# Implications of the Government Shutdown on Inflation Estimates

Each month, the Bureau of Labor Statistics (BLS) releases estimates of the Consumer Price Index (CPI) and the Producer Price Index (PPI). The government shutdown, which ended late on October 16, caused a delay in the release of these statistics and many of the statistics and data products that rely on them. But the shutdown will also affect the accuracy of these statistics for months to come. This article outlines the impact of the shutdown, particularly on the accuracy of the CPI.

The repercussions on CPI estimates will continue for at least seven months. Some of these repercussions will occur later this month, but the majority of the influence will occur the next month, in November, when the monthly overall inflation estimates derived from the CPI will be subject to significant error. However, year-over-year inflation estimates will continue to be quite reliable.

## October Impact: Delay and Potential Processing Error

There is always a half-month delay between the collection of data and the construction of the CPI: Releases in the middle of the month of October pertain to data that were collected during September. Putting this differently, the September inflation rate (the difference between September's CPI and the previous month's CPI) becomes known in mid-October. Likewise, October data are released in November.

Since the October release pertains to September data, and all of these data were collected prior to the shutdown, the chief October impact of the shutdown will be that the release of the CPI will be delayed. Commodity analysts in the BLS usually spend the entire month processing data flowing in from field offices around the country. Up until the shutdown on October 1, these analysts were able to process some of the data that had been obtained in September, but as they return to work, they will have a hard time catching up. The early parts of the month are typically periods of heightened activity, and there are strict limits on the amount of overtime work that these analysts can undertake. October's CPI may also be subject to processing error; under normal conditions, processing error is miniscule, but under rushed conditions it is easy to imagine some processing errors inadvertently creeping in.

Of course, the fact that many prices will not be collected in October will have repercussions later on. In fact, these repercussions do not end until May of 2014.

## November through May Impact: Sampling Error

There are two kinds of errors that might enter the November release of October CPI data. First, it is possible that there will be some processing error. During the months of October and early November, commodity analysts will be rushing to catch up their processing of the October data, subject again to the constraint of limited overtime.

Second, and more importantly, is sampling error. All statistics are prone to some sampling error, leading to uncertainty surrounding those statistics. By definition, statistics are based upon a sample of the data, rather than the entire universe of data. An estimate of the average is only an estimate; most likely, the estimate is a little too high or a little too low.

Statisticians measure the amount of uncertainty (or the degree of accuracy) in a given statistic with another statistic, the standard error. The standard error of a statistic can be used to construct confidence intervals, or likely ranges for the true value given the specific estimate obtained from the sample. In particular, the chance that an estimated statistic is farther than one standard error away from the true value is about 30 percent, while the chance that a statistic is off by more than two times the standard error is less than 5 percent. For example, if the standard error is 0.4 percent, then we know that there is less than a 5 percent chance that the statistic misses the true value by 0.8 percent or more. All else equal, a bigger sample yields a more accurate statistic; in other words, a bigger sample yields a statistic with a smaller standard error.

Since the CPI price collection relies upon field staff visiting shops, some of the October data will never be collected. As a result, the November CPI release, which is based upon October data, will have a much bigger standard error due to the smaller sample. We can estimate how much bigger by weighing the potential size of the October sample against typical sample sizes, historical standard errors, and the likely inflation rate.

The October sample will be half its usual size. Price collection happens during the working days of the month. The government was shut down for 11 working days, so the missing data represent about 50 percent of the price quotes (since there are 21 working days a month on average).

The monthly standard error was most recently estimated by the BLS to be 0.03 percent for the 2011 CPI, based upon 83,300 price quotes. A standard error estimate of 0.03 percent is probably still the best estimate for post-2012 data. The median monthly percentage price change in the CPI for this period was 0.14 percent (roughly corresponding to an annualized average of about 1.6 percent), and the available evidence suggests that the noise in CPI estimates does not fall appreciably when inflation is low. However, with approximately half of the price quotes missing, the standard error would rise to at least 0.042 percent.

This level of error gives rise to considerable uncertainty about the true monthly inflation rate. For example, suppose that the October CPI ends up being estimated at its median, 0.14 percent, and we wish to have a wide-enough confidence interval so that we are wrong only 5 percent of the time. In this case, the range of uncertainty about this 0.14 percent estimate would be that true monthly inflation in September was somewhere between 0.05 percent and 0.22 percent.

## Impact on Annual CPI Statistics

While the monthly inflation rate will be subject to this uncertainty, other commonly used statistics computed using CPI data will have smaller errors. For example, the estimated standard error in year-over-year inflation under ordinary circumstances is 0.07 percent, but that is compared to a median of about 1.88 percent in 2013. Because the year-over-year inflation rate is computed based upon twelve separate one-month inflation estimates, even if one particular month has a standard error as large as 0.042 percent, this will cause only a modest increase in the uncertainty of this twelve-month measure. Furthermore, in the situation we are examining, errors in the October CPI (released in November) start to be cancelled out in the November CPI (released in December).Why doesn't the October CPI error just disappear in the November CPI (which is released in December)? If the prices of all goods and services were collected each month, then this is exactly what would happen. For example, if the October inflation estimate happened to be too high because of missing price quotes, then - once those prices were once again collected - the November inflation estimate would be too low, owing to all those price changes being properly accounted for, and that would be the end of it. Any errors due to a small sample that cause a problem in one month would be exactly reversed in the next month, so that the price level - the index itself, not the inflation estimate - would go back to where it would have been, had all the data actually been collected in October.

But since not all prices are collected every month, not all of the error will be reversed right away. In fact, the price index will not return to its original course for another six months. This period is so long for cost reasons. The BLS has divided all the goods and services it collects prices on into three categories: goods whose prices are collected each month in all cities; goods whose prices are collected only every other month in most cities (exceptions are Chicago, Los Angeles, and New York City, where all commodities and services except rents are priced monthly); and rents. Rents are collected only every six months; if the rental price on a particular rental unit is collected in January, then the rent on that unit will next be collected in July.

Because of this, pricing errors that relate to monthly items (such as food) will be reversed in the November inflation estimate. But pricing errors that relate to bimonthly items (such as vehicles in Cleveland or women's shoes in Baltimore) will not be reversed until the December inflation estimate is released (in January). To see how this works, consider a hypothetical example.

Suppose that the true average price increase of automobiles in Cleveland between August and December is 1.0 percent per month. Of course, some cars rise more in price, and some rise less in price. Suppose that the BLS normally collects 30 vehicle prices per month, but owing to the shutdown, it was only able to collect 15 vehicle prices in October. And suppose that these vehicles just happened to be cars that experienced quite rapid increases in price, so that the estimated October price increase for Cleveland automobiles happened to be 1.9 percent. The missing price quotes are not used in the October CPI, but the BLS still estimates the missing prices. It does so by assuming that those prices also rose by 1.9 percent.

In December, the BLS field staff is once again able to visit all the dealerships in their Cleveland sample. Those rapid-price-increase cars are again priced, and their two-month price changes enter the inflation estimate as usual. But this time the field staff is also able to collect prices from those other vehicles, the ones that did not experience much inflation. The estimated inflation rate is based upon the actual price versus the estimated October price - so the estimated inflation rates are negative for those cars. As a result, the December inflation estimate will be about 0.1 percent.

This means that over the four-month period, September to December, the average inflation rate for cars in Cleveland ends up being about 1.0 percent, as it should be. (For a more detailed description of BLS methods used in constructing the CPI, see chapter 17 in the BLS Handbook of Methods, available at www.bls.gov.)

Meanwhile, since rents are only collected every six months, errors would only be removed in the April collection. In other words, any error in the October rent inflation estimate would be reversed in the April inflation estimate.

In terms of CPI inflation estimates, then, the following summarizes the errors owing to the shutdown:

- October - delays and possible processing errors in the September CPI estimate
- November - sampling error in the October CPI estimate
- December - unwinding of October sampling error in monthly items in the November CPI estimate
- January - unwinding of October sampling error in bimonthly items in the December CPI estimate
- May - unwinding of October sampling error in rents in the April CPI estimate

## Other Aggregate Statistics

The CPI is not the only statistic that will be affected by the government shutdown. The Federal Reserve System focuses on the price index associated with the Personal Consumption Expenditure estimate in the national accounts. This index is called the PCE-PI. Since CPI data movements underlie most of the PCE-PI computation, most of the errors and any delays in the CPI would be reflected in the PCE-PI. Furthermore, the PCE-PI computation will be affected by other data products produced by the BLS. The BLS produces Producer Price Indexes, which will also be delayed and subject to errors over the coming months. These data are used fairly intensively in the PCE-PI as well.

These delays and errors don't just influence inflation estimates: any errors in PCE-PI translate directly into errors in aggregate consumption estimates. Furthermore, aggregate GDP computations will also suffer from missing producer price data; these directly impact productivity estimates and aggregate output estimates. However, aggregate GDP computations occur quarterly, based upon three months of data. Most of the error in the CPI that was induced by the small sample will disappear by December.

## Implications of Uncertainty in Price Measures

Monetary policymakers are keenly interested in inflation, and one of the main challenges they face is distinguishing signal from noise in the current inflation data. Even in the best of times, some part of the inflation data is simply noise - transitory movements in inflation, either up or down, that go away in a month or two.

Some of these transitory movements are due to sampling error in the CPI. Some are due to temporary movements in prices that will reverse themselves in a few months. Analysts within the Federal Reserve System spend enormous time and effort to try to determine whether the latest aggregate price movement is mostly transitory or mostly persistent and what the true underlying trends in inflation are.

An increase in the standard error of the CPI reduces its usefulness to policymakers. It makes it hard to judge whether a number like 1.5 percent reflects real inflation, or whether it is simply error. For example, if the inflation rate is mistakenly reported as too high, the monetary authority might begin raising interest rates prematurely, threatening the recovery. If the inflation rate is mistakenly reported as too low, the monetary authority might keep interest rates too low for too long, which could ignite inflation.

To avoid policy errors, the usual advice - based on the "Brainard" theory of policy practice under uncertainty - is for policymakers to react more cautiously than they otherwise would, when faced with data that is measured with more error than usual.

Similarly, an increase in uncertainty about inflation estimates reduces the usefulness of those estimates to consumers, workers, and producers, and also makes planning errors more likely. For example, in the hypothetical cars-in-Cleveland scenario above, consumers tracking auto prices might be alarmed by the seemingly rapid rise in car prices and be prompted to buy too quickly. Cleveland auto dealers might be encouraged to raise their prices more, thinking that they are only doing what everyone else is doing.

The government shutdown caused increased uncertainty in the economy for a host of reasons. The increased uncertainty for policymakers owing to increased uncertainty in the CPI is another contributor to that overall uncertainty. But since the shutdown was resolved in mid-October, the degree of increased uncertainty in the CPI over the coming months will not seriously damage the Federal Reserve System's ability to determine the current state of the economy.