RE: st: OLS and IV have opposite sign

["Millimet, Daniel" <millimet@mail.smu.edu>]

The bias from incorrectly treating a covariate as exogenous is additive: E[beta-hat] = beta + bias.  So, if the bias is larger in absolute value than beta, and IV provides a consistent estimate of the true value, beta, there is no reason why they cannot be of the opposite sign.  Of course, given recent work on heterogeneous treatment effects, it could also be that IV estimates the local average treatment effect (for compliers) and this parameter has no simple relationship to the OLS estimate.

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Daniel L. Millimet, Professor
Department of Economics
Box 0496
SMU
Dallas, TX 75275-0496
phone: 214.768.3269
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web: http://faculty.smu.edu/millimet
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-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Shikha Sinha
Sent: Monday, October 15, 2012 3:33 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: OLS and IV have opposite sign

I am estimating the effect of family size (no of children) on probability of work by mother. The endogenous variable is no of children and I instrument this by gender of first born. If the first child is female then family size should be greater.

I understand that IV correct the bias and OLS coeff may be upward or downward biased. One can sign the bias (+) or (-) by examining the correlation between the omited variable and endogenous, but What I do not understand why the sign would change and what determines the opposite sign. I get a negative OLS while a positive IV coeff.

Thanks,
Shikha

On Mon, Oct 15, 2012 at 1:11 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> Shikha Sinha <shikha.sinha414@gmail.com>:
> The econometric reason is simple if you believe the exclusion 
> restriction.  Tell us what the endog var is, what the excluded 
> instruments are, and someone on the list will provide a (verbal) 
> description of the bias producing a negative OLS coef estimate 
> (evidently no longer visible in the consistent IV estimate).  Then 
> someone else will weigh in on whether the exclusion restriction makes 
> sense, probably...
>
> On Mon, Oct 15, 2012 at 3:58 PM, Shikha Sinha <shikha.sinha414@gmail.com> wrote:
>> Dear all,
>>
>> I am estimating an Ordinary least square (OLS) and Instrument 
>> variable
>> (IV) model, however the signs are opposite to each other. The OLS 
>> coeff is negative, while the IV coeff is positive. Could anyone 
>> explain what the signs in these two models are different- is there 
>> any econometric reason for this?
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