Using the "lag" variable for a panel regression

[Benjamin Rey]

Dear Community,

I'm starting this thread because I seem to be having some trouble with my lag (and possibly more).

As stated in an other thread, I'm analyzing the effects of the exchange rates on Swiss watch exports, and Swiss total exports. The panel contains 10 countries its time is quarterly from 2006Q1 to 2017Q4.

I created lags on the Exchange rates n-1, n-2, n-3.

Due to strong variations between various currency pairs, I standardized each of them with "std".

Quick overview of my 480 line data:

So after using "std" to standardize my exchange rates "exrate2", I also created three lags for "exrate2_L1" "exrate2_L2" "exrate2_L3". (instead of lagging the export numbers)

I attempted conducting an xtreg and got the following:

. xtset countrynum qdate
       panel variable:  countrynum (strongly balanced)
        time variable:  qdate, 2006q1 to 2017q4
                delta:  1 quarter


. xtreg Watchexports exrate2

Random-effects GLS regression                   Number of obs     =        480
Group variable: countrynum                      Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.1734                                         min =         48
     between = 0.0016                                         avg =       48.0
     overall = 0.0417                                         max =         48

                                                Wald chi2(1)      =      98.62
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
Watchexports |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     exrate2 |  -41.01679   4.130305    -9.93   0.000    -49.11204   -32.92154
       _cons |   331.0792   61.16525     5.41   0.000     211.1975    450.9608
-------------+----------------------------------------------------------------
     sigma_u |  193.18872
     sigma_e |  89.635446
         rho |   .8228582   (fraction of variance due to u_i)
------------------------------------------------------------------------------

Added the lagged independent variables:

. xtreg Watchexports exrate2 exrate2_L1 exrate2_L2 exrate2_L3

Random-effects GLS regression                   Number of obs     =        450
Group variable: countrynum                      Number of groups  =         10

R-sq:                                           Obs per group:
     within  = 0.1774                                         min =         45
     between = 0.4358                                         avg =       45.0
     overall = 0.0486                                         max =         45

                                                Wald chi2(4)      =      92.36
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

------------------------------------------------------------------------------
Watchexports |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     exrate2 |   .4325143   12.19669     0.04   0.972    -23.47257     24.3376
  exrate2_L1 |  -41.41257   19.06705    -2.17   0.030    -78.78329   -4.041838
  exrate2_L2 |   7.802177   19.09005     0.41   0.683    -29.61364    45.21799
  exrate2_L3 |  -8.273314   11.92493    -0.69   0.488    -31.64574    15.09911
       _cons |   336.8466   41.79914     8.06   0.000     254.9218    418.7714
-------------+----------------------------------------------------------------
     sigma_u |  130.20494
     sigma_e |  86.010766
         rho |  .69620148   (fraction of variance due to u_i)
------------------------------------------------------------------------------

The one including lagged values has shockingly high P values. So there must be something wrong with the way I'm proceeding.

Really hard for me to interpret the results when I know I'm doing something wrong in the process...

[Carlo Lazzaro]

Benjamin:
in all likelihood, the shocking p-values are due to the quasi-extreme multicollinearity of exrate2 exrate2_L1 exrate2_L2 exrate2_L3.
Check whether your model is correctly specified and/or you gave a fair an true view of the data generating process.

[Benjamin Rey]

[...]due to the quasi-extreme multicollinearity of exrate2 exrate2_L1 exrate2_L2 exrate2_L3.[...]

Thank you. Indeed it seems the way I used the lags is not appropriate.

What would be the best way to use the lags? By generating a new separate regression?

[Carlo Lazzaro]

Benjamin:
I would sponsor a different approach: does including lags the way you did give a fair and true view of the data generating process (something that you can check skimming through the literature of your research field)?
Moreover (and possibly more relevant): is it reasonable to assume that an unique predictors (regardless being lagged or not) explains all the variation in your regressand?