A Bivariate Distribution for Inflation and Output Forecasts

The contribution of this paper is to derive a bivariate distribution for inflation and output uncertainty with a well-defined role for subjective judgements. The marginal distributions for inflation and output growth are derived from uncertainty in the macro variables that are deemed to be important for future inflation and output growth. The uncertainty in the macro variables is based on their historical standard deviations, but we allow these to be subjectively adjusted if there is reason to be more or less uncertain than historically. We also allow for a subjective assessment of the balance of risk, i.e. whether the distributions are symmetric or not. Given the marginal distributions for inflation and output growth we derive a bivariate distribution using the translation method. Having derived the bivariate distribution we are in a position to discuss inflation forecast uncertainty conditional on the growth of output (or vice versa). The analysis can readily be extended to the case of more than two variables.