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Diffusion of New Pharmaceutical Drugs in Developing and
Developed Nations1
Ramarao Desiraju
Associate Professor of Marketing
College of Business Administration, University of Central Florida
Orlando, FL 32816
Email: [email protected]
Phone: 407-823-6521
Harikesh Nair
Assistant Professor of Marketing,
Graduate School of Business, Stanford University,
518 Memorial Way, Stanford, CA - 94305.
Email: [email protected]
Phone: 650-736-4256
Fax: 650-725-9932
Pradeep Chintagunta
Robert Law Professor of Marketing
Graduate School of Business, University of Chicago
1101 East 58th Street, Chicago, IL 60637
E-Mail: [email protected]
Phone: 773-702-8015
First version: June 30, 2003
This version: May 24, 2004
1 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.
Diffusion of new pharmaceutical drugs in developing and
developed nations
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
fifteen 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 include: (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.
Keywords: Diffusion, cross-country analysis, pharmaceuticals, Hierarchical Bayes.
1
1. Introduction
Many developing nations, with their relatively large populations, have attractive potential buyer
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 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 sub-
category of pharmaceutical drugs, we examine the diffusion speed, maximum penetration potential,
and the effects of prices and per capita health care expenditures in fifteen 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. Mahajan, Muller and
Bass 1990; Dekimpe, Parker and Sarvary 2000a). 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 (see e.g., Talukdar, Sudhir and 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, Parker and Sarvary 2000a). We explore
whether these findings hold in the context of our data.
2
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. Further, the level of heath care provision among the population is also lower. For example,
the more developed countries spend around 5 to 10 percent of their GDP on health care, compared to
2 to 5 percent 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 (“formularies”) based on drug prices. In Europe, governments maintain “positive”
and “negative” 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 and Lilien
1997) notes that not accounting for the effect of marketing mix elements may result in exaggerated
3
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 cross-national comparisons. In such
instances, observations at a given point in time may be capturing a different stage in each country's
diffusion curve; therefore across-country comparisons could be biased if each country's temporal
stage in the diffusion curve is not controlled for (Dekimpe, Parker and Sarvary 2000a). This issue is
mitigated to a great extent in our analysis since 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., Lenk and
Rao 1990, Putsis and Srinivasan 2000, Rossi and 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.
4
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 since 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 variables procedure to correct for this
endogeneity. The proposed instrumental variables procedure is embedded within the HB framework
and the model is estimated using the Gibbs sampler.
Our main empirical findings include: (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 significant statistically. 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 five 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.
5
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 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 et al. (1997) and
Rizzo (1999) who estimate oligopolistic demand functions of individual categories of pharmaceuticals;
Rosenthal et al. (2002) and Wosinska (2002) who study the role of DTC in enhancing category
demand; and Chintagunta and Desiraju (2002) who examine demand and competition among multi-
market 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 (2002). These
studies, though 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
(2003) 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 (see e.g., Coleman, Katz and
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
6
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 anti-ulcer drugs in the US, use the
Bass (1969) model to characterize network effects in drug diffusion. Analogously, though 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.2
As noted in the introduction, most existing cross-national 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 - since 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 et al. (2000b); while those studies explicitly account for non-industrialized 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, ( )itX , and the population ( )iM t :
( )( )
( ) ( ) ( )( )
i i
i i i i
i i
dX tX t M t X t
dt M t
θα
α= − (1.1)
where, i
α 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
2 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.
7
analog to the above equation.3 Denoting the realized sales in each period (, 1it i t
X X −= − ) as itx , we can
write the following discrete-time version of the model in (1.1):
( ), 1 , 1
i
it i t i it i t
i it
x X M XM
θα
α− −= − (1.2)
The logistic formulation in (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, p1%) to another (say, p2%). As noted in Van den Bulte (2000), in
the continuous time analog of the logistic model, this time difference equals
( ) ( )2 1 1 2
1ln 1 1
i
p p p pθ
− − , and is inversely proportional to iθ . Therefore, the parameter
iθ 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 i
θ -s.
If we let ity denote the empirical instantaneous growth rate
, 1it i tx X − , and let
iγ denote
i iθ α− , then (1.2) can be rewritten to obtain the following estimation equation:
( ), 1it i i i t it ity X Mθ γ ε−= + + (2)
where, it
ε represents deviations from the model-predicted growth rate, and is assumed to be a mean
zero error term, distributed standard normal with variance 2σ . As seen from (2), the appealing
property of the logistic framework is that the diffusion speed i
θ is linearly related to the empirical
instantaneous growth rate, ity . This makes the formulation appealing for studying diffusion speed.
Given that cumulative variables are regressors in (2), a priori, we can expect some serial
correlations in the residuals. We allow for first order auto-correlation in it
ε and
specify, 1it i t it
ε ρε υ−= + , where it
υ is a mean-zero white noise term assumed to be orthogonal to all
3 Noting that ( ) [ ] ( )( ) *
i i i iX t M t F tα= , where ( )
iF t is the cumulative distribution function of sales, we see that the
continuous differential equation in (1.1), is equivalently ( ) ( ) ( )[ ]1= −i i ii
F t F tdF t dt θ , the solution to which is a
logistic function, ( ) ( )( )01 1 it t
iF t e
θ− −
= + (Fisher and Pry, 1971). Essentially, our model focuses on the imitation
process; this is reasonable since previous research (e.g., Coleman et al 1966) suggests that word-of-mouth is an
important influence in pharmaceutical sales growth.
8
included variables.4 While accommodating for serial correlation in the residuals is straightforward,
the presence of this correlation introduces a non-trivial econometric problem: with persistence in the
residuals, it
ε will contain , 1i t
ε − ; and since the lagged variable,, 1i t it
X M− , in (2) contains , 1i t
ε − , it will be
correlated with it
ε . Hence, we have an errors-in-variables or endogeneity problem. To see this, note
that equation (2) corresponding to month (t - 1) is:
, 1−i ty ( ) ( ) ( ), 1 , 2 , 1 , 2 , 2 , 2 , 1 , 1θ γ ε− − − − − − − −= = − = + +i t i t i t i t i t i i i t i t i tx X X X X X M , implying that
, 1i tX − is correlated
with , 1i t
ε − . If the residuals are serially correlated, then it
ε is a function of , 1i t
ε − , implying that
( ), 1, 0corr i t itX ε− ≠ , thus making , 1i t
X − endogenous in (2). In essence, the estimation equation (2)
becomes a canonical linear model with a lagged dependant variable and serially correlated errors,
which gives inconsistent estimates unless the endogeneity is controlled for (e.g., see Johnston and
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
(2), when serial correlation is present in the residuals.5
The solution to the endogeneity problem is to find a set of exogenous instruments itZ
that are
correlated with the endogenous variable, 1i t
X − , but are uncorrelated with the residuals itε .
Intuitively, we should only use variation in , 1i t
X − that is “explained” by the exogenous variables itZ
for estimation. All other unexplained variation in , 1i t
X − is possibly correlated with itε 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
4 In our estimation section, we report evidence for such serial correlation in the residuals. A regression of the
residuals from our “base model” in section 5 on lagged values, εit = ρεi,t-1 + υit, gave an estimate of 0.2715 for ρ
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. 5 For instance, using OLS for estimating the linearized version of the Bass diffusion model, xt = a + b Xt + cXt2 +
εt, would result in biased and inconsistent estimates for a, b and c, if there exists serial correlation in εt.
9
both time-invariant variables (e.g. country characteristics) and time-varying variables (e.g. prices) on
the diffusion speed. We therefore allow i
θ in (2) to be influenced by both time-varying and time-
invariant control variables. Since by construction, i i i
γ θ α= − , this implies that we need to also allow
iγ to be a function of the same variables.6 Formally, we specify:
0
1 1
J KW D
it i ij ij ik ikt
j k
W Dθ θ θ θ= =
= + +∑ ∑ (3.1)
0
1 1
J KW W
it i ij ij ik ikt
j k
W Dγ γ γ γ= =
= + +∑ ∑ (3.2)
where the W-s are time-invariant covariates, the D-s are time varying covariates, and a t-subscript
has been added to θ and γ to reflect the effect of the time-varying variables. Note that with these
parameterizations, the estimation equation (2) still remains linear, with the .iθ terms entering (2) as
main effects of the control variables, and the .iγ terms entering (2) as interactions of the control
variables with , 1i t it
X M− . For expositional convenience, we denote all the model parameters that
vary by country as i
β :
( )0 1 1 0 1 1, ,.., , ,.., , , ,.., , ,.., , '= W W D D W W D D
i i i iJ i iK i i iJ i iKβ θ θ θ θ θ γ γ γ γ γ (4)
We allow all the parameters in (4) to vary across countries according to the following hierarchical
set-up. In the first stage of the hierarchy, we specify:
( )~ ,i MVN ββ µ Ω (5)
where, βµ is the mean of the i
β -s, and Ω is the precision matrix for the distribution of the i
β -s
around this mean. The uncertainty about the parameters of the above distribution is specified in the
second stage of the hierarchy as:
( )2~ Normal ,β βµ µ σ (6)
6 Alternatively, we could allow αi to be a function of the control variables, and estimate the parameters
describing the dependence of both θi and αi on these variables from the data. We do not pursue this approach
since we are interested mainly in the effect of the control variables on the diffusion speed, θi, and in obtaining
estimates of the aggregate potential for each country (αi), for which the current approach is appropriate.
Furthermore, the alternative model would be significantly more complicated to estimate since αi enters (2) non-
linearly.
10
( )~ Wishart ,R rΩ (7)
Finally, the priors for the residual standard deviation and the auto-correlation parameter are
specified as:
( )~ InverseGamma ,a bσ (8)
( )~ Uniform 1,1ρ − (9)
We adopt a Bayesian method to estimating the hierarchical model above for two reasons: (i) we seek
direct inference about the country-specific parameters i
β 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 i
β and its population). This requires a method that
enables pooling of information across countries to develop posterior estimates of i
β 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 fifteen 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
SSRI (selective serotonin reuptake inhibitor) antidepressant drugs, and span from the first quarter
of 1987 through the last quarter of 1993. Figure 1 presents plots of the cumulative sales of the drug
in these countries.
[Tables 1 and Figure 1 here]
11
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 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.
[Table 2 here]
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 ten year period starting 1988; see
Chintagunta and Desiraju 2002), 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 non-SSRI 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
12
symptoms of gastrointestinal upset, sleep impairment, impaired libido, and anorgamia (see e.g.,
Morrison 1999) that sometimes prevent their use. Further, in several countries, there is a belief that
non-allopathic 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.
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 , 1it i t
x X − in (2) which uses only variation in , 1it i t
x X − that
is explained by a set of exogenous instruments. We then use the predicted values as data, and
estimate the entire hierarchical diffusion system (5)-(9) using a Bayesian procedure.7 Further, to
assess the robustness of the analysis, we drop the last observation for each country from the data
and re-estimate 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 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 (i
β ) for each country. With access to the full data on diffusion, we can infer
about the parameter specific to each country based on our knowledge of the marginal distribution of
iβ and the value of the country-specific variables. To update our inferences to this full data, we must
simply compute the posterior distribution of i
β given [ ] , 1 111
, ,, ,− ==
=
T
J K
i t ij ikt kjt
it it X W Dy x 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 dataset. Once the country-
7 For other Bayesian applications in the cross-country context, see e.g., Neelamegham and Chintagunta (1999),
Talukdar et al. (2002), and for an overview of hierarchical Bayesian methods in marketing see, Rossi and
Allenby (2003).
13
specific parameter vector i
β 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 sub-section. The first sub-section focuses
on exploratory regressions; the second on the mean parameters of the full model specified in (2)-(9);
and the third sub-section presents the country-specific 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 “base model” – 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).8 The LM approach facilitates a test of
autocorrelation in the presence of a lagged dependant variable. Running the test for the “base model”
8 The LM test involves first obtaining the residuals from a regression of the dependant variable on all exogenous
variables and the lagged dependant variable, and second, running an auxiliary regression of these residuals on
lagged residuals, all exogenous variables and the lagged dependant variable. The corresponding test-statistic for
the null hypothesis of no first-order auto correlation is nR2 (where n is the number of observations), and is
distributed χ2(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 “second method”).
14
in Table 3.1 gave a value of 187.72 for the LM test statistic. The critical value ( )21χ 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 sales per population variable. As discussed in the appendix, the instrument is
constructed as the predicted value from a regression of the endogenous variable, 1i t it
X M− , on the
entire set of exogenous variables itZ . The regression of
, 1i t itX M− , on
itZ had an R2 = 0.727, indicating
a good fit. Further, the regression as a whole was significant (F = 96.68, k = 4, N = 262). A regression
of , 1i t it
X M− on the instrument ,i t
z− alone had an R2 = 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, 1i t it
X M− .
[Tables 3.1, 3.2, 4, 5 and 6 here]
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
, 1i tε − would increase
, 1i tX − ; and since it
ε is auto correlated and contains , 1i t
ε − , , 1i t
X − and itε are
positively correlated. Therefore, since the coefficient on , 1i t it
X M− is negative, if the endogeneity
problem is uncorrected, we would expect it to be biased toward 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 “base model” specification
15
gave a test statistic of 13.44. The corresponding critical value ( )21χ is 3.84, which rejects OLS over
2SLS, indicating that ignoring the endogeneity of , 1i t it
X M− 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 equations (2)-(9).
Note that these results correspond to a hierarchical linear model with autocorrelated errors, in
which predicted values from the instrumental variables regression, , 1−i t it
X M , are used as “data”.9
The full model specification uses two country-specific control variables, viz., prices (which are time
varying and correspond to the iktD variable in equations 3.1 and 3.2) and per-capita health
expenditures (which are time-invariant and correspond to the ijW variable in equations 3.1 and 3.2).
Recall that these enter the estimation equation (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 βµ corresponds to a constant, prices, per capita health expenditure,
instrumented lagged cumulative sales per population and interactions of prices and per capita health
expenditure with the instrumented lagged cumulative sales per population variable.
Here we present the results for the posterior mean parameters ( βµ in equation 5); the next
sub-section presents the results at the individual country level. Table 4 reports the posterior mean
and standard deviation for the mean parameters.10 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
9An alternative approach to account for the endogeneity would be to specify Xi,t-1/Mit ~ N(Zitλ, Σ) and model the
correlation between εit and the elements of Σ (e.g., Geweke, Gowrishankaran and Town 2003). This approach
would have the advantage that the uncertainty associated with using the predicted value of Xi,t-1/Mit is also
accounted for in the estimation. Exploring this approach would be an interesting avenue for future research. 10 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 represents 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.
16
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
macro level 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 σ (the standard deviation of the estimation error in equation 2) is
0.34. This indicates some unexplained variation in the dependant variable, ity , across countries and
time periods after controlling for the health expenditures, prices and the diffusion effect (lagged
cumulative sales per population). Further, the estimated posterior mean for ρ 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.
5.3. Posteriors parameters at the country level
Our main focus is on the country-specific parameters, and we summarize our findings in this sub-
section. 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
17
the lowest impact; of course, Australia, Canada and Italy have non-significant 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 Tables 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 since the mean 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
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 affects 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
the individual country level. The mean diffusion speed for each country in Table 6, iθ , represents the
mean of the posterior distribution of the average value of it
θ (that is the mean of the left-hand side of
equation 3.1) computed across all the observations for that country. The maximum penetration
potential in Table 6, iα , is computed as i iθ γ− , where iγ is the mean of the posterior distribution of
the average value of it
γ (that is the mean of the left-hand side of equation 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
18
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, since 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
below average diffusion speeds; further, 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, iα , 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 Netherlands. The remaining developed
nations have higher potentials. The difference between developing and developed countries adds to
the existing finding in Talukdar et al. (2000) 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
19
place through which new drugs can diffuse into the population, penetration potentials and diffusion
speeds for these countries are naturally lower.
[Insert Table 7 here]
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. Further, 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 non-urban 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 cross-country data, it is
possible that researchers can 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, since 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 - for example, at the city or regional
20
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 welfare-oriented 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;
further, 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. Further, in this product category, we find that even though its impact is
relatively small, higher prices tend to reduce diffusion speed. We also find that a macro level
covariate, per capita healthcare expenditures has a significant positive effect on diffusion speed,
particularly in developed nations.
21
An area that is worthy of research attention is the impact of other elements of the marketing
mix (e.g., 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.
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Appendix: 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 , 1it i t
x X − in (2) which uses only the variation in , 1it i t
x X −
that is explained by a set of exogenous instruments. We then use the predicted values as data, and
estimate the entire hierarchical diffusion system (5)-(9) using a Bayesian procedure. We discuss the
procedure in the two sub-sections below.
A1. Instrumental variables procedure
Our proposed instrument for , 1i t it
X M− 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 it
ε , are uncorrelated with
cumulative sales of the drug in other countries in that period. Denote by ,i t
z− , the mean value of
, 1c t ctX M− , averaged over all countries c i≠ . Then, by the argument presented above,
,i tz− is
correlated with , 1i t it
X M− but is uncorrelated with
itε . Therefore,
tz is a reasonable instrument for
, 1it i tx X − . Note that since 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
24
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, ,i t
z− , as itZ . We first run a
regression of the endogenous variable, , 1i t it
X M− , on the entire set of exogenous variables itZ :
, 1i t it it itX M Z λ ω− = +
Let the predicted value of , 1i t it
X M− from the regression, itZ λ= , be denoted as
, 1−i t itX M . Recall that
the endogeneity problem occurs since , 1i t it
X M− is correlated with εit in (2). It is easy to see from
above that while ( )corr ,it it
ω ε need not be zero, we ensure by construction that it itZ ε⊥ . Therefore, the
variation in the predicted value, , 1−i t it
X M , represents only the variation in , 1i t it
X M− that is
“explained” by the exogenous variables itZ . We can now proceed by simply using the predicted value,
, 1−i t it
X M , in place of the endogenous variable, , 1i t it
X M− , wherever it appears in the estimation
equation (2). Since , 1−i t it
X M is not correlated with it
ε in (2), there is no longer an endogeneity
problem. The approach is similar in spirit to a 2-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 , 1−i t it
X M instead of , 1i t it
X M− 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.
A2. Bayesian estimation
The Bayesian inference problem here is to obtain the posterior distribution of the entire set of
parameters, ( )2, ,iβ σ ρΘ = given the priors and the data. Following Chib (1993), we factor the joint
prior for Θ as: ( )2, ,ip β σ ρ = ( ) ( ) ( )ip p pβ σ σ ρ . Thus ( )2
,iβ σ are a priori assumed independent of
25
ρ . 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 i
β ; in practice, we take diffuse priors over βµ , σ
and ρ , and induce a small amount of shrinkage with our Ω prior. The exact prior settings are as
follows: The priors for βµ are independent normal with βµ set to be zero, and 2σ set to 1e-6 for all
six elements of βµ . We introduce a mild amount of shrinkage with our Ω 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 = 6 (i.e., the rank of Ω ). The priors for σ are 0.001a = , 0.001b = , and are
chosen to be non-informative. A diffuse uniform prior is set on ρ 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 et al. 1995).
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.
26
Table 1: Introduction timing across countries
Country Quarter of
introduction
Belgium First quarter 1987
South Africa First quarter 1987
USA First quarter 1988
Spain Fourth quarter 1988
Italy Fourth quarter 1988
Mexico First quarter 1989
Canada First quarter 1989
United
Kingdom
First quarter 1989
France Third quarter 1989
Netherlands Third quarter 1989
Brazil Fourth quarter 1989
Colombia First quarter 1990
Venezuela Second quarter 1990
Australia Third quarter 1990
Portugal Second quarter 1991
Note: 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.
Table 2: Cumulative sales, average prices in each market
Country Cumulative Sales Average Prices Std. Dev. (for prices)
Belgium 137.58 15.35 2.09
South Africa 157.78 31.40 8.98
USA 19792.88 135.61 17.56
Spain 540.66 19.04 4.65
Italy 509.80 12.71 1.48
Canada 1075.20 126.55 6.35
UK 660.32 36.92 9.17
Mexico 73.21 17.14 3.70
France 3171.92 12.41 1.77
Netherlands 156.33 53.59 3.34
Brazil 191.42 20.35 3.87
Colombia 18.44 19.52 2.40
Venezuela 6.49 16.23 0.69
Australia 121.49 31.39 4.79
Portugal 56.57 19.83 4.58
Note: Sales are in kilograms, measured at the end of the observation period; Prices are in equivalent
unadjusted U.S. dollars.
27
Table 3.1: Results from pooled regression – no instruments for (Lagged cumulative sales)/population
Parameter
t-
statistic Parameter
t-
statistic Parameter
t-
statistic
Constant 0.4368 4.348 0.3543 2.086 0.4582 1.4203
Per capita health expenditure 0.1730 2.060 0.1675 1.730 0.1081 1.6651
(Lagged cumulative sales)/population -0.0009 -3.811 -0.0011 -3.536 -0.0054 -3.9918
Prices -0.000028 -0.546 -0.000029 -0.565 -0.000048 -0.9429
Number of firms in market 0.0722 0.240 0.0858 0.2897
Number of firms in market*Prices 0.0008 0.501 0.0023 0.5288
Prices*(Lagged cumulative sales)/population 0.0022 3.0885
(Per capita health expenditure)*(Lagged cumulative
sales)/population -1.25E-05 -1.6563
Observations 262
R2 0.235 0.244 0.314
Note: Data are pooled across all countries and time-periods. Dependant variable is sales/(lagged cumulative sales) in all regressions.
Table 3.2: Results from pooled regression – using instruments for (Lagged cumulative sales)/population
Parameter
t-
statistic Parameter
t-
statistic Parameter
t-
statistic
Constant 0.3114 3.1017 0.2745 2.6246 -0.0745 -0.2182
Per capita health expenditure 0.4852 4.6005 0.5709 4.6213 0.6607 4.7104
Instrumented [(Lagged cumulative sales)/population] -0.0024 -6.0318 -0.0019 -3.4948 -0.0019 -3.1784
Prices -
0.0000074 -0.1498
-
0.0000038 -0.0768
-
0.0000045 -0.1508
Number of firms in market -0.0005 -1.0638 0.2287 0.6804
Number of firms in market*Prices 3.81E-07 0.0776 0.0026 0.7552
Prices* Instrumented [(Lagged cumulative sales)/population] 0.0004 0.9413
(Per capita health expenditure)* Instrumented [(Lagged cumulative
sales)/population]
-1.42E-05 -1.1279
Observations 262
R2 0.354 0.363 0.381
Note: Data are pooled across all countries and time-periods. Dependant variable is sales/(lagged cumulative sales) in all regressions. The
variables: “Number of firms in market”, and “Number of firms in market*Prices”, were dropped from the subsequent analysis since they are
statistically insignificant.
28
Table 4: Posteriors for the mean parameters ( βµ ), ρ and σ
Parameter Std. dev.
Constant 1.8590 0.3779
Per capita health expenditure 1.6320 0.7088
Instrumented (Lagged cumulative sales)/population -0.00150 0.000582
Prices -0.00015 0.000095
(Per capita health expenditure)*Instrumented (Lagged cumulative
sales)/population -0.00192 0.001140
Prices*Instrumented (Lagged cumulative sales)/population -0.00002 0.000037 ρ 0.8539 0.0106 σ 0.3369 0.0158
Table 5: Posterior estimates for each country
Notes: 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.
Country 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
Param. Std. dev. Param. Std. dev. Param. Std. dev. Param. Std. dev. Param. Std. dev. Australia 0.3947 0.5508 -0.0005 0.0002 -0.00015 0.00012 -0.00015 0.00215 0.00005 0.00006
Belgium 0.7474 0.3186 -0.0010 0.0015 -0.00015 0.00011 -0.00104 0.00146 0.00000 0.00005
Brazil 1.6490 1.4090 -0.0016 0.0012 -0.00014 0.00007 -0.00190 0.00245 -0.00002 0.00007
Canada 0.3558 0.3152 -0.0010 0.0003 -0.00015 0.00012 -0.00099 0.00194 0.00001 0.00002
Colombia 2.7360 1.8810 -0.0026 0.0010 -0.00015 0.00013 -0.00257 0.00320 -0.00007 0.00008
France 2.0810 0.3182 -0.0017 0.0011 -0.00014 0.00011 -0.00247 0.00119 -0.00003 0.00006
Italy 0.5137 0.3322 -0.0011 0.0002 -0.00015 0.00012 -0.00111 0.00151 0.00001 0.00006
Mexico 1.6310 1.2970 -0.0019 0.0011 -0.00015 0.00011 -0.00183 0.00246 -0.00002 0.00006
Netherlands 5.8240 0.7375 -0.0030 0.0015 -0.00013 0.00022 -0.00534 0.00377 -0.00014 0.00009
Portugal 3.5520 1.0730 -0.0019 0.0015 -0.00014 0.00014 -0.00345 0.00283 -0.00007 0.00007
South Africa 0.6901 1.2950 -0.0015 0.0010 -0.00015 0.00012 -0.00116 0.00257 0.00000 0.00005
Spain 1.2860 0.4584 -0.0016 0.0009 -0.00015 0.00010 -0.00200 0.00176 -0.00002 0.00005
UK 2.3300 0.4369 -0.0019 0.0014 -0.00014 0.00011 -0.00289 0.00172 -0.00005 0.00005
USA 0.5305 0.3030 -0.0010 0.0007 -0.00015 0.00012 -0.00098 0.00146 0.00001 0.00002
Venezuela 0.1816 1.8540 -0.0003 0.0019 -0.00015 0.00013 -0.00082 0.00316 0.00004 0.00008
Average 1.6335 -0.0015 -0.00015 -0.00191 0.00002
29
Table 6: Posterior mean diffusion speed
Country Mean diffusion speed ( )iθ 1 Maximum penetration level ( )iα 2
Belgium 0.4259 1615.7
South Africa 0.4424 1112.7
USA 0.2133 34340.8
Spain 0.6823 1028.4
Italy 0.3635 1326.6
Canada 0.3361 19320.1
UK 0.4415 1608.4
Mexico 1.5580 792.9
France 0.8946 1280.0
Netherlands 0.6194 1108.2
Brazil 0.2464 271.2
Colombia 0.3564 1277.0
Venezuela 0.3246 1361.0
Australia 0.2889 2100.9
Portugal 0.2608 1489.4
Average 0.4971 4668.9 1Computed as the mean of the posterior distribution of the average of
itθ across all observations for each country, for the last
10,000 draws of the chain. 2in Kg-s/million people
30
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 %
of GDP
Population per
physician
Population per
hospital bed
Women aged between
15 and 49 (in
thousands)
Brazil 6,100 4.2 680.90 299.88 39,466
Colombia 5,300 4.0 1,198.58 733.43 9,022
Mexico 7,700 3.2 1770.63 801.37 21,559
South Africa 4,800 5.6 1716.67 NA 9379
Venezuela 9,300 3.6 633.44 385.00 4,935
Australia 22,100 7.7 437.53 183.28 4, 474
Belgium 14,573 7.5 311.18 120.83 2, 438
France 20,200 8.9 346.44 109.05 14,116
Italy 18,700 7.5 210.02 131.28 14,420
Netherlands 19,500 7.9 412.00 169.80 3,967
Portugal 11,000 7.0 480.46 226.67 2,544
Spain 14,300 6.6 277.13 208.74 10,114
UK 19,500 6.1 NA 160.91 14,160
Canada 24,400 9.1 469.30 67.30 7,154
USA 27,500 12.7 420.61 194.39 65,806
31
Figure 1: Cumulative sales in each country
Cumulative Sales
0
100
200
300
400
500
1 4 7
10
13
16
19
22
25
28
Quarters
BRAZIL
SOUTH AFRICA
COLOMBIA
VENEZUELA
Cumulative Sales
0
500
1000
1500
2000
2500
3000
3500
1 4 7
10
13
16
19
22
25
28
Quarters
Australia
Canada
Cumulative Sales
0
10000
20000
30000
40000
50000
60000
70000
1 4 7
10
13
16
19
22
25
28
Quarters
France
Canada
USA
Cumulative Sales
0
500
1000
1500
2000
2500
1 4 7
10
13
16
19
22
25
28
Time
Belgium
Netherlands
Portugal
Spain
UK
Italy
