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In one discussion, 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?

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  • $\begingroup$ IMHO, these two words should be the same in any DID setting. $\endgroup$
    – Phil Nguyen
    Commented Jun 5, 2021 at 3:42

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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.

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  • $\begingroup$ So, is it mostly the coefficients of post*treat variable? $\endgroup$
    – Phil Nguyen
    Commented Jun 5, 2021 at 8:45
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    $\begingroup$ 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. $\endgroup$
    – Thomas Bilach
    Commented Jun 5, 2021 at 18:12
  • $\begingroup$ 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 ? $\endgroup$
    – Phil Nguyen
    Commented Jun 6, 2021 at 22:34
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    $\begingroup$ 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. $\endgroup$
    – Thomas Bilach
    Commented Jun 8, 2021 at 18:22

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