<p>Given that you have one value for this <span class="math-container">$M/N$</span> allocation variable per individual, it can be considered a time-invariant explanatory variable.  If you estimate this model without including individual fixed effects (which control for all unobserved time-invariant differences between individuals), you will be estimating a pooled cross-section regression, which will allow you to get an estimate of <span class="math-container">$a_{1}$</span> but which will ignore the panel dimension of your data.  As a result, the estimate of this coefficient and all other coefficients will be based on the assumption that the model applies in the same manner to every individual (individuals are not unique) and that there are no effects across time.  (You could include dummy variables for each year in the model and do a joint test on those dummies to see if the assumption about the effect of time is valid, though you would not be able to include any other variables that vary only over time.)</p>

<p>If you, however, wanted to estimate a fixed effects model because you thought that there are unique attributes of individuals that do not vary across time (in other words, you thought that outcomes of the same individual were correlated in different periods), you would not be able to use this kind of time-invariant explanatory variable in the model.  This is because in a fixed effects model, coefficients are identified using only variation over time within each individual.  So if a variable varies only across individuals, but not over time, then its effects cannot be identified at all in a fixed-effects model.</p>

CC BY-SA 4.0
2019-05-24T00:44:09.450Z
2019-05-24T00:44:09.450Z
AlexK
<p>I run the following function:
<span class="math-container">$$Y_{it} = a_0+a_1*X_{it}+K*a_3+\epsilon_{it}$$</span></p>

<p>where <span class="math-container">$X_{it}=M_{it}/N_{it}$</span> is a generated variable. I got data <span class="math-container">$Y_{it}$</span> for the period from 2010 to 2015. Due to data unavailable , I just got data <span class="math-container">$M_{it}$</span> and <span class="math-container">$N_{it}$</span>(two resources) in 2010, <span class="math-container">$K$</span> is other control variables.</p>

<p>Actually, I run this
<span class="math-container">$$Y_{i2010-2015} = a_0+a_1* M_{i2010}/N_{i2010} +K*a_3+\epsilon_{it}$$</span></p>

<p>Is there any problem to run this model? Can I use coefficient <span class="math-container">$a_1$</span> to explain the allocation of resources?</p>

CC BY-SA 4.0
2019-05-24T01:35:43.840Z
My answer below assumes that you have multiple observations of $Y$ per individual (one per $t$ year).  I am now not sure what your $Y_{i2010-2015}$ notation means.  Does it mean you have one combined $Y$ value per individual only?
AlexK
CC BY-SA 4.0
2019-05-24T01:39:35.083Z
@AlexK it is multiple observations of $Y_{it}$ per individual .
XJ.C
<econometrics>
ratio independent time-invariant variable
XJ.C
# ratio independent time-invariant variable

(Asked by: username_0 on 2019-05-23)

I run the following function:
$$Y\_{it} = a\_0+a\_1\*X\_{it}+K\*a\_3+\epsilon\_{it}$$

where $X\_{it}=M\_{it}/N\_{it}$ is a generated variable. I got data $Y\_{it}$ for the period from 2010 to 2015. Due to data unavailable , I just got data $M\_{it}$ and $N\_{it}$(two resources) in 2010, $K$ is other control variables.

Actually, I run this
$$Y\_{i2010-2015} = a\_0+a\_1\* M\_{i2010}/N\_{i2010} +K\*a\_3+\epsilon\_{it}$$

Is there any problem to run this model? Can I use coefficient $a\_1$ to explain the allocation of resources?

**Tags:** econometrics
> **Comments:**
> **username_1**: My answer below assumes that you have multiple observations of $Y$ per individual (one per $t$ year).  I am now not sure what your $Y_{i2010-2015}$ notation means.  Does it mean you have one combined $Y$ value per individual only?  
> **username_0**: @AlexK it is multiple observations of $Y_{it}$ per individual .  

---

## 1 answers

### Answer by username_1 on 2019-05-24. Score: 1 | Accepted answer

Given that you have one value for this $M/N$ allocation variable per individual, it can be considered a time-invariant explanatory variable. If you estimate this model without including individual fixed effects (which control for all unobserved time-invariant differences between individuals), you will be estimating a pooled cross-section regression, which will allow you to get an estimate of $a\_{1}$ but which will ignore the panel dimension of your data. As a result, the estimate of this coefficient and all other coefficients will be based on the assumption that the model applies in the same manner to every individual (individuals are not unique) and that there are no effects across time. (You could include dummy variables for each year in the model and do a joint test on those dummies to see if the assumption about the effect of time is valid, though you would not be able to include any other variables that vary only over time.)

If you, however, wanted to estimate a fixed effects model because you thought that there are unique attributes of individuals that do not vary across time (in other words, you thought that outcomes of the same individual were correlated in different periods), you would not be able to use this kind of time-invariant explanatory variable in the model. This is because in a fixed effects model, coefficients are identified using only variation over time within each individual. So if a variable varies only across individuals, but not over time, then its effects cannot be identified at all in a fixed-effects model.


---

