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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