Which economic states are sustainable under a slightly constrained tax-rate adjustment policy

Krawczyk, Jacek B. and Judd, Kenneth L. (2014): Which economic states are sustainable under a slightly constrained tax-rate adjustment policy.

Abstract

Viability theory is the study of dynamical systems that asks what set of initial conditions will generate evolutions which obey the laws of motion of a system and some state constraints, for the length of the evo- lution. We apply viability theory to Judd’s (JPE, 1987) dynamic tax model to identify which economic states today are sustainable under only slightly constrained tax-rate adjustments in the future, when the dynamic budget constraint and consumers’ transversality condition at infinity are satisfied. We call the set of such states the economic viability kernel. In broad terms, knowledge of the viability kernel can tell the planner what economic ob- jectives are achievable and assist in the choice of suitable controls to realise them. We observe, unsurprisingly, that a very high consumption economy lies outside such kernels, at least for annual tax-adjustment levels limited by 20%; higher consumption levels can only be sustained when capital is abundant. Furthermore, we notice that the sizes of the kernel slices for a given taxation level do not diminish as the tax rate rises, hence high taxation economies are not necessarily more prone to explode, or implode, than their low taxation counterparts. In fact, higher tax rates are neces- sary to keep many consumption choices viable, especially when capital approaches the constraint-set boundaries.

• Item Type: MPRA Paper
• Language: English
• Keywords: taxation policy, macroeconomic modeling, dynamic systems, vi- ability theory; VIKAASA
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E61 - Policy Objectives ; Policy Designs and Consistency ; Policy Coordination; E - Macroeconomics and Monetary Economics > E6 - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook > E62 - Fiscal Policy

References

Aubin JP (1991) Viability Theory. Systems & Control: Foundations & Appli- cations, Birkha ̈user, Boston, DOI 10.1007/978-0-8176-4910-4

Aubin JP (1997) Dynamic Economic Theory: A Viability Approach. Springer Verlag

Aubin JP (2001) Viability kernels and capture basins of sets under dif- ferential inclusions. SIAM J Control Optimization, 40:853–881, DOI 10.1137/S036301290036968X

Baker B, Kotlikoff LJ, Leibfritz W (1999) Generational accounting in New Zealand. In: Auerbach AJ, Kotlikoff LJ, Willi L (eds) Generational Ac- counting around the World, University of Chicago Press, pp 347 – 368

Bonneuil N, Boucekkine R (2008) Sustainability, optimality and viability in the Ramsey model, manuscript, 39 pages

Bonneuil N, Saint-Pierre P (2008) Beyond optimality: Managing children, assets, and consumption over the life cycle. Journal of Mathematical Eco- nomics 44(3-4):227–241

Brock WA, Turnovsky SJ (1981) The analysis of macroeconomic policies in perfect foresight equilibrium. International Economic Review 22(1):179– 209

Cardaliaguet P, Quincampoix M, Saint-Pierre P (1999) Set valued numerical analysis for optimal control and differential games. Stochastic and differ- ential Games: Theory and Numerical Methods, Ann Internat Soc Dynam Games 4:177–274

Clement-Pitiot H, Doyen L (1999) Exchange rate dynamics, target zone and viability

Clement-Pitiot H, Saint-Pierre P (2006) Goodwin’s models through viability analysis: some lights for contemporary political economics regulations. In: 12th International Conference on Computing in Economics and Finance, Cyprus, conference maker

De Lara M, Doyen L, Guilbaud T, Rochet MJ (2006) Is a management frame- work based on spawning stock biomass indicators sustainable? A viability approach. ICES Journal of Marine Science

Gaitsgory V, Quincampoix M (2009) Linear programming approach to de- terministic infinite horizon optimal control problems with discounting. SIAM J Control Optim 48:2480–2512, DOI 10.1137/070696209

Judd KL (1987) The welfare cost of factor taxation in a perfect-foresight model. Journal of Political Economy 95, No. 4:675–709

Krastanov M (1995) Forward invariant sets, homogeneity and small-time local controllability. Nonlinear Control and Differential Inclusions (Banach Center Publ 32) Polish Acad Sci Warsaw pp 287–300

Krawczyk JB, Judd KL (2012) Viable economic states in a dy- namic model of taxation. In: 18th International Conference on Computing in Economics and Finance, Prague, Czech Repub- lic, URL https://editorialexpress.com/cgi-bin/conference/download.cgi? db name=CEF2012&paper id=116, Conference Maker

Krawczyk JB, Kim K (2004) A viability theory analysis of a macroeco- nomic dynamic game. In: Eleventh International Symposium on Dynamic Games and Applications, Tucson, AZ, US

Krawczyk JB, Kim K (2009) “Satisficing” solutions to a monetary policy problem: A viability theory approach. Macroeconomic Dynamics 13:46– 80, DOI 10.1017/s1365100508070466

Krawczyk JB, Pharo A (2011) Viability Kernel Approximation, Analysis and Simulation Application – VIKAASA Manual. SEF Working Paper 13/2011, Victoria University of Wellington, URL http://hdl.handle.net/10063/1878 Krawczyk JB, Pharo A (2014) Viability Kernel Approximation, Analysis and Simulation Application – VIKAASA Code. URL http://code.google.com/ p/vikaasa/

Krawczyk JB, Serea OJ (2009) Computation of viability kernels for three and four meta-state monetary-policy macroeconomic problems. In: Work- shop on Perturbations, Game Theory, Stochastics, Optimisation and Ap- plications, University of South Australia, URL www.unisa.edu.au/maths/ research/JerzyFilar/default.asp

Krawczyk JB, Serea OS (2013) When can it be not optimal to adopt a new technology? A viability theory solution to a two-stage optimal control problem of new technology adoption. Optimal Control Applications and Methods 34(2):127 – 144, DOI 10.1002/oca.1030, URL http://www.vuw.ac. nz/staff/jacek krawczyk/somepapers/oca1030.pdf

Krawczyk JB, Sethi R (2007) Satisficing solutions for New Zealand mon- etary policy. Tech. rep., Reserve Bank of New Zealand, No DP2007/03., URL http://www.rbnz.govt.nz/research and publications/articles/details. aspx?id=3968

Krawczyk JB, Pharo A, Simpson M (2011) Approximations to viability ker- nels for sustainable macroeconomic policies. Tech. rep., VUW SEF Work- ing paper: 01/2011, URL http://hdl.handle.net/10063/1531

Krawczyk JB, Sissons C, Vincent D (2012) Optimal versus satisfactory decision making: a case study of sales with a target. Computational Management Science 9:233–254, DOI: 10.1007/s10287-012-0141-7

Krawczyk JB, Pharo A, Serea OS, Sinclair S (2013) Computation of viability kernels: a case study of by-catch fisheries. Computational Management Science 10(4):365–396, DOI 10.1007/s10287-013-0189-z, URL http://dx.doi. org/10.1007/s10287-013-0189-z

Martinet V, Doyen L (2007) Sustainability of an economy with an exhaustible resource: A viable control approach. Resource and Energy Economics 29(1):17–39

Martinet V, Thebaud O, Doyen L (2007) Defining viable recovery paths toward sustainable fisheries. Ecological Economics 64(2):411–422, DOI 10.1016/j.ecolecon.2007.02.036

Pujal D, Saint-Pierre P (2006) Capture basin algorithm for evaluating and managing complex financial instruments. In: 12th International Confer- ence on Computing in Economics and Finance, Cyprus, conference maker

Quincampoix M, Veliov VM (1998) Viability with a target: Theory and ap- plications. Applications of Mathematical Engineering pp 47–58

Veliov V (1997) Stability-like properties of differential inclusions. Set-Valued Analysis 5(1):73–88, DOI 10.1023/A:1008683223676, URL http://dx.doi.org/ 10.1023/A%3A1008683223676

Veliov VM (1993) Sufficient conditions for viability under imperfect mea- surement. Set-Valued Analysis, 1(3):305–317, DOI 10.1007/bf01027640