<p>In a simple OLS regression we calculate the estimator Beta by dividing the covariance of x and y by the variance of x. </p>

<p>How do we calculate the estimator Beta if we regress the mean of a variable (at time t) on the mean of its lagged variable (at time t-1) ?:</p>

<p><a href="https://i.sstatic.net/1T7GH.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1T7GH.png" alt="OLS regression of mean of y on the mean of y lag"></a></p>

CC BY-SA 4.0
2019-03-25T14:30:01.717Z
Its the same. Just treat $y_{t-1}$ as you would treat x.
BB King
CC BY-SA 4.0
2019-03-25T15:22:59.433Z
But both my dependant and independent variables are the mean of a certain variable. How can I calculate the variance and the co-variance if I already use the mean as my variables?
R-User
CC BY-SA 4.0
2019-03-25T16:56:17.377Z
hi: assuming that the absolute of $b$ is less than 1 and that $u$ is an error term, then the unconditional mean of your model is $a$.  Note there are estimation issues when using OLS with lagged dependent variables in finite samples because the classical OLS assumptions don't hold. One way to deal with this is to maximize the likelihood numerically rather than using OLS. If your sample size is large, don't worry about it. No idea what you mean by the variables being means of other variables. They should be changing over time so I'm not clear what you mean by them being means ?
mark leeds
CC BY-SA 4.0
2019-03-25T20:38:45.217Z
What @BBKing means is that in your equation the dependent and independent variables can be considered random variables, even though they are calculated instead of coming from raw data.  A mean of a random variable is also a random variable and it has its own distribution properties, including variance.  If this is a theoretical exercise, just assume that you have multiple mean values of IV and DV for different samples.
AlexK
CC BY-SA 4.0
2019-03-26T15:55:48.880Z
@AlexK: In the example I saw in a paper, it was assumed that the error term equals 0 and the intercept is 0 as well. Then, they just divided the mean of yt by the mean of yt-1 to get b. Is that correct and how can that be explained with the original calculation of the OLS-coefficient?
R-User
CC BY-SA 4.0
2019-03-26T20:31:07.170Z
Can you provide a link?  That's not the formula for beta.
AlexK
<econometrics><regression>
How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?
R-User
# How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?

(Asked by: username_0 on 2019-03-25)

In a simple OLS regression we calculate the estimator Beta by dividing the covariance of x and y by the variance of x.

How do we calculate the estimator Beta if we regress the mean of a variable (at time t) on the mean of its lagged variable (at time t-1) ?:

[![OLS regression of mean of y on the mean of y lag](https://i.sstatic.net/1T7GH.png)](https://i.sstatic.net/1T7GH.png)

**Tags:** econometrics, regression
> **Comments:**
> **username_1**: Its the same. Just treat $y_{t-1}$ as you would treat x.  
> **username_0**: But both my dependant and independent variables are the mean of a certain variable. How can I calculate the variance and the co-variance if I already use the mean as my variables?  
> **username_2**: hi: assuming that the absolute of $b$ is less than 1 and that $u$ is an error term, then the unconditional mean of your model is $a$.  Note there are estimation issues when using OLS with lagged dependent variables in finite samples because the classical OLS assumptions don't hold. One way to deal with this is to maximize the likelihood numerically rather than using OLS. If your sample size is large, don't worry about it. No idea what you mean by the variables being means of other variables. They should be changing over time so I'm not clear what you mean by them being means ?  
> **username_3**: What @BBKing means is that in your equation the dependent and independent variables can be considered random variables, even though they are calculated instead of coming from raw data.  A mean of a random variable is also a random variable and it has its own distribution properties, including variance.  If this is a theoretical exercise, just assume that you have multiple mean values of IV and DV for different samples.  
> **username_0**: @AlexK: In the example I saw in a paper, it was assumed that the error term equals 0 and the intercept is 0 as well. Then, they just divided the mean of yt by the mean of yt-1 to get b. Is that correct and how can that be explained with the original calculation of the OLS-coefficient?  
> **username_3**: Can you provide a link?  That's not the formula for beta.  

---

## 0 answers

