Academic Articles Hospitals Supply of Medical Services

Payer type and the returns to bypass surgery: evidence from hospital entry behavior

It is often very difficult to determine price data for various medical procedures. With the exception of Medicare or Medicaid data, hospitals often do not publish their prices for each service and even when the prices are provided they rarely correspond to the true prices paid. Published prices often do not take into account different discounts negotiated by each insurance company with the hospital. How can we determine the returns to performing a surgical operation without any price data?

Chernew, Gowrisankaram and Fendrick (2001) attempt to solve this problem. They model hospital entry behavior into the coronary artery bypass graft (CABG) market as a function of the predicted patients flow to the hospital after entry. For instance if a hospital in a poor neighborhood would enter the CABG market, they may attract only the uninsured, Medicaid, and Medicare patients. If these types of insurance compensate doctors at a lower rate than FFS insurance, entry would likely be unprofitable for the hospital. On the other hand, a hospital in a wealthy suburb may attract FFS patients whose insurance would pay physicians at a higher rate than Medicaid or Medicare. Entry would be profitable in this case.

Estimation – Predicted Volume

To estimate the predicted volume at a hospital, the authors use a conditional choice model based on McFadden (J Pub E 1974). The latent utility function for individual ‘i’ choosing hospital ‘j’ is:

  • U_{ij}=X_{i,j}β_i + f(D_ij)λ_i + ε_{ij}
  • ε_{ij} ~ Type I extreme value

Here, ‘X‘ are a vector of covariates and ‘D_ij‘ is the distance from the individual’s home zip code to hospital ‘j‘. Using McFadden’s derivation (see also Wooldrige pp. 500-504), we find the probability that person ‘i’ is treated at hospital ‘j’ is:

P(Y_{ij}=1) = exp(X_{ij}β_i + f(D_ij)λ_i) / [Σ_k exp(X_{ik}β_i + f(D_ik)λ_i)]

The predicted volume for hospital ‘j’ for payer type ‘h’ is simply the sum of P(Y_{ij}=1) over all individuals ‘i’ who have payer type ‘h’. The estimation of Q_h,j must be performed for each type of insurance payers.

  • Q_h,j= Σ_i P(Y_{ij}=1)

Estimation – Entry Decision

Now that the predicted volumes are estimated, the authors must try to predict whether or not a hospital will enter the CABJ market. A hospital will enter if the total net revenue will exceed profits. In other words, the hospital will enter if and only if:

  • Σ_h [Q_{h,j}*(P_{h} – AVC_{h}) ] + K_j > 0
  • K_j=Z_j*γ + ν_j
  • Σ_h [Q_{h,j}*R_{h}] + Z_j*γ + ν_j > 0

Here, ‘Q_{h,j}’ is calculated from the regression above, ‘R_h‘ is the average net revenue for patient with insurance type h, and the fixed cost ‘K_j’ is made up an observable (‘Z’) and unobservable (‘ν_j’) component. If ν_j ~ iid N(0,1), the we can use a standard probit to estimate the probability of entry.

  • P(entry_j|no CABJ at t-1)=Φ[Σ_h Q_{h,j}*R_{h}] + Z_j*γ]

Entry will be determined by the predicted volume of patients by payer type. The authors also test the robustness of their specification by later allowing serial correlation and then instituting a cox hazard model into their formulation.


The paper uses data from the California Office of Statewide Health Planning and Development (OSHPD) which has over 300,000 hospital discharges between 1984 and 1994. The authors find that when a hospital will attract many FFS patients, it is approximately 20% more likely that the institution will enter the CABJ market. On the other hand, when a hospital attracts many Medicaid patients it is approximately 60% less likely to enter the CABJ market.

This paper’s main contribution is to create a novel estimation method for the estimation of price on hospital entry without needing explicit price data.