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5 questions · 1 formulas

Fixed vs random effects

FE: within variation, drops time-invariant X. Hausman small p → FE

Trap: FE cannot estimate a time-invariant variable's coefficient.

Normal DistributionD–A level★ High priority — official Canvas example

In a regression with ln(price) as dependent variable, pool dummy coefficient = 0.0774. Best interpretation?

→ A) A house with a pool is on average about 7.74% more expensive than a house without a pool, holding the other regressors fixed.

Canvas Example MCQ — Q53

  • A) A house with a pool is on average about 7.74% more expensive than a house without a pool, holding the other regressors fixed.
  • B) A house with a pool is on average $7,740 more expensive than a house without a pool.
  • C) A house with a pool is on average 7.74% less expensive than a house without a pool.
  • D) A house with a pool is on average $77,740 more expensive than a house without a pool.
  • E) None of A-D is close; write the correct answer.

For a dummy in log-Y, the standard approximation is 100b% = 7.74%. Exact effect = 100(e^0.0774-1) ≈ 8.05%. The source MCQ is testing the approximation.

Rule: Know both approximate and exact dummy-in-log effects.

Panel DataD–A levelNormal priority

You want to estimate a panel data regression model. Your key variable of interest is time-invariant. Therefore, you should estimate a_______

→ B) Random effects model

Old Exam — Oct 2023, Q17

Given: Time-invariant key regressor: fixed effects wipes it out; random effects can estimate its coefficient.

  • A) Fixed effects model
  • B) Random effects model
  • C) A fixed effects (FE) model because time-invariant variables are not eliminated with FE model.

A time-invariant regressor has no within-person variation and is eliminated by FE. To estimate its coefficient, use RE (subject to RE assumptions) -> B.

Rule: Time-invariant variable -> FE cannot estimate its coefficient. Small Hausman p-value -> reject RE, prefer FE.

Panel DataD–A levelNormal priority

You have done a Hausman test to see if a random effects or a fixed effects models should be used. The p-value of the Hausman test is 0.0003. Therefore you conclude that ___________.

→ A) Fixed effects model should be used.

Old Exam — Oct 2023, Q18

Given: Hausman p=0.0003: reject RE consistency; prefer FE.

  • A) Fixed effects model should be used.
  • B) Random effects model should be used.

Hausman H0: RE is consistent. p=0.0003 is tiny -> reject H0 -> prefer FE -> A.

Rule: Time-invariant variable -> FE cannot estimate its coefficient. Small Hausman p-value -> reject RE, prefer FE.

Panel DataD–A levelNormal priority

In this course (AI2152) we have studied the NLS panel data set. Suppose that you want to estimate panel data models and that you have collected data on individuals with following variables: Variable definitions: Which one of the following statements is true?

→ B) You want to estimate a random effects model when you are interested the coefficient of the variable black.

Old Exam — Dec 2022, Q28

Given: Panel setup: BLACK is time-invariant for each person; UNION varies over time.

  • A) You want to estimate a fixed effects model when you are interested the coefficient of the variable black.
  • B) You want to estimate a random effects model when you are interested the coefficient of the variable black.
  • C) Both fixed and random effects model are appropriate when you are interested the coefficient of the variable black.
  • D) The variable union is a so-called time-invariant variable.
  • E) None of the above (A, B, C, D) is close to be correct.

Fixed effects eliminate variables that do not change over time within each individual. BLACK is time-invariant, so its coefficient cannot be estimated by FE; RE can estimate it -> B.

Rule: Time-invariant variable -> FE cannot estimate its coefficient. Small Hausman p-value -> reject RE, prefer FE.

Panel DataE-levelNormal priority

You need the coefficient on a time-invariant variable (e.g. building type) in panel data. Which estimator?

→ B) Random effects (or pooled OLS)

Formula Battle — method recognition (built from the Formula Book)

  • A) Fixed effects
  • B) Random effects (or pooled OLS)
  • C) First differences
  • D) Any — they all work

FE removes everything constant over time. Correct method: Random effects (or pooled OLS).

Rule: FE cannot estimate time-invariant regressors