Choose estimators for panel rent regressions
Overview
This question evaluates expertise in panel-data econometrics and time-series diagnostics, testing skills in fixed-effects specification, robust standard-error selection, unit-root and cointegration testing, error-correction interpretation, and multicollinearity handling for elasticity estimation.
Freddie Mac
Oct 13, 2025, 9:49 PM
Data Scientist
Onsite
Statistics & Math
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Panel Rent–Vacancy Elasticity and Inference: Design, SEs, and Time-Series Diagnostics
Context
You have a monthly property-level panel from 2010-01 to 2025-06. For property i in MSA m at month t, you observe:
- rent_it (asking rent), vacancy_it (vacancy rate), amenities_i (time-invariant),
- msa_unemp_mt (MSA unemployment), CPI_t (national CPI), interest_t (national rate).
You observe serial correlation and heteroskedasticity. Answer the following:
Tasks
- Model specification: Write a regression to estimate the elasticity of rent with respect to vacancy using property and month fixed effects. Justify log transforms and seasonal terms.
- Standard errors: Specify which SEs you would use and why. Compare two-way clustering by property and month versus Driscoll–Kraay versus Newey–West, including finite-sample implications.
- Nonstationarity: Test for unit roots and cointegration in ln(rent) and ln(vacancy). If both are I(1), outline Engle–Granger or Johansen steps to fit an Error Correction Model (ECM) to avoid spurious regression.
- Interpretation: With an estimated coefficient β = −0.35 on ln(vacancy), compute the predicted percent change in rent when vacancy increases by 2 percentage points (from 8% to 10%) at the MSA level.
- Multicollinearity: Diagnose multicollinearity among macro regressors and propose remedies (orthogonalization, ridge, Bayesian priors). Explain how these affect inference.
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