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Econometrics-I-8

Regression fit if drop without lppt r-squared=.99573

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Unformatted text preview: Regression fit if drop? Without LPPT, R-squared= .99573 Compare R2, was .99605, F(1,27) = [(.99605 - .99573)/1]/[(1-.99605)/(36-9)] = 2.187 = 1.4722 (with some rounding difference) &#152;&#152;&#152;&#152;&#152;™ ™ 38/50 Part 8: Hypothesis Testing Robust Tests p The Wald test generally will (when properly constructed) be more robust to failures of the narrow model assumptions than the t or F p Reason: Based on “robust” variance estimators and asymptotic results that hold in a wide range of circumstances. p Analysis: Later in the course – after developing asymptotics. &#152;&#152;&#152;&#152;&#152;™ ™ 39/50 Part 8: Hypothesis Testing Particular Cases Some particular cases: One coefficient equals a particular value: F = [(b - value) / Standard error of b ]2 = square of familiar t ratio. Relationship is F [ 1, d.f.] = t2[d.f.] A linear function of coefficients equals a particular value (linear function of coefficients - value)2 F = ---------------------------------------------------- Variance of linear function Note square of distance in numerator Suppose linear function is k wk bk Variance is kl wkwl Cov[bk,bl] This is the Wald statistic. Also the square of the somewhat familiar t statistic. Several linear functions. Use Wald or F. Loss of fit measures may be easier to compute. &#152;&#152;&#152;&#152;&#152;™ ™ 40/50 Part 8: Hypothesis Testing Hypothesis Test: Sum of Coefficients = 1?---------------------------------------------------------------------- Ordinary least squares regression ............ LHS=LG Mean = 5.39299 Standard deviation = .24878 Number of observs. = 36 Model size Parameters = 9 Degrees of freedom = 27 Residuals Sum of squares = .00855 <******* Standard error of e = .01780 <******* Fit R-squared = .99605 <******* Adjusted R-squared = .99488 <*******--------+------------------------------------------------------------- Variable| Coefficient Standard Error t-ratio P[|T|>t] Mean of X--------+------------------------------------------------------------- Constant| -6.95326*** 1.29811 -5.356 .0000 LY| 1.35721*** .14562 9.320 .0000 9.11093 LPG| -.50579*** .06200 -8.158 .0000 .67409 LPNC| -.01654 .19957 -.083 .9346 .44320 LPUC| -.12354* .06568 -1.881 .0708 .66361 LPPT| .11571 .07859 1.472 .1525 .77208 LPN| 1.10125*** .26840 4.103 .0003 .60539 LPD| .92018*** .27018 3.406 .0021 .43343 LPS| -1.09213*** .30812 -3.544 .0015 .68105--------+------------------------------------------------------------- &#152;&#152;&#152;&#152;&#152;™ ™ 41/50 Part 8: Hypothesis Testing Hypothesis Test: Sum of Coefficients Do the three aggregate price elasticities sum to zero? H0 :β7 + β8 + β9 = R = [0, 0, 0, 0, 0, 0, 1, 1, 1], q = [0] Variable| Coefficient Standard Error t-ratio P[|T|>t] Mean of X--------+------------------------------------------------------------- LPN| 1.10125*** .26840 4.103 .0003 .60539 LPD| .92018*** .27018 3.406 .0021 .43343 LPS| -1.09213*** .30812 -3.544 .0015 .68105 &#152;&#152;&#152;&#152;&#152;™ ™ 42/50 Part 8: Hypothesis Testing Wald Test &#152;&#152;&#152;&#152;&#152;™ ™ 43/50 Part 8: Hypothesis Testing Using the Wald Statistic--> Matrix ; R = [0,1,0,0,0,0,0,0,0 / 0,0,1,0,0,0,0,0,0]$--> Matrix ; q = [1/-1]$--> Matrix ; list ; m = R*b - q $ Matrix M...
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Regression fit if drop Without LPPT R-squared=.99573...

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