Wednesday, February 4, 2009

Working with the Monthly Data

Holbrook Working published a paper in 1960 that is now famous only in geek circles. The paper is called "Note on the Correlation of First Differences of Averages in a Random Chain."

WORKING EXAMPLE. Despite its user unfriendliness, the paper has a basic idea that is quite helpful for anyone interested in where our economy is headed for the next quarter or two.

To appreciate the idea, consider a series that is continuously updated and hard to predict, such as the S&P 500 index. This series is updated every second or so (at least during trading hours). It is hard to use changes in the S&P index to predict changes going forward. For example, the fact that the index fell in the morning (that is, was lower at noon than it was at 9:30am) does not suggest that it will also fall in the afternoon (that is, would be lower at 4p than it was at noon). Nevertheless, the fact that the morning's AVERAGE index was lower than the index was, say, when the market opened in the morning tells us that this afternoon's average will be somewhat lower than the morning's average!

The reason is that, given that the morning average was lower that the morning's open, it must be that the index was relatively high soon after the open, and fell sometime thereafter. The morning average includes those early morning highs, but the afternoon average will not.

LESSON FOR MACRO FORECASTING. The lesson applies to GDP just as well as to the S&P index. People produce and spend every day, but the BEA reports to us the AVERAGE spending for all the days of the quarter. The fact that 2008 Q3 GDP was lower than 2008 Q2 by itself suggests that, other things the same, 2008 Q4 may be lower than 2008 Q3. The reason has nothing to do with the possibility that negative growth begets more negative growth. Rather, the fact that 2008 Q3 GDP was down means that spending fell sometime between July 1 and September 30. As long as the fall did not all occur on July 1, then the 2008 Q3 average has the benefit of some high spending days early in July that Q4 does not, even if every single day in Q4 were at least as good as September 30.

This is why I pay attention to the monthly data when trying to make forecasts for quarterly averages.

So what's going to happen in 2009 Q1? A good forecast, IMO, depends very much on when economic activity dropped in such a way to make the Q4 average worse than Q3's. If it dropped in, say, August, then I more optimistic than if it dropped in November. A (hypothetical) November drop means that the 2008 Q4 average we were given last Friday from BEA includes some high spending in October that I don't expect to carry over to January, given that it did not even carry over to December.

Below I show a couple of pretty important income and spending indicators that the BEA measures monthly and released on Monday. One of them is real disposable personal income per person -- the average amount of income, adjusted for inflation, that people have after paying taxes and receiving transfers. The other is an index of the volume of consumer spending (the number and quality of items they buy, not the amount spent on those items).

Real disposable personal incomes reached their low in September and have increased every month since. If you just compared the quarterly averages, Q4 might look close enough to Q3 to suggest that 2009 Q1 can't be good. But the underlying monthly income pattern is pretty promising.



The real consumption data are less amazing, but still suggest that 2009 Q1 begins in about the same spot that 2008 Q4 did. Moreover, given the movement of spending away from brick and mortar and toward on-line, it is possible that the BEA's seasonal adjustments allocate too much consumption to November and too little to December.



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