Linear regression with AR(1) disturbance

[Victoria Romanova]

Dear Colleagues,

Currently, I am conducting research and selected panel regression (FE) with AR(1) disturbance. And I have some questions. First of all, what is the theoretical model of linear regression with AR(1) disturbance and how it could be written? Second, how should I interpret rho_ar, sigma_u, sigma_e and rho_fov. Thank you for your help in advance!

FE (within) regression with AR(1) disturbances Number of obs = 140
Group variable: Countryid Number of groups = 28

R-squared: Obs per group:
Within = 0.0822 min = 5
Between = 0.0275 avg = 5.0
Overall = 0.0235 max = 5

F(2,110) = 4.92
corr(u_i, Xb) = -0.7658 Prob > F = 0.0089

------------------------------------------------------------------------------
Y | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
X3 | 11.10673 4.665076 2.38 0.019 1.861643 20.35181
X6 | 5.932966 2.57744 2.30 0.023 .8250849 11.04085
_cons | -64.4357 19.73932 -3.26 0.001 -103.5544 -25.317
-------------+----------------------------------------------------------------
rho_ar | .09722836
sigma_u | 10.590696
sigma_e | 7.8843345
rho_fov | .64341014 (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(27,110) = 3.11 Prob > F = 0.0000

[Carlo Lazzaro]

Victoria:
welcome to this forum.
Too broad a question indeed.
Take a look at any decent panel data econometrics textbook, -xtreg- and -xtregar- entries in Stata .pdf manual.
In addition, as per FAQ, you're kindly requested to report, via CODE delimiters, what you typed (-xregar,fe-?) and what Stata gave you back (as you did, but in an improvable way). Thanks.

[Jeff Wooldridge]

As Carlo said, more information would help. I think I see N = 28, T = 5. You shouldn't do anything fancy with such a data set as the sample sizes are small. In particular, with T = 5 you shouldn't be using an AR(1) model along with fixed effects. That estimator only has good properties with T is pretty large.

You should just do regular fixed effects. While N = 28 is pretty small for clustering, you don't have much of a choice. I would also include time dummies (fixed effects) because the results are not usually believable otherwise:

xtreg Y X1 ... XK i.time, fe vce(cluster Countryid)

The clustering accounts for any serial correlation and heteroskedasticity -- provided N = 28 is large enough for the asymptotic approximations to work.