Some reporting is required depending on state or federal financial support, i.e. if students qualify for financial aid, most institutions have to report placement rates.
But there is no guarantee those numbers mean a damn either.
The goal of retraining is also not necessarily to help workers find better paying jobs, but any paying job. If their previous field is obsolete, than retraining for any viable occupation is an improvement.
The main issue is not retraining, but supporting growth industries that will absorb excessive unemployment. For the US, I think industries which have that potential are renewable power generation, at every level, from design to manufacturing to service and repair; robotics, especially development of consumer-level maintenance robots such as Roomba and drone delivery vehicles (instead of 2000 lb vehicles to deliver pizzas, how about 200 lb ones, either aerial or ground.);and higher education.
The US has one of the premier higher education systems in the world and already caters to a growing number of international students. While it is important for regions to develop their own systems, the US can still be a leader in this area. As the middle class continues to grow world-wide so will the demand for higher education. Instead of being the world’s policeman, the US could focus on being the world’s professor, not to cherry-pick and enable brain drain, but to educate students for their home country, especially for Africa and Latin America where demand is greater than supply.
Many cities already rely on being a ‘college town’ as the main driver for their local economy. I would say that is where our comparative advantage lies. The cultural environment of those towns and cities create a richer environment for students than most areas, especially in Africa and Latin America.
No one industry will provide the ‘magic’ fix, and no industry will scale up to the necessary size without significant government collaboration (which could be mostly regulatory, not financial, but most likely both.) Economic development with gov support is not new, and has been effective in many areas, particularly in Asia and in the US (easements for the railroads and utilities for example). Ideological restraints, not technological barriers, prevent us from following suit. The key issues of such policies are transparency and equity, but they have been shown to be effective and efficient.
Complaints that job training programs do not all have 90% placement rates (or even 50%) miss the point of those programs - that their graduates qualify for an existing occupation, not an obsolete one. Their goal is not to aim for full employment, but mitigate the damage from structural unemployment. They may lead to gluts in supply for certain jobs, but it is better than a glut in supply for non-existent jobs. I would rather be a well-trained, but unemployed auto mechanic than a carriage maker. When a recession ends, I know which will lead to greater opportunities.