Can I take log and lag on my independent variables in a regression?

[Emma Obed]

Hello,
Please can someone answer me if it is possible to take log and lag (both at the same time) on my independent variables in a regression?
Thank you.

Example

xtreg logres L1.logres err_d4 err_d3 err_d2 L2.ka_open L2.logsdebt L2.logeqty_gdp L2.logtrade , re robust

[Jorrit Gosens]

Yes, you can. There are no reasons why that would be incompatible. If you assume a log-log relation between your variables, and a lagged effect of independent/explanatory variables on your outcome/dependent variable, then your model specification is fine.

[Emma Obed]

That's great. Thank you so much.

[Richard Williams]

However, since you are using the lagged independent variable, consider using xtabond, xtdpdml, or one of the other programs designed for dynamic data modeling.

[Emma Obed]

Thanks Sir,
I have tried xtabond2 but the results of xtreg seems better.
*I stand to be corrected.

Please kindly look below my results. I would as well appreciate your suggestion on which regression to present as main results. Or your advice on which step to take.
Thank you.


# xtreg (with fixed-effects)

	(1)	(2)	(3)
	logres	logres	logres
L.logres	0.815***	0.815***	0.668***
	(6.10)	(6.10)	(5.22)
err_d4	-0.344	-0.344	-0.319
	(-1.58)	(-1.58)	(-1.77)
err_d3	0.121	0.121	0.152
	(1.17)	(1.17)	(1.78)
err_d2	0	0	0
	(.)	(.)	(.)
L2.ka_open	-0.545	-0.545	-0.490
	(-2.04)	(-2.04)	(-1.22)
L2.logsdebt	0.0624	0.0624	0.0524
	(1.99)	(1.99)	(1.69)
L2.logeqty_gdp	-0.0277	-0.0277	-0.0249
	(-1.23)	(-1.23)	(-1.02)
L2.logtrade	0.106	0.106	0.209
	(0.38)	(0.38)	(0.59)
_cons	0.0161	0.0161	0.229
	(0.02)	(0.02)	(0.24)
Year-effect	no	no	yes
Country-effect	no	yes	no
N	109	109	109
R-sq	0.665	0.665	0.717

# xtreg (with random-effects)

	logres	logres	logres
L.logres	0.927***	0.815***	0.899***
	(24.45)	(5.32)	(22.19)
err_d4	-0.0195	-0.267	0.00755
	(-0.17)	(-0.80)	(0.06)
err_d3	0.181**	0.198	0.182*
	(2.70)	(0.52)	(2.37)
err_d2	0.152*	0.0763	0.152*
	(2.21)	(0.22)	(2.01)
L2.ka_open	-0.168**	-0.545	-0.141
	(-2.94)	(-1.78)	(-1.72)
L2.logsdebt	-0.00379	0.0624	-0.00945
	(-0.52)	(1.74)	(-1.18)
L2.logeqty_gdp	-0.00615	-0.0277	-0.00894
	(-0.97)	(-1.07)	(-1.04)
L2.logtrade	0.190*	0.106	0.208*
	(2.26)	(0.33)	(2.31)
_cons	-0.697*	-0.609	-0.664
	(-2.42)	(-0.63)	(-1.89)
Year-effect	no	no	yes
Country-effect	no	yes	no

#And the xtabond2 (I just tried)

Dynamic panel-data estimation, one-step	system	GMM
Group variable: ccode	Number of obs =	109
Time variable : year	Number of groups =	25
Number of instruments = 57	Obs per group: min =	1
F(8, 24) = 2005.58	avg =	4.36
Prob > F = 0.000	max =	9
Robust
logres Coef. Std. Err.	t	P>t [95% Conf.	Interval]
logres
L1. .9632041 .0499732	19.27	0.000 .8600645	1.066344
err_d4 .0332534 .1422133	0.23	0.817 -.2602606	.3267673
err_d3 .204235 .1612294	1.27	0.217 -.1285261	.536996
err_d2 .078498 .1248907	0.63	0.536 -.1792637	.3362598
ka_open
L2. -.2502539 .1131818	-2.21	0.037 -.4838496	-.0166582
logsdebt
L2. .0031773 .0116287	0.27	0.787 -.0208232	.0271778
logeqty_gdp
L2. -.0004218 .0086298	-0.05	0.961 -.0182328	.0173892
logtrade
L2. .1374197 .1377279	1.00	0.328 -.1468366	.4216761
_cons -.5263714 .5030866	-1.05	0.306 -1.564691	.5119484

[Jeff Wooldridge]

It's not legitimate to say you will use a procedure because you like the results better. Unless your T is large, the fixed effects estimates can be badly biased. If T is "large," you can get away with fixed effects. But how large is enough depends on several factors.

JW

Edit: I see that T = 25. This is likely enough to justify FE estimation. The bias should be relatively small. As another comment, you should really have both time and country effects if you want your findings to be most convincing.

[Emma Obed]

Well noted. I will do that.
Thanks to you all, I appreciate your responses.

But please I realized that the p-values of the xtabond regression are not significant. Please what about that?

And please @JW, do you mean I can justify Fe and use as main results or use xtabond2? Because I see T=25 at the xtabond regression. Thanks.

[Emma Obed]

Please I still welcome comments from everyone. Thank you.