Hello,
I have a question about how to remove seasonality in Panel data. I want to evaluate how sales of a specific product change as its price increases (due to a totally exogenous input reason). The price increase is gradual and ongoing for 2-3 years and the rate of change differs between stores (due to, among other things, how much they have in stock). I have monthly data from a few hundred stores, spread across the country, with information about current price, quantity sold, income level, store size etc.

I have verified with Hausman test that I can use a random effects model (estimates are vertically identical to fixed effect model). And I control for heteroscedasticity and within-group autocorrelation by using Eicker–Huber–White standard errors (clustered standard errors at store level) which allows correlation between but not within stores.

The problem is that sales are severely affected by seasonality and I want to make sure that I have sufficiently controlled for that. I have data from the month before the price begin to change (the exogenous event) until one year after all stores reach price unity, in total about 48 months. To control for seasonality, I have used monthly time dummies (i.month).

My questions are:
  • Are monthly time dummies enough to remove seasonality?
  • What is the difference in interpretation between using i.month and the i.date command in Stata (creates 48 dummies, one for each individual month)?
  • Is the time from which I have data, about 4 years, enough to remove seasonality and to provide me with an accurate estimations of the effect size? I could include more observations at the end of the data-set (but there is no price variation so what would be the point?) but not before my current starting point.

Help would really be appreciated = )