Applied Public Economics 3. Efficiency Costs of Taxation PDF

Applied Public Economics 3. Efficiency Costs of Taxation Michael Gerfin University of Bern Spring 2024 Outline 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 2 / 53 Introduction Definition Incidence: eff...

Applied Public Economics 3. Efficiency Costs of Taxation Michael Gerfin University of Bern Spring 2024 Outline 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 2 / 53 Introduction Definition Incidence: effect of policies on distribution of economic pie Efficiency or deadweight cost: effect of policies on size of the pie Focus in efficiency analysis is on quantities, not prices 3 / 53 Introduction Efficiency Cost: Introduction Government raises taxes for one of two reasons: 1 2 To raise revenue to finance public goods To redistribute income But to generate $1 of revenue, welfare of those taxed falls by more than $1 because the tax distorts behavior How to implement policies that minimize these efficiency costs? Start with analysis of how to measure efficiency cost of a given tax system 4 / 53 Marshallian Surplus 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 5 / 53 Marshallian Surplus Marshallian Surplus: Assumptions Simplest analysis of efficiency costs: Marshallian surplus Two assumptions: 1 Quasilinear utility: no income effects, money metric 2 Competitive production 6 / 53 Marshallian Surplus Partial Equilibrium Model: Setup Two goods: x and y Consumer has wealth Z, utility u(x) + y, and solves max u(x) + y s.t. (p + τ )x(p + τ, Z) + y(p + τ, Z) = Z x,y Producers use y to produce x Production function is concave, so marginal cost of producing x is increasing With perfect optimization, supply function for x is implicitly defined by the marginal condition p = c′ Equilibrium quantity Q(τ ) is defined by D(p + τ ) = S(p) Consider the effect on Q and on surplus of introducing a small tax dτ > 0 7 / 53 Marshallian Surplus Graphical derivation of Excess Burden 8 / 53 Marshallian Surplus Graphical derivation of Excess Burden 9 / 53 Marshallian Surplus Efficiency Cost: Qualitative Properties 1 Excess burden increases with square of tax rate the larger the tax, the larger will be the base of the triangle 2 Excess burden increases with elasticities the larger the elasticities, the larger will be the reduction in quantity (the height of the triangle) 10 / 53 Marshallian Surplus Graphical derivation of Excess Burden 11 / 53 Marshallian Surplus Graphical derivation of Excess Burden 12 / 53 Marshallian Surplus Graphical derivation of Excess Burden 13 / 53 Marshallian Surplus Tax Policy Implications With many goods, the most efficient way to raise tax revenue is: 1 Tax inelastic goods more (e.g. medical drugs, food) 2 Spread taxes across all goods to keep tax rates relatively low on all goods (broad tax base) These are two countervailing forces; balancing them requires quantitative measurement of excess burden 14 / 53 Marshallian Surplus Excess Burden of Tax Excess burden of introducing a tax τ is 1 EB(τ ) = − dQdτ 2 1 dQ = − (dτ )2 2 dτ 1 dQ 2 = − τ 2 dτ (the third line uses the fact that for the introduction of a tax τ = dτ ) 15 / 53 Marshallian Surplus Marginal Excess Burden of Tax Increase Consider EB from raising tax by ∆τ given pre-existing tax τ :    dQ dQ  2 2 EB(∆τ ) = −(1/2) (τ + ∆τ ) − −(1/2) ∆τ dτ {z dτ } | | {z } EB(τ +∆τ ) = = = EB(τ )  dQ  (τ + ∆τ )2 − τ 2 dτ  dQ  −(1/2) · 2τ · ∆τ + (∆τ )2 dτ dQ dQ −τ ∆τ − (1/2) (∆τ )2 dτ dτ −(1/2) First term is first-order in ∆τ ; second term is second-order ((∆τ )2 ) 16 / 53 Marshallian Surplus Excess Burden of Tax Increase 17 / 53 Marshallian Surplus The Fiscal Externality Tax revenue is given by R(τ ) = Q(τ ) × τ Then the change in tax revenue caused by a tax change is ∂R ∂τ = Q + τ dQ dτ ⇒ ∂R = ∂τ × Q + τ × dQ This change consists of two elements 1 Mechanical revenue change: ∂τ × Q 2 Behavioral revenue change: τ × dQ Mechanical change is the change ignoring behavioral changes Behavioral change is change in quantity times original tax rate This revenue loss due to behavioral changes is also called the fiscal externality, τ dQ It corresponds to the first order term in the M EB formula 18 / 53 Sufficient Statistics 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 19 / 53 Sufficient Statistics Structural vs Sufficient Statistics Approach Difference between structural and quasi-experimental methodologies Modern literature focuses on deriving “sufficient statistic” formulas that can be implemented using quasi-experimental techniques Now develop general distinction between structural and sufficient statistic approaches to welfare analysis in a simple model of taxation No income effects (quasilinear utility) Constant returns to production (fixed producer prices) Permit multiple goods 20 / 53 Sufficient Statistics Sufficient Statistic 21 / 53 Sufficient Statistics Sufficient Statistics vs Structural Methods N goods: x = (x1 ,..., xN ); prices (p1 ,...pN ); wealth Z Normalize pN = 1 (xN is numeraire) Government levies a tax t on good 1 Individual takes t as given and solves max u(x1 ,..., xN −1 ) + xN s.t. (p1 + t)x1 + N X p i xi = Z i=2 To measure EB of tax, define social welfare as sum of spending on numerraire. income individual’s utility and tax revenue: minus... W (t) = {max u(x1 ,..., xN −1 )+Z −(p1 +t)x1 − x Goal: measure N −1 X pi xi }+tx1 i=2 dW dt (social welfare loss caused by tax change) 22 / 53 Sufficient Statistics Sufficient Statistics vs Structural Methods Structural method: estimate demand system, recover u Sufficient statistics: apply envelope theorem to derive dW dt Private sector makes choices to maximize private surplus W (t) = {max u(x1 ,..., xN −1 ) + Z − (p1 + t)x1 − x | N −1 X pi xi } + tx1 i=2 {z } private surpus only nr we need Private surplus corresponds to indirect utility V (p1 + t,..., pN , Z), so we can apply Roy’s identity (dV /dt = −αx1 with α = 1 because of quasi-linear preferences) dW dx1 dx1 = −x1 + x1 + t =t dt dt dt → dx1 dt is a “sufficient statistic” for calculating dW dt 23 / 53 Taxable Income Elasticity 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 24 / 53 Taxable Income Elasticity Feldstein 1995, 1999 Following Harberger, large literature in labor estimated effect of taxes on hours worked to assess efficiency costs of taxation Feldstein observed that labor supply involves multiple dimensions, not just choice of hours: training, effort, occupation Taxes also induce inefficient avoidance/evasion behavior Structural approach: account for each of the potential responses to taxation separately and then aggregate Feldstein’s alternative: elasticity of taxable income with respect to taxes is a sufficient statistic for calculating deadweight loss 25 / 53 Taxable Income Elasticity Feldstein Model: Setup Government levies linear tax t on reported taxable income Agent makes 2 labor supply choices: l1 , l2 (hours and effort) Each choice li has disutility ψi (li ) and wage wi Agents can shelter $e of income from taxation by paying cost g(e) Taxable Income (Z) is Z = w1 l1 + w2 l2 − e Consumption is given by taxed income plus untaxed income minus sheltering costs: c = (1 − t)Z + e − g(e) Agent’s utility is quasi-linear in consumption: u(c, e, l) = c − ψ1 (l1 ) − ψ2 (l2 ) 26 / 53 Taxable Income Elasticity Feldstein Taxable Income Formula Social welfare: W (t) = {(1 − t)Z + e − g(e) − ψ1 (l1 ) − ψ2 (l2 } + tZ Differentiating and applying envelope theorem yields dW dZ dZ = −Z + Z + t =t dt dt dt first order conditions for li ((1 − t)wi = ψi′ (li )) and e (g ′ (e) = t) are always satisfied Intuition: marginal social cost of reducing earnings through each margin is equated at optimum → irrelevant what causes change in Z 27 / 53 Taxable Income Elasticity Kleven and Schulz 2014 Use full population of tax returns in Denmark since 1980 (large sample size, panel structure, many demographic variables, stable inequality) A number of reforms changing tax rates differentially across three income brackets and across tax bases (capital income taxed separately from labor income) Show compelling visual DD-evidence of tax responses around the 1986 large reform Define treatment and control group in year 1986 (pre-reform), follow the same group in years before and years after the reform (panel analysis) 28 / 53 Taxable Income Elasticity Kleven and Schulz 2014 29 / 53 Taxable Income Elasticity Kleven and Schulz 2014 30 / 53 Taxable Income Elasticity Saez (2010), Bunching Saez observes that only non-parametric source of identification for elasticity in a cross-section is amount of bunching at kinks Intuition: discontinuous reduction in wage rate at kink yields source of non-parametric identification All other cross-sectional tax variation is contaminated by smooth heterogeneity in tastes Derives an estimator for the taxable income elasticity using amount of bunching at kinks ε= excess mass at kink dz/z ∗ = dt/(1 − t) % change in N T R Currently a popular approach because it yields credible estimates Saez, E. (2010), Do tax payers bunch at kink points?ı̀, American Economic Journal: Economic Policy, 180-212 31 / 53 Taxable Income Elasticity Bunching at kink points preferences for labour supply are comparable these people would have chosen similar levels 32 / 53 Taxable Income Elasticity Bunching at kink points all these guys here go there income distribution expected to look like a v 33 / 53 Taxable Income Elasticity Bunching at kink points Earned Income Tax Credit Schedule for Single Earners with One Child in 2008 EITC Credit Amount ($1000) 4k This income level maximizes tax refund generate incnetives to enter labor markets subsidies wages for single mothers but prorgamme was expanded t=0 3k t=0,2 2k 1k 0k $0k $5k $10k $15k $20k $25k $30k $35k Family Earnings 34 / 53 Taxable Income Elasticity Bunching at kink points U.S. Income Distributions for EITC-Eligible Individuals with Children in 2008 5% Percent of Tax Filers 4% 3% 2% 1% 0% $0 $10K $20K $30K $40K Total Earnings (Real 2010 $) One child Two children 35 / 53 Taxable Income Elasticity Bunching at kink points no automatic implementation, you must ask the tax office 36 / 53 Taxable Income Elasticity Bunching at kink points not large 37 / 53 Taxable Income Elasticity Why not more bunching at kinks? 1 Small structural elasticity 2 Noise in income generation process 3 Price misperceptions and salience effects 4 Optimization frictions Chetty, Friedman, Olsen, Pistaferri (2011) Chetty, Friedman, Saez (2012) Kleven and Waseem (2012) 38 / 53 Taxable Income Elasticity Optimization Frictions Standard methods assume that agents can costlessly adjust hours of work In practice, most hours changes occur with job switches And many individuals may be inattentive to change in tax rates Implies that long-run impacts of policies may not be identified from short run variation 39 / 53 Taxable Income Elasticity Optimization Frictions and Identification Chetty (2012) formalizes how frictions affect identification of elasticities Agents can choose any xt that generates a utility loss less than exogenous threshold δ: U (x∗i ) − U (xi ) < δpx∗i A given price p produces a choice set X(p, δ) instead of a single point x∗ (p) 40 / 53 Taxable Income Elasticity Chetty (2009) 41 / 53 Taxable Income Elasticity Chetty (2009) 42 / 53 Taxable Income Elasticity Chetty (2009) 43 / 53 Taxable Income Elasticity Chetty (2009) 44 / 53 Taxable Income Elasticity Chetty (2009) 45 / 53 Taxable Income Elasticity Optimization Frictions and Identification Identification problem: Multiple observed elasticities εb can be generated by a model with a given structural elasticity when δ>0 Conversely, multiple structural elasticities consistent with observed εb Note that this is not a finite-sample problem; does not disappear as sample size approaches ∞ One focus of current research: how to deal with such frictions andrecover ε? 46 / 53 Salience Effects 1. Introduction 2. Marshallian Surplus 3. Sufficient Statistics Approach 4. Taxable Income Elasticity 5. Welfare Analysis with Salience Effects 47 / 53 Salience Effects Welfare Analysis with Salience Effects: Setup Representative consumer has wealth Z and utility u(x) + y (quasi-linear) Let{x∗ (p, tS , Z), y ∗ (p, tS , Z)} denote bundle chosen by a fully-optimizing agent Let {x(p, tS , Z), y(p, tS , Z)} denote empirically observed demands Budget constraint (p + tS )x(p, tS , Z) + y(p, tS , Z) = Z 48 / 53 Salience Effects Efficiency Cost with Salience Effects Define excess burden (EB) as loss in consumer surplus minus tax revenue (no income effects, quasi-linear utility) Two demand curves: price-demand x(p, 0, Z) and tax-demand x(p0 , tS , Z) (identical for fully rational consumer) Two steps in efficiency calculation: 1 2 Use tax-demand x(p, tS , Z) to calculate change in demand Use price-demand x(p, 0, Z) to recover change in surplus supply is perfectly elastic and able to shift the tax 100% to consumers. 49 / 53 Salience Effects Efficiency Cost with Salience Effects Price demand curve Agents act along the tax curve Consumer surplus before the introduction of tax Full incidence on the consumers Utility loss to consumers (if they are less rational) Tax demand curve F determines true utility (willingness to pay) Tax curve must be steeper because the reactions to tax changes are less pronounced than price changes. TAX REVENUES P0 price before taxation rational reaction We must end up with the same quantity x_0 To make the graphical analysis easier to interpret, we make the simplifying assumption that supply is perfectly elastic (flat inverse supply function) 50 / 53 Salience Effects Efficiency Cost with Salience Effects: Fig. 2 Surplus before tax: triangle ABC Introduction of tax shifts supply curve to p0 + ts Consumer reacts along tax-demand curve: x0 → x1 Impact on consumer surplus using price-demand curve positive surplus: triangle DGC (p0 + tS < wtp for demand x∗1 ) negative surplus : triangle DEF (p0 + tS > wtp for demand x1 − x∗1 ) Tax revenue is rectangle GBEH The resulting EB is triangle AF H ∂x line AH: tS ∂t S = x0 − x1 S line HF : tS ∂x/∂t ∂x/∂p 51 / 53 Salience Effects Efficiency Cost with Salience Effects: Fig. 2 Alternatively, start from EB of fully optimizing agent, EB ∗ , which is given by triangle AID For the not fully optimizing agent, two adjustment to EB ∗ are necessary subtract the additional revenue earned by the government because the agent under-reacts to the tax (rectangle HIDE) add the private welfare loss due to the optimization error (triangle DEF ) 52 / 53 Salience Effects Efficiency Cost: No Income Effects Without income effects, excess burden of introducing a small tax SLOPE OF THE BLUE LINE tS is S ∂x/∂t 1 · ∂x/∂tS EB(tS ) ≃ − · (tS )2 · 2 ∂x/∂p 1 = − · θ · (tS )2 · ∂x/∂tS 2 Quantituy loss influences welfare change Inattention reduces excess burden Intuition: tax tS induces behavioral response equivalent to a fully perceived tax of θtS. If θ = 0, tax is equivalent to a lump sum tax and EB = 0 because agent continues to choose first-best allocation. if nobody pays attention, excess burden is 0 as people stay where they are 53 / 53