Short answer: It depends on what you want the minimum wage to do. If the goal is to ensure full‑time workers can afford basic necessities, then yes—tying it to the cost of living (some form of indexing) is the most direct way to keep its real value from eroding. If the top priority is maximizing entry‑level job availability or minimizing compliance costs for very small firms, you might choose slower or less automatic adjustments.
How policymakers typically approach it
•Index to prices (inflation/CPI): Keeps purchasing power steady year to year. Simple and predictable, but won’t track local housing spikes well.
•Index to wages (e.g., a share of the median wage): Keeps the floor aligned with overall pay levels and productivity trends, but can amplify swings if the labor market weakens.
•Index to local cost of living: Better matches regional realities (housing, transportation), but is more complex and data‑heavy; national floors may still be needed.
Pros of automatic indexing
•Prevents silent erosion between infrequent legislative hikes.
•Smaller, regular changes help businesses plan and reduce “shock” adjustments.
•Depoliticizes routine updates.
Trade‑offs and cautions
•One national index can be too low for high‑cost cities and too high for low‑cost areas.
•Indices can mismeasure fast‑rising housing costs or local conditions.
•Very large or abrupt increases can stress some small employers; phased‑in schedules and guardrails (e.g., caps on annual changes) help.
•Evidence generally finds small overall employment effects for modest increases, with larger risks if the floor is pushed far above typical local wages.
Good policy design options
•Set a clear target (for example, 50–60% of the local median wage, or a “living‑wage” market basket for a full‑time worker), then index annually.
•Use a federal floor indexed to national inflation, plus room for states/cities to layer higher, locally indexed floors.
•Build in periodic reviews (e.g., every 3–5 years) to recalibrate the level and the index.
•Pair the wage floor with complements like the Earned Income Tax Credit/child benefits, childcare and housing supports, and help for small firms (training, tax credits).
If you tell me your jurisdiction and policy goals (e.g., “cover basic needs for a single adult” vs “limit impacts on very small businesses”), I can suggest a concrete indexing formula and example numbers.