A Note on Reliefs for Traveling Expenses to Work

Transcription

1 A Note on Reliefs for Traveling Exenses to Work by Matthias Wrede niversity of Bamberg and Technical niversity of Aachen, Germany * July 1999 Abstract Assuming that higher traveling exenses reduce traveling time, this aer considers reliefs for traveling exenses to ork hen a distorting age tax is levied. While the decision on traveling exenses ould not be distorted if traveling costs ere comletely deductible, taxation ould still not be neutral ith resect to the leisure-consumtion choice. Moreover, the aer shos that second-best otimum taxation requires less than comlete deductibility of traveling exenses to ork. Keyords: Income taxation, reliefs, traveling exenses to ork, otimum taxation JEL-lassification: H21, H24 * Matthias Wrede, Deartment of Economics, niversity of Bamberg, D Bamberg, Germany, matthias.rede@soi.uni-bamberg.de

2 - 1 - A Note on Reliefs for Traveling Exenses to Work I. Introduction Tax rules concerning traveling exenses to ork are quite different in the various industrialized countries. While traveling exenses to ork are not deductible in many countries like the nited States, the nited Kingdom and even several continental Euroean countries, tax alloances are granted by other countries like the Scandinavian countries and Germany [see OED (1993),. 37]. The main argument in favor of a relief is that orkers should not be distorted by the income tax hen choosing their lace of ork. ritics, hoever, argue that rather than the lace of ork the location of residence matters and that referential treatment of far-off domiciles by the tax code not only reduces tax revenue but it is also inefficient. Hoever, this aer ill not analyze tax alloances for traveling exenses to ork against the background of the discussion of hether the choice of the lace of ork or the choice of the location of residence is causal for commuting [see, e.g., Krause-Junk (1996), Olbertz (1986), Richter and Theile (1998)]. Furthermore, equity considerations, hich are discussed concerning ork-related exenses by, e.g., Baldry (1998), ill also be ignored. The focus ill be on a articular efficiency asect of traveling exenses. Reliefs also affect traveling exenses if both the lace of ork and the domicile are given. Normally, higher traveling exenses result in less traveling time. By buying a more exensive and thus faster car and by traveling by car instead of traveling by train (or bicycle), the commuting time can be reduced. Hence, the deductibility of traveling exenses to ork guarantee that the decision uon them and therefore the decision on the commuting time is not distorted by the income tax. Since, at first sight, the neutrality regarding the traveling time says something for the comlete deductibility of traveling exenses, it is the urose of this aer to analyze in detail the tax treatment of traveling exenses to ork assuming that less traveling time requires higher traveling costs.

3 - 2 - The remaining art of the aer is organized as follos. Section to resents a model and derives the first-best efficiency conditions. Section three characterizes the market equilibrium and section four develos a second-best tax rule. Finally, section five concludes. II. Traveling exenses and efficiency The model considers a one-erson economy here the individual derives utility from rivate consumtion and leisure F. Preferences are reresented by a ell-behaved utility function (, F). F indicates the total time endoment and L the orking time in the roduction of goods. Furthermore, it is assumed that the individual has to send some time T to travel from home to the location here roduction takes lace. Labor, leisure and traveling time add u to the total time endoment. To goods are roduced in the economy. One good can be either used as rivate consumtion good or ithout additional costs as ublic good G. The other good covers the traveling exenses to ork, hich are not exogeneously given. At least to some extent, they are used for reducing traveling time. Hence, the more is used by the orker, the less traveling time is needed: T T( ), here T < 0 and T > 0. In order to simlify the analysis, a linear one-factor technology ith fixed technical coefficients is assumed. Measured in units of time, the unit costs of the first and the second good are given by 1 a and 1 a, resectively. While L denotes labor in the roduction of (and G), L denotes labor in the roduction of. solution of If some quantity G of the ublic good is required, the first-best otimum is the (1) Max (, F), F, L,, L, L s.t. + G a L, a L, F F + L + T( ), L L + L, c

4 - 3 - here the first to constraints describe the roduction technology, the third condition is the time constraint, and the fourth condition covers the division of labor. On the one hand, an interior solution is characterized by (2) F a. The marginal rate of substitution beteen leisure and consumtion is equal to the marginal rate of transformation beteen leisure and consumtion, i.e., the marginal roductivity of labor in the consumtion good sector. On the other hand, efficiency requires (3) a T ( ) 1. The amount of saved traveling time roduced by one additional unit of orking time in the roduction of should be equal to its oortunity costs. III. Traveling exenses and labor income taxation Suose that lum-sum taxes are unavailable and that the ublic good is financed by a linear labor income tax. Suose further that traveling exenses to ork are at least artially deductible. Denote the roducer rices of goods and labor by,, and, resectively. The age tax rate is indicated by τ. If a fraction δ of the traveling exenses is deductible from the tax base of the ersonal income tax such that the government effectively subsidizes traveling exenses at a rate (4) θ τδ, the government budget constraint can be ritten as (5) τl θ G. c The household sells labor and buys both tyes of goods at rices net of taxes and tax reliefs. 1 Therefore, the utility maximizing household solves 1 Because of the technology, rofit income is absent.

5 (6) Max (, F), L, s.t. L F F L T( ) , Rearranging the first-order conditions yields (7) F and T. The marginal rate of substitution beteen leisure and consumtion is equal to the real age net of the age tax. The marginal roductivity of time saring traveling exenses is equal to the relative rice of net of taxes and reliefs. If markets are cometitive, an equilibrium here rofits (8) ( a ) L and ( a ) Π Π L are zero is characterized by (9) a and a. In the remaining art of the aer, the rice of the consumtion good ill be normalized to some fixed ositive value. If the rice of is given, the equilibrium rice of and the age rate are determined by the technical coefficients. Hence, all roducer rices are constant. ombining the first-order conditions of the utility-maximization roblem and the rofit-maximization roblem leads to F (10) ( ) 1 τ a and a T 1 1 θ τ. In general, both efficiency conditions (2) and (3) are violated. Hoever, if traveling exenses ere comletely deductible, i.e., if (11) θ τ or equivalently δ 1,

6 - 5 - one of them ould be fulfilled. Deciding uon traveling exenses, the household ould take the real oortunity costs into account. Nevertheless, the leisure-consumtion decision ould be still distorted. Since the main theorem of second best theory suggests that counting efficiency conditions is, in general, misleading, the advantage of comlete deductibility of traveling exenses is questionable. In order to discuss the merits and demerits of comlete deductibility, a standard second-best-otimum-taxation aroach has to be undertaken. IV. Traveling exenses and second-best-otimum taxation tility maximization of the household generates the labor suly function L(, x ), the demand function function ( ) ( ), x, and the indirect utility V, x. Since all roducer rices are constant, is suressed. sing the first-order conditions of the utility maximization roblem, one easily verifies (12) T > and 1 ( 1 0 T <. The otimization roblem of the government is ( ) (13), Max V x τ, θ s.t. ( ) ( ) ( ) (( ) ( ) ) G τl 1 τ, 1 θ + θ 1 τ, 1 θ 0. c The solution can be described by (14) τ L τ θ L θ + µ λ, µ µ λ, µ here µ is the Lagrange multilier associated ith the government budget constraint and λ is the marginal utility of income. sing the roerties of the household utility maximum and rearranging yields (15) θ τ ( LT 1 L + 1.

7 - 6 - This formula can be used to derive the folloing to main results of the aer. The elasticities of labor suly are (16) ε ( ) L, 1 τ L and ε ( ) L, 1 θ L. Proosition 1: Traveling exenses to ork shouldn t be deductible at all, i.e., θ δ 0, if (17) ε ε L, L L, T is fulfilled. Hence, non-deductibility of traveling exenses to ork is otimal only under very secial circumstances. alculating the artial derivatives of the labor suly function and using 2 LL, hich is the second artial derivative of the utility function ith resect to labor after inserting the constraints, i.e., of ( 1 ) ( 1 ) able to derive an illuminating formula for the subsidy: ([ ] ( )) τ L θ, F L T, one is (18) θ τ + ( LL τ 1 T Since the second-order conditions require LL < 0, this formula roofs the folloing roosition. Proosition 2: Traveling exenses to ork should never be deducted comletely from the tax base of the labor income tax, i.e., θ τ or equivalently δ 1 are never otimal. The economic exlanation for that result is straightforard. If traveling costs ere comletely deductible form the tax base, the choice of traveling exenses ould be efficient, but due to the high age tax rate, the leisure-consumtion choice ould be 2 ( 2 ( 1 ( 1 ) LL FF F

8 - 7 - heavily distorted. Introducing a small distortion of traveling exenses results in elfare losses hich are much smaller than the elfare gains from reducing the large distortion in the leisure-consumtion decision. V. oncluding remarks This aer considered reliefs for traveling exenses to ork in the resence of a distorting age tax. The focus of the analysis as neither on the choice of the locations of ork and home nor on the distance beteen them. Taking the vie that higher traveling exenses reduce traveling time, the aim as hether deductibility increases traveling exenses to an inefficient amount. It turns out that the relationshi beteen traveling time and orking time is of articular imortance in ansering this question. While the decision on traveling exenses and, therefore, the decision on traveling time ould not be distorted if traveling costs ere comletely deductible, taxation ould still not be neutral ith resect to the leisure-consumtion choice. sing a standard second-best otimum taxation aroach, it has been shon that non-deductibility of traveling exenses to ork is otimal only under very secial conditions and, even more imortantly, that second-best otimum taxation requires less than comlete deductibility of traveling exenses to ork. The analysis is of consequence to the treatment of traveling exenses to ork by the income tax la, for instance in Germany. In Germany, the necessary cost of transortation beteen the home and the lace of ork are deductible. Hoever, since 1955, only a secific amount er km (the so called Kilometerauschale ) times the distance beteen the home and the lace of ork is deductible from the income tax base if a car is used. The deductible amount er km, hich as 0,50 DM in 1955, as reduced to 0,36 in 1967 and has been increased since 1989 u to 0,70 DM in Since the result of this aer as that traveling exenses to ork should be only artially deductible form the tax base, the deductible amount er km should be less than the comlete cost er km. The analysis suorts, therefore, the existing treatment of traveling exenses to ork by the German income tax la. Hoever, if the oortunities

9 - 8 - of tax evasion are taken into account the aer backs the roosal of the income-taxreform commission led by P. Bareis hich roosed in 1994 a fixed deductible amount er km (0,20 DM) irresective of the means of transortation (the so called Entfernungsauschale ) [see Einkommensteuer-Kommission (1994)].

10 - 9 - References Baldry, Jonathan (1998). Income Tax Deductions for Work Related Exenses: the Rationale Examined. Australian Economic Paers Einkommensteuer-Kommission (1994). Thesen zur Steuerfreistellung des Existenzminimums ab 1996 und zur Reform der Einkommensteuer. Bonn. Krause-Junk, Gerold (1996). mstrittene Kilometerauschale. Wirtschaftsdienst 1996/I OED (1993). Taxation in OED ountries. Paris. Olbertz, Peter (1996). Die Aufendungen des Arbeitnehmers für Fahrten zischen Wohnung und Arbeitsstätte gemäß 9 Ab. 1 Satz 3 Nr. 4 EStG und das objektive Nettorinzi. Betriebs-Berater Richter, Wolfram F. and arsten Theile (1998). Aufendungen für Fahrten zischen Wohnung und Arbeitsstätte: Ein Vorschlag zur Verirklichung einkommensteuerlicher Entscheidungsneutralität. Steuer und Wirtschaft 4/