Say there is a rich country without a minimum wage. Some people rightfully dislike challenging labor. For example, in a remote college town, some people fold student laundry at $4/hr for 40 hours a week, and work at the local library for $6/hr for another 20 hours a week, yielding a weekly salary of $280. The federal government determines that $280/week is necessary, and therefore requires a $7/hr minimum wage based on a 40 hour work week. Some time later an economist uses regression analysis to show that neither employment nor output fell, how could this be?
Though wages at existing jobs probably increased without reducing net employment to some extent, through some third-order mechanism, a simpler and more tangible answer is available. Suppose individuals in the above example had a target wage of $250, without which they would die. The available hours for employment doing laundry or working at the library are no longer high enough to meet the target. Therefore, some such individuals started working as low-end construction workers earning $11/hr part-time, a job which they never wanted given its physical rigor.
Small increases in the minimum wage at non-random times over a long history may not demonstrate this effect. But there are lots of people who may be working jobs that are mentally, emotionally, or physically strenuous because easier labor has been criminalized. Hence, demonstrating that there is not a significant decline in employment after the minimum wage, by itself, does not show anything.
Lots of people could be truck drivers or natural gas workers in North Dakota, probably earning way more than they do today. They choose not to because they don’t want to drive around the country all day or leave their families as modern-day migrant workers. People have the right to make this choice. If it is offensive for whatever reason that some people are not rich enough, we should give them cash instead of criminalizing their choices.