Fixed Effects panel model with the lagged independent variable

[Kamola Abdurasulova]

Hi everyone,


I have panel data, and I want to use Fixed Effects (FE) within the estimator method. One of my independent variables is income. If I add the lag of income into the regression (I assume that the income from the previous period affects my dependent variable), is my model still an FE? or should I consider the dynamic panel model estimation? Thank you very much beforehand!

[Andrew Musau]

A dynamic model is one that has a lagged dependent variable on the RHS. There is no issue with lagging a regressor in a fixed effects model. If the regressor is exogenous, then its lag is still exogenous.

webuse grunfeld, clear
xtset company year
xtreg mvalue L.invest, fe

Res.:

. xtreg mvalue L.invest, fe

Fixed-effects (within) regression               Number of obs     =        190
Group variable: company                         Number of groups  =         10

R-squared:                                      Obs per group:
     Within  = 0.1128                                         min =         19
     Between = 0.8380                                         avg =       19.0
     Overall = 0.6971                                         max =         19

                                                F(1, 179)         =      22.76
corr(u_i, Xb) = 0.7909                          Prob > F          =     0.0000

------------------------------------------------------------------------------
      mvalue | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
      invest |
         L1. |    1.26864    .265901     4.77   0.000     .7439366    1.793344
             |
       _cons |   924.7426   43.50694    21.26   0.000     838.8902    1010.595
-------------+----------------------------------------------------------------
     sigma_u |  1142.0025
     sigma_e |  315.00571
         rho |  .92929406   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(9, 179) = 93.50                     Prob > F = 0.0000

.

[Kamola Abdurasulova]

Thank you very much!

[Jeff Wooldridge]

To add to Andrew's helpful comment: lagging a variable cannot make it strictly exogeneous, which is required for FE. But there may be less bias. Still, if you are lagging the variable because you think it can react to shocks to the error, you would then want to try instrumental variable strategies (xtabond2).


Also, to study dynamic effects, you could include the current variable and its lag -- as is often done in policy analysis.

[Kamola Abdurasulova]

Thank you very much, Professor Wooldridge!