Public Economics Flashcards
government roles in modern economy (5)
price intervention (taxes, welfare etc); regulation (min wages); taxation; spending; macro-economic stabilisation (fiscal policy)
where is the tax base more elastic
tax base is more elastic at the top because the rich have more avenue to respond to taxation to reduce their tax burden
what do top 1% earners do when tax rate increases
reduce working hours, migrate, tax avoid/evade
How much tax income you raise is a result of 2 things:
- how elastic is your tax base? will people migrate if you raise taxes? 2. what are the citizens political preferences?
contract curve
all pareto efficient point
first fundamental theorem of welfare economics
private market outcomes are pareto efficient under a set of conditions. outcome due to market conditions will be efficeint but it is not necessarily fair
pareto efficiency
no one can be made better off without making someone else worse off
second fundamental theorem of welfare economics
under a broad set of conditions, any pareto-efficeint allocation can be achieved through a redistribution of initial endowments and then letting the markets work freely. if initial outcome unfair, pick another allocation (take from one and give to another), then go away and let them trade freely until they reach a new point
first welfare theorem assumptions (4)
no externalities, perfect competition (no price makers, free entry), perfect information, rational agents
when the first welfare theorem assumptions hold…
no need for a government
when the first welfare theorems do not hold…
market failure –> govt intervention may be desirable
internality
cost you impose on the future version of yourself
fallacy of 2nd welfare theorem
it requires lump-sum taxes based on individual characteristics and not behaviour (1st best tax) but govt doesnt have enough info to do this, so govt use distortionary taxes and transfers leads to conflict between efficiency and equity (2nd best taxation)
efficiency-equity trade off
as a result of private actions, you arrive at an allocation that isn’t fair. you redistribute. if you redistribute using taxes, you end up inside the utility possibility frontier. you must give up some efficiency to gain equity.
wealth tax - economic efficiency
a wealth tax could discourage investment and savings, impacting economic growth and job creation. it could correct inefficiencies and imbalances caused by extreme wealth concentration
wealth tax - fairness and equity
means to address increasing income & wealth inequality, ensuring that the wealthiest pay their fair share. it penalises success and could lead to double taxation
wealth tax - administrative challenges
valuation of assets, especially non-liquid assets like real estate and art. concerns about costs of complexities of admin and compliance.
excess burden
measure of the costs of substituting away from taxed activities - more leisure time, find loopholes in tax code, migrate. measures the cost of the changes in behaviour caused by the substitution effect
lump-sum taxes
the only taxes that create no excess burden as taxpayers cannot avoid or evade them. they create no behavioural responses and hence no excess burden
substitution effect
refers to the change in demand or supply due to a relative price change caused by the tax
income effect
change in demand for a good or service caused by a change in a consumer’s purchasing power, due to a change in real income. generally reinforces substitution effect of reducing consumption
when does income effect not reinforce substitution effect after tax
labour supply - lower disposable income means lower consumption of leisure and therefore higher labour supply
tax incidence
the effects of tax policies on prices and the distribution of utilities
effects of a tax change or introduction
effect on price –> distributional effects on consumers, profits of prodcuers, shareholders, farmers etc
economic incidence vs statutory incidence
statutory incidence is who is legally required to pay the tax, economic incidence is who ultimately ends up paying the tax
partial equilibrium incidence assumptions (5)
two good economy: one relative price, no close substitutes/complements; tax revenue not spent on the taxed good; perfect competition among producers
excise or specific tax
tax levied on a quantity
ad-valorem tax
tax levied on price
partial equilibrium incidence model setup
two goods x and y. government levies an excise tax on good x. let p denote the pre tax price of x and q = p + t be the taxed price
partial equilibrium incidence model: demand
consumer has wealth Z and utility u(x,y). price elasticity of demand: eD = ∂D/∂q * q/D(q) = ∂logD/∂logq
price elasticity of demand
percentage change in quantity demanded following a change in price - elasticities are unit free
partial equilibrium incidence model: supply
cost of production c(S) units of y to produce S units of x. cost of production is increasing and convex: c’(S)>0 & c’‘(S)>=0. profit at pretax price is: pS - c(S). with perfect optimisation, the supply function for good x is implicitly defined by the marginal condition: p = c’(S(p)). price elasticity of supply: eS = ∂S/∂p * p/S(p)
partial equilibrium incidence model: equilibrium
equil condition: Q = S(p) = D(p + t).
perfectly inelastic demand graph
vertical demand curve
perfectly elastic demand graph
horizontal demand curve
formula for tax incidence
implicitly differentiate D(p+t)=S(p). incidence on consumers: dq/dt = 1 + dp/dt = eS / (eS - eD)
the more open an economy is to capital movements….
the more the burden is likely to fall on labour
evans, ringel, and stech 1999
idea: suppose federal govt implements a tax change, compare cigarette prices before and after the change: D = [P_A1 - P_A0]. identification assumption - absent the tax change, there would have been no change in cigarette price
evans, ringel, and stech 1999: difference-in-differences
what if price fluctuates because of climatic conditions or trends in demand? relax ID assumption using diff-in-diff: DD = [P_A1 - P_A0] - [P_B1 - P_B0]. state A: experienced a tax change (treatment), state B: does not experience a tax change (control). captures changes due to external factors. identification assumption for DD - ‘parallel trends’ absent the policy change, P1 - P0 would have been the same for A and B
tax is …
regressive on an absolute level
general equilibrium analysis
all prices are flexible, move beyond 2-good partial equil model to analyse impacts on all prices. typical goal: trace out full incidence of taxes back to original owners of factors. capital owners vs. labour vs. landlord etc
static general equilibrium model
many sectors or many factors of production
dynamic general equilibrium model
characterise impacts over time or across generations
static vs dynamic GE models
static models assume that all prices and quantities adjust immediately. in practice, adjustment of capital stock and reallocation of labour takes time. dynamic GE models incorporate these effects. static models can be viewed as a description of steady states
deadweight loss of commodity taxation
consume X units of commodity at price p, govt imposes per unit tax t. q = p+t is consumer price. Change in DWL from small tax change: dDWL = - t dX. PED = (dX/X) / (dq/q). Obtain: dDWL/dt = t/q * e * X
partial equilibrium analysis deadweight loss
consumer demand function Xi = Xi(qi). Assume: no income effect (uncompensated demand = compensated demand); independent market (no cross price effects). Choose optimal tax rate to minimise DWL: ∑_(i=1)^n DWL_i subject to revenue requirement R = t1X1 + … + tnXn >= R0. Lagrange: ∑DWLi - λ(R - R0). FOC: (∂DWLi/∂ti) / (∂R/∂ti) = λ = (∂DWLi/∂R). use dDWL/dt = t/q * e * X from before to obtain ramsey rule
ramsey rule
ti/qi = (λ / 1 + λ) (1/ei). The tax rate on a good should be inversely related to its elasticity of demand. tax inelastic goods at higher rates, DWL is higher the more elastic a good is.
optimal tax rule
choose tax rates such that the equiproportionate reduction in demand is equal across all commodities
issues with differentiation in taxes (4)
ignorance - lack knowledge of elasticities; admin and complexity - costly, complex, line drawing problem; creation of new goods - how to treat new goods?; political economy - lobbying, bribery
income tax marginal DWL
dDWL = - τ * w * dh = τ / (1-τ) * e * wh * dτ, where e = (dh/h) / (d(1-τ) / (1-τ))
income tax DWL insights
first $ of tax had no DWL, marginal DWL is increasing in marginal tax rate, marginal DWL is increasing in labour supply elasticity, marginal DWL is increasing in the earnings level wh
optimal income tax problem + simplifications
objective: a social welfare function W = W(U1, .., Un). choice: tax function T(Z) where z = wh is earnings. constraints: govt budget constraint and individual optimising behaviour. problem: design T(.) to max SWF subject to GBC and individual optimisation. Simplify by: restricting tax system (linear or piecewise linear taxes), consider special SWF
Linear income tax problem
constant marginal tax rate and guaranteed minimum income G>0: T(z) = τz - G –> flat tax or negative income tax. Average tax rate: a = T(z)/z = τ - G/z. Implies ∂a/∂z = G / z^2, which is positive for G>0. System is progressive
rawlsian SWF
W = min(U1, .., Un) so gov only care about the worst off person. Assume worst of person unable to work and lives on transfer G. Rawlsian gov wants to maximise G –> optimal income tax maximises revenue –> goes to top of Laffer curve
laffer curve and optimal taxation
laffer rate is optimum under rawlsian social preferences. laffer rate represents an upper bound on tax rates: any tax system above is pareto inefficeint, any tax system below may be optimal under some SWF. laffer rate is only value-free statement on optimal tax policy
high-income laffer rate setup
top MTR applies to income above z. denote ¯z the average income among taxpayers above z. total rev at top: R = τ(¯z - z)N. marginal change dτ creates: a mechanical revenue effect dM = dτ (¯z - z)N; a behavioural revenue effect dB = τ dz N.
high income laffer rate
determined by dR = dM + dB = 0 and is: τ* = 1 / (1 + eα) where e = (d¯z / ¯z) / (d(1-τ) / (1-τ)) is the elasticity of taxable income and α = ¯z / (¯z - z*) >= 1
tax base
amount of economic activity subject to the tax
deadweight loss occurs because
economic agents move away from the taxed activity, substituting toward its alternatives
what is the Lagrange multiplier of the Ramsey problem
the marginal cost of public funds. It represents the additional deadweight loss generated by extracting an additional unit of revenue on the good i
fiscal externality
a situation in which an economic agent’s behaviour changes the cost of some subsidy or alters the revenues collected from some tax, thereby affecting the well-being of taxpayers in general
simple model with no behavioural response (utilitarianism)
government maximises utilitarian objective: ∫_0^∞ u(z-T(z))h(z)dz subject to resource constraint: ∫T(z)h(z)d(z)≥E. Because incomes z are fixed, the lagrange is: L=[u(z-T(z))+λT(z)]h(z) and FOC is: [-u^’ (z-T(z))+λ]h(z)=0. Hence utilitarianism with fixed earnings implies full redistribution of income
issues with the simple model (utilitarianism)
no behavioural response: 100% redistribution would destroy incentives to work and thus assumption that z is exogenous is unrealistic. many people would object to 100% redistribution
linear labour income tax model
govt uses linear tax rate τ to fund a demogrant R and on-transfer spendings E taken as exogenous. Individual i maximises utility u^i (c,z) subject to budget constraint c=(1-τ)z+R, leads to the FOC:
(1-τ) (∂u^i)/∂c+(∂u^i)/∂z=0. Individual utility maximisation implicitly defines compensated (Marshallian) earnings supply function z_u^i (1-τ,R). Summing individual earnings function z_u^i (1-τ,R), we obtain aggregate earnings Z_u (1-τ,R). government’s budget constraint is R+E=τZ_u (1-τ,R(τ)). Revenue maximising tax rate τ^* is such that Z(1-τ)-τ dZ/d(1-τ) =0 or:
τ^/(1-τ^ )=1/ε or τ^*=1/(1+ε)
welfarism
social welfare based solely on individual utilities
most widely used welfarist SWFs
Utilitarian: SWF=∫u^i
Rawlsian: SWF=min_i〖u^i 〗
General Pareto weights: SWF=∫_i〖w^i u^i 〗 with w^i≥0 exogenously given.
general principle of tax design
if the idea is to encourage (or discourage) something, it is best to use the tax (or subsidy) most directly focused on that end
what is the advantage of taxing bad things rather than subsidising good things
it provides government with additional resources rather than using them up
externality
damage (or benefit) that a transaction or action confers on those who have no say in whether it takes places and whose interest are ignored. the first party bears no cost (or receives no benefit) for the effect they have on the second
public solutions to externalities
pigouvian corrective taxation, regulation, permits
private solution to externalities
coasian bargaining
coase theorem
if transaction costs are low and sources of damages can be identified, once property rights are completely defined, private bargaining will restore efficiency irrespective of initial assignments of property rights.
carbon tax example
pigouvian response: tax greenhouse gas emissions in general and fossil fuels in particular at a level that reflect global damage. some or all of this tax will be passed to consumers, reducing demand and then supply. alternative: create rights to emit CO2, sell them, allow private markets to trade them. this can replicate effects of tax and raise same revenue for govt
time inconsistency
planning rationally today on future actions that, when the time comes, will be rational not to take
vertical equity
how the tax burden varies by level of well-being e.g, rich vs middle-class vs poor families
horizontal equity
how the tax burden varies across families at the same level of wellbeing
the benefit principle
tax burden should be related to what benefit government provides - people that will benefit from HS2 should pay for HS2 - not easy to determine who benefits from governemnt goods so could end up being regressive as poor tend to use more public services than rich
the ability-to-pay principle
tax burden should be higher for those more “able” to pay
utilitarianism in tax context
objective should be “greatest amount of happiness on the whole”
edgeworth proposition
assuming everyone has the same utility function, a levelling tax system maximises the sum of utilities
the principle of horizontal equity
people at an equal level of wellbeing should pay the same tax. what are legitimate and illegitimate bases for distinguishing tax burden? Age, medical expenses, kids, smoking? how do we measure wellbeing?
implicit tax biases
impossible to eliminate. people differ in terms of their preferences over goods and leisure. some who likes goods is willing to work to acquire them, suffers more from a tax on income. to avoid this, some academics like the idea of taxing people on the basis of their potential wage rate rather than actual wage income
the marriage tax impossibility theorem
no tax system can simultaneously be marriage neutral, horizontally equitable, and progressive
absent externalities, any effect on behaviour is a symptom of…
an efficiency cost
labour supply theory basic model
utility maximisation: max u = u(c,l) subject to: c = wl + y, where w is wage rate and y is non-labour income. Optimal labour supply satisfies -(u_l^’)/(u_c^’ )=w, labour supply function l=l(w,y), Uncompensated elasticity of labour supply: ε^u=w/l ∂l/∂w, Income effect parameter: η=w ∂l/∂y≤0, Compensated elasticity of labour supply: ε^c=w/l (∂l^c)/∂w, Slutsky equation: ∂l/∂w=(∂l^c)/∂w+l∂l/∂y→ ε^u=ε^c+η
labour supply theory: convexity assumption
in standard model, workers supply labour where IC is tangent to budget set. if this point occurs at negative hours, a non-negativity constraint implies a corner solution at zero hours. marginal changes in taxes lead to marginal changes in hours worked.
estimating labour supply
ln(l) = β_0+β_1ln(1-τ)w+β_2 lny+β_3 x+v where x is a vector of observable controls and v is an error term. β_1 is (uncompensated) labour supply elasticity
potential problems in estimating labour supply
omitted variable bias: w is correlated with unobserved variables that impact l directly -> positive correlation between w and l -> upward bias. reverse causality: τ is endogenous to l in a nonlinear tax system -> w might also be endogenous to l. other issues: measurement error in w; functional form sensitivity; non-participation in labour market
why does modern public finance literature focus on taxable income elasticities instead of labour supply elasticity?
what matters for policy is the total behaviour response to tax rates (not hours worked but also occupational choices, avoidance etc) and data availability: taxable income is precisely measured
elasticity of taxable income
ETI=(1-τ)/z ∂z/∂(1-τ), where z is taxable income and τ is marginal tax rate.
ETI estimation + Identifying Assumption
denote s_t is top income share, τ_t is top MTR. if legislated change in τ_t occurs between time 0 and 1, ETI: ε ̂=(ln(s_1)-ln(s_0))/(ln(1-τ_1 )-ln(1-τ_0 ) ). IA = absent the tax change, the top income share would have remained constant
diff-in-diff estimate of ETI (Feldstein 1995 empirical strategy)
ε ̂=(∆ ln(z^T) -∆ln(z^C)) / (∆ ln(1-τ^T )-∆ln(1-τ^C ) ), where T is treatment group and C is control group. exploit differences in marginal tax cuts across the income distribution
problems with feldstein’s approach
- if inequality increases for non-tax reasons, the ETI is biased upwards as diff-in-diff attributes all differential increases in top incomes to the tax reform. 2. defining treatment and control by pre-reform income level creates a mean reversion problem, for tax cuts at the top, this biases the ETI downwards. 3. when treatment and control are affected, diff-in-diff requires homogenous elasticities. if elasticities are increasing in income, the ETI is biased upwards
economic effects of taxing the top 1% (3)
- supply side: top earners work less and earn less when top tax rate increases, top tax rate shouldn’t be too high. 2. tax avoidance/evasion: eliminate loopholes then increase top tax rates. 3. rent-seeking: top earners extract more pay (at expense of 99%) when top tax rates are low, high top tax rates desirable
real changes vs tax avoidance: charitable giving
test using charitable giving behaviour of top income earners. because charity is tax deductible, incentives to give are stronger when tax rates are higher, under tax avoidance scenario, reported incomes and reported charitable giving should move in opposite directions. empirically, charitable giving of top earners has grown in close tandem with top incomes -> incomes at the top have grown for real
supply side or rent seeking?
if rent seeking: growth in top 1% incomes should come at expense of bottom 99% (and conversely). two macro preliminary tests: in US, top 1% incomes grow slowly from 1933-1975 and fast afterwards. bottom 99% income grow fast 1933-1975 and slowly after -> consistent with rent seeking. look at cross-country correlation between economic growth and top tax rate cuts -> no correlation supports trickle up
distortionary taxes
change economic behaviour and can lead to inefficiencies in the market
when would you use distortionary taxes
Governments need to use distortionary
taxes only because people are of different types in terms of their ability and governments do not (or
cannot) observe their types.
Why can non-convex budget sets rationalize the presence of large extensive labour supply responses to variations in taxes? Explain where such non-convexities in the budget set may come from.
The standard labour supply model based on convex budget set predicts smooth changes in labour supply with smooth changes in wage rate. But with non-convex budget sets we may observe large changes in hours worked and participation as a result of a small change in tax rates. These non-convexities may arise from commuting costs, child-care costs, or jumps/discontinuities in the tax and transfer schedule.
