The link between the minimum wage and unemployment is a touchstone with many of us who broadly believe in free markets, because if we're wrong about this, then we might be wrong about a lot of things.

The supply and demand model is one of economics's most enduring, intuitive, tractable, and predictive frameworks. Yes, there are always going to be many examples it doesn't apply to. Some things are too complex to be framed in that way, or beset with market failures. But basic market transactions should work the way it says. Slapping a blunt price floor on something as basic as labour should have very perverse effects.

And broadly, this is what the literature says. I know this because I've read nearly every minimum wage paper ever written. But it's not what all of the literature says. Everyone now agrees that in most cases minimum wage hikes do not lead to immediate appreciable drops in employment considered over the whole population.

The debate is mostly over which control groups and other methodological techniques we should use. Two new papers illustrate that minimum wage defenders should not see the work of Card & Krueger and Dube as the last and only word. There is more coming out all the time.

The first (pdf) is of Danes. When Danes turn 18 they face a sharply higher minimum wage, and a lot of them get fired on their birthday or soon after. But total wage payments are about the same—many get fired, but some get more per hour.

On average, the hourly wage rate jumps up by 40 percent when individuals turn eighteen years old. Employment (extensive margin) falls by 33 percent and total labor input (extensive and intensive margin) decreases by around 45 percent, leaving the aggregate wage payment nearly unchanged. Data on flows into and out of employment show that the drop in employment is driven almost entirely by job loss when individuals turn 18 years old. We estimate that the relevant elasticity for evaluating the effect on youth employment of changes in their minimum wage is about -0.8.

In this methodology the actual rules stayed the same for the whole study, but eligibility changed over the lifespan. By contrast, a new NBER paper looks at the imposition of a considerably higher minimum wage in Seattle on the low-wage sector: those who might be affected. Seattle rapidly hiked its minimum wage from $9.47 to $11, in 2015, and then to $13, in 2016.

Their results were in some ways starker than the Danish findings, since the higher wage per hour was far more than outweighed by the lower total hours.

Using a variety of methods to analyze employment in all sectors paying below a specified real hourly rate, we conclude that the second wage increase to $13 reduced hours worked in low-wage jobs by around 9 percent, while hourly wages in such jobs increased by around 3 percent. Consequently, total payroll fell for such jobs, implying that the minimum wage ordinance lowered low-wage employees’ earnings by an average of $125 per month in 2016.

Is it too soon to predict that eventually we'll all agree that the supply & demand model broadly works, even in the case of low wage labour?