Diffusion of new pharmaceutical drugs in developing and developed nations

Intern. J. of Research in Marketing 21 (2004) 341 – 357 www.elsevier.com/locate/ijresmar

Diffusion of new pharmaceutical drugs in developing and developed nations Ramarao Desirajua,*, Harikesh Nairb, Pradeep Chintaguntac a College of Business Administration, University of Central Florida, Orlando, FL 32816, USA Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637, USA c Graduate School of Business, University of Chicago, 1101 East 58th Street, Chicago, IL 60637, USA

b

Received 3 July 2003; received in revised form 22 December 2003; accepted 13 May 2004

Abstract In the context of introducing new products around the world, it is important to understand the relative attractiveness of various countries in terms of maximum penetration potential and diffusion speed. In this paper, we examine these market characteristics for a new category of prescription drugs in both developing and developed countries. Using data from 15 countries and a logistic specification in the hierarchical Bayesian framework, we report the differences in diffusion speed and maximum penetration potential between developing and developed nations. Our methodology accounts for the limited number of data observations, as well as serial correlation and endogeneity problems that arise in the analysis. The principal findings are as follows. (i) Compared to developed countries, developing nations tend to have lower diffusion speeds and maximum penetration levels. (ii) Laggard developed countries have higher speeds. However, laggard developing countries do not have higher diffusion speeds. (iii) Per capita expenditures on healthcare have a positive effect on diffusion speed (particularly for developed countries), while higher prices tend to decrease diffusion speed. The paper concludes by identifying useful avenues for additional research. D 2004 Elsevier B.V. All rights reserved. Keywords: Diffusion; Cross-country analysis; Pharmaceuticals; Hierarchical Bayes

1. Introduction Many developing nations, with their relatively large populations, have attractive potential buyer

* Corresponding author. Tel.: +1 407 823 6521; fax: +1 407 823 3801. E-mail address: [email protected] (R. Desiraju). 0167-8116/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ijresmar.2004.05.001

segments that may exceed the size of an entire developed nation’s market. In an era of less prevalent trade barriers, more common consumer preferences across the globe, and market saturation in developed nations, there is an increasing need to understand the market characteristics of these developing nations. In particular, as firms introduce their products and services across countries, it is important to assess the relative attractiveness of various nations in terms

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of their market potential, the likely speed of diffusion, and the impact of marketing mix elements (such as prices) on that speed. These factors have important strategic value, and in this paper, we explore such market characteristics in both developing and developed nations. In the context of the diffusion of a new subcategory of pharmaceutical drugs, we examine the diffusion speed, maximum penetration potential, and the effects of prices and per capita health care expenditures in 15 countries (ordered first by entry date and then alphabetically): Belgium, South Africa, USA, Spain, Italy, Mexico, Canada, UK, France, Netherlands, Brazil, Colombia, Venezuela, Australia, and Portugal. Over the last three decades, the marketing literature on new product diffusion has focused mainly on durable products in varying subsets of industrialized countries (c.f. Dekimpe, Parker, & Sarvary, 2000a; Mahajan, Muller, & Bass, 1990). In recent years, there has been an increasing effort to study the diffusion process in the other parts of the world. Our study adds to this growing literature as follows. First, by studying diffusion of new drugs, we aim to add to the existing empirical findings in other product categories; collectively, these can help develop empirical generalizations. For instance, extant research reports that developed nations tend to have significantly higher maximum penetration levels than developing nations (e.g., see Talukdar, Sudhir, & Ainslie, 2002). Similarly, a consistent finding in the literature is that laggard countries (i.e., where the product is introduced later) tend to have faster diffusion patterns (Dekimpe et al., 2000a). We explore whether these findings hold in the context of our data. Our analysis focuses on developing and developed nations. Pharmaceutical markets in these countries exhibit important differences that can lead to differences in diffusion speed and penetration potentials. As noted earlier, developing countries tend to have much larger populations than developed ones and are thus likely to have higher penetration potentials. By definition, developing countries also tend to be less economically advanced. The level of economic development of a country, along with the resources devoted to healthcare, has a significant influence on its health system, particularly on the supply and quality of health resources. Lower economic development often implies a less educated and more rural

population that has a lower demand for scientific medicine. Furthermore, the level of health care provision among the population is also lower. For example, the more developed countries spend around 5% to 10% of their GDP on health care compared to 2% to 5% in most developing countries. We expect such factors to result in significantly lower diffusion speeds in developing countries. Next, prices of the drug can affect the demand and speed of diffusion. In the US, for instance, organizations such as HMOs in the market determine the approved list of drugs to be prescribed by affiliated doctors (bformulariesQ) based on drug prices. In Europe, governments maintain bpositiveQ and bnegativeQ lists to reflect drugs that will and will not be reimbursed. Some countries have a tiered system, in which some drugs will be reimbursed at higher rates than others. In addition, both developing and developed nations have large uninsured population segments that are fully liable for the cost of the drug. We thus expect higher drug prices to lower the speed of diffusion within a country, all other factors held equal. Furthermore, we expect developing countries, with their lower income populations, to have higher sensitivity to prices than developed countries. In our diffusion framework, we capture these differences by allowing aggregate per capita health care expenditures and drug prices to affect the diffusion speed differently in developing and developed countries. It is worth noting that most diffusion studies do not examine the impact of marketing mix elements, such as prices, on the diffusion process. Recent literature (c.f. Van den Bulte & Lilien, 1997) notes that not accounting for the effect of marketing mix elements may result in exaggerated estimates of the contagion parameter. For example, if there is a systematic decline in prices that leads to increased adoption and prices are not included in the model, the increased adoption is likely to be attributed to the diffusion parameter. We take a step towards bridging this gap in the literature and explicitly incorporate the impact of prices on the diffusion process. Finally, left censoring—that is, the problem of data not including observations from the inception of the category in each country—is often a concern in crossnational comparisons. In such instances, observations at a given point in time may be capturing a different

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stage in each country’s diffusion curve; therefore, cross-country comparisons could be biased if each country’s temporal stage in the diffusion curve is not controlled for (Dekimpe et al., 2000a). This issue is mitigated to a great extent in our analysis because we obtained data from the inception of the category in each country included in the study. The diffusion framework we employ is a discrete time version of the logistic model presented in Van den Bulte (2000). The logistic model is attractive for our purposes since it directly addresses the issue of measuring diffusion speed and allows for a straightforward comparison of markets in a cross-national setting. We adopt a hierarchical Bayes (HB) approach to estimate the parameters of the model. A significant advantage of the HB approach in the diffusion context is that it enables the pooling of information across countries to develop more precise estimates of model parameters. In contrast, standard estimators of the diffusion parameters would need far more data to obtain reliable estimates. In many real world settings where managers seek forecasts of sales when products have just been introduced, such data may not be available. HB estimators are very useful in such sparse data situations, and researchers have been calling for more work with these methods (e.g., see Lenk & Rao, 1990; Putsis & Srinivasan, 2000; Rossi & Allenby, 2003). In addition, the HB approach allows us to obtain posterior estimates of diffusion parameters specific to each country in a statistically consistent manner that takes into account the uncertainty associated with the model and the available data. In estimating the model, like many past diffusion studies, we find evidence for significant persistence (or serial correlation) in the unobserved shocks to diffusion. The persistence in the diffusion shocks introduces an errors in variables or endogeneity problem inasmuch as lagged cumulative sales included as a covariate in the estimation equation contains unobserved shocks from previous time periods that are correlated with current period shocks. If uncorrected, this could lead to inconsistent estimates. We implement an instrumental variable procedure to correct this endogeneity. The proposed instrumental variable procedure is embedded within the HB framework, and the model is estimated using the Gibbs sampler.

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Our main empirical findings include the following. (i) Compared to developed countries, developing nations tend to have lower diffusion speeds and maximum penetration levels. (ii) Laggard developed countries have higher speeds. However, laggard developing countries do not have higher diffusion speeds. (iii) Per capita expenditures on healthcare have a positive effect on diffusion speed (particularly for developed nations). Higher prices tend to decrease diffusion speed (i.e., estimates of the price coefficients are negative for all countries); however, except for Brazil, the coefficients are not statistically significant. These results add to our current understanding of the variation in diffusion speed across countries, especially in the context of comparing developed and developing nations. The rest of this paper is organized as follows. The next section provides a review of the relevant literature. The subsequent two sections discuss our model, the data, and estimation issues. Section 5 presents the results, and the penultimate section explores the underlying reasons for the differences between the two types of nations. The final section concludes the paper with suggestions for further research.

2. Relevant literature Here, we focus on two streams of literature, (1) the recent wave of research on the marketing and diffusion of pharmaceutical drugs and (2) the research that examines developing nations and compares them with developed nations. Each of these is discussed below. Recent years have seen dramatic increments in marketing spending by pharmaceutical companies; for instance, direct to consumer advertising (DTC) spending increased from less than a billion US dollars in 1996 to more than 2.5 billion in 2000 and is expected to grow even more in the coming years. The increased spending has drawn attention from practitioners and academics on analyzing the effects on demand and the return on investment (ROI) from such marketing activities. Research that has focused on studying aggregate pharmaceutical demand includes Berndt, Bui, Lucking-Reiley and Urban (1997) and Rizzo (1999) who estimate oligopolistic

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demand functions of individual categories of pharmaceuticals; Rosenthal, Berndt, Donohue, Epstein and Frank (2002) and Wosinska (2002) who study the role of DTC in enhancing category demand; and Chintagunta and Desiraju (in press) who examine demand and competition among multimarket pharmaceutical firms in several developed countries. A parallel set of studies that focused mainly on studying the ROI from pharmaceutical marketing activities include Association of Medical Publications (AMP) (2001), Wittink (2002) and Narayanan, Desiraju, and Chintagunta (in press). These studies, although related to our work, are different in that maximum penetration levels and diffusion speed are not central to their analysis. Other recent studies on pharmaceuticals use individual–physician level data to understand prescription behavior of physicians. For example, Kamakura and Kossar (1998) examine the adoption/timing of physician’s drug prescription decisions; Manchanda, Rossi, and Chintagunta (in press) model physician prescription behavior within a framework that allows response parameters to be affected by the process by which detailing is set across physicians. These studies, too, are not explicitly concerned with understanding the diffusion of the drug within and across countries. Past research that focused on the diffusion of pharmaceuticals includes Hahn, Park, Krishnamurthi, and Zoltners (HPKZ) (1994) and the papers cited therein. Since word of mouth has long been known to be an important influence on pharmaceutical sales (e.g., see Coleman, Katz, & Menzel, 1966), these researchers have argued that the diffusion framework is appropriate to study the sales growth of pharmaceutical drugs. HPKZ, for instance, expand the diffusion framework to account for repeat purchases and estimate a repeat rate parameter for 21 new pharmaceutical product categories. Interestingly, only about eight among the 21 categories studied had a repeat rate that was significantly different from zero at the 0.05 level; the maximum of these rates was 25%, while the lowest was 7.7% (see Table 2, the panel on HPKZ1, p. 233). Other researchers who examined the sales growth of pharmaceuticals, however, do not explicitly account for repeat rates. For example, Berndt, Pindyck, and Azoulay (1999), who study antiulcer drugs in the US, use the Bass (1969) model

to characterize network effects in drug diffusion. Analogously, although we employ the diffusion framework in our analysis, repeat purchases are not explicitly taken into account. In light of HPKZ’s findings, our analysis can be viewed as being applicable to categories with very low repeat rates; for other categories, the analysis may be seen as an upper bound benchmark.1 As noted in the introduction, most existing crossnational diffusion studies focus on developed nations. In contrast, we examine both developing and developed nations. In addition, our specification and analysis revolve around diffusion speed—because one of our goals is to compare these speeds across national markets. This focus distinguishes our study from both Talukdar et al. (2002) and Dekimpe, Parker, and Sarvary (2000b); while those studies explicitly account for nonindustrialized nations, neither is explicitly concerned with diffusion speed.

3. Model The new product growth model that we employ follows the logistic specification in Van den Bulte (2000). The model specifies the growth rate of sales for a new product in country i at time t, as a function of cumulative sales at the beginning of period t, X i (t), and the population M i (t): dXi ðt Þ hi ¼ Xi ðt Þðai Mi ðt Þ  Xi ðt ÞÞ dt ai M i ð t Þ

ð1:1Þ

where a i represents the maximum penetration level and indicates that the maximum possible sales in each period is linearly related to the population in the country. We consider the discrete time analog to the above equation.2 Denoting the realized sales in each 1

In the sense that any sales growth from repeat purchases may be interpreted as arising from new purchases and can inflate the latter’s effect. 2 Noting that X i (t)=[a i M i (t)]*F i (t), where F i (t) is the cumulative distribution function of sales, we see that the continuous differential in Eq. (1.1) is equivalent to dF i (t)/dt =h i F i (t) [1F i (t)], the solution to which is a logistic function, F i (t)=1/ (1+e hi (ttn )) (Fisher & Pry, 1971). Essentially, our model focuses on the imitation process; this is reasonable inasmuch as previous research (e.g., see Coleman et al., 1966) suggests that word of mouth is an important influence in pharmaceutical sales growth.

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period (X it X i,t1) as x it , we can write the following discrete time version of the model in Eq. (1.1): xit ¼


hi Xi;t1 ai Mit  Xi;t1 ai Mit

ð1:2Þ

The logistic formulation in Eq. (1.2) is useful for studying diffusion speed because of the following reason: begin with a simple definition of diffusion speed, stated as the amount of time required to move from one level of market penetration (say, p 1%) to another (say, p 2%). As noted in Van den Bulte (2000), in the continuous time analog of the logistic model, this time difference equals 1/h i ln[ p 2 (1p 1)/ p 1(1p 2)] and is inversely proportional to h i . Therefore, the parameter h i is a measure of the aggregate diffusion speed for the category in country i, and a comparison of diffusion speeds across countries can be made on the basis of their estimated h i –s. If we let y it denote the empirical instantaneous growth rate x it /X i,t1, and let c i denote h i /a i , then Eq. (1.2) can be rewritten to obtain the following estimation equation: 
ð2Þ yit ¼ hi þ ci Xi;t1 =Mit þ eit where e it represents deviations from the modelpredicted growth rate and is assumed to be a mean zero error term distributed standard normal with variance r 2. As seen from Eq. (2), one property of the logistic framework is that the diffusion speed h i is linearly related to the empirical instantaneous growth rate, y it . This makes the formulation appealing for studying diffusion speed. Given that cumulative variables are regressors in Eq. (2), a priori, we can expect some serial correlations in the residuals. We allow for first-order autocorrelation in e it and specify e it =qe i,t-1 +t it , where t it is a mean zero white noise term assumed to be orthogonal to all included variables.3 While accommodating for serial correlation in the residuals is straightforward, the presence of this correlation

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introduces a nontrivial econometric problem; with persistence in the residuals, e it will contain e i,t1 ; and inasmuch as the lagged variable, X i,t1/M it , in Eq. (2) contains e i,t1 , it will be correlated with e it . Hence, we have an errors-in-variables or endogeneity problem. To see this, note that Eq. (2) corresponding to month (t1) is y i,t1 =x i,t1/X i,t2 =(X i,t1X i,t2)/ (X i,t2)=h i +c 1 (X i,t2/M i,t1)+e i,t1, implying that X i,t1 is correlated with e i,t1. If the residuals are serially correlated, then e it is a function of e i,t1, implying that correlation (X i,t1, e it )p0, thus making X i ,t 1 endogenous in Eq. (2). In essence, the estimation in Eq. (2) becomes a canonical linear model with a lagged dependent variable and serially correlated errors, which gives inconsistent estimates unless the endogeneity is controlled for (e.g., see Johnston & Dinardo, 1997). Note that this problem is not specific to the framework that we use; the endogeneity issue is a problem for all diffusion studies that employ a linearized estimation equation similar to Eq. (2) when serial correlation is present in the residuals.4 The solution to the endogeneity problem is to find a set of exogenous instruments Z it that are correlated with the endogenous variable X i,t1 but are uncorrelated with the residuals e it . Intuitively, we should only use variation in X i,t1 that is bexplainedQ by the exogenous variables Z it for estimation. All other unexplained variation in X i,t1 is possibly correlated with e it and should be ignored. The use of instrumental variables enables us to do precisely this, and we discuss the details of the procedure later in the estimation section. Recall that the main goal of our analysis is to understand differences in the diffusion speed (and thus indirectly in the growth rate) across countries. Furthermore, we wish to study the effect of both time-invariant variables (e.g., country characteristics) and time-varying variables (e.g., prices) on the diffusion speed. We therefore allow h i in Eq. (2) to be influenced by both time-varying and timeinvariant control variables. By construction, c i =h i /a i ,

3

In our estimation section, we report evidence for such serial correlation in the residuals. A regression of the residuals from our bbase modelQ in Section 5 on lagged values, e it =qe i,t 1 +t it , gave an estimate of 0.2715 for q with a t-statistic of 12.3, indicating significant persistence in the residuals. Running the Durbin (1970) h-test, we rejected the null of no first order autocorrelations in the residuals.

4 For instance, using OLS for estimating the linearized version of the Bass diffusion model, x t =a+b X t +cX t2 + e t , would result in biased and inconsistent estimates for a, b and c, if there exists serial correlation in e t .

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and this implies that we need to also allow c i to be a function of the same variables5. Formally, we specify, hit ¼ hi0 þ

j X

hW ij Wij þ

J ¼1

cit ¼ ci0 þ

J X

K X

hD ik Dikt

ð3:1Þ

rfInverseGammaða; bÞ

ð8Þ

qfUniformð1; 1Þ

ð9Þ

k¼1

cW ij Wij

j¼1

þ

K X

cW ik Dikt

ð3:2Þ

k¼1

where the W-s are time-invariant covariates, the D-s are time varying covariates, and a t-subscript has been added to h and c to reflect the effect of the timevarying variables. Note that with these parameterizations, the estimation Eq. (2) still remains linear, with the h i terms entering Eq. (2) as main effects of the control variables, and the c it terms entering Eq. (2) as interactions of the control variables with X i,t1/M it . For expositional convenience, we denote all the model parameters that vary by country as b i : W D D W W bi ¼ ðhi0 ; hW i1 ; . . . ; hiJ ; hi1 ; . . . ; hiK ; ci0 ; ci1 ; . . . ; ciJ ; D cD i1 ; . . . ; ciK ; ÞV

ð4Þ

We allow all the parameters in Eq. (4) to vary across countries according to the following hierarchical set-up. In the first stage of the hierarchy, we specify 
bi fM V N lb ; X ð5Þ where l b is the mean of the b i -s, and X is the precision matrix for the distribution of the b i -s around this mean. The uncertainty about the parameters of the above distribution is specified in the second stage of the hierarchy as 
lb fNormal l¯ b ; r¯ 2 ð6Þ XfWishartð R; rÞ 5

Finally, the priors for the residual standard deviation and the autocorrelation parameter are specified as

ð7Þ

Alternatively, we could allow ai to be a function of the control variables and estimate the parameters describing the dependence of both h i and a i on these variables from the data. We do not pursue this approach because we are interested mainly in the effect of the control variables on the diffusion speed, h i , and in obtaining estimates of the aggregate potential for each country (a i ), for which the current approach is appropriate. Furthermore, the alternative model would be significantly more complicated to estimate inasmuch as a i enters Eq. (2) nonlinearly.

We adopt a Bayesian method to estimating the hierarchical model above for two reasons. (i) We seek direct inference about the country-specific parameters b i and potential functions of these parameters (for example, we are interested in estimating the size of the potential market for country i which is a function of its diffusion parameters b i and its population). This requires a method that enables pooling of information across countries to develop posterior estimates of b i specific to country i conditional on all the observed data. (ii) Since we are making inferences in many situations on the basis of few observations, the method should properly account for parameter uncertainty and be free from approximations that rely on large sample asymptotic theory.

4. Data and estimation 4.1. Overview of data Our data obtained from a proprietary source and IMS are comprised of quarterly observations on sales and average prices of a new category of antidepressant drugs in 15 countries (ordered first by entry date and then alphabetically): Belgium, South Africa, USA, Spain, Italy, Mexico, Canada, UK, France, Netherlands, Brazil, Colombia, Venezuela, Australia, and Portugal. The data are on selective serotonin re-uptake inhibitor (SSRI) antidepressant drugs and span from the first quarter of 1987 through the last quarter of 1993. Fig. 1 presents plots of the cumulative sales of the drug in these countries. Table 1 provides the introduction timing of the category in the different markets. The time period of the data includes the initial launch of the drugs in each country, and the observations begin with the introduction of the category. The availability of data from the inception of the category mitigates the left censoring problem common to many past diffusion studies. Even with this controlled for, there could still be a censoring

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347

Fig. 1. Cumulative sales in each country.

problem to the extent that we do not observe factors such as newspaper articles and trade-press reports about the drug that build demand prior to entry in countries where the drug is introduced later (we thank an anonymous reviewer for pointing this out). A variable representing the time since introduction in the lead country included to control for such effects turned out to be insignificant in all empirical specifications we considered. Hence, using these criteria, this issue does not seem to be very important for SSRI antidepressant drugs. Nevertheless, the availability of actual data on these factors could enable us to better calibrate and understand the influence of these effects on diffusion. Descriptive statistics of the data are provided in Table 2. In each country, the price variable captures the average selling price charged by the manufacturer (and is not the retail price) expressed in equivalent US dollars. The sales units are in terms of kilograms of the drug. In addition to prices, we also use per capita expenditures on health care to explain differences in

diffusion speed across countries. The per capita expenditures variable is expressed in constant 1989 dollars and is obtained from the Global Market Information Database provided by Euromonitor. To obtain a perspective on this category of drugs, note that the estimated shares of the SSRI-s among all antidepressants vary from country to country; for example, in the USA, the share has been around 33% (estimated by averaging quarterly shares over a 10year period starting 1988; see Chintagunta & Desiraju, in press), while in Italy, it is about 9%, and in France and the UK, it is around 20%. This limited penetration is primarily due to the availability of alternative nonSSRI drugs (such as tricyclics and monoamine oxidase inhibitors) for treating depression. While SSRI-s are as a class, often the first choice for treating depression, they do also have several side effects, such as symptoms of gastrointestinal upset, sleep impairment, impaired libido, and anorgamia (e.g., see Morrison, 1999) that sometimes prevent their use. Furthermore,

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Table 1 Introduction timing across countries Country

Quarter of introduction

Belgium South Africa USA Spain Italy Mexico Canada United Kingdom France Netherlands Brazil Colombia Venezuela Australia Portugal

First quarter 1987 First quarter 1987 First quarter 1988 Fourth quarter 1988 Fourth quarter 1988 First quarter 1989 First quarter 1989 First quarter 1989 Third quarter 1989 Third quarter 1989 Fourth quarter 1989 First quarter 1990 Second quarter 1990 Third quarter 1990 Second quarter 1991

To facilitate highlighting any impact of order of entry, in Tables 1, 2, and 6, the countries are ordered first by entry date and then alphabetically.

in several countries, there is a belief that nonallopathic medications are more effective in treating depression and related disorders. For these reasons, the SSRI-s did not have relatively high penetration rates for the duration of our data. With this brief background on the market for SSRI drugs, we now turn to the procedure for estimating the model.

set and gives us confidence in the robustness of our results. Further details of the instrumental variables procedure and the Gibbs sampler used for estimation are presented in the Appendix. As a significant byproduct of the Gibbs sampling procedure, we obtain the distribution of the posterior coefficients (b i ) for each country. With access to the full data on diffusion, we make inferences about the parameter specific to each country based on our knowledge of the marginal distribution of b i and the value of the country-specific variables. To update our inferences to this full data, we must simply compute the posterior distribution of b i given { y it , x it , X i,t1, J K T [Wij ]j=1 [D ikt ] k=1 }t=1 and the information in the entire set of countries. This is given automatically by the posterior distributions constructed from the Gibbs sampler run with all the countries in the data set. Once the country-specific parameter vector b i is obtained, it is straightforward to obtain estimates of other quantities of interest (e.g., mean diffusion speed and maximum penetration potential) for that country.

5. Results Three sets of results are presented here, each in a separate subsection. The first subsection focuses on

4.2. Estimation We conduct the estimation in two steps. We first use an instrumental variables procedure to obtain a predicted value for the endogenous variable x it /X i,t1 in Eq. (2) which uses only variation in x it /X i,t1 that is explained by a set of exogenous instruments. We then use the predicted values as data and estimate the entire hierarchical diffusion system [Eqs. (5)–(9)] using a Bayesian procedure.6 Furthermore, to assess the robustness of the analysis, we drop the last observation for each country from the data and reestimate the model parameters (the results of this analysis are available from the authors on request)—this generated little changes to the reported results for the full data 6 For other Bayesian applications in the cross-country context, e.g., see Neelamegham and Chintagunta (1999), Talukdar et al. (2002), and for an overview of hierarchical Bayesian methods in marketing, see Rossi and Allenby (2003).

Table 2 Cumulative sales average prices in each market Country

Cumulative sales

Average prices

Standard deviation (for prices)

Belgium South Africa USA Spain Italy Canada UK Mexico France Netherlands Brazil Colombia Venezuela Australia Portugal

137.58 157.78 19,792.88 540.66 509.80 1075.20 660.32 73.21 3171.92 156.33 191.42 18.44 6.49 121.49 56.57

15.35 31.40 135.61 19.04 12.71 126.55 36.92 17.14 12.41 53.59 20.35 19.52 16.23 31.39 19.83

2.09 8.98 17.56 4.65 1.48 6.35 9.17 3.70 1.77 3.34 3.87 2.40 0.69 4.79 4.58

Sales are in kilograms measured at the end of the observation period. Prices are in equivalent unadjusted US dollars.

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Table 3.1 Results from pooled regression—no instruments for (lagged cumulative sales)/population Constant Per capita health expenditure (Lagged cumulative sales)/population Prices Number of firms in market Number of firms in market*prices Prices*(lagged cumulative sales)/population (Per capita health expenditure)* (lagged cumulative sales)/population Observations R2

Parameter

t-Statistic

Parameter

t-Statistic

Parameter

t-Statistic

0.4368 0.1730 0.0009 0.000028

4.348 2.060 3.811 0.546

0.3543 0.1675 0.0011 0.000029 0.0722 0.0008

2.086 1.730 3.536 0.565 0.240 0.501

0.4582 0.1081 0.0054 0.000048 0.0858 0.0023 0.0022 1.25E–05

1.4203 1.6651 3.9918 0.9429 0.2897 0.5288 3.0885 1.6563

0.235

262 0.244

0.314

Data are pooled across all countries and time periods. Dependent variable is sales/(lagged cumulative sales) in all regressions.

exploratory regressions; the second on the mean parameters of the full model specified in Eqs. (2)– (9); and the third subsection presents the countryspecific parameter estimates which address the principal research questions of our paper. 5.1. Exploratory regressions The results from regressions of sales on lagged cumulative sales and other explanatory variables are presented in Table 3.1. The first regression—the bbase modelQ—has per capita health expenditures, lagged cumulative sales per population, and prices as variables. The second has two additional controls for competitive conditions in the market, viz., the number of firms in the market and interactions of the number of firms with prices. The third adds interactions of prices and per capita health expenditures with lagged cumulative sales per population. The data are pooled across all countries and time periods in all the regressions. Referring to Table 3.1, we see that all parameters have the expected sign. The effect of per capita expenditures is positive and significant; that of the past installed base (lagged cumulative sales/population) is negative and significant, and the effect of prices is negative but insignificant. Both the competitive variables are insignificant here and also in our subsequent analysis and hence were dropped from the final chosen specification. We tested for the presence of serial correlation in the residuals using the Breusch–Godfrey Lagrange

multiplier (LM) test (Breusch, 1978; Godfrey, 1978).7 The LM approach facilitates a test of autocorrelation in the presence of a lagged dependent variable. Running the test for the bbase modelQ in Table 3.1 gave a value of 187.72 for the LM test statistic. The critical value v 2 is 3.84, indicating that we reject the null of no first-order autocorrelation. Furthermore, the coefficient on lagged residuals in the auxiliary regression was significant (t=16.57). The results for the other specifications in Table 3.1 were similar. Thus, to summarize, we find significant evidence for persistence in the residuals for these data. As noted earlier, this implies that the resulting endogeneity problem cannot be ignored. Finally, White tests rejected heteroscedasticity in the residuals for all specifications. We now discuss the results after using instruments to control for the endogeneity. Table 3.2 presents the results from the corresponding regressions to Table 3.1 when we instrument for the lagged cumulative

7 The LM test involves first obtaining the residuals from a regression of the dependent variable on all exogenous variables and the lagged dependent variable, and second, running an auxiliary regression of these residuals on lagged residuals, all exogenous variables and the lagged dependent variable. The corresponding test statistic for the null hypothesis of no firstorder autocorrelation is nR 2 (where n is the number of observations) and is distributed v 2(1) under the null. Furthermore, a statistically significant coefficient on lagged residuals in the auxiliary regression provides additional evidence of first-order autocorrelation (this is sometimes referred to as Durbin’s bsecond methodQ).

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Table 3.2 Results from pooled regression—no instruments for (lagged cumulative sales)/population Constant Per capita health expenditure Instrumented [(lagged cumulative sales)/population] Prices Number of firms in market Number of firms in market*Prices Prices*instrumented [(lagged cumulative sales)/population] (Per capita health expenditure)*Instrumented [(lagged cumulative sales)/population] Observations R2

Parameter

t-Statistic

Parameter

t-Statistic

Parameter

t-Statistic

0.3114 0.4852 0.0024

3.1017 4.6005 6.0318

0.2745 0.5709 0.0019

2.6246 4.6213 3.4948

0.0745 0.6607 0.0019

0.2182 4.7104 3.1784

0.0000074

0.1498

0.0000038 0.0005 3.81E07

0.0768 1.0638 0.0776

0.0000045 0.2287 0.0026 0.0004

0.1508 0.6804 0.7552 0.9413

1.42E05

1.1279

0.354

262 0.363

0.381

Data are pooled across all countries and time periods. Dependent variable is sales/(lagged cumulative sales) in all regressions. The variables bnumber of firms in marketQ and bnumber of firms in market*pricesQ were dropped from the subsequent analysis inasmuch as they are statistically insignificant.

sales per population variable. As discussed in the Appendix, the instrument is constructed as the predicted value from a regression of the endogenous variable X i,t1/M it on the entire set of exogenous variables Z it . The regression of X i,t1/M it on Z it had an R 2=0.727, indicating a good fit. Furthermore, the regression as a whole was significant ( F=96.68, k=4, N=262). A regression of X i,t1/M it on the instrument z¯ i,t alone had an R 2=0.406, with F=51.25 (k=4, N=262). We conclude that our exogenous instruments do a reasonable job of predicting the endogenous variable X i,t1/M i . Table 3.2 reveals that after using instruments, the coefficient on the endogenous variable becomes more negative. This is consistent with what we expect a priori. Recall that a higher value of e i,t1 would increase X i,t1; and inasmuch as e it is autocorrelated and contains e i,t1, X i,t1, e it , and e i,t1 are positively correlated. Therefore, inasmuch as the coefficient on X i,t1/M it is negative, if the endogeneity problem is uncorrected, we would expect it to be biased towards zero. This is consistent with the observed direction of change in the coefficient with instruments and suggests that the instruments are working properly. Finally, a Hausman test of 2SLS versus OLS for the bbase modelQ specification gave a test statistic of 13.44. The corresponding critical value v 2 (1) is 3.84, which rejects OLS over 2SLS, indicating that ignoring the endogeneity of X i,t1/M it can significantly bias the parameters.

5.2. Posteriors for the mean parameters We now discuss the estimated posterior coefficients for the full model specified in Eqs. (2)–(9). Note that these results correspond to a hierarchical linear model with autocorrelated errors, in which predicted values from the instrumental variables regression, X i,t1/M it , are used as bdataQ.8 The full model specification uses two country-specific control variables, viz., prices (which are time varying and correspond to the D ikt variable in Eqs. (3.1) and (3.2)) and per capita health expenditures (which are time-invariant and correspond to the Wij variable in Eqs. (3.1) and (3.2)). Recall that these enter the estimation Eq. (2) both as main effects and as interactions with the instrumented lagged cumulative sales per population variable. Thus, in the final specification, the mean parameter vector Ab corresponds to a constant, prices, per capita health expenditure, instrumented lagged cumulative sales per population and interactions of prices and per

8 An alternative approach to account for the endogeneity would be to specify X i ,t1/M it ~N(Z i k,R) and model the correlation between e it and the elements of R (e.g., see Geweke, Gowrisankaran, & Town, 2003). This approach would have the advantage that the uncertainty associated with using the predicted value of X i ,t 1/M it is also accounted for in the estimation. Exploring this approach would be an interesting avenue for future research.

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capita health expenditure with the instrumented lagged cumulative sales per population variable. Here, we present the results for the posterior mean parameters (l b in Eq. (5)); the next subsection presents the results at the individual country level. Table 4 reports the posterior mean and standard deviation for the mean parameters.9 Tables 5 and 6 present the results at the individual country level. From Table 4, we note that the posterior mean for the parameter on lagged cumulative sales per population is 0.0015 and is statistically significant. Thus, the diffusion process is affected by past cumulative sales and suggests that the installed base of past adopters (as measured by cumulative sales) impact the sales growth of antidepressant drugs. The posterior mean for the parameter measuring the impact of per capita healthcare expenditures on diffusion speed is 1.6320 and is significant. The implication is that the rate of diffusion of drugs within countries is affected by a country’s healthcare expenditures. This is consistent with the extant findings in the literature that macrolevel country covariates affect new product growth. The posterior mean for the parameter measuring the impact of price on diffusion speed is 0.000147, suggesting that higher prices reduce the diffusion speed, all else held equal. However, the effect is not statistically significant. The estimated posterior mean for r (the standard deviation of the estimation error in Eq. (2)) is 0.34. This indicates some unexplained variation in the dependent variable, c it , across countries and time periods after controlling for the health expenditures, prices, and the diffusion effect (lagged cumulative sales per population). Furthermore, the estimated posterior mean for q of 0.85 indicates a significant first-order serial correlation in the residuals. Although not reported, the distribution of the posterior means when the last observation is dropped from the data (estimated as a robustness check) is similar.

9 Recall that all parameters are treated as having a distribution in Bayesian estimation. The means and standard deviations reported in Tables 4, 5, and 6 represent the mean and standard deviation of the marginal posterior distributions of the parameters, given the priors and the observed data. These are obtained in a straightforward fashion from the Gibbs sampler. Trace plots, marginal distributions, and autocorrelations plots for the posteriors are available from the authors on request.

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Table 4 Posteriors for the mean parameters (l b ), q, and r

Constant Per capita health expenditure Instrumented (lagged cumulative sales)/population Prices (Per capita health expenditure)* instrumented (lagged cumulative sales)/population Prices*instrumented (lagged cumulative sales)/population q r

Parameter

Standard deviation

1.8590 1.6320 0.00150

0.3779 0.7088 0.000582

0.00015 0.00192

0.000095 0.001140

0.00002

0.000037

0.8539 0.3369

0.0106 0.0158

5.3. Posterior parameters at the country level Our main focus is on the country-specific parameters, and we summarize our findings in this subsection. We first discuss the country-specific counterparts of the mean parameters discussed in the previous subsection and then compare the implied diffusion speeds and maximum penetration levels among the countries in our sample, focusing mainly on the differences between the markets in developing and developed countries. Section 6 presents anecdotal evidence to explain some underlying reasons for our results. 5.3.1. Country-specific parameter estimates Country-specific effects of heath expenditures on diffusion speed are presented in the first two columns of Table 5. Among the developed nations with statistically significant coefficients, we find that The Netherlands has the largest impact from health expenditures, while USA and Belgium have the lowest impact; of course, Australia, Canada, and Italy have nonsignificant coefficients and therefore experience limited impact from these expenditures. Among the developing countries, these expenditures all have the correct sign but are not significant statistically. From Table 5, we note that the posterior means for prices all have the correct signs for each of the countries in the sample; the size of the effect, however, varies across countries. From Table 5, we note that while its coefficient is negative in all the countries, price has a statistically significant impact only in one country (Brazil). This was expected because the mean

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Table 5 Posterior estimates for each country Country

Per capita health expenditure

Instrumented (lagged Prices cumulative sales)/ population

(Per capita health expenditure)* Prices*instrumented instrumented (lagged cumulative (lagged cumulative sales)/population sales)/population

Parameter Standard Parameter Standard Parameter Standard Parameter deviation deviation deviation Australia Belgium Brazil Canada Colombia France Italy Mexico Netherlands Portugal South Africa Spain UK USA Venezuela Average

0.3947 0.7474 1.6490 0.3558 2.7360 2.0810 0.5137 1.6310 5.8240 3.5520 0.6901 1.2860 2.3300 0.5305 0.1816 1.6335

0.5508 0.3186 1.4090 0.3152 1.8810 0.3182 0.3322 1.2970 0.7375 1.0730 1.2950 0.4584 0.4369 0.3030 1.8540

0.0005 0.0010 0.0016 0.0010 0.0026 0.0017 0.0011 0.0019 0.0030 0.0019 0.0015 0.0016 0.0019 0.0010 0.0003 0.0015

0.0002 0.0015 0.0012 0.0003 0.0010 0.0011 0.0002 0.0011 0.0015 0.0015 0.0010 0.0009 0.0014 0.0007 0.0019

0.00015 0.00015 0.00014 0.00015 0.00015 0.00014 0.00015 0.00015 0.00013 0.00014 0.00015 0.00015 0.00014 0.00015 0.00015 0.00015

0.00012 0.00011 0.00007 0.00012 0.00013 0.00011 0.00012 0.00011 0.00022 0.00014 0.00012 0.00010 0.00011 0.00012 0.00013

0.00015 0.00104 0.00190 0.00099 0.00257 0.00247 0.00111 0.00183 0.00534 0.00345 0.00116 0.00200 0.00289 0.00098 0.00082 0.00191

Standard deviation

Parameter Standard deviation

0.00215 0.00146 0.00245 0.00194 0.00320 0.00119 0.00151 0.00246 0.00377 0.00283 0.00257 0.00176 0.00172 0.00146 0.00316

0.00005 0.00000 0.00002 0.00001 0.00007 0.00003 0.00001 0.00002 0.00014 0.00007 0.00000 0.00002 0.00005 0.00001 0.00004 0.00002

0.00006 0.00005 0.00007 0.00002 0.00008 0.00006 0.00006 0.00006 0.00009 0.00007 0.00005 0.00005 0.00005 0.00002 0.00008

The means and standard deviations of the posterior distribution of the parameters (for the last 10,000 draws of the chain) for each country are reported.

Table 6 Posterior mean diffusion speed Country

Mean diffusion speed (hˆi )a

Maximum penetration level (aˆ i )b

Belgium South Africa USA Spain Italy Canada UK Mexico France Netherlands Brazil Colombia Venezuela Australia Portugal Average

0.4259 0.4424 0.2133 0.6823 0.3635 0.3361 0.4415 1.5580 0.8946 0.6194 0.2464 0.3564 0.3246 0.2889 0.2608 0.4971

1615.7 1112.7 34340.8 1028.4 1326.6 19320.1 1608.4 792.9 1280.0 1108.2 271.2 1277.0 1361.0 2100.9 1489.4 4668.9

a

Computed as the mean of the posterior distribution of the average of h it across all observations for each country for the last 10,000 draws of the chain. b In Kg-s/million people.

price effect across all countries was not significant and suggests that, while higher prices tend to reduce diffusion speed, they do not play a significant role for antidepressant medications. The possible substantive reasons underlying this result are discussed in Section 6. Among the developed countries, the main effect of lagged cumulative sales is highest for The Netherlands and lowest for Australia, with USA, Italy, Canada, and UK having values in between. Among the developing countries, the effect is significant only for Colombia. The lagged cumulative sales significantly affect sales growth via an interaction with per capita health expenditures in Spain, France, and Portugal. Overall, while all the developed countries experience the diffusion effect from an installed patient base (as captured via lagged cumulative sales), only one developing country experiences this effect. 5.3.2. Country-specific diffusion speeds and penetration levels We now turn to Table 6 to highlight the mean diffusion speeds and maximum penetration levels at

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the individual country level. The mean diffusion speed for each country in Table 6, hˆi , represents the mean of the posterior distribution of the average value of h it (that is the mean of the left-hand side of Eq. (3.1)) computed across all the observations for that country. The maximum penetration potential in Table 6, a i , is computed as hˆi /cˆ i , where cˆi is the mean of the posterior distribution of the average value of c it (that is the mean of the left-hand side of Eq. (3.2)) computed across all the observations for that country. A significant advantage of the Gibbs sampler is that these can be computed directly by making draws from the stationary distribution of the parameters for each country. Note that the mean diffusion speed and penetration potentials computed as above also reflect the effects of time-varying variables, viz., prices in each country. One could instead report the diffusion speed (and analogously, the maximum penetration potential) without including the effects of time-varying variables. We adopt the former approach as it allows the diffusion speed to also reflect the variation in sensitivities to prices across countries. One striking feature of Table 6 is that all the developing countries (except Mexico) have belowaverage diffusion speeds; furthermore, among these countries, diffusion speed does not increase for laggard countries (i.e., where the drugs are introduced later). In contrast, except for Portugal, laggard European countries have higher diffusion speeds than other European countries; a similar pattern holds between Canada and USA—Canada, the later entrant has a higher speed. It is worth noting that the above results for laggard developed countries are consistent with those found in earlier research. However, the pattern for the developing countries is the first we have seen in the literature and suggests that future research should understand this in more detail. Turning to the maximum penetration potential, a i , measured in terms of sales per million of the population, we note that Brazil and Mexico have the lowest values, while USA and Canada have the largest values. Venezuela, Colombia, and South Africa have penetration potentials that are roughly on par with those of Spain, Italy, France, and The Netherlands. The remaining developed nations have higher potentials. This difference between developing and developed countries adds to the existing finding in Talukdar

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et al. (2002) that for durable goods, developing countries have lower penetration levels than developed countries.

6. Discussion As noted in the introduction, developing counties are, by definition, economically less advanced than developed nations. Lower economic development in turn translates to inadequate infrastructure for delivering health care to the population. Table 7 indicates that developing nations have a relatively smaller number of doctors or hospital beds per capita. With limited health care delivery systems in place through which new drugs can diffuse into the population, penetration potentials and diffusion speeds for these countries are naturally lower. The lack of comprehensive health care delivery infrastructure in developing countries also implies that only urban populations are likely to contribute to new pharmaceutical product growth. Since urban areas constitute only a fraction of the total national population, diffusion speed and penetration rate tend to be low. Furthermore, restricted communication between urban and rural areas limits the role of the installed base of users in the diffusion process. The predominance of a rural population also implies that laggard developing countries may not experience faster speeds due to a ceiling effect— given that new products are not likely to diffuse through nonurban areas, there is a cap on the incremental (rate of) growth that the laggard countries can achieve. Table 7 also indicates significant variation in the number of women aged between 15 and 49 across countries. Ingram and Scher (1998) observe in their review of epidemiological studies that gender is significantly correlated with depression. More specifically, the lifetime prevalence rates for depression is higher in women (7.0%) than in men (2.2%); these differences occur across a variety of ethnic groups (e.g., African Americans, Hispanic, Caucasian) even when differences in education, income, and occupations are controlled. Other factors such as socioeconomic status are not particularly correlated with these mental disorders. With access to more crosscountry data, it is possible that researchers can

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Table 7 Some relevant economic and demographic characteristics of the various countries (circa 1990, based on data availability) Country

GDP (per capita in US dollars)

Healthcare expenditures as percent of GDP

Population per physician

Population per hospital bed

Women aged between 15 and 49 (in thousands)

Brazil Colombia Mexico South Africa Venezuela Australia Belgium France Italy Netherlands Portugal Spain UK Canada USA

6100 5300 7700 4800 9300 22,100 14,573 20,200 18,700 19,500 11,000 14,300 19,500 24,400 27,500

4.2 4.0 3.2 5.6 3.6 7.7 7.5 8.9 7.5 7.9 7.0 6.6 6.1 9.1 12.7

680.90 1198.58 1770.63 1716.67 633.44 437.53 311.18 346.44 210.02 412.00 480.46 277.13 NA 469.30 420.61

299.88 733.43 801.37 NA 385.00 183.28 120.83 109.05 131.28 169.80 226.67 208.74 160.91 67.30 194.39

39,466 9022 21,559 9379 4935 4474 2438 14,116 14,420 3967 2544 10,114 14,160 7154 65,806

measure the extent to which these gender ratio differences further explains differences in penetration potentials across countries after controlling for population size. Finally, we speculate that low price sensitivity of patients in this category of pharmaceuticals drives our empirical finding that prices do not significantly decrease diffusion speed. However, as we do not have patient-level data, we are unable to explore this issue further. Here, it is also worth noting that our results were obtained with aggregate country-level data, which does not have information on region-to-region variation in sales and prices within each country. With access to data on sales and prices at a finer level of aggregation, e.g., at the city or regional level, we might be able to measure the various effects with greater precision. The availability of such data would be an important advance in further understanding the diffusion process within and across countries. Overall, developing countries, with a welfareoriented ideology, have been undertaking major efforts to bring health services to rural people through networks of health centers and extensive training and use of auxiliary personnel. There are currently numerous initiatives to allocate health manpower to rural areas and generally to extend health service coverage. This may be seen as an opportunity for drug companies to invest in these countries to develop the appropriate infrastructure, which will in turn help grow pharmaceutical sales.

7. Conclusions For a variety of reasons, developing countries are increasingly becoming economically important. Both practitioners and academics have an interest in understanding the markets in these countries, and in this paper, we take a step in that direction. Our empirical analysis reveals some important differences in the diffusion process between developing and developed countries. In line with previous research, we find that maximum penetration levels tend to be lower in developing countries; furthermore, we find that among developed countries, laggard markets—where the product is introduced later—have faster growth rates. We also find that this result does not generalize to the developing countries; there, diffusion speeds tend to be smaller (compared to developed countries), and laggard countries do not have higher growth rates. We find that cumulative past sales are significant in explaining diffusion speed, particularly in developed nations, implying that the size of the installed base of past adopters is an important factor for drug diffusion. Moreover, in this product category, we find that although its impact is relatively small, higher prices tend to reduce diffusion speed. We also find that a macrolevel covariate, per capita healthcare expenditures, has a significant positive effect on diffusion speed, particularly in developed nations. An area that is worthy of research attention is the impact of other elements of the marketing mix (e.g.,

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detailing in the context of prescription drugs) on new drug diffusion. Inclusion of these marketing mix elements in the analysis may further help explain some of the differences across various national markets. Future research should also explore the role of repeat purchases in pharmaceutical diffusion. We believe our analysis serves as a useful starting point for future researchers and hope that our effort here will help spark further research in this area.

Acknowledgements The authors are grateful to Dipak Jain and IMS for help in obtaining the data used in this study, to Sridhar Narayanan for help with WinBUGS, and to Puneet Manchanda for useful comments. Thanks are also due to Donald Lehmann and Marnik Dekimpe, the reviewers of the original proposal submitted to MSI, seminar participants at the MSI conference on Global Marketing 2003, and three anonymous referees for helpful comments and suggestions. All errors are the authors’ responsibility.

Appendix A. Estimation details We conduct the estimation in two steps. We first use an instrumental variables procedure to obtain a predicted value for the endogenous variable x it /X i,t1 in (2) which uses only the variation in x it /X i,t1 that is explained by a set of exogenous instruments. We then use the predicted values as data, and estimate the entire hierarchical diffusion system Eqs. (5)–(9) using a Bayesian procedure. We discuss the procedure in the two subsections below. A.1. Instrumental variables procedure Our proposed instrument for X i,t1/M it is motivated by the idea that the cumulative sales of the drug in all other countries in a period is a reasonable predictor of the cumulative sales of the drug in country i in that period. It is also reasonable to believe that unobserved determinants of diffusion and/or measurement error in country i in period t, i.e., the residuals e it , are uncorrelated with cumulative sales of the drug in other countries in that period.

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Denote by z¯ i ,t , the mean value of X c,t 1/M ct averaged over all countries c p 1. Then by the argument presented above, z¯ i,t is correlated with X i,t1/M it but is uncorrelated with e it . Therefore, z¯ t is a reasonable instrument for x it /X i,t1. Note that as the product is initially launched in multiple countries, there are no time periods in which we do not have instruments for a particular country. This formulation of using the mean value of the endogenous variable across other independent units as an instrument is similar in spirit to the methods suggested by Hausman and Taylor (1981) for individual panel data across households and to Hausman, Leonard, and Zona (1994), and Nevo (2001) for aggregate sales data across regions. Denote the first stage instrument matrix composed of a constant, the exogenous variables (viz. per capita health expenditure and prices), and the instrument, z¯ i ,t , as Z it . We first run a regression of the endogenous variable, X i,t1/M it , on the entire set of exogenous variables Z it : Xi;t1 =Mit ¼ Zit k þ xit Let the predicted value of X i,t1/M it from the regression, Z it k, be denoted asˆ Xi;t1 =Mit . Recall that the endogeneity problem occurs when X i,t1/M it is correlated with e it in Eq. (2). It is easy to see from above that while correlations (x it , e it ) need not be zero, we ensure by construction that Z it 8e it . Therefore, the variation in the predicted value, ˆ Xi;t1 =Mit represents only the variation in X i,t1/M it that is bexplainedQ by the exogenous variables Z it . We can now proceed by simply using the predicted value, ˆ Xi;t1 =Mit , in place of the endogenous variable, X i,t1/ M it , wherever it appears in the estimation Eq. (2). Inasmuch as X i,t1/M it is not correlated with e it in Eq. (2), there is no longer an endogeneity problem. The approach is similar in spirit to a two-step implementation of two-stage least squares. We now describe the hierarchical Bayesian method that is used to estimate all the model parameters. Note that by using ˆ Xi;t1 =Mit instead of X i,t1/M it at this stage, the endogeneity of the lagged per capita cumulative sales variable is already controlled for. The model that needs to be estimated is a standard hierarchical linear model with autocorrelated errors.

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A.2. Bayesian estimation The Bayesian inference problem here is to obtain the posterior distribution of the entire set of parameters, H=(b i , r 2, q) given the priors and the data. Following Chib (1993), we factor the joint prior for H as p(b i , r 2, q)=p(b i |r)p(r)p(q). Thus, (b i , r 2) are a priori assumed independent of q. The chosen priors for these parameters form natural conjugates for the country-level parameters in the hierarchical set-up and result in proper standard full conditional distributions that are easily sampled. Both the setting of prior hyperparameters and the nature of the prior distribution have the potential to influence the posterior distribution of b i ; in practice, we take diffuse priors over l b, r, and q and induce a small amount of shrinkage with our X prior. The exact prior settings are as follows. ¯ The priors for l b ¯are independent normal with l b set to be zero, and r 2 set to 1e–6 for all six elements of l b . We introduce a mild amount of shrinkage with our X prior and set the scale matrix of the Wishart, R=diag(1.0, 1.0, 0.01, 0.01, 0.01, 0.01) and the degrees of freedom r to be the lowest possible value equals 6 (i.e., the rank of X). The priors for r are a=0.001, b=0.001, and are chosen to be noninformative. A diffuse uniform prior is set on q over the stationary interval (1, 1). Draws from the posterior distribution of the parameters are obtained using the Gibbs sampler implemented within the WinBUGS Bayesian analysis software (Spiegelhalter, Thomas, Best, & Gilks, 1994). The first 20,000 draws are used as burn-in, and the last 10,000 draws are used to generate all posterior parameter estimates and standard deviations. Convergence was assessed using visual inspection of the chains and using the Gelman–Rubin statistic from running parallel chains.

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