A frequent topic of investigation in health economics is to estimate the elasticity of the demand for medical procedures with respect to wait times. A paper by Martin, Rice, Jacobs and Smith in the Journal of Health Economics uses quarterly data from 200 English hospitals between 1995-2002 in order to separately estimate the supply and demand curves for elective surgery. On the demand side, patients care about the cost of the surgery as well as the quality of the doctor. Quality is comes in two forms: clinical quality (i.e.: health-related outcome measures such as QALYs) and responsiveness (i.e.: notions of patient autonomy and convenience). Clinical quality is measure by the mortality rate of each surgery, the staff sickness rate and the staff surgery rate. Responsiveness is measured by patient wait times. On the supply side, hospital managers care about the volume of care and quality of care as well as managerial effort. One issue to deal with is that British patients can elect to have either NHS or private treatment, but if NHS treatment is chosen then provider choice is usually limited. Price is approximately the same for each person; the only difference in terms of cost is implicit cost of the accessibility of private facilities. Thus, the authors include a term for ease of access to private acute hospital beds. More private hospital bed availability should decrease demand for NHS services.
The major problem with estimating supply and demand separately is that the residuals of the two regressions could be correlated. Since the demand and supply equations are overidentified (i.e.: there are explanatory variables in the demand equations which do not appear in the supply equation, and vice versa), the authors can use a seemingly unrelated regressions (SUR) framework. Also, because of the time series nature of the data, a lagged dependent variable is also employed in some specifications.
As predicted the authors find that longer wait times decrease demand. The estimated elasticities are similar to figures found in earlier studies [Martin and Smith 1999 (-.021), Gravelle et al. 2003 (-0.21), and Dusheiko et al. 2005 (-0.10)]. The SUR estimates give a lower elasticity of demand than those obtained with OLS. A more surprising result is that longer wait times increase supply in terms of the number of admissions from the waiting list and the number of outpatient referrals seen. The authors found the elasticity of supply with respect to wait time was small however 0.05 to 0.10, whereas Martin and Smith (1999) found an elasticity of supply of 2.93 and a later paper [Martin and Smith (2003)] found an estimated elasticity of supply of 5.29.
- Martin; Rice; Jacobs; Smith (2007) “The market for elective surgery: Joint estimation of supply and demand” JHE, vol 26, issue 2, pp. 263-285.