<p><strong>extrapolation</strong> - means making predictions or estimations outside the range of your original sample.</p>
<p>For example, if you estimate relationships between calorie intake and weight to be:</p>
<p><span class="math-container">$$\hat{Y}=50+0.001X$$</span></p>
<p>Using sample where calorie intake (<span class="math-container">$X$</span>) ranges from 1000-5000 per day, and weight of individuals ranges from 40 to 120 kg, it you try to use the same model to estimate the weight of someone eating 10000 calories (that is using model above we would have <span class="math-container">$\hat{Y}=50+0.001 \cdot 10000 \implies \hat{Y}= 150$</span> that estimate 150kg for someone eating 10000 calories would be extrapolation.</p>
<p>However, do not confuse this with any prediction as trying to estimate what weight a person eating 4000 would have, is not extrapolation anymore as 4000 calories and corresponding weight of 90kg is within range of data in our sample.</p>
<p>In your example of DiD the extrapolation involves estimating potential outcomes of treated individuals from the non-treated sample.</p>
<p><strong>imputation</strong> - is replacement of missing data with substituted values.</p>
<p>For example, suppose you have data on GDP for 2011, 2012 and 2014 but you miss GDP for 2013. Instead of leaving that one observation missing you could impute the missing value for example by linear interpolation.</p>
<p>In your case above, as far as I can understand from the passage, the unobserved potential non-treated outcomes for the treated are being imputed.</p>

CC BY-SA 4.0
2021-09-30T22:17:31.327Z
Thanks a heap, @1muflon1, it is a very clear explanation in "*extrapolation*" case. I am just thinking, whether they mean that they use the extrapolate method to imputate the potential treated outcome. I mean. They initially set the potential treated outcome as missing for all. Then they use the extrapolated method to get the value for potential treated outcome after treatment (imputation)?
Nguyen Lis
CC BY-SA 4.0
2021-09-30T22:19:37.123Z
I mean, they extrapolate to imputate, is it a correct thought? So, I try to add on your last sentence "the unobserved potential non-treated outcomes for the treated are being imputed **by extrapolation method**"
Nguyen Lis
CC BY-SA 4.0
2021-10-01T12:00:47.623Z
@NguyenLis I do not have time to read their paper but just based on that exert you provided it looks like yes they extrapolate from their untreated sample to imput*e* (not imputate which is incorrect spelling) those values
1muflon1
CC BY-SA 4.0
2021-09-30T10:18:12.143Z
2021-09-30T10:18:12.143Z
1muflon1
<p>I am using an imputation estimator for Diff-in-Diff proposed by <a href="https://scholar.harvard.edu/borusyak/publications/revisiting-event-study-designs" rel="nofollow noreferrer">Borusyak, 2021</a>. The way to calculate it is</p>
<p>Estimation proceeds in three steps:</p>
<blockquote>
<ol>
<li>Estimate a model for non-treated potential outcomes using the non-treated (i.e. never-
treated or not-yet-treated) observations only.
The benchmark model for diff-in-diff designs is a two-way fixed effect
(FE) model:</li>
</ol>
</blockquote>
<blockquote>
<p>Y_it = a_i + b_t + eps_it, but
other FEs, controls, etc., are also allowed.</p>
</blockquote>
<blockquote>
<ol start="2">
<li><strong>Extrapolate</strong> the model from Step 1 to treated observations, <strong>imputing</strong> non-treated potential outcomes Y_it(0), and obtain an
estimate of the treatment effect tau_it = Y_it - Y_it(0) for each
treated observation. (See What if imputation is not
possible)</li>
</ol>
</blockquote>
<blockquote>
<ol start="3">
<li>Take averages of estimated treatment effects corresponding to the estimand of interest.</li>
</ol>
</blockquote>
<p>Even I am using it but I do not fully understand the meaning of &quot;<strong><a href="https://dictionary.cambridge.org/dictionary/english/extrapolate" rel="nofollow noreferrer">extrapolate</a></strong>&quot; and &quot;<strong><a href="https://dictionary.cambridge.org/dictionary/english/imputation" rel="nofollow noreferrer">imputation</a></strong>&quot; words even after search from the dictionary. I decided to ask here rather than in English Learner because it relates more in economic-and-finance context.
I may think that &quot;extrapolate&quot; because the author apply the coefficient of the regression on untreated for the treated to get the potential outcome of the treated if the treatment does not happen, but I totally get lost regarding the word &quot;imputation&quot;</p>
<p>Is there any intuitive way to explain these two words?</p>

<econometrics>
What do "extrapolate" and "imputation" mean?
Nguyen Lis
# What do "extrapolate" and "imputation" mean?

(Asked by: username_0 on 2021-09-30)

I am using an imputation estimator for Diff-in-Diff proposed by [Borusyak, 2021](https://scholar.harvard.edu/borusyak/publications/revisiting-event-study-designs). The way to calculate it is

Estimation proceeds in three steps:

> 1. Estimate a model for non-treated potential outcomes using the non-treated (i.e. never-
>    treated or not-yet-treated) observations only.
>    The benchmark model for diff-in-diff designs is a two-way fixed effect
>    (FE) model:

> Y\_it = a\_i + b\_t + eps\_it, but
> other FEs, controls, etc., are also allowed.

> 2. **Extrapolate** the model from Step 1 to treated observations, **imputing** non-treated potential outcomes Y\_it(0), and obtain an
>    estimate of the treatment effect tau\_it = Y\_it - Y\_it(0) for each
>    treated observation. (See What if imputation is not
>    possible)

> 3. Take averages of estimated treatment effects corresponding to the estimand of interest.

Even I am using it but I do not fully understand the meaning of "**[extrapolate](https://dictionary.cambridge.org/dictionary/english/extrapolate)**" and "**[imputation](https://dictionary.cambridge.org/dictionary/english/imputation)**" words even after search from the dictionary. I decided to ask here rather than in English Learner because it relates more in economic-and-finance context.
I may think that "extrapolate" because the author apply the coefficient of the regression on untreated for the treated to get the potential outcome of the treated if the treatment does not happen, but I totally get lost regarding the word "imputation"

Is there any intuitive way to explain these two words?

**Tags:** econometrics

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## 1 answers

### Answer by username_1 on 2021-09-30. Score: 3 | Accepted answer

**extrapolation** - means making predictions or estimations outside the range of your original sample.

For example, if you estimate relationships between calorie intake and weight to be:

$$\hat{Y}=50+0.001X$$

Using sample where calorie intake ($X$) ranges from 1000-5000 per day, and weight of individuals ranges from 40 to 120 kg, it you try to use the same model to estimate the weight of someone eating 10000 calories (that is using model above we would have $\hat{Y}=50+0.001 \cdot 10000 \implies \hat{Y}= 150$ that estimate 150kg for someone eating 10000 calories would be extrapolation.

However, do not confuse this with any prediction as trying to estimate what weight a person eating 4000 would have, is not extrapolation anymore as 4000 calories and corresponding weight of 90kg is within range of data in our sample.

In your example of DiD the extrapolation involves estimating potential outcomes of treated individuals from the non-treated sample.

**imputation** - is replacement of missing data with substituted values.

For example, suppose you have data on GDP for 2011, 2012 and 2014 but you miss GDP for 2013. Instead of leaving that one observation missing you could impute the missing value for example by linear interpolation.

In your case above, as far as I can understand from the passage, the unobserved potential non-treated outcomes for the treated are being imputed.

> **Comments:**
> **username_0**: Thanks a heap, @1muflon1, it is a very clear explanation in "*extrapolation*" case. I am just thinking, whether they mean that they use the extrapolate method to imputate the potential treated outcome. I mean. They initially set the potential treated outcome as missing for all. Then they use the extrapolated method to get the value for potential treated outcome after treatment (imputation)?  
> **username_0**: I mean, they extrapolate to imputate, is it a correct thought? So, I try to add on your last sentence "the unobserved potential non-treated outcomes for the treated are being imputed **by extrapolation method**"  
> **username_1**: @NguyenLis I do not have time to read their paper but just based on that exert you provided it looks like yes they extrapolate from their untreated sample to imput*e* (not imputate which is incorrect spelling) those values  

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