Unable to find the correct AIC and BIC while conducting the ADF test. Need solution!

[Mir Adnan Ali]

Hello all,
I'm using AIC and BIC to find the appropriate lag to be used in the ADF test. The approach I used was to manually write the regression equation corresponding to the dicky fuller equation, and then use the command estat ic. However, the issue I faced was when I used trend in the ADF test. The coefficient of the constant term is different in the ADF test and the regression table, which I found by manually writing the regression equation. Below is the code and also the output. I assume that due to this discrepancy the correct AIC and BIC will be different. How can I resolve this issue?

[Justin Niakamal]

It's probably how you've defined your trend variable. You should be able to replicate dfuller if you replace year with the following trend variable

sum year
gen trend = year - r(min)

See below

 webuse air2, clear
(TIMESLAB: Airline passengers)

.
.  
. dfuller air, lags(2) trend regress

Augmented Dickey–Fuller test for unit root

Variable: air                             Number of obs  = 141
                                          Number of lags =   2

H0: Random walk with or without drift

                                       Dickey–Fuller
                   Test      -------- critical value ---------
              statistic           1%           5%          10%
--------------------------------------------------------------
 Z(t)            -7.085       -4.026       -3.445       -3.145
--------------------------------------------------------------
MacKinnon approximate p-value for Z(t) = 0.0000.

Regression table
------------------------------------------------------------------------------
       D.air | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         air |
         L1. |  -.4565681   .0644396    -7.09   0.000    -.5840014   -.3291349
         LD. |      .5086   .0745238     6.82   0.000     .3612247    .6559752
        L2D. |   .1033717   .0876976     1.18   0.241    -.0700557    .2767992
             |
      _trend |   1.232306   .1819661     6.77   0.000     .8724568    1.592155
       _cons |   39.48703   7.153964     5.52   0.000     25.33963    53.63443
------------------------------------------------------------------------------

.
. gen T = _n -1

. reg d.air l.air l(1/2)d.air c.T

      Source |       SS           df       MS      Number of obs   =       141
-------------+----------------------------------   F(4, 136)       =     20.11
       Model |  60062.8156         4  15015.7039   Prob > F        =    0.0000
    Residual |  101570.887       136  746.844754   R-squared       =    0.3716
-------------+----------------------------------   Adj R-squared   =    0.3531
       Total |  161633.702       140  1154.52644   Root MSE        =    27.328

------------------------------------------------------------------------------
       D.air | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         air |
         L1. |  -.4565681   .0644396    -7.09   0.000    -.5840014   -.3291349
         LD. |      .5086   .0745238     6.82   0.000     .3612247    .6559752
        L2D. |   .1033717   .0876976     1.18   0.241    -.0700557    .2767992
             |
           T |   1.232306   .1819661     6.77   0.000     .8724568    1.592155
       _cons |   39.48703   7.153964     5.52   0.000     25.33963    53.63443
------------------------------------------------------------------------------