Spatial sorting, not displacement: short-term rentals and long-term rents in Medellín

We estimate the causal effect of short-term rental (STR) penetration on long-term rental prices and rental supply in Medellín, using an annual city-block panel that combines two independent rental records with Airbnb listing counts. The raw correlation between STR intensity and rents (≈ 0.12) vanishes once neighborhood fixed effects are added and disappears once STR activity is instrumented with a shift-share (Bartik) instrument that interacts a predetermined 2014 land- use-mix index with city-wide tourism demand shocks (international arrivals, online searches, the exchange rate). The estimated causal effect on long-term rents is small and, under weak-instrument-robust inference, never a positive premium; it is statistically indistinguishable from zero in the broad-coverage record and, at most, a slight negative in the high-stratum one — and over-identification tests (adding distance to a pre-existing landmark) do not reject instrument validity. On the supply side, co-movement dominates over displacement in the broad-coverage record, while a valid over-identified specification in the high-stratum record points to a bounded contraction that we treat as suggestive rather than conclusive, given restricted coverage and the gap between published listings and available stock. Attributing the recent rise in rents specifically to STR finds no empirical support.