# st: two stage least square questions

 From Zhiqiang Feng To statalist@hsphsun2.harvard.edu Subject st: two stage least square questions Date Mon, 21 May 2007 11:12:08 +0100

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.

Zhiqiang

Zhiqiang Feng

Research Fellow
Longitudinal Study Centre for Scotland
University of St Andrews
St Andrews, UK

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