Generalized Economics of Exchange Rates and Policy Options: Empirical Evidence

The minmax solution of foreign exchange rates is a consistent efficiency test for micro and macro efficiency. Deviations from the competitive equilibrium lead to persistent devaluation and output declines. The optimal fiscal and monetary policy is estimated with a minimum and shrinking variance of errors. The necessary and sufficient Lagrange multiplier, nonlinear stability, and convergence probability are defined. A family of evolution equations yields the minmax solution, which is equilibrium level of outcomes to be evaluated, when the response coefficient of strategies alternates in sign around the equilibrium. The larger the conditional convergence probability is, the steeper the wave curvature of the objective welfare and asset allocation would be, and the faster the convergence time is. Beyond the equilibrium, the positive sign of coefficient synergy tends to blow up and becomes transformed into a negative response. Thus we solve the optimization problem at all horizons and times. The Lagrange multiplier is a coordinator and indicates the evolution direction and the convergence probability towards the stable equilibrium. The generalized solution is found consistent with real data and satisfies the equality and inequality constraints of resources, when resources are potential rather than constant.