<p>In econometrics, identification can take several forms depending on the type of model you are working with (see <a href="http://fmwww.bc.edu/EC-P/wp957.pdf" rel="nofollow noreferrer">this survey</a> for a more comprehensive description). However, in general, identification pertains to the idea that either your econometric model or the exogenous variation in your data (or both) allows you to tease out the parameters that truly describe the data generating process. </p>

<p>To be more specific, suppose that you are studying outcome <span class="math-container">$y$</span> which depends (stochastically) on <span class="math-container">$x$</span> so that the data is generated according to <span class="math-container">$F(y|x)$</span> where <span class="math-container">$F$</span> is some distribution function. Then you have an econometric model that depends on a parameter, <span class="math-container">$\theta$</span> (this can be a vector of parameters), and for each parameter, it spells out a conditional distribution of <span class="math-container">$y$</span> in terms of <span class="math-container">$x$</span>. That is your econometric model is a function <span class="math-container">$M(\theta)=G(y|x; \theta)$</span>. We say that the model is identified if there exists a unique parameter, <span class="math-container">$\theta^*$</span>, in the domain of <span class="math-container">$M$</span> such that <span class="math-container">$M(\theta^*)=F(y|x)$</span>. </p>

<p>In reduced-form work, <span class="math-container">$M$</span> is assumed to be linear (or in general to be an injective function and have a relatively simple form), so ensuring identification has more to do with your data, <span class="math-container">$F$</span>, having the right properties (mainly having enough exogenous variation).</p>

<p>In contrast, structural work typically deals with data that is not experimental or quasi-experimental so <span class="math-container">$M$</span> cannot credibly be assumed linear. Instead, you develop a rich enough model and identification requires <span class="math-container">$M$</span> to be invertible. If <span class="math-container">$M$</span> is invertible, then you have that <span class="math-container">$M^{-1}(F(y|x))=\theta^*$</span>.</p>

<p>I think that in relation with identification, linear algebra tools are mainly useful to prove the invertibility of <span class="math-container">$M$</span>. However, it can prove also useful when it comes to designing an estimation strategy, and when implementing the estimation strategy in the computer, etc. </p>

CC BY-SA 4.0
2020-04-28T00:56:56.560Z
2020-04-28T00:56:56.560Z
Regio
<p>Hi: There is a book from 1966 that contains various papers on identification. It is called "Studies in Econometric Method" and it's edited by Hood and Koopmans. It looks like it assumes that one has a grasp of the necessary linear algebra.  It's a cowles foundation monograph so not trivial but, atleast from that book, you could probably figure out what linear algebra concepts are necessary to understand the papers.</p>

CC BY-SA 4.0
2020-04-28T19:25:38.117Z
2020-04-29T01:53:52.230Z
2020-04-29T01:53:52.230Z
mark leeds
<p>I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) that probably there are concepts in Linear Algebra (or Multivariate Mathematical Analysis if that is the case) that probably would make their life easier had they known that beforehand. Since I'm currently studying a more rigorous approach to linear algebra (nothing fancy, but definitely proving everything), I would like to understand this "Identification Strategy" concept that I remember "learning" in an introductory econometrics course where I'm pretty sure no one even mentioned what was the math behind it, which I think is extremely important. </p>

<p>If you could be clear and didactic I would appreciate a lot. </p>

<p>Thank you!</p>

CC BY-SA 4.0
2020-04-27T21:27:14.150Z
Do you want to know what the concept of identification is or the linear algebra concepts that go into econometrics? Identification strategy has nothing to do with linear algebra. What do you mean “*model the idea of Identification Strategy*”?
Brennan
CC BY-SA 4.0
2020-04-28T23:09:24.153Z
From Regio's answer, I think I know the direction now. Thanks.
Caio Velasco
<econometrics><mathematical-economics><linear-algebra>
What are the concepts in Linear Algebra that model the idea of Identification Strategy in Econometrics?
Caio Velasco
# What are the concepts in Linear Algebra that model the idea of Identification Strategy in Econometrics?

(Asked by: username_0 on 2020-04-27)

I just would like to know what concepts one should know before talking about identification strategies in econometrics. I see people studying such concepts but I'm not sure they realize (or even know) that probably there are concepts in Linear Algebra (or Multivariate Mathematical Analysis if that is the case) that probably would make their life easier had they known that beforehand. Since I'm currently studying a more rigorous approach to linear algebra (nothing fancy, but definitely proving everything), I would like to understand this "Identification Strategy" concept that I remember "learning" in an introductory econometrics course where I'm pretty sure no one even mentioned what was the math behind it, which I think is extremely important.

If you could be clear and didactic I would appreciate a lot.

Thank you!

**Tags:** econometrics, mathematical-economics, linear-algebra
> **Comments:**
> **username_1**: Do you want to know what the concept of identification is or the linear algebra concepts that go into econometrics? Identification strategy has nothing to do with linear algebra. What do you mean “*model the idea of Identification Strategy*”?  
> **username_0**: From Regio's answer, I think I know the direction now. Thanks.  

---

## 2 answers

### Answer by username_2 on 2020-04-28. Score: 1 | Accepted answer

In econometrics, identification can take several forms depending on the type of model you are working with (see [this survey](http://fmwww.bc.edu/EC-P/wp957.pdf) for a more comprehensive description). However, in general, identification pertains to the idea that either your econometric model or the exogenous variation in your data (or both) allows you to tease out the parameters that truly describe the data generating process.

To be more specific, suppose that you are studying outcome $y$ which depends (stochastically) on $x$ so that the data is generated according to $F(y|x)$ where $F$ is some distribution function. Then you have an econometric model that depends on a parameter, $\theta$ (this can be a vector of parameters), and for each parameter, it spells out a conditional distribution of $y$ in terms of $x$. That is your econometric model is a function $M(\theta)=G(y|x; \theta)$. We say that the model is identified if there exists a unique parameter, $\theta^\*$, in the domain of $M$ such that $M(\theta^\*)=F(y|x)$.

In reduced-form work, $M$ is assumed to be linear (or in general to be an injective function and have a relatively simple form), so ensuring identification has more to do with your data, $F$, having the right properties (mainly having enough exogenous variation).

In contrast, structural work typically deals with data that is not experimental or quasi-experimental so $M$ cannot credibly be assumed linear. Instead, you develop a rich enough model and identification requires $M$ to be invertible. If $M$ is invertible, then you have that $M^{-1}(F(y|x))=\theta^\*$.

I think that in relation with identification, linear algebra tools are mainly useful to prove the invertibility of $M$. However, it can prove also useful when it comes to designing an estimation strategy, and when implementing the estimation strategy in the computer, etc.


---

### Answer by username_3 on 2020-04-28. Score: 0

Hi: There is a book from 1966 that contains various papers on identification. It is called "Studies in Econometric Method" and it's edited by Hood and Koopmans. It looks like it assumes that one has a grasp of the necessary linear algebra. It's a cowles foundation monograph so not trivial but, atleast from that book, you could probably figure out what linear algebra concepts are necessary to understand the papers.


---

