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13A.4 THE PROOF OF EQUATION (13.6.2)

Since there is no intercept in the model, the estimate of a, according to the formula for the regression through the origin, is as follows:

Substituting for Y from the true model (13.2.8), we obtain a = Zip™ = pLXU (2)

EX2 EX?

Statistical theory shows that if ln ui ~ N(0, a2) then ui = log normal [ea?/2, ea2(ea?-1)] (3)

Therefore,

where use is made of the fact that the X's are nonstochastic and each ui has an expected value of ea /2.

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