Analyze omitted-variable bias in regression

Q: Analyze omitted-variable bias in regression

This question evaluates understanding of omitted-variable bias and heteroscedasticity in linear regression, testing competency in how omitting a relevant covariate and having non-constant error variance impact OLS point estimation and inference.

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Question

Omitted-Variable Bias, Heteroscedasticity, and Remedies

Setup

True data-generating process (DGP): Y = β0 + β1·Temp + β2·Occupancy + ε
Assumptions: E[ε | Temp, Occupancy] = 0 and Var(ε | Temp, Occupancy) = σ²(Temp) (heteroscedasticity depending on Temp).
Mistake: You fit OLS on Y ~ Temp only (Occupancy omitted).

Tasks

Derive the expected (asymptotic) bias of the OLS estimator of β1 when regressing Y on Temp only. Express it in terms of Cov(Temp, Occupancy) and Var(Temp).
State the sign of the bias when hotter days are more occupied.
Explain how weighted least squares (WLS) and heteroscedasticity-robust standard errors (robust SEs) affect estimation vs inference in this setting.
Design a test to detect remaining heteroscedasticity: name the test and its null hypothesis.
Propose a practical heteroscedasticity diagnostic you would include in a production training report.

Analyze omitted-variable bias in regression

Quick Overview

Omitted-Variable Bias, Heteroscedasticity, and Remedies

Setup

Tasks

Solution

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