From Free Exchange at The Economist:

In the first [paper] Isaac Sorkin of the University of Michigan argues that firms may well substitute machines for people in response to minimum wages, but slowly. Mr Sorkin offers the example of sock-makers in the 1930s, which took years to switch to less labour-intensive machines after the federal minimum wage was brought in. He also explains how this finding squares with other research. Most studies look at past minimum wage increases that were not inflation-proofed. Firms may decide not to go through the hassle of investing in labour-saving machines if the minimum wage will affect them less over time. But they could respond differently to a more permanent increase.

Mr Sorkin crunches the numbers, using a model of the American restaurant industry in which companies choose between employees and machines. He investigates the effect of a permanent (ie, inflation-linked) increase in the minimum wage and shows that the tiny short-run effects on employment normally seen are fully consistent with a long-run response over 100 times larger. The lack of evidence for a big impact on employment in the short term does not rule out a much larger long-term effect.

In a second paper, written with Daniel Aaronson of the Federal Reserve Bank of Chicago and Eric French of University College London, Mr Sorkin goes further, offering empirical evidence that higher minimum wages nudge firms away from people and towards machines. The authors look at the type of restaurants that close down and start up after a minimum-wage rise. An increase in the minimum wage seems to push some restaurants out of business. The eateries that replace them are more likely to be chains, which are more reliant on machines (and therefore offer fewer jobs) than the independent outlets they replace. This effect has not been picked up before because the restaurants which continue to operate do not change their employment levels, so the jobs total does not shift much in the short run.