Econometrics-I-18

# Leads to the lr test the wald test the usual the

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Leads to the LR test. The Wald test: The usual. The Lagrange multiplier test: Underlying basis: Reexamine the first order conditions. Form a test of whether the gradient is significantly “nonzero” at the restricted estimator. ™  29/47

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Part 18: Maximum Likelihood Estimation Testing Hypotheses Wald tests, using the familiar distance measure Likelihood ratio tests: LogLU= log likelihood without restrictions LogLR= log likelihood with restrictions LogLU > logLR for any nested restrictions 2(LogLU – logLR)  chi-squared [J] ™  30/47
Part 18: Maximum Likelihood Estimation Testing the Model +---------------------------------------------+ | Poisson Regression | | Maximum Likelihood Estimates | | Dependent variable DOCVIS | | Number of observations 27326 | | Iterations completed 7 | | Log likelihood function -106215.1 | Log likelihood | Number of parameters 4 | | Restricted log likelihood -108662.1 | Log Likelihood with only a | McFadden Pseudo R-squared .0225193 | constant term. | Chi squared 4893.983 | 2*[logL – logL(0)] | Degrees of freedom 3 | | Prob[ChiSqd > value] = .0000000 | +---------------------------------------------+ Likelihood ratio test that all three slopes are zero. ™  31/47

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Part 18: Maximum Likelihood Estimation Wald Test --> MATRIX ; List ; b1 = b(2:4) ; v11 = varb(2:4,2:4) ; B1'<V11>B1\$ Matrix B1 Matrix V11 has 3 rows and 1 columns. has 3 rows and 3 columns 1 1 2 3 +-------------- +------------------------------------------ 1| .31954 1| .4856275D-04 -.4556076D-06 .2169925D-05 2| -.52476 2| -.4556076D-06 .00048 -.9160558D-05 3| -.04987 3| .2169925D-05 -.9160558D-05 .2988465D-05 Matrix Result has 1 rows and 1 columns. 1 +-------------- 1| 4682.38779 LR statistic was 4893.983 ™  32/47
Part 18: Maximum Likelihood Estimation Chow Style Test for Structural Change ™  33/47 Does the same model apply to 2 (G) groups? For linear regression we used the "Chow" (F) test. For models fit by maximum likelihood, we use a test based on the likelihood function. The same model is fit t ( 29 1 o the pooled sample and to each group. Chi squared = 2 log log Degrees of freedom = (G-1)K. G g pooled g L L = -

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Part 18: Maximum Likelihood Estimation Poisson Regressions ---------------------------------------------------------------------- Poisson Regression Dependent variable DOCVIS Log likelihood function -90878.20153 (Pooled, N = 27326) Log likelihood function -43286.40271 (Male, N = 14243) Log likelihood function -46587.29002 (Female, N = 13083) --------+------------------------------------------------------------- Variable| Coefficient Standard Error b/St.Er. P[|Z|>z] Mean of X --------+------------------------------------------------------------- Pooled Constant| 2.54579*** .02797 91.015 .0000 AGE| .00791*** .00034 23.306 .0000 43.5257 EDUC| -.02047*** .00170 -12.056 .0000 11.3206 HSAT| -.22780*** .00133 -171.350 .0000 6.78543 HHNINC| -.26255*** .02143 -12.254 .0000 .35208 HHKIDS| -.12304*** .00796 -15.464 .0000 .40273 --------+------------------------------------------------------------- Males Constant| 2.38138*** .04053 58.763 .0000 AGE| .01232*** .00050 24.738 .0000 42.6528 EDUC| -.02962*** .00253 -11.728 .0000 11.7287 HSAT| -.23754*** .00202 -117.337 .0000 6.92436 HHNINC| -.33562*** .03357 -9.998 .0000 .35905 HHKIDS| -.10728*** .01166 -9.204 .0000 .41297 --------+------------------------------------------------------------- Females Constant| 2.48647*** .03988 62.344 .0000 AGE| .00379*** .00048 7.940 .0000 44.4760 EDUC| .00893*** .00234 3.821 .0001 10.8764 HSAT| -.21724*** .00177 -123.029 .0000 6.63417 HHNINC| -.22371*** .02767 -8.084 .0000 .34450 HHKIDS| -.14906*** .01107 -13.463 .0000 .39158 --------+------------------------------------------------------------- ™  34/47
Part 18: Maximum Likelihood Estimation Chi Squared Test Namelist; X = one,age,educ,hsat,hhninc,hhkids\$ Sample ; All \$ Poisson ; Lhs = Docvis ; Rhs = X \$ Calc ; Lpool = logl \$ Poisson ; For [female = 0] ; Lhs = Docvis ; Rhs = X \$ Calc ; Lmale = logl \$ Poisson ; For [female = 1] ; Lhs = Docvis ; Rhs = X \$ Calc ; Lfemale = logl \$ Calc ; K = Col(X) \$ Calc ; List ; Chisq = 2*(Lmale + Lfemale - Lpool) ; Ctb(.95,k) \$ +------------------------------------+ | Listed Calculator Results | +------------------------------------+ CHISQ = 2009.017601 *Result*= 12.591587 The hypothesis that the same model applies to men and women is rejected.

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