Using percentage change as a dependent variable

[Clara Etcheverry]

Hello,
I am doing a regression with stata.
If I use percentage change of the profit as my dependent variable what is the correct modeling method?Can I supply use OLS? How can I do?
Thank you very much

[Nick Cox]

You could use regress or any other relevant regression command. There is not much information in #1: for example, do you have panel data?

Show us a quantile plot of your percentage change outcome so that we can see whether there might be a problem with long tails or outliers.

[Clara Etcheverry]

Thank you. Yes, I use regress. The Y (change in profit) can be negative or positive because it is a variation rate in percent. Is it a problem in theory?

[Clara Etcheverry]

Yes it is panel data

[Nick Cox]

Quantile plot?

[Clara Etcheverry]

for dataset A

[Clara Etcheverry]

For dataset B

[Jeff Wooldridge]

Because profit can be negative as well as positive, I guess that's why you're not taking the log and using it in, say, fixed effects analysis -- correct? Having said that, you're free to start with any model you want. Using percentage change is already a kind of differencing of your dependent variable, but that may be warranted.

Seems like you have firm level data and probably want to model the percentage change in profits in terms of other firm characteristics? Is it descriptive or supposed to be causal?

[Clara Etcheverry]

Thank you very much for your answer!

"Because profit can be negative as well as positive, I guess that's why you're not taking the log and using it in, say, fixed-effects analysis -- correct?" Yes.

Having said that, you're free to start with any model you want. Using percentage change is already a kind of differencing in your dependent variable, but that may be warranted.

Seems like you have firm-level data and probably want to model the percentage change in profits in terms of other firm characteristics? Is it descriptive or supposed to be causal? It is more descriptive. It is just to show a correlation after a structural econometrics model. This structural econometrics model allows me to compute the profits. Then, I do a counterfactual where I compute new profits and I compute the variation in profit between the estimated profits and the counterfactual profits. This evolution in % is the dependent variable. The explanatory variables are the retailers' strategy dummies. I want to show that the variation in profit is correlated to the retailers' strategy.

[Jeff Wooldridge]

Do the retailers' strategies change over time? Even if they do, you might just want to use pooled OLS and cluster at the retailer level to get proper standard errors. Or use random effects. But if you have enough time variation in strategy, you can use fixed effects and hope to obtain a more causal estimate of strategy on profit growth.

[Nick Cox]

Thanks for the plots. You used qnorm not quantile but the results are still helpful.

Outliers and long tails don't seem evident. That is good news. Your distributions fall into two quite distinct groups. That needs a story!

[Clara Etcheverry]

Thank you very much for your answers!

Each retailer adopts one strategy and it does not change over time. With one strategy we observe an increase in profits and with the other strategy, there is a decrease in profits.

[Jeff Wooldridge]

Then just use a pooled OLS regression and cluster your standard errors. Something like this:

reg pcprofits i.strategy x1 ... xk i.year, vce(cluster id)

where x1 ... xk are other control variables and "id" is the retailer identifier.

[Clara Etcheverry]

Thank you very much !!