It looks like another case where we have a skills mismatch. In a NYT column criticizing Sean Hannity's housing investments, Bill Sapotio tells us that the housing industry:
"[...]still needs some 200,000 workers, with some of that shortfall no doubt linked to current immigration policy, or the fear of it. The need is so great that the Home Depot Foundation is putting up $50 million to help train and hire skilled workers."
The problem with this story is wages are not rising especially rapidly in construction. According to the Bureau of Labor Statistics, the average hourly pay of production and non-supervisory workers in the sector rose 3.9 percent. That's not bad, but before the recession, they were rising over 4.0 percent annually and sometimes over 5.0 percent.
Average Hourly Wage in Construction: Production and Non-Supervisory Workers
Source: Bureau of Labor Statistics.
If there actually is a shortage of construction workers as this piece claims, then we seem to have more evidence of employers who lack the skills necessary to do their job. They apparently don't understand that if you want to hire more workers, you have to offer higher pay.