Debt and convergence: Evidence from the EU member states

•We add debt interaction terms in growth regressions to study convergence effects.•Higher debt levels are associated with slower convergence among EU member states.•Convergence slowdown is 3 to 5 times stronger for public compared to private debt.•Public debt relationship with convergence could partly reflect private debt effects.•Convergence may stop at very high levels of total, public, and private debt.