P vuong if model a is correct then the likelihood

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p Vuong: If model A is correct, then the likelihood function will generally favor model A and not model B ™    21/27
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Part 9: Hypothesis Testing - 2 Davidson and MacKinnon Strategy p Obtain predictions from model A = AFit p Obtain predictions from model B = Bfit p If A is correct, in the combined model (A,Bfit), Bfit should not be significant. p If B is correct, in the combined model (B,Afit), Afit should not be significant. p (Unfortunately), all four combinations of significance and not are possible. ™    22/27
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Part 9: Hypothesis Testing - 2 Application Model A LogG(t) = 1 + 2logY(t) + 3logPG(t) + 4logPNC(t) + 5logPUC(t) + 6logPPT(t) + 7logG(t-1) + Model B LogG(t) = 1 + 2logY(t) + 3logPG(t) + 4logPNC(t) + 5logPUC(t) + 6logPPT(t) + 7logY(t-1) + w ™    23/27
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Part 9: Hypothesis Testing - 2 B does not add to Model A ™    24/27
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Part 9: Hypothesis Testing - 2 A Does Add to Model B ™    25/27
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Part 9: Hypothesis Testing - 2 Voung p Log density for an observation is Li = -.5*[log(2) + log(s2) + ei2/s2] p Compute Li(A) and Li(B) for each observation p Compute Di = Li(A) – Li(B) p Test hypothesis that mean of Di equals zero using familiar “z” test. p Test statistic > +2 favors model A, < -2 favors model B, in between is inconclusive. ™    26/27
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Part 9: Hypothesis Testing - 2     27/27
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