Determinants for Spatial Location of Pharmacies

Jewczak, Maciej Article Determinants for Spatial Location of Pharmacies Comparative Economic Research. Central and Eastern Europe Provided in Cooperation with: Institute of Economics, University of Łódź Suggested Citation: Jewczak, Maciej (2012) : Determinants for Spatial Location of Pharmacies, Comparative Economic Research. Central and Eastern Europe, ISSN 2082-6737, Łodz University Press, Łodz, Vol. 15, Iss. 4, pp. 87-103, https://doi.org/10.2478/v10103-012-0028-4 This Version is available at: https://hdl.handle.net/10419/259120 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0 10.2478/v10103-012-0028-4 MACIEJ JEWCZAK* Determinants for Spatial Location of Pharmacies Abstract The topic of drug reimbursement is an important subject when one makes a decision on the construction of the reform of the health sector. Any change in the reimbursement list ends with a hot debate in the media and in everyday life. Incomprehensible pricing strategies used by pharmacies, force patients to seek those places that offer the necessary medication at the lowest possible price. Recognizing the economic opportunities for a profitable business, in recent years, a significant increase in the number of pharmacies is observed, and therefore, the number of these entities makes the process of selling drugs, especially those from the reimbursement list, almost impossible to control. The article aims to reveal the spatial dependence for the pharmaceutical market on the example of pharmacies in poviat districts of Poland. An attempt is made to assess the prevalence of spatial dependence between the number of pharmacies and other determinants indicating health care resources, ageing process and the state of health of Poles. The summary of the study is to build a spatial model with its diagnosis for the number of pharmacies according to various socio-economic factors. 1. Introduction In recent studies, both theoretical and empirical, the distinguishing between health economics and health care economics should be considered. As far as the health economics are concerned it is the scientific discipline that treats *University of Łódź 88 Maciej Jewczak health as an economic issue. Following that definition, health economics relates to the process of manufacturing, exchange and consumption of health services. The issues of health economics continuously evolve under the influence of both internal and external surroundings of health care system and the health consideration of the population. On the other hand, the health care economics interests in the analyses of the health care functioning and the manner of financing of the health services in different organizational health care system types. Contemporary research in the field of health care economics, in major part, considers mostly the characteristics of the connection between the condition of national economy or/and the area of health care and health (in a broad meaning). Due to the diversity of the health care system problems the need for the interdisciplinary research and the use of appropriate research instruments induces. The health economics is the science of allocating resources to the health system and within the system. In another words, health economics determines the subject of interest for economists working in this field, as well as, the methods of application of economic principles in health care. In practice, several characteristic approaches to analysis can be used. One can highlight many important attributes of the economy, but in health economics three should be noted. First of all, the scarcity of social resources. The classical economic analysis is based on the assumption that individuals must resign from a certain part of one resource in exchange for another. This means that on the national level, the growth in health expenditure to GDP results in reduction of other expenses. The opportunity cost (cost of giving up to get something else) of health care can be substantial. While most, pay attention to the monetary costs of goods and services, economists consider time as the most important scarce resource. Individuals sell time in exchange for remuneration, and most probably would refuse to work overtime, even if offered the rate of pay higher than normal, because it is not profitable. In a similar vein, many individuals resign from the use of admission free health care services because the costs of arrival at the health establishment and waiting for the service are too high. Rational decision-making is another important attribute. Typically, economists examine economic problems of human behavior, assuming that the individual makes a rational decision. While rationality is defined as making the best possible choice to meeting the objectives of the limitations of resources, some of the individual’s behavior in the health care system may seem irrational. But when it comes to disputes about the rational behavior, economists often point out that the so-called irrational behavior often makes sense, but only if the achieved benefits are properly understood. The important characteristic of recent Determinants for Spatial Location… 89 research in health care is the use of models in the analyses. In economics, models are developed to illustrate the ongoing or future possible processes, though should be understood as a reflection of reality. However, the models can be useful. This article focuses mainly on the quantitative analyses of the health care system characteristics and attempts to apply the spatial statistics and spatial model in health economics. 2. Methods The rapid development of the methodological principles and their application enabled the extensive use of the spatial econometrics methods and models in economic research in many other scientific fields, for instance: labor market economic growth, social interactions, environmental protection and health care. In the economical spatial studies, the impact of exogenous variables on the endogenous variable must also include an interactive combination between the observations. This follows from the fact that space is not consisting of mutually insulated units. The spatial interaction between two objects may also affect other objects. It should be noted that according to the Tobler’s law, the closer the objects are geographically, the spatial interactions are more significant. 2.1. Testing the spatial dependence The term of spatial autocorrelations refers to spatial clustering of similar values and their interdependence or interactions in reference to the geographical location of the objects. The study of interdependence relationships in geographic space requires the assumption on the existence of the functional relationship between the values of observed variables (Anselin 1988, p. 11). By definition, this means a lack of independence between the observations and the direct application of the Tobler’s law. Spatial autocorrelation is a degree of correlation of the observed values of variable in a given location with the values of the same variable in another location. This means that the tested variable at the same time determine and is determined by its implementation in other locations. When testing for spatial dependence, two types of relations are considered: positive and negative 90 Maciej Jewczak autocorrelation. Confirming the positive autocorrelation, means in terms of location, the spatial accumulation: high or low values of observed variables. On the other hand, negative autocorrelation can be interpreted as the reverse of the positive autocorrelation - high values of observed variables adjoin to low and vice versa (Suchecki 2010, pp. 103-105). There are several types of indicators for testing the spatial dependence. The most commonly used statistic is Moran’s I (Cliff and Ord 1973) , It is used to test the presence of global spatial autocorrelation according to the scheme described by standardized weights matrix W. Let us consider the variable x of observed values x i in n different regions (i = 1, 2, ..., n). Then the value of the Moran’s I statistics can be describe as follows (Suchecki 2010, p. 113) . ( ) ( ) ( ) ∑ ∑∑ = = = − −− = n ii n i n jjiij xx xxxxw I 1 2 1 1 (1) where: n – number of observations, x i , x j – values of x variable in locations i and j, x – mean value of x variable, w ij – elements of spatial weights matrix W. While testing for spatial autocorrelation, a structure of hypothesis is examined, the null hypothesis for lack of spatial dependence against the alternative hypothesis for occurrence of spatial dependence. If the adjoined spatial objects are similar in reference to the descriptive characteristics, forming spatial clusters, then the value of Moran’s I statistics is positive. If the adjoined spatial objects are varied (the spatial structure is regular, no clusters are formed) then the value of Moran’s I statistics is negative. The Moran’s I statistics ranges from (-1) to 1. For better visualizing of the type of Moran’s I statistics, scatterplots are created and statistical significance graph is analyzed, the percentage of permutations for spatially random layout of variables is calculated. On this basis, it can be concluded about the existence or absence of spatial autocorrelation. The value of probability (p-value) is called the pseudosignificance level and is the ratio of the number of permutations for which I i > I 0 to the number of all permutations made plus 1. The greater the p-value is, the less likely is the actual presence of autocorrelation. Apart from the need to study global spatial autocorrelation, the literature indicates to obtain a detailed picture of the phenomenon of spatial dependence. Therefore, local indicators for spatial association analysis (Anselin 1995, pp. 93–115) (LISA) should be performed. It involves the study of correlation between the values of the variable in particular location in comparison to Determinants for Spatial Location… 91 locations adjoined. Local Moran’s I statistics I i are calculated as follows (Suchecki 2010, p. 123): ( ) ( ) ( ) ∑ ∑ = = − − − = n jjij n ii i i xxw xx n xx I 1 1 2 1 (2) here: n – number of observations, x i , x j – values of x variable in locations i and j, x – mean value of x variable, w ij – elements of spatial weights matrix W. 2.2. Spatial weights matrix W In the construction of the measures of the spatial interactions, the spatial weights play a fundamental role. The spatial weights form the spatial weights matrix W and are calculated on the basis of distance or neighborhood matrices. The weight matrices can be constructed with the assumptions of different types and orders of contiguity (Suchecki 2010, pp. 33-34). The weight matrices are usually symmetric and in the analysis of spatial interaction, row standardization of the elements is assumed. This involves creating the transformed matrix, in which the sum of the elements in each row equals to 1. The values of the matrix elements are standardized with a closed interval <0,1>. For the construction of statistical measures, the standardization of the elements of the weights matrix is highly desirable, because of the possibilities of comparing different spatial processes and different models, therefor it is easier to interpret the processes of spatial autocorrelation and autoregression. 2.3. Spatial modeling Spatial modeling improves the construction of the econometric model. If the analysis starts from the simple linear regression model, the application of cross-sectional sample as a localized data requires taking into account the spatial interactions that may occur between the studied units, which are expressed through the introduction of the model matrix of weights W. The interactions may relate to the endogenous variables – spatial autoregression is assumed, exogenous variables – cross spatial regression is assumed and random component – spatial autocorrelation of errors is assumed (Suchecki 2010, 92 Maciej Jewczak p. 239). For the purpose of this article Spatial Autoregressive and Spatial Error Model are further described. Spatial Autoregressive Model (or Spatial Lag Model) (Arbia 2006) assumes that the values of the endogenous variable in one location are dependent on spatially lagged mean values of the endogenous variable in adjoin locations. Formally, SLM model can be described as follows (Suchecki 2010, pp. 248250): 2 , :N( , ) ρ σ + +y = Wy X β ε ε 0 I (3) where: y – endogenous variable, X – exogenous variables matrix, β – vector of structural parameters, W – spatial weights matrix, ρ – spatial autoregression parameter, Wy – spatially lag endogenous variable, ε – independent random component. In SLM models the significance of ρ parameter is tested. Spatial Error Model can be tested, when in regression an autocorrelation in linear random component is assumed: 2 , ~ N( , ) λ σ + +y = X β ξ ξ= Wξ ε,ε0 I (4) where: y – endogenous variable, X – exogenous variables matrix, β – vector of structural parameters, W – spatial weights matrix, λ – spatial autocorrelation parameter, Wξ – spatially lag error (mean error from adjoin locations), ε – independent random component. In SEM models the significance of λ parameter is verified. SEM model assumes the existence of spatial interactions (autocorrelation), caused by random factors (not included in modeling) or measurement errors (Suchecki 2010, p. 250). 3. Data set and research assumptions 3.1. Data source and specification The source of data for the analysis is Local Data Bank of Central Statistical Office 1 . At the time of constructing the research the most current data was dated to 2010. The data used in the analysis was gathered on the NUTS 4 2 1 http://www.stat.gov.pl/bdlen/app/strona.html?p_name=indeks [day of access 14.07.2012]. 2 In accordance to the Nomenclature of Units for Territorial Statistics. Determinants for Spatial Location… 93 level – for 379 Polish poviats. As a subject of the research the number of pharmacies in Poland was accepted and a data set of potential explanatory variables was considered. The first group of explanatory variables was connected strictly with the health care and included: • number of medical establishments, • number of doctors, pharmacists. The second group of explanatory variables included: • gross monthly average income, • number of people at age: o working, o pre-working, o post-working, • number of people threatened with: o work environment, o work nuisance, o mechanical factors. 3.2. Main and specific objectives The main objective of the article was to identify the spatial dependence on the example of the number of pharmacies in Polish districts. Apart from the main objective, some specific objectives were assumed as well. An attempt to verify the presence of spatial dependence between the number of pharmacies and explanatory variables 3 was made. As a summary of the research a spatial model for the number of pharmacies was designed and specified, depending on various factors. 3.3. Research hypotheses For the purpose of the research hypotheses were formed. Firstly, if a patient goes to the doctor/medical establishment, then the pharmacy should be located close to that doctor/medical establishment. Secondly, people at post3 Group consisting of data for: gross monthly average income, number of doctors, number of medical establishments, number of people at post-working age, number of people at risk because of the work environment. 94 Maciej Jewczak work age need an easy access to medicines. Thirdly, people who work and claim to be threatened because of their work environment need access to medicines. 4. Results 4.1. Baseline study In the period 2003-2010, an increase in the number of pharmacies and their employees has been observed. The average growth rate noted for the number of pharmacies and the number of pharmacists amounted to 2.38% and 1.03%, respectively. The figure 1 below presents the tendencies observed in those time series and indicates that annually the number of pharmacies increased by 231,15 objects on average, and the number of pharmacists increased by 352,14 employees on average, ceteris paribus. Both parameters for the time variable t of the linear trend functions were significant. Figure 1. Number of pharmacists and pharmacies Source: developed by author, on the basis of CSO data in Microsoft Excel Software. Comparing the ranks, a regularity is observed: on average, there are 2 pharmacists in a pharmacy, which is consistent with the guidelines of Ministry of Health. Determinants for Spatial Location… 101 Table 5. SEM summary of output: Spatial Error Model - Maximum Likelihood Estimation Dependent Variable : LA Number of Observations: 379 Mean dependent var : 29.807388 Number of Variables : 5 S.D. dependent var : 42.894081 Degree of Freedom : 374 Lag coeff. (Lambda) : 0.443498 R-squared : 0.975087 R-squared (BUSE) : - Sq. Correlation : - Log likelihood :-1270.366036 Sigma-square : 45.836938 Akaike info criterion : 2550.73 S.E of regression : 6.7703 Schwarz criterion : 2570.419753 REGRESSION DIAGNOSTICS DIAGNOSTICS FOR HETEROSKEDASTICITY TEST DF VALUE PROB Breusch-Pagan test 4 13020.8 0.0000000 DIAGNOSTICS FOR SPATIAL DEPENDENCE TEST DF VALUE PROB Likelihood Ratio Test 1 45.41532 0.0000000 Variable Coefficient Std.Error z-value Probability CONSTANT 2,966 0,804 3,687 0,000 LZOZ 0,200 0,022 8,886 0,000 LLEK 0,023 0,003 7,900 0,000 LZSP 0,002 0,000 4,860 0,000 LWPOP 0,001 0,000 12,916 0,000 LAMBDA 0,443 0,061 7,219 0,000 Source: developed by author, on the basis of CSO data in GeoDa 0.95. 102 Maciej Jewczak After the final estimation, the coefficients of the explanatory variables turned out to be significant, assuming the 5% level of error. The impact of each exogenous variable was consistent with previously made assumptions. The most important fact was the significance of λ parameter, which confirmed the existence of spatial dependence and indicated the influence of random factors or measurement errors on the number of pharmacies in Poland. Diagnosis for spatial dependence (Likelihood Ratio test) was significant, which indicated that application of SEM model for explaining the changes in the number of pharmacies in Poland in 2010 eliminated the problem of spatial autocorrelation in data, but did not deal with the problem of heterogeneity. 5. Discussion and Conclusions The implementation of spatial interactions improved the fit of model: Table 6. Criterions of fit for OLS and EM Criteria 5 OLS SEM Log likelihood -1293,07 < -1270,37 Akaike 2596,15 > 2550,73 Schwarz 2615,84 > 2570,42 Source: developed by author, on the basis of CSO data in GeoDa 0.95. All of the criteria received for SEM model indicated the better usage of that model, comparing with the OLS. Unfortunately, due to the high heterogeneity of Polish poviats it was not possible to deal with the problem of heteroskedasticity. The model adjusted for spatial dependence (SEM) – eliminated the problem of spatial dependence in the data. Apart from the strictly technical results and findings of the analyses, it should be emphasized that the methods of spatial econometrics can be widely used in health care analyses, for instance, in developing a tool/model for defining the determinants for the number of pharmacies in Poland. It was confirmed, that on average when five new medical establishments are found in a poviat, then a pharmacy appears in that region, as well. The methods for revealing the spatial dependence allowed to identify the areas of occurrence of spatial autocorrelation for the number of pharmacies and the number of people at 5 It is not possible to compare the R 2 of OLS and SEM models, instead values of Log likelihood, Akaike and Schwarz criterions are used. Better model has higher values of Log likelihood, lower values of Akaike and Schwarz criterions. Determinants for Spatial Location… 103 risk due to the work environment. Moreover, the research confirmed the need to incorporate spatial interaction factor in the modeling of health care on the example of the number of pharmacies. References Anselin L., (1988), Spatial Econometrics: Methods and Models, Kluwer Academic Publishers, Dordrecht Anselin L., (1995), Local Indicators of Spatial Association – LISA, Geographical Analysis 27(2) Arbia G., (2006), Spatial Econometrics: Statistical Foundations and Applications to Regional Convergence, Springer–Verlag, Berlin Cliff A.D., Ord J.K., (1973), Spatial Autocorrelation, Pion, London Suchecki B. (ed.), (2010), Ekonometria przestrzenna. Metody i modele analizy danych przestrzennych, C.H.Beck, Warszawa Streszczenie DETERMINANTY LOKALIZACJI PRZESTRZENNEJ APTEK Tematyka refundacji leków to istotne zagadnienie przy podejmowaniu wszelkich decyzji dotyczących kształtu reform dla sektora opieki zdrowotnej. Każdorazowa zmiana wykazu leków refundowanych kończy się gorącą debatą w mediach i w codziennym życiu. Niezrozumiałe strategie cenowe, stosowane przez apteki, zmuszają pacjentów do poszukiwania tych miejsc, które oferują niezbędny lek w jak najniższej cenie. Dostrzegając możliwości dobrego biznesu ekonomicznego, na przestrzeni ostatnich lat, obserwuje się znaczący wzrost liczby aptek, a w związku z tym, liczebność tych podmiotów uniemożliwia pełną kontrolę w procesach sprzedaży leków, zwłaszcza tych z list refundowanych. Celem artykułu jest wykazanie przestrzennych zależności obserwowanych na rynku farmaceutycznym na przykładzie liczby aptek w powiatach Polski. Podjęta została próba oceny występowania przestrzennych zależności pomiędzy liczebnością aptek a liczbą lekarzy, liczbą zakładów opieki zdrowotnej, jak również innych determinant wskazujących na proces starzenia się społeczeństwa i stanu zdrowia Polaków. Podsumowaniem badań jest próba budowy modelu przestrzennego i jego diagnoza dla liczby aptek w zależności od różnych czynników społeczno-gospodarczych.