GENERIC DRUG INDUSTRY DYNAMICS
`
`David Reiffen and Michael R. Ward*
`
`Absiract-—Because ofits uniqueinstitutional and regulatory features, the
`generic drug industry provides a useful laboratory for understanding how
`competition evolves. We exploit these features to estimate a system of
`structural relationships in this industry, including the relationship between
`price and the number of competitors, and between drug characteristics and
`the entry process. Our methodology yields a number offindings regarding
`industry dynamics, We find that generic drug prices fall with increasing
`number of competitors, but remain above long-run marginal cost unt!
`there are eight or more competitors, We also find the size and time paths
`of generic revenues,rents, and the numberoffirms are greatly affected by
`expected market size. Finally, we show how estimates derived from a
`system of structural equations can be used to simulate the effect of
`changes in an exogenous variable.
`
`L.__
`
`Introduction
`
`oth the economics literature and the business press
`suggest that a typical pattern for a “new” industry [or
`what Jovanovic and MacDonald (1994)call an invention] is
`to have an initial phase in which a small numberoffirms
`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).
`Althoughthis pattern seemsto characterize many industrics,
`the length of time during which early movers retain their
`profits, how prices adjust during the entry process, and the
`degree of shakeout vary widely across industries (Gort &
`Klepper, 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. There 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 obsery-
`
`Received for publication October 15, 2002. Revision accepted for
`publication October 28, 2003.
`* Commodity Futures Trading Commission and University of Texas at
`Arlington,respectively.
`We would like to thank our former employer, the Federal Trade Com-
`mission, for acquiring the data; David Balan, Denis Breen, Bill Crowder,
`George Deltas, Craig Depken, Haj Hadeishi, Ron Hansen, Dan Hosken,
`Paul Pautler, and Mick Vaman for their helpful comments on previous
`drafts of this paper; Dr. James Loverde for technical advice: and Sara
`Harkavy for assistance. The views expressed in this paper are solely those
`ofthe authors, and not necessarily those of their current or past employers.
`‘Bresnahan and Reiss (1991) also look at industries with multiple (in
`their case, geographic) markets in cach industry. Their work focuses on
`characterizing how the static equilibrium varies across markets, rather
`than intramarket dynamics.
`
`able to researchers.” 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 mustsink significant
`costs to apply for approvalprior to knowing when, or how
`many, rivals will enter the market. Hence,
`firms must
`determine if their expected post-entry 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. Two simul-
`taneously determined relationships are the effect of avail-
`able rents on the pattern of entry over time andthe 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 ofthe
`hands ofindividualfirms, so that the number offirms at any
`point in time is not determined by the currentprice, yet the
`price is affected by the number of competitors. Thus we can
`estimate the effect of the numberoffirms oncurrentprice,
`assumingthat 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 developan iterative estimator to determinethe effects
`of rents on entry. A zero-expected-profit condition is ex-
`ploited that equates the expected numberofentrants 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
`numberof 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 work, we find that
`generic drug prices fall with an increase in the number of
`competitors. Though estimating the relationship between
`market structure and prices is a necessary component of
`estimating our system of structural relationships, the esti-
`
`? We usc the terms market, generic drug, and chemical interchangeably.
`All three terms simply refer to a prescription drug whose patent has
`expired.In particular, the use of the term market may not correspond to its
`antitrust meaning.
`
`The Review of Economics and Statistics, February 2005, 81(1): 37-49
`© 2005 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology
`
`1
`
`Exhibit 2066
`Slayback v. Sumitomo
`IPR2020-01053
`
`Exhibit 2066
`Slayback v. Sumitomo
`IPR2020-01053
`
`

`

`38
`
`THE REVIEW OF ECONOMICS AND STATISTICS
`
`mated effect of entry on price is also of independentinterest,
`for this relationship has been an area of ongoing interest in
`the industrial organization literature? 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. Finally, we find that the flow of generic
`industry profits increases as revenues grow, butbegin falling
`after 5 to 12 months, as entry reduces price-cost margins. In
`addition, we find that this pattern is accelerated in larger
`markets because competitors enter more quickly.
`An advantage ofestimatingthe set of structural relation-
`ships that 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 estimatesto inform policy, we simulatethe effect of
`an actual change in the competitive environment
`in this
`industry.
`In response to a scandal
`involving illegitimate
`approvals, the FDAincreased 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
`FDAapproval for qualified applicants. Our estimates pro-
`vide a meansof determining the effect of the higher entry
`costs on long-run generic prices.
`
`Il, Background
`
`Before marketing a new chemical entity, a prospective
`manufacturer must obtain FDA approval. To obtain a new
`drug approval (NDA)from the FDArequires 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 1990s,
`its producer had spent over $335 million (in 2000 dollars)
`on development, and an additional $467 million on clinical
`and othertesting.‘ In addition, the clinical trial process took
`approximately 8 years.
`Prior to 1984, producing a generic version of mostexist-
`ing drugs involved a similar application process. Although
`the generic producerdid notface the cost of drug discovery,
`it still bore the costs of demonstrating the safety and
`efficacy of its version. The Waxman-Hatch 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. Theability
`
`3 See Bresnahan (1989) for a discussion and analysis of this literature.
`* See DiMasi, Hansen, and Grabowski (2003). This figure represents the
`expected cost of a successful drug, in the sense that it is adjusted for the
`probability that a drug never obtains an NDA,
`
`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) was approximately
`$603,000 in the early 1990s (and approximately $338,000 in
`the period immediately following passage of the Act).
`Not surprisingly,
`this expedited approval process has
`increased the number offirms 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
`approvalofrivals’ ANDAapplications. The time it takes the
`FDAto process applications can be both considerable and
`variable. In the vast majority of cases, the initial ANDA
`application is found deficient, requiring the applicant to
`conduct additional tests or submit additional material. Of-
`ten, approval is granted only after the applicant has gone
`through two or three resubmissions. Hence, from the appli-
`cant’s perspective, the time betweeninitial submission and
`FDAapproval 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.
`
`Til. Modeling Industry Dynamics
`
`Two features of the entry process in this industry are
`important
`to understanding industry dynamics. First, an
`entrant’s timing ofentry into the marketis 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 drug 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-
`neric profits will depend greatly on whenit gains approval
`relative to other generic producers. Firms gaining approval
`earlier face fewer competitors initially, and are able to sell
`for a longer time. There is some evidence that earlier
`entrants carn greater profits even after rivals have entered.>
`
`‘In addition to anecdotal evidence from industry participants, Cook
`(1998) shows that sales are highly concentrated among firms in cach
`
`

`

`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 carn a positive return
`on its application-related costs, whereas firms obtaining
`approval later in the process are likely not to recover their
`sunk costs. Thus,
`in contrast to markets 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.
`Specifically (assuming n identical applicants), the expected
`profit for each firm from applying for an ANDAis
`
`A. The Effect of Generic Industry Structure on Profits
`
`Generic price-cost 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 numberoffirms that already
`have an ANDAforthat drug. To address this question, we
`estimate a regression of the form
`
`=
`
`il
`ot
`
`V
`
`Py
`Nol
`a + Y a,D,+ Dy Xp,
`i=]
`i
`
`(2)
`
`ExpectedProfit= Ein~?(Som). =Fn) 74
`
`(1)
`
`where Pi is the price in the post-patent-expiration period
`whenthere are i generic firms with FDA approval producing
`chemical k, and P,, is the price of the branded version of
`where II, is total generic industry profits at time ¢ with i
`product k during the year prior to patent expiration.” D;is a
`firmsin the market, p;, is the probability that i firms are in
`dummy variable that equals 1 when there are i generic
`the market at time¢, A is the cost of applying for an ANDA,
`producers of chemical k and 0 otherwise, and the Xy are
`andBis the discountfactor. V is defined as the present value
`variables representing demand or cost shifters for drug k.
`of the stream of expected rents for all generic producers of
`Using dummy variables for the number of generic pro-
`a drug. The goal of the empirical analysis in this paper is to
`ducers imposes no specific structure on the relationship
`estimate the kcy parameters of equation (1). Specifically, we
`between price and the number of competitors. This contrasts
`estimate the interrelationships that allow us to calculate the
`with some previous work, in which a specific structure on
`Tl, and p; as functions of exogenous, drug-specific vari-
`the relationship is assumed (for example, an a priori func-
`ables. The remainder of this section details the estimation
`tional form is imposed on the effect of more firms on
`generic prices).§ Each such specification makes implicit
`procedure.In brief, each H,, can be thoughtofas the product
`assumptions aboutthe pattern ofprice effects that can result
`of two factors: total revenue and price-cost margins. Ac-
`from entry. For example,
`the implicit assumption made
`cordingly, we calculate the IT, by combining the results of
`when the numberoffirmsis used as an explanatory variable
`regressions of each of price-cost margins and revenues
`is that the effect of an increase by | in the numberoffirms
`against explanatory variables, such as time since patent
`is independentof the initial number of firms. By allowing
`expiration. Given these estimates, we can then determine [];,
`the marginal effect of an additional firm to vary with the
`conditional on any given i and 7. To calculate the probability
`number of firms, we can examine questions such as the
`that a given Il, occurs (p,), we estimate two structural
`numberof firms necessary to lead to approximately mar-
`relationships: the relationship between the numberof appli-
`ginal cost pricing. Allowing the marginal effect to vary is
`cants for ANDAs ({n) and rents in a market (V), and the
`also important to our goal of accurately measuring the rents
`relationship between the timing of FDA approval and rents.
`associated with any specific number of generic competitors.
`Thus, for any given levels of rents (and given set of
`This relationship can be viewed as structural only if one
`exogenous variables), we can use these two relationships to
`views the numberoffirms at any time as exogenous. One
`calculate p;. Note that because total rents both determine
`standard criticism of empirical studies of the relationship
`and are determined by p,, these relationship must be esti-
`between market structure and prices is that structure is not
`mated simultaneously.
`exogenous, but rather is determined by the profitability of
`
`market; even in markets with more than ten firms, the top two generic
`producers typically sell more than 60% ofthe units. Bond and Lean (1977)
`and Berndt et al. (1995) provide several examples of drugs for which the
`first entrant had a substantial advantage.
`§ Consequenily, in contrast to the markets examined here, in a market
`with sequential entry, changes in the profits cared by the first entrant will
`not change subsequentfirms’ incentive to enter. Another important differ-
`ence between generic drug markets (where entry decisions can be viewed
`as simultaneous) 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 inducing entry, even if
`firms outside the market have the same cntry costs as the incumbents.
`
`7 We use the branded price before patent expiration, rather than the
`contemporaneous branded price, because the latter is likely to be deter-
`mined jointly with the generic price (as noted in foomote 21, the empirical
`evidence on the importance ofthis relationship is mixed). In contrast, the
`branded price before there is any geacric entry is likely to be independent
`of the number of generic
`jucers in
`periods,
`5 For example,
`in other studies of generic drug Sapgenn: generic
`Price is assumed to vary linearly with j, the number of
`(Frank and
`Satkever, 1997); with j and j? (Caves, Whinston, & Hurwicz, 1991); or
`with j and 1/j (Wiggins & Maness, 2004). These papers are discussed at
`greater length in section Y.
`
`

`

`40
`
`THE REVIEW OF ECONOMICS AND STATISTICS
`
`entering the market.” 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
`ANDAsadjusts in responseto the available rents. However,
`in the generic drug industry, the nature of the FDA review
`process makesit unlikely that the number offirms at a point
`in time is affected by currentprice, within the time series of
`prices for any one drug. Most ANDA applications are
`submitted before the gencric market even exists, and the
`number of competitors at any point in time depends on the
`FDAreview 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 because there are unobserved
`differences 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 mode]
`allows there to be differences across drugs in the average
`relationship between generic prices and pre-patent-expiration
`branded prices (see Greene, 2003).!° Finally, we tested this
`potential endogeneity using a Hausman test and cannot reject
`the null hypothesis that market structure is exogenousin the
`pricing equation (Hausman, 1978).!!
`In principle, N in equation (2) could be the maximum
`numberofentrants observed in the data. In practice, we take
`N to be the minimum numberof entrants such that the price
`effect of further entry is negligible. The interpretation of ap
`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 «,, such as a, are the increments in the
`ratio Over @ when there are i producers. Because ag reflects
`the ratio below which additional entry does not lead to
`lower prices, we view (a + Zy;Xxy) Pp, as the long-run
`marginal production cost of drug k (where X,, is the mean
`value of X; for drug k). Under this assumption, a/(ay +
`a, + Dy, X,;) is a measure of the price-cost margin with i
`generic producers.
`The other relationship required for calculating V condi-
`tional on the p;, is the relationship between generic revenue
`
`° This criticism dates back at least to Demseuz (1973). For more formal
`analysis, see Bresnahan (1989).
`Other studies have allowed for drug-specific effects by including
`market-specific dummy variables. Either assumption allowscalculation of
`the average effect of increasing the number of competitors in a market.
`'' Following Frank and Salkever (1997) and Caveset al, (1991), we use
`time since patent expiration and pre-patent branded revenues as insiru-
`ments for the number of generic firms, Because we do not have enough
`instruments to estimate equation (2), our endogeneity tests employ several
`common functional forms of the number of competitors.
`
`and market-specific variables. Our estimation of this rela-
`tionship is of the form
`
`J
`In (Puy Qui) = ty + 1; In (Pre Qe) + Dy Xys
`pez
`
`(3)
`
`where P;, Qy, is total monthly generic industry revenue at
`time ¢ in market kK, Ps, Qj, is the branded firm’s average
`monthly revenue during the year prior to patent expiration,
`and the X, are other variables that might affect generic
`revenue. The X,; will include many of the same variables as
`equation (2).
`
`B. The Effect of Industry Profitability on Entry
`
`The model we use to examine entry decisions treats each
`of M firms as homogeneous in regardto their ability to enter
`and produce a generic drug. We assume that generic rents
`are notsufficient to allow all Mf 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 numberofrival producers of the
`drug. We conceptualize the entry decision as each firm
`choosing independently and simultaneously whether to en-
`ter each market. This reflects the reality that cach 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 k with some probability ry, where that jr, may
`depend on the expected rents in the market.'? The symmet-
`ric Nash equilibrium in each market consists of a 1; that is
`commonto each firm, and that has the property that each
`firm optimally chooses it, given that all of its rivals have
`chosen that same p44. The jy, 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 changingits strategy to
`entering with probability 1 (and entering with probability 0
`if expected profits are negative). Comparing across drugs,
`the equilibrium js, will be increasing in the expected rents
`associated with that drug, 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 whetherto enter is independentof 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
`
`"2 An alternative equilibrium concept is employed by Berry (1992), who
`assumes that firms’ entry costs differ. Given variation in entry costs, a
`pure-strategy equilibrium can emerge, in which only low-enwy-cost firms
`enter.
`
`

`

`GENERIC DRUG INDUSTRY DYNAMICS
`
`41
`
`This function is defined in terms of the hazard proportion-
`ality parameter as S;, = exp(—A, f). Then, using equation
`(4) and the binomial formula, we calculate the probability
`that i firms have ANDAsin market k in period 1 as
`
`pur = Din) ogg (I SuSE.
`
`!
`
`7)
`
`C. The Endogeneity of Rents and Identification
`
`Equations (2), (3), and (7) together make up the compo-
`nents of equation (1) and thus allow for the calculation of
`industry rents,
`
`derive the density function of the number of entrants in
`market k as
`
`(ny) = exp(— na) wr’! ,
`
`(4)
`
`where 1, is the equilibrium entry probability. The zero-
`expected-profits condition implies that E[mJA = E[V]. Be-
`cause E[n,] = Mp, with the Poisson distribution, this yields
`E[V./Mp, = 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 j1,. There is reason to
`believe, however, that application costs increased substan-
`tially in 1989, 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).
`Weattempt to capture this in a dummy variable, Stringent,
`that equals | for the period after mid-1989 and 0 otherwise.
`Consequently, we estimate the relationship between p, and
`the cost and benefit of applying as
`
`Hi = V, exp(, + 2 Siringeni,)
`
`(5)
`
`from a cross section of 31 drugs. This relationship charac-
`terizes how the numberof 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 onthe total numberofapplications, as
`detailed below.
`For any given numberof 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 numberofentrants. 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 byrents available and FDA regime.Specifically, we
`posit a probability X of any firm that has not yet been
`approved obtaining an ANDA during month f. We estimate
`the following relationship for Ag
`
`In Ay = 8, + 6,V, + 8, Stringent, .
`
`(6)
`
`Wepostulate that A, may be increasing in V, because
`firms apply earlier in high-V, markets and/or have a greater
`incentive to file accurately. Because the value of \ may also
`depend on the regulatory environment, equation (6) in-
`cludes Stringent, 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 \; from
`equation (6) to determine the survivorship function, where
`surviving means the applicant has not yet been approved.
`
`V, = x p'|> Pilly,
`
`- Se" [5 uso" Py0. .
`
`tet
`
`-
`
`i=t
`
`:
`
`P; :
`ike
`
`a’)
`
`However, equation (7), governing 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, 4, shifting the prob-
`abilities p toward more firmsat any point in time, which by
`equation (1’) 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-moye 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 (V*, A*, 4.*) if equations (2) and (3)
`indicate that per-firm profits are decreasing in the number of
`firms, and equations (5) and (6) indicate that A and p. are
`such that the expected number of firms at every point in
`time is increasing in V. To see why (V*, A*, *) represents
`a fixed point, consider an alternative V, V7 > V*. Because
`ve > V*, the \ and pt 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 A and p will be less than V*.
`Hence, V’s above V* map to lower V’s, and V’s below V*
`map to higher V’s,
`The actual calculation of the fixed point follows this same
`logic. In the first iteration, we calculate V, using equation
`(1‘) based on arbitrary values of \ and p, along with the
`parameters estimated in equations (2) and (3). We then
`estimate the \ and j., using equations (5) and (6) with V; on
`the right-hand side. These are used to calculate fin), the
`density of 2, and the pj, according to equations (4) and (7).
`
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`THE REVIEW OF ECONOMICS AND STATISTICS
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`We combine the m and pj, from this iteration with the atx,
`calculated from equations (2) and (3) to calculate V>. 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 A, p, and V are the equilibrium. If the
`predicted V is sufficiently different from the initial value, we
`repeat
`the process, using V; as the right-side value in
`recstimating equations (5) and (6), and then calculating V,
`based on the new \ and p and the unchanged 7. In this
`way, we iterate through a series of V> until we obtain
`convergence.
`
`IV. Data
`
`Ourprimary source for price and quantity data is Generic
`Spectra® from IMS Inc., a proprietary vendor of informa-
`tion to the pharmaceutical industry. The IMS data provide
`information on 31 drugs that went off patent in the late
`1980s and early 1990s, 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 pharmaciesand other dispens-
`ers. A small proportion, perhaps 5%, of sales are made
`directly by manufacturers. The sales by distributors are
`captured by IMS directly monitoring the shipments of a
`high percentageof distributors (98% ofall 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 generic product. We calculate this
`price separately for all generic 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. According to IMS,
`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 first and the average generic seller.
`For drugs with multiple strength-form com