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Dynamic Entry with Cross Product Spillovers:An Application to the Generic Drug Industry

Ron Gallant1 Han Hong2 Ahmed Khwaja3

1Duke University and New York University

2Stanford University

3Yale University

Summer Institute in Competitive StrategyHaas School of Business, UC-Berkeley

21st July 2010

Gallant, Hong, & Khwaja (2010) Dynamic Entry with Cross Product Spillovers 21st July 2010 1 / 73

Introduction

Outline

Introduction

Research Overview

Institutional Background

Model: Set Up and Solution

Particle Filters: A Brief Review

Estimation

Data and Results

Conclusions and Future Work


Introduction

Motivation

I Long standing interest in spillovers of experience:

I Learning curves in psychology (e.g., Ebbinghaus 1885, Bills 1934).

I Learning curves in engineering (e.g., Wright 1936).

I Experience curves in economics/strategy/marketing (e.g., Arrow1962, Bass 1980, Dolan & Jeuland 1981, Spence 1981, Shen &Villas-Boas 2010)

I Spillovers can have significant strategic implications, i.e., potentialpath to market dominance (Bruce Henderson/BCG Matrix 1972).

I Develop method to estimate dynamic models of strategicinteractions with endogenous latent state variables that areserially correlated.


Introduction

MotivationI Two examples:

I NFL on Fox (HBS Case 9-704-443)I Buy the broadcasting rights to NFL in 1993.I Expected annual loss potential $500 - $700 mil.

I Murdoch’s purchase of WSJ?

I Traditionally focus has been on experience spillovers for a singleproduct (e.g., Benkard 2003 - Lockheed L-1011) we examinecross-product spillovers.

I On supply/production side spillovers may arise due to, e.g.,I Learning by doing.I Economies of scope.I Firm or Managerial attributes.I Supplier networks.


Introduction

Motivation

Empirical Models of Entry(E.g., πnjt ,anjt ,n = 1,2 firms, j = 1,2 products, t = 1,2 time periods)

No Product Spillovers Product Spillovers

Static π11(a11, a21) = 0∑2

j=1[π1j({a1j , a2j}2j=1)] = 0

Dynamic∑2

t=1[π11t(a11t , a21t)] = 0∑2

t=1

∑2j=1[π1jt({a1jt , a2jt , a1jt−1, a2jt−1}2

j=1)] = 0


Introduction

MotivationEmpirical Models of Entry


Static E.g., Bresnahan & Reiss (1990, 1991), E.g., Ellickson et al. (2008),Berry (1992), Scott-Morton (1999), Jia (2008)Mazzeo (2002), Seim (2006),Vitorino (2008), Datta & Sudhir (2008)Ellickson & Misra (2008),Zhu & Singh (2009), Shen (2010) etc.

Dynamic E.g., Hitsch (2006), Benkard (2004), GHK (2010)Ching (2009)


Introduction

Truth in Advertising!

Empirical Models of Entry(E.g., πnjt ,anjt ,n = 1,2 firms, j = 1,2 products, t = 1,2 time periods)


Static π11(a11, a21) = 0∑2

j=1[π1j({a1j , a2j}2j=1)] = 0

Dynamic∑2

t=1[π11t(a11t , a21t)] = 0∑2

t=1[π1t(a1t , a2t , a1t−1, a2t−1)] = 0


Research Overview

Outline

Introduction

Research Overview




Estimation

Data and Results



Research Overview

Model Overview

Dominant Firms(enter = 1, not enter = 0)

Drug ANDA Date Mylan Novopharm Lemmon Geneva Total RevenueEntrants ($ mil.)

· · · · · · · ·· · · · · · · ·Tolmetin Sodium 27 Nov. 91 1 1 1 1 7 59.11Clemastine Fumarate 31 Jan. 92 0 0 1 0 1 9.08Cinoxacin 28 Feb. 92 0 0 0 0 1 6.28Diltiazem Hydrochloride 30 Mar. 92 1 1 0 0 5 439.13Nortriptyline Hydrochloride 30 Mar. 92 1 0 0 1 3 187.68Triamterene 30 Apr. 92 0 0 0 1 2 22.09Piroxicam 29 May 92 1 1 1 0 9 309.76· · · · · · · ·· · · · · · · ·

I On average 8 market opportunities in a year.I Each firm makes decisions about entry at each opportunity.I Opportunity to enter a product market presents itself just once - no

late movers or second chances.I Firm makes entry decision in a strategic setting thinking not just

about payoff from current opportunity but also spillovers of entry.


Research Overview

Modeling Spillovers

I Model spillovers as the effect of past actions on a firm’sunobserved ability to profit.

I For convenience model spillovers through unobservable “cost."

I Can’t separately identify revenue and cost spillovers.I No different from existing entry literature (an exception is Datta &

Sudhir, 2008).I Limitation: black box, single dimensional approach.

I Specify spillovers as effect of past actions on costs.I ci,t = µc + ρc (ci,t−1 − µc)− κcAi,t−1 + σceit .

I Also costs are serially correlated as important to allow for firmlevel persistence in spillovers.


Research Overview

Econometric Challenge: Serial Correlation

I Serial correlation imposes a severe computational challenge:I E.g., (in discrete choice estimation) if IID error:

I Uj,t(Xj,t , β, εj) = Uj,t(Xj,t , β) + εj

I Pr(dj,t | Xj,t) =∫ε1, . . . ,

∫εJ

I(Uj − Ui > εi − εj ∀i 6= j)f (ε)dε1 . . . dεJ

I

(=

exp(Uj,t (Xj,t ,β))∑Jj′=1

exp(Uj′,t (Xj′,t ,β)))

)I E.g., if error term is serially correlated:

I Uj,t(Xj,t , β, ρ, εj,t , εj,t−1) = Uj,t(Xj,t , β) + εj,t + ρεj,t−1

I Do GHK (maybe) to get Pr(dj,t | Xj,t)

I If error term is serially correlated and dynamic forward lookingagents:

I Uj,t(Xj,t , β, ρ, εj,t , εj,t−1) = Uj,t(Xj,t , β) + δEMAX (Xt+1) + εj,t + ρεj,t−1

I Need to solve dynamic programming problem (to get EMAX (Xt+1))and do GHK to get Pr(dj,t | Xj,t)


Research Overview

Econometric Challenge: Two Step Estimation

I A static, single agent example of two step estimation:I Decision to buy a TV of brand j ∈ {1,2}.I Characteristics of TV: (Xj ,Zj ) - observable, µj - unobservable.I Probability of failure of brand j is pj (Zj , µj ).I Utility from brand j is Uj (Xj , β, µj )

I 1st step: estimate beliefs about uncertain events pj directly from(observable) data.

I 2nd step: estimate structural payoff parameters (β) by plugging theestimated beliefs (p̂j ) in expected utility function(maxj∈{1,2}[p̂jUj + (1− p̂j )Uj ]).

I Inconsistent 1st step estimates will contaminate 2nd stageestimates if some unobservable (to researcher) variable (µ) createsa correlation between payoff function and an agent’s beliefs.


Research Overview

Econometric Challenge: Two-Step EstimationI Two-Step estimation, e.g,. Hotz & Miller 1993, Bajari, Benkard &

Levin 2004, Pakes, Ostrovsky & Berry 2003.I In dynamic games:

I 1st step: estimate player’s beliefs about the actions of theircompetitors directly from the data (assume private information isIID).

I 2nd step: estimate structural parameters of payoff functionssubstituting the 1st step belief estimates in the Bellman equation.

I Advantage is computational tractability.

I Serially correlated unobserved heterogeneity in costs rules outtwo step estimators - it creates a correlation between beliefs aboutactions of competitors and payoffs.

I Aguirregabiria & Mira (2007) and Arcidiacono & Miller (2010) usefinite mixtures to incorporate discrete (exogenous) unobservedheterogeneity in Two-Step estimation.


Research Overview

Method Overview

I Dynamic Game between forward looking firms:I Current actions of a player affect it’s current and future payoffs.I Current actions of competitors affect a player’s current payoffs and

actions, and hence it’s future payoffs.

I Solve game using dynamic programming:

I Approximate value functions using local linear approximation (e.g.,Keane & Wolpin (1997)).

I Integrate out unobserved state variable (i.e., costs) in likelihoodusing sequential importance sampling.

I Use Bayesian MCMC to recover model parameters.


Research Overview

Key Findings

I Find evidence of large cross product spillovers of experience.

I Immediate effect of entry on costs is 7%.

I Average annual cumulative effect (over 8 entry opportunities) is51%.

I Costs shocks can be big and can wipe out the benefits ofexperience allowing for “leap-frogging."

I Immediate effect of a one standard deviation shock on costs is 37%.

I Spillovers are important in entry decisions and hence evolution ofmarket structure.

I Stylized model fits data well, i.e., low classification error rates.



Outline

Introduction

Research Overview




Estimation

Data and Results




Generic Drugs: A Big Industry

I U.S. generic pharmaceutical sales in 2007: $58.5 billion (brandedpharmaceutical sales $228 billion).

I Generics make up 65% of all prescriptions in U.S. and exist for8,730 of 11,487 drugs in FDA’s Orange Book.

I Preparation of ANDA can take a long time and is costly ($250,000- $20 mil., revenues in one-firm markets: $10 mil.).

I Drug Price Competition and Patent Term Restoration Act orHatch-Waxman Act of 1984 allowed Abbreviated New DrugApplications (ANDAs).

I 1989 “generic scandal.” Four reviewers found to be taking bribesto hasten approval of ANDAs at FDA.



Generic Drugs: Suitable Application?

I High frequency of sequential entry opportunities.I Potential economies of scope (organizational experience, portfolio

of drugs etc.).I Oligopolistic industry where firms take a long term perspective.I Large payoffs and big sunk costs (FDA examines plant before

approval) so entry decisions are very important.I FDA does not reveal when and from whom it receives applications.I Few late sequential movers who withdraw in response to rivals’

approvals.I Size and heterogeneity of entry cost relative to market revenue

lead to small number of entrants supported by each market.



Outline

Introduction

Research Overview




Estimation

Data and Results




Model Set Up 0

Scott-Morton (1999)

I Simultaneous move static game.I Heterogenous observable (multidimensional) fixed costs, identical

marginal costs.I Complete information, firms know each other’s revenue and costs.

GHK (2009)

I Simultaneous move dynamic game.I Heterogenous unobservable (unidimensional) costs that are

endogenous to past actions.I Complete information, firms know each other’s revenue and costs.



Model Set Up I

I There are i = 1, . . . , I, firms.

I Firms maximize PDV of profits over t = 1, . . . ,∞I Each period t a market opens and firms make entry decisions:

I If enter Ai,t = 1;, else Ai,t = 0.

I Number of firms in the market at time t , is Nt =∑I

i=1 Ai,t .

I Lump sum profits for firm i from market opportunity t areΠi,t = Rγ

t /Nt − Ci,t .

I Lump sum revenue (Rt ) from market opportunity t is exogenouslydetermined and shared equally among dominant firms.



Model Set Up II

I Serially correlated costs are endogenous to past entry decisions(source of dynamics):

I ci,t = µc + ρc (ci,t−1 − µc)− κcAi,t−1 + σceit ,

I where ci,t = log Ci,t .

I Firms move simultaneously.

I Equilibrium selection: pick equilibrium with entrants with thelowest total costs (see e.g., Berry 1992, Scott-Morton 1999).



Bellman Equation: Choice Specific Value Function

Vi(Ai,t ,A−i,t ,Ci,t ,C−i,t ,Rt )

= Ai,t(Rγ

t /Nt − Cit)

+

β E[Vi(AE

it+1,AE−it+1,Cit+1,C−it+1,Rt+1)|Ait ,A−it ,Cit ,C−it ,Rt

]I Entry decision of firm i : Ai,t .I Cost of firm i : Ci,t .I Entry decisions of competitors −i : A−i,t .I Costs of competitors −i : C−i,t .I Total number of entrants: Nt .I Revenue: Rt .I Equilibrium actions in period t + 1: AE

i,t+1,AE−i,t+1.



Pure Strategy Markov Perfect Equilibrium

Simultaneous Best Response (no firm has an incentive to deviate)

Vi(AEi,t ,A

E−i,t ,Ci,t ,C−i,t ,Rt ) ≥ Vi(Ai,t ,AE

−i,t ,Ci,t ,C−i,t ,Rt) ∀ Ai,t , ∀ i , t

where

Vi(AEit ,A

E−it ,Cit ,C−it ,Rt )

= AEit

(Rγ

t /NEt − Cit

)+

β E[Vi(AE

it+1,AE−it+1,Cit+1,C−it+1,Rt+1) |AE

it ,AE−it ,Cit ,C−it ,Rt

],

and number of firms in equilibrium:

AEi,t , AE

−i,t , ⇒ NEt



Bellman Equation: Ex Ante Value Function

Since a game of complete information, Ct ,Rt known implies that AEt

known:

Vi(Ci,t ,C−i,t ,Rt ) = Vi(AEi,t ,A

E−i,t ,Ci,t ,C−i,t ,Rt ).

Vi(Ci,t ,C−i,t ,Rt )

= AEi,t

(Rγ

t /NEt − Cit

)+

β E[Vi(Cit+1,C−it+1,Rt+1)|AE

it ,AE−it ,Cit ,C−it ,Rt

]



Model: Solution I

I Main computational burden is finding a fixed point forVi(Ci,t ,C−i,t ,Rt ).

I The value function is approximated by a local linear function ofstate variables (e.g., Keane & Wolpin 1997).

I The integral is computed by Gauss-Hermite quadrature.



Model: Solution II

I For a three player game:

V (Ct ,Rt ) =(

V1(C1t ,C−1t ,Rt ),V2(C2t ,C−2t ,Rt ),V3(C2t ,C−3t ,Rt ))

I At each centroid K :

VK = bK + BK s ,

where VK is 3× 1, bK is 3× 1 , BK is 3× 4, and s is 4× 1.

I Map s, the log of the state variable S = (C1,C2,C3,R), to acoarse grid. Grid points determine both the centroid K and whichlinear approximator is to be used at s.



Model: Solution III For a three player game:

V (Ct ,Rt ) =(



VK = bK + BK s ,





Model: Solution II

I For a three player game:

V (Ct ,Rt ) =(



VK = bK + BK s ,





Model: Solution Algorithm I

I Guess a value for the value functions at a given state at iterationj = 0, i.e., (b(0)

K ,B(0)K ).

I Use guesses in computing the choice specific value functions atiteration j + 1:

Vi(Ai,t ,A−i,t ,Ct ,Rt )

= Ai,t(Rγ

t /Nt − Cit)

+ β E[Vi(Ct+1,Rt+1)|Ait ,A−it ,Ct ,Rt

]



Model: Solution Algorithm II

I This involves taking expectations over the evolution of the futurestate variables (Gauss-Hermite quadrature procedure).

I With choice specific value functions, compute the best responsestrategy profile at iteration j + 1:

Vi(AEi,t ,A

E−i,t ,Ct ,Rt ) ≥ Vi(Ai,t ,AE

−i,t ,Ct ,Rt).

I The best response strategy profile at iteration j + 1 is used tocompute the iteration j + 1 ex ante value functions:

Vi(Ct ,Rt )

= AEi,t

(Rγ

t /NEt − Cit

)+ β E

[Vi(Ct+1,Rt+1)|AE

it ,AE−it ,Ct ,Rt

]



Model: Solution Algorithm III

I The iteration j + 1 ex ante value functions are used to compute theiteration j + 2 choice specific value functions:

Vi(Ct ,Rt ) = Vi(AEi,t ,A

E−i,t ,Ct ,Rt ).

I Use multivariate regression to update value function:(b(0)K ,B(0)

K ),(b(1)

K ,B(1)K ), . . . ,(b(∗)

K ,B(∗)K )

I The entire procedure is repeated till a fixed point is obtained.



Outline

Introduction

Research Overview




Estimation

Data and Results




An Example: Stochastic Volatility Model (Polson form)

xt = φxt−1 + σet

yt = β exp(xt ) ut

et ∼ N(0,1)

ut ∼ N(0,1)

x0 ∼ N[0, σ2/(1− φ2)]

(et ,ut ) ∼ iidE(etut ) = ρ

I Agrees with the notational conventions of the particle filter literature.

I Will assume ρ = 0 for simplicity.

I See Douced, de Freitas, & Gordon (2001) for more details.



Generic Particle Filter Problem

x0 ∼ p(x0)

xt ∼ p(xt |xt−1)

yt ∼ p(yt |xt )

y1:t = {y1, . . . , yt}x0:t = {x0, . . . , xt}

Goal:I Estimate the posterior p(x0:t |y1:t ) recursively.I Estimate the filtering distribution p(xt |y1:t ) recursively.I Approximate integrals of the form

∫ft (x0:t ) p(x0:t |y1:t ) dx0:t



Particle Filter Algorithm

1. Initialization, t = 0.I For i = 1, . . . ,N sample x (i)

0 from p(x0) and set t to 1.2. Importance sampling step.

I For i = 1, . . . ,N sample x̃ (i)t from p(xt |x (i)

t−1) and setx̃ (i)

0:t = (x (i)0:t−1, x̃

(i)t ) .

I For i = 1, . . . ,N compute weights w̃ (i)t = p(yt |x̃ (i)

t ) .I Normalize the weights.

3. Selection stepI For i = 1, . . . ,N sample with replacement the particles

x (i)0:t from the set {x̃ (i)

0:t} according to the weights.I Increment t and go to step 2



Why Does This Work?

I It is an application of importance sampling applied sequentiallywith a particular choice of importance function that simplifies thealgebra.

I The selection step corrects for a defect in importance samplingthat arises when it is applied sequentially.

I Details follow.I In what follows, the hidden Markov state x can be either scalar or

vector and the same for the observation y .



Importance Sampling

We want to compute the integral∫

f (x)p(x) dx , where p(x) is a densityfunction with support X ⊂ <d . Suppose we can find a density functionπ(x) whose support includes X from which we can draw a samplex (1), . . . , x (N). Then∫

f (x)p(x) dx =

∫f (x)w(x)π(x) dx

wherew(x) =

p(x)

π(x)

whence ∫f (x)p(x) dx .

=1N

N∑i=1

f (x (i))w(x (i))



For Importance Sampling to Work Well

I The variance with respect to π(x) of f (x)w(x) must be small.

I To satisfy this requirement for general f (x) one tries to make thevariance of w(x) small.

I Making the variance of w(x) small is usually accomplished bymaking sure that π(x) has fatter tails than p(x) .

I For example, if p(x) has exponential tails like exp−x′Σ−1x/2, then

choose π(x) to be a density with polynomial tails like themultivariate t-distribution.

I Importance sampling is hard to get to work well when the dimension of xis large because it is hard to draw a sample that lands where f (x)w(x) islarge.



Normalized Weights

Let

w̃ (i) =w(x (i))∑Nt=i w(x (i))

then ∫f (x) p(x) dx =

∫f (x)w(x)π(x) dx∫

w(x)π(x) dx

.=

1N∑N

i=1 f (x (i))w(x (i))1N∑N

i=1 w(x (i))

=N∑

i=1

w̃ (i)f (x (i))



Why are Normalized Weights Relevant?N∑

i=1

w̃ (i) = 1 &∫

f (x) p(x) dx .=

N∑i=1

w̃ (i)f (x̃ (i)),

I Implies that we are integrating f (x) with respect to a discretedistribution that puts probability w̃ (i) on the points {x̃ (i)}.

I That means we could alternatively generate a random sample{x (i)} from this discrete distribution and use the formula∫

f (x)p(x) dx .=

N∑i=1

f (x (i))

I A random sample can be generated by sampling the points {x̃ (i)}with replacement with probability w̃ (i).

I This turns out to be the critical fact that allows importancesampling to be used recursively.



Why Follow It with a Selection Step?

When importance sampling is done recursively what happens as tincreases is that a few of the weights w̃ (i)

t increasingly dominate sothat most particles effectively die out.

What resampling does is eliminate some of the particles that havenegligible weight, replace them with particles that have larger weight,and adjust the weights. The result is more equal weights. This is calledbootstrap selection.

After completing a bootstrap selection, each particle has weight 1/N.


Estimation

Outline

Introduction

Research Overview




Estimation

Data and Results



Estimation

Estimation Overview

1. Given a parameter value, generate values for the latent variableusing the importance sampler.

2. Compute equilibrium of dynamic game as function of theobserved and unobserved state variables (given parameter value).

3. Use the equilibrium outcome to compute a likelihood of observeddata and latent state variables.

4. Integrate out the latent state variables using importancesampler to obtain a likelihood that depends only observedvariables.

5. Use this likelihood to make the accept/reject decision of theMCMC algorithm to generate MCMC chain of parameters.


Estimation

Likelihood: Misclassification ProbabilityI Since this a game of pure strategies the likelihood may not exist

we resolve this by assuming a misclassification probabilityqa = 1− pa, 0 < pa < 1 for an observed (ex post) action profileAo

t , i.e.,

p(Aot | rt , xt , yt−1, θ) =

I∏i=1

(pa)I(Aoit =Ait )(1− pa)I(Ao

it 6=Ait )

I Interpretation:I Small probability qa that planned entry decisions are not realized.I Measurement error by researcher.I Error or tremble by firm.


Estimation

Boundedly and Fully Rational Games

I We call the game as previously described with this modifiedlikelihood Boundedly Rational.

I Easier to compute (see also Che, Sudhir, & Seetharaman 2007).

I The modified game where the Value Functions and BellmanEquations account for the vector of qa is called a Fully Rationalgame.


Estimation

Sequential Importance Sampling Overview I

I Initial density c0 ∼ p(c0)

I Transition density ct ∼ p(ct |ct−1)

I Observation density At ∼ p(At |ct )

I Let A1:t = {A1, . . . ,At}I Let c0:t = {c0, . . . , ct}I Can estimate posterior p(ct |A1:t ).I Can estimate filtering distribution p(c0:t |A1:t ).I Can approximate integrals such as

∫ft (c0:t )p(c0:t |A1:t ).


Estimation

Sequential Importance Sampling Overview II

Integrating ct from likelihood:

p(A1:t |θ) =T∏

t=2

p(At |A1:t−1, θ)

=T∏

t=2

∫p(At |ct , θ)p(ct |A1:t−1, θ)dct

.=

T∏t=2

N∑i

p(At |c it , θ)

where are {c(i)1:t} drawn from p(c1:t |A1:t−1, θ) = p(A1:t |c0:t ,θ)p(c0:t ,θ)∫

p(A1:t |c0:t ,θ)p(c0:t ,θ)dc0:t.


Estimation

Revenues and Costs Specification

Notation: let xt = log Xt .

Revenue:

rt = µr + σr e0,t (1)

Cost has two components: (i) Cu,i,t , known by all firms but not us, & (ii)Ck ,i,t , known to everyone.

ci,t = cu,i,t + ck ,i,t (2)cu,i,t = µc + ρc (cu,i,t−1 − µc) + σceit (3)ck ,i,t = ρc ck ,i,t−1 − κcAi,t−1 (4)


Estimation

Sequential Importance Sampling: Set Up I

I Observable states: yt = (A1t , . . . ,AIt , ck ,1,t , . . . , ck ,I,t , rt ).

I Unobservable states: xt = (cu,1,t , . . . , cu,I,t )

I Firm entry decision density:p(At |rt , xt , yt−1, θ) =

∏Ii=1(pa)I(Ait =Ac

it )(1− pa)I(Ait 6=Acit )

I Measure of goodness of fit: pa

I Parameters: θ = (µc , ρc , σc , κc , µr , σr , β, pa)


Estimation

Sequential Importance Sampling: Implementation I

I For t = 0I Start N particles by drawing x (i)

0 for i = 1, . . . ,N from the initialdensity (6).

I Compute

p(y0|θ) =

∫p(y0|y−1, x0, θ) p(y−1, x0|θ) dx0

.=

1N

N∑i=1

p(y0|y−1, x(i)0 , θ).


Estimation

Sequential Importance Sampling: Implementation II

I For t = 1, . . . ,nI For each particle draw x̃ (i)

t from the transition density (5) and set

x̃ (i)0:t = (x (i)

0:t−1, x̃(i)t ).

I For each particle compute the particle weights w̃ (i)t using the

observation density (7); i.e.

w̃ (i)t = p(yt |yt−1, x̃

(i)t , θ)

I This involves solving the game and is computationally very costly.I We use a piecewise linear approximation to the value function in our

computations.


Estimation

Sequential Importance Sampling: Implementation III

I For t = 1, . . . ,nI Compute

p(yt |y1:t−1, θ) =

∫p(yt |yt−1, xt , θ) p(xt |y1:t−1, θ) dxt

.=

1N

N∑i=1

p(yt |yt−1, x(i)t , θ)

I Normalize the weights so that they sum to one.I For i = 1, . . . ,N sample with replacement the particles x (i)

0:t from theset {x̃ (i)

0:t} according to the weights.


Estimation

Sequential Importance Sampling: Implementation IV

I Done. The likelihood is:

p(y1:t |θ) = p(y0, θ)n∏

t=1

p(yt |y1:t−1, θ).

I Compute Posterior using MCMC (Metropolis-Hastings).


Estimation

MCMC Set Up: Priors (Uninformative)

I Unobservable cost dynamicsI−∞ < µc <∞I −1 ≤ ρc ≤ 1I 0 < σc

I Experience effectI 0 5 κc

I RevenueI−∞ < µr <∞I 0 < σr


Estimation

MCMC Set Up: Priors (Dogmatic)

I β = 0.96875I Corresponds to 20% annualized, ave data freq is 1.5 mos.I Discount rate is poorly identifiedI 20% for the drug industry is well documented

I γ = 0.9375I R − Rγ is the revenue conceded ex ante to marginal firmsI γ is poorly identifiedI A regression of entrants on revenue over the entire sample bracketsγ between 0.908 and 1.0

I pa = 0.9375I Imposed for convenienceI pa affects the particle survival rateI Nothing else is affected for pa > 0.7


Data and Results

Outline

Introduction

Research Overview




Estimation

Data and Results



Data and Results

Data: Estimation Sample

I Focus on markets for on the orally ingested generics in the form ofpills.

I Dominant firms Mylan, Novopharm, Lemmon, Geneva, and a“composite” firm, i.e., “Other.”

I Estimation sample period is 1990-94 (40 markets).I Data from 1984 to 1989 used to prime the recursion:

I ck,i,t = ρc ck,i,t−1 − κcAi,t−1

I Data used in estimation: total market revenues and entrydecisions of firms.


Data and Results

Table 1. Data

Dominant Firms(enter = 1, not enter = 0)

Drug / Active Ingredient ANDA Date Mylan Novopharm Lemmon Geneva Total RevenueEntrants ($’000s)

Sulindac 03 Apr. 90 1 0 1 1 7 189010Erythromycin Stearate 15 May 90 0 0 0 0 1 13997Atenolol 31 May 90 1 0 0 0 4 69802Nifedipine 04 Jul. 90 0 1 0 0 5 302983Minocycline Hydrochloride 14 Aug. 90 0 0 0 0 3 55491Methotrexate Sodium 15 Oct. 90 1 0 0 0 3 24848Pyridostigmine Bromide 27 Nov. 90 0 0 0 0 1 2113Estropipate 27 Feb. 91 0 0 0 0 2 6820Loperamide Hydrochloride 30 Aug. 91 1 1 1 1 5 31713Phendimetrazine 30 Oct. 91 0 0 0 0 1 1269Tolmetin Sodium 27 Nov. 91 1 1 1 1 7 59108Clemastine Fumarate 31 Jan. 92 0 0 1 0 1 9077Cinoxacin 28 Feb. 92 0 0 0 0 1 6281Diltiazem Hydrochloride 30 Mar. 92 1 1 0 0 5 439125Nortriptyline Hydrochloride 30 Mar. 92 1 0 0 1 3 187683Triamterene 30 Apr. 92 0 0 0 1 2 22092Piroxicam 29 May 92 1 1 1 0 9 309756Griseofulvin Ultramicrocrystalline 30 Jun. 92 0 0 0 0 1 11727Pyrazinamide 30 Jun. 92 0 0 0 0 1 306Diflunisal 31 Jul. 92 0 0 1 0 2 96488Carbidopa 28 Aug. 92 0 0 1 0 4 117233Pindolol 03 Sep. 92 1 1 0 1 7 37648Ketoprofen 22 Dec. 92 0 0 0 0 2 107047Gemfibrozil 25 Jan. 93 1 0 1 0 5 330539Benzonatate 29 Jan. 93 0 0 0 0 1 2597Methadone Hydrochloride 15 Apr. 93 0 0 0 0 1 1858Methazolamide 30 Jun. 93 0 0 0 1 3 4792Alprazolam 19 Oct. 93 1 1 0 0 7 614593Nadolol 31 Oct. 93 1 0 0 0 2 125379Levonorgestrel 13 Dec. 93 0 0 0 0 1 47836Metoprolol Tartrate 21 Dec. 93 1 1 0 1 9 235625Naproxen 21 Dec. 93 1 1 1 1 8 456191Naproxen Sodium 21 Dec. 93 1 1 1 1 7 164771Guanabenz Acetate 28 Feb. 94 0 0 0 0 2 18120Triazolam 25 Mar. 94 0 0 0 0 2 71282Glipizide 10 May 94 1 0 0 0 1 189717Cimetidine 17 May 94 1 1 0 0 3 547218Flurbiprofen 20 Jun. 94 1 0 0 0 1 155329Sulfadiazine 29 Jul. 94 0 0 0 0 1 72Hydroxychloroquine Sulfate 30 Sep. 94 0 0 0 0 1 8492

Mean 0.45 0.28 0.25 0.25 3.3 126901

46


Data and Results

Main Results

I Estimate model for 2 cases for Boundedly Rational and FullyRational models:

I 3 dominant firmsI 4 dominant firms

I Focus on Boundedly Rational results.I κc = 0.07, i.e., immediate effect of entry on costs is 7%, average

annual cumulative effect is 51%.I σc = 0.37, i.e., cost shocks can be big and nullify the benefits of

experience allowing for “leap-frogging.".I Spillovers are important in entry decisions and hence evolution of

market structure.I Stylized model fits data well, i.e., low classification error rates (3

firm case: 0.09, 4 firm case: 0.11).


Data and Results

Table 2. Posterior Distribution: Boundedly Rational Model

Number of Potential Entrants(excluding “other” firms)

Parameter 3 firms 4 firms

µc 10.05 10.07(0.017) (0.0014)

ρc 0.9866 0.9873(0.00086) (5.6e-05)

σc 0.3721 0.3675(0.026) (3.0e-04)

κc 0.06655 0.07067(0.0015) (1.1e-04)

µr 9.906 10.008(0.083) (0.0037)

σr 1.591 1.682(0.060) (0.0023)

γ 0.9375 0.9375

β 0.9688 0.9688

pa 0.9375 0.9375

CER firm 1 0.0857 0.1208CER firm 2 0.0788 0.0876CER firm 3 0.1038 0.1061CER firm 4 0.1374

CER all firms 0.0894 0.1130

MCMC Reps 3000000 3000000

stride 375 375

47


Data and Results

Table 3. Posterior Distribution: Fully Rational Model

Number of Potential Entrants(excluding “other” firms)

Parameter 3 firms 4 firms

µc 10.06 10.07(0.016) (0.0012)

ρc 0.9877 0.9873(0.00095) (4.5e-05)

σc 0.3714 0.3676(0.037) (0.00035)

κc 0.06634 0.0704(0.0012) (0.00010)

µr 9.941 10.009(0.064) (0.0032)

σr 1.531 1.682(0.059) (0.0016)

γ 0.9375 0.9375

β 0.9688 0.9688

pa 0.9375 0.9375

CER firm 1 0.0861 0.1045CER firm 2 0.0786 0.0837CER firm 3 0.0971 0.0860CER firm 4 0.1351

CER all firms 0.0873 0.1023

MCMC Reps 3000000 3000000

stride 375 375

48


Data and Results

Histogram of mu_c

Den

sity

10.00 10.02 10.04 10.06 10.08 10.10

010

2030

Histogram of rho_c

Den

sity

0.985 0.986 0.987 0.988

020

040

060

0

Histogram of sigma_c

Den

sity

0.364 0.366 0.368 0.370 0.372 0.374 0.376 0.378

050

100

150

Histogram of kappa_c

Den

sity

0.062 0.064 0.066 0.068 0.070

050

150

250

Histogram of mu_r

Den

sity

9.6 9.7 9.8 9.9 10.0 10.1

01

23

45

6

Histogram of sigma_r

Den

sity

1.4 1.5 1.6 1.7

02

46

8

Figure 1. Marginal Posterior Distributions, Three Firm Model.

35


Data and Results

Histogram of mu_c

Den

sity

10.062 10.064 10.066 10.068 10.070

020

040

0

Histogram of rho_c

Den

sity

0.98720 0.98725 0.98730 0.98735 0.98740

050

0015

000

Histogram of sigma_c

Den

sity

0.3668 0.3670 0.3672 0.3674 0.3676 0.3678

050

015

00

Histogram of kappa_c

Den

sity

0.0703 0.0704 0.0705 0.0706 0.0707 0.0708

040

0080

00

Histogram of mu_r

Den

sity

10.005 10.010 10.015

050

100

150

Histogram of sigma_r

Den

sity

1.678 1.680 1.682 1.684

010

030

0

Figure 2. Marginal Posterior Distributions, Four Firm Model.

36


Data and Results

Results: Plot of log cost in the 3 firm model.

I Top firm, Mylan, seems to have a cost advantage.I Broad trends in costs are similar for all firms.


Data and Results

0 10 20 30 40

910

1112

MYLAN’s log cost

o

o

o

o

o

oo

o

oo

o o

oo o

o

o oo

0 10 20 30 40

910

1112

NOVOPHARM’s log cost

o

o

o

o

o

o o

oo

o

o

o

0 10 20 30 40

910

1112

LEMMON’s log cost

o

o

o

o

o

o

oo

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o

o

0 10 20 30 40

46

810

12

log total revenue

3 2 0 1 1 0 1 0 0 3 0 3 1 0 2 1 0 3 0 0 1 1 2 0 2 0 0 0 2 1 0 2 3 3 0 0 1 2 1 0 0

44


Data and Results

Results: Overplots of log cost of 3 dominant firms

I Costs for 3 dominant firms are similar in 3 and 4 firm models.


Data and Results

0 10 20 30 40

78

910

1112

1314

MYLAN’s log cost

o o o o o o o o o o o o o o o o o o o

0 10 20 30 40

78

910

1112

1314

NOVOPHARM’s log cost

x x x x x x x x x x x x

0 10 20 30 40

78

910

1112

1314

LEMMON’s log cost

* * * * * * * * * * *

Figure 4. Cost and Entry Decisions of the Dominant Firms.

38


Data and Results

Predicted & Actual Entry

0 10 20 30 40

0.0

0.4

0.8

MYLAN’s entry decisions

x

x

x

x

x

x

x

x x

x

x

x

x x

x x

x

x

x xx x

x

x

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x x

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x x

o o

o

o

o o

o

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o o o

o o

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o o o

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0 10 20 30 40

0.0

0.4

0.8

NOVOPHARM’s entry decisions

x

xx x

x

x x x x

x

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x x

x

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xx x x x

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0 10 20 30 40

0.0

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0.8

LEMMON’s entry decisions

x

x

x

x x x x x x

x

x

xx

x

x

xx

x

x x

x x

x

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x

x x x

x

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x x

x x x x x x x

o o

o o o o o o o

o

o

o o

o o o o

o

o o

o o

o o

o

o o o o o o o

o o

o o o o o o o

46


Data and Results

Results: AlternativesI Two other possible games:

I “Myopic” game: (β = 0, κc = 0).I “Static” game: (β = 0, κc > 0).I 3 firm case: “myopic” game matches our game in 49% and “static”

game in 84% of cases respectively.I 4 firm case: numbers are 31% and 68% respectively.

I Is it really the dynamic spillover effect of entry on future costs orthe converse (alternatively are σc and κc correlated)?

I Re-running MCMC chain setting κc to 0.25, 0.125 and 0.0625 hasvery little effect on σc .



Outline

Introduction

Research Overview




Estimation

Data and Results




Contribution

I Estimated a dynamic entry game of cross product spillovers.I Stylized model fits data reasonably well.I Spillovers affect entry and market structure.I Leap-frogging may happen as cost shocks can wipe out gains from

experience.

I Developed method to estimate dynamic models of strategicinteractions allowing for endogenous latent state variables to beserially correlated.

I Method is generally applicable if a firm’s strategic choices arediscrete, e.g., entry/exit, introduction/discontinuation ofbrands/products/models, start-up/shut-down/relocation ofstores/firms/factories, technology adoption/upgrades etc.

I Spillovers may be positive or negative.




I Allow for multidimensional measures of experience.

I Allow for mixed discrete-continuous choices, e.g., introduction ofnew product and advertising or pricing decision.

I Extend to dynamic games of incomplete information.


dynamic entry with cross product spillovers: an ...doubleh/computationaleconometricss/khwaja...i nfl...

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