I did not realize you were planning to leave out the fixed effects and
call b0(i)+v(i,t) a composite error term, in which case, yes, you have
an endogeneity problem because the fixed effect b0 is correlated with
p. Since you have panel data, I assumed you would run a fixed effects
model (e.g. -xtivreg2, fe-) or some other model (e.g. -xtivreg2, fd-)
so that b0 is not an issue. The remaining issue is the important one:
both price and quantity are determined by the intersection of two
curves, both of which are shifting over time (which is not shown in
how you have written the equations--i.e. put income and weather and
other factors in there). Unless you have exogenous variation shifting
one curve but not the other, you can identify neither supply nor
demand curves. Hence find an instrument and use -xtivreg2- not
-xtreg-.
I guess the issue is that IV is consistent but inefficient and you
have small N, so you will have low power. But I cannot see that you
have a better alternative. Unless there is some good reason you can
treat p as exogenous (maybe related to the small N?)...
On Fri, Sep 5, 2008 at 3:39 AM, <[email protected]> wrote:
> Many thanks for your helpful suggestions!
> And sorry about posting twice, my fault - I wasn't sure the e-mail made it to the list at all, but still...
>
> But I don't understand why p(i,t) isn't endogeneous in (2).
> It is not uncorrelated to the composite error term b0(i)+v(i,t) as E[p(i,t)*(b0(i)+v(i,t))] = E[p(i,t)*b0(i)] + E[p(i,t)*v(i,t)],
> where p(i,t) being stationary could be written as p(i,t) = [a0(i)/(1-a1)] + SUM_s a1^s*u(i,t-s).
> Hence, the first expectation becomes E[p(i,t)*b0(i)] = b0(i) * [a0(i)/(1-a1)], which is not equal to zero (the second becomes zero, however).
>
> Thus, I intended to -reg- the first differences of q(i,t) on p(i,t),
> eliminating time-invarying variables and ending up with a consistent estimate of b1,
> the parameter of interest - d.p is a valid instrument for itself in d.q.
>
> Is there an error in my thinking?
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