Constructing bivariate density forecasts of inflation and output growth using copulae: modelling dependence using the Survey of Professional Forecasters

Traditionally density forecasts of inflation and output growth are published separately without any obvious indication of how they are related. But ‘flexible’ inflation targeting motivates concern with the underlying bivariate density forecast. This paper, therefore, suggests use of copulae to model the dependence between known marginal density forecasts. Estimated copula functions are used to back-out the ‘most likely’ (i.e. the most data consistent) bivariate density forecast given knowledge of the marginal densities. In an application to the Survey of Professional Forecasters we find that the dependence between the inflation and output growth density forecasts over the period 1982-2006 was negative but time-varying. Conditional copula functions are then estimated to try and explain this time-variation.