Do I have a problem with simultaneity here??


I am modelling the demand for imported rice for a sample of countries. The price of imports, one of the explanatory variables, is assumed to be exogenous (small country assumption). However I can't tell if another of my explanatory variables (price of domestic rice) is simultaneously determined with the dependent variable. Intuitively, it seems it is: an influx of imports would depress the price of locally-produced rice.

However I have the following system of equations:

Domestic supply/demand for rice
Demand for domestically produced rice, Qd(H), is a function of income Y, its own price P(H) and the exogenous price of imported substitutes P(I):

Qd(H) = F [ Y, P(I), P(H) ]

and supply of domestic rice Qs(H) is a function of its domestic price and a vector of input prices, W:

Qs(H) = G [ P(H), W ]

In equilibrium we have Qd(H) = Qs(H). So the home price P(H) can be implicitly defined by the exogenous variables Y, P(I) and W:

P(H) = H [ Y, P(I), W ]

Import demand

Import demand is a function of income, the good's own price and the price of locally-produced substitutes:

Qd(I) = J [ Y, P(I), P(H) ]

This gives us the two equations:

(1) Import demand function
Q(I) = A+ P(I) + P(H) + Y
(2) Domestic price function
P(H) = B + P(I) + W + Y

It seems to me then that, beause P(H) is a function of exogenous variables only, there can't be simultaneity between the quantity of imports Q(I) and the price of local rice P(H) in the import demand function.

So the question I'm asking is, should I be worried about simultaneity between Q(I) and P(H)??

Your comments are gratefully recieved, many thanks