Title: Side constrained optimisation to capture capacity of choices in the multinomial logit model: case study of income tax policy in the USA prior to the 2009 economic crisis

Authors: Saeed Asadi Bagloee; Glenn Withers

Addresses: Infrastructure Engineering Department, The University of Melbourne, Victoria 3010, Australia ' Research School of Economics, The Australian National University, Australian Capital Territory 0200, Australia

Abstract: The choices' limited capacities of the discrete choice models must be taken into account. We propose a convex optimisation formulation in which the exponential formulation of the logit model is upheld in the Karush-Kuhn-Tucker (KKT) conditions. The capacities of the choices are then added to the formulation as side constraints. A solution algorithm based on the successive coordinate descent is proposed. For numerical evaluation, we investigate US income tax policies for the years prior to the 2009 crisis using multinomial logit models. The tendency of the states for choice of income tax versus other tax sources is assessed and it is found that: 1) all states show a propensity to levy more income tax; 2) this propensity has a ceiling cap similar to what is already known from the 'Laffer curve'; 3) residents in the states with already high income tax are more likely to be subjected to even heavier income tax within caps.

Keywords: convex optimisation; successive coordinate descent; SCD; logit; income tax; behavioural model; Laffer curve; economic crisis; recession; USA.

DOI: 10.1504/IJOR.2019.102073

International Journal of Operational Research, 2019 Vol.36 No.1, pp.123 - 149

Received: 07 Jul 2016
Accepted: 12 Nov 2016
Published online: 06 Sep 2019 *

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