<p>The difference-in-differences “estimator” is a method used to “estimate” a target parameter of interest. That parameter is also commonly referred to as the causal “estimand” (<em>that which is to be estimated</em>), at least in econometric circles. I also see it used quite frequently in reference to “treatment effects” in applied clinical trials. In short, it’s a quantity to be estimated in a statistical model.</p>

CC BY-SA 4.0
2021-06-05T08:45:03.253Z
So, is it mostly the coefficients of  **post*treat** variable?
Phil Nguyen
CC BY-SA 4.0
2021-06-05T18:12:21.820Z
Yes. But in the interest of being precise, the causal *estimand* is the target parameter. The coefficient we obtain for the target quantity (i.e., the product term) *is* the difference-in-differences estimate. It's inappropriate to call the coefficient in your regression output your causal estimand. Rather, it's your *estimate* of the causal *estimand*. Just be mindful of this subtle difference when you're writing up your findings.
Thomas Bilach
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2021-06-06T22:34:42.247Z
Thanks Thomas, in a standard DID y = a1 + a2*post + a3*treat  +  a4*post*treat. So. in short, I may understand that **causal estimand** is **post * treat**, and **difference-in-differences estimator** is **a4**, is it correct ?
Phil Nguyen
CC BY-SA 4.0
2021-06-08T18:22:02.303Z
No. Ignore the variables for a moment. The parameter $\alpha_4$ attached to the product term is the *causal estimand*. It's something we want to *estimate*. Once we actually estimate it using software, then we call $\hat{\alpha}_4$ our difference-in-differences estimate.
Thomas Bilach
CC BY-SA 4.0
2021-06-05T07:27:14.013Z
2021-06-05T08:07:16.787Z
2021-06-05T08:07:16.787Z
Thomas Bilach
<p>In <a href="https://stats.stackexchange.com/a/527119/319998">one discussion</a>, I saw the answer containing two words that I think can be used interchangeably, but I am not sure if it's the case.</p>
<blockquote>
<p>I simply state in other posts that the &quot;generalized&quot; **difference-in-differences <strong>estimator</strong> may accommodate intermittent exposures.</p>
</blockquote>
<blockquote>
<p>Now it's important to note that the <strong>causal estimand</strong> is plausibly unbiased if we assume constant treatment effects.</p>
</blockquote>
<p>So, I want to know whether <strong>difference-in-differences estimator</strong> and <strong>causal estimand</strong> have similar meanings and are they all about the coefficient of the variable <strong><span class="math-container">$Treatment \times Post$</span></strong> in a DiD setting?</p>

CC BY-SA 4.0
2021-06-05T03:42:44.870Z
IMHO, these two words should be the same in any DID setting.
Phil Nguyen
<econometrics><definition><causal-inference>
What are the meanings of "difference-in-differences" and "causal estimand"?
Phil Nguyen
# What are the meanings of "difference-in-differences" and "causal estimand"?

(Asked by: username_0 on 2021-06-05)

In [one discussion](https://stats.stackexchange.com/a/527119/319998), I saw the answer containing two words that I think can be used interchangeably, but I am not sure if it's the case.

> I simply state in other posts that the "generalized" \*\*difference-in-differences **estimator** may accommodate intermittent exposures.

> Now it's important to note that the **causal estimand** is plausibly unbiased if we assume constant treatment effects.

So, I want to know whether **difference-in-differences estimator** and **causal estimand** have similar meanings and are they all about the coefficient of the variable **$Treatment \times Post$** in a DiD setting?

**Tags:** econometrics, definition, causal-inference
> **Comments:**
> **username_0**: IMHO, these two words should be the same in any DID setting.  

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## 1 answers

### Answer by username_1 on 2021-06-05. Score: 5 | Accepted answer

The difference-in-differences “estimator” is a method used to “estimate” a target parameter of interest. That parameter is also commonly referred to as the causal “estimand” (*that which is to be estimated*), at least in econometric circles. I also see it used quite frequently in reference to “treatment effects” in applied clinical trials. In short, it’s a quantity to be estimated in a statistical model.

> **Comments:**
> **username_0**: So, is it mostly the coefficients of  **post*treat** variable?  
> **username_1**: Yes. But in the interest of being precise, the causal *estimand* is the target parameter. The coefficient we obtain for the target quantity (i.e., the product term) *is* the difference-in-differences estimate. It's inappropriate to call the coefficient in your regression output your causal estimand. Rather, it's your *estimate* of the causal *estimand*. Just be mindful of this subtle difference when you're writing up your findings.  
> **username_0**: Thanks Thomas, in a standard DID y = a1 + a2*post + a3*treat  +  a4*post*treat. So. in short, I may understand that **causal estimand** is **post * treat**, and **difference-in-differences estimator** is **a4**, is it correct ?  
> **username_1**: No. Ignore the variables for a moment. The parameter $\alpha_4$ attached to the product term is the *causal estimand*. It's something we want to *estimate*. Once we actually estimate it using software, then we call $\hat{\alpha}_4$ our difference-in-differences estimate.  

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