Calibrated forecasting and merging

Consider a finite-state stochastic process governed by an unknown objective probability distribution. Observing the system, a forecaster assigns subje ctive probabilities to future states. The resulting subjective forecast mer ges to the objective distribution if, with time, the forecasted probabiliti es converge to the correct (but unknown) probabilities. The forecast is cal ibrated if observed long-run empirical distributions coincide with the fore casted probabilities. This paper links unobserved reliability of forecasts to their observed empirical performance by demonstrating full equivalence b etween notions of merging and of calibration, and discusses implications of this equivalence for the literature of forecasting and learning. Journal o f Economic Literature Classification Numbers: C5, C11, C73, D83. (C) 1999 A cademic Press.