Most discussions of xtreg and xtregar emphasize xtreg's ability to use robust standard errors. However, as I understand it, xtreg is not consistent on the parameters under serial correlated errors, but xtregar is consistent if the error structure is only a one period serial correlation.
All of these discussions seem to assume that the two estimators give somewhat similar parameter estimates.
I've hit data where I get massively different betas between the two estimators. Here is an example:
. xtregar oee c.numlines ,fe
FE (within) regression with AR(1) disturbances Number of obs = 43,657
Group variable: sitexline Number of groups = 1,124
R-squared: Obs per group:
Within = 0.0043 min = 1
Between = 0.0303 avg = 38.8
Overall = 0.0178 max = 59
F(1,42532) = 184.43
corr(u_i, Xb) = -0.1303 Prob > F = 0.0000
------------------------------------------------------------------------------
oee | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
numlines | .7376822 .0543185 13.58 0.000 .6312169 .8441475
_cons | 70.71834 .1576968 448.44 0.000 70.40925 71.02743
-------------+----------------------------------------------------------------
rho_ar | .54586885
sigma_u | 12.837564
sigma_e | 7.2494405
rho_fov | .75821216 (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(1123,42532) = 14.33 Prob > F = 0.0000
.
.
. xtreg oee c.numlines if e(sample),fe robust
Fixed-effects (within) regression Number of obs = 44,795
Group variable: sitexline Number of groups = 1,138
R-squared: Obs per group:
Within = 0.0001 min = 1
Between = 0.0146 avg = 39.4
Overall = 0.0173 max = 60
F(1,1137) = 0.60
corr(u_i, Xb) = 0.1393 Prob > F = 0.4390
(Std. err. adjusted for 1,138 clusters in sitexline)
------------------------------------------------------------------------------
| Robust
oee | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
numlines | .0719856 .092992 0.77 0.439 -.1104697 .2544409
_cons | 74.14837 .5735115 129.29 0.000 73.02311 75.27363
-------------+----------------------------------------------------------------
sigma_u | 13.830154
sigma_e | 8.2724051
rho | .73649924 (fraction of variance due to u_i)
I understand that xtregar loses an observation for each panel due to the serial correlation correction, but we're only talking 1000 observations on a 40000 observation estimation.
Any ideas what is going on would be appreciated.
Phil
All of these discussions seem to assume that the two estimators give somewhat similar parameter estimates.
I've hit data where I get massively different betas between the two estimators. Here is an example:
. xtregar oee c.numlines ,fe
FE (within) regression with AR(1) disturbances Number of obs = 43,657
Group variable: sitexline Number of groups = 1,124
R-squared: Obs per group:
Within = 0.0043 min = 1
Between = 0.0303 avg = 38.8
Overall = 0.0178 max = 59
F(1,42532) = 184.43
corr(u_i, Xb) = -0.1303 Prob > F = 0.0000
------------------------------------------------------------------------------
oee | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
numlines | .7376822 .0543185 13.58 0.000 .6312169 .8441475
_cons | 70.71834 .1576968 448.44 0.000 70.40925 71.02743
-------------+----------------------------------------------------------------
rho_ar | .54586885
sigma_u | 12.837564
sigma_e | 7.2494405
rho_fov | .75821216 (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(1123,42532) = 14.33 Prob > F = 0.0000
.
.
. xtreg oee c.numlines if e(sample),fe robust
Fixed-effects (within) regression Number of obs = 44,795
Group variable: sitexline Number of groups = 1,138
R-squared: Obs per group:
Within = 0.0001 min = 1
Between = 0.0146 avg = 39.4
Overall = 0.0173 max = 60
F(1,1137) = 0.60
corr(u_i, Xb) = 0.1393 Prob > F = 0.4390
(Std. err. adjusted for 1,138 clusters in sitexline)
------------------------------------------------------------------------------
| Robust
oee | Coefficient std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
numlines | .0719856 .092992 0.77 0.439 -.1104697 .2544409
_cons | 74.14837 .5735115 129.29 0.000 73.02311 75.27363
-------------+----------------------------------------------------------------
sigma_u | 13.830154
sigma_e | 8.2724051
rho | .73649924 (fraction of variance due to u_i)
I understand that xtregar loses an observation for each panel due to the serial correlation correction, but we're only talking 1000 observations on a 40000 observation estimation.
Any ideas what is going on would be appreciated.
Phil
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