In many instances, statistics are collected at a higher frequency than a user requires. In the example here, the unemployment rate is collected monthly, but we often have other labor market data collected annually. The question here is how to aggregate the high-frequency data into a lower-frequency statistic. In FRED, we have three options: average, sum, or end of period. In the graph, we compare annual unemployment data taking either the average over the year or the end-of-period observation. The choice of whether to use seasonal adjustment doesn’t affect the average. By definition, seasonal adjustment implies that December, the last month of the year, does not have a systematically different unemployment rate from any other month. However, averaging or summing will systematically give lower measures of variation than the end-of-period observation. The reason is simple, even without too much formal math: Suppose every month our observation is the annual number plus some monthly “noise” term. Either summing or taking the average, we essentially allow these monthly variations to cancel each other out. Taking an observation from the end of period includes all of the month-specific variation. In the graph, we can see that the red line, which takes annual unemployment as the final month’s observation, is more volatile. In fact, from 1979-2014, its coefficient of variation is 25.56%; the blue line, which takes the average, has a coefficient of variation of 24.86%.
How this graph was created: Search for “unemployment” and select the seasonally adjusted civilian unemployment rate. Using the pull-down menu, change “Frequency” to “Annual.” The default “Aggregation Method” is “Average,” and we will keep that. Then, “Add Data Series” and again search for “unemployment.” Add a new series using “unrate,” the same data as last time. Again, change it to an annual frequency. But this time, change the aggregation method to “End of Period.”
Suggested by David Wiczer.