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# Re: st: OLS and IV have opposite sign

 From Austin Nichols To statalist@hsphsun2.harvard.edu Subject Re: st: OLS and IV have opposite sign Date Mon, 15 Oct 2012 17:14:53 -0400

```Shikha Sinha <shikha.sinha414@gmail.com>
I recommend you practice using the data from the paper that pioneered
the approach:
http://economics.mit.edu/faculty/angrist/data1/data/angev98

My guess is that your sample size is too small for IV's consistency to
manifest itself, and you are understating your SEs.  Perhaps you have
a positive point estimate whose confidence interval includes a very
wide range of negative effects?

The usual story is that the apparent negative impact of a birth on
labor supply is biased upward in magnitude (down on the number line)
by selection; those who are intrinsically less likely to work are more
likely to give birth.  So the true effect, while negative, is smaller
in magnitude than the biased OLS coef.  This need not be true in every
context, of course, but I find your estimate of a positive impact of
childbirth on probability of work by mother implausible on its face.

On Mon, Oct 15, 2012 at 4:32 PM, Shikha Sinha <shikha.sinha414@gmail.com> wrote:
> 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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