cost frontier - how to deal with negative price values in data

[Guest]

Hi

My task is to build a cost frontier that shows the cost of producing electricity. I consider the following variables: total costs, electricity output, labor price, fuel price, and capital price. My data is on plant level and also only for a specific year.
Since I have information about the capital price, I am using an approach to approximately estimate the capital price of each plant: (total costs-labor expenses-fuel expenses)/(total capacity).
I have found that approach in a research paper.

However, my problem is that out of 400 observations (plants) I have 18 with a negative capital price. Since I'm forced to use a ln function, I need to have non negative values. Also it does not make sense to have negative capital prices, even if the plant is amortized, because a negative price would mean that the plant receives money.

Are there any common practices in stata to solve that problem? Dropping the observations would bias my estimation. I was thinking of setting those capital prices to a very low positive value (0.00001), so that the influence on the total costs is rather negligible.

Thank you very much for your help in advance!

[Charlie Joyez]

Dropping the observations would bias my estimation.

So will keeping abnormal values.

You should contact your data provider and ask to know to what correspond the negative capital costs. (Although I do think it could make sense, capital is not an usual good).

However keeping observations you know (or think) they are not true, is even worth than removing them (in my view), and quite hard to justify.

If the negative values are an error (e.g due to an estimation), you should remove them, or try to estimate the "real capital cost" from the other observations.

If they are not an error, you could consider reshaping the values to only have positive values. I would be more careful about setting them to 0.00001, it depends on the other values of this variable. (If the mean is above 1000 with a limited variability, setting a few values to 0.00001 will cause bias). However, if the "normal" values are very far from the negatives one you have, then it is probably errors.

Anyway what you could do before obtaining any answer from your data supplier is to compare whether including or not these 18 observations significantly change the result of your estimation. If the model is well specified, it should not.

Best,
Charlie

[Guest]

Hi Charlie

Thank you for your fast answer.

If they are not an error, you could consider reshaping the values to only have positive values. I would be more careful about setting them to 0.00001, it depends on the other values of this variable. (If the mean is above 1000 with a limited variability, setting a few values to 0.00001 will cause bias). However, if the "normal" values are very far from the negatives one you have, then it is probably errors.

Considering the distribution of the capital prices, I think the negative values are not errors. How would you reshape the variable to have only positive values? I was thinking of adding a constant "a", but I'm not sure if that is going to bias my estimation, since it is based on ln values of the variable. => ln (x+a)=ln(x)+ln(1+a/x)

Anyway what you could do before obtaining any answer from your data supplier is to compare whether including or not these 18 observations significantly change the result of your estimation. If the model is well specified, it should not.

I will try that, hopefully it does not make too much of a difference.