Hospital competition, hospital efficiency and the impact of spatial interaction effects in Turkey

Hospital competition, hospital efficiency and

the impact of spatial interaction effects in

Turkey

1413309

MSc Student Economics, Faculty of Economics and Business, University of Groningen Master’s Thesis Economics

University of Groningen

Department of Economics, Econometrics and Finance Supervisor: Prof. dr. J.P. Elhorst

ABSTRACT

The common approach to assess the performance of public enterprises like hospitals consists of two stages. To determine whether resources are properly utilized, the efficiency in the use of resources is explored first by means of data envelopment analysis (DEA). The calculated DEA scores are then regressed against environmental variables reflecting features of organizational design and local circumstances. Whereas previous studies used simple OLS regression models for this purpose, treating hospitals as being independent from each other, we find empirical evidence in favour of spatial interaction effects both in the dependent variable and the independent variables. To model and to estimate the magnitude of these interaction effects, we apply a spatial Durbin model with controls for hospital fixed effects and time-period fixed effects, using a panel of 746 hospitals in Turkey in 2005, 2006, 2007 and 2008. We find that the relative location of a hospital, the effect of being located closer or further away from hospitals in other towns, matters in that a change in some environmental variables not only has a significant direct effect on the efficiency level of a hospital itself, but also a significant indirect effect on the efficiency level of other hospitals. We also find evidence in favour of a break-even point at the positive effect of scale economies and the negative effect of too much market power on efficiency.

Preface

Since I was a child, I was interested in the health care sector. I grew up in a family of doctors and nurses and because of them I developed a lot of feeling with this sector during my childhood. When I started studying economics, I had not realized that the health care sector would be such an important economic subject as it is nowadays. Moreover, the sector is a very important subject in modern economics, which gave me the trigger to search in the direction of the health care sector for the subject of my thesis.

This thesis would not have been possible without the guidance and support of several individuals. First and foremost I would like to express my gratitude towards my supervisor, prof. dr. J.P. Elhorst, who has been an inspiring and helpful guide during the writing process of this thesis. With critical remarks when necessary and a lot of patience and understanding, prof. dr. J.P. Elhorst encouraged me to finish this final piece of work. I also want to thank his Turkish colleague, dr. M. Ensar Yesilyurt for his expertise on the Data Envelopment Analyses (DEA) and for providing the efficiency scores resulting from DEA, which was an important input variable in the model we used.

I would like to thank my family and close friends for their support, and especially my father, who was telling me over and over again that the clock was ticking. ‘It is five to twelve’ was his favourite quote the last few months. Also Jack Johnson for providing his music. Without his soothing melodies I would not have survived this tribulation.

This research and the associated results are a very current topic in the economy nowadays. It is very interesting to see that the results of the research correspond with my presumption that a very high degree of specialization in the health care sector is harmful for the efficiency. While one can see that the trend in the health care sector, stimulated by the government, is in the direction of specialization and concentration. This shows that it is important for the sector and for government policy to securely guard the break-even point of the relation between specialization and concentration on the one hand and efficiency on the other hand.

1. Introduction

This study measures the efficiency level of hospitals in Turkey and especially the influence of spatial interaction effects among Turkish hospitals within certain areas. We use data from 746 hospitals over 4 years and are interested in neighbourhood relationships between these different hospitals and the extent to which they influence each other’s efficiency levels. The hypothesis being tested in this paper is whether hospitals do compete with each other.

This research contributes to the economic literature because previous studies only use simple OLS regression models to draw a conclusion on the scores obtained from DEA, while we use a spatial interaction model to set out the competitive structure among hospitals. Previous studies treat hospitals as being independent from each other, but in this study we analyse competitive relationships dependent on the distance between hospitals. The evidence we find from the results of the model can also be used to reinterpret current policy questions of the health care sector.

The health care structure in Turkey is highly complex. During our observation period, there were three different agencies that managed the financial side of the Turkish medical care system. The SSK which covers private sector employees, Bag-Kur which covers the self-employed and Emekli Sandik, a pension fund, which covers retired officers. These programs were inefficient and it was difficult for these agencies to communicate with each other when people move from one system to another system, for example, when they retire. The system also uses a Yesil Kart also known as Green card. This card gives the poor, homeless and unemployed access to free healthcare. There is a significant lack of human recourses in the health care sector in Turkey relative to the population. The Physician density was half of the OECD average in 2006 and the nurse density was only one-fifth of the OECD average. Furthermore, besides the lack of human resources, the resources where inadequately distributed among the areas (especially before 2003).1 About the percentages of people who are covered by a health insurance are serious contradictions. According to the Turkey Statistical Institute, 64% of the population is covered by health insurance, while the ratio is 85% according to National Planning Organization. Especially the percentages of the coverage of SSK and Bag-Kur are very

deviating. Their total coverage is 46.2% according to Turkey Statistical Institute2 and 68.6% according to the National Planning Organization. In 2005, 5.4% of GDP was used for healthcare. In 2008 the expenditures increased to 6.1%. More important to show is the comparison with the average of the European Union. In 2005 the healthcare expenditure per capita was 383.8 in Turkey compared to 2,648.3 in the European Union.

Studies to measure hospital efficiency are widespread because public pressure and executive interest for cost containment ask for monitoring the organizational causes of excess resource utilization. Efficiency measurement was a first step towards the evaluation of a coordinated health system, and is one of the most important means to control for a rational distribution of human capital and economic resources.

Data envelopment analysis (DEA) has proven to be an effective tool to measure effectiveness in the health care sector and it has been used all over the world. It was first used to measure hospital efficiency in the United States for more than 25 years ago. Efficiency is a measure to determine to what extent an organization functions as it should to create the largest possible output with a fixed number of inputs, or to what extent the allocation of inputs leads to the lowest possible costs and creates the highest possible profit. A firm is technically efficient if it uses a minimum amount of resources as input to create a fixed amount of output, or in other words, uses a fixed amount of input to create a maximum feasible output. Another variation of efficiency is allocative efficiency, which is more complicated than technical efficiency because it requires information on the relative prices of inputs and outputs. An organization is allocative efficient if it produces a given level of outputs at the lowest possible cost, which is the same as maximizing benefits for a given cost constraint. The difference here is that technical efficiency implies a minimum of wasted resources and does not imply benefit maximizing or minimizing costs. Combining the technical efficient and allocative efficient measures will provide a measure of total economic efficiency

Techniques to measure efficiency can be divided into four classes. They can be parametric or non-parametric, and in addition can be stochastic or deterministic. Each set of techniques has its own strengths and weaknesses. Whereas parametric techniques are

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based methods in general and assume a specific functional form for the frontier, non-parametric techniques do not have such a specific functional form. Parametric techniques may suffer from model misspecification, because the efficiency scores are sensitive to distributional assumptions regarding the error term. Deterministic measuring techniques do not contain a random error component, and therefore may be sensitive to extreme observations since the assumption is that the observed distance to the frontier is due to inefficiency. Stochastic models on the other hand are less sensitive to extreme observations since part of the distance to the frontier can be attributed to random error. In this paper we use a deterministic, non-parametric DEA approach to determine the efficiency of the use of resources in hospitals. The mathematics behind this DEA analysis will be explained in section 3.

The following step is to regress the calculated DEA scores on environmental variables reflecting features of organizational design and local circumstances. Whereas previous studies used simple OLS regression models for this purpose, treating hospitals as being independent from each other, this paper tests for spatial interaction effects, both in the dependent variable and in the independent variables. In the spatial econometric literature there is growing interest for such relationships based on spatial panels. Elhorst (2012) explains three popular spatial panel data models, the spatial lag model, the spatial error model and the spatial Durbin model. Each of the models can be used under different circumstances and an econometric researcher should ask himself which type of spatial interaction effects should be accounted for; a spatially lagged dependent variable, spatially lagged independent variables, a spatially autocorrelated error term, or maybe a combination of these three. These spatial interaction models require a spatial weights matrix that reflects the intensity of the geographic relationship between observations in a neighbourhood, e.g., the distances between neighbours, the lengths of shared borders, or whether they fall into a specified directional class such as "west". Furthermore, it is important to determine whether or not spatial-specific and/or time-specific affects should be accounted for and if so, whether they should be treated as fixed or as random effects. For the data in this paper, the spatial specific effects will be defined as hospital fixed effects.

model is the best fitting model. The rest of this paper is organized as follows. In section 2 the used data will be described, therefore we have to give a little information on the organization of hospitals in Turkey. In section 3 the mathematics behind the DEA will be described. We will test whether we have to expand the model with cross-sectional or time-period fixed effects where after we will search for interaction effects using the LM-tests. Eventually, the search for the right spatial panel data model and finally the mathematics behind the Spatial Durbin model, which is shown to be the best fitting model in this paper. In section 4 we will analyse the results from the Spatial Durbin model and will try to find an answer to the hypothesis, whether hospitals compete. Therefore we have to find the direct and indirect (spill over) effects between hospitals nearby. If hospital A scores very well, do neighbour hospitals score automatically worse? Which can be interpreted as competition. Or do neighbour hospitals profit from each other’s knowledge? Then we expect to find similar efficiency scores between neighbours, which can be explained as collaboration instead of competition. In section 5 we give concluding remarks to the research.

2. Data

For the spatial interaction model we have included a variable representing the urbanization and development level of an area, Development index (DI), calculated by the State Planning Institution (SPI). This variable is an indication of the economic and social development of the towns where the hospitals are located. The variable will be used as a dummy variable from the index of the SPI. Another variable to put socio-economic structure into the model is using a variable as the income in provinces. In the literature, for example Chen et al. (2005) and Bates et al. (2006), the variable income in cities or provinces in which the hospitals are located is used to capture the socio-economic structure. In this study we use green card holders as a reference for socio-economic structure. This variable is interesting and gives a better representation of the poverty in different areas. We use a variable for population density (DEN) in this study to be able to test whether population density instead of population causes an increase in demand for the hospital services due to urbanization.

Finally, another group of variables used in the literature to analyse efficiency of hospitals is the competition structure and market power. Matarrodona and Junoy (1998), Bates (2006) and Nahra et al. (2009) used the number of hospitals in local markets for this purpose. Furthermore, the Herfindahl Index (HI) and/or market share has been used in the literature in order to analyse the market power according to the demand for services and the used number of beds. The Herfindahl index is a measure of the size of the hospital in relation to the total health care sector and an indicator of the amount of competition among hospitals. The Herfindahl index is defined as the sum of the squares of the market shares of the 50 largest hospitals (or summed over all the hospitals if there are fewer than 50) within the sector, where the market shares are expressed as fractions. The result is proportional to the average market share, weighted by market share. As such, it can range from 0 to 1.0, moving from a huge number of very small firms to a single monopolistic producer. Increases in the Herfindahl index generally indicate a decrease in competition and an increase of market power, whereas decreases indicate the opposite.

Again Matarrodona and Junoy (1998) and Lynch and Ozcan (1994) and Cellini et al. (2000) used a Herfindahl index based on beds and Rosko and Chilingirian (1999), Cellini et al. (2000) and Chen et al. (2005) used a Herfindahl index based on patients3. Additionally, Lee et al.                                                                                                                          

(2009) used the number of beds to measure capacity. In our study, two different HI have been tested: The number of ambulatory offered by the hospital is Herfindahl index (HIambulatory) and the number of beds in a hospital is Herfindahl index (HIbed). This HIambulatory describes the relative simple treatments where patients are treated outpatient or policlinic in a hospital. HIbed describes the more complicated treatments in a hospital where patients need to stay overnight.

3. Theoretical structure and model analyses

3.1 DEA analyses

As mentioned above, DEA has proven to be an ideal method for cases with several outputs, therefore the method is considered to be a suitable method for this analysis. More than twenty years ago Sherman (1984) first applied DEA to measure the efficiency of seven US hospitals. Since then it has been applied many times to several studies for health care organisations. The main advantages to use DEA for the health care sector are its flexibility, versatility and it is easiness to use. DEA requires no information on relative prices and the model can easily accommodate multiple inputs and outputs. Of course every model also has its weaknesses and practical limitations. For DEA, for example, the lack of restrictions on prices can lead to difficulties. When the number of observations is small relative to the sample size, efficiency scores can be overrated. It might be possible that a large proportion of organisations may be identified as efficient due to a lack of degrees of freedom. It then might be necessary to discriminate among the efficient units and look at information on the relative values of the inputs and outputs.

A number of additional techniques have been developed over time to improve and extend DEA toward the measurement of both allocative and technical efficiency. Examples of the studies are the cone-ratio approach of Charnes et al. (1989) and the assurance-region approach                                                                                                                                                                                                                                                                                                                                                                                                        

(AR) of Thompson et al. (1986). These approaches impose reasonable bounds on the input and output weights in the equations (1) and (2) that will be introduced below.

When relative prices are known, allocative efficiency can be estimated using allocative efficiency DEA models, as first developed by Färe et al. (1985). Numerous extensions and diagnostics have been developed to address the limitations of deterministic methods. According to Banker (1993), stochastic DEA is a variation of the original DEA model that can separate inefficiency from random error.

This section explains the basic DEA model following O’neill et al. (2008), and the adjusted DEA model used in this study. DEA is the non-parametric mathematical programming approach to frontier estimation. To explain DEA intuitively we consider an example with our input variables: specialist physician, practitioner physician and number of beds and our output variables: the number of ambulatory visits, the number of small operations, the number of medium operations, the number of big operations and the number of births. The most efficient hospital for example is hospital X and has an efficiency score of 100% while a less efficient hospital, hospital Y, has an efficiency score of 70%. This means that hospital Y should be able to produce the same output with 70% of the initial input if it would operate as efficient as hospital X does.

The basic DEA model, also known as the CCR ratio model named after it’s inventors Charmes, Cooper en Rhodes (1978), can be formulated as follows: suppose there are n decision making units (DMU’s), who use m inputs to produce s outputs. Let xij be the amount of input i

(i= 1,…, m) used by DMUj ( j = 1,…, n); and let yrj be the amount of output r (r = 1,…., s)

produced by DMUj ( j = 1,…, n). Note that, in all DEA models, xij and yrj are treated as

constants. The variables ur (r = 1,…, s) and vi (i=1,…, m) are weights. The technical efficiency

of the representative hospital (DMU0)is then given by:

max(u, v) r=1u s

∑

∑

∑

∑

The set of constraints in equation (2) limits all efficiency scores to a maximum value of unity. The variables ur and vi are stated in ‘efficiency units’ that are obtained by solving the

maximization problem; it evaluates the behaviour of DMU0 relative to the performance of all

The CCR ratio model generalizes the definition of efficiency from its usual one-output-to-one-input ratio in order that the resulting measure could include multiple outputs and multiple inputs without recourse to externally imposed weights. The CCR ratio model provides a basis for DEA with longstanding approaches to efficiency evaluation in other fields, in particular welfare economics and its concept of ‘‘Pareto–Koopmans’’ efficiency which is similar to the concept of technical efficiency mentioned in section 1.

Accoring to Charmes, Cooper en Rhodes (1978) the model in equation (1) is a fractional programming problem. By fixing the denominator, the model will transform into an input orientated form and can be explained as follows (the µr results from the ur in equation 1)

0 1 max r s r ry

∑

∑

∑

∑

An output-oriented model results if, in equation (1), the numerator is fixed to 1 and the denominator is minimized. To come to the output-orientated model, we first take the dual problem of equations (4)-(7), which result in the input-oriented dual form of DEA, as follows:

subject to

∑

∑

λ

Variable θ0 represents the radial (technical) efficiency of DMU0 and variable λj is the

weight placed by DMU0 on DMUj. Those DMUs for which λj > 0 include DMU0’s efficient

reference set. Movement toward the best practice frontier is achieved by reducing current levels of inputs while maintaining the same level of outputs. DMUs for which the optimal solution θ< 1 are inefficient.

If the goal is to increase outputs for a fixed quantity of inputs we can use the output-orientated model. The corresponding dual form of the output-oriented model is given by

max φ (12) subject to

∑

∑

λ

The majority of DEA studies in health care, including this one, use the input-oriented model, equations (9)-(11) since the goal is to reduce costs rather than to increase the volume of services provided. The CCR model in equations (9)-(11) assumes constant returns-to-scale (CRS), but in this study we have to use variable returns-to-scale (VRS). That is because limitations as imperfect competition and financial difficulties prevent hospitals from working on an optimal scale. The CRS method will overlap technical and scale efficiencies, while the use of VRS enables us to differentiate between the values of technical and scale efficiency and, therefore, will be accurately in measuring pure efficiency.

The model can be easily modified to operate with variable returns-to-scale (VRS) by adding the following convexity constraint:

∑

This formulation is called, alternatively, the VRS model and the BCC model, after its developers, Banker, Charnes, and Cooper (1984).

The efficiency scores obtained from the data envelopment analyses will be used as the dependent variable in the spatial interaction model therefore we will not discuss these results in detail here or in the next section. The results will be included in the discussion of the results of the spatial interaction model in section 4.

3.2 Spatial interaction

lagged dependent variable and spatially lagged independent variables. For detailed information of the different models we refer to Elhorst (2012).

The first step is to run an ordinary least squares (OLS) model and include spatial fixed effects (hospital fixed effects) and time period fixed effects. Hospital fixed effect control here for all space-specific time invariant variables whose omission could bias the estimates in a typical cross sectional study. Time-period specific effects control for all time-specific effects whose omission could bias the estimates in a typical time-series study. Table 1 shows that both the hospital fixed effects and the time-period fixed effects are jointly significant.

In an OLS model, spatial dependence can be incorporated in two ways: as an additional regressor in the form of a spatially lagged dependent variable (Wy), or in the error structure (E[εiεj] ≠0). To test for spatial dependence, a spatially lagged dependent variable or spatial error

autocorrelation, we use an LM test conditional upon including hospital and time period fixed effects. Furthermore we use a robust LM test, to test for a spatially lagged dependent variable in the local presence of spatial error autocorrelation and the other way around. The LM test and the robust LM test follow a chi-squared distribution with one degree of freedom.

In our spatial interaction model we make use of two different spatial weight matrices to reflect the intensity of the geographic relationship between observations in a neighbourhood. The first is an inverse distance matrix between neighbours (Wd), a province based approach with hospitals in different towns. The second weight matrix is the common boundary matrix (Wbc), this matrix is based on hospitals in the same city.

Table 1. Estimation results of hospital efficiency using panel data models without spatial interaction effects

Determinants (1) Wbc (2) Wd

Hospital and time-period fixed effects Hospital and time-period fixed effects

Density -0.175 (-1.99) -0.175 (-1.99) Greenc/pop -0.034 (-0,54) -0.034 (-0.54) HIbed -0.357 (-14.66) -0.357 (-14.66) HIambulatory 0.354 (20.61) 0.354 (20.61) σ2 0.0339 0.0339 R2 _{0.1474 0.1474} LogL 742.64 742.64 LM spatial lag 1.216 (0.27) 1.6009 (0.21) LM spatial error 0.750 (0.39) 1.9388 (0.16) Robust LM spatial lag 0.779 (0.38) 0.0136 (0.91) robust LM spatial error 0.314 (0.58) 0.3514 (0.54) LR hospital fixed effects 2850,99 (p-value 0.00) 2833.66 (p-value 0.00) LR time-period fixed effects 160,11 (p-value 0.00) 162.11 (p-value 0.00)

Notes: t-values in parentheses.

The results of the LM and robust LM tests (table 1) are not providing any information about the choice between the error and the lag model. When using the classic LM test, both the hypothesis of no spatially lagged dependent variable and the hypothesis of no spatially autocorrelated error term can be rejected at the 1% as well as 5% level. These results are the same for both the Wbc and Wd matrices.

in the error terms (E[εiεj] ≠0). However, the spatial structure can also be specified in a different

way, when taking into account spatially lagged exogenous variables (Wx) instead of spatially lagged endogenous variables (Wy). To test for this type of interaction we consider the Spatial Durbin model, which is a spatial lag model with an additional set of spatially lagged exogenous (independent) variables (Wx).

The literature shows that even if we could have rejected the non-spatial model in favour of the spatial lag or spatial error model based on these LM-tests, we have to be careful to conclude that one of these models best fits the data. According to LeSage and Pace (2009), the Spatial Durbin model should always be taken into consideration

3.3. Spatial Durbin model

The spatial Durbin model with hospital and time period fixed effects reads as,

y

=

λ

w

y

+

φ

+

∑

x

β

+

w

x

θ

+

∑

c

+

α

+ v

where yit is the dependent variable for the efficiency of hospital i at time t (i = 1, …, N; t=1, ...,

T). The variable ∑jwijyjt is the interaction effect of the dependent variable yit with the dependent

variable yjt in neighbouring hospitals, where wij is the i,j-th element of a pre-specified

nonnegative N x N spatial weights matrix W describing the spatial setting of the spatial units in the sample. The response parameter of ∑j wijyjt, λ, is restricted to the interval (1/rmin, 1), where

rmin equals the most negative purely real characteristic root of Wd or Wbc after this matrix has

been row-normalized (for mathematical details see LeSage and Pace, 2009, pp.88-89). Then we have Φ, which is a constant term parameter, and xit, which is a 1xK vector of exogenous variables

and β in its turn is a corresponding 1xK vector of fixed but unknown parameters. ∑jwijxijt is the

interaction effect of the dependent variable yit with the independent variable xijt with wij again as

term, for i and t with zero mean and variance σ2. Time specific effects are denoted by the αi and

finally ci stands for hospital fixed effects.

The last step, before we can move on to the rest of the details and the results of the spatial Durbin model, is to test whether we can simplify the model to either the spatial lag or the spatial error model. According to Burridge (1981), the first hypothesis for this simplification is H0: θ=0.

This hypothesis examines whether the spatial Durbin model can be simplified to the spatial lag model. The second hypothesis in this context is H0: θ+ λβ=0 and examines whether the model

can be simplified to the spatial error model. Both tests follow a chi-squared distribution with K degrees of freedom. There are two ways to test for this simplification. The first is when the spatial lag and the spatial error model are estimated themselves and the second is from the output of the spatial Durbin.

When the spatial lag and spatial error models are estimated too, a Likelihood Ratio (LR) test will provide information for the feasibility of simplification. An LR is based on the likelihood ratio, which expresses how many times more likely the data are under the used model than under the simplified model. It is a statistical test used to compare the fit of two models, one of which is a special case of the other. This likelihood ratio, can then be used to compute a p-value, or compared to a critical value to decide whether to reject the model in favour of the alternative simplified model. The likelihood ratio expresses how many times more likely the data are under one model than the other.

The second possibility, which we have chosen for in this study, is to provide the information on simplification of the model from the output of the spatial Durbin model. Therefore we use the Wald test. The Wald test is a parametric statistical test named after the statistician Abraham Wald with a great variety of uses. The Wald test can be used to test the true value of the parameter based on the sample estimates. As can be found in the literature LR tests have the disadvantage that they require more models to be estimated, while Wald tests are more sensitive to the parameterization of nonlinear constraints.

If both hypothesis H0: θ=0 and H0: θ+ λβ=0 are rejected, we may assume that the spatial

Durbin model best describes the data. If we can adopt H0: θ=0 and the (robust) LM test also

describes the data. If we cannot reject H0: θ+ λβ=0, we have to assume that the spatial error

model best fits the data, provided that the (robust) LM tests also indicated this. Finally, if the LM test and the LR- or Wald-test both point to another model we have to adopt the spatial Durbin model anyway because this model generalizes both the spatial lag and the spatial error model.

According to Elhorst (2012), the spatial econometrics literature is divided about starting with the spatial Durbin model and test for simplification (specific-to-general approach), or the other way around (general-to-specific approach). In this study the testing procedure is somewhat mixed. First, the non-spatial model is estimated to test for rejection in favour of the spatial lag and the spatial error model with use of LM tests. In case the non-spatial model is rejected or the provided evidence is not convincing enough to reject the non-spatial model, the spatial Durbin model is estimated from where we can test whether it can be simplified to the spatial lag or spatial error model or not. If both tests point to either the spatial lag or the spatial error model, it is safe to conclude that that model best describes the data. By contrast, if the non-spatial model is rejected in favour of the spatial lag or the spatial error model while the spatial Durbin model is not, one better adopts this more general model.

4. Results

LM tests and robust LM tests do not provide convincing (significant) evidence to reject the non-spatial interaction model in favour of the spatial lag model or the spatial error model. Therefore, according to the specific-to-general approach, we run the spatial Durbin model in order to test whether the Wald test gives providing evidence whether or not this model can be simplified to the spatial lag or the spatial error model. Table 2 and 3 report the results from the spatial Durbin model for two different spatial weight matrices.

second W matrix gives non-zero weights if hospitals are within a given distance (Wd) of each other, which is a province-based approach in this study.

Using Wbc in the model does not provide any evidence in favour of spatial interaction effects. In table 2 we can see that none of the interaction effects based on Wbc is significant. Therefore we can assume that the model with this weight matrix Wbc is not contributing to our hypotheses. Furthermore, when looking at the indicators R-squared and the Log-likelihood function values in table 2 and 3, we see that the model in which we use the spatial weight matrix Wbc, where hospitals with the same weight are located in the same city, produces a less satisfactory result than if we look at the same values in the model where we use the weight matrix Wd. From these values we can draw the conclusion that, apart from the insignificant values of the variables in the model using Wbc, the model in which we use Wd fits the data better.

Running the spatial Durbin model, continuing with the weight matrix Wd, provides the following outcomes reported in table 3. Here we find empirical evidence in favour of the interaction variables. Two of them, Wd*Density and Wd*HIbed, are significant.

The next step is to test whether or not the spatial Durbin model can be simplified to the spatial lag of the spatial error model. We examine this by means of the Wald test and the Likelihood ratio test (LR test). Looking at table 3, we see that the test results of both the Wald and the LR tests for both the spatial lag and for the spatial error model are significant at the 1% level. This means that the hypothesis that the spatial Durbin model can be simplified to the spatial lag of the spatial error model must be rejected and therefore that we can assume that the spatial Durbin model best fits the data in this study.

In interpreting the results, we make a distinction in direct and indirect effects.

on another hospital Y. In other words, if the results of hospital X show a positive coefficient for one of the independent variables, what does that mean for the effect on hospital Y.

If we look at the direct effects, we see a negative but significant result for the Herfindahl index of complicated treatments, where patients have to stay overnight (HIbed). This means that the larger the market power of a hospital measured by the number of patients who need a bed to stay overnight, the less efficient the hospital will be. Patients that need to stay overnight after an operation or a hospitalization do have more complex or life threatening disorders. The more market power a hospital has on this point, the less efficient it will be according to the results. This sounds logically if we argue as follows; large hospitals having too much monopoly power are not competing anymore. If a large hospital is the only hospital in a wide area that is able and allowed to do some specific complex operations or life threatening treatments, it is no longer challenged to be the most efficient one. Furthermore, it is no longer forced to be very precise and because of the high market power there is a change of the occurrence of overtreatment because highly specialized hospitals are inclined to give more attention to diagnostics which is cost increasing and therefore less efficient. This arises from the persuasion that nobody else is capable of doing those treatments. Another factor of the negative influence of high market power which reduces the efficiency, is the fact that such a specialized hospital is forced to treat the serious risk cases because ‘who else is going to do it’.

In the health care sector we see more often a trend in specialization of hospitals. Governments give direction to this trend with the philosophy that more specialization implies economies of scale and economies of scale means cost efficiency and health care quality. On the one hand this is a generally accepted economic theory, but on the other hand we see according to the results of this study a negative effect if the specialization is accompanied with market power (HIbed). This market power has a negative effect on the efficiency of a hospital and as we will see later on in the discussion of the results, it has also a negative effect on the neighbouring hospitals.

Intuitively this can be explained by the fact that the policlinic treatments are less complicated than the patients that need to stay overnight, which means that these kinds of treatments are more competitive because they are easier to fulfill than the treatments under HIbed.

Furthermore there are significant indirect effects if we look at the results in table 3. The indirect effects are interesting because they tell us something about the interaction effects of hospitals. The effect of changes in an independent variable of hospital X, that will influence the efficiency of neighbour hospital Y. We start with the variable density, which was not significant when we analyzed the direct effects, but is significant as an indirect effect. The effect is negative, which means that the larger the population density in the area of hospital X, the lower the efficiency of hospital Y outside this area. The indirect effect is a so-called spillover effect that measures the influence of the impact of a change in the parameters of hospital X, on the efficiency of hospital Y. This effect might be explained by the fact that large cities with a high population density have large hospitals. Governments tend to spend their money in such important hospitals and the productivity of the hospitals is high. The negative spillover effect can be explained by the fact that areas with high densities often do not have neighbour areas with high densities too (think of the city and the suburbs around it). The relatively smaller hospitals in the neighbourhood are forced to operate on a smaller scale and besides that, it is likely that the smaller hospitals receive less money from the government.

reasoning is exactly the other way around. In conclusion we can say here that market power does not contribute to hospital efficiency.

Table 2. Estimation results of hospital efficiency: spatial Durbin model specification with hospital and

time-period specific effects for Wbc.

Coefficient Direct effect Indirect effect Total effect

Density -0.107 (-0.89) -0.106 (-0.85) -0.125 (-0.66) -0.230 (-1.22) Greenc/pop 0.010 (0.12) 0.013 (0.15) -0.053 (-0.86) -0.040 (-0.50) HIbed -0.358 (-12.73) -0.357 (-12.49) -0.009 (-0.19) -0.366 (-6.33) HIambulatory 0.354 (17.84) 0.355 (17.74) -0.011 (-0.29) 0.344 (8.06) Wbc*Density -0.124 (-0.67) Wbc*Greenc/pop -0.053 (-0.86) Wbc*HIbed -0.003 (-0.06) Wbc*HIambulatory -0.015 (-0.40) Wbc*dep.var. 0.015 (0.50) R2 0.715 σ2 _0.045 LogL 743.984

Wald test spatial lag 1.43 (p=0.840) LR test spatial lag 2.43

(p=0.658) Wald test spatial error 1.39

(p=0.845) LR test spatial error 0.68

Table 3. Estimation results of hospital efficiency: spatial Durbin model specification with hospital and

time-period specific effects for Wd.

Coefficient Direct effect Indirect effect Total effect

Density -0.043 (-0.39) -0.038 (-0.35) -2.872 (-3.67) -2.910 (-3.77) Greenc/pop 0.087 (1.07) 0.087 (1.07) -0.258 (-1.06) -0.171 (-0.76) HIbed -0.363 (-12.93) -0.362 (-13.12) -0.535 (-2.12) -0.897 (-3.54) HIambulatory 0.361 (18.19) 0.362 (18.58) -0.171 (-0.94) 0.191 (1.06) Wd*Density -3.566 (-3.80) Wd*Greenc/pop -0.298 (-1.04) Wd*HIbed -0.754 (-2.40) Wd*HIambulatory -0.127 (-0.57) Wd*dep.var. -0.239 (-1.53) R2 0.718 σ2 0.045 LogL 759.523

Wald test spatial lag 24.48 (p=0,000) LR test spatial lag 32.56

(p=0.000) Wald test spatial error 24.43

(p=0.000) LR test spatial error 33.03

5. Conclusion

This paper presents the results from a spatial Durbin model with the use of data of hospitals in Turkey to test whether we can find evidence in favour of spatial interaction effects and especially for competition between hospitals. Competition is a key factor for providing efficiency as we can see in our results. We found evidence in favour of a relation between efficiency and scale economies, which means the more a hospital is treating, the more efficient the hospital will be. Therefore we can conclude that specialization is increasing the efficiency but we also find evidence for a break-even point in that the more hospitals are specialized, the more market power it has and the lower the efficiency is. This effect is especially notable at the more complicated treatments where patients need to stay overnight and not at the polyclinic treatments.

We found also an interesting result in the indirect spatial interaction effects of this growing market power of complicated treatments. The growing market power in complicated treatments of for example hospital X has a negative influence on the efficiency of hospital X itself as we could conclude from the paragraph above, but it also has a negative effect on neighbouring hospitals Y. This is plausible because the higher the market power of hospital X, the lower the market power of neighbour hospital Y will be. Hospitals with low market power are forced to operate on a smaller scale and, as generally accepted in economic literature, this means that the efficiency must be lower. The higher the market power, the larger the scale, and the more efficient the production process will be. For lower market power, the reasoning is exactly the other way around. In conclusion we can say here that too much market power or that monopoly positions are not encouraging for hospital efficiency.

logic behind this thought seems convincing. The more often a surgery is performed, the more routine a treating team creates and the less complication will occur. Fewer complications logically mean lower costs. Moreover, if hospitals specialize it is no longer necessary that every hospital has all the expensive facilities such as a 24x7 emergency department, which is also a cost reducing factor for the health care sector.

specialization and market power and where too much market power will lead to a reduction in efficiency.

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