Consider a linear structural relationship model where we assume that ξi, has an improper distribution, ξi ~ uniform(-ˆž, ˆž).
(a) Show that for each i,

(Completing the square in the exponential makes the integration easy.)
(b) The result of the integration in part (a) looks like a pdf, and if we consider it a pdf of Y conditional on X, then we seem to have a linear relationship between X and Y. Thus, it is sometimes said that this "limiting case" of the structural relationship leads to simple linear regression and ordinary least squares. Explain why this interpretation of the above function is wrong.

Transcribed Image Text:

(zi )2 (2m) σ6σε