# st: Re: Re: Re: Re: marginal effects

 From "Marina.Balboa" To Subject st: Re: Re: Re: Re: marginal effects Date Fri, 25 Jul 2003 19:52:42 +0200

```Thank you Scott for your help. It seems that the relation between the
marginal effects of the unconditional expected value and the latent variable
is the same for all the variables, including the constant. I will see if
papers include the constant when they report marginal effects of the
unconditional expected value and the interpretation.

Sincerely,
Marina Balboa

----- Original Message -----
From: "Scott Merryman" <smerryman@kc.rr.com>
To: <statalist@hsphsun2.harvard.edu>
Sent: Friday, July 25, 2003 3:44 AM
Subject: st: Re: Re: Re: marginal effects

> ----- Original Message -----
> From: "Marina.Balboa" <Marina.Balboa@ua.es>
> To: <statalist@hsphsun2.harvard.edu>
> Sent: Thursday, July 24, 2003 3:20 AM
> Subject: st: Re: Re: marginal effects
>
>
> > Thank you Scott very much for your helpful explanation. Just one
question,
> > please. What about the constant? If I want to report the results of
> >
> > mfx compute, predict(ys(0,.))
> >
> > Does not the model on the observed variable y have a constant, like the
> > model with the latent variable?
> >
> > Or does it have a constant that I may infer like this (using your
example):
> >
> > > . xttobit price mpg, ll(4000) i(foreign) nolog
> > >
> > > Random-effects tobit regression                 Number of obs      =
> > 74
> > > Group variable (i): foreign                     Number of groups   =
> > 2
> > >
> > > Random effects u_i ~ Gaussian                   Obs per group: min =
> > 22
> > >                                                                avg =
> > 37.0
> > >                                                                max =
> > 52
> > >
> > >                                                 Wald chi2(1)       =
> > 25.39
> > > Log likelihood  = -597.93768                    Prob > chi2        =
> > 0.0000
> > >
> >
> --------------------------------------------------------------------------
> > ----
> > >        price |      Coef.   Std. Err.      z    P>|z|     [95% Conf.
> > Interval]
> >
> -------------+------------------------------------------------------------
> > ----
> > >          mpg |  -327.9141    65.0826    -5.04
> > 0.000    -455.4736   -200.3545
> > >        _cons |   13099.53   1578.574     8.30   0.000     10005.58
> > 16193.48
> >
> -------------+------------------------------------------------------------
> > ----
> > >     /sigma_u |   707.8464   527.0417     1.34   0.179    -325.1364
> > 1740.829
> > >     /sigma_e |   2762.649   252.5473    10.94   0.000     2267.665
> > 3257.632
> >
> -------------+------------------------------------------------------------
> > ----
> > >          rho |   .0616045   .0871224                      .0016116
> > .4454072
> >
> --------------------------------------------------------------------------
> > ----
> > >
> > >   Observation summary:        63     uncensored observations
> > >                               11  left-censored observations
> > >                                0 right-censored observations
> > >
> >
> > > . mfx compute, nose predict(ys(4000,.))
> > >
> > > Marginal effects after xttobit
> > >       y  = E(price*|price>4000) (predict, ys(4000,.))
> > >          =  6495.1777
> >
> --------------------------------------------------------------------------
> > -----
> > >                         variable |          dy/dx                 X
> >
> ---------------------------------+----------------------------------------
> > -----
> > >                              mpg |       -252.7986            21.2973
> >
> --------------------------------------------------------------------------
> > -----
> > >
> > > . ****The marginal effects for the unconditional expected value of y
> > >
> > > .
> > >
> > >
> > > Hope this helps,
> > > Scott
> >
> > the relation between  the mpg coefficients
is: -252.7986/-327.9141=0.7709
> >
> > the constant of the model that I'm interested in is:
> > 13099.53*0.7709=10099
> >
> > Thank you very much for your help and any hint you could give me about t
his.
> > Sincerely,
> > Marina Balboa
> >
>
> This procedures seems to generate the same coefficient for the constant
that one
> would get after -dtobit- , but I am unsure of the interpretation of the
marginal
> effects of a constant.
>
>
> Scott
>
>
> . clear
>
> . use "C:\Stata8\auto.dta", clear
> (1978 Automobile Data)
>
> . replace price = 4000 if price <4000
>
> . qui tobit price mpg, ll(4000)
>
> . dtobit
>
> Marginal Effects: Latent Variable
> --------------------------------------------------------------------------
----
> variable |      dF/dx   Std. Err.      z    P>|z|     X_at   [    95%
I.   ]
> ---------+----------------------------------------------------------------
----
>      mpg |  -293.3453   60.82228    -4.82   0.000
21.2973  -412.555 -174.136
>    _cons |   12125.15   1316.403     9.21   0.000         1   9545.05
14705.3
> --------------------------------------------------------------------------
----
>
> Marginal Effects: Unconditional Expected Value
> --------------------------------------------------------------------------
----
> variable |      dF/dx   Std. Err.      z    P>|z|     X_at   [    95%
I.   ]
> ---------+----------------------------------------------------------------
----
>      mpg |  -218.8408   45.37451    -4.82   0.000
21.2973  -307.773 -129.908
>    _cons |   9045.577   982.0601     9.21   0.000         1   7120.77
10970.4
> --------------------------------------------------------------------------
----
>
> Marginal Effects: Conditional on being Uncensored
> --------------------------------------------------------------------------
----
> variable |      dF/dx   Std. Err.      z    P>|z|     X_at   [    95%
I.   ]
> ---------+----------------------------------------------------------------
----
>      mpg |  -155.8101   32.30571    -4.82   0.000
21.2973  -219.128 -92.4921
>    _cons |   6440.265   699.2065     9.21   0.000         1   5069.84
7810.68
> --------------------------------------------------------------------------
----
>
> Marginal Effects: Probability Uncensored
> --------------------------------------------------------------------------
----
> variable |      dF/dx   Std. Err.      z    P>|z|     X_at   [    95%
I.   ]
> ---------+----------------------------------------------------------------
----
>      mpg |  -.0331409   .0068714    -4.82   0.000
21.2973  -.046609 -.019673
>    _cons |   1.369848   .1487217     9.21   0.000         1   1.07836
1.66134
> --------------------------------------------------------------------------
----
>
>
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```