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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 17:20:43 -0400

```Shikha Sinha <shikha.sinha414@gmail.com>:
Sorry--I read your post a bit too quick--you are using the gender of
firstborn, not genders of first 2 kids, so
http://elsa.berkeley.edu/~moretti/sons.pdf
is the relevant inspiration.  Are you limiting to married/cohab women?
If not, then an increase in number of children "caused" by the chance
birth of a daughter instead of a son might be also be predictive of
single motherhood, which might be correlated with increased work.  I
to interpret your findings for you...

On Mon, Oct 15, 2012 at 5:14 PM, Austin Nichols <austinnichols@gmail.com> wrote:
> 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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