No. There is no economic requirement that the minimum wage "keep up" with the cost of living, and forcing it to do so via indexing or large hikes often harms the low-skilled workers it intends to help.
Basic Economics, Not Slogans
Wages are prices for labor. They emerge from productivity (what a worker adds to output), supply and demand for skills, and local conditions—not from a moral formula tying them to a basket of consumer goods. The "cost of living" is itself an outcome of productivity, housing/land-use rules, energy policy, monetary inflation, and taxes. Artificially raising the price floor on low-skill labor does not magically raise the value those workers create. When the mandated wage exceeds a worker's marginal revenue product, employers respond by:
•Hiring fewer people (or none)
•Cutting hours
•Automating or substituting capital
•Raising prices (which hits low-income consumers hardest)
•Relocating or closing
This is not theory-only. It is the standard prediction of price-floor analysis, visible in teen/unskilled unemployment rates, which are chronically higher precisely where minimum wages bind hardest.
Evidence Over Intentions
•Employment effects are real: Meta-analyses and studies by economists such as David Neumark, William Wascher, and others consistently find disemployment effects, especially for young, low-skilled, and minority workers. The famous Card-Krueger fast-food study claimed otherwise but has been heavily criticized for data and methodology problems; later work (including re-analyses and studies of Seattle's large hike) found reduced hours and earnings for the targeted group. Congressional Budget Office estimates of U.S. federal hikes routinely project hundreds of thousands of lost jobs alongside earnings gains for some.
•Indexing locks in the damage: Tying the minimum to CPI or a "living wage" measure means it ratchets upward even in recessions or when productivity stagnates, amplifying unemployment exactly when labor markets are weak. It also ignores massive geographic variation—$15+ may be irrelevant in rural Mississippi and binding in high-cost coastal cities, yet a national or blunt rule cannot fine-tune this.
•Living standards rose without constant real-minimum increases: Real wages and consumption for lower-income households have climbed over decades primarily through productivity growth, cheaper goods (trade, innovation), and dual-income households—not because the statutory minimum tracked a price index. Periods of high real minima have coincided with higher youth unemployment.
•Cost-of-living drivers are often policy failures: Housing costs (the biggest item for many) explode under zoning, environmental reviews, and NIMBY restrictions—not because the minimum wage lagged. Inflation is a monetary phenomenon. Fixing those is higher-leverage than mandating wages.
Trade-offs and Better Levers
Supporters correctly note that some workers who keep their jobs get a raise and that very modest minima in tight markets show smaller effects. That does not establish a "need" for permanent COL matching. Concentrated benefits (visible raises) plus diffuse costs (unseen job loss, slower hiring, higher prices) make it politically attractive regardless of net effects. If the goal is helping the poor:
•Earned Income Tax Credit and similar wage subsidies raise incomes without pricing people out of jobs.
•Remove barriers to work and mobility: occupational licensing, housing supply restrictions, poor K-12 skills formation, and policies that increase low-skill labor supply faster than demand.
•Growth and skills matter more than floors. Workers with higher productivity command higher pay in competitive markets; the long-run path out of low wages is human capital and capital deepening, not legislation.
A minimum wage that is low enough to be mostly non-binding can set a weak norm against exploitation without large distortions. Treating it as an automatic COL escalator turns it into a blunt, ongoing intervention whose costs fall disproportionately on the least employable. For data and literature, see work from the NBER, CBO scorekeeping on wage hikes, and reviews by Neumark et al. Claims that "studies show no downside" usually cherry-pick or ignore the broader body of evidence.