I'm not an academic economist, so what do I know, but I think the authors aare missing something else.
I think the productivity was in some part driven by minimum wage laws. At lower wages, developing, installing and maintaining ordering kiosks and smart phone ordering apps makes less sense, because fast food cashiers are so cheap. When fast food cashiers become more expensive (and the technology costs come down) kiosks and apps make more sense. The same amount of food sold without the cost of cashiers is the resultant increase in productivity.
So my theory in a nutshell was that cashiers added little value. Substituting capital for labor led to labor productivity gains.
I think the productivity was in some part driven by minimum wage laws. At lower wages, developing, installing and maintaining ordering kiosks and smart phone ordering apps makes less sense, because fast food cashiers are so cheap. When fast food cashiers become more expensive (and the technology costs come down) kiosks and apps make more sense. The same amount of food sold without the cost of cashiers is the resultant increase in productivity.
So my theory in a nutshell was that cashiers added little value. Substituting capital for labor led to labor productivity gains.