<p>Your model has <span class="math-container">$\beta_3 * t$</span>, which is a <em>linear</em> time trend, not time dummies. If that's correct, you are controlling for only a linear trend. Because oil prices do not have a <em>perfect</em> linear trend, you can include them.</p>
<p>But I am not sure you really want the linear trend specification instead of time dummies (say, <span class="math-container">$\beta_{3t}$</span>). For a model with common time effects (year dummies), time series variables are not allowed due to perfect collinearity. Thus, if the time series variables are the key variables, you have a trouble. But if you only want to control for them, you can just omit them because any common time effects will be eliminated by the time dummies.</p>
<p>Country-pair fixed effects are similar. You cannot use time-invariant variables if those fixed effects are included.</p>
<p>One possible solution is to take the correlated random effects approach, but there is the issue of RE <span class="math-container">$\ne$</span> FE. You will have to defend your RE model. That's a different issue.</p>

CC BY-SA 4.0
2021-02-27T02:13:35.687Z
2021-02-27T02:13:35.687Z
chan1142
<p>I'm estimating this equation for the trade flows between various countries at time t: (<span class="math-container">$i$</span> and <span class="math-container">$j$</span> are countries)</p>
<p><a href="https://i.sstatic.net/D9Dc5.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/D9Dc5.png" alt="enter image description here" /></a></p>
<p>The last 3 terms are control variables, one of which is <strong>oil prices</strong>. Can I add oil prices as a control variable if I already have a time fixed effects term, <span class="math-container">$ \beta_3 $</span>. Further, can I have country pair fixed effects, <span class="math-container">$\beta_6$</span>, when I'm also controlling for variables that are fixed for two countries across time (for example, if the two countries were in a colonial relationship in the past, this variable wouldn't change with time and would stay fixed for the two countries for the entire period).</p>

CC BY-SA 4.0
2021-02-27T10:13:04.227Z
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1muflon1
<international-trade><paneldata>
Can I add a variable that varies only with time in Least Squares Regression model with a time-fixed effects term?
Karthik
# Can I add a variable that varies only with time in Least Squares Regression model with a time-fixed effects term?

(Asked by: username_0 on 2021-02-26)

I'm estimating this equation for the trade flows between various countries at time t: ($i$ and $j$ are countries)

[![enter image description here](https://i.sstatic.net/D9Dc5.png)](https://i.sstatic.net/D9Dc5.png)

The last 3 terms are control variables, one of which is **oil prices**. Can I add oil prices as a control variable if I already have a time fixed effects term, $ \beta\_3 $. Further, can I have country pair fixed effects, $\beta\_6$, when I'm also controlling for variables that are fixed for two countries across time (for example, if the two countries were in a colonial relationship in the past, this variable wouldn't change with time and would stay fixed for the two countries for the entire period).

**Tags:** international-trade, paneldata
> **Comments:**
> **username_1**: Welcome to Economics:SE. Thank you for your question; please consider revising it to be more in line with our community expectations. Like many other stacks, [we expect questions to provide evidence of prior research](https://economics.stackexchange.com/help/how-to-ask). That helps us to understand the question, and avoids our repeating work you've already done. Our [help center](https://economics.stackexchange.com/help), and [other stacks](https://interpersonal.meta.stackexchange.com/questions/3224/how-do-i-write-a-good-question) provide additional resources to assist with revisions.  

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## 1 answers

### Answer by username_2 on 2021-02-27. Score: 3

Your model has $\beta\_3 \* t$, which is a *linear* time trend, not time dummies. If that's correct, you are controlling for only a linear trend. Because oil prices do not have a *perfect* linear trend, you can include them.

But I am not sure you really want the linear trend specification instead of time dummies (say, $\beta\_{3t}$). For a model with common time effects (year dummies), time series variables are not allowed due to perfect collinearity. Thus, if the time series variables are the key variables, you have a trouble. But if you only want to control for them, you can just omit them because any common time effects will be eliminated by the time dummies.

Country-pair fixed effects are similar. You cannot use time-invariant variables if those fixed effects are included.

One possible solution is to take the correlated random effects approach, but there is the issue of RE $\ne$ FE. You will have to defend your RE model. That's a different issue.


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