<p>A two-way FE model is:</p>
<p><span class="math-container">$y_{it} = \beta_0 +\beta_1 x_{it} +\gamma_i + \delta_t +u_{it}$</span></p>
<p>The <span class="math-container">$\delta_t$</span> absorb average time effects, but there may still be unit-specific trends, which could be modelled with:</p>
<p><span class="math-container">$y_{it} = \beta_0 +\beta_1 x_{it} +\alpha_i t +\gamma_i + \delta_t +u_{it}$</span></p>
<p>There is not a violation of multicollinearity and it is more general than before. If instead we had a <em>general</em> time trend, rather than unit specific, it would violate multicollinearity.</p>
<p><span class="math-container">$y_{it} = \beta_0 +\beta_1 x_{it} +\alpha t +\gamma_i + \delta_t +u_{it}$</span></p>
<p>Also, there has been some literature that has cautioned against the use of individual-specific time trends because such can absorb part of a heterogeneous treatment effect. <a href="http://Meer,%20J.,%20&amp;%20West,%20J.%20(2016).%20Effects%20of%20the%20minimum%20wage%20on%20employment%20dynamics.%20Journal%20of%20Human%20Resources,%2051(2),%20500-522." rel="nofollow noreferrer">Meer and West 2016</a>.</p>

CC BY-SA 4.0
2021-09-16T09:44:16.790Z
Thank @Micheal , can I ask an example of controlling for "unit-specific trends" is unit's lag variable?
Phil Nguyen
CC BY-SA 4.0
2021-09-16T09:46:04.177Z
"general time trend" would be perfect colinear with time fixed effect, is it what you mean then? Thanks
Phil Nguyen
CC BY-SA 4.0
2021-09-16T09:59:21.170Z
Lag variable is different than time trends.  A lag variable might be as follows:
$y_{it} = \beta_0 +\beta_1 x_{it} + \beta_2 Z_{it-1} +\gamma_i +\delta_t +u_{it}
$Z$ is used generically. $Z$ could be a lagged $X$ variable, or instead a lagged outcome variable. There are issues with lagged outcome variables, and I'm guessing that's not relevant to your case.
Michael Gmeiner
CC BY-SA 4.0
2021-09-16T09:59:37.220Z
""general time trend" would be perfect colinear with time fixed effect, is it what you mean then?"  Yes.
Michael Gmeiner
CC BY-SA 4.0
2021-09-16T10:05:36.860Z
Can I ask for an example of adding a unit-specific trends if it is convenient? Thanks a heaps
Phil Nguyen
CC BY-SA 4.0
2021-09-16T10:15:59.463Z
The second equation in my answer does this. The coefficient, $\alpha_i$, differs for each individual, measuring an unit-specific time trend.
Michael Gmeiner
CC BY-SA 4.0
2021-09-16T09:04:30.987Z
2021-09-16T09:04:30.987Z
Michael Gmeiner
<p><a href="https://www.mendeley.com/catalogue/b1e55330-f605-363c-b07f-3ab67325e929/?utm_source=desktop&amp;utm_medium=1.19.8&amp;utm_campaign=open_catalog&amp;userDocumentId=%7B47d22c8f-e7ba-3ead-9833-eeae8a94d5f0%7D" rel="nofollow noreferrer">Borusyak, 2021</a> has a sentence</p>
<blockquote>
<p>While our baseline setting is for panel data with two-way fixed
effects, we show how our formal results extend naturally in a number
of ways. We allow for <strong>more general panel-type specifications that can
include, for instance, unit-specific trends or time-varying covariates</strong></p>
</blockquote>
<p>It is quite contradictory to my understanding. Because to me, when you consider &quot;two-way fixed effects&quot;, you also control for unit and period fixed effects. Why the author used the word &quot;<strong>more general panel-type specifications that can include, for instance, unit-specific trends or time-varying covariates</strong>&quot; here. I mean, the &quot;more general panel-type specifications&quot; as he described is &quot;two-way fixed effects&quot;, not &quot;more general&quot;</p>

<econometrics><nonexpert>
What is "panel-type specifications" more general than "two-way fixed effects"?
Phil Nguyen
# What is "panel-type specifications" more general than "two-way fixed effects"?

(Asked by: username_0 on 2021-09-15)

[Borusyak, 2021](https://www.mendeley.com/catalogue/b1e55330-f605-363c-b07f-3ab67325e929/?utm_source=desktop&utm_medium=1.19.8&utm_campaign=open_catalog&userDocumentId=%7B47d22c8f-e7ba-3ead-9833-eeae8a94d5f0%7D) has a sentence

> While our baseline setting is for panel data with two-way fixed
> effects, we show how our formal results extend naturally in a number
> of ways. We allow for **more general panel-type specifications that can
> include, for instance, unit-specific trends or time-varying covariates**

It is quite contradictory to my understanding. Because to me, when you consider "two-way fixed effects", you also control for unit and period fixed effects. Why the author used the word "**more general panel-type specifications that can include, for instance, unit-specific trends or time-varying covariates**" here. I mean, the "more general panel-type specifications" as he described is "two-way fixed effects", not "more general"

**Tags:** econometrics, nonexpert

---

## 1 answers

### Answer by username_1 on 2021-09-16. Score: 3 | Accepted answer

A two-way FE model is:

$y\_{it} = \beta\_0 +\beta\_1 x\_{it} +\gamma\_i + \delta\_t +u\_{it}$

The $\delta\_t$ absorb average time effects, but there may still be unit-specific trends, which could be modelled with:

$y\_{it} = \beta\_0 +\beta\_1 x\_{it} +\alpha\_i t +\gamma\_i + \delta\_t +u\_{it}$

There is not a violation of multicollinearity and it is more general than before. If instead we had a *general* time trend, rather than unit specific, it would violate multicollinearity.

$y\_{it} = \beta\_0 +\beta\_1 x\_{it} +\alpha t +\gamma\_i + \delta\_t +u\_{it}$

Also, there has been some literature that has cautioned against the use of individual-specific time trends because such can absorb part of a heterogeneous treatment effect. [Meer and West 2016](http://Meer,%20J.,%20&%20West,%20J.%20(2016).%20Effects%20of%20the%20minimum%20wage%20on%20employment%20dynamics.%20Journal%20of%20Human%20Resources,%2051(2),%20500-522.).

> **Comments:**
> **username_0**: Thank @Micheal , can I ask an example of controlling for "unit-specific trends" is unit's lag variable?  
> **username_0**: "general time trend" would be perfect colinear with time fixed effect, is it what you mean then? Thanks  
> **username_1**: Lag variable is different than time trends.  A lag variable might be as follows: $y_{it} = \beta_0 +\beta_1 x_{it} + \beta_2 Z_{it-1} +\gamma_i +\delta_t +u_{it} $Z$ is used generically. $Z$ could be a lagged $X$ variable, or instead a lagged outcome variable. There are issues with lagged outcome variables, and I'm guessing that's not relevant to your case.  
> **username_1**: ""general time trend" would be perfect colinear with time fixed effect, is it what you mean then?"  Yes.  
> **username_0**: Can I ask for an example of adding a unit-specific trends if it is convenient? Thanks a heaps  
> **username_1**: The second equation in my answer does this. The coefficient, $\alpha_i$, differs for each individual, measuring an unit-specific time trend.  

---

