Università Commerciale Luigi Bocconi Econpubblica Centre for Research on the Public Sector

WORKING PAPER SERIES

Market structure and technology: evidence from the

Italian National Health Service

Silvana Robone Alberto Zanardi

Working Paper n. 102

October 2004

www.econpubblica.uni-bocconi.it

MARKET STRUCTURE AND TECHNOLOGY: EVIDENCE FROM THE ITALIAN NATIONAL HEALTH SERVICE

Silvana Robone – University of Bologna

Alberto Zanardi* - University of Bologna and Econpubblica-Bocconi University

Abstract

A key feature of Sutton's theory is that industries evolve to distinct market configurations in terms of concentration depending upon whether the markets have a large size, whether the corresponding products are essentially homogeneous, whether they are differentiated by research and development (R&D) and advertising. This paper aims to test empirically the consistency of the technological profiles and market structure of the health care sector in Italy with Sutton's predictions. The results of the analysis offer some empirical support in differing relationships between industry concentration levels and technological characteristics across health care productions.

Keywords: health services, market structure, technology JEL classification: I11, L1, L8, O33 Corresponding author: Alberto Zanardi, Dipartimento di Scienze Economiche, Università di Bologna, email: zanardi@economia.unibo.it

* The authors would like to thank the Italian Ministry of Health, Francesco Taroni and Roberto Labanti of the Regional Health Agency of Emilia-Romgna and Daniele Fabbri of the University of Bologna for providing the data-set employed in this work. We are also grateful to the participants to the 2003 Italian Society of Public Economics Conference and to the 2003 Italian Association of Health Economics Conference for useful comments. Financial support from MURST is gratefully acknowledged.

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1. Introduction

In the past few decades health care markets have been deeply affected by two different

radical structural changes. On one hand, the rapid pace of technological development

and the diffusion of new technologies to providers, by improving the quality of care and

introducing new and costlier products, have greatly contributed to cost increasing in the

health care industry. On the other hand, even in the diversity of national experiences, a

clear trend has emerged towards a decentralization of public intervention in health care

to sub-national layers of government (regional as well as local bodies). During the '90s

radical reforms towards regionalization have reshaped the national health service in

Canada, Italy, Spain and Sweden, determining the rise of regional health services

differentiated on the basis of organization, institutions and services, and increasing the

decisional autonomy of the agents operating in the health care markets, on both the

demand and the supply side. On the demand side, patients have gained the right to

freely choose the facilities that best meet their requirements of high-quality medical

care, whereas on the supply side, hospitals and other health structures, apart from

fulfilling a series of essential services, have become more autonomous in concentrating

their own resources on specific health care productions started by technological

innovations. As a whole, these dramatic changes have greatly contributed to make the

functioning of health care markets more similar to traditional industrial sectors, where it

is generally assumed that consumers are free to choose their supplier, suppliers are free

to choose which product to offer and the quality of it, and technology plays a crucial

role.

With reference to the Italian National Heath Service in particular, a series of empirical

contributions (Fabbri and Fiorentini (1996), Degli Esposti et al. (1996), Ugolini and

Fabbri (1998), Spampinato (2001)) has stressed the relevance of the relation between

interregional mobility of patients and the technological complexity of health services

provided by different Regions: patients are more willing to move far from their

territorial area of residence, and therefore to bear the implied costs of transaction, if they

need health services characterized by high specialization, thus affecting the structure of

the health care industry (market concentration).

Industrial organization literature has largely investigated the relationship between

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technology and market structure. In this regard a standard reference is offered by the

theoretical and empirical contribution by John Sutton. A key feature of Sutton's research

approach (Sutton (1991, 1998)) is that industries evolve to distinct market

configurations in term of concentration depending upon whether the corresponding

products are essentially homogeneous or whether they are differentiated by research and

development (R&D) and advertising. Sutton develops his analysis with reference to

manufacturing sectors. A series of contributions (Robinson and Chiang (1996), Lyons

and Matraves (1996), Matraves (1999), Giorgetti (2000), Marin and Siotis (2002),

Gruber (2002), Giorgetti (2003), de Juan (2003), Buzzacchi and Valletti (2003))

perform empirical tests for several industries in the EU and the US that support Sutton's

prediction about market size and market structure. What has been argued before about

the ongoing dramatic changes in health care suggests, as a promising path of research,

to resort to the same interpretative tools to study the structure of medical care markets

currently prevailing. In particular, the aim of this paper is to test empirically the

existence of the relation between technological profiles and market structure claimed by

Sutton’s theory in a specific economic framework, that of medical care services

provided by the Italian National Health Service.

This paper is organized as follows. In Section 2 Sutton's theoretical framework is briefly

discussed. Section 3 describes the data about the health services provided by the Italian

National Health Service that is at the basis of our empirical application. Section 4

illustrates the statistical tests developed to try out Sutton’s empirical predictions about

market concentration and product homogeneity, and about market concentration and

market size. Section 5 concludes and outlines some possible directions for future

research.

2. Technology and market structure: the Sutton’s approach

Sutton (1991, 1998) investigates the relationship between an industry’s R&D intensity

(measured by the ratio of R&D spending on sales) to its level of concentration

(measured by the combined market share of some specified number of top firms).

Theoretical and empirical literature has at length debated on this relationship without

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reaching a common view. On the theoretical ground, it was initially the direction of

causation (from concentration to R&D intensity, or vice versa) to be disputed1.

However, starting from the 70’s the view that concentration and R&D intensity were

both endogenous variables became widely accepted, and therefore they should be

simultaneously determined within an equilibrium system. On the empirical ground, no

clear consensus appears to emerge in empirical cross-industry analyses about the sign

and the form of the relationship between R&D intensity and concentration: beside

papers that report a positive correlation, others emphasize a negative relationship or no

correlation at all.

The starting point of the theory, developed by Sutton (Shaked and Sutton (1982, 1987),

Sutton (1989, 1991, 1998)) lies in the observation that R&D (and advertising) outlays

can both be considered as sunk costs incurred by the firm with a view to enhance

consumers’ willingness-to-pay for the firm's product: R&D (and advertising) outlays are

choice variables to the firms and so their levels must be determined endogenously as

part of the specification of industry equilibrium (endogenous sunk costs).

In particular Sutton focuses on what he calls the escalation mechanism. This describes

the way in which firms may respond to an increase in the size of the market, relative to

the set up costs incurred by entering the industry, through raising their R&D spending.

In particular � denotes the escalation parameter, that measures the additional profits an

entrant firm that spends in R&D more than the incumbent firms operating in an initially

fragmented market can attain.

A crucial question related to � arises: what are its determinants? Can the value of � be

related to observable industry characteristics?

In general terms, � can be thought to be a function of two parameters:

• � , a cost parameter which measures the degree to which product quality and

consumers’ willingness-to-pay rises with R&D spending;

• � , a substitution parameter which measures the strength of the links between

different technological trajectories in the market and their associated product groups

1 The latter stance is mainly based on appeal to the structure/conduct/performance paradigm developed by Bain (1956). Within that paradigm, is it claimed that a one-way chain of causation runs in each industry from structure (the level of concentration) to conduct (the degree of collusion), and from conduct to performance (profitability). Structure, in this setting, is explained by the degree of scale economies in the industry and by observed levels of advertising and R&D outlays relative to industry sales.

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both on the demand side (substitution) and the supply side (scope economies in

R&D).

Fig. 1 illustrates the relationship between � and the parameters � and � . When � is

low (that is R&D is effective and the increase in quality is highly evaluated by the

consumers) and � is high (progress on one trajectory leads to the stealing of consumers

from rivals on other trajectories because of relevant scope economies in R&D and close

substitutability between different goods associated with various trajectories) then � is

high and as a consequence both high R&D intensity and high level of concentration will

result. On the other hand if the degree of substitution is low, in spite of the effectiveness

of R&D spending, concentration may be low.

In this paper we are interested in two predictions put forward by Sutton (1991):

a) in exogenous sunk cost markets the lower bound to equilibrium concentration

converges monotonically to zero as the ratio between the market size and the

set up costs increases (see fig.2);

b) in endogenous sunk cost markets (like in R&D intensive markets) Sutton

predicts that concentration remains bounded away from zero as the ratio

between the market size and the set up costs increases (see fig.3).

We recall that Sutton (1991) approximates the set up costs incurred by firms on entering

an industry with the costs of acquiring a single plant of minimum efficient scale. The

intuition behind the previous predictions is the following. In exogenous sunk cost

markets a continuing increase in market size relative to set up costs gives additional

entrants the opportunity to build a profitable scale of operations. Differently, in

endogenous sunk cost markets a firm is willing to suffer short-term losses from

incurring in endogenous sunk costs in order to gain long-term revenues. As market size

(relative to set up) costs increase, long term revenues increase. Through this

mechanism, increasing market size leads to a competitive escalation in short term

spending; eventually, when this competitive escalation of spending becomes too high

for a new entrant to handle, entry is blocked. Of course, the degree to which

concentration is bounded away from zero is an empirical matter.

In Sutton (1998), building on the definition of � and the notion of an equilibrium

configuration, Sutton derives a non-convergence theorem, which represents the key

result of his contribution. According to the non-convergence theorem, in any

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equilibrium configuration it holds that �≥C1 , that is the one-firm sales concentration

ratio C1 is bounded below by � , independently of the size of the market. Since � and

� are not directly observable, Sutton reformulates the non-convergence theorem in

terms of two observable industry characteristics whose joint behavior reveal

information about the value of � and thereby places a lower bound on the level of

concentration: the industry’s R&D/sales ratio and h , an homogeneity index which

measures the extent to which the industry’s sales are divided among products associated

with different technological trajectories. In particular, h represents the share of industry

sales accounted for by the largest product category.

Two distinct empirical predictions regarding the joint distribution of R&D intensity,

concentration, and product homogeneity have been derived:

c) in the industries where R&D intensity is low, the lower bound to concentration

converges to zero as the size of the market becomes large, independently of the

degree of product homogeneity (see fig. 4);

d) on the contrary, in the industries where R&D intensity is high, the lower bound

to concentration increases from zero with the h index (see fig. 5);

The intuition behind these general empirical predictions is as follows. If R&D is

ineffective in raising consumers' willingness-to-pay for the firm's products, it can be

shown that R&D intensity is necessarily low. So if we construct a set of industry for

which the R&D/sales ratio is high, then we know that for this group R&D effectiveness

is high. Whether this necessarily implies a high level of concentration depends on the

strength of the linkages between sub-markets, that in its turn depends on the scope

economies and the degree of substitutability across products associated with different

R&D trajectories. Where these are high, concentration will necessarily be high since, if

all firms have a low market share, an escalation of R&D spending will be profitable: a

high-R&D-spending firm can capture sales from low-R&D-spending rivals on its own

trajectory and on others. On the contrary, when the scope economies and the degree of

substitutability across products are low, in spite of the effectiveness of R&D spending,

concentration may be low: there are many product groups, associated with different

R&D trajectories ( h is low), and therefore escalation can yield only poor returns.

On the other hand, when R&D intensity is low, the absence of an escalation mechanism

involving R&D makes the market able to support an indefinite number of firms, and

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therefore the theory predicts that the lower bound to concentration is zero independent

of h .

In conclusion, in the effort to be as general as possible, the empirical predictions by

Sutton place only weak restrictions on observable industry characteristics (R&D

intensity, market size, product homogeneity, market concentration). This generality is

exploited by Sutton (1991, 1998) by following two different paths of analysis: on one

hand, by developing a statistical test of his empirical predictions based on data from a

selection of industrial sectors; on the other hand, by discussing a series of industry cases

(from flow-meters to turbine generators) that, through a detailed collection of qualitative

information, enable to go further in probing the validity of the theory, than that which

would have been possible solely on the basis of the econometric analysis.

As discussed in Section 1, the aim of this work is to test empirically the existence of the

relation between technological profiles and market structure claimed by Sutton’s

theoretical framework with reference to the medical care services provided by the

Italian National Health Service.

3. The Data

The analysis is based on a data-set provided by the Italian Ministry of Health reporting

health services (including both hospitalization and day-hospital services) offered in

2001 by all the medical care facilities operating within the National Health Service. For

any single health service produced, the data-set reports a set of essential information:

the corresponding Diagnosis Related Group (DRG) according to the classification

adopted by the Italian Ministry of Health, the fares corresponding to each DRG, the

medical care facilities where the service was provided together with the Region where

those facilities were operative, and the Region where the patient resided. The data

includes all the 20 Italian Regions and all the 492 DRGs classified by the Italian

Ministry of Health2. Moreover, the Ministry of Health groups the DRGs into 25 Main

2 More precisely no medical care services corresponding to DRG numbers 109, 351, 438 and 474 for the hospitalization services and numbers 109, 168, 169, 185, 186, 187, 391, 438 and 474 for the day-hospital services are included in the data-set referred to 1999, even if those DRG are provided in the classification system adopted by the Ministry of Health.

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Diagnostic Categories (MDCs) representing specific diagnostic groups. Due to

incomplete information, some observations have been excluded from the data-set3.

In addition to data on the size and the composition of medical care productions, our

analysis relies on information about their technological characteristics. Failing direct

information about the value of means of production employed in the provision of health

care services classified by DRG, we tried to derive a proxy of the technological

intensity of each DRG by resorting to the more detailed information available on the

health services provided by combining two different data-sets available for the health

services provided in the case of a specific Italian Region, Emilia-Romagna. The first

one reports the number of health care services provided by every regional hospital,

distinctly by DRG and hospital ward; the second one relates to the total costs classified

by main items (such as medical staff, paramedic staff, executive staff, non-durable

goods purchases, etc.) incurred by hospital wards for each regional hospital. The basic

cost items by hospital wards and the services provided (measured in terms of

hospitalization days) classified by hospital wards and DRG have then been aggregated

across hospitals. Among the cost items the category of capital costs (depreciation plus

capital goods hiring) have been distinguished from other costs. A capital intensity index

has then been derived for each DRG as the weighted average of the ratio capital

costs/total costs referred to each hospital ward, the weights given by the share of the

total number of services each hospital ward provides for each DRG4. Analogously, for

each MDC the corresponding capital intensity index has been calculated as the weighted

average of capital intensity index of the DRGs pertaining that MDC, the weights given

by the share of the total production of that MDC referred to each DRG. The capital

intensity indexes, derived in such a way, have been assumed as a proxy of the

3 In order to perform statistical tests on the data, we have excluded from the data-set those observations that do not report complete information about the corresponding DRG, the hospital where the service is provided, the Region where the hospital is operative. A number of health services corresponding to DRGs (468, 469, 470, 476, 477, 480, 481, 482 and 483), which the official classification does not include in any MDC, have been removed as well. 4 More precisely, if we denote by i the i-th DRG and by j the j-th category of hospital department, capital intensity index it is derived as:

��=

jij

ij

j j

ji

s

s

c

kt

where k , c and s respectively denote capital costs, total costs and the number of provided services measured in terms of hospitalization days.

8

technological intensity of each MDC ( tech )5.

Tab. 1 reports for each MDC some essential information about the number of health

services offered, the number of DRGs and of hospitals operating in each market. As

expected, for all MDCs hospitalization services greatly outnumber day-hospital

services. Moreover, both hospitalization and day-hospital services show a strong

variability in their size measured in terms of the corresponding number of health

services (the coefficient of variation is equal respectively to 0.98 and to 0.82). For

example, within hospitalization services, MDC size ranges from 1,303,341 services

provided (5 - Cardio-vascular apparatus diseases) to 6,694 (22 - Burns), whereas for

day-hospital services it ranges from 334,881 (17 - Myelo-proliferative diseases) to 38

(24 - Serious multiple traumatisms). Variability is also strong as far as the number of

DRGs belonging to each MDC for both hospitalization and day-hospital services (the

coefficient of variation is equal respectively to 0.70 and to 0.71). Differently, variability

is much less strong as far as the number of hospitals operating in each MDC (the

coefficient of variation is equal to 0.22 for hospitalization services and to 0.39 for day-

hospital services).

In order to interpret the market structure of the Italian National Health Service through

Sutton’s theoretical framework, some correspondences between the theoretical setting

discussed in Section 2 and the data just described need to be established. Thus:

• the classification of health services by MDCs identifies 25 different markets

(industries). Within each market, health services referred to each DRG included

in that market make up a sub-market (a technological trajectory);

• within each market (sub-market) hospitals operate as firms;

• the number of services provided, multiplied by their corresponding fares (set by

the National Health Service), represents the sales revenue of the hospital-firm;

• the share of each hospital in each market (sub-market) is identified by the sales

revenue gained by that hospital over the total revenue gained in that market (sub-

market).

As discussed in Section 2, the empirical predictions regarding the joint distribution of

5 The values of tech may obviously differ between hospitalization services and day-hospital services for the same MDC. As a matter of fact, even if a unique capital intensity index is provided for each DRG regardless of the distinction between hospitalization and day-hospital services, the distribution of

9

R&D intensity, concentration, size and product homogeneity can be derived from

Sutton's theoretical framework. In order to test the consistency of the data from the

Italian National Health Service with those two empirical predictions, four indexes have

to be worked out for each MDC (distinctly for hospitalization services day-hospital

services):

• the technological intensity index tech as defined before, which is here used as a

proxy for the R&D intensity in the MDC;

• the concentration index 4C , defined as the sum of market shares corresponding

to the four firms providing the largest number of health services in the MDC;

• the homogeneity index h , determined as the fraction of sales revenue

corresponding to the largest DRG (in terms of number of health services

produced) in each MDC;

• the market size to set up costs ratio index size , determined as the ratio between

the revenue gained in the MDC and the set up costs to enter that market; costs

approximated by Sutton (1991) with the costs of acquiring a single plant of

minimum efficient scale. We approximate them by the revenue of the median

hospital.

Tab. 2 reports the values of tech , 4C , h and size for each MDC (denoting

hospitalization and day-hospital services respectively by h and d) sorted by descending

values of tech (fig. 6 and fig. 7 report the corresponding values in terms of percentage

deviation form the average). The tech -index ranges from a minimum of 0.047 to a

maximum of 0.077, showing a very low variability of the composition by sub-markets

across MDCs (coefficient of variation equal to 0.088). The h -index ranges from a

minimum of 0.105 to a maximum of 0.974, showing a marked variability (coefficient of

variation equal to 0.563); 4C shows more variability than h and tech , ranging from a

minimum of 0.030 to a maximum of 0.473 (coefficient of variation equal to 0.879): on

average hospitalization services show a concentration index (0.067) lower than day-

hospital services (0.153). The size -index ranges from a minimum of 7.28 to a

maximum of 23.05, and its coefficient of variation is 0.134, which is a pretty low value.

provided services across DRGs within a given MDC is usually different when the two categories of health

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4. Empirical results

The consistency of the empirical predictions by Sutton (1991, 1998) with the market

structure of the Italian National Health Service is tested here by jointly considering the

MDCs corresponding to hospitalization services and those corresponding to day-

hospital services, in order to get a data sample large enough (50 observations) to ensure

statistical significance to the test.

Given that Sutton states different predictions according to the R&D intensity of the

considered industries, first of all we have split our sample of MDCs into two sets, the

first one characterized by a relatively high level of technological intensity and a control

group for which the technological intensity is relatively low. A rather crude way to

proceed is to rank the MDCs by tech -index, and to choose as cutoff level the average

value (0.063)6. In order to distinguish more sharply the high- tech group from the low-

tech one, we do not consider the MDCs whose tech -index is near to the cutoff level

and we drop the 5% of MDCs from the high- tech group (2 MDCs) and the 5% of

MDCs from the low one (3 MDCs). Thus, 21 MDCs make up the group characterized

by a relatively high level of technological intensity, which we refer to as the high- tech

MDCs group, while 24 MDCs make up the low- tech MDCs group (see tab.2).

The partitioning of the sample of MDCs into the high-tech and low-tech groups makes

it possible to stress some preliminary points. For high-tech MDCs, the tech -index goes

from 0.063 to 0.077 (average value equal to 0.067), the h -index from 0.117 and 0.974

(average value equal to 0.311), while the 4C -index ranges from 0.032 and 0.473

(average equal to 0.091). On the contrary, for the low- tech MDCs, the tech -index

ranges from a minimum of 0.047 to a maximum of 0.062 (average value equal to

0.059), the h -index from 0.173 to 0.869 (average value equal to 0.425), while the 4C -

index values are between 0.032 and 0.340 (average value equal to 0.123).

4.1. Market concentration and market size

Fig.8 and fig.9 illustrate the relationship between the 4C -index and the size -index

services are compared. 6 Notice that our choice of the cut-off point is to some extent arbitrary and that other criteria could be adopted to define it.

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respectively for the high-tech and the low-tech MDCs. Our interest lies in comparing

these scatter diagrams with the predicted lower bounds shown in fig.2 and fig.3. As

mentioned in Section 2, the theory states that for the high- tech group, the lower bound

to concentration converges monotonically to zero as market size increases, while for

the low- tech group concentration remains bounded away from zero as market size

increases.

Following Sutton (1991), in order to estimate a lower bound to the scatters of

observations shown in fig.8 and fig.9 we adopt the methodology based on Smith (1985,

1994), involving the use of a two-step procedure. The first step of the procedure

requires making some a priori decision about the form of the schedule f(z) that

describes the lower bound. Then we may obtain a consistent estimator of the actual

schedule by choosing parameters minimizing the sum of residuals )( ii zfy − , subject

to the constraint that all residuals shall be non-negative. The second step involves

checking that the pattern of the estimated residual fits a two parameters Weibull

distribution7.

The three parameters Weibull distribution is defined on the domain �≥t by:

��

���

��

���

��

� −−−=≤�

�

�exp1)(Prob

ttT (1)

where 0� > and 0� > . The three constants (� , � , � ) respectively denote a shape, a

scale parameter and a location parameter. Notice that the location parameter �

represents the lower bound to the support of the distribution. If 0� = the distribution

comes down to a two-parameters Weibull.

The procedure rests on the assumption that the distribution of residuals is identical at all

values of the independent variable. This assumption would be unrealistic if applied

directly to the scatters of fig.8 and fig.9, considering the presence of an upper limit of

14 =C . For this reason we take the logit transformation of 4C :

���

����

�

−=

4

4*4 1

lnC

CC (2)

7 We chose to use a Weibull distribution as the distribution generating the level of concentration in the MDCs because it is a flexible functional form. In fact we can assume different shapes and different

12

The first step of the estimate procedure is to make some assumptions regarding the form

of the schedule describing the lower bound and to estimate the parameter of the

schedule. A reasonable family of candidate schedules would be:

���

����

�+=

sizeC

lnb

a*4 (3)

Fig.8 and fig.9 show the estimated schedules describing the lower bound in the high and

low-tech MDCs groups. The estimated parameter a is equal to –9.263 for the high- tech

MDCs group while it is equal to –21.875 for the low- tech one. Considering the values

estimated for the parameter b , we find a higher slope of the lower bound for the low-

tech MDCs group than for the high- tech one, equal respectively to 17.535 and to

55.308. The parameters a and b are significant at a confidence level higher than 99%

for both the two groups of MDCs8. For this result it is therefore apparent that the

relationship between the estimated schedules in the high and low- tech MDCs groups

gives support to the predictions of the theory as presented in Section 2.

Secondly, it is necessary to check that the associated set of residuals fits a Weibull

distribution. We prove that the set of residuals fits the Weibull distribution well, both in

the high and low- tech MDCs groups. Moreover, we test the null hypothesis that in both

groups the residuals fit a two parameter Weibull distribution, that is the parameter

0� = . To check the null hypothesis we need to test the two-parameter Weibull against

the three-parameter Weibull; this can be done using a likelihood ratio test. In fact, twice

the difference of the fitted negative log likelihood (NLLH) between the three and the

two-parameter Weibull has an approximate chi-square distribution with one degree of

freedom. The results of the test prove that the null hypothesis that the residuals fit a two

parameter Weibull distribution ( 0� = ) cannot be rejected9.

position in the plane according to the values given to its parameters. For this reason it has been widely used in fitting bounds to various empirical distributions. 8 In fact for the high-tech MDCs group the t-value associated with the parameter a is –36,48 while the one referred to the parameter b is 24,89. For the low tech MDCs group the t-value associated to the parameter a is –23,13 while the one corresponding to the parameter b is 20,04. In order to calculate these t values, we have computed the standard errors of the parameter a and b following Smith’s procedure (1994). The standard errors are obtained from a ’s and b ’s empirical distributions, which have been calculate by generating error terms from a Weibull distribution characterized by the estimated parameters. 9 Considering that twice the difference of NLLH is 0.948 and 3.120 for the high and for the low-tech MDCs group respectively and that the 5% rejection point of the chi-square distribution is 3.84, the null hypothesis cannot be rejected.

13

To test the null hypothesis that the estimated schedules for both types of industries

converge to the same value as the market size goes to infinitive, we can observe the

values assumed by *4C for the high- tech MDCs group and for the low- tech one when

size goes to infinitive. For the first group it is equal to –9.263 (which corresponds to

4C = 0.010%), while for the second one it is equal to –21.875 (which corresponds to

4C = 0.000%). These results are consistent with the empirical predictions a) and b) by

Sutton (see Section 2). Finally, the estimated value of � is inferior to 2 for both the low

and the high- tech MDCs group, which indicates that Smith’s methodology is

appropriate because a maximum likelihood approach would be inadequate in such

cases10.

4.2. Market concentration and market homogeneity

Fig.10 and fig.11 illustrate the relationship between the 4C -index and the h -index

respectively for the high- tech and the low- tech MDCs. We are interested in comparing

these scatter diagrams with the predicted lower bounds shown in fig.4 and fig.5. As

mentioned in Section 2, the theory states that for the high- tech group, the lower bound

to concentration is an increasing function of h that passes through the origin, whereas

for the control group it is zero everywhere. Actually, at a first observational exploration,

the data from the Italian National Health Service does not seem to contrast those

theoretical predictions: the high- tech group does not include observations where high

values of h are coupled with low values of 4C (except for the second MDC (Eye

diseases – day-hospital services) that may be treated as an outlier), whereas some low-

tech MCDs are characterized by both low product homogeneity and low concentration.

This rough empirical evidence encourages us to turn to a formal statistical test

procedure in order to try out Sutton (1998)’s predictions. Notice that Sutton’s theory

makes no general prediction as to the functional form of the lower bound. However in

the limiting case where all sub-markets are completely independent, the theory states

that the bound for the high- tech group takes the form of a ray through the origin. Thus,

making this simplifying assumption for the lower bound, we can represent each

10 For further details on this point we refer to Sutton (1991, 116-117).

14

observation ( 4C , h ) by the ratio h

C4 and test the prediction that the values of h

C4 in

the high- tech group of MDCs, are drawn from a distribution whose support is bounded

away from zero. A conventional approach in modeling draws from a distribution that

has a finite lower bound is to model the observations h

C4 as drawn from a Weibull

distribution. In particular, the three parameters Weibull distribution is defined as in

Section 4.1. We check if the observations h

C4 can actually be well described by a

Weibull distribution and we conclude that modeling the observations h

C4 as a three-

parameter Weibull distribution is an acceptable assumption for both high and low- tech

MDCs groups11.

Based on this result, we can now turn to test the null hypothesis that the location

parameter of the Weibull distribution (which, as mentioned, represents the lower bound)

is equal to zero in the high- tech MDCs group. In order to test this hypothesis, we could

follow the approach (Smith (1985)) used in Section 4.1 or an alternative approach

(Mann, Scheuer and Fertig (1973)). The former consists in testing directly the

hypothesis that 0� = , subject only to the assumption that the observations are drawn

from a Weibull distribution with unknown shape (� ) and scale (� ) parameters. As this

method allows to bypass the estimation of the shape and scale parameters of the

distribution and to construct directly a confidence interval for the lower bound, it

involves less computational problems than the first approach. Since we are only

interested in the location parameter, the Mann-Scheuer-Fertig test appears to be more

11 In order to check whether the observations

hC4 can actually be well described by a Weibull distribution

for some parameter values (� , � , � ), we choose some reasonable value for the location parameter �

(lower bound) and test whether the residuals �4 −=h

CR , can be well described as a two-parameter

Weibull distribution. After ranking the R ’s in ascending order, we define their cumulative distribution

)(RF and we call ���

����

�

−=

)(11

lnRF

y . We then plot y against Rln distinctly for high-tech and low-tech

MDC groups. In both cases the points roughly lie on a straight line (for simplicity, we omit to show the

15

expedient for the present context.

In general terms, the Mann-Scheuer-Fertig test relies on the properties of the order

statistics niX , of a sample drawn from an extreme value distribution, that is the log

transformation of a Weibull distribution. Denote with T a random variable drawn from

a two-parameter Weibull distribution (that is, as said before, when 0� = ). Then, the

variable TX ln= distributed as an extreme value distribution is defined by:

���

��� −−−=≤

bu

expexp1)(Probx

xX (4)

where �lnu = and �/1b = respectively denote the location and the scale parameters of

the extreme value distribution. Now consider the order statistic niX , of a sample of

n observations drawn from the distribution X . In the case that 0� = , as stressed by

Mann, Scheuer and Fertig (1973), “the right-hand tail of the extreme value density

function is ‘shorter’ than that of the usual appropriate alternative distributions, while

that of the left-hand tail is ‘longer’… Thus the ‘upper’ gaps between successive order

statistics will tend to be smaller than the ‘lower’ gaps”. This is not true if the sample is

drawn from the distribution for which 0� > , since in that case the left-hand tail is

attenuated.

As shown by Pyke (1965), the spacings nini XX ,,1 −+ between ranked observations

from any distribution having a density are asymptotically exponential and

asymptotically independent. It follows that the ratios:

)()( 1,1

1,1

++

++−−

=ini

inii XEXE

XXl (5)

are asymptotically exponentially distributed with mean one and asymptotically

independent. Denote the ratios il as leaps and the numerators 1,1 ++ − ini XX as gaps. To

calculate the expected value of order statistics for the standardized extreme value

distribution with 0� = and 1b = we can resort to the published tables of the expected

values of the reduced extreme-value order statistics (Mann, Scheuer and Fertig (1973),

Balakrishnan and Chan (1992)). These values correspond to the expected values of the

graphics). Therefore, we can conclude that modeling the observations h

C4 as a three-parameter Weibull

distribution is an acceptable assumption for both groups of observations.

16

transformed order statistics b/)u( ,, −= XY nini . For each successive pair of

observations in the sample, calculate the ratio:

)()('

,,1

,,1

nini

ninii YEYE

YYl

−−

=+

+ (6)

Now partition in two the sample of il ' (in number 1n − ) by setting r as the integer part

of 2)1n( − . The test statistic is given by the ratio of the sum of leaps in the top half of

the sample to the sum of leaps over the whole sample, that is:

�

�

= −

=

−

−=1

1

1

'

'

n

ii

n

rnii

l

l

S (7)

Considering that S is asymptotically distributed as a Beta distribution, the observed

value of S can be compared with percentile values of the Beta distribution with

parameters 2)1n( − and 2)1n( − for n odd or 2)2n( − and 2n for n even12. If the

calculated value of S exceeds its tabulated percentile the hypothesis, that the location

parameter � of the associated Weibull distribution is equal to zero, is rejected.

Now apply this procedure to the data from the Italian National Health Service described

above. For the group of 21 high-tech MDCs the computed value of the test statistic S

turns out to be equal to 0.712. Therefore for those MDCs the null hypothesis that the

lower bound is equal to zero can be rejected with a confidence of 95 %– 99 % and this

result is consistent with the empirical prediction c) by Sutton. Otherwise, when the

control group of 24 low-tech MDCs is considered, the computed value of S equals

0.532. This means that we can reject the null hypothesis with a confidence level inferior

to 75%: therefore, the null hypothesis that the lower bound is equal to zero cannot be

rejected, again consistently with the empirical prediction d).

17

6. Final remarks

A key feature of Sutton's theory is that industries evolve to distinct market

configurations in terms of concentration depending upon whether the markets have a

large size, whether the corresponding products are essentially homogeneous, whether

they are differentiated by research and development (R&D) and advertising. This paper

aims to test empirically the consistency of the technological profiles and market

structure of the health care sector in Italy with Sutton's predictions. The results of the

analysis offer some empirical support in differing relationships between industry

concentration levels and technological characteristics across health care productions.

However, the relevance of this outcome needs to be validated by further research in

order to overcome some limitations affecting the initial analysis. An interesting

perspective that should be adequately investigated is to focus on health interregional

mobility, that is, to confine the analysis only to the sub-sample of health services

provided to patients not resident in the Region where those services were produced.

Testing Sutton’s predictions on mobile patients only, would allow the investigation of

the robustness of these predictions.

12 For samples including less than 25 observations the approximation provided by the Beta distribution becomes unsatisfactory. However, Monte Carlo estimates for small samples are reported by Mann, Scheuer and Fertig (1973).

18

References

Bain, Joe S. (1956), Barriers to New Competition, Cambridge, Harvard University

Press. Balakrishnan, Narayanaswamy and Ping S. Chan (1992), "Extended Tables of Means,

Variances and Covariances of Order Statistics from the Extreme Value Distribution for Sample Size up to 30", Report, Department of Mathematics and Statistics, McMaster University, Hamilton, Canada.

Buzzacchi, Luigi and Tommaso L. Valletti (2003), “Firm Size Distribution: Testing the "Independent Submarkets Model" in the Italian Motor Insurance Industry”, London School of Economics, mimeo.

Degli Esposti Giandomenico et.al (1996), "Matrici di mobilità per DRGs: analisi descrittiva ed applicazioni per la programmazione e le politiche sanitarie regionali", Mecosan, 19, 53-62.

Fabbri, Daniele and Gianluca Fiorentini (1996), "Mobilità e consumo sanitario: metodi per la valutazione di benessere", Mecosan, 19, 37-52.

Giorgetti, Maria L. (2000), "La verifica empirica del modello di Sutton per i settori manufatturieri italiani", L'industria, 21, 543-564.

Giorgetti, Maria L. (2003), "Lower Bound Estimation - Quantile Regression and Simplex Method: an Application to Italian Manufacturing Sectors", Journal of

Industrial Economics, 51, 113-120. Gruber, Herald (2002), “Endogenous Sunk Costs in the Market for Mobile

Telecommunications: the Role of Licence Fees", Economic and Social Review, 33, 55-64.

de Juan, Rebeca (2003), "The Independent Submarkets Model: an Application to the Spanish Retail Banking Market", International Journal of Industrial Organization, 21, 1461-1487.

Lyons, Bruce R. and Catherine Matraves (1996), "Industrial Concentration", in Stephen Davies and Bruce R. Lyons (eds.), Industrial Organization in the European Union:

Structure, Strategy and the Competitive Mechanism, Oxford University Press, 86-104.

Mann, Nancy R., Ernest M. Scheuer and and Kenneth W. Fertig (1973), "A New Goodness-of-Fit Tst for the Two-Parameter Weibull or Extreme-Value Distribution with Unknown Parameters", Communications in Statistics, 2, 383-400.

Marin, Pedro L. and Georges Siotis (2002), Innovation And Market Structure: An

Empirical Evaluation Of The 'Bound Approach' In The Chemical Industry, CEPR Discussion Paper, 3162, January.

19

Matraves, Catherine (1999), "Market Structure, R&D and Advertising in the Pharmaceutical Industry", Journal of Industrial Economics, vol. 47, 169-194.

Pyke, Roland (1965), "Spacings", Journal of Royal Statistical Society, B 27, 395-449. Robinson, William T. and Jeongwen Chiang (1996), "Are Sutton's Predictions Robust?:

Empirical Insights into Advertising, R&D, and Concentration", Journal of

Industrial Economics, 44, 389-408. Shaked, Avner and John Sutton (1982), "Relaxing Price Competition through Product

Differentiation", Review of Economic Studies, 49, 3-13. Shaked, Avner and John Sutton (1987), "Product Differentiation and Industrial

Structure", Journal of Industrial Economics, 36, 131-146. Spampinato, Grazia Concetta (2001), "Mobilità sanitaria regionale e federalismo",

Politiche sanitarie, 2, 44-56. Smith, Richard L. (1985), “Maximum Likelihood estimation in a class of non-regular

cases”, Biometrika, 72, 67-92. Smith, Richard L. (1994), “Nonregular Regression”, Biometrika, 81, 173-183. Sutton, John (1989), "Endogenous Sunk Costs and Industrial Structure"", in G. Bonanno

and D. Brandolini (eds.), Market Structure in the New Industrial Economics, Oxford, Oxford University Press.

Sutton, John (1991), Sunk Costs and Market Structure, Cambridge, MIT Press. Sutton, John (1998), Technology and Market Structure, Cambridge, MIT Press. Ugolini, Cristina and Daniele Fabbri (1998), "Mobilità saniatria ed indici di entropia",

Mecosan, 26, 9-24.

Tab. 1 MDCs description

# % # % # % # % # % # %1 Nervous system diseases 734336 7.95 172201 5.70 35 7.40 34 7.41 1284 4.91 856 5.422 Eye diseases 377790 4.09 299627 9.91 13 2.75 13 2.83 1015 3.89 676 4.283 Ear, nose, mouth and throat diseases 401040 4.34 96928 3.21 26 5.50 26 5.66 1145 4.38 761 4.814 Respiratory apparatus diseases 601622 6.52 97971 3.24 29 6.13 29 6.32 1198 4.59 741 4.695 Cardio-vascular apparatus diseases 1303341 14.11 221505 7.33 44 9.30 40 8.71 1242 4.75 823 5.216 Digestive system apparatus 974565 10.55 177934 5.89 40 8.46 39 8.50 1183 4.53 815 5.167 Hepatobiliary and pancreatic diseases 371101 4.02 102369 3.39 18 3.81 18 3.92 1152 4.41 743 4.708 Muscle-skeletal system diseases and diseases of connective tissue 1166688 12.63 285063 9.43 50 10.57 49 10.68 1258 4.82 864 5.479 Skin, subcutaneous tissue and breast diseases 368064 3.99 241705 7.99 28 5.92 28 6.10 1181 4.52 836 5.2910 Endocrine, nutritional and metabolic diseases 201828 2.19 174089 5.76 17 3.59 17 3.70 1174 4.49 753 4.7611 Kidney and urinary system diseases 424576 4.60 142067 4.70 32 6.77 31 6.75 1164 4.46 777 4.9212 Male reproductive system diseases 172739 1.87 70290 2.32 18 3.81 18 3.92 1109 4.24 759 4.8013 Female reproductive system diseases 308454 3.34 145298 4.81 17 3.59 17 3.70 1081 4.14 731 4.6214 Gestation and birth 758348 8.21 152461 5.04 15 3.17 15 3.27 751 2.87 547 3.4615 Neonatal period diseases 146001 1.58 5301 0.18 6 1.27 6 1.31 740 2.83 343 2.1716 Diseases of the blood, of the hemopoietic organs and of the immune system 90835 0.98 78601 2.60 8 1.69 7 1.53 1138 4.36 765 4.8417 Myelo-proliferative diseases 259117 2.81 334881 11.08 17 3.59 17 3.70 1144 4.38 788 4.9918 Infectious diseases 76803 0.83 15858 0.52 9 1.90 9 1.96 1088 4.16 603 3.8219 Mental diseases 226231 2.45 53662 1.77 9 1.90 9 1.96 1148 4.39 629 3.9820 Alcohol/drugs abuse and induced organic mental diseases 33457 0.36 1752 0.06 5 1.06 5 1.09 910 3.48 200 1.2721 Traumatisms, poisonings and toxic effects of medicines 83756 0.91 16352 0.54 17 3.59 17 3.70 1133 4.34 678 4.2922 Burns 6694 0.07 480 0.02 6 1.27 3 0.65 621 2.38 122 0.7723 Factors affecting health and health services demand 122166 1.32 113428 3.75 7 1.48 7 1.53 1185 4.54 777 4.9224 Serious multiple traumatisms 10328 0.11 38 0.00 4 0.85 2 0.44 694 2.66 24 0.1525 HIV infections 14428 0.16 23378 0.77 3 0.63 3 0.65 387 1.48 195 1.23

Total 9234308 100.00 3023239 100.00 473 100.00 459 100.00 26125 100.00 15806 100.00

number of hospitals

day-hospital services hospitalisation services day-hospital services

number of services number of DRGs

MDC descriptionMDC

identification number

hospitalisation services day-hospital services hospitalisation services

Tab. 2 Technogical intensity, homogeneity, market concentration and size of the MDCsMDC description tech h C 4 size

high

- tec h

MD

Cs

2d - Eye diseases 0.0772 0.6788 0.0472 20.27892h - Eye diseases 0.0770 0.5727 0.0818 23.045112h - Male reproductive system diseases 0.0718 0.1975 0.0325 19.842412d - Male reproductive system diseases 0.0700 0.1815 0.0583 18.886811h - Kidney and urinary system diseases 0.0694 0.1670 0.0429 20.808711d - Kidney and urinary system diseases 0.0675 0.1483 0.0867 19.757822h - Burns 0.0671 0.4052 0.2018 16.519324h - Serious multiple traumatisms 0.0666 0.3513 0.0650 16.539322d - Burns 0.0661 0.5292 0.4729 12.347624d - Serious multiple traumatisms 0.0659 0.9737 0.3947 7.275223h - Factors affecting health and health services demand 0.0657 0.4618 0.0793 19.87091d - Nervous system diseases 0.0655 0.3136 0.0787 19.712223d - Factors affecting health and health services demand 0.0652 0.6634 0.1760 20.05905h - Cardio-vascular apparatus diseases 0.0651 0.1178 0.0411 21.81358h - Muscle-skeletal system diseases and diseases of connective tissue 0.0647 0.2276 0.0421 21.52341h - Nervous system diseases 0.0647 0.2033 0.0451 21.38045d - Cardio-vascular apparatus diseases 0.0641 0.2711 0.0848 19.98178d - Muscle-skeletal system diseases and diseases of connective tissue 0.0640 0.1218 0.0532 19.94763h - Ear, nose, mouth and throat diseases 0.0633 0.1686 0.0386 21.228915h - Neonatal period diseases 0.0632 0.2620 0.0589 19.01633d - Ear, nose, mouth and throat diseases 0.0630 0.1726 0.1140 19.52959h - Skin, subcutaneous tissue and breast diseases 0.0628 0.1047 0.0681 20.56319d - Skin, subcutaneous tissue and breast diseases 0.0626 0.2910 0.0709 19.938913h - Female reproductive system diseases 0.0625 0.4182 0.0490 20.03166h - Digestive system apparatus 0.0623 0.1191 0.0299 21.20287h - Hepatobiliary and pancreatic diseases 0.0622 0.1750 0.0376 20.380613d - Female reproductive system diseases 0.0621 0.3691 0.0501 19.028221h - Traumatisms, poisonings and toxic effects of medicines 0.0621 0.1873 0.0649 19.205614h - Gestation and birth 0.0620 0.3576 0.0426 20.412114d - Gestation and birth 0.0620 0.7463 0.0710 18.68196d - Digestive system apparatus 0.0619 0.2509 0.0720 19.593421d - Traumatisms, poisonings and toxic effects of medicines 0.0610 0.3233 0.1918 17.61254h - Respiratory apparatus diseases 0.0608 0.1734 0.0430 21.056010h -Endocrine, nutritional and metabolic diseases 0.0606 0.2700 0.0693 19.964418h - Infectious diseases 0.0606 0.3323 0.0417 19.130725h - HIV infections 0.0606 0.5989 0.2412 18.05527d - Hepatobiliary and pancreatic diseases 0.0605 0.5580 0.1321 19.576225d - HIV infections 0.0605 0.8695 0.3403 16.900218d - Infectious diseases 0.0604 0.2843 0.1399 17.39704d - Respiratory apparatus diseases 0.0602 0.2022 0.1029 19.373916h - Diseases of the blood, hemopoietic organs and immune system 0.0599 0.4999 0.0448 19.049416d - Diseases of the blood, hemopoietic organs and immune system 0.0597 0.4684 0.1341 19.212115d - Neonatal period diseases 0.0597 0.5646 0.2473 15.765010d - Endocrine, nutritional and metabolic diseases 0.0592 0.3730 0.1107 20.164417h - Myelo-proliferative diseases 0.0568 0.2485 0.0819 21.216517d - Myelo-proliferative diseases 0.0559 0.6216 0.1324 20.954420d - Alcohol/drugs abuse and induced organic mental diseases 0.0531 0.5782 0.2586 14.243920h - Alcohol/drugs abuse and induced organic mental diseases 0.0525 0.5886 0.0936 18.002819d - Mental diseases 0.0503 0.2261 0.2169 19.141919h - Mental diseases 0.0470 0.5001 0.0319 20.5478average value 0.0626 0.3698 0.1101 19.1153

low

-tech

MD

Cs

high

- tec h

MD

Cs

Fig. 1 Determinants of αααα

�������������� ��������

�������������������������

��������������������

���������������� �

���������������������������

�������������������

β → α (β, σ) ← σ

����

����������

concentration

market size

Fig. 2 Lower bound for concentration in exogenous sunk industries

concentration

market size

Fig. 3 Lower bound for concentration in endogenous sunk industries

h

concentration

Fig. 4 Lower bound for concetration in low R&D intensity industries

concentration

h

Fig. 5 Lower bound for concentration in high R&D intensity industries

Fig.6 Technological intensity, homogeneity, market size and market concentration in the high-tech MDCs (% deviation from the average)

-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

9d - Skin, subcutaneous tissue and breast diseases

9h - Skin, subcutaneous tissue and breast diseases

3d - Ear, nose, mouth and throat diseases

15h - Neonatal period diseases

3h - Ear, nose, mouth and throat diseases

8d - Muscle-skeletal system diseases and diseasas of connective tissue

5d - Cardio-vascular apparatus diseases

1h - Nervous system diseases

8h - Muscle-skeletal system diseases and diseseas of connective tissue

5h - Cardio-vascular apparatus diseases

23d - Factors affecting health and health services demand

1d - Nervous system diseases

23h - Factors affecting health and health services demand

24d - Serious multiple traumatisms

22d - Burns

24h - Serious multiple traumatisms

22h - Burns

11d - Kidney and urinary system diseases

11h - Kidney and urinary system diseases

12d - Male reproductive system diseases

12h - Male reproductive system diseases

2h - Eye diseases

2d - Eye diseases

tech h C4 size

Fig.7 Technological intensity, homogeneity, market size and market concentration in the low-tech MDCs (% deviation from the

average)

-1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00

19h - Mental diseases

19d - Mental diseases

20h - Alcohol/drugs abuse and induced organic mental diseases

20d - Alcohol/drugs abuse and induced organic mental diseases

17d - Myelo-proliferative diseases

17h - Myelo-proliferative diseases

10d - Endocrine, nutritional and metabolic diseases

15d - Neonatal period diseases

16d - Diseases of the blood, hemopoietic organs and immune system

16h - Diseases of the blood, hemopoietic organs and immune system

4d - Respiratory apparatus diseases

18d - Infectious diseases

25d - HIV infections

7d - Hepatobiliary and pancreatic diseases

25h - HIV infections

18h - Infectious diseases

10h -Endocrine, nutritional and metabolic diseases

4h - Respiratory apparatus diseases

21d - Traumatisms, poisonings and toxic effects of medicines

6d - Digestive system apparatus

14d - Gestation and birth

14h - Gestation and birth

21h - Traumatisms, poisonings and toxic effects of medicines

13d - Female reproductive system diseases

7h - Hepatobiliary and pancreatic diseases

6h - Digestive system apparatus

13h - Female reproductive system diseases

tech h C4 size

Fig. 8 Market concentration and market size in high - tech MDCs

-9

-8

-7

-6

-5

-4

-3

-2

-1

0 1.9 2.4 2.9 3.4 3.9

log size

C4*

lower bound MDCs

Fig. 9 Market concentration and market size in low - tech MDCs

-9

-8

-7

-6

-5

-4

-3

-2

-1

0 2.5 2.7 2.9 3.1 3.3 3.5 3.7 3.9 4.1

log size

C4*

low-tech lower bound low-tech MDCs high-tech lower bound

3d

15h 3h 8d

5d 1h 8h 5h

23d

1d 23h

24d

22d

24h

22h

11d 11h

12d 12h

2h 2d

0

.1

.2

.3

.4

.5

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

C4

Fig. 10 Market concentration and product homogeneity in high-tech MDCs

h

13d 21h

14h 14d 6d

21d

4h 10h

18h

25h

7d

25d

18d 4d

16h

16d

15d

10d 17h

17d

20d

20h

19d

19h 0

.1

.2

.3

.4

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

C4

Fig. 11 Market concentration and product homogeneity in low-tech MDCs

h