econometrics (Page 332)

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118 PART ONE: SINGLE-EQUATION REGRESSION MODELS whereµ1 =mean of Y1 µ2 =mean of Y2 σ1 =standard deviation of Y1 σ2 =standard deviation of Y2 ρ=coefficient of correlation between Y1 andY2 4.2.By applying the second-order conditions for optimization (i.e., secondderivative test), show that the ML estimators ofβ1, β2, and σ 2 obtained by solving Eqs. (9), (10), and (11) do in fact maximize the likelihood function
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