Journal of Law, Economics, and Organization

Journal of Law, Economics, and Organization Advance Access published online on April 22, 2009
Journal of Law, Economics, and Organization, doi:10.1093/jleo/ewp002

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Early Entrant Protection in Approval Regulation: Theory and Evidence from FDA Drug Review

Daniel Carpenter^*

Harvard University

Susan I. Moffitt

Harvard University

Colin D. Moore

Harvard University

Ryan T. Rynbrandt

Collin County Community College

Michael M. Ting

Columbia University

Ian Yohai

Harvard University

Evan James Zucker

Harvard Medical School

^* Department of Government, Harvard University, Cambridge, Massachusetts. Email: dcarpenter{at}gov.harvard.edu.

	Abstract

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
Early entrant protection in approval regulation exists when the first incumbents in an exclusive market niche receive more favorable regulatory treatment than later entrants. We show that this pattern can prevail for two reasons: regulatory capture and consumer co-optation. We consider a decision-theoretic model of dynamic product approval by an uncertain regulator. The model predicts early entrant protection even when later entrants offer quality improvements over market incumbents. We then test the model using duration analyses of New Drug Application approval times for 1080 new molecular entities submitted to the US Food and Drug Administration (FDA) from 1950 to 2006 and later approved. FDA approval times are shown to be increasing in order of market entry for the entire period studied and across numerous subsamples. A standard deviation rise in the log of order of entry is associated with a 3.6-month increase in expected FDA approval time. The entry-order gradient appears to be heavily influenced by disease-level variables but not by firm-level effects, supporting a consumer co-optation explanation and disfavoring capture and producer rent-seeking accounts. The gradient appears heightened by the 1962 Kefauver-Harris Amendments but unaffected by the 1992 Prescription Drug User Fee Act; the influence of some disease-level factors upon the gradient may have been reduced by the 1992 statute. (JEL C44, I18, L51, H11)

	1. Introduction

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
Government regulation is often associated with reduced or delayed firm entry into markets. Such a characterization is especially apt for those markets in which the government directly determines entry through an approval or licensing process. In these markets, firms must literally wait for the government to allow them into the market, assuming of course that the firm is successful in its entry application. In this article, we argue that one approval process—US Food and Drug Administration (FDA) review of new molecular entities—serves to give decided advantages to the earliest entrants to pharmaceutical markets, in the sense that those who enter markets sooner receive quicker regulatory approvals. We call this pattern early entrant protection,¹ and in this article we offer a formalized explanation for it. We also document and quantify early entrant protection with precise estimates of its magnitude.

Early entrant protection links the power of the state to crucial regulatory outcomes. Consider "the industry" in the capture theory of regulation to represent market incumbents or "earlier entrants." As interpreted by capture theory, early entrant protection would provide market incumbents with added and prolonged shelter from competition. Incumbent firms will usually benefit from regulatory impediments to competition (e.g., regulatory delay in approving later entrants), whereas consumers will usually lose out from regulatory hurdles to market entry through delayed price and quality competition. If early entrant protection exists, then, it has notable distributive consequences for firms and consumers alike. Indeed, these consequences form the basis for a capture-theoretic explanation for early entrant protection, inasmuch as earlier entrants will find it in their interest to lobby the regulator to delay market entry for their competitors.

We think something else—something that may look like capture but is quite different —is going on. Our analysis focuses upon a rather different explanation for early entrant protection: the political co-optation of organized consumers by an astute regulator. If organized consumers—acquired immune deficiency syndrome (AIDS) patients, for example—can impose costs upon a regulator by protesting or otherwise lobbying for regulatory approval of products beneficial to them, then one effect of product approval will be to dampen this political demand for yet-to-be-approved products. Under simple and flexible assumptions regarding the ability of products to "satisfy" organized consumers, analysis of the model shows that the earlier entrants to a market always have the greatest marginal satisfaction; hence, their more rapid approval represents a way for the regulator to co-opt noisy citizens by throwing them a bone.

We formalize this logic in a repeated optimal stopping model of product approval by an uncertain yet politically responsive regulator. The model predicts early entrant protection even when firms are unorganized and have no differential clout. A key prediction of the model is that early entrant protection should hold even when the regulator expects products to improve in the future. The model also issues in several predictions about the effect of product development or R&D on regulatory approval. The first amounts to a "curse of investment" for those markets in which the regulator delays current aspirants to the market because it expects high-quality entrants to submit products with more frequency in the future. A flip-side of this prediction is that we should witness less early-entrant protection when the pipeline of future therapies is "closer" temporally to the present.

We conclude by offering two hypotheses that we believe can be tested in future work and that each have important implications for the functioning of health policy and health markets. First, our framework predicts a greater prevalence of Type I errors (ex post "bad" approvals, of which Vioxx is purported to be one) for products early in the sequence. Second, we conjecture that early entrant advantages in government regulation give firms seeking entry a strong incentive to tailor product development to market niches with few entrants, even when doing so is short-term unprofitable.²

Our empirical analysis is premised upon a simple but oft-forgotten fact about health policy: there is no single market for pharmaceutical products. Instead, there exist hundreds of somewhat overlapping market niches defined by primary indications or diseased populations. To consider an obvious example, no antidepressant medication known as a selective serotonin reuptake inhibitor currently competes directly or indirectly with beta-blockers or statin medications for the treatment of cardiovascular ailments. The two classes of drugs treat starkly different medical conditions. To some extent this niche exclusivity is shaped by regulation, though this is not the focus of our analysis here.

We calculate the order of market entry for pharmaceuticals in a given therapeutic class and show it to be consistently and positively associated with FDA approval times for new drugs. This relationship is remarkably robust. It prevails in the early years of drug regulation, before the Kefauver-Harris Amendments of 1962, and it prevails in the period from 1962 to the present. It prevails within any number of therapeutic categories, from cardiovascular drugs to neurological drugs. It prevails across estimations with numerous controls for the burden of disease and other factors salient to drug approval. We also show that the relationship has a remarkably stable functional form when it is in evidence, in the sense that log-linear protection functions are to be preferred to linear ones.

More broadly, our model and results are consistent with recent arguments that regulatory regimes in licensure and product approval do not conform well to traditional capture and rent-seeking explanations (Carpenter 2004b; Law and Kim 2005; Law 2006; Law and Marks 2007). Institutions of pharmaceutical regulation in the United States, Europe, and elsewhere give the state the discretionary power to permit entry of some firms into some markets while denying or delaying that of others. Yet although regulators may shed favor upon earlier entrants in approval regulation settings, these observational patterns alone cannot support an inference of capture or rent-seeking (Carpenter 2004b). The analysis and results reported here are broadly consistent with these newer, alternative accounts of regulation.

We now turn to elaborate the basic dynamics of our model.

	2. A Dynamic Model of Approval Regulation with a Farsighted Regulator

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
In a product approval, a repeated learning problem confronts a regulator, who must for each product study an entry application (with accompanying data) and decide when the apparent benefits of the product outweigh the costs or risks associated with its use. We assume that product approval regulators guard their reputation for protecting consumer safety or expertise and so view their approval decisions as fundamentally irreversible (or reversible only at cost) (for a growing literature on reputation effects in bureaucratic and regulatory behavior, see Wilson 1989; Carpenter 2001, 2002, 2004b; Krause and Douglas 2005; Krause and Corder 2007). Early approvals benefit both producing firms and organized consumers who may demand new products, and these interests can make it politically costly for the agency to delay. Regulatory delay is useful to the rational agency because it buys time and information—the ability to review the firm's potential new product more carefully and to request more studies. As in financial options, there is an informational value to waiting, which is marginally decreasing as the agency learns more.³ The problem facing the agency is that of stopping the review only once the payoff of approval exceeds both the reputational losses associated with the danger of the product and the value of waiting for more information.

2.1 Assumptions and Parameters
We stylize the model for the drug approval process as it operates in the United States and other countries. Let all drugs be indexed by i, diseases by j, and firms by k. The model assumes an exogenous industry production process in which the agency expects drugs to be submitted at a constant rate over time. Drugs are assumed to treat one disease only.⁴

All drugs in the model are characterized by two parameters. First, let _ij (0 < _ij 1) be the curing probability of the drug (which can be interpreted as the fraction of people with disease j that drug i will cure). We assume that _ij is fixed and known with certainty throughout the agency's decision problem. Second, let µ_i be the danger of the drug or the expected number of people who will be harmed or killed by the drug over a given interval of time. Normalizing the interval to 1, µ_i can be considered to be the rate of harming consumers. The greater the danger of the drug, the more its approval will harm the agency's reputation for protecting public safety. We assume throughout that a drug's danger is independent of its curing power, which implies cov(µ_i, _i) = 0.

The agency observes a series of experiments (e.g., clinical trials) in which a product either harms or does not harm the consumer. Observed harm in regulatory review evolves according to a Wiener process X_it = X(t), a linear function of underlying danger (µ), plus a random component, or

(1)

where µ (with superscript suppressed) and > 0 are constants, and where z(t) is a standard normal variable with mean 0 and variance t. The agency learns about µ by applying Bayes' Rule to the stochastic history of X(t). Without loss of generality, if X(t) starts at 0, then for any t > 0, it is normally distributed with mean µt and variance ²t. We assume that is the same across drugs but that µ differs across them, according to a normal distribution with mean m and variance s. For any drug review of length t and accumulated harm X(t) = x, the dual [x,t] constitutes a sufficient statistic for the agency's problem. Given these sufficient statistics (Chernoff 1969), Bayesian estimates of µ are

(2a)

(2b)

Notice that

(3)

The posterior variance S(t) may be thought of as the agency's uncertainty about the true value of µ. Hence, the value of waiting for another moment is an increasing function of S(t).⁵

We assume that, once a product is approved, the agency cannot recover any loss from a bad approval. This may be true even when (as in real-world settings) agencies have the option to recall a bad product, or to induce producers to recall it. Our logic again follows from reputation protection (Carpenter 2004b). Once a product has done sufficient harm that it must be recalled, the FDA cannot recover its reputational losses by recalling the drug. Everyone will know that the agency has made a "bad" decision. In this respect, the decision to approve a product (or to leave it on the market for too long) is reputationally irreversible.⁶ Upon the approval of the product, the agency pays the parameter µ, which can be learned only through preapproval review.

2.1.1 The Political Demand for Drugs and the Approval Payoff.
What makes regulatory delay costly is less economics than politics. In recent years, the FDA has appeared highly responsive to the demands of (potential) drug consumers such as AIDS activists, cancer sufferers and their advocate, and lobbyists for the mentally ill (Olson 1995; Vogel 1996; Carpenter 2002). Firms also attempt to place pressure upon the agency for quick approvals. Organized consumers and producers not only lobby the agency directly but also apply pressure indirectly through elected politicians.

We define the agency's approval payoff from approving a drug as a function (g) of disease attributes such as prevalence, severity, public salience, and the political organization of patients and the submitting firm. Generally, the payoff may be written

(4)

where L_J is disease J's prevalence, or the number of persons with disease J;⁷ _J is the political multiplier of disease J, a positive parameter. We can interpret _j as the expected number of citizens, for every citizen afflicted by disease J, who will apply pressure upon the agency or the politicians governing it. In some (but not all) cases, this parameter may not only capture the political impact of disease severity but will also be affected by the political organization of disease J's patients and advocates, that is, "public salience";

N_J – 1 is the number of marketed drugs that already treat disease J;

_K is the political clout of the submitting firm K.

2.1.2 The Agency's Optimal Policy.
With the approval payoff described as above, the problem facing the agency is the optimal stopping of the process _t, consistent with the following objective.

(5)

where is the discount factor, t_app is a given approval time, µ* is the agency's estimate of danger at the optimal stopping time [as given in (2)], denotes an elementary event in the probability space , and y is a variable of integration. The optimal policy is a first-passage-time strategy with the following time-dependent barrier (for a derivation, see Carpenter [2004b]):

(6)

where F denotes the integral of the flow value function f, and F[(t), t] is the second partial derivative of F with respect to , evaluated at at time t. We define by G*(t) the approval distribution, or the probability of approval at time t under the optimal policy, and we define E[t_app] as the expected approval time under the optimal policy. Conditioned upon the event of approval, E[t_app] is strictly decreasing in the payoff A.⁸

	3. Early Entrant Protection with a Farsighted Regulator

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
In the past two decades, the FDA has shown considerable responsiveness to pressure from organized patients and disease-specific advocacy groups.⁹ The most visible case of FDA reaction to these forces was the quickening of drug approvals for AIDS drugs in the 1980s and early 1990s (Epstein 1996). To capture the influences of disease-specific political advocacy upon pharmaceutical regulation, we specify the agency's approval payoff as a function of the political organizations of consumers (and of producers). We also provide a flexible functional form for the effect of past and future drugs on the approval payoff for the present drug. The approval payoff may be defined intuitively as follows.

For any drug i, which treats disease j and is submitted by firm k, the agency's payoff from approving the drug (denoted by A) is equivalent to the sum of all individuals with disease J who have no presently available pharmaceutical alternatives now and whom drug i would be expected to cure, where each consumer is weighted by their relative political organization (a political multiplier), and where the drug itself is weighted by the firm's political clout, and where each consumer is discounted by the approval probability and waiting time for drugs that may cure her (both therapeutically and "politically") in the future [the value an individual would attach to a "pipeline" of future therapies if it were known].

We assume that the political demand for a drug differs from the economic demand for it in an important way. Political demand is greater for those individuals who have no therapeutic alternatives for their disease. In other words, if individuals are taking a drug that ameliorates their condition in some way, then they have less political demand for any more drugs for their disease, even if these drugs would improve their condition or would be available at a lower cost. In other words, the model rests upon the assumption that, once individuals have adopted a drug, their contribution to the political demand pool drops.

In short, although individuals as consumers may maximize their health status and care about price, individuals as citizens satisfice with respect to the agency. The reason is that citizens have "traceability" constraints (Arnold 1990). They do not blame the agency for the high price of drugs—even if it is apparent that the regulatory process boosts drug prices. If the price of a drug is too high or if citizens are weakly satisfied with a drug they are taking, they blame not the agency but the producers. Among recent students of pharmaceutical regulation, Epstein (1997), Carpenter (2002), and Hilts (2003) provide argument and evidence for this characterization.

3.1 The Value of Products over Time
We associate with each drug a therapeutic value (which is simply _ij) and a political value, which denotes the possibly time-variant nature of the severity and newsworthiness of the indication disease, the target population's political organization, and the sponsoring firm's political clout. For the Nth drug in any sequence, denote this political value by _N(_J, _K|N_J) where : ²⁽⁺⁾(0, 1) maps positive variables into a value on the unit interval. We assume that _N(J) is strictly increasing in all its arguments. Hence, the greater a disease's prevalence, the greater a drug's political value, ceteris paribus, and the same is true for political organization () and firm clout ().

The immediate and unconditional value of a drug is the product of its curing value and its political value. If the agency knew that the one and only one drug were ever to be submitted for a disease, then the curing value of that drug would be equal to _1J1(J)L_J.¹⁰ Yet because drugs may already exist to treat disease j = J, the payoff for any drug is not so simple. Previously approved drugs and potentially approvable future therapies also influence the farsighted regulator's judgment.

Consider first the effect of past drug approvals upon the current drug's approval payoff. After approval of the drug, (1 – _1J1(J))L_J persons remain in the "demand pool" for the drug. If one drug (drug 1) has already been approved, then the expected curing of drug 2 would be _2J2J(1 – _1J1(J))L_J. So for any series of drugs i = 1,2, ... N, the total curing of the Nth drug conditioned upon past approvals is, suppressing J,

(7)

Pharmaceutical producers constantly introduce new drugs, and a farsighted agency will take into account this stream of future submissions as well. If the agency expects a sufficient number of high-quality drugs to be submitted for disease J in the very near future, then the approval payoff for the current drug is also lower.

To incorporate into the approval payoff, the set of drugs that will be submitted and may be approved in the future, define as the time that the Nth drug (the one currently under consideration) is submitted. Let E be the expectation operator computed at time . Let c_iJ be the mean of the curing distribution f(_iJ). Then the approval payoff for the Nth drug submitted for disease J can be written as:

(8)

The term in brackets on the second line of equation (8) is called the pipeline value and will be denoted as A. Intuitively, the pipeline value is the expected fraction of diseased population that remains after the political and therapeutic curing of the full stream of future drugs, each weighted by the probability of their approval under the optimal policy, and each fully discounted. The pipeline value is 0 only if the regulator firmly expects a "cure-all" to be approved with probability 1 immediately upon the submission of the drug. This event has negligible probability (Billingsley 1999). Hence with probability 1 almost surely, the pipeline value for any drug is positive. Since the function _N is also positive, the approval payoff is always positive for problems we consider.

Our analysis relies heavily upon the assumptions that the regulator can anticipate both (1) the quality of drugs later in the pipeline and (2) the political value of drugs later in the pipeline, if in fact political and epidemiological conditions can be anticipated. For health regulators such as the FDA, this is probably a reasonable assumption insofar as changing conditions of disease may be predicted by epidemiologists and insofar as the FDA knows a lot about the pipeline of future submissions because it regulates clinical trials.¹¹

Another characterization embedded in our model is that the regulator is not learning within therapeutic class. One might posit that the effect of learning from drugs approved earlier in a sequence of therapies should be to shorten the amount of time needed to acquire the same amount of information about subsequent drugs that treat the same or similar diseases.¹² Our model assumes no learning spillovers from one drug to another drug in a therapeutic class, and this represents a useful avenue for extension of the model. In part, we think that such spillovers are more likely to occur within molecules—to supplemental applications (sNDAs) that occur when a previously approved molecule is applied to new diseases—than for substantively distinct molecular forms.

We define early entrant protection (EEP) as the systematic advantage in expected time to approval for the first drugs approved for a disease relative to drugs developed later on. Let the protection function β(N_J) be the increased expected approval time by which an otherwise identical drug with identical history but with entry order N_J + 1 gets approved, given that N_J drugs have already been approved.

Strong early entrant protection: Expected approval times are a strictly increasing function of the order of entry, such that E[t_app(i = N_J + 1)] > E[t_app(N_J)] for all N_J. That is β(N_J) > 0 for all N_J.

Weak early entrant protection: One drug has a lower expected approval time than all subsequent drugs. For weak early entrant protection, β(N_J) > 0 only for N_J greater than some value N, where Nsatisfies E[t_app(N)] > E[t_app(N)] N N.

Analysis of the model suggests that early entrant protection depends critically upon how the curing power of therapies unfolds over a sequence of drugs submitted for a given disease.¹³ An instructive result comes when we assume that this unfolding is stationary.

Proposition 1.
Concave early entrant protection under a stationary quality and political value. For any disease j = J, consider a sequence of disease-specific drugs i = 1, ... N_J. Then _i,J is the curing probability for drug i for disease J. Let f() be a stationary curing distribution for any disease, such that E[_i] = c for all i J. Then if , strong early entrant protection holds: E[t_app(i = N_J + 1)] > E[t_app(N_J)] for all N_J. Moreover, expected approval times are concave in N_j.

Proof.
Proofs of all comments and lemmata are in the Appendix.

The essential lesson of Proposition 1 is that if neither drug quality nor a drug's political value is expected to rise over time, then early entrant protection is inevitable. Even if a drug's political value is expected to rise, the increase must "outweigh" the decline in marginal curing that occurs under stationary quality. Because the political multiplier can change over sequences of drugs—the regulator might expect a disease's size to grow, might expect a firm to get more powerful, or might expect a disease lobby to respond more or less to the introduction of new therapies—the conditions for early entrant protection become somewhat more restricted.

Concavity bestows the greatest regulatory advantages upon the first entrant to any market niche. Beyond the fact that the first entrant receives the quickest review, it is also true that the second entrant has the largest expected delay relative to the previous entrant, so that the "degree" of protection given to the first entrant is the greatest.

3.1.1 The Generality of Early Entrant Protection.
This pattern of induced regulatory favor for earlier entrants is in fact more general. For any two drugs i = N and N + 1 with identical levels of danger (µ_N = µ_N+1), the expected approval time for the Nth is always shorter unless the (N + 1)th offers an improvement in curing power.

Proposition 2.
Given two drugs with identical danger (µ_N = µ_N+1), then unless the (N + 1)th drug improves upon the curing of the Nth, EEP must hold. The inverse is not true.

3.1.2 Early Entrant Protection when Drugs Improve over Time.
It is useful to consider the case of stochastic improvement, where newer drugs will be expected to have superior curative power relative to older ones, a process presumably driven by technological change and related factors.

Proposition 3.
Early Entrant Protection for Improvement Functions over the Curing Distribution. Let the improvement function satisfy (1) dE[_iJ]/dN > 0. Then at least two forms of early entrant protection prevail.

1. For ₁ sufficiently high, there is strong early entrant protection.
   
2. For any infinite sequence of drugs with monotonic improvement, there is always weak early entrant protection, or protection for some set of drugs submitted and approved early in the sequence.
   

Proposition 3 shows that early entrant protection holds even when the regulator expects later entrants to a market niche to offer quality improvements. And unlike the predictions of earlier models (Carpenter 2004b), none of the results here depend upon restrictions of the stochastic improvement function.

3.1.3 Hypotheses.
We introduce hypotheses from the model for testing, in three sets. The first hypothesis holds under most conditions of the model and generally posits early entrant protection. The second hypotheses (1.2 and 1.3) are mutually exclusive and explore the functional form between order of entry and expected approval time.

Hypothesis 1.1:
The expected approval time of products is a monotonically nondecreasing function of the order of entry.

Hypothesis 1.2:
The expected approval time of products is a linearly nondecreasing function of the order of entry.

Hypothesis 1.3:
The expected approval time of products is a concavely nondecreasing function of the order of entry.

A second set of hypotheses concerns the political or administrative mechanisms underlying early entrant protection. Depending on how firm clout and political demand unfold over therapies (see the Appendix for details), the entry-order gradient may be positively or negatively conditioned upon either firm-level or disease-level attributes.

Hypothesis 2.1 (Producer Capture):
The entry-order gradient is conditioned upon firm-level attributes.

Hypothesis 2.2 (Consumer Politics):
The entry-order gradient is conditioned upon disease-level factors.

A final set of hypotheses posits the behavior of a farsighted regulator. Hypothesis 3.1 suggests that early entrant protection will be mitigated when the submission rate is high. The reason is that, when the first drug (or first few drugs) for any disease is being considered, the agency will discount their marginal curing value by the expectation that other cures are likely to be submitted soon. In this way, early entrants may themselves be slowed down by the prospect of promising therapies in the pipeline. Hypothesis 3.2 extends this logic to the approval process. If the agency expects future political and therapeutic cures to be approved quickly upon submission, then the present value of the product currently under consideration is less.

Hypothesis 3.1:
For any sequence of drugs, the likelihood and severity of EEP is decreasing in the product innovation rate _j and the expected approval rate G*(·).

Hypothesis 3.2:
General administrative factors accelerating the product approval rate will reduce the likelihood and gradient of EEP.

	4. Empirical Tests

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
The fundamental prediction of the repeated regulation model is that order of entry into any given pharmaceutical market will be positively associated with approval time, ceteris paribus (Hypothesis 1.1). We now turn to test this basic hypothesis and to assess the functional form that early entrant protection assumes in pharmaceutical markets (Hypotheses 1.2 and 1.3). In doing so, we make use of a new data set of 1089 new molecular entities (NMEs) submitted to the FDA (and subsequently approved) over the last half century. This data set is much larger and more complete than those used by other students of FDA review times, for example, Dranove and Meltzer (1994), Olson (1997, 1999, 2001), and Carpenter (2002, 2004a).¹⁴ Of these drugs, we are able to retrieve reliable review time data for 1080 NMEs, and these form the basis for our estimations. Table 1 displays summary statistics. Notice that the standard deviation (SD) of our order of entry variable is about 15.

View this table: [in this window] [in a new window]   Table 1. Descriptive Statistics for Selected Variables

 
We use a variety of regression analyses to test our hypotheses. At the most flexible, we employ a Cox semi-parametric regression model to avoid constraints of parametrically imposed hazard functions. We also employ several parametric estimators, including the log-normal and the Weibull. In all maximum likelihood duration analyses, we include frailty (random effects) terms that are grouped by the primary indication (disease) of the NME, and in many specifications, we include a battery of indicator variables for the drug's sponsoring firm. Hence, our models "control" for all disease-level and firm-level effects, and most of our statistical leverage is given by drug-to-drug changes in relevant variables (principally, order of entry, which varies over markets and over time). We also conduct some linear regressions on approval times in order to retrieve elasticities and to restrict some of our comparisons to small disease-specific samples.

At least three potential confounding forces are of interest. First, it is possible that our order-of-entry variable, being correlated with the passage of time, simply picks up trends in approval time of the past 50 years. In most of the analyses reported here, we looked for temporal variation in approval time in two ways, by including a trend variable and by including a dummy variable measuring whether the drug in question was submitted before or after the Kefauver-Harris Amendments of 1962. The addition of these variables does not suffice to explain the order-of-entry effect, as the relationship persists (in some cases, is strengthened) when these variables are added.

A second possibility is that our order-of-entry variable, which varies across therapeutic categories as well as over time, is simply picking up therapeutic variations across medical conditions. To address this concern explicitly, we add a set of disease-specific "frailty" parameters to all the models here, which amounts to 227 "random effects" variables (assumed to be Gamma distributed in the Cox model, and inverse Gaussian distributed in the log-normal duration model).¹⁵ We also regress approval time on order of entry for estimate disease-specific samples (Table 3).

A third possibility is that order of entry is highly correlated with technological improvement in drugs. As the model suggests, we would expect early entrant advantage to hold nonetheless. Yet empirically, it is important to try to control for "importance" or "quality" of the drug. The frailties estimated have disease-specific means and so are of little help here. We follow Dranove and Meltzer (1994) and Kyle (2006) and use medical databases to proxy for the importance of drugs. Using a program written in Java by the authors, we searched the MEDLINE database for all hits for any given drug based upon either its trade name or its generic name and recorded the hits by year. Unlike Dranove and Meltzer and Kyle, we construct the following two variables: (1) total MEDLINE hits in the years before submission, and (2) total MEDLINE hits in the years before submission where "safety," toxic*," and hazard-related terms occur. This addresses the concern that a drug may receive considerable scientific and medical attention because of its safety hazards and side effects; hence, the measures of Dranove and Meltzer (1994) and Kyle (2006) may pick up "negative" features of drugs as well as positive ones.

Our two variables—a "residualized MEDLINE count" and a "residualized MEDLINE safety count"—are constructed by taking the aggregate counts for the years before submission for each drug, then regressing these on a battery of 227 dummy variables for the drug's indication, and then retrieving the residuals. By doing this we hope to have "purged" the counts of variations in citations that occur because of medical specialties, therapeutic class considerations, and other factors that are unobservable but vary at the level of disease.¹⁶

Table 2 displays the most general models estimated. The dependent variable is the approval time (in months) from New Drug Application (NDA) submission to NDA approval as conducted by Center for Drug Evaluation and Research (CDER). For partial-likelihood Cox regression and maximum-likelihood duration models,¹⁷ Table 2 presents the results of three models, one where order of entry enters the regression linearly and two others where it enters the regression nonlinearly (logarithmically). It is important to note that the coefficient representation for the Cox model differs from that of the log-normal models. In the Cox model, a coefficient estimate above 1 implies an increase in the hazard rate and a reduction in expected review time. Only for a negative coefficient estimate is a similar inference supported for the log-Normal models. (See the table notes for proper interpretation.)

View this table: [in this window] [in a new window]   Table 2. Tests for Entry-Order Effects, Linearity versus Log-Linearity (cell entries are coefficient estimates for the relevant model; see notes for proper interpretation; standard errors are in parentheses)

 
In all six models presented in Table 2, the order of market entry is positively associated with approval time, consistent with Hypothesis 1.1. Using the accelerated failure-time model for marginal effects estimates, we calculate that for every 1-unit rise in the natural logarithm of entry order, the expected approval time rises by 2.90 months; 1 SD rise in logged entry order (1.23) thus yields a 3.57-month increase in expected FDA approval time. Yet across both estimation procedures—and across many regressions not reported here—the model with logged order of entry offers superior predictive power to the model with linear order of entry. The relevant comparison can be gleaned from the log-likelihood values (computed at convergence) and the adjusted R-square values for the linear model.

Less parametric approaches support the concavity findings reported in Table 2. We created a battery of 40 dummy variables for the first 40 entrants in any primary indication niche. For instance, if a drug was the first entrant into a niche, ENTRANT01 would be scored one and ENTRANT02 through ENTRANT40 would be scored 0. We then substituted this battery of variables for the single variable representation used in Table 2, running the same model. In Figure 1, we report the coefficient estimates—represented as hazard ratios, or multipliers—accompanied by their respective upper and lower 95% confidence intervals for all ENTRANT categories in which there are 20 or more data points (the first 12 entrants into any market niche). Note that since the hazard is being represented here, Hypothesis 1b predicts the (stochastic) convexity of the successive hazard ratios. The more formal test for this functional relationship occurs in Table 2, but the nonparametric functional relationship appears intuitively in Figure 1. From Figure 1, the first four entrants exhibit higher hazard rates than do all subsequent entrants. In addition, Wald's test rejects the equivalence of the first entrant's hazard rate to that of any and all months following the fourth.

View larger version (7K): [in this window] [in a new window] [Download PowerPoint slide]   Figure 1. Approval Hazard Ratio by Order of Entry [Cox Model Estimates, Gamma-distributed Family].

 
Another way of examining the data is to break the data into subsamples based on the primary indication of the drug and to run disease-specific regressions. Doing so is one way of addressing the concern that the approval times and administrative processes represented in Table 2 are not truly comparable because the drugs treat different diseases. For each of 227 diseases, we regressed the logged approval time upon the logged order of entry, the year of the drug's submission, and the residualized MEDLINE "total" and "safety-related" importance measures. Since the dependent variable and the relevant independent variable are both expressed in terms of their natural logarithms, the coefficients can be interpreted roughly as elasticities.

In Table 3, the coefficient (elasticity) estimates from these regressions are reported for all those samples where coefficient estimates for all regressors could be retrieved. In many cases, the samples are so small so as to preclude valid statistical inference; yet we report the elasticity estimates nonetheless. Of the 50 regressions thereby retrieved, only 10 yield a negative elasticity estimate, and only two of these estimates are statistically significant. Of the other 40 diseases for which a positive relationship is observed, 21 regressions yield a statistically significant (p < 0.05 for a two-tailed test) and positive relationship between order of entry and approval time. When we pay attention to those estimates with statistical significance at p < 0.10 with two-tailed tests, we observe fully 30 positive elasticity estimates, with just three negative estimates. Larger elasticities appear for contraceptives (where there would appear to be less heterogeneity in effectiveness), for bacterial and respiratory infections, for anti-inflammatory medicines, and for nonanalgesic drugs for chronic pain. Except for anti-emetic drugs, cancer diseases do not appear to exhibit large entry-order gradients.

View this table: [in this window] [in a new window]   Table 3. Disease-Specific Entry-Order Gradients, Expressed as Elasticities (robust standard errors in parentheses)

 
4.1 Firm versus Disease-Level Conditioning of the Entry-Order Gradient
We then turn to assess Hypotheses 2a and 2b. We do so through two methods. We first conduct an "analysis of variance" in which approval times are regressed upon the logged order of entry variable alone. We then retrieve the predicted values from this regression and regress this variable on two sets of dummy variables, one the set of all sponsoring firms and the other the set of all diseases. We then compare the aggregate performance of these two models. The results appear in Table 4A. Here the evidence is quite clear. Whereas the firm-effects model accounts for less than one-fifth of the variance of the entry-order predictions, the disease-effects model accounts for almost 70% of that variance.

View this table: [in this window] [in a new window]   Table 4. Conditioning of Entry-Order Gradient on Firm versus Disease Factors

 
Another way of examining the firm- or disease-level conditioning of the entry-order gradient is to use interaction terms. If producer capture theory (Hypothesis 2.1) is correct, the entry-order gradient should be conditioned upon other observable features of firms, such as their size and experience. Intuitively, if industry rent-seeking undergirds early entrant protection, then we should expect to observe larger firms enjoying greater protection than smaller firms. That is, the "slope" of early entrant protection should be conditioned upon the particular clout with which firms can lobby the regulator for delayed entry for their competitors. We assume that larger, older firms can marshal greater political clout than smaller firms can, and we predict that early entrant protection should hence be greater for larger, older firms. We test this prediction by way of two interaction terms. We first interact order of entry with firm sales. We next interact order of entry with the count of previous firm submissions. A capture-theoretic perspective would predict a positive coefficient estimate for both of these variables.

If the consumer co-optation account (Hypothesis 2.2) is correct, the gradient should be conditioned upon observable features of diseases, particularly their political and social relevance (Carpenter 2002). Although a producer capture perspective suggests that order-of-entry effects will be conditioned on firm size and age, a co-optation perspective suggests that the order-of-entry effects will be shaped by consumer organization and political clout. We include three such variables representing consumer political organization here. The first two—the raw aggregate of groups representing the primary indication disease and the budget of the wealthiest of these groups—are described in previous research (Carpenter 2002). A third is media coverage of disease, which assays the extent to which organized advocates can establish their condition as newsworthy (Colby and Cook 1995; Epstein 1999). Carpenter (2002, 2004) used Washington Post coverage of the primary indication disease. In lieu of this variable—which produces small and insignificant interaction estimates—we focus here on broadcast news coverage, which permits for a larger sample and measure broadcast news coverage by consulting the Vanderbilt TV News Archive, which is also searchable electronically.¹⁸ Because these measures are available only for recent decades, we consider a subsample of new molecular entities submitted from 1977 to 2000 in these analyses. In addition, because firm sales data and epidemiological data are not available for all of our drugs, our sample size shrinks to 349 molecules.

Coefficient estimates for the interaction terms of these models appear in Table 4B. From z-scores and associated Wald tests, there is no statistically significant conditioning of the entry-order gradient upon firm experience, regulatory familiarity (number of previous submissions), or upon firm size (sales). For both the disease advocacy groups estimate and the broadcast news coverage moving average; however, there is a statistically significant relationship between entry-order interactions of these variables and approval times.

From these two analyses, it would appear that there is much more support for consumer co-optation (Hypothesis 2.2) than producer capture (Hypothesis 2.1). It is not clear that Hypothesis 2.1 can be rejected entirely; yet it seems evident from Table 4 that disease-level factors explain a much greater fraction of the entry-order effect in new drug approval than do firm-level factors.

4.2 Conditioning of Entry-Order Gradient upon Historical Factors
It is unlikely that the entry-order gradient estimated in Table 2 is homogeneous over time, particularly over a time span of 56 years. We are interested in two particular change-points in the history of US pharmaceutical regulation that might have altered it: the 1962 Kefauver-Harris Drug Amendments (which followed upon the thalidomide tragedy) and the 1992 Prescription Drug User Fee Act (which established a per-application tax upon drug producers, the proceeds from which pay for FDA personnel for drug reviews and other regulatory tasks). To assess whether either or both of these junctures was associated with a change in the entry-order gradient, we add models with interactions between indicator variables for whether the drug was submitted after 1962 (or 1992) and the logged order-of-entry variable. The results suggest that whereas there is no observable change in the entry-order gradient associated with the Prescription Drug User Fee Act (PDUFA), where was a heightening of early entrant advantage after the 1962 Amendments were passed. Our theoretical model does not speak directly to an explanation, but one reason for this increase in early entrant advantage may be that, in the wake of the 1962 Amendments, the criterion of unmet medical need drops off more quickly after one or two drugs are approved for the disease in question.

Our data on primary indication diseases and firm-level covariates are of more recent vintage, allowing us to observe whether the covariation of the entry-order gradient with disease- and firm-level factors was affected by the PDUFA legislation and associated changes. In models on a reduced data, we include two sets of interaction terms—interaction of each of the disease-level and firm-level covariates with the order of entry and a further interaction of this entire battery of interactions with the 1992 PDUFA indicator. Cox and parametric lognormal duration models are then estimated, and the results appear in the 2nd and 4th columns of estimates in Table 5.¹⁹

View this table: [in this window] [in a new window]   Table 5: Conditioning of Entry-Order Gradient on Time (cell entries are coefficient estimates for the relevant model; standard errors are in parentheses)

 
Results of this analysis continue to suggest that the entry order gradient is most heavily conditioned upon the disease-level factor of group organization. Although the PDUFA law does not appear to have influenced the overall entry-order gradient, it would appear that the interaction of disease-level and firm-level covariates with the order-of-entry variable was changed by the 1992 law (or contemporaneous changes). In particular, the greater the number of advocacy groups representing a disease, the higher is the entry-order gradient. (The average approval time is, however, considerably reduced in the presence of greater numbers of advocacy groups, so the context of this result should be kept in mind.) This boosting of the entry-order gradient appears to have been ameliorated, however, by the user-fee law or associated developments. After 1992, there is no appreciable increase in the entry-order gradient. Put differently, the observed effect of group organization is not dampened by order of entry after 1992, whereas before 1992 it was reduced by order of entry.

4.3 Pipeline Value (Hypotheses 3.1 and 3.2).
We turn finally to a rough assessment of whether the entry-order effects are anticipatory of the "pipeline" of future therapies. This is a difficult hypothesis to test because although it is possible to write a closed-form expression for the pipeline value, computing that value is quite another matter. (We have investigated different computational approaches but have decided against reporting these due to instability of the estimates.) We instead focus on two variables that shape the pipeline value. The first is the stock of all new drug applications that arrive at the time that the drug is considered; because this represents the agency's backlog, we expect this variable to inflate approval times. The second is the general approval rate for all NDAs in the year that the current molecule is submitted. This is a measure of the approval probability (G*) in ensuing years. We assume that both these are observable by the agency.²⁰

Estimates presented in Table 6 suggest modest evidence that the entry-order gradient is shaped by factors affecting the pipeline value but in ways that contradict the model. The log of NDAs received is associated with an increased hazard rate of approval (in the Cox model) and shorter expected approval times (in the log-Normal model). Meanwhile, the ratio of NDAs received to NDAs approved is associated with higher hazard rates and lower approval times, and the relationship observed for this ratio variable is stronger than that observed for the logged NDAs received variable. The aggregate approval rate, when interacted with order of entry, would appear to enhance the entry-order gradient, as the interaction reduces the hazard rate (the order of entry variable alone decreases it) and lengthens expected approval time (the order of entry variable alone lengthens it). These estimated relationships contradict Hypotheses 3.1 and 3.2, as expected future generosity (a better approval rate) does not reduce the marginal value of earlier drugs and does not reduce the entry-order gradient. We note, however, the potential endogeneity of these measures and the difficulty of computing exact pipeline values from observed data.

View this table: [in this window] [in a new window]   Table 6. Conditioning of Entry-Order Gradient on Pipeline Factors

 
4.4 Other Predictions: Regulatory Error and Consequences for Product Development
We consider, finally, two possibilities for generating predictions from the repeated regulation model here, both of which would entail considerable expansion and elaboration of the model. The first concerns regulatory error. If the regulator (and the groups pressuring it) place a premium on the first few drugs approved for any disease, then we might expect these drugs to have been approved more erroneously (Type I errors; see Heimann 1997, Ting 2002, Carpenter and Ting 2007). We might also expect the regulator to erroneously delay products (commit Type II errors) in markets where there are already many entrants.

There is support for this prediction in a study by Olson (2004).²¹ In that study, observational evidence is presented supporting the hypothesis that newer therapies for the same medical condition are associated with greater safety risks to patients. Olson measures the number of reported Adverse Event Reports (AERs) as collected by the FDA. Other measures of postmarket safety problems are possible (see Carpenter and Ting 2007), and the relationships between order of market entry and postmarket outcomes are perhaps worth a separate treatment.

A second set of predictions concerns investment and R&D behavior by firms. If firms anticipate EEP, then we should witness specific kinds of investment behavior. Firms expecting EEP to prevail should target product development and regulatory submissions to those market niches with few (or few effective) entrants, and particularly to those with well-organized sufferers and advocates. (Firms might also try to create disease organization where none exists, but there appear to be limits on the ability of firms to do this and retain credibility.) Although we have not modeled firm behavior here (for an attempt, see, Carpenter and Ting 2007), it is plausible that strategic firms might target little-entered markets even to the neglect of short-run profits. (This is in direct contrast to the predictions of Acemoglu and Linn (2004).) Once the basic molecule received regulatory approval, firms would then rely on "supplemental" applications to access more lucrative markets. Hence, a rational firm might respond to early entrant protection by first submitting a promising cancer drug for pancreatic or stomach cancer, and then apply later to add an indication for metastatic breast cancer. Our model would need to be expanded to reflect this, but it is worth noting that such a pattern is noted in many casual and journalistic descriptions of the industry, including interviews that we have done.

	5. Conclusion

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
We have presented a theoretical rationale for early entrant protection in approval regulation—a pattern in which the first arrivals to any market receive the quickest approval times from a gatekeeping regulator. Perhaps most important, our theoretical and empirical efforts suggest that this pattern can hold in the absence of regulatory capture of the agency by industry. The empirical pattern of early entrant protection—observed as a positive slope between the order of market entry for a drug and its regulatory approval time—is strongly conditioned upon variables representing the political and social organization of advocates for the medical condition treated by the drug in question. There is no evidence that the relationship between order of entry and approval time is conditioned upon firm or industry attributes such as size or sales. The relationship is, however, robust to the inclusion of firm-level covariates and firm-level fixed effects.

We have purposefully sidestepped the question of whether early entrant protection represents a desirable public policy outcome. We can envision several arguments here, arguments that we seek to address in future research. First, it is quite possible that by delaying price competition (prolonging monopolies) and the arrival of superior products in a market, early entrant protection serves to harm consumers and weaken investment in "second-generation" pharmaceutical therapies. Second, and on the other hand, it is also possible that early entrant protection preserves incentives to "get in the market first" and to develop products quickly. In this way, the empirical patterns observed here may not weaken investment but may promote it, inasmuch as early entrant protection represents something of a tournament (in which the prize of quick approvals goes to the earliest market arrivals).

Finally, we recall our model (and the reality) of an uncertain regulator. In a world where the true importance or quality of a drug cannot be known with certainty, the FDA must use clear and defensible criteria to allocate scarce resources across drugs and, implicitly, across human disease conditions. The number of previously approved therapies for a primary indication, although blunt, may indeed serve as a useful measure of "unmet medical need." Our statistical results are consistent with the interpretation that FDA regulators have used these kinds of consideration, approving drugs more quickly when there are fewer existing therapies available for the primary indication disease target. In terms of political economy, our analyses suggest that the weights given to different disease over the past half century appear to reflect the politics of disease-based and patient-based organizations.

	Appendix: Selected Definitions and Proofs

Top Abstract 1. Introduction 2. A Dynamic Model... 3. Early Entrant Protection... 4. Empirical Tests 5. Conclusion Appendix: Selected Definitions... References

 
Define a probability space (, , P), where all events , is a -field corresponding to , and P offers a probability measure on the space. We can write _t as the filtration of this space, which includes the full stochastic history and the realization of all experiments. For any t, sufficient statistics can be generated from _taccording to equation (2).

All propositions for early entrant protection make use of the following lemma.

Lemma 2.
Given two drugs with identical danger (µ_N = µ_N+1), the absence of early entrant protection for the Nth relative to the (N + 1)th requires

(A-1)

Proof.
Let _N(·)_N(_J, _K|N_J – 1) and _N+1(·) _N+1(_J, _K|N_J). Strong early entrant protection cannot hold if for any two drugs i = N, N + 1, it is the case that A_N A_N+1, or

Cancel like terms in the telescoping products on both sides of the inequality to get (A-1).

Proof of Proposition 1.
Strong early entrant protection cannot hold if for any two drugs i = N, N+1, it is the case that A_N A_N+1, or (A-1). Now assume stationarity of c_i. Then suppressing some subscripts, (A-1) reduces to

Because the probability of immediate approval is 0, this relation cannot be satisfied unless either the series {c_i} or the series {_i} is weakly increasing, or both are. For concavity, notice that the likelihood of early entrant protection is decreasing in e^{–(E[t_sub]+E[t_app*])}G* because longer expected approval times raise the left-hand side of the equation. We have already established that E[t_app*]is increasing in N_J, ceteris paribus. Hence, is monotonically decreasing in . From this it can be seen that .

For Propositions 2 and following, we shall need the following lemma.

Lemma 3.
Let [where 0 < β; 0 < β] and let the improvement for _N+1 be represented as . Then there is strong early entrant protection unless

(A-2)

Proof.
Rewrite (A-1) as

(A-2)

Proof of Proposition 2.
Immediate. If {} is stationary, then unless > 0, (A-2) cannot be satisfied.

Proof of Proposition 3.
Let any ₁ and ₂ satisfy the conditions of Lemma 3, in which case dE[]/dN > 0. Then strong early entrant protection exists for any sequence of drugs whose movements uniformly satisfy (A-5).

For weak early entrant protection, note that whether or not there is improvement, for any countable series. Then for any sequence i = 1, ... N_J, ... N (Npossibly infinite), there exists an N_J for which A_NJ A_NJ+1. Choose = A_NJ > 0. Then there exists some such that . As lim sup is a decreasing series, weak EEP prevails for such a series, even if infinite.

Proof of Hypothesis 2.1. Let (·) > 0 and let one of the following two constraints hold on the relevant cross-partial:

Then , respectively, as is nondecreasing in is nonzero if either . These conditions prevail if the first or second cross-partial restriction holds, respectively. The proof for disease-related factors is identical if is substituted for throughout.

Proof of Hypotheses 3.1 and 3.2: We need only show that the left-hand side of (A-5) is strictly decreasing in _j. By assumption, E[t_sub(_J)]is decreasing in _J. Hence, is monotonically decreasing in . A similar proof holds for any general determinant of E[t_app*].

	Acknowledgments

 
Daniel Carpenter acknowledges the National Science Foundation (NSF) (SES-0076452 and SES-0351048), a Robert Wood Johnson Foundation Investigator Award in Health Policy Research, and the Harvard University Department of Government for support. The authors also acknowledge the University of Michigan College of Literature, Science and the Arts and the University of Michigan, Department of Political Science. We thank David Dranove and David Meltzer for sharing data, and acknowledge John deFigueredo, David Epstein, Richard Frank, Sanford Gordon, Jacob Hacker, Gregory Huber, Robert Lieberman, Jane Mansbridge, Mary Olson, Ariel Pakes, Craig Volden, Gregory Wawro, audiences at Yale University and Columbia University, the Editors, and an anonymous reviewer for helpful comments. Susan I. Moffitt acknowledges the Robert Wood Johnson Foundation Scholars in Health Policy Fellowship. Professor Ting acknowledges NSF grant SES-0519082.

	Footnotes

 
¹ One thoughtful reader suggested "early entrant advantage," which seems near perfectly substitutable and will be used occasionally in the course of our argument.

² This last result is a "conjecture" because deriving it as a prediction from our model would require a fuller model of firm R&D that confronts a potential regulatory "veto." See Carpenter and Ting (2007) for relevant analyses.

³ We use the term "risk" only in its decision-theoretic sense. The agency is always "danger averse," but the model is constructed under the assumption of risk neutrality.

⁴ A more thorough exposition of a more restricted model appears in Carpenter (2004b). There are important differences in the "early entrant protection" section of that article, however, and theoretically, the early entrant protection analysis in Carpenter (2004b) is a special case of the broader model developed here. The one-drug-one-disease assumption can be relaxed without affecting the general results of the model.

Clearly the exogeneity assumption here is violated in practice. Where the agency becomes more stringent in its product approval decisions, firms will develop fewer drugs and do so more slowly (Peltzman 1973; Grabowski and Vernon 1983; Thomas 1990). For a model that endogenizes submissions, see Carpenter and Ting (2007).

⁵ We rely throughout on the scale invariance of Brownian diffusions (Miroschnichenko 1975: 389–91).

⁶ Other functional forms are possible, including a "geometric" Brownian motion exp(µ), under which none of the substantive results of the model differ.

⁷ We assume L constant through the agency's decision, which is an absolute requirement for the solution concept of smooth pasting. To get around this, one could assume that a rapidly growing disease has a high political multiplier.

⁸ See Carpenter (2004b), Propositions 1 through 3 for a demonstration of the claims in this paragraph. See the Appendix for more details on the probability space and its filtration.

⁹ Some of these are connected to the pharmaceutical industry; many are not.

¹⁰ The product assumption is one that we use to purchase tractability and space. It may be possible to create a separate function h(, ):(0, 1) x (0, 1)(0, 1) that would allow for more general relationships. As long as h was strictly nondecreasing in its arguments, results like those that we state here would obtain.

¹¹ We note a paradox in the specification of the model. At the time a new drug is submitted, the regulator anticipates the quality of drugs in the pipeline and anticipates changes in the political value of these drugs. However, once review begins, this sequence of expectations is fixed. Unanticipated changes to the quality or political value of drugs in the pipeline cannot, once review begins, be taken into account. For this reason, our regulator is highly "anticipatory" (has considerable foresight) but has restricted learning capability. Allowing our regulator to learn from unanticipated changes in the quality or political value of future drugs during the review of the current drug would require that the smooth pasting equation (Carpenter 2004b) satisfy a highly nonlinear and multidimensional set of constraints. We have examined this possibility and have found mathematical analysis to be untenable in terms of producing closed form solutions.

We note that this stationarity of expectations about future drugs also amounts to an exogeneity assumption about them. Future drug submissions are not altered by perturbations or trembles to the regulator's current strategies. The model assumes, in other words, that there is no time inconsistency problem that allures the regulator. The agency does not consider changes in the quality or political value of the drugs that are unanticipated. This assumption is in fact realistic during the course of review for any drug, as pharmaceutical regulators often wish to project an image and reputation of scientific and behavioral consistency (Carpenter 2004a, 2004b). Firms, medical professionals, and scientific advisory committees are important audiences for the regulator in this respect. We thank an anonymous reviewer for suggesting this point and its discussion.

¹² We acknowledge the anonymous reviewer for making this point.

¹³ Carpenter (2004b) develops several predictions from analysis of a model similar to that here, but his model fails to consider the possibility that the effect of firm or consumer politics could change as entry-order changes. If _iJ is constant for an entire sequence of products, then the analysis here reduces to that of Carpenter (2004b).

¹⁴ We thank Dranove and Meltzer, however, for sending us their FDA approval time data, which allowed us to increase the size of our data by 40% and permitted a more than doubling of their original data.

¹⁵ For some of the models estimated with smaller NME samples sizes, the number of random effects falls to 177 or less.

¹⁶ Two notes on this procedure are in order. First, the searches were conducted in PubMed, which considers abstracts before 1966 as being contained in the OLDMEDLINE database; hence, that database is included in our searches. Second, the retrieved residual is a variable with known error, and one might fairly wonder why a two-stage process is not used to retrieve the final standard errors. Note, however, that the only "purging" done is via a fixed-effect for the primary indication of the drug in question, so this step (which would be very complicated for the nonlinear models we estimate) can be avoided.

¹⁷ We use different estimation procedures as a robustness check upon our results. Each procedure has its own drawbacks, namely proportional hazards assumption for the Cox model, a parametric assumption for the log-normal model (although one that is predicted by our formal model), and the absence of stochastic nuance in the linear regressions.

¹⁸ To measure broadcast coverage, a research team again agreed upon a list of search terms for diseases and tallied the total number of nightly newscast stories on the three major networks in which a disease was mentioned in a given year. This was done for each disease in the sample (over 300) for each year from 1975 to 2000. Search terms were adjusted to ensure that superfluous "hits" were excluded. A research team searched under "stroke AND disease" using a Boolean operator, for instance, to avoid hundreds of golf stories. We conducted a similar tabulation for the Vanderbilt database, for each disease yearly from 1977 to 2000. These measures rely on disease coverage before the drug's submission, so endogeneity of media coverage to drug approval is ruled out. If anything, drugs that are approved more quickly should result in the media having less time to cover them before they are approved.

¹⁹ Note that because data on two of the variables from Table 4—real-dollar, deflated firm sales at the time of NDA submission and the budget of the disease advocacy group with the largest budget—contain many missing observations, we restrict our attention to three covariates in Table 5: number of national and regional disease advocacy groups for the primary indication disease, Vanderbilt TV news coverage of the disease in the four years previous to NDA submission, and number of previously approved NMEs for the sponsoring firm at the time of NDA submission.

²⁰ We acknowledge that both of these variables—the NDAs received and the aggregate NDA approval rate—are endogenous to the model. NDAs received may be endogenous because strategic firms will respond to any tightening or loosening of the regulatory acceptance rate (see Carpenter and Ting [2007] for a formal model elaborating this relationship). The aggregate approval rate may be affected by the drug under consideration. It is for this reason that we look at all new drug applications when computing these two variables—as opposed to the select NMEs that are a small subsample of all NDAs.

²¹ We thank an anonymous reviewer for this suggestion.

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