Ann Reg Sci (2010) 44:299–314 DOI 10.1007/s00168-008-0259-2 ORIGINAL PAPER
A spatiotemporal analysis of public pharmaceutical expenditure Jorgen Lauridsen · Mickael Bech · Fernando López · Mariluz Maté Sánchez
Received: 26 January 2007 / Accepted: 14 June 2008 / Published online: 19 July 2008 © Springer-Verlag 2008
Abstract A regression model for per capita public pharmaceutical expenditure, based on aggregate data from fifty Spanish provinces, observed annually for the period 1996–2002 is analyzed. The necessity of simultaneously controlling for dynamic patterns and spatial autocorrelation is demonstrated. As the aim of the present and related studies of small-area variation is to control for spatial association rather than to formulate it as an explicit part of a model, the traditional application of parametric spatial autocorrelation or spatial autoregression specifications seems unnecessarily restrictive and superfluous. The present study analyzes the effects of spatial association using a non-parametric spatial filtering approach. The importance of adjusting for spatial association is confirmed, but it is further shown that the parametric and the non-parametric approaches may lead to substantially different conclusions regarding explanation of pharmaceutical expenditure variations. Thus, the need for further evidence on the implications of spatial association—and the recognition that this is more than just spatial autocorrelation and/or spatial autoregression—when analyzing complex large area behavior using small area data is demonstrated. JEL Classification
I11 · L65 · R15 · C21 · C23
J. Lauridsen (B) · M. Bech Institute of Public Health – Health Economics, University of Southern Denmark, Campusvej 55, 5230 Odense M, Denmark e-mail:
[email protected] M. Bech Odense University Hospital, Odense, Denmark F. López · M. M. Sánchez Department of Quantitative and Computering Methods, Polytechnical University of Cartagena, Cartagena, Spain
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1 Introduction During the last decade, the public pharmaceutical expenditure in Spain has grown at a rate superior to the total public health care expenditure (Darbá 2003a,b). Thus, the public pharmaceutical expenditure makes up an increasing proportion of the total public health care expenditure. Pharmaceutical expenditure made up 16.8% in 1991 and had in 2002 increased to 23% of the total health care expenditure (LopezCasasnovas et al. 2005). This growth is not specific to Spain, but is a general feature of the European Union countries (Ess et al. 2003); however, the Spanish pharmaceutical expenditure as a share of public health care expenditure exceeds European Union (EU) averages (Lopez-Casasnovas 2005). It is thus crucial to analyze the causes of this growth differential in order to focus on a rational use of medicine. The regulation of the pharmaceutical market in Spain is shared between national regulatory bodies and the regional authorities. There are notable differences in health resources supply and health care expenditure across regions (Lopez-Casasnovas et al. 2005) and there is evidence of regional variation in prescription rates and expenditure per prescription resulting in regional heterogeneity in pharmaceutical expenditure and in the pharmaceutical expenditure as a share of the total regional health care expenditure (Costa-Font and Puig-Junoy 2004). There are very few studies on pharmaceutical expenditure from the regional perspective, although it is possible to find a few works dealing with the analysis of regional health care expenditure (see e.g. Kitchener et al. 2003; Levaggi and Zanola 2003; Lopez-Casasnovas and Saez 2001; Moscone and Knapp 2005; Costa-Font and Moscone 2008). Despite the ample body of evidence of variations in the use of procedures in the literature on small-area variation (Folland et al. 2003; Ham 1988; Joines et al. 2003; Wennberg and Gittelsohn 1973; Westert et al. 2004), few studies have examined the geographical variability in the use of pharmaceuticals (see e.g. Dubois et al. 2002; Metge et al. 1999; Morgan 2005). The causes of variation discussed in the literature are the prevalence of diseases, mixed opinions of the effectiveness of surgery, practice style, health supply resource and differing patient preferences. Only a few studies of small-area variation have considered spatial variation in medical practice. Westert et al. (2004) studied spatial disparities in hospital discharges (measured by coefficients of variations) and found these disparities to be approximately unchanged during the 1980s and 1990s. Joines et al. (2003) found that hospitalization rates for low back problems varied significantly across the counties of North Carolina. Furthermore they found that counties with similar rates clustered geographically and they concluded that spatial effects are important and should be considered in small area studies. Moscone and Knapp (2005) explored the spatial patterns of mental health expenditure and established—similar to Joines et al.—the importance of controlling for spatial autocorrelation. Moscone and Knapp’s study found a positive significant spatial autocorrelation suggesting that adjacent local authorities mimic the behavior of their neighbors and tend to have similar mental health expenditure. The present study focuses on the provincial variations in the determination of public pharmaceutical expenditure in Spain and contributes to the literature on small-area variation and determinants of health care expenditure. The aim of the study is to analyze the determinants of the province-level pharmaceutical expenditure in Spain while
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controlling for spatial effects. However, in contrast to the above mentioned studies, which apply parametric specifications, we apply an exploratory technique denoted spatial filtering (SAF) developed by Griffith (1996, 2000, 2003). The advantage of the SAF methodology is that spatial association is controlled for by screening it out of the variables prior to the analysis, rather than relying on a restrictive parametric model of the spatial association as a part of the analysis. Specifically, spatial association may potentially be more than just spatial autocorrelation. Spatial association may be present when the spatial units are small and the boundaries cut through clusters of provinces, whereby a certain degree of heterogeneity within the provinces may be expected. In that case association between provinces is probably not due to spatial autocorrelation but to some sort of trend or regional phenomenon (cultural, historical, etc.). Furthermore, in order to obtain efficient results, the SAF approach is combined with a seemingly unrelated regression (SUR) framework in order to capture intertemporal residual correlation and time-varying residual variances. Though it cannot be concluded that the filtering approach is definitely superior to a parametric approach for the case studied, it is clearly superior to the unadjusted SUR approach and thus merits further attention. Finally, it should be noticed that economic theories from the public expenditure literature on welfare competition, yardstick competition and benefit spill over may explain the existence of spatial spillover. In the present paper, we are not aiming on testing these theories but rather to present a non-parametric filtering approach to separate the spatial and from the non-spatial components.
2 The Spanish pharmaceutical market In Spain, the prices of publicly financed pharmaceuticals are fully or partially controlled, and the price index of the medicines has been largely unchanged in the last decade. However, older drugs are replaced by newer, more expensive, drugs (Dubois et al. 2000; Gerdtham and Lundin 2004; Morgan 2005) and a larger quantity is consumed because of increases in the intensity of medication in terms of defined daily doses per patient (Darbá 2003b; Rovira et al. 2001). The Spanish national health system is a decentralized system in which the regulation of the pharmaceutical market is shared between national regulatory bodies and the regional authorities—called autonomous communities (AC). In this context, to ensure better administration of pharmaceutical administration several legal modifications have been introduced. These laws have increased the control of regional governments on heath expenditures and the organization of the clinical care provision for different ACs (Antoñanzas et al. 2007). See Fig. 1 for a map of provinces by AC. Even though cost containment has been a major priority for publicly financed pharmaceuticals this has not resulted in significant savings in public expenditure (Costa-Font and Puig-Junoy 2004; Darbá 2003a,b). The average price for pharmaceuticals is below EU averages, with older drugs priced significantly below the EU average (Puig-Junoy 2004). There seems to be significant regional heterogeneity in the use of generics (Costa-Font and Puig-Junoy 2004). New drugs are not priced significantly below the EU average and these drugs account for the largest market share
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Fig. 1 Provinces by ACs
(Costa-Font and Puig-Junoy 2004; Darbá 2003a,b). Different cost containment policies such as negative lists of excluded drugs, regulation of profits, repayments from pharmaceutical companies, reference pricing system and promotion of the use of generic drugs have had little effect on the overall increase in pharmaceutical expenditure. The ACs have gradually become significant actors in the pharmaceutical policy along with the decentralization process starting in the early 1980s until the completion of the devolution process in 2002. Funding is mainly centrally collected and distributed to the ACs. Until 2001, the regional health care financing was decided in a separate negotiation between the Minister of Health and the corresponding Regional Ministers in the 17 ACs, mainly allocating funds as block grants following the lines of an unadjusted capitation formula (Lopez-Casasnovas et al. 2005). Since 2002 the health care expenditure is allocated as part of the general financing using a capitation formula with some demographic adjustments. Health care expenditure accounts for around 40% of the ACs’ total funding. The ACs have some possibilities of raising funding by levying higher taxes; however, various central funds strive to maintain territorial equity. There are some inter-regional inequalities in health expenditure per capita, but the coefficient of variation in regional health care expenditure per capita is one of the lowest among health care systems for which territorial health care expenditure may be identified (Lopez-Casasnovas and Saez 2001). There appear to be significant differences in hospital specialization, physician density and technology and it has been suggested that this diversity can be partly explained by differences in particular gross
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domestic product (GDP) and population structures (Lopez-Casasnovas et al. 2005). The regional inequality in health expenditure is, however, not correlated with inequality in health outcomes (Lopez-Casasnovas et al. 2005). There is evidence of significant regional variation in prescription rates and expenditure per prescription resulting in significant regional heterogeneity in pharmaceutical expenditure as a share of the total regional health care expenditure (Costa-Font and Puig-Junoy 2004).
3 Spatial spillover and economic theory A number of factors may determine the pharmaceutical expenditure such as policy makers and regulation but other supply and demand variables such socio-demographic variables, morbidity and mortality, accessibility of pharmacies and hospitals etc. may also be involved. These determinants may, however, not be randomly distributed across the geographical units but may have an underlying spatial patterns. A non-random underlying spatial pattern may if ignored bias the significance of the determinants (Case et al. 1993; Revelli 2002) and invalidate conclusions. Spatial mechanisms may emerge from several sources. Competition and learning effects among spatially clustered regions may lead to spatial clustering of health care behaviour, i.e. endogenous spatial spillover may be involved. Pharmacetical expenditure in one regional jurisdiction which induce or contain pharmaceutical expenditure may exert influence beyond the regional borderline because of competitive or learning effects as suggested in the public economics literature (see e.g. Costa-Font and Pons-Novell 2007; Brueckner 2003; Revelli 2002, 2005, 2006). The strategic interaction between regional jurisdictions involves that one jurisdiction’s level of a decision variable is directly or indirectly is affected by the level of surrounding jurisdictions’ choice of level. The level may be influenced directly through the levels on the decision variable in the surrounding jurisdiction or indirectly through the surrounding jurisdictions’ characteristics which causes a spatial auto-correlation in the sense that the policies and the behaviour of patients, doctors and physicians of nearby provinces appear to be more correlated than those of far-away ones. In this sense, changes in utilization patterns might result from differences in supply inducement incentives by doctors in treatment intensity and differences in the types of inputs chosen. For instance, those regions that exhibit high levels of physician density tend to display lower levels of in-patient care due to some substitution taking place (Skinner and Wennberg 2000). Furthermore, the population size of the system is a well known determinant in the sense that larger regional health services are likely to exhibit economies of scale in the provision of health care (Costa-Font and Moscone 2008). On the other hand, political decision making may have influence on the pharmaceutical expenditure. In principle, we would expect left wing governments to increase public health care expenditures at a faster rate than right-wing governments. Parties of the left may favour spending on social welfare (Henrekson 1988). However, recent evidence indicates that the left gains credibility through expenditure cuts, while the right gains credibility through tax revenue increases (Tavares 2004). Due to this result, it is expected that the pharmaceutical expenditure decisions would be more influenced
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by the effectiveness in the management of the neighbours than by their own political decisions market. 4 Methodology The basic linear regression model reads for one year as yt = X t β + υt , υt ∼ N (0, σ 2 I ),
(1)
where X t is an N by K dimensional matrix of explanatory variables, yt is an N dimensional vector of endogenous observations, β is a K dimensional coefficient vector, and υt is a residual with variance σ 2 . To enable β to change over the years, we further add interaction variables between X t and a time trend T , i.e. terms on the form X t × T . As the model is estimated with regional data, dependencies between the crosssections have to be taken into account to avoid biased conclusions (Anselin 1988). To make the concepts of spatial association operational in a one-period model, specify an N by N matrix W so that wi j equals 1 if provinces i and j are neighbours (i = j) and 0 otherwise, and divide each element in W with the number of non-zero elements in the row it belongs to. Then the product W yt defines a variable, which for each province holds the average of yt in the neighbouring municipalities. Traditionally, control for spatial association is obtained by adding spatial parameters to the model in question. One approach is to control for endogenous spatial association by applying the spatially autoregressive (SAR) specification (Anselin 1988) yt = λ(W yt ) + X t β + υt ,
(2)
where λ is a parameter specifying the degree of association, formally restricted to the interval between (−1) and (+1), but for most practical purposes restricted to be nonnegative. Alternatively, control for exogenous spatial association may be obtained by applying the spatial distributed lag (SDL) specification of (Florax 1992) yt = X t β + (W X t )δ + υt .
(3)
Finally, a SAR–SDL specification obtained by combining (2) and (3) may be applied. One further approach commonly applied is to defer the spatial association to the residuals, thus obtaining the spatially autocorrelated (SAC) specification (Anselin 1988): yt = X t β + εt , εt = λW εt + υt ,
(4)
which is merely a restricted case of the SAR–SDL, obtained by imposing the spatial Durbin restriction δ = −λβ. However, as the frequent aim is to control for spatial association rather than estimating it explicitly as a part of the model, these restrictive parametric specifications may
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well be superfluous and may even hamper the very purpose of efficiently controlling for spatial association. Specifically, spatial association may potentially be more than just spatial autocorrelation. Spatial association may occur when the spatial units are small and the boundaries cut through clusters of provinces, whereby a certain degree of heterogeneity within the provinces may be expected. In that case association between provinces is probably not due to spatial autocorrelation but to some sort of trend or regional phenomenon (cultural, historical, etc.). Therefore, the present study suggests the application of spatial filtering along the lines of Griffith (1996, 2000, 2003) in order to obtain a non-parametric separation of the spatial and non-spatial components of the series that enter the regression model. The approach is based on the eigenfunction decomposition suggested by Griffith (1996, 2000). Filtering relies on a decomposition of Moran’s I (MI) statistic MI =
z t W z t z t z t
(5)
as a measure of the global spatial autocorrelation structure, where z t is the meanadjusted version of some variable to be investigated. An intuitive way of understanding Moran’s I is that it is equivalent to the regression coefficient from a regression of the average of z t in the contiguous provinces (i.e., the spatial lag W z t ) on z t itself. Moran’s I can be expressed as a weighted sum of the eigenvalues of the matrix C = (In − ii /n)W (In − ii /n),
(6)
where In is the n dimensional identity matrix and i an n vector of ones (Tiefelsdorf and Boots 1995; Griffith 1996). The eigenvectors of C are utilized to separate spatial from non-spatial components. Generally, spatial dependencies are represented by the system of eigenvectors, which identify distinct geographic map patterns. The nonspatial part of a variable is given by the Ordinary Least Squares (OLS) residuals of a regression of that variable on the significant eigenvectors, for each variable from each time period (Griffith 1996, 2000). Griffith (2003) suggested an assessment of sub, where MImax denotes stantial spatial autocorrelation on the basis of the ratio MIMI max the largest Moran coefficient of any eigenvector of the C matrix. According to his qualitative classification we apply a threshold value of 0.25 for the selection of eigenvectors. Finally, the filtered variables, say X t∗ , replace X t in the SUR regression, and the significant eigenvectors are further added to this regression. Furthermore, when applying pooled data for T years, the residuals are intercorrelated across years, and the variances within years vary over time. Thus, the residual covariances read as E(υt υs ) = σts2 t, s = 1, . . . , T.
(7)
Thus, to obtain efficient estimates, we integrate the SAF methodology with the Zellner (1962) Feasible Generalised Least Squares (F-GLS) approach to obtain Seemingly Unrelated Regression (SUR) estimates for β.
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To provide devices for comparison of alternative models, some quantities are applied. One is a pseudo-R-square (R 2 ), calculated as the square of the correlation between y and its predicted values. As this measure is readily calculated for the nonfiltered and the filtered SURs, it is not defined for the SUR–SAR specification. A second device, which similar to the R-square measures can be used as a goodnessof-fit measure for comparison of models, is the familiar Akaike information criterion (AIC). Finally, the condition number is reported for all models in order to inspect potential presence of multicollinearity problems.
5 Data Data for 50 Spanish provinces (excluding the autonomous cities of Ceuta and Melilla) were collected. These provinces correspond with the NUT-3 level of aggregation according to EUROSTAT. The provinces are assembled in 17 Autonomous Communities (AC). The ACs correspond with the NUT-2 level of aggregation according to EUROSTAT and they present a higher degree of heterogeneity than the provinces. Regarding the decentralisation process, 7 of the ACs took over independent responsibilities during the 1980s and 1990s (Cataluña 1981; Andalucía 1984; Comunidad Valenciana y País Vasco 1987; Galicia y Navarra 1991; and Canarias 1994), while the last ten took responsibility for health care regulation in 2002. Until then these 10 ACs were centrally regulated. The data were collected annually from 1996 to 2003 from two sources, The National Statistical Institute (INE) and the Ministry of Health and Consumption (MSC). The dependent variable is Public Pharmaceutical Expenditure (EXP) per capita. This variable includes the expenditure on extra-hospital drugs managed by the administration, but does not take private purchase into account. To capture influence of wealth, Gross Domestic Product per capita (GDP) is included as an explanatory variable. Furthermore, to capture influence of health care system, the variables number of pharmacists per 1000 inhabitants (PHARM), number of hospital beds per 1000 inhabitants (BEDS), and number of medical doctors per 1000 inhabitants (MED) are included. Finally, to capture influence of population structure, population proportions of females (FEM), foreigners (FOREIGN), people over 65 years (OLD), and 0–4 year old children (CHILD) are included. Table 1 presents the data applied, including means and standard deviations (average over 8 years). The variables describing the population control for socio-demographic risk factors and are considered to be proxies for need, whereas GDP controls for ability to pay. The variables describing the health care system do not solely reflect supply factors but are a result of interactions between demand and supply factors. Some health system variables may be considered to be substitutes of utilization of pharmaceuticals while others are complementary. A priori, one would expect the number of pharmacists to be complementary, whereas we have no unambiguous a priori hypothesis for hospital beds and medical doctors. Figure 2 shows the distribution of variables (average over 8 years) by provinces. Spatial patterns are predominant, though not of a unique nature. For the expenditure, a clear indication of spatial association is seen. Comparing the maps in Fig. 2 to the
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Table 1 Data applied for the study Variable
Description
Source
EXP
Pharmaceutical expenditure per capita
MSC, Institute of Sanitary Information
Mean
164.899 9241.57
Standard deviation 31.710
GDP
GDP per capita
INE, National Statistical Inst.
PHARM
Pharmacists per 1,000 inhabitants
INE, social indicators, 2004
1.206
1766.14 0.225
BEDS
Hospital beds per 1,000 inhabitants
MSC, National Hospital catalogue
0.004
0.001
MED
Medical doctors per 1,000 inhabitants
INE, Social indicators, 2004
4.183
0.739
FEM
Population proportion of females
INE, National Statistical Inst.
0.506
0.006
FOREIGN
Population proportion of foreigners
INE, National Statistical Inst.
0.018
0.019
OLD
Population proportion over 65 years
INE, National Statistical Inst.
0.185
0.042
CHILD
Population proportion from 0 to 4 years
INE, National Statistical Inst.
0.090
0.016
map of ACs in Fig. 1, this association seems to be of an intra- as well as a supraAC nature. Further, there appear to be some tendencies to North/West–South/East contrasts. With respect to GDP, medical doctors, hospital beds and, to some extent, pharmacists a clear North–South contrast is evident. This is also the case for some of the population characteristics, especially elderly, children and to some extent females, while foreigners seem to cluster especially over the East coast provinces.
6 Results Prior to estimation and testing, Moran’s I is computed as an overall measure for spatial autocorrelation for the variables considered for each year (see Table 2). With the exception of FEM in 1993, all variables exert significant spatial autocorrelation throughout at the 5 percent level and most of them even on the 1 percent level. Hence, control for spatial association is urgent in order to ensure efficient estimation. Bech et al. (2006) estimated a multiplicative Cobb-Douglas type specification, which was linearized by applying log transforms of the variables. Bech et al. (2006) investigated different models including parametric control for spatial autoregression and spatial autocorrelation and found the SAR specification to be superior to the SDL and the combined SAR–SDL. The SAC was discarded, as the Durbin restriction was tested and found not to hold true. Their SUR model without spatial adjustments is shown together with their suggested optimal SAR–SUR in the first two columns of Table 3.
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Fig. 2 Unfiltered variables (averaged over 8 years) by provinces
For the unadjusted SUR, GDP is found to have a positive impact on expenditure, but the effect is significantly reduced over time and will even be negative after two years. Turning to characteristics of health care system, number of pharmacists (PHARM) is found to have an increasing, but weakly significant, positive effect on expenditure. Number of hospital beds (BEDS) is insignificant, while number of medical doctors (MED) has an insignificant positive effect, which is significantly reduced over time. Regarding population characteristics, population proportions of females (FEM) and old people (OLD) exert positive effects on expenditure that do not change significantly over time. Population proportion of young children (CHILD) has a positive impact on expenditure, but this effect is seen to be significantly reduced over time. Finally, the general time trend (T) seems to be insignificant. Considering the SAR–SUR, the coefficient for the spatial endogenous lag (W × EXP) is large and highly significant, and the AIC is better for this model than for the former. Thus, endogenous spatial association seems to be a highly relevant part of the specification. Furthermore, substantial changes are observed for the coefficients
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Table 2 Moran’s I for each variable by year EXP
GDP
PHARM BEDS
MED
FEM
FOREIGN OLD
CHILD
1996 0.305*** 0.770*** 0.287*** 0.270*** 0.323*** 0.142*
0.190**
0.308*** 0.631***
1997 0.291*** 0.760*** 0.267*** 0.347*** 0.277*** 0.152**
0.210**
0.314*** 0.649***
1998 0.250*** 0.753*** 0.277*** 0.315*** 0.283*** 0.162**
0.228***
0.320*** 0.656***
1999 0.219*** 0.734*** 0.254*** 0.316*** 0.275*** 0.170**
0.227***
0.325*** 0.691***
2000 0.203**
0.715*** 0.258*** 0.381*** 0.245*** 0.178**
0.254***
0.325*** 0.647***
2001 0.245*** 0.727*** 0.239*** 0.339*** 0.230*** 0.199**
0.292***
0.325*** 0.641***
2002 0.277*** 0.697*** 0.203**
0.370*** 0.212**
0.256*** 0.357***
0.327*** 0.634***
2003 0.287*** 0.701*** 0.183**
0.315*** 0.203**
0.282*** 0.402***
0.333*** 0.632***
Significance indicated at 1% (***), 5% (**) and 10% (*) levels
of the exogenous variables as compared to the unadjusted SUR. The effect of GDP and the time trend in this effect are reduced to about half of the effects obtained from the unadjusted SUR. The effect of number of pharmacists is almost multiplied by four and changes from insignificant to significant, while its time trend is substantially reduced and loses any indication of significance. For hospital beds, the coefficient as well as its time trend is still insignificant. The effect of medical doctors as well as its time trend is practically unchanged. For the population structure variables, the effects are drastically reduced. Regarding the time trends of the latter effects, a substantial increase for old people and a substantial decrease for children are found, while the time trends of the effects of females and foreigners are practically unchanged. Before turning to the filtered SUR, an inspection of the spatially filtered variables may be instructive. These are shown in Fig. 3. Comparing the patterns of the spatially filtered variables to the patterns of the unfiltered variables of Fig. 2 throughout reveals that substantial amounts of the spatial patterns have been removed by the filtering. Especially, the clear North-South contrast of Fig. 2 is considerably less predominant, as are the spatial clustering tendencies of several variables. The filtered SUR is reported in the third column of Table 3. The number of significant eigenvectors applied for filtering of each variable occurs in squared brackets. It is seen that the lowest numbers are for children and females (6 and 7, respectively). This is presumably due to the quite uniform North-South patterning of these variables, while the more scattered variables seem to require more eigenvectors. Thus, for example, hospital beds and old people require the highest number of eigenvectors (10 and 11 respectively). Next, considering the log likelihood and the AIC, the model seems to be superior to the unadjusted SUR, while the R 2 hardly favours any of the models. On the other hand, the log likelihood and the AIC slightly favour the SAR–SUR over the filtered SUR. Regarding the effects of determinants, several differences are obtained as compared to the unadjusted SUR as well as the SAR–SUR. The effect of GDP is positive and much higher than for any of the former variables, while the time trend of this effect is comparable to that of the unadjusted SUR. Considering the characteristics of health care system, the effect of pharmacists is positive and much higher than those obtained in models [1] and [2], while the time trend of this effect is comparable to
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Table 3 SUR models [1] SUR (unadjusted)
[2] SUR (SAR adjusted)
[3] SUR (filtered)
Constant
7.075*** (0.673)
3.281*** (0.603)
4.844*** (0.016)
GDP
0.042 (0.035)
0.024 (0.030)
0.106*** (0.040) [8]
PHARM
0.018 (0.034)
0.062** (0.031)
0.119*** (0.042) [9]
BEDS
0.001 (0.016)
−0.009 (0.015)
−0.020 (0.021) [10]
MED
0.061 (0.039)
0.062* (0.035)
0.078 (0.057) [8]
FEM
1.832*** (0.673)
0.943 (0.607)
1.891** (0.810) [7]
FOREIGN
0.012** (0.006)
0.002 (0.006)
−0.008 (0.007) [8]
OLD
0.212*** (0.055)
0.144*** (0.049)
0.243*** (0.060) [11]
CHILD
0.175*** (0.045)
0.078** (0.039)
0.085 (0.055) [6]
T
0.118 (0.073)
0.008 (0.069)
0.064*** (0.003)
T × GDP
−0.020*** (0.004)
−0.009** (0.004)
−0.020*** (0.006) −0.004 (0.007)
T × PHARM
0.008* (0.004)
0.002 (0.004)
T × BEDS
0.002 (0.003)
0.004 (0.003)
0.006 (0.004)
T × MED
−0.013** (0.005)
−0.009* (0.005)
−0.014 (0.010)
T × FEM
−0.090 (0.064)
−0.108* (0.059)
−0.063 (0.125)
T × FOREIGN
0.001 (0.001)
0.001 (0.001)
0.003*** (0.001)
T × OLD
0.002 (0.006)
0.009* (0.005)
0.004 (0.009)
T × CHILD
−0.032*** (0.007)
−0.013* (0.006)
−0.013 (0.011)
Log L
1367.88
1420.06
1382.45
AIC
−2625.76
−2730.13
−2626.91
R2
0.78
Condition number
20.74
20.74
22.40
W × EXP
0.651*** (0.003)
0.77
Standard errors in parentheses. Significance indicated at 1% (***), 5% (**) and 10% (*) levels. The number of eigenvectors applied for filtering of each variable is reported in squared brackets
these. The effects of hospital beds and medical doctors as well as the time trends of these effects are insignificant and comparable to those obtained in models [1] and [2]. For the population characteristics, the effects of foreigners and children resemble those obtained by the SAR–SUR, while the effects of females and old people rather resemble those obtained by the unadjusted SUR. Thus, in terms of a priori expectations, the filtered SUR seems to provide a much better logical explanation of the variation in expenditure, since the spatial effects are controlled for in a detailed and specific manner due to the spatial filtering. Furthermore, to examine the potential risk of multicollinearity, the condition numbers are reported for all models. It is seen that the condition number of the filtered SUR is only marginally higher than for the unadjusted SUR and the SAR adjusted SUR. Assuming that a condition number exceeding 30 or 40 should be considered an indication of potential collinearity problems, none of the reported condition numbers give rise to concern. Finally, Fig. 4 provides a comparison of the residuals of the SAR–SUR and the spatially filtered SUR specifications. While a strong North/West–South/East contrast
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Fig. 3 Filtered variables (averaged over 8 years) by provinces
is predominant for the SAR–SUR residuals, only weak tendencies of spatial patterns are found for the filtered SUR. There appears to be a slight tendency to high residuals along the East coast, in a belt in the middle of the country, and in the North/West provinces of the Galicia and Asturias ACs. Furthermore, for the filtered SUR as well as for the SAR–SUR, the spatial patterns of the residuals seem to be only to a small extent ascribable to intra-AC effects. Thus, to summarize, the message of previous studies still holds true: It is essential to control for spatial association when analysing large area behavior using pooled smallarea cross section data. Using any of the parametric and non-parametric approaches to control for spatial association led to substantially different effects of determinants as compared to the spatially unadjusted model. On the other hand, substantial differences were also found between the parametric and the non-parametric approaches. Therefore, the message needs a modification: not only is it essential to control for spatial association, but it is also important to consider different approaches, as they may potentially lead to substantial differences in results obtained, due to the obviously complex nature of the large area behavior studied.
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Fig. 4 Residuals (averaged over 8 years) by provinces
7 Conclusions The present study analyzes determination of public pharmaceutical expenditure and adds to previous knowledge regarding not only the necessity but also the involved implications of adjusting for spatial association. A dynamic non-parametric spatial filtering approach is suggested as an alternative to more restrictive parametric specifications applied previously. The results from the spatially filtered model are compared to results from an unadjusted model and from a parametric spatial autoregressive model. The conclusion is equivocal: The importance of adjusting for spatial association in order to obtain proper conclusions regarding the effects of determinants is confirmed, but it is further shown that the parametric and the non-parametric approaches may lead to substantially different conclusions regarding explanation of pharmaceutical expenditure variations, due to the complex supra-provincial nature of the pharmaceutical market and its determinants. The study reveals an especially interesting result in regard to GDP, which is a key variable in many economic studies of small-area variation and health care expenditure. The elasticity for GDP is positive and significant in the filtered SUR model, whereas it is small and insignificant in the other models. Also, the number of pharmacists seemed at first to have a small and insignificant positive coefficient whereas the model taking spatial autocorrelation into account show a larger and significant coefficient. This result has important policy implications for a decentralized health care system such as the Spanish system. In summary, the complexity of controlling for spatial association is clearly illustrated, and the need for further evidence, not only on the implications of spatial association, but also on the implications of using different approaches to control for these, is demonstrated. Acknowledgments The authors have no conflicts of interest and the project has received no external funding. We thank the two anonymous reviewers and editor for their constructive comments to earlier versions of the manuscript. This work has been carried out with the financial support of project SEJ200602328/ECON of the Ministerio de Ciencia y Tecnología del Reino de España.
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