This is the output in terms of heteroskedasticity
-
Login or Register
- Log in with
- You are not logged in. You can browse but not post. Login or Register by clicking 'Login or Register' at the top-right of this page. For more information on Statalist, see the FAQ.
-
-
Francesca:
the model looks ok to me.
Hiwever, you might have a minor heteroskedasticity issue: just impose cluster robust SEs and see if the 95% CIs do differ vs default SEs.Kind regards,
Carlo
(Stata 19.0)Comment
-
Carlo, thank you very much again. I invoked robust standard errors. You can find below the output with robust standard errors and without. It seems to me that CI are smaller in the model without robust standard errors, do you agree?
Code:xtreg TobinsQ ROA DE LNTA 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] -------------+---------------------------------------------------------------- ROA | 1.677901 .5152768 3.26 0.001 .6621507 2.693651 DE | -.2066595 .0689203 -3.00 0.003 -.3425202 -.0707989 LNTA | -1.350005 .2896686 -4.66 0.000 -1.92102 -.7789899 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) ------------------------------------------------------------------------------ . . xtreg TobinsQ ROA DE LNTA YoYSales RDCS i. Years, fe 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(9,839) = 21.76 corr(u_i, Xb) = -0.7982 Prob > F = 0.0000 ------------------------------------------------------------------------------ TobinsQ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- ROA | 1.677901 .4205996 3.99 0.000 .8523498 2.503452 DE | -.2066595 .0667669 -3.10 0.002 -.3377094 -.0756097 LNTA | -1.350005 .129184 -10.45 0.000 -1.603567 -1.096443 YoYSales | .7732031 .1465645 5.28 0.000 .485527 1.060879 RDCS | -.7317888 .1967754 -3.72 0.000 -1.118019 -.3455589 | Years | 2014 | .1331407 .1034784 1.29 0.199 -.0699663 .3362476 2015 | .0866756 .1058546 0.82 0.413 -.1210953 .2944466 2016 | .2196538 .1098901 2.00 0.046 .0039619 .4353456 2017 | .679877 .1150542 5.91 0.000 .4540491 .9057048 | _cons | 30.76325 2.699273 11.40 0.000 25.46513 36.06137 -------------+---------------------------------------------------------------- sigma_u | 3.1345762 sigma_e | 1.0474911 rho | .89954618 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(211, 839) = 14.60 Prob > F = 0.0000 .
However, I would like to ask your opinion on the following:
-Why if my observation years go from 2013 (included) to 2017(included), I see only years from 2014 when I insert years dummy variable?
-How can I control for the company effect if I don't invoke robust standard errors?
-When I do the Hausman test, do I need to include the dummy variables for the years or is not necessary?
-If my F value increase, it means that the model increase in significance, right?
Many thanks in advance,
Francesca
Comment
-
Francesca:
- I would keep the model with clustered robust SE (and this comment answers to your question #2, too) because SEs are actually higher (and for some coefficients they almost double) than the default ones;
- 2013 is omitted by default to shelter your regression from the so called dummy trap (https://en.wikipedia.org/wiki/Dummy_...(statistics));
- yes, include the dummy variables for year in both the -fe- and -re- regressions, that now should be compared via the community-contributed command -xtoverid- as you invoked non default SEs which are not supported by -hausman-;
- not quite. The F-test investigates whether your coefficients jointly differ from zero.Kind regards,
Carlo
(Stata 19.0)Comment
-
Thank you very much Carlo as always and sorry for the delay in the response!
First of all, merry Christmas and happy holidays! I just realized that for my model I did not take into account potential outliers that should be eliminated. Do you think this is a major issue or can I avoid to check for outliers?
Many thanks again and my best wishes,
FrancescaComment
-
Francesca:
I do reciprocate best wishes for the Xmas season to you and your dears.
Sticking with statistics, eliminating outliers (unless you're 100% sure that they are the result of a mistaken data entry) is, in general, a very bad idea. What we call outliers, are, in general, expressions of the data generating process undelying our samples. For instance, it is frequent that the statistical distribution of the total cost of a given activity is positively skewed (gamma distribution).
In sum, think very carefully about eliminating "weird" observations: personally, I do not advise that approach.Kind regards,
Carlo
(Stata 19.0)Comment
-
Thank you very much Carlo! However, I would have another concern. When I apply robust standard errors and plot again to check for heteroskedasticity, it seems to stay the same as before invoking for robust standard errors (I attach the graph below). Is it normal?Comment
-
This is the output after invoking robust standard errorsAttached FilesComment
-
-
Would it be better to apply the natural logarithm to some of the variables? If I do so and plot for heteroskedastity, these are the output I get:
The R-sqared increase from 17% to 27% and the heteroskedasticity improves:Code:xtreg LNTobinsQ LNTA ROA LNDE lnYoYSales i.Years, fe Fixed-effects (within) regression Number of obs = 1,049 Group variable: Company1 Number of groups = 210 R-sq: Obs per group: within = 0.2717 min = 4 between = 0.0011 avg = 5.0 overall = 0.0058 max = 5 F(8,831) = 38.76 corr(u_i, Xb) = -0.7684 Prob > F = 0.0000 ------------------------------------------------------------------------------ LNTobinsQ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LNTA | -.3862058 .0367041 -10.52 0.000 -.4582493 -.3141622 ROA | .9756964 .1211722 8.05 0.000 .7378569 1.213536 LNDE | -.0886246 .0141089 -6.28 0.000 -.1163178 -.0609314 lnYoYSales | .0513431 .009779 5.25 0.000 .0321487 .0705375 | Years | 2014 | .0703752 .0295889 2.38 0.018 .0122975 .1284529 2015 | .0508165 .030604 1.66 0.097 -.0092537 .1108866 2016 | .1006498 .0316692 3.18 0.002 .0384888 .1628109 2017 | .266613 .0331686 8.04 0.000 .2015089 .3317171 | _cons | 8.532238 .7666167 11.13 0.000 7.027505 10.03697 -------------+---------------------------------------------------------------- sigma_u | .98246626 sigma_e | .29886225 rho | .91530234 (fraction of variance due to u_i) ------------------------------------------------------------------------------ F test that all u_i=0: F(209, 831) = 19.11 Prob > F = 0.0000
Attached FilesComment
-
-
Thank you very much in advance.
Comment
-
Francesca:
what you experienced (#37) occurred to everybody when trying to get familiar with -regress- (and I lead the queue of those frightened with looking at the same graph before/after invoking robust standard errors)..
Indeed, re-checking for heteroskedasticity after invoking cluster robust standard error is not useful at all: the graph will remain the same because the -robust- option correct the standard errors, not the residuals.
As far as your second question is concerned, actually there seem to be heteroskedasticity in your last graph (the distribution of the systematic error seems to widen when the value of the fitted values increase). It is worth checking whether heteroskedasticity depends on misspecification.
Logging some variables at random makes little methodological sense (by the way, from your code I fail to get which variables, if any, have already been logged): logging the regressand and/or the predictors means creating different regression models, which coefficients can be difficult to undestand and/or disseminate.
If the heteroskedasticity is not due to model misspecification, invoking cluster robust standard error is, in general, enough.
Kind regards,
Carlo
(Stata 19.0)Comment
-
Just to add on to Carlo's helpful comments, you're fixating way too much on heteroskedasticity. It's much more likely that serial correlation is a bigger issue, if you think of these problems the way they are traditionally taught. How come you're testing for heteroskedasticity and not serial correlation?
The point is, you should test for neither. The clustering accounts for any kind of heteroskedasticity and any kind of serial correlation. You're not changing the estimates -- it's still standard fixed effects -- but you're computing robust standard errors. They're robust to heteroskedasticity and serial correlation, and that's why almost all empirical researchers compute them now and do not even bother to check if either is a problem. The standard errors work in either case.
Two things about taking the log of TobinsQ. First, note that you've lost 11 observations, which is due to TobinsQ <=0 in 11 cases. And you've lost two firms entirely. So you don't want to do this. And even if you did, it makes no sense to compare R-squareds across different transformations of the dependent variable. It's possible to compute an R-squared that is comparable, but, since you are losing data taking the logs, you shouldn't do that. It is often true that the R-squared using logs is higher but that doesn't mean you should do it, especially when the samples aren't comparable.
Do you have any negative values of TobinsQ, or just zeros?
Above I suggested that you stop with the results in post #33, using the results with clustered standard errors. That's still my suggestion. Is someone insisting you test for heteroskedasticity?Comment
-
Dear Carlo and Jeff, thank you very much for your support, it is really important to me! First of all, apologies for my late response and wish you all the best for the new year!
I understand that heteroskedasticity is definitely not a big issue (most of all after applying robust standard errors) and thank you for your patience in explaining me why. I was looking at previous thesis with regression analysis as a reference and I noticed that they were checking on heteroskedasticity before and after some transformations. That's why I was erroneously looking at heteroskedasticity too much. The minimum value of my Tobin's Q is 0,18 and now I also understand why it doesn't make sense to apply the log. So, really thank you.
However, I would like to kindly ask you another clarification on my analysis:
-When I run the regression including time effect, therefore years' dummy variables, what is a good explanation to the fact that only one year is statistically significant?
Below I provide an output for your reference:
Many thanks in advance!Code:. xtreg TobinsQ LNTA ROA DE YoYSales RDS 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 = 0.1768 min = 5 between = 0.0030 avg = 5.0 overall = 0.0071 max = 5 F(9,211) = 10.54 corr(u_i, Xb) = -0.7614 Prob > F = 0.0000 (Std. Err. adjusted for 212 clusters in Company1) ------------------------------------------------------------------------------ | Robust TobinsQ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LNTA | -1.201734 .2806209 -4.28 0.000 -1.754914 -.6485543 ROA | 1.799148 .4931036 3.65 0.000 .827107 2.771189 DE | -.2142444 .0701898 -3.05 0.003 -.3526075 -.0758813 YoYSales | .8832866 .2885457 3.06 0.002 .3144848 1.452088 RDS | -.9375915 1.432355 -0.65 0.513 -3.76115 1.885967 | Years | 2014 | .1154523 .0818341 1.41 0.160 -.0458648 .2767695 2015 | .0553842 .1094215 0.51 0.613 -.1603152 .2710835 2016 | .1661806 .0992611 1.67 0.096 -.02949 .3618511 2017 | .6106977 .1347841 4.53 0.000 .3450019 .8763936 | _cons | 27.29121 5.722012 4.77 0.000 16.01158 38.57085 -------------+---------------------------------------------------------------- sigma_u | 2.9067784 sigma_e | 1.0554858 rho | .88350911 (fraction of variance due to u_i) ------------------------------------------------------------------------------ .
FrancescaComment
-
Francesca:
best wishes for the just begun 2020 to you, too.
You should better consider the joint statistical significance of -i.year- via:
Code:testparm(i.year)
It may well be that -i.year-, when adjusted for the remaining predictors, does not play a relevant role (jointly speaking) in explaining the variation of the regressand within the same panel (as you're dealing with -fe- specification).Kind regards,
Carlo
(Stata 19.0)Comment
-
Thank you very much Carlo!
Now that I am going to interpret the coefficients, I am wondering if my interpretation is correct. This is the output I get, for example, from my first model:
is it correct stating the following?Code:. xtreg TobinsQ LNTA ROA DE YoYSales RDS 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 = 0.1768 min = 5 between = 0.0030 avg = 5.0 overall = 0.0071 max = 5 F(9,211) = 10.54 corr(u_i, Xb) = -0.7614 Prob > F = 0.0000 (Std. Err. adjusted for 212 clusters in Company1) ------------------------------------------------------------------------------ | Robust TobinsQ | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- LNTA | -1.201734 .2806209 -4.28 0.000 -1.754914 -.6485543 ROA | 1.799148 .4931036 3.65 0.000 .827107 2.771189 DE | -.2142444 .0701898 -3.05 0.003 -.3526075 -.0758813 YoYSales | .8832866 .2885457 3.06 0.002 .3144848 1.452088 RDS | -.9375915 1.432355 -0.65 0.513 -3.76115 1.885967 | Years | 2014 | .1154523 .0818341 1.41 0.160 -.0458648 .2767695 2015 | .0553842 .1094215 0.51 0.613 -.1603152 .2710835 2016 | .1661806 .0992611 1.67 0.096 -.02949 .3618511 2017 | .6106977 .1347841 4.53 0.000 .3450019 .8763936 | _cons | 27.29121 5.722012 4.77 0.000 16.01158 38.57085 -------------+---------------------------------------------------------------- sigma_u | 2.9067784 sigma_e | 1.0554858 rho | .88350911 (fraction of variance due to u_i) ------------------------------------------------------------------------------ .- When the natural logarithm of total assets increases by one unit, the change in Tobin’s Q equals a decrease of 1,2 units;
- When the return on assets increases by one unit, the change in Tobin’s Q equals an increase of 1,8 units;
- When the debt-equity ratio increases by one unit, the change in Tobin’s Q equals a decrease of 0,2 units;
- When the year-over-year sales increase by one unit, the change in Tobin’s Q equals an increase of 0,9 units;
- When the research and development expenditure intensity increases by one unit, the change in Tobin’s Q equals a decrease of 0,9 units.
Many thanks in advance,
Francesca
Comment
Comment