Fixed effects and interaction terms

[Isabella Blengini]

Hello,
I have a little question. I am analyzing a simple fixed effects model. I have my firms classified by class (so each class is an individual id) and I have interactions between my independent variable (the exchange rate) and the dummy associated to the class. Basically I want to study how the same appreciation of the exchange rate affects the performance of the different classes. I observed that if I run my regression without interaction terms, I get reasonable results. If I run the regression without fe and only with interaction terms and I get beautiful results, super intuitive. But when I include fixed effects and interaction terms, results stop being intuitive. My question is: is there a rigorous way to check which specification is more correct? I am sorry for the stupid question, I typically do theoretical models :-)
Many thanks,

ISabella

[Carlo Lazzaro]

Isabella:
welcome to this forum.
As per FAQ, it would be really helpful for interested listers to see what you typed and what Stata gave you back. Thanks.
As you can easily figure out, it is really difficult to guess what you mean by intuitive/counterintuitive results without taking a look at them.

[Isabella Blengini]

Dear Carlo,
many thanks for your message. I made my posts visible to everybody, I hope this is what you meant.
Here I give you the details of my situation:
I have 6 different classes: class 1 is the luxury one, class 6 is the economic one. I want to see how the average price of a hotel room changes with exchange rate appreciations. When I use either pure fixed effects or only interactions between exchange rate and classes, results are very smooth: in general, a strengthening of the ER affects the economy class more than the luxury one. This is also what I find with fe: on average, the price of economy class is lower than the luxury one. When I mix the two specifications, things becomes less linear. In general, as I do not have many observations, I feel that the inclusion of too many dummies (I also have to control for quarters and for years) creates problems.
I know that this is far from sophisticated as a model, but I wanted to keep things simple and intuitive, plus I do not have a lot of experience with empirical analysis. Any comments are more than welcome. Many thanks again!

	(1)	(2)	(3)
	Ln_average price	Ln_average price	Ln_average price
L. Ln_average price	0.398***	0.348***	0.388***
	(15.39)	(13.20)	(14.96)
L.ln_RER	0	0	-0.196
	(.)	(.)	(-1.54)
L_class1ER	-0.0706	-0.238*
	(-0.55)	(-1.66)
L_class2ER	-0.169	-0.376***
	(-1.33)	(-2.62)
L_class3ER	-0.210	-0.295**
	(-1.64)	(-2.06)
L_class4ER	-0.236*	-0.168
	(-1.85)	(-1.15)
L_class5ER	-0.250*	0.282*
	(-1.96)	(1.90)
L_class6ER	-0.267**	-0.447***
	(-2.09)	(-2.71)
Class2		0.147	-0.466***
		(0.29)	(-22.20)
Class3		-0.436	-0.658***
		(-0.86)	(-22.88)
Class4		-1.164**	-0.783***
		(-2.22)	(-22.98)
Class5		-3.340***	-0.852***
		(-6.00)	(-23.08)
Class6		-0.0177	-0.930***
		(-0.03)	(-22.94)
quarter1	0.0766***	0.0788***	0.0771***
	(11.29)	(11.85)	(11.43)
quarter2	0.0196***	0.0219***	0.0201***
	(2.92)	(3.33)	(3.02)
quarter3	-0.00335	-0.00250	-0.00312
	(-0.51)	(-0.39)	(-0.48)
quarter4	0	0	0
	(.)	(.)	(.)
Year Dummy	yes	yes	yes
_cons	3.965***	5.041***	4.606***
	(6.57)	(7.40)	(7.58)
N	1102	1102	1102
R2	0.979	0.980	0.979

t statistics in parentheses
* p<0.10, ** p<0.05, *** p<0.01

[Carlo Lazzaro]

Isabella:
some comments about your results.
1) what strikes me is the sky-rocketing R2 of all your regression models. Are you sure that you do not have an overfitting issue?
2) As you did not post the Stata codes you used, I cannot say anything about the way you ran your regression models. I surmise that you ran a pooled OLS regression on your data (by the way: your sample size seems large enough) and plugged in -i.hotel- among your set of predictors when you investigated fixed effects. If that were the case, you should have reported adjusted-R2, too as it allows comparing different -regress-models.
3) With panel data, regression effect with fixed effect specification is better performed via -xtreg,fe-.
4) As far as interactions and categorical variables are concerned, you can rely on -fvvarlist- notation, instead of creating them by hand.
5) Eventually, the best way to post what you typed and what Stata gave you back is via CODE delimiters (see the FAQ). You can also share an example/excerpt of your dataset via -dataex-.

[Phil Bromiley]

To add to Carlo's helpful comments, it may be that the high R2 reflects the lagged dv. It is highly likely that you need to handle the endogeneity of the lagged dv. In addition to fvvarlist notation, you should consider using L. lag notation instead of creating lags previously.

[Isabella Blengini]

Many thanks to both of you, Carlo and Phil. I am also getting very worried about this R2. It is always there, if I use the lag of the dependent variable or not. I do not understand what is going on there. And yes Phil, typically I use the L. lag notation but I did not know that there was a fwarlist notation. I will explore it for sure.

Many thanks again and happy Sunday!

[Carlo Lazzaro]

Isabella:
as far as the "weird" R2 is concerned, you may want to take a look at -estat vif- outcome (to be typed after -regress-).
I reciprocate Happy Sunday.

[Isabella Blengini]

Many thanks Carlo! I will do that!