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From |
Nicolai Borgen <nicolai.borgen@sosgeo.uio.no> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Multiple endogenous variables IV. Estimating the first stage regression with only a subset of the instruments |

Date |
Tue, 25 Oct 2011 14:59:45 +0200 |

I have a question regarding the use of instrumental variables when having multiple endogenous variables. I am estimating the economic return of attending different educational institutions X1, X2 and X3. For simplicity, the models are presented without control variables and constant. [A1] Y= δ1*X1 + δ2*X2 + δ3*X3 + ε Since I have strong reasons to suspect that X1, X2 and X3 is correlated with ε, it is necessary to use an instrumental variable approach to estimate the return. I therefore use proximity (in km) between municipality of adolescence and these institutions as instruments (Z1, Z2 and Z3). Using regression commands such as ivregress and ivreg2 in STATA, all instruments are included in the first stage for each endogenous variable X1, X2 and X3: [B1] X1 = B1*Z1 + B2*Z2 + B3*Z3 + ε [C1] X2 = B1*Z1 + B2*Z2 + B3*Z3 + ε [D1] X3 = B1*Z1 + B2*Z2 + B3*Z3 + ε My problem occurs because X1 and X2 are located in the same city, and Z1 and Z2 are therefore perfectly collinear. Thus, in [B1] and [C1] either Z1 or Z2 is dropped. My model is therefore basically under-identified. Based on this, I have the following two questions: (1) Is it possible to estimate the first stage regression using a subset of the instruments? [B2] X1 = B1*Z1 + ε [C2] X2 = B2*Z2 + ε [D2] X3 = B3*Z3 + ε (2) This STATA page http://www.stata.com/support/faqs/stat/ivr_faq.html shows an example of how to perform the two-step computations for the instrumental variable estimator without using ivregress or ivreg2. Is this a feasible solution? Are there any STATA commands I can use that do this? Many thanks, Nicolai Borgen University of Oslo * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: RE: Multiple endogenous variables IV. Estimating the first stage regression with only a subset of the instruments***From:*"Millimet, Daniel" <millimet@mail.smu.edu>

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