Demand system estimation. Let Y denote total expenditure on consumer durables, nondurables, and services and Ed, En, and Es are the expenditures on the three categories. As defined, Y = Ed + En + Es. Now, consider the expenditure system Prove that if all equations are estimated by ordinary least squares, then the sum of the expenditure coefficients will be 1 and the four other column sums in the preceding model will bezero.

Edad + BaY+Yad Pa + Van Pn + Yds Ps + Ed, En an+BnY+ Ynd Pa + Ynn Pn + Yns Ps + En = Es = s + BsY+Ysd Pd + Ysn Pn + Yss Ps + Es.