<p>Let’s say we have a certain DGP <span class="math-container">$y=c+ax+bz+ error$</span>. I take this to mean that conditional on the values of <span class="math-container">$x$</span> and <span class="math-container">$z$</span> in a certain instance (and no additional information )the expected value of <span class="math-container">$y$</span> can be inferred by plugging the values into the above equation. Now let’s say <span class="math-container">$x$</span> and <span class="math-container">$z$</span> are correlated. A different DGP may now be <span class="math-container">$y=d+mx+error$</span> where m may be higher(or lower) than <span class="math-container">$a$</span> due to the correlation of <span class="math-container">$x$</span> and <span class="math-container">$z$</span>. Now wouldn’t <span class="math-container">$y=d+mx+error$</span> also be a valid DGP given that the expected value of <span class="math-container">$y$</span> conditional on <span class="math-container">$x$</span> (and no other information) is given correctly?</p>

CC BY-SA 4.0
2019-12-29T03:13:06.953Z
the DGP refers to the true process which generates the data. It is different from a model of the data. So it doesn't really make sense to talk about validity in terms of the DGP since the DGP is the truth. Once you have the DGP then you can think about models that try to describe that DGP and whether they are useful or not.
Andrew M
CC BY-SA 4.0
2019-12-29T03:22:52.453Z
It does not make sense to compare two different DGP's since they are referring to two completely different realities. On the other hand for a given DGP you can consider many different models and discuss whether they are valid or not so if y=c+ax+bz+e is the DGP then a model could be y=d+mx+error. Note then with your model you will not be able to recover the "true" DGP parameters of c and a unless b=0 or using other methods (i.e. instrumental variables etc).
Andrew M
CC BY-SA 4.0
2020-01-22T04:37:02.207Z
@afreelunch I used the quotes because it was meant that the truth depends on how we define it. What we say is the true process in one setting may not be the true process in another. I was trying to highlight that fact. Was not trying to fudge anything.
Andrew M
<econometrics>
What defines a data generating process
robot112
# What defines a data generating process

(Asked by: username_0 on 2019-12-28)

Let’s say we have a certain DGP $y=c+ax+bz+ error$. I take this to mean that conditional on the values of $x$ and $z$ in a certain instance (and no additional information )the expected value of $y$ can be inferred by plugging the values into the above equation. Now let’s say $x$ and $z$ are correlated. A different DGP may now be $y=d+mx+error$ where m may be higher(or lower) than $a$ due to the correlation of $x$ and $z$. Now wouldn’t $y=d+mx+error$ also be a valid DGP given that the expected value of $y$ conditional on $x$ (and no other information) is given correctly?

**Tags:** econometrics
> **Comments:**
> **username_1**: the DGP refers to the true process which generates the data. It is different from a model of the data. So it doesn't really make sense to talk about validity in terms of the DGP since the DGP is the truth. Once you have the DGP then you can think about models that try to describe that DGP and whether they are useful or not.  
> **username_1**: It does not make sense to compare two different DGP's since they are referring to two completely different realities. On the other hand for a given DGP you can consider many different models and discuss whether they are valid or not so if y=c+ax+bz+e is the DGP then a model could be y=d+mx+error. Note then with your model you will not be able to recover the "true" DGP parameters of c and a unless b=0 or using other methods (i.e. instrumental variables etc).  
> **username_1**: @afreelunch I used the quotes because it was meant that the truth depends on how we define it. What we say is the true process in one setting may not be the true process in another. I was trying to highlight that fact. Was not trying to fudge anything.  

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