County specific time trend

[Chuan Tang]

Hi, all

I have read some posts about adding a county specific time trend into the model (e.g., Link for post). Suppose that I have three variables for county, year, and month respectively.

I know the correct way to specify a county specific yearly time trend is to add

c.year ## i.county

into a 'fe' model

Now, if I also want to specify not only the county specific yearly time trend, but county specific monthly time trend as well, can I do it by adding the following term into my model?

c.year #c.month# i.county

or adding them separately, like:

c.year ## i.county     c.month ## i.county

if not, what's the correct way to achieve that?

Many thanks!

[Clyde Schechter]

Probably neither of these.

First you need to clarify what you mean by a monthly time trend. Do you mean that you expect there to be periodicity in your outcome so that there are effects that operate in January of every year, and other effects that operate in February of every year, etc., through December of every year. To do this, your month variable has to be just a number between 1 and 12 that reflects the month of the year of the observation but is independent of the year. This would be manifested in the outcome variable as a monthly disturbance pattern that recurs every year, perhaps superimposed on a steady upward or downward trend over the years. Then in that case what you want is:

c.year##i.county i.month##i.county

Note, by the way that this would not be a monthly time trend. It is recurring effects reflecting the month of the year. It is seasonal variation (in 1-month seasons). A monthly time trend is, in theory, possible but it would be very unusual because the data would then exhibit a "saw tooth" pattern where the outcome variable trends upward from January through December within a year and then abruptly drops back to the low January level again at the start of the next year.

If you really mean by a monthly time trend a long-term trend in time and you want to study it in a fine-grained monthly way instead of in a coarse-grained yearly way, then your month variable would be coded to represent both the month and year (as a Stata internal format monthly variable--see -help datetime- if you don't know what that is), and you would simply use

c.month##i.county

and omit the yearly trend altogether.

[Chuan Tang]

Hi, Clyde:

Thanks for your prompt response. I realize that what I need is the second solution in your post. Your answer helps me to understand the problem much better.

chuan