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DYNAMIC ENTRY WITH DEMAND AND SUPPLY SIDE SPILLOVERS.

I. INTRODUCTION

One of the most significant decisions a firm makes is whether or not to enter a new market. In a dynamic environment, a firm's current decision not only affects its current profit, but also has spillovers upon its future profitability (e.g., Fitzgerald, Haller, and Yedid-Levi 2016; Piveteau 2016; Rodrigue and Tan 2016). Rodrigue and Tan (2016), for instance, find that firms can increase their future sales through decreasing their current price and building their brand's reputation. Similarly, Erdem (1998), Che, Erdem, and Oncu (2015), and Ching and Lim (2016) document the fact that consumers' "correlated learning" improves a firm's performance in a new product market if it has experience in a related product market. (1) This improvement implies that a firm's decision to enter a product market is determined not only by the profits associated with this market, but also the enhanced profitability in future markets. Much of the literature, however, attributes entry spillovers to the supply side of a firm, in particular, the type of spillovers which reduce a firm's cost in later markets given that it has previous entry experience (Benkard 2004; Gallant, Han, and Khawaja 2017). The cost reduction has been deemed the primary determinant of the "overentry" phenomenon. This phenomenon is a well-known empirical pattern where many firms enter small markets which only can accommodate a small number of firms, and some or all of them receive negative profits.

In this paper, we disentangle the effect of different types of spillovers on firm-level entry decisions by separately identifying demand and supply side spillovers on firm-level profitability. We note that our identification arises from our functional form since we lack the firm-level market share data. Specifically, we use differences in the relative rates of entry across markets and differences in the absolute rate of entry across markets to shed light on how demand and supply side spillovers may manifest themselves in the pharmaceutical industry.

We also compare the different policy implications of supply and demand side spillovers through counter-factual experiments. The identification is crucial for a firm's market entry decision. For instance, when demand spillovers play the role, a firm can increase its market share in other product markets through entering an uncorrelated product (under the same brand). In contrast, when supply side spillovers play the role, a firm must enter a similar product market in order to enjoy production cost reductions in other products.

Demand side spillovers have received little attention, especially in dynamic settings. This type of spillover may also improve a firm's profitability in the later markets if previous entry allows the firm to increase its market share in future markets. The increase in market share may result from brand loyalty or an enlarged customer base from previous market entry. There are a number of explanations for brand loyalty, such as the cost of establishing new trading relationships, learning how to use a new product, uncertainty over product quality, or product compatibility with existing products. Erdem (1998), for example, finds that consumers are willing to purchase their oral hygiene products under the same brand. This loyalty allows a supplier with more product varieties to obtain more market power or share in a new market than competitors offering a smaller range of products (Che, Erdem, and Oncu 2015; Ching and Lim 2016; Hendricks and Sorensen 2009; Klemperer and Padilla 1997). In the pharmaceutical industry, demand side spillovers, which are usually referred to as the firm's reputation, also play a significant role (e.g., Gilbert, Ural, and Lopz 2012; Keyl 2006; Mason and Bearden 1980; Reiffen and Ward 2005; Scott-Morton 1999). Gilbert, Ural, and Lopz (2012), for instance, demonstrate that the generic firms can enhance the efficiency of sales by engaging in an "Umbrella Strategy." Mason and Bearden (1980) find that physicians and pharmacists will be less likely to prescribe or use generic drugs if the manufacturers have an unknown reputation.

Supply and demand side spillovers have distinct policy implications. In particular, in an industry where new products are introduced over time, each firm sequentially makes its market entry decision. If the decisions are affected by supply side spillovers, a policymaker can decrease the cost of entry in initial markets to achieve the policy goal of increasing the total market entry rate over time. In contrast, in the presence of demand side spillovers, lowering the entry costs in initial markets will decrease the subsequent markets entry rate. The intuition for the different policy implications is straightforward: supply side spillovers increase the profitability of firms at the aggregate level. Decreasing entry barriers in initial markets attracts more entrants in future markets because, on average, firms have lower costs and higher profitability in later markets. In contrast, demand side spillovers only reallocate share toward more experienced firms (which have entered more markets and have a larger market share in the later markets). The more experienced firms squeeze out less experienced firms, and cause the entry rate to fall in future markets. Misidentifying the two types of spillovers will invalidate some market-associated policies. This paper contributes to this literature by separately identifying demand and supply side spillovers and quantifying their impact on firm profits and entry decisions.

In the generic pharmaceutical industry, future benefits from current entry could arise from future cost reductions, or from an increased customer base, brand reputation, or loyalty. The supply channel is frequently mentioned in the learning literature (learning by firms), in which firms accumulate experience during the production process (Spence 1981). This experience reduces the subsequent costs associated with the entry in future markets. The demand channel is usually caused by consumer learning (e.g., Che, Erdem, and Oncu 2015; Ching and Lim 2016; Erdem 1998; Hendricks and Sorensen 2009). In particular, when consumers' quality perceptions are correlated across different generic drugs under the same brand, the previous experience in one generic drug serves as a quality signal of other drugs belonging to the same brand. As such, the experience in one product potentially increases the demand in other products.

A contribution of this paper is that we extend the static model with demand side spillovers to a dynamic structural model with firm-level strategic responses to the spillovers. Regardless of which channel determines entry, a firm may enter a currently unprofitable market to gain an advantage in future markets.

Starting from Bresnahan and Reiss (1991), there is an increasing amount of empirical literature which studies firm-level entry and exit decisions. The early literature focuses on a static entry game. Berry (1992) analyzes airlines' decisions to set up nonstop flights between city-pairs; Scott-Morton (1999) estimates which characteristics of generic drug market openings attract more entrants; Mazzeo (2002) studies the U.S. motel market by allowing the representative motel to simultaneously choose their service quality and locations. Seim (2006) further extends Mazzeo (2002) by adding firm side heterogeneities to investigate the location and product quality decisions of videotape firms. Ching (2010b) uses a structural model to analyze the generic firms' entry decision when both firms and consumers are uncertain about the quality of the generic drugs but learns via consumers' experience. Benkard (2004) first identifies dynamic supply side spillovers in the aircraft industry. He concludes that production experience of an airplane module reduces the cost of producing a similar module of that airplane later. Gallant, Han, and Khawaja (2017) (henceforth GHK) similarly estimate supply side spillovers in the pharmaceutical industry to explain firm-level over-entry patterns, when new drug market openings appear. They find that each entry reduces future costs by approximately 7% at the next entry opportunity.

In contrast to Benkard (2004) and GHK (2017), Foster, Erdem, and Oncu (2015) and Foster, Haltiwanger, and Syverson (2016) stress demand side spillovers. They attribute firms' market share growth to their past sales, a firm with more accumulated sales tends to have larger market share, and this effect leads to slow convergence of the size gap between new and incumbent firms. Gavazza (2011) also emphasizes demand side spillovers in the U.S. fund market. In this market, fund families offer a large number of funds rather than low fees to gain more market power and share. He finds that the four largest fund families doubled their market shares between 1992 and 2007 by offering more funds.

Another strand of literature focuses on estimating entry games. In contrast to the former literature, there are two main methodological challenges that need to be addressed. One challenge in our dynamic game setting is that a firm's entry decision depends not only on their own state, but also on their rivals' entry decisions. This strategic interaction invalidates the methods proposed by Rust (1987), and Hotz and Miller (1993). In these papers, the individual's decision only depends on his own state, whereas in our paper, the estimation is based on the noncooperative equilibrium among firms. The second challenge is the continuous state variables. The continuity features rule out the method of Aguirregabiria and Mira (2007), which requires the conditional choice probabilities (CCP) at all possible states. Instead, the estimation technique here follows GHK (2017), and uses Bayesian Markov Chain Monte Carlo (MCMC) methods to overcome these difficulties.

In this paper, we find that past entry experience has an important impact on firm performance in subsequent markets. When only supply side spillovers are allowed, the costs in the future markets may fall by as much as 7%. This result is close to its counterpart in GHK (2017). In contrast, when we incorporate demand side spillovers, the supply spillover effect becomes insignificantly different from zero, whereas demand spillovers increase a firm's future market share by 3%-4% at the next market opening. The results show that demand side spillovers dominate supply spillovers in the pharmaceutical industry when both of them are considered together.

In order to compare our findings with those in GHK (2017), we take the strategic competition among the top three pharmaceutical firms into account. Nonetheless, to check the robustness of our findings, we also estimate versions which consider strategic competition among the top four or top five generic pharmaceutical firms. Across each model estimation, our parameter estimates exhibit very similar features. Although we focus on the setting with three strategic firms in the main text, the results for each model are available in Table 1. (2) The results indicate that lowering entry barriers will not encourage long-run competition in the pharmaceutical industry, as experienced firms will squeeze out new firms in future markets by attenuating market share for new ones.

Differing from Ching (2010b), in which he considers the impact of early entry on the firm-level profits in the same market, this paper identifies the early entry impact across markets. We find that past entry experience has an important impact on firm performance in subsequent markets. Our estimation method also deviates from Jmai, Jain, and Ching (2009), in which they use past iterations to locally approximate the value function. Local approximation only works well when there is a unique equilibrium. In a setting with multiple possible equilibria, a small deviation from past states may substantially change the equilibrium and the approximated value functions. This leads to biased local approximation. In addition, this paper has significant differences from Amisano and Giorgetti (2013), in which they use a reduced form approach to investigate the impact of early market entry on the firm-level profit in the submarkets of the pharmaceutical industry. The structural approach in this paper allows us to conduct counterfactual policy experiments, which indicate different implications of supply and demand side spillovers.

The rest of the paper is organized as follows: in Section II, the background of generic pharmaceutical industry and the corresponding data are introduced. A dynamic model containing both demand and supply side spillovers is formally presented in Section III. Section IV discusses the model's solution, and Section V presents the likelihood function. We introduce the choice of priors for all parameters in Section VI. In Section VII, we report the estimate results and evaluate the model's performance relative to that of the benchmark model. Section VIII conducts counterfactual experiments of the proposed model and discusses the implications for policymakers and firms. Finally, Section IX concludes.

II. BACKGROUND AND DATA

Generic drugs, substitutes for brand-name drugs, are almost bioequivalent to the brand-name drugs, but less expensive. Generic pharmaceutical sales account for a considerable share of gross domestic product (GDP) in the United States. In 2007, total sales were valued at $58.5 billion. In the same year, 65% of prescriptions in the United States were made up of generics. In order to promote generics as well as lower drug prices, the Drug Price Competition and Patent Term Restoration Act of 1984 (usually referred to as the Waxman-Hatch Act) was enacted to lower entry barriers for generic firms by permitting abbreviated new drug applications (ANDAs). This act promotes market entry, because generic firms only need to submit bioequivalence studies, instead of repeating all the expensive and time consuming tests that the manufacturer of the pioneer branded product went through to gain the Food and Drug Administration (FDA) approval. The Waxman-Hatch act has resulted in a lot of biologically equivalent drugs. According to a report of the FDA in 2004, there were 941 new drug and biological license application approvals between 1995 and 2004; only one-third were defined by the FDA as "containing an active substance that has never before been approved for marketing in any form in the United States."

Although the Waxman-Hatch act lowers entry barriers, there remains a significant sunk entry cost associated with submitting an ANDA, even if it is much less than the cost of inventing a new drug. These sunk entry costs range from $250,000 to $20 million. In addition, the generic drug market is risky. Empirical evidence shows that only 3 out of every 20 approved drugs bring in sufficient revenue to cover their costs (Ogbru 2002). These significant sunk costs and uncertainties in each market cause the number of entrants to be small.

As discussed in Scott-Morton (1999), entry is rarely announced, because firms who have private information do not want to signal the common market value, attract potential entrants, and increase competition. They also fear that the delay in the approval will invite competition. There are few late sequential movers who withdraw in response to rivals' approvals. As such, simultaneous entry decisions are a striking feature of the pharmaceutical industry.

The original data were assembled by Scott-Morton (1999), and were sorted by GHK (2017) later. This dataset consists of all ANDA approvals between 1984 and 1994. To implement the estimation, the variables we are using for each market opportunity include the ANDA approval date, market revenue in the year before the patent expires, and entry decision of potential entrants.

In 1989, the notorious "generic scandal" was exposed, in which some FDA reviewers confessed to accepting bribes to expedite ANDAs, and some data submitted by firms were falsified in order to pass the FDA process. During this "scandal period," the market structure may be different from the postscandal period. Because of the possibility of structural change, the data points in the scandal period are disposed of to avoid biasing the analysis. As a result, we focus on the period after the scandal, 1990-1994. In this period, there are 40 market openings for which the previous revenue data are not missing, and 51 firms who entered at least once. Following GHK (2017), this analysis focuses on the top three pharmaceutical firms. As a robustness check, we provide the estimation results for the top four and top five pharmaceutical firms. The top three dominant firms in the sample after 1989 are My Ian, which entered 45% of the markets, Novopharm which entered 28%, and Lemmon which entered 25% of the markets. The detailed data are included in Table 2.

The number of entrants is negatively correlated with time t, which implies that the later markets attract fewer firms to enter. In order to stress this point, we regress the number of entrants on t by controlling for the market revenue as follows:

[n.sub.t] = [a.sub.1] + [a.sub.2][rev.sub.t] + [a.sub.3]t + [[epsilon].sub.t],

where n, is the total number of entrants in market t, and rev, is the revenue in market t. The result shows that [a.sub.2] is negative and significant (3 )([a.sub.2] = -0.046(0.0008)). This fact is coincidental with the impact of demand rather than supply spillovers: some frequent entrants (the top three firms) accumulate brand loyalty in the early markets and squeeze out nonfrequent entrants in later markets.

III. MODEL

In this section, we present a dynamic model of firm entry with both demand side and supply side spillovers. Because of the computational burden of solving the model in markets with many entrants, we restrict the strategic interaction to the three dominant firms. The remaining firms are referred to as "other firms," and their small size and market share are assumed not to affect the top firms' entry decisions. In this analysis, the market share occupied by other firms is simply neglected. However, we make use of all firms' entry decisions to underscore the potential demand side spillovers. Each dominant firm maximizes his discounted profits in an infinite series of market openings t = 1, 2... [infinity] . Each market (4) opening opportunity is defined as the time when a drug's patent protection expires. In a bid to maximize the discounted profits, each firm makes their entry decision at market t based on the current profits associated with market t and the impact of the decision on future profitability. Since market openings appear in the time horizon, in the following context, t will be used interchangeably to denote a market opening or the time period associated with it. If a firm decides to enter a market, he collects profits over all future periods, instead of realizing all profits in one period. However, this feature makes the dynamic model hard to estimate, because two time horizons are entangled in this model: one is within each market t, the other is over different market openings. To make the model computationally feasible, we follow GHK (2017) and assume firms realize all profits in each market in a lump-sum form.

When market t opens, firm r's entry decision is denoted by [A.sub.it] = {0, 1}. If firm i chooses to enter market t, [A.sub.it] = 1, otherwise, [A.sub.it] = 0. In each market t, firm decisions are observed by whether they submit an ANDA or not. The number of total entrants in market t is given by

(1) [mathematical expression not reproducible]

The possible sources of dynamics are through cost and market share. If a firm entered a previous market, their profitability may be enhanced later. This increase in profits could be the result of a cost reduction from previous experience, (5) or a demand increase from an enlarged customer base. (6)

To separately identify the sources of dynamics, we impose some structure on the model. Particularly, current costs, [C.sub.it] are determined by previous entry decisions and random shocks.

We assume evolution of cost is governed by the following equation:

(2) [mathematical expression not reproducible]

where [u.sub.c] is a location parameter representing the average log cost; [k.sub.c] is the direct cost spillover effect in current market t if firm i enters market t-1, and the cost spillovers last more than one period through the persistence parameter [[rho].sub.c] [[sigma].sub.v][e.sub.it] is the cost shock which follows a normal distribution with zero mean and variance [mathematical expression not reproducible]. The cost shock captures unobservable firm-level heterogeneity in production cost and market entry cost. Equation (2) implies that if [k.sub.c] is positive, a firm's past entry experience reduces their cost in later markets. More importantly, the impact of supply side spillovers on a firm's future profit is uncorrelated with the number of markets the firm's competitors have entered. This implies that supply side spillovers rely only on the firm's own absolute entry history.

The firm-level expected market share is generated by consumers' heterogeneous preference toward different products in a market. In particular, consumers in general prefer a brand which has been known or used before (e.g., Che, Erdem, and Oncu 2015; Erdem 1998). (7) Therefore, a firm with more market entry experience could ensure a larger expected market share, whereas a firm that rarely entered markets before only anticipates a small market share. As a result, firm i's expected market share [S.sub.it] conditional on all firms entering market t is governed by the following equation:

(3) [mathematical expression not reproducible]

where the parameter X measures the magnitude of the demand spillovers. Equation (3) implies that if [lambda] is positive, a firm's previous entry experience increases its market share given that his rivals keep the same strategies.

Several features of Equation (3) are worthy of addressing here (8): first, given the value of X, the impact of entry on the future demand is decreasing in the total number of markets a firm has entered. This feature is consistent with the literature. On one hand, according to Ching (2010a), entry in related products markets builds a firm's reputation through attracting consumers according to their degree of price sensitivity. More price sensitive consumers are attracted in early periods; on the other hand, according to Erdem and Keane (1996), when consumers are risk averse and uncertain about a new product, they use the quality signals from related products to update their prior beliefs. As the information they already have grows (experience with related products), additional signals provide less information. Second, the impact of previous entry on market share depends on the entry history of other firms. This feature is consistent to Erdem and Keane (1996) and Che, Erdem, and Oncu (2015). In particular, when consumers' quality perceptions are correlated across products under the same brand, the more products offered by a brand will decrease consumers' purchase likelihood of other brands. As such, if competitors entered a larger number of early markets, consumers are more certain about their product quality, and it is more difficult for the representative firm to attract consumers through entry. As such, demand side spillovers rely on different firm-level relative market entry histories. Third, our identification of this model relies on the functional form of demand side spillovers. Due to data limitations, we need the demand and supply side spillovers to affect the firm-level profit differently.

In the case that a potential entrant does not enter the market, its expected market share will be split by the other firms in proportion to their conditional market shares. The actual market share for firm i in market t is defined in the following equation

(4) [mathematical expression not reproducible]

We assume, as in GHK (2017), that this is a game with complete information. Hence, all firms observe each other's costs as well as their expected market shares. (9) Total revenue in market t is approximated by the revenue in the previous year, when the drug was on patent. Therefore, when firms make their entry decision at market t, the revenue [R.sub.t] associated with this market is treated as known, because firms can observe the previous year's revenue.

The uncertainties originate from the corresponding costs and revenue in future markets. The realization of revenue [R.sub.t+1] =exp([r.sub.t+1]) is assumed to take the following form:

(5) [mathematical expression not reproducible]

where, [u.sub.r] is a location parameter, and [e.sub.r ,t + 1] is a random shock to the revenue in market t +1, with standard normal distribution. Firms take Equation (5) into consideration when they make decision at time f.

This structure allows us to write the profits [[pi].sub.it] for dominant firm i in market; as:

(6) [[pi].sub.it] = [A.sub.it] ([[rho].sub.it] [R.sub.t] - [C.sub.it]).

The firm's discounted profits at time t are

(7) [mathematical expression not reproducible]

where [beta] is a discount parameter within the interval (0, 1). The firm maximizes the sum of discounted profits by making his entry decision in each market given the actions of other firms.

The choice specific Bellman equation can be written as:

(8) [mathematical expression not reproducible]

where [S.sub.it] = ([A.sub.it], [A.sub.it], [C.sub.it], [C.sub.-it] [[rho].sub.it][R.sub.t], [[rho].sub.it][R.sub.t])--i represents all the other firms with respect to firm i, [mathematical expression not reproducible] is the equilibrium strategy for firm i, and [mathematical expression not reproducible] is the equilibrium strategy vector of other firms. The choice-specific value function (8) gives the discounted profits for firm i if he chooses action [A.sub.it] at time t and all firms play equilibrium actions from t+1 onwards. The expectation is over the distribution of cost shocks, revenue, and actual market shares in market t + 1 conditional on all the realizations of states and actions taken at time t.

The best response strategy profile [mathematical expression not reproducible] as the stationary pure strategy Markov perfect equilibrium of the dynamic game satisfies: (9) [mathematical expression not reproducible]

The value function (not the choice specific value function) is

(10) [mathematical expression not reproducible]

Our estimation strategy relies on the pure strategy Markov perfect equilibrium. We first consider how to calculate the equilibrium. Without knowing what actions the rivals will take, a representative firm needs to compare his discounted profits under every possible action profile of his rivals. Within Bayesian estimation, the required parameters can be drawn from prior distributions, and updated by comparing likelihoods computed under different sets of parameters. (10)

A second difficulty is the number of equilibria. One possibility is that there may be no pure strategy equilibrium at some given set of parameters, another is multiple equilibria at some given set of parameters, and finally the model may deliver a unique Nash equilibrium in each market. If there is no equilibrium, we simply dispose of that set of parameters, and draw a new set of parameters. In other words, the parameters are only updated when they generate an equilibrium in pure strategies. When there are multiple equilibria, we follow Berry (1992) in the selection of equilibrium. Specifically, when there are multiple equilibria, the equilibrium with the minimum total cost will be chosen as the equilibrium to be used in estimation. The details about estimating the model under pure strategies and unique equilibrium are discussed in Section IV.

IV. SOLVING THE MODEL

In the estimation, a nested approach is employed to solve the dynamic model. The broad outline of the computational strategy is as follows: (1) Draw a set of parameters by means of the MCMC algorithm. (2) For each set of parameters, generate the state variables over the sample period. (3) Solve the dynamic game to compute the equilibrium outcome as a function of the state variables. (4) Use the equilibrium outcome to compute likelihood relying on the observed entry data. (5) Use the likelihood depending only on observed variables to make an acceptance-rejection decision within the MCMC algorithm. Repeat steps (1)-(5) to generate an MCMC chain which is drawn from the posterior distribution of the parameters. In the above outline, the two main tasks are computing the equilibrium and calculating the likelihood. In this section, we describe the details for solving the equilibrium of the dynamic game. In Section V, we discuss how to calculate the likelihood function with the solved equilibrium and latent parameters.

Within the dynamic model, we look for a stationary Markov perfect equilibrium, which requires solving the fixed point of the Bellman Equation (10). At each market opening t, firms make their entry decisions. The strategy profile [A.sub.t] played by all firms at time t is denoted as

(11) [A.sub.t] = {[A.sub.1t], [A.sub.2t], [A.sub.3t]).

The equilibrium strategy profile should be a function of state variables ([C.sub.1t], [C.sub.2t], [C.sub.3t], [[rho].sub.it] [R.sub.it] [[rho].sub.2t][R.sub.t] [[rho].sub.3t] [R.sub.t],), costs, and market share of all firms. The vector of the log of the state variables at time t is

(12) [mathematical expression not reproducible]

Given a set of parameters, the game is solved as follows:

1. Approximate the value function at each market opening (by a linear equation, V*([s.sub.t]) = b* + B*[s.sub.t], where b* is a constant vector, and B* is a coefficient matrix.

2. Search for the fixed point of V* (s) = [mathematical expression not reproducible] by initializing the value function [V.sup.0](s)--0 + 0 X [s.sub.t], where the superscript indicates the number of iterations. Here, the search starts with ([b.sup.0], [B.sup.0]) being set to 0.

3. Compute the best response strategy for each firm over the sample period. The best response strategy requires the formula of the expected future value function

[mathematical expression not reproducible]

for each firm i. We obtain the above formula as follows: at each [s.sub.t], given any strategy profile [A.sub.j] of all firms, we generate the next period state variables [S.sub.tj], where j= 1,2,..., J. The variable [S.sub.tj] is the future possible states around s,, but shifted by strategy profile [A.sub.j]. Each [S.sub.tj] contains the dynamic effect of strategy profile [A.sub.j] and systematic cost shocks and demand shocks. The expectation is the sum of the value function at different [S.sub.ij].

(13) [mathematical expression not reproducible]

4. Calculate the value function at all possible strategy profiles, and make use of Equation (9) to select the best response strategy profile [mathematical expression not reproducible]. We record the value function with the best response strategy profile for each market t as [mathematical expression not reproducible]

5. Regress [V.sup.0]([s.sub.t]) on a constant and state variables to get [b.sup.1] and [B.sup.1]. The new ([b.sup.1], [B.sup.1]) is an update of ([b.sup.0], [B.sup.0]).

6. Iterate Step 3 to Step 5 to find the new equilibrium profile under new coefficients ([b.sup.1], [B.sup.1]) to update ([b.sup.1], [B.sup.1]) to ([b.sup.2], [B.sup.2]). Keep doing this until ([b.sup.k], [B.sup.k]) becomes stable.

7. The fixed point of the value function is V*(s) = [b.sup.k]+[B.sup.k]s.

To summarize the procedure, we first solve the equilibrium by guessing the coefficients of the value function. After solving the corresponding equilibrium given the coefficients, the value function V (*) at each state s, can be computed. T value functions are calculated over the sample periods, and these values are regressed on state variables to update the coefficients of value function. This procedure continues until all coefficients become stable. In the procedure, it is possible that no equilibrium exists for some sets of parameters. In this case, these parameters are considered to be an irrelevant portion of the parameter space, and are rejected in the MCMC likelihood comparison step.

Our model may also deliver multiple equilibria. For example, suppose we have a situation where one firm entering a market is profitable, but two entrants make a loss for both. In this situation, either firm entering the market is an equilibrium. Alternatively, it may be that taking the same strategy as a rival is profitable for the firm. (11) In the later case, having both firms enter or having both stay out of the market are equilibria.

We follow Berry (1992) to deal with multiple equilibria by adopting a selection rule. The rule is to select the equilibrium with the minimum total cost of all firms as the equilibrium. Specifically, at market t, there is a total cost of [C.sub.t] = [C.sub.1t] + [C.sub.2t] + [C.sub.3t] associated with an action profile [A.sub.t] = ([A.sub.1t] [A.sub.2t], [A.sub.3t]). The action profiles are ordered by their associated total cost: the first action profile is associated with the lowest total costs and the last action profile contains highest total costs. The equilibrium action profile with the smallest costs is the selected equilibrium action profile.

The procedure of solving for the equilibrium given a set of parameters described in this section can be treated as an inner routine. The outer routine consists of sequentially drawing different sets of parameters, comparing their corresponding likelihood functions, and saving the draws which increase the likelihood function with a certain probability. We will discuss the construction of the likelihood function next.

V. LIKELIHOOD COMPUTATION

Because we are estimating a game of pure strategies, a density for the strategy profile A, that depends only on state [S.sub.t] = ([C.sub.it] [C.sub.2t] [C.sub.3t] [[rho].sub.1t] [R.sub.t], [[rho].sub.2t][R.sub.t] [[rho].sub.3t][R.sub.t]) and the model parameters would generate a value of one for the likelihood when the prediction is coincident with observed actions, and a value of zero for likelihood when the prediction is not. This feature would generate a mass of one on a single value of [A.sub.t].

To solve this problem, we follow GHK (2017) by defining a misclassification probability [q.sub.a] = a-[p.sub.a], 0< [p.saub.a] < 1, and the likelihood function for an observed action profile [mathematical expression not reproducible] is defined as follows

(14) [mathematical expression not reproducible]

where [A.sub.it] is predicted entry decision computed from the model given state [S.sub.t] and 0 is the set of parameters to be estimated.

(15) [theta]= ([u.sub.1], [[sigma].sub.1], [u.sub.c], [[sigma].sub.c], [[sigma].sub.r], [[rho].sub.c], [k.sub.c], [lambda])

The full likelihood for the data is (16) [mathematical expression not reproducible]

We interpret the misclassification probability as follows. Consider a firm which decides to enter a market and submit its ANDA. However, with some probability its ANDA will be rejected, even if it decides to enter. This rejection does not allow his entry decision to be realized, and the rejection probability is the misclassification probability (Table 3).

Between 1990 and 1994, there are 40 markets in total without missing revenue data after the scandal. In the first period, there is no information about the demand and supply spillovers. We use two prescandal periods' entry behavior to generate the firm-level entry histories. Alternatively, the first period is treated as the initial period, in which all firms are ex ante equivalent. The results suggest no significant difference between the two approaches.

VI. PARAMETER ESTIMATION

As discussed in Section IV, the estimation method contains an inner routine and an outer routine. For the outer routine, an MCMC method is used to draw the parameters from a one-move-at-a-time random walk proposal density. Given the old draw [[theta].sup.0], a new draw is made from a conditional distribution q([theta]*|[[theta].sup.0]). Denote the likelihood by L([theta]), and the prior by [pi]([theta]). The actual next period parameter 8 is generated as follows:

1. Draw 0[theta]* according to q([theta]*|[[theta].sup.0]).

[mathematical expression not reproducible]

2. If there is no equilibrium at parameter [theta]*, set [theta]' = [[theta].sup.0], otherwise with probability a, set [theta]' = [theta]* and with probability (1 - a) set [theta]' = [[theta].sup.0].

We choose q([theta]*|[[theta].sup.0]) to be a conditional normal distribution, in which [theta]* is drawn from a normal distribution with mean [[theta].sup.0], so as to facilitate the outer routine computation. In this way, q([theta]*|[[theta].sup.0]) = q([[theta].sup.0]|d*), and the acceptance probability in Step 2 can be written as

Because we do not want to impose too many restrictions on the parameters, we use a non-informative prior [pi]([theta]) with flat tails: log[u.sub.1]~ U[-3, 3], log [u.sub.c].~U[-3, 3], log [[sigma].sub.1]~U[-3, 3], log [[sigma].sub.c]~U[-3,3], log [[sigma].sub.r]~ U[-3,3], [k.sub.c]~U[-1, 1], [[rho].sub.c]~U[0,1], and [lambda]~U[0, 2]. The time discount parameter [beta] and the misclassification parameter [p.sub.a] are not estimated in the program. Following the literature, we set fi = 0.95, and [p.sub.a] = 0.9375.

VII. RESULTS

GHK (2017) claim that firms' overentry behavior is caused by supply spillovers, which reduce the total costs by 7%. To make the estimates comparable to GHK (2017), we first estimate the model under supply side spillovers only by shutting off the demand side spillovers, [lambda] = 0, and updating the remaining parameters. We then repeat the exercise with both demand and supply side spillovers. The key parameter in the second column of Table 3 is [k.sub.c], which is the measure of supply spillovers. The estimate of [k.sub.c] is close to its counterpart in GHK (2017), likewise, the other parameters are close to those previously estimated in the literature. The results from the model with supply side spillovers imply that firms can reduce future costs by 7% if they enter the current product market. In the third column, we report the results when both demand and supply spillovers are introduced in the model. It is not surprising to find that the magnitude of the supply side spillovers falls after introducing demand spillovers, while the parameter governing demand side spillovers, [lambda], is positive and significant. Although it is not surprising that the supply side spillovers fall after adding demand side spillovers, it is surprising to see that past entry experience has a negative impact on costs in the later markets. (12) However, we cannot confidently determine the sign of the supply side spillovers given its large degree of variation in the posterior distribution of [k.sub.c]. It is worthwhile to point out that [lambda] itself is not a direct measure of the market share increase, but the market share increase can be calculated from [lambda]. The detailed market share increase caused by demand side spillovers is presented in Table 4. The difference in the value of [k.sub.c] across columns implies that in the pharmaceutical industry, the pattern of firm-level overentry behavior is largely determined by demand spillovers. Moreover, if we ignore demand spillovers, researchers will incorrectly estimate the supply spillover effect.

In order to compare the goodness of fit of the two models (the model with supply side spillovers only vs. the model with both supply and demand side spillovers), we calculate the predicted market entry rate and the average predicted market revenues based on the coefficients in column 2 and column 3, respectively. (13) All results are in Tables 5 and 6. Results indicate, on one hand, that the model with demand and supply side spillovers (our preferred specification) fits the data better than the model with only supply side spillovers; on the other hand, the model with supply side spillovers tends to overpredict the firm-level entry rate relative to the model with both spillovers. The reason is that with significant supply side spillovers, all firms, on average, tend to enter more frequently in subsequent markets. Following GHK (2017), we conduct a series of robustness checks. First, we allow the value function to assume different forms across the state space, and the results are reported in Table 7; second, we extend the competition between the top three firms to the top four firms to alleviate the concern that only considering the top three firms is too restrictive. (14) The results are reported in Table 1. All results indicate that the demand side spillovers dominate the supply side spillovers.

To shed more light on the role of demand spillovers, we define [f.sub.1] ([A.sub.ij], [A.sub.-i,j]) as firm i's market share in market t + 1 conditional on having entered market t, and [f.sub.2]([A.sub.ij], [A.sub.-i,j]) as firm i's market share in market t+ 1 given that he has not entered market t:

(17) [mathematical expression not reproducible]

(18) [mathematical expression not reproducible]

Then, firm i's marginal market share from entering market f, conditional on the actual entry history, can be computed as follows:

(19) [mathematical expression not reproducible]

where MM[S.sub.it] is the marginal market share of firm i at market t.

The average marginal share increase caused by demand spillovers, or in other words by reputation building, for each firm over all markets is reported in Table 4. Market-specific results are reported in Table 8. Table 4 shows that in our sample, past entry increases the current market share of each firm by 3% to 4% on average, given that his rivals keep the same entry decision. The increase in market share enhances firms' profitability, and hence gives them the incentive to enter markets even if they are associated with relatively low revenue.

As discussed above, firm-level market-entry decisions depend on expected profits. We use a simple example to show how the two types of spillovers differently affect these expected profits. Consider two firms that face a market opening. Firm i has no previous entry experience, but firm j has entered many past markets. Since firm i has no entry history, it cannot benefit from its own cost reduction (supply spillovers) nor reputation (demand spillovers). While supply spillovers alone affect firm i's expected profit by changing firm/s entry probability, (15) demand spillovers not only increase firm /s entry probability, but also decrease firm i's postentry market share. In this example, the impact of supply spillovers on firm i is indirect (through increasing the entry probability of firm j by reducing its cost), but the demand spillovers have both indirect and direct impact on firm i (through increasing firm j's profits, and hence the entry probability by reallocating market shares from firm i to firm/.

VIII. POLICY EXPERIMENTS

To distinguish the different implications of demand side spillovers and supply side spillovers, three experiments have been performed. The objective of these experiments is to measure how a policymaker could encourage entry by lowering entry barriers in different scenarios. In the first experiment, the average number of entrants before and after the barrier reduction is computed by assuming no spillovers. The second and third experiments repeat the exercise with supply spillovers and demand spillovers, respectively.

A. Three Counterfactual Experiments

In each experiment, 50 market openings are simulated, and a policymaker is able to decrease the total costs of potential entrants by 20% in the first 10 markets by lowering the entry cost. Specifically, in the first 10 markets, the cost location parameter becomes 0.8[u.sub.c].. The features of markets and potential entrants are characterized by the parameters estimated in the last section. In particular, the revenue, and costs associated with each market are respectively drawn from N([u.sub.r] [[sigma].sub.r]), and N([u.sub.c], [[sigma].sub.c]). For the cases of no spillovers or only demand spillovers, we use the parameters from the third column of Table 3. For the case of only supply side spillovers, we use the parameters from the second column of Table 3.

One concern is that if the model with only supply side spillovers is misspecified, the entry cost parameter, [k.sub.c] may be biased; what can we conclude from the change of market entry rate in this case? The answer to this question is that in the counterfactual experiment, we are comparing the market entry rate before and after entry cost reduction under each circumstance. As such, in the case with only supply side spillovers, we are only concerned with how the market entry rate changes without stressing the change magnitude. (16)

The first and second columns are the entry rate before and after the cost reduction, while the third column reports the change in the Herfindahl index before and after the cost reduction. (17)

Table 9 first shows that with and without the cost reduction (lowering entry barrier), if an industry is characterized by supply spillovers only, then that industry tends to have the highest entry rate. (18) This result is reasonable in the sense that supply spillovers increase firms' average profitability in later markets, whereas demand spillovers only shift the market share among firms, which raise the profitability for one firm by hurting the other firms. Second, in the benchmark and supply spillovers case, a policymaker could enhance the market entry rate and competition by lowering entry barriers, but in the demand spillover case, lowering entry barriers results in a lower entry rate and less competition (increased concentration). The reason is that with demand spillovers, firms that enter early markets have an advantage over late comers, and they will squeeze out other firms in later markets, even in those high revenue markets, as the market share left for other firms is too small to make profits.

B. Insights and Implications

For Policymakers. The above results indicate that if a policymaker is about to lower entry barriers to encourage entry in an industry with demand spillovers, he is likely to increase the concentration in this industry and induce a lower entry rate, possibly even lower than in the benchmark case, in future markets. The difference in the changes of the average market entry rate across the supply and demand spillovers cases indicates the drawback of misspecification in the nature of spillovers.

For Firms. As mentioned in Benkard (2004), supply spillovers that appear across products share some similarities. If a firm takes advantage of supply side spillovers to maximize its long-run profit, it would increase its competitiveness (production cost reductions) in one product market through entering a related product market. In particular, for generic drug firms, if they enter every heart disease medicine market, they may reduce their production cost in the future heart disease medicine. In contrast, our results demonstrate that in the generic drug market, demand side spillovers work. As such, generic drug firms are able to increase their market share in one drug market through entering other unrelated drug markets. For instance, a generic drug firm is able to increase its profitability in a future heart disease medicine market through entering any drug markets as long as these drugs are under the same brand. Therefore, it is quite important for a firm manager to identify which kind of spillovers are at work before they extend their product scope.

IX. CONCLUSION

This paper investigates cost and demand spillovers that affect firm-level entry decisions in the pharmaceutical industry. The former spillover is caused by economies of scope and the latter one results from reputation building. In contrast to previous literature which attributes overentry in the pharmaceutical industry to economies of scope, this paper finds that reputation building plays a significant role in firm-level entry patterns. The results indicate that when the impact of reputation building on demand is neglected, the estimated effect of economies of scope tends to be biased upward. After both types of spillovers are taken into account, reputation building is shown to have an important impact on firm-level profits in the pharmaceutical industry. Furthermore, ignoring the impact of reputation on firm-level profits leads to misleading results. Lowering entry barriers increases competition in models of supply side factors alone, but decreases competition when demand side factors are dominant. This suggests that subsidizing only new firms might be a way to increase competition when the impact of reputation on firm demand is of significance. In contrast, when only economies of scope play their role, the policymaker does not need to distinguish between firms. Subsidizing all firms can increase competition. The verification of this policy conjecture for the pharmaceutical industry, however, is left for future research.

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YONG TAN (*)

(*) I am grateful to Joel for his continuous advice and helpful comments. I am indebted to Andrea and Chen for their suggestions in improving this paper. I also thank the financial support from National Natural Science Foundation of China (71703067), National (Major) Social Science Foundation of China (18VSJ017), and Major Bidding Project of Ministry of Education of China (16JZD019). Finally, I give my special gratitude to my wife Ying. Without her physical and psychological supporting, I would struggle more so in my Ph.D. studies. Also, thank you for bringing our son Xiao, Zhuren into my life.

Tan: Associate Professor, School of International Economics and Trade, Nanjing University of Finance and Economics, Nanjing, 2100023, China. Phone +86-18105155848, E-mail yongtan_econ@ 163.com

ABBREVIATIONS

ANDAs: Abbreviated New Drug Applications

CCP: Conditional Choice Probabilities

FDA: Food and Drug Administration

GDP: Gross Domestic Product

GHK: Gallant, Han, and Khawaja

MCMC: Markov Chain Monte Carlo

MMS: Marginal Market Share

(1.) Note that when Rodrigue and Tan (2016), Piveteau (2016), and Fitzgerald, Haller, and Yedid-Levi (2016) focus on the dynamic spillvers over time in one market, Erdem (1998) addresses the dynamic spillovers across different markets.

(2.) Due to the computational burden associated with estimating the strategic model, GHK (2017) only estimate supply side spillovers in an empirical model which has strategic competition among the top three or four pharmaceutical firms. We extend the estimation of our model with both supply and demand spillovers to a setting with strategic interaction among the top five firms. However, as the number of firms in the model increases, the number of possible equilibria increases exponentially, which substantially raises the computational burden associated with estimating the model.

(3.) We also repeat the regression for the top three firms. where n, is the number of entrants of the top three firms, and the negative correlation still holds [a.sub.2] = -0.012(0.0001)

(4.) To make the results comparable to GHK (2017), we focus on the drug markets in which the drugs have the form of pills. Differing from Amisano and Giorgetti (2013), each market is identified as a therapeutic class. As such, there is no submarket in each therapeutic class

(5.) There are a number of sources for cost reductions. for instance, by entering more markets, a firm may achieve economies of scope by reducing fixed entry costs (Dubois et al. 2015), distribution costs, market establishment costs (Keyl 2006), or research costs (Appelt 2015; Branstetter et al. 2011; Henderson and Cockburn 1996).

(6.) The increase in demand arises due to a reputation effect: physicians and pharmacists are reluctant to prescribe the drugs they are not familiar with (Gilbert, Ural, and Lopz 2012; Mason and Bearden 1980); patients are more willing to use the drugs in which they have less uncertainty regarding the quality (Ching 2010a, 2010b).

(7.) This is usually caused by quality correlations or correlated quality perceptions across products under the same brand.

(8.) This equation shares very similar features to the demand structure in McFadden (1974).

(9.) Since a firm's market entry history is observable, the expected market share is given by Equation (3).

(10.) More details can be found in Doucet, Freitas, and Gordon (2001).

(11.) This case can be interpreted as firms choosing to protect their comparative advantage in future markets. That is. they may use the same strategy as their rival to keep themselves in a safe position.

(12.) There are a number of explanations for the negative impact of past entry on future profitability. These include diseconomies of scale or diseconomies of scope with respect to technological investment costs. For instance. Henderson and Cockburn (1996) claim that in the pharmaceutical industry, economies of scope in research is the determinant of supply side spillovers. However, generic drug firms invest relatively less in research, as such there is little room for economies of scope.

(13.) We thank an anonymous referee for pointing out the importance of comparing the two model specifications.

(14.) We thank an anonymous referee for suggesting to extend the exercise to more firms to make the results more convincing. Due to the computational burden, we only extend the three-firm case to the four-firm case.

(15.) Since firm; entered many past markets, the supply spillovers increase its likelihood to enter the current market. This increased entry likelihood lowers firm i"s postentry expected profit.

(16.) We thank an anonymous referee for pointing out this issue. The magnitude of the increase in the entry rate with supply spillovers after cost reduction is biased, but it still sheds light on how the entry rate changes with only supply side spillovers.

(17.) In the case where we only have demand side spillovers, firm-level market share varies across firms: firms which have entered more markets have larger market shares. Therefore, the number of firms in a market is not sufficient to measure the market competitiveness. Instead, the Herfindal index is computed as a robust measure of market competitiveness.

(18.) We need to be aware that the mean of [u.sub.r] is higher in the supply spillovers' case than that of the no spillovers' and demand spillovers' case. This higher average revenue partly leads to a higher entry rate in the supply spillovers' case.

doi: 10.1111/coep.12391
TABLE 1
Posterior Distribution with Supply and Demand Spillovers (Four-Firm
and Five-Firm Cases)

Parameter        Four-Firm Case            Five-Firm Case

[u.sub.c]             9.9943(0.1583)      10.0112(0.1624)
[u.sub.r]            10.2412(0.2319)      10.5368(0.2217)
[[sigma].sub.c]       0.2483(0.1027)       0.2674(0.0993)
[[sigma].sub.r]       1.6397(0.0200)       1.6014(0.0563)
[k.sub.c]            -0.1696(0.1612)      -0.0987(0.1321)
[lambda]              0.1379(0.0125)       0.1436(0.0211)
[[rho].sub.c]         0.8530(0.1127)       0.8793(0.1422)
[beta]                0.95                 0.95
[p.sub.a]             0.9375               0.3795
MCMC Rep         10,000               10,000

Notes: Table 1 reports the parameter of estimates after accounting for
the strategic interaction among the top four and top five dominant
generic firms' market entry decisions. The results show that demand
side spillovers still dominate supply side spillovers.

TABLE 2
The Data

Drug Active Ingredient              ANDA Date           Mylan

Sulindac                            April 3, 1990        1
Erythromycin stearate               May 15, 1990         0
Atenolol                            May 31, 1990         1
Nifedipine                          July 4, 1990         0
Minocycline hydrochloride           August 14, 1990      0
Methotrexate sodium                 October 15, 1990     1
Pyridostigmine bromide              November 27, 1990    0
Estropipate                         February 27, 1991    0
Loperamide hydrochloride            August 30, 1991      1
Phendimetrazine                     October 30, 1991     0
Tolmetin sodium                     November 27, 1991    1
Clemastine f'umarate                January 31, 1992     0
Cinoxacin                           February 28, 1992    0
Diltiazem hydrochloride             March 30, 1992       1
Nortriptyline hydrochloride         March 30, 1992       1
Triamterene                         April 30, 1992       0
Piroxicam                           May 29, 1992         1
Griseofulvin ultramicrocrystalline  January 30, 1992     0
Pyrazinamide                        January 30, 1992     0
Diflunisal                          July 31, 1992        0
Carbidopa                           August 28, 1992      0
Pindolol                            September 3, 1992    1
Ketoprofen                          December 22, 1992    0
Gemfibrozil                         January 25, 1993     1
Benzonatate                         January 29, 1993     0
Methadone hydrochloride             April 15, 1993       0
Methazolamide                       January 30, 1993     0
Alprazolam                          October 19, 1993     1
Nadolol                             October 31, 1993     1
Levonorgestrel                      December 13, 1993    0
Metoprolol tartrate                 December 21, 1993    1
Naproxen                            December 21, 1993    1
Naproxen sodium                     December 21, 1993    1
Guanabenz acetate                   February 28, 1994    0
Triazolam                           March 25, 1994       0
Glipizide                           May 10, 1994         1
Cimetidine                          May 17, 1994         1
Flurbiprofen                        June 20, 1994        1
Sulfadiazine                        July 29, 1994        0
Hydroxychloroquine sulfate          September 30, 1994   0
Mean                                                     0.45

                                               Total     Revenue
Drug Active Ingredient       Novopham  Lemmon  Entrants  ($'000)

Sulindac                       0         1       7       189,010
Erythromycin stearate          0         0       1        13,997
Atenolol                       0         0       4        69,802
Nifedipine                     1         0       5       302,983
Minocycline hydrochloride      0         0       3        55,491
Methotrexate sodium            0         0       3        24,848
Pyridostigmine bromide         0         0       1         2,113
Estropipate                    0         0       2         6,820
Loperamide hydrochloride       1         1       5        31,713
Phendimetrazine                0         0       1         1,269
Tolmetin sodium                1         1       7        59,108
Clemastine f'umarate           0         1       1         9,077
Cinoxacin                      0         0       1         6,281
Diltiazem hydrochloride        1         0       5       439,125
Nortriptyline hydrochloride    0         0       3       187,683
Triamterene                    0         0       2        22,092
Piroxicam                      1         1       9       309,756
Griseofulvin
ultramicrocrystalline          0         0       1        11,727
Pyrazinamide                   0         0       1           306
Diflunisal                     0         1       2        96,488
Carbidopa                      0         1       4       117,233
Pindolol                       1         0       7        37,648
Ketoprofen                     0         0       2       107,047
Gemfibrozil                    0         1       5       330.539
Benzonatate                    0         0       1         2,597
Methadone hydrochloride        0         0       1          1858
Methazolamide                  0         0       3         4,792
Alprazolam                     1         0       7       614,593
Nadolol                        0         0       2       125,379
Levonorgestrel                 0         0       1        47,836
Metoprolol tartrate            1         0       9       235,625
Naproxen                       1         1       8       456,191
Naproxen sodium                1         1       7       164,771
Guanabenz acetate              0         0       2        18,120
Triazolam                      0         0       2        71,282
Glipizide                      0         0       1       189,717
Cimetidine                     1         0       3       547,218
Flurbiprofen                   0         0       1       155,329
Sulfadiazine                   0         0       1            72
Hydroxychloroquine sulfate     0         0       1         8,492
Mean                           0.28      0.25    3.3     126,901

Notes: Table 2 reports the postscandal data used in the study. Three
dominant firms' entry decisions are denoted as 1 if entry, 0
otherwise. Total entrants include all small firms. Revenue is the
realized revenue 1 year before the patent expires.

TABLE 3
The Posterior Distribution

                 Posterior Distribution   Posterior Distribution
                 with Supply Spillovers   with Supply and Demand
Parameter        Only                     Spillovers

[u.sub.c]            10.3488 (0.2993)          10.5238 (0.2188)
[u.sub.r]            11.8320 (0.4253)          10.2971 (0.2275)
[[sigma].sub.c]       0.4811 (0.0452)           0.2485 (0.0881)
[[sigma].sub.r]       1.6902 (0.0138)           1.6625 (0.0127)
[k.sub.c]             0.0677 (0.0206)          -0.0787 (0.1363)
[[rho].sub.c]         0.8405 (0.1086)           0.8553 (0.1098)
[beta]                0.95                      0.95
[p.sub.a]             0.9375                    0.9375
[lambda]                                        0.1664 (0.0128)
MCMC Rep         10,000                    10,000

TABLE 4
The Average Marginal Market Share (AMMS) Gain from Entry

        AMMS

Firm 1  0.0406
Firm 2  0.0331
Firm 3  0.0313

TABLE 5
Goodness of Fit of Entry

                      Predicted Entry  Predicted Entry Rate
        Actual Entry  Rate Supply      Demand
        Rate (%)      Spillovers (%)   Spillovers (%)

Firm 1     45            42.5             37.5
Firm 2     27.5          40.0             27.5
Firm 3     25            35.0             22.5

Notes: Table 5 reports the goodness of fit of the structural model
with demand and supply side spillovers. The second column is the
actual firm-level entry rate in all 40 markets. The third column is
the predicted firm-level entry rate in all 40 markets with supply side
spillovers, and the fourth column reports the predicted entry rate
with demand side spillovers. The predicted entry rate is computed with
the posterior mean of parameters in columns 2 and 3 of Table 3,
respectively.

TABLE 6
Goodness of Fit of Market Revenue

                     Average           Average
Average             Predicted     Predicted Revenue
Actual           Revenue Supply        Demand
Revenue            Spillovers        Spillovers

10.4737(2.1213)  11.8320(1.4223)  10.2971 (1.6625)

Notes: Table 6 reports the mean of actual market revenues and the
average predicted market revenues with supply side spillovers and
demand side spillovers, respectively. The standard deviation is in
the parenthesis.

TABLE 7
Posterior Distribution with Supply and Demand Spillovers (with Split
State-Space)

Parameter        Three-Firm Case

[u.sub.c]        10.7887 (0.3866)
[u.sub.r]        10.6395 (0.2389)
[[sigma].sub.c]   0.2810 (0.0887)
[[sigma].sub.r]   1.5025 (0.0966)
[k.sub.c]        -0.0732 (0.0893)
[lambda]          0.1722 (0.0656)
[[rho].sub.c]     0.8951 (0.1489)
[beta]            0.95
[p.sub.a]         0.9375
MCMC Rep         10.000

Notes: Table 7 reports the parameters of estimates after I split the
state space by market revenue. In particular. I allow the coefficients
of value function V*([S.sub.t]) = b + [BS.sub.t], to be different when
the realized market revenues are all above or below the median market
revenue. The results show that demand side spillovers still dominate
supply side spillovers.

TABLE 8
Market Share Increase for Each Firm in Each Market

Drug Active Ingredient              MMS for Firm 1  MMS for Firm 2

Sulindac                              0.03794         0.036921
Erythromycin stearate                 0.03%           0.036921
Atenolol                              0.0396          0.035716
Nifedipine                            0.040232        0.035716
Minocycline hydrochloride             0.040232        0.037787
Methotrexate sodium                   0.040232        0.036579
Pyridostigmine bromide                0.041174        0.036579
Estropipate                           0.041174        0.036579
Loperamide hydrochloride              0.040232        0.034324
Phendimetrazine                       0.041174        0.036579
Tolmetin sodium                       0.040232        0.034324
Clemastine fumarate                   0.040789        0.035716
Cinoxacin                             0.040789        0.035716
Diltiazem hydrochloride               0.040232        0.034324
Nortriptyline hydrochloride           0.041174        0.035163
Triamterene                           0.041566        0.035163
Piroxicam                             0.041174        0.032753
Griseofulvin ultramicrocrystalline    0.041566        0.035163
Pyrazinamide                          0.041566        0.035163
Diflunisal                            0.041449        0.034324
Carbidopa                             0.041174        0.03336
Pindolol                              0.040789        0.031843
Ketoprofen                            0.041449        0.034324
Gemfibrozil                           0.041174        0.031843
Benzonatate                           0.041566        0.031843
Methadone hydrochloride               0.041566        0.031843
Methazolamide                         0.041566        0.031843
Alprazolam                            0.041449        0.030177
Nadolol                               0.041544        0.031016
Levonorgestrel                        0.041069        0.031016
Metoprolol tartrate                   0.041386        0.02914
Naproxen                              0.041386        0.02914
Naproxen sodium                       0.041386        0.02914
Guanabenz acetate                     0.040645        0.031755
Triazolam                             0.040645        0.031755
Glipizide                             0.040645        0.02981
Cimetidine                            0.040153        0.027749
Flurbiprofen                          0.03868         0.028269
Sulfadiazine                          0.036786        0.028269
Hydroxychloroquine sulfate            0.036786        0.028269

Drug Active Ingredient              MMS for Firm 3

Sulindac                              0.034713
Erythromycin stearate                 0.036921
Atenolol                              0.035716
Nifedipine                            0.034713
Minocycline hydrochloride             0.034713
Methotrexate sodium                   0.03336
Pyridostigmine bromide                0.03336
Estropipate                           0.03336
Loperamide hydrochloride              0.030816
Phendimetrazine                       0.03336
Tolmetin sodium                       0.030816
Clemastine fumarate                   0.03336
Cinoxacin                             0.035716
Diltiazem hydrochloride               0.034324
Nortriptyline hydrochloride           0.031843
Triamterene                           0.031843
Piroxicam                             0.029231
Griseofulvin ultramicrocrystalline    0.031843
Pyrazinamide                          0.031843
Diflunisal                            0.031843
Carbidopa                             0.034324
Pindolol                              0.034324
Ketoprofen                            0.034324
Gemfibrozil                           0.032753
Benzonatate                           0.035163
Methadone hydrochloride               0.035163
Methazolamide                         0.035163
Alprazolam                            0.032753
Nadolol                               0.031016
Levonorgestrel                        0.031016
Metoprolol tartrate                   0.02838
Naproxen                              0.025724
Naproxen sodium                       0.025724
Guanabenz acetate                     0.02838
Triazolam                             0.02838
Glipizide                             0.026482
Cimetidine                            0.023855
Flurbiprofen                          0.02195
Sulfadiazine                          0.02195
Hydroxychloroquine sulfate            0.02195

TABLE 9
The Average Entry before and after Cost Reduction

                   Average Number of Entrants
                      No Cost Reduction

Benchmark                  1.08
Supply spillovers          1.68
Demand spillovers          1.24

                   Average Number of Entrants   Change of Herfindahl
                     with Cost Reduction        Index Before and
                                                After Cost Reduction

Benchmark              1.21                           -0.06
Supply spillovers      1.80                           -0.10
Demand spillovers      1.13                           +0.03
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Author:Tan, Yong
Publication:Contemporary Economic Policy
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2019
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