GENERIC DRUG INDUSTRY DYNAMICS
`
`David Reii’fen and Michael R. Ward’
`
`Abstractmaecatlse of its unique institutional and regulatory features. the
`generic drug industry provider I useful laboratory for understanding how
`competition evolves. We exploit these features to mtimate a system of
`structural relationships in this industry. including the relationship between
`price and the number ofcompetitors. and between drug characteristics and
`the entry process. Our methidology yields a number of findings regarding
`industry dynamics. We find that generic drug prices fall with increasing
`mimber of competitors. but remain above long-run marginal cost until
`there are eight or more competitors, We also find the size and time paths
`of genenc revenues. rents. and the number of firms are greatly aflected by
`expected market size Finally. we show how estimates du'lved from a
`system of structural equations can be used to simulate the effect of
`changes in an exogenous variable.
`
`I.
`
`Introduction
`
`0th the economics literature and the business press
`suggest that a typical pattern for a “new" industry [or
`what Jovanovic and MacDonald 0994) call an invention] is
`to have an initial phase in which a small number of firms
`each earn significant profits, followed by a phase in which
`rapid entry of new firms leads to increased competition and
`dissipation of some of those profits. often accompanied by
`a shakeout. whereby only a few large firms remain (espe-
`cially if subsequent innovations increase the optimal scale).
`Although this pattern seems to characterize many industries.
`the length of time during which early movers retain their
`profits. how prices adjust during the entry process. and the
`degree of shakcout vary widely across industries (Gon &
`Kleppor. 1982). Because the factors that influence the tim-
`ing of entry and exit are idiosyncratic to each industry,
`empirical studies of this process tend to focus on a single
`industry (see. for example. Gisser. 1999; Klepper & Simons.
`2000). and in a sense constitute a single data point. making
`generalizations tenuous.
`Several characteristics of the generic drug industry result
`in it being a useful laboratory for understanding how com-
`petition evolves within a market. First. each chemical rep-
`resents a distinct experiment. here are a large number of
`individual experiments within the same industry, providing
`multiple observations on similar dynamic processes.‘ Sec-
`ond. information about the market for each drug is observ-
`
`is. 2009. Revision accepted for
`
`Received for publication October
`publication October- 28. 2003.
`' Commodity Futures Trading Commission and University of‘l'exas at
`Arlington. respectively.
`We world like to thank our former employer. Ihe Federal Trade Com-
`mism'on. for admiring the data; David Balm. Denis an. Bill Crowda.
`George Deltas. Craig Deplten. Haj Hadeishi. Ron Hansen. Dan Beckett.
`Paul Pruner. and Mick Vaman for their helpful comments on previous
`drafts of this paper: Dr. lanes Loverde for technical advice: and Sara
`Harkavy for assistance. The views cxpreswd in this paper are solely those
`of the authors. and not necessarily those of their current or past employers.
`' Bresnahan and Reiss (I991) also loolt at industries with multiple (in
`their case. geographic) markets in each industry. Their work focuses on
`characterizing how the static equilibrium varies across markets. rather
`than intramarkct dymicr.
`
`able to researchers.2 For example. because a market begins
`when the patent on an existing drug expires. the date at
`which the market opens to competitors is known in advance
`and the potential revenue can be projected with some
`accuracy by both participants and researchers. Because
`entry occurs at observable points in time. the consequences
`of changes in the number of producers on pricing is mea-
`surable. Moreover, because entry requires Food and Drug
`Administration (FDA) approval, firms must sink significant
`costs to apply for approval prior to knowing when. or how
`many. rivals will enter the market. Hence.
`firms must
`determine if their expected postoentry rents are sufficient to
`justify the costs sunk prior to entry.
`These features enable us to impose restrictions from
`economic theory that identify the key structural relation—
`ships describing the evolution of these markets. No simul-
`taneously determined relationships are the effect of avail-
`able rents on the pattern of entry over time and the effect of
`changes in industry structure (namely. entry) on rents. The
`latter relationship can be estimated because the process of
`FDA approval takes the timing of entry decisions out of the
`hands of individual firms. so that the number of firms at any
`point in time is not determined by the current price. yet the
`price is affected by the number of competitors. Thus we can
`estimate the effect of the number of firms on current price.
`assuming that current industry structure is exogenous. Com-
`bining that with estimates of revenue. we are able to
`calculate the expected rents conditional on the number of
`competitors and the elapsed time since market opening
`We develop an iterative estimator to determine the effects
`of rents on may. A unexpected-profit condition is ex-
`ploited that equates the expected number of entrants to the
`ratio of total generic industry rents to sunk entry costs per
`firm. At
`the same time.
`the rents available to potential
`entrants will depend on the number of entrants. We estimate
`the probability of any number of competitors in each time
`period as a function of the available rents. We then use these
`estimates, together with the industry rents conditional on the
`number of firms and time. to calculate the available rents.
`Equilibrium is obtained when the rents predicted by the
`entry parameters equal the rents assumed in their estimation.
`Our structural estimates yield a number of empirical
`findings. First. consistent with previous worit. we find that
`generic drug prices fall with an increase in the number of
`competitors. Though estimating the relationship between
`market strucnrrc and prices is a necessary component of
`estimating our system of structural relationships. the esti-
`
`7 We use the terms market. generic drug. and chemical interchangeably.
`All three terms simly refer to a prescription drug whose patent has
`expired. In particular. the use of the term mire! may notcorrecpond to its
`antitrust meaning.
`
`"it Review of (immune: and Statistics. February 2003. BTU): 37-49
`0 2005 by the Presktent and Fellow: of Harvard College aid the Massachusetts institute of Technology
`
`1
`
`Exhibit 2066
`Slayback v. Sumitomo
`|PR2020—01053
`
`Exhibit 2066
`Slayback v. Sumitomo
`IPR2020-01053
`
`

`

`38
`
`THE REVIEW OF ECONOMICS AND STATISTICS
`
`mated effect of entry on price is also of independent interest.
`for this relationship has been an area of ongoing interest in
`the industrial organization literature.3 We calculate that
`prices for the initial generic monopolist are 20%-30% (or
`perhaps even more) above long-run marginal costs. Generic
`prices steadily decline with an increase in the number of
`producers and begin to approach long-run marginal cost
`when there are 10 or more competitors. Second. more firms
`enter, and enter more quickly,
`in markets with greater
`expected rents. Fatally. we find that the flow of generic
`industry profits increases as revenues grow, but begin falling
`after 5 to l2 months, as entry reduces price-cost margins. In
`amnion, we find that this pattern is awelerated in larger
`markets because competitors enter more quickly.
`An advantage of estimating the set of stnrctural relation-
`ships tint constitute the equilibrium is that one can trace
`through the effect of changes in market characteristics on
`the equilibrium. This can be particularly valuable in evalu-
`ating the effects of alternative policies. To illustrate the use
`of these estimates to inform policy. we simulate the effect of
`an actual change in the competitive environment
`in this
`industry.
`In response to a scandal
`involving illegitimate
`approvals. the FDA increased its scrutiny of generic drug
`applications in mid-1989. Though the policy may have
`allowed the FDA to discover. and therefore reject. more
`substandard applications, it also raised the cost of obtaining
`FDA approval for qualified applicants. Our estimates pro-
`vide a means of determining the effect of the higher entry
`costs on long—run generic prices.
`
`II. Background
`
`Before marketing a new chemical entity. a prospective
`manufacttn'er must obtain FDA approval. To obtain a new
`drug approval (NDA) from the FDA requires demonstrating
`that a drug is safe and efficacious. which is both expensive
`and time-consuming.
`It has been estimated that for the
`average drug that was obtained FDA approval in the 19905.
`its producer had spent over $335 million (in 2000 dollars)
`on development. and an additional $467 million on clinical
`and other testing.‘ In addition, the clinical trial process took
`approximately 8 years.
`Prior to 1984. producing a generic version of most exist-
`ing drugs involved a similar application process. Although
`the generic producer did not face the cost of drug discovery.
`it still bore the costs of demonstrating the safety and
`efficacy of its version. The WaxmamHatch Act in 1984
`created an abbreviated new drug approval (ANDA) proce-
`dure that reduced the regulatory burden for generic produc-
`ers by requiring only that they demonstrate bioequivalence
`to a drug that was already approved by the FDA. The ability
`
`’See Bresnahan (I989) for a discussion and analysis of this literature.
`‘ See DiMasi. Hansen. and Grabowslti (2003). This figure represents the
`expected cost ofa successful drug. in the sense that it is taijustnd for the
`probability that a drug never obtains an NBA.
`
`to avoid safety and efficacy testing considerably reduced the
`cost of obtaining FDA approval. As discussed below. we
`estimate that the cost of applying for an ANDA (including
`the cost of the requisite testing) wm approximately
`$603,000 in the early 19905 (and approximately $338,000 in
`the period immediately following passage of the Act).
`Not surprisingly.
`this expedited approval process has
`increased the number of firms producing generic versions of
`previously patented drugs. Cook (1998) reports that for 13
`major drugs with patents expiring between 1990 and 1993.
`11 had generic entry within 2-months of patent expiration.
`In contrast. she notes that in Caves. Whinston. and Hur-
`wicz's (1991) study of pre-Waxman-Hatch entry (between
`1976 and 1982). only 2 of the top 13 drugs had generic entry
`within 1 year of patent expiration.
`Entry still requires significant up-front expenditures. with
`a payoff that depends both on the FDA's decisions with
`respect
`to a firm’s application, and the timing of FDA
`approval of rivals” ANDA applications. The time it takes the
`FDA to process applications cart be both considerable and
`variable. In the vast majority of cam. the initial ANDA
`application is found deficient, requiring the applicant to
`conduct additional tests or submit additional material. 0f-
`ten, approval is granted only after the applicant has gone
`through two or three resubmissions. Hence. from the appli-
`cant's perspective. the time between initial submission and
`FDA approval is quite variable. Scott Morton (1996) calcu-
`lates that between 1984 and 1994 the time between the
`initial application and approval of ANDAs averaged ap—
`proximately 19 months. with considerable year-to-year vari-
`ation. in addition. entry requires time to obtain an approved
`source of materials and adequate production facilities. In
`total. the applicant has to anticipate 2 to 3 years elapsing
`from the time it begins preparing to enter until it can begin
`selling a generic drug.
`
`III. Modding lndtutry Dynamics
`
`No features of the entry process in this industry are
`imponant
`to understanding industry dynamics. First. an
`entrant‘s tinting of entry into the market is largely not under
`its control. Not only is the date of its approval by the FDA
`uncertain, but each applicant lacks knowledge of when, or
`how many. other ANDAs for that dnrg will be approved.
`Thus, potential entrants make their entry decisions simulta-
`neously (although actual entry will typically be sequential).
`Second. an individual entrant’s share of the aggregate ge-
`netic profits will depend greatly on when it gains approval
`relative to other generic producers. Firms gaining approval
`earlier face fewer competitors irtitially. and are able to sell
`for a longer time. There is some evidence that earlier
`entrants earn greater profits even after rivals have entered.5
`
`’ In addition to anecdotal evidmce from industry participants. Cook
`(I998) shows that sales are highly concentrated arming firms in each
`
`

`

`GENERIC DRUG INDUSTRY DYNAMICS
`
`39
`
`Together these two features create a “lottery" for prospec—
`tive producers of a generic version of a drug. If a firm
`obtains early approval. it is likely to earn a positive return
`on its application-related costs, whereas firms obtaining
`approval later in tire process are likely not to recover their
`sunk costs. Thus,
`in contrast to markes in which entry
`decisions are sequential and competition results in the last.
`or marginal entrant earning zero profit, here the number of
`firms adjusts until
`the average firm earns zero profit.6
`Specifically (assuming I: identical applicants), the expected
`profit for each firm from applying for an ANDA is
`
`A. The Effect of Generic Industry Structure on Profit:
`
`Generic pricecost margins are estimated as a function of
`observable market characteristics. including the number of
`generic competitors. We are interested in a specific aspect of
`the relationship between margins and the number of com—
`petitors, an aspect that is not explicitly examined elsewhere:
`how the marginal effect of an additional competitor on a
`drug's prices changes with the number of firms that already
`have an ANDA for that drug. To address this question. we
`estimate a regression of the form
`
`_ _L g .
`BPl
`ErpeaedProfit —- E["]
`
`n
`
`V
`
`(Emilia)‘A=Em‘A.
`
`(1)
`
`where H, is total generic industry profits at time t with i
`firms in the market. pi, is the probability that I firms are in
`the market at time t. A is the cost of applying for an ANDA,
`and B is the discount factor. V is defined as the present value
`of the stream of expected rents for all generic producers of
`a drug. The goal of the empirical analysis in this paper is to
`estimate the key parameters of equation (1). Specifically. we
`estimate the interrelationships that allow us to calculate the
`11,-, and p. as functions of exogenous. drug-specific vari-
`ables. The remainder of this section details the estimation
`
`procedure. In brief. each Huerta be thought of as the product
`of two factors: total revenue and price-cost margins. Ac-
`cordingly. we calculate the IL, by combining the results of
`regressions of each of price-cost margins and revenues
`against explanatory variables. such as time since patent
`expiration. Given these estimates. we can then determine IL,
`conditional on any given i and I. To calculate the probability
`that a given II, occurs (p..). we estimate two strucurral
`relationships: the relationship between the number of appli-
`cants for ANDAs (n) and rents in a market (V). and the
`relationship between the timing of FDA approval and rents.
`Thus. for any given levels of rents (and given set of
`exogenous variables), we can use these two relationships to
`calculate 9... Note that because total rents both determine
`and are determined by pk. these relationship must be esti-
`mated simultaneously.
`
`markat; even in markets with mom: than m firms. the top two generic
`[reducers typically sell more than 60%ofthe units. Bond and Lean (I977)
`and Banal er a]. 0993) provide severaI examples of drug: for which the
`first entrain had a substantial atlvuruge.
`‘Consequently. in contrast to the markets examined here. in a market
`with sequential entry. din-gee in the profits earned by the first entrant will
`not change subsequent firms' incentive to enter. Another important differ
`ence between generic drug markets (where entry decisions can be viewed
`as aimuhaneout) and other markets is that an exogenous change in the
`number of competitors (for example. due to a merger several years after
`patent expiration) can lead to higher prices without iruiticing entry. even if
`firms omside the market have the same entry costs as the incumbents.
`
`(2)
`
`where P", is the price in the postvpatentexpiration period
`when there are t‘ generic firms with FDA approval producing
`chemical k. and P“ is the price of the branded version of
`product It during the year prior to patent expiration.’ D,- is a
`dummy variable that equals 1 when there are i generic
`producers of chemical k and 0 otherwise. and the X” are
`variables representing demand or cost shifters for drug It.
`Using dummy variables for the number of generic pro-
`ducers imposes no specific structure on the relationship
`between price and the number of competitors. This contrasts
`with some previous work, in which a specific structure on
`the relationship is assumed (for example. an a priori func-
`tional form is imposed on the effect of more firms on
`generic prices)" Each such specification makes implicit
`assumptions about the pattern of price effects that can result
`from entry. For example.
`the implicit assumption made
`when the number of firms is used as an explanatory variable
`is that the effect of an increase by l in the number of firms
`is independent of the initial number of firms. By allowing
`the marginal effect of an additional firm to vary with the
`number of firms. we can examine questions such as the
`number of firms necessary to lead to approximately mar-
`ginal cost pricing. Allowing the marginal effect to vary is
`also important to our goal of accurately measuring the rents
`associated with any specific number of generic competitors.
`This relationship can be viewed as structural only it one
`views the number of firms at any time as exogenous. One
`standard criticism of empirical studies of the relationship
`between market structure and prices is that structure is not
`exogenous. but rather is determined by the profitability of
`
`7 We use the branded price before pacnt exp'ntion. rather than the
`contemporaneous branded price, because the Iarter is likely to be deter-
`nrined jointly with the generic price (a noted in footnote 2 l. the anpirical
`evidence on tit importance of this relationship is mixed). In “It!!!“ the
`branded price before there is any generic entry is likely to be independent
`of the number of generic producers in futtue periods
`3For example.
`in other studies of generic drug common. generic
`price is assumed to vary Enemy with j. the number of
`(Frank and
`Sanrevcr. I997); with j and [1 (Caves. Whinston. a Hurwicz. FBI): or
`mmjand thflViuinsa Mane“. 2004).mediscussedu
`greatu length in section V.
`
`

`

`40
`
`THE REVIEW OF ECONOMICS AND STATISTICS
`
`entering the market.9 This criticism implies that the ob-
`served cross—sectional relationship between price and the
`number of firms is an equilibrium relationship reflecting
`market-specific differences. and not a structural one reflect~
`ing the effect of more competitors on price. That is. as
`equation (1) illustrates. the number of firms applying for
`ANDAs adjusts in response to the available rents. However.
`in the generic drug industry. the nature of the FDA review
`process makes it unlikely that the number of firms at a point
`in time is affected by current price. within the time series of
`prices for any one drug. Most ANDA applications are
`submitted before the generic market even exists. and the
`number of competitors at any point in time depends on the
`FDA review process (most applications must be resubmitted
`multiple times). Hence.
`though the eventual number of
`approvals for a drug is related to the aggregate rents. the
`actual number of FDA-approved firms at any point in time
`may plausibly be considered independent of the contempo-
`raneous price. A potential endogeneity issue arises when
`aggregating across drugs bemuse there are unobserved
`difi‘erences between drugs that might affect both prices and
`the number of entrants. We control for these between-drug
`effects by estimating a random—effects model. This model
`allows there to be differences across drugs in the average
`relationship between generic prices and pre-patent—expiration
`branded prices (see Greene. 2003).lo Finally. we tested this
`potential cndogeneity using a Hausman test and cannot reject
`the null hypothes's that market structure is exogenous in the
`pricing equation (l-lausrnan, 1978).“
`In principle. N in equation (2) could be the maximum
`number of entrants observed in the data. In practice. we take
`N to be the minimum number of entrants such that the price
`effect of further entry is negligible. The interpretation of a.)
`is the ratio of the generic price when there are more than N
`generic producers to the branded price that prevailed before
`patent expiration. if all other independent variables were
`equal to 0. The other 01,-, such as as, are the increments in the
`ratio over 010 when there are r‘ producers. Because no reflecrs
`the ratio below which additional ”entry does not lead to
`lower prime, we view ((10 + 23x”) P“ as the long-run
`marginal production cost of drug k (where X” is the mean
`value of )9 for drug 1:). Under this assumption. afluo +
`a, + 27, x”) is a measure of the price-cost margin with i
`generic producers.
`The other relationship required for calculating V condi-
`tional on the Dr, is the relationship between generic revenue
`
`“This criticism dates back a least to Demsetz (I973). For more formal
`analysis. see Blesaahan (I989).
`'° Other- studies have allowed for drug-specific effects by including
`market-specific dummy variables. Either assumption allows calculation of
`the avenge ell'ect of increasing the number of competitors in a market.
`“ Following Frank and Salkever(l997) and Caves et al. (199]). we use
`time s'mce patent expiration and pie-patent branded revenues as instru-
`meras for the number of genetic firms. Because Ive do not leave enough
`instruments to atimale equation (2). our endogeneity tests employ several
`common ftmctioaal forms of the number of competitors.
`
`and market-specific variables. Our estimation of this rela-
`tionship is of the form
`
`J
`
`In (a, 9..) = to + n In (Pat 9..) + 2 1.x...
`1-2
`
`(3)
`
`where Pk. Q” is total monthly generic industry revenue at
`time t in market It. PM (2.. is the branded film’s average
`monthly revenue during the year prior to patent expiration.
`and the XE,- are other variables that might affect generic
`revenue. The XV will include many of the same variables as
`equation (2).
`
`B. The Efl'ccr of Industry Pmfitabiliry an Entry
`
`The model we use to examine entry decisions traits each
`of M timts as homogeneous in regard to their ability to enter
`and produce a generic dmg. We assume that generic rents
`are not sufficient to allow all M potential entrants to prof-
`itably enter any market. but that they are sufficient to allow
`one firm to earn profits in any market. We also make the
`natural assumption that each firm’s profits from producing a
`drug are decreasing in the number of rival producers of the
`dmg. We conceptualize the entry decision as each firm
`choosing independently and simultaneously whether to en-
`ter each market. This reflects the reality that each generic
`producer must
`independently decide whether to enter a
`market. at a point usually 2 to 3 years prior to patent
`expiration. The symmetric (mixed strategy) Nash equilib-
`rium in this case will consist of each firm i choosing to enter
`market It with some probability p“, where that M may
`depend on the expected rents in the market.'2 The symmet-
`ric Nash equilibrium in each market consists of a pk that is
`common to each firm. and that has the property that each
`firm optimally chooses it. given that all of its rivals have
`chosen that same [L‘- The p.) in the Nash equilibrium yields
`zero expected profits.
`the logic being that
`if an entry
`probability generates sufficiently few expected entrants so
`that each entrant expects to earn positive profits. then any
`firm would be better off unilaterally changing its strategy to
`entering with probability l (and entering with probability 0
`if expected profits are negative). Comparing across drugs,
`the equilibrium in will be increasing in the expected rents
`associated with that dnig. so that we expect to see more
`entrants for higher-V. drugs
`One feature of this stylized game is that, because each
`firm‘s decision whether to enter is independent of all other
`firms‘ decisions. the equilibrium distribution of the number
`of entrants will follow a binomial distribution. We use the
`Poisson distribution as an approximation of the binomial to
`
`'1 An alternative equilibrium concept is employed by Berry (I992). who
`assumes that fimts' uttry costs differ. Given variation in entry costs. a
`pure-strategy equilibrium can emerge. in which only low-entry-cost firms
`Clllfl.
`
`

`

`GENERIC DRUG INDUSTRY DYNAMICS
`
`41
`
`This function is defined in terms of the hazard proportion-
`ality parameter as Sh = expo-M t). Then. using equation
`(4) and the binomial formula, we calculate the probability
`that i fimts have ANDAs in market It in period t as
`
`p... = Slim) 62%“ — su)‘ .r'.
`
`(7)
`
`C. The Endogeneity Qfltentr and Identification
`
`Equations (2). (3). and (7) together make up the compo—
`nents of equation (I) and thus allow for the calculation of
`industry rents.
`
`derive the density function of the number of entrants in
`market It as
`
`fin.) = exp( - u.) ui‘lnt! .
`
`(4)
`
`where u, is the equilibrium entry probability. The zero-
`expected-profits condition implies that Eh.“ == E[VI. Be-
`cause Eln.) = MN with the Poisson distribution, this yields
`Elm/Mm. = A; that is. applications costs are equal
`to
`expected rents divided by the expected number of entrants.
`This implies that holding M and A constant. there should be
`a direct relationship between V). and us. There is reeson to
`believe. however. that application costs increased substan-
`tially in I989. when it was discovered that some ANDAs
`had been fraudulently obtained. and that the FDA reacted by
`increasing its scrutiny of applications (Scott Morton. 1996).
`We attempt to capture this in a dummy variable. Sm'ngem.
`that equals l for the period after mid-1989 and Oodterwise.
`Consequently. we estimate the relationship between it; and
`the cost and benefit of applying as
`
`P4 = Vt €XP(¢: + 4’2 Sifi"gemk)
`
`(5)
`
`from a cross section of 3l drugs. This relationship charac-
`terizes how the number of entrants adjusts to changes in the
`costs and benefits of FDA approval. it also provides us with
`a means of estimating the time series of entry within each
`market. because the expected number of producers at each
`point in time depends on the total number of applications. as
`detailed below.
`For any given number of applicants. the pattern of entry
`will depend on the FDA review process. Our second entry
`equation characterizes the timing of entry. conditional on
`the total number of entrants. To reflect the stochastic nature
`(from the applicants' perspective) of the FDA review pro-
`cess, we model the rate of entry as a proportional hazard
`function in which the proportionality parameter is possibly
`affected by rents available and FDA regime. Specifically. we
`posit a probability x of any firm that has not yet been
`approved obtaining an ANDA during month t. We estimate
`the following relationship for M:
`
`In A, = 6. + 62V, + 83 Sm‘ngenn.
`
`(6)
`
`We postulate that )t. may be increasing in Vb because
`firms apply earlier in high-Vt markets and/or have a greater
`incentive to file accurately. Because the value of X may also
`depend on the regulatory environment. equation (6) in-
`cludes Stringenr. our postscandal dummy variable. These
`parameters are estimated from data on the time to entry for
`all entrants in each of 31 generic drugs.
`Combining equations (4) and (6) allows us to calculate
`the time path of expected entry. as a function of rents and
`the FDA regime. Specifically. we use the estimate of M from
`equation (6) to determine the survivorship function, where
`surviving means the applicant has not yet been approved.
`
`VA 3‘ 2 B' ( 2 Danna:
`
`- 2 B’ (2 p... ; p. 9.).
`
`"I
`
`‘
`
`all
`
`n
`
`Pi I —
`In
`
`(1')
`
`However. equation (7). goveming the entry process. also
`depends on the magnitude of the expected available rents
`through equations (5) and (6). Larger expected rents V
`generate larger probabilities of entry. u. shifting the prob-
`abilities p toward more firms at any point in time. which by
`equation (I ’) tends to reduce expected rents V. Because V is
`endogenous. via equation (1'). we develop an iterative
`process to estimate the parameters of equations (5) and (6).
`The mixed—strategy simultaneous-move Nash equilibrium
`suggested above will represent a stable fixed point in the
`mapping of V onto V under certain conditions. Specifically.
`the system of equations consisting of equations (1 ’). (5) and
`(6), along with subsidiary relationships embodied in those
`equations [for example. equation (2) within equation (1')].
`will have a fixed point (W, h“. pf) if equations (2) and (3)
`indicate that per-finn profits are decreasing in the number of
`firms. and equations (5) and (6) indicate that )t and p. are
`such that the expected number of firms at every point in
`time is increasing in V. To see why (V*. A“, pt“) represents
`a fixed point, consider an alternative V. Va > V“. Because
`V' > V", the x and p. based on V” will lead to more firms
`at each point in time if the second stability condition
`holds. Consequently. if the first stability condition holds,
`the V resulting from this it and y. will be less than V‘.
`Hence. V‘s above V" map to lower V‘s. and V5 below V“
`map to higher Vs.
`The actual calculation of the fixed point follows this same
`logic. la the first iteration. we calculate V. using equation
`(1') based on arbitrary values of h and it. along with the
`parameters estimated in equations (2) and (3). We then
`estimate the h and ‘L. using equations (5) and (6) with VI on
`the right-hand side. These are used to calculate fin), the
`density of at, and the pit, according to equations (4) and (7).
`
`

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`42
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`THE REVIEW OF ECONOMICS AND STATISTICS
`
`We combine the n, and pin from this iteration with the arm
`calculated from equations (2) and (3) to calculate V2. We
`then compare V2 with V. and if the two values are suffi-
`ciently close. we view the process as convergent; that is.
`these values of )t. p, and V are the equilibrium. If the
`predicwd Vis sufficiently different from the initial value. we
`repeat
`the process. using V; as the right-side value in
`reestimating equations (5) and (6). and then calculating V3
`based on the new A and p. and the unchanged pm. In this
`way. we iterate through a series of V; until we obtain
`convergence.
`
`IV. Data
`
`Our primary source for price and quantity data is Generic
`Spectra" from [MS Inc., a proprietary vendor of informa-
`tion to the pharmaceutical industry. The [MS data provide
`information on 31 drugs that went off patent in the late
`1980s and early l9908. and subsequently faced competition
`from generic producers (see table 4). It includes information
`on monthly price and quantity for the patent holder and
`generic entrants for 3 years subsequent to patent expiration
`and 3 years prior to patent expiration (for the patent holder).
`These data include prices derived from two distinct sources:
`product shipments and price surveys. For both sources the
`data are provided separately for each strength (for example.
`50 mg) and form (for example. oral solid) of the drug.
`The shipment-based data on revenues and quantities are
`derived primarily from shipments by distributors (who pur-
`chase from manufacturers) to pharmacies and other dispens-
`ers. A small proportion, perhaps 5%. of sales are made
`directly by manufacturers. The sales by distributors are
`captured by 1M5 directly monitoring the shipments of a
`high percentage of distributors (98% of all such shipments
`are contained in their sample). This is combined with
`estimates of direct sales of manufacturers. which are esti-
`mated from a sample of invoices. Our measure of price per
`kilogram is the average revenue for a particular strength and
`form derived by dividing total generic revenue by the
`number of kilograms of genetic product. We calculate this
`price sepmately for all genetic sales. and for sales by the
`first generic entrant"
`The second set of prices in Generic Spectra is obtained
`from a sample of pharmacies. It includes data on average
`transaction prices paid by pharmacies. Awording to [M5,
`the measured acquisition price would reflect all relevant
`discounts, with the exception of year-end quantity discounts
`provided by some manufacturers. We calculate acquisition
`prices for both the