iii) generics roducers to set rices rather than quantities. By modelling cometition as a simultaneous game rather than a Stackelberg one), we avoid the strong assumtion that firms can commit to rices. We also avoid the assumtion of a Cournot cometition, which has limited emirical suort in the harmaceutical market. Our study is not the first to assume that generics roducers set rices. There exists several studies that allow for rice cometition between brand-name and generics roducers. 12 However, these studies assume that only one generic roducer is resent in the market. Thus, the contribution of our aer in regard to this literature is to allow for several generics roducers. There is one recent aer by Ghislandi 2011) that allows for more than one generic roducer in the market. By considering an infinitely reeated two-stage game, where at stage 1 the firms set rices that determine the reference rice and at stage 2 the firms set rices taking the reference rice as given, he shows that an otimal reference ricing scheme should only deend on generic rices in order to avoid collusion among generics roducers. However, in Ghislandi 2011) there is either erfect cometition à la Bertrand) or collusion among the generics roducers, and he is not concerned with the imact of reference ricing on generic entry. Thus, our aer differs significantly from his both in terms of research question and modeling framework. Another related aer is Bardey et al. 2013), who study the otimal reimbursement schemes 11 A similar set-u is considered by Wiggins and Maness 2004). 12 See, for instance, Brekke et al. 2007, 2011) and Miraldo 2009). 5

6 for drugs in a set-u with harmaceutical innovation, allowing for a reference rice based on minimal and maximal market rices. They show that the otimal reference ricing is more lenient than the one that would be otimal in the static case without entry and innovation. Our analysis comlements theirs by focusing on generic entry rather than entry of atented drugs) and by showing that reference ricing may be dominated by ure coinsurance even if drug diversity is not an issue, and the ayer exclusively minimises total exenditures. Furthermore, we consider the case where the maximum reimbursement is comuted using different and less extreme) formulae. Finally, our aer contributes to the interretation of the results from the emirical literature on the effect of reference ricing on generic cometition. Several aers have analysed the imact of reference ricing and tend to find that it stimulates generic cometition and leads to lower rices and exenditures see, for instance, Aronsson et.al, 2001, Pavcnik, 2002, Brekke et al., 2009, 2011, and Kaiser et al., 2014). An excetion is Danzon and Chao 2000), who argue that reference ricing might be counterroductive in curbing harmaceutical exenditures. 13 Moreover, Ekelund 2001) analyse the Swedish harmaceutical market and find weak) evidence of a negative effect of reference ricing on generic entry, whereas Rudholm 2001) find no effect of reference ricing on generic entry in Sweden. A study by Moreno-Torres et al. 2009) on the Sanish market find that reference ricing has a negative effect on generic entry, whereas a recent study by Brekke et al. 2015) on the Norwegian market find that reference ricing has a ositive effect on generic entry. Our aer suggests that the mixed emirical findings can be exlained by the resence and strictness of rice ca regulation. The rest of the aer is organised as follows. In Section 2 we resent our basic model. In Section 3 we derive the equilibrium for a ure coinsurance or fixed ercentage) reimbursement scheme. In Section 4 we derive the equilibrium with endogenous and exogenous) reference ricing, and comare this with the equilibrium under ure coinsurance. In Section 5 we introduce rice ca regulation. In Section 6 we conduct a welfare analysis. Section 7 concludes the aer. The roofs of all Lemmas and Proositions are relegated to the Aendix. 13 Danzon and Ketcham 2004) rovide emirical evidence that reference ricing leads to a rice convergence towards the reference rice, imlying that brand-name drug rices dro whereas generic rices increase. 6

7 2 Model Consider a harmaceutical market with a brand-name drug that has lost atent rotection and faces cometition from generics roducers, indexed by i = 1,..., n. Each generic drug roducer can enter the market by incurring a fixed sunk) cost f. 14 Suose the market is reresented by a Salo circle with circumference 1 and a uniform distribution of consumers with total mass equal to 1, and that the n generics roducers that enter the market are symmetrically located on the circle. 15 We assume that there are two different tyes of consumers in the market. At each oint on the circle, a share λ of the consumers are brand biased, whereas the remaining share 1 λ are brand neutral. Brand-biased consumers have a reference for the brand-name drug and will only buy a generic alternative if the coayments out-of-ocket ayments) are sufficiently lower. 16 The reason for a brand reference may be that consumers erceive the brand-name drug to be of higher quality or less risky than generic drug versions due to, for instance, marketing effort by the brand-name roducer during the atent eriod or ast consumtion of the brand-name drug. 17 We model this by assuming that there are mismatch costs associated with buying a generic drug instead of the brand-name drug. The utility of an arbitrary brand-biased consumer located at x [0, 1] on the circle is given by u bb v c b x) = v c i g t b x zg i if consuming the brand-name drug if consuming generic drug i, 1) with i = 1,..., n. The arameter v denotes the gross utility reservation rice) of medical treatment, c b and c i g are the coayments out-of-ocket ayments) of the brand-name drug and the generic drug i, resectively, and t b x zg i is the mismatch switching) cost of consuming 14 The fixed costs cature all relevant sunk costs associated with market entry of the generics roducers, including the costs of setting u a new roduction line, obtain aroval and marketing licence, etc. 15 This assumtion is reasonable given that consumers are uniformly distributed and there is rice cometition among firms see Economides, 1989), and catures the fact that generic drugs can be erceived as horizontally differentiated by consumers e.g., due to different roduct name, ackage, resentation form, etc.). 16 We use the term coayments for the out-of-ocket ayments made by the atients when demanding a given drug. Thus, coayments should not be confused with the term co-ay used in, for instance, the US Medicare rogram, which is a deductible. 17 Brand loyalty is a standard assumtion in the literature on cometition between brand-name and generic drug roducers; see, e.g., Frank and Salkever 1992, 1997), Grabowski and Vernon 1992), Brekke et al. 2007, 2011). 7

8 a generic drug i located at zg. i Thus, in the segment of brand-biased consumers, the degree of brand bias varies across consumers and is reflected by the consumer locations on the circle. The remaining consumers are assumed to be brand neutral and will always refer a generic drug if it is cheaer than the brand-name drug. Thus, as long as the rice of the brand-name drug is higher than the rice of generic drugs, these consumers will only choose between different generic alternatives, which we assume are considered imerfect substitutes in a strictly horizontal sense. The utility of an arbitrary brand-neutral consumer located at x who consumes generic drug i, located at zg, i is given by u bn x) = v c i g t g x zg i. 2) Notice the different interretations of the arameters t b and t g. Whereas t b reflects the degree of vertical differentiation between brand-name and generic drugs for brand-biased consumers, t g reflects the degree of horizontal differentiation between different generic drugs for brandneutral consumers. 18 We assume throughout the aer that t g t b, i.e., the mismatch cost for brand-biased consumers is weakly) higher than for the brand-neutral consumers. It is arguably a reasonable assumtion that the vertical differentiation among brand-name and generic drug versions is weakly) stronger than the horizontal differentiation between different generic drug versions. Alying this model to rice cometition in off-atent drug markets, we will look for equilibria where the market is fully covered imlying that total demand is erfectly rice inelastic) and where both the brand-name and the generics roducers have ositive sales. In such equilibria, a fraction of the brand-biased consumers will buy the brand-name drug with the remaining ones buying the most referred generic drug), whereas all brand-neutral consumers will buy generic drugs. Note that, in the brand-biased demand segment, each generic drug roducer cometes directly with the brand-name roducer and only indirectly with the other generic drug roducers i.e., a rice change by generic drug roducer i will trigger a rice resonse by the brand-name roducer, which in turn triggers rice resonses by the remaining generic drug roducers j i). 18 Technically, the difference between brand-biased and brand-neutral consumers lies in their ercetions about the location of the brand-name drug. Whereas brand-biased consumers erceive the brand-name drug to be located at every single oint on the circle, brand-neutral consumers erceive the brand-name drug to be co-located with the generic drugs. 8

9 However, in the brand-neutral segment, there is direct cometition between different generics roducers. In the brand-neutral demand segment, demand allocations are determined by the locations of the consumers who are indifferent between the neighboring generic drugs i and i + 1. These consumers are located a distance 1/2n) + c i+1 g c i g) /2tg ) from the location of generic drug i. With the assumtion of full market coverage, demand allocations in the brand-biased segment are determined by the location of the consumers who are indifferent between the brand-name drug and their most referred generic drug i. These consumers are located a distance c b c i g) /tb from the location of the generic drug i. 19 Taking into consideration that in each demand segment there are two locations of indifferent consumers, one on each side of generic drug i, the total demand for this drug is given by ) Dg i = 2λ cb c i ) 1 g + 1 λ) t b n + ci+1 g + cg i 1 2c i g. 3) 2t g The demand for the brand-name drug is given by total demand minus the sum of demands for generic roducts: D b = λ 1 2n t b c b 1 n n i=1 c i g )). 4) Observe that the demand for the generics roducer i in the brand-biased segment is ositive only if the coayment for the generic drug is strictly lower than the coayment of the brandname drug, otherwise all brand-biased consumers refer to buy the brand-name drug. However, some consumers are willing to buy the brand-name drug as long as c b c i g) < tb /2n, i.e. the difference in coayments is not too large. This condition will always be satisfied in the equilibria we consider. All roducers including the brand-name roducer) are assumed to have constant and identical marginal costs of roduction, which we set to zero without loss of generality. The rofit 19 Technically, for this to be the location of the indifferent brand-biased consumers, we also need ) c b c i g /tb to be smaller than 1/2n) + ) c i+1 g cg) i /2tg, ensuring that i is the most referred generic drug of the indifferent consumer. Since we focus on symmetric equilibria, where the most referred generic drug is the closest one, this condition trivially holds under the assumtion of ositive sales. 9

10 functions of the brand-name roducer and generics roducer i are then given by π b = b D b, 5) π i g = i gd i g f, 6) where b and i g are the rices of the brand-name drug and the generic drug i, resectively, and f is the sunk) entry cost of generics roducer. We consider a two-stage game, where at Stage 1 the atent rotection of the brand-name drug exires and n generics roducers simultaneously) decide whether to enter symmetrically) the market deending on the exected rofits relative to the fixed entry cost. At Stage 2 there is Bertrand) rice cometition between all brand-name and generics) firms in the market. 20 The outcome of this rice cometition deends on the regulatory olicies in lace. We will consider, and comare, two different reimbursement schemes: ure coinsurance or fixed ercentage reimbursement) and reference ricing. These are the two most commonly used reimbursement schemes in Euroean countries see, e.g., Carone et al., 2012) Pure coinsurance Suose that the coayment is a fixed ercentage of the rice of the demanded roduct. If we let α 0, 1) be the coinsurance rate, the coayments for the brand-name drug and the generic drug i are c b = α b and c i g = α i g, resectively. With this coayment rule, the rofit maximisation roblems of the brand-name roducer and the generics roducer i, at the second stage of the game, are given by, resectively, max π b = b λ b 1 2nα t b b 1 n n i g i=1 )), 7) 2λα max π i i g = i g b i ) 1 g + 1 λ) g t b n + α i+1 g + g i 1 2 i 2t g) )). 8) g 20 As exlained in the Introduction, a Stackelberg ricing game with the brand-name roducer as a first mover) is not lausible due to the standard time inconsistency roblem. The brand-name roducer has an incentive to reotimise its rice once the generics roducers enter the market, resulting in a Bertrand rice equilibrium. 21 In Euroean countries, it is uncommon for consumers to urchase sulementary rivate insurance covering out-of-ocket exenditures. See OECD 2014). 10

11 The first-order conditions of the rofit-maximisation roblems defined above are given by π b b = λ 1 2αn t b 2 b 1 n )) n = 0, 9) i g i=1 π i g i g = 2λα t b b 2 i ) 1 g + 1 λ) n + α i+1 g 2t g ) + g i 1 ) 2α i g = 0, i = 1,..., n. 10) t g Alying symmetry i g = g for all i = 1,..., n), the candidate equilibrium rices are given by b n) = 1 λ) t b λ) t g ) t b 4nα 1 λ) t b + 3λt g ) 11) g n) = 2 λ) t g t b 2nα 1 λ) t b + 3λt g ) 12) As exected, a higher number of generics roducers will lead to lower rices of all drugs in the market. The following Lemma defines the condition for the existence of this equilibrium: Lemma 1 Under ure coinsurance, there is a unique Nash equilibrium in the rice game, for a given number of firms, if either λ is sufficiently high or t g is sufficiently low relative to t b. The equilibrium is given by 11)-12). Equilibrium existence requires that the brand-name roducer has no incentive to deviate unilaterally from its candidate equilibrium strategy by setting the rice equal to or slightly below) the generics rice and thereby cature all demand from both segments. Such a deviation is not rofitable if either the brand-biased segment is sufficiently large or if the degree of vertical differentiation between brand-name and generic drugs is sufficiently large relative to the degree of horizontal differentiation between generics drugs. A similar condition is required for equilibrium existence in all reimbursement scenarios subsequently considered in this aer. 22 Assuming that the condition stated in Lemma 1 is satisfied, the demand and market share) of the brand-name drug is given by 22 Notice also that D b b n), g n) ) = λ 1 λ) t b λ) t g ). 13) 2 1 λ) t b + 3λt g ) b n) g n) = 1 λ) t b + 2t g 2λ 1)) t b, 4nα 1 λ) t b + 3λt g) which is ositive under the general conditions for equilibrium existence rovided in Lemma 1. 11

12 A noteworthy feature of the equilibrium under ure coinsurance is that the brand-name market share does not deend on the number of generic cometitors. In this equilibrium, generic entry will reduce brand-name and generic drug rices and therefore coayments) roortionally, leaving the brand-name market share unchanged. The equilibrium rofits of the two tyes of drug suliers are given by π b b n), g n) ) = λt b 1 λ) t b λ) t g ) 2 8nα 1 λ) t b + 3λt g ) 2, 14) π g b n), g n) ) = 2 λ)2 t b t g 1 λ) t b + 2λt g ) 4n 2 α 1 λ) t b + 3λt g ) 2 f. 15) In a free-entry equilibrium i.e., the subgame erfect Nash equilibrium of the full game), the equilibrium number of generics roducers, n, is the highest integer number that satisfies the following weak inequality, 2 λ) 2 t b t g 1 λ) t b + 2λt g ) 4 n ) 2 α 1 λ) t b + 3λt g ) 2 f 0. 16) 4 Reference ricing Suose now that the reimbursement scheme is based on reference ricing. Let the reference rice set by the regulator, which defines the maximum rice to be reimbursed, be given by r. We will focus on the case in which r lies somewhere between the rices of brand-name and generic drugs, which is the most frequently observed case in ractice. 23 The consumers coayments for the brand-name drug and for generic drug i, resectively, are then given by c b = αr + b r 17) and c i g = α i g. 18) Alying the terminology of Brekke et al. 2011), we will distinguish between two different 23 It is not common to set the reference rice below the lowest generic drug rice. Moreover, if the reference rice is higher than the brand-name drug rice, we have a de facto ure coinsurance scheme, as described in the revious section. 12

13 cases: i) exogenous reference ricing, where r does not deend on actual drug rices, and ii) endogenous reference ricing, where r is endogenously determined as a function of the rices chosen by the drug suliers. Although most countries that use reference ricing ractice some form of endogenous reference ricing, the case of exogenous reference ricing is arguably the best aroximation to reimbursement schemes where the reference rice is not frequently udated or where udates are not based on redefined rules. There are also a few examles of countries that exlicitly use an exogenous reference ricing scheme, such as Belgium and Norway Exogenous reference ricing Alying the coayment rules given by 17)-18), the rofit maximisation roblems of the brandname roducer and the generics roducer i, at the second stage of the game, are given by, resectively, max π i g i = i g g max π b = b λ b 1 2n t b αr + b r α n 2λ αr + b r α i ) 1 g + 1 λ) t b n + α n i=1 i+1 g i g )) + i 1 g 2t g, 19) 2 i ))) g. 20) We will here look for a Nash equilibrium in the rice game that imlies an interior solution, with i g < r < b. Assuming an interior solution, the first-order conditions of the rofit-maximisation roblems defined above are given by π b b = λ 1 2n t b 2 b 1 α) r α n )) n = 0, 21) i g i=1 π i g i g = 2λ b 1 α) r 2α i ) 1 g + 1 λ) t b n + α i+1 g 2t g ) + g i 1 ) 2α i g = 0, i = 1,..., n. t g 22) Alying symmetry i g = g for all i = 1,..., n) and simultaneously solving 21)-22), the equilibrium candidate rices are b r, n) = t b 1 λ) t b λ) t g ) + 2nr 1 α) 1 λ) t b + 2λt g ), 23) 4n t b 1 λ) + 3λt g ) 24 See Carone et al. 2012) for a detailed overview. 13

14 g r, n) = t g 2 λ) t b 2 1 α) λnr). 24) 2nα 1 λ) t b + 3λt g ) As for the case of drug reimbursement based on ure coinsurance, drug rices are monotonically decreasing in the number of generic firms. It is worth noting, though, that changes in the reference rice, r, have oosite effects on brand-name and generic drug rices. As long as the reference rice lies between generic and brand-name rices, a reduction in the reference rice makes the brand-name drug relatively more exensive for consumers, which, all else equal, shifts demand from brand-name to generic drugs. The otimal resonse from a generic brand-name) roducer is therefore to increase reduce) its rice. The conditions for these rices to constitute a Nash equilibrium in the rice game are given by the following Lemma: Lemma 2 Under exogenous reference ricing, there is a unique Nash equilibrium with an interior solution in the rice game, for a given number of firms, if the following conditions are satisfied: i) r < r < r, where r := 2 λ)t b t g 2n1 λ)αt b +λ2α+1)t and r := t b 1 λ)t b +1+λ)2t g) g) 2n1 λ)1+α)t b +2λ2+α)t ; ii) g) λ is sufficiently high or t g is sufficiently low relative to t b. The equilibrium is given by 23)-24). Assuming that these conditions are satisfied, the brand-name market share and the rofits of both tyes of drug roducers are, in equilibrium, given by 25 D b b r, n), g r, n) ) = λ 1 λ) t 2 b λ) t bt g α) nr 1 λ) t b + 2λt g ) ) 2t 1 λ) t b + 3λt g ) 25) and π b b r, n), g r, n) ) = λ t b 1 λ) t b λ) t g ) + 2nr 1 α) 1 λ) t b + 2λt g )) 2 8nt b 1 λ) t b + 3λt g ) 2, π g b r, n), g r, n) ) = 1 λ) t b + 2λt g ) 2 λ) t b 2 1 α) λnr) 2 t g 4αn 2 t b 1 λ) t b + 3λt g ) 2 f. 27) Note that changes in the reference rice affect equilibrium rofits in a way that corresonds to the equilibrium rice resonses. For a given number of firms, a lower reference rice benefits generics roducers at the exense of the brand-name roducer. Since π g b r, n), g r, n) ) is 25 Notice also that b r, n) g r, n) = 2nr 1 α) 1 λ) αt b + 2λ 1 + α) t g) t b 2 2 λ) t g 2αt g λ + 1) αt b 1 λ)), 4nα 1 λ) t b + 3λt g) which is ositive for r r, r). 26) 14

15 monotonically decreasing in n, the number of generics roducers in a free-entry equilibrium, n, is given by the highest integer number that satisfies the following weak inequality, 1 λ) t b + 2λt g ) 2 λ) t b 2 1 α) λn r) 2 t g 4α n ) 2 t b 1 λ) t b + 3λt g ) 2 f 0, 28) and that simultaneously satisfies the conditions in Lemma Endogenous reference ricing Under endogenous reference ricing systems, the reference rice is calculated as a function of one or more drug rices in the market. 26 A formulation that is sufficiently general to cature several realistic ossibilities is r = 1 β) b + β n n i g, 29) where the reference rice is a linear combination of the brand-name drug rice and the average rice of all generic drugs. A higher value of β 0, 1) imlies that cheaer drugs are given larger weights when calculating the reference rice. In a symmetric equilibrium, β = 1 imlies that the reference rice is equal to the lowest rice in the market. Notice also that β = 0 is equivalent to a ure coinsurance scheme. Alying the coayment rules given by 17)-18), and where r is given by 29), the rofit maximisation roblems of the brand-name roducer and the generics roducer i, at the second stage of the game, are given by, resectively, i=1 max π b = b λ b 1 2nθ t b b 1 n n i g i=1 )), 30) max π i g i = i g g λ 2 1 α) β θ b t b n )) n i g α i 1 g + 1 λ) n + α i+1 g + g i 1 2 i ))) g, 2t i=1 g 31) where θ := α + 1 α) β 0, 1). The first-order conditions of these rofit maximisation 26 Some countries base the reference rice only on the lowest generic drug rice in a reference grou, while others set the reference rice at the average or median rice. See, for instance, Carone et al. 2012) for an overview of the different reference ricing schemes in Euroe. 15

16 roblems are π i g i g = 2λ t b θ b 1 α) β n π b b = λ 2 i g + j i 1 2nθ t b j g 2 b 1 n n i=1 i g )) = 0 32) 2α i 1 g +1 λ) n + α i+1 g + i 1 g 4 i )) g = 0 2t g Note here how the endogeneity of the reference rice gives the suliers of generic drugs incentives to rice strategically in order to influence the reference rice. By reducing its rice, a generics roducer will enforce a reduction in the reference rice, which makes the brand-name drug more exensive and therefore shifts demand towards generic drugs. This effect, which is catured by the second term in the first arenthesis in 33), is stronger when β is higher or when n is lower which imlies a larger weight on each single generic drug rice in the reference rice formula). Reference ricing also gives the brand-name roducer incentives to reduce its rice second term in 32)), because demand becomes more elastic for rices above r. Alying symmetry i g = g for all i = 1,..., n) and simultaneously solving 33)-32), the equilibrium candidate rices are 33) b β, n) = nα 1 λ) t b λ) t g ) + 2βt g 1 α) n + λ)) t b, 34) 4nθ nα 1 λ) t b + 3λt g ) + λβt g 1 α) n + 2)) g β, n) = 2 λ) t b t g 2 nα 1 λ) t b + 3λt g ) + λβt g 1 α) n + 2)). 35) As for the case of ure coinsurance or exogenous reference ricing, it is straightforward to confirm that all drug rices are decreasing in n. They are also monotonically decreasing in β. The more weight the rices of generic drugs carry in the reference rice formula, the lower are the rices set by all drug suliers in the market. The condition for these rices to constitute a Nash equilibrium in the rice game is given by the following Lemma: Lemma 3 Under endogenous reference ricing, there is a unique Nash equilibrium in the rice game, for a given number of firms, if either λ is sufficiently high or t g is sufficiently low relative to t b. The equilibrium is given by 34)-35). 16

17 Given that this condition is satisfied, the equilibrium brand-name market share is given by 27 D b b β, n), g β, n) ) = λ 2 nα 1 λ) t b λ) t g ) + 2βt g 1 α) n + λ). 36) nα 1 λ) t b + 3λt g ) + βλt g 1 α) n + 2) It is easily confirmed that the brand-name market share is increasing in n. The reason for this erhas surrising result is related to the fact that changes in n have artly counteracting effects on the ricing incentives of brand-name and generics roducers. An increase in n makes the demand for all drug tyes more elastic, which all else equal leads to lower rices. This is the dominant effect for both brand-name and generic drugs. However, an increase in n also has a counteracting effect on the ricing incentives of generics roducers. A higher number of generic drugs imlies that the rice of each of these drugs has a smaller weight in the reference rice formula, which reduces the incentive for each generic roducer to strategically reduce its rice in order to induce a lower reference rice. Thus, increased generic cometition leads to a larger rice reduction for brand-name than for generics roducers, to the extent that the equilibrium brand-name market share increases. The equilibrium rofits of both tye of drug suliers are given by π b b β, n), g β, n) ) = λt b nα 1 λ) t b λ) t g ) + 2βt g 1 α) n + λ)) 2 8nθ nα 1 λ) t b + 3λt g ) + βλt g 1 α) n + 2)) 2, 37) π g b β, n), g β, n) ) = t bt g 2 λ) 2 nα 1 λ) t b + 2λt g ) α) βλt g ) 4n nα 1 λ) t b + 3λt g ) + βλt g 1 α) n + 2)) 2 f. 38) Since π g b β, n), g β, n) ) is monotonically decreasing in n, the number of generics roducers in a free-entry equilibrium, n, is given by the highest integer number that satisfies the following weak inequality, t b t g 2 λ) 2 n α 1 λ) t b + 2λt g ) α) βλt g ) 4n n α 1 λ) t b + 3λt g ) + βλt g 1 α) n 2 f 0, 39) + 2)) and that simultaneously satisfies the condition in Lemma Notice also that b β, n) g β, n) = nα 1 λ) t b + 2 2λ 1) t g) + 2βt g 1 α) λ + λ 1) n)) t b, 4nθ nα 1 λ) t b + 3λt g) + βλ 1 α) n + 2) t g) which is ositive under the general conditions for equilibrium existence given by Lemma 3. 17

18 4.3 Pure coinsurance versus reference ricing Let us now comare the two reimbursement systems considered ure coinsurance and exogenous or endogenous) reference ricing and see how the choice of reimbursement scheme affects equilibrium drug rices and rofits for a given number of firms, and how it consequently affects generic entry. Proosition 1 Suose that the conditions given by Lemmas 1-3 are satisfied. Then, for a given number of firms, the rice equilibrium under reference ricing is characterised by lower rices for all drugs and a higher brand-name market share, comared with the rice equilibrium under ure coinsurance. These results hold regardless of whether the reference rice is exogenous or endogenous. The intuition for the rice reducing effect of reference ricing is fairly straightforward. Since reference ricing makes demand for the brand-name drug more rice elastic for rices above the reference rice), the brand-name roducer will resond by lowering its rice. Although reference ricing makes generic drugs relatively cheaer all else equal), and therefore gives the generics roducers an isolated incentive to raise rices, the strategic comlementarity of rice setting ensures that generic rices also dro. 28 As shown by Proosition 1, this second effect dominates for the entire set of arameter values that ensure equilibrium existence. Furthermore, if the reference rice is endogenous, the generic roducers also have an extra incentive to reduce rices, since such rice reductions will reduce the reference rice and therefore make the brandname drug more exensive for consumers. 29 In many ways, though, the key result in Proosition 1 is not that reference ricing leads to lower rices, which is intuitive and exected, but that the reduction in brand-name rices is roortionally larger than the reduction in generic rices, imlying that the market share of the brand-name drug increases. When reference ricing whether endogenous or exogenous) leads to a reduction in both rice and demand for generics roducers, the imlications for generic entry follow directly: 28 For the case of exogenous reference ricing, note the difference between switching from ure coinsurance to reference ricing and changing the reference rice within the latter system. Whereas generic rices are lower under reference ricing than under ure coinsurance for any r r, r), a reduction in r under an exogenous reference ricing system leads to an increase in generic drug rices, as discussed in Section Note that the results in Proosition 1 hold also for the secial case of λ = 1. Thus, our results do not deend crucially on the resence of a brand-neutral consumer segment. 18

19 Corollary 1 Suose that the conditions given by Lemmas 1-3 are satisfied. Then, in a free entry equilibrium, the number of generic drugs is weakly) higher under ure coinsurance than under exogenous or endogenous) reference ricing. In some sense, this result might be seen as counterintuitive, since reference ricing is a reimbursement scheme designed to give generics roducers a cometitive advantage vis-à-vis brand-name roducers. Indeed, for given drug rices, a switch from ure coinsurance to reference ricing will shift demand towards generic drugs and therefore benefit generics roducers. However, as Proosition 1 shows, such a switch will also trigger rice resonses such that the generics roducers end u with lower rofits. Thus, a switch from ure coinsurance to reference ricing will lead to fewer generic drugs in a free entry equilibrium. 4.4 Can reference ricing lead to higher rices? When taking into account the effect on generic entry, the intended cost-containing effect of reference ricing is no longer obvious. In our model it is not analytically feasible to give a recise characterisation of the required conditions for reference ricing to lead to higher rices or not. However, we have constructed a set of numerical examles which illustrate both ossibilities and therefore allow us to gain some further insights into the effects of reference ricing. Tables 1 and 2 show the effects of going from a reimbursement system with ure coinsurance to a reimbursement system based on reference ricing. We consider two different cases regarding demand: Table 1 illustrates Case 1, where consumers are almost exclusively brand biased, whereas Table 2 shows Case 2, with a larger brand-neutral demand segment, but where the degree of vertical differentiation between brand-name and generic drugs is larger than the degree of horizontal differentiation between generic drugs. In each of the two cases, we vary the arameters α and β to show how the exact design of the reimbursement system affects the comarison between ure coinsurance and reference ricing, and we also consider both tyes of reference ricing: endogenous and exogenous. 30 [Table 1 here] [Table 2 here] 30 In all numerical examles, the arameters are chosen such that the conditions for equilibrium existence are satisfied. 19

20 Consider first the effects of introducing endogenous reference ricing. In all arameter configurations considered, the introduction of endogenous reference ricing leads to fewer generic drugs in the free entry equilibrium the only excetion is for α = 0.4 in Case 2, where reference ricing has no effect on entry). This negative entry effect contributes to an increase in average drug rices av := D b b + 1 D b ) g ), and therefore higher total drug exenditures, for three different arameter configurations: α = 0.4; β = 0.5) and α = 0.6; β = 0.5) in Case 1, and α = 0.6; β = 0.5) in Case 2. In all of these three cases, the increase in the average drug rice is caused by a combination of two effects: i) all drug rices increase because of less generic cometition), and ii) a large share of consumers choose the most exensive drug. Endogenous reference ricing Even with the limited amount of different arameter configurations on dislay, a relatively clear attern can still be detected. Endogenous reference ricing will not lead to higher drug rices if the coinsurance rate α is sufficiently low or if the weight β on the cheaest drugs in the reference rice formula is sufficiently large. This has a fairly intuitive exlanation. A low coinsurance rate imlies that drug demand is very inelastic over all relevant rice intervals) in a ure coinsurance system, which in turn imlies that equilibrium drug rices are relatively high. The introduction of reference ricing will therefore have a large effect on the rice elasticity of demand for rices above the reference rice). The direct rice-reducing effect of reference ricing will therefore outweigh the effect of less generic cometition, leading to an overall reduction in drug rices. This also aears to be the case if β is given a sufficiently large value in the reference rice formula. A higher value of β imlies that each generic roducer can more effectively reduce the reference rice by reducing the rice of its drug. This stimulates rice cometition and increases the direct rice-reducing effect of reference ricing. It is worth noticing, though, that in all examles where endogenous reference ricing leads to a higher average drug rice, the increase in exenditures is entirely borne by the consumers, who face an increase in average drug coayments c av ) as a combined result of a higher coayment for the brand-name drug because of reference ricing) and higher drug rices because of less generic cometition). 31 For the third-arty ayer, on the other hand, the introduction 31 Average drug coayment is given by α av under ure coinsurance, and by α 1 D b ) g + D b r)+ b r) D b under reference ricing. 20

21 of endogenous reference ricing always yields a reduction in drug ayments av c av ) in the examles considered in Tables 1 and Even if reference ricing leads to higher rices for all drugs, the increase in atient coayment for the brand-name drug is large enough to yield savings for the ayer. This suggests that endogenous reference ricing is likely to be more beneficial for the third-arty ayer than for consumers. Exogenous reference ricing The rightmost column in Tables 1 and 2 shows the effect of introducing exogenous reference ricing. For each arameter configuration, we have chosen a value of the reference rice such that the Nash equilibrium exists and yields an interior solution, with g < r < b. 33 Since the exact choice of the reference rice for each case is rather arbitrary, a comarison of the effects for different values of the coinsurance rate α) is somewhat less meaningful. Likewise, a comarison between the effects of endogenous and exogenous reference ricing must also be done with some care, since there is no obvious way of making a like-for-like comarison. Nevertheless, some aarently clear atterns can still be identified. First, exogenous reference ricing aears to have a stronger negative effect on generic entry, even if the exogenous reference rice is higher than the equilibrium endogenous reference rice. In addition, and artly as a result of less generic cometition, the equilibrium brand-name market share is consistently higher under exogenous reference ricing. The imlication for average drug rices is striking: in all but one case, going from ure coinsurance to exogenous reference ricing leads to higher average drug rices the excetion is for α = 0.4 in Case 2). Furthermore, in 4 out of the 5 different arameter configurations where exogenous reference ricing leads to a higher average drug rice, the increase in drug exenditures is aid not only by consumers, but also by the third-arty ayer the only excetion is for α = 0.2 in Case 1). In sum, these numerical examles suggest that reference ricing is more likely to yield rice reductions if the reference rice is endogenously determined, and if a larger weight is given to 32 We have, unsuccessfully, tried to find numerical examles of endogenous reference ricing leading to higher exenditures also for the ayer. Although we cannot rule out this ossibility, the clear attern emerging from our model is that, if endogenous reference ricing leads to an increase of total exenditures, this increase is likely to be borne by the atients and not by the ayer. 33 If r is given a sufficiently low value, all firms will otimally rice above the reference rice. But this is equivalent to the case of ure coinsurance with α = 1. Such equilibria would offer little insurance to consumers and is to our knowledge not alied in ractice, and are therefore disregarded. 21

22 low-riced drugs in the reference rice formula. 5 Reference ricing and rice ca regulation We have so far assumed that the harmaceutical firms freely can set rices without any constraints excet for the demand-side cost sharing rules defined by the reimbursement schemes. In ractice, however, most countries also aly suly-side regulations that constrain the firms rice setting in order to control the medical exenditures. The most common rice control scheme is to enforce maximum rices that harmaceutical firms can charge for a given roduct. 34 In this section, we therefore analyse the effect of introducing reference ricing in markets with rice ca regulation. In the revious section, we find that reference ricing always reduce generic entry due to the aggressive rice resonse by the brand-name roducer. However, in markets with rice regulation, the brand-name roducer s rice setting is constrained by a binding rice ca. A key question is therefore whether reference ricing actually can stimulate generic cometition in the resence of rice regulation. We consider the case where drug roducers are subject to rice ca regulation and are not allowed to set rices in excess of, regardless of the reimbursement system. We assume that the rice ca binds for the brand-name roducer but not for the generics roducers; otherwise generic cometition will not take lace. With a binding rice ca, the Nash equilibrium in the rice game under ure coinsurance and for a given number of firms) is then a corner solution with the following rices: b =, 40) g, n) = 1 λ) t b + 2nαλ) t g nα 1 λ) t b + 4λt g ), 41) where the candidate equilibrium rice g is found by inserting b = into 10), alying symmetry, and solving for g. The following Lemma states the condition for equilibrium existence: Lemma 4 Under ure coinsurance, and for a given number of firms, the unique Nash equilibrium in the rice game is a corner solution, given by 40)-41), if the following conditions 34 In Euroe, rice ca regulation is highly common; see Carone et al. 2012). 22