EC426 Public Economics Optimal Income Taxation Class 4, question 1. Monica Rodriguez

Transcription

1 EC426 Public Economics Optimal Income Taxation Class 4, question 1 Monica Rodriguez

2 a) What is the role of the economics of information (Mankiw and Weinzierl, 2010)? Optimal Income Taxation Theory Vickrey (1945) and Mirrlees (1971). Given the revenue that the government has decided to collect, how should it choose the rates of the various taxes to maximize social welfare? Ideally we would like to tax ability to pay: Abilities determines wage; but abilities are assumed to be unobservable (private information). Available information to the government determines what fiscal instruments it may use. Assumption: government only observable data is total income (function of productivity and effort). Taxing income, however distorts labour supply. But any exogenous variable correlated with productivity should be a useful indicator to determine the optimal tax liability. Can you think of any for which we have data?

3 a) What is the role of the economics of information (Mankiw and Weinzierl, 2010)? Mankiw and Weinzierl (2010): Why not to consider another variable to determine the optimal tax liability, taxpayers height? Two arguments: Theory: any exogenous variable correlated with productivity should be a useful indicator (Saez 2001, Kaplow 2007). Empirical evidence on height as a explanatory variable for higher earnings (Judge et.al 2004, Persico et. al 2004, Case et. al 2008). If the policy seems absurd, provide an explanation to leave optimal income taxation framework intact. Otherwise, reconsider whether this approach captures the notions of redistributive justice.

4 a) What is the role of the economics of information in (Mankiw and Weinzierl, 2010)? Assumptions Utilitarian social welfare Individual utility additively separable, CRA in consumption and isoelastic in labour. Data for US adult white males aged in height groups: short, medium and tall, across 18 wage bins. Main results Simulations suggest that a tall person should pay more in tax than a short person of the same income. The average tax rate for tall individuals is always above that for short individuals. Consistency with results attributed to optimal tax models when ability is observable: given a wage, lower expected utility for taller individuals than for short ones. Gain in welfare when compared with a benchmark model (in which government could not observe height).

5 a) What is the role of the economics of information in (Mankiw and Weinzierl, 2010)? What matters for optimal height taxation is the consistent statistical relationship between exogenous height and income. A possible counterargument: height tax would open the possibility to make taxes based on demographic characteristics more natural and dangerously expanding the scope for government information collection and policy personalization. (MW 2010). But modern tax systems already condition on much personal information (e.g. number of children, marital status, personal disabilities). If the government s problem is made more realistic by allowing to observe other variables correlated with ability, such as height, he should use those other variables in addition to income for setting optimal policy.

6 b) What is the incentive-compatibility constraint in optimal income taxation? Individuals problem: Choose labour effort, l i, to max l i u i (c i, l i ) Subject to: c i = w i l i T(w i l i ) Where: c i consumption w i wage (earning abilities) associated to each individual i T w i l i tax schedule y i w i l i pretax income u c > 0; u l < 0; u x > 0 for x = c, l

7 b) What is the incentive-compatibility constraint in optimal income taxation? Government s problem: Choose a tax schedule T(wl) to max T(wl) Ψ u c w, l w f w dw Where: Ψ social welfare function, weights the utilities of the agents according to redistributives objectives; increasing and concave function. f w distribution density of abilities

8 b) What is the incentive-compatibility constraint in optimal income taxation? And faces two types of contraints: 1) Feasibility (revenue constraint) T wl w f w dw R 2) Individual s behaviour Individuals will respond to the given tax schedule optimally. Need to consider: participation constraint of the lowest-skilled individual, possible discontinuities for the highest-skilled individual, incentive compatibility constraints.

9 b) What is the incentive-compatibility constraint in optimal income taxation? Equivalently, another way to see the problem: max T(wl) Ψ u c w, l w f w dw The government would like that every individual choose on her own a specific consumption and pre-tax income bundle intended for her. (Revelation principle). Then we need to impose that the intended pair to be chosen is the solution to the maximisation problem faced by the household. Let c(w i ) and l(w i ) represent the consumption and labour effort levels that the government intends that a household of ability w i choose. We have that: u i (c(w i ), l(w i )) u i (c(w j ), l(w j )) for all i j. Note the potential infinity constraints: need to be compared between all other individuals!

10 c) Compare the role of the constraint in linear income taxation with that in non-linear income taxation. Under the linear case, the tax schedule now given by: T(wl) = twl g Where: t marginal, constant tax rate, g lump sum subsidy. Here, the individual s budget constraint: c = wl twl g = (1 t) wl g Individual budget is convex. This tax structure eliminates the requirement to consider IC constraint as the individual behaviour can be determined as a function of the two parameters that describe the tax schedule: g and t. Therefore, the choice of the optimal policy corresponds to a standard maximisation problem.

11 c) Compare the role of the constraint in linear income taxation with that in non-linear income taxation. Instead, in the non-linear scenario, the IC must be made explicit: u i (c(w i ), l(w i )) u i (c(w j ), l(w j )) for all i j. Assuming that the MRS between consumption and labour effort is smaller for more productive individuals, it can be shown that this condition is equivalent to: A first order condition u c c (w) + u l l (w) = 0 A second order condition equivalent to l(w i ) 0 As second order implies the first order condition, we now have a single condition for every level of w i.

12 c) Compare the role of the constraint in linear income taxation with that in non-linear income taxation. Graphically: c u b c u b u a u b u a y y w a l a w b l b w a l a w b l b Linear income tax Non-linear income tax

13 References Kaplow, L. (2008) The Theory of Taxation and Public Economics, Princeton University Press, Chapter 4. Mankiw, N.G., Weinzierl, M. and Yagan, D. (2009) Optimal Taxation in Theory and Practice, Journal of Economic Perspectives, 23, Mankiw, N.G and Weinzierl, M. (2010). The Optimal Taxation of Height: A Case Study of Utilitarian Income Redistribution, American Economic Journal: Economic Policy, American Economic Association, vol. 2(1), pages , February. Myles,Gareth D. (1995). Public Economics, Cambridge University Press. Salanié, B. (2003) The Economics of Taxation, Cambridge Massachusetts: MIT Press.