Ec 426 Public Economics I Who pays taxes

Ec 426 Public Economics I Who pays taxes? General equilibrium tax incidence A B Atkinson Room R 515 Office hour: email tony. atkinson@nuffield. ox. ac. uk for appointment. 1

My background • Teaching economics since 1967 at Cambridge, Essex, MIT, UCL, LSE, Oxford, and Harvard. • Engagement with public policy: - Member, Royal Commission on Distribution of Income and Wealth, 1978; - Chairman, Taxation Review Committee, Fabian Society, 1989; - Member, Pension Law Review Committee, 1992; - Report on Social Indicators for the EU, formed basis for Laeken indicators (Structural Indicators) 2001; - Member, Conseil d’Analyse Economique, advising French Prime Minister, 1997 -2001; - Report on new methods of development financing for UN General Assembly, 2004; - Member, High-Level Group on the future of social policy in an enlarged European Union, 2004; - “Atkinson Review” for UK Government of the measurement of government output, 2004 -5; - Member of the European Statistics Governance Advisory Board established by Council of Ministers and European Parliament, 2009 -12. 2

Tax Incidence 1. 2. 3. 4. Why does tax incidence matter? Incidence in a single market Two sector general equilibrium model Incidence of corporate profits tax 5. What is missing from the model? 3

1. Why does tax incidence matter? A government imposes a tax, with a legal obligation for a person (or legal entity) to pay the tax, but who really pays the tax? Incidence depends on the market reactions. A tax may be shifted on to others. Indeed, it is assumed in discussions of UK VAT increase that it led to faster inflation. The degree of shifting affects how we think about the distributional impact of tax changes. What is the distributional effect of a switch from direct to indirect taxation? What is the effect of increasing employer payroll taxes? “The theory of tax incidence has a number of practical results. For example, United States Social Security payroll taxes are paid half by the employee and half by the employer. However, economists think that the worker is bearing almost the entire burden of the tax because the employer passes the tax on in the form of lower wages. The tax incidence falls on the employee. ” 4

Distributional effect of taxation “across the entire period [1977 to 2007], the tax system as a whole (including indirect taxes) has had virtually no impact on the shares of each fifth of the income distribution [in the UK]” Report of the National Equality Panel, January 2010, page 50, from ONS annual Redistribution of Income (ROI) analysis. On what is this based? Comparing for household h Gross income Yh with Yh – Th - ∑ti Xhi where Th denotes income tax paid and ti is rate of indirect tax on good I, and Xhi is the consumption of good I by household h. The calculation assumes that Yh and Xhi are unchanged. Income tax fully borne by income recipient and indirect taxes fully passed on to consumers. No account is taken of employer social 5 security tax or of corporation tax.

2. Incidence in a single market Price to producer Demand curve after tax introduced Demand curve before tax introduced Tax ● Supply curve Effect of indirect tax In the constant elasticity case, the consumer price = ● (1+t) to the power of εs/(εs+εd) Quantity 6

Price to producer Assumption underlying official ROI analysis Demand curve before tax introduced Tax ● Totally elastic supply curve ● Demand curve after tax introduced Quantity 7

Labour market and cut in payroll tax Wage received by worker Demand curve after tax reduced Supply curve Demand curve by employers ● In constant elasticity case, tax at rate t reduces net wage by factor ● (1+t) to the power of εd/(εs+εd) Quantity of labour 8

Wage received by worker Demand curve by employers • • E 1 • Tax cut can reduce employment if economy moves from E 3 Supply curve Demand curve after tax reduced E 2 • E 3 Market reactions and complications Backward-bending labour supply curve and nonunique market equilibria Number of worker hours 9

What is missing from Partial Equilibrium Analysis? • • What lies behind supply (demand) curves? Effect on factors of production and incomes Inter-relation between markets Input-output effects 10

3. Two sector general equilibrium analysis Two sector/two factor model allows for a variety of taxes AND models the whole economy Capital Sector X t. KX Labour Value added t. LX t. X VAT Sector Y t. KY t. LY t. Y Corporation tax Both t. K t. L Payroll tax 11

Demand side Assume consumer demands are homothetic and that government spends revenue in same way as consumers. Relative demands are then function only of the relative prices: e. g. X/Y = (p. X/p. Y)-ε X/Y Closed economy p. X/p. Y w/r Atkinson Stiglitz Lecture 6 45 o w/r 12

Production side: assume constant returns to scale, perfectly competitive pricing, and full mobility of factors. Unit costs and hence prices are X/Y p. X = c. X(r, w); p. Y = c. Y(r, w) Eg Cobb-Douglas case p. X= rα w(1 -α) ; p. Y = r βw(1 -β) p. X/p. Y X more labour intensive if α < β w/r Assume X more labour intensive 45 o w/r Pricing relationship 13

p. X/py = c. X[r, w(1+t. L)]/ c. Y[r, w(1+t. L)] X/Y Eg Cobb-Douglas case p. X/p. Y = [w(1+t. L)/r] β-α Not lose sight of purpose = model effect of taxes: e. g. effect of payroll tax X more labour intensive if α < β p. X/p. Y w/r 45 o Assume X more labour intensive Effect of payroll tax, given the assumption that X more labour intensive. w/r BUT not only effect. 14

Factor market clearing X/Y Assume fixed supplies of capital, K 0 and labour, L 0. Factor market KX + KY = c. KX X + c. KY Y = K 0 LX + LY = c. LX X + c. LY Y = L 0 If cij fixed, then only one X/Y (at most) clears market. If cij variable, then different combinations of X/Y and w/r clear market. If w/r rises, both sectors use less labour. Equilibrium can only be reestablished if there is a switch of outputs towards the labourintensive sector (X). w/r Assume X more labour intensive 45 o w/r 15

X/Y where w/r = K 0/L 0 /[β/(1 -β)] Cobb-Douglas example The market clearing equations (where both factors fully used) are: * X α(r/w)-(1 -α) + Y β (r/w)-(1 -β) = K 0 X (1 -α) (r/w)α + Y (1 -β) (r/w)β = L 0 w/r • where w/r • Solving these equations, we obtain the values of X and Y that ensure factor market equilibrium for given (r/w). We have to ensure that the values of outputs are non-negative. This is guaranteed where β/(1 -β) ≥ (K 0/L 0) /(w/r) ≥ α/(1 -α) = K 0/L 0 /[α/(1 -α)] * Obtained using the fact that the factor demands are given by derivatives of the cost function. 16

X/Y Putting it together: Demand “Supply” • • • w/r • • Demand px/py w/r 17

Supply X/Y Putting it together: “Demand” and Supply “Demand” w/r • • px/py w/r 18

4. Incidence of corporate profits tax Harberger (Journal of Political Economy 1962) used this model to examine incidence of the corporate income tax. Corporation tax = tax on use of capital in the corporate sector. It is a partial factor tax. Effects: • not enter the demand side; • affects the pricing relationship; • affects the choice of production techniques. Outcome depends on whether corporate sector is capitalintensive or labour-intensive. 19

Begin by assuming Fixed coefficients and X/Y Demand curve Corporate sector is capital intensive (Y). Determined by full employment condition p. X/p. Y = p. X/p. Y c. X[r, w]/c. Y[r(1+TKY), w] Corporation tax in this case is the same as a partial excise tax, and reduces return to factor used intensively in its production. What would happen if the corporate sector were X? w/r Effect of the tax 20

Effect of the tax “Demand curve” X/Y Supply curve Now allow variable coefficients. Corporate sector is capital intensive (Y). ●● p. X/p. Y w/r Effect of the tax 45 o w/r 21

“Demand curve” Effect of the tax X/Y Supply curve Suppose now that the corporate sector is labour intensive (X). ● ● p. X/p. Y w/r Effect of the tax 45 o w/r 22

Algebraic version: see Atkinson and Stiglitz, pp 166 -70 Three key equations of proportionate change: d. X/X – d. Y/Y = - σD [dp. X/p. X – dp. Y/p. Y] + T 1 dp. X/p. X – dp. Y/p. Y = θ* [dw/w – dr/r] + T 2 λ* [d. X/X – d. Y/Y] = σS [dw/w – dr/r] + T 3 where T 1, T 2 and T 3 show the effects of taxes. and σD is the aggregate elasticity of substitution in demand σS is the aggregate elasticity of substitution in supply and θ* and λ* are measures of relative factor intensity. 23

Solve for induced changes in w/r (dw/w – dr/r) [σS + σD θ*λ*] = λ*T 1 - σD λ*T 2 - T 3 The square bracket on the LHS is positive, since θ* and λ* have the same sign (in the absence of taxes and other distortions). Effect of corporation tax in sector X: T 1 = 0 T 2 is positive, but effect depends on sign of λ*, which is positive where X relatively labour-intensive T 3 is negative and magnitude depends on elasticity of substitution in X sector. w/r most likely to fall where • Little scope for factor substitution in taxed sector • Elasticity of substitution in demand is larger; • Larger difference in factor intensities. 24

5. What is missing from the model? • • • Open economy (tax competition); Unemployment; Imperfect competition; Other market imperfections; Other taxes and subsidies; Input-output relationships; Demand influences; Variable factor supplies; Environmental impact. 25