Organisational determinants of production and efficiency in general practice: a population-based study

In principle, citizens can choose to be outside the list system but as less than 2% of the population has done this, it is of no analytical importance in the present study.

This is due to the fact that log transformation does not apply when some inputs have the value 0.

A third relevant input parameter is capital or technological endowment. Unfortunately, data on technological equipment in general practice are not available. Omission of this input parameter is not perceived as majorly problematic as the level of technological endowments is probably relatively low in Danish general practices. Technological equipment mostly consists of simple diagnostic equipments such as lung function spirometry machines, urin stix and virus test, and the variation across practices is likely to be minor. It should be noted that the presence of nurses may pick up some of the effect if there is correlation between employing nurses and level of investments in diagnostic equipment.

One often used approach to assessing determinants of efficiency has been to apply a two-step approach where the efficiency estimates are estimated in step 1 where after these estimates are regressed on a set of variables assumed to influence efficiency. This approach has been widely criticised, and various solutions have been suggested among these the Batese and Coelli one-step maximum-likelihood estimator [3]; [8] (see [21] chapter 7 for a good overview of other solutions).

From (3), the marginal productivities can be derived at the mean of the involved variables as \( f_{\text{GP}}^{'} = \hat{\beta }_{1} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \hat{\beta }_{3} (\overline{\text{GP}} )^{{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \hat{\beta }_{5} (\overline{\text{GP}} )^{{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }} (\overline{\text{NS}} )^{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} } \) and \( f_{\text{NS}}^{'} = \hat{\beta }_{2} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \hat{\beta }_{4} (\overline{\text{NS}} )^{{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }} + \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} \hat{\beta }_{5} (\overline{\text{NS}} )^{{ - \raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} }} (\overline{\text{GP}} )^{\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} } \) respectively.

Thurston and Libby refer to two different approaches to calculating elasticities. In one approach, the elasticity is evaluated at the mean level of production as defined in (6), while the other approach involves the estimation of elasticities for each GP. In the latter, the elasticity is then presented as the mean elasticity between GPs, i.e. \( \eta_{\text{GP,NS}} = \frac{1}{N}\sum\nolimits_{i = 1}^{N} {\frac{{q_{i} \cdot f_{\text{GP,NS}}^{''} }}{{f_{\text{GP}}^{'} \cdot f_{\text{NS}}^{'} }}} \). This approach has the advantage that confidence intervals can be derived directly without the use of bootstrapping [41]. However, it has the disadvantage that the elasticity can only be calculated if the GP has a positive value of both inputs. If this is not the case, it is not possible to derive the first-order derivatives and hence \( \eta_{\text{GP,NS}} \) cannot be derived. This entails that GPs that do not employ nurses will not be included in this approach. We use both approaches and compare the results.

Notice that the minimum value of weekly nurse hours is 0. This is because 48% of the practices did not employ nurses.

The effect of the various GP- and practice-specific variables on the efficiency is shown in the lower part of Table 3. Notice that u in Eq. 2 and hence in Table 3 should be defined as inefficiency as it is estimated as the distance to the (optimal) production frontier. Hence, a positive sign of the beta coefficients in the lower part of Table 3 indicates that the specific variable increases inefficiency and hence reduced efficiency.