# Subjects with different order of magnitude values in panel data

I have quarterly sales data for a variety of stores and would like to estimate the effect of a regulation on sales. A panel type model would appear to be appropriate in this case, with the regulation as a dummy variable.

However, the quantity of sales varies by two-orders of magnitude between stores. How should I account for this?

Apologies for any problems with the question, I am something of a beginner.

• using logs sometimes helps. Log-log models are popular in econometrics, because they are easy to interpret, that is another bonus of using them. – mpiktas Feb 23 '11 at 8:23

## 1 Answer

Actually the @mpiktas comment is the answer to your particular question. Sales models are usually multiplicative by the nature (some intuition could be found in Market response models book). There is also a number of reasons for logs discussed for ARIMA models in my earlier post. In your case it is the scale effect that troubles you, therefore log transformation works well here. Another useful trick is to divide by some size variable (plot of the store, number of workers, etc.), so moving to fractions could help also.

In addition to your question. What you have to pay attention to are other important explanatory variables: location variables or density of the population, size, variety of products (categories) and there average prices, number of workers, distances to the rival shops etc. that will matter (omitting them will cause you some estimates with poor properties: probably biased and inconsistent). Regulation can't be put as the solo explanatory variable in this context.

• Given that a small minority of my sales data is in the range 0.0 to 1.0, should I add 1 to all my sales figures before using a log transformation? – fmark Mar 6 '11 at 1:02
• @fmark, if you don't have exactly zeroes than there is no problem to take log transformation (the only case for zero is if the store sells nothing during a quarter!, but it is a strange case). You have this small range probably due to units you measure your sales. In log-log regression this will be absorbed into intercept term. However, if you do have some true zeroes then we will think about other useful tricks (by the way no need for logs in dummies). – Dmitrij Celov Mar 6 '11 at 9:05