Choose estimators for panel rent regressions
Problem Description
You are provided with a monthly property-level panel dataset spanning from January 2010 to June 2025. For each property i within a specific Metropolitan Statistical Area (MSA) m at a given month t, the following variables are observed:
rent_it: Asking rentvacancy_it: Vacancy rateamenities_i: Time-invariant property amenitiesmsa_unemp_mt: MSA-level unemployment rateCPI_t: National Consumer Price Indexinterest_t: National interest rate
Preliminary analysis indicates the presence of both serial correlation and heteroskedasticity in the data.
Your tasks are as follows:
-
Model Specification:
- Write a regression model to estimate the elasticity of rent with respect to vacancy.
- The model must include both property and month fixed effects.
- Justify the use of log transformations for relevant variables and the inclusion of seasonal terms.
-
Standard Errors:
- Specify and justify which type of standard errors you would use for this model.
- Compare the implications of using two-way clustering by property and month versus Driscoll–Kraay standard errors versus Newey–West standard errors, specifically addressing their finite-sample properties.
-
Nonstationarity:
- Describe how you would test for unit roots and cointegration in
ln(rent)andln(vacancy). - If both series are found to be integrated of order one (I(1)), outline the steps for fitting an Error Correction Model (ECM) using either the Engle–Granger or Johansen approach to mitigate the risk of spurious regression.
- Describe how you would test for unit roots and cointegration in
-
Interpretation:
- Given an estimated coefficient β = −0.35 on
ln(vacancy), compute the predicted percentage change in rent when the vacancy rate increases by 2 percentage points (e.g., from 8% to 10%) at the MSA level.
- Given an estimated coefficient β = −0.35 on
-
Multicollinearity:
- Explain how you would diagnose multicollinearity among the macro regressors (
msa_unemp_mt,CPI_t,interest_t). - Propose and explain potential remedies such as orthogonalization, ridge regression, or incorporating Bayesian priors, detailing how each method affects statistical inference.
- Explain how you would diagnose multicollinearity among the macro regressors (
AI interview prep
Core dilemma
Achieving robust and unbiased causal inference for rent-vacancy elasticity in a complex panel data setting, while rigorously addressing issues of heteroskedasticity, serial correlation, nonstationarity, and multicollinearity, and ensuring the model's interpretability for business stakeholders.
3 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Choose estimators for panel rent regressions
Problem Description
You are provided with a monthly property-level panel dataset spanning from January 2010 to June 2025. For each property i within a specific Metropolitan Statistical Area (MSA) m at a given month t, the following variables are observed:
rent_it: Asking rentvacancy_it: Vacancy rateamenities_i: Time-invariant property amenitiesmsa_unemp_mt: MSA-level unemployment rateCPI_t: National Consumer Price Indexinterest_t: National interest rate
Preliminary analysis indicates the presence of both serial correlation and heteroskedasticity in the data.
Your tasks are as follows:
-
Model Specification:
- Write a regression model to estimate the elasticity of rent with respect to vacancy.
- The model must include both property and month fixed effects.
- Justify the use of log transformations for relevant variables and the inclusion of seasonal terms.
-
Standard Errors:
- Specify and justify which type of standard errors you would use for this model.
- Compare the implications of using two-way clustering by property and month versus Driscoll–Kraay standard errors versus Newey–West standard errors, specifically addressing their finite-sample properties.
-
Nonstationarity:
- Describe how you would test for unit roots and cointegration in
ln(rent)andln(vacancy). - If both series are found to be integrated of order one (I(1)), outline the steps for fitting an Error Correction Model (ECM) using either the Engle–Granger or Johansen approach to mitigate the risk of spurious regression.
- Describe how you would test for unit roots and cointegration in
-
Interpretation:
- Given an estimated coefficient β = −0.35 on
ln(vacancy), compute the predicted percentage change in rent when the vacancy rate increases by 2 percentage points (e.g., from 8% to 10%) at the MSA level.
- Given an estimated coefficient β = −0.35 on
-
Multicollinearity:
- Explain how you would diagnose multicollinearity among the macro regressors (
msa_unemp_mt,CPI_t,interest_t). - Propose and explain potential remedies such as orthogonalization, ridge regression, or incorporating Bayesian priors, detailing how each method affects statistical inference.
- Explain how you would diagnose multicollinearity among the macro regressors (