58 3.5.3. Model Speci? cation I – First Differences We use OLS regressions to test the existence of a statistically signi? cant relationship between drug expenditure and political interests. We hypothesise the following relationship: . (3.1) Thus we assume that the amount of drug expenditure in year t per insured person (Expt) is dependent on the age structure of the insurants (Age??t), the basic wage total per SHI member (BWaget), the share of co-payments on total drug expenditure (CPayt) and politicians’ interests (PDumt). Since the estimations are based on annual values (from 1983 to 2004) we presume static relationships. All monetary variables represent real values de? ated with the pharmaceutical price index (2000 = 100 %). Starting in 1993, the data for the new German Laender are included. Before we can start the regression analysis, it is ? rst necessary to check the time series for stationarity, i.e. if their means and variances are constant over time. If the time series is non-stationary, the problem of spurious regressions arises and OLS results will be inef? cient. Therefore we use the Augmented Dickey-Fuller (Dickey and Fuller 1979) and the Philips-Perron (Philips and Perron 1988) tests to verify the existence of unit roots. It can be supposed that the time series of drug expenditure, age ratios and total wages are probably trend dependent. Accordingly, a trend variable has been included into the stationary tests. Only co-payments reveal no consistent time trend and hence only the constant term has been considered. Table 3.1: Stationarity Tests. Augmented Dickey-Fuller Philips-Perron Variable Regression t-Statistic t-Statistic log (Exp) Level 1st diff erence c, t c -3,2 -4,612*** -2,887 -5,835*** log (Age??) Level 1st diff erence c, t c -0,781 -2,851* -1,047 -2,811* log (BWage) Level 1st diff erence c, t c -0,715 -3,247* -0,715 -3,215* log (CPay) Level 1st diff erence c c -1,67 -3,944*** -1,67 -4,312*** Note: *** Non-stationarity rejected at a 1% critical level; * at a 5% or 10% critical level. c = constant, t = trend; t-statistics based on MacKinnon critical t-values. As table 3.1 shows, it is not possible to reject the existence of a unit root for any of the time series. However, non-stationarity can be rejected for all variables in ? rst differences. So we can assume that the variables are I(1), i.e. they are integrated of order one, and follow a random walk. 59 Since the variables are I(1) we run the model in ? rst differences (? indicates differenced values). The theoretical equation is speci? ed in a double-log functional form including no constant but an error term: (3.2) . 3.5.4. Results The results of the estimated regressions are presented in table 3.2. The age dependency ratio (Age??) and the share of co-payments (CPay) are the only variables which are highly signi? cant in all regressions. Thus at ? rst glance we can already state that the ageing population enforces drug consumption whereas higher co-payments entail demand reductions. For further interpretations we must look at the models in more detail. Table 3.2: Regression results. Variable Model 1 (Basic) Model 2 (Opportunistic) Model 3 (Partisan) Model 4 (Partisan & Opportunistic) Model 5 (Partisan & Opportunistic & Corporatistic) Age?? 1,228** (2,63) 1,049** (2,135) 1,378*** (3,404) 1,477*** (3,145) 1,466*** (3,29) BWage 0,921** (2,651) 0,658 (1,57) 0,44 (1,267) 0,915** (2,759) 0,906** (2,828) CPay -0,184*** (-5,052) -0,177*** (-4,813) -0,196*** (-6,193) -0,198*** (-5,533) -0,197*** (-5,763) PDum -0,025 (-1,11) 0,023** (2,717) 0,014 (1,668) 0,016* (2,05) Adj. R2 0,476798 0,483401 0,613737 0,595365 0,622468 Durbin/Watson 1,808 1,838 1,967 2,142 2,362 Note: *** indicates signi? cance at the 1% level, ** at the 5% level, and * at the 10% level. We start with the basic model 1, which contains no political dummy variable. With less than 50 %, the value of the coef? cient of determination, the adjusted R2, shows a quite unsatisfying ? t, which indicates that at least one additional explanatory variable might be missing. Including opportunistic behaviour (model 2) only marginally improves the results. Neither the political dummy variable (PDum) nor wages (BWage) are signi? cant. Additionally, the dummy has a negative sign, which is extremely implausible. It must be assumed that the purely opportunistic model is not adequately speci? ed. In contrast, all estimations that consider partisan behaviour (models 3, 4 and 5) clearly deliver improved outcomes: the adjusted R2 rises to around 60 %. Compared to all other regressions, the purely partisan model 3 provides the highest degree of signi? cance of the dummy variable, but still exhibits problems with the relevance of wages. Model 4 overcomes this obstacle, but in turn the political dummy loses signi? cance.