The U.S. can't afford to put President Trump's $1 trillion infrastructure spending plan into action, former Federal Reserve Chairman Alan Greenspan told CNBC Thursday. 

Infrastructure spending does not have a return on investment until the projects are complete, Greenspan warned, and will only serve to deepen the public sector's debt obligations. 

"The question is who is financing this trillion dollars in infrastructure. At the moment, we can't afford it," Greenspan told CNBC Thursday. 

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