omitting continuous variable in categorical by continuous interaction

[Atreya De]

Hello,

I'm having a difficult time understanding why omitting a continuous variable in a panel setting would be potentially mis-specified. I've checked some other threads, i.e., https://www.statalist.org/forums/for...n-with-dummies but I'm still having trouble.

I have an example below that shows essentially the same results, i.e., the same marginal effects, coefficient estimates, and degrees of freedom. Is this model really mis-specified - reghdfe lnw i.hispanic#c.exper, absorb(id)?

. use https://stats.idre.ucla.edu/stat/stata/examples/alda/data/wages_pp, clear

.
. reghdfe lnw i.hispanic c.exper i.hispanic#c.exper, absorb(id)
(dropped 38 singleton observations)
note: 1bn.hispanic is probably collinear with the fixed effects (all partialled-out value
> s are close to zero; tol = 1.0e-09)
(MWFE estimator converged in 1 iterations)
note: 1.hispanic omitted because of collinearity

HDFE Linear regression                            Number of obs   =      6,364
Absorbing 1 HDFE group                            F(   2,   5512) =     332.74
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.5008
                                                  Adj R-squared   =     0.4237
                                                  Within R-sq.    =     0.1077
                                                  Root MSE        =     0.3241

----------------------------------------------------------------------------------
             lnw | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
      1.hispanic |          0  (omitted)
           exper |   .0408981   .0019789    20.67   0.000     .0370186    .0447776
                 |
hispanic#c.exper |
              1  |   .0112029    .003912     2.86   0.004     .0035338     .018872
                 |
           _cons |    1.72312   .0079086   217.88   0.000     1.707616    1.738624
----------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          id |       850           0         850     |
-----------------------------------------------------+

. di "`e(df_m)'"
2

.
. reghdfe lnw i.hispanic#c.exper, absorb(id)
(dropped 38 singleton observations)
(MWFE estimator converged in 1 iterations)

HDFE Linear regression                            Number of obs   =      6,364
Absorbing 1 HDFE group                            F(   2,   5512) =     332.74
                                                  Prob > F        =     0.0000
                                                  R-squared       =     0.5008
                                                  Adj R-squared   =     0.4237
                                                  Within R-sq.    =     0.1077
                                                  Root MSE        =     0.3241

----------------------------------------------------------------------------------
             lnw | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-----------------+----------------------------------------------------------------
hispanic#c.exper |
              0  |   .0408981   .0019789    20.67   0.000     .0370186    .0447776
              1  |    .052101   .0033746    15.44   0.000     .0454855    .0587165
                 |
           _cons |    1.72312   .0079086   217.88   0.000     1.707616    1.738624
----------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
          id |       850           0         850     |
-----------------------------------------------------+

. di "`e(df_m)'"
2

[George Ford]

what do you mean mis-specified?

If id is a person, then hispanic won't change. So, it is perfectly correlated with the fixed effect. Just drop hispanic from the model.

Model 1 tells you the difference in the coefficient beween non-hispanic and hispanic. The t-stat on the interaction is a direct test of the difference.

Model 2 estimates different coefficients for each group. You see that 0.0408981 + 0.0112029 = 0.052101. To test whether they are equal, you'll have to do a post-estimation test. Or, just take the t-stat from Model 1.

I assume exper is changing over time.