<p><a href="https://doi.org/10.1080/10691898.2020.1807429" rel="nofollow noreferrer">This paper</a> uses a differece-in-differences (DID) approach to assess the effect of adding quizzes and assignments on exam grades. The data come from 3 different sections that one of the authors taught, with the following characteristics:</p>
<ul>
<li>Section 1: no quizzes or assignments</li>
<li>Section 2: assignments only</li>
<li>Section 3: quizzes only</li>
</ul>
<p>They do separate DIDs: first they compare Section 2 to Section 1, then Section 3 to Section 1. They fit the model (directly copied from the paper):</p>
<p><span class="math-container">$$
O_{it} = \beta_0 + \beta_1T + \beta_2A + \beta_3A\times T+\beta_4X_{it}+\epsilon_{it}
$$</span></p>
<p>where <span class="math-container">$O_{it}$</span> is the outcome measure (exam score) for <span class="math-container">$i^{th}$</span> student in period <span class="math-container">$t$</span>, <span class="math-container">$T$</span> and <span class="math-container">$A$</span> are indicators for the treated group and <span class="math-container">$X_{it}$</span> is a vector of covariates: gender, student residency status (i.e., domestic vs. international), and GPA. As best as I can tell from their Section 2.3, the study is a panel DID: the same students in each section are measured for midterm 1 and midterm 2.</p>
<p>I don't get how these covariates can be used in this DID. None are time-varying, so aren't they all just part of a student fixed effect that should get removed with differencing?</p>

CC BY-SA 4.0
2023-06-13T00:00:46.640Z
Thanks for the interesting paper. The paper says that $T$ is the period dummy so it should be OK. Also, there are no student fixed effects so $X_{it}$ should be fine.
chan1142
CC BY-SA 4.0
2023-06-14T02:38:21.400Z
Why would GPA, gender, and residency not be fixed effects?
sams
CC BY-SA 4.0
2023-06-15T04:40:27.310Z
That's about what we mean by "fixed effects". Econometricians mean by "fixed effects" unobservable student effects possibly correlated with other covariates ($X_{it}$), and that's what I meant. Please let me change the wording to "there are no student dummies" from "there are no student fixed effects".
chan1142
CC BY-SA 4.0
2023-06-16T12:46:58.150Z
In the study, if it's being conducted the way I'm understanding it, its the same students being compared in both time periods that occur within the same semester. GPA, gender, and student resident status aren't changing in that semester, so don't they all get absorbed into a student-level fixed effect that ends up being differenced out when estimating the model?
sams
CC BY-SA 4.0
2023-06-18T01:03:15.667Z
The data set is a panel data set, but the model has no student-level fixed effect on the right-hand side. What do you mean by "they all get absorbed into a student-level fixed effect"? It's a pooled OLS, not an FE regression.
chan1142
CC BY-SA 4.0
2023-06-19T02:32:55.200Z
GPA is one of the X_{it} covariates. Presumably, GPA doesn't vary by time in this study because it's the same students within each class measured before and after. Why is it included in the analysis?
sams
CC BY-SA 4.0
2023-06-19T11:14:17.810Z
For example, supppse we used the first difference estimator (https://en.m.wikipedia.org/wiki/First-difference_estimator). Wouldn't all the \delta GPA  values then be 0?
sams
CC BY-SA 4.0
2023-06-20T05:49:55.123Z
Now I think I understand your concern. Regarding "why is it included in the analysis?", I think time-invariant controls are unnecessary. They do not change the DID results, and they do no harm, either. That's for balanced panel data. I'm interested in what happens for unbalanced panel data.
chan1142
<paneldata><fixed-effects><difference-in-difference>
Individual level covariates used in this difference-in-difference paper: a mistake?
sams
# Individual level covariates used in this difference-in-difference paper: a mistake?

(Asked by: username_0 on 2023-06-12)

[This paper](https://doi.org/10.1080/10691898.2020.1807429) uses a differece-in-differences (DID) approach to assess the effect of adding quizzes and assignments on exam grades. The data come from 3 different sections that one of the authors taught, with the following characteristics:

* Section 1: no quizzes or assignments
* Section 2: assignments only
* Section 3: quizzes only

They do separate DIDs: first they compare Section 2 to Section 1, then Section 3 to Section 1. They fit the model (directly copied from the paper):

$$
O\_{it} = \beta\_0 + \beta\_1T + \beta\_2A + \beta\_3A\times T+\beta\_4X\_{it}+\epsilon\_{it}
$$

where $O\_{it}$ is the outcome measure (exam score) for $i^{th}$ student in period $t$, $T$ and $A$ are indicators for the treated group and $X\_{it}$ is a vector of covariates: gender, student residency status (i.e., domestic vs. international), and GPA. As best as I can tell from their Section 2.3, the study is a panel DID: the same students in each section are measured for midterm 1 and midterm 2.

I don't get how these covariates can be used in this DID. None are time-varying, so aren't they all just part of a student fixed effect that should get removed with differencing?

**Tags:** paneldata, fixed-effects, difference-in-difference

> **Comments:**
> **username_1**: Thanks for the interesting paper. The paper says that $T$ is the period dummy so it should be OK. Also, there are no student fixed effects so $X_{it}$ should be fine.  
> **username_0**: Why would GPA, gender, and residency not be fixed effects?  
> **username_1**: That's about what we mean by "fixed effects". Econometricians mean by "fixed effects" unobservable student effects possibly correlated with other covariates ($X_{it}$), and that's what I meant. Please let me change the wording to "there are no student dummies" from "there are no student fixed effects".  
> **username_0**: In the study, if it's being conducted the way I'm understanding it, its the same students being compared in both time periods that occur within the same semester. GPA, gender, and student resident status aren't changing in that semester, so don't they all get absorbed into a student-level fixed effect that ends up being differenced out when estimating the model?  
> **username_1**: The data set is a panel data set, but the model has no student-level fixed effect on the right-hand side. What do you mean by "they all get absorbed into a student-level fixed effect"? It's a pooled OLS, not an FE regression.  
> **username_0**: GPA is one of the X_{it} covariates. Presumably, GPA doesn't vary by time in this study because it's the same students within each class measured before and after. Why is it included in the analysis?  
> **username_0**: For example, supppse we used the first difference estimator (https://en.m.wikipedia.org/wiki/First-difference_estimator). Wouldn't all the \delta GPA  values then be 0?  
> **username_1**: Now I think I understand your concern. Regarding "why is it included in the analysis?", I think time-invariant controls are unnecessary. They do not change the DID results, and they do no harm, either. That's for balanced panel data. I'm interested in what happens for unbalanced panel data.  

---

## 0 answers

