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The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV herehere.

In one approach, the Stata command would be something like

reg y i.a##i.b##i.c controls, vce(cluster clustvarname)

$c_i$ is unobserved heterogeneity of the observational unit, while $\lambda_t$ is unobserved heterogeneity of time. In the basic two-period model, $\lambda_t$ is a binary variable, but in a multi period environment, you have the ability to more flexibly model time. You would also have a third aspect of unobserved heterogeneity. These (the main effects) can be modeled by adding fixed effects, but for a DDD, you will also need to model the interaction (second order) effects and of course include a term for your triple interaction (the variable of interest).

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

In one approach, the Stata command would be something like

reg y i.a##i.b##i.c controls, vce(cluster clustvarname)

$c_i$ is unobserved heterogeneity of the observational unit, while $\lambda_t$ is unobserved heterogeneity of time. In the basic two-period model, $\lambda_t$ is a binary variable, but in a multi period environment, you have the ability to more flexibly model time. You would also have a third aspect of unobserved heterogeneity. These (the main effects) can be modeled by adding fixed effects, but for a DDD, you will also need to model the interaction (second order) effects and of course include a term for your triple interaction (the variable of interest).

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

In one approach, the Stata command would be something like

reg y i.a##i.b##i.c controls, vce(cluster clustvarname)

$c_i$ is unobserved heterogeneity of the observational unit, while $\lambda_t$ is unobserved heterogeneity of time. In the basic two-period model, $\lambda_t$ is a binary variable, but in a multi period environment, you have the ability to more flexibly model time. You would also have a third aspect of unobserved heterogeneity. These (the main effects) can be modeled by adding fixed effects, but for a DDD, you will also need to model the interaction (second order) effects and of course include a term for your triple interaction (the variable of interest).

3 added 690 characters in body
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The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

In one approach, the Stata command would be something like

reg y i.a##i.b##i.c controls, vce(cluster clustvarname)

$c_i$ is unobserved heterogeneity of the observational unit, while $\lambda_t$ is unobserved heterogeneity of time. In the basic two-period model, $\lambda_t$ is a binary variable, but in a multi period environment, you have the ability to more flexibly model time. You would also have a third aspect of unobserved heterogeneity. These (the main effects) can be modeled by adding fixed effects, but for a DDD, you will also need to model the interaction (second order) effects and of course include a term for your triple interaction (the variable of interest).

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

In one approach, the Stata command would be something like

reg y i.a##i.b##i.c controls, vce(cluster clustvarname)

$c_i$ is unobserved heterogeneity of the observational unit, while $\lambda_t$ is unobserved heterogeneity of time. In the basic two-period model, $\lambda_t$ is a binary variable, but in a multi period environment, you have the ability to more flexibly model time. You would also have a third aspect of unobserved heterogeneity. These (the main effects) can be modeled by adding fixed effects, but for a DDD, you will also need to model the interaction (second order) effects and of course include a term for your triple interaction (the variable of interest).

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The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + \delta_t +controls + \epsilon$$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, $\delta_t$ are the year dummies, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + \delta_t +controls + \epsilon$

where $\alpha$ is the intercept, $\delta_t$ are the year dummies, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

The DDD formula is slightly different than both of those. It is

$Y = \alpha + a + b + c + a*b + a*c + b*c + a*b*c + controls + \epsilon$

where $\alpha$ is the intercept, and $\epsilon$ is the is the error term.

That is, you also have to include the main effects, $a$, $b$, and $c$. Assuming you are examining a single event that occurs at a point in time, one of these three main effects could be modeled by year dummies. See equation 1.3 on page 2 of the Wooldridge Imbens lecture and a related post on CV here.

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