<p>The first model you presented is for a case where the <em>treatment</em> is applied, the <em>effect</em> occurs, and then no further effects from the treatment are observed.</p>
<p>The second model imagines that the treatment could be preceded by some sort of anticipation effect (such as investors anticipating that the Fed will change interest rates). The maximum number of periods this anticipation could take before the treatment occurs is L (leads). Similarly, some effects could be delayed (some investors didn't check the newspaper until the following week). These delayed effects can occur up until K periods later (lags).</p>
<p>Empirical work in my area tends to recognize that lags and leads are plausibly relevant, and in the case that the first model is true and there are no confounding dynamics, all the lags and leads should be zero.  However, in practice there seems to often be some significance to these lags and leads even if the circumstances seem to suggest an event best described by the first model.</p>

CC BY-SA 4.0
2021-07-12T16:28:44.073Z
2021-07-19T15:36:17.803Z
2021-07-19T15:36:17.803Z
RegressForward
<p>When reading about the Difference-in-Differences for multiple groups and time periods, I see a term called &quot;<strong>static or dynamic/event-study</strong>&quot;. Can you help me to distinguish these two settings intuitively? I tried to google but I cannot find any intuitive answer.</p>
<p><strong>Static</strong> event study</p>
<p><span class="math-container">$\begin{equation}
  y_{it} = \mu_i + \mu_t + \tau D_{it} + \varepsilon_{it},
\end{equation}$</span>         (1)</p>
<p>where <span class="math-container">$\mu_i$</span> are unit fixed effects, <span class="math-container">$\mu_t$</span> are time fixed effects, and <span class="math-container">$D_{it}$</span> is an indicator for receiving treatment.</p>
<p><strong>Dynamic</strong> event study</p>
<p><span class="math-container">$\begin{equation}
y_{it} = \mu_i + \mu_t + \sum_{k = -L}^{-2} \tau^k D_{it}^k + \sum_{k = 1}^{K} \tau^k D_{it}^k + \varepsilon_{it},
\end{equation}$</span>                 (2)</p>
<p>where <span class="math-container">$D_{it}^k$</span> are lag/leads of treatment (k periods from initial treatment date).
Side question: what does L mean in the second equation?</p>
<p><a href="https://kylebutts.com/did2s/articles/Two-Stage-Difference-in-Differences.html" rel="nofollow noreferrer">Reference</a> updated</p>

CC BY-SA 4.0
2021-07-07T12:59:15.307Z
Can you please add links to sources where you read that?
1muflon1
CC BY-SA 4.0
2021-07-08T05:15:38.467Z
Thank you so much 1muflon1, I updated the reference
Phil Nguyen
<econometrics>
What are the dynamic and static event-study?
Phil Nguyen
# What are the dynamic and static event-study?

(Asked by: username_0 on 2021-07-07)

When reading about the Difference-in-Differences for multiple groups and time periods, I see a term called "**static or dynamic/event-study**". Can you help me to distinguish these two settings intuitively? I tried to google but I cannot find any intuitive answer.

**Static** event study

$\begin{equation}
y\_{it} = \mu\_i + \mu\_t + \tau D\_{it} + \varepsilon\_{it},
\end{equation}$ (1)

where $\mu\_i$ are unit fixed effects, $\mu\_t$ are time fixed effects, and $D\_{it}$ is an indicator for receiving treatment.

**Dynamic** event study

$\begin{equation}
y\_{it} = \mu\_i + \mu\_t + \sum\_{k = -L}^{-2} \tau^k D\_{it}^k + \sum\_{k = 1}^{K} \tau^k D\_{it}^k + \varepsilon\_{it},
\end{equation}$ (2)

where $D\_{it}^k$ are lag/leads of treatment (k periods from initial treatment date).
Side question: what does L mean in the second equation?

[Reference](https://kylebutts.com/did2s/articles/Two-Stage-Difference-in-Differences.html) updated

**Tags:** econometrics
> **Comments:**
> **username_1**: Can you please add links to sources where you read that?  
> **username_0**: Thank you so much 1muflon1, I updated the reference  

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## 1 answers

### Answer by username_2 on 2021-07-12. Score: 3 | Accepted answer

The first model you presented is for a case where the *treatment* is applied, the *effect* occurs, and then no further effects from the treatment are observed.

The second model imagines that the treatment could be preceded by some sort of anticipation effect (such as investors anticipating that the Fed will change interest rates). The maximum number of periods this anticipation could take before the treatment occurs is L (leads). Similarly, some effects could be delayed (some investors didn't check the newspaper until the following week). These delayed effects can occur up until K periods later (lags).

Empirical work in my area tends to recognize that lags and leads are plausibly relevant, and in the case that the first model is true and there are no confounding dynamics, all the lags and leads should be zero. However, in practice there seems to often be some significance to these lags and leads even if the circumstances seem to suggest an event best described by the first model.


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