Funnily enough every time this is studied the correlation is never really there. Minimum wages going up are typically a result of things getting more expensive not vice versa.

It's pretty easy to reason about too: the big organisations handling huge sums of money in a country have a much greater impact on an economy than the group of people (about 1%) making the bare minimum possible in order to to survive.

The only way it goes up explicitly because of minimum wage is if a business owner decides to maliciously meddle with supply and demand pricing to explicitly target people who might get a minimum wage increase—but no business owner intending to continue to do business would hand their competitor an advantage like that.

Minimum wage increases are generally proven to benefit pretty much everyone at all economic levels (yes, even business owners, because their customers are able to be more liberal with spending)

Minimum wage raises have almost no effect on inflation rates, or "shrinkflation" for that matter. The rises in minimum wage have been frequent over the last few years but it's almost entirely been cost push inflation that's caused the cost of living to be so much higher and so swiftly over the last few years. Longer term here's actually been huge wage stagnation for most. Which is its own issue. Off the back of the cost push causation, the UA invasion by Russia, covid etc profiteering by companies is definitely happening too.

New Labour had the longest period of sustained low inflation since the 1960s, despite overseeing a massive increase in wages for the lowest paid.

Increasing minimum wage doesn't really affect inflation.