Residuals in a panel data model

[Alex Brown]

Hi
I am running a regression (using panel data) looking at the effect of income on food consumption and controlling for age. I am trying to determine if I need a squared term for age so wish to create a scatter plot of residuals against my independent variable as I have read this will show if there is a non- linear relationship- is this correct?
Therefore do I run:
xtreg fruvege age_dv, fe robust
predict fit, xbu
gen fit_2=fit^2
xtreg fruvege age_dv fit_2, fe robust
test fit_2=0

twoway (scatter fit_2 lnm)

in which case I get this:



What does this mean? what am I doing wrong?
Thank you for any help.

[Carlo Lazzaro]

Alex:
it would seem that you're interested in a Pregibon test (https://www.jstor.org/stable/2346405):

xtreg  fruvege fit fit^2, fe robust
test sq_fit

If -test- turns out to be significant, your model is misspecified.
A toy-example of a misspecified model is reported below:

. use "http://www.stata-press.com/data/r15/nlswork.dta"
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. xtreg ln_wage age

Random-effects GLS 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

                                                Wald chi2(1)      =    3140.35
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         age |   .0185667   .0003313    56.04   0.000     .0179174    .0192161
       _cons |   1.120439   .0112038   100.01   0.000      1.09848    1.142398
-------------+----------------------------------------------------------------
     sigma_u |  .36972456
     sigma_e |  .30349389
         rho |  .59743613   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. predict fit, xb
(24 missing values generated)

. g sq_fit=fit^2
(24 missing values generated)

. xtreg ln_wage fit sq_fit

Random-effects GLS 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 = 0.1015                                         avg =        6.1
     overall = 0.0870                                         max =         15

                                                Wald chi2(2)      =    3388.51
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
     ln_wage |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         fit |   7.572907   .4384755    17.27   0.000      6.71351    8.432303
      sq_fit |   -1.96055   .1306854   -15.00   0.000    -2.216689   -1.704412
       _cons |  -5.475764   .3662055   -14.95   0.000    -6.193514   -4.758015
-------------+----------------------------------------------------------------
     sigma_u |   .3654049
     sigma_e |  .30245467
         rho |  .59342665   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. test sq_fit

 ( 1)  sq_fit = 0

           chi2(  1) =  225.06
         Prob > chi2 =    0.0000

.

You can investigate your specification further by adding grade 3 and 4 polynomials of -xb- as predictors of your accessory regression.

[Alex Brown]

I will look into this. Many thanks

[Carlo Lazzaro]

Alex:
you may also take a look at the really valuable: https://www.stata.com/bookstore/heal...s-using-stata/, Chapter 4.