Rounding Error

The BLS is considering a change in the reporting of the CPI. Instead of one digit past the decimal they'd report three digits. Here is the problem (Key Inflation Index ... [$]):

The Bureau of Labor Statistics is contemplating a change in the widely followed consumer-price index that could have a big impact on how markets and policy makers interpret the latest inflation data.

The agency, part of the Department of Labor, is considering publishing the index and its subindexes to three decimal places instead of one, an agency official said. Doing so would greatly reduce the frequency with which rounding produces a misleading inflation rate.

No decision has been announced. If it goes ahead, the change would probably take effect early next year.

The consumer-price index is currently one of the most closely watched economic statistics on Wall Street because it is critical in the Federal Reserve's interest-rate decisions.

In recent months, markets have moved considerably depending on whether the monthly change in the index was 0.2% or 0.3%. (Investors and the Fed focus most closely on the "core" index, which excludes the volatile food and energy components.) July's figure is due out on Wednesday.

Each month, the bureau surveys prices for about 80,000 items in 200 categories and converts the result to an index number. Component indexes are then combined into a variety of aggregates, such as the all-items and the core index. The change in the indexes is then calculated as the inflation rate. June's index, at 202.3, was up 0.2% from May's index reading of 201.9, and up 4.3% from the June 2005 index of 193.9. So the monthly inflation rate was 0.2%, and the 12-month inflation rate was 4.3%. (The index is equal to 100 in 1984.)

But because of rounding, these inflation figures can be misleading -- in two ways. One is that the percentage change is rounded. For example, an increase of 0.249% would be rounded down to 0.2%, while an increase of 0.251% would be rounded up to 0.3%. The difference between 0.2% and 0.3% seems large, but without rounding the difference is trivial. Economists, however, can adjust for that problem by calculating the percentage changes in the indexes themselves.

The second, more serious way the figures can be misleading results from the fact the BLS rounds the indexes as well before publishing them. Suppose the index for one month is 198.945, and then rounded down to 198.9, and the index for the next month is 199.355, and then rounded up to 199.4. The change in the rounded numbers is 0.251%, which rounds up to 0.3%, but the change in the unrounded numbers is only 0.206%, which rounds down to 0.2%.

The difference between 0.2% and 0.3% can have a huge impact on the market.

A working paper by Elliot Williams of the BLS notes the February 2005 consumer-price index released in March that year showed core monthly inflation at 0.3%, above economists' expected 0.2%. Bond prices tumbled and yields rose on the news. But Mr. Williams says the unrounded index would have shown a change of 0.2%, "and would have constituted essentially no news for inflation projections or bond prices."

Mr. Williams's paper found that between 1986 and 2005, using a seasonally adjusted index rounded to just one decimal place produced an inaccurate monthly overall inflation rate 24% of the time and an inaccurate core inflation rate 16% of the time. Using an index rounded to three decimal places reduces the incidence of errors to less than 1% of the time for both. "Increasing the precision of reported CPI levels would go a long way toward making the errors which arise from rounding error negligible," he wrote. (Staff papers don't represent official BLS views.)

Over time, rounding errors tend to offset each other and thus are less of a factor in annual inflation rates than monthly inflation rates.

It sounds like there are significant benefits to the change. What is the cost? In MS Excel, changes in the number of digits past the decimal is easily handled. Does the BLS have Excel?

Comments

[spencer]

Reporting to three digits past the decimal points gives an impression of a precision
in the data that is not there in reality.

Does any one really believe that a difference of one decimal in the reported inflation rate is of economic significance?

If the brokerage houses want to make suckers out of traders that like to bet on the number why should the governemnt interfer?

Is there any evidence that this has created a problem for policy makers-- for example the Fed raising rates because the monthly CPI rounded up to 0.3 rather then 0.2 ?

Yes, I would have thought markets were more sophisticated than that.

[Elliot]

@John: "What's the cost?"

The cost ends up being not insignificant. For the BLS, a whole slew of the internal processing steps need to be double-checked, and the published tables need to be re-layed-out. Downstream consumers of the data need to be able to deal with the changes as well. But it's worth it to get things right.

@spencer: "impression of a precision in the data that is not there in reality"

Just the opposite: increasing the precision in the index allows differences in inflation rates which are within the BLS sampling variation to be reported accurately. Previously, the rounding was distorting the numbers. The change fixes a problem with BLS methodology.