RESET test for omitted variables

[Julia Raciniewska]

Hello,

I am trying to run diagnostics of my model and I would like to clarify the following uncertainty. I have panel data and I am using fixed effects. Initially, I estimated a model without lagged dependent variable as a regressor but due to suspecting autocorrelation, later I have included it. When I am running Ramsey's RESET test should I run it on the initial or second model? Result for the first one tells about omitted variables, however when the lagged variable is included - there are no omitted variables. How can I interpret this?

[Carlo Lazzaro]

Julia:
how did you perform Ramsey test after -xtreg, fe-?

[Julia Raciniewska]

Carlo Lazzaro oh sorry - performed it before, for simple ols. Then decided to use FE, robust with lagged dependent variable as I also had heteroskedasticity

[Carlo Lazzaro]

Julia:
as -estat ovtest- is not supported by -xt- suite, you can test non-linear relationship between predictors and regressand via Pregibon test (see -help linktest-):

use http://www.stata-press.com/data/r15/nlswork.dta
. xtreg ln_wage age, fe

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

R-sq:                                           Obs per group:
     within  = 0.1026                                         min =          1
     between = 0.0877                                         avg =        6.1
     overall = 0.0774                                         max =         15

                                                F(1,23799)        =    2720.20
corr(u_i, Xb)  = 0.0314                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0181349   .0003477    52.16   0.000     .0174534    .0188164
       _cons |   1.148214   .0102579   111.93   0.000     1.128107     1.16832
-------------+----------------------------------------------------------------
     sigma_u |  .40635023
     sigma_e |  .30349389
         rho |  .64192015   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23799) = 8.81                 Prob > F = 0.0000

. predict u, xb
(24 missing values generated)

. g sq_u=(u)^2
(24 missing values generated)

. xtreg ln_wage u sq_u, fe

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(2,23798)        =    1451.88
corr(u_i, Xb)  = 0.0440                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           u |   7.143466    .478902    14.92   0.000     6.204788    8.082144
        sq_u |  -1.816243    .141469   -12.84   0.000    -2.093531   -1.538955
       _cons |  -5.167788   .4037984   -12.80   0.000    -5.959259   -4.376317
-------------+----------------------------------------------------------------
     sigma_u |   .4039153
     sigma_e |  .30245467
         rho |  .64073314   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.74                 Prob > F = 0.0000

. test sq_u

 ( 1)  sq_u = 0

       F(  1, 23798) =  164.83
            Prob > F =    0.0000

.* the statistical significance means that the model is, as expected with one predictor only, misspecified*

If you suspect/detect autocorrelation and/or heteroskedasticity in the distribution of the idiosyncratic error, just invoke the -cluster- or -robust- option.
Conversely, lagging the dependent variable, will imply moving from static to dynamic panel data models (a totally different kind of beast).

[Julia Raciniewska]

Carlo:
Thank you very much for your response and advice! I have one extra question on different topic, when I do -estat vce, corr- after runing me fixed effects regression with lagged dependent variable, there is high correlation between one of my x and yt-1. Is that a big issue, and should I then drop the lagged d. variable?

[Carlo Lazzaro]

Julia:
I would advice to get rid of lagging the regressand altogether, as, under -xtreg-, the estimates you get are inconsistent.
Use -cluster- or -robust- option with -xtreg-, instead.

[Julia Raciniewska]

Carli:
thank you very much for all your advice!

[Jaspal Channa]

Hi Carlo,

As you cannot run Ramsey RESET after a fixed effects regression, should I just run Ramsey RESET after using the LSDV version of my FE model to produce estimates?

Many thanks,
Jaspal

[Carlo Lazzaro]

Jaspal:
welcome to this forum.
You can use a modified version of the -linktest- command to check for model misspecification, as you can see from the following toy-example:

. 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 age i.year, fe

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

R-sq:                                           Obs per group:
     within  = 0.1060                                         min =          1
     between = 0.0914                                         avg =        6.1
     overall = 0.0805                                         max =         15

                                                F(15,23785)       =     188.00
corr(u_i, Xb)  = 0.0467                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0125992   .0102163     1.23   0.217    -.0074253    .0326238
             |
        year |
         69  |   .0748621   .0159011     4.71   0.000      .043695    .1060292
         70  |   .0478697   .0235673     2.03   0.042     .0016763     .094063
         71  |   .0865577   .0327939     2.64   0.008     .0222795     .150836
         72  |   .0856757   .0424903     2.02   0.044     .0023919    .1689594
         73  |   .0880069    .052344     1.68   0.093    -.0145906    .1906044
         75  |   .0778607   .0720304     1.08   0.280    -.0633235    .2190449
         77  |    .108365   .0922272     1.17   0.240    -.0724063    .2891363
         78  |   .1309518   .1028143     1.27   0.203    -.0705707    .3324743
         80  |   .1142649    .122792     0.93   0.352    -.1264152     .354945
         82  |   .1090451   .1431112     0.76   0.446    -.1714619    .3895522
         83  |   .1211272   .1532018     0.79   0.429    -.1791581    .4214125
         85  |   .1465637   .1736146     0.84   0.399    -.1937321    .4868594
         87  |   .1382642   .1941163     0.71   0.476     -.242216    .5187445
         88  |   .1799741   .2079871     0.87   0.387    -.2276938     .587642
             |
       _cons |   1.203731   .1952306     6.17   0.000     .8210667    1.586396
-------------+----------------------------------------------------------------
     sigma_u |   .4058746
     sigma_e |  .30300411
         rho |  .64212421   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23785) = 8.80                 Prob > F = 0.0000

. predict fitted, xb
(24 missing values generated)

. g sq_fitted=fitted^2
(24 missing values generated)

. xtreg ln_wage fitted sq_fitted , fe

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

R-sq:                                           Obs per group:
     within  = 0.1086                                         min =          1
     between = 0.0962                                         avg =        6.1
     overall = 0.0845                                         max =         15

                                                F(2,23798)        =    1449.33
corr(u_i, Xb)  = 0.0519                         Prob > F          =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      fitted |   4.791882   .4570443    10.48   0.000     3.896046    5.687718
   sq_fitted |  -1.125657   .1355632    -8.30   0.000    -1.391369   -.8599442
       _cons |    -3.1774   .3839526    -8.28   0.000    -3.929971   -2.424828
-------------+----------------------------------------------------------------
     sigma_u |  .40489607
     sigma_e |  .30248347
         rho |  .64180514   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(4709, 23798) = 8.78                 Prob > F = 0.0000

. test sq_fitted=0

 ( 1)  sq_fitted = 0

       F(  1, 23798) =   68.95
            Prob > F =    0.0000

The resulst of -test- shows evidence of model misspecification.

[Jaspal Channa]

Hi Carlo,

Thanks very much for your help! I tried it but got the results below. I'm not sure what to make of them?

 xtreg lnyrslost lnalc lngdpnethe lnhe lnhrs lnlru lnobese lnoop lnpol lnpopstruc year2-year17, fe

Fixed-effects (within) regression               Number of obs     =        527
Group variable: c_id                            Number of groups  =         35

R-sq:                                           Obs per group:
     within  = 0.8838                                         min =          7
     between = 0.5104                                         avg =       15.1
     overall = 0.5897                                         max =         17

                                                F(25,467)         =     142.12
corr(u_i, Xb)  = 0.3047                         Prob > F          =     0.0000

------------------------------------------------------------------------------
   lnyrslost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       lnalc |   .2364279   .0337759     7.00   0.000     .1700564    .3027995
  lngdpnethe |  -.2018354   .0418138    -4.83   0.000    -.2840018    -.119669
        lnhe |  -.0614547    .040874    -1.50   0.133    -.1417745    .0188651
       lnhrs |   .4635103   .1449492     3.20   0.001     .1786769    .7483437
       lnlru |  -.0137754   .0103706    -1.33   0.185    -.0341542    .0066033
     lnobese |   .2000181   .0877928     2.28   0.023     .0275001     .372536
       lnoop |     .04865   .0222948     2.18   0.030     .0048394    .0924606
       lnpol |   .0221281    .026256     0.84   0.400    -.0294664    .0737227
  lnpopstruc |    .134221   .0747912     1.79   0.073    -.0127479    .2811899
       year2 |  -.0190149   .0134847    -1.41   0.159    -.0455131    .0074834
       year3 |  -.0328363   .0148058    -2.22   0.027    -.0619305   -.0037421
       year4 |  -.0547662   .0163505    -3.35   0.001    -.0868958   -.0226366
       year5 |  -.0813504    .018457    -4.41   0.000    -.1176195   -.0450813
       year6 |  -.0979063   .0209637    -4.67   0.000    -.1391012   -.0567115
       year7 |  -.1041513   .0243929    -4.27   0.000    -.1520847   -.0562179
       year8 |  -.1145426   .0277315    -4.13   0.000    -.1690365   -.0600487
       year9 |   -.149305   .0309592    -4.82   0.000    -.2101415   -.0884684
      year10 |  -.1706807   .0328238    -5.20   0.000    -.2351814     -.10618
      year11 |   -.199391   .0350153    -5.69   0.000     -.268198   -.1305841
      year12 |  -.2170585   .0382028    -5.68   0.000    -.2921293   -.1419878
      year13 |  -.2455363   .0407991    -6.02   0.000    -.3257087   -.1653638
      year14 |  -.2567588   .0439462    -5.84   0.000    -.3431156    -.170402
      year15 |  -.2828465   .0465216    -6.08   0.000     -.374264   -.1914289
      year16 |  -.3011785   .0493891    -6.10   0.000    -.3982308   -.2041261
      year17 |    -.30004   .0526682    -5.70   0.000    -.4035359   -.1965441
       _cons |   6.024674   1.164144     5.18   0.000     3.737065    8.312282
-------------+----------------------------------------------------------------
     sigma_u |  .26531306
     sigma_e |  .04742289
         rho |  .96904003   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(34, 467) = 215.81                   Prob > F = 0.0000

. 
. 
. predict fitted, xb
(40 missing values generated)

. gen sq_fitted = fitted^2
(40 missing values generated)

. xtreg lnyrslost fitted sq_fitted, fe

Fixed-effects (within) regression               Number of obs     =        527
Group variable: c_id                            Number of groups  =         35

R-sq:                                           Obs per group:
     within  = 0.8840                                         min =          7
     between = 0.5160                                         avg =       15.1
     overall = 0.5934                                         max =         17

                                                F(2,490)          =    1866.49
corr(u_i, Xb)  = 0.3112                         Prob > F          =     0.0000

------------------------------------------------------------------------------
   lnyrslost |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      fitted |   .3421513    .855178     0.40   0.689    -1.338117     2.02242
   sq_fitted |   .0383396   .0498308     0.77   0.442    -.0595689     .136248
       _cons |   2.820235     3.6682     0.77   0.442    -4.387108    10.02758
-------------+----------------------------------------------------------------
     sigma_u |  .26461935
     sigma_e |   .0462686
         rho |  .97033454   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(34, 490) = 326.92                   Prob > F = 0.0000

.

Many thanks,
Jaspal

[Carlo Lazzaro]

Jaspal:
despite you omitted to -test- sq_fitted=0, since its coefficients does not reach statistical significance, your regression model does not support evidence of misspecification.

[Jaspal Channa]

Thank you Carlo. God bless!

[Jeff Wooldridge]

I'd be careful constructing the "link" test by hand. I assume that when you used the built-in command, Stata is properly compute the standard error that accounts for the first-step estimation of beta. The procedure proposed by Carlo is sound but I don't think the standard error is correct.

I prefer a modification of RESET in which I can compute a valid standard or or joint F test. I will also not that it's almost always a good idea to cluster your standard errors to account for serial correlation and heteroskedasticity.

xtreg y x1 x2 ... xK, fe vce(cluster id)
predict xbhat, xb
gen xbhatsq = xbhat^2
gen xbhatcu = xbhat^2
xtreg y x1 x2 ... xK xbhatsq xbhatcu, fe vce(cluster id)
test xbhatsq xbhatcu

I should also point out that RESET is not a general misspecification test no matter how many times this is said. It is a pure test of functional form. Therefore, you might want to expand your model to include squares and interactions to see if the are important -- if the test rejects. For example, in Carlo's example, I'm pretty sure the square of age would be important, and it is omitted from the equation.

[Jaspal Channa]

Thanks for your advise Jeff!

Do you mind clarifying the difference between a general misspecification test and a pure test of functional form?

Best,
Jaspal

[Jaspal Channa]

Just to add another quick question, I am not sure whether or not the clustered errors are appropriate. My model does not have serial correlation, but does have heteroskedasticity. Do I have to use the robust errors? They remove the significance of a few of my findings.

Many thanks,
Jaspal