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  • Parallel trend assumption using leads and lags

    I am running some robustness checks to my diff-in-diff specification. In particular, I am trying to check if the parallel trend assumption is satisfied. I am following the suggestion reported here https://stats.stackexchange.com/ques...mon-trend-betw.

    Thus, given my dataset, I am running an -xtreg, fe- where log_GON is my dependent variable and the diff-in-diff variable would be treated_decr*post_decr, i.e. the interaction between the dummy of being in the treated group and being post the date of implementation of the policy I am interested in. The year of implementation is 1995. Thus following the suggestion in the link I am running a diff-in-diff model with leads and lags for the diff-in-diff term and I am planning to test if the two pre-treatment terms, i.e. the ones in 1994 and 1993 are jointly non significant.

    The code and the outcomes are the following


    Code:
    xtreg log_GON treated_decr#1994.year treated_decr#1993.year treated_decr#1996.year ///
    treated_decr#1997.year treated_decr#1998.year c.year c.year#i.state ///
    if (state == 2|state == 5|state == 6|state == 8) & year >= 1985, cluster(state) fe basel
    Code:
    Fixed-effects (within) regression               Number of obs     =        128
    Group variable: state                           Number of groups  =          4
    
    R-sq:                                           Obs per group:
         within  = 0.3827                                         min =         32
         between = 0.1068                                         avg =       32.0
         overall = 0.0748                                         max =         32
    
                                                    F(3,3)            =          .
    corr(u_i, Xb)  = -0.9994                        Prob > F          =          .
    
                                           (Std. Err. adjusted for 4 clusters in state)
    -----------------------------------------------------------------------------------
                      |               Robust
              log_GON |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
    ------------------+----------------------------------------------------------------
    treated_decr#year |
              0 1993  |          0  (base)
              0 1994  |  -.4768764   .1315696    -3.62   0.036    -.8955894   -.0581633
              0 1996  |  -.4627052   .4205494    -1.10   0.352    -1.801081    .8756705
              0 1997  |  -.0429162   .4332989    -0.10   0.927    -1.421867    1.336034
              0 1998  |  -.0507665   .2062129    -0.25   0.821    -.7070279    .6054949
              1 1993  |  -.7470444   3.39e-08 -2.2e+07   0.000    -.7470445   -.7470443
              1 1994  |  -.8624563   2.99e-08 -2.9e+07   0.000    -.8624564   -.8624562
              1 1996  |  -.6488787   2.18e-08 -3.0e+07   0.000    -.6488787   -.6488786
              1 1997  |  -.5308411   1.78e-08 -3.0e+07   0.000    -.5308412   -.5308411
              1 1998  |  -.1217581   1.38e-08 -8.8e+06   0.000    -.1217582   -.1217581
                      |
                 year |   .0501079   4.00e-09  1.3e+07   0.000     .0501078    .0501079
                      |
         state#c.year |
                  SA  |  -.0288139   .0015684   -18.37   0.000    -.0338051   -.0238227
                 Tas  |  -.0237483   .0015684   -15.14   0.001    -.0287395    -.018757
                  WA  |  -.0365106   .0015684   -23.28   0.000    -.0415019   -.0315194
                      |
                _cons |  -52.61188   2.378725   -22.12   0.000    -60.18204   -45.04172
    ------------------+----------------------------------------------------------------
              sigma_u |  31.831812
              sigma_e |  .47882443
                  rho |  .99977378   (fraction of variance due to u_i)
    -----------------------------------------------------------------------------------
    and then the test gives me

    Code:
    test 1.treated_decr#1993b.year 1.treated_decr#1994.year
    Code:
    ( 1)  1.treated_decr#1993b.year = 0
     ( 2)  1.treated_decr#1994.year = 0
           Constraint 2 dropped
    
           F(  1,     3) = 4.9e+14
                Prob > F =    0.0000
    My main doubt is about the specification. It makes sense to me but I am not 100% sure about it because I removed treated_decr#1992.year on purpose to keep it as a baseline but I would add treated_decr#1995.year, the real diff-in-diff coefficient of interest.

    Do you have any hint?



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