More bad news for the middle class: When the economy recovers, jobs in the middle won’t. That is the conclusion of an important new study that connects a long-term trend in the labor market with the business cycle of recession and rebound.

Nir Jaimovich, an economist at Duke University, and Henry E. Siu, an economist at the University of British Columbia, take as their starting point one of the most important continuing changes in Western developed societies. That shift is what economists, most notably David Autor of the Massachusetts Institute of Technology, have called the ‘‘polarization’’ of the job market. Maarten Goos and Alan Manning, extending the research to Britain, have more colorfully dubbed it the dual rise of ‘‘lousy and lovely’’ jobs.

Their point is that, thanks to technology, more and more ‘‘routine’’ tasks can be done by machines. The most familiar example is the increasing automation of manufacturing. But machines can now do ‘‘routine’’ white-collar jobs, too — things like the work that used to be performed by travel agents and much of the legal ‘‘discovery’’ that was done by relatively well-paid associates with expensive law degrees.

The jobs that are left are the ‘‘lovely’’ ones, at the top of the income distribution – white-collar jobs that cannot be done by machines, like designing computer software or structuring complex financial transactions. A lot of ‘‘lousy’’ jobs are not affected by the technology revolution, either – nonroutine, manual tasks like collecting the garbage or peeling and chopping onions in a restaurant kitchen.

An extensive body of economic research has shown that job polarization is happening throughout the Western developed world. It accounts for many of the social and political strains we have experienced over the past three decades, particularly the increasing divide between the people at the top and at the bottom of the economic heap, and the disappearance of those in the middle who were once both the compass and the backbone of our societies.