Theoretical Economics and the Second-Order Economic Theory. What is it?

Abstract: The economic and financial variables of economic agents determine macroeconomic variables. Current models consider agents' variables that are determined by the sums of values and volumes of agents' trades during some time interval {\Delta}. We call them first-order economic variables. We describe how the volatilities and correlations of market trade values and volumes determine price volatility. We argue that such a link requests consideration of agents' economic variables of the second order that are composed of sums of squares of agents' transactions during {\Delta}. Almost any variable of the first order should be complemented by its second-order pair. Respectively, the sums of agents' second-order variables introduce macroeconomic variables of the second order. The description of the first- and second-order macroeconomic variables establishes the subject of second-order economic theory. We highlight that the complexity of second-order economic theory essentially restricts any hopes for precise predictions of price probability and, at best, could provide estimates of price volatility. That limits the predictions of price probability to Gauss's approximations only.