Here's a clue to what Rowe is talking about - raises in the minimum wage have a direct impact on the SPEED that automation is implemented. Rowe (nor anyone) is saying minimum raise is the ONLY cause of automation.
Let's see if I can keep this simple enough for even you....a fast food employee makes $8/hour. The cost of a machine to replace what he/she does costs $12/hour. Employee keeps job until the cost of the automation gets below the wage cost. Now, via increase in the minimum wage, the same employee has to make $15/hour. Guess who is now out of a job?????
The reason to automate are many, the cost of minimum wage is near the bottom of the reasons.
What the employee makes is not the full cost of employing them either.