# How do we calculate Beta in a OLS regression of the mean of y on the mean of lag of y?

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) ?:

• Its the same. Just treat $y_{t-1}$ as you would treat x. – BB King Mar 25 '19 at 14:30
• 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 Mar 25 '19 at 15:22
• 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 Mar 25 '19 at 16:56
• 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 Mar 25 '19 at 20:38
• @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 Mar 26 '19 at 15:55