Inequality, welfare and the progressivity (?) of the UK tax/benefit system. Sam Hinds
Utility possibility frontier (i) First we consider the utility possibility diagram discussed in the lecture under a range of scenarios. Throughout we assume total income is fixed and is to be divided in some way to yield utility to two agents, A and B. On each diagram I note the Nozick, Pareto, Bentham, Rawls and Egalitarian optima.
Utility possibility frontier (ii) Case (i) Utility is equal to income for both A and B
Utility possibility frontier (iii) Case (ii) Utility is proportional to income for both A and B, but each utility function is different
Utility possibility frontier (iv) Case (iii) Everyone has the same utility function but utility depends on other people s income Altruism: Envy:
Welfare axioms (i) Suppose social welfare is to be measured by mean (1 Gini): which of the welfare axioms (if any) is violated by this SWF? (1) Anonymity - If x is a permutation of x then W (x ) = W (x) -> fine (2) Population principle - W (x ) W (x) W (x,...,x ) W (x,...,x) -> fine, if we replicate the population exactly then both the mean income and Gini coefficient are unchanged (3) Transfer principle - If xi < xj then, for small δ, W(x1,...,xi +δ,...,xj δ,...,xn) W(x1,...,xn ) -> fine, the transfer does not change mean income but improves the Gini coefficient in both, preserving the ordering (4) Scale invariance - W (x ) W (x) W (λx ) W (λx) -> fine as long as λ is positive (cancels out in Gini formula and multiplied the mean)
Welfare axioms (ii) Suppose social welfare is to be measured by mean (1 Gini): which of the welfare axioms (if any) is violated by this SWF? 5. Monotonicity - Increase anyone's income and welfare increases -> fine (effect on mean income dominates) 6. Decomposability - Adding the same subgroup to each distribution leaves the ranking unchanged -> Not ok, the Gini coefficient is not decomposable which means that we can get a reversal in the welfare measure when adding the same subgroup (e.g. see Cowell, 1988 -> we can add a group so that mean income remains the same but the impact on the Gini reverses the ranking)
The progressivity (?) of the UK tax/benefit system Government intervention, through taxes and benefits, alters the incomes of households available for consumption, investment etc The UK tax and benefits system aids redistribution efforts through progressivity of direct taxation for example, whereby those higher up the income distribution are taxed at a higher rate and as such contribute a larger proportion of their income to distributive efforts. However, other instruments such as VAT (value-added-tax) can hinder redistribution efforts as they are regressive, levied at a constant rate for the entire population (meaning they take a higher proportion of the income of poorer households).
The UK tax and benefit system 2 4 3 1 Jones (2008) studies four tiers of the UK tax/benefit system: 1. Original income; 2. Gross income (net of cash benefits); 3. Disposable income (also net of direct taxes); and 4. Post tax income (also net of indirect taxes).
Lorenz dominance To analyse how different elements of the UK tax system affect inequality we can use the notion of Lorenz dominance: Lorenz dominance: x L x if s q sq for all q, with > for some q (i.e. the qth cumulative for the dominant distribution is above or the same as the dominated) If the distribution post tax/benefit dominates the distribution pre tax/benefit then the tax/benefit is progressive (and vice versa)
Cash benefits Cash benefits include contributory benefits (recouped through National Insurance (NI) payments made by workers) and noncontributory benefits. They include state retirement pensions, child tax credits and housing benefits. Of the main categories of benefits, 87% goes to the bottom two quintiles with the majority going to the bottom Not surprisingly the Gross Income distribution Lorenz dominates the Original Income distribution indicating cash benefits are progressive: Type of income 1 st quintile 1:2 quintile 1:3 quintile 1:4 quintile Original income 3 10 25 49 Gross income 7 18 34 57
Direct taxes Direct taxes include income tax, National Insurance (NI) and council tax. Higher income groups pay both higher amounts of and higher proportions of their income in direct tax (the top quintile paid an average of 18,500 per household in 2006/7 while the bottom quintile paid 1,200). The exception to this is council tax which is levied on housing characteristics. Similar to cash benefits, as shown below, the Disposable Income distribution Lorenz dominates the Gross Income distribution meaning direct taxation, on the whole, is progressive: Type of income 1 st quintile 1:2 quintile 1:3 quintile 1:4 quintile Gross income 7 18 34 57 Disposable income 7 19 35 57
Indirect taxes Indirect taxes include VAT, sin and other taxes and the amount paid by a household is related to expenditure rather than income. The proportion paid in indirect tax tends to be lower for households at the top of the distribution compared with those lower down (16% in the top quintile and 20% for the bottom). As a result of taking up a higher proportion of income of those further down the distribution, indirect taxes are regressive and the Post Tax distribution is Lorenz dominated by the Disposable income distribution: Type of income 1 st quintile 1:2 quintile 1:3 quintile 1:4 quintile Disposable income 7 19 35 57 Post tax income 6 17 33 55
Summary At the first tier, the top quintile group receive 51% per cent of all original income and the bottom only receives 3%. However, at the final tier, the bottom quintile have a larger of final income of 6% while the top has a lower of 44% This indicates the tax/benefit system as a whole is progressive
References: Petersen, H.G. (2004) Redistribution and the efficiency/justice trade-off, Studi Economici, no. 82, 2004:1 Cowell, F.A. (1988) Inequality decomposition: Three bad measures, Bulletin of Economic Research, 40:4 Jones, F. (2008) The effects of taxes and benefits on household income, 2006/07, Economic and Labour Market Review, 2,