Paneldata Analysis-Steps to follow

[Christian Mueller]

Hello,
for my research I have to do a paneldata analysis and I would like to know if there are steps to follow in order to get valid and robust results. I have paneldata for a time period of 50 years and five independent variables.
What I did until now is the following:
1. xtreg y x i e z u, re robust (Random effects regression)
2.Xttest0 (Test if pooled OLS is appropriate)
3. Xtoverid (Test if fixed effects or random reffects to choose)
As result I got that I have to choose the fixed effects model. How can I check now for these points in my panel data in order to obtain unbiased results:

4. Multicollinearity
5. Homoscedasticity
6. Autocorrelation
7. Normally distributed error term
8. How can I decide whether or not to include time-fixed effects?
9. Is there something like a model specification test which says that my model is appropriate?

Thank you for your help

Christian

[Carlo Lazzaro]

Christian:
welcome to the list.
-xtreg- and -xtreg postestimation- entries in Stata .pdf manual covers all the topics you're interested in (I would add to the list -hausman- specification test).
For the future, posting what you typed and what Stata gave you back will increase your chances of getting more helpful replies (as per FAQ). Thanks.

[Christian Mueller]

Hello Carlo,

thank you for your answer. Now in more detail. I want to estimate the effect of some variables on capital expenditures:

1.xtreg capx_at_w Tobin_Q_w cashflow_w leverage_w che_w, re robust
2. xttest0 (Test if pooled OLS is appropriate)
Output: Breusch and Pagan Lagrangian multiplier test for random effects

capx_at_w[conm,t] = Xb + u[conm] + e[conm,t]

Estimated results:
| Var sd = sqrt(Var)
---------+-----------------------------
capx_at_w | .0069986 .0836577
e | .003402 .0583269
u | .0047764 .0691118

Test: Var(u) = 0
chibar2(01) = 1.4e+05
Prob > chibar2 = 0.0000


3.xtoverid (Test if fixed effects or random effects are appropriate)
Output:
Test of overidentifying restrictions: fixed vs random effects
Cross-section time-series model: xtreg re robust cluster(conm)
Sargan-Hansen statistic 528.762 Chi-sq(4) P-value = 0.0000


So finally I choose the fixed effects model because RE and pooled OLS are not appropriate.


4.xtreg capx_at_w Tobin_Q_w cashflow_w leverage_w che_w, fe robust
Output:

Fixed-effects (within) regression Number of obs = 114411
Group variable: conm Number of groups = 8788

R-sq: within = 0.1146 Obs per group: min = 1
between = 0.0068 avg = 13.0
overall = 0.0345 max = 53

F(4,8787) = 615.73
corr(u_i, Xb) = -0.1984 Prob > F = 0.0000

(Std. Err. adjusted for 8788 clusters in conm)
------------------------------------------------------------------------------
| Robust
capx_at_w | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
Tobin_Q_w | .0139907 .0003026 46.24 0.000 .0133976 .0145837
cashflow_w | 1.52e-06 1.15e-06 1.32 0.188 -7.44e-07 3.78e-06
leverage_w | -3.22e-06 4.10e-07 -7.86 0.000 -4.02e-06 -2.42e-06
che_w | -.0000153 1.26e-06 -12.16 0.000 -.0000178 -.0000129
_cons | .0584618 .0006402 91.32 0.000 .0572069 .0597167
-------------+----------------------------------------------------------------
sigma_u | .07619167
sigma_e | .05832688
rho | .63050365 (fraction of variance due to u_i)


So what I would like to know is, whether this regression is now valid and unbiased. Do I have to check for multicollinearity, homoscedasticity, autocorrelation and normally disbributed errors terms or am I finished now and the model is good?
Thanks for your help!

[Christian Mueller]

For a better reading:

capx_at_w	Coeff	std.err	t	p	conf intervall
Tobin_Q_w	0.0139	0.00306	46.24	0.000
cashflow_w	1.52e-0.6	1.15e-0.6	1.32	0.188
leverage_w	-3.22e-0.6	4.10e-0.7	-7.86	0.000
che_w	-0.000153	1,26e-0.6	-12.16	0.000
cons

[Carlo Lazzaro]

Christian:
yes, you have to check for the model specification items that you have listed, exception made for autocorrelation and heteroskedasticitty, which are managed by the -robust()- option of standard errors.
As a closing-out remark, I notice that your R-sq within is quite low: this results may be consistent with the outcome of other researches published or may be due to a limited number of predictors (put differently, your regression model may suffer from omitted variable bias and possible endogeneity).
For the future, please consider posting what you typed and what Stata gave you back via CODE delimiters (this topic, among others, is covered in the FAQ).

[Christian Mueller]

Hello Carlo,
thank you again for your answer. Two mor questions.
1. You said that I don´t have to test for heteroskedasticity. But if I execute the following commands I get:

xtreg capx_at_w Tobin_Q_w cashflow_w leverage_w che_w, fe robust

Xttest3 (test for heteroscedastitcity)

Output:

Modified Wald test for groupwise heteroskedasticity
in fixed effect regression model

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

chi2 (8788) = 4.9e+40
Prob>chi2 = 0.0000


This output tells me that there is still heteroscedasticity although I used roubst standdard errors. How is this possible?


2. How can I test for endogenity? I did not find a command.


Thank you for your help

Christian

[Carlo Lazzaro]

Christian:
1) With such a large sample the -xttest3- (since it is not a Stata official command, you are kindly requested to report wher you download it from. The reason for this seemingly pedanti requirement are reported in the FAQ) may end up statistically significant; I would not be worried about its outcome;
2) Endogeneity has more to do with the theory of your resarch field than with formal tests. For instance: can you rule out that an omitted variable embedded in residuals can influence one or more predictors and the dependent variable at the same time?

[Christian Mueller]

Hell Carlo,
thank you again. But I have got the same problem with the command xtserial.
I did the following steps:
1.xtreg capx_at_w Tobin_Q_w cashflow_w leverage_w che_w, fe cluster (conm)
2. Xtserial (Test for autocorrelation)
Output:
xtserial capx_at_w Tobin_Q_w cashflow_w leverage_w che_w

Wooldridge test for autocorrelation in panel data
H0: no first-order autocorrelation
F( 1, 7704) = 1931.843
Prob > F = 0.0000

How is it possible that there is still autocorrelation although I corrected for it with fe cluster(conm)?
Thank you!

[Bertha Rohenkohl]

I may be wrong, but I think the idea of correcting the fixed effects model using vce(cluster id) is exactly to correct your standard errors allowing for autocorrelation.

What I mean is, for panel data the post estimation tests will always tell you to reject H0 of no autocorrelation even after you corrected it. But this result doesn't have any meaning, as you have already managed this issue using vce(cluster id).

[Carlo Lazzaro]

Christian:
I share Bertha's standpoint.

[Christian Mueller]

Ok thank you for the answers!
Just to summarize: These are the assumptions underlying regressions models:

1. var (e(it))=o^2 homoscedasiticity
Controlled for by using robust()-option.

2.cov(e(it) e(is)=0 no autocorrelation
Controlled for by using robust()-option

3.e(it)=normally distributed (normally distributed residuals)
Can I check for this with the following command:
xtreg capx_at_w Tobin_Q_w cashflow_w leverage_w che_w, fe cluster (conm)
predict residuals, e
kdensity residuals, normal

4. No multicollinearity
How to check for this? "Estat vif" command does not work.

5.E(e(it)=0 Expected value of erro e is zero

How to check for this?

6. cov (e(it), x(kit))=0 exogenity of independent varialbe
How to check for this?

7. Linear model
How to check if linear model is appropriate?

If finally all these assumptions are fulfilled I assume that the model is appropriate.

Thank you for your help!

[Carlo Lazzaro]

Christian:
- # 5:

predict e_res, e
kdensity e_res

:

- ##4 and 6: -estat vce-; -estat vce, corr-;

#7: you may want to include a squared terms and see what happens.

[Christian Mueller]

Thank you Carlo!
I have got anohter question:
1. In a regression analysis is it necessrary that all the variables are normally disributed? Or is it just the residuals of the regression which have to be normally distributed?
Thank you for your answer!

[Carlo Lazzaro]

Christian:

...just the residuals of the regression have to be normally distributed...

[Cláudio Carvalho]

Christian:
- # 5:

predict e_res, e
kdensity e_res

:

- ##4 and 6: -estat vce-; -estat vce, corr-;

#7: you may want to include a squared terms and see what happens.

Carlo, predict e_res, e is for the expected value or for the prediction of the idiosyncratic error component (http://www.stata.com/manuals13/xtxth...timation.pdf)? If so, what is the command for doing what Christian pretend to do? Must be "ue"?... Thanks