# Re: st: Re: Re: RE: Nonlinear IV estimation in STATA

 From "Austin Nichols" To statalist@hsphsun2.harvard.edu Subject Re: st: Re: Re: RE: Nonlinear IV estimation in STATA Date Mon, 1 May 2006 11:00:39 -0400

```Elaine--
I believe Mark pointed out that you need two excluded instruments when
you treat P and P^2 as two endogenous variables in a linear
specification. If demand is Q = B(A-P)^2 and you have two excluded
instruments and you're willing to make different assumptions about the
distribution of the error term...
You can estimate Q = a + bP + cP^2 + v
where a=B(A^2) and b=-2AB and c=B right?
So B=(c) and A=(-b/2c).
You can get SEs for A and B via -nlcom- I think.
You can also test whether a=(b^2/4c) to see if your model fits the
data (interpret a rejection as E(v)!=0 if you like).
I guess you want Q=0 whenever (A-P)<0 too, but I don't think the log
fixes that particular problem for you.

On 4/28/06, Elaine Tan <elaine.tan@econ.hku.hk> wrote:
```
```Hi - Information that I left out earlier: B measures size of market demand,
A is maximum willingness to pay.

----- Original Message -----
From: "Elaine Tan" <elaine.tan@econ.hku.hk>
To: <statalist@hsphsun2.harvard.edu>
Sent: Saturday, April 29, 2006 11:43 AM
Subject: st: Re: RE: Nonlinear IV estimation in STATA

> Thanks - the demand function is modelled as:
>
> Q = B(A-P)^2
>
> rewritten as: lnQ = lnB + 2 ln(A-P) + u
>
> So the function is nonlinear in A. I think I need nonlinear IV regression
> to estimate A?
```
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```