The NYT had an article reporting on how the reduction of immigration had led to a shortage of workers in many industries, highlighting the case of residential construction. While there have been modest increases in real wages in residential construction, the data don't provide evidence of a serious shortage of workers.
Since 2000, the inflation-adjusted average hourly wage for production and nonsupervisory workers in the industry has increased by 14.3 percent, an average of 0.7 percent annually, as shown below.
Real Wages in Residential Construction
Source: Bureau of Labor Statistics.
While this is better than in some industries, this pace of wage growth is well below the economy-wide average rate of productivity growth. It is difficult to argue that the industry is hit by a labor shortage if wages are not even keeping pace with productivity growth, although it is not surprising that employers, like the ones quoted in this piece, complain about having to pay high wages.