Why im I getting a positive result with log-linear regression and a negative with linear-linear?

[david schtrutz]

Hi!

I'm working on a project where I want to see the effect off an aviation tax on total passangers that travel with aviation, using the difference in difference model.

Code I use in Stata: reg TotalpassengersSweden dummy_Treat_Aviation AfterTax Interactionterm,r

Code I use in Stata with log: reg log_TotalpassengersSweden dummy_Treat_Aviation AfterTax Interactionterm,r

This is the result I get. Why isn't the log function negative? I understand that the total passengers in kolumn (1) decrease. But wouldn't the log function also be negative?
I interpret the result like this:
(1): The result from the tax (with the DiD-model) shows that number of passengers decrease with 2,2 millions.
(2): The result from the tax makes the total passengers to increase with 11.8%

Do I interpret the result correct? Or how should the result be interpreted? If I'm wrong, why is the log function negative?
It feels strange that the linear-linear function shows a decrease and the log-linear a positive result. Also that the log-function is significant and the linear-linear is not.
Regards
David

[Nick Cox]

I'd present all of your data here and full details of your output, not just selected items.

With a R-square like that and a very small sample size, your models may be struggling to show all that you want them to show.

[david schtrutz]

The first one is the linear-linear. The other one is the log-linear.

avia=Travel with aviation
train=Travel by train

Does this help to answer my question?

[FernandoRios]

Dear David
Couple of answers to your questions

- Why isn't the log function negative?
Keep in mind that while the effect you observe seems negative, compared to the scale of your data, the effect is rather small, and your Confidence interval suggests that you cannot reject the H0 that the interaction term is zero or negative.
Second. Loglinear and linear models cannot be fully compared because one is trying to capture a nonlinear relationship between dep and indep variables. So, what your model suggests to me is that you may have a model specification problem. That is one the reason why your estimated effect changes signs.
Third. To some extent, Using logs is like compressing/re-weighting your data. changing the "weight" on how each pair of observations is treated during the regression. With a log model. you are
reducing the impact of high value observations in the dependent variable, towards the log center of the data.

Perhaps a couple of other thoughts about your problem:
1) try qreg . Conditional quantile regression is often more robust to outliers, if that is the problem of your regression.
2) try rreg. This regression command is also robust to outliers.
3) To help with the interpretation, rescale your dependent variable. Say, divide your dep variable by 1000000. This will make your table a bit easier to understand.
HTH
Fernando

[david schtrutz]

Thank you for a good answer!
I will try the things you wrote to solve the problem

[david schtrutz]

Dear David
Couple of answers to your questions

- Why isn't the log function negative?
Keep in mind that while the effect you observe seems negative, compared to the scale of your data, the effect is rather small, and your Confidence interval suggests that you cannot reject the H0 that the interaction term is zero or negative.
Second. Loglinear and linear models cannot be fully compared because one is trying to capture a nonlinear relationship between dep and indep variables. So, what your model suggests to me is that you may have a model specification problem. That is one the reason why your estimated effect changes signs.
Third. To some extent, Using logs is like compressing/re-weighting your data. changing the "weight" on how each pair of observations is treated during the regression. With a log model. you are
reducing the impact of high value observations in the dependent variable, towards the log center of the data.

Perhaps a couple of other thoughts about your problem:
1) try qreg . Conditional quantile regression is often more robust to outliers, if that is the problem of your regression.
2) try rreg. This regression command is also robust to outliers.
3) To help with the interpretation, rescale your dependent variable. Say, divide your dep variable by 1000000. This will make your table a bit easier to understand.
HTH
Fernando

Regressions:

I tried to do the things you told me but it is still positive. Since we have an interaction term, what could be the interpretation of what we have if it is positive? Should I interpret the result as a passengers increase with 11.8% after the aviation tax?? Could I say that my result in the linear-linear model is incorrect and that the log-linear model is more trust worthy since it is significant? This is just a simple model of DiD Estimator, so I do not really get why there would be a specification problem

Code I use in Stata for the DiD estimator: reg TotalpassengersSweden dummy_Treat_Aviation AfterTax Interactionterm,r

Code I use in Stata for the DiD estimator with log: reg log_TotalpassengersSweden dummy_Treat_Aviation AfterTax Interaction

Your answers are appreciated!