If the government had not been shut down on October 1, the Bureau of Labor Statistics (BLS) would be releasing the consumer price index (CPI) for September this morning. September’s data, together with the data for July and August, provide the basis for the annual cost of living adjustment (COLA) for Social Security.

While we do not yet have September’s data, based on the data from the prior two months, it is likely that the COLA will end up being either 1.5 or 1.6 percent, depending on exactly what the September data show. It is unfortunate that this number is not yet available.

It is striking to note that the COLA provided for by the current index, the consumer price index for wage and clerical workers (CPI-W) is likely to show a lower rate of inflation than the BLS experimental elderly index (CPI-E), which is designed to reflect the purchasing patterns of the elderly. The biggest differences between the two indices are the weights assigned to health care and housing, with both components accounting for a much larger share of the CPI-E than the CPI-W.

The price of medical care services was up 3.1 percent in August from its year ago level. The price of the CPI’s shelter component was up 2.4 percent from its year ago level. As a result of the more rapid price increases in these components, the CPI-E would likely show a rate of inflation that 0.1-0.2 percentage points higher than the CPI-W. This would suggest that the rate of inflation seen by seniors is somewhat higher than the COLA they are now getting for Social Security.

However, this gap would increase if the COLA indexation switched to the chained CPI (CCPI-U). This index typically shows a rate of inflation that is 0.2-0.3 percentage points lower than the CPI-W. The reason for the difference is that CCPI-U incorporates the impact of substitution on consumption costs. If the price of apples rises less rapidly than the price of oranges, and people switch from consuming oranges to apples, then the CCPI would lower the weight it assigns to oranges and increases the weight it assigns to apples. This leads it to show a lower measured rate of inflation, which arguably reflects actual patterns in consumption.

While the CCPI-U may be picking up substitution patterns for the population as a whole, it is not clear that it accurately reflects substitution patterns among seniors. The goods disproportionately consumed by seniors, health care and housing, don’t lend themselves to easy substitution. Furthermore, it is not clear that seniors can substitute for other goods with the same ease as the rest of the population. Unfortunately, neither BLS or the proponents of adopting the chained CPI for the COLA have done research on this topic.

In short, there is some reason to believe that the current COLA already does not adequately compensate seniors for the rate of inflation they experience. This problem would be worse if the basis for the COLA is changed to the chained CPI.