xtreg vs xtscc

[Prateek Bedi]

Hi,

I am trying to estimate the impact of directors' remuneration on firm performance. My unbalanced data set comprises 1696 firms and 16 time periods (in particular, years). I have 7 independent variables in total. In existent literature, fixed effects model (xtreg, fe) has been used as a common methodology to estimate parameters. Below is my model.

xtreg Profitability4 Size2 Leverage1 CurrentRatio SalesGro CapitalExpenditure2 WPromoterSharesin1 AD_Totalremuneration i.Year, fe

I checked for serial correlation in the error term using the command xtserial and found presence of serial correlation. Below is the output for the same.

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
    F(  1,    1084) =    216.002
           Prob > F =      0.0000

Then, I checked for group-wise heteroskedasticity (using command xttest3) and found presence of the same. Below is the concerned output.

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

H0: sigma(i)^2 = sigma^2 for all i

chi2 (1264)  =  2.6e+36
Prob>chi2 =      0.0000

Finally, I checked for cross-sectional dependence using xtcdf and found presence of cross-sectional dependence. Here is the result.

quietly: xtreg Profitability4 Size2 Leverage1 CurrentRatio SalesGro CapitalExpenditure2
>  WPromoterSharesin1 AD_Totalremuneration i.Year, fe

. predict res, r
(15,392 missing values generated)

. xtcdf Profitability4 res

xtcd test on variables Profitability4 res
Panelvar: CompanyID
Timevar: Year
------------------------------------------------------------------------------+
    Variable    |  CD-test   p-value   average joint T | mean ρ   mean abs(ρ) |
----------------+--------------------------------------+----------------------|
 Profitability4 +  119.953    0.000         13.24      +  0.03       0.31     | 54693 com
> binations of panel units ignored (insufficient joint observations).
      res       +  1.985      0.047          8.29      +  0.00       0.17     | 843986 co
> mbinations of panel units ignored (insufficient joint observations).
------------------------------------------------------------------------------+
 Notes: Under the null hypothesis of cross-section independence, CD ~ N(0,1)
        P-values close to zero indicate data are correlated across panel groups.

I have the following questions:

1. I would like to know if I have run the xtcdf correctly. Also, what does presence of cross-sectional dependence mean intuitively?
2. Since my data set exhibits serial correlation, heteroscedasticity and cross-sectional dependence, should I use xtreg, fe cluster(CompanyID) or xtscc, fe? What are the relevant criteria for choosing one of the these two commands?
3. While using xtscc, I realised that it does not support use of factor variables. In that case, should I manually create time dummies and introduce them in the model?
4. How should we select the number of lags in case of xtscc?

Thanks and Regards,
Prateek

[Jeff Wooldridge]

Prateek: You don't have enough time periods to use xtscc. It's useful in cases where T is sufficiently large to use asymptotic approximations in the time series dimension.

You have to be careful in interpreting the tests for cross-sectional correlation even when using the residuals. Heterogeneous coefficients can be mistaken for cross-sectional correlation. And testing y itself is not informative because you haven't removed the time effects or the firm effects. Plus, without some ordering of the firms in space, you can't use spatial-correlation robust standard errors.

With your data structure, I recommend the usual FE estimator and compute standard errors robust to serial correlation and heteroskedasticity:

xtreg Profitability4 Size2 Leverage1 CurrentRatio SalesGro CapitalExpenditure2 WPromoterSharesin1
                AD_Totalremuneration i.Year, fe vce(cluster CompanyID)

[Prateek Bedi]

Thanks a lot, Prof. Jeff Wooldridge for answering my query. I have two follow-up questions:

1. Actually, I used residuals and tested Y because that is the way it was done in the help file. I agree that I haven't removed time and firm effects. According to you, what should be the correct specification to test cross-sectional dependence in the context of my model?
2. I did not understand what is meant by ordering of firms in space. Could you please elaborate on the same?

As a side note, it feels so good to hear from a stalwart like you. I would like to convey my respect and gratitude to you for your remarkable body of work in Econometrics and beyond. Your textbooks on Econometrics (Introductory Econometrics: A Modern Approach and Econometric Analysis of Cross-Section and Panel Data) are like the foundation stones on which students like me build their understanding of the subject. Your research papers are like the go-to-guide for naive researchers like me. Whenever I have a discussion regarding any concept in Econometrics with my friends/professors, we refer to your books for the final word. In my circle of fellow researchers, you are as popular as a rockstar. I am glad that you answered my query because I got a chance to tell you that you are doing some brilliant work for present as well as future generations. Please keep spreading the light of knowledge like this.

May God bless you with the best of health and happiness.

[Sergio Lopez]

Good afternoon,

I would be very grateful if somone can answer my question.

I have a database with 40 countries and about 20 years for each one. The dependent variable is the percentage of invoicing currency and I have 10 independent variables. The database is unbalanced and with quite a few missing values and I have checked that there is Heteroskedasticity and I assume that there is cross-sectional dependence, so far I had used xtreg, fe vce(cluster country), but I have been strongly advised to use xtscc, and the results I have obtained with this are much more consistent [p value is lower for almost all my results, compared to the xtreg results]. I can split the database into advanced and developing countries which would leave me with 20 countries on each side. My question is whether I can use xtscc despite not having a large number of years (T = N).

[Joro Kolev]

You can do whatever you want, the computer will not break. But Daniel Hoechle's xtscc is linear regression with Driscoll-Kraay standard errors, and those are justified as T goes to infinity. Using xtscc makes, or does not make sense depending on your belief: Is 20 time series observations infinity?

Even more importantly, what kind of correlation you believe you have? Correlation of observations within a country, or you re also worried about correlation across countries?

If I were you, I would use -xtreg- with robust and clustered standard errors by country. And I would not split the sample because 40 is already small.

Good afternoon,

I would be very grateful if somone can answer my question.

I have a database with 40 countries and about 20 years for each one. The dependent variable is the percentage of invoicing currency and I have 10 independent variables. The database is unbalanced and with quite a few missing values and I have checked that there is Heteroskedasticity and I assume that there is cross-sectional dependence, so far I had used xtreg, fe vce(cluster country), but I have been strongly advised to use xtscc, and the results I have obtained with this are much more consistent [p value is lower for almost all my results, compared to the xtreg results]. I can split the database into advanced and developing countries which would leave me with 20 countries on each side. My question is whether I can use xtscc despite not having a large number of years (T = N).

[Ali Maleki]

Hello, I am new to the stata community. Can you help me whether xtreg, xtgls or xtscc should be used for the panel data with the following characteristics?
I have three panel data (N=12 countries T=40 years) with three different dependent variables (but same independent variables) . data is not sample but the populations.
all three have autocorrolation
2 of them have heteroskedasticity, but one does not have.

Husman test and Breusch and Pagan test for the three says
1- niether fixed effext nor random effect is not suitable for two of them
2-fixed effext is suitable for one else.

Can you please help me how can I choose between the three xtreg, xtgls or xtscc and also ( fixed effect or random effect?)?

I read some helps but more confuses how to go with the three commands.

[Carlo Lazzaro]

Duplicate post #6; replied at https://www.statalist.org/forums/for...xtgls-vs-xtscc