PS 4 Panel Models 11 December 2014 PS 4 Panel Models Pooled OLS vs - - PowerPoint PPT Presentation

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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

SLIDE 1

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

SLIDE 2

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

SLIDE 3

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

SLIDE 4

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

mitted? What’s with the constant?

Model1_OLS Model1_FE Model1_Dem~d

.0233121 .0297916 .0297916 y99 .0419392 .0590909 .0590909 y00 .1053677 .1285602 .1285602 lpassen

.0769015
.3695845
.3695845

concen .2733854 .1500383 .1500383 ldist .4339374 _cons 2.443014 7.173499 3.30e-09

PS 4 Panel Models

SLIDE 5

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

SLIDE 6

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

.0233121 .0281082 .0297916 y99 .0419392 .0535282 .0590909 y00 .1053677 .1210173 .1285602 lpassen

.0769015
.279287
.3695845

concen .2733854 .1527638 .1500383 ldist .4339374 .3833817 _cons 2.443014 4.064902 7.173499

PS 4 Panel Models

SLIDE 7

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

SLIDE 8

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

SLIDE 9

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

SLIDE 10

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

ne-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