<p>No in pure time series we generally don't use fixed effects. If you have data on lets say monthly frequency you could include dummies for months in general, e.g. having February, March, April ... dummies but you would include them as a general dummies where all Februaries are part of the February dummy rather having a separate dummy for each time period.</p>
<p>You can also include dummies for time periods where you think that the period was special in some way. For example, you could include a special dummy for all crisis years. Similarly, you could include some dummies for structural breaks and so on.</p>
<p>Furthermore, dynamic OLS model is more of an umbrella term. For example, the above would hold for ARDL/Pesaran error correction model. There might be dynamic models that have further issues, it is always best to survey literature on the particular model you are actually using then just generalizing.</p>
<p>PS:</p>
<blockquote>
<p>I know that one should control for year fixed effects when you have panel data.</p>
</blockquote>
<p>This is actually not generally valid statement. Yes more often than not you want to control for year  fixed effects in panel data but not always.</p>

CC BY-SA 4.0
2020-09-03T22:10:12.507Z
2020-09-04T01:32:19.637Z
2020-09-04T01:32:19.637Z
1muflon1
<blockquote>
<p>...I know that one should control for year fixed effects when you have
panel data...</p>
</blockquote>
<p>Inserting time (e.g. seasonal) dummies in also standard for stationary time series models. If the dummies are seasonal, such a component would be called <em>additive seasonality</em>.</p>
<blockquote>
<p>Also, does it even make sense to control for year fixed effects when
the independent and main dependent variable are non-stationary, but
cointegrated?</p>
</blockquote>
<p>It's not clear from your question the context that would motivate such a model but in principle one can consider such models.</p>
<p>(Presumably, you are considering the possibility that deviation from the long-run equilibrium relationship---the stationary error term in a cointegration regression---now has seasonality or time trend.)</p>
<p>In a cointegration regression
<span class="math-container">$$
y_t = \beta x_t + \epsilon_t \quad (*)
$$</span>
where <span class="math-container">$x$</span> and <span class="math-container">$y$</span> are I(1), and <span class="math-container">$\epsilon$</span> is I(0), the OLS <span class="math-container">$\hat{\beta}$</span> is super-consistent, even when <span class="math-container">$\epsilon_t$</span> is correlated with <span class="math-container">$x_t$</span>.
So if there is additive seasonality being omitted in the model and
<span class="math-container">$\epsilon_t = D_t + \nu_t$</span>, where <span class="math-container">$D_t$</span> is seasonal dummy and <span class="math-container">$\nu_t$</span> is true error term, <span class="math-container">$\hat{\beta}$</span> remains super-consistent.</p>
<p>For testing for cointegration, however, specification may matter.
For example, the Engel-Granger test computes ADF statistic of the residuals from <span class="math-container">$(*)$</span> (but with a different the asymptotic distribution under the null than ADF).
If there is omitted seasonality, the asymptotic distribution can be different from that of Engel-Granger and their critical values may not be valid.</p>

CC BY-SA 4.0
2020-09-04T10:40:36.273Z
2020-09-04T10:40:36.273Z
Michael
<p>I am estimating a dynamic OLS model since I have variables that are non-stationary, but cointegrated. In addition, the data is a standard time-series (i.e. one observation per one time period) so technically not panel. I know that one should control for year fixed effects when you have panel data. My question is should I still control for year fixed effects even though my data technically isn't panel. Also, does it even make sense to control for year fixed effects when the independent and main dependent variable are non-stationary, but cointegrated?</p>

<econometrics><time-series>
Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables
guest123
# Year Fixed Effects in a Dynamic OLS Regression with Cointegrated Variables

(Asked by: username_0 on 2020-09-03)

I am estimating a dynamic OLS model since I have variables that are non-stationary, but cointegrated. In addition, the data is a standard time-series (i.e. one observation per one time period) so technically not panel. I know that one should control for year fixed effects when you have panel data. My question is should I still control for year fixed effects even though my data technically isn't panel. Also, does it even make sense to control for year fixed effects when the independent and main dependent variable are non-stationary, but cointegrated?

**Tags:** econometrics, time-series

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## 2 answers

### Answer by username_1 on 2020-09-03. Score: 3

No in pure time series we generally don't use fixed effects. If you have data on lets say monthly frequency you could include dummies for months in general, e.g. having February, March, April ... dummies but you would include them as a general dummies where all Februaries are part of the February dummy rather having a separate dummy for each time period.

You can also include dummies for time periods where you think that the period was special in some way. For example, you could include a special dummy for all crisis years. Similarly, you could include some dummies for structural breaks and so on.

Furthermore, dynamic OLS model is more of an umbrella term. For example, the above would hold for ARDL/Pesaran error correction model. There might be dynamic models that have further issues, it is always best to survey literature on the particular model you are actually using then just generalizing.

PS:

> I know that one should control for year fixed effects when you have panel data.

This is actually not generally valid statement. Yes more often than not you want to control for year fixed effects in panel data but not always.


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### Answer by username_2 on 2020-09-04. Score: 1

> ...I know that one should control for year fixed effects when you have
> panel data...

Inserting time (e.g. seasonal) dummies in also standard for stationary time series models. If the dummies are seasonal, such a component would be called *additive seasonality*.

> Also, does it even make sense to control for year fixed effects when
> the independent and main dependent variable are non-stationary, but
> cointegrated?

It's not clear from your question the context that would motivate such a model but in principle one can consider such models.

(Presumably, you are considering the possibility that deviation from the long-run equilibrium relationship---the stationary error term in a cointegration regression---now has seasonality or time trend.)

In a cointegration regression
$$
y\_t = \beta x\_t + \epsilon\_t \quad (\*)
$$
where $x$ and $y$ are I(1), and $\epsilon$ is I(0), the OLS $\hat{\beta}$ is super-consistent, even when $\epsilon\_t$ is correlated with $x\_t$.
So if there is additive seasonality being omitted in the model and
$\epsilon\_t = D\_t + \nu\_t$, where $D\_t$ is seasonal dummy and $\nu\_t$ is true error term, $\hat{\beta}$ remains super-consistent.

For testing for cointegration, however, specification may matter.
For example, the Engel-Granger test computes ADF statistic of the residuals from $(\*)$ (but with a different the asymptotic distribution under the null than ADF).
If there is omitted seasonality, the asymptotic distribution can be different from that of Engel-Granger and their critical values may not be valid.


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