# On the design of an optimal non-linear tax/pension system with habit formation

## Abstract

We study the optimal tax/pension design in a two-period model where individuals differ in both productivity and discount rates or projection bias and where their utility of the retirement period consumption is not independent of the earlier standard of living. We consider both welfarist and paternalistic social objectives. The paternalistic government attempts to correct the projection bias by using a higher discount factor. We derive general mathematical expressions that characterize optimal tax/pension design (marginal tax/subsidy rates). They suggest that the pattern of marginal labor income taxes depends on habit formation. Negative marginal labor income tax rates are possible. To gain a better understanding, we examine numerically the properties of an optimal lifetime redistribution policy with habit formation. We find support for non-linear tax/pension program in which some types of individuals are taxed while some are subsidized. The effect of changes in the degree of habit formation is explored in the numerical simulations as well as the implications of different degrees of correlation between skill and projection bias.

## Keywords

Optimal taxation Habit formation## JEL Classification

H21 H55## References

- Akerlof, G. A. (1978). The economics of “tagging” as applied to the optimal income tax, welfare programs and manpower planning.
*American Economic Review*,*68*, 8–19. Google Scholar - Akerlof, G. (2002). Behavioral macroeconomics and macroeconomic behavior.
*American Economic Review*,*92*(3), 411–433. CrossRefGoogle Scholar - Benartzi, S., & Thaler, R. (2007). Heuristics and biases in retirement savings behaviour.
*Journal of Economic Perspectives*,*21*, 81–104. CrossRefGoogle Scholar - Boadway, R., Marchand, M., Pestieau, P., & del Mar Racionero, M. (2002). Optimal redistribution with heterogeneous preferences for leisure.
*Journal of Public Economic Theory*,*4*, 475–498. CrossRefGoogle Scholar - Blomquist, S., & Christiansen, V. (2004). Taxation and heterogeneous preferences.
*CESifo working paper 1244*. Google Scholar - Choi, J., Laibson, D., Madriand, B., & Metrick, A. (2003). Optimal defaults.
*American Economic Review Papers and Proceedings*,*93*, 180–185. CrossRefGoogle Scholar - Cremer, H., Pestieau, P., & Rochet, J.-C. (2001). Direct versus indirect taxation: the design of the tax structure revisited.
*International Economic Review*,*42*, 781–799. CrossRefGoogle Scholar - Cremer, H., De Donder, P., Maldonado, D., & Pestieau, P. (2008). Habit formation and labor supply.
*CESifo Working Paper No. 2351*. Google Scholar - Cremer, H., De Donder, P., Maldonado, D., & Pestieau, P. (2009). Forced saving, redistribution and non-linear social security scheme.
*Southern Economic Journal*,*76*(1), 86–98. CrossRefGoogle Scholar - Cuff, K. (2000). Optimality of workfare with heterogeneous preferences.
*Canadian Journal of Economics*,*33*, 149–174. CrossRefGoogle Scholar - Diamond, P. A. (1977). A framework for social security analysis.
*Journal of Public Economics*,*8*, 275–298. CrossRefGoogle Scholar - Diamond, P. A. (2003).
*Taxation, incomplete markets, and social security. The 2000 Munich Lectures*. Cambridge: MIT Press. Google Scholar - Diamond, P. A., & Kőszegi, B. (2003). Quasi-hyperbolic discounting and retirement.
*Journal of Public Economics*,*87*, 1839–1872. CrossRefGoogle Scholar - Diamond, P. A., & Mirrlees, J. (2000). Adjusting one’s standard of living: two period models. In P. J. Hammond & G. D. Myles (Eds.),
*Incentives, organization and public economics, papers in honour of Sir James Mirrlees*(pp. 107–122). Oxford: Oxford University Press. Google Scholar - Diamond, P. A., & Spinnewijn, J. (2009). Capital income taxes with heterogeneous discount rates.
*NBER Working paper 15115*. Google Scholar - Duesenberry, J. S. (1949).
*Income, saving and the theory of consumer behaviour*. Cambridge: Harvard University Press. Google Scholar - Feldstein, M. (1985). The optimal level of social security benefits.
*Quarterly Journal of Economics*,*100*(2), 300–320. CrossRefGoogle Scholar - Haveman, R., Holden, K., Romanov, A., & Wolfe, B. (2007). Assessing the maintenance of savings sufficiency over the first decade of retirement.
*International Tax and Public Finance*,*14*(4), 481–502. CrossRefGoogle Scholar - İmrohoroğlu, A., İmrohoroğlu, S., & Joines, D. H. (2003). Time inconsistent preferences and social security.
*Quarterly Journal of Economics*,*118*(2), 745–784. CrossRefGoogle Scholar - Judd, K. L., & Su, C.-L. (2006).
*Optimal income taxation with multidimensional taxpayers types*.*Computing in economics and finance 2006*(Vol. 471). Society for Computational Economics. Google Scholar - Laibson, D., Repetto, A., & Tobacman, J. (1998). Self-control and saving for retirement.
*Brookings Papers on Economic Activity*,*1*, 91–196. CrossRefGoogle Scholar - Loewenstein, G., O’Donoghue, T., & Rabin, M. (2003). Projection bias in predicting future utility.
*Quarterly Journal of Economics*,*118*(4), 1209–1248. CrossRefGoogle Scholar - Mirrlees, J. (1971). An exploration in the theory of optimum income taxation.
*Review of Economic Studies*,*38*, 175–208. CrossRefGoogle Scholar - Pirttilä, J., & Tuomala, M. (1997). Income tax, commodity tax and environmental policy.
*International Tax and Public Finance*,*4*, 379–393. CrossRefGoogle Scholar - Pollak, R. (1970). Habit formation and dynamic demand functions.
*Journal of Political Economy*,*78*(4), 745–763. CrossRefGoogle Scholar - Ryder, H., & Heal, G. (1973). Optimal growth with intertemporally dependent preferences.
*Review of Economic Studies*,*40*, 1–33. CrossRefGoogle Scholar - Sandmo, A. (1993). Optimal redistribution when tastes differ.
*Finanzarchiv*,*50*(2), 149–163. Google Scholar - Sen, A. (1974). Informational bases of alternative welfare approaches: aggregation and income distribution.
*Journal of Public Economics*,*3*(4), 387–403. CrossRefGoogle Scholar - Tarkiainen, R., & Tuomala, M. (1999). Optimal nonlinear income taxation with a two-dimensional population: a computational approach.
*Computational Economics*,*13*, 1–16. CrossRefGoogle Scholar - Tarkiainen, R., & Tuomala, M. (2007). On optimal income taxation with heterogeneous work preferences.
*International Journal of Economic Theory*,*3*, 35–46. CrossRefGoogle Scholar - Tenhunen, S., & Tuomala, M. (2010). On optimal lifetime redistribution policy.
*Journal of Public Economic Theory*,*12*(1), 171–198. CrossRefGoogle Scholar