Dear statalist,

I am trying to estimate a fixed-effect model to evaluate the effect of program intervention. I have daily data 12 months before the intervention and 12 months after the intervention.
As a benchmark model, I first estimate the following, and the ATE is identified by the coefficient of the interaction between the treatment and post variables (b3),

yit =b1TREATi + b2POSTit +b3TREATi*POSTit +controls +fixed effects+eit

Code:
gen TREAT_POST=el_TREAT*POST_treat

xtset newid new_day
xtreg daily_water i.POST_treat TREAT_POST i.month Mtemp Sun_D Rain_D away i.dow i.year,fe cl(newid)

After this, I want to estimate and plot the ATEs in each month after the treatment period. I use the following code to generate the ATEs. From this model, I presume that the coefficients for the interaction between month_treat and POST are ATEs for each month after the treatment period.

Code:
gen month_treat=month*el_TREAT
xtreg daily_water i.month_treat##i.POST_treat Mtemp Sun_D Rain_D away i.dow i.year,fe cl(newid)
Now, my question is to make sure that I am estimating the correct model to get the desired results. That means, am I using the appropriate code to get the desired results(Monthly ATEs after the treatment)?

I put the sample data and model results below.

Many thanks for your help in advance!

Code:
Fixed-effects (within) regression        Number of obs     =    262,435
Group variable: newid        Number of groups  =        415

R-sq:        Obs per group:
within  = 0.1783        min =        260
between = 0.1623        avg =      632.4
overall = 0.1639        max =        731

        F(36,414)         =      32.03
corr(u_i, Xb)  = 0.0656        Prob > F          =     0.0000

    (Std.    Err. adjusted for 415 clusters    in newid)
            
    Robust
daily_water       Coef.    Std. Err.    t    P>t     [95% Conf.    Interval]
            
month_treat 
1    -14.05208    4.755825    -2.95   0.003    -23.40066    -4.703508
2     -13.3265    4.876675    -2.73   0.007    -22.91263    -3.740371
3    -.1929066    5.669033    -0.03   0.973    -11.33659    10.95077
4    -2.404938    5.429825    -0.44   0.658     -13.0784    8.268526
5     4.115936    5.508886    0.75   0.455    -6.712939    14.94481
6     4.275163    5.780306    0.74   0.460    -7.087246    15.63757
7     3.327438    5.874876    0.57   0.571    -8.220867    14.87574
8     4.405579    5.138175    0.86   0.392    -5.694587    14.50574
9     8.603835    4.601088    1.87   0.062    -.4405733    17.64824
10     4.321167    3.383359    1.28   0.202    -2.329539    10.97187
11    -1.052435    3.101057    -0.34   0.734    -7.148215    5.043346
12            0    (omitted)

1.POST_treat   -4.729409    3.57058    -1.32   0.186    -11.74814    2.289318

month_treat#POST_treat 
1 1     8.122836    7.652072    1.06   0.289    -6.918924    23.1646
2 1     8.110173    7.870883    1.03   0.303    -7.361705    23.58205
3 1    -9.648266    7.453082    -1.29   0.196    -24.29887    5.002335
4 1    -7.793852    7.782507    -1.00   0.317    -23.09201    7.504304
5 1    -9.078844    7.394379    -1.23   0.220    -23.61405    5.456366
6 1    -7.826685    7.525708    -1.04   0.299    -22.62005    6.966679
7 1    -9.695505    6.62882    -1.46   0.144    -22.72585    3.334836
8 1    -11.36933    6.432636    -1.77   0.078    -24.01403    1.275367
9 1    -14.44174    7.03736    -2.05   0.041    -28.27515    -.6083234
10 1    -10.67377    6.98552    -1.53   0.127    -24.40528    3.05774
11 1    -2.222318    7.668682    -0.29   0.772    -17.29673    12.85209
12 1    -7.011918    6.918561    -1.01   0.311    -20.61181    6.587971

Mtemp   -.4811931    .0891859    -5.40   0.000    -.6565069    -.3058794
Sun_D    .0053095    .0103424    0.51   0.608    -.0150206    .0256396
Rain_D   -.2029803    .0736975    -2.75   0.006    -.3478483    -.0581123
away   -165.7579    5.145493    -32.21   0.000    -175.8725    -155.6434

dow 
1    -19.45075    1.844929    -10.54   0.000    -23.07735    -15.82416
2    -18.78981    1.754284    -10.71   0.000    -22.23823    -15.3414
3    -18.33057    1.733601    -10.57   0.000    -21.73832    -14.92281
4    -18.02998    1.639566    -11.00   0.000    -21.25289    -14.80706
5     -19.4266    1.868959    -10.39   0.000    -23.10043    -15.75277
6    -.6209718    1.246531    -0.50   0.619    -3.071291    1.829348

year 
2016     10.58831    3.006831    3.52   0.000     4.677755    16.49887
2017     7.982201    3.661211    2.18   0.030     .7853198    15.17908

_cons    192.2065    2.591394    74.17   0.000     187.1125    197.3004
            
sigma_u   78.626063
sigma_e   104.21317
rho   .36274481    (fraction    of variance due to u_i)





[CODE]
* Example generated by -dataex-. To install: ssc install dataex
clear
input byte month float(newid daily_water el_TREAT POST_treat)
3 2 234 1 0
3 2 70 1 0
3 2 175 1 0
3 2 77 1 0
3 2 89 1 0
3 2 124 1 0
3 2 262 1 0
3 2 225 1 0
3 2 135 1 0
3 2 143 1 0
3 2 8 1 0
3 2 1 1 0
3 2 6 1 0
3 2 1 1 0
3 2 1 1 0
3 2 1 1 0
3 2 5 1 0
3 2 50 1 0
3 2 67 1 0
3 2 229 1 0
3 2 306 1 0
3 2 96 1 0
3 2 74 1 0
3 2 100 1 0
3 2 335 1 0
3 2 115 1 0
3 2 204 1 0
3 2 144 1 0
3 2 99 1 0
3 2 74 1 0
3 2 89 1 0
4 2 59 1 0
4 2 156 1 0
4 2 396 1 0
4 2 117 1 0
4 2 171 1 0
4 2 163 1 0
4 2 252 1 0
4 2 66 1 0
4 2 53 1 0
4 2 112 1 0
4 2 229 1 0
4 2 211 1 0
4 2 77 1 0
4 2 83 1 0
4 2 114 1 0
4 2 101 1 0
4 2 101 1 0
4 2 319 1 0
4 2 237 1 0
4 2 104 1 0
4 2 79 1 0
4 2 108 1 0
4 2 61 1 0
4 2 125 1 0
4 2 265 1 0
4 2 175 1 0
4 2 85 1 0
4 2 125 1 0
4 2 85 1 0
4 2 91 1 0
5 2 241 1 0
5 2 134 1 0
5 2 205 1 0
5 2 74 1 0
5 2 101 1 0
5 2 134 1 0
5 2 141 1 0
5 2 116 1 0
5 2 259 1 0
5 2 223 1 0
5 2 134 1 0
5 2 86 1 0
5 2 65 1 0
5 2 209 1 0
5 2 302 1 0
5 2 183 1 0
5 2 100 1 0
5 2 65 1 0
5 2 131 1 0
5 2 298 1 0
5 2 109 1 0
5 2 269 1 0
5 2 264 1 0
5 2 82 1 0
5 2 68 1 0
5 2 482 1 0
5 2 57 1 0
5 2 239 1 0
5 2 254 1 0
5 2 282 1 0
5 2 150 1 0
6 2 327 1 0
6 2 114 1 0
6 2 93 1 0
6 2 251 1 0
6 2 55 1 0
6 2 134 1 0
6 2 240 1 0
6 2 101 1 0