Combining disaggregate forecasts or combining disaggregate information to forecast an aggregate

To forecast an aggregate, we propose adding disaggregate variables, instead of combining forecasts of those disaggregates or forecasting by a univariate aggregate model. New analytical results show the effects of changing coefficients, mis-specification, estimation uncertainty and mis-measurement error. Forecastorigin shifts in parameters affect absolute, but not relative, forecast accuracies; mis-specification and estimation uncertainty induce forecast-error differences, which variable-selection procedures or dimension reductions can mitigate. In Monte Carlo simulations, different stochastic structures and interdependencies between disaggregates imply that including disaggregate information in the aggregate model improves forecast accuracy. Our theoretical predictions and simulations are corroborated when forecasting aggregate US inflation pre- and post 1984 using disaggregate sectoral data.