Interpretation of results to capture dummy effect

[Jack Lee]

Hello,

I am currently doing my dissertation on how technological approach affects export in goods for developing countries. I am trying to incorporate a dummy variable for 2008 financial crisis to capture the effect of financial crisis of export in goods for developing countries.

To simplify, my regression: Export in Goods=technological approach+dummy variable for 2008 financial crisis.
My coefficient on technological approach=2.4
My coefficient on dummy variable for 2008 financial crisis= -0.2
Dummy covers a period from 2008-2010, while my data covers a period from 2002-2010.

Is it possible to interpret my regression results as below:
Before the period of financial crisis (dummy=0), GDP increases by 2.4% when there is a 1% increase in technological approach.
During the period of financial crisis (dummy=1), GDP increases by 2.2% (2.4-0.2) when there is a 1% increase in technological approach.

Thanks in advance!

[Carlo Lazzaro]

Jack.
as per FAQ, please post what you typed and what Stata gave you back via CODE delimiters, so that interested listers can see all the stuff with just one look. Thanks.

[Jack Lee]

Carlo Lazzaro
Sorry I am quite new to this forum and did not familiarise myself with the FAQ. Thanks for the advice!

lgerd=ln(Technological Approach)

Jack

[Clyde Schechter]

Is it possible to interpret my regression results as below:
Before the period of financial crisis (dummy=0), GDP increases by 2.4% when there is a 1% increase in technological approach.
During the period of financial crisis (dummy=1), GDP increases by 2.2% (2.4-0.2) when there is a 1% increase in technological approach.

It is possible, but it would be wrong! :-). As best one can guess from the names of your variables, you do not have an interaction term in the model. So the interpretation of the financialcrisis indicator is that it is associated with an absolute decrease of 0.103... in ltcg. If ltcg is itself a log-transformed version of some outcome tcg (just a guess from the name), then this corresponds to a decrease in tcg itself of about 10% (tcg multiplies by a factor of 0.902 = exp(-.103).)

Also, the coefficients in your attached output do not match what you described in your post, so I think it best not to try to give further advice on interpreting them as there seems to be some confusion on your part or mine as to what the model results are.

[Minhaj uddin]

Hello,
I have some confusion related to interpretation in the case of interaction term.

Actually, in my case, I have my data of firms broadly divided into domestic and foreign and I want to test the impact of crisis on both groups. For that, if I choose to run the following model:

ROA=α+β1⋅COVID+β2⋅(COVID ×Foreign)+ϵ

what will be the interpretation from this model. I mean, for domestic, I can conclude if the crisis had a significant impact or not, but for foreign, I can only conclude if the impact is significantly different to domestic or not.

My doubt is: how to know for the foreign firm, if that impact is significant or not, irrespective of domestic? Much like the domestic firms, as shown by β1.

[Clyde Schechter]

So, let's go from model equations to code. Presumably you are going to run something like

xtreg roa i.covid##i.foreign, fe

possibly with time effects, other covariates, and perhaps clustered vce.

If you follow that up with

margin foreign, dydx(covid)

you will get the marginal effect of the covid pandemic on roa separately for foreign and domestic firms.

[Minhaj uddin]

Thanks you sir


Here is what I got from the margin command

. margin domestic , dydx( Covid )

Average marginal effects                                 Number of obs = 1,698
Model VCE: Robust

Expression: Linear prediction, predict()
dy/dx wrt:  1.Covid

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
0.Covid      |  (base outcome)
-------------+----------------------------------------------------------------
1.Covid      |
    domestic |
          0  |    .677036   .3212124     2.11   0.035     .0474712    1.306601
          1  |    .226094   .1547929     1.46   0.144    -.0772946    .5294825
------------------------------------------------------------------------------
Note: dy/dx for factor levels is the discrete change from the base level.

From the above result, is it appropriate to conclude that COVID had a significant positive impact on the ROA of the foreign firms and insignificant on the domestic ROA?

I have another question related to the model selection. If I estimate the two separate models for domestic and foreign firms, will the difference in their coefficients be the same as the coefficient on the interaction term in the above model? According to you, which type of model is more appropriate—a separate or one with an interaction term?

[George Ford]

estimate them together.

[George Ford]

The sum of the two coefficients is the foreign effect. You can test that using margins. You can also create a domestic dummy and estimate the coefficients for each, but then you've got to test to see if they are equal. Or, run both models and get the results that way.

[Clyde Schechter]

From the above result, is it appropriate to conclude that COVID had a significant positive impact on the ROA of the foreign firms and insignificant on the domestic ROA?

I'm the wrong person to ask this because I do not believe statistical significance is a useful concept in this kind of situation and I consider it misleading. That said, yes, the finding for foreign (domestic = 0) firms is statistically significant, and that for domestic firms is not. My fear is that like so many people, you will then go further and interpret the latter finding as meaning that there is no impact on domestic firms. That is a common misinterpretation of statistical significance. The correct interpretation is that the data are inconclusive as to the sign and magnitude of the effect of COVID, if any, on ROA in domestic firms. Do note that most of the confidence interval for domestic firms lies in positive territory, and it only goes a short distance into negative territory. So this is weakly suggestive of a positive impact in domestic firms as well, but the data are not strong enough to justify a "verdict" on the matter.

If I estimate the two separate models for domestic and foreign firms, will the difference in their coefficients be the same as the coefficient on the interaction term in the above model?

Assuming we are talking about the model I showed in #6, yes, the interaction coefficient will be the same as you would find for the difference of the coefficients in two separate models. Now, if you also have other variables in the regression, then to get the same result requires a little care in how you set up the interaction.

According to you, which type of model is more appropriate—a separate or one with an interaction term?

Appropriate for what purpose? If your goal is to estimate the difference in the marginal effects of COVID on ROA in domestic and in foreign firms, both approaches give the same answer and are equally appropriate. The interaction approach is, in my opinion, simpler to use because the computer does all the arithmetic for you. Then again, it requires using the -margins- command, which some people aren't comfortable doing, at least initially. I think it's a matter of taste.

If, however, you are interested in testing hypotheses about the difference between the effects, then the two approaches have different pros and cons. While you can calculate the difference in the coefficients across two models, that won't give you the standard error of the difference, nor any test statistics, p-values, or confidence intervals. The interaction approach gives you the difference directly read out as the coefficient of the interaction term--and it comes with the standard error and the others already there.

Now, it is also possible to get the standard error etc. out of two separate models by using -mixed- instead of -xtreg, re-, and feeding those regression results to the -suest- command and then running a -test- command. But that approach is much more cumbersome, as it involves a large number of steps. Also, getting all the notation right in the -test- command is a bother. And if you're not familiar with -mixed-, it, too, has a syntax that is different from -xtreg, re- and takes a bit of getting used to. The reason you have to use -mixed- instead of -xtreg, re- for this is that -suest- does not accept -xtreg- results. So for all those reasons, I would avoid the two-model approach in this particular situation.

[Minhaj uddin]

Thank you so much, Dr. Clyde and Dr. George; this is extremely helpful.