Short answer: It depends on your goal.
If the goal is to keep a constant basic standard of living for low‑wage workers, then yes—the minimum wage should generally track the cost of living. If the goal is to minimize potential employment or price effects, some prefer a looser link (or indexing to median wages/productivity instead of prices).
How indexing to cost of living helps
•Preserves purchasing power so the wage floor doesn’t quietly erode between legislated hikes.
•Increases predictability for workers and employers; avoids big, disruptive jumps.
•Limits political drift where the real value falls for years.
Trade‑offs and caveats
•One national index can miss large regional cost differences; local variation matters.
•Mechanical indexation during inflation spikes can fuel persistence; many proposals use smoothing, caps, or multi‑year averages.
•Some small, thin‑margin sectors (restaurants, care) feel costs more; gradual phase‑ins help.
•Minimum wage alone is a blunt anti‑poverty tool; many beneficiaries aren’t in poor households. It works better paired with tax credits (e.g., EITC), childcare, and housing supports.
What research tends to find (on average)
•Moderate, predictable increases show small to negligible employment effects overall; very large or abrupt hikes in low‑wage regions carry higher risk.
•Prices rise modestly in affected sectors; earnings at the bottom increase and wage inequality narrows.
•Poverty reductions are stronger when combined with refundable tax credits and benefits.
Practical policy designs
•Pick a benchmark: CPI (prices) to maintain living standards, or a share of the median wage to maintain relative position; some blend both.
•Allow regional or city‑level rates to reflect local costs.
•Set a multi‑year path to a target, then index annually with guardrails (caps/floors, pause triggers in recessions).
•Review exemptions (tipped/training wages) and enforcement so the policy works as intended.
Bottom line: A minimum wage that roughly keeps pace with the cost of living—implemented with regional tailoring, gradual phase‑ins, and safeguards—is a reasonable default. It shouldn’t stand alone; pairing it with earned income tax credits and support for housing and childcare delivers better, more reliable gains for low‑income households.
If you want, tell me your country/state or whether you’re asking as a voter, policymaker, or employer, and I can tailor specifics.