A tail of three occasionally-binding constraints: a modelling approach to GDP-at-Risk

We build a semi-structural New Keynesian model with financial frictions to study the drivers of macroeconomic tail risk (‘GDP-at-Risk’). We analyse the empirically observed fat left tail of the GDP distribution by modelling three key non-linearities emphasised in the literature: 1) an effective lower bound on nominal interest rates, 2) a credit crunch in bank credit supply when bank capital depletes, and 3) deleveraging by borrowers when debt service burdens become excessive. We obtain three key results. First, our model generates a significantly fat-tailed distribution of GDP – a finding that is absent in most linear New Keynesian and RBC models. Second, we show how these constraints interact with each other. We find that an economy prone to debt deleveraging will experience significantly more credit crunch and effective lower bound episodes than otherwise. Moreover, as the effective lower bound becomes more proximate, the frequency of credit crunch episodes increases significantly. As a rule of thumb, we find that each 50 basis point decline in monetary policy headroom requires additional capital buffers of 1% of assets or 2%–2.5% points lower debt service burdens to hold the risk level constant. Third, we use the model to generate a historical decomposition of GDP-at-Risk for the United Kingdom. The implied risk outlook deteriorates significantly in the run-up to the Global Financial Crisis, driven by depleted capital buffers and increasing debt burdens. Since then, GDP-at-Risk has remained elevated, with greater bank resilience and lower debt offset by the limited capacity of monetary policy to cushion adverse shocks.