In summary the Indo-Europeanist’s data and method do not allow the question ‘When was PIE spoken?’ to be answered in any really meaningful or helpful way.
Source, in full
Clackson, James (2013). The Origin of the Indic Languages – The Indo- European Model, in Perspectives on the Origin of Indian Civilization (ed. Marcantonio, Angela and Jha, Girish Nath), Dartmouth: Center for Indic Studies, University of Massachusetts and New Delhi: D.K. Printworld (P) Ltd.