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Econometric take home APPS_Part_15

# Econometric take home APPS_Part_15 - To compute the Wald...

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59 To compute the Wald statistic, we require the unrestricted regression. The parameter estimates are given above. The sums of squares are 465.708, 785.399, and 145.055 for i = 1, 2, and 3, respectively. For the common estimate of σ 2 , we use the total sum of squared GLS residuals, 1396.162. Then, W = (10/2){[(1396.162/30)/(465.708/10) - 1] 2 + ...} = 25.21. The Wald statistic is far larger than the LM statistic. Since there are two restrictions, at significance levels of 95% or 99% with critical values of 5.99 or 9.21, the two tests lead to different conclusions. The likelihood ratio statistic based on the FGLS estimates is χ 2 = 30ln(1396.162/30) - 10ln(465.708/10) ... = 6.42 which is between the previous two and between the 95% and 99% critical values. Applications As usual, the applications below require econometric software. The computations can be done with any modern software package, so no specific program is recommended. --> read \$ Last observation read from data file was 200 End of data listing in edit window was reached --> REGRESS ; Lhs = I ; Rhs = F,C,one \$ +----------------------------------------------------+ | Ordinary least squares regression | | LHS=I Mean = 145.9582 | | Standard deviation = 216.8753 | | WTS=none Number of observs. = 200 | | Model size Parameters = 3 | | Degrees of freedom = 197 | | Residuals Sum of squares = 1755850. | | Standard error of e = 94.40840 | | Fit R-squared = .8124080 | | Adjusted R-squared = .8105035 | | Model test F[ 2, 197] (prob) = 426.58 (.0000) | +----------------------------------------------------+ +--------+--------------+----------------+--------+--------+----------+ |Variable| Coefficient | Standard Error |t-ratio |P[|T|>t]| Mean of X| +--------+--------------+----------------+--------+--------+----------+ F | .11556216 .00583571 19.803 .0000 1081.68110 C | .23067849 .02547580 9.055 .0000 276.017150 Constant| -42.7143694 9.51167603 -4.491 .0000 --> CALC ; R0=Rsqrd \$ --> REGRESS ; Lhs = I ; Rhs = F,C,one ; Cluster = 20 \$ +----------------------------------------------------+ | Ordinary least squares regression | | LHS=I Mean = 145.9582 | | Standard deviation = 216.8753 | | WTS=none Number of observs. =

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