THE ROLE OF LABOUR DEMAND ELASTICITIES IN TAX INCIDENCE ANALYSIS WITH HETEROGENEOUS LABOUR


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1 THE ROLE OF LABOUR DEMAND ELASTICITIES IN TAX INCIDENCE ANALYSIS WITH HETEROGENEOUS LABOUR Kesab Battarai 1,a and 1, a,b,c Jon Walley a Department of Economics, University of Warwick, Coventry, CV4 7AL, UK b Department of Economics, University of Western Ontario, London Ontario ONT N6A 5C2 Canada c National Bureau of Economic Researc, 1050 Mass. Ave. Cambridge, MA , USA Abstract Weter labour bears full burden of ouseold level income and consumption taxes ultimately depends on te degree of substitutability among different types of labour in production. We find more variation in incidence patterns across ouseolds wit less tan perfectly substitutable eterogeneous labour tan wit perfectly substitutable omogeneous labour in production. Tis finding is based on results obtained from omogeneous and eterogeneous labour general equilibrium tax models calibrated to decile level income and consumption distribution data of UK ouseolds for te year We use labour supply elasticities implied by te substitution elasticity in ouseolds' utility functions and derive labour demand elasticities from te substitution elasticity in te production function. Key words: Elasticities, labour demand, labour supply, welfare, incidence, redistribution JEL classification: J20, H22, C68 Marc Battarai and Walley acknowledge financial support from te ESRC under an award for a project on General Equilibrium Modelling of UK Policy Issues. We are tankful to Baldev Raj and two referees for comments on earlier versions of tis paper.
2 I. Introduction 1 Tis paper builds on te observation tat existing empirically based incidence analyses drawing eiter on sifting assumptions 2, or on general equilibrium tax models treat labour as bearing te burden of its own income and payroll taxes 3. Te implicit assumption is tat labour is a omogenous input wic is perfectly mobile across industries and yields leisure wic is consumed by ouseolds. A key set of parameters in incidence analyses conducted wit tese models ave been presumed to be te labour supply elasticities wic are te subject of some attention in bot calibration and sensitivity analysis. Labour demand elasticities do not enter tese analyses. We argue tat wit omogeneous labour in production, te implicit labour demand function facing eac ouseold is igly elastic since, if small relative to te aggregate, eac is a price taker in labour markets. Te implication is tat labour will bear most of te burden of its own labour taxes, independently of labour supply elasticities used. Conventional sensitivity analysis on labour supply elasticities will sow little variation in tax incidence profiles. On te oter and, varying labour demand elasticities will allow for te sifting of tax burdens to oter groups or ouseolds. We investigate differences in model analyses of tax incidence using comparable nested models in wic labour is eiter omogenous or eterogeneous in production, so tat labour demand elasticities also enter. Eac model is calibrated to a ten decile ouseold data set containing data on consumption, taxes, and leisure for te UK for Labour supply elasticity calibration is based on estimates from Killingswort (1983), wit te labour 2 See Pecman and Okner (1974), and Gillespie (1965) as examples of tis approac. 3 See Soven and Walley (1972) for a simple 2 sector 2 ouseold Harberger tax model; Piggott and Walley (1985) for a 100 ouseold model of te UK; Ballard, Fullerton, Soven and Walley (1985) for a 15 ouseold model of te US; and Auerbac and Kotlikoff (1987) for a 55 overlapping generations dynamic structure applied to US data.
3 2 demand elasticity used in calibration in te eterogeneous labour model drawing on estimates from Hamermes (1993). Significant differences in incidence profiles are found across te two models. Te eterogeneous model sows significant variations in incidence profiles as labour demand elasticities cange, wile te omogeneous good model sows little sensitivity to labour supply elasticities. Te implication drawn is te need to more carefully specify labour demand elasticities in tax incidence analyses.
4 II. Tax Incidence Models wit Heterogeneous and Homogeneous Labour Supply 3 It seems clear tat if labour supplied by ouseold groups is eterogeneous wit imperfect substitutability in production across skill levels, ten bot labour demand and labour supply elasticities are needed in tax incidence analyses. If labour is treated as omogeneous across ouseolds, ten if eac ouseold is small and a taker of wage rates, tey implicitly face a perfectly elastic labour demand function. In tis case, varying te labour supply elasticity will not cange te conclusion tat labour bears te burden of teir own income taxes, even if tax rates differ across ouseolds. If te labour demand elasticity is less tan infinite, as labour supply functions sift due to ouseold specific taxes, some of te burden of te tax is sifted elsewere. Te implication is tat if eterogeneous labour models are used for tax incidence analysis and model parameters calibrated to bot labour demand and labour supply elasticities, tax incidence results can differ 4 (and potentially sarply so) from tose generated by te omogenous labour model conventionally used. We coose te ouseold as te basic unit of tax incidence analysis not only because consumption and labourleisure coice decisions are made at te ouseold level, but also it is adapted in te data on income and consumption used in te empirical analysis of incidence profiles in te paper. A eterogeneous labour ouseold tax model
5 4 We consider an economy wit ouseolds differentiated according to teir skill levels, wic, for our empirical application, we take to be collinear wit income ranges. Eac ouseold is endowed wit a fixed amount of time, wic it can divide between leisure and work. A production function specifies ow te various labour types combine to yield a single consumption good. Eac of tem buys te consumption good using income earned by selling its labour on te market along wit transfers received from government, effectively buying back its leisure at its net of tax wage. Houseolds maximize utility by coosing bundles of consumption goods and leisure subject to teir budget constraint. Hours of work (labour supply), consumption and leisure are tus obtained by solving eac ouseold s optimization problem. Taxes distort te consumptionleisure coice of ouseolds. Tax rates are ouseold specific, and government budget balance olds wit transfers te sole expenditure item. In empirical implementation, we use a single tax rate on labour income for eac ouseold to represent te composite of income and payroll taxes, and a composite indirect tax rate for eac ouseold wic reflects sales (VAT) and excise taxes. Tese latter rates differ by ouseold due to differing consumption patterns in te data. More specifically, we assume CES preferences for eac ouseold as σ 1 U = σ α C + ( 1 α ) L σ 1 σ σ σ 1 (1) were U is utility, α is te sare of income spent on te consumption good, (1α ) is te sare parameter on leisure, C and L are consumption and leisure respectively of 4 One reason for te relative absence of eterogeneous labour models in empirically based general equilibrium work is te seeming difficulty of solution in te nonnested production function case. We solve it using te new PATH algoritm developed and employed wit GAMS by Micael Ferris (see Appendix 2 for details).
6 ouseold, and σ 5 is te elasticity of substitution between consumption and leisure of ouseold. Te income for ouseold equals te time endowment valued at te net of tax wage plus transfers received from government, i.e. ( 1 t I w L RH (2) I = ) + were I is te full income of ouseold, w is te gross of tax wage rate for ouseold, and t I is te ouseold specific income tax rate. L is te time endowment of ouseold to be divided between labour supply and leisure, and RH are transfers received by ouseold. Maximization of utility (1), subject to (2), yields demand functions for consumption and leisure for eac ouseold as, C α = P( 1+ t C σ ) α (P( 1+ t C )) 1 σ I + ( 1 α )(w ( 1 t I )) 1 σ (3) σ (1 α ) I L = (4) w (1 t I ) α ( P(1 + t σ + w t σ C )) 1 (1 α )( (1 1 I )) were w is te gross of tax wage rate for labor of type (supplied by ouseold ), P is te price of te consumption good, and t C is te consumption (or indirect) tax rate faced by ouseold. Te budget balance condition for ouseolds implies tat on te expenditure side = P( 1+ tc ) C + w (1 tl L (5) I ) Eac ouseold supplies labour to te market wic reflects te difference between its labour endowment and its demand for leisure, LS = L L (6)
7 were 6 LS is labour supplied by ouseold. Te economy wide labour supply is te sum of labour supplied across te individual ouseolds. In equilibrium, equation (6) is also te labour market clearing condition for labour of type. In te model, we assume tat te labour eac ouseold supplies is differentiated by skill level from te labour supplied by all oter ouseolds, and we represent tis troug a CES production tecnology for te single output Y in wic all labour types enter, i.e. σ p σ p 1 σ p 1 σ p Y = λ δ LS (7) were LS is te input (labour supply) of type, δ is te sare parameter in production on eac category of labour, λ is a units term and σ p is te elasticity of substitution among labour types in production. Producers pay te gross of tax wage rate wen iring labour from eac ouseold, and ouseolds receive te net of income tax wage. For simplicity, we assume tat only one consumption good is produced in tis economy, and producers maximize profit, Π, given by Π = PY w LS (8) were te P is price of te consumption good, and LS is te labour input of type. Profit maximization results in te labour demand function for eac labour type as, LD 1 = δ + λ δ Π w w σ p 1 σ p σ p 1 (9) were LD is labour demand of type, and in equilibrium also equals labour supply LS.
8 7 Te government in tis economy raises revenues, R, by taxing income and consumption, i.e, I c (10) R = t w LS + t PC We assume a single period in wic all output is consumed (tere is no saving). In equilibrium, P and te ouseold wage rates, w, are endogeneously determined suc tat tere is market clearing in te consumption good Y = C (11) and tere is market clearing for eac labour type, LS = LD. (12) As transfers to ouseolds are te only government expenditure item, government budget balance also requires tat in equilibrium R = RH. Tus, for eac ouseold, in equilibrium labour supplied of eac type equals its use in production, and a profile of skill specific equilibrium wage rates will be determined. For convenience, in tis model, we can coose te numeraire of tis system to be tat te price of te consumption good is equal to 1. A omogeneous labour tax model In contrast to te eterogeneous labour model, wen labour is omogeneous in production we need only specify a model wit labour as te single input into production. We
9 8 assume a constant marginal product of labour production function, wic is linear in (total) labour 5. Y = λ LS (13) A single wage applies to all ouseolds labour supply because of te omogeneity of labour inputs, and te relationsip between te wage rate and te price of te consumption good is given by P w = λ. (14) Houseolds still differ in teir preferences as in (1), still face ouseold specific income and consumption tax rates, but unlike in te eterogeneous labour model face a common wage rate. Equilibrium in tis case is given by market clearing for te single labour type in te model; wit, in tis case, one single wage rate endogenously determined. Tis omogeneous labour model is tus a special case of te model presented above, and nests into te more general eterogeneous labour model. 5 Tis is a special case of te production function (7) in te model above, for te case were σ p becomes infinite.
10 III. Implementation of Homogeneous and Heterogeneous Labour Tax Incidence Models 9 We perform tax incidence analyses using two models above by calibrating 6 eac to a base year data set, specifying labour demand and labour supply elasticity values, and performing counterfactual equilibrium analyses. Te base case data set we use reflects te UK economy for te UK tax year 1994/95 7. We use data on incomes, taxes and benefits by ouseold decile compiled by te UK Treasury and reported in te UK government statistical publication Economic Trends (1996). Tis source reports data for non retired ouseolds grouped by income 8 decile, benefits received bot in cas and in kind, and direct and indirect taxes paid by eac ouseold decile. Base case data For modelling purposes, we require a base case data set wic is fully model admissible. Tis means tat all variables wic appear in eac model sould be identified in te data set, and all of te model equilibrium conditions need to be satisfied. Among tese are conditions tat te value of consumption across ouseolds sould equal te value of production (a zero profit condition in production implies tat income received from supplying labour equals te value of production). All ouseolds sould also be represented by data wic satisfies ouseold budget balance, and government expenditures equal government receipts (government budget balance). 6 Calibration, ere, denotes te exact calibration of eac model to a model admissible data set wic is constructed from unadjusted data from a variety of statistical sources. Tis is te sense of calibration discussed by Mansur and Walley (1984) and differs from te calibration procedures used by real business cycles researcers (see Kydland and Prescott (1982)). In tis latter work, no readjustments are made to data, and model parameter values cosen by reference to literature sources wit a view to seeing ow close model solution can be made to actual data. See also Watson (1993). 7 April 5 t 1994 to April 4 t Tis is te year used in recording tax and ouseold income data by te UK tax autorities. 8 Te income concept used in te publised data is ouseold equivalized disposable income.
11 10 Te basic data we use, wile aving most of te information we need, is deficient for our purposes in number of respects. Houseold leisure consumption is not identified. Government budget balance is violated in te data, since all taxes paid by ouseolds are identified but only tose government expenditures leading directly to direct ouseold benefits (cas transfers, education, and ealt care appear, but defence, for instance, is missing). In te basic data, government expenditures in aggregate are tus substantially less tan tax revenues. Also, individual ouseold budget constraints do not automatically old. A series of adjustments and modifications are terefore necessary to te basic data set before it can be used for model calibration. Tese are set out in more detail in Appendix 1, but can be summarised as follows. We scale te in kind portion of government benefits for eac decile suc tat government expenditures equal taxes collected. Transfers received by eac decile in te model are tus te sum of cas and in kind benefits provided by government. We use wage rate data by ouseold and UK time use survey data to construct data on te value of leisure time by ouseold for eac decile, valuing time at te net of tax wage. We ten make furter adjustments to ensure full consistency of te data set to te model, including modifications suc tat ouseold budget constraints old in te data. Te resulting model admissible data set across ten UK ouseolds is displayed in Table 1. In tis data, gross income is concentrated in te iger deciles, wit transfers concentrated in te lower deciles. Te ouseold profile of leisure consumption reflects te interaction of ours (falling as we move to te iger income ranges) and wage rates at wic leisure is valued (rising by income range). Te two tax rate profiles are for average (not marginal) tax rates. For income taxes tey rise by income range, but not by as muc as migt be tougt from an examination of tax rate scedules. Tis is because of income tax allowances, caps on social (national) insurance contributions, untaxed ousing capital
12 11 income, and UK tax selters (pensions, savings in tax seltered veicles), all of wic ave a major influence on te average tax rate profile. Te indirect tax rates fall by income range due to te influence of excise taxes, particularly on petrol, but also on drink, bot of wic are a considerably larger fraction of expenditures for te poor tan te ric. Houseolds 10 Table1 Model admissible ouseold data set by deciles of income for nonretired ouseolds, UK 1994/95 9 (a) Gross of tax labor income a (b) Transfers a (c) Income and oter direct taxes paid a,11 (d) Indirect taxes paid a,12 (e) Consumption gross of indirect taxes a,13 (f) Leisure a,14 (g) Income tax rate 15 () Indirect tax rate 16 Decile (Poor) Decile Decile Decile Decile Decile Decile Decile Decile Decile (Ric) Notes: All figures in tis table noted wit superscript a are millions of, for te tax year 1994/95. Using information on elasticities, we calibrate bot te omogeneous and eterogeneous labour models to tis bencmark equilibrium data set. To do tis, we first take te bencmark data set from Table 1 in value terms, and decompose it into separate price and quantity observations. Following Harberger (1962), and Soven and Walley (1992) we coose units bot for labour by type, and for consumption, as tose amounts 9 See Appendix 1 for more detail. 10 Tese ouseolds are grouped by original ouseold income as in Economic Trends (1995). Original income is pre tax / pre transfer income. 11 Tis includes all social insurance contributions. 12 Tis includes VAT and all excises (especially on petrol, tobacco, drink). 13 Tis is gross of indirect taxes. 14 Tis is from UK time use survey data; leisure time is valued at te net of tax wage. 15 Tis includes income tax and social insurance contributions. 16 Tis includes te VAT plus specific excise taxes.
13 12 wic sell for 1 in te base case equilibrium. Using tis convention all prices and wages are one in te base case, and all quantities are as given by te base case observations in Table 1. Te calibrated versions of eac model replicate tis base case data as a model solution. Elasticities Te elasticity parameters needed for te models are te ten ouseold specific substitution elasticities in consumption (CES preferences) wic are used in bot models, and te substitution elasticity in production (in te CES production function) in te eterogeneous labour model. Direct estimates of tese elasticities are not available in te literature. Elasticities in consumption over goods and leisure must be inferred from literature estimates of labour supply elasticities. Elasticities of substitution in production between labour types must be inferred from literature estimates of labour demand elasticities for various types of labour. From te production function (7), we can use te first order conditions for profit maximization and te derived labour demand function (9). Te elasticity of labour demand in production is given by e LD LD w = and differentiating (9) w.r.t. w gives w LD e LD = w σ σ p 1 p δ + δ Π w δ σ p 1 Πw w σ p 1 (15) In te base case all gross of tax wage rates are unity, and if, in addition, ouseold labour sares are small, e LD effectively collapses to p σ. We coose te elasticity of substitution between labour types in production wic, from (15), we can calibrate numerically to values of labour demand elasticities found in te literature (Hamermes
14 13 (1993)), and use oter sensitivity cases discussed below to reflect ranges around a central case value. As tere are ten ouseold demand elasticities in te model around te base case equilibrium, and only one free parameter, σ p, in calibration we coose σ p suc tat elasticities across ouseolds (wic do not vary tat muc) are witin a desired range. Labour supply elasticities, in contrast, are found using te leisure demand function (4). Point estimates of labour supply elasticities for eac ouseold in te neigbourood of te bencmark equilibrium can be generated by noting tat LS w w LS LS L w L L = = ( 1 ) η LE (16) L w L LS LS We use te leisure demand function (4) to derive te leisure demand elasticity, η LE wic is given by η LE 1 σ α w = ( 1)( 1 ) σ + 1 σ α P + ( 1 α ) w σ 1 σ (17) Te point estimate of te labour supply elasticity for eac ouseold, given σ, is : e LS = σ ( σ + α P p 1)(1 α ) w 1 σ + (1 α ) w 1 σ 1 σ L LS (18) In te neigbourood of te base case, were te price of goods and all wage rates are unity, tis collapses to e LS = σ + 1 σ L ( σ p 1)(1 α ) w (19) LS and if ( α ) 1 is small 17 L els σ. LS We coose values for labour supply elasticities from literature estimates and using (16) tese imply leisure demand elasticities. Using tose as point estimates around te
15 14 bencmark equilibrium, and using (18), elasticities of substitution in preferences are determined for eac ouseold decile. Te equation (18) yields an implicit function for σ, wic we solve numerically. Table 2 Model production and consumption side elasticities, and literature justification A. Range of labour supply elasticities based on tose reported in Killingswort (1983) Range of values Labour supply elasticity assumed for eac ouseold Range of elasticities of substitution in consumption implied for ouseold deciles Hig Mid (central case) Low B. Range of labour demand elasticities based on tose reported in Hamermes (1993) Range Range of labour demand elasticities by decile Elasticity of substitution used in production Hig to Mid Range (central to case) Low to Table 2 sets out te elasticity ranges we use for in te two models and te implied substitution elasticities in consumption and production. Tese are approximately consistent wit ranges of parameter estimates reported by Hamermes (1993) for labour demand, and Killingswort (1983) for labour supply. In te model, tere are 10 separate labour demand elasticities for eac labour type. Tese elasticities vary, and ence we calibrate te model to point estimates of tese elasticities in te neigbourood of te bencmark equilibrium. In addition, tere is only one free model parameter (te elasticity of substitution among labour types in production) so tat exact calibration for eac ouseold type labour demand elasticity is not feasible. We tus 17 Typically, owever, consumption sare parameters on leisure are not small.
16 15 vary te single production side elasticity until te ouseold labour demand elasticities, wic are similar across ouseolds, are witin te desired range. IV. Results We ave used te eterogeneous and omogeneous labour models described above and calibrated to UK data for te 1995/96 tax year to investigate te beaviour of tax incidence results across models. We do tis for different tax experiments, different labour supply elasticity (consumption/leisure substitution ) configurations, freezing te labour demand elasticity specification; and for different labour demand elasticity specifications, freezing te labour supply elasticity specification. Te essence of tax policy analysis lies in comparing welfare canges between bencmark and counterfactual equilibria. How muc a typical ouseold as gained or lost because of canges in policy in money metric terms, or ow muc money is required to bring im/er back to teir original welfare can be measured at eiter original or new prices. Te Hicksian equivalent variation (EV) is a money metric measure of te welfare cange between bencmark and counterfactual scenarios using bencmark (old) prices. It is te difference in money metric utility at old prices corresponding to bencmark and counterfactual model solutions; i.e. N EV = E( U, P ) E( U, P ) (20) were superscripts N and O represent new and old values for te variable on wic tey appear, U is te utility, and E is te expenditure function wic depends on prices and utility level. If utility functions are of te linear omogeneous type, ten original and new equilibria can be tougt of in terms of a radial expansion of te utility surface. In tis case te cange
17 16 in money metric welfare between bencmark and counterfactual solutions of te model is proportional to te cange in utility or te percentage cange along te radial projection between te two consumption points. EV 0 U N U 0 = I (21) 0 U were N and O represent new and old values of te variables as before, and I represents te income. In Table 3 we report tax incidence calculations for a case were we replace te pre existing pattern of labour income tax rates by ouseold by a yield preserving uniform rate income tax across ouseolds. We consider cases were we freeze labour supply elasticities first at 0.3, and ten at 1.0, and vary te ranges we use for labour demand elasticities in te eterogeneous labour model. We compare model results across te omogeneous labour model and te various specifications of te eterogeneous model for tese labour supply elasticities. Table 3 Comparing omogeneous and eterogeneous labour models Specification Experiment: replacing existing labour income taxes by yield preserving uniform rate Elasticity specification: Labour supply elasticity 0.3 and 1.0 in two cases, labour demand elasticities range from to Results: Welfare gains/losses by decile in terms of Hicksian EV as a fraction of base income (wit low labour supply elasticity (0.3)) Decile Homogen eous Labour model Heterogeneous Labour model Labour demand elasticities ranges as specified in Table 2 Low Middle Hig (0.58 to 0.67) (1.05 to 1.24) (1.8 to2.1) 1 poor
18 ric Results: Welfare gains/losses by decile in terms of Hicksian EV as a fraction of base income (wit low labour supply elasticity (1.0)) Decile Homogen eous Labour model Heterogeneous Labour model Labour demand elasticities ranges as specified in Table 2 Low Middle Hig (0.58 to 0.67) (1.05 to 1.24) (1.8 to2.1) 1 poor ric Results in Table 3 sow te redistribution across ouseolds in tese cases. Ricer ouseolds gain because teir taxes fall, and poorer ouseolds lose since te replacement tax is at a uniform rate and teir taxes rise. However, tere is considerable variation in te redistribution profile across te two elasticity cases for te eterogeneous labour model. Considerably more redistribution occurs in te ig elasticity case since wage rate canges in response to te tax replacement are small; low income ouseolds bear most of te burden of teir iger taxes, and ig income ouseolds gain by most of teir tax saving. As one moves across labour demand elasticity specifications te redistributive effects from te tax canges become larger, wit wage canges less pronounced. Labour demand elasticities ave a significant influence on te perceived tax incidence effects from te tax
19 18 replacement. From various sensitivity analyses, we find tat as labour demand elasticities increase, te income tax incidence profile in te eterogeneous labour model approaces tat of te omogeneous labour model for any given value of te labour supply elasticity. In Table 4 we explore ow te model comparisons cange as we vary labour supply elasticities. We consider te same tax replacement, i.e. replacing te existing profile of income tax rates by a uniform rate income tax across ouseolds, but only consider te mid range specification of labour demand elasticities, canging labour supply elasticities in bot omogeneous and eterogeneous labour models. Results in Table 4 sow tat te incidence profile canges relatively little between eterogeneous and omogeneous labour models as labour supply elasticities increase. Te low income ouseolds lose about 56 percent of te base year income in bot eterogeneous and omogeneous labour models irrespective of different values of labour supply elasticities. For middle range values of labour demand elasticities (irrespective to any specific value of labour supply elasticity), income tax incidence profiles of replacing base case labour income taxes by yield preserving labour income tax rates become comparable across two models. Table 4 Impacts of Varying Labour Supply Elasticities on Incidence Profile Comparisons Specification Experiment: replacing existing labour income taxes by yield preserving uniform rate Elasticity specification: Labour supply elasticity 0.3, mid range demand elasticities in te eterogeneous labour model. Results: Welfare gains/losses by ouseolds, Hicksian EV as a fraction of base income Decile Labour supply elasticity Labour supply elasticity Labour supply elasticity (1.0) (0.15) (0.3) Homogen Heterogen Homogen Heterogen Homogen Heterogen
20 eous labour Model eous labour model eous labour Model eous labour model eous labour Model eous labour model 1 poor ric As final sets of results in Table 5 we present incidence results for tree different yield preserving tax canges; te first one only involves income taxes, te second one involves income and sales taxes, and te last one involves only sales taxes. We use a 0.3 labour supply elasticity and mid range labour demand elasticities. Table 5 Incidence Comparison for Different Tax Canges for te Heterogeneous Labour and Homogeneous Labour Models Specification Labour supply elasticity set at 0.3 Labour demand elasticities set at mid range values in te eterogeneous labour model. Results: Welfare gains/losses by ouseolds, Hicksian EV as a fraction of base income Only income tax Income and sales tax Only sales tax Decile Homogen eous labour Model Heterogen eous labour model Homogen eous labour Model Heterogen eous labour model Homogen eous labour Model Heterogen eous labour model 1 poor
21 ric In bot te income tax case and te combined income and sales tax case we find low income ouseolds lose and ig income ouseolds gain wen base case taxes are replaced by yield preserving tax rates, but te pattern of gains is different in te upper tail of te distribution across eterogeneous and omogeneous models.
22 V. Conclusions 21 In tis paper we analyze ow labour demand elasticities, long neglected in empirically based tax incidence analysis, affect incidence conclusions. Using a data set for te UK for tax year 1994/95 covering 10 ouseold deciles we use two models to evaluate te incidence effect of various tax canges, specially te replacement of te existing pattern of income tax rates by a uniform rate yield preserving alternative. We consider two models, one wit labour eterogeneous in production, i.e. 10 different labour types (one for eac decile) in production; and te oter wit labour omogeneous across ouseolds i.e. only one type of labour in production. Te substitution elasticity among labour types in production determines labour demand elasticities. Our results suggest tat labour demand elasticities do indeed matter for tax incidence conclusions.
23 References: 22 Auerbac Alan J. and L. J. Kotlikoff (1987), Dynamic Fiscal Policy, Cambridge University Press. Ballard Carles L., D. Fullerton, J.B. Soven and J. Walley (1985) A General Equilibrium Model for Tax Policy Evaluation, University of Cicago Press, Cicago. Dirkse S. P. and M. C. Ferris (1995) CCPLIB: A collection of nonlinear mixed complementarity problems Optimization Metods and Software. 5: Dex S., A.Clark and M.Taylor (1995), Houseold Labour Supply Employment, Department Researc Series No. 43 (ESRC Center for Microsocial Cange, University of Essex). Economic Trends (1996), Office of National Statistics, London. Gillespie W. (1965) Effect of Public Expenditure in Distribution of Income, in R. Musgrave (ed.) Essays in Fiscal Federalism, Brookings, Wasington DC, pp Hamermes D. S. (1993) Labour Demand, Princeton University Press, New Jersey. Harberger A.C. (1962) Te Incidence of te Corporation Income Tax, Journal of Political Economy, 70, Killingswort M. (1983) Labour Supply, Cambridge University Press. Kydland F. E., and E. C. Prescott Time to Build and Aggregate Econometrica 50, Nov., Fluctuations. Mansur A. and J. Walley (1986), Numerical Specification of Applied General Equilibrium Models: Estimation, Calibration and Data, in Scarf Herbert E and Soven Jon B. (ed.) Applied General Equilibrium Analysis, Cambridge University Press. Pecman J.A and B.A. Okner (1974) Wo Bears te Burden of Taxes? Brookings Institute, Wasington D.C. Piggott J. and J. Walley (1985) UK Tax Policy and Applied General Equilibrium Analysis, Cambridge University Press. Soven J.B. and J. Walley (1992) Applying General Equilibrium, Cambridge University Press. Soven J.B. and J. Walley (1972) A General Equilibrium Calculation of te Effects
24 of Differential Taxation of Income from Capital in te U.S. Journal of Public Economics 1, Watson Mark W. (1993) Measures of Fit for Calibrated Models, Journal of Political Economy, Vol. 101, no. 6 pp
25 Appendix 1 Data Sources 24 Tis appendix presents details on various data sources and adjustments tat underlie Table 1. Te main data sources are Table 3A (Appendix 1) of Economic Trends, 1995/96, p. 36, New Earnings Survey 1995 and Time Use Survey reported in Dex et al. (1995). Te gross income in column (a) of Table 3A comprises original income and direct taxes (see Table 1 in text). Original income includes wages and salaries, imputed income from benefits in kind, selfemployment income, occupational pensions, annuities and oter income. Direct taxes include employees national insurance (NI) contributions. Te ouseold average direct tax rate to be income and oter taxes divided by gross of tax income plus transfers. A1 Components of Gross of tax labour income in Table 1 (see Text) ( million 1995/1996 UK Tax year) H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 Total Original income Direct taxes Total Te UK Economic Trends data distinguises five different concepts of income: original, income, gross income, disposable income, post tax income and final income. Original income plus cas benefits equal gross income, disposable income is gross income minus direct taxes. Post tax income is disposable income minus indirect taxes Final income equals post tax income plus in kind benefits. Table A2 Gross consumption by Houseolds in Table 1 (see Text) ( million 1995/1996 UK Tax year) Decile H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 Total Gross income Transfers Direct taxes Total Te transfers presented in column (b) of Table 1 in te text include direct cas benefits, in kind transfers, and consumption of publicly provided goods services suc as national defence. Direct cas benefits consist of retirement pension contributions, unemployment benefit, invalidity pension and allowance, sickness and industrial injury benefit, widow s benefits, and statutory maternity pay/allowance. Noncontributory benefits include income support, cild benefit, ousing benefit, invalid care allowances, attendance allowance, disability living allowance, industrial injury disablement benefit, student maintenance awards, government training scemes, family credit and oter noncontributory benefits. Benefits in kind consist of education, national ealt service, ousing subsidy, rail travel subsidy, bus travel subsidy, scool meals and welfare milk.
26 25 Te gross consumption of eac ouseold, included in column (e) of Table 1 in te text, is derived by adding cas, in kind and noncontributory benefits to original income and subtracting te direct and indirect taxes paid by te ouseold. Consumption tus is gross of indirect taxes tat include taxes on final goods and services, VAT, duty on tobacco, beer and cider, wines and spirits, ydrocarbon oils, veicle excise duty, TV licences, stamp duty on ouse purcase, customs duties, betting taxes, fossil fuel levy, and Camelot national lottery fund. It also includes intermediate taxes suc as commercial and industrial rates, employer s NI contributions, duty on ydrocarbon oils, veicle excise and oter duties. Table A3 Te Value of Leisure Consumption by Houseolds in Table 1 (see text) H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 Total Earnings/week/ouse olds ( ) Working weeks Leisure weeks Value of leisure by ouseold ( million) Te value of leisure reported in Table 1 in te text as been obtained by multiplying nonworking weeks by te weekly earnings rate. Te number of nonworking weeks is te difference between te working weeks and 104 weeks. Te total working week represents te total labour endowment per ouseold wit two working members. Earnings per week for top and bottom deciles, and first and tird quartiles are taken from te New Earnings Survey Tese are interpolated for oter deciles. Working weeks are derived by dividing te original income by te weekly earnings.
27 26 Appendix 2 Solution Metod of te Model Bot omogeneous and eterogeneous labour models discussed in tis paper are set up as a mixed complementarity problems and solved in GAMS software using te PATH solver. Dirkse and Ferris (1995) state te basic idea beind te PATH solver in terms of a "zero finding problem". For any function F: R n R n wit lower bound  l and an upper bound u + te problem is to find z R n suc tat eiter z i = l i and F i (z) 0 or z i = l i and F i (z) 0 or l i z i u I and Fi(z) = 0 PATH constructs a solution using a damped Newton metod suc as 0 = FB = F ( ) ( ) x + x x x ( B) B were x B is te Euclidean projection of x onto te Box B := [ l, u]. A vector x solves tis nonlinear equation only if z = xb solves te MCP. A more detailed explanation of tis algoritm is beyond te scope of tis paper, many tecnical papers on te topic are available in Ferris's omepage : ttp:// GAMS syntax (Brook, Kendrick and Meeraus (1992)) permits us to generate a non linear mixed complemetarity model by declaring and assigning sets, data, parameters, variables, equations in te model. PATH is invoked by te "OPTION MCP = PATH" statement in te GAMS code and a command line "solve <model name> using MCP" instructs GAMS to solve te model using te PATH solver. We use batc files to compute incidence profiles across various scenarios for different values of elasticities and tax rates for ouseolds.
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