A lot of it gets lost to private contractors and consultants. Privatization is nice if you don't have the labor pool to do the work with public employees, but it's very wasteful and costly because everyone down the line needs to get their chunk of the pie. Public can run at cost or over budget and still be a huge success because no one is clamoring for a >30% profit margin. It also invites nepotism.
European cities also generally use private contractors for construction. The Paris subway expansion, which is proceeding at a fraction of the per-mile cost of New York's Second Avenue subway, is being done by private contractors: https://tunneltalk.com/France-25Oct2018-Grand-ParisExpress-n....
