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Nagase Effect

How do medical care costs respond to different coinsurance rates? The RAND Health Insurance Experiment (Manning, et al. AER 1987) demonstrated that moral hazard is problem; individuals with lower coinsurance rates tend to use more medical services.

In 1935, Kozo Nagase formulated a mathematical heuristic to describe how coinsurance rates affected medical expenditures in Japan. The formula is as follows:

  • y= 1 – 1.6*x + 0.8*x2

Here y is the amount of medical expenditures and x is the coinsurance rate. This formula produces the following values

Coins Rate Relative Med. Exp
0% 1
25% 0.65
50% 0.4
75% 0.25
100% 0.2

A recent paper by Bessho and Ohkusa however claims that medical expenses and coinsurance rates are not related, at least not in the case of acute light illness (i.e.: cold, flu, hay fever, menstrual cramps, sprains, constipation, etc.). The authors use Record Card data in which individuals between 20 and 69 years of age keep logs of household members’ illness related behavior between May and November 2001. The analysis looks at the duration between the first onset of sickness and the decision to visit the doctor.

The econometric specification creates the function λ(k,x) which is equal to the probability of visiting a hospital or physician on the k-th day since they feel sick conditional on exogenous variables, x, and conditional on that they did not consult a doctor during the preceding k-1 days. The problem then becomes a recursive binary choice model where one can use maximum likelihood estimation to find the correct parameters for the following equation:

  • P(k|x)=λ(k,x) Π_{j=1 to k-1} [1-λ(j,x)]

The authors also take into account the fact that some observations are censored by the length of time the individuals were observed. Bessho and Ohkusa find that there is no statistically significant correlation between coinsurance rates and the probability of a physician or hospital visit. Since public insurance covers the majority of acute light illnesses, adverse selection is not a problem. Also, since the patient is the one deciding when to see the physician, supplier-induced demand should not be present.  One issue could be the wait times a patient experiences between calling a physician to make an appointment and the actual date of the appointment.  There is also the problem of whether or not the self-reported record cards are accurate.

Manning; Newhouse; Duan; Keeler; Leibowitz; Marquis; (1987) “Health Insurance and the demand for medical care: Evidence from a randomized experimentAmerican Economic Review, vol 77(3), pp. 251-277.

Nagase, Kozo (1935) Disease Statistics, Tokyo, Kenho Hoken Ihosha (In Japanese).

Bessho; Ohkusa (2006) “When do people visit a doctorHealth Care Management Science, vol 9, pp 5-18.