# Math Help - Two Stage Least Squares

1. ## Two Stage Least Squares

You are given a dependent variable y, and independent variable x such that the regression would be ( x and y are endogenous):
$y=\beta_{0} + \beta_{1}x + \epsilon$

There is the possibility that the coefficients estimated from the model is affected by x and y having measurement errors in them.
You are also given the lagged (by one period) dataset of x and y (x_1 and y_1 respectively).

How would you go about fixing this error?

May I ask if my approach is correct?
I would use the lagged data to estimate the true values of x & y, so that the errors are no longer correlated so that the model would look as follows

$y_1=\beta_{0} + \beta_{1}x_1 + \epsilon \\ x = x_1 + u_{1} \\ y = y_{1} + u_{2}$

Then this would be the equivalent of running a two way least squares regression with x_{1} and y_{1} as instrumental variables?

Thank you in advance for any feedback

2. ## Re: Two Stage Least Squares

I would have to look it up to confirm your approach, but it sounds like the correct approach in applying a two-stage OLS using the autocorrelation to account for the measurement error. I've just never seen it used like that (due to my ignorance, not because I can say it isn't used like that). If you don't get additional help here, I'd also query at the talk stats forums.