<p>You're definately on the right track. What you are doing is estimating the inverse demand and inverse supply in your market. The variables <strong><em>Visits Print and Prod</em></strong> can be used as "shifters" i.e. instruments for the quantity in the equation in which they are not present. <strong><em>Visits</em></strong> can be used as an instrument for quantity, when estimating the inverse supply equation and <strong><em>Print and Prod</em></strong> can be used as instruments for quantity when estimationg the inverse demand equation. </p>

<p>A well known example of how this works is Grady's article on Fulton fish market. You can find STATA code that replicates that article here: <a href="https://www.stata.com/data/s4poe/chap11.do" rel="nofollow noreferrer">https://www.stata.com/data/s4poe/chap11.do</a> .</p>

<p>The data sets for the stata code are here: <a href="http://www.principlesofeconometrics.com/poe4/data/stata/" rel="nofollow noreferrer">http://www.principlesofeconometrics.com/poe4/data/stata/</a> .</p>

<p>Of course you should test the validity of the assumptions behind the use of IV in your SEM with the Hausman, Sargan-Wu and Stock-Yogo tests.</p>

CC BY-SA 4.0
2019-07-30T14:28:46.920Z
2019-07-30T14:28:46.920Z
Grada Gukovic
<p>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: <a href="https://economics.stackexchange.com/questions/19077/equilibrium-price-ols-regression">Equilibrium Price - OLS Regression</a>. 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>

<p><span class="math-container">$P_{Dt} = \beta _{0} + \beta _{1} Q_{t} + \beta_{2} Visits + u_{t}$</span></p>

<p><span class="math-container">$P_{St} = \alpha _{0} + \alpha _{1} Q_{t} + \alpha_{2} Print_{t} + \alpha_{3} Prod_{t} + u_{t}$</span></p>

<ul>
<li><p><span class="math-container">$P_{Dt, St}$</span> = Inverse Demand and Inverse Supply</p></li>
<li><p><span class="math-container">$Q_{t}$</span> = Quantity of Display Advertisement</p></li>
<li><p><span class="math-container">$Visits$</span> = Index of web traffic/visits (akin to income effect)</p></li>
<li><p><span class="math-container">$Print$</span> = Price of print advertisement (substitution effect)</p></li>
<li><p><span class="math-container">$Prod$</span> = Creative production costs (factor of production)</p></li>
</ul>

<p>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!</p>

<econometrics>
Estimating Equilibrium Price for Advertising using Simultaneous Equations Model
Witeswa18
# Estimating Equilibrium Price for Advertising using Simultaneous Equations Model

(Asked by: username_0 on 2019-07-29)

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](https://economics.stackexchange.com/questions/19077/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!

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2019-07-30. Score: 1 | Accepted answer

You're definately on the right track. What you are doing is estimating the inverse demand and inverse supply in your market. The variables ***Visits Print and Prod*** can be used as "shifters" i.e. instruments for the quantity in the equation in which they are not present. ***Visits*** can be used as an instrument for quantity, when estimating the inverse supply equation and ***Print and Prod*** can be used as instruments for quantity when estimationg the inverse demand equation.

A well known example of how this works is Grady's article on Fulton fish market. You can find STATA code that replicates that article here: <https://www.stata.com/data/s4poe/chap11.do> .

The data sets for the stata code are here: <http://www.principlesofeconometrics.com/poe4/data/stata/> .

Of course you should test the validity of the assumptions behind the use of IV in your SEM with the Hausman, Sargan-Wu and Stock-Yogo tests.


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