This paper introduces incomplete insurance against idioyncratic labour income risk into an otherwise standard New Keynesian business cycle model with involuntary unemployment. Following an adverse monetary policy shock that lowers aggregate demand, job creation is discouraged and unemployment risk persistently rises. Imperfectly insured households rationally respond to the rise in indosyncratic income uncertainty by increasing precautionary saving, thereby cutting consumption and depleting

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... gate demand even further; this in turn magnifies the initial labour market contraction and further raises unemployment risk. A Bayesian estimation of the model is used to assess the contribution of time-varying precautionary saving to movements in aggregate consumption.