C. VAN DE VOORDE ET AL for specialist care, given that specialist care Based on the robust standard errors(which are treats on average more severe conditions, and in general, larger than the standard WLs esti- (b)a higher price sensitivity for GP home mates), the estimation results indicate that hy visits than for GP office visits because the pothesis I(zero price elasticity) can be rejected for monetary price is a much smaller share of the all types of care for the general population and total price in the latter case the wopi. but not for the low-income woPi We could have estimated each of Equations (1) However, given the lack of price variation, the nd(2)separately, but in order to perform statis estimation results for this latter group are not ative, and we show them only for the tical tests of differences in the parameters across sake of completeness. For the general population Inforn equations, it is convenient to estimate (D)as a GP home visits can be seen to be much more system of nine and (2)as a system of tions. For our central exercise, we will assume price-sensitive (-0.39)than GP office visits Ix equa that e( EirikEurt'k)=0forj≠ i'and k≠k 0.16) or specialist visits (-0.10). Similarly, out-of-pocket price elasticities are negative and significant, but much lower in absolute value for he higher-income WoPI group, ranging from RESULTS -0.08 for gp home visits to -0.06 for gP office and specialist visits. The value of the F-test for the hypothesis j: a,=2=ay is 70.28, which Levels model implies that the hypothesis of equal price elastic ities for the active population and the WOPI is The WLSVD estimation results of Equation (1) very clearly rejected for the nine cases are presented in Table 1. We do not report the(279)estimates of the fixed regional effects, which are not very informative as such. Differences model Almost all of them are very significant. These fixed effects capture all time-invariant inter- The WLSDV estimates of Equation (2)are pre- regional variation. This includes the effects of sented in Table 2. Again, we do not provide the local demand and supply conditions, the age dis- results for the 31 regional dummies, but the esti- tribution of the membership of the local sickness mates of the coefficients yink-3) are all significant funds, the overall pattern of morbidity and mor- in each of the regressions. Coupled with the sig tality, the differences in income distribution, nificant estimates for two of the three time trend which can all be assumed to have been reasonably Bok-3y, this suggests that both the time trends and stable over the period 1986-1995 regional utilization differences are very differ The adjusted Durbin-Watson test statistic indi- ent for all subgroups. In general, the estimated cates the presence of positive autocorrelation in price elasticities are lower (in absolute value) than all nine equations, and the White test indicates in Table 1. The coefficients are all negative, heteroscedasticity in two of the equations for though no longer significantly different from zero specialist visits, despite the application of in the case of the high-income WOPI. If we could weighted least squares. The serial correlation may assume that the low-income WOPI's utilization also be indicative of some misspecification. Exper- behaviour provides a more accurate control for iments with alternative specifications(e.g. non-lin- unobserved variables than the time trends in lev- ear time trends) hardly changed the value of the els, then we have to conclude that failure to use djusted Durbin-Watson. Nor did the autocorre- this control group results in an overestimation of lation disappear when we introduced a separate the price sensitivity trend for each region. Dynamic specifications However, the results strongly suggest that the with lagged price variables were not feasible ow- differences in time trends and fixed effects are not ng to the limited number of post-reform observa- sufficient to correct for the heterogeneity of the tions. As autocorrelation and heteroscedasticity different groups. The estimated price elasticities affect the efficiency, but not the consistency of the are significantly different between the active pop- coefficient estimates, we decided to retain the ulation and the WOPI (F= 42.21). Therefore, the basic specification and to compute robust stan- low-income WOPI cannot be an adequate control dard errors using Arellano's method [17]. group for the two experimental groups at the Copyright a 2001 John Wiley Sons, Ltd Health Econ.10:457-471(2001)466 C. VAN DE VOORDE ET AL. for specialist care, given that specialist care treats on average more severe conditions, and (b) a higher price sensitivity for GP home visits than for GP office visits because the monetary price is a much smaller share of the total price in the latter case. We could have estimated each of Equations (1) and (2) separately, but in order to perform statis￾tical tests of differences in the parameters across equations, it is convenient to estimate (1) as a system of nine and (2) as a system of six equa￾tions. For our central exercise, we will assume that E(itjkitjk )=0 for j
j and k
k. RESULTS Le
els model The WLSVD estimation results of Equation (1) for the nine cases are presented in Table 1. We do not report the (279) estimates of the fixed regional effects, which are not very informative as such. Almost all of them are very significant. These fixed effects capture all time-invariant inter￾regional variation. This includes the effects of local demand and supply conditions, the age dis￾tribution of the membership of the local sickness funds, the overall pattern of morbidity and mor￾tality, the differences in income distribution, which can all be assumed to have been reasonably stable over the period 1986–1995. The adjusted Durbin–Watson test statistic indi￾cates the presence of positive autocorrelation in all nine equations, and the White test indicates heteroscedasticity in two of the equations for specialist visits, despite the application of weighted least squares. The serial correlation may also be indicative of some misspecification. Exper￾iments with alternative specifications (e.g. non-lin￾ear time trends) hardly changed the value of the adjusted Durbin–Watson. Nor did the autocorre￾lation disappear when we introduced a separate trend for each region. Dynamic specifications with lagged price variables were not feasible ow￾ing to the limited number of post-reform observa￾tions. As autocorrelation and heteroscedasticity affect the efficiency, but not the consistency of the coefficient estimates, we decided to retain the basic specification and to compute robust stan￾dard errors using Arellano’s method [17]. Based on the robust standard errors (which are, in general, larger than the standard WLS esti￾mates), the estimation results indicate that hy￾pothesis 1 (zero price elasticity) can be rejected for all types of care for the general population and the WOPI, but not for the low-income WOPI. However, given the lack of price variation, the estimation results for this latter group are not very informative, and we show them only for the sake of completeness. For the general population, GP home visits can be seen to be much more price-sensitive (−0.39) than GP office visits (−0.16) or specialist visits (−0.10). Similarly, out-of-pocket price elasticities are negative and significant, but much lower in absolute value for the higher-income WOPI group, ranging from −0.08 for GP home visits to −0.06 for GP office and specialist visits. The value of the F-test for the hypothesis
j:
j1=
j2=
j3 is 70.28, which implies that the hypothesis of equal price elastic￾ities for the active population and the WOPI is very clearly rejected. Differences model The WLSDV estimates of Equation (2) are pre￾sented in Table 2. Again, we do not provide the results for the 31 regional dummies, but the esti￾mates of the coefficients ij(k−3) are all significant in each of the regressions. Coupled with the sig￾nificant estimates for two of the three time trends j(k−3), this suggests that both the time trends and the regional utilization differences are very differ￾ent for all subgroups. In general, the estimated price elasticities are lower (in absolute value) than in Table 1. The coefficients are all negative, though no longer significantly different from zero in the case of the high-income WOPI. If we could assume that the low-income WOPI’s utilization behaviour provides a more accurate control for unobserved variables than the time trends in lev￾els, then we have to conclude that failure to use this control group results in an overestimation of the price sensitivity. However, the results strongly suggest that the differences in time trends and fixed effects are not sufficient to correct for the heterogeneity of the different groups. The estimated price elasticities are significantly different between the active pop￾ulation and the WOPI (F=42.21). Therefore, the low-income WOPI cannot be an adequate control group for the two experimental groups at the Copyright © 2001 John Wiley & Sons, Ltd. Health Econ. 10: 457–471 (2001)