# Which estimate of parameter is better in regression?

Suppose my true Model is:

$$y = Xb + u \tag 1$$

But I am estimating:

$$y = Xb + Zd + u \tag 2$$

I can get the estimate of $$b$$ from $$(2)$$ by using $$Mz$$ operator as:

$$\hat{b} = (X'MzX)^{-1}(X'MzY)$$

Why is an estimate from the first equation is better than the second?

• Is this a question from a course or textbook? If so, please add the [self-study] tag & read its wiki. Nov 27, 2016 at 23:12
• @gung done. Thanks any help though? Nov 28, 2016 at 1:45
• I am sure you know the variance covariance matrix for $b$ when estimating model (1)? There likewise is an expression for the variance of the coefficients corresponding to $b$ when estimating (2). Can you derive that one as well? Nov 28, 2016 at 5:00