How to account for cross sectional dependence in unbalanced panel which is irregularly spaced?

[Neharika Sobti]

Hi
I have a long panel with T= 1400 and N is fixed to 5. It is an unbalanced panel and my cross sectional units are Monday, Tuesday, Wednesday, Thursday and Friday. So i expect that there should be some cross sectional dependence given the objective. Now , i ran random effects model as BP LM test xttest0 and found that random effects are present, then i checked for cross sectional dependence wherein xttest2 and xtcsd, pesaran abs both provide evidence of cross sectional dependence.

Now how to account for it in model? Should I use Seemingly unrelated regression with GLS or is there a model with random effects. Kindly help.

[Carlo Lazzaro]

Neharika:
welcome to this forum.
See -help xtregar-.

[Neharika Sobti]

Dear Carlo Sir
Thanks but what should i write xtregar depvar indepvar, re?Is that It? Is it accounting for cross sectional dependence across entity and heteroscdasticity?

[Carlo Lazzaro]

Neharika:
another option could be -xtgls-.

[Neharika Sobti]

Dear Sir

Can you kindly guide how can i implement xtsur command with this issue? like my data set is in a panel form wherein my i have one dependent variable and 5 independent variable for each entity. Do i need to reframe my data or can it done in panel set form?

[Jeff Wooldridge]

This is a multiple time series setup, not panel data in the usual sense. And I'm a bit puzzled about the "cross-sectional" dimension because that seems to be day-of-the week. So, I assume t is time and you want to group outcomes for a week. If so, that's not really a panel data setup. Why not treat it as a time series -- which is what it is? Then include dummy variables for the different days of the week, and maybe interact those day-of-week dummy variables with explanatory variables. You can then compute Newey-West standard errors.

If you still want to treat each group of five days as a unit, you can use the Driscoll-Kraay approach (-xtscc- is user written). It allows any kind of "cross-sectional" dependence.

[Neharika Sobti]

Dear Prof. Wooldridge
Thank you sir for your reply. You are right that I have 5 sets of time series , one for each day of the week. My objective is to understand the determinant of a dependent variable for each day of the week and assess whether I find the relationships to be same for all day of the week or different but at same time I have a strong assumption that there is bound to be some cross sectional dependence between Monday with Tuesday and so on ..
Firstly, I tried to run simple OLS with newey west for all 5 day of the week separately - this method will not account for cross sectional dependence neither will pooled data. Secondly I tried to run a panel regression with random effects but I get problem of cross sectional dependence and heteroscedasticity. Like you mentioned Driscoll-Kraay approach (-xtscc- is user written) , it is suitable for balanced data with regularly spaced data , I have unbalanced panel with irregularly spaced data. Its not working. So i checjed and saw maybe SUR model with GLS a suitable model for my objective. Can you pls suggest that SUR with GLS a suitable model or should i use simple time series with dummies but how to account for cross sectional dependence in that?

[Neharika Sobti]

Any help on using SUR model?

[Neharika Sobti]

Kindly reply.

[Jeff Wooldridge]

If you use a standard SUR then you're assuming independence over time. That's much worse than assuming no cross-sectional independence. And what does that even mean here? It means correlation across days of the week, I think.

Use the xtscc command with the FE option and let Stata choose the optimal lag for you in the Newey-West variance estimator. SUR is much too restrictive with this kind of time series data -- at least the way Stata implements it, not allowing for a Newey-West estimator.

[Neharika Sobti]

Sir I am unable to use xtscc as my panel is irregularly spaced . This is the error i am getting. How to resolve this?

[Neharika Sobti]

Any solution to force my irregularly spaced data to be regular to use xtscc command.

[Jeff Wooldridge]

Just re-index the data starting consecutively from 1, 2, 3, and so on. Define a "cross-sectional" identify as id = 1, 2, 3, 4, 5.

[Neharika Sobti]

Thank you Prof. Wooldridge
I was able to perform xtscc command with fe . But I have a doubt that since I have a large panel with T>>N , can the xtpcse i.e. , Beck and Katz (1995) proposed OLS coefficient estimates with panel-corrected standard errors (PCSEs) a better solution or should I stick to Driscoll and Kraay (1998) xtscc? I am not able to decide because both methods helps to resolve cross sectional dependence in large T panels.

[Jeff Wooldridge]

Beck and Katz is too restrictive. They assume an AR(1) model across time, and do not allow for variances that change across t. The Driscoll-Kraay assumptions are much weaker. They don't restrict heteroskedasticity, and any kind of weak dependence in the time series is allowed.