## Healthcare Economist

Unbiased Analysis of Today's Healthcare Issues

## Productivity Spillovers: The Case of AMI

Written By: Jason Shafrin - Sep• 23•13

The Healthcare Economist has written a lot about the fact that there exists significant regional variation in health care spending.  Is this due to a provider cultural norms?  Or are other factors at play?

A paper by Chandra and Staiger (2007) claim that productivity spillovers may explain this results.  I summarize their proposition in more detail below.

### Roy Model

The authors generate a propose a simple Roy model with two treatments. Treatment 1 is non-intensive and treatment 2 is intensive. Assume that people value the treatments based on how it effects their survival and how much it costs.

• Si = βiSZ + αiSPi + εiS, where i∈{1,2}
• C= βiSZ + αiSP+ εiS, where i∈{1,2}

The term Z represents provides information on patient characteristics and the term Pi represents the share of patients in a given area (e.g., HRR) that receive treatment i.  We can combine these benefits and costs into a single utility function as follows:

• Ui =Si – λCi = βiZ + αiPi + εi, where i∈{1,2}

where  βi = βiS – λβiC­­, αi = αiS – λαiC­­, and εi = εiS – λεiC­­ .  The term λ represents the value of an additional life year.  The term Z represents the appropriateness of each treatment given the patient’s health and the term Pi captures the productivity spillover, which is positive if αi>0.  In other words, when  αi>0, the benefits of increased specialization outweigh the costs.  The expected utility gain from someone choosing the intensive treatment is:

• E[U2 – U1 | U2 – U1>0] = βZ + αP2 – α1+ E[ε | U2 – U1>0]

This equation has a simple Tobit structure.  Thus, patients who choose the intesnive treatmetn will have a higher expected utility gain from treatmetn if they are more apporpriate (i.e., higher βZ) or live in more intesnive region (αP2).

### Model Implications

The model derived above implies the following:

• The utility associated with nonintensive management is worse in areas that are intensive. This occurs because a high prevalence of intensive surgical treatment crowds out good medical management.
• In intensive areas, patient utility will be higher among patients who are most appropriate for intensive management, but lower among patients who are more appropriate for medical management. In other words, the area’s specialization in intensive management helps patients who are appropriate for this type of care through higher survival or lower costs, but patients who require less intensive management are harmed by the area’s specialization in intensive management.
• Marginal patients receiving the intensive treatment in intensive areas will be less appropriate for the treatment than the average patient receiving the intensive treatment.
• Among those receiving intensive treatment, the benefit to receiving intensive treatment in the intensive area is larger than the benefit in the nonintensive area.

This model is able to generate a number of relationships typically observed in the data. The author explain.

In particular, our productivity spillovers model can generate (1) substantial differences across areas in the use of intensive procedures that are unrelated to average patient outcomes, (2) a negative correlation between surgical intensity and the quality of medical management of a condition, and (3) large returns to receiving the intensive intervention, particularly in high-intensity areas.

### Empirical Results

The authors wish to test if the performance of cardiac catheterization has geographic spillovers. The authors use data from the Medicare National Claims History (NCH) file to identify all AMI discharges. Because the patients that are unobservably more likely to respond positivtely to cardiac catheterization are also the patients most likely to receive this treatment, we have an endogeneity issue. To address this problem, the authors use an instrumental variables approach. The instrument is the differential distance (measured as the distance between the patient’s zip code of residence and the nearest catheterization hospital minus the distance to the nearest non-catheterization hospital.

The results of the authors’ analysis–which largely coincide with the predictions of their model–are the following:

• As predicted by the Roy model, as the area’s intensity increases, the marginal patient is 4.5 percentage points less likely to be appropriate for intensive treatments
• Risk-adjusted cath rates are positively associated with cardiovascular surgeons per capita (physicians who perform cardiac surgery) and the number of cath labs per capita. These correlations are consistent with the view that a higher level of support services available in high-intensity areas may contribute to the externalities.
• “The survival return to intensive management in intensive areas is roughly three times the return observed in low-intensity areas; there is no statistically significant difference in the costs associated with the different areas…As predicted by our model, the most appropriate patients in high-intensity areas have the highest survival returns (and lowest costs) associated with intensive management, whereas the lowest survival returns (and highest costs) are seen among the less appropriate patients in low-intensity areas”
• Patients appropriate for intensive management clearly benefit from being treated in intensive areas. However, as the productivity externality predicts, patients least appropriate for intensive treatments are harmed as a result of being treated in intensive areas.

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