بازار برای عمل جراحی انتخابی : برآورد مشترک عرضه و تقاضا

This paper develops models of the demand for and supply of elective (non-emergency) surgery using a panel of quarterly data for 200 English hospitals over the period 1995–2002. Unusually, distinct measures of supply (outpatients seen and inpatient admissions) and demand (outpatient referrals and decisions to admit) are available for each observation. These offer the opportunity to estimate separate empirical models of supply and demand using ordinary least squares (OLS) regression methods. However, the strong correlation between the residuals of these models suggests some merit in the deployment of seemingly unrelated regression (SUR) methods. Although both static and dynamic SUR estimations leave the results largely qualitatively unchanged, SUR estimation can have a considerable quantitative effect relative to the OLS results. For example, SUR estimation generates a lower elasticity of inpatient demand with respect to waiting time than that obtained via OLS. The results offer an important justification for more careful econometric modelling of hospital behaviour than has traditionally been employed in the health economics literature.

Numerous empirical models of the supply of and demand for health care have been reported in the literature. Typically, these model demand as a function of price, indirect costs to the patient, and various measures of quality, such as waiting time (Cullis et al., 2000). Models of supply depend more heavily on institutional arrangements, but typically require modelling of revenue sources, case mix and quality of care, as well as a range of ‘environmental’ factors that affect the provider's ability to produce care. In the hospital sector, examples include Goddard and Tavakoli (1998), Gravelle et al. (2003), Martin and Smith, 1999 and Martin and Smith, 2003 and Windmeijer et al. (2005). In this paper we concentrate on the market for elective (non-emergency) hospital surgery in a system of public health care (the English National Health Service). To date, most empirical modelling of supply and demand has been hampered by the availability of only one measure of the quantity of health care—namely, the amount delivered by a provider in a specified period. This quantity results from the interaction of supply and demand, and so the empirical analyst must either be content to model quantity as a reduced form equation, making policy inferences difficult, or resort to advanced econometric methods in an effort to model supply and demand separately. In contrast, in this study we have available distinct measures of supply and demand for each period, offering the opportunity to develop quite straightforwardly separate models of supply and demand. However, separate estimation of supply and demand models may ignore important information contained in the data and lead to serious estimation inefficiencies. Specifically, if the residuals from the supply and demand models are correlated, it may be the case that there are important variables omitted from the empirical models. Simultaneous modelling of supply and demand, using the methods of seemingly unrelated regressions (SUR), can take advantage of these correlation structures to offer more secure coefficient estimates. After deploying routine OLS methods, this paper employs SUR methods to model important links between supply and demand equations. As in most markets, some notion of price will often play an important part in any model of elective surgery, even in a public service system. Even if patients pay no direct price for care, there might be important variations in the opportunity cost of using different providers that we should seek to model. And on the supply side the provider's revenue stream must be modelled. In addition, one of the most important influences on the market for surgery is likely to be the notion of the quality of care. Health care quality can be considered under two broad headings: clinical quality, as expressed in health-related outcome measures such as quality-adjusted life years (QALYs), and responsiveness, the extent to which the health system performs in relation to non-health expectations, embracing notions such as patient autonomy and convenience (WHO, 2000). The routine collection and public dissemination of quality data is intended to affect both the demand for and supply of health care. On the demand side, patients and their representatives (such as general practitioners) might seek out the higher performing providers. On the supply side, given the right incentives, providers may strive to improve their reported quality. This paper therefore also seeks to incorporate quality measures into the model of elective surgical procedures in UK. The arguments set out above suggest that quality indicators will affect both the demand for and supply of elective surgery. This paper provides empirical estimates of the elasticities associated with such measures. Given the UK policy preoccupation with waiting times, we concentrate on variables associated with waiting. However, the models are of general relevance to examining the role of quality in supply decisions, and we therefore take the opportunity to examine the influence of the limited range of other quality measures available over the study period. This paper builds on previous studies that have estimated supply and demand functions for elective care. Martin and Smith, 1999 and Martin and Smith, 2003 estimated demand and supply models in which waiting time acts as a price that simultaneously deters demand and encourages supply. These studies were forced to assume that waiting lists were in equilibrium with the queue length relatively stable. Because we now have available separate measures of supply (outpatients seen and inpatient admissions) and demand (outpatient referrals and decisions to admit), this paper drops the assumption of equilibrium and estimates jointly supply and demand functions. In addition, because the waiting time data employed previously were based on individual records of patient care, the demand results were more robust than the rather rudimentary supply side findings. Here, with the hospital as the unit of analysis and access to a considerable database of hospital characteristics, modelling of the supply side is considerably strengthened, and we are also able to model for the first time both outpatient and inpatient care. The next section sets out a simple theoretical model of the determinants of demand and supply. Section 3 outlines the specific institutional context in UK, Section 4 describes the English hospital dataset that forms the centrepiece of the empirical study, and Section 5 provides estimation details. Both static and dynamic versions of the supply and demand models are presented in Section 6, first using OLS techniques, and then applying seemingly unrelated regression (SUR) methods. The paper concludes with an assessment of the implications of the study for modelling waiting times.

This study has estimated supply and demand functions for elective surgery in the English NHS over the period 1995–2002. The estimated models reflect four advances: first, no assumption of equilibrium has been made so that NHS waiting lists are free to vary according to levels of supply and demand; second, an extensive database on hospital characteristics has been deployed to ensure that the models are sensitive to variations in hospital circumstances and, in particular, to the quality of service provided; third, the supply and demand models are applied to both outpatient and inpatient services; and fourth, the joint estimation of supply and demand functions has revealed that OLS can generate misleadingly large elasticities on some variables if others are imperfectly measured or are omitted altogether. The results are consistent with economic theory. On the demand side, longer waiting times serve to depress demand (in the form of additions to the waiting list and outpatient referrals) to a modest but measurable extent. On the supply side, longer waiting times serve to stimulate activity (in the form of admissions from the waiting list and outpatient referrals seen), again to a small but measurable extent. In addition, we found that a number of variables – such as measures of case mix and the number of beds – also affected the supply of elective care in the anticipated fashion in the static model but that in the dynamic model most of the supply/demand shifters became statistically insignificant. We view these two sets of results as complementary: the static models investigate the role of supply/demand shifters while the dynamic models ascertain the level of supply/demand persistence in the data. In the dynamic models we do not place great weight on the supply/demand shifters, but instead view these, together with their respective within hospital means, as conditioning variables to enable us to derive consistent estimates of the parameter on the lagged dependent variable. Sensitivity analysis shows that the persistence effect is relatively insensitive to the specification of the conditioning variables. Indeed, the persistence effect is so strong that the inclusion of the lagged dependent variable in the dynamic model, combined with the lack of variability in many of the supply/demand shifters, renders most of the latter variables – which were significant in the static model – insignificant in the dynamic model. We also found that the demand response to waiting times was more rapid than the supply response, both for the static and dynamic models. Our results are generally consistent with those obtained by other studies of the demand for and supply of NHS health care. The Martin and Smith (1999) study was based on Hospital Episodes Statistics (population) admissions data for routine surgery for 1991–1992 and employed the electoral ward as the unit of analysis. Their model was an equilibrium one – it assumed that queue lengths were reasonably stable – and obtained an elasticity of inpatient demand with respect to the mean wait of about −0.21. Gravelle et al. (2003) estimated the same model as that employed in this study but applied the model to English Health Authority data for 24 quarters from 1987 to 1993 for routine inpatient surgical admissions. They obtained an elasticity with respect to the proportion of patients waiting more than 3 months of about −0.21 although they were unable to detect any significant ‘needs’ effect on demand. Gravelle et al. (2002) modelled the determinants of inpatient admission rates for cataract surgery across general practices in North Yorkshire Health Authority over the period 1995–1998. They found that increases in waiting times have the anticipated negative effect on demand and that the elasticity of demand with respect to waiting time was −0.25. Finally, Dusheiko et al. (2005b) investigated the impact of the UK's GP fundholding scheme under which general practices could elect to hold a budget to meet the costs of elective surgery for their patients. This study found that the elasticity of elective admissions with respect to the mean waiting time was −0.10. There are fewer estimates of the elasticity of supply. Martin and Smith (1999) reported an elasticity of supply with respect to waiting time for all routine surgical specialties of 2.93 and, in a later study, obtained an elasticity of 5.29 (Martin and Smith, 2003). These are substantially larger than the elasticities we have found in this study (ranging from 0.050 to around 0.100). One reason for this difference might be the very rudimentary nature of the supply model in these earlier studies compared with the more comprehensive equation estimated here. The difference may also be due to differences in estimation procedures (cross-section versus panel, or the year used, or the technique used (IV versus OLS, SUR)). It might also reflect the fact that the elasticity in equilibrium differs from that in disequilibrium. In their linear supply equation for inpatient care, Gravelle et al. (2003) report a coefficient of 0.17 on their mean waiting time variable. This implies an elasticity of 0.083 (at the mean of the variable). This is of a similar magnitude to figures we have obtained yet the two studies employ different units of analysis (Health Authorities rather than hospitals) and different time periods (1987–1993 rather than 1995–2002). Most recently, in a study of a single hospital in Scotland over the period 1997–2001, Windmeijer et al. (2005) report a slightly higher positive elasticity of overnight inpatient admissions with respect to waiting times (0.40) and a more modest response for day cases (with an elasticity of 0.13). They also employ the number of outpatients seen as a measure of outpatient demand and report an elasticity of outpatient visits with respect to the mean wait of −0.31. We found that the residuals from OLS estimation of the individual demand and supply functions were highly correlated and, as a consequence, the SUR estimator was employed. We cannot be certain about the reason for this correlation, but we believe that it is most likely attributable to the omission of a time varying measure of need from the estimated supply and demand models. The SUR estimator transforms the OLS errors so that they are no longer correlated and then applies this transformation to the other variables in the models which are then estimated by OLS. Thus the SUR estimator can be viewed as ‘purging’ the other variables of their correlation with the time-varying element of the need for health care. Qualitatively, SUR estimation yielded similar results to OLS estimation but, for some variables, SUR estimation reduced the absolute size of the estimated coefficients, particularly on the waiting time variable in the demand equation, and on the beds variable in the supply equation. However, SUR estimation of both the static and dynamic models left the broad structure of our results unchanged, with waiting time having a positive impact on supply and a negative – albeit less marked – effect on the demand for NHS health care. From a policy perspective this reduction in the demand elasticity is good news for it suggests that any increase in demand following a reduction in waiting times might be less than had previously been anticipated. These results offer an important justification for more careful econometric modelling of hospital behaviour than has traditionally been employed in the health economics literature.