Income tax deduction of commuting expenses in an urban CGE study: The case of German cities

Transport Policy 28 (2013) 11–27

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Income tax deduction of commuting expenses in an urban CGE study: The case of German cities Georg Hirte n, Stefan Tscharaktschiew 1 Technische Universit¨ at Dresden, Faculty of Traffic Sciences ‘‘Friedrich List’’, Institute of Transport & Economics, Chair of Spatial Economics & Regional Science, 01062 Dresden, Germany

a r t i c l e i n f o

abstract

Available online 7 July 2012

Granting the right to deduct commuting expenses from the income tax base has regularly been under debate during the last decades. This paper provides for the first time an insight into the magnitude of the effects of this kind of commuting subsidy under different funding schemes. The economic and spatial effects are calculated by applying a spatial CGE approach calibrated to a German urban area. The findings suggest that effects on urban sprawl characterized by suburbanization, spatial expansion of the city, and increasing commuting distance are surprisingly small. Concerning welfare, we found that the current level of tax deductions in Germany is too small in the case of income tax funding. If one considers further changes in the tax system welfare can be considerably enhanced by raising tax deductions above that level. In particular this refers to a tax structure where energy taxes are used to make traveling by car less attractive and tax deductions are used to lower the negative impact of taxes on labor supply. & 2012 Elsevier Ltd. All rights reserved.

Keywords: Urban general equilibrium model Commuting subsidies Income tax deduction

1. Introduction Commuting expenses reduce the income tax liability in many European countries, e.g. in Belgium, Denmark, Finland, France, Germany,2 Luxembourg, the Netherlands, Norway and Switzerland (see Potter et al., 2006). In Germany this regulation has often been changed and has been under debate for decades. Advocates of income tax deductions3 emphasize that they reduce distortions concerning individual labor supply (Wrede, 2000, 2001; Sinn, 2003), eliminate spatial misallocations in particular concerning working location decisions (Wrede, 2009; Sinn, 2003; Gasche, 2004),4 or they may serve to internalize positive agglomeration externalities (Borck and Wrede, 2009). In contrast, objections against tax deductions arise since commuting subsidies might induce negative externalities and, thus, constitute a ‘bad’ (Richter, 2006) and since costs resulting from privately caused decisions concerning commuting should not be subsidized

n

Corresponding author. Tel.: þ49 0351 463 36805; fax: þ 49 0351 463 36819. E-mail addresses: [email protected] (G. Hirte), [email protected] (S. Tscharaktschiew). 1 Tel.: þ49 0351 463 36817; fax: þ 49 0351 463 36819. 2 For example in Germany income tax deduction of commuting expenses caused total income tax savings (or governmental income tax losses) of commuters of about 4 billion h in 2006 (Bach et al., 2007). 3 In the following we only use the term ‘tax deduction’. 4 Commuting costs might deter individuals from choosing the more productive job. Thus, granting deductions eliminates this effect. 0967-070X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.tranpol.2012.05.003

(Richter, 2004, 2006; Gasche, 2004; Wrede, 2004).5 Further, Kloas and Kuhfeld (2003) and Bach et al. (2007) refer to equity reasons. They suggest to abolish tax deductions because highincome households benefit the most, as they found in their descriptive analyses. Eventually, there is reasoning that tax deductions discriminate in favor of commuters who avoid high rents in central cities but at the same time benefit from subsidized living at low-rent suburbs (see e.g. Wrede (2004) by drawing conclusions from his related work).6 By summarizing his different contributions Wrede (2004) considers a deduction rate of slightly less than the current rate of 0:30 h=km as optimal. Richter (2006) derives that commuting expenses should be deductible only if they are indispensable for earning income. He suggests that a criterion to decide on this could be whether there is some compensation payment, such as higher wages, for commuting. This so-called net-principle is the main reasoning in favor of tax deductions in Germany. The German Advisory Board for Economic Development (SVR, 2003) assumes that commuting expenses occur on account of mixed reasons. Thus, it suggests that about 50% are occupational caused, though, it does not provide a thorough foundation for that. In contrast, Richter (2004) in referring to his theoretical paper (see Richter, 2006)

5 Sinn (2003), Gasche (2004), Wrede (2004) and Richter (2004) are German contributions which are, at least partly, based on theoretical analyses. 6 There are also many policy oriented statements or reports recommending to reduce or abolish tax deductions. For example, Bach (2003) or Donges et al. (2008).

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presumes that employer do not pay higher wages for commuters. Accordingly, so he is reasoning, commuting is privately caused and, thus, should not be tax deductible at all.7 This short review shows that the pros and cons of tax deductions are well known. However, in the urban/transport economics literature there is a lack of quantitative studies analyzing economic and spatial effects of the tax deductibility of commuting expenses. Of course, there is some literature connected to the problem of tax deduction. Because it changes commuting costs studies on the effects of changes in commuting costs on labour supply might provide some insights into the effects of tax deductions, too. Gutie´rrez-i-Puigarnau and van Ommeren (2010) and van Ommeren and Gutie´rrez-i-Puigarnau (2011) examine the effects of employer induced increases in commuting distance on labor supply and absenteeism. According to their findings in the earlier paper an increase in commuting distance and, thus, an increase in commuting costs imply a reduction of daily working hours but no noticeable effect on the number of working days. If, however, absenteeism is taken into account, absenteeism and thus effective working days are varied, too (Gutie´rrez-i-Puigarnau and van Ommeren, 2011). Concerning these results one should be aware that their studies only look at employer induced changes in distance. In that case employees already have a contract with the employer and there might be restrictions concerning the variation of workdays. With reference to tax deductions, one might deduce from these results that both, daily working hours as well as working days per week will increase due to commuting subsidies. Interestingly there are only two ‘technical’ papers focusing on tax deduction of commuting expenses (see Wrede, 2001, 2000). However, the models used in the literature do not simultaneously implement spatial location and labor supply decisions along with distortionary taxation because such an approach is not analytically solvable. Moreover, the models rely on restrictive assumptions concerning the design of the income taxation scheme and the structure of households living in the urban area—they usually neglect household heterogeneity. Hence, optimal deduction rates are not yet fully derived since the different lines of reasoning are yet not integrated in one unified approach. Consequently, it is not at all clear how efficiency effects concerning residential and employment location distortions, labor supply distortions, effects on externalities such as congestion, or effects on travel mode choice and on welfare distribution behave if all those features are simultaneously considered. This is a serious gap in the debate because the consequences of not integrating these important features are not clear in advance.8 Would this either imply a lower or a higher deduction rate than the current level? Is there a strong effect on urban sprawl and the environment, e.g. characterized by changes in travel related CO2 emissions? This is our point of departure. We – to the best of our knowledge for the first time – apply a spatial computable general equilibrium polycentric city model (SCGE) calibrated to an average German metropolitan area to analyze the impact of tax deduction

7 Gutie´rrez-i-Puigarnau and van Ommeren (2010), however, provide evidence for Germany that there is on average some compensation if the increase in commuting distance is caused by employer relocation. 8 Of course, there is a large body of literature on transport subsidies in general applying either non-spatial or spatial approaches (see e.g. De Borger and Wuyts, 2009; Parry and Small, 2009; Borck and Wrede, 2005, 2008, 2009; Su and DeSalvo, 2008; Brueckner, 2005; Van Dender, 2003; Calthrop, 2001; Martin, 2001; Zenou, 2000). Tscharaktschiew and Hirte (2012) provide a review of the corresponding literature and summarize the main findings. Nonetheless, except for Tscharaktschiew and Hirte (2012), all these papers neglect the simultaneous consideration of these features and there is no corresponding study focusing on income tax deduction of commuting expenses.

of commuting expenses.9 Because commuting is particularly significant within metropolitan areas and since theory stresses spatial effects we look at the impacts of tax deduction policies within a city framework. The model is in the tradition of Anas and Xu (1999), Anas and Rhee (2006, 2007) which had been extended by Tscharaktschiew and Hirte (2010a,b) in different ways. In the model residential, employment and shopping location decisions as well as labor supply decisions are endogenous. Moreover, the approach takes household heterogeneity, important institutional features such as progressive income taxation and further taxes, travel mode choice and endogenous automobile congestion, gasoline consumption and CO2 emissions into account. Because one reasoning against tax deductions is that they raise suburbanization we consider land supply endogeneity in the suburbs (endogenous city fringe). Those features have never been simultaneously treated in a spatial economic model when studying tax deduction of commuting expenses, though most of them has been discussed in the literature on tax deductions. Our focus is on the optimal tax deduction rate and the impact of varying the deduction rate on the urban economy. In addition, we go one step further in comparison to the literature where it is usually assumed that subsidies are either financed by lump-sum or income taxes. This might be useful from a systematic point of view. Nonetheless, if policymakers adjust taxes it is more appropriate to consider taxes which are less distortionary than the income tax. Therefore we implement revenue neutral tax reforms where different taxes are used to finance tax deductions of commuting expenses. In particular, the following funding schemes are considered: income tax, sales tax and energy tax10 funding. This allows to consider a wide range of differentiated funding related effects. For example, funding tax deduction by sales or energy taxes also implies an increase in (full) shopping trip costs, i.e. the costs of nonproductive time use while in particular energy tax funding may also induce changes in travel mode choice. In addition to a pure theoretical or econometric approach11 the SCGE analysis provides an extension of the theory where pure theory cannot be used on account of complexity. But this comes at the costs that specific functions and parameter values have to be assumed. Therefore, exactly speaking the results apply to the specific case under consideration, an ‘average’ large German metropolitan area featuring the specific parameters used. Nevertheless the results allow to draw conclusions concerning other feasible parameter configurations under the same institutional settings and theoretical frameworks. For this reason, we put a lot of effort into the calibration. Here we try, e.g. to replicate features common to different cities such as Berlin, Munich, Frankfurt, Stuttgart or Hamburg to allow drawing more general conclusions concerning the German case. Our results suggest that the current level of the tax deduction rate is below the optimal level if it is financed by income taxes. The optimal deduction rate, on the one hand, is about the same size as monetary round-trip commuting costs but, on the other hand, still considerably smaller than full economic (incl. time cost) round-trip commuting cost. If, however, a change in the tax base occurs the subsidy should be even higher. With respect to 9 Other commuting subsidies in such a framework are examined in Tscharaktschiew and Hirte (2012). 10 In Germany energy taxes encompass a gasoline tax and an eco-tax component. From a resident’s perspective both components are institutionally identical. Therefore, they are considered together as energy tax. We further do not consider lump-sum tax funding (see Tscharaktschiew and Hirte, 2012). 11 Using an econometric approach, though statistically more sound, is limited due to data restrictions. It is, e.g., not yet possible to link income tax data with detailed labor market data. In addition, differentiated spatial data, e.g. with respect to commuting patterns, are not available.

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

urban welfare and environmental effects the combination of an increase in tax deductibility with energy tax funding turns out to be the best policy among those considered. In this case there is a significant decline in the congestion externality and in travel related CO2 emissions. Furthermore, the different funding schemes cause heterogeneous redistribution effects. Surprisingly, the analyses also suggest quite small effects on urban sprawl. According to these findings, tax deductibility of commuting expenses contributes only to a minor extent to larger commuting distances and suburbanization. The paper proceeds as follows: the next section provides a short theoretical discussion of the efficiency aspect of tax deduction under different funding schemes. In the subsequent sections we describe the simulation model and the calibration. Then we present and explain the main results. The paper closes with a general discussion and some conclusions.

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Solving (2) for D and inserting into (1) yields the consolidated full economic budget constraint: ðp þcx þ ytxÞz þrðxÞq þ y‘ ¼ yE,

ð3Þ

where

y¼

ð1tI ÞwðyÞLCX þ tI dX L þ TX

ð4Þ

is the value of time (VOT) of the representative urban worker. Differentiating utility subject to (3) with respect to z, q, ‘, y and x yields the first-order conditions (FOC) for the optimal decisions with respect to the non-spatial variables z, q and ‘ u‘ y , ¼ uz p þ cx þ ytx

u‘ y , ¼ uq rðxÞ

ð5Þ

as well as the first-order conditions for the optimal spatial location decisions encompassing the working location choice (provided D 4 0)

2. Theoretical background

ð1tI Þw0 ðyÞL ¼ ðC þ yTtI dÞ

In the following we discuss a worker’s decisions in a stylized urban setting. This shows that tax deduction of commuting expenses may distort a worker’s non-spatial as well as spatial decisions and how the results might be affected by the differentiated funding schemes considered. This also provides a basis for discussing the efficiency effects in the full-fledged spatial model of the urban economy employed in the simulations.

and the condition for the optimal residential location (slope of the bid-rent curve)

2.1. A simple spatial model to illustrate basic effects The city is assumed to be monocentric concerning shopping activities, i.e. there is a Central Shopping District (CSD), but not with respect to housing and employment. The place of residence (employment) is defined by its distance from the CSD, denoted by xðyÞ. We assume, for the time being, that y rx. Accordingly, commuting distance is denoted by X ¼ xy. Each identical worker chooses the number of shopping trips z, which is equivalent to the level of consumption, housing consumption q and leisure ‘, the residential location x as well as the working location y to maximize utility u ¼ uðz,q, ‘Þ subject to a monetary budget and a time constraint. The budget constraint is ðp þ cxÞz þ rðxÞq ¼ ½ð1tI ÞwðyÞLCX þ tI dXD:

ð1Þ

It states that expenditures for shopping (including shopping trip cost) and housing equal (labor) income net of taxes and commuting costs plus tax deductions of commuting expenses. The monetary cost of each shopping trip is p þ cx where p denotes the mill price of the composite consumption good and c denotes monetary travel cost per round-trip shopping kilometer. The price of housing per square meter and period is rðxÞ where r 0 o0 and r 00 4 0. The daily net return to labor ð1tI ÞwðyÞL is the after tax wage where the hourly wage rate wðyÞ differs according to the location of the workplace and w0 o 0 and w00 4 0; tI is the marginal wage tax rate; and L is the fix number of working hours per workday. C are monetary commuting costs per round-trip kilometer; d is the tax deduction rate of commuting expenses; and D is the endogenous number of workdays (working shifts). Consequently, while daily working hours L are fixed, total labor supply of the household, L  D, leisure as well as shopping trip activities are endogenously determined. The time constraint is ðLþ TXÞD þ txz þ ‘ ¼ E:

r 0 ðxÞ ¼ 

ðc þ ytÞz ðC þ yTtI dÞD  : q q

ð6Þ

ð7Þ

These conditions show that the marginal income tax rate, tI , distorts all decisions. Tax deductions can neutralize the effect of the income tax on the VOT if dX ¼ wðyÞL. While this eliminates the distortions regarding the non-spatial decisions (5) it, however, does not eliminate the distortions concerning the spatial location decisions (6) and (7). As a consequence, there is no optimal subsidy or tax deduction rate eliminating all distortions arising from income taxation. 2.2. The model with German institutions Because further distortionary taxes exist in Germany tax interaction effects and tax revenue recycling effects are important issues (see also Parry and Bento, 2001). Therefore we have to discuss the effects of tax deductions simultaneously with other taxes which might be used to finance the commuting subsidy. In the following we extend the previous model by adding German consumption taxes and energy taxes and take different travel modes, m, into account. In Germany energy taxes are levied with amount tg per unit of gasoline consumed. Gasoline consumption per round-trip kilometer of shopping and commuting, respectively, are denoted by f ðmÞ and FðmÞ where individual demand depends on the travel mode m used for the corresponding trip purpose. The taxes on general consumption and on the energy tax liability, tz , as well as on other monetary travel expenditures (services), tp ðmÞ, are distinguished because travel expenditures might be subject to a lower sales tax rate depending on travel mode m.12 The German income taxation scheme is progressive and exactly implemented in the simulation model. For the time being we assume that there is a general tax allowance, P, and, in addition, workers are allowed to deduct dXD from the income tax base; thus, the tax liability is tI ðwðyÞLDPdXDÞ. Then, the monetary budget constraint turns into ½ð1 þ tz Þp þ ð1þ tp ðmÞÞcðmÞx þ ð1 þ tz Þtg f ðmÞxz þrðxÞq ¼ ½ð1tI ÞwðyÞLð1 þ tp ðmÞÞCðmÞXð1 þ tz Þtg FðmÞX þ tI dXD þ tI P:

ð8Þ

ð2Þ

The time endowment E is used for working, commuting, shopping trips and leisure. T and t denote travel time per round-trip kilometer required for commuting and shopping, respectively.

12 In Germany the sales tax rate on public transport fares (7% in 2011) differs from that imposed on general consumption and private travel activities (19% in 2011).

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G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

The worker’s time constraint is ðLþ TðmÞXÞD þ tðmÞxz þ ‘ ¼ E:

ð9Þ

After forming the consolidated full economic budget constraint the corresponding first-order conditions for the worker’s choice problem encompass the FOCs concerning non-spatial decisions u‘ yðmÞ , ¼ ð1þ tz Þp þ ½ð1 þ tp ðmÞÞcðmÞ þð1 þ tz Þtg f ðmÞ þ yðmÞtðmÞx uz

ð10Þ

u‘ yðmÞ , ¼ rðxÞ uq

ð11Þ

and the FOCs concerning the employment location decision (12) and residential location decision (13) ð1tI Þw0 ðyÞL ¼ ð1 þ tp ðmÞÞCðmÞð1þ tz Þtg FðmÞyðmÞTðmÞ þ tI d; ð12Þ ½ð1þ tp ÞcðmÞ þ ð1 þ tz Þtg f ðmÞ þ yðmÞtðmÞz r ðxÞ ¼  q 0



½ð1 þ tp ÞCðmÞ þ ð1þ tz Þtg FðmÞ þ yðmÞTðmÞtI dD , q

ð13Þ

where

yðmÞ ¼

ð1tI ÞwðyÞL½ð1 þ tp ÞCðmÞ þ ð1þ tz Þtg FðmÞtI dX Lþ TðmÞX

ð14Þ

is the VOT of a worker facing commuting distance X. Eliminating the distortion in the leisure-housing decision (11) requires deductions to neutralize all taxes in the VOT, hence, tI dX ¼ tI wðyÞL þ tp CX þ ð1 þ tz Þtg FX. This allows neither to eliminate the distortions in the leisure-consumption decision (10) nor to eliminate the distortions in the spatial location decisions (12) and (13). The FOCs also show that the way in which deductions are financed is important because each tax enters the FOCs in another way. 2.3. Tax deductions, tax funding and the VOT Next we focus on the VOT as a crucial variable concerning the workers’s individual decisions. The VOT represents the (average) net return to labor as well as the opportunity costs of time. Therefore it provides a link between labor supply and location decisions, two of the features we integrate in our approach. Deriving the impact of a revenue neutral change in the deduction rate on the VOT also requires to consider the effect of the tax instrument used for funding deductions. Differentiating (14) with respect to the tax deduction rate (given prices) yields  dy tI X @y dth  @y dy @y dx ¼ þ h þ þ , ð15Þ dd Lþ TðmÞX @t dd x,y @y dd @x dd |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} direct effect

funding effect

relocation effects

system of FOCs. We refrain from doing this and focus on the funding effect in the following. Calculating the funding effect gives  @y dth  1 ¼ L þTðmÞX @th dd x,y 8 > dtI > > ½wðyÞLdX > > dd > > > > dtz > > g > t FðmÞX > > dd > > < dtp  CðmÞX > dd > > > > dtz > > ½CðmÞ þ tg FðmÞX > > > dd > > > > dtg > z > t ÞFðmÞX ð1þ : dd

if dtz , if dtp ,

ð16Þ

if dtz , tp ¼ tz , if dtg :

According to (16) each tax discussed affects the VOT negatively.13 There is, however, a remarkable difference between income and other taxes. While the funding effect is negative and proportional to commuting distance X for sales tax ðdtz ,dtp Þ and energy tax funding ðdtg Þ, the impact of commuting distance in the case of income tax funding ðdtI Þ is positive. The reason for the latter is that tax deductions depend on the marginal income tax rate. As a consequence, income tax funding favors longer commuting trips while the other funding schemes punish longer commuting trips. Accordingly, ceteris paribus urban sprawl14 and congestion are expected to be more pronounced with income tax funding than under other policies. However, with income tax funding there is a further effect, wðyÞL, independent from commuting distance. This effect lowers the VOT to a relatively large extent compared with the commuting distance dependent effects under the alternative funding schemes. But since a lower VOT discourages labor supply and, in addition, favors slower travel modes such as walking, the effects on urban sprawl, congestion and emissions are in fact ambiguous. Furthermore, the effects of sales and energy tax funding depend on the travel mode chosen. The higher the gasoline usage the stronger the adverse effects on the VOT imposed by energy tax and sales tax funding. This provides an incentive for commuters to diminish these adverse effects by switching to alternative, i.e. less gasoline intensive travel modes, such as walking or public transport. As this lowers emissions and congestion it improves welfare. The magnitude of the funding effect also depends on the degree of change in the respective tax rate. This, in turn, depends on the tax base and the respective behavior of the household, e.g. travel mode choice. Because there is a tax allowance on income, the income tax rate presumably increases more than other tax rates to finance the same change in the deduction rate. This induces stronger efficiency losses in comparison to funding by other than the income tax. 13

For the case of income tax funding the implies assuming wðyÞLdX 4 0. There is no standardized procedure how to measure urban sprawl. Nechyba and Walsh (2004) point out that a common way to document the presence of urban sprawl is to look first at the evolving relationship of population levels between suburbs and central cities. Anas and Rhee (2006) use changes in the daily average travel time per worker as a measure of sprawl. Ewing et al. (2002) operationalize, or measure, sprawl using several variables that represent different aspects of development patterns (e.g. neighborhood mix of homes, jobs, and services). Brueckner (2000) defines sprawl as an excessive spatial growth of cities while Su and DeSalvo (2008) refer to the decentralization of urban population. We measure sprawl as changes in average commuting distance, the spatial expansion of the urban area and the decentralization of jobs and residences. It should be noted, however, that from an economist’s point of view urban sprawl need not necessarily be faulted as socially undesirable unless market failures distort the operation of forces that cause sprawl such as decreasing transport costs (see Brueckner, 2000 for an excellent discussion). 14

where h A fI,z,p,gg denotes the tax used for funding the subsidy. The first term on the right-hand side represents the direct effect of a change in the tax deduction rate d. An increase in d directly raises the VOT by tI X=½L þ TðmÞX which is the higher the higher the marginal tax rate (the higher the income), and the longer the commuting distance. The second term on the right-hand side is the funding effect accruing on account of changes in tax rates required to finance tax deductions. The third and fourth term on the right-hand side comprise relocations of the places of employment and of residence as a response to the change in deductions and the corresponding change in tax rates. We cannot derive the exact effects without simultaneously differentiating the whole

if dtI ,

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

15

Let us summarize:

 Tax deductions raise the value of time entailing higher labor







supply primarily of high-skilled workers. Unfortunately, this is likely to be attended with more sprawl, more congestion and higher emissions. Tax funding impairs this positive effect on labour supply through lowering the VOT. This, in turn, mitigates the adverse effects of tax deductions on urban sprawl, congestion and emissions. Income tax funding rewards long-distance commuting while the other funding schemes sanction longer commuting trips. However, there is a countervailing effect of income tax funding on the VOT which is independent from commuting distance. As a consequence, the net effect on, e.g. congestion is in fact ambiguous. Energy tax funding discriminates against commuting by automobile, sales taxes do it to some degree, too. Hence, both imply less road traffic and, thus, less congestion and emissions.

3. The spatial simulation model 3.1. The general setting The spatial urban computable general equilibrium model we employ is a modification of the model described in Tscharaktschiew and Hirte (2010b, 2012). Here we add an endogenous city fringe to the model required to look at the impact of tax deductions on urban sprawl. The model explicitly takes into account the interactions between different markets (land, labor, commodities), households and firms. All location decisions of households and firms are endogenously determined. Households can vary in idiosyncratic tastes for locations within the urban area such that decisions of households create mixed land use and various possible travel patterns. Hence, the endogenous spatial structure is not restricted to the assumption of a monocentric city. This allows the reflection of employment decentralization that characterizes today’s urban areas (see Anas et al., 1998). The metropolitan area encompasses I¼9 zones (locations), where the innermost zone i¼5 is assumed to be the city center.15 All zones have a length of di ¼ 4:5 km (km) so that the whole urban area expands over 40.5 km. The zones 3–7 shape the city of the complete circular urban area while zones 2 and 8 (1 and 9) form the surrounding inner (outer) suburbs. In each zone i ðiA IÞ there is a given homogeneous land area, Ai , available for residences, establishments (firms) and roads. Supply of land increases with distance from the city center. The urban locations are linked via a transport network with distance dij between the center of the zones.16 It is assumed that the urban economy is closed in the sense that the total population in the urban area is fixed and exogenously given. Hence, there is no interurban migration and utility levels of households are endogenous. There are two main household types in the urban economy: non-working households and working households characterized by skill level h ðhA HÞ. In the latter case, each household encompasses one working member. Households with working members are differentiated in regard to the exogenously given skill levels of their members either as 15 Note that due to accessibility advantages the innermost zone of the city will in fact endogenously become the city center where, e.g. land rents are higher compared with other locations. 16 To simplify matters it is assumed that there is no spatial differentiation within a zone. Instead all individuals traveling within a zone face the same travel distance to reach a destination within a zone.

Fig. 1. Income taxation scheme Germany (Tariff 2009, see EStG, 2009).

low-skilled or high-skilled households. Households decide where to reside, where to work (working HH), where and how much to shop, how much labor to supply and, thus, how often to commute (working HH), how much land to rent, and which travel mode to use. All these decisions are endogenously determined and implicitly determine commuting and shopping trip distances, frequencies and, along with travel speeds, travel times. Concerning consumption it is assumed that residents have a preference to go shopping at different locations implying that there is spatial product differentiation. Households face monetary travel cost and opportunity cost of travel time. They maximize utility subject to a monetary budget and a time constraint (similar to (8) and (9)). Income is taxed according to Germany’s progressive tax tariff (see Fig. 1), where commuting expenses are deductible. The average tax rate increases with an increase in taxable income. Basically the treatment of tax deductibility of commuting expenses is implemented as it is applied in Germany. This means it is taken into account that the individual taxpayer could also deduct a general employee tax allowance (see also the parameter P in the theoretical model) from the income tax base ð920 h=yearÞ as long as this allowance exceeds aggregate commuting and further noncommuting expenditures.17 Travel mode choice, where tm A fwalking,public transport, automobileg denotes the travel modes available for trips in the urban area, is endogenously determined (see Appendix A.1). Individual automobile travel causes congestion (travel time delays), gasoline consumption, and CO2 emissions. Empirically derived functional relationships (see Appendix A.2) specify automobile travel times, gasoline consumption and CO2 emissions per vehicle km which are a function of traffic congestion and, thus, endogenously determined.18 All in all, since location and travel decisions are endogenous urban residents may therefore respond to commuting subsidies in a variety of ways affecting, in turn, congestion and emission externalities. A sufficiently large number of firms produce in each zone i zone specific commodities/services by applying a Cobb–Douglas technology that combines land and labor supplied by low-skilled and high-skilled workers. Within each zone there is competition

17 Consequently, this treatment allows to account for the fact that commuters whose residential and employment locations are close to each other could actually not directly benefit from higher tax deductions up to a certain deduction level because in such a case aggregate deductible commuting and (non-commuting) expenses do not exceed the general employee tax allowance. The reason is that a rational taxpayer would apply the general employee tax allowance which is not related to commuting distance traveled. 18 This implies that gasoline consumption per vehicle km is (indirectly) related to population density due to its dependency on the traffic flow–road capacity ratio.

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G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

implying price taking behavior of firms which sell their products/ services at the competitive mill price (see Appendix A.3). The federal government levies progressive income taxes, sales taxes and energy (gasoline) taxes, grants tax deductions to commuters and income transfers to non-working households and redistributes – according to fiscal interdependencies among public authorities in Germany – shares of its revenues to the local urban government. The federal tax revenues not redistributed to the urban private households and the city government are used for public consumption consisting of purchasing locally produced commodities. The city government receives its shares of federal tax revenues and levies a local lump-sum tax to finance local goods such as roads. Infrastructure costs consist of opportunity costs due to land used for infrastructure. Absentee landowners use their rent income and an external transport sector monetary travel costs (except for travel-related taxes) accruing from urban travel activities to purchase urban commodities. At spatial urban general equilibrium, endogenous land rents,19 wages and commodity prices clear the spatially differentiated markets for land, low-skilled labor, high-skilled labor and commodities (see Appendix A.4). A typical working household faces the following decision: given a feasible combination of residential location i and working location j ðj A IÞ the household decides on demand for commodities (shopping), housing and leisure. The household then chooses its utility maximizing home and work location, i.e. the preferred location within its location choice set fi,jg given utility attached to fi,jg derived from consumption/leisure choices as well as idiosyncratic tastes reflected by a stochastic utility component.20 Except for the fact that there is no decision concerning the place of work, non-working households face an equivalent decision problem, depending on the specific location choice set fig.21 3.2. Utility maximization Depending on residential location i and working location j (only working households), urban households derive utility from consumption zijk in shopping location k ðk A IÞ, lot size qij (m 2 ) as an approximation for housing, and leisure ‘ij (h). The random utility function of a typical low-skilled ðh ¼ 1Þ or high-skilled ðh ¼ 2Þ working household facing location choice set fi,jg is !1=Z I X Z ðzijk Þ þ b ln qij þ g ln ‘ij þ eij , ð17Þ U ij ¼ uij þ eij ¼ a ln k¼1

where 0 o a, b, g o 1, a þ b þ g ¼ 1.22 The idiosyncratic taste constant eij represents the stochastic part of the random utility function and varies among the households for each location choice set fi,jg. The shopping subutility function for visiting different shopping locations over a certain period of time is represented by a CES utility function. The working head of the household residing in location i, working in location j, travels from zone i to (every) zone k to purchase the composite commodity zk produced and sold there, taking into account full economic shopping costs in the whole urban area, i.e. the commodity price plus monetary travel cost and opportunity cost of travel time. The constant elasticity of substitution 1=ð1ZÞ, Z o 1 (Dixit and Stiglitz, 1977) reflects spatial taste variety in shopping. We further assume that separate 19 Except for the outer suburbs where land rents are fixed while the city fringe is endogeneous. 20 But note that both decisions are in fact made simultaneously. 21 Therefore we focus on the decision problem of the working population group hereafter. 22 The utility function of non-working households is the same, where the location choice set is restricted to fig.

trips are made to each production (shopping) zone, purchasing/ consuming one unit of the local good/service per trip. Hence, we ignore trip chaining. The monetary budget constraint and the time constraint of a typical urban worker facing location choice set fi,jg are similar to (8) and (9), where monetary travel costs cij and travel times tij from zone i to zone j are determined as expected values over the available travel modes tm (see Appendix A.1). Taxable income is whj LDij þRmax½P; U þ ddij Dij . Hence, from a worker’s perspective the income tax deduction rate d is only relevant if deductible commuting expenses per year, ddij Dij , plus other work related expenses, U,23 exceed the general employee tax allowance P. In contrast to a typical working household, non-working households receive transfer income from the federal government, e.g. pension benefits. Their time endowment E can be allocated to leisure and traveling. 3.3. Location decision Given optimized spatial consumption (shopping) patterns, housing demand and leisure demand, the household compares (indirect) utility U~ ij associated with all location choice sets fi,jg and chooses the most preferred combination of locations, taking into account his idiosyncratic tastes eij . Because these tastes are stochastically distributed among households for each fi,jg, the probability of a household to choose the specific location choice set fi,jg is Cij ¼ Prob ½U~ ij 4 U~ ij~ ,8i~ a i ¼ Prob½u~ ij þ eij 4 u~ ij~ þ eij~ , 8ij~ a ij, where Cij is the probability that a randomly selected household most-prefers the location choice set fi,jg. Assuming that each eij is independent and identically Gumbel distributed 2 (i.i.d.) with pffiffiffi mean zero, variance s and dispersion parameter L ¼ p=ðs 6Þ, the choice probabilities are given by the multinomial logit model24: expðLu~ ij Þ : PI ~ a¼1 b ¼ 1 expðLu ab Þ

Cij ¼ PI

ð18Þ

In (18) the dispersion parameter, L, is important (Anas, 1990).25 At one extreme, as L-1 ðs-0Þ, there is taste homogeneity since taste idiosyncrasies vanish and all households (of the same type) choose identically. In this case, the Cij corresponding to the highest u~ ij approaches one and all others converge to zero. At the other extreme, as L-0 ðs-1Þ, there is infinite taste heterogeneity since idiosyncrasies swamp the deterministic and systematic part of utility and households choose randomly ðCij ¼ 1=I2 Þ. 4. Model calibration The model calibration ensures that the benchmark city found as the result of the basic simulation exhibits

 a representative household composition (e.g. the relative shares of low-skilled and high-skilled workers),26 23 For example expenditures caused by a double housekeeping or expenditures for work related clothing. 24 See, e.g. Train (2003) who provides a discussion on the properties of the logit probabilities. 25 The location choice probabilities of non-working households are P Ci ¼ expðLu~ i Þ= Ia ¼ 1 expðLu~ a Þ. 26 The total number of households in the urban area is assumed to be 1.75 m. In 2007 in Germany, the share of households with adult working age persons (the economic head of the household is at 18–65 years of age) amounted to about 70% (Federal Statistical Office, 2009). Assuming that a percentage of 5 of all households with adult working age persons is actually not working, the number of working households 1,163,750. Accordingly, the number of non-working households amounts to 586,250. The percentage of high-skilled workers – reflecting an educational attainment achieved by studying at universities of applied sciences

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

17

Table 1 Some results of the benchmark compared with empirical evidence. Average (over all locations and persons) Gross wage ðh=hÞ Gross wage (h/h) Average income tax rate (%) Work days (days/year) Percentage commuters (commuting distance o 10 one-way km) One-way commuting distance (km) Ratio shopping trips/commuting trips Share travel costs on disposable income VOT vs. gross wage/net wage Number of jobs in i Job–Housing–Balance Number of workers residing in i

[1] [2] [3] [4] [5] [6] [7] [8] [9]

Urban area City

Suburb/City



Empirical evidence

Source

19.23 19.56 20.6 219 55 12 1.29 0.09 52%/77% 0.75/1.37

20.04 (Germany 2007) 19.26 (Berlin 2007) 20.3 (2004) 215–223 (2004) 52 (2004) 12–13 1.32 (2002) 0.10 47%/78% 0.87/1.54 (Hannover)

[1] [1] [2] [3] [4] [5] [6] [7] [8] [9]

0.79/1.33 (Hamburg) 0.86/1.39 (Munich) 0.89/1.56 (Stuttgart)

[9] [9] [9]

¨ Arbeitskreis Volkswirtschaftliche Gesamtrechnungen der Lander (2009). Federal Statistical Office (2008b). IAB (2005). Federal Statistical Office (2005). Federal Ministry of Transport, Building and Urban Affairs (2009). Federal Ministry of Transport, Building and Urban Affairs (2004). Federal Statistical Office (2009). Small and Verhoef (2007)/De Borger and Van Dender (2003). Siedentop (2007).

 economic characteristics (e.g. rents, wages, incomes, income 

Urban model

tax rates, federal tax revenues), travel characteristics (e.g. modal split, relative importance of trip purposes, travel demand elasticities, average commuting distances and average automobile travel speeds, average gasoline consumption (fuel economy) and CO2 emission per vehicle kilometer) and spatial patterns (e.g. residential and employment densities,27 job-housing-balance,28 the share of urban land allocated to roads29)

which are representative for an ‘average’ German metropolitan area. A detailed description of the calibration including the chosen parameter values and the results of the benchmark simulation can be found in Tscharaktschiew and Hirte (2010b). Here we only list selected benchmark results and repeat a comparison of some benchmark results with empirical evidence (see Table 130) suggesting that there is an appropriate fit of data. Moreover, we computed, based on the benchmark calibration, general equilibrium long run travel demand elasticities to make sure that they are in line with the empirical literature. Travel demand is measured as the total distance traveled by all residents per year with the respective travel mode (see Table 231). (footnote continued) or a common university as well as advanced degrees (e.g. PhD) – is assumed to be 20% compared to a percentage of 20.5 in Munich, 17.5 in Frankfurt/Main, 20.9 in Stuttgart, or 20.3 in Dresden (Stadt Frankfurt/Main, 2009). 27 In the benchmark urban area population as well as employment densities endogenously peak in the city center and decrease with distance from the center as observed in real urban areas. 28 The benchmark urban economy reflects a realistic spatial pattern regarding the job-housing-balance which is defined as the ratio of the number of jobs in a specific location to the number of employees residing in that location. According to evidence cited by Siedentop (2007) the job-housing-balance exceeds unity for central cities and falls short of unity in the suburbs which is fully in line with the spatial pattern of the benchmark city. 29 The total land area allocated to roads amounts to 15.3% in the model benchmark city (zones 3–7). For comparison, for example in the city of Berlin (Munich), the share of land area allocated to roads amounted to 15.3 % (17.2%) in 2007 (Berlin: Federal Statistical Office, 2008a; Munich: Statistical Office Munich, 2009). 30 This table is reproduced from Tscharaktschiew and Hirte (2010b). 31 This table is taken from Tscharaktschiew and Hirte (2010b).

Using these data and travel demand elasticities the main results of the benchmark equilibrium simulation are reported in Table 3.32

5. Simulation and results 5.1. Research design Our research design is as follows: we vary the deduction rate in the range of 0:0 r d r1:3 h=km. The benchmark level is 0:30 h=km. This implies that we consider an upper ceiling of the tax deductibility rate which, on the one hand, exceeds monetary commuting costs but, on the other hand, falls below full economic commuting costs (see Table 4). We implement four scenarios differing in the way tax deductions are financed:

 Policy 1 (income tax funding): varying the (marginal) income tax rates,

 Policy 2 (general sales tax funding): adjusting the sales tax rate  

holding constant the reduced sales tax rate on public transport, Policy 3 (energy tax funding): adjusting the energy tax rate, Policy 4 (multiple sales tax funding): adjusting, first, the reduced sales tax rate on public transport (holding the general sales tax rate fix) and, then, adjusting the general sales tax. If deductions are raised the reduced sales tax rate is incrementally increased until it reaches the level of the general sales tax rate, then both tax rates are raised together. If deductions decline the reduced sales tax rate is incrementally lowered until zero, then the general sales tax rate is additionally lowered.

Policies 2, 3 and 4 also constitute a change in the tax base away from income to consumption and energy taxation. We distinguish two scenarios concerning the adjustment of the sales tax rate.

32

This table is taken from Tscharaktschiew and Hirte (2010b).

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G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

Table 2 Travel demand elasticities. Elasticity

Urban model

Empirical evidence

Source

Own-price elasticity of travel demand for private automobile with respect to gasoline price

 0.2

Own-price elasticity of travel demand for public transport with respect to transit fare

 0.7

Cross-price elasticity of travel demand for public transport (tram) with respect to gasoline price

þ 0.3

(  0.1) to (  0.3)  0.3  0.2 (  0.1) to (  0.5)  0.4 (on average) (  0.5) to (  0.6) (Bus) (  0.4) to (  1.0) (Metro) (  0.1) to (  1.1) (Rail) (  0.0) to ( 0.8) þ0.3 (on average) (þ 0.1) to (þ 0.8) (Range)

[1] [2/4/5] [6/7] [3] [1] [2] [2] [2] [3] [2] [2]

[1] [2] [3] [4] [5] [6] [7]

Small and Verhoef (2007). Goodwin (1992). Oum et al. (1992). Goodwin et al. (2004). Graham and Glaister (2004). Hymel et al. (2010). Steiner and Cludius (2010).

Table 3 Some results of the benchmark simulation. Rents/wages/prices/output/shopping/jobs Zone

Zone 1(9)

Zone 2(8)

Zone 3(7)

Zone 4(6)

Zone 5

Rent ðh=m2 =yearÞ Gross-wage (low-skilled) [h/h] Gross-wage (high-skilled) [h/h] Price ðh=unitÞ Output (million units/year) Shopping [million units/year] Jobs low-skilled Jobs high-skilled

23.19 15.64 33.71 60.12 115.477 49.889 106,377 20,961

27.99 15.29 35.14 67.53 100.294 41.907 106,328 24,201

36.46 14.79 36.50 74.79 87.528 34.806 104,136 26,925

55.94 14.42 37.70 83.11 75.332 27.887 100,828 29,125

171.54 14.13 38.67 100.00 57.926 18.497 95,662 30,326

Private households

Working HH (low-skilled) Working HH (high-skilled) Non-working HH

Disposable income [h/year] 26,590–27,427 54,128–55,684 22,308

Income tax [h/year] 6136–6624 24,190–25,499 4807

Time allocation

Work days (Commutes)

Travel (h/year)

Leisure (h/year)

Working HH (low-skilled) Working HH (high-skilled) Non-working HH

207–219 243–252 –

460–536 403–467 215–303

2289–2307 2081–2105 4197–4285

Public household (total federal tax revenues) Tax

Income tax

Sales tax

Energy tax

Sum

[1000 million h=year] Share

14.514 0.541

11.862 0.442

0.432 0.017

26.808 1.000

Gasoline consumption (automobile) Zone Zone specific (liters/100 vkm) Urban area average Total urban area

Zone 1(9) Zone 2(8) 6.6 6.8 8.3 l/100 vkm 664.817 million liters/year

Zone 3(7) 7.0

Zone 4(6) 8.1

Zone 5 15.6

Zone 1(9) Zone 2(8) 154 (39) 160 (40) 195 (49) gCO2 =vkm 1,555,673 (388,918) tCO2 =year

Zone 3(7) 165 (41)

Zone 4(6) 189 (47)

Zone 5 365 (91)

CO2 emissions (automobile) Zone Zone specific (g/vkm) Urban area average Total urban area

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

19

Table 3 (continued ) CO2 emissions (public transport) Urban area average Total urban area

72 gCO2 =pkm 362,825 tCO2 =year

CO2 emissions (total) Total urban area

1,555,673þ388,918 þ 362,825¼2,307,416 tCO2 =year

Table 4 Average (full economic) commuting cost (benchmark). Commuting cost component

Urban worker Low-skilled

Monetary commuting cost (h/round-trip km) Commuting time cost (h/round-trip km) Full economic commuting cost (h/round-trip km)

High-skilled

0.73 0.88 1.61

1.00 1.20 2.20

Table 5 Spatial effects of different tax deduction rates under different funding schemes. Tax deduction rate ðh=kmÞ

Income tax funding Average commuting distancea (%) Suburban expansion (km2)/(%) Spatial allocation of residences and jobs Residences in the cityb (total)/(%) Jobs in the cityb (total)/(%) General sales tax funding Average commuting distancea (%) Suburban expansion (km2)/(%) Spatial allocation of residences and jobs Residences in the cityb (total)/(%) Jobs in the cityb (total)/(%) Energy Tax Funding Average commuting distancea (%) Suburban expansion (km2)/(%) Spatial allocation of residences and jobs Residences in the cityb (total)/(%) Jobs in the cityb (total)/(%) Multiple sales tax funding Average commuting distancea (%) Suburban expansion (km2)/(%) Spatial allocation of residences and jobs Residences in the cityb (total)/(%) Jobs in the cityb (total)/(%)

0.0

0.6

1.2

 1.8  2.2/  0.24

þ1.5 þ1.3/ þ 0.14

þ5.4 þ2.8/ þ 0.32

þ 1595/þ 0.2 þ 633/þ 0.1

 1486/  0.2  392/  0.1

 4131/  0.6  1408/  0.2

 1.8  3.3/  0.37

þ1.5 þ4.2/ þ 0.47

þ4.7 þ12.4/ þ1.39

þ 1916/þ 0.3 þ 633/þ 0.1

 2223/  0.3  366/  0.1

 6412/  0.9  1223/  0.2

 1.8  3.4/  0.39

þ1.5 þ4.6/ þ 0.52

þ5.4 þ13.8/ þ1.55

þ 1971/þ 0.3 þ 698/þ 0.1

 2378/  0.3  554/  0.1

 6997/  1.0  1996/  0.3

–0.9  1.8/  0.20

þ0.6 þ1.5/ þ 0.17

þ3.9 þ9.6/ þ 1.08

þ 1155/þ 0.2 þ 369/þ 0.1

 949/  0.1 þ95/0.0

 5067/  0.7  720/  0.1

Changes in relation to the benchmark. a b

Averaged over all travel patterns and workers. Gains (losses) of the city ¼losses (gains) of the suburbs.

Raising the general sales tax rate but holding the reduced tax rate constant, i.e. Policy 2, implies additionally a raise in the subsidy to public transport. In contrast, raising the reduced sales tax rate on public transport until it reaches the level of the general sales tax rate i.e. Policy 4, also implies a reduction in the subsidy to public transport.

5.2. Spatial and economic effects 5.2.1. Spatial effects Starting with spatial effects, Table 5 displays the results for three selected levels of the tax deduction rate. The results are shown as changes compared to the benchmark level.

20

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

Fig. 2. Effects of tax deductibility of commuting expenses on commuting trips.

Fig. 3. Effects of tax deductibility of commuting expenses on congestion.

The general pattern is in accordance with intuition. Abolishing tax deductions lowers average commuting distances and causes an incremental shrinkage of the city as well as a decline concerning suburbanization of residences and jobs. Raising the commuting subsidy induces diametrical effects which are, however, surprisingly small. A doubling of the deduction rate from currently 0:30 h=km to 0:60 h=km leads to a very small increase in the average commuting distance of only 0.6% to 1.5%. An increase to 1:20 h=km, after all an increase by 300% compared with the initial level, increases the average commuting distance by at most 5.4%. Also very small is the percentage change in the city size. The urban area increases by 0.14% to 0.52% as a response to a doubling of the deduction rate. This is very small in comparison with the results of Su and DeSalvo (2008) who found much higher effects for car subsidies in the U.S. (an elasticity of about 0.1). One reason for this weak impact in our study is that funding subsidies provokes a countervailing raise of the tax rate used for funding. Another reason is that shopping trip costs do hardly change by commuting subsidies. Furthermore, we consider different types of individuals where non-working households do not receive commuting subsidies and low-skilled workers face only a small subsidy on account of their low marginal wage tax rate. Given that, abolishing commuting subsidies is not an instrument to lower urban sprawl substantially. The gross effects on residential and job relocation are also relatively small. Even raising the tax deduction rate to 1:20 h=km prompts at most 7000 workers or a percentage of around unity to relocate from the city to the suburbs. These findings query the standard objection against commuting subsidies, namely, that they are an important cause for suburbanization. Accordingly, abolishing the tax deduction rate of commuting expenses is not a very effective device to reduce sprawl or commuting distances.

income tax is used to finance subsidies. In this case (curve with rhombuses in Fig. 2), aggregate labor supply and commuting do hardly change if the subsidy rate increases. Despite this relatively small effects on aggregate labor supply, there are strong changes in congestion and, more important, even different signs of the effects. Fig. 3 displays the changes in congestion costs for different subsidy levels and different taxes used for funding. All changes are printed as percentage changes compared with the benchmark ðd ¼ 0:30 h=kmÞ. With income tax funding (curve with rhombuses, Policy 1) and general sales tax funding (curve with triangles, Policy 2) a reduction of the deduction rate reduces while an increase aggravates congestion. The changes range from a reduction of 2% to an increase by about 5% and 8% if the deduction rate achieves its upper ceiling, thus the increase is slightly stronger with consumption tax funding. Congestion accumulates faster than aggregate commuting trips. Raising incomes when commuting subsidies are increased also raise the number of shopping trips. Moreover, an increase in tax deductions causes the VOT to increase which in turn favors mode choice toward faster travel modes such as automobile contributing the most to congestion. Recall that Policy 4 (curve with circles) implies abolishing the advantage for public transport if the commuting subsidy is raised and expanding the subsidy to public transport if the tax deduction rate is lowered. The first change boosts automobile usage and, thus, aggravates congestion. The second change shifts demand toward public transport and mitigates congestion. These effects explain the strong change in congestion around the benchmark level of the tax deduction rate. The most interesting result is Policy 3 (curve with squares). Because the energy tax constitutes a tax mainly on automobile usage, reducing the tax more than offsets the positive effect of a lower deduction rate on congestion. Therefore congestion exacerbates. In contrast, road congestion strongly declines if the energy tax rate is raised for funding higher tax deduction rates because more and more residents switch their travel mode choice toward public transport.33 Consequently, all road users still using private cars now benefit from a reduction in congestion, i.e. they benefit from lower travel times and higher fuel economy (lower gasoline consumption).34 For example, doubling the deduction

5.2.2. Aggregate labor supply and congestion Fig. 2 displays changes in the number of aggregate commuting trips which, due to the complementarity of commuting trips and working days, is proportional to changes in labor supply. Abolishing tax deductions reduces commuting trips and labor supply by about 0.5%, while a raise of the deduction rate increases both. Doubling the deduction rate from 0:30 h=km to 0:60 h=km raises labor supply by about 0.5% in case of energy tax and general sales tax funding. Policy 2 and Policy 3, as well as Policy 4 (though to a smaller degree) shift the marginal tax burden from labor to consumption. Consumption and shopping trips are, therefore, getting relatively more expensive in comparison to commuting trips and labor supply. For this reason commuting and labor supply increase. This effect, however, almost vanishes if the

33 Note that in Germany the right to deduct commuting expenses from the income tax base is independent from travel mode choice. 34 Recall the U-shaped character of the gasoline consumption function (A.4). Generally, a reduction in congestion (higher travel speeds) could also imply an increase in gasoline consumption. On the city level, however, travel speeds are relatively low such that an increase in travel speed implies a reduction in gasoline consumption (per vehicle kilometer).

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

Income Tax Funding

21

General Sales Tax Funding

500

8%

500

8%

400

6%

400

6%

4%

300

4%

300

2%

2%

200

200 0%

0% 100

-2%

0

100

-2%

-4%

0

-4%

-100

-6%

-100

-6%

-200

-8%

-200

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.0

0.2

Income tax deduction rate [€/km]

0.4

0.6

0.8

1.0

1.2

Income tax deduction rate [€/km]

Energy Tax Funding

Multiple Sales Tax Funding

500

8%

500

400

6%

400

4%

300

2%

200

A

1

B

2

8%

C

6% 4%

300

2% 200 0%

0% 100

-2%

0

-4%

-100 -200 0.0

-8%

0.2 0.4 0.6 0.8 1.0 Income tax deduction rate [€/km]

100

-2%

0

-4%

-6%

-100

-8%

-200 0.0

1.2

-6% -8% 0.2

0.4

0.6

0.8

1.0

1.2

Income tax deduction rate [€/km]

CO2 emissions (right axis) Urban Welfare [million €/year] (left axis)

Absentee Landowners [million €/year] (left axis)

Multiple Sales Tax Funding: A: General sales tax funding with full sales tax exemption of public transport fares 1: General sales tax rate = 0.19 and full sales tax exemption of public transport fares B: Funded by a higher/lower sales tax on public transport fares with sales tax rate on general consumption = 0.19 2: Full sales tax on public transport fares and general consumption (uniform sales tax rate = 0.19) C: Sales tax funding (uniform higher sales tax rate (> 0.19) on public transport fares and general consumption)

Fig. 4. Aggregate welfare effects of tax deductibility of commuting expenses.

rate reduces congestion by about 10% where the effect is nonlinear. As a result, reducing congestion implies that more time is available for labor and/or leisure and a higher share of disposable income is available for, e.g. general consumption (because gasoline expenditures decline35). To summarize, a high deduction rate funded by an increase in the energy tax discriminates in favor of public transport usage and imposes the strongest positive effect concerning congestion while the other policies increase the congestion externality. 5.3. Aggregate welfare and environmental effects Fig. 4 displays the aggregate welfare effects measured by the equivalent variation (left axis) as well as changes in travel related CO2 emissions (right axis). Urban welfare is printed as the solid dotted lines and welfare of absentee landowners by the dashed lines with dots. The solid lines with triangles depict changes in CO2 emissions.

0:90 h=km which is larger than the current rate.36 However, the welfare gains achievable are at best about 70 mh or about 40 h per household and year on average. Abolishing tax deductions lowers welfare by about 60 mh. There are opposite effects present. On the one hand, the net reduction of income taxes for commuters occurring if deductions are increased lowers the taxation of productive time use (see Kleven, 2004). This raises welfare. On the other hand, the increase in tax deduction rates implicitly lowers the taxation on the externality and, thus, lowers welfare (see Sandmo, 1975). A comparison with absentee landowners shows that gains and losses are also capitalized in rents, as the similar run of the curves indicates. The effects on travel related CO2 emissions are small. Even a shift of the deduction rate to 1:30 h=km raises CO2 emissions only by about 3% in comparison to the benchmark, whereas abolishing tax deductions lowers CO2 emissions only by about 2%.

5.3.1. Income tax funding (Policy 1) Income tax funding of commuting subsidies is the case usually discussed in the literature. Concerning this policy the upper left panel of Fig. 4 reveals that the optimal deduction rate is around

5.3.2. General sales tax funding (Policy 2) Funding tax deductions by general sales taxes induces the same sign but stronger effects than income tax funding (see the upper right panel of Fig. 4). Abolishing tax deductions lowers welfare twice as strong as compared with income tax funding. An increase in tax deductions implies a much stronger and almost

35 But note that the ‘‘rebound-effect’’, i.e. lower expenditure for gasoline per vehicle km due to higher fuel economy increases travel demand, constitutes a countervailing effect that works against the gasoline expenditure saving.

36 If the urban fringe were exogenous the optimal deduction rate is smaller ð0:50 h=kmÞ but, nevertheless, higher than the benchmark level (see Tscharaktschiew and Hirte, 2012).

22

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

Fig. 5. Aggregate distribution effects of tax deductibility of commuting expenses.

linear increase in welfare. At a deduction rate of 1:00 h=km welfare improves by about 430 mh. Because this policy induces a relative reduction of distortionary labor taxation it constitutes a shift toward stronger taxation of time used nonproductively. This also slightly dampens the negative effect of the deductions on congestion by raising the full economic travel cost of shopping. Because of the similar pattern in regard to changes in congestion the effects on CO2 emissions are almost the same as in the case of income tax funding.

5.3.4. Multiple sales tax funding (Policy 4) The trends are the same than with consumption taxes. However, the strong impact on congestion caused by changes in the sales tax on public transport implies that welfare effects around the benchmark level differ from the welfare effects with general sales tax funding. In particular, a local welfare maximum is reached at a deduction rate of 0:22 h=km and a global minimum at the deduction rate of 0:41 h=km. Also with respect to this funding procedure effects are capitalized into land rents but the effect is less distinctive.

5.3.3. Energy tax funding (Policy 3) The results regarding energy tax funding are displayed in the lower left panel of Fig. 4. Abolishing tax deductibility diminishes welfare, which is almost the same compared with sales tax funding. The gains from raising deductions are higher compared to those accruing under income consumption tax funding. Taxing gasoline taxes nonproductive use of time (e.g. travel) and, in addition, imposes a stronger taxation on the congestion externality implying positive effects on urban welfare (see the discussion concerning policy impacts on congestion in Section 5.2.2). The most outstanding result is that this policy is the only one considered which achieves a strong reduction concerning CO2 emissions, while the other policies entail a raise in emissions. The reduction mainly stems from, first, a switch in travel mode choice away from emission intensive automobile road traffic and, second, a reduction in congestion and associated with this lower automobile emissions per vehicle kilometer.

5.4. Aggregate distribution effects Fig. 5 displays distribution effects based on aggregated equivalent variations of the different household groups.37 In each scenario the non-working households (dashed curves) benefit from a decrease and suffer from an increase in the deduction rate. First, they also contribute to financing the commuting subsidy and second, they also suffer from congestion, even though to a smaller extent than working city residents. The dotted lines in Fig. 5 represent the equivalent variation of low-skilled households. In general low-skilled workers benefit 37 Aggregate distribution effects take the relative shares of the calibrated number of the different household types into account. Because the number of urban households differs among the different household types aggregate distribution effects may differ from those accruing on an individual household level basis (see below).

G. Hirte, S. Tscharaktschiew / Transport Policy 28 (2013) 11–27

from commuting subsidies which are – according to the current institutional arrangement of the tax deduction policy in Germany– also granted for public transport usage. Their gains are the lower the stronger their contribution to financing the subsidy and the higher their labor supply is taxed which is the case with income tax funding (Policy 1). Because their relative tax burden is the lowest under energy tax funding they prefer Policy 3. However, with multiple sales tax funding (Policy 4) their benefits and losses around the benchmark deviate from general trends. Here, a reduction of the subsidy to public transport required to finance higher tax deductions adversely affects the low-skilled workers. Welfare changes of the high-skilled workers are printed as solid curves in Fig. 5. They are very differently affected depending on the funding scheme. Income tax funding (Policy 1) makes them worse off because this directly taxes their labor supply and counteracts the positive effect of the deductibility (see also (16)). Their tax burden is the lowest with sales tax funding (Policy 2). With energy tax funding (Policy 3), however, two opposite effects are at work. While they benefit from a reduction in congestion they suffer from the stronger taxation of automobile travel. Because of the fact that the congestion externality decreases with an increase in gasoline taxation the first effect is relatively strong close to the benchmark level, whereas the latter effects is predominant for higher deduction rates implying a decline in welfare. To summarize: from the perspective of the non-working households the best policy is a deduction rate of about 0:18 h=km together with a stronger subsidy on public transport (multiple sales tax funding). The low-skilled workers as a whole are better off with energy tax funding and higher deductions and the group of high-skilled workers as a whole gains the most under general sales tax funding and higher deductions. 5.5. Acceptance of policies An individual worker is probably more concerned with changes in his relative wealth as well as in his individual payoffs in comparison to other income groups. This will be important concerning his acceptance of policies. Therefore we also consider the equivalent variations of different groups in per capita terms to gain an insight into the level of acceptance of different policies. Of course, the inhabitants of the metropolitan area cannot decide on federal policy. Nonetheless, metropolitan areas might lobby in favor of one of those policies. Three large cities are even able to vote on such a policy in the Federal Council of Germany (Bundesrat) because they coincide with a German state (Berlin, Hamburg, Bremen). Furthermore, cities’ inhabitants vote on representatives for the German parliament (Bundestag). While aggregate distribution effects imply that higher deductions cause a redistribution in favor of the low-skilled workers, focusing on distribution effects in per capita terms reveals that the high-skilled workers benefit considerably more than the low-skilled with higher deductions by general sales tax or multiple sales tax funding. There is no policy most favored by more than one group of urban households in terms of individual welfare. The non-working households prefer reducing deductions along with multiple sales tax funding, low-skilled workers prefer higher deductions financed by energy taxes, whereas high-skilled workers most favor higher tax deductions financed by general sales taxes. Though, lower skilled workers constitute a small majority (931,000) in comparison to the other households (819,000), they might not be able to push their representatives to vote for this policy. To achieve this it is useful that more than one group agrees on a specific policy. Given that, higher deductions financed by energy taxes or general sales taxes are the two policies

23

unambiguously advantaging both groups of workers in comparison to the benchmark—though the distribution effects are totally different. Unfortunately, because high-skilled workers lose with income tax funding and even with a low level of multiple sales tax funding and low-skilled workers might lose with multiple sales tax funding both groups have to worry if they push a raise in deductions when the funding scheme applied by policymakers is uncertain. If their representatives have to compromise to achieve higher deductions this might be even worse for them than the benchmark. Moreover, if only a small change in tax deductibility is politically feasible, the low-skilled workers might even be better off if deductions are reduced under multiple sales tax funding, though the possible gains per household are less than 100 h=year. These could be the reasons why the current policy arrangement seems to be acceptable by the working households. Even the non-workers might tolerate the current situation because reducing deductions provide them a welfare gain of at most 50 h=year which is only fraction of their yearly income.

6. Discussion and conclusions In this paper we have examined the tax deductibility of commuting expenses by applying a spatial urban general equilibrium simulation model calibrated to an average German metropolitan area. Although there is large body of literature analyzing commuting subsidies or transport subsidies in general, only a restricted number of papers theoretically analyzes commuting subsidies in the form of tax deductions. This paper contributes to the literature by providing for the first time an insight into the magnitude of the effects of tax deduction policies by implementing several institutional details of the German tax system in regard to tax deduction (in particular progressive income taxation). In addition, the approach takes into account the following features that have never been simultaneously treated in a spatial setting when studying tax deduction of commuting expenses: endogenous labor supply decisions and location decisions where the urban area is not restricted to be monocentric, household heterogeneity by considering multiple household types differentiated by skills and employment status, commuting and noncommuting (shopping) trips, different funding schemes, travel mode choice, travel related externalities such as congestion, and feedback effects between urban land, labor and commodity markets. Concerning income tax funding our results suggest that the optimal tax deduction rate in terms of welfare of the inhabitants of the metropolitan area is higher than the current deduction rate in Germany. This rate would then be close to monetary commuting costs needed for a commuting round-trip but would still be far below full economic commuting costs needed for such a trip (see Table 4). However, if negative effects of urban sprawl or higher CO2 emissions and further externalities are taken into account the optimal deduction rate is likely to be lower than calculated here. Moreover, the maximum aggregate welfare gain is very low and amounts to about 50 mh=year (on average about 30 h=year per household). The results also indicate that the tax deduction rate hardly contributes to urban sprawl according to the definition of sprawl used here, regardless of the funding scheme. There is the expected positive relationship (raising the tax deduction rate raises average commuting distance; the spatial expansion of the urban area; and contributes to suburbanization) but the magnitude of the effect is very small—i.e. the response of commuting distance, the size of the urban area, and relocations to suburban areas with respect to a higher tax deduction rate is quite inelastic. Hence, according to

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the simulation results the tax deductibility of commuting expenses is suggested to be of minor importance only with respect to urban sprawl, at least in the case of German cities. Positive effects of tax deductions on labor supply and negative effects on congestion are also very small due to countervailing effects on the VOT accruing under income tax funding. However, one might ask why shall income taxes be used for funding? Usually the reasoning is that income tax deductions shall be financed by income taxes in order to avoid mixing a tax reform (change in the tax base) with a commuting subsidy policy via tax deductions. However, in a spatial world with externalities and other time consuming activities funding subsidies by other taxes could be justified from an optimal tax point of view (see Kleven, 2004; Sandmo, 1975). Therefore, we have also looked at alternative funding procedures. Then the positive labor supply effects of the subsidy can be combined with a less harmful tax on general consumption or energy (fuel). This is equivalent to a change in the tax base in favor of taxing nonproductive time use, e.g. shopping trips, or in favor of taxing externalities, e.g. congestion, caused particularly by road traffic. These are the reasons why using the energy tax for funding (Policy 3) provides the highest urban welfare gain. Moreover, this policy is the only one considered reducing travel related CO2 emissions. Under this policy the high-skilled workers and low-skilled workers gain. In addition, non-working households are hardly affected by this policy. The switch to consumption or energy taxation implies that the optimal deduction rate is beyond our ceiling of 1:30 h=km. In these cases, granting higher deductions indirectly constitutes a tax switch away from labor taxation, usually argued to provide a distinctive potential to raise economic efficiency. But what does this result mean? First, if one wants to examine tax deductions of commuting expenses it is necessary to distinguish different household types, different travel modes, different travel purposes as well as endogenous labor supply and location decisions. This allows to differentiate the properties of different taxes and subsidies which overlap concerning labor supply but are distinct concerning travel mode choice or travel purposes. Second, given the findings of the analyses here further research shall focus on these interrelations of tax deductions and different taxes available for funding. Does our findings really imply that tax deductibility of commuting expenses should be raised to such a high level? Concerning our research design the answer is yes. If, however, the whole tax system is debatable it might be much more promising to directly switch the tax base from income toward energy or consumption accompanied by the abolishment of commuting subsidies. Then, longer commuting distances would not be rewarded and, thus, urban sprawl as well as emissions should be even lower than under the policy arrangement considered here. This, however, is a task for future research. Eventually, two problems should be stressed. First, the findings are preliminary in the sense that the spatial CGE approach is calibrated by looking at some observations only. So, how can we say something on the reliability or robustness of the results? Usually, CGE simulations should be accompanied by a number of sensitivity analyses where important parameter values are varied. In the spatial CGE approach we apply we face the following problem: varying parameters would require to conduct a new calibration and calculate a new benchmark case for each change in a parameter value and, further, many parameters cannot be changed without providing a spatial equilibrium which is far away from a benchmark consistent with data. Because calibration is extremely time consuming in this complex model and because it is also hard to find those parameter values which can be used for sensitivity analysis without generating unrealistic results, we did not perform an extended sensitivity analysis. Instead we put

huge effort into the benchmark calibration to make it more reliable. After calibrating we were able to replicate some important features found in data on German cities. Also, travel demand elasticities we use are in the range provided by empirical studies. This gives us some confidence concerning the findings. Second, the results are found in a specific theoretical model solved by numerical simulations. There are some features which might affect the results, in particular labor supply decisions. For example, adding a combined labor supply decision on working days and on daily working hours might be important. In that case, one might deduce from the work of Gutie´rrez-i-Puigarnau and van Ommeren (2010) and van Ommeren and Gutie´rrez-iPuigarnau (2011) that the effects on travel and congestion should be lower and the stimulus of labor supply via raising daily working time might be higher. Consequently, this could affect the optimal tax deduction rate.

Acknowledgements We are grateful to the anonymous reviewers for their valuable comments and suggestions.

Appendix A. The spatial simulation model A.1. Travel mode choice Individual expected travel costs ciz and travel times t iz for all residents in the urban area depend on the travel mode tm used to travel from zone i to zone z A ½j,k. Let c1,tm be the travel mode specific travel cost rate per km (commuting, shopping) except for gasoline costs and taxes; c2,auto be the (private) automobile gasoline cost per liter; and let c3,tm be other travel mode specific fixed costs, i.e. costs not depending on the distance traveled. Then, aggregate monetary one-way travel costs from zone i to zone z with travel mode tm are38 1,tm ctm diz þ c2,auto  g auto þ c3,tm Þð1þ ttm Þ, iz ¼ ðc iz

ðA:1Þ

where c2,auto ¼ ðpg þ tg Þ. The pure gasoline (producer) price is denoted by pg; the energy tax imposed by the federal government by tg ; and ttm is the sales tax rate depending on travel mode tm. Gasoline consumption (l) for an automobile trip from zone i to auto zone z is denoted by g auto is iz . Note that gasoline consumption g iz endogenously determined, depending on traffic speed which is endogenous as well (see Appendix A.2). Travel times from zone i to zone z are assumed to be exogenous in the case of travel modes tm¼walking and tm¼ public transport. Hence, there is no congestion in public transport (e.g. a tram using a separated train path/corridor). By assuming that an exogenously given specific average speed of travel mode tm is given by v tm (km/h), one-way travel time t tm iz (h) from zone i tm to zone z with travel mode tm is then t tm iz ¼ diz =v . However,

automobile travel times t auto are endogenously determined, iz depending on, e.g. road infrastructure capacity and traffic volume (see Appendix A.2). These travel mode specific one-way travel costs ctm iz and travel times t tm iz can be transformed into traveler specific expected twoway travel costs and travel times which enter the budget and 38 Note that when the specific superscript auto, denoting travel mode tm ¼ automobile, is used in (A.1), then the respective travel cost component applies exclusively to the travel mode automobile.

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time constraint of residents X X tm tm t iz ðtm,F,KÞ ¼ 2 ptm ciz ðtm,F,KÞ ¼ 2 ptm iz c iz , iz t iz , tm

ðA:2Þ

tm

where ptm iz is the probability that a traveler chooses travel mode tm for a trip from zone i to zone z: That means, it is assumed that over a certain period of time, a traveler will choose the available travel modes tm with some probability, depending on utility (derived from full economic travel cost) associated with travel mode tm on relation iz. These mode choice probabilities are computed by using a mode choice model in multinomial logit form.

A.2. Automobile congestion, gasoline consumption and CO2 emission Each commuting and shopping trip in the urban area is associated with travel time and monetary travel costs. Concerning the latter gasoline is only required for traveling by automobile. In addition, emissions of CO2 only accrue by using travel modes other than walking. Automobile travel time, gasoline consumption as well as CO2 emissions are all endogenously determined, depending on traffic speed. In order to determine travel times, gasoline consumptions and CO2 emissions, empirical functional relationships are employed. Before determining relation, i.e. zone-to-zone specific values which enter the budget and time constraints, it is necessary to calculate zone specific travel times, gasoline consumptions and emissions. The individual automobile travel time (h) needed to travel 1 km in zone i is given by the Bureau of Public Roads type congestion function which is extensively used in transport analyses (see e.g. Small and Verhoef, 2007): "  f 2 # Fi t auto ðF ,K Þ ¼ f 1 þf , ðA:3Þ i i i0 1 i Ki where f1, f 2 4 0; fi0 is the inverse of the free of congestion traffic speed; and Fi denotes total automobile traffic flow,39 i.e. traffic demand, traversing zone i. Road capacity Ki in zone i is proportional to Ri , the land allocated to roads in zone i, where K i ¼ wRi ðw 40Þ. The individual consumption of gasoline (l) needed to travel 1 km by automobile in zone i is given by the function (see FGSV, 2002) 2 3 !2 1 1 e4e0 þ e1 auto g auto ðF i ,K i Þ ¼ þ e2 t auto ðF i ,K i Þ5, ðA:4Þ i i 740 t i ðF i ,K i Þ where e0 ¼ 17:7766, e1 ¼ 0:0023606, e2 ¼ 1461:87 are positive and exogenously given constant parameters; 1/740 is the inverse of the assumed gasoline density in grams per liter used to convert gasoline consumption in gram into liter; and e is an exogenously given efficiency parameter used to obtain a reasonable benchmark consumption of gasoline. Due to the fact that the amount of CO2 emissions corresponds with gasoline consumption in a direct way, individual emissions in grams discharged by traveling 1 km by automobile in zone i are 39 Because all location decisions and thus the spatial patterns of travel activities are endogenous, traffic flow Fi traversing zone i is endogenous as well. It can be determined by taking into account the location choice sets along with labor supply and consumption decisions (shopping) of all residents in the urban area where, for the sake of simplicity, it is not focused on trip scheduling issues. The endogeneity of the spatial patterns (and travel mode choice as well) implies that each policy causing adjustments in, e.g. spatial patterns may affect traffic conditions in the urban area.

25

then given by the function 2 3 !2 ef 4 1 auto auto emi ðF i ,K i Þ ¼ e e0 þe1 auto þ e2 t i ðF i ,K i Þ5, 740 t i ðF i ,K i Þ dir

indir

dir

ðA:5Þ indir

where ef ¼ ef þef with ef ¼ 2340 g CO2 =l, ef ¼ 585 gCO2 =l is used to convert gasoline consumption in liters into CO2 emissions in grams. The emission factors efdir and efindir encompass direct and indirect emissions, respectively. Direct emissions accrue from the combustion of gasoline on the road, whereas indirect emissions originate in upstream processes such as the extraction and preparation of gasoline.40 Note that gasoline consumption per vehicle kilometer as well as emissions in zone i depend directly on automobile travel speed 1=t auto ðF i ,K i Þ and thus i indirectly on traffic flow Fi and road capacity Ki.41 Moreover, emissions from public transport are denoted by ASCE, a given average social (indirect) CO2 emission rate (g/passenger km) caused by electrically operated vehicles. Note that, in contrast to automobile CO2 emissions, ASCE does not vary across urban space. This is due to the assumption that public transport is not affected by traffic congestion. Since (A.3)–(A.5) constitute zonal automobile travel times, gasoline consumptions and emissions all per vkm, they must be converted into relation (zone-to-zone) specific measures which enter the budget and time constraint of residents. Using Oi  ftauto ,g auto ,emauto g, one-way automobile travel times, gasoline i i i consumptions and emissions are Oii ¼ di Oi =2 for intrazonal trips P and Oij ¼ ðdi Oi þdj Oj Þ=2 þ j1 ðd O Þ for interzonal trips.42 a ¼ iþ1 a a

A.3. Urban firms Within each zone i competitive firms in the input and output markets employ a Cobb–Douglas production function that combines land and labor to produce the zone specific composite commodities. Each commodity is sold at the zone in which it is produced. Firms producing at the same zone i are identical. Let Mhi be the aggregate labor input of skill level h (h/period) in zone i and let Qi be the aggregate land input in zone i, the production function of the zone specific aggregate output Xi can then be written as follows: fi

X i ¼ Bi Q i

H Y

h

ðM hi Þdi ,

ðA:6Þ

h¼1 h

where Bi is the productivity (scale-) parameter, di is the output elasticity with respect to labor characterized by skill level h, fi is PH h the output elasticity with respect to land and h ¼ 1 di þ fi ¼ 1, 8i A I: Given the production technology, profit maximization P h h maxðMh ,Q i Þ pi ¼ pi X i  H h ¼ 1 wi M i r i Q i in all locations i yields i

40 The indirect emission factor efindir is taken from Fritsche (2007). Considering indirect emission implies that emissions generated by processes required to satisfy transport demand of households are imputed to the households keeping in mind that, in a less local approach, calculating overall emissions may require subtracting those emissions elsewhere in the context of emission inventory (see Satterthwaite (2008) for a discussion of the allocation of emissions). 41 The function was developed by the German Road and Transportation Research Association (FGSV) based on real data. It is used in a standardized Cost-Benefit-Analysis for road infrastructure investment decisions. The crucial point is that the run of the function is U-shaped, that is at low travel speeds gasoline consumption and thus CO2 emissions per vehicle kilometer are high and become higher the lower the speed of travel. As travel speed increases, gasoline consumption and emissions fall until a certain threshold of travel speed, then raising again when travel speed increases further. 42 The first term on the right-hand-side of Oij is divided by 2 because traffic originating and terminating in a zone is assumed to traverse one half of the zone length.

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~ h , 8h A H and Q~ i with the profit maximizing input demands M i corresponding first-order conditions with respect to skill specific h labor di pi X i =M hi ¼ whi and land fi pi X i =Q i ¼ r i , respectively.

The location specific prices of goods/services supplied by firms are determined from the zero profit condition h f Q h di r i H h ¼ 1 ðwi Þ pi ¼ i Q : ðA:10Þ f h dhi Bi fi i H h ¼ 1 ðdi Þ

A.4. Model closure

It states that prices equal marginal (and average) cost since free entry in each zone insures that profit maximizing firms make zero economic (normal) profit in the competitive markets. According to the conditions described above, solving for the spatial urban general equilibrium requires to find land rents, wages, commodity prices, firm outputs, export quantities for each zone i and, based on it, the entire set of endogenous variables (see Table 3) using simulations. We have checked whether the equilibrium conditions are fulfilled, i.e. whether all excess demands equal zero, that the monetary budget constraints as well as the time constraints of all residents in the city and the zero profit condition of all city firms are met. In addition, the uniqueness of the equilibrium was explored numerically. Using a broad range of different starting values, the solution algorithm converges to the same equilibrium.

At spatial urban general equilibrium, the budget constraints of the federal as well as the local urban government must hold. Endogenous land rents, wages and commodity prices clear the spatially differentiated markets for land, low-skilled labor, highskilled labor and commodities. Furthermore, firms in each location must make zero economic profits. In each zone i, market clearing in the local land market requires

C1i N 1 q~ 1i þ

X

h,2 ~ h,2 q ij þ Q~ i þ Ri ¼ Ai : Ch,2 ij N

ðA:7Þ

ðh,jÞ

The left-hand side is the sum of lot size (housing) demands of all non-working households ðN 1 Þ residing in zone i and all working households ðN h,2 Þ residing in zone i and commuting to all employment locations plus land demands of all the firms in zone i plus the land allocated to roads. The right-hand side is the available (developable) land in zone i. Spatial equilibrium in the local labor market regarding skill level h in zone i requires X

h,2

h

h,2 ~ ~ , D ai L ¼ M Ch,2 i ai N

ðA:8Þ

a

The left-hand side is the supply of labor by all workers working in zone i and the right-hand side is the demand for labor by all the firms producing and selling in zone i. In the local market i for the composite commodity, market clearing requires X

X

a

ðh,a,bÞ

C1a N 1 z~ 1ai þ

h,2 ~ h,2 z abi þ EXP i ¼ X~ i : Ch,2 ab N

ðA:9Þ

The left-hand side is the quantity of the composite commodity purchased in zone i by all households who live and work in all the zones in the urban area plus the quantity EXPi of the composite commodity that must be exported to balance payments to economic agents outside the urban economy under consideration. It is assumed that the composite commodity produced in a zone i can be exported at price pi at zero transport costs. EXPi is determined by the ‘balance of payment’. The sum of tax payments to the federal government not redistributed to private households or the city government, land rents paid to absentee landowners and travel expenses paid to the absentee transport sector must be equal to the value of commodities sold to these agents. It is assumed that absentee landowners use their rent income to buy urban commodities. The transport sector buys intermediate urban commodities so that its zero profits condition holds. Outside commodity demands of the different locations are derived from a Cobb–Douglas function. The expenditure shares for the local commodities are exogenous but demand quantities depend on location specific prices.43 43 The full formulas of the public budget constraints and the ‘balance of payment’ are suppressed because they contain several expressions aggregating e.g. tax revenues and transport costs over households, locations and tax/cost categories. However, to provide an example, aggregate federal income tax revenue P 1 1 P Inc,1 h,2 can be determined as follows: þ ðh,i,jÞ Ch,2 TaxInc,h,2 : The first i Ci N Taxi ij N ij term refers to non-working households while the second term to working households.

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