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As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$

_{(I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here? Maybe I should also note it's not obvious that stronger assumptions achieve identification when weaker ones do, as stronger assumptions may lead to "inexistence" of the desired parameters when weaker ones don't.)}

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|x] = 0$ would be enough to (causally) identify $\beta$, but $E[x\epsilon] = 0$ would not be sufficient anymore.

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$

_{(I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here? Maybe I should also note that it's not obvious stronger assumptions achieve identification when weaker ones do, as stronger assumptions may lead to "inexistence" of the desired parameters when weaker ones do not.)}

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|x] = 0$ would be enough to (causally) identify $\beta$, but $E[x\epsilon] = 0$ would not be sufficient anymore.

My questions are:

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$

_{(I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here? Maybe I should also note it's not obvious that stronger assumptions achieve identification when weaker ones do, as stronger assumptions may lead to "inexistence" of the desired parameters when weaker ones don't.)}

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|X] = 0$ would be enough to (causally) identify $\beta$, but $E[X\epsilon] = 0$ would not be sufficient anymore.

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$

_{(I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here? Maybe I should also note it's not obvious that stronger assumptions achieve identification when weaker ones do, as stronger assumptions may lead to "inexistence" of the desired parameters when weaker ones don't.)}

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|x] = 0$ would be enough to (causally) identify $\beta$, but $E[x\epsilon] = 0$ would not be sufficient anymore.

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$ (I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here?).

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|X] = 0$ would be enough to (causally) identify $\beta$, but $E[X\epsilon] = 0$ would not be sufficient anymore.

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?

As others, it seems (Identification of parameters problem), I get confused about the use of the word "identification" in econometrics. It seems some people talk about "identification" in the sense described in Identification of parameters problem, i.e., a parameter vector $\theta_1$ is identified provided :

"there does not exist a different parameter vector $\theta_1$ that would induce the same data generating process, given our model specification $M$".

If I understand this correctly, it means that in a simple linear model $y = x'\beta + \epsilon$, for example, $\beta$ is identified under identification assumption $E[x\epsilon] = 0$ as well as under the stronger $E[\epsilon|x] = 0$

_{(I guess I should add $E(\epsilon^2)<\infty$ and the invertibility of $E(xx')$ as auxiliary identification assumptions here? Maybe I should also note it's not obvious that stronger assumptions achieve identification when weaker ones do, as stronger assumptions may lead to "inexistence" of the desired parameters when weaker ones don't.)}

At the same time, many people seem to talk about an "identification strategy" as a way to single out causal effects. For example, I feel like I often hear people ask "what is your identification strategy?" as a shortcut for asking "what is your strategy for convincing people that the effect you measured is causal?

In that sense, if I again understand things correctly, $E[\epsilon|X] = 0$ would be enough to (causally) identify $\beta$, but $E[X\epsilon] = 0$ would not be sufficient anymore.

• Does that seem like a fair description of econometricians' use of the term "identification"?
• Is there really such a ubiquitous ambiguity in people's use of the word "identification"?
• Or is there no ambiguity, one commonly accepted use of the term "identification", and I am the one who is missing something?