Econometrics-I-9

# &#152&#152;™™ ™ 16/27 ln = i v i i i i i

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Unformatted text preview: &#152;&#152;™™ ™ 16/27 ( ) ln + = + . i v i i i i i i i i i = f y e TE = + v u y + ′ α- ′ α x x x ε β β Part 9: Hypothesis Testing - 2 Application to Spanish Dairy Farms Input Units Mean Std. Dev. Minimum Maximum Milk Milk production (liters) 131,108 92,539 14,110 727,281 Cows # of milking cows 2.12 11.27 4.5 82.3 Labor # man-equivalent units 1.67 0.55 1.0 4.0 Land Hectares of land devoted to pasture and crops. 12.99 6.17 2.0 45.1 Feed Total amount of feedstuffs fed to dairy cows (tons) 57,941 47,981 3,924.1 4 376,732 N = 247 farms, T = 6 years (1993-1998) &#152;&#152;™ ™ 17/27 Part 9: Hypothesis Testing - 2 Stochastic Frontier Model &#152;&#152;™ ™ 18/27 Part 9: Hypothesis Testing - 2 &#152;&#152;&#152;™ ™ 19/27 Part 9: Hypothesis Testing - 2 &#152;&#152;&#152;™ ™ 20/27 Part 9: Hypothesis Testing - 2 Nonnested Regression Models p Davidson and MacKinnon: If model A is correct, then predictions from model B will not add to the fit of model A to the data. p Vuong: If model A is correct, then the likelihood function will generally favor model A and not model B &#152;&#152;&#152;™ ™ 21/27 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. &#152;&#152;&#152;™ ™ 22/27 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 &#152;&#152;&#152;™ ™ 23/27 Part 9: Hypothesis Testing - 2 B does not add to Model A &#152;&#152;&#152;™ ™ 24/27 Part 9: Hypothesis Testing - 2 A Does Add to Model B &#152;&#152;&#152; ™ 25/27 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. &#152;&#152;&#152; &#152;™ 26/27 Part 9: Hypothesis Testing - 2 &#152;&#152;&#152; &#152; 27/27...
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