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Efficient and equitable taxation. Criteria for evaluating tax systems. Tax systems can be evaluated along different dimensions: Efficiency (minimization of distortions) Equity/fairness (distributional considerations) Administrative costs Amount of revenues generated (Leviathan)
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Criteria for evaluating tax systems • Tax systems can be evaluated along different dimensions: • Efficiency (minimization of distortions) • Equity/fairness (distributional considerations) • Administrative costs • Amount of revenues generated (Leviathan) • Avoidance of tax evasion • Not all these criteria are compatible • Well known equity/efficiency trade-off
Optimal commodity taxation - 3 • The reduction of the value of time endowment, in the case where w and T are fixed, implies that • The reduction is equal across all commodities, since the endowment wT is fixed • Individual does not change the allocation of value between X, Y and l • Tax t is lump sum→ no EB • Problem: taxing leisure time is impossible → one can tax only commodities X and Y • A certain amount of EB is inevitable • The goal of optimal commodity taxation is taxing X and Y at a rate such that EB be minimized • Intuitive solution could be taxing X and Y at same rate t (= neutral taxation) • Not efficient!!!
Diagram of the Marginal Excess Burden PX Marginal excess burden = areafbae = 1/2∆x[uX + (uX + 1)] = ∆X MarginalExcessBurden f g P0 + (uX + 1) ExcessBurden i b P0 + uX h c P0 j e a DX ∆x ∆X X2 X1 X0 X per year
Numerical example of Ramsey rule • ΔPx=20%=τx • Variation of the P of X due to the tax (e.g., VAT) • Quantity demanded before tax X0=4 • Elasticity of X to changes of P : εx=-0.3 • ΔX= τx*εx=0.2*(-0.3)=-0.06 • % change of quantity demanded of X due to tax • X1=X0+(X0*ΔX)=4+(-0.24)=3.76 • Quantity of X demanded after tax
Cornett-Hague rule • When taxing income, choice is labour/leisure • A lump sum tax, with EB=0 implies taxing leisure l as well as all commodities • You cannot tax leisure → distortion → leisure should be taxed more • Tax commodities associated to leisure with high tax rates • Tax supercars, holidays, restaurants 12
Efficient taxation and vertical equity • Ramsey rule suggests taxing heavily primary goods (e.g. Bread, medicines) and mildly luxury goods (Ferrari) • Bread has low elasticity, luxury goods high elasticity • Ramsey rule considers only efficiency, not equity • → Trade off between efficiency and equity • Tax systems must consider vertical equality too • Distribute EB in an equitable way between individuals with different AtP (Ability to Pay) • Departure from Ramsey rule are a function of • Egalitarian preferences within society • Differences in consumption between rich and poor → if rich and poor consume goods in the same proportion, taxing goods at different rates cannot affect the distribution of Y 13
Optimal tariffs/user fees • So far hypothesis that commodities are produced within the private sector. • What changes when state produces goods? Usually (in theory, reality is much different) in cases of natural monopoly • Natural monopoly characterized by AC continuously decreasing over the range of demand → one firm is likely to have a cost advantage over the later entrants → keeping the market competitive is difficult • Networks (utilities, railways etc.)
Optimal User Fees A Natural Monopoly $ • Marginal Cost Pricing with Lump Sum Taxes • Benefits received principle • Average Cost Pricing • A Ramsey Solution PM ACM ACZ P* MCZ MRZ DZ ZM ZA Z* Z per year
Diagram of natural monopoly - 2 • Zm, Pm: price and quantity of a pure monopolist • Inefficient because Pm>MCz • Government can (not will) prove more efficient than market in production of Z by setting P=MCz • At P*=MCz there is a loss (dark grey area) • Which is the best solution?
Optimal user fees - 1 • Average cost pricing • PA=AC: no losses, but ZA<Z* → inefficient quantity • Marginal cost pricing with lump sum taxes • P*=MC and loss covered by lump sum taxes • 2 problems • Lump sum taxes do not exist → their replacement may engender inefficiencies greater than efficiency gains associated with the production of Z* • It seems equitable that those who benefit from the service also pay for it (benefits-received principle) → no general taxes such as lump sum → but: if a skier falls in a crevasse, should he pay for the helicopter that rescues him?
Optimal user fees - 2 • Two part tariffs • Lump sum tax to have access to the service + tax P*=MC to consume the service • If efficient quantity is Z* and demanders are 1000, each one pays an access tariff equal to Z*/1000 then P*=MC related to amount of Z consumed • Loss thus covered in a non distorting way • 2 problems • Access tariff may reduce the number of consumers • Not a serious problem for services with inelastic demand such as utilities (energy, water, garbage collection) • Access tariff does not discriminate between rich and poor • If distributional aspects are to be taken into account, Feldstein advise to set P*>MC directly
Optimal income taxation: Edgeworth • Important because income • Is an important component of tax revenues (over 75% in Italy) • Best proxy for individual AtP • First analysis of optimal income taxation is Edgeworth model (see lecture on income redistribution), based on 4 hypotheses • Goal is maximizing the sum of individual utilities=social welfare • All individuals have identical U functions of only Y • U’’<0 • Total Y is fixed • Result: justification for a progressive tax system that redistributes Y until individual MU are all the same • t(Y)=100%
Mirlees (1971): equity-efficiency trade-off • Modern studies of optimal Y taxation recognize that hypothesis 3 is main difficulty • Total Y (and LS) is not fixed → individuals can choose between leisure l and work w→ taxes on Y are distortive → the cost of achieving greater equality by taxing Y at 100% rate is not 0 → higher tax rates engender less revenues to redistribute → equity/efficiency trade-off • Mirlees (1971) reformulates problem → choose t(Y) s.t. Max W(U) with elastic L • Constraint: after tax distribution of Y should not alter the before tax rank ordering of individual Y • Results: • A tax system approximately linear, with all its administrative advantages → essentially, a proportional taxation of Y • Y tax is a much less powerful tool for income redistribution than generally believed • Marginal Y tax rates should be very moderate → moderate application of tax progressivity
Stern (1987): flat income tax • Stern (1987) reformulates basic Edgeworth model considering the choice between l and w • REV=-a+τY→ linear income tax (aka flat tax) • -a is a subsidy to low income earners • Linear income tax is progressive even when MARTAX is constant: the higher Y, the higher AVGTAX • Problem is finding a and τ that minimize EB • Stern (1987) makes 3 points: • If REV that government targets is 20% of Y, τ=19% minimizes EB → much less of 100% of Edgeworth, and also less than 35% top marginal statutory income tax rate of U.S. today • The more elastic the LS → the lower τ→ higher elasticity of LS implies higher EB of taxing income • Even more extreme SWF do not lead to 100% tax rates → a maximin SWF à la Rawls (1971) implies τ=80% • Gruber and Saez (2002) relax Stern’s hypothesis of a single tax rate, using a model with up to 4 rates • Conclusion: people with higher Y should be taxed with lower marginal tax rates → regressive income tax makes high income people increase LS → increased revenues can be used to lower tax revenues on low income people • Switzerland has adopted a similar income tax system
Tax Revenue t = marginaltax rate α = lump sumgrant Income Optimal Income Taxation—Modern Studies • Supply-side responses to taxation • Linear income tax model (flat income tax) • Revenues = -α + t * Income
Politics and time inconsistency • Time inconsistency (Kydland and Prescott, 1977): a rational government that decides today an optimal policy to maximize citizens’ welfare, if it has the opportunity to re-optimize and change policy tomorrow it will do so • Applied to taxation: if a tax on K is applied today with a promise that K will not be taxed in the future any more → a tax on K tomorrow is a lump sum tax → investment choices had already been done under the promise of no taxation tomorrow → this creates the incentive for the government to renege the promise • Rational individuals anticipate this event → savings decrease • Time inconsistency of optimal policies is a threat to government credibility • Constitutional constraints provide a technology for government to solve time inconsistency problems → Constitutions as ‘commitment technology’
Politics and Leviathan • Optimal theory of taxation is purely normative → no consideration of incentives/constraints that lead governments to choose taxes to minimize EB • Real world tax systems are quite different from optimal ones • Brennan and Buchanan (1980): A Leviathan model where an un-responsive, un-democratic government maximizes tax revenues rather than SWF generates predictions much closer to real world outcomes • Constitutional constraints to taxation (e.g., balanced budget requirements, supermajorities for tax increases, prohibition of taxing certain assets, progressive taxation, budget organized around earmarked taxation) can be rationalized as ex ante precautions against a Leviathan government • Citizens may ex ante prefer inefficient tax systems to prevent governments from taxing too much or to behave in time inconsistent ways
Equity criteria • Equity is a widespread criterion for evaluation of tax systems, with deep roots in public opinion and embedded in Constitutions (France, Italy) • Equity broadly requires correlating taxes to individual ability to pay • Horizontal equity → individuals with equal AtP should pay the same tax • Two more equity criteria featured in literature • Vertical equity → individuals with higher AtP should pay higher taxes • Marginal tax ≤1 → avoid changes in rank ordering of tax bases before and after tax
Horizontal equity: outcome based • Ambiguous concept → Proxied by what? Income? Consumptions? Wealth? Else? • Problem is that it is based on (observable) results → outcomes • If A and B have same income but A worked more → A shouldn’t be taxed in the same way as B • # of hours worked is alternative concept • If A and B taxed differently because A studied more → horizontal equity again violated • Feldstein (1991) proposes a definition of horizontal equity based on U • 2 individuals with same U before taxes must have same U after taxes • Taxes must not violate order of U • Problem: how to measure U? • Keep the tax system constant and let people optimize
Horizontal equity: rule based • Buchanan: only redistributions generated by equitable procedures can be considered equitable • Equal opportunities, which does not imply equal results • The rules that govern the selection of taxes are more important for judging fairness than the outcomes themselves → rule definition of horizontal equity • Nozick (1975) • Maintaining that society must redistribute income is meaningless, because only individuals, not society, possess income • A distribution of income is unacceptable only if it is the result of improper rules (e.g. theft) • Ethical value of the status quo • Another view is that redistribution is not so important provided that social classes are mobile (‘social elevators’) • What matters is that individuals below poverty line be not always the same
Administrative costs • So far (and quite often) hypothesis that administering the tax system has no cost • Sometimes the case: the IRS in the U.S. spends 0.44$ for every 100$ of revenues raised • In less developed systems, administrative costs are substantial → hyperinflation in Latin America • Choice of tax assignment to various government levels explained in terms of administrative costs • Low cost taxes such as property → low level governments • High cost taxes such as taxes on K → central government • Compliance costs (time spent to prepare tax declarations, professional advice) can be substantial → Kaplow (2008) estimates it at 10% of revenues • Under-researched field (but: political economy of taxation)
Tax evasion • Tax evasion is related both to administration of tax systems and to EB • Need to distinguish tax avoidance from tax evasion • Tax avoidance is changing behaviour to minimize tax liability → legal • Tax evasion is failing to pay legally due taxes • Positive analysis of tax evasion suggests that individual evade taxes until MB equals MC • MC of tax evasion depend on: • ρ = probability of being audited and found • Penalty associated with tax evasion • MB of tax evasion depend on • t = marginal tax rate = MB of not declaring Y and evading → more progressive the tax system, more convenient evading • R*=optimal evasion
Positive Analysis of Tax Evasion MC = p * marginalpenalty MC = p * marginalpenalty $ $ MB = t MB = t (Dollars of underreporting) (Dollars of underreporting) R* R* = 0
Measuring tax evasion • Correlating income to expenditures (living standards) • Some expenditures are not declared • Sector studies → assume that all individuals working in certain sectors should have approximately the same income, controlling for conditioning factors • Especially common for retail, liberal professions etc. • A very rigid instrument, often unfair • Lobbying against these studies has proven successful • Surveys • Problem: people falsely report • Measuring the preference for cash payments in the economy (e.g., amount of cash circulating) • Cash does not imply a legal record
Size of hidden economy, EU 27 - 2012 Note: Derived from Schneider (2013)
Remedies against tax evasion • Increasing psychic costs of being caught evading (dishonour) • Work choices → model deals only with optimal evasion, assuming Y given • The higher is t, the higher the probability that individuals choose to work in underground economy → lowering tax progressivity reduces the incentives to evade • Changing the probability to audit → probably the most effective measure • Improving tax morale → people evade because the government does not provide enough services of enough good quality for the taxes collected
Limits to contrasting tax evasion • Eliminating the entire underground economy may not be optimal • Certain activities exist because tax rate is 0 in the underground economy (evasion) → taxing them at t>0 may make them disappear • If the underground economy employs low-income people or people with high elasticity of LS wrt tax, better tax them at very low rates • Tax amnesties • Extreme resource when the tax administration is inefficient → perverse effects for the incentives to comply → if individuals expect more amnesties, the incentives to declare fall • If a government must make a tax amnesty, it must also credibly show that after it the tax administration will become more efficient • E.g. amnesty removes a backlog of cases, after which the administration will efficiently consider the current cases • In Italy there have been ‘tombstone amnesties’ (=settles entirely the position of the taxpayer) in 1973, 1982, 1991, 1995, 2003 → a signal that the tax administration was inefficient
