The Economic Consequences of Commuting Distance

Wages and commuting: quasi-natural experiments' 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-natural experiment setting by examining how wages respond to changes in commuting distance induced by firm relocations. This setup enables us to test for the relevance of job search frictions within labour market models. Due to the quasiexperimental setup, we are able to avoid a range of endogeneity issues. We demonstrate that a one kilometre increase in commuting distance induces an almost negligible wage increase in the year after the relocation, but a more substantial wage increase of about 0.15% three years later. This paper examines individual-level compensating wage differentials for commuting distance, i.e. wage differences for commuting for workers belonging to the same firm. We address endogeneity of distance by employing exogenous shocks in commuting distance due to firm relocations. As emphasised by Manning (2003) and Gibbons and Machin (2006), despite the large number of empirical studies that examine the relationship between wages and commuting, * Ismir Mulalic, Technical University of Denmark, Bygningstorvet 116B, 2800 Kgs. Lyngby, Denmark, e- mail: imu@transport.dtu.dk. We thank Mogens Fosgerau and Bruno De Borger, two anonymous referees and Steve Pischke for useful suggestions on earlier draft. Seminar participants at the 10th IZA/SOLE Transatlantic Meeting of Labor Economists, 5th Kuhmo-Nectar Conference, NECTAR 2011 conference, SERC Annual conference (London School of Economics), Department of Economics at the University of Copenhagen, and DTU Transport at the Technical University of Denmark also provided helpful comments. We are grateful to Statistics Denmark for providing the data. Research support from the Danish Council for Strategic Research is acknowledged.

there are reasons to believe that these studies do not estimate the causal effect of commuting on wages. The effect of commuting costs on wages is interesting for policy reasons (Gibbons and Machin, 2006). For example, economists usually assume that employers do not compensate workers when road tolls are introduced, whereas our results suggest that this assumption may not hold. The focus of the paper here is, however, more fundamental and is related to labour market theory. Our starting point is that evidence on the relationship between wages and commuting is informative about the relevance of labour market theories that assume the presence of job search frictions -- including wage posting, bargaining and efficiency wage theory -- which receive a lot of attention in the urban economics literature that analyses spatial aspects of markets (Ross and Zenou, 2008; Zenou, 2009). As discussed in more detail later, these theories tend to imply individual-level compensating wage differentials for commuting. We employ the static frictionless economic model with homogeneous individuals as a 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 offer a wage-workplace location package to workers (the wage gradient) and do not pay individual-level compensation for commuting. To test for the presence of an individual-level compensating wage differential, we use a quasi-natural experimental setup and analyse dynamic wage responses given changes in commuting distance due to firm relocations. We use Danish register data on all workers of all large firms that relocate in the year 2004. To understand our main methodological contribution, we emphasize that in traditional cross-section analyses of the effect of commuting on wages (White, 1977; Zax, 1991), one does 2

not deal with the endogeneity of commuting which may arise due 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/employer characteristic, because it affects both worker productivity, and therefore wages, and commuting. By including worker fixed effects one solves for the endogeneity issue caused 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 to another employer. In the current paper, we estimate the effect of commuting on wages for workers employed by firms that relocate while using worker fixed effects. In this way, we are able to deal with both the endogeneity caused by unobserved worker characteristics as well as by unobserved job/employer characteristics. 1 Moreover, by using firm fixed effects, we are able to exploit intrafirm variation in commuting distance which deals with the wage gradient. 2 One important issue is that wage responses to firm relocations may differ in the short and the long run. The theories we are interested in are static and focus on long-run compensation. Empirical studies tend to estimate short-run compensation because they use yearly panel data and include worker fixed effects to address endogeneity issues related to unobserved variables (Manning, 2003). Although the advantages of including worker fixed effects outweigh the disadvantages (we will do the same in the current paper), the short-run responses are likely much smaller than the long-term responses one is interested in. We address this issue by focusing on 1 An alternative method of dealing with endogeneity caused by unobserved worker characteristics is to use an 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 income plays a role in the choice of the residence location (Wheaton, 1974). 3

wage responses immediately after 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's workplace and the residence location. Hence, any meaningful model that includes the cost of commuting must make assumptions about the labour market as well as the housing market. We start with a discussion of frictionless static models with homogeneous workers that dominate the urban economics literature. These models start from the assumption that worker utility depends positively on the wage, but negatively on commuting costs, and therefore on commuting distance and house prices. Wages and house prices are endogenously determined. Frictionless models assume that firms freely choose workplace locations and workers freely choose a job and a residence from a given set of locations (job and residential relocation costs are zero). For a firm, productivity at workplace locations is given (but may depend on the presence of other firms and therefore agglomeration externalities, see Fujita and Ogawa (1982) and Lucas and Rossi Hansberg (2002)). Employment is not homogeneously 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 location, but does not depend on the length of the commute of the worker. In other words, firms offer wagelocation packages and ignore where workers live (e.g. Fujita et al., 1997). Hence, a firm may employ workers who differ in their commuting costs but who are compensated by differences in house prices (Lucas and Rossi Hansberg, 2002). 3 Non-homogeneous space is essential to generate positive commuting. Given homogeneous space we end in a backyard economy with zero commuting according to a spatial impossibility theorem (Starrett, 1978). 4

Now suppose that due to an exogenous shock in productivity at a certain workplace location, a firm relocates to another workplace location, which changes the commuting costs of all workers. The firm will adjust the wage of all workers in the same way. Workers who decide not to change residence location will stay with the firm only when the commuting costs change is compensated by the wage change, and will otherwise move to another employer (Herbert and Stevens, 1960; Fujita and Ogawa, 1982; Lucas and Rossi Hansberg, 2002). Alternatively, workers may move to a new residence location and stay with the firm. At the new residence location, house prices may be higher or lower than in the previous residence location and therefore for workers who change residence, there is no systematic one-to-one relationship between the change in wages and change in commuting costs. The above-mentioned literature assumes homogeneous workers. Allowing for heterogeneity in worker preferences does not change these results. For example, one may assume that workers have different preferences regarding the desirability of being employed by a certain employer (Gibbons and Katz, 1992). 4 In this case, the firm will offer the same wage to inframarginal and marginal workers (independent of their commuting distance). However, given an infinitesimal increase in commuting distance due to a firm relocation (and no wage change), marginal workers will move to another employer (or change residence), whereas inframarginal workers may not change employer (or residence). We now make several adjustments to the frictionless model. First, and most importantly, we assume the presence of job search frictions: firms (with job vacancies) and (unemployed) workers have to search for each other. The contact rate between workers and firms is finite, see Manning (2003), and does not depend on the distance between the worker and the firm. Second, 4 One may also allow for heterogeneity in preferences regarding commuting. Workers with a stronger dislike of commuting will then sort themselves in jobs with a shorter commute. 5

residence location is fixed, because residential moving costs are infinite (the presence of compensating differentials can also 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 commuting distance within a Nash bargaining framework where the surplus of the match is shared between workers and employers (Pissarides, 2000). 5 It can then be shown that workers and firms will only form a match when the distance is less than a certain maximum (defined by the condition that the worker's utility of a job match for that distance is equal to the utility of being unemployed). 6 In addition, conditional on forming a match, wages will be higher for workers with a longer commute (e.g. Marimom and Zilibotti, 1999; Van Ommeren and Rietveld, 2005). This result is intuitive because a long distance makes the job match less attractive to workers. This result does not hold in the extreme case when residential moving costs are zero. Zenou (2009) demonstrates this for a monocentric city model with wage bargaining and endogenous house prices. Workers with long commutes are then fully compensated through lower housing prices. Consequently, conditional on the presence of residential moving costs, wage bargaining models imply individual-level wage compensation differentials for commuting distance. We emphasise that this finding is not confined to wage bargaining models. It also holds for other labour markets with similar assumptions. See, for example, Manning (2003) who uses a 5 It is similar to assuming Rubenstein s infinite horizon, alternating offer bargaining game with no outside options (Rubenstein, 1982). In this setup, 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. 6

wage posting model. 7 Now suppose that workers are confronted with an exogenous change in their commuting distance due to a firm relocation and bargain again with their employer. When the new commuting distance is increased, it may exceed the maximum commuting distance and workers will leave the firm (they prefer to be unemployed and search for another employer). If workers stay with the firm, workers confronted with an increased distance will bargain for a higher wage and workers confronted with a decreased distance will settle for a lower wage. Hence, firm relocation implies an individual-level compensating differential for commuting. Given heterogeneity in worker preferences regarding the desirability to work for a certain employer, workers who are keen to work for a certain employer ( inframarginal workers) will lose more when not forming a match with this employer than those were not so keen ( marginal workers), see Harding et al. (2003). So, given wage bargaining, 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 heterogeneous workers receive different levels of compensation for commuting. In fact, the results by Van Ommeren and Rietveld (2005) based on a standard wage bargaining model imply that given a change in commuting distance (due to a firm relocation), all workers will receive the same wage change for a unit change in commuting. In addition, the model implies that workers who are confronted with a higher commuting distance due to the firm relocation that exceeds the maximum commuting distance will leave after the firm relocation. 8 7 Efficiency wage theory also suggests that firms pay higher wages to workers with long commuting distances in order to reduce shirking. Van Ommeren and Gutiérrez-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 in commuting distance, these workers are more likely to move to another firm. 7

This discussion of worker heterogeneity ignores that workers may differ in their preferences regarding commuting. Due to search frictions, workers with different preferences regarding commuting may then end up working for the same firm (and residing in the same residence location). Workers who are not so keen to commute will bargain for higher wages. Given an increase in commuting distance, these workers are more likely to move job. This suggests that the distribution of commuting compensation based on the sample of non-movers is less dispersed than for the full population and that the average estimate based on a sample of non-movers is a conservative estimate. We now proceed to the dynamic wage responses that we are interested in. There are several 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 and Pissarides, 1999; Bertola and Garibaldi, 2001), implying that wages adjust immediately after 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 is negligible. Another reason is that nominal wage reductions are rare (even when inflation is low, see Fehr and Goette (2005)). Therefore, given a firm relocation, workers that are confronted with a commuting distance increase may immediately receive a higher nominal wage, while those who are confronted with a commuting distance decrease will keep the same nominal wage. Consequently, real wage reductions will take longer to materialise (see, similarly, Neumark and Sharpe (1996) who argue that the impact on labour given a major firm event (e.g. a hostile takeover) may take several years). Note that this implies that wage responses may not be symmetric with respect to increases and decreases in 8

distance in the short run, but are likely to be symmetric in the long run. 9 In addition, there is suggestive evidence that workers underestimate the effect of changes in commuting time on well-being in the short run, but not in the long run (Simonsohn, 2006; Stutzer and Frey, 2008), which also suggests that the long-run effects are stronger. 2. Identification Strategy of Individual-Level Compensation for Commuting Models with search frictions predict individual-level worker compensation for commuting. One complication when estimating this effect is that commuting distances are usually self-chosen by workers. Our approach entails estimating wage responses to changes in commuting distance of large firms that relocate (defined here as firms with at least 10 workers). When firms are large, the change in a worker's commuting distance can be assumed to be due to an exogenous treatment (conditional on the average change in the commuting distance for workers of that firm). We aim to obtain the average treatment effect of an increase in commuting distance. 10 A focus on firms that relocate may create a selection bias because the set of relocating firms may not be random as firms differ in relocation propensities. We will show that selection bias is likely 9 Another reason to expect asymmetric responses is that commuters have reference-dependent preferences (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. 10 We do not have a discrete treatment, as in most of the treatment literature. In that literature, some individuals are treated and others are not. We analyse a situation where all workers are treated, but there are differences in levels of treatment. The idea to use workplace relocation as a source of exogenous change in distance is also exploited in Zax (1991), Zax and Kain (1996) and Gutiérrez-i-Puigarnau and Van Ommeren (2010). Workplace relocations are quite common. About 7 8% of Dutch firms are involved in relocation decisions each year (Weltevreden et al., 2007). In Great Britain, 0.5% of workers state that they have changed residence in the previous year because of a workplace relocation (National Statistics, 2002). 9

minimal, because summary characteristics of relevant variables (e.g. wages, commuting distance, wage growth, workforce size) of relocating and non-relocating firms are almost identical. 11 We measure wages on an annual basis. For this reason, we select workers that have been employed at least one year with a relocating firm. One advantage of making this minor selection is that it reduces the possibility that the relocating event was known before the worker started to work at this firm (firms usually do not announce long in advance that they consider relocating). We focus on wage responses of workers who do not leave the firm in the period after the relocation (i.e., we obtain the average treatment 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 reverse causation. This is relevant, because the choice of residence location depends on income (Wheaton, 1974). Second, it controls for the housing market compensation that workers may receive when changing residence (e.g., a worker employed in a city centre who moves residence from the centre to the suburbs is not only confronted with a longer commuting distance, but also with lower house prices). Third, by keeping residential location constant, we solve the complication that some firms reimburse residential relocation costs (Van Ommeren and Rietveld, 2007). Because residential mobility rates are low in Denmark, the selection bias that will occur due to choosing workers that do not move residence is likely limited. However, in a sensitivity analysis, we will focus on this issue. 11 Van Dijk and Pellenbarg (2000) show that small firms relocate more frequently. Because we focus on firms 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 section 4.3. 10

To describe our identification strategy more formally, let W i,f,t denote the worker i s wage in year t of firm f. We assume the following specification of wages: log W i,f,t = α 0 + α 1 d i,f,t + α 2 X i,f,t + α 3t Z i,f + φd f,t + ε i + u i,f,t (1) where d i,f,t is the worker's distance of commuting; X i,f,t includes controls for worker and firm characteristics that vary over time (e.g. size of the firm), Z i,f refers to time-invariant variables for which a time-varying effect is present (e.g., educational level, type of industry of firm), d f,t is the average commuting distance of the firm, ε i is a worker fixed effect, and u i,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 distance (Manning, 2003). Note that d f,t aims to capture the location-specific productivity level related to the firm and therefore may capture the presence of any spatial wage gradient (within the municipality), as reported by empirical studies (Timothy and Wheaton, 2001). We are particularly interested in the value of α 1, as in a frictionless market α 1 = 0, whereas α 1 > 0 for markets with search frictions. We estimate all models in terms of first-differences, that is, we use within-workers variation, and variables are formulated as changes from one time period to another, implying: log W i,f = α 1 d i,f + α 2 X i,f + α 3 Z i,f + φ d f + v i,f (2) where denotes the time-difference operator, where α 3 = α 3t - α 3t-1 and where v i,f = u i,f,t u i,f,t 1. In (2), we allow for the effect of time-invariant characteristics Z i,f on wage differences. One may argue that specification (1) may be improved by including year-specific firm fixed effects, because we control then perfectly for the presence of a spatial wage gradient and control for any unobserved firm heterogeneity (e.g., a firm-specific compensation related to the relocation; teleworking policies). Given time differencing, this implies that one may estimate the following equation: 11

log W i,f = α 1 d i,f + α 2 X i,f + α 3 Z i,f + δ f + v i,f (3) where δ f 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 decentralized bargaining regime based on flexible wage structures since the early 1980s (Iversen, 1996). Although unions and their employer counterparts determine the general wage level, workers bargain for additional individual bonuses. Therefore, individual wage bargaining 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 is only 4.7 years (compared to an EU average of 8.2 years). In contrast, due to steep housing transaction taxes and rent control, residential mobility rates are moderate and substantially 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 cars is 180%). In addition, 40% of the population lives in the Copenhagen metropolitan area with excellent public transport supply. As the climate is mild and the country is flat, bicycle use is very common. As a result, less than one third of the workers commute by car. The average oneway commuting time is 20.5 minutes, which is about the European average. Many workers travel relatively short distances (about half of them commute less than 12.5 kilometres one-way), predominantly using a bicycle or public transport. For these workers, even small increases in distance (e.g. 1 kilometre) may increase commuting time non-negligibly. For 12

example, for a cyclist who travels at a speed of 16 km/h, an increase of one kilometre one-way increases the commute by almost eight minutes per day, about 1.67% of a standard working day. Workers with a one-way commute that exceeds 12.5 kilometres are entitled to a tax deduction which roughly compensates for the monetary commuting expenses. 13 These deductions imply, per kilometre, a (net) wage compensation of about 0.1% for distances longer than 12.5 kilometres and a compensation of about 0.05% for distances longer than 50 kilometres. 14 Because commuting time is the main component of the overall commuting costs and the elasticity of commuting time with respect to distance is about 0.5 (Van Ommeren and Dargay, 2006), there will be diminishing marginal costs of distance. In combination with income-tax reductions, one expects that for longer distances, marginal wage compensation will be small. 3.2. The Data The data used in the empirical analysis are derived from annual register data from Statistics Denmark for the years 2003 2007. We observe the full population of establishments, 15 which we refer to as firms, and their workers. We observe all firm relocations for the year 2004 (but not for other years). We will analyse changes in annual wages between 2003 and 2005 the short-run as well as changes between 2003 and 2007 the long-run. For each year we have for December 31, information on worker s residence and workplace municipality, annual net wages, and a range of explanatory variables that is much more extensive than is usual for register data (for workers: educational level, age, gender, full- 13 These income tax reductions for workers with long commutes can be found in many European countries (Potter et al., 2006). 14 For example, in 2003, workers were entitled to deduct 3.2 DKK from gross income per kilometre for distances 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. 13

time versus part-time; for firms: number of workers, revenue and industry). To protect worker privacy, Statistics Denmark does not provide the exact residence and workplace addresses (within the municipality), but provides us with the commuting distances for the shortest route between these addresses on December 31. 3.3. Selection of Sample and Descriptive Statistics We select workers who had been employed for at least one year on January 1, 2004 by a firm with ten or more workers that relocated in the year 2004 (1043 firms). In most register datasets, the number of hours worked is not reported. Fortunately, we have information about whether jobs are full-time or part-time. Empirical evidence indicates that labour supply hardly changes given changes in commuting distance (Gutiérrez-i-Puigarnau and Van Ommeren, 2010). Nevertheless, it seems prudent to keep labour supply constant, so we have selected workers who work full-time or part-time during the whole period of observation. Employers seldom reimburse commuting expenses explicitly (viz. through a fringe benefit), so we ignore this issue. We exclude observations with missing information and observations for which the commuting distance exceeds 100 kilometres or the change in distance exceeds 50 kilometres. 16 Given these selection criteria, we exclude 68 firms. Our econometric approach is then based on a sample of 975 firms and 19,283 workers (about 20 workers per firm). This sample contains a subsample of workers who did not change employer or residence from January 2004 until the end of 2005 (7,459 workers) and another subsample of workers who did not make these changes until the end of 2007 (4,523 workers), see Table A1 in Appendix A. For both subsamples of workers, the commuting distance changes only in the year 2004 due to a 16 In an earlier version of this paper, we excluded observations with large changes in wages as they were assumed to be outliers. We obtained similar results, excluding these observations. 14

firm relocation. The correlation between changes in commuting distance and changes in wages for the selected subsamples is 0.034 for 2005 and 0.043 for 2007, suggesting that variation in distance might be relevant for determining variation in wages. We will initially focus on these two subsamples and later analyse selection issues. We have also regressed the change in commuting distance on pre-move covariates discussed later on (including commuting distance, wage, and firm fixed effects). It appears that changes in commuting distance are hardly explained by these covariates, as indicated by the R 2 which is equal to only 0.03 (in the short run) and 0.06 (in the long run). So, from a statistical point of view, changes in commuting distance are close to random. 17 About 55% of workers who were employed in January 2004 left their employer by the end of 2005. Hence, the annual mobility rate is about 33% (and above the national average of 25%, as one may expect for firms that relocate). For workers who have not changed employer or residence before the end of 2005, mobility drops to 13% in 2006/2007 (consistent with the stylised fact that job mobility depends negatively on job tenure). Moving residence is much less common than moving employer. In Table A2, Appendix A, it is shown that the selected firms are comparable in number of workers, wages, revenue, as well as the change over time in these variables to firms that did not 17 Furthermore, of the many individual explanatory variables included, only two variables, the pre-move commuting distance and age, have statistically significant effects in the short and long run analyses. Their effect sizes are very small. For example, a 10 years increase in age reduces the average change in commuting distance by only 200-300 m. Increasing the pre-move distance by 10 kilometres has a similar effect size. 15

relocate. 18 For example, relocating firms have, on average, 49 workers, whereas other firms have 53 workers. Importantly, the selected firms are also representative in terms of average commuting distance. The commuting distance distributions of workers belonging to relocating firms and other workers are also similar (see Figure B1, Appendix B). This suggests that our selected sample is representative for the population of firms and workers (the selected sample is also quite representative in terms of other indicators such as industry). 19 Another way to examine selectivity issues, is to analyse wage changes over time for a sample of workers who do belong to firms that do not relocate and to compare results with the selected sample (in these analyses, we exclude the change in distance variable). Both samples provide essentially identical effects for worker (e.g. age, educational level) as well as firm characteristics (firm size, change in firm size). Table 1 shows summary statistics of variables of interest before the firm relocation (in January 2003), the commuting distance in 2005 (after the firm relocation, but before any job or residence change) as well as the changes of commuting distance over time. We will focus first on the subsamples of workers who did not change employer or residence (the first two columns of Table 1). For these workers, as would occur given random changes in firm relocation, the average change in commuting distance is a few hundred metres, so close to zero (see also Figure B2, Appendix B). The average absolute change in distance for the selected sample is about 1.8 18 The difference in average workforce growth between relocating and nonrelocating firms is minimal. Both types of firms reduce the workforce by less than one worker. The variation in workforce reduction is somewhat larger for relocating firms. 19 In the selected sample, the number of firms is somewhat less than in the full sample, particularly in the long run. One of the main reasons is that some firms, when relocating, change identity according to the tax system (e.g., because the owner has changed). Consequently, according to the tax authorities, workers in these firms change employer. Arguably, this type of selection is random and therefore not problematic. 16

and 1.2 kilometres in the short-run and long-run, respectively, with relatively large standard deviations of 4.6 kilometres in the short-run and 2.5 kilometres in the long-run. Hence, although, firms tend to relocate over a rather short distance, the high standard deviation indicates that we have substantial variation in distance changes. The summary statistics of the selected sample and a sample that consists of workers who moved residence or employer (the last two columns of Table 1) are remarkably similar. 20 This is in line with the general idea that job moving in Denmark is not specific 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 year in 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 3 to 4 times higher in the movers sample (because changes in distance through residence or employer moves 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 the long run. This is in line with the standard result in the job search literature that workers 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 kilometres. In our interpretation of the empirical results, we will particularly focus on the results for a marginal increase in distance for a representative worker with a distance of 10 kilometres (the median distance), because this worker is not affected by income taxation rules regarding commuting. 20 The sample size of job and residence changers for the period 2003-2005 is somewhat less than those reported in Table A1 of Appendix A, because of missing information and because some workers leave the labour market or move more than once, whereas we only consider workers who move once. The sample size of these changers for the period 2003-2007 is much less than those reported in Table A1 (and even less than for 2003-2005), because the probability of leaving the labour market or moving more than once is quite large over a long period. 17

Table 1 Summary Statistics, Means and Standard Deviations for Different Samples Workers that remain at firms that relocate and did not Employer and residence movers change residence 2003-2005 2003-2007 2003-2005 2003-2007 Commuting distance, 2003 (km) 16.362 (17.141) 10.642 (11.408) 18.596 (16.943) 15.223 (15.561) Commuting distance, 2005 (km) 16.677 (17.326) 10.903 (11.510) 17.497 (17.393) 15.705 (15.760) Change in commuting distance, (km) 0.315 (4.922) 0.261 (2.813) -1.099 (13.219) 0.483 (9.124) Abs. change in commuting distance, (km) 1.788 (4.596) 1.222 (2.548) 7.631 (10.849) 4.253 (8.086) Change in log wage 2003-2005 0.079 (0.146) 0.146 (0.252) 0.067 (0.176) 0.132 (0.413) Distance between 12.5 and 50 km, 2003 (dummy) 0.425 (0.494) 0.260 (0.437) 0.530 (0.499) 0.370 (0.483) Distance> 50 km, 2003 (dummy) 0.059 (0.236) 0.015 (0.123) 0.060 (0.238) 0.044 (0.205) Annual net wage (1,000 DKK) 372.227 (173.722) 366.930 (175.431) 347.747 (191.994) 345.766 (133.782) Worker s age 39.591 (9.808) 39.396 (9.682) 38.859 (10.340) 37.819 (9.990) Male 0.662 (0.473) 0.642 (0.479) 0.702 (0.458) 0.657 (0.475) Vocational education 0.422 (0.494) 0.414 (0.493) 0.446 (0.497) 0.406 (0.491) Short-cycle higher education 0.070 (0.256) 0.071 (0.256) 0.066 (0.249) 0.070 (0.256) Medium-cycle higher education 0.109 (0.311) 0.106 (0.307) 0.088 (0.283) 0.106 (0.308) Bachelor 0.017 (0.130) 0.017 (0.128) 0.017 (0.128) 0.020 (0.140) Long-cycle higher education 0.109 (0.312) 0.111 (0.314) 0.076 (0.265) 0.106 (0.308) PhD-degree 0.006 (0.076) 0.004 (0.066) 0.007 (0.083) 0.005 (0.067) Number of obs. 7459 4523 11525 4178 Notes: standard deviations are in parentheses. 4. Empirical Results We will first focus on the long run. The econometric results of several specifications of firstdifferences models for changes between 2003 and 2007 based on specification (2) are shown in Table 2. We are mainly interested in the effect of changes in commuting distance on changes in wages, so we have experimented with several functional forms for distance (linear, loglinear). 18

Theoretical considerations marginal commuting costs fall in distance and because of income tax advantages for longer distances as well as empirical considerations given a linear spline functions, we find that the marginal effect of distance is strongly diminishing suggest that the inclusion of a logarithm of distance is preferred to a linear specification. We emphasise that our results are robust with respect to specification (also for specifications which are not explicitly discussed). 21 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 change employer or residence. The reported standard errors are clustered by firm. The first column [1] in Table 2 shows the results given a spline specification of log distance with given nodes at a one-way distance of 12.5 and 50 kilometres, i.e. at the distance where workers are 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 as for firm characteristics such as average change in commuting distance, number of employees, change in number of employees and industry (111 industry dummies) as these characteristics may influence wage growth. Furthermore, we include 278 regional (municipality) fixed effects, which capture changes in wage growth between regions (most Danish regions are small except for the municipality of Copenhagen). 21 For example, the log specification implies that the marginal effect of distance is extremely large for short distances (e.g., hundred meters), 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. When including the square of distance, the results remain robust. 19

Given this specification, for distances up to 12.5 kilometres, the distance elasticity of the wage is equal to 0.015 with a standard error of 0.007, and thereby statistically significant. The estimated effects of the control variables are in line with the usual findings. 22 These results suggest that above 12.5 kilometres, and also above 50 kilometres, the distance 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 is constant over distance. Therefore, we will proceed by assuming that the elasticity is constant over distance. Given this assumption, the distance elasticity is equal to 0.015 with 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 kilometres (i.e. a worker who does not receive an income tax reduction). For this worker, an increase in distance by 1 kilometre induces, on average, a wage increase of 0.147% (calculated as [log(11) - log(10)] 0.015). This is an economically significant effect. Given a daily labour supply of 7.4 hours and the average hourly wage of 165.59 DKK, the daily wage increase is then about 1.80 DKK (0.00147 7.4 165.59 DKK). Given a commuting speed of 30 km/h (the speed that applies to travel trips over 10 kilometres), an additional 1 km commute (one way) increases the daily commute by 4 minutes, and the 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, because it assumes that workers travel each day to their workplace, which is not the case due to business travel, teleworking and absenteeism. 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 setup, variation over time in the average commuting distance is limited, so one may need a much larger dataset to estimate this effect precisely. 20

Table 2 Changes in Log Wage between 2003 and 2007 [1] [2] [3] [4] [5] Firm fix. Employer Abs. chg. in eff. movers dist.>500m Change in log distance 0.015** (0.007) 0.015** (0.007) 0.014* (0.008) 0.016** (0.008) 0.017** (0.007) Change in log (distance -12.5) (when dist.>12.5) 0.002 (0.011) Change in log (distance - 50) (when dist. > 50) -0.027 (0.034) Change in average log distance (per firm) -0.005 (0.010) -0.005 (0.010) -0.028 (0.021) -0.001 (0.012) Male 0.031*** (0.011) 0.031*** (0.011) 0.033** (0.014) -0.104*** (0.032) 0.030* (0.016) Worker s age -0.007*** -0.007*** -0.007*** -0.006*** (0.002) -0.007*** Vocational education 0.044*** (0.013) 0.044*** (0.013) 0.040*** (0.015) -0.028 (0.055) 0.082*** (0.027) Short-cycle higher education -0.010 (0.011) -0.010 (0.011) -0.004 (0.013) -0.094** (0.042) -0.001 (0.027) Medium-cycle higher education 0.079** (0.032) 0.079** (0.032) 0.068** (0.034) -0.202* (0.110) 0.159*** (0.055) Bachelor 0.031** (0.014) 0.031** (0.014) 0.036** (0.016) -0.202 (0.042) 0.035 (0.031) Long-cycle higher education -0.051 (0.081) -0.051 (0.080) -0.018 (0.052) -0.391*** (0.125) -0.070 (0.069) PhD-degree 0.039*** (0.011) 0.039*** (0.011) 0.038*** (0.012) 0.047 (0.036) 0.095*** (0.021) Change in log number of employees 0.001 0.001-0.003 (0.006) 0.002 (0.002) Log number of employees -0.004 (0.004) -0.004 (0.004) -0.032** (0.015) 0.004 (0.007) Regional fixed effect (278) yes yes yes yes yes Dummies indicating industry yes yes no yes yes (111 industries) Firm fixed effects no no yes no no R 2 0.129 0.129 0.432 0.134 0.177 No. of observations 4523 4523 4523 2714 1605 Notes: Dependent variable is change in logarithm of wage; ***,**,* indicate that estimates are significantly different from zero at the 0.01, at the 0.05 and the 0.10 levels, respectively; standard errors (clustered by firm) are in parentheses. To interpret this result, it is useful to note that transport economists using stated preference data typically find that the commuter's value of time is about 50% of the gross wage rate (Small and Verhoef, 2007). For example, Brownstone and Small (2005) find that the average value of commuting time varies among different industrialized cities in the US from 20% to 100% of the gross wage rate. Using revealed preference data, it is common to find higher estimates. For 21

example, Fu and Ross (2007) find that the value of commuting time is about 90% of the wage. Small et al. (2005) also find that the 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 the overall commuter costs per hour travelled, i.e. the hourly costs of commuting including monetary expenses, are about twice the wage rate. Given the assumption that the overall worker costs of commuting time are twice the wage, our result implies that workers receive 8% of their commuting costs. This effect is in line with labour market models with search frictions, but cannot be explained by perfectly competitive models without these frictions. When we assume a lower worker cost of commuting, let's say, the cost of one hour commuting is equal to the wage rate, the compensation will be equal to 16% of the hourly wage. 23 These levels of compensating differentials for commuting because of search frictions are lower than, but not completely out of line with, those implied by a number of wage bargaining studies. For example, the results by Cahuc et al. (2006) imply a compensation between 0 and 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 focus on critical selection issues. Before we focus on selection issues, we address the importance of including firm fixed effects and controlling for explanatory variables. 23 Fosgerau et al. (2007) report a value of time of about 50% per hour for Danish commuters using stated preference data. 22

4.2.1. Firm fixed effects One criticism of the above estimation procedure is that we do not control sufficiently enough 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 have controlled for this (the wage gradient) using the average change in the commuting distance of the relocating firm (as well as changes in municipality). It may be the case that this control is not sufficient. To address this issue, we have estimated a specification with firm fixed effects (see column [3]). Individual-level workers compensating differentials for commuting are now solely identified using intrafirm compensating differentials. We find that the estimates are almost identical with a marginal effect of 0.014 (and a standard error of 0.008). 4.2.2. Inclusion of control variables We have argued above that changes in commuting distance due to firm relocation can be interpreted as the outcome of a quasi-natural experiment. If this is true, the results must not change substantially if we exclude all control variables, because these control variables are largely orthogonal to changes in commuting distance. This appears to hold. Without any control variable, we find an elasticity of 0.016 with a standard error of 0.06. If we include firm fixed effects, but no other control variables, we find an elasticity of 0.012 and the same standard error. 4.2.3. Selection of workers that do not change residence We have examined to what extent the selection regarding that workers do not move residence causes a selection bias. Clearly, this is a less important issue, because only 20% of workers move residence during the period of observation. Residential moving costs are high in Denmark, due to 23

substantial transaction costs in the housing ownership market as well as due to rent control and public housing regulation in the rental market. In such a market, combined with high job mobility rates, it is usually not rational for workers to move residence closer to the current employer, since the anticipated employment duration will be short. 24 This makes it likely that moving residence is mainly due to change in housing consumption and in general is unrelated to the relocation of the firm. Nevertheless, to address this selection bias, we have estimated standard Heckman selection models using the presence of children in the age category between 6 and 18 as an instrument in the selection step. The idea here is that children in this age category strongly reduce residential mobility as these children go to school, which increases the cost of residential moving. As one may argue that the presence of children affects wage growth, we have estimated these models controlling for the number of children (irrespective of children s age). The full results are reported in Table C1 in Appendix C. It appears that the effect of commuting distance on wages is essentially the same as discussed in Table 2. 4.2.4. Other selection issues The results discussed above were based on a sample of workers who did not change from fulltime to part-time (or the other way around) during the whole period of observation. We have reestimated the model including workers who changed from full-time to part-time (or the other time round) during the period of observation, while controlling for part-time work. This generates almost identical results than those reported here. In addition, we have re-estimated models including workers with a company car (0.3% of the sample). Including these workers does not affect the estimation results. We have experimented with less selective criteria 24 Interestingly, Zax (1991) has noted that given spatial differences in house prices, moving residence farther away after a firm relocation is a rational choice for workers when firms relocate towards workers. 24

regarding the size of the firm. Our results remain robust up to the point of selecting firms with at least five workers. One may also wonder to what extent our main results are robust in the sense that they only hold for a subgroup of observations. For example, it may be thought that workers with relative short commuting distances (before the firm relocation) are much more sensitive to changes in commuting distance (because these workers have sorted themselves into jobs close to the residence). We have therefore re-estimated the model selecting only workers with a commute of less than 12.5 kilometres (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 meters are usually economically of little or no importance, but are relatively common in our data (65% of the observations). We find that the effects become slightly more pronounced if one excludes 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 of changes in commuting on changes in wages. To avoid endogeneity issues due to relocation in the housing market, he employs a selected sample of workers who voluntarily change the length of their commute when they move employer. In the current paper, our focus is on workers confronted with an exogenous commuting distance change when their employer relocates. We have also followed the approach by Manning (2003), so we estimate (2) for workers who move 25

employer. 25 These results 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 current data, 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 same way to increases and decreases in distance. To test for the latter, we have estimated models where we allow these effects to differ, see Table D1, Appendix D. The earlier point estimate of 0.015 is within the 95% confidence intervals of both estimates. However, we find that the effect is only positive and significant when distances decrease (and the estimates are statistically different using a F-test). It appears however that this result is not robust to specification. For example, we have re-estimated the model excluding 30 observations with extreme wage changes (0.7% of the number of observations). We now find that there is no statistical difference between the effects of increases and decreases in distance (at the 5% significance level), and the point estimate of the increases in distance effect is now higher. 26 Consequently, we believe that the data indicate that wages respond in the same way to increases and decreases in distance, in the long-run. 4.5. The Competitive Market Model without Search Frictions According to the competitive labour market model without search frictions, within-firm variation of commuting distance is not relevant to explain wages. If one assumes that the model without search frictions is the true one, then one may estimate the effect of distance by using an estimator 25 One slight technical complication is that some workers move employer more than once after they have left the firm. To simplify the estimation procedure, we focus on 2,714 workers who moved once (before the end of 2007). 26 When we exclude even more wage outliers (e.g. 3% of the number of observations), we find the same result. 26

that uses only between-firm variation in distance (and other indicators), so we identify the effect of changes in the firm-average distance. We emphasise that this estimate may introduce a bias because one cannot control for unobserved firm characteristics that may be relevant (e.g., teleworking policies). The results are reported in Table 3. We find that the effect of distance, so α 1 + φ, is positive (and significant at the 10% level). The effect size is about the same as the estimate of α 1 reported in Table 2. This suggests that φ, which captures the wage gradient, is negligible (consistent with our findings in Table 2). This makes sense in the current context where commuting distance changes due to firm relocation are usually small so most firms relocate within the local labour market. Table 3 Changes in Log Wage, Between-Firm Estimates 2003-2007 2003-2005 Change in log distance 0.017* (0.009) 0.009* (0.005) Dummy indicating male 0.027 (0.030) 0.043 (0.032) Worker s age -0.008*** -0.005*** Dummy indicating worker with vocational education 0.075* (0.044) 0.025 (0.071) Dummy indicating worker with short-cycle higher education -0.049 (0.050) -0.013 (0.042) Dummy indicating worker with medium-cycle higher education 0.095 (0.125) 0.015 (0.100) Dummy indicating worker with bachelor -0.017 (0.047) 0.104** (0.048) Dummy indicating worker with long-cycle higher education -0.336 (0.421) -0.187 (0.170) Dummy indicating worker with PhD-degree 0.016 (0.033) 0.004 (0.035) Change in logarithm of firm s number of employees 0.002 (0.003) 0.003 (0.002) Logarithm of firm s number of employees 0.013* (0.007) 0.001 (0.007) Regional fixed effect yes yes Dummies indicating industry yes yes R 2 0.433 0.487 No. of observations of firms 4523 7459 Notes: Dependent variable is change in logarithm of wage; ***,* indicate that estimates are significantly different from zero at the 0.01 and 0.1 levels respectively; standard errors (clustered by firm) are in parentheses. 27

Table 4 Changes in Log Wage between 2003 and 2005 [1] [2] [3] [4] [5] Firm fix. eff. Abs. chg. in dist.>500m Workers that remain at firms 2003-2007 0.002 (0.002) Change in log distance 0.001 0.001 0.001 0.001 Change in log (distance -12.5) 0.003 (when distance >12.5) (0.005) Change in log (distance - 50) -0.002 (when distance > 50) (0.012) Change in average log distance 0.001 0.006 0.003 0.042** (per firm) (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 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 of 0.0001 0.0001 0.0004 0.0001 employees (0.0009) Log number of employees 0.001 0.001 0.004 0.001 (0.002) (0.004) (0.002) Regional fixed effect (271) yes yes yes yes yes Dummies indicating industry yes yes no yes yes (111 industries) Firm fixed effects no no yes no no R 2 0.112 0.112 0.394 0.151 0.119 No. of observations 7459 7459 7459 2682 4523 Notes: Dependent variable is change in logarithm of wage; ***,**,* indicate that estimates are significantly different from zero at the 0.01, at the 0.05 and the 0.10 levels, respectively; standard errors (clustered by firm) are in parentheses. 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 by considering the effect on wage changes between 2003 and 2005. Again we have estimated a large number of specifications (see Table 4). We now find that the effect is much smaller with a point estimate of 28

around 0.001. For a worker with a distance of 10 kilometres, an increase in distance by 1 kilometre induces, on average, a wage increase of 0.01%. 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 the long-run effect. 27 Finally, and in contrast with the long-run, and in line with theoretical considerations, we find that the effect of increases in distance exceeds the effect of decreases in distance. For example, given the specification used in Table 4, we find that the increase in distance is about 0.02 with a standard error of 0.005 whereas the effect of a decrease in distance is insignificant. 5. Conclusion This paper analyses the effect of commuting distance on wages using matched register data for firms and workers for Denmark. We deal with the endogeneity of commuting distance by means of a quasi-natural experimental approach using changes in distance that are due to firm relocations. We show that an increase in commuting distance implies a moderate wage increase three years after the firm relocation (a 1 kilometre increase induces a wage increase of about 0.15%), while this effect is much smaller the year after the relocation. The estimated effect implies individual-level compensating differentials for commuting distance as predicted by labour market models that allow for job search frictions, and due to the quasi-natural experimental set-up excludes a range of other competing explanations frequently mentioned in the literature. Our findings are consistent with the notion that individual-level wage setting is an important characteristic of the Danish labour market. This study therefore implies 27 If we re-estimate models while excluding wage outliers, short-run and long-run effect increases. Hence, we arrive at the same conclusion. 29

that employers have market power and pay below workers' productivity (Marimom and Zilibotti, 1999; Pissarides, 2000). Technical University of Denmark VU University Technical University of Denmark 30

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Appendix A Table A1 Sample Selection Procedure Workers Firms 1 Full sample 19,283 975 2 Change in residence (2004-2005) 2,419 6 3 Employer change (2004-2005) 10,697 367 4=1-2-3 Short-run subsample (exclude residence and employer changes) 7,459 603 5 Change in residence (2006 and 2007) 1,181 9 6 Employer change (2006 and 2007) 2,023 78 7=4-5-6 Long-run subsample (exclude residence and employer changes) 4,523 524 Notes: Firms with 10 or more workers that relocated between January 2004 and December 2004 and workers with constant full/part-time job (without change in working hours). This excludes a few records with missing information. Table A2 Summary Statistics of Firms Variable Non-relocating firms Relocating firms in 2004 Workers 53.364 (300.173) 49.137 (191.787) Revenue (million DKK) 95.436 (780.174) 93.485 (488.743) Wages (million DKK) 17.453 (94.252) 16.024 (52.065) Change in number of person's full year's work -0.543 (42.107) -1.309 (116.189) Change in revenue (million DKK) 12.974 (279.557) 7.670 (230.273) Change in wages (million DKK) 0.991 (17.348) 1.162 (20.973) Commuting distance (km) 19.026 (33.275) 20.175 (35.582) Number of observations 16,708 1,160 Notes: Firms with 10 or more workers; changes between 2005 and 2003; standard deviations are in parentheses. 35

Appendix B. Fig. B1 Commuting Distances (km) in 2003 (a) population (2,699,855 obs.) (b) workers of firms that relocate and who do not change employer/residence 2003-2007 (4,523 obs.) (c) workers of firms that relocate and who do not change employer/residence 2003-2005 (7,459 obs.) 36

Fig. B2 Change in Commuting Distances (km) a) 2003-2005 b) 2003-2007 37

Appendix C Table C1 Heckman Selection Models: Wage Differences and Not Moving Residence Wage differences Not moving residence 2003-2007 2003-2005 2003-2007 2003-2005 Change in log distance 0.015** (0.006) 0.001 Change in average log distance (per firm) -0.011 (0.011) 0.006 (0.009) 0.090** (0.037) -0.012 (0.040) Male 0.036*** (0.012) 0.005 (0.005) -0.041 (0.044) 0.021 (0.045) Worker s age -0.009*** -0.003*** (0.0003) 0.017*** (0.003) 0.030*** (0.002) One child 0.017 (0.010) -0.001 (0.004) 0.058 (0.065) 0.130** (0.055) Two children -0.017* (0.010) 0.002 (0.004) 0.304*** (0.069) 0.474*** (0.076) Three children (or more) 0.0002 (0.017) 0.003 (0.007) 0.221* (0.123) 0.467*** (0.128) Children 6-18 years old (instrument) 0.112** (0.057) 0.274*** (0.063) Vocational education 0.056*** (0.015) 0.007 (0.006) -0.172** (0.079) -0.249*** (0.072) Short-cycle higher education 0.0002 (0.014) 0.013* (0.007) -0.161** (0.071) -0.211*** (0.071) Medium-cycle higher education 0.104*** (0.031) 0.026** (0.012) -0.331*** (0.122) -0.369*** (0.138) Bachelor 0.044*** (0.016) 0.016*** (0.006) -0.177*** (0.059) -0.236*** (0.060) Long-cycle higher education -0.035 (0.073) -0.026* (0.014) -0.096 (0.196) 0.117 (0.216) PhD-degree 0.037*** (0.012) 0.015*** (0.004) 0.136** (0.053) 0.009 (0.051) Change in log number of workers 0.001 0.0001 Log number of workers -0.004 (0.004) 0.001 (0.002) Regional fixed effect yes yes no no Dummies indicating industry yes yes no no Sigma 0.256 (0.009) 0.138 (0.002) Rho -0.633 (0.053) 0.017 (0.013) Lambda -0.162 (0.018) 0.002 (0.002) No. Observations 5704 8287 5704 8287 Notes: Model accounts for selection regarding residence change; ***,**,* indicate that estimates are significantly different from zero at the 0.01, at the 0.05 and the 0.10 levels, respectively; standard errors (clustered by firm) are in parentheses; all explanatory variables in the selection equation are from 2003, so prior to the firm relocation. 38

Appendix D Table D1 Changes in Log Wage between 2003 and 2007 with Distinction between Decrease and Increase in Distance [1] [2] Change in log distance (increase) -0.009 (0.023) 0.014 (0.012) Change in log distance (decrease) 0.019*** (0.007) 0.008** (0.004) Change in average log distance (per firm) -0.003 (0.011) 0.0004 (0.008) Male 0.031*** (0.011) 0.024 (0.011) Worker s age -0.007*** -0.007*** Vocational education 0.044*** (0.013) 0.037*** (0.012) Short-cycle higher education -0.011 (0.011) -0.016 (0.012) Medium-cycle higher education 0.077** (0.032) 0.072** (0.031) Bachelor 0.031** (0.014) 0.021 (0.015) Long-cycle higher education -0.052 (0.081) 0.011 (0.033) PhD-degree 0.040*** (0.011) 0.029*** (0.009) Change in log number of employees 0.001 0.001 Log number of employees -0.004 (0.004) -0.005 (0.004) Regional fixed effect (278) yes yes Dummies indicating industry (111 industries) yes yes R 2 0.133 0.132 No. of observations 4523 4493 Notes: Dependent variable is change in logarithm of wage; [2] excludes observations for which absolute change in log wage >1.1 ; ***,**,* indicate that estimates are significantly different from zero at the 0.01, at the 0.05 and the 0.10 levels, respectively; standard errors (clustered by firm) are in parentheses. 39