Managing rational routes to randomness

Abstract

Within the seminal cobweb model of Brock and Hommes, firms adapt their price expectations by a profit-based switching behavior between free naïve expectations and costly rational expectations. Brock and Hommes demonstrate that fixed-point dynamics may turn into increasingly complex dynamics as the firms' intensity of choice increases. We show that policy-makers are able to manage rational routes to randomness by adjusting profit taxes. As suggested by our analytical and numerical analysis, policy-makers should increase (decrease) profit taxes if destabilizing expectations generate higher (lower) profits than stabilizing expectations to alter the composition of applied expectation rules and thereby to promote market stability. Our results are not restricted to cobweb models: a huge body of literature demonstrates that rational routes to randomness may emerge in many different markets. KeywordsCobweb models; discrete choice approach; intensity of choice; profit taxes; stability analysis; policy implications. JEL ClassificationD84; E30; Q11.

Piecewise-Linear Maps and Their Application to Financial Markets

“…Examples in this direction include, among others, the work on price limiters by He and Westerhoff [55], on shortselling constraints by Anufriev and Tuinstra [56] and on profit taxes by Schmitt and Westerhoff [57]. It seems that the mathematical progress which has been made in the analysis of piecewise-linear models may be used to revisit these models.…”

Nonlinear asset-price dynamics and stabilization policies

“…We briefly remark that similar experiments exist for other markets that entail nonlinearities. For instance, Schmitt and Westerhoff [70] show that the nonlinear cobweb model by Brock and Hommes [15] may be stabilized if firms have to pay a profit tax. However, Schmitt et al [69] warn that profit taxes may also harbor a number of surprising and possibly undesirable side effects.…”

Evolutionary Competition and Profit Taxes: Market Stability Versus Tax Burden

“…An important question is whether policy makers can stabilize such dynamics. Extending the model by Brock and Hommes (1997), Schmitt and Westerhoff (2015) demonstrate that policy makers may be able to manage rational routes to randomness by introducing a proportional tax on firms' profits. The basic idea of their paper is that an increase in the tax rate reduces profit differentials between free naive expectations and costly rational expectations.…”