Richardson (1981)
The main focus of Richardson (1981) was to test the hypothesis that GPs generated their own demand. Two systems of equations were estimated: one assumed GPs were price takers and included a supply equation; the other assumed GPs had the ability to set prices, and did not include a supply equation or equilibrium assumption. The data used were 1976 pooled cross-sectional data from the Medibank system (Medibank was the predecessor to the current Medicare). The data were analysed at a Statistical Division level (56 observations).
This approach is subject to the technical criticisms outlined in McGuire (2000), but was the first such study in Australia. The most problematic of the results was the finding of a positive net price elasticity in the GP demand equation, which was inconsistent with all other analyses (including Richardson and colleagues later work). Richardson drew a range of conclusions from the equations, focusing on the significant role of GP density in the demand equation which gave credence to the inducement hypothesis.
Richardson (2001), Richardson & Peacock (2006)
Richardson (2001) (further developed in Richardson & Peacock 2006) used 1996 data for Statistical Sub-divisions (SSDs: 187 observations) to re-estimate the equilibrium equations of Richardson (1981). The model was summarised as:
) ˆ , , , ˆ ( 1 C O D SES INC P f QD n (1) ) / ( * Q DOC DOC QS (2) ) , ˆ ( 2 RES P f DOC g (3) D S Q Q (4)
where QD,QS represent the services per capita demanded and supplied, Q the services per capita actually provided, Pg, Pn represent gross price and net price per service, SES represents a set of socio-economic indicators, DOC represents the number of GPs per capita in an area measured as Full Time Equivalent GPs (FTEGPs), RES represents a set
of indicators of a desirable residential location for a GP, and ^ indicates an endogenised variable. Table 2.3 summarises the results of this analysis.
Table 2.3: Richardson (2001) model
Equation Estimated coefficients
Supply Demand
Dependent variable FTEGP/10,000 Q/Capita
OLS OLS 2SLS Net price -0.28** -0.42** Gross price 0.16* FTEGP/10,000 0.39** 0.40** Population density 6.82** Hosp/10,000 -0.31** Urban dummy 1.12** Vic -1.52** ACT -2.53** NT -0.46** WA -0.99** % Aboriginal -4.29** -4.01** Constant 1.95 3.57 3.86 R2 0.69 0.83
** significant at 1% level, * significant at 5% level.
Note that only statistically significant variables have been provided. It is not clear if insignificant variables have been dropped from the estimation, or simply not reported.
The coefficients on full time equivalent GPs per 10,000 population in the demand equation were interpreted as indicating that supplier-induced demand was statistically significant. Contrary to Richardson (1981), the estimated price elasticity at the mean was -0.23 (comparable for example with -0.22 reported by Manning, Newhouse et al.
1987). The Richardson (2001) estimate of the GP density elasticity at 0.46 was very high by comparison with Cromwell & Mitchell (1986) who estimated the physician elasticity as 0.09 for surgery and Fuchs (1978) who estimated the elasticity for surgery at 0.3.
Doessel (1997) suggested that the methods of Richardson (1981) were subject to the technical concerns outlined by Ramsey & Wasow (1986), as well as potential identification problems. The substantive identification issues were documented by Auster & Oaxaca (1981) and Folland, Goodman et al. (2001, p. 211). Richardson
(2001) addressed the Auster and Oaxaca issue by use of a measure of supply which was not perfectly correlated with observed demand. The Folland, Goodman et al issue
(which is outlined in Section 2.4.1) was addressed in Richardson & Peacock (1999) where they argued that this was not of concern in the context of estimation of the two stage least squares equation where the variable of interest (GP density in this case) is endogenous and so introduced in a stochastic predicted form.
There are many critiques of the approach to supplier-induced demand based on
aggregate data and 2SLS estimation. Ramsey & Wasow (1986) and Dranove & Wehner (1994) provided the strongest and clearest critiques.
Ramsey & Wasow (1986) argued that all the papers up to that time exploring supplier- induced demand had major econometric flaws. Their concern with the Fuchs & Kramer (1972) paper (the nearest to Richardson (2001) of those considered) was the apparent omission of important variables and concerns with endogeneity of instruments.
Dranove & Wehner (1994), as noted earlier, showed both that in their specification, which closely followed Fuchs (1986), the system was under-identified as a number of instruments were invalid as they were not uncorrelated with the error in the demand equation, and that there were substantial border crossing biases.
Richardson & Peacock (1999) reported that they used the Hausman approach as
outlined in Godfrey (1988, p. 191) to show that the demand equation was well specified (i.e. showed no evidence of correlation between the instruments and the residuals), and argued that they had addressed the technical issues of Ramsey & Wasow (1986).
They further argued that the problem of boundary crossing was resolved as FTE GPs were divided between areas if the GP worked in more than one area. This, however, does not remove the problem, as the GP (or part GP) was still associated with the area in which they provided services, while patient data were associated with the area in which the patients resided. Border crossing issues remained as the GPs in an area provided services to patients who may or may not have been residents of the area. At the extreme, in inner city areas with small populations, many services may have been provided to people who worked in the city and lived in the suburbs.
To prove the relevance of GP supply in the demand equation, Richardson (2001) re- estimated the equation without GP supply and showed the residuals from this equation were highly correlated with GP supply, and also undertook more formal tests that GP supply was relevant to the demand equation. Richardson put considerable emphasis on this result as evidence that GP supply should be included in any model of demand. However, a strong correlation between numbers of services and numbers of GPs in an area was not surprising, and the real question was correlation with demand. This test cannot answer this question, particularly as the specification included so few other exogenous demand predictors.
Richardson (2001) did not report any test of omitted variables for the demand equation, and the small number of variables reported is of concern. The supply equation was tested for omitted variables but not for instrument strength.
Freebairn (2001) reviewed Richardson (2001) and provided a strong critique on both the theory of SID and econometric issues. The latter have all been discussed above. The theoretical concern is that the effect of GP supply need not be SID but may be an availability effect. This is a valid concern, and one which was not acknowledged. These factors are addressed in more detail in the context of the modelling in this thesis in Chapter 7.
Richardson (2001) has addressed the relevant identification issues and provided tests for the most likely areas of misspecification. While the endogeneity tests were appropriate, the potential for omitted variable and border crossing biases remained.
Richardson, Peacock et al. (2006)
Richardson, Peacock et al. (2006) addressed the question of the determinants of bulk
billing and charging levels using a basic model similar to that of Richardson (2001). The equations were structured as shown above, with the addition of:
4 3(... ) e DOC f EB (5) 5 4(... ) e DOC f BB (6)
where BB = bulk billing rate and EB = average extra billing per service when billed (also referred to as the gap payment or co-payment).
Incorporating the identities reflecting relationships between bulk billing, gross and net fees, and gap payments and simplifying led to :
8 4 3 2 1 0 d DOC d D d S d BB e d Fee Gross (7)
Equations (5), (6) and (7) were estimated using 2SLS. Equations were estimated separately for specialists and GPs. Equation (7) was modelled with and without bulk billing.
It is not clear that equation (7) was a validly specified structural equation as, while bulk billing was associated with gross fees in a mathematical sense, it was not clear that this was so in a behavioural sense. In other words it was not at all clear that the decision of a GP to bulk bill a certain group of patients defined the average gross fee charged. It was equally arguable that the decision process worked in the opposite direction, with the gross fee set by market factors and the GPs desired income. The bulk billing rate and the co-payment level would then be jointly set to generate the required gross fee. Later work in this thesis supports the latter view.
Richardson, Peacock et al. (2006) concluded that:
overall fees increased with number of GPs in an area if the bulk billing rate was included in the equation (although the effect was very small). This effect disappeared if the bulk billing rate was not included in the equation:
o This is consistent with the view above that including bulk billing in the equation
was a mis-specification;
o It is, however, surprising that fees should stay stable when the supply of GPs
increased;
including a variable for the level of the Medicare rebate in the fees equation showed that an increase in the rebate would be reflected in the fees and absorbed by the GPs rather than reducing charges faced by patients:
o While this conclusion is supported by later analysis in this thesis, it is not a
correct interpretation of the Richardson, Peacock et al. (2006) analysis;
o As the Medicare rebate for any service was fixed across Australia at any point of
time, the variable labelled ‘rebate’ in their cross-sectional data reflected
variability in service mix, not in rebate. The areas with high ‘rebate’ were areas with higher proportions of longer consultations. Conclusions cannot be drawn about the impact of changing the MBS rebate since the variable did not reflect the government rebate but the service mix;
bulk billing increased with more GPs as would be expected;
extra billing, when applied, increased when the number of GPs was higher:
o This is not implausible as a ‘compensating effect’ if levels of GP supply do not
affect overall fees and bulk billing rates increase with GP supply; and overall the authors noted that the effects were quantitatively very small, and
indicated “that fees are highly insensitive to the competitive supply of doctors”.
Richardson & Peacock (2003)
This paper was entitled “Will more doctors increase or decrease death rates?” and used the same broad structure as their previous papers with the addition of an equation for standardised death rates. The data comprised Medicare information at the Statistical Sub-Division Level for 1994–95, 1991 census data, and published mortality data. The equation added to the model was:
4 3 2 2 1 0 d DOˆC d (DOˆC) d M e d SMR (8)
where variables were as previously defined, except that SMR was the standardised mortality rate for the specified area, and M the exogenous mortality-related variables.
As in previous modelling, an equation was estimated for GP density although the
specification was varied. This generated a significant negative coefficient for gross fees charged in the GP density equation, meaning GPs were less likely to work in areas with higher fees. This is implausible, and inconsistent with Richardson and colleagues’ previous work.
This unexpected result was probably due to inclusion in the GP density equation of a variable reflecting GP workloads which appears to have been treated as exogenous. Not only should this be endogenous, but it is also not clear it belongs in the equation. While some GPs will prefer to work in practices with lower (or higher) workloads, there was no reason that this would apply to geographic areas. This suggests that the negative sign on the GP workload variable was due to an arithmetic relationship – the number of services per capita in any area was broadly stable, so GP density and GP workload had an inverse arithmetic relationship.
The modelling showed a strong relationship between GP numbers, GP numbers squared and SMR. The model as described in Equation 8 appears to have used the squared value of the projected GP density rather than treating GP density squared as a separate variable in its own right and independently instrumenting this squared variable. This method would not be valid, being what Wooldridge (2002, p. 236) calls a ‘forbidden regression’. It was also likely (although not reported in the paper) that the variables GP density and GP density squared were extremely highly correlated.
GP density had a negative coefficient and GP density squared a positive coefficient in these models, with the turning point near to the average density, and death rates increasing with numbers of GPs beyond this point.19
19 Connelly & Doessel (2004), looking at Table 6, column 6.1 of Richardson & Peacock (2003) argued
that the turning point of the estimated equation which had coefficients of -26.11 for GP numbers and 1.88 for GP numbers squared was 13.88 which was outside the range of realistic values. However taking the partial derivative with respect to GP numbers gives (0=-26.11 +2*GP numbers), leading to a turning
Connelly & Doessel (2004) used a different specification and a different estimation strategy, including treatment of income and education as endogenous, and use of a three stage least squares structure, and also use different Australian data to Richardson & Peacock (2003). In doing so they found that “medical expenditure is not only health- improving (mortality reducing) but also subject to increasing marginal product.” Connelly & Doessel (2004) used medical expenditure rather than GP numbers as potential determinants of mortality so direct comparison is difficult, but their very different result and the problems with the Richardson & Peacock (2003) specification give cause for concern.