# Estimating Equilibrium Price for Advertising using Simultaneous Equations Model

I am attempting to build a simultaneous equations model that estimates the equilibrium price of display advertisement, but I have only seen textbook examples with Quantity being the dependent variable - this question is similar: Equilibrium Price - OLS Regression. However, I assume that quantity is also endogenous, and I think I should use two stage least squares to produce unbiased estimates. Display advertisement is bought/sold in online marketplaces, and that led me to believe this model would provide a good fit.

$$P_{Dt} = \beta _{0} + \beta _{1} Q_{t} + \beta_{2} Visits + u_{t}$$

$$P_{St} = \alpha _{0} + \alpha _{1} Q_{t} + \alpha_{2} Print_{t} + \alpha_{3} Prod_{t} + u_{t}$$

• $$P_{Dt, St}$$ = Inverse Demand and Inverse Supply

• $$Q_{t}$$ = Quantity of Display Advertisement

• $$Visits$$ = Index of web traffic/visits (akin to income effect)

• $$Print$$ = Price of print advertisement (substitution effect)

• $$Prod$$ = Creative production costs (factor of production)

If anyone has experience modeling structural equations with price as the dependent variable I would really appreciate hearing your thoughts on how I should create a predicted value for Quantity and finalize a reduced form equation. Thanks!