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Comparing Regression Models for Hausman Test: Fixed Effects vs. Random Effects

This notice provides guidance on comparing R2 between Fixed Effects (FE) and Random Effects (RE) models for constructing an Arellano-Bond panel data estimator. Discusses implications of R2 changes after within-panel means subtraction and the importance of identifying groups using the ID variable. Detailed steps for estimating fixed and random effect models, conducting Hausman test, and interpreting group information are included.

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Comparing Regression Models for Hausman Test: Fixed Effects vs. Random Effects

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  1. Notice R2 and compare to FE in next regression

  2. Areg constructs within Panel means rather than Estimate LSDV model Data must Be sorted by ID Big jump in R2 ID is the variable That identifies Groups for Fixed-effects Number of groups (N in class notation)

  3. To estimate fixed and random effect models, You must defined the dimension of the daya

  4. This the R2 after within panel Means have been subtracted How much variation is left for you To explain? Notice the Z’s have been Dropped from the analysis

  5. Store the fixed-effects estimates to be used in Construction of the Hausman test

  6. Slightly lower R2 than in the OLS model Group information .3782/(.3782+.2342) Most of the variance is between group, not within

  7. Ask for Hausman test after the RE model is estimated Test statistic P-value Easily reject null in this case

  8. Get between group estimates

  9. Summary of Results (X’s)

  10. Summary of Results (Z’s)

  11. Rate of return to tenure • Yit =β0 + Eitβ1 + Eit\2β2 + Titβ3 + Tit2β4 + Unionitβ5 + EDUCiγ1 + Blackiγ2 + εit dY/dT = β3 + 2 Titβ4 Return to tenure OLS FE RE 5 years 0.0232 0.0128 0.0255 10 years 0.0157 0.0078 0.0170 20 years 0.0007 -0.0022 0.0000

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