Short answer: It depends on your goal.
If the goal is that a full‑time worker can meet basic needs, then yes—tying the minimum wage to the cost of living (via an inflation or cost‑of‑living index) is the most direct way to keep its purchasing power from eroding. Without indexation, the real value falls whenever prices rise, and periodic, politicized “catch‑up” hikes create long gaps and sharper shocks.
What “keep up” can mean
•Inflation indexing: Adjust annually by a price index (e.g., CPI). Preserves purchasing power on average, but may miss big local housing or childcare cost swings.
•Regional cost‑of‑living indexing: Adjust by metro/state costs. Better matches local realities but is more complex and contentious to measure.
•Median‑wage anchoring: Keep the minimum at a stable share of the typical wage (often 45–55%). Ensures low pay doesn’t drift far behind overall pay levels.
Pros of indexing
•Predictability for workers and businesses.
•Avoids real pay cuts caused by inflation.
•Reduces large, abrupt legislative hikes.
Potential trade‑offs
•Uniform national indexing can misfit high‑ and low‑cost regions.
•Measurement error (which index? CPI, rent, childcare?) can over‑ or under‑shoot.
•Some price pass‑through in low‑wage sectors; employment effects are generally small for modest, gradual increases but risks rise with very large jumps or in weaker local economies.
Practical design options
•National floor indexed to inflation + local add‑ons for high‑cost areas.
•Annual adjustments with guardrails (e.g., caps/bands) and multi‑year phase‑ins.
•Pair with complementary policies (Earned Income Tax Credit, childcare, housing, healthcare) to boost incomes without putting the entire burden on employers.
•Periodic reviews to recalibrate if indexed changes outpace local conditions.
Bottom line: If your policy objective is a stable, needs‑based wage floor, indexing to living costs (ideally with regional tailoring and guardrails) is a sensible default. If your objective prioritizes maximum local flexibility or minimizing mandated labor costs, you might prefer occasional legislative adjustments complemented by tax credits and safety‑net supports.