ESCoE Research Seminar

Transcription

1 ESCoE Research Seminar A Democratic Measure of Income Growth Presented by Martin Weale, Economic Statistics Centre of Excellence, Centre for Macroeconomics and King s College, London 01 May 2018

2 A Democratic Measure of Income Growth Andrew Aitken and Martin Weale March 2018

3 National Accounts William Petty, FRS ( )- inventor of the term Political arithmetic - the study of the economic and demographic statistics of a state Produced the first national accounts James Meade ( ) and Richard Stone ( ) The first modern national accounts in 1941 (simultaneous with those in the Netherlands and Palestine) A focus on national income rather than output Now integrated with measurement of GDP

4 That s your bloody GDP, not ours - Newcastle heckler It is well-known that GDP growth is not a good measure of growth in welfare. 1. It is gross of depreciation. A welfare measure has to be net. 2. Account needs to be taken of net income from abroad. 3. Money net income should be deflated by the price of consumption, not the price of output. 4. Some adjustment for population growth is needed. Real net national income growth per capita is a much better indicator of change in welfare. But aggregate or average real growth weights individual growth rates according to the level of income of each household. A plutocratic indicator of welfare growth. High earners count for more. A democratic measure takes the growth in the real income of each household and averages this across all households. 3

5 Democratic Growth Sig Prais (1959) developed a democratic price index. It calculates the change in prices based on the spending pattern of an average household. CPI uses total spending, so high spenders have more influence. Tony Atkinson (1971) developed inequality-averse measures of income. We take the geometric mean of household income (A special case of Atkinson s inequality aversion) and deflate using Prais democratic price index. The output is the growth rate in real household income averaged across all households. We discuss the role of this as an indicator of welfare accruing. 4

6 Atkinson Inequality Aversion YY = nn ii=1 yy 1 ρρ ii nn 1 1 ρρ nn ii=1 (ρρ 1) If ρρ = 1 then YY = yy ii Assume now that there is an aggregate price measure P and quantity measure (real income) Q so that Y=PQ. Each household has a price index p i and a quantity index q i with y i = p i q i so that Now take logs And differentiate YY nn ii=1 PPPP = pp ii llllllll = llllllll + llllllll = llllll YY = PP PP + QQ QQ = nn ii=1 nn ii=1 1 ρρ qqii 1 ρρ nn nn 1 1 ρρ pp 1 ρρ 1 ρρ ii qqii 1 ρρ llllllll pp ρρ 1 ρρ 1 ρρ ρρ iipp ii qqii + qqii pp ii qqii nn 1 ρρ 1 ρρ ii=1 pp ii qqii 5

7 A General Measure PP nn ii=1 PP + QQ QQ = ( pp ii pp ii )pp ii 1 ρρ qqii 1 ρρ +( qq ii qq ii )pp ii 1 ρρ qqii 1 ρρ nn 1 ρρ 1 ρρ ii=1 pp qqii ii The household weights are yy ii 1 ρρ If ρ=1 all households are given equal weight = nn ppii 1 ρρ qq yy pp ii ii +( ii 1 ρρ ii=1 )yy qq ii ii nn 1 ρρ ii=1 yy ii If ρρ > 1 then poor households are given more weight than rich households. In the special case with ρρ = 1 YY YY = PP PP + QQ QQ = PP = PP nn ii=1 pp ii/pp ii nn and we can derive nn ii=1 pp ii/pp ii + qq ii /qq ii nn is the Prais Index QQ QQ = YY YY PP PP to get the democratic growth rate. 6

8 Towards a Welfare Interpretation If saving is the only source of income growth, the rate of change of real income is the real rate of return on saving qq iiii = rr iiii (qq iiii ππ ttcc iiii ) pp iiii Gives a relationship between current income and current and future consumption tt qq iiii = (rr iiii ππ ττcc iiii ee tt rr iiiidddd ττ /pp iiii )dddd and, with inter-temporally efficient allocation, a welfare interpretation of saving dd dddd uu ii cc iiττ ee θθθθ zz iiii ddττ = pp iiii (rr tt xx iiii ππ ττcc iiii ee ττ tt rr iiiidddd /pp iiii )dddd ππ ttcc iiii /pp iiii iiii tt The rate of change of life-time utility is saving multiplied by the marginal utility of money, (Sefton and Weale 2006) Requires individual homotheticity (constant expenditure shares) Otherwise there is no single measure of real income even for an individual household and the Divisia measure is path-dependent 7

9 How Limiting is the Divisia Assumption? Redding and Weinstein( CEP Paper 2016) argue that demand functions are homothetic but prone to preference shocks. Consider a CES utility function uu ii = cc iiii δδ iiii 1 σσ The price index is 1 σσ σσ pp ii And the expenditure shares are = (ππ jj δδ iiii ) σσ 1 σσ jj ωω iiii = (ππ jj δδ iiii ) σσ 1 σσ (ππ jj δδ iiii ) σσ 1 jj σσ Differentiating ddpp ii pp ii pp ii 1 σσ = ddππ jj ππ jj jj (ππ jj δδ iiii ) 1 σσ + ddδδ jj δδ jj jj (ππ jj δδ iiii ) 1 σσ So ddpp ii pp ii = ddππ jj ππ jj jj And Divisia is valid if ωω iiii + ddδδ jj ωω δδ iiii jj jj ddδδ jj ωω δδ iiii = 0 jj jj Using scanner data Redding and Weinstein suggest this condition is met

10 Aggregating with Unit Inequality Aversion Suppose we also have an exogenous source of growth, h iiii so that qq iiii = rr iiii and qq iiii qq iiii = qq iiii ππ ttcc iiii pp iiii + h iiii rr iiii dd yy iiii zz iiii / xx iiii Set ss iiii = h iiii rr iiii h iiττ ee rr iiθθ ddθθ tt Then qq iiii ττ tt dddd uu ii cc iiττ ee θθθθ ddττ NN tt ddττ QQ tt(1) QQ tt (1) = rr iiii ii=1 yy iiii zz iiii xx iiii + h iiii rr iiii h iiττ ee rr iiθθddθθ ddττ tt dd dddd uu ii cc iiττ ee θθθθ ddττ + ss iiii tt qq iiii /NN ττ tt

11 Aggregate Income and a Market Social Welfare Function The growth rate of the aggregate (plutocratic) price index, used to calculate real income is the average of the growth rate of the individual price indices, weighted by the consumption, not the income, of each household. Aggregate utility is, with αα ii market weights, defined as UU = ii αα ii uu tt ii (cc iiττ )ee θθθθ ddττ ZZ MM ππ ii, XX tt is indirect utility with resources efficiently allocated, i.e. if ZZ MM (ππ tt,xx tt ) zz = αα ii (ππ tt,xx iiii ) XX ii tt xx iiii Households with high marginal utility of income have low weights The price index in the national accounts is computed using consumption weights rather than income weights. Then QQ CC tt (0) QQ CC tt (0) = rr tt dd YY tt ZZ MM / XX tt dddd αα iiuu ii ii cc iiττ ee θθθθ ddττ + HH tt rr tt HH ττ ee ττ tt rr θθddθθ ddττ tt QQ CC tt (0) 10

12 The Price Index as a Constant-scaling Cost of Living Index Write indirect utility as a function of prices, household money consumption and the elasticity of substitution zz ii ππ tt, xx iiii, σσ = 1 1 σσ xx iiii pp ii ππ tt 1 σσ = llllll A utilitarian welfare function σσ 1 xx iiii pp ii ππ tt σσ = 1 ZZ UU ππ tt, xx 1tt, xx NNNN, σσ = 1 NN(1 σσ) ii xx iiii pp ii ππ tt 1 σσ

13 Introduce a common scaling factor, µ t ZZ UU ππ tt, xx 1tt, xx NNNN, σσ = NN 1 ii NN(1 σσ) μμ tt xx iiii pp ii ππ tt 1 σσ μμ tt ZZ UU ZZUU + ddμμ jj ππ jjjj = 0 tt ππ jjjj It shows how much incomes need to change so that social welfare is unaffected by price changes. μμ tt = μμ tt ii xx iiii pp ii (ππ tt ) ii xx iiii pp ii (ππ tt ) 1 σσ pp ii (ππ tt ) pp ii (ππ tt ) 1 σσ The rate of growth of the scaling factor is the growth rate of each household s price index weighted by real consumption to the power 1-σ. If σ=1, we have the democratic price index.

14 Income, Consumption and Welfare The utility accruing from income is the utility accruing from consumption plus saving multiplied by the marginal utility of consumption. zz yy ii ππ tt, xx iiii, yy iiii = zz ii ππ ii, xx iiii + (yy iiii xx iiii ) zz ii ππ tt, xx iiii xx iiii Consider a first-order Taylor approximation zz yy ii ππ tt, xx iiii, yy iiii zz ii ππ ii, yy iiii Income is an indicator of welfare accruing YY PP tt PP YY tt = It then follows that ii yy iiii pp ii (ππ tt ) yy iiii ii pp ii (ππ tt ) YY QQ tt QQ YY tt 1 σσ = pp ii(ππ tt ) pp ii (ππ tt ) 1 σσ qq ii(ππ tt ) ii qq ii (ππ tt ) qq iiii 1 σσ qq iiii 1 σσ ii The weights are based on real rather than nominal incomes, but with σ=1 this is the democratic growth rate.

15 Application Adjust household income for household size Use democratic CPI produced by Tanya Flower and Philip Wales at ONS Results for household disposable income after housing costs taken from Households Below Average Income dataset 14

16 Three Measures of Central Tendency of Nominal Household Income ( per week) after Housing Costs Geometric Mean Median Mean Data Source: Households below Average Income 15

17 6% Growth Rates of Democratic and Plutocratic Price Indices (% p.a.) 5% 4% 3% 2% 1% 0% -1% Average Democratic Price Index Plutocratic Price Index

18 Growth Rates of Real Democratic and Plutocratic Income (% p.a.) 5% 4% 3% 2% 1% 0% -1% -2% -3% -4% -5% Average Real Democratic Income mean

19 Application to National Income Results so far relate to household income. National income includes components not allocated to households 1. Undistributed income of corporations 2. Tax revenues spent on government-provided consumption and investment 3. Income accruing to pension funds Also major doubts about the accuracy of survey data

20 Allocation of Gross National Disposable Income ( mn Fiscal Years) 2,000,000 1,800,000 1,600,000 1,400,000 1,200,000 1,000, , , , , HHldNPISH Govt Fin Cos ICCos

21 Allocation of Net National Disposable Income ( m Fiscal Years) 1,800,000 1,600,000 1,400,000 1,200,000 1,000, , , , , HHldNPISH Govt Fin Cos ICCos

22 Pension Rights and Financial Companies ( m Fiscal Years) 80,000 60,000 Before deducting accrual of pension rights 40,000 20, ,000 After deducting accrual of pension rights -40, Fin Cos Pension Accruals This graph shows the disposable income (saving) of financial companies before and after adjusting for accruals of pension rights

23 Allocating the Whole of National Income to Households to deliver a Democratic Measure of National Income Growth Govt cons Govt saving Reallocated Income bn 2015 Initial Income Pensions Dividends UK total economy Non-financial corporations Financial corporations General government Households and NPISH

24 The Scale of misreporting, 2013 Component National Accounts Total Microsource Total Coverage Rate (%) Macro resources (received): Operating surplus 130,150 68, Mixed income 110,469 63, Wages and salaries 711, , Net property income received 149,811 34, Social benefits other than STiK 332, , Social transfers in kind 273, , A Total 1,707,497 1,239, Macro uses (paid): Current taxes on income and wealth 195, , Employers actual social contributions 136,091 59, Households social contributions 67,528 62, B Total 399, , Household Gross Disposable Income (A-B) 1,308, , Memo: Gross Prop. Inc. excl. Rent 75,903 21, Source: Office for National Statistics and own calculations

25 Imputation Issues and Approaches Scaling widely used (e.g. in ONS work on consumption) Scaling preserves zeroes Scaling will not work for sources of income omitted from LCFS- e.g. undistributed accruals to pension funds. We found a higher proportion of zeros in LCFS than in other sources (e.g. SPI and HBAI) Need to model both the probability of a non-zero receipt and the magnitude of the receipt conditional on being nonzero In contrast to scaling, this has to be stochastic - there is not going to be any covariate which exactly identifies non-zero recipients in HBAI or SPI

26 Heckman Modelling Could use Heckman s approach to model jointly the probability of receiving interest/dividends and the amount conditional on receipt No obvious exclusion restriction: the model has to be identified by making the assumption of joint normality The distribution in fact departs substantially from normality This may not matter for the coefficients but it does for the stochastic imputation

27 Categorical Imputation using Ordered Probit Models (i) We adopt a more flexible approach structured round an ordered probit model We convert the data in our source datasets (SPI for investment income/was for pensions) into a large number of categories (89 for investment income and 32 for pensions) and fit ordered probit models to these Covariates have to be variables available both in the source surveys and in LCFS Simulating these models provides stochastic categorical estimates which can be imputed into LCFS

28 Categorical Imputation using Ordered Probit Models (ii) Compute a fitted value for each latent variable, and add on random terms from the multivariate normal distribution Each latent variable is allocated to the relevant category underpinning the probit model Where it lies between 2 cut points, the distance between 2 categories is interpolated on the basis of the latent variable

29 The Upper Tail Reconciliation with the macro data requires appropriate handling of the upper tail Use a Pareto type-1 distribution for observations xx ii > xx mm of the form: 1 FF xx = (xx mm /xx) αα with αα > 0 where the expected value conditional on xx > xx mm is xx mm αα/ αα 1 if αα > 1 but infinite otherwise The expected value is used for imputed observations in the top category

30 Individuals and Households SPI is based on tax records and provides data on individuals but not households This is because income tax is levied on individuals WAS and LCFS provide both individual and household data Investment income is imputed on an individual basis while pension rights are imputed on a household basis

31 Taxation Revisions to tax paid need to be consistent with revisions to taxable household income We calculate each individual s tax bill on the basis of their income as recorded in LCFS and then recalculate it in the light of the imputations we make We add the difference on to the LCFS figure for tax paid

32 Covariances Need to take into account correlation between random components of imputed variables Use best source of data for pension wealth (WAS) and investment income (SPI), therefore not able to jointly estimate our models to estimate correlations simultaneously with parameters Estimate a correlation matrix using WAS (which does allow joint estimation but is not the ideal source) for the random components

33 Pension income Use ordered probit with waves 3 and 4 of WAS to allocate pension and insurance income to categories Include age, age 2, No. adults, No. children, tenure type, marital status, labour or pension income Estimate separately for under 65 (with & without labour income) and over 65 (with & without pension income) Waves 1 and 2 do not provide satisfactory income measures for use as covariates

34 Compare the performance of the Heckman and Ordered Probit approaches with wave 4 of WAS Assess the ability of the models to match the distribution of pension rights in the data. Examine both the full ordered probit model and the model relying on dummy variables only

35 The Distribution of Pension Rights simulated for 2013 using Heckman and Ordered Probit Models applied to WAS Data

36 Investment income Use ordered probit with SPI to allocate investment income to categories Include age bands, log labour income, regional dummies Estimate separately for men and women and by year Currently working on imputing dividends and interest income separately

37 The Distribution of Investment Income in the 2013 SPI and the Distribution Fitted by the Ordered Probit Models (Unweighted)

38 Covariances Implementation (i) Assuming few households have more than two adult members, three correlations are needed ρρ 12 - the correlation between the latent variables driving investment income for each of the two adults ρρ 13 - the correlation between the latent variables driving investment income of the first adult and that driving pension rights ρρ 23 - the correlation between the latent variables driving investment income of the second adult and that driving pension rights

39 Covariances Implementation (ii) Base covariances on coarse multivariate OP models fitted to WAS. Use financial asset holdings of first and second household members as proxies for investment income, together with household holding of pension rights. The model cannot be estimated for all types of household We use the estimated correlations we can find and take the arithmetic average

40 Covariances Implementation (iii) Wave 3 Wave 4 Mean <65 Empl Inc <65 No Empl Inc >64 Pens Inc <65 Empl Inc < 65 No Empl Inc ρρ ρρ ρρ There is a strong correlation between the investment income of the two household members with possibly material implications for household income inequality. Correlations between investment income and pension rights are much weaker.

41 Simulations Examine the effect of including imputed pension and investment income on measures of inequality such as Gini & geometric mean of income Present results from 5 simulations Preliminary due to top-coding of labour income in LCFS data

42 Estimates of the Gini Coefficient: LCFS Data and with Pension Income and Investment Imputations (20 draws)

43 The Geometric Mean of Equivalised Household Income ( p.a.): Original Data and Including Pension Fund Income and Imputed Investment Income (20 draws)

44 Future work Currently using top-coded version of LCFS, waiting for access to full version of data Imputing dividends and interest receipts separately Extend existing democratic price indices to cover public consumption (drawing heavily on ONS work on Earnings, Taxes and Benefits dataset) Produce a democratic measure of real disposable national income in the Autumn.