Economic Theory as Successive Approximations of Statistical Moments

This paper highlights the links between the descriptions of macroeconomic variables and statistical moments of market trade, price, and return. We consider economic transactions during the averaging time interval Δ as the exclusive matter that determines the change of any economic variables. We regard the stochasticity of market trade values and volumes during Δ as the only root of the random properties of price and return. We describe how the market-based n-th statistical moments of price and return during Δ depend on the n-th statistical moments of trade values and volumes or equally on sums during Δ of the n-th power of market trade values and volumes. We introduce the secondary averaging procedure that defines statistical moments of trade, price, and return during the averaging interval Δ2>>Δ. As well, the secondary averaging during Δ2>>Δ introduces statistical moments of macroeconomic variables, which were determined as sums of economic transactions during Δ. In the coming years, predictions of the market-based probabilities of price and return will be limited by Gaussian-type distributions determined by the first two statistical moments. We discuss the roots of the internal weakness of the conventional hedging tool, Value-at-Risk, that could not be solved and thus remain the source of additional risks and losses. One should consider economic theory as a set of successive approximations, each of which describes the next array of the n-th statistical moments of market transactions and macroeconomic variables, which are repeatedly averaged during the sequence of increasing time intervals.