<p>Assume a certain market can be described by</p>

<ul>
<li>Demand Function: $$Q_{d, t} = \alpha_0 + \alpha_1 P_t + \mu_{1, t}$$</li>
<li>Supply Function: $$Q_{s, t} = \beta_0 P_t + \mu_{2, t}$$</li>
</ul>

<p>The price in this market is determined by the <strong><em>equilibrium point</em></strong>, that is $Q_d$ = $Q_s$ = $Q_t$ . Now let $\alpha_1$ be <em>0</em>, so that the demand is perfectly inelastic.</p>

<p>Now - is it possible to model the $P_t$ as a linear regression function of $Q_t$ so that: $$ P_t = \gamma_0 + \gamma_1 Q_t + \epsilon_t.$$</p>

<p>The standard simultaneous equation model problem is not present because of the perfectly inelastic demand. Yet I am unsure wether it is possible to model the price like this - several scientific papers I read did exactly that. Yet, Since the Price is still determined by an equilibrium situation and I can determine which $Q_t$ is present by looking at the given value of $P_t$ and the other way around I am of the opinion that there still is some sort of reverse causality present, which in turn implies that I have to replace $Q_t$ by an exogenous regressor so that</p>

<p>$$ P_t = \gamma_0 + \gamma_1 (regressor) + \epsilon_t.$$</p>

<p>Am I right? Or does the assumption of perfect inelasticity "dismantle" the issue of simultaneous equations in the regression context.</p>

CC BY-SA 3.0
2018-02-24T16:08:31.190Z
Is this a time series regression?
london
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2018-02-24T20:15:38.357Z
Yes. I am talking about time series data.
shenflow
CC BY-SA 3.0
2018-02-25T01:06:33.743Z
For your supply function, did you mean  $Q_{s, t} = \beta_0+ \beta_1 P_t + \mu_{2, t}$ instead of  $Q_{s, t} = \beta_0 P_t + \mu_{2, t}$?
EconJohn
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2018-02-25T07:59:54.527Z
No. I am assuming that there is no intercept present. You could write the function as you did and set it to 0 - but does this have an impact on the issue?
shenflow
CC BY-SA 3.0
2018-02-25T10:43:08.630Z
@shenflow, see this http://rstudio-pubs-static.s3.amazonaws.com/195495_d47be7c818424a3c9bfa5452dd17c6c6.html
london
CC BY-SA 3.0
2018-02-25T11:49:33.293Z
I am aware of that, the classical SEM problem is described in that article. But it does not answer the issue I am having. I am looking at a case where one of the 2 formulas is **completely price inelastic** so that one of the coefficients is 0. What this essentially means is that the SEM model reduces to one formula when it comes to determining the equilibrium price, because it is only part of one formula (the coefficient is 0 in the other one).
shenflow
CC BY-SA 3.0
2018-02-25T11:50:32.637Z
One might think that this solves the problem, but in my opinion, there still is some reverse causality present. The price still determines the demand and the demand still determines the price although I only have one formula that is composed of those 2 variables.
shenflow
CC BY-SA 3.0
2018-02-25T21:46:35.710Z
@shenflow be sure to tag the users to get their attention by using the @ symbol and their name.
EconJohn
CC BY-SA 3.0
2018-02-26T06:29:04.730Z
Thank you for reminding. @london please see the comments above.
shenflow
CC BY-SA 3.0
2018-02-28T12:08:07.977Z
@shenflow, I see that, and the link I posted above has a section about how to control for reverse causality. Have you considered using 2SLS method?
london
<econometrics><regression>
Econometrics - Simultaneous Equations and Perfect Inelasticity in the Context of Regression
shenflow
# Econometrics - Simultaneous Equations and Perfect Inelasticity in the Context of Regression

(Asked by: username_0 on 2018-02-24)

Assume a certain market can be described by

* Demand Function: $$Q\_{d, t} = \alpha\_0 + \alpha\_1 P\_t + \mu\_{1, t}$$
* Supply Function: $$Q\_{s, t} = \beta\_0 P\_t + \mu\_{2, t}$$

The price in this market is determined by the ***equilibrium point***, that is $Q\_d$ = $Q\_s$ = $Q\_t$ . Now let $\alpha\_1$ be *0*, so that the demand is perfectly inelastic.

Now - is it possible to model the $P\_t$ as a linear regression function of $Q\_t$ so that: $$ P\_t = \gamma\_0 + \gamma\_1 Q\_t + \epsilon\_t.$$

The standard simultaneous equation model problem is not present because of the perfectly inelastic demand. Yet I am unsure wether it is possible to model the price like this - several scientific papers I read did exactly that. Yet, Since the Price is still determined by an equilibrium situation and I can determine which $Q\_t$ is present by looking at the given value of $P\_t$ and the other way around I am of the opinion that there still is some sort of reverse causality present, which in turn implies that I have to replace $Q\_t$ by an exogenous regressor so that

$$ P\_t = \gamma\_0 + \gamma\_1 (regressor) + \epsilon\_t.$$

Am I right? Or does the assumption of perfect inelasticity "dismantle" the issue of simultaneous equations in the regression context.

**Tags:** econometrics, regression

> **Comments:**
> **username_1**: Is this a time series regression?  
> **username_0**: Yes. I am talking about time series data.  
> **username_2**: For your supply function, did you mean  $Q_{s, t} = \beta_0+ \beta_1 P_t + \mu_{2, t}$ instead of  $Q_{s, t} = \beta_0 P_t + \mu_{2, t}$?  
> **username_0**: No. I am assuming that there is no intercept present. You could write the function as you did and set it to 0 - but does this have an impact on the issue?  
> **username_1**: @username_0, see this http://rstudio-pubs-static.s3.amazonaws.com/195495_d47be7c818424a3c9bfa5452dd17c6c6.html  
> **username_0**: I am aware of that, the classical SEM problem is described in that article. But it does not answer the issue I am having. I am looking at a case where one of the 2 formulas is **completely price inelastic** so that one of the coefficients is 0. What this essentially means is that the SEM model reduces to one formula when it comes to determining the equilibrium price, because it is only part of one formula (the coefficient is 0 in the other one).  
> **username_0**: One might think that this solves the problem, but in my opinion, there still is some reverse causality present. The price still determines the demand and the demand still determines the price although I only have one formula that is composed of those 2 variables.  
> **username_2**: @username_0 be sure to tag the users to get their attention by using the @ symbol and their name.  
> **username_0**: Thank you for reminding. @username_1 please see the comments above.  
> **username_1**: @username_0, I see that, and the link I posted above has a section about how to control for reverse causality. Have you considered using 2SLS method?  

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## 0 answers

