Why logit regression and marginal effects can't generate the same z-statistics?

[Jae Li]

Dear Stata experts,

I've run logit regression and its marginal effect at follow. However, they should have the same z-statistics but I couldn't manage to get it, do you possibly know why is it? Can you please fix it if possible? Many thanks to you in advance!

logit perf inv profit book_lev MTT, cluster(permno)

Iteration 0:   log pseudolikelihood = -18638.798  
Iteration 1:   log pseudolikelihood = -17116.388  
Iteration 2:   log pseudolikelihood = -13925.904  
Iteration 3:   log pseudolikelihood = -13667.722  
Iteration 4:   log pseudolikelihood = -13661.271  


Logistic regression                             Number of obs     =    102,384
                                                Wald chi2(84)     =    4529.30
                                                Prob > chi2       =     0.0000
Log pseudolikelihood =  -13661.16               Pseudo R2         =     0.2671

                                                         (Std. Err. adjusted for 10,947 clusters in permno)
-----------------------------------------------------------------------------------------------------------
                                          |               Robust
                                    perf|      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------------------+----------------------------------------------------------------
                                     inv  |   .5335151   .2469513     2.16   0.031     .0494995    1.017531
                                   profit |  -1.891079   .0930199   -20.33   0.000    -2.073395   -1.708763
                                 book_lev |   1.609226   .1046438    15.38   0.000     1.404128    1.814324
                                      MTT |  -.5021871   .0129645   -38.74   0.000     -.527597   -.4767773



. margins, dydx(*)

Average marginal effects                        Number of obs     =    102,384
Model VCE    : Robust

Expression   : Pr(perf), predict()
dy/dx w.r.t. : inv profit book_lev MTT

-----------------------------------------------------------------------------------------------------------
                                          |            Delta-method
                                          |      dy/dx   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------------------------------+----------------------------------------------------------------
                                     inv  |    .018774   .0086892     2.16   0.031     .0017435    .0358045
                                   profit |  -.0665456   .0033517   -19.85   0.000    -.0731148   -.0599764
                                 book_lev |   .0566274   .0037265    15.20   0.000     .0493236    .0639312
                                      MTT |  -.0176716   .0004976   -35.51   0.000    -.0186468   -.0166963

[Clyde Schechter]

However, they should have the same z-statistics

That's just not true. Either you misunderstood whoever told you that, or they don't know what they're talking about.

[Jae Li]

@Clyde Schechter Thank you Clyde for replying me so quickly! Do you mean they are supposed to be different? Many thanks for your time!

[Clyde Schechter]

Yes, they are supposed to be different. They might occasionally, by coincidence, turn out the same, but that would be very unusual.

[Jae Li]

@Clyde Schechter Good to know that and thank you very much for your confirmation!