Econometric take home APPS_Part_7

Econometric take home APPS_Part_7 - LOGI | .99299135...

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LOGI | .99299135 .25037574 3.966 .0003 9.67214751 LOGPNC | -.15471632 .26696298 -.580 .5653 4.38036654 LOGPUC | -.48909058 .08519952 -5.741 .0000 4.10544881 LOGPPT | .01926966 .13644891 .141 .8884 4.14194132 T | .03797198 .00751371 5.054 .0000 26.5000000 LOGPD | 1.73205775 .25988611 6.665 .0000 4.23906603 LOGPN | -.72953933 .26506853 -2.752 .0087 4.23689080 LOGPS | -.86798166 .35291106 -2.459 .0181 4.17535768 Calc;r1=rsqrd$ Regr;lhs=logg;rhs=one,logpg,logi,logpnc,logpuc,logppt,t$ +----------------------------------------------------+ | Ordinary least squares regression | | LHS=LOGG Mean = 1.570475 | | Standard deviation = .2388115 | | WTS=none Number of observs. = 52 | | Model size Parameters = 7 | | Degrees of freedom = 45 | | Residuals Sum of squares = .1014368 | | Standard error of e = .4747790E-01 | | Fit R-squared = .9651249 | | Adjusted R-squared = .9604749 | | Model test F[ 6, 45] (prob) = 207.55 (.0000) | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |t-ratio |P[|T|>t]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ Constant| -13.1396625 2.09171186 -6.282 .0000 LOGPG | -.05373342 .04251099 -1.264 .2127 3.72930296 LOGI | 1.64909204 .20265477 8.137 .0000 9.67214751 LOGPNC | -.03199098 .20574296 -.155 .8771 4.38036654 LOGPUC | -.07393002 .10548982 -.701 .4870 4.10544881 LOGPPT | -.06153395 .12343734 -.499 .6206 4.14194132 T | -.01287615 .00525340 -2.451 .0182 26.5000000 Calc;r0=rsqrd$ Calc;list;f=((r1-r0)/2)/((1-r1)/(n-10))$ +------------------------------------+ | Listed Calculator Results | +------------------------------------+ F = 34.868735 The critical value from the F table is 2.827, so we would reject the hypothesis. ?======================================================================= ? b. Nonlinear restriction ?======================================================================= Since the restricted model is quite nonlinear, it would be quite cumbersome to estimate and examine the loss in fit. We can test the restriction using the unrestricted model. For this problem, f = [ γ nc - γ uc , γ nc δ s - γ pt δ d ] The matrix of derivatives, using the order given above and " to represent the entire parameter vector, is G = = . The parameter estimates are ∂∂ f f 1 2 / / α α 0 0 0 11 0000 0 000 0 0 0 −− δδ γ s d pt nc γ Thus, f = [-.17399, .10091] . The covariance matrix to use for the tests is G s 2 ( X X ) -1 G The statistic for the joint test is χ 2 = f [ G s 2 ( X X ) -1 G ] -1 f = .4772.
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Econometric take home APPS_Part_7 - LOGI | .99299135...

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