ORGANIZACIONES INTERNACIONALES NO GUBERNAMENTALES

The basic formulation used by Connelly (1999) followed the same supply and demand arrangements as Richardson (1981), and he also estimated a system of equations including or excluding a supply equation (although as discussed above he used a direct form of the supply equation). Connelly focused on a production function equation with mortality reflecting health produced. His data were 1991–92 MBS data for Queensland classified by postcode (postcodes are generally smaller than SLAs), and linked with census and other population data.

The major differences between the Connelly (1999) and Richardson (2001) specifications were the:

 primacy of the production function;

 use of mortality as a potential determinant of demand for GP services;

 incorporation of some border crossing effects by inclusion of measures of numbers of GPs and average fees in the areas contiguous with the postcode of interest;  inclusion of estimated average travel costs within and between areas;

 use of system estimation rather than equation by equation estimation; and  use of the translog formulation.20

20 _{This functional form includes every conceivable quadratic and interaction term, regardless of the} theoretical plausibility. Connelly (1999) manages this large volume of variables by a two step process of eliminating insignificant terms to provide a more manageable final set of variables.

Connelly (1999) also included spatial autoregressive (AR) terms to accommodate any geographic serial correlation in the error terms (with rich suburbs located near each other and poor suburbs located near each other, or with areas of high GP density located next to and serving areas of low GP density). He tested for spatial autocorrelation using a Durbin-Watson type statistic and, finding spatial autocorrelation existed, applied AR adjustments to all models.

Connelly noted the high degree of collinearity between own prices and cross prices. To address this issue he estimated one set of models where cross prices and own prices were entered separately in the demand equations, and another set where they were

entered as ratios, although the latter proved not acceptable and are not discussed further.

To assess the stability of estimation, he used two different estimation methods: iterative ordinary least squares (IOLS) and full information maximum likelihood (FIML)

techniques. Although the FIML approach to estimation had many theoretical

advantages, the results from the different model structures and estimation methods were little different.

Table 2.6 shows results (in terms of elasticities at the mean) for his model IIA which included a supply equation, had prices entered separately and was estimated using FIML. The table shows elasticities derived from the large number of quadratic and interaction terms estimated under the translog functional form.

Table 2.4: Connelly model IIA (FIML) – Elasticities

Equation Production Location Demand Supply

Dependent variable Mortality Number of

GPs

Services provided

Services provided Note: all dependent and independent variables in natural logarithm form.

Note: *= significant at 1% ,**= significant at 5%, ***= significance at 10 %

Specialist revenue -0.003 0.01* Percentage of population

aged 65 or over 0.18*

Percentage of population

aged under 15 -0.08

Percent age of population

female 0.84

Percentage of population of non English speaking background

-0.01

Services 0.07***

Revenue per GP 0.01

Population -0.07*

Gross own price -1.38

Cost index -7.13*

Number of GPs 0.17*** 1.22*

GPs per hectare -0.02 0.05*

Net own price -0.31*

Cross price

(i.e.neighbouring area) 0.36*

Travel costs within area -0.19*

Travel costs between -0.06

Average personal income -0.55** -0.73*

Crude mortality rate 0.07*

Percentage of population

Indigenous Australian 0.09* -.05

Mean years of schooling 0.10 -0.09

AR(1) 0.08 0.2* 0.07*** 0.11**

AR(2) 0.14*

R2 0.91 0.99 0.90 0.75

While the approach was system based rather than equation by equation, and had a more complete specification with less obvious concerns than some of those of Richardson and colleagues, it generates broadly similar results. The results were generally in line with expectations, with negative price elasticity of demand and a positive cross price, and mortality higher where there were older people and where incomes were lower. The positive relationship between numbers of GP services and mortality was consistent with

Richardson & Peacock (2003) but not Connelly & Doessel (2004). The positive effect of GP numbers on demand suggested SID (an availability effect), although of much smaller magnitude than Richardson (2001). The location equation was surprising in having a negative population effect and negligible revenue effect.

The R2 values in the location equation seem implausibly high for cross-sectional data, and while this could be due to the pseudo R2 (Berndt 1991, p. 468) used in the FIML context, similar R2 values occurred in the OLS modelling. While Connelly took

comfort from the very high values (most ranging from 0.90 to 0.99, the supply equation had a lower R2 of 0.75), in cross-sectional modelling these are extremely high and suggest some specification issues may have been present.

Connelly noted that the comparable equations in systems with and without a supply equation had fundamentally the same results. Based on this, he suggested that the supply equation was superfluous. Equally it could be argued that it was a reasonable part of the system, which gave advantages in interpretation of overall markets.

The FIML system was used by Connelly (1999) to accommodate endogeneity although it is not clear how it allowed for endogeneity of the terms which are squares of

endogenous terms or interactions with endogenous terms, and it may have suffered from the forbidden regression problem (Wooldridge 2002, p. 236) faced by Richardson & Peacock (2003). The FIML approach addressed the system nature of the GP market, and in particular accommodated the correlation of errors between equations. In practice, the only non trivial correlations (around 0.55) were between the supply and demand equations. Despite this correlation, the FIML approach gave virtually the same answers as the IOLS.

Connelly undertook wide ranging tests of his modelling for spatial serial correlation, heteroskedasticity and for omitted variables, and concluded that the results were robust. Issues of concern which remained include the extreme R2 values, in particular the R2 of 0.99 for the location equations does not seem plausible for cross-section data, as he found a negative elasticity for population as a determinant of GP numbers.

crossing outside major cities would tend to lead to alternating over-supply and under- supply of GPs, and considerable border crossing in practice is from suburbs to central business districts and so can cross many postcodes.

Overall the Connelly modelling provides mostly plausible results, and has addressed the main econometric issues in the context of cross-sectional modelling. The two concerns are the possibility of omitted variables (e.g. some areas being transport hubs which attract patients and GPs but not population), the extreme R2 values and the implausible coefficients in the location equation which lead to concerns about its specification. While border crossing has been addressed, it is not clear that it has been fully resolved.