Applied Public Economics PDF Spring 2024

Applied Public Economics 1. Introduction and Motivation Michael Gerfin Maximilian von Ehrlich University of Bern Spring 2024  Course Outline 1 Introduction and Motivation 2 Tax incidence 3 Efficiency costs of taxation 4...

Applied Public Economics 1. Introduction and Motivation Michael Gerfin Maximilian von Ehrlich University of Bern Spring 2024  Course Outline 1 Introduction and Motivation 2 Tax incidence 3 Efficiency costs of taxation 4 Optimal taxation 5 Empirical Welfare Analysis 6 International taxation 7 Taxation of Savings and Wealth 8 Public goods 2 / 49  Contents of first lecture 1. Introduction 2. Role of the Government 3. Applied Public Economics 4. Behavioral Public Economics 5. Eliciting the people’s view 3 / 49  Introduction What is Public Economics? Study of the role of the government in the economy Government is instrumental in many aspects of economic life 1 Government in charge of huge regulatory structure 2 Taxes: governments in advanced economies collect 35-50% of National Income in taxes 3 Expenditures: taxes fund public goods (infrastructure, defense) and welfare state (retirement benefits, health care, income support) We pool a large share of our incomes through government 4 / 49  Introduction Size of Public Sector 5 / 49  Introduction Size of Public Sector 6 / 49  Introduction A Bigger Picture View Of Government Sometimes, economics takes a narrow minded view of individual behavior: purely selfish and rational interacting through markets This view sets limits to fully understand public economics Social interactions are critical for humans we naturally cooperate at many levels: families, communities, nations, global treaties Humans reveal their social nature from the size and design of their “governments” (informal and formal) Replacing social institutions by markets does not always work 7 / 49  Introduction 3 Questions 1 When should the government intervene in the economy? 2 What is the effect of those interventions on economic outcomes? 3 Why do governments choose to intervene in the way that they do? 8 / 49  Role of the Government 1. Introduction 2. Role of the Government 3. Applied Public Economics 4. Behavioral Public Economics 5. Eliciting the people’s view 9 / 49  Role of the Government Q1: When should government intervene in the economy? 1 Market Failures Market economy sometimes fails to deliver an outcome that is efficient Then government intervention may improve the situation 2 Redistribution Market economy generates substantial inequality in economic resources across individuals Inequality is an issue because we are “social beings” People willing to pool their resources (through government taxes and transfers) to help reduce inequality 10 / 49  Role of the Government Market Failures Imperfect competition: (example: monopoly) → requires regulation (typically studied in Industrial Organization) Imperfect/Asymmetric Information: (example: health insurance markets) Healthy people drop out of private market → unraveling Mandated coverage could make everyone better off Externalities: (example: greenhouse carbon emissions) markets incomplete due to lack of prices (e.g. pollution) require interventions (such as corrective taxation) Individual failures People do not behave as “fully rational individuals” example: myopic people may not save enough for retirement intervention by forcing to save via social security paternalistic? 11 / 49  Role of the Government Inequality and Redistribution Even when the private market outcome is efficient, it may not have good distributional properties 2nd Welfare Theorem: Any Pareto efficient outcome can be reached by 1 Suitable redistribution of initial endowments (individualized lump-sum taxes based on indiv. characteristics and not behavior) 2 Then letting markets work freely In general, redistribution of initial endowments is not feasible Government can redistribute income through tax and transfer system (distortionary) Then redistribution creates an equity-efficiency trade-off 12 / 49  Role of the Government Q2: What Are the Effects of Alternative Interventions? 1 Direct effects effects of government interventions that would be predicted if individuals did not change their behavior in response to the interventions relatively easy to compute 2 Indirect Effects effects of government interventions that arise only because individuals change their behavior in response to the interventions (sometimes called unintended effects) empirical public economics analysis tries to estimate indirect effects to inform the policy debate Example: increasing top income tax rates mechanically raises tax revenue but top earners might find ways to avoid taxes, reducing tax revenue relative to mechanical calculation 13 / 49  Role of the Government Q3: Why Do Governments Intervene in the Way They Do? 1 Political Economy theory of how the political process produces decisions that affect individuals and the economy example: how the level of taxes and spending is set through voting and voters’ preferences 2 Public choice sub-field of political economy from a libertarian perspective that focuses on government failures situations where the government does not act in the benefit of society (e.g., government captured by special interests or a self-perpetuating bureaucracy) This question is not addressed in this course 14 / 49  Role of the Government Normative vs. Positive Public Economics 1 Normative analysis: what should the government do if we can choose optimal policy? how high should taxes be? should health insurance be mandated? 2 Positive analysis: what are the observed effects of government programs and interventions? do higher taxes reduce labor supply? does mandatory health insurance increase health care spending? Positive economics is a required first step before we can complete normative economics Positive analysis is primarily empirical, and normative analysis is primarily theoretical 15 / 49  Role of the Government Methodology Public economics is at the frontier of a methodological transformation in applied microeconomics Data-driven approach to answering important policy questions Combines a broad set of skills: applied theory, applied econometrics, simulation methods Useful skill set for many applied fields in economics Applied Public Economics is not feasible without a good knowledge of modern econometric tools 16 / 49  Applied Public Economics 1. Introduction 2. Role of the Government 3. Applied Public Economics 4. Behavioral Public Economics 5. Eliciting the people’s view 17 / 49  Applied Public Economics Connecting Theory to Data Modern public economics tightly integrates theory with empirical evidence to derive quantitative predictions what is the optimal income tax rate? what is the optimal unemployment benefit level? Traditional approach: theoretical models and numerical simulations but: theory often makes weak predictions: e.g. optimal tax rate between 0 and 100% numerical simulations rely on strong assumptions Recent work derives robust formulas that can be implemented using well-identified empirical estimators difference-in-differences, IV, regression discontinuity Students interested in these approaches are encouraged to take the course Causal Analysis also offered this semester 18 / 49  Applied Public Economics Connecting Theory to Data Curry et al. (2020), Technology and Big Data Are Changing Economics:Mining Text to Track Methods, AEA Papers & Proceedings, forthcoming 19 / 49  Applied Public Economics Connecting Theory to Data Curry et al. (2020), Technology and Big Data Are Changing Economics:Mining Text to Track Methods, AEA Papers & Proceedings, forthcoming 20 / 49  Applied Public Economics Data types used in economic research Curry et al. (2020), Technology and Big Data Are Changing Economics:Mining Text to Track Methods, AEA Papers & Proceedings, forthcoming 21 / 49  Applied Public Economics “Big Data” Compelling implementation of quasi-experimental methods requires a lot of data Recent availability of very large datasets has transformed research in applied microeconomics government data: tax records, Medicare corporate data: retailer data (scanner data), health insurance companies, Facebook unstructured data: Twitter, newspapers, Swisscom 22 / 49  Applied Public Economics What are the benefits of Big Data? 1 Higher quality information: virtually no missing data or attrition 2 Longitudinal tracking over long periods 3 Very large sample sizes Can develop new research designs Can zoom in to subgroups 4 Ability to measure new variables (e.g. non-market inter- actions, networks, emotions) 23 / 49  Behavioral Public Economics 1. Introduction 2. Role of the Government 3. Applied Public Economics 4. Behavioral Public Economics 5. Eliciting the people’s view 24 / 49  Behavioral Public Economics What is behavioral economics? In the last years, a large body of research has incorporated insights from psychology – such as loss aversion, present bias, and inattention – into economic models Still, the neoclassical model remains the benchmark for most economic applications The debate about behavioral economics is often framed as a question about the foundational assumptions of neoclassical economics Are individuals rational? Do they optimize in market settings? Potentially fruitful to approach the debate on behavioral economics from a more pragmatic, policy-oriented perspective 25 / 49  Behavioral Public Economics Policy-oriented behavioral public economics The pragmatic approach starts from a policy question and incorporates behavioral factors to improve empirical predictions and policy decisions The implications of behavioral economics for public policy can be classified into three domains Each of these domains has a intellectual tradition in economics → from a pragmatic perspective, behavioral economics is a natural progression of neoclassical economic methods 26 / 49  Behavioral Public Economics Domain 1: New policy tools Insights from psychology offer new tools that expand the set of outcomes that can be achieved through policy changing default options framing incentives as losses instead of gains 27 / 49  Behavioral Public Economics Domain 2: Better predictions about the effects of policies Incorporating behavioral features such as inertia or inattention into neoclassical models can yield better predictions about the effects of economic incentives such as retirement savings subsidies or income tax policies These behavioral features can help econometricians develop new counterfactuals to identify policy impacts 28 / 49  Behavioral Public Economics Domain 3: New welfare implications Behavioral biases may generate a gap between welfare from a policy maker’s perspective, which depends on an agent’s experienced utility (his actual well-being), and the agent’s decision utility (the objective the agent maximizes when making choices) Accounting for these gaps between decision and experienced utilities improves predictions about the welfare consequences of policies The difference between the policy maker’s and agent’s objectives in behavioral models parallels non-welfarist approaches to optimal policy 29 / 49  Behavioral Public Economics Example : Chetty et al (2014) Denmark has two types of tax-deferred savings accounts capital pensions paid out as a lump sum upon retirement annuity pensions paid out as annuities In 1999, the tax deduction for contributing to capital pension accounts was reduced from 59% to 45% for individuals in the top income tax bracket (≈ DKr 250k) Chetty et al. (2014) analyze how this change affected payments to the capital pension Control group: individuals in the lower income brackets 41 million observations on the savings of all Danish citizens from 1995-2009 Source: Chetty, R., J. Friedman, S. Leth-Peterson, T. Nielsen, and T. Olsen (2014), Active vs. Passive Decisions and Crowd-out in Retirement Savings Accounts: Evidence from Denmark, QJE 30 / 49  Behavioral Public Economics Chetty et al (2014): results The greenish lines refer to periods before the reform, the reddish lines to periods after the reform. Incomes below 250k DKr. are the control group, which shows no change over time. Savings behavior of treatment group strongly changes after reform. 31 / 49  Behavioral Public Economics Chetty et al (2014) The estimated effect is driven by the 19%, who stopped to pay into the capital pension (left spikes). The other 81% did not react to the reform. About half of the reduction in capital pension contributions was offset by increased contributions to annuity pension accounts, the rest was almost entirely offset by increased saving in taxable accounts 32 / 49  Behavioral Public Economics Chetty et al. (2014) Lessons from this analysis: Responses that appear to be consistent with optimization in the aggregate may mask significant deviations from optimization at the individual level any optimizing agent at an interior optimum should change capital pension contributions by some non-zero amount when the subsidy is reduced Standard policy tools suggested by neoclassical theory are not very successful in increasing savings rates they induce only a small group of individuals to respond these individuals simply shift assets between accounts 33 / 49  Eliciting the people’s view 1. Introduction 2. Role of the Government 3. Applied Public Economics 4. Behavioral Public Economics 5. Eliciting the people’s view 34 / 49  Eliciting the people’s view Large-scale online surveys and experiments New strand of research using large-scale online surveys and experiments to understand how people think how they form their perceptions, beliefs, and attitudes how their views on economic and social policies emerge Examples Kuziemko et al (2015), “How Elastic are Preferences for Redistribution: Evidence from Randomized Survey Experiments”, American Economic Review) Stantcheva (2021), “Understanding Tax Policy: How do people Reason?”, QJE Alesina et al (2021), “Immigration and Redistribution”, Review Of Economic Studies Ferrario & Stantcheva (2022), “Eliciting People’s First-Order Concerns: Text Analysis of Open-Ended Survey Questions”, AER P&P 35 / 49  Eliciting the people’s view Understanding Tax Policy: How do people reason? Elements of survey Background Socioeconomic Questions: apart from typical (age, income) highest level of education achieved, main source of news, and political orientation political orientation: classify themselves in terms of their views on economic policy, ranging from “very conservative” to “very liberal”; what they consider their political affiliation to be (Republican/Democrat/Independent/Other/Nonaffiliated) Knowledge: level of the top federal taxes, the threshold for the top income tax bracket, the top tax rates in the 1950s, the share of households paying no income tax, the average tax rate for the median household or the top household, the share of total income that goes to the top 1%, or the occupational composition of the top 1% of earners 36 / 49  Eliciting the people’s view Understanding Tax Policy: How do people reason? Elements of survey Information Treatment: randomly chosen subsample of respondents was shown one of three versions of an instructional video that provided information about the policy (see following slides) Reasoning about taxes: respondents are asked to think in more detail about how tax policy works. What behavioral responses, efficiency effects, and effects on the broader economy will it trigger? What are the distributional consequences for different groups? What fairness concerns do people have? Example: in the income tax module, respondents are asked to what extent they believe people will engage in the following behaviors if their taxes were to increase: save less, work less, stop working altogether, evade taxes, and so on; whether taxing away the income of different groups is fair or unfair. 37 / 49  Eliciting the people’s view Understanding Tax Policy: How do people reason? Elements of survey Policy Views: Respondents were asked about their views on the current tax systems (Is it fair?) and for opinions regarding policy actions (increasing tax to fund specific programs) Views of Government: respondents expressed their views about the role and capacity of the government to deal with the issue at hand (e.g. to what extent they think the government has the tools and ability to reduce income inequality) and their general attitudes toward government (e.g. trust) 38 / 49  Eliciting the people’s view Redistribution Treatment Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 39 / 49  Eliciting the people’s view Efficiency Treatment Stantcheva (2021), Understanding Tax Policy: How Do People Reason?,QJE 40 / 49  Eliciting the people’s view Economist Treatment Stantcheva (2021), Understanding Tax Policy: How Do People Reason?,QJE 41 / 49  Eliciting the people’s view Main Considerations About Income Tax Stantcheva (2021), Understanding Tax Policy: How Do People Reason?,QJE 42 / 49  Eliciting the people’s view Perceived Behavioral Responses Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 43 / 49  Eliciting the people’s view Perceived Efficiency Costs Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 44 / 49  Eliciting the people’s view Social Preferences Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 45 / 49  Eliciting the people’s view Support for Increasing Taxes Depends on Goal Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 46 / 49  Eliciting the people’s view Construction Of Policy Index Goal: policy index that increases when respondents support more progressive taxes and are more favorable to government intervention to reduce inequality Apply unsupervised, clustering machine learning algorithm based on latent Dirichlet allocation Algorithm identifies probability distributions over answers and assigns them to respondent “profiles” based on their frequency Income tax policy index: combines variables on whether the respondent thinks that progressive taxation is an important tool to reduce inequality, whether they support increasing taxes on higher-income to expand programs targeted to low incomes or to increase investments, and whether they believe that the government should have responsibility in reducing income inequality between the rich and the poor. Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 47 / 49  Eliciting the people’s view Decomposing Tax Policy Views Stantcheva (2021), Understanding Tax Policy: How Do People Reason?, QJE 48 / 49  Eliciting the people’s view Impact of Information Treatments Stantcheva (2021), Understanding Tax Policy: How Do People Reason?,QJE 49 / 49 Applied Public Economics Tax Incidence Michael Gerfin University of Bern Spring 2024  Contents 1. Introduction 2. Partial Equilibrium Incidence 3. Tax Incidence: Empirical Applications 4. Tax Incidence with Salience Effects 2 / 50  Introduction Introduction Tax incidence is the study of the effects of tax policies on prices price changes are functions of supply and demand curves these depend on production and utility functions hence price changes induced by taxes have impact on producer and consumer rents Economic and statutory incidence are equivalent when prices are constant What happens to market prices when a tax is introduced or changed? Increase tax on cigarettes by $1 per pack Introduction of Earned Income Tax Credit (EITC) Food stamps program Effect on price → distributional effects on smokers, profits of producers, shareholders, farmers,... 3 / 50  Introduction Introduction Tax incidence is an example of positive analysis Typically the first step in policy evaluation An input into thinking about policies that maximize social welfare Theory is informative about signs and comparative statics but is inconclusive about magnitudes Incidence of cigarette tax: elasticity of demand w.r.t. price is crucial Labor vs. capital taxation: mobility of labor, capital are critical 4 / 50  Partial Equilibrium Incidence 1. Introduction 2. Partial Equilibrium Incidence 3. Tax Incidence: Empirical Applications 4. Tax Incidence with Salience Effects 5 / 50  Partial Equilibrium Incidence Partial Equilibrium Model: Setup Two goods: x and y Government levies an excise tax on good x Excise or specific tax: levied on a quantity (e.g. gallon, pack) Ad-valorem tax: fraction of prices (e.g. sales tax) Let p denote the pre-tax price of x and q = p + t denote the tax inclusive price of x Good y, the numeraire, is untaxed Perfect competition → firms are price-taking 6 / 50  Partial Equilibrium Incidence Partial Equilibrium Model: Demand Consumer has wealth Z and utility function u(x, y) Utility maximization gives demand D as a function of price q, D(q) ∂D q ∂ log D Let εD = ∂q D(q) = ∂ log q denote the price elasticity of demand 7 / 50  Partial Equilibrium Incidence Partial Equilibrium Model: Supply Producers use y to produce x Production function is concave, so marginal cost of producing x is increasing With perfect optimization, profit maximization gives supply S as a function of pre-tax price p, S(p) (because the tax will never be part of profit) ∂S p Let εS = ∂p S(p) denote the price elasticity of supply 8 / 50  Partial Equilibrium Incidence Partial Equilibrium Model: Equilibrium The equilibrium condition Q = S(p) = D(p + t) defines p as a function of t, p(t) dp Goal of analysis: characterize dt , the effect of a tax on price First consider some graphical examples to build intuition, then analytically derive formula 9 / 50 Partial Equilibrium Incidence Graphical Example I 10 / 50 Partial Equilibrium Incidence Graphical Example II 11 / 50  Partial Equilibrium Incidence Formula for Tax Incidence Implicitly differentiate equilibrium condition D(p(t) + t) = S(p(t)) to obtain incidence on producers: dp ∂D 1 = ∂S ∂D dt ∂p ( ∂p − ∂p ) dp εD ⇒ = dt εS − εD Incidence on consumers is: dq dp εS =1+ = dt dt εS − εD 12 / 50  Partial Equilibrium Incidence Formula for Tax Incidence in a Picture 13 / 50  Empirical Applications 1. Introduction 2. Partial Equilibrium Incidence 3. Tax Incidence: Empirical Applications 4. Tax Incidence with Salience Effects 14 / 50  Empirical Applications Applications 1 Doyle and Samphantharak (2008), $2.00 Gas! Studying the effects of a gas tax moratorium, Journal of Public Economics 2 Hastings and Washington (2010), The First of the Month Effect: Consumer Behavior and Store Responses, AEJ: Econ. Policy More examples are in the exercises 15 / 50  Empirical Applications Doyle and Samphantharak, 2008 Question: who bears the burden of the gas tax? Setting: Gas prices spike above $2.00 in 2000, near election, political desire to provide tax relief Repeal and subsequent reinstatement of sales tax in Indiana and Illinois Reforms known to be temporary and timing of reinstatement was known ex-ante Exogenous change, independent of market price 16 / 50  Empirical Applications Doyle and Samphantharak, 2008 Homogeneous product (no quality differences) Highly important tax: total revenue in the US 8 billion $ per year (EIA, 2005) Fall and rise in price → potential asymmetries in response can be identified Effects on retail prices and cross-border competition 17 / 50  Empirical Applications Doyle and Samphantharak, 2008 Institutional Background Election year in Indiana (IN) plus exceptional gas prices Governor of IN declares energy emergency IN suspends 5% sales tax on gas starting July 1 for 60 days Suspension was extended three times and tax was reinstated on Oct 30 Gas prices had already fallen in September which suggests that reinstatement was not tied to market conditions Illinois (IL) suspends 5% sales tax on gas starting July 1, reinstates on Dec 31 18 / 50  Empirical Applications Doyle and Samphantharak, 2008 Institutional Background Excise taxes were not affected by the moratorium Sales tax is levied from the retailer Posted gas prices include any taxes (salient tax) Station owners can deduct excise tax from the tax base when computing the sales tax Sales tax applies to ca. 90% (80%) of posted price in IL (IN) Full-shifting therefore implies 4.5% change in price in IL and 4% change in prices in IN 19 / 50  Empirical Applications Empirical Approach Difference-in-Difference estimation comparing treated states with neighboring states (MI, OH, MO, IA, WI) There should be a sharp discontinuity at the time of tax repeal and reinstatement Start with graphical evidence Next consider regression equation (controls for area characteristics X , brand FE), s = station, b = brand, t=time, P = retail price, W SP = whole sale price ln Pbst = γ0 + γ1 T reated + γ2 P ostref orm + γ3 (T reated · P ostref orm) + γ4 ln(W SP )s + γ5 X + δb + εbst 20 / 50  Empirical Applications Graphical Analysis: Effect of tax repeal Local linear regression of difference in log prices (IL,IN vs. neighbors) Effect of about -2.7% 21 / 50  Empirical Applications Graphical Analysis: Effect of tax increase Prices rose by about 4% (2.8%) in IN (IL) 22 / 50  Empirical Applications Diff-in-Diff Results: Tax-Repeal 23 / 50  Empirical Applications Diff-in-Diff Results: Tax-Repeal γ3 /0.04 = 0.72 (IN) and γ3 /0.045 = 0.64 (IL) measures relative incidence Estimated effects imply an approx. 70% pass-through rate (70% of the tax decrease reflected in lower price for consumers) The elasticity of demand is thought to be in range from -0.05 to -0.25 (Hughes et al., 2006) Recall that dq εS dqdt = ⇒ εS = εD dt (εS − εD ) (1 − dqdt) A pass-through rate of 0.7 implies a supply elasticity in the range of 0.1 − 0.6 24 / 50  Empirical Applications Diff-in-Diff Results: Tax Reinstatement 25 / 50  Empirical Applications Diff-in-Diff Results: Tax Reinstatement When the tax was reinstated, retail prices rose by roughly 4% Point estimates suggest that prices decrese less in response to the tax cut compared to the response to the tax increase However, the 3% and 4% changes are not statistically significantly different Full shifting of the tax changes cannot be rejected for the October reinstatement, but can be rejected in the July repeal and the January reinstatement 26 / 50  Empirical Applications Hastings and Washington 2010 Question: How does food stamps subsidy affect grocery store pricing? Food stamps typically arrive at the same time for a large group of people, e.g. first of the month Use this variation to study: 1 Whether demand changes at beginning of month (violating permanent income hypothesis) 2 How much of the food stamp benefit is taken by firms by increased prices rather than consumers (intended recipients) 27 / 50  Empirical Applications Hastings and Washington: Data Scanner data from several grocery stores in Nevada Data from stores in high-poverty areas (> 15% food stamp recipients) and in low-poverty areas ( 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  2  dQ 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  = −(1/2) dτ dQ  · 2τ · ∆τ + (∆τ )2  = −(1/2) dτ dQ dQ = −τ ∆τ − (1/2) (∆τ )2 dτ dτ 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 N X max u(x1 ,..., xN −1 ) + xN s.t. (p1 + t)x1 + p i xi = Z i=2 To measure EB of tax, define social welfare as sum of individual’s utility and tax revenue: spending on numerraire. income minus... N X −1 W (t) = {max u(x1 ,..., xN −1 )+Z −(p1 +t)x1 − pi xi }+tx1 x i=2 dW Goal: measure dt (social welfare loss caused by tax change) 22 / 53  Sufficient Statistics Sufficient Statistics vs Structural Methods Structural method: estimate demand system, recover u dW Sufficient statistics: apply envelope theorem to derive dt Private sector makes choices to maximize private surplus N X −1 W (t) = {max u(x1 ,..., xN −1 ) + Z − (p1 + t)x1 − pi xi } + tx1 x 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 dW → dt is a “sufficient statistic” for calculating 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 dz/z ∗ excess mass at kink ε= = 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 4k This income level maximizes tax refund t=0 generate incnetives EITC Credit Amount ($1000) to enter labor 3k markets t=0,2 subsidies wages for single mothers but 2k prorgamme was expanded 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% 4% Percent of Tax Filers 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 Use tax-demand x(p, tS , Z) to calculate change in demand 2 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 Utility loss to Price demand curve Agents act along the tax curve consumers (if they are less rational) Consumer surplus Tax demand curve before the introduction of tax F determines true utility (willingness to pay) Full incidence Tax curve must be on the consumers TAX REVENUES steeper because the reactions to tax changes are less P0 price before pronounced than taxation price changes. We must end up with the same quantity x_0 rational reaction 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 ∂tS = 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 tS is SLOPE OF THE BLUE LINE 1 ∂x/∂t S EB(tS ) ≃ − · (tS )2 · · ∂x/∂tS 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 Applied Public Economics 4. Optimal Labor Income Taxation Michael Gerfin University of Bern Spring 2024  Contents 1. Social Welfare Function 2. Optimal Linear Tax 3. Optimal Top Income Tax 4. A Tale of Three Elasticities 2 / 57  Overview of Optimal Taxation Realised earnings are functions of people being shown how From an efficiency perspective, government should be financed purely through lump-sum taxation With redistributional concerns, ideally levy individual-specific lump sum taxes Tax higher-ability individuals a larger lump sum Problem: cannot observe individuals’ types Therefore must tax economic outcomes such as income or consumption, which leads to distortions 3 / 57  Mirrlees (1971) Pioneer work on optimal income taxation based on structural approach Mirrlees model had a profound impact on information economics E.g. models with asymmetric information in contract theory But until late 1990s, had little impact on practical tax policy Since late 1990s, e.g. Diamond (1998), Piketty (1997), and Saez (2001) have connected Mirrlees model to practical tax policy/empirical tax studies sufficient statistic formulas in terms of labor supply/taxable income elasticities instead of primitives new approach summarized in Diamond-Saez JEP’11 and Piketty-Saez Handbook’13 4 / 57  Social Welfare Function 1. Social Welfare Function 2. Optimal Linear Tax 3. Optimal Top Income Tax 4. A Tale of Three Elasticities 5 / 57  Social Welfare Function Social Welfare Function Throughout this chapter we assume that the goal of the government is to maximize social welfare The only reason to tax is to redistribute income Transfers are negative taxes, so the sum of all taxes is zero Tax function is given by T (z), where z is taxable income Individual i has quasi-linear preferences of the form they could be just two different dimensions ui = u(ci , zi ) = ci − v(zi ), of labour supply where c = z − T (z) is after-tax income and v(·) is an increasing convex function reduce your overtime, which is easier Population is of size one (sum equals mean) 6 / 57  Social Welfare Function more influential increases in change Social Welfare Function of utility in poor people rather than rich people transforms individual utility into social welfare, a concave function because we want to have test for the redistribution in society. The social welfare function, W , is Z W = G(ui )f (wi )dw G(·) is function that transforms individual utilities into individual social welfare contributions. With redistributive tastes G(u) is increasing and concave. With quasi-linear utility we need G in order to have social preferences for redistribution f (wi ) is distribution of wages w (skills) in society (exogenous) 7 / 57  Social Welfare Function Government’s revenue constraint Government’s revenue constraint is: Z T (zi )f (wi )dw = 0 This model can also be written in sums N X −1 W =N G(ui ) i=1 XN 0 = N −1 T (zi ) i=1 8 / 57  Social Welfare Function increase the total value of Social Welfare Weights society if you give an individual one USD1 Let gi = g(zi ) be the social marginal welfare weight for an individual with earnings zi in terms of public funds It is defined as gi = G′ (ui )ui,c /α α is the marginal value of one dollar tax revenue, which corresponds to the multiplier on the gov’t budget constraint in the Lagrangian for the social welfare maximization ui,c is marginal utility of consumption, equal to 1 ∀ i with quasi-linear preferences Intuitively, gi measures the dollar value to society (in terms of public funds) of increasing consumption of individual i by $1 With quasi-linear preferences gi = G′ (ui )/Ḡ′ R ′ ′ α ′ R = G (ui )f (wi )dw = Ḡ (mean of G (ui )) gi f (wi )dw = 1 (mean of gi ) 9 / 57  Social Welfare Function Properties of gi Distinguish two polar cases and an intermediate case Polar case 1: Society has no preferences for redistribution gi = 1 ∀ i Polar case 2: Society has Rawlsian preferences maximize welfare of the worst-off individuals (here zi = 0) then gi = 0 ∀ zi > 0 g1 = N/N0 ∀ zi = 0, where N0 is the number of people with zi = 0 (need to make sure gi averages to 1) Intermediate case: Society has Utilitarian preferences gi > 1 for individuals with low income and gi < 1 for individuals with high income This is illustrated in the following graph 10 / 57 Social Welfare Function Properties of gi Johns rawisl..theory of justice, regartding the way public polcies should be "formulated". Due to our insufficency to understand natural behav, we weight lss than one 11 / 57  Social Welfare Function Derivation of α = Ḡ′ Derivation of marginal social welfare weight with quasi-linear utility: ui = ci − v(zi ) Z Z max L = G(ui )f (wi )dw + α [T (zi )] f (wi )dw T (z) Z Z dL ∂G(ui ) ∂u dc dT = f (wi )dw + α f (wi )dw = 0 dT ∂u ∂c dT dT Z = G′ (ui )(1)(−1) f (wi )dw + α = 0 Z α = G′ (ui ) f (w)dw = Ḡ′ 12 / 57  Social Welfare Function Derivation of α = Ḡ′ , discrete case Derivation of marginal social welfare weight with of quasi-linear utility: ui = ci − v(zi ) X X max L = G(ui )) + α (T (zi ) T (z) dL X ∂G ∂u dc X dT = ui )∂u +α =0 dT ( ∂c dT dT X = G′ (ui )(1)(−1) + αN = 0 X = −G′ (ui ) + αN = 0 X α = G′ (ui )/N = Ḡ′ 13 / 57  Optimal Linear Tax 1. Social Welfare Function 2. Optimal Linear Tax 3. Optimal Top Income Tax 4. A Tale of Three Elasticities 14 / 57  Optimal Linear Tax Linear Tax Rate Tax system consists of 1 Lump-sum grant R given to everybody (universal basic income) 2 Marginal tax rate τ on taxable income z T (z) = τ · z − R with linear tax rate τ and lump-sum transfer R funded by taxes τ · Z , where Z denotes aggregate earnings After tax income is c = (1 − τ ) · z + R Population of size one (continuum) with quasi-linear preferences ui = u(ci , zi ) = ci − v(zi ) 15 / 57  Optimal Linear Tax Linear Tax Rate why is ν' the slope rate of the curve? it is the marginal rate of substitution between the two arguments of utility function. Ci Individual i chooses z to maximize ui = (1 − τ ) · zi + R − v(zi ) FOC is (1 − τ ) = v ′ (zi ) This implicitly defines taxable income z as a function of the net-of-tax rate (1 − τ ): z = z(1 − τ ) Individual choices of taxable income Rzi (1 − τ ) aggregate to economy wide earnings Z(1 − τ ) = zi f (wi )dw note that Z(1 − τ ) means Z is function of (1 − τ ) dU/dthing on x-c*x_i*j slope ind, curveL -MRS= dzU/dthing on y-c*x_i*j 16 / 57  Optimal Linear Tax The slope is 1, which means that for each additional unit of taxable income z, the Linear Tax Rate disposable income c increases by the same amount. In other words, if you make one more dollar, you get to keep that dollar. The red line represents the situation with a tax. The slope of this line is 1−t, where t is the tax rate. If the tax rate is, for instance, 20%, then t=0.2 and the slope of the red line is 1 − 0.2 = 0.8. This means that for each additional dollar of taxable income, If each dollar the disposable income I am earning., only increases by 80 consumption cents because 20 cents comes up at 1-t are paid in tax. venit impozabil in RO The reason why the red curve is less steep is that the tax effectively removes a portion of each additional dollar earned. The steeper the slope, the more of each dollar you keep. Thus, a slope of less than 1 reflects the impact of taxes taking away part of your income, resulting in a less steep line that shows the relationship between your taxable income and your disposable income after taxes. 17 / 57  Optimal Linear Tax Revenue-Maximizing Linear Tax Rate Tax rate τ max maximizes tax revenue R = τ Z, so R′ = Z + τ max dZ/d(τ ) = Z − τ max dZ/d(1 − τ ) = 0 Solving for τ max yields 1 1−τ dZ τ max = with e = 1+e Z d(1 − τ ) e is the elasticity of aggregate earnings with respect to the net-of-tax rate (1 − τ ) τ > τ max is inefficient: cutting τ increases individuals welfare and government revenue So-called Laffer curve 18 / 57 Optimal Linear Tax Principle of diminishing returns from taxation. At a 0% tax rate, the Laffer Curve government would collect no revenue, but at a 100% tax rate, the government also would collect no revenue because there would be no incentive for people to earn taxable income. The curve suggests that there is an optimal tax rate (τ*) where tax revenue is maximized. Beyond this point, any increase in tax rates would actually lead to a decrease in total revenue. there must be a tax level that maximizes tax elasticity. he wanted to convince Reagan that taxes were too high 19 / 57  Optimal Linear Tax Optimal Linear Tax Rate Labour income i can keep + transfer Government chooses τ to maximize Utility + tasx revenues Z W = G[(1 − τ )zi + τ Z(1 − τ ) − v(zi )]f (w)dw | {z } u(ci ,zi ) Z = G[(1 − τ )zi − v(zi ) + τ Z]f (w)dw The argument of the G function can be interpreted as an analogue of the definition of social welfare in the pure efficiency analysis (1 − τ )zi − v(zi ) is private surplus τ Z is tax revenue here, tax revenue enters private utility because it is transferred back to individuals 20 / 57  Optimal Linear Tax Perturbation Argument Apply perturbation argument to derive optimal tax rate all effects start from optimal individual choices zi conditional on τ and within the marginally change τ by dτ people's reaction G function this has an mechanical effect, a behavioral effect, and a private change utility effect effect on argument in the G-function in tax the first two relate changes in tax revenue, the third is the private surplus change we know from the efficiency analysis how to compute these effects at optimal τ the social welfare weighted net effect of these changes must be zero 21 / 57  Optimal Linear Tax Effect of dτ on ui Mechanical effect on tax revenue τ Z: dM = Z × dτ Behavioral effect on tax revenue τ Z: dB = τ × dZ Utility effect on income level zi : dui = −zi × dτ Difference to pure efficiency analysis: here dM relates to average income Z, while dui relates to zi , and there is variation in zi (otherwise no need for redistribution) Utility enters social welfare through function G 22 / 57  Optimal Linear Tax dW/dτ Analyze change in W caused by dτ (leaving f (w)dw implicit) Z dW = 0 = G′i (dM + dB + dui ) Z = (G′i dM + G′i dB + G′i dui ) Z Z Z = Gi dM + Gi dB + G′i dui ′ ′ Z Z Z = dM G′i + dB G′i + G′i dui Z = dM Ḡ′ + dB Ḡ′ + G′i dui Z = dM + dB + (G′i /Ḡ′ )dui Z = dM + dB + gi dui 23 / 57  Optimal Linear Tax Condition for optimal tax rate R dM + dB + gi dui = 0 Replacing dM, dB and dui by their quantities, we get R dτ Z + τ dZ + gi (−zi dτ ) = 0 Denote gi zi by Z g (welfare weighted average income) R Then the weighted average private utility effect is dU = −Z g × dτ Putting it together: Z × dτ + τ dZ − Z g × dτ = 0 24 / 57  Optimal Linear Tax Rewrite dB Taxable income elasticity with respect to net-of-tax rate (1 − τ ) 1−τ dZ e= Z d(1 − τ ) dB dZ dB = τ × dZ = −τ dτ d(1 − τ ) τ 1−τ dZ = − × × Zdτ 1−τ Z d(1 − τ ) τ ⇒ dB = − × e × Zdτ 1−τ in the first line the second equality follows from the fact dτ = −d(1 − τ ) in second line multiply by Z/Z and (1 − τ )/(1 − τ ), then rearrange to get elasticity 25 / 57  Optimal Linear Tax Condition for optimal tax rate Using the rewritten dB we get τ Z × dτ − × e × Zdτ − Z g × dτ = 0 1−τ This simplifies to τ Z − Zg = ×e×Z 1−τ Then τ 1 Z − Zg 1 = (Z − Z g )/(e × Z) = = (1 − ḡ) 1−τ e Z e where ḡ = Z g /Z (ratio of welfare weighted average income to actual average income) 0 ≤ ḡ < 1 if g(z) is decreasing with z 26 / 57  Optimal Linear Tax Optimal Linear Tax Rate Solving for τ gives after some rearrangements only a function of e, elasticity income, and g, equity ∗ 1 − ḡ preferences in society τ = 1 − ḡ + e Formula captures the equity-efficiency trade-off robustly (τ ∗ ↓ ḡ, τ ∗ ↓ e) Without efficiency costs (e = 0), τ ∗ = 1 If society does not value redistribution at all, ḡ = 1 and τ ∗ = 0 If social preferences are Rawlsian, ḡ = 0 and τ ∗ is the revenue maximizing tax rate Formula is implicit because both e and ḡ vary with τ Formula is general as it applies to many models for the income generating process (only aggregate elasticity e matters) 27 / 57  Optimal Top Income Tax 1. Social Welfare Function 2. Optimal Linear Tax 3. Optimal Top Income Tax 4. A Tale of Three Elasticities 28 / 57  Optimal Top Income Tax Top 1% Share Over Time Source: Lampart et al. (2023), Verteilungsbericht, SGB Dossier 154 29 / 57  Optimal Top Income Tax Top 1% Share and Top Marginal Tax Rate Piketty et al (2014) Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities, American Economic Journal: Economic Policy 30 / 57  Optimal Top Income Tax Top 1% Share and Top Marginal Tax Rate Piketty et al (2014) Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities, American Economic Journal: Economic Policy 31 / 57  Optimal Top Income Tax CEO Compensation and Top Marginal Tax Rate Source: Piketty, Saez, & Stantcheva (2014), “Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities”, American Economic Journal: Economic Policy 32 / 57  Optimal Top Income Tax Growth and Change in Top Marginal Tax Rate Source: Piketty, Saez, & Stantcheva (2014), “Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities”, American Economic Journal: Economic Policy 33 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate Derivation of optimal top tax rate Consider constant τ above fixed income threshold z ∗ Use perturbation argument again Assume there is a continuum of measure one of individuals above z ∗ Let z(1 − τ ) be their average income (depends on net-of-tax rate 1 − τ ), with top taxable income elasticity etop = [(1 − τ )/z] · dz/d(1 − τ ) 34 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate 35 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate Mechanical effect in tax revenue: dM = [z − z ∗ ]dτ Behavioral effect dz dB = τ · dz = −τ dτ d(1 − τ ) τ 1−τ dz = − · · zdτ 1−τ z d(1 − τ ) τ ⇒ dB = − · etop · zdτ 1−τ Weighted private utility effect: dU = −g top dM = −g top [z − z ∗ ]dτ where g top is the average social welfare weight of the rich 36 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate Optimal τ such that dW = dM + dU + dB = 0 dW = dM + dU + dB  top ∗ top τ = dτ (1 − g )(z − z ) − e z 1−τ   ∗ top top z τ = dτ (z − z ) (1 − g ) − e (z − z ∗ ) 1 − τ   z τ = dM 1 − g top − etop (z − z ∗ ) 1 − τ 37 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate Define a = z/(z − z ∗ )   top top z τ dW = dM 1 − g − e (z − z ∗ ) 1 − τ   top top τ = dM 1 − g − e a 1−τ τ Optimal τ requires dW = 0 ⇒ 1 − g − etop a 1−τ top =0 Solving for τ gives ∗ 1 − g top τtop = 1 − g top + etop a 38 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate ∗ 1 − g top τtop = 1 − g top + etop a ∗ decreases with g top (redistributive tastes) τtop ∗ decreases with etop (efficiency) τtop ∗ decreases with a (thickness of top tail) τtop 39 / 57  Optimal Top Income Tax Empirical estimate of a = z/(z − z ∗ ) 40 / 57  Optimal Top Income Tax Optimal Top Income Tax Rate In US tax return data, a = z/(z − z ∗ ) very stable above z ∗ = $400K with a ≈ 1.5 (CH: a ≈ 1.9, DK: a ≈ 3) Top income distribution can be very well approximated by Pareto distribution with fixed parameter a Pareto distribution f (z) = a · k a /z 1+a with k and a constant Assuming g top = 0 and etop = 0.25 (mid-range estimate in literature) the optimal top tax rate is 1/(1 + 0.25 · 1.5) = 0.73 41 / 57  Optimal Top Income Tax Top income shares in Switzerland Source: Schaltegger and Gorgas (2011), The Evolution of Top Incomes in Switzerland 42 / 57  Optimal Top Income Tax Top income shares in Switzerland Source: Schaltegger and Gorgas (2011), The Evolution of Top Incomes in Switzerland a = β/(β − 1) 43 / 57  Optimal Top Income Tax Tax Reforms in Switzerland Source: Lampart et al. (2023), Verteilungsbericht, SGB Dossier 154 44 / 57  A Tale of Three Elasticities 1. Social Welfare Function 2. Optimal Linear Tax 3. Optimal Top Income Tax 4. A Tale of Three Elasticities 45 / 57  A Tale of Three Elasticities Piketty, Saez & Stantcheva (2014) Piketty et al (2014) analyze the channels through which the top 1% income share has increased 1 Standard supply side channel (with elasticity e1 ) 2 Avoidance and income shifting (with elasticity e2 ) 3 Compensation bargaining and rent seeking (with elasticity e3 ) In the most simple case e = e1 + e2 + e3 , where e is the total taxable income elasticity In the standard case, e2 = e3 = 0, and the previous result holds (assuming g top = 0) dz/z e = e1 = d(1−τ )/(1−τ ) and τ ∗ = 1/(1 + a · e1 ) Piketty et al (2014) Optimal Taxation of Top Labor Incomes: A Tale of Three Elasticities, American Economic Journal: Economic Policy 46 / 57  A Tale of Three Elasticities Tax avoidance Assume agent can shelter $x with cost f (e), and taxable income is z = y − x, where y is real income Examples for avoidance reductions in current cash compensation for e.g. deferred compensation such as stock-options outright tax evasion such as using offshore accounts z is taxed a constant rate τ , x is taxed at a constant rate 0≤t 0: pay for luck βl ≥ β: no filtering of luck component 54 / 57  A Tale of Three Elasticities Piketty et al., 2014: empirical analysis In order to measure β estimate by OLS payit = βpit + γi + µt + αXit + εit , where γi is firm FE, µt is time FE and Xit are CEO controls To decompose p regress p on luck measure l pit = πlit + γi + µt + δXit + νit , and generate p̂it = π̂lit + γ̂i + δ̂Xit , which is the part of p attributed to luck Finally, to estimate βl regress payit = βl p̂it + γi + µt + αXit + εit , The last two steps are nothing else but 2SLS with the luck measure l as instrument for performance p 55 / 57  A Tale of Three Elasticities Piketty et al., 2014: empirical analysis Performance measures: (1) net income and (2) shareholder wealth Measure of pay: Total CEO Pay Measure of luck: Mean asset-weighted performance of other firms in industry Data: Forbes 800 + Execucomp, COMPUSTAT-CRSP Years: 1970-2010 56 / 57  A Tale of Three Elasticities Piketty et al., 2014: empirical analysis there is pay for luck (CEOs are rewarded for industry wide performance) (cols. 2 and 5) pay for luck has increased since 1987 when top tax rates are lower (Panel A vs Panel B) sensitivity of workers’ wages to industry performance has not been affected by the change in top tax rates (cols. 3 and 6) 57 / 57 Applied Public Economics 5. Empirical Welfare Analysis Michael Gerfin University of Bern Spring 2024  Introduction Contents 1. Introduction 2. Marginal Value of Public Funds 3. Examples 2 / 23  Introduction Goals of Public Economics What government policies improve social welfare the most? Should we spend more (or less) on health insurance? Should we raise top marginal income tax rates? Large body of existing research analyzing the causal impact of a wide range of these types of policy changes How do we translate those estimates into a statement about the desirability of the policy change? 3 / 23  Introduction Normative Evaluation of Policy Changes How to nest causal effects into normative welfare framework? Key questions to answer: What types of causal effects do we need? What else do we need to know? What are the key assumptions needed? New approach: for each policy change, construct its implied Marginal Value of Public Funds (MVPF) Aggregate Benefits MV PF = Net Government Costs 4 / 23  Marginal Value of Public Funds 1. Introduction 2. Marginal Value of Public Funds 3. Examples 5 / 23  Marginal Value of Public Funds Definition of M V P F The above definition can be restated more concretely as W T P of population affected by the policy MV PF = Net Impact on Government Costs where W T P is willingness to pay Typically both nominator and denominator have the same sign reducing a tax rate has a positive W T P of the beneficiaries of the reform, but also additional costs for the government (in terms of lower revenues) increasing the tax rate has a negative W T P of the affected population, but it has also a negative impact on net government costs because tax revenues increase so we can interpret increased spending/reduced tax revenue as positive costs, and increased tax revenues/reduced spending as negative costs 6 / 23  Marginal Value of Public Funds used in the context of welfare economics, λ quantifies the additional utility an individual gains specifically when discussing the Marginal Value of from a small increase in their income. Each additional Public Funds (MVPF) and the Willingness to Pay currency unit an individual receives becomes slightly less valuable as their income grows (diminishing WTP (WTP) for a given policy. marginal utility). measures how much additional utility (or satisfaction) an δu/δt is the marginal utility of the policy or reform individual gains from a small increase in the policy variable t W T P is willingness to pay for reform out of own income It is defined as the effect of the reform on utility, du/dt, normalized by the marginal utility of income λ The division effectively normalizes the utility gained from the policy by how du WTP = dt /λ much utility is gained from income, giving a measure of Willingness to Pay (WTP) for the policy in income-equivalent terms. Remember Roy’s identity: du/dt = −λ · x, where x denotes the RI is a way to derive demand functions consumption/income level before the reform from utility functions Hence W T P = −x Quasi-linear utility functions assume that the marginal utility of income is constant. Real-world scenarios and utility functions don't adhere to this simpl. so we do not need to assume quasi-linear utility (λ = 1) for this allows for a more general utility framework where the marginal utility of income can to work vary, λ differs from 1 W T P as defined here is equivalent to the compensating and the equivalent variation used when income effects are present The change in utility due to a small change in the policy (t) can be related directly to how the individual values their current level of income or consumption (x), adjusted by the marginal utility of income (λ). This relationship is crucial for understanding how changes in policies affect individual welfare. Compensating Variation is the amount of money one would need to give to an individual to offset the harm from a policy change or to make them as well off as before the change. Equivalent Variation is the amount of money one would have to take away from an individual before a policy change to make them as well off as they would be after the change. 7 / 23  Marginal Value of Public Funds A higher WTP indicates a greater value of the policy to the individuals, suggesting that they derive significant benefits from it. Net Government Costs NC = C-R, C is policy implementation and R is revenue generation NC_new​+δR−δC=0 C>R⇒ΔC_other​0 Another way to think about the net costs of a policy is to consider budget-neutral reforms positive net costs then imply that other policies must be cut negative net costs imply that other policies can be expanded Hence positive net costs are equivalent to lower revenues and ΝC>0 a need to identify other policy areas where costs can be reduced vice versa As already shown the effect of a tax change on government revenue is equal to x + t · dx dt (mechanical plus behavioral effect) Because the effect on revenues and on costs have opposite signs, the denominator in the definition of M V P F is equal to −(x + t · dx dt ) 8 / 23  Marginal Value of Public Funds Putting it together essentially tells us how many units of benefit are generated We can now write M V P as for each unit of government −x x spending MV PF = dx = dx −(x + t · dt ) (x + t · dt ) It is sometimes convenient to normalize the willingness to pay by the mechanical cost to the government if we cut taxes, those guys 1 1 will benefit with $3 MV PF = = (1 + xt · dx dt ) (1 + e) where e is the elasticity of demand wrt. t, an object we know how to estimate What does the M V P F tell us? The M V P F measures a policy’s “bang-for-the-buck” every $1 of net spending on a tax cut delivers $MVPF of benefits to the recipients of that tax cut every $1 of net revenue raised through a tax increase imposes a cost equivalent to $MVPF to those affected by the tax increase 9 / 23  Marginal Value of Public Funds Infinite M V P F Define M V P F = ∞ if W T P > 0 and Cost < 0 (and −∞ if W T P < 0 and Cost > 0 Preserves ordering (M V P F = ∞ is better than other policies with finite M V P F Policy “pays for itself” (“Laffer” effect) 10 / 23  Marginal Value of Public Funds Construction of Policies that Increase Welfare Take two policies: policy 1 and policy 2 Consider budget neutral policy reform: increase spending on policy 1 financed from less spending (greater revenue) from policy 2 To first order, combined policy increases social welfare if and only if η̄1 M V P F1 > η̄2 M V P F2 η̄j is average social welfare weight of the population affected by policy j M V P F normalizes the net government spending on each policy so that we construct hypothetical budget neutral policies Motivates comparing policies with similar distributional incidence η̄1 ≈ η̄2 11 / 23  Examples 1. Introduction 2. Marginal Value of Public Funds 3. Examples 12 / 23  Examples Example: Tax Rate Change M V P F of a policy reducing income tax rate τ by dτ Average earnings in the population is E(zi ) = Z Government revenue is R = τ Z Changing τ leads to a change in revenue R dR dZ =Z +τ dτ dτ which is minus the cost of the reform consisting of mechanical and behavioral effect Consider the W T P here the envelope theorem is useful (again) to first order, individuals do not value their change in incomes if you earn $100 and taxes go from 10% to 9%, the W T P for the decrease is $1, re