Econometric take home APPS_Part_20

Econometric take home APPS_Part_20 - +-+ | Groupwise...

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79 +--------------------------------------------------+ | Groupwise Regression Models | | Estimator = 2 Step GLS | | Groupwise Het. and Correlated (S2) | | Nonautocorrelated disturbances (R0) | | Test statistics against the correlation | | Deg.Fr. = 45 C*(.95) = 61.66 C*(.99) = 69.96 | | Test statistics against the correlation | | Likelihood ratio statistic = 320.2052 | | Log-likelihood function = -853.084972 | +--------------------------------------------------+ +--------+--------------+----------------+--------+--------+ |Variable| Coefficient | Standard Error |b/St.Er.|P[|Z|>z]| +--------+--------------+----------------+--------+--------+ F | .10806238 .00241169 44.808 .0000 C | .15079551 .00386063 39.060 .0000 Constant| -20.1588844 .79950153 -25.214 .0000 CREATE ; WI = (SDI(firm,firm))^2 $ REGRESS; Lhs = I ; Rhs = F,C,one ; Wts = WI $ +----------------------------------------------------+ | Ordinary least squares regression | | LHS=I Mean = 6.993136 | | Standard deviation = 18.01824 | | WTS=WI Number of observs. = 200 | | Model size Parameters = 3 | | Degrees of freedom = 197 | | Residuals Sum of squares = 11690.82 | | Standard error of e = 7.703521 | | Fit R-squared = .8190465 | | Adjusted R-squared = .8172094 | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |t-ratio |P[|T|>t]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ F | .07847124 .00459121 17.092 .0000 96.8424912 C | .09896094 .00761314 12.999 .0000 23.8374846 Constant| -2.96519441 .66964256 -4.428 .0000
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Chapter 11 Nonlinear Regression Models Exercises 1. We cannot simply take logs of both sides of the equation as the disturbance is additive rather than multiplicative. So, we must treat the model as a nonlinear regression. The linearized equation is y αα α α β ββ β 00 0 0 xx x x +− + () ( l o g ) ( β 0 ) where α 0 and β 0 are the expansion point. For given values of α 0 and β 0 , the estimating equation would be ( ) ( ) yx + ε * x x x x x x −++ = + ααα α β α β 000 0 0 (log ) (log ) or ( ) ( ) x x x x += + β α (log ) (log ) β 0 + ε * . Estimates of α and β are obtained by applying ordinary least squares to this equation. The process is repeated with the new estimates in the role of α 0 and β 0 . The iteration could be continued until convergence. Starting values are always a problem. If one has no particular values in mind, one candidate would be α 0 = y and β 0 = 0 or β 0 = 1 and α 0 either x y / x x or y / x .
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Econometric take home APPS_Part_20 - +-+ | Groupwise...

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