Choose estimators for panel rent regressions

You have monthly panel data for properties i in MSAs m from 2010-01 to 2025-06: rent_it, vacancy_it, amenities_i, msa_unemp_mt, CPI_t, interest_t. You observe serial correlation and heteroskedasticity. (1) Write a regression to estimate the elasticity of rent to vacancy with property and month fixed effects; justify log transforms and seasonal terms. (2) Specify which standard errors you would use and why: two-way clustering by property and month vs Driscoll–Kraay vs Newey–West; discuss finite-sample implications. (3) 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 ECM and avoid spurious regression. (4) Interpret beta = -0.35 on ln(vacancy): compute the predicted percent change in rent for a 2 percentage-point vacancy increase from 8% to 10% at the MSA level. (5) Diagnose multicollinearity among macro regressors; propose remedies (orthogonalization, ridge, Bayesian priors) and how they affect inference.