EFFECTS OF COST SHARING ON PHYSICIAN UTILIZATION the graphs that any response in utilization be- difference between the equation of the experimen haviour has to be measured as a deviation from tal group and the control group, for k= 1, 2 the time trend until the e co- ayment change Third, we have pooled the data for all 31 regions, In gajk-In qu3=a, (In Pujk-In pa3) but have allowed for nal heterogeneity in utilization levels by estimating a fixed effects Bk-3T+∑7k-3R+4mk-3(2) model using the weighted least-squares dummy variables(WLSDV) method. The 7k estimate the where regional fixed effects. Finally, we have tested for the presence of heteroskedasticity using the White -1=/3-a test [15], and for the presence of autocorrelation Bxk-3)=Bk-B3 using the adjusted Durbin-Watson statistic for nel data [16]. Where either autocorrelation or ik-3)-70k-7y heteroskedasticity is a problem, we have used Eank-3)=fark -er Arellano's [17 method to compute heteroscedas- ticity and serial correlation consistent standard As we will automatically obtain two separate errors in panel data models for within-group esti- estimates of a,(for j=l,., 3), one from the mators of linear regression models [18]. This re- difference equation for the general population and quires re-estimation of Equation (1), using the another from the equation for high-income WOPI method of within-group deviations from time (call them %wk) for k=l, 2), we can test whether means on transformed variables and computing the homogeneity assumption is rejected by testing White's[19] robust estimates for the standard for ax=ay2 for j=l,-.,3 Testing strategy Diferences mode Estimation of Equation()provides j*k parame- This model assumes that the low-income woP each combination of k and ]), whereas estimation can be regarded as an appropriate control group, of Equation(2)provides j*(k-1)parameter vec. groups can be measured as a deviation from the tors [awey, Bok-3y Yunk-3(i=\- sog/ues of these differential utilization of experimental and control hypotheses concerning the relative groups as a function of the price differential. a parameters crucial homogeneity assumption is inescapable for 1. Estimated price elasticities are negative for all his approach to work, namely that the price groups and for all types of care elasticity in the control group is equal to that in 2. In terms of between-group differences, we ex- the experimental group, i.e. that ak=r3 Vj and pect the general population to be more price- k=1. 2. In other words we have to assume that responsive than the 'needy groups(high-and fter correction for any possible differences in low-income WOPI). One argument for this time trends and regional effects, both groups are homogeneous with respect to their price-sensitiv- or pothesis is the better average health status he general population. It is also possible te ity. It is then as if both groups are drawn from the argue that the utilization by the WOPI is less same population and only one of the groups is price elastic, because they can be persuaded ubjected to price variation. The main problem more easily by the physicians to take more with this approach is that, in general, one can treatment. our data do not allow us to distin never be certain about the validity of the homo- guish the demand and the supply effects, as we geneity assumption In our case, however, we can are only capable of estimating the overall price test whether the price elasticities of the two exper- effect. For the low-income WOPI, price-sensi- imental groups are equal tivity can hardly be measured owing to lack of The ces for the estimation procedure price variation in the period considered and 3. In terms of between-visits differences we ex pect(a)a higher price sensitivity for GP than Copyright a 2001 John Wiley Sons, Ltd Health Econ.10:457-471(2001)EFFECTS OF COST SHARING ON PHYSICIAN UTILIZATION 465 the graphs that any response in utilization be￾haviour has to be measured as a deviation from the time trend until the co-payment change. Third, we have pooled the data for all 31 regions, but have allowed for regional heterogeneity in utilization levels by estimating a fixed effects model using the weighted least-squares dummy variables (WLSDV) method. The ijk estimate the regional fixed effects. Finally, we have tested for the presence of heteroskedasticity using the White test [15], and for the presence of autocorrelation using the adjusted Durbin–Watson statistic for panel data [16]. Where either autocorrelation or heteroskedasticity is a problem, we have used Arellano’s [17] method to compute heteroscedas￾ticity and serial correlation consistent standard errors in panel data models for within-group esti￾mators of linear regression models [18]. This re￾quires re-estimation of Equation (1), using the method of within-group deviations from time means on transformed variables and computing White’s [19] robust estimates for the standard errors. Differences model This model assumes that the low-income WOPI can be regarded as an appropriate control group, and that any price response of the other two groups can be measured as a deviation from the control group behaviour. We then focus on the differential utilization of experimental and control groups as a function of the price differential. A crucial homogeneity assumption is inescapable for this approach to work, namely that the price elasticity in the control group is equal to that in the experimental group, i.e. that
jk=
j3
j and k=1, 2. In other words, we have to assume that, after correction for any possible differences in time trends and regional effects, both groups are homogeneous with respect to their price-sensitiv￾ity. It is then as if both groups are drawn from the same population and only one of the groups is subjected to price variation. The main problem with this approach is that, in general, one can never be certain about the validity of the homo￾geneity assumption. In our case, however, we can test whether the price elasticities of the two exper￾imental groups are equal. The consequences for the estimation procedure are as follows. Starting from Equation (1), and assuming that
j1=
j2=
j3=
j
j, we take the difference between the equation of the experimen￾tal group and the control group, for k=1, 2 ln qitjk−ln qitj3=
j(ln pitjk−ln pitj3) +j(k−3)Tt+
31 i=1 ij(k−3)Ri+itj(k−3) (2) where
j=
j1=
j3=
j2 j(k−3)=jk−j3 ij(k−3)=ijk−ij3 itj(k−3)=itjk−itj3 As we will automatically obtain two separate estimates of
j (for j=1, . . . , 3), one from the difference equation for the general population and another from the equation for high-income WOPI (call them
j(k) for k=1, 2), we can test whether the homogeneity assumption is rejected by testing for
j(1)=
j(2) for j=1, . . . , 3. Testing strategy Estimation of Equation (1) provides j k parame￾ter vectors [
jk, jk, ijk (i=1, . . . , 31)] (one for each combination of k and j), whereas estimation of Equation (2) provides j (k−1) parameter vec￾tors [
j(k) , j(k−3), ij(k−3) (i=1, . . . , 31)]. Based on the Rand HIE results, we can formulate some hypotheses concerning the relative values of these parameters 1. Estimated price elasticities are negative for all groups and for all types of care. 2. In terms of between-group differences, we ex￾pect the general population to be more price￾responsive than the ‘needy’ groups (high- and low-income WOPI). One argument for this hypothesis is the better average health status of the general population. It is also possible to argue that the utilization by the WOPI is less price elastic, because they can be persuaded more easily by the physicians to take more treatment. Our data do not allow us to distin￾guish the demand and the supply effects, as we are only capable of estimating the overall price effect. For the low-income WOPI, price-sensi￾tivity can hardly be measured owing to lack of price variation in the period considered. 3. In terms of between-visits differences, we ex￾pect (a) a higher price sensitivity for GP than Copyright © 2001 John Wiley & Sons, Ltd. Health Econ. 10: 457–471 (2001)