Panel data: interpreting coefficient

[Leonhard Maier]

Dear all,

I'm new to this forum. I have a straightforward question. I have a panel of annual data (20 countries, 100 years for each country). How do I interpret the coefficient for a dummy that indicates a certain time period (say, it is 1 in five post-crisis years, and zero otherwise), when the dependent variable is a growth rate (first difference of the natural log times 100)? Thank you very much for your help.

[Carlo Lazzaro]

Leonhard:
welcome to the list.
As per FAQ, your chances of getting helpful replies are conditional on posting what you typed and what Stata gave you back (via CODE delimiters, please. See FAQ again on this topic, too). Thanks.

[Leonhard Maier]

Dear Carlo, thank you very much for your helpful comment. I typed:

 reg d.lntop1 postcrisis5, robust

. Notice that we are not talking about the difference in the natural log times 100, but just the difference in the natural log (not multiplied by 100). Thus, d.lnytop1 is the first-difference of a (logged) top1 income share variable. The dummy is a variable that indicates that a given country is in a five-year post-financial crisis period in a given year. The output is as follows:

Linear regression Number of obs = 1046
F( 1, 1044) = 4.78
Prob > F = 0.0290
R-squared = 0.0036
Root MSE = .07226

------------------------------------------------------------------------------
| Robust
D.lntop1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
postcrisis5 | .0127337 .0058235 2.19 0.029 .0013067 .0241607
_cons | -.0050392 .0024461 -2.06 0.040 -.0098391 -.0002394
------------------------------------------------------------------------------

I am not interested in whether this regression has any predictive power or is appropriate for any matters, I am only wondering how to interpret the .0127337. Thank you very much for your help.

[Carlo Lazzaro]

Leonhard:
thanks for providing further details amd using CODE delimiters for posting waht you typed (to avoid formatting issue, next time please use that approach for posting what Stata gave you back, too. Thanks).
I'm a little bewildered from your regresion code, as you mentioned a panel data regression in your first post, which usually calls for -xt- prefixed Stata commands.
That said, you specified a log-linear univariate regression model.
The interpretation of -postcrisis5- coefficient should be the following one: switching from a pre to a post.crisis period, increases the -depvar- of (exp(.0127337) -1)*100%=1.2815119%

[Leonhard Maier]

Thank you very much. Sure I will use CODE delimiters also for the output. Yes, I use xtreg for the panel regressions but I just wanted to make this more simple for the example. Thank you so much! Your explanation makes very much sense. Let me just mention that the counterfactual are not pre-crisis years but "all other years" in the sample. Thus it would be switching from a "normal" to a post-crisis period.

I would greatly appreciate if use could answer one simple question. You said that switching to post-crisis increases the -depvar- by 1.28%. The -depvar- used here is the log first difference of the top1 income share, so the 1.28% increase would refer strictly to this log first difference, right? Or to the "original" dependent variable before first-differencing, ie, the log top1 income share in levels?

Could I add another brief question: How to interpret the coefficient when I type:

 reg d.lntop1 l1.d.lngdp, robust

, meaning I regress the log first difference of the top1 income share on the lagged log first difference of real GDP per capita. The output would be as follows:

  

Linear regression                                      Number of obs =    1037
                                                       F(  1,  1035) =    1.07
                                                       Prob > F      =  0.3006
                                                       R-squared     =  0.0015
                                                       Root MSE      =  .07195

------------------------------------------------------------------------------
             |               Robust
    D.lntop1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lngdp |
         LD. |   .0650807   .0628337     1.04   0.301    -.0582153    .1883767
             |
       _cons |  -.0052213   .0026485    -1.97   0.049    -.0104183   -.0000243 
------------------------------------------------------------------------------

Specifically, is (exp(.0650807) -1)*100% then the effect of a one UNIT or PERCENTAGE or PERCENTAGE POINT increase in lagged (logged) real GDP per capita, or in its first differences?. Many questions, I apologize, elasticities are confusing sometimes.. Thank you very much!

Leo

[Leonhard Maier]

Moreover, is it generally valid to include both the post-crisis dummy and the lagged log first difference of real GDP on the right-hand side of the regression model?

[Carlo Lazzaro]

Leonhard:
- the 1.28% increase would refer strictly to the log first difference. You can test yourself what happens when you change the -depvar- and keeps the predictor unchanged;
- I would say that 1 percent point change in lagged log first difference of real GDP per capita corresponds to an (exp(.0650807) -1)*100% increase in log first difference of the top1 income share.

[Carlo Lazzaro]

Leonhard:
I cannot reply to you last question, since I do not the literature of your research field.

[Leonhard Maier]

Thank you very much! Best, Leo