Small N and large T panel analysis

[Pallavi Rajkhowa]

Hi! I am using panel data with N=6 and monthly data from 2000 to 2017 i.e., T=216. The specific industry I am studying has only six firms, therefore N cannot be larger than 6. I am studying the impact of a policy change that was introduced in a staggered manner across the six firms.

Can I use a fixed effect estimator with such a small N? If I use seemingly unrelated regression, will it be correct to use the dataset in a wide format and then run the surgeg command? What alternative models are suitable with small N and large T?

Further, if I have to add lagged variable of the dependent variable into my specification can Arellano and Bond estimator be used for small N and large T?

[Carlo Lazzaro]

Pallavi:
welcome to this forum.
The commands you should consder are: -xtgls- and -xtregar-.
Take a comprehensive look at their entries in Stata .pdf manual.

[Phil Bromiley]

To add to Carlo's helpful comment, be aware that xtgls does not include fixed or random effects. On the other hand, xtregar doesn't allow for heterskedasticity.

[Pallavi Rajkhowa]

Pallavi:
welcome to this forum.
The commands you should consder are: -xtgls- and -xtregar-.
Take a comprehensive look at their entries in Stata .pdf manual.

Thank you Carlos! Your comment has been very helpful. I have a follow-up question. When I use the xtgls command with the option panel (core), I get an error " panels must be balanced". However, my dataset is strongly balanced with the time variable having values that are a constant difference apart. Any comment why I might be getting this error?

[Pallavi Rajkhowa]

To add to Carlo's helpful comment, be aware that xtgls does not include fixed or random effects. On the other hand, xtregar doesn't allow for heterskedasticity.

Thanks Phil! I will keep this in mind!

[Carlo Lazzaro]

Pallavi:
can you plase share what you typed and what Stata gave you back via CODE delimiters (from -xtset- onwards)? Thanks.

[Jeff Wooldridge]

What you really have is closer to multiple time series, but you can still use certain panel data commands. I would use the user-written command -xtscc- with the fixed effects option. This just estimates 6 different firm intercepts, which is no problem because of your large T. I don't think I'd estimate a separate intercept for each time periods, but you'll have to deal with time effects somehow -- seasonal dummies and linear trends (maybe interacted with firm dummies?).

-xtscc- computes Driscoll-Kraay standard errors, which allow any correlation across firm and general serial correlation across time. The problem with -xtgls- and -xtregar- is that they do not allow for robust inference -- at least, not through Stata 15. If you like the results from FE with the D-K standard errors, I'd stop there.

Also, with large T and small N, just include the lags directly in the -xtscc-- command. The bias from using fixed effects with a lagged dependent variable is small when T is large. You should not use Arellano-Bond, as it requires large N.

[Pallavi Rajkhowa]

What you really have is closer to multiple time series, but you can still use certain panel data commands. I would use the user-written command -xtscc- with the fixed effects option. This just estimates 6 different firm intercepts, which is no problem because of your large T. I don't think I'd estimate a separate intercept for each time periods, but you'll have to deal with time effects somehow -- seasonal dummies and linear trends (maybe interacted with firm dummies?).

-xtscc- computes Driscoll-Kraay standard errors, which allow any correlation across firm and general serial correlation across time. The problem with -xtgls- and -xtregar- is that they do not allow for robust inference -- at least, not through Stata 15. If you like the results from FE with the D-K standard errors, I'd stop there.

Also, with large T and small N, just include the lags directly in the -xtscc-- command. The bias from using fixed effects with a lagged dependent variable is small when T is large. You should not use Arellano-Bond, as it requires large N.

Thank you for your detailed comment! xtscc seems to be working well. I have a follow up question. I also have a dummy variable that takes the value of 1 on a specific month indicating introduction of a policy change across all firms. Would it make sense to estimate using first difference variables with fixed effects. Also, I would be grateful if you could please suggest a few readings on panel data using small N and large T.

Best regards,
Pallavi

[cess Jadhav]

Hello everyone, I have a similar question. I am using panel data with N=93 and T=10. I also found that the model has the issue of heteroskedasticity and autocorrelation. in this regard, Should I use Driscoll-Kraay xtscc, xtgls, xtpcse method to correct the problem, where N>T.

Thank you

[Carlo Lazzaro]

Cess:
you're seemingly dealing with a N>T panel dataset.
Therefore, you should go -xtreg- (I assume that your regressand is continuous) and invoke -robut- or -cluster- options for standard errors if you detected heteroskedasticity and/or autocorrelation.

[cess Jadhav]

Dear Carlo Lazzaro,

Yes, regressand is a continuous variable. I will try these robust and cluster id options, get back to you.

Thank you

[Carlo Lazzaro]

Cess:
you can choose one of them indifferently, as they do the very same job under -xtreg-.

[cess Jadhav]

Dear Carlo,

The cluster id options results are better than vce_robust). Thank you.

Jadhav Chakradhar

[Carlo Lazzaro]

Cess:
how can it be?

. use "https://www.stata-press.com/data/r16/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage c.age##c.age, fe vce(cluster idcode)

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1087                                         min =          1
     between = 0.1006                                         avg =        6.1
     overall = 0.0865                                         max =         15

                                                F(2,4709)         =     507.42
corr(u_i, Xb)  = 0.0440                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0539076    .004307    12.52   0.000     .0454638    .0623515
             |
 c.age#c.age |  -.0005973    .000072    -8.30   0.000    -.0007384   -.0004562
             |
       _cons |    .639913   .0624195    10.25   0.000     .5175415    .7622845
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. xtreg ln_wage c.age##c.age, fe rob

Fixed-effects (within) regression               Number of obs     =     28,510
Group variable: idcode                          Number of groups  =      4,710

R-sq:                                           Obs per group:
     within  = 0.1087                                         min =          1
     between = 0.1006                                         avg =        6.1
     overall = 0.0865                                         max =         15

                                                F(2,4709)         =     507.42
corr(u_i, Xb)  = 0.0440                         Prob > F          =     0.0000

                             (Std. Err. adjusted for 4,710 clusters in idcode)
------------------------------------------------------------------------------
             |               Robust
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0539076    .004307    12.52   0.000     .0454638    .0623515
             |
 c.age#c.age |  -.0005973    .000072    -8.30   0.000    -.0007384   -.0004562
             |
       _cons |    .639913   .0624195    10.25   0.000     .5175415    .7622845
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------

.

[cess Jadhav]

Dear Carlo,

Thank you so much for the help

Jadhav Chakradhar