Dear Members,
I ran the following 2 regressions(2 Models)

Code:
 
Model One
xtreg cash_ta2_w L.epu  ///
> receb_ta_w payab_ta2_w inven_ta_w ///
> ncfo_ta_w size_w fixed_ass_w lever_w stbankborr2_w ltbankborr2_w rd_ta_w i.divid_du
> m ///
> sgrowth_w oppro_ta_w  nw_ta_w fcfvol  ///
> gdp_grow_annual real_int_rate /// 
> ,fe vce(robust)

Fixed-effects (within) regression               Number of obs     =     45,328
Group variable: id                              Number of groups  =     10,683

R-sq:                                           Obs per group:
     within  = 0.2054                                         min =          1
     between = 0.2196                                         avg =        4.2
     overall = 0.2146                                         max =         15

                                                F(18,10682)       =      66.17
corr(u_i, Xb)  = -0.0817                        Prob > F          =     0.0000

                                   (Std. Err. adjusted for 10,683 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
     cash_ta2_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            epu |
            L1. |   .0036138   .0012607     2.87   0.004     .0011425    .0060851
In Model 1, the variable of interest(epu) is lagged one period and all other variables are at time " t".

Code:
Model 2
 
 xtreg cash_ta2_w L.epu  ///
> L.receb_ta_w L.payab_ta2_w L.inven_ta_w ///
> L.ncfo_ta_w L.size_w L.fixed_ass_w L.lever_w L.stbankborr2_w L.ltbankborr2_w L.rd_t
> a_w L.i.divid_dum ///
> L.sgrowth_w L.oppro_ta_w  L.nw_ta_w L.fcfvol  ///
> L.gdp_grow_annual L.real_int_rate /// 
> ,fe vce(robust)

Fixed-effects (within) regression               Number of obs     =     42,093
Group variable: id                              Number of groups  =     10,261

R-sq:                                           Obs per group:
     within  = 0.0419                                         min =          1
     between = 0.1941                                         avg =        4.1
     overall = 0.1626                                         max =         15

                                                F(18,10260)       =      19.52
corr(u_i, Xb)  = 0.1863                         Prob > F          =     0.0000

                                   (Std. Err. adjusted for 10,261 clusters in id)
---------------------------------------------------------------------------------
                |               Robust
     cash_ta2_w |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
            epu |
            L1. |    .001941   .0012023     1.61   0.106    -.0004157    .0042977
                |
In Model 2, all the variables including the variable of interest(epu) is lagged one period.

Now comparing models 1 &2 , model one has a higher within r^2 as well as variable of interest is significant(if I am allowed to use the word) at 1% level.
My doubts
1. Can we have models like Model 1, where covariates are at some other time period than the variable of interest?, Or, should we be consistent?
2. How to decide which specification is correct, if theory cant help you here much?