Wages and Commuting: Quasi-natural Experiments' Evidence from Firms that Relocate

WAGES AND COMMUTING: QUASI-NATURALEXPERIMENTS’ EVIDENCE FROM FIRMS THAT RELOCATE*

Ismir Mulalic, Jos N. Van Ommeren and Ninette Pilegaard

We examine individual-level compensating differentials for commuting distance in a quasi-naturalexperiment setting by examining how wages respond to changes in commuting distance induced byfirm relocations. This set-up enables us to test for the relevance of job search frictions within labourmarket models. Due to the quasi-experimental set-up, we are able to avoid a range of endogeneityissues. We demonstrate that a 1 km increase in commuting distance induces an almost negligiblewage increase in the year after the relocation but a more substantial wage increase of about 0.15%three years later.

This article examines individual-level compensating wage differentials for commutingdistance, i.e. wage differences for commuting for workers belonging to the same firm.We address endogeneity of distance by employing exogenous shocks in commutingdistance due to firm relocations. As emphasised by Manning (2003) and Gibbons andMachin (2006), despite the large number of empirical studies that examine therelationship between wages and commuting, there are reasons to believe that thesestudies do not estimate the causal effect of commuting on wages.

The effect of commuting costs on wages is interesting for policy reasons (Gibbonsand Machin, 2006). For example, economists usually assume that employers do notcompensate workers when road tolls are introduced, whereas our results suggest thatthis assumption may not hold. The focus of the article here is, however, morefundamental and is related to labour market theory. Our starting point is thatevidence on the relationship between wages and commuting is informative about therelevance of labour market theories that assume the presence of job search frictions– including wage posting, bargaining and efficiency wage theory – which receive a lotof attention in the urban economics literature that analyses spatial aspects ofmarkets (Ross and Zenou, 2008; Zenou, 2009). As discussed in more detail later,these theories tend to imply individual-level compensating wage differentials forcommuting.

We employ the static frictionless economic model with homogeneous individuals asa benchmark. Workplace and residence locations are assumed to be chosen by workers.Wages are determined by the productivity level at the firm location. Hence, firms offera wage–workplace location package to workers (the wage gradient) and do not payindividual-level compensation for commuting.

* Corresponding author: Ismir Mulalic, Technical University of Denmark, Bygningstorvet 116B, 2800 Kgs.Lyngby, Denmark. Email: [email protected].

We thank Mogens Fosgerau and Bruno De Borger, two anonymous referees and Steve Pischke for usefulsuggestions on earlier drafts. Seminar participants at the 10th IZA/SOLE Transatlantic Meeting of LaborEconomists, 5th Kuhmo-Nectar Conference, NECTAR 2011 conference, SERC Annual conference (LondonSchool of Economics), Department of Economics at the University of Copenhagen and DTU Transport at theTechnical University of Denmark also provided helpful comments. We are grateful to Statistics Denmark forproviding the data. Research support from the Danish Council for Strategic Research is acknowledged.

[ 1086 ]

The Economic Journal, 124 (September), 1086–1105. Doi: 10.1111/ecoj.12074 © 2013 Royal Economic Society. Published by John Wiley & Sons, 9600

Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA.

To test for the presence of an individual-level compensating wage differential, we usea quasi-natural experimental set-up and analyse dynamic wage responses given changesin commuting distance due to firm relocations. We use Danish register data on allworkers of all large firms that relocate in the year 2004.

To understand our main methodological contribution, we emphasise that intraditional cross-section analyses of the effect of commuting on wages (White, 1977;Zax, 1991), one does not deal with the endogeneity of commuting, which may arisedue to the presence of unobserved worker and job/employer characteristics (see also,Fu and Ross, 2007). Teleworking is a relevant example of an unobserved job/employercharacteristic, because it affects both worker productivity, and therefore wages, andcommuting. By including worker fixed effects one solves for the endogeneity issuecaused by unobserved time-invariant worker characteristics (Manning, 2003). However,this does not address the endogeneity due to unobserved job/employer characteristics,because it identifies the effect of distance mainly through workers who move job toanother employer.

In this article, we estimate the effect of commuting on wages for workers employedby firms that relocate while using worker fixed effects. In this way, we are able to dealwith both the endogeneity caused by unobserved worker characteristics as well as byunobserved job/employer characteristics.1 Moreover, by using firm-fixed effects, we areable to exploit intra-firm variation in commuting distance, which deals with the wagegradient.2

One important issue is that wage responses to firm relocations may differ in the shortand the long run. The theories we are interested in are static and focus on long runcompensation. Empirical studies tend to estimate short run compensation becausethey use yearly panel data and include worker fixed effects to address endogeneityissues related to unobserved variables (Manning, 2003). Although the advantages ofincluding worker fixed effects outweigh the disadvantages (we will do the same in thisarticle), the short run responses are likely much smaller than the long-term responsesone is interested in. We address this issue by focusing on wage responses immediatelyafter as well as several years after the firm relocation.

1. Labour Market Models of Commuting

By construction, the length of a worker’s commute is determined by the worker’sworkplace and the residence location. Hence, any meaningful model that includes thecost of commuting must make assumptions about the labour market as well as thehousing market. We start with a discussion of frictionless static models withhomogeneous workers who dominate the urban economics literature. These modelsstart from the assumption that worker utility depends positively on the wage butnegatively on commuting costs, and therefore on commuting distance and houseprices. Wages and house prices are endogenously determined.

1 An alternative method of dealing with endogeneity caused by unobserved worker characteristics is to usean instrumental variable approach. This is not easy in the current setting.

2 Another issue which we address is that commuting distance is endogenous because household incomeplays a role in the choice of the residence location (Wheaton, 1974).

© 2013 Royal Economic Society.

[ S E P T E M B E R 2014] W AG E S A N D COMMU T I N G 1087

Frictionless models assume that firms freely choose workplace locations and workersfreely choose a job and a residence from a given set of locations (job and residentialrelocation costs are zero). For a firm, productivity at workplace locations is given butmay depend on the presence of other firms and therefore agglomeration externalities(Fujita and Ogawa, 1982; Lucas and Rossi-Hansberg, 2002). Employment is nothomogeneously distributed over space.3

In equilibrium, firm profits are zero and workers’ utility levels do not vary over space.It follows that the wage is equal to the marginal productivity at the workplace locationbut does not depend on the length of the commute of the worker. In other words,firms offer wage-location packages and ignore where workers live (Fujita et al., 1997).Hence, a firm may employ workers who differ in their commuting costs but who arecompensated by differences in house prices (Lucas and Rossi-Hansberg, 2002).

Now suppose that due to an exogenous shock in productivity at a certain workplacelocation, a firm relocates to another workplace location, which changes thecommuting costs of all workers. The firm will adjust the wage of all workers in thesame way. Workers who decide not to change residence location will stay with the firmonly when the commuting costs change is compensated by the wage change and willotherwise move to another employer (Herbert and Stevens, 1960; Fujita and Ogawa,1982; Lucas and Rossi-Hansberg, 2002). Alternatively, workers may move to a newresidence location and stay with the firm. At the new residence location, house pricesmay be higher or lower than in the previous residence location and therefore forworkers who change residence, there is no systematic one-to-one relationship betweenthe change in wages and change in commuting costs.

The above-mentioned literature assumes homogeneous workers. Allowing forheterogeneity in worker preferences does not change these results. For example,one may assume that workers have different preferences regarding the desirability ofbeing employed by a certain employer (Gibbons and Katz, 1992).4 In this case, the firmwill offer the same wage to inframarginal and marginal workers (independent of theircommuting distance). However, given an infinitesimal increase in commuting distancedue to a firm relocation (and no wage change), marginal workers will move to anotheremployer (or change residence), whereas inframarginal workers may not changeemployer (or residence).

We now make several adjustments to the frictionless model. First, and mostimportantly, we assume the presence of job search frictions: firms (with job vacancies)and (unemployed) workers have to search for each other. The contact rate betweenworkers and firms is finite, see Manning (2003), and does not depend on the distancebetween the worker and the firm. Second, residence location is fixed, becauseresidential moving costs are infinite (the presence of compensating differentials canalso be shown given finite moving costs Van Ommeren and Rietveld, 2007). Third,unemployed workers receive a benefit which is less than marginal productivity. Fourth,given a contact, workers and employers bargain about the wage conditional on the

3 Non-homogeneous space is essential to generate positive commuting. Given homogeneous space we endin a backyard economy with zero commuting according to a spatial impossibility theorem (Starrett, 1978).

4 One may also allow for heterogeneity in preferences regarding commuting. Workers with a strongerdislike of commuting will then sort themselves in jobs with a shorter commute.


1088 TH E E CONOM I C J O U RN A L [ S E P T E M B E R

commuting distance within a Nash bargaining framework where the surplus of thematch is shared between workers and employers (Pissarides, 2000).5 It can then beshown that workers and firms will only form a match when the distance is less than acertain maximum (defined by the condition that the worker’s utility of a job match forthat distance is equal to the utility of being unemployed).6 In addition, conditional onforming a match, wages will be higher for workers with a longer commute (Marimomand Zilibotti, 1999; Van Ommeren and Rietveld, 2005). This result is intuitive becausea long distance makes the job match less attractive to workers. This result does not holdin the extreme case when residential moving costs are zero. Zenou (2009) demon-strates this for a monocentric city model with wage bargaining and endogenous houseprices. Workers with long commutes are then fully compensated through lowerhousing prices. Consequently, conditional on the presence of residential moving costs,wage bargaining models imply individual-level wage compensation differentials forcommuting distance. We emphasise that this finding is not confined to wagebargaining models. It also holds for other labour markets with similar assumptions.See, for example, Manning (2003) who uses a wage posting model.7

Now suppose that workers are confronted with an exogenous change in theircommuting distance due to a firm relocation and bargain again with their employer.When the new commuting distance is increased, it may exceed the maximumcommuting distance and workers will leave the firm (they prefer to be unemployed andsearch for another employer). If workers stay with the firm, workers confronted with anincreased distance will bargain for a higher wage and workers confronted with adecreased distance will settle for a lower wage. Hence, firm relocation implies anindividual-level compensating differential for commuting.

Given heterogeneity in worker preferences regarding the desirability to work for acertain employer, workers who are keen to work for a certain employer (‘inframar-ginal’ workers) will lose more when not forming a match with this employer than thosewho were not so keen (‘marginal’ workers), see Harding et al. (2003). So, given wagebargaining, keen workers will receive a lower wage than those who are not so keen, see,for example, Wolinsky (1996). However, this does not imply that heterogeneousworkers receive different levels of compensation for commuting. In fact, the results byVan Ommeren and Rietveld (2005) based on a standard wage bargaining model implythat given a change in commuting distance (due to a firm relocation), all workers willreceive the same wage change for a unit change in commuting. In addition, the modelimplies that workers who are confronted with a higher commuting distance due to thefirm relocation that exceeds the maximum commuting distance will leave after thefirm relocation.8

5 It is similar to assuming Rubenstein’s (1982) infinite horizon, alternating offer bargaining game with nooutside options. In this set-up, the share is given. In a frictionless market, employers have no market power,so the share is zero, see Pissarides (2000). There is little evidence on the value of this share (Shimer, 2005;Mortensen and Nagypal, 2007; Gertler et al., 2008).

6 When the job arrival rate is infinite, which describes the frictionless model, this maximum is zero.7 Efficiency wage theory also suggests that firms pay higher wages to workers with long commuting

distances to reduce shirking. Van Ommeren and Guti�errez-i-Puigarnau (2011) show that absenteeism,which might be interpreted as a form of shirking, increases with commuting distance.

8 Note that the maximum commuting distance will be less for ‘marginal’ workers, so given an increase incommuting distance, these workers are more likely to move to another firm.


2014] W A G E S A N D COMMU T I N G 1089

This discussion of worker heterogeneity ignores that workers may differ in theirpreferences regarding commuting. Due to search frictions, workers with differentpreferences regarding commuting may then end up working for the same firm (andresiding in the same residence location). Workers who are not so keen to commute willbargain for higher wages. Given an increase in commuting distance, these workers aremore likely to move job. This suggests that the distribution of commuting compen-sation based on the sample of non-movers is less dispersed than for the full populationand that the average estimate based on a sample of non-movers is a conservativeestimate.

We now proceed to the dynamic wage responses that we are interested in. There areseveral reasons to believe that wage changes will be different in the long and short run.For example, in the long run, wages are thought to be closer to the marginal product,because workers have received more job offers from alternative employers. In addition,although one may assume that wages are renegotiated continuously (Mortensen andPissarides, 1999; Bertola and Garibaldi, 2001), implying that wages adjust immediatelyafter a firm relocation, it has been observed that wages are typically renegotiated yearly(Antel, 1985). It is then plausible that compensation shortly after firm relocation isnegligible. Another reason is that nominal wage reductions are rare (even wheninflation is low, Fehr and Goette, 2005). Therefore, given a firm relocation, workerswho are confronted with a commuting distance increase may immediately receive ahigher nominal wage, while those who are confronted with a commuting distancedecrease will keep the same nominal wage. Consequently, real wage reductions willtake longer to materialise; see, similarly, Neumark and Sharpe (1996) who argue thatthe impact on labour given a major firm event (e.g. a hostile takeover) may take severalyears. Note that this implies that wage responses may not be symmetric with respect toincreases and decreases in distance in the short run but are likely to be symmetrical inthe long run.9 In addition, there is suggestive evidence that workers underestimate theeffect of changes in commuting time on well-being in the short run but not in the longrun (Simonsohn, 2006; Stutzer and Frey, 2008), which also suggests that the long runeffects are stronger.

2. Identification Strategy of Individual-level Compensation for Commuting

Models with search frictions predict individual-level worker compensation forcommuting. One complication when estimating this effect is that commuting distancesare usually self-chosen by workers. Our approach entails estimating wage responses tochanges in commuting distance of large firms that relocate (defined here as firms withat least 10 workers). When firms are large, the change in a worker’s commutingdistance can be assumed to be due to an exogenous treatment (conditional on theaverage change in the commuting distance for workers of that firm). We aim to obtain

9 Another reason to expect asymmetric responses is that commuters have reference-dependentpreferences (De Borger and Fosgerau, 2008) and the pre-relocation commute is used as a reference point.In the long run, this effect may disappear when commuters adjust their reference point.



the average treatment effect of an increase in commuting distance.10 A focus on firmsthat relocate may create a selection bias because the set of relocating firms may not berandom as firms differ in relocation propensities. We will show that selection bias islikely minimal, because summary characteristics of relevant variables (e.g. wages,commuting distance, wage growth, workforce size) of relocating and non-relocatingfirms are almost identical.11

We measure wages on an annual basis. For this reason, we select workers who havebeen employed at least one year with a relocating firm. One advantage of making thisminor selection is that it reduces the possibility that the relocating event was knownbefore the worker started to work at this firm (firms usually do not announce long inadvance that they consider relocating). We focus on wage responses of workers who donot leave the firm in the period after the relocation (i.e. we obtain the averagetreatment effect of non-job movers).12

Finally, we select workers who do not change residence after the firm relocation.Keeping residence location constant is fundamental to our identification strategy. First,it guarantees that changes in commuting distance are exogenous, avoiding reversecausation. This is relevant, because the choice of residence location depends onincome (Wheaton, 1974). Second, it controls for the housing market compensationthat workers may receive when changing residence (e.g. a worker employed in a citycentre who moves residence from the centre to the suburbs is not only confronted witha longer commuting distance but also with lower house prices). Third, by keepingresidential location constant, we solve the complication that some firms reimburseresidential relocation costs (Van Ommeren and Rietveld, 2007). Because residentialmobility rates are low in Denmark, the selection bias that will occur due to choosingworkers who do not move residence is likely limited. However, in a sensitivity analysis,we will focus on this issue.

To describe our identification strategy more formally, let Wi,f ,t denote the worker i’swage in year t of firm f . We assume the following specification of wages:

logðWi;f ;tÞ ¼ a0 þ a1di;f ;t þ a02X i;f ;t þ a03tZ i;f þ u �df ;t þ ei þ ui;f ;t ; ð1Þwhere di,f,t is the worker’s distance of commuting; Xi,f ,t includes controls for worker andfirm characteristics that vary over time (e.g. size of the firm), Zi,f refers to time-invariantvariables for which a time-varying effect is present (e.g. educational level, type ofindustry of firm), �df ;t is the average commuting distance of the firm, ei is a worker fixedeffect and ui,f ,t is the overall error. By including worker fixed effects, we deal with time-invariant unobserved variables that cause spurious correlation between wages and

10 We do not have a discrete treatment, as in most of the treatment literature. In that literature, someindividuals are treated and others are not. We analyse a situation where all workers are treated but there aredifferences in levels of treatment. The idea to use workplace relocation as a source of exogenous change indistance is also exploited in Zax (1991), Zax and Kain (1996) and Guti�errez-i-Puigarnau and Van Ommeren(2010). Workplace relocations are quite common. About 7%–8% of Dutch firms are involved in relocationdecisions each year (Weltevreden et al., 2007). In Great Britain, 0.5% of workers state that they have changedresidence in the previous year because of a workplace relocation (National Statistics, 2002).

11 Van Dijk and Pellenbarg (2000) show that small firms relocate more frequently. Because we focus onfirms with at least 10 workers, we focus on a relatively homogeneous firm type with respect to relocation.

12 The wage response for non-movers may differ from the wage change of workers who leave the employer,which is examined by Manning (2003). We will come back to this in subsection 4.3.



distance (Manning, 2003). Note that �df ;t aims to capture the location-specificproductivity level related to the firm and therefore may capture the presence of anyspatial wage gradient (within the municipality), as reported by empirical studies(Timothy and Wheaton, 2001). We are particularly interested in the value of a1, as in africtionless market a1 = 0, whereas a1 > 0 for markets with search frictions.

We estimate all models in terms of first-differences, i.e., we use within-workers’variation and variables are formulated as changes from one time period to another,implying the following:

D logðWi;f Þ ¼ a1Ddi;f þ a02DX i;f þ a03Z i;f þ uD �df þ vi;f ; ð2Þwhere D denotes the time-difference operator, where a3 = a3t � a3t�1 and wherevi,f = ui,f ,t � ui,f ,t�1. In (2), we allow for the effect of time-invariant characteristics Zi,fon wage differences.

One may argue that specification (1) may be improved by including year-specificfirm-fixed effects, because we then control perfectly for the presence of a spatial wagegradient and control for any unobserved firm heterogeneity (e.g. a firm-specificcompensation related to the relocation; teleworking policies). Given time differencing,this implies that one may estimate the following equation:

D logðWi;f Þ ¼ a1Ddi;f þ a02DX i;f þ a03Z i;f þ df þ vi;f ; ð3Þwhere df denotes the firm-fixed effect.

3. Institutional Context, Data and Descriptives

3.1. Institutional Context of Denmark

The Danish labour market has experienced a trend towards a more decentralisedbargaining regime based on flexible wage structures since the early 1980s (Iversen,1996). Although unions and their employer counterparts determine the general wagelevel, workers bargain for additional individual bonuses. Therefore, individual wagebargaining is thought to be important for almost all jobs.

Job mobility is extremely high and even the highest in Europe (Mortensen, 2001).This applies to most categories of workers and is not caused by a minor share of(unskilled) workers being extremely mobile (Madsen, 2002). Average job duration isonly 4.7 years (compared to an EU average of 8.2 years). In contrast, due to steephousing transaction taxes and rent control, residential mobility rates are moderate andsubstantially less than for example in the UK and the US (OECD, 1999).

Denmark has an extremely high level of car taxation (the ad valorem tax on new carsis 180%). In addition, 40% of the population lives in the Copenhagen metropolitanarea with excellent public transport supply. As the climate is mild and the country isflat, bicycle use is very common. As a result, less than one third of the workerscommute by car. The average one-way commuting time is 20.5 minutes, which is aboutthe European average.

Many workers travel relatively short distances (about half of them commute less than12.5 km one way), predominantly using a bicycle or public transport. For theseworkers, even small increases in distance (e.g. 1 km) may increase commuting timenon-negligibly. For example, for a cyclist who travels at a speed of 16 km/hour, an



increase in 1 km one-way increases the commute by almost 8 min/day, about 1.67% ofa standard working day.

Workers with a one-way commute that exceeds 12.5 km are entitled to a taxdeduction which roughly compensates for the monetary commuting expenses.13 Thesedeductions imply, per kilometre, a (net) wage compensation of about 0.1% fordistances longer than 12.5 km and a compensation of about 0.05% for distances longerthan 50 km.14 Because commuting time is the main component of the overallcommuting costs and the elasticity of commuting time with respect to distance is about0.5 (Van Ommeren and Dargay, 2006), there will be diminishing marginal costs ofdistance. In combination with income tax reductions, one expects that for longerdistances, marginal wage compensation will be small.

3.2. The Data

The data used in the empirical analysis are derived from annual register data fromStatistics Denmark for the years 2003–7. We observe the full population of establish-ments,15 which we refer to as firms, and their workers. We observe all firm relocationsfor the year 2004 (but not for other years). We analyse changes in annual wagesbetween 2003 and 2005 – the short run – as well as changes between 2003 and 2007 –the long run.

For 31 December each year, we have information on worker’s residence andworkplace municipality, annual net wages and a range of explanatory variables that ismuch more extensive than is usual for register data (for workers: educational level, age,gender, full-time versus part-time; for firms: number of workers, revenue and industry).To protect worker privacy, Statistics Denmark does not provide the exact residence andworkplace addresses (within the municipality) but provides us with the commutingdistances for the shortest route between these addresses on 31 December.

3.3. Selection of Sample and Descriptive Statistics

We select workers who had been employed for at least one year on 1 January 2004 by afirm with 10 or more workers who relocated in the year 2004 (1,043 firms). In mostregister data sets, the number of hours worked is not reported. Fortunately, we haveinformation about whether jobs are full-time or part-time. Empirical evidence indicatesthat labour supply hardly changes given changes in commuting distance (Guti�errez-i-Puigarnau and Van Ommeren, 2010). Nevertheless, it seems prudent to keep laboursupply constant, so we have selected workers who work full-time or part-time during thewhole period of observation. Employers seldom reimburse commuting expensesexplicitly (viz. through a fringe benefit), so we ignore this issue. We excludeobservations with missing information and observations for which the commuting

13 These income tax reductions for workers with long commutes can be found in many Europeancountries (Potter et al., 2006).

14 For example, in 2003, workers were entitled to deduct 3.2 DKK from gross income per kilometre fordistances between 12.5 and 50 km, corresponding to an average net wage increase of about 0.1%.

15 The statistical unit is an administrative unit used to register enterprises liable to VAT.



distance exceeds 100 km or the change in distance exceeds 50 km.16 Given theseselection criteria, we exclude 68 firms. Our econometric approach is then based on asample of 975 firms and 19,283 workers (about 20 workers per firm).

This sample contains a subsample of workers who did not change employer orresidence from January 2004 until the end of 2005 (7,459 workers) and anothersubsample of workers who did not make these changes until the end of 2007 (4,523workers), see Table A1 in online Appendix A. For both subsamples of workers, thecommuting distance changes only in the year 2004 due to a firm relocation. Thecorrelation between changes in commuting distance and changes in wages for theselected subsamples is 0.034 for 2005 and 0.043 for 2007, suggesting that variation indistance might be relevant for determining variation in wages. We will initially focus onthese two subsamples and later analyse selection issues.

We have also regressed the change in commuting distance on pre-move covariatesdiscussed later on (including commuting distance, wage and firm-fixed effects). Itappears that changes in commuting distance are hardly explained by these covariates,as indicated by the R2 which is equal to only 0.03 (in the short run) and 0.06 (in thelong run). So, from a statistical point of view, changes in commuting distance are closeto random.17

About 55% of workers who were employed in January 2004 left their employer by theend of 2005. Hence, the annual mobility rate is about 33% (and above the nationalaverage of 25%, as one may expect for firms that relocate). For workers who have notchanged employer or residence before the end of 2005, mobility drops to 13% in2006/2007 (consistent with the stylised fact that job mobility depends negatively on jobtenure). Moving residence is much less common than moving employer.

In Table A2, online Appendix A, it is shown that the selected firms are comparablein number of workers, wages, revenue, as well as the change over time in these variablesto firms that did not relocate.18 For example, relocating firms have, on average, 49workers, whereas other firms have 53 workers. Importantly, the selected firms are alsorepresentative in terms of average commuting distance. The commuting distancedistributions of workers belonging to relocating firms and other workers are alsosimilar (see Figure B1, online Appendix B). This suggests that our selected sample isrepresentative of the population of firms and workers (the selected sample is also quiterepresentative in terms of other indicators such as industry).19

Another way to examine selectivity issues, is to analyse wage changes over timefor a sample of workers who do belong to firms that do not relocate and to

16 In an earlier version of this article, we excluded observations with large changes in wages as they wereassumed to be outliers. We obtained similar results, excluding these observations.

17 Furthermore, of the many individual explanatory variables included, only two variables, the pre-movecommuting distance and age, have statistically significant effects in the short and long run analyses. Theireffect sizes are very small. For example, a 10-year increase in age reduces the average change in commutingdistance by only 200–300 metres. Increasing the pre-move distance by 10 km has a similar effect size.

18 The difference in average workforce growth between relocating and non-relocating firms is minimal.Both types of firms reduce the workforce by less than one worker. The variation in workforce reduction issomewhat larger for relocating firms.

19 In the selected sample, the number of firms is somewhat less than that in the full sample, particularly inthe long run. One of the main reasons is that some firms, when relocating, change identity according to thetax system (e.g. because the owner has changed). Consequently, according to the tax authorities, workers inthese firms change employer. Arguably, this type of selection is random and therefore not problematic.



compare results with the selected sample (in these analyses, we exclude the changein distance variable). Both samples provide essentially identical effects for worker(e.g. age, educational level) as well as firm characteristics (firm size, change in firmsize).

Table 1 shows the summary statistics of variables of interest before the firmrelocation (in January 2003), the commuting distance in 2005 (after the firmrelocation but before any job or residence change) as well as the changes ofcommuting distance over time. We focus first on the subsamples of workers who didnot change employer or residence (the first two columns of Table 1). For theseworkers, as would occur given random changes in firm relocation, the averagechange in commuting distance is a few hundred metres, so close to zero (see alsoFigure B2, online Appendix B). The average absolute change in distance for the

Table 1

Summary Statistics, Means and Standard Deviations for Different Samples

Workers who remain atfirms that relocate and did

not change residenceEmployer and residence

movers

2003–5 2003–7 2003–5 2003–7

Commuting distance, 2003 (km) 16.362 10.642 18.596 15.223(17.141) (11.408) (16.943) (15.561)

Commuting distance, 2005 (km) 16.677 10.903 17.497 15.705(17.326) (11.510) (17.393) (15.760)

Change in commuting distance (km) 0.315 0.261 �1.099 0.483(4.922) (2.813) (13.219) (9.124)

Absolute change in commutingdistance (km)

1.788 1.222 7.631 4.253(4.596) (2.548) (10.849) (8.086)

Change in log wage 2003–5 0.079 0.146 0.067 0.132(0.146) (0.252) (0.176) (0.413)

Distance between 12.5 and 50 km,2003 (dummy)

0.425 0.260 0.530 0.370(0.494) (0.437) (0.499) (0.483)

Distance > 50 km, 2003 (dummy) 0.059 0.015 0.060 0.044(0.236) (0.123) (0.238) (0.205)

Annual net wage (1,000 DKK) 372.227 366.930 347.747 345.766(173.722) (175.431) (191.994) (133.782)

Worker’s age 39.591 39.396 38.859 37.819(9.808) (9.682) (10.340) (9.990)

Male 0.662 0.642 0.702 0.657(0.473) (0.479) (0.458) (0.475)

Vocational education 0.422 0.414 0.446 0.406(0.494) (0.493) (0.497) (0.491)

Short-cycle higher education 0.070 0.071 0.066 0.070(0.256) (0.256) (0.249) (0.256)

Medium-cycle higher education 0.109 0.106 0.088 0.106(0.311) (0.307) (0.283) (0.308)

Bachelor degree 0.017 0.017 0.017 0.020(0.130) (0.128) (0.128) (0.140)

Long-cycle higher education 0.109 0.111 0.076 0.106(0.312) (0.314) (0.265) (0.308)

PhD degree 0.006 0.004 0.007 0.005(0.076) (0.066) (0.083) (0.067)

Number of observations 7,459 4,523 11,525 4,178

Note. Standard deviations are in parentheses.



selected sample is about 1.8 and 1.2 km in the short run and long run, respectively,with relatively large standard deviations of 4.6 km in the short run and 2.5 km inthe long run. Hence, although, firms tend to relocate over a rather short distance,the high standard deviation indicates that we have substantial variation in distancechanges.

The summary statistics of the selected sample and a sample that consists of workerswho moved residence or employer (the last two columns of Table 1) are remarkablysimilar.20 This is in line with the general idea that job moving in Denmark is notspecific to certain groups (e.g. the young). For example, workers in our sample of non-movers are only slightly older than those in the sample of movers (less than one yearin the short run, less than two years in the long run). There are two main exceptions.One exception is that the absolute change in distance is three to four times higher inthe movers sample (because changes in distance through residence or employermoves are much larger than for firm relocations). The other exception is that the non-movers have a shorter commuting distance in 2003 than the movers, particularly in thelong run. This is in line with the standard result in the job search literature thatworkers with a long distance have higher job and residential mobility rates (Manning,2003).

In our data, 52% of workers have a commute of less than 12.5 km. In ourinterpretation of the empirical results, we will particularly focus on the results for amarginal increase in distance for a representative worker with a distance of 10 km (themedian distance), because this worker is not affected by income taxation rulesregarding commuting.

4. Empirical Results

We focus first on the long run. The econometric results of several specifications of first-differences models for changes between 2003 and 2007 based on specification (2) areshown in Table 2. We are mainly interested in the effect of changes in commutingdistance on changes in wages, so we have experimented with several functional formsfor distance (linear, loglinear). Theoretical considerations –marginal commuting costsfall in distance and because of income tax advantages for longer distances – as well asempirical considerations – given a linear spline functions, we find that the marginaleffect of distance is strongly diminishing – suggest that the inclusion of a logarithm ofdistance is preferred to a linear specification. We emphasise that our results are robustwith respect to specification (also for specifications which are not explicitlydiscussed).21

20 The sample size of job and residence changers for the period 2003–5 is somewhat less than thosereported in Table A1 of online Appendix A, because of missing information and because some workers leavethe labour market or move more than once, whereas we only consider workers who move once. The samplesize of these changers for the period 2003–7 is much less than those reported in Table A1 (and even less thanfor 2003–5), because the probability of leaving the labour market or moving more than once is quite largeover a long period.

21 For example, the log specification implies that the marginal effect of distance is extremely large forshort distances (e.g. 100 metres), which may be inaccurate. So, we have also estimated models including log(distance + 1). The results remain robust to this specification and generally provide higher estimates. Whenincluding the square of distance, the results remain robust.



4.1. Wage Changes Between 2003 and 2007 (‘The Long Run’)

We first focus on the results using the subsamples of workers who do not changeemployer or residence. The reported standard errors are clustered by firm. The firstcolumn (1) in Table 2 shows the results given a spline specification of log distance withgiven nodes at a one-way distance of 12.5 and 50 km, i.e. at the distance where workersare entitled to an income tax reduction associated with commuting. In this specification,we further control for worker characteristics such as gender, age and education as well asfor firm characteristics such as average change in commuting distance, number ofemployees, change in number of employees and industry (111 industry dummies) asthese characteristics may influence wage growth. Furthermore, we include 278 regional

Table 2

Changes in Log Wage Between 2003 and 2007

(1) (2) (3) (4) (5)

Firm fixedeffects

Employermovers

Absolute change indistance > 500 m

Change in log distance 0.015** 0.015** 0.014* 0.016** 0.017**(0.007) (0.007) (0.008) (0.008) (0.007)

Change in log (distance � 12.5)(when distance > 12.5)

0.002(0.011)

Change in log (distance � 50)(when distance > 50)

�0.027(0.034)

Change in average log distance(per firm)

�0.005 �0.005 �0.028 �0.001(0.010) (0.010) (0.021) (0.012)

Male 0.031*** 0.031*** 0.033** �0.104*** 0.030*(0.011) (0.011) (0.014) (0.032) (0.016)

Worker’s age �0.007*** �0.007*** �0.007*** �0.006*** �0.007***(0.001) (0.001) (0.001) (0.002) (0.001)

Vocational education 0.044*** 0.044*** 0.040*** �0.028 0.082***(0.013) (0.013) (0.015) (0.055) (0.027)

Short-cycle higher education �0.010 �0.010 �0.004 �0.094** �0.001(0.011) (0.011) (0.013) (0.042) (0.027)

Medium-cycle higher education 0.079** 0.079** 0.068** �0.202* 0.159***(0.032) (0.032) (0.034) (0.110) (0.055)

Bachelor degree 0.031** 0.031** 0.036** �0.202 0.035(0.014) (0.014) (0.016) (0.042) (0.031)

Long-cycle higher education �0.051 �0.051 �0.018 �0.391*** �0.070(0.081) (0.080) (0.052) (0.125) (0.069)

PhD degree 0.039*** 0.039*** 0.038*** 0.047 0.095***(0.011) (0.011) (0.012) (0.036) (0.021)

Change in log number ofemployees

0.001 0.001 �0.003 0.002(0.001) (0.001) (0.006) (0.002)

Log number of employees �0.004 �0.004 �0.032** 0.004(0.004) (0.004) (0.015) (0.007)

Regional fixed effect (278) Yes Yes Yes Yes YesDummies indicating industry(111 industries)

Yes Yes No Yes Yes

Firm fixed effects No No Yes No No

R2 0.129 0.129 0.432 0.134 0.177Number of observations 4,523 4,523 4,523 2,714 1,605

Notes. Dependent variable is change in logarithm of wage; ***, **, * indicate that estimates are significantlydifferent from zero at the 0.01, 0.05 and 0.10 levels respectively; standard errors (clustered by firm) are inparentheses.



(municipality) fixed effects, which capture changes in wage growth between regions(most Danish regions are small except for the municipality of Copenhagen).

Given this specification, for distances up to 12.5 km, the distance elasticity of thewage is equal to 0.015 with a standard error of 0.007, and thereby statisticallysignificant. The estimated effects of the control variables are in line with the usualfindings.22 These results suggest that above 12.5 km, and also above 50 km, thedistance elasticity is of similar magnitude. This is confirmed by a standard F-test(F = 0.10; p-value = 0.748) which does not reject the hypothesis that the elasticity isconstant over distance. Therefore, we will proceed by assuming that the elasticity isconstant over distance. Given this assumption, the distance elasticity is equal to 0.015with a standard error of 0.007, see column (2).

To interpret this result, it is useful to focus on a worker with a distance of 10 km(i.e. a worker who does not receive an income tax reduction). For this worker, anincrease in distance by 1 km induces, on average, a wage increase of 0.147%(calculated as [log(11) � log(10)] 9 0.015). This is an economically significant effect.Given a daily labour supply of 7.4 h and the average hourly wage of 165.59 DKK, thedaily wage increase is then about 1.80 DKK (0.00147 9 7.4 9 165.59 DKK). Given acommuting speed of 30 km/hour (the speed that applies to travel trips over 10 km),an additional 1 km commute (one way) increases the daily commute by 4 minutes, andthe implied hourly compensation is then about 27 DKK, so 16% of the net hourly wage.This estimate is an underestimate of the effect of the actual distance travelled, becauseit assumes that workers travel each day to their workplace, which is not the case due tobusiness travel, teleworking and absenteeism.

To interpret this result, it is useful to note that transport economists using statedpreference data typically find that the commuter’s value of time is about 50% of thegross wage rate (Small and Verhoef, 2007). For example, Brownstone and Small (2005)find that the average value of commuting time varies among different industrialisedcities in the US from 20% to 100% of the gross wage rate. Using revealed preferencedata, it is common to find higher estimates. For example, Fu and Ross (2007) find thatthe value of commuting time is about 90% of the wage. Small et al. (2005) also find thatthe value of time is about 93% of the average wage. Consistent with the latter studies,Timothy and Wheaton (2001) and Van Ommeren and Fosgerau (2009) report that theoverall commuter costs per hour travelled, i.e. the hourly costs of commutingincluding monetary expenses, are about twice the wage rate.

Given the assumption that the overall worker costs of commuting time are twice thewage, our result implies that workers receive 8% of their commuting costs. This effect isin line with labour market models with search frictions but cannot be explained byperfectly competitive models without these frictions. When we assume a lower workercost of commuting, let us say, the cost of 1 hour commuting is equal to the wage rate,the compensation will be equal to 16% of the hourly wage.23 These levels of

22 We do not find strong evidence of an effect of the change in the average commuting distance,suggesting the absence of a spatial wage gradient as estimated by Timothy and Wheaton (2001). Note,however, that in our quasi-experimental set-up, variation over time in the average commuting distance islimited, so one may need a much larger data set to estimate this effect precisely.

23 Fosgerau et al. (2007) report a value of time of about 50% per hour for Danish commuters using statedpreference data.



compensating differentials for commuting because of search frictions are lower thanbut not completely out of line with, those implied by a number of wage bargainingstudies. For example, the results by Cahuc et al. (2006) imply a compensation between 0and 33%. Mortensen and Nagypal (2007) propose in their survey paper a value of 50%.

4.2. Sensitivity Analyses

We now provide robustness checks of these results. Most of the robustness checks focuson critical selection issues. Before we focus on selection issues, we address theimportance of including firm-fixed effects and controlling for explanatory variables.

4.2.1. Firm-fixed effectsOne criticism of the above estimation procedure is that we do not control sufficientlyenough for changes in firm location. According to standard urban economic theory,wages depend on the workplace location of the firm. In the current analysis, we havecontrolled for this (the wage gradient) using the average change in the commutingdistance of the relocating firm (as well as changes in municipality). It may be the casethat this control is not sufficient. To address this issue, we have estimated aspecification with firm-fixed effects (see column (3)). Individual-level workerscompensating differentials for commuting are now solely identified using intrafirmcompensating differentials. We find that the estimates are almost identical with amarginal effect of 0.014 (and a standard error of 0.008).

4.2.2. Inclusion of control variablesWe have argued earlier that changes in commuting distance due to firm relocation canbe interpreted as the outcome of a quasi-natural experiment. If this is true, the resultsmust not change substantially if we exclude all control variables, because these controlvariables are largely orthogonal to changes in commuting distance. This appears tohold. Without any control variable, we find an elasticity of 0.016 with a standard errorof 0.06. If we include firm-fixed effects but no other control variables, we find anelasticity of 0.012 and the same standard error.

4.2.3. Selection of workers who do not change residenceWe have examined to what extent the selection regarding that workers do not moveresidence causes a selection bias. Clearly, this is a less important issue, because only20% of workers move residence during the period of observation. Residential movingcosts are high in Denmark, due to substantial transaction costs in the housingownership market as well as due to rent control and public housing regulation in therental market. In such a market, combined with high job mobility rates, it is usually notrational for workers to move residence closer to the current employer, as theanticipated employment duration will be short.24 This makes it likely that movingresidence is mainly due to change in housing consumption and in general is unrelatedto the relocation of the firm. Nevertheless, to address this selection bias, we have

24 Interestingly, Zax (1991) has noted that given spatial differences in house prices, moving residencefarther away after a firm relocation is a rational choice for workers when firms relocate towards workers.



estimated standard Heckman selection models using the presence of children in theage category between 6 and 18 as an instrument in the selection step. The idea here isthat children in this age category strongly reduce residential mobility as these childrengo to school, which increases the cost of residential moving. As one may argue that thepresence of children affects wage growth, we have estimated these models controllingfor the number of children (irrespective of children’s age). The full results arereported in Table C1 in online Appendix C. It appears that the effect of commutingdistance on wages is essentially the same as discussed in Table 2.

4.2.4. Other selection issuesThe results discussed above were based on a sample of workers who did not change fromfull-time to part-time jobs (or the other way around) during the whole period ofobservation. We have re-estimated the model including workers who changed fromfull-time to part-time jobs (or the other time round) during the period of observation,while controlling for part-time work. This generates almost identical results to thosereported here. In addition, we have re-estimated models including workers with acompany car (0.3% of the sample). Including these workers does not affect theestimation results. We have experimented with less selective criteria regarding the sizeof the firm. Our results remain robust up to the point of selecting firms with at least fiveworkers.

One may also wonder to what extent our main results are robust in the sense thatthey only hold for a subgroup of observations. For example, it may be thought thatworkers with relative short commuting distances (before the firm relocation) are muchmore sensitive to changes in commuting distance (because these workers have sortedthemselves into jobs close to the residence). We have therefore re-estimated the modelselecting only workers with a commute of less than 12.5 km (before the relocation).Now, the point estimate of the distance is only marginally higher (about 10%).

Another issue is that changes in distance smaller than 500 metres are usuallyeconomically of little or no importance but are relatively common in our data (65% ofthe observations). We find that the effects become slightly more pronounced if oneexcludes these observations (see column (5)). Now, the elasticity increases to 0.017(with a standard error of 0.007).

4.3. Employer Movers

Manning (2003) focuses on the same question as we do and estimates the effect ofchanges in commuting on changes in wages. To avoid endogeneity issues due torelocation in the housing market, he employs a selected sample of workers whovoluntarily change the length of their commute when they move employer. In thecurrent article, our focus is on workers confronted with an exogenous commutingdistance change when their employer relocates. We have also followed the approach byManning (2003), so we estimate (2) for workers who move employer.25 These results

25 One slight technical complication is that some workers move employer more than once after they haveleft the firm. To simplify the estimation procedure, we focus on 2,714 workers who moved once (before theend of 2007).



are reported in Table 2, column (4). We now find an almost identical effect of 0.016(with a standard error of 0.008). This finding indicates that, at least with the currentdata, both approaches provide the same answer.

4.4. The Effect of Increases in Distance Versus Decreases in Distance

We have argued above that one expects that in the long run wages respond in the sameway to increases anddecreases in distance. To test for the latter, wehave estimatedmodelswhere we allow these effects to differ, see TableD1, online AppendixD. The earlier pointestimate of 0.015 is within the 95% confidence intervals of both estimates. However, wefind that the effect is only positive and significant when distances decrease (and theestimates are statistically different using an F-test). It appears, however, that this result isnot robust to specification. For example, we have re-estimated the model excluding30 observations with extreme wage changes (0.7% of the number of observations). Wenow find that there is no statistical difference between the effects of increases anddecreases in distance (at the 5% significance level), and the point estimate of theincreases in distance effect is now higher.26 Consequently, we believe that the dataindicate that wages respond in the same way to increases and decreases in distance, in thelong run.

4.5. The Competitive Market Model Without Search Frictions

According to the competitive labour market model without search frictions, within-firm variation in commuting distance is not relevant to explain wages. If one assumesthat the model without search frictions is the true one, then one may estimate theeffect of distance by using an estimator that uses only between-firm variation indistance (and other indicators), so we identify the effect of changes in the firm-averagedistance. We emphasise that this estimate may introduce a bias because one cannotcontrol for unobserved firm characteristics that may be relevant (e.g. teleworkingpolicies). The results are reported in Table 3. We find that the effect of distance,a1 + u, is positive (and significant at the 10% level). The effect size is about the same asthe estimate of a1 reported in Table 2. This suggests that u, which captures the wagegradient, is negligible (consistent with our findings in Table 2). This makes sense inthe current context where commuting distance changes due to firm relocation areusually small so most firms relocate within the local labour market.

4.6. Wage Changes Between 2003 and 2005 (‘The Short Run’)

We have also examined the short run effect of a change in commuting distance byconsidering the effect on wage changes between 2003 and 2005. Again we haveestimated a large number of specifications (see Table 4). We now find that the effect ismuch smaller with a point estimate of around 0.001. For a worker with a distance of10 km, an increase in distance by 1 km induces, on average, a wage increase of 0.01%.

26 When we exclude even more wage outliers (e.g. 3% of the number of observations), we find the sameresult.



Although the standard errors tend to be much smaller for the short run estimates(where we have more observations), the short run effect is not statistically significant.So we conclude that the short run effect is either absent or only a small fraction of thelong run effect.27 Finally, and in contrast with the long run, and in line with theoreticalconsiderations, we find that the effect of increases in distance exceeds the effect ofdecreases in distance. For example, given the specification used in Table 4, we findthat the increase in distance is about 0.02 with a standard error of 0.005 whereas theeffect of a decrease in distance is insignificant.

5. Conclusion

This article analyses the effect of commuting distance on wages using matched registerdata for firms and workers for Denmark. We deal with the endogeneity of commutingdistance by means of a quasi-natural experimental approach using changes in distancethat are due to firm relocations. We show that an increase in commuting distance

Table 3

Changes in Log Wage, Between-firm Estimates

2003–7 2003–5

Change in log distance 0.017* 0.009*(0.009) (0.005)

Dummy indicating male 0.027 0.043(0.030) (0.032)

Worker’s age �0.008*** �0.005***(0.001) (0.001)

Dummy indicating worker with vocationaleducation

0.075* 0.025(0.044) (0.071)

Dummy indicating worker with short-cyclehigher education

�0.049 �0.013(0.050) (0.042)

Dummy indicating worker with medium-cyclehigher education

0.095 0.015(0.125) (0.100)

Dummy indicating worker with bachelor degree �0.017 0.104**(0.047) (0.048)

Dummy indicating worker with long-cyclehigher education

�0.336 �0.187(0.421) (0.170)

Dummy indicating worker with PhD degree 0.016 0.004(0.033) (0.035)

Change in logarithm of firm’s number ofemployees

0.002 0.003(0.003) (0.002)

Logarithm of firm’s number of employees 0.013* 0.001(0.007) (0.007)

Regional fixed effect Yes YesDummies indicating industry Yes Yes

R2 0.433 0.487Number of observations of firms 4,523 7,459


27 If we re-estimate models while excluding wage outliers, short run and long run effect increase. Hence,we arrive at the same conclusion.



implies a moderate wage increase three years after the firm relocation (a 1 km increaseinduces a wage increase of about 0.15%), while this effect is much smaller the year afterthe relocation.

The estimated effect implies individual-level compensating differentials for com-muting distance as predicted by labour market models that allow for job searchfrictions, and due to the quasi-natural experimental set-up excludes a range of othercompeting explanations frequently mentioned in the literature. Our findings areconsistent with the notion that individual-level wage setting is an important charac-teristic of the Danish labour market. This study therefore implies that employers have

Table 4

Changes in Log Wage Between 2003 and 2005

(1) (2) (3) (4) (5)

Firm fixedeffects

Absolute changein distance> 500 m

Workers whoremain at firms

2003–7

Change in log distance 0.001 0.001 0.001 0.001 0.002(0.001) (0.001) (0.001) (0.001) (0.002)

Change in log(distance � 12.5) (whendistance > 12.5)

0.003(0.005)

Change in log (distance � 50)(when distance > 50)

�0.002(0.012)

Change in average log distance(per firm)

0.001 0.006 0.003 0.042**(0.002) (0.009) (0.002) (0.018)

Male 0.005 0.005 0.005 0.011 0.009(0.005) (0.005) (0.005) (0.008) (0.006)

Worker’s age �0.003*** �0.003*** �0.003*** �0.004*** �0.003(0.0003) (0.0003) (0.0003) (0.0004) (0.0004)

Vocational education 0.007 0.007 0.003 0.014 0.012(0.006) (0.006) (0.007) (0.011) (0.007)

Short-cycle higher education 0.013* 0.013* 0.011 0.015 0.011(0.007) (0.007) (0.007) (0.011) (0.008)

Medium-cycle higher education 0.026** 0.026** 0.028** 0.026 0.019(0.012) (0.012) (0.013) (0.021) (0.017)

Bachelor degree 0.016*** 0.016*** 0.017*** 0.028*** 0.009(0.006) (0.006) (0.006) (0.010) (0.008)

Long-cycle higher education �0.026* �0.026* �0.024* 0.012 �0.048(0.014) (0.014) (0.015) (0.032) (0.036)

PhD degree 0.015*** 0.015*** 0.016*** 0.029*** 0.018***(0.005) (0.005) (0.005) (0.008) (0.005)

Change in log number ofemployees

0.0001 0.0001 0.0004 0.0001(0.001) (0.0009) (0.001) (0.001)

Log number of employees 0.001 0.001 0.004 0.001(0.001) (0.002) (0.004) (0.002)

Regional fixed effect (271) Yes Yes Yes Yes YesDummies indicating industry(111 industries)

Yes Yes No Yes Yes

Firm fixed effects No No Yes No No

R2 0.112 0.112 0.394 0.151 0.119Number of observations 7,459 7,459 7,459 2,682 4,523




market power and pay below workers’ productivity (Marimom and Zilibotti, 1999;Pissarides, 2000).

Technical University of DenmarkVU UniversityTechnical University of Denmark

Submitted: 24 April 2012Accepted: 6 June 2013

Additional Supporting Information may be found in the online version of this article:

Appendix A. Sample Selection Procedure and Summary Statistics for Firms.Appendix B. Distribution of Commuting Distance.Appendix C. Selection of Workers who do not change Residence.Appendix D. The Effect of Increases in Distance Versus Decreases in Distance.

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Wages and Commuting: Quasi-natural Experiments' Evidence from Firms that Relocate

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