# st: Re: Re: Re: marginal effects

 From "Scott Merryman" To Subject st: Re: Re: Re: marginal effects Date Thu, 24 Jul 2003 20:44:38 -0500

```----- 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
>
> 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% C.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% C.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% C.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% C.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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