Re: st: two stage least square questions

["Austin Nichols" <austinnichols@gmail.com>]

Zhiqiang Feng--
No, you cannot use the fitted values or residuals from a first stage
using a different dep var in the second stage as you propose.  You
can, however, simply model the effect of "any_commute" (binary X1' in
your notation) on Y directly; see
http://www.stata.com/statalist/archive/2007-05/msg00338.html

though you undoubtedly still have a selection problem--commuting and
wages can be observed only for the employed.

On 5/21/07, Zhiqiang Feng <zf2@st-andrews.ac.uk> wrote:
> Hi, everyone,
>
> We like to do a two stage least square (2SLS) regression. We have looked
> at some information in the forum. For example, the email communications
> on "Re: st: 2SLS with Probit in the first-stage regression" in 2004.
> However, our questions are somewhat different.
>
> We are interested in the impact of commuting on health.
>
> So the regression is:
>
> Y = a + b1X1 + b2X2 + e
>
> here Y is defined as health status of subjects, a continuous variable.
> X1 is commuting time, a continuous and endogenous variable.
>
> We like to instument X1 with Z1 and Z2, so the second regression is:
>
> X1 = a + b1Z1 + b2Z2 + b3X2 + e
>
> However, we think Z1, Z2 and X2 are associated with the decision on
> whether subjects take up commuting instead of on commuting time, so we
> prefer to use X1 as a binary variable indicating whether to commute, say
> X1', in the second regression,.
>
> X1' = a + b1Z1 + b2Z2 + b3X2 + u
>
> We wonder if this is possible or CORRECT as we try to use the same
> variable (commuting) differently in the first (as binary) and second (as
> continuous) regressions.
>
> Any help would be appreciated.
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