Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice PS 4 Panel Models 11 December 2014 PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q1 Run pooled OLS: reg lfare y98 y99 y00 lpassen concen ldist Both the White and the Breusch-Pagan tests strongly reject homoscedasticity in this model. The Wooldridge test rejects the null of (first order) zero-autocorrelation. PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q2 To demean variables: egen Mconcen = mean(concen), by(id) generate concen_dev = concen- Mconcen PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q3 Coefficients for the pooled OLS and fixed effects model. Why omitted? What’s with the constant? Model1_OLS Model1_FE Model1_Dem~d --------------------------------------------------- y98 .0233121 .0297916 .0297916 y99 .0419392 .0590909 .0590909 y00 .1053677 .1285602 .1285602 lpassen -.0769015 -.3695845 -.3695845 concen .2733854 .1500383 .1500383 ldist .4339374 0 0 _cons 2.443014 7.173499 3.30e-09 PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q4 xtreg lfare y98 y99 y00 lpass conc ldist98 ldist99 ldist00, fe test ldist98 = ldist99 = ldist00 = 0 ( 1) ldist98 - ldist99 = 0 ( 2) ldist98 - ldist00 = 0 ( 3) ldist98 = 0 F( 3, 3439) = 3.55 Prob > F = 0.0139 And the same can be done in pooled OLS (with an additional variable). PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q5 The RE model lies in between the other two in many ways. Model1_OLS Model1_RE Model1_FE --------------------------------------------------- y98 .0233121 .0281082 .0297916 y99 .0419392 .0535282 .0590909 y00 .1053677 .1210173 .1285602 lpassen -.0769015 -.279287 -.3695845 concen .2733854 .1527638 .1500383 ldist .4339374 .3833817 0 _cons 2.443014 4.064902 7.173499 PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q6 xtreg lfare y98 y99 y00 lpassen concen ldist, fe scalar sigma_u2 = e(sigma_e)^2 scalar sigma_e2 = e(sigma_u)^2 scalar T = e(N) scalar lambda = 1 - (sigma_e2/(sigma_e2+(T*sigma_u2)))^0.5 di lambda .91221833 This means that the RE model is close to the FE model, a result we could also see in Q5 by looking closely at the coefficients. PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q7 xtreg lfare y98 y99 y00 lpassen concen ldist, fe eststo fixed xtreg lfare y98 y99 y00 lpassen concen ldist, re eststo random hausman fixed random\\ PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q7 Test: Ho: difference in coefficients not systematic chi2(5) = (b-B)’[(V_b-V_B)^(-1)](b-B) = 771.13 Prob>chi2 = 0.0000 (V_b-V_B is not positive definite) PS 4 Panel Models
Pooled OLS vs Fixed Effects Pooled OLS vs Fixed Effects vs Random Effects Policy Advice Q8 Our best estimate of the impact of concentration on the price comes from the FE model and is 0 . 1500383. This is a log-lin relationship meaning that we expect the average one-way fare to increase by 0 . 15% if the market share of the largest competitor on the route increases by one percentage point. PS 4 Panel Models
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