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We analyze Ramsey optimal monetary policy in a New Keynesian model with skill loss from long-term unemployment and endogenous growth through learning-by-doing. The competitive equilibrium is shown to be inefficient, despite imposing the Hosios condition, due to firms failing to internalize the effects of current hiring on (i) future labor productivity through learning-by-doing; and (ii) future training costs of other firms. These externalities are complementary to each other, thereby justifying marked deviations from price stability. In a calibrated version of the full model, we show significant deviations of the optimal policy from constant inflation, and from Taylor-type rules, in response to productivity shocks.