I would have to see some reliable data before I would believe that "most" of the engineering jobs are going overseas.
Nevertheless, I have no doubt that the demand for chemical engineers is down in the traditional petroleum and chemical industries. Part of that may be the result of government policies that are unfriendly to such industries. (How difficult would it be to get approval to build a new refinery in the United States these days?)
More important, perhaps, is that those are "mature" industries. (That sounds much better than saying "dying" industries.) Even if the business climate were to improve drastically, it is doubtful that the petroleum and chemical industries would ever need as many chemical engineers as they once did.
The chemical engineering profession is either going to adapt or whither away. Chemical engineers appear to be adapting. They are going into nontraditional fields such as biotechnology, pharmaceuticals, materials, and food engineering. Even so, it would not surprise me if the numbers of chemical engineers declines.
Mechanical engineering is also going to follow chemical engineering. Many of the same plants that employ chemical engineers to run the processes employ mechanical engineers to run the equipment. I agree that many mechanical engineers will be forced to adapt, but the final numbers are still going to be lower in mechanical engineering.
Chemical and mechanical engineering have been the biggest fields for some time, and if you're admitting that those fields are declining, then we get back to my point. It's silly to encourage young people to go into fields where they will immediately find themselves scrambling to adapt to loss of jobs. They'd be much better off going into fields where the training matches the available jobs.
Undoubtedly, government policies are having a big negative impact on these industries. The high cost of natural gas is killing the chemical industry. One reason that the cost of natural gas is rising so much is that government policy is pushing us away from coal and nuclear energy. We have good supplies of coal. Coal is reasonably inexpensive, doesn't kill the ducks when spilled in a lake, and doesn't go boom when spilled on the ground. If we'd use more of our coal (and nuclear) for utility power, we'd have less demand for natural gas and therefore cheaper natural gas. This policy change would help the chemical industry tremendously.
Bill