Impact of weather on the economy

The March 6 issue of BusinessWeek reports an increase in retail sales and housing starts this January (What Got The Economy's Bouce Going). The hypothesis is that the cause is the relative warm weather (an average of 39.6F). So how can this be tested? BW mention a study by James O'sullivan, an economist with UBS, that tries to quantify the impact of warm January weather on retail sales and housing starts. They describe it as follows:

He looked at the historical relationship between data from several economic reports and deviations from the average December and January temperatures. December temperatures were used to capture any weather-related distortions that could carry over into January.

This doesn't tell us much about the model. The clue is in the reported results:

Based on these past relationships, the above-average January temperatures provided a 1.4-percentage-point boost to retail sales. Housing starts got a weather-related increase of approximately 200,000 units at an annualized rate, while the balmy temperatures may have accounted for all of the 0.7% rise in manufacturing output.

Here's my guess: this is a set of regression models! For retail sales, it might look like this:

log(retail sales) = a + b*(deviation from average Dec-or-Jan temp)+ noise

The model for housing starts:

housing starts = a + b*(deviation from average Dec-or-Jan temp)+ noise

The model for manufacturing output:

log(housing starts) = a + b*(deviation from average Dec-or-Jan temp)+ noise

How do we know whether there is a log on the left hand side? Well, if the results are reported in percentages (a unit change in X is associated with a percentage change in Y), then there is most likely a log. In contrast, if the results are reported in the units of Y (for instance, units of housing starts), then there is no log.

A final interesting note made in the article is that "government's seasonal adjustment process, which tries to account for typical seasonal variation, can go awry when patterns are atypical". I'll describe how these seasonal adjustments are done in a future post.