[Carlo Lazzaro]

Francesca:
if you logged a coefficient but not the regressand, a 1% change in the logged predictors causes a (0.01xBeta1) variation in the regressand.
In your case, a 1% reduction in LNTA causes a reduction of (0.01*-1.201734)=-0.012 in Tobin’s Q.

[Francesca Sossella]

Thank you very much Carlo. While, for the other variables, is it correct to consider variations in units (as in my example) or in percentages?

Many thanks,

Francesca

[Francesca Sossella]

In addition, serial correlation and multicollinearity are the same thing?

Thanks,

Francesca

[Carlo Lazzaro]

Francesca:
I would stick with unit change.
Not quite:
serial correlation=autocorrelation (of the systematic espilon error term).
Multicollinearity occurs when two predictors are highly correlated and their contribution in explaining variation of the conditional mean of the regressand is impossible to disentagle.

[Francesca Sossella]

Thank you very much Carlo for all your help. Now that I am writing comments to my models I cannot find a good explanation to the fact that my models have low R squared (around 20%), please see below one of the outputs:

xtreg TobinsQ LNTA ROA DE YoYSales RDCS i. Years, fe vce(cluster Company1)

Fixed-effects (within) regression               Number of obs     =      1,060
Group variable: Company1                        Number of groups  =        212

R-sq:                                           Obs per group:
     within  = 0.1893                                         min =          5
     between = 0.0031                                         avg =        5.0
     overall = 0.0070                                         max =          5

                                                F(9,211)          =      10.82
corr(u_i, Xb)  = -0.7982                        Prob > F          =     0.0000

                             (Std. Err. adjusted for 212 clusters in Company1)
------------------------------------------------------------------------------
             |               Robust
     TobinsQ |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        LNTA |  -1.350005   .2896686    -4.66   0.000     -1.92102   -.7789899
         ROA |   1.677901   .5152768     3.26   0.001     .6621507    2.693651
          DE |  -.2066595   .0689203    -3.00   0.003    -.3425202   -.0707989
    YoYSales |   .7732031   .2754733     2.81   0.005     .2301706    1.316236
        RDCS |  -.7317888   .3324677    -2.20   0.029    -1.387173    -.076405
             |
       Years |
       2014  |   .1331407    .082901     1.61   0.110    -.0302795    .2965609
       2015  |   .0866756   .1132684     0.77   0.445     -.136607    .3099582
       2016  |   .2196538   .1044505     2.10   0.037     .0137535    .4255541
       2017  |    .679877   .1435643     4.74   0.000     .3968728    .9628811
             |
       _cons |   30.76325   6.044455     5.09   0.000     18.84799     42.6785
-------------+----------------------------------------------------------------
     sigma_u |  3.1345762
     sigma_e |  1.0474911
         rho |  .89954618   (fraction of variance due to u_i)
------------------------------------------------------------------------------

I found one explanation in the fact that also previous studies on the topic found a low R squared. Do you have any further suggestions for the explanation of why the R squared can be relatively low?

Many thanks,

Francesca

[Carlo Lazzaro]

Francesca:
regression models often fall halfway between creating new research appraoches and avoiding re-inventing the wheel.
If your model does not complain about misspecification problem, I would play on the safe side of the matter, stating that your results confirm what others reported.
As I recommended you repeatedly before, please discuss with your supervisor each of the many research steps that you have taken autonomously, in order to avoid misunderstandings during the last mile of your research effort.

[Francesca Sossella]

Thank you very much Carlo and sorry for the late response. Yes, I am trying to keep in touch with my supervisor as much as I can, even if it's hard sometimes, unfortunately.
However, when it comes to the Hausman test, that makes me choose between fixed and random effects, I am wondering if I got the meaning of the difference between the two. Do you think the following explanation is correct?

In a fixed effect model, a parameter’s estimate of a dummy variable is considered part of the intercept of the regression, while in a random effect model the estimator of a dummy variable is considered to be a random error component. In addition, the fixed effect model captures the time-constant omitted variables, but fail to incorporate the time-varying omitted variables, if any, since they are perfectly correlated with the fixed-effect dummies. In addition, the fixed effect model does not incorporate time-invariant explanatory variables. On the other hand, the random effect model allows to estimate time-invariant regressors but, if individual effects are correlated with explanatory (or independent) variables, the random effect model would be incompatible, while the fixed effect could still be applied.

Thank you very much in advance.

Francesca

[Carlo Lazzaro]

Francesca:
the main difference between fixed and effect specification is that, while the first one allows a weak endogeneity via the correlation between the vector of the regressors and the panel-wise error term, the second one does not (although this assumption oftentimes does not hold). In both cases (and despite their definitions) we talk about random parameters, whereas their difference is indeed a matter of correlation. One of the best explanation I've ever found about that difference is reported in the help file of the community-contributed programme -xtoverid-.
In addition, the -fe- estimator wipes out all the time invariant predictors, including those that were omitted and lurked behind residual.
As an aside, both specification rule out any correlation between the vector of regressors and the idiosyncratic error (ie, epsilon, the error component that varies for both panel units and time).
As far as -hausman- is concerned, it is important to stress that it actually tests the intersection of the regressors included in both -fe- and -re- specifications (for instance, time-invariant predictors that are kicked out from -fe- but estimated in -re- are not included in -hausman-, because they actually appear under -re- only).
The null hypothesis is that both -fe- and -re- are consistent but, if the null is not rejected, the -re- estimator is more efficient whereas the opposite happens when the null is rejected.
I would recommend you to take a look at any decent textbook on panel data econometrics and grasp what you need about the theoretical foundations of your research.

[Francesca Sossella]

Thank you very much Carlo! And sorry again for my late response, I am back to work.

Good news: my supervisor said I did a really good job, so really thank you very much for all your help and support!

I would have one last doubt, if you can kindly help on this. Back on the interpretation of the coefficient (please see what follows).

. . xtreg TobinsQ LNTA ROA DE YoYSales RDS i. Years, fe vce(cluster Company1)

Fixed-effects (within) regression               Number of obs     =      1,240
Group variable: Company1                        Number of groups  =        248

R-sq:                                           Obs per group:
     within  = 0.1775                                         min =          5
     between = 0.0039                                         avg =        5.0
     overall = 0.0080                                         max =          5

                                                F(9,247)          =      11.83
corr(u_i, Xb)  = -0.7769                        Prob > F          =     0.0000

                             (Std. Err. adjusted for 248 clusters in Company1)
------------------------------------------------------------------------------
             |               Robust
     TobinsQ |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        LNTA |  -1.192326    .259264    -4.60   0.000    -1.702976   -.6816754
         ROA |   .0187411    .004765     3.93   0.000     .0093558    .0281264
          DE |  -.2090798   .0663855    -3.15   0.002    -.3398335    -.078326
    YoYSales |   .8738011   .2685996     3.25   0.001     .3447635    1.402839
         RDS |  -1.030589   1.402473    -0.73   0.463     -3.79292    1.731741
             |
       Years |
       2014  |   .1005881   .0711572     1.41   0.159    -.0395641    .2407403
       2015  |   .0632616   .0966094     0.65   0.513    -.1270216    .2535449
       2016  |   .1696639   .0892839     1.90   0.059     -.006191    .3455188
       2017  |   .6047159   .1218185     4.96   0.000     .3647804    .8446515
             |
       _cons |   27.11054   5.300276     5.11   0.000     16.67103    37.55004
-------------+----------------------------------------------------------------
     sigma_u |  2.8756923
     sigma_e |  1.0068194
         rho |   .8908054   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

• When the total assets increases by one unit percentage, the change in Tobin’s Q equals a decrease of 1,2 units percentage;
• When the return on assets increases by one unit percentage (1%), the change in Tobin’s Q equals an increase of 0,018 units percentage (-0,18%);
• When the debt-equity ratio increases by one unit percentage, the change in Tobin’s Q equals a decrease of 0,2 units percentage;
• When the year-over-year sales increase by one unit percentage, the change in Tobin’s Q equals an increase of 0,9 units percentage;
• When the research and development expenditure intensity increases by one unit percentage, the change in Tobin’s Q equals a decrease of 1.03 units percentage.

Mathematically speaking, should be the same using units or percentages, right?

Many thanks in advance,

Francesca

[Francesca Sossella]

Sorry, I deleted this message since I already modified what necessary in the last one.

Thanks,

Francesca

[Carlo Lazzaro]

Francesca:
I would replace unit(s) percentage with percentage points (which, in turn, differ from percentage).