Lower bounds of uncertainty and upper limits on the accuracy of forecasts of macroeconomic variables

Abstract

We consider the randomness of values and volumes of market deals as a major factor that describes lower bounds of uncertainty and upper limits on the accuracy of the forecasts of macroeconomic variables, prices, and returns. We introduce random macroeconomic variables, whose average values coincide with usual macroeconomic variables, and describe their uncertainty by coefficients of variation that depend on the volatilities, correlations, and coefficients of variation of random values or volumes of trades. The same approach describes bounds of uncertainty and limits on the accuracy of forecasts for growth rates, inflation, interest rates, etc. Limits on the accuracy of forecasts of macroeconomic variables depend on the certainty of predictions of their probabilities. The number of predicted statistical moments determines the veracity of macroeconomic probability. To quantify macroeconomic 2nd statistical moments, one needs additional econometric methodologies, data, and calculations of variables determined as sums of squares of values or volumes of market trades. Forecasting of macroeconomic 2nd statistical moments requires 2nd order economic theories. All of that is absent and for many years to come, the accuracy of forecasts of the probabilities of random macroeconomic variables, prices, and returns will be limited by the Gaussian approximations, which are determined by the first two statistical moments.