6
Let us consider Situation 1.
Let us assume that $\rho$ is observed. If it does not work when $\rho$ is observed, there is no reason why it (using a proxy of $\rho$ as instrument) should work when $\rho$ is not observed.
$\rho$ is endogenous so we can't just include it as a regressor in an equation. Thus, let us consider IV estimation.
Obvious instruments for ...
5
I think this is already answered in the paper itself and in addition I think this is due to the way how they define 'simultaneous equations' topics.
First as authors of that paper opine:
This presumably reflects
declining use of an orthodox multi-equation framework, especially in macroeconomics. The reduced coverage of Simultaneous equations has made space ...
1
Let's start by writing down the profit functions:
$$
\pi_1 = p_1 q_1 - c_1 q_1 = (p_1 - c_1) q_1 = (p_1 - c_1)(a_1 + b_{11} p_1+b_{12} p_2)
$$
and similarlily:
$$
\pi_2 = (p_2 - c_2)(a_2 + b_{21} p_1 +b_{22} p_2)
$$
In a simultaneous equilibrium, both firms simultaneously maximize their profits taking the strategies of the players as given.
Doing this will ...
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