Talk to the founders of Silicon Valley startups and they will tell you that the single greatest obstacle they face after they obtain funding is the dearth of skilled talent. They say this is limiting their ability to innovate. A group of tech CEOs told President Obama in March that five companies alone — IBM, Intel, Microsoft, Oracle, and Qualcomm — had 10,000 job openings in the US. They called this “one of the biggest economic challenges facing our nation” and asked the president to address the need for more qualified, highly-skilled professionals, domestic and foreign, and to urgently enact immigration reform.

Polarization is often stark around highly-skilled immigration, one of the issues at the heart of the tech sector’s pleas. It can be difficult to separate fact from fiction.

Take academics Hal Salzman of Rutgers, Norm Matloff of UCLA, and Ron Hira of RIT, who insist that there is no skilled labor shortage. They published papers through big labor think tank Economic Policy Institute that support its arguments against immigration reform and the expansion of H-1B visas for foreign workers. Salzman says that the US graduates far more workers in Science, Engineering, Technology, and Mathematics (STEM) than the tech industry needs and that foreign workers are causing Americans to get discouraged and join other professions. Matloff claims that foreign students have talent lesser than, or equal to, their American peers. Hira says that claims of a shortage are a ploy by tech companies to bring wages down and to replace Americans with foreign workers.

The comment boards of articles about immigration are often filled with heart-wrenching stories of American engineers who can’t find employment. They too blame foreigners for their woes. So what gives? Could there indeed be a vast conspiracy by the technology industry to exclude Americans from the innovation economy?

The truth is we’re not seeing the full picture around highly-skilled immigration. To get there, we need to better understand and debunk myths around three key issues: labor mobility, wages, and the rate of invention.

While there are unemployed engineers in the US at the same time that there are severe shortages of talent in the tech centers, this is really a mismatch of skill, location, and need.

Issue 1: Labor mobility The demand for technology workers cannot be accounted for by merely tallying the numbers of native-born STEM degree-graduates. Many leave the field for other pursuits like finance and law — which sometimes pay higher wages. Skill requirements (such as programming languages and computer platforms) also shift rapidly, rendering skills of significant parts of the workforce obsolete.

But more importantly, the US has amongst the highest rate of home ownership in the world — which makes it difficult for some workers to move. This is made worse by depressed home prices and the high cost of living in places like Silicon Valley and New York City — where tech job demand is high.

In a report titled “The Search for Skills,” Neil Ruiz, Jill Wilson, and Shyamali Choudhury of the Brookings Institution analyzed demand for H-1B workers in metropolitan areas. They found that supply and demand for skilled labor varies by region. Demand for H-1B’s is highest in tech centers like New York, Silicon Valley, Los Angeles, Washington, D.C., Virginia, Chicago, and Boston. Not coincidentally, these places are among those with the lowest unemployment rates for engineers.

They also found the same trend in regions that house America’s research centers. Places such as Columbus, Ind., where engine manufacturer Cummins is based, and Rochester, Minn., home of medical giant Mayo Clinic, are among the regions with the highest demand for H-1Bs and lowest unemployment rates for bachelor’s degree holders (3% in Columbus and 1.5% in Rochester for 2010). In other words, where there is demand for skilled workers, there is also the most innovation economic growth.

Issue 2: Wages One argument that opponents of skilled immigration make is that if there were indeed an engineering shortage, salaries would rise. Salzman says he analyzed U.S. census data to determine that engineering salaries have remained flat or declined over the past two decades. So there is no engineering shortage, he argues, and therefore foreign workers are discouraging natives from entering STEM fields.

This analysis is deeply flawed. You can’t draw reasonable conclusions about the needs of technology firms by looking at data at the computer industry level. It is a very diverse industry in which there is rapid creation and destruction. Workers with the right skills receive large salary increases while those with obsolete skills see their careers stagnate. This is what defines the tech world and fuels innovation.

Indeed when Jonathan Rothwell and Neil Ruiz of Brookings analyzed salaries in occupations that were receiving the most H-1B requests, they found that wage growth in these was actually stronger than the national average. They also found that H-1B workers are paid more than US native-born workers with a bachelor’s degree ($76,356 versus $67,301 in 2010) and even within the same occupation and industry for workers with similar experience. This also counters the argument that foreign workers have lesser skills. Companies would only pay such a premium if this group — which includes foreign students graduating from US universities — were the “best and brightest” and did have the skills that companies need.

Issue #3: Invention A growing body of research has found that a higher concentration of H-1B holders in STEM fields actually boosts invention. In their National Bureau of Economic Research work “How Much Does Immigration Boost Innovation?” Jennifer Hunt and Marjolaine Gauthier-Loiselle found that each 1% increase in the population of immigrant college graduates increased overall patents per capita by 9-18%.

In another research paper, “The Supply Side of Innovation,” William Kerr of Harvard Business School and William Lincoln of the University of Michigan studied the impact of the concentration of H-1B visa holders in certain metro areas with regard to innovation. Kerr and Lincoln reported a 10% growth in H-1B population corresponded to a 6%-12% growth in invention (measured as patents) by the largest immigrant groups — Indians and Chinese — and a 0.5% to 1% growth in patents by US natives. In other words, total invention increases with higher admission of skilled foreign workers, primarily through the direct contributions of immigrant inventors.

Ultimately, the debate shouldn’t be about shortages or gluts. Having more engineers and scientists means there will be more innovation and the economic pie will grow larger. In the global competition for highly-skilled workers, US companies and institutions must also seek the best talent, wherever they can find it. Consider that only 4% of the world’s undergraduate engineering degrees go to US citizens. In contrast, 56% are earned in Asia and 17% of engineering degrees are awarded to Europeans.

The U.S., without doubt, has to improve its education system and graduate more high-quality engineers and scientists. But asking US technology and engineering companies to restrict their search geographically — unless they prove that there is a shortage of talent — makes as much sense as telling the National Basketball Association that it must only recruit players who were born within the United States.