Also, the BLS OES data still suggests that the majority of H1Bs make below the median in their field. Its possible there is large reporting bias, but the existence of a visa premium makes sense, and it seems likely some employers would find a way to use it to their benefit.
Obviously, a lot depends on the trends. People on H1B Visas eventually either become permanent residents or leave the country. And if they become permanent residents no longer in the H1B program, how does a study report them?I clearly make less than the median, because I am a junior staff in the pool. But, I cannot stay on H1B longer than 5 years, and almost everybody went through the same process. The initial claim that there is a systemic problem with the H1B program is quite extraordinary, and the soundbites can be interpreted innocuously by someone living the ordinary reality of the H1B program. I would be interested in a more convincing study.
In other words, people here on a H1B Visa can make the same as American workers with the same experience and still depress the mean wage of all employees. A high influx of new workers means you can implement more of an "up or out" attitude towards current workers. Experience counts for more if the probability of a new employee being good is lower. In other words, an employee's replacement value, how much better he is than the average expected replacement, is higher if the overall quality of the replacement pool is lower.
This can actually be more of a problem than just lowering wages for new employees. How does the influx of H1B workers affect the average age of programmers and engineers a company has? And what does that mean career wise, especially for employees in their 40's and 50's? Forcing a young person to realize they may not be competitive in the career field they chose has a completely different impact than waiting for a couple decades before telling a worker he just isn't all that special (and, presumably, even if not definitely, it would be the "just good enough" experienced workers that would experience the biggest impact).