Log minimum wage on log poverty line, 238 province-years, 34 provinces. The first specification asks whether a province's wage follows its own costs; the second removes whatever was happening to the whole country at once.

specification	β	se	se, clustered	t	95% CI
province FE	+1.146	0.034	0.042	27.12	+1.063 – +1.229
+ year FE	−0.262	0.206	0.218	−1.20	−0.689 – +0.164

The first interval is nowhere near zero; the second comfortably contains it. The apparent tracking was the national inflation trend the whole time.

cross-section, one year at a time

year	n	r	ρ	elasticity	r²
2015	34	0.557	0.510	0.646	23.4%
2016	34	0.471	0.354	0.568	16.6%
2017	34	0.522	0.426	0.528	22.7%
2018	34	0.531	0.452	0.519	22.9%
2019	34	0.542	0.465	0.515	24.2%
2020	34	0.517	0.416	0.497	21.9%
2022	34	0.496	0.412	0.493	21.1%

Even ignoring time, the poverty line accounts for a median 22.7% of the variation in what provinces set. Most of what fixes a minimum wage is not what that province costs.