There are 2 big reasons workers' wages haven't risen for so long

• A decline in union participation helps explain stagnant wages for US workers.
• Research points to automation as another factor in labor's falling share of national income.
• The same trend is taking place all over the world, not just the United States.

Federal Reserve Chair Janet Yellen and other top economists say productivity is the key to long-run wage growth for American workers. That would be true - if only the fruits of economic expansion were actually trickling down to average incomes.

"If the labor market continues to improve we will see some pickup in wage growth, but we have at the moment low productivity growth," Yellen told Congress in her last official testimony in her current term as Fed Chair, which ends early next year. "That wage growth would be greater over time if productivity growth picks up."

Two new studies indicate the process might not be so simple. That's because for decades now the benefits of a more productive economy have flowed increasingly to corporations at the expense of workers.

It's happening for a bunch of reasons, research shows. The two main ones: a sharp decline in worker unionization and the automation of certain types of work that has further eroded the bargaining power of labor.

A new report from the International Monetary Fund zeroes in on one particular trend: "The US labor share of income has been on a secular downward trajectory since the beginning of the new millennium."

"Across both state and industry, we show the decline in the labor share is broad-based but the extent of the fall varies greatly," write IMF economists Yasser Abdih and Stephan Danninger. "In addition to changes in labor institutions, technological change and different forms of trade integration lowered the labor share."

The IMF research finds the share of US national income going to workers in the form of wages and benefits has declined 3.5 percentage points since 2000. Before that period "while the labor share displayed some ups and downs, there was no notably long-term trend."

Trade and globalization also played some role in the process, the paper suggest, because the sectors most deeply affected were also those most exposed to international trade, such as information technology, manufacturing, transportation, mining, and agriculture.

The findings come with a rather stern warning about social and growth effects from the decline in labor's share of the economic pie, which has become a major political issue in the United States and other Western nations.

It also serves another reminder that the IMF has recently begun delivering advice to rich nations of the sort it used to reserve for emerging markets.

The result has been rising income inequality, which tends to rise as the labor share of national income shrinks.

"This income inequality, in turn, entails large social costs. It deprives lower-income households of the ability to stay healthy and accumulate physical and human capital and has been shown to negatively affect the pace and sustainability of economic growth," the study says.

"The downward trend in the labor share is a widespread and global phenomenon," the authors add.

A second paper by economists from the Organization for Economic Cooperation and Development (OECD) focuses specifically on the global nature of the trend in declining worker unionization. On average across OECD countries, just 17% of workers belong to a union, down from 17% oil 1985 the paper finds.

As for solutions, the paper offers a few outlines, but recognizes the lack of easy policy options, particularly given the changing nature of work.

"The picture that emerges from the data discussed above is complex, but confirms the broad decline in the use of collective bargaining to set the terms of employment," write Sandrine Cazes and co-authors. "Some innovative responses are beginning to emerge, but we don't know yet how well they will work."

Rising part-time work and the advent of contract labor, often happening outside of an office or factory context, poses "a major challenge for collective bargaining systems given that they are still largely based on the concept of a standard work relationship."

Unions better get to work.