1. Econometric model: Y = β_0+ β_1 Z+u OLS estimates: (β_1 ) ̂=15 and (β_0 )...

1. Econometric model: Y = β_0+ β_1 Z+u OLS estimates: (β_1 ) ̂=15 and (β_0 ) ̂= -37. Based on the information above:

a. Write out the SRF.

b. In one sentence explain the meaning of (β_1 ) ̂=15

c. Write out the mean independence assumption.

Expert Solution

The econometric model y^=βO+β1Z+u is a population regression function (PRF).

(a) The sample regression function (SRF) is written simply by inserting the hat (^) above every dependent variable (Y) and parameters (b0 and b1) concerned.

The SRF would be y^=βO^+β1^Z+u. The purpose of SRF is to determine the PRF which is not possible in real life to compute PRF.

(b) β1 is a slope which implies that a unit change in Z, the value of Y changes by β1 only, everything remains constant. Similarly, when β1=15, it means when Z increases by 1 unit then Y increases by 15, everything else remains constant.

(c) Y is mean independent of Z if and only if its conditional mean E(Y | Z=z) equals it's unconditional mean E(Y) for all z such that the probability that Z = z is not zero.

Rahul Sunny answered 3 years ago

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