Interpretating Estimators of a Panel data regression with Random Effects

[John Riveros]

Greetings Community of Stata, This is my first post, I've been estimating Kaldorian laws for my country (colombia) which has 32 Departaments as Administrative territorial entities so i generated a Id_dpto variable to identify them across the time in the panel structure. This is a short panel since N>T Panel. (it has 16 years and 26 groups and arround 380 observations) also unbalanced.

So I've made a single panel regression with random effects (since hausmann test fail to reject the null hypothesis, P>chi^2= 0.6147) but i'm not interesting in the random intercept, I'm more interested in finding the impact of the growth of the industrial sector over the growth in the colombian economy as general (using an estimation of the pib of each departament over the industrial pib of each one). Results give me this.

.         xtreg G_y_dpto G_pib_s_ind_dpto, re

Random-effects GLS regression                   Number of obs     =        389
Group variable: id_dpto                                Number of groups  =         26

R-sq:                                                         Obs per group:
within  = 0.0107                                          min =          1
between = 0.1929                                        avg =       13.8
overall = 0.0094                                          max =         16

Wald chi2(1)      =       3.37
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0064


G_y_dpto                       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

G_pib_s_ind_dpto               .0533818   .0290758     1.94   0.006    -.0036058    .1103693
_cons                          .0389222   .0065268     5.96   0.000       .02613    .0517144

sigma_u           0
sigma_e   .12278606
rho           0   (fraction of variance due to u_i)

I'm wondering about the interpretation of my estimator related to "G_pib_s_ind_dpto" which is the growth of the industrial pib.

I followed the examples in -xtreg- about random effects. it gives an interpretation of the estimator like OLS. which is like "the return of the X has the impact of Bi over Y".

I followed Wooldrige book of panel data analysis and it has different interpretations over and over of the Bi coefficients.

So it would be wrong to say this ?. The growth of 1% of the industrial pib at a departamental level across the time, increases by 0.053% the growth of the departamental pib ceteris paribus.

if not... What would be the correct way to interpretate the estimator related to my independent variables?

[Carlo Lazzaro]

John:
as per -sigma_u-=0, you should switch to a pooled OLS.

[John Riveros]

Thank you Mr Carlo Lazzaro , Breush-Pagan confirmed the sigm_u=0. However, testing the Kaldorian theory distribution by elasticities, the panel regression gives me this result

Random-effects GLS regression        Number of obs     =        387
Group variable: id_dpto        Number of groups  =         26

R-sq:        Obs per group:
within  = 0.7793        min =          2
between = 0.9787        avg =       14.9
overall = 0.9777        max =         16

        Wald chi2(2)      =    2317.51
corr(u_i, X)   = 0 (assumed)        Prob > chi2       =     0.0000

        
log_pib_s_ind_dpto       Coef.    Std. Err.    z    P>z     [95% Conf. Interval]
        
log_salarios_ind_r      .404073    .0349672    11.56   0.000     .3355386    .4726075
log_beneficios_ind_r    .631426    .0262867    24.02   0.000      .579905     .682947
_cons                  1.353984    .4377034    3.09   0.002     .4961007    2.211867
        
sigma_u   .33106121
sigma_e   .17047745
rho   .79041033    (fraction    of variance due to u_i)

This time breush-pagan rejects the null hypothesis so a fixed/random model is better to estimate.
Sigma_u differs from 0.
Hausman gave me the result that random effects would be better.

So what would be the correct way to interpretate the estimators related to my independent variables? For example. that 0.404073 estimator related log of salaries.

[Carlo Lazzaro]

John:
a 1% increase in salaries is estimated to increase the dependent variable of about 0.404073%.