Time FEs with xtregar

[Gabriel Mihalache]

Hello! Can anyone explain why xtregar will not allow the inclusion of the time variable (as fixed effect, with i.year, for example) in the varlist? The "time variable" is the one I used in xtset.
Is there a standard workaround? Thank you!

[Andrew Musau]

Ha?

webuse grunfeld, clear
xtset company year
xtregar invest mvalue kstock i.year, fe

Res.:

.         . xtregar invest mvalue kstock i.year, fe

FE (within) regression with AR(1) disturbances  Number of obs     =        190
Group variable: company                         Number of groups  =         10

R-squared:                                      Obs per group:
     Within  = 0.6513                                         min =         19
     Between = 0.7838                                         avg =       19.0
     Overall = 0.7798                                         max =         19

                                                F(20,160)         =      14.94
corr(u_i, Xb) = -0.1416                         Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .0938865   .0104378     8.99   0.000     .0732729    .1145001
      kstock |   .4076907   .0373936    10.90   0.000      .333842    .4815393
             |
        year |
       1936  |   22.60707   15.23516     1.48   0.140    -7.480873    52.69502
       1937  |   29.02835   20.63253     1.41   0.161    -11.71886    69.77557
       1938  |   32.19837   23.69301     1.36   0.176    -14.59298    78.98973
       1939  |   17.30833   25.51947     0.68   0.499    -33.09011    67.70676
       1940  |   50.88403   27.01934     1.88   0.061    -2.476513    104.2446
       1941  |   79.24101   27.76837     2.85   0.005     24.40121    134.0808
       1942  |   73.97942   28.25514     2.62   0.010      18.1783    129.7805
       1943  |   56.66199   28.31439     2.00   0.047     .7438482    112.5801
       1944  |   58.95475   28.56968     2.06   0.041     2.532449     115.377
       1945  |   49.74642   28.40551     1.75   0.082    -6.351667    105.8445
       1946  |   75.78518   28.05301     2.70   0.008     20.38324    131.1871
       1947  |   57.76681   26.94116     2.14   0.034     4.560676    110.9729
       1948  |   51.01013   26.04522     1.96   0.052    -.4266119    102.4469
       1949  |   20.19058   24.97134     0.81   0.420    -29.12536    69.50651
       1950  |   18.35979   23.75434     0.77   0.441     -28.5527    65.27228
       1951  |   36.28607   21.77871     1.67   0.098    -6.724731    79.29688
       1952  |   32.36863   18.82811     1.72   0.088    -4.815034    69.55229
       1953  |   30.71474   14.03026     2.19   0.030     3.006356    58.42313
       1954  |          0  (omitted)
             |
       _cons |  -124.2761   10.59512   -11.73   0.000    -145.2004   -103.3518
-------------+----------------------------------------------------------------
      rho_ar |  .68127018
     sigma_u |  96.029876
     sigma_e |  39.732352
     rho_fov |  .85383317   (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9,160) = 12.27                      Prob > F = 0.0000

.

[Andrew Musau]

The "time variable" is the one I used in xtset.

OK, did you do this?

xtset year

and then

xtregar ... i.year, fe

In this case, the year fixed effects are already included by xtset, so i.year would be collinear with the time effects and should not be added again.

[Gabriel Mihalache]

Thank you for your reply! Using your example, I get this error:

. webuse grunfeld, clear

. xtset company year

Panel variable: company (strongly balanced)
 Time variable: year, 1935 to 1954
         Delta: 1 year

. xtregar invest mvalue kstock i.year, fe
time variable may not be included in varlist
r(198);

[Andrew Musau]

I should have indicated that my version of Stata is StataNow 18.5. Is your version Stata 19/ StataNow 19.5? There may be some statistical reason for not doing this (i.e., applying the AR(1) correction after the time dummies are partialled out), but it is not discussed in the xtregar manual (https://www.stata.com/manuals/xtxtregar.pdf). There should be a way to force Stata to do this—either by using version control or by cloning the time variable. However, what you should be more concerned about are the statistical properties of such a procedure. Perhaps if you write to Technical Services, an expert can provide the underlying reasoning.

webuse grunfeld, clear
xtset company year
version 18: xtregar invest mvalue kstock i.year, fe

or

webuse grunfeld, clear
xtset company year
clonevar time = year
xtregar invest mvalue kstock i.time, fe

[Joro Kolev]

I am getting the same error in Stata 18. Probably Andrew has a newer version of Stata, and apparently up to Stata 18 the factor variable notation has not been implemented in -xtregar-.

Just generate the dummies manually, like this:

. . webuse grunfeld, clear

. 
. 
. 
. . xtset company year

Panel variable: company (strongly balanced)
 Time variable: year, 1935 to 1954
         Delta: 1 year

. xtregar invest mvalue kstock i.year, fe
time variable may not be included in varlist
r(198);

. tab year, gen(yr)

       Year |      Freq.     Percent        Cum.
------------+-----------------------------------
       1935 |         10        5.00        5.00
       1936 |         10        5.00       10.00
       1937 |         10        5.00       15.00
       1938 |         10        5.00       20.00
       1939 |         10        5.00       25.00
       1940 |         10        5.00       30.00
       1941 |         10        5.00       35.00
       1942 |         10        5.00       40.00
       1943 |         10        5.00       45.00
       1944 |         10        5.00       50.00
       1945 |         10        5.00       55.00
       1946 |         10        5.00       60.00
       1947 |         10        5.00       65.00
       1948 |         10        5.00       70.00
       1949 |         10        5.00       75.00
       1950 |         10        5.00       80.00
       1951 |         10        5.00       85.00
       1952 |         10        5.00       90.00
       1953 |         10        5.00       95.00
       1954 |         10        5.00      100.00
------------+-----------------------------------
      Total |        200      100.00

. xtregar invest mvalue kstock yr*, fe
note: yr20 omitted because of collinearity.

FE (within) regression with AR(1) disturbances  Number of obs     =        190
Group variable: company                         Number of groups  =         10

R-squared:                                      Obs per group:
     Within  = 0.6513                                         min =         19
     Between = 0.7838                                         avg =       19.0
     Overall = 0.0180                                         max =         19

                                                F(20,160)         =      14.94
corr(u_i, Xb) = -0.0017                         Prob > F          =     0.0000

------------------------------------------------------------------------------
      invest | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      mvalue |   .0938865   .0104378     8.99   0.000     .0732729    .1145001
      kstock |   .4076907   .0373936    10.90   0.000      .333842    .4815393
         yr1 |  -96356.17   44014.77    -2.19   0.030      -183281   -9431.333
         yr2 |  -65601.06   29972.83    -2.19   0.030    -124794.4   -6407.667
         yr3 |  -44657.49   20406.63    -2.19   0.030    -84958.58   -4356.399
         yr4 |  -30390.47   13889.82    -2.19   0.030    -57821.49   -2959.451
         yr5 |  -20687.82   9449.858    -2.19   0.030    -39350.36   -2025.284
         yr6 |  -14033.98   6425.021    -2.18   0.030    -26722.76   -1345.196
         yr7 |  -9495.432   4364.444    -2.18   0.031    -18114.78   -876.0849
         yr8 |  -6428.035   2960.811    -2.17   0.031    -12275.34   -580.7253
         yr9 |  -4352.041   2004.415    -2.17   0.031    -8310.563   -393.5196
        yr10 |  -2923.638   1352.812    -2.16   0.032    -5595.309   -251.9674
        yr11 |   -1961.28    908.943    -2.16   0.032    -3756.353   -166.2073
        yr12 |  -1273.342   606.6414    -2.10   0.037    -2471.399   -75.28522
        yr13 |  -840.4285    401.292    -2.09   0.038    -1632.941   -47.91619
        yr14 |  -539.9785   261.2814    -2.07   0.040    -1055.983    -23.9735
        yr15 |  -361.5073   165.9385    -2.18   0.031    -689.2194   -33.79517
        yr16 |  -220.7546   100.9425    -2.19   0.030     -420.106   -21.40312
        yr17 |  -105.6904   56.52777    -1.87   0.063    -217.3272    5.946425
        yr18 |  -43.43064   26.28637    -1.65   0.100    -95.34365    8.482359
        yr19 |          0  (omitted)
        yr20 |          0  (omitted)
       _cons |  -189.9274   16.52428   -11.49   0.000    -222.5612   -157.2936
-------------+----------------------------------------------------------------
      rho_ar |  .68127018
     sigma_u |  96.029876
     sigma_e |  39.732352
     rho_fov |  .85383317   (fraction of variance because of u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9,160) = 12.27                      Prob > F = 0.0000

.

[Andrew Musau]

I am getting the same error in Stata 18. Probably Andrew has a newer version of Stata, and apparently up to Stata 18 the factor variable notation has not been implemented in -xtregar-.

Just generate the dummies manually, like this:

Thanks for testing this, the issue must have been with older versions of Stata then. Does cloning the time variable like in #5 work for you?

[Gabriel Mihalache]

Great! Thank you Joro and Andrew for your help. This will be fine. Greatly appreciated!