log-log regression panel interpretation

[Chiara Tasselli]

Happy Sunday to all,
someone could help me with a table interpretation:
in need to interpret the coefficient of lwage .
where lhours is the log of the hours worked by individual i, lwage is the log annual wage of individual i... I know that is an elasticity but what the difference between cross section and panel data interpretation?

eg: if the regression had been cross-section I would have interpreted it as an increase in hours worked of 1 percent causes wages to increase by 0,20 percent. isn't it?
But here with a panel how I should interpret it?

xtreg lhours lwage age wealth

Random-effects GLS regression                   Number of obs     =     14,252
Group variable: id                              Number of groups  =     10,593

R-squared:                                      Obs per group:
     Within  = 0.0268                                         min =          1
     Between = 0.1213                                         avg =        1.3
     Overall = 0.1069                                         max =          3

                                                Wald chi2(3)      =    1461.90
corr(u_i, X) = 0 (assumed)                      Prob > chi2       =     0.0000

------------------------------------------------------------------------------
      lhours | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       lwage |   .2047036   .0056303    36.36   0.000     .1936685    .2157387
         age |  -.0031516   .0002673   -11.79   0.000    -.0036756   -.0026277
      wealth |  -.0003943   .0000233   -16.92   0.000      -.00044   -.0003487
       _cons |   5.675673   .0544222   104.29   0.000     5.569007    5.782338
-------------+----------------------------------------------------------------
     sigma_u |  .19164361
     sigma_e |  .14282326
         rho |  .64291967   (fraction of variance due to u_i)

Many thanks you all for you time

[Clyde Schechter]

First, unless this data comes from an experiment, it is not legitimate to say that anything caused anything else. You should use causation-neutral language such as "is associated with."

That aside, the percent differences (not "changes"--causal language again) are related precisely as you say they are. That it is cross sectional rather than panel data has no effect on that.

The difference in interpretation that you should be aware of (and might or might not state explicitly when presenting your results) is that with panel data, you are describing relationships that apply within individuals, whereas with cross sectional data you are describing relationships that apply across individuals. Thus with panel data, you might be able to say that if over time a person's wage increases by 1%, the expected hours worked will be 0.2% higher. But with cross sectional data you say that comparing people whose wages differ by 1%, the expected hours worked among the group with higher wages is 0.2% higher.

[Carlo Lazzaro]

Chiara:
as an aside to Clyde's helpful reply, I would add:
1) I would investigate whether -age- has a non-linear relationship with the regressand (-c.age##c.age-);
2) the contribution of -lwage- to variations in the regressand should be read adding the usual sentence "when adjusted for the other predictors";
3) even though after Joshua D. Angrist

and

Guido W. Imbens

' Nobel “for their methodological contributions to the analysis of causal relationships” (

https://www.nobelprize.org/prizes/li...omic-sciences/

), replacing association/correlation with causation is getting more and more tempting, I do share Clyde's word of methodological caution;
4) you went -xtreg,re-

which takes both within and between panel variation. Conversely, (pooled) OLS focuses on between variation and ignore most of the within-panel variation. In addition, both pooled OLS and -xtreg,re- assumes no correlation between -ui- and the vector of regressors (an assumption that oftem does not hold).

[Chiara Tasselli]

Many thanks to both for the useful correction and advice,
I only wanna be more precise in my question by underlining that I was comparing a simple OLS (not pooled) with panel data. A mean by running the OLS model for only 1 year of the panel. Does thing changes?
Thank you so much for your time and knowledge: very useful advices.