Unbiased Analysis of Today's Healthcare Issues

Substitution and Price Indices

Written By: Jason Shafrin - Apr• 15•10

In this post, I discussed how to construct the Laspeyres, the Paasche, and the Fisher price index.  In practice, the Laspeyres tends to overstate the price increase and the Paasche tends to understate the price increases.  Let us look at the following example to see why this is the case.

In this spreadsheet, I use the example of a doctor’s visit to an internist and a doctor’s visit to a nurse practitioner.  Assume that there is no health insurance.  In the first period, it costs $200 to see the internist and $100 to see the nurse practitioner.  In this case, 10 patients visit each type of provider (20 total visits).  However, in the second period, the price for an internist visit rises to $350 (75% increase) while the price of a visit to a nurse practitioner only rises to $125 (25% increase).  Because of the difference in both the rate and level of price increases, some patients will stop seeing the internist and will instead visit the nurse practitioner.

Because the change in prices is between 25% (for the NP) and 75% (for the internist), we know the resulting price index value will be between 1.25 and 1.75.  If we use the Laspeyres index and weight the price changes by the initial quantities, the value of the price index in period 2 is 1.58.  However, if we use the Paasche index and weight the price changes by the terminal quantities, then the price index value in the second period is only 1.45.

The Laspeyres overstates the price increase, because it does not take into account the fact that people switched from the expensive internist to the cheaper nurse practitioner.  On the other hand, the Paache index understate the price increases because it ignores the fact that some people had to switch from their preferred provider (internist) to a less preferred provider (NP) because of the price change.  It ignores that some people are getting lower quality care when they switch to the NP.  [Disclaimer! This is just a simple example where I assume internists care is superior to NP care when I realize that in reality, this may or may not be the case].

One could apply the Fisher index as well which is the geometric mean of the Laspeyres and the Paasche.   The Fisher index takes into account the substitution between goods or services over time.  In this case, the price index value is a more reasonable 1.52.

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