Theory of variable-structure systems (VSS) and its applications to economic dynamics

This study examines the economic dynamics when economic agents incur information and decision errors due to the presence of market frictions, transaction costs, or agents' C-D gaps; to determine whether Leon Walras's disequilibrium model of tatonnement is compatible with the theme prevalent among Austrian economists that views market as a process; and to provide a viable alternative to the standard but somewhat restricted concept of "saddle-path stability."; The method used is the variable-structure system (VSS) approach and its associated sliding mode control. The solution concept of Filippov for differential equations with discontinuous right-hand sides is used to define the dynamics along the user-chosen switching surface.; The findings indicate four major conclusions: (1) By using the Filippov solution concept to reinterpret the Walrasian pricing rule as a simple switching mechanism, the disequilibrium model of tatonnement is shown to be more representative of Walras's idea than the pledges model. (2) Under the transaction-costs or C-D gap constrained model, the behavioral regularities of flexible accelerator do not simulate optimizing behavior and are not an approximation of maximizing so as to always choose most preferred alternatives. Rather, they represent self-stabilizing rules of thumb used by agents to cope with possible information and tracking errors. (3) The reversal of saddle-path instability into dynamic stability is attained through the idea of regime switching in the presence of transaction costs or C-D gaps. Transaction costs or C-D gaps are thus shown to be an important stabilizing factor. (4) When the disequilibrium dynamics are introduced for the study of exchange-rate movements, the overshooting of exchange rate over its long-run level may not occur. The exchange-rate dynamics with regime switching also illustrate that the perfect-foresight or rational-expectations model may provide an effective equilibrium concept underlying an adaptive expectations adjustment process.