<p>Unmeasured covariate is simply some omitted variable.  For example, suppose that the true model that explains wages is given by:</p>
<p><span class="math-container">$$w_i = \beta_0 + \beta_1 E_i + \beta_2 A_i + e_i$$</span></p>
<p>where <span class="math-container">$w_i$</span> is wage, <span class="math-container">$E_i$</span> your education and <span class="math-container">$A_i$</span> innate ability or talent.</p>
<p>Unfortunately in real life we have no statistics about talent/ability of an individual. Consequently in real life we can only estimate the following regression:</p>
<p><span class="math-container">$$w_i = \beta_0 + \beta_1 E_i +e_i$$</span></p>
<p>However, the model above suffers from omitted variable bias (e.g. problem of having unmeasurable covariates see discussion in Verbeek Guide to Modern Econometrics pp 55).</p>
<p>The Diff-in-Diff solves this issue because as explained in the previous question you asked <a href="https://economics.stackexchange.com/questions/44278/how-to-clarify-the-description-of-common-trend-assumption-description-in-a-paper">here</a>, even if the outcome is different due to unobserved variable between groups or individuals, you can argue that you can get treatment effect from observing change in trend between treatment and control. This controls for any time invariant unobservable, like for example innate ability or IQ between groups because the differences in these time invariant unobservable is already reflected in difference in outcomes, but it should not affect trend after intervention, since for example if your level of ability grants you \$1000 extra dollars in your monthly wage, it should do so before and after some intervention and so any increase in your wage above what would be given by the trend (for which you use control group) can be argued to be attributed to the intervention.</p>

CC BY-SA 4.0
2021-06-02T23:51:57.937Z
Thanks @1muflon1. Of my curiousity, what does $R_i$ stands for in your second equation, I mean, which variable it is in theory or applied model.
Phil Nguyen
CC BY-SA 4.0
2021-06-03T00:01:05.103Z
@Knowledge-chaser sorry that was a typo it was supposed to be E_i, R is next key right of E I accidentally must have hit it - I already corrected the text
1muflon1
CC BY-SA 4.0
2021-06-03T00:54:25.437Z
And the very last point is "*This controls for any time invariant unobservable, like for example innate ability or IQ between groups because the differences in these time invariant unobservable is already reflected in difference in outcomes*". I assume outcome is dependent variable, so you mean that all differences in time invariant unobservable reflected in error term (normally epsilon) would be reflected already in the value of dependent variable?
Phil Nguyen
CC BY-SA 4.0
2021-06-03T00:58:11.397Z
And can I simplify the sentence of the author "**The DID design is meant to control for these unmeasured confounders even though the underlying variables are not measured explicitly**" to "**The DID is meant to control for omitted variables even though these variables are still in error terms**" ?
Phil Nguyen
CC BY-SA 4.0
2021-06-03T01:27:42.827Z
@Knowledge-chaser 1. in response to the first question, yes by outcomes I mean dependent variable. 2. No, the second sentence would not be correct. There are different ways how DiD can be specified a popular one is via fixed effects. If you use fixed effects specifications the unobservable are captured by fixed effects, fixed effects regression would look like this  $w_{it}=β_i+β_1E_{it}+e_{it}$, note now each panel member will have its own intercept and it is this 'individualized intercept' (in proper terminology fixed effect) that captures the effect of unobservables not error term
1muflon1
CC BY-SA 4.0
2021-06-03T01:28:01.970Z
if the unobservables would still in error term there would still be bias
1muflon1
CC BY-SA 4.0
2021-06-02T11:12:12.273Z
2021-06-03T00:00:28.613Z
2021-06-03T00:00:28.613Z
1muflon1
<p>When reading a DID paper, I faced a common phrase &quot;<strong>unmeasured covariates</strong>&quot;, for example</p>
<blockquote>
<p>In a similar manner, the coefficient on <span class="math-container">$P_t$</span> captures the combined
effects of any <strong>unmeasured covariates</strong> that change between the two
periods but affect outcomes the same way in both groups</p>
</blockquote>
<p>or</p>
<blockquote>
<p>A key point is that the group effects and time trends stem from
underlying differences in <strong>unmeasured covariates</strong> across groups and time
periods. The DID design is meant to control for these unmeasured
confounders even though the underlying variables are not measured
explicitly</p>
</blockquote>
<p>I cannot fully understand these sentence due to the lack of understanding &quot;<strong>unmeasured covariates</strong>&quot; phrase</p>

<nonexpert>
Is there any simple explanation or alternative word for "unmeasured covariates"?
Phil Nguyen
# Is there any simple explanation or alternative word for "unmeasured covariates"?

(Asked by: username_0 on 2021-06-02)

When reading a DID paper, I faced a common phrase "**unmeasured covariates**", for example

> In a similar manner, the coefficient on $P\_t$ captures the combined
> effects of any **unmeasured covariates** that change between the two
> periods but affect outcomes the same way in both groups

or

> A key point is that the group effects and time trends stem from
> underlying differences in **unmeasured covariates** across groups and time
> periods. The DID design is meant to control for these unmeasured
> confounders even though the underlying variables are not measured
> explicitly

I cannot fully understand these sentence due to the lack of understanding "**unmeasured covariates**" phrase

**Tags:** nonexpert


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## 1 answers

### Answer by username_1 on 2021-06-02. Score: 2 | Accepted answer

Unmeasured covariate is simply some omitted variable. For example, suppose that the true model that explains wages is given by:

$$w\_i = \beta\_0 + \beta\_1 E\_i + \beta\_2 A\_i + e\_i$$

where $w\_i$ is wage, $E\_i$ your education and $A\_i$ innate ability or talent.

Unfortunately in real life we have no statistics about talent/ability of an individual. Consequently in real life we can only estimate the following regression:

$$w\_i = \beta\_0 + \beta\_1 E\_i +e\_i$$

However, the model above suffers from omitted variable bias (e.g. problem of having unmeasurable covariates see discussion in Verbeek Guide to Modern Econometrics pp 55).

The Diff-in-Diff solves this issue because as explained in the previous question you asked [here](https://economics.stackexchange.com/questions/44278/how-to-clarify-the-description-of-common-trend-assumption-description-in-a-paper), even if the outcome is different due to unobserved variable between groups or individuals, you can argue that you can get treatment effect from observing change in trend between treatment and control. This controls for any time invariant unobservable, like for example innate ability or IQ between groups because the differences in these time invariant unobservable is already reflected in difference in outcomes, but it should not affect trend after intervention, since for example if your level of ability grants you \$1000 extra dollars in your monthly wage, it should do so before and after some intervention and so any increase in your wage above what would be given by the trend (for which you use control group) can be argued to be attributed to the intervention.

> **Comments:**
> **username_0**: Thanks @username_1. Of my curiousity, what does $R_i$ stands for in your second equation, I mean, which variable it is in theory or applied model.  
> **username_1**: @Knowledge-chaser sorry that was a typo it was supposed to be E_i, R is next key right of E I accidentally must have hit it - I already corrected the text  
> **username_0**: And the very last point is "*This controls for any time invariant unobservable, like for example innate ability or IQ between groups because the differences in these time invariant unobservable is already reflected in difference in outcomes*". I assume outcome is dependent variable, so you mean that all differences in time invariant unobservable reflected in error term (normally epsilon) would be reflected already in the value of dependent variable?  
> **username_0**: And can I simplify the sentence of the author "**The DID design is meant to control for these unmeasured confounders even though the underlying variables are not measured explicitly**" to "**The DID is meant to control for omitted variables even though these variables are still in error terms**" ?  
> **username_1**: @Knowledge-chaser 1. in response to the first question, yes by outcomes I mean dependent variable. 2. No, the second sentence would not be correct. There are different ways how DiD can be specified a popular one is via fixed effects. If you use fixed effects specifications the unobservable are captured by fixed effects, fixed effects regression would look like this  $w_{it}=β_i+β_1E_{it}+e_{it}$, note now each panel member will have its own intercept and it is this 'individualized intercept' (in proper terminology fixed effect) that captures the effect of unobservables not error term  
> **username_1**: if the unobservables would still in error term there would still be bias  

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