Someone asked this recently, so I am posting a response here.

For as long as I've been in the statistics/biostatistics profession, students haven't had difficulties finding jobs after graduation. There aren't enough biostat and stat MS and PhD grads to come close to satisfying current demand. Quite a number of companies have more than 100 PhD (bio)stat grads and would be willing to hire as many as they could find, if they could find more. Even if one industry might decrease their demand for our grads, a couple more industries crop up, needing our students ever more badly. Currently rapidly growing are the internet marketing companies (Amazon, Google) and the social-media companies (Facebook, Twitter). News organizations are beginning to hire some statisticians. And any company large enough to need one statistician is likely to need five more in short order. Lately HMO, health care and hospital type organizations have been increasing their share of our students. The traditional employers like Biotech and Biopharm have not slacked off their hiring. And more Biotech and Biopharm companies seem to be created every week. Lets not forget public policy, county, state and federal health departments, survey companies (political, marketing), JD Powers, Consumers Reports, and so on. Did I mention academia? Academia is still growing for statisticians too.

Outsourcing would have to go to people somewhere. Presumably the fear is that the jobs might go to China and India, having the largest populations out there. Chinese undergrads very much want to come here, apparently because there are many more jobs and much better jobs here than in China. I've heard that it pays US companies to outsource statistics but I find it very difficult to believe there are sufficient even partially trained people any where on the planet to be able to outsource many biostat jobs. And anyone you out-source to will need to be managed by someone who knows more statistics than they do. India and China are not yet training many statisticians, though both train some really great people.

For decades, many people with only basic statistical skills have found jobs as statisticians because there are so few statisticians. UCLA has thousands of researchers, most of whom could use a statistician to help with their research. There are now maybe 50 PhD statisticians, (not all faculty) on campus, and we don't begin to make a dent in the demand. Thus there are psychometricians, econometricians, quantitative social, educational and political scientists, computer scientists and many others who operate as statisticians because they can run software and fit basic and some complex models. The outside world isn't much different.

There has always been a good demand for statisticians, and the demand should be increasing as society is increasingly valuing the tools we understand and the services we supply.