Short answer: It depends on what you want the minimum wage to do.
If the goal is to ensure full-time workers can cover basic needs, then yes—tying the minimum wage to the cost of living (inflation and, ideally, local prices) helps preserve purchasing power and prevents political delays from eroding wages.
Reasons to keep it aligned with cost of living
•Maintains real wages: Prevents inflation from quietly lowering pay at the bottom.
•Predictability: Automatic adjustments help workers and businesses plan.
•Equity and turnover: Modest increases tend to raise low-end pay, reduce turnover, and narrow inequality; average employment effects in research are small to near zero for typical increases.
Reasons to be cautious or use complements
•Local variation: A single national number can be too high for some regions and too low for others.
•Business impact: Some firms (especially small, low-margin ones) may cut hours, benefits, or raise prices; effects are larger for big jumps.
•Targeting: Minimum wages aren’t tailored to family size; tools like the Earned Income Tax Credit (EITC), housing and childcare supports can better target need.
•Cyclicality: Automatic increases during downturns can be procyclical unless there are pause/cap rules.
Common policy designs
•Index to inflation (e.g., CPI) once the wage is set, to stop erosion.
•Use regional adjustments (regional price parities or local cost indexes) to reflect local living costs.
•Tie growth partly to median wages or productivity, not just prices, if the goal includes sharing economic gains.
•Phase-ins, youth/training wages, and small-business schedules to ease transitions.
•Pair with EITC and housing/childcare supports for affordability without concentrating all pressure on employers.
Bottom line: Many economists favor automatic inflation indexing (often with regional variation) after setting an appropriate level, because it preserves purchasing power and predictability. Whether the minimum should fully match a “living wage” is a normative choice; achieving that typically works best when combined with targeted supports rather than relying on the minimum wage alone.