The Decline of Drudgery and the Paradox of Hard Work

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1106 June 2014 The Decline of Drudgery and the Paradox of Hard Work Brendan Epstein Miles S. Kimball NOTE: International Finance and Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IDFPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at www.ssrn.com.

The Decline of Drudgery and The Paradox of Hard Work (cid:3) Brendan Epstein and Miles S. Kimball y z Abstract We develop a theory that focuses on the general equilibrium and long-run macroeconomic consequences of trends in job utility. Given secular increases in job utility, work hours per capita can remain approximately constant over time even if the income e⁄ect of higher wages on labor supply exceeds the substitution e⁄ect. In addition, secular improvements in job utility can be substantial relative to welfare gains from ordinary technological progress. These two implications are connected by an equation (cid:135)owing from optimal hours choices: improvements in job utility that have a signi(cid:133)cant e⁄ect on labor supply tend to have large welfare e⁄ects. Keywords: Labor supply, work hours, drudgery, income e⁄ect, substitution e⁄ect, job utility. JEL classi(cid:133)cations: E24, J22, O40. The views in this paper are solely the responsibility of the authors and should not be interpreted as (cid:3) re(cid:135)ectingtheviewsoftheBoardofGovernorsoftheFederalReserveSystemorofanyotherpersonassociated with the Federal Reserve System. The authors are thankful, without implicating, for comments received by seminar participants at the University of Michigan and also during visits to the Board of Governors of the Federal Reserve System, Brown University, the Federal Reserve Bank of Atlanta, the Federal Reserve Bank of Philadelphia, the Federal Reserve Bank of Richmond, and McMaster University. Board of Governors of the Federal Reserve System (e-mail: Brendan.Epstein@frb.gov). y Professor, University of Michigan, and NBER (mkimball@umich.edu). z

1 Introduction In his 1930 essay, (cid:147)Economic Possibilities for Our Grandchildren,(cid:148)Keynes predicted that a large increase in leisure would take place over the following century, but robust signs of such a leisure boom have failed to materialize. As shown in Figure (1), for a large set of OECD countries, from 1956 through 2009 aggregate (real) consumption per working-age population (ages 15-64) rose by100%andmore, while workhours per working-age populationhave been dramatically (cid:135)at in comparison.1 It is not unreasonable to think, as Keynes did, that the extent to which consumption has increased, along with long-run growth in real wages, should have led to a prominent trend decline in work hours driven by the income e⁄ect overtaking the substitution e⁄ect. Indeed, there is good reason to think that income e⁄ects are substantial (see, for instance, Kimball and Shapiro 2008). Why are people still working so hard? And, what are the welfare e⁄ects of this paradox of hard work? Work Hours per Population Private Consumption per Population 2.5 2.5 Australia Australia Euro Euro 2 Japan 2 Japan US US 1.5 1.5 1 1 0.5 0.5 0 0 0.5 0.5 1960 1970 1980 1990 2000 2010 1960 1970 1980 1990 2000 2010 Figure 1: Left panel: di⁄erence between the natural logarithm of work hours per working age population (15-65) and its corresponding value in 1956. Right panel: di⁄erence between the natural logarithm of private consumption per working age population (15-65) and its corresponding value in 1956. Data are at yearly frequency. Consumption is takenfromthePennWorldTables(pwt.sas). Hoursperpopulationaretheproductofhoursworkedperworkerandthe employment-to-population ratio. Hours worked per worker are from the Groningen Total Economy Database (which ismaintainedbytheConferenceBoard,conference-board.org). Dataontheworking-agepopulation(ages15-64)and 1SeePrescott(2004),Alesina,Glaeser,andSacerdote(2006),Rogerson(2006,2007,and2009),Faggioand Nickell (2007), Ljungqvist and Sargent (2007), Ohanian, Ra⁄o, and Rogerson (2008), Shimer (2009), Fang and McDaniel (2011), McDaniel (2011), Guner, Kaygusuz and Ventura (2012), and Epstein and Ramnath (2014) for complementary work related to cross-country di⁄erences in hours worked per population. 1

employment are from the OECD (stats.oecd.org). Countries: Australia, Canada, Euro (simple average of countryspeci(cid:133)cratiosoverAustria,Belgium,Finland,France,Germany,Italy,Netherlands,Spain,Sweden,Switzerland,and the United Kingdom), Japan and United States. In principle there are four alternative, but not mutually exclusive, explanations through which the paradox of hard work can be rationalized (detailed just below). Of the set of explanations for the paradox of hard work, in this paper we focus on job utility. Economists have long understood that cross-sectional di⁄erences in job utility at a particular time give rise to compensating di⁄erentials. We develop a theory that focuses on a less-studied topic: understanding the long-run macroeconomic consequences of trends in job utility. The four rationalizations of the paradox of hard work are as follows. 1. Assuming that the elasticity of intertemporal substitution is large. However, empirical evidence suggests the contrary. Hall (1988) (cid:133)nds this elasticity to be approximately zero, BasuandKimball(2002)(cid:133)ndthatplausiblevaluesarelessthan0.7, andKimball, Sahm, and Shapiro (2011) (cid:133)nd a value of approximately 0.08.2 2. An increasing ratio of e⁄ective marginal wages to consumption. This could be the result,forinstance,ofareductionintheprogressivityofthetaxsystem,anintensi(cid:133)cation of competition for promotions within (cid:133)rms, and increasing educational debts.3 3. Anything that keeps the marginal utility of consumption high. This could be, for example, because of habit formation, whether internal and external ("keeping up with the Joneses"), and from the introduction of new goods.4 4. Anything that serves to keep the marginal disutility of work low. This can be, for instance, the result of technological progress in household production, non-separability betweenconsumptionandleisure (King, Plosser, andRebelo (1988), BasuandKimball (2002)), and jobs getting nicer.5 2Seealso,forexample,Altonji(1982),Card(1994),PattersonandPesaran(1992),Fuhrer(2000),Vissing- Jorgensen (2002), and Yogo (2002). 3For additional discussion, see, for instance, Shapiro and Kimball (2008). 4See, for instance, Abel (1990), Fuhrer (2000), Luttmer (2005), Rayo and Becker (2007), and Struck (2013). 5It follows that our research is broadly related to many literatures. These literatures include, but are not limited to, work by MaCurdy (1981), Altonji (1982 and 1986), Hansen (1985), Mankiw, Rotemberg and Summers (1985), Rogerson (1988), Blundell, Meghir, and Neves (1993), Mulligan (1998), Blundell and MaCurdy (1999), Blundell, Chiappori, Magnac, and Meghir (2001), Mulligan (2001), Coulibaly (2006), Krusell, Mukoyama, Rogerson, and Sahin (2008), Francis and Ramey (2009), Prescott, Rogerson, and Wallenius (2009), and Prescott and Wallenius (2011). 2

We propose an intertemporal framework for thinking about the causes and e⁄ects of secular increases in job utility, that is, of jobs getting nicer. Some of the questions that our framework provides answers to are the following. Howdo(on-the-job)e⁄ort,amenities,job-enjoymenttechnology,andlabor-augmenting (cid:15) technology interact? What are the key determinants of long-run labor supply given job utility? (cid:15) How does job utility matter for (cid:133)rms(cid:146)optimization problems and (cid:133)rms(cid:146)ongoing ability (cid:15) to operate, attract workers, and establish job parameters given long-run changes in labor-augmenting technology and job-enjoyment technology? What are the long-run welfare e⁄ects of changes in job utility? (cid:15) In turn, the answers to these questions lead to two contributions to the macro and labor economics literatures. First, we show that secular improvements in job utility(cid:151)the decline of drudgery(cid:151)can induce work hours to remain approximately constant over time even if the income e⁄ect of higher wages on labor supply exceeds the substitution e⁄ect of higher wages. Therefore, the paradox of hard work is not necessarily evidence that the elasticity of intertemporal substitution is large, that preferences are strongly non-separable, or that preferences have some other feature such as habit formation. Second, we show that secular improvements in job utility can be very substantial in comparison to the welfare gains from ordinary (say, labor-augmenting) technological progress. These two implications are connected by an equation: improvements in job utility that have a signi(cid:133)cant e⁄ect on labor supply tend to have large welfare e⁄ects. This paper proceeds as follows. Section 2 relates our work to the static theory of compensating di⁄erentials. Section 3 provides a general overview of our framework. Then, Section 4 discusses the variables we focus on and how our formulation maps into the real world. Sections 5 and 6 focus, respectively, on the optimization problems of individuals and (cid:133)rms. Section 7 deals with the economy(cid:146)s general equilibrium. Then, Section 8 addresses the welfare consequence of changes in job utility. Finally, section 9 concludes. 3

2 The Static Theory of Compensating Di⁄erentials The natural point of reference for our analysis is the theory of compensating di⁄erentials, spelled out originally in the (cid:133)rst ten chapters of Book I of (cid:147)The Wealth of Nations(cid:148)(Smith, 1776). A standard modern reference on compensating di⁄erentials is Rosen (1986). 2.1 Worker and Firm Choices The solid line in the left panel of Figure 2 is a wage/job-utility frontier: jobs o⁄ering lower job utility will, in principle, compensate by o⁄ering higher real wages (in the (cid:133)gure W is the real wage and J is job utility). Thus, all else equal, individuals face a trade-o⁄between these two variables. Conditional on individual preferences, a particular worker optimizes by choosing a feasible point on the (solid) frontier in the (W;J) plane. The solid line in the right panel of Figure 2 is a job-utility/output frontier: in order to improve job utility (cid:133)rms must divert part of their resources away from the production of output (Y). Given its idiosyncratic costs of job utility in terms of output, a particular (cid:133)rm optimizes by choosing a feasible point on the (solid) frontier in the (Y;J) plane. J J a' a c d' b d W Y Figure 2: Theory of compensating di⁄erentials. Left panel: real wage (W) / job utility (J) frontier faced by workers. Right panel: job utility / output (Y) frontier faced by (cid:133)rms. 2.2 Movements Along the Frontiers Suppose higher output and higher real wages came from movements along the solid frontiers (a to b in the left panel and c to d in the right panel). As argued in Kimball and Shapiro (2008), income e⁄ects on labor supply are substantial. So, the higher real wage implied by moving from point a to point b would tend to reduce work hours. In addition, if work hours 4

are increasing in job utility, then lower job utility implied by moving from point a to point b also puts downward pressure on work hours. 2.3 Movements of the Frontiers However, the frontiers themselves can shift (the dashed lines in Figure 2). As the economy(cid:146)s choicesetexpands,optimalchoicescanentailmovingtopointssuchasa andd,inwhichcase 0 0 job utility, output, and real wages all rise, and increases in job utility emerge as potentially o⁄setting to income e⁄ects. The theory we develop in this paper focuses attention on understanding the dynamic general equilibrium implications and endogenous foundations of such intertemporal changes in the economy(cid:146)s choice set. This understanding is complementary to the long-standing static, partial equilibrium microeconomic framework of compensating di⁄erentials. 3 The Social Planner(cid:146)s Perspective There are no distortions in our model so the planning version of the economy is equivalent to a decentralized economy with perfect competition. Both perspectives are valuable, and we begin with the social planning perspective. Consider individuals who obtain utility from consumption and non-work time. A standard assumption is that any time devoted to work always subtracts from utility. Our alternative assumption is that process bene(cid:133)ts and process costs of work(cid:151)what we call (cid:147)job utility(cid:148)(cid:151)matter as well. The problem that an idealized social planner would face helps summarize our overall framework. Thesocialplanner(cid:146)sprobleminvolveschoosingconsumption, capital, workhours devoted to particular jobs, e⁄ort demands by a particular job (per hour of work), and amenities provided by a particular job in order to maximize a household(cid:146)s lifetime utility given (cid:133)rms(cid:146)production structures and other standard constraints. 3.1 Baseline Assumptions We consider a small open economy in which agents can freely borrow and lend at the exogenously determined real interest rate r (equal to (cid:26), the rate at which all economic agents 5

discount the future). Capital is freely mobile across (cid:133)rms and boarders. We assume that all bene(cid:133)ts and costs to (cid:133)rms and workers other than the utility from leisure and consumption are proportional to work hours. These assumptions jointly guarantee that there will never be any disagreement between workers and (cid:133)rms about job parameters other than the wage. Furthermore, given fully mobile capital and the exogenous world interest rate, we can focus on steady state analysis since the absence of state variables implies that changes between steady states occur instantaneously. The model is cast in continuous time (we omit time indexes in order to avoid notational clutter). 3.2 Individuals and Firms The economy is inhabited by i = 1,...,I (cid:133)rms all of which are producers of the same (cid:133)nal good and a continuumof individuals whose mass is normalized to one. Households each have only one individual, so we will use the terms household and worker interchangeably. Utility depends on consumption, the division of time into work time and non-work time, and job utility per hour of work. Job utility depends on e⁄ort, amenities, and job-enjoyment technology (we elaborate on all of these further below). Firms produce output using capital and e⁄ective labor input (the product of hours, e⁄ort and labor-augmenting technology), and can vary in their real wage and job utility o⁄erings. 3.3 Planning Problem Table 1 below lays out our notation. In that notation, the planning problem is: max e (cid:26)t (C;T H; H J (E ;A ;(cid:9) ))dt C,Hi,Ei,Ai,Ki (cid:0) U (cid:0) i i i i i i Z P s.t. _ Y (K ;Z E H )+(cid:5) = C +K (cid:14)K + A H , i i i i i i (cid:0) i i i P P and H = H. i i P _ For any variable X, X refers to its change over time. 6

Table 1: Variables and Parameters Variable Description Parameter Description Instantaneous utility (cid:26) Discount rate U J Job utility function T Time endowment t Denotes time (cid:9) Job-enjoyment technology i C Total consumption of (cid:133)nal output (cid:5) Non-labor, non-interest income H Total work hours (cid:14) Depreciation rate H Work hours devoted to ith (cid:133)rm i E ith (cid:133)rm e⁄ort demands i A ith (cid:133)rm amenities provision i Y ith (cid:133)rm (cid:133)nal output i K ith (cid:133)rm capital use i Z ith (cid:133)rm labor-augmenting technology i 4 From Planning Problem to Real World Our objective is to deal with many real world features of jobs without adding too much to the complexity of our model. So, we have a broad interpretation of consumption, work hours, e⁄ort, amenities, and job utility that allows each to address multiple dimensions of the real world. For example, job-enjoyment technology is meant to capture both innovations in the nature of work proper and innovations in the nature of the work environment. 4.1 Consumption and Work Hours 4.1.1 Consumption Consumption, C, is meant to capture all the richness of how resources other than time a⁄ect life outside of working hours. For instance, a broad notion of consumption necessarily accounts for fringe bene(cid:133)ts. 4.1.2 Work Hours Work hours, H, is meant to capture every way in which a person(cid:146)s job interferes with the quantityandenjoymentofnon-worktimeandhomeproduction. Forexample,ifanindividual is unable to stop thinking about work issues while at home and this interferes with other activities at home, then that can be considered an e⁄ective reduction in leisure and hence an increase in H. Also, consider time spent away from home due to work-related travel. Travel may boost the utility of non-work time if it provides pleasant and interesting experiences. However, work-related travel can also hamper the enjoyment of non-work time because of 7

being away from friends and family. In either case, an adjustment to H may be warranted. 4.2 Job Utility 4.2.1 E⁄ort E⁄ort, E, is meant to capture all aspects of a job that generate proportionate changes in e⁄ective productive input from labor. E⁄ort has many dimensions. For example, the intensity of a worker(cid:146)s concentration on a task while at his or her work station, the amount of time spent at the water cooler or in other forms of on-the-job leisure, own time spent cleaning and beautifying the work place, time spent in o¢ ce parties or morale building exercises during work hours, and amount of time spent pursuing worker interests that have some productivity to the (cid:133)rm but would not be the boss(cid:146)s (cid:133)rst priority, are all dimensions of e⁄ort. 4.2.2 Amenities Amenities, A, are job characteristics whose cost to the (cid:133)rm is in terms of goods. The real-world characterization of amenities is just as rich as the characterization of e⁄ort. For instance, amenities include the number of parking spots, the quality of air conditioning, and the quality and capacity relative to the number of employees of the o¢ ce gym.6 4.2.3 Job-Enjoyment Technology Job-enjoyment technology a⁄ects the mapping of e⁄ort and amenities into overall job utility. Therefore, changes in this technological component can be interpreted as capturing innovations in the nature of work proper, or innovations related to the work environment. Innovations in the Nature of Work Proper Innovations in the nature of work proper come in many forms. For example, working in groups, establishing clear guidelines about what is expected from the worker, allowing workers to have greater discretion in the way projects are carried out, developing creative ways to give workers feedback on their performance (including constructive criticism techniques rather than, say, yelling at the worker about what he or she is doing wrong), improving the organizational structure of the (cid:133)rm in 6See Epstein and Nunn (2013) for a treatment of amenities in an environment with search frictions. 8

termsofwhodoeswhat, howtheydoitandwhentheydoit, andallowingindividualsgreater (cid:135)exibility in determining the time during which work is carried out all count historically as innovations in the nature of work proper. Innovations in the Nature of the External Work Environment Innovations related to the external work environment come in many forms as well. In particular, think of the advent of air conditioning, the distribution, design, and allocation of physical work space (such as cubicalization or open o¢ ce environments), the provision of on-site childcare, exercise, and laundry facilities, and the institution of measures to reduce the incidence of sexual harassment. 4.2.4 Interpretation of the Job Utility Function The job utility function J itself is the optimum over many possible ways of doing things. i For example, consider two production techniques, as shown in Figure 3 in (E;J) space. Production technique 1, yielding 1, results in relatively higher job utility at lower levels Ji of e⁄ort, while production technique 2, yielding 2, results in relatively higher job utility Ji at higher levels of e⁄ort. Then, J is the upper envelope (bold) of these two techniques. i The analytical framework that we develop is robust to such non-concavities in job-utility functions. J J 2 J 1 E Figure 3: The job-utility function, J , as the upper envelope of the two di⁄erent production techniques 1 and 2. i Ji Ji 4.2.5 Reducing the Number of Dimensions for the Arguments of Job Utility The function J = ( ; ;(cid:9) ) maps , , and (cid:9) into the hourly utility associated with i i i i i i i i J E A E A being at work. is a vector describing all dimensions of what the average hour of work i E 9

is like that a⁄ects productivity (aspects of e⁄ort, including the fraction of time spent in each di⁄erent activity at work). is the amenities counterpart to this. Recall that (cid:9) is i i A job-utility technology. and are determined optimally by (cid:133)rms. i i E A The reduced form job utility function comes from maximizing over these vectors, subject to keeping e⁄ort-related productivity and the cost of amenities the same, that is, J (E ;A ;(cid:9) ) = max ( ; ;(cid:9) ) i i i i i i i i i, i fJ E A g E A s.t. E = E ( ), i i i E A = p , i A i (cid:1)A i where p is a vector of real amenity prices. So, the number E (cid:151)hourly e⁄ort per worker(cid:151) i i A givese⁄ectiveproductiveinputfromanhouroflaborbeforemultiplicationbylabor-augmenting technology, whilethenumberA summarizestheexpenditureonamenitiesperhourofwork.7 i We allow for J to be either positive or negative and we allow for the possibility that i job utility is increasing in e⁄ort at relatively small levels of e⁄ort, but we assume it must be decreasing in e⁄ort at relatively high levels of e⁄ort if only because physical and mental exhaustion eventually push J toward (otherwise there would be no upper limit to i (cid:0)1 feasible E ).8 We also assume that @J =@A > 0 and @J =@(cid:9) . i i i i i 7The relative price of amenities can simply be thought of as being part of the overall technological component (cid:9) . Indeed, think of production of (cid:133)rm is kth ammenity as i k =(cid:18)kYK, Ai i i where(cid:18)k istechnologyandYK istheamountofthe(cid:133)rm(cid:146)stotaloutput,Y ,devotedtoproducingtheamenity. i i i Then, the (cid:133)rm(cid:146)s total expenditure on amenity k is (1=(cid:18)k) k = YK and we de(cid:133)ne pk (1=(cid:18)k). Thus, for instance, an increase in technology (cid:18)k decreases the relat i iv A e i price i of the kth amenity A . i E (cid:17) xcept w i hen the real i prices of amenities are visible in markets it might be impossible to distinguish between an improvement in job-enjoyment technology and a fall in the price of an amenity. 8We consider this to be the more intuitive case, although our results are unaltered by assuming that job utility is always decreasing in e⁄ort. 10

5 The Household 5.1 Optimization We now focus on the decentralized version of the representative worker(cid:146)s optimization problem. We show that this problem can be broken into three optimization subproblems that jointly answer the following question: Once job utility is accounted for, what are the key determinants of labor supply? 5.1.1 Main Problem Given (cid:133)nancial wealth M and job opportunities, the worker chooses consumption C, total work hours H, work hours devoted to each job H , to maximize utility i max e (cid:26)t(U (C)+(cid:8)(T H)+ H J )dt, C;H;Hi (cid:0) (cid:0) i i i Z P s.t. _ M = rM +(cid:5)+ W H C, (1) i i i (cid:0) P H = H, i i P and H 0. i (cid:21) Overall (cid:135)ow utility comes from consumption utility U, utility from o⁄-the-job leisure (cid:8), W is the real wage o⁄ered by the ith job, which the worker takes as given. We assume that i U > 0, U < 0, (cid:8) > 0, and (cid:8) < 0. The choice of job is represented simply as the choice of 0 00 0 00 whether to devote strictly positive work hours to any one job in particular. Here, we assume that utility is additively separable between consumption C and all the dimensions of labor. (A companion paper relaxes that assumption, and yields broadly similar results as those we obtain in the present paper). 11

5.1.2 Optimization Subproblems The current-value Hamiltonian associated with the worker(cid:146)s problem is = U (C)+(cid:8)(T H)+ H J H (cid:0) i i i +b(H H )+ (cid:22) PH +(cid:21)(rM +(cid:5)+ W H C). (cid:0) i i i i i i i i (cid:0) P P P This maximization problem can be broken down into four optimization subproblems: max = max U (C) (cid:21)C +(cid:21)(rM +(cid:5)) H C f (cid:0) g + max (cid:8)(T H)+bH H f (cid:0) g + max (cid:22) H + H (J +(cid:21)W ) b H . Hi f i i i i i i i (cid:0) i i g P P =Bi P | {z } Above, (cid:21) is the costate variable giving the marginal value of real wealth; the Euler equation _ is (cid:21) = (cid:26) r = 0. b is the multiplier on the work-hours constraint. (cid:22) is the multiplier on the i (cid:0) nonnegativity constraint for hours at each possible job.9 Finally, B denotes the marginal i hourly net job bene(cid:133)ts associated with a job of type i. The four optimization subproblems nested within maximization of the current-value Hamiltonian are: (1) the consumption decision; (2) job choice; (3) the decision about work hours for each job; and (4) the overall hours decision. In the additively separable case here we normalize J and (cid:8) so that (cid:8) (T) = 0.10 Given i 0 this normalization, J > 0 means that a worker would be willing to spend at least some time i on a job even if unpaid, should that be the only job available. On the other hand, J < 0 i means that a worker would never do such a job unless paid. 9The worker(cid:146)s problem would be dramatically di⁄erent if it were possible to devote negative work hours to unpleasant, badly paid jobs. 10ConsiderU+(cid:8)~+HJ~ with(cid:8)~ (T)=(cid:20),where(cid:20)isaconstant. De(cid:133)ne(cid:8)(X)=(cid:8)~(X) (cid:20)X andJ =J~+(cid:20). i 0 i i (cid:0) Then, (cid:8) (T)=0, and 0 = U +(cid:8)~(T H)+ H J~ (cid:20)T U (cid:0) i i i (cid:0) = U +(cid:8)(T H)+ H J +(cid:20)(H H ). (cid:0) Pi i i (cid:0) i i P =P0 | {z } 12

Choice of Consumption As shown in the left panel of Figure 4, the solution to the (cid:133)rst optimization sub-problem, max U (C) (cid:21)C , is to choose consumption to satisfy the (cid:133)rst C f (cid:0) g order condition U = (cid:21). 0 V B B V d(’T H) U(’C) C H C H T Figure 4: Household solution to choice of consumption, C, and total work hours, H. Choice of Jobs and Hours at Each Job Job choice involves surveying all possible job types and choosing the job or jobs with the highest B . At an optimum B = max B . It i i i follows that if total work hours are spread across more than one job type it must be the case that each job with positive hours for the individual is o⁄ering the same level of (hourly marginal net) job bene(cid:133)ts(cid:151)although they need not be o⁄ering the same combination of real wage and job utility. Formally, the level of hourly net job bene(cid:133)ts for all jobs with strictly positive hours is B = maxB . We elaborate on the fraction of time devoted to each job later. i i Choice of Overall Work Hours Combining the job choice with the choice of work hours at each job, optimization requires H = 0 if J +(cid:21)W < b and J +(cid:21)W = b when H > 0. i i i i i i This implies that b = B: the marginal bene(cid:133)t of overall work hours is equal to the marginal bene(cid:133)t of hours at the job with the highest job bene(cid:133)ts. Therefore, total work hours should be chosen to satisfy (cid:8) = B. In words, at the optimal level of work hours, the marginal 0 utility from o⁄-the-job leisure is equal to job bene(cid:133)ts B of the most attractive job. Thus, therightpanelofFigure4showsthedeterminationoftheoptimalchoiceofH. Notethatthe labor-hours supply function is(cid:8), andtheequivalenttoamarketclearingpriceforworkhours 0 is job bene(cid:133)ts B. (We postpone discussion of the determination of the general equilibrium value of B to Section 7.). 13

5.2 Implications Three questions follow immediately. First, how do long-run changes in work hours depend on job utility? Second, assuming there is more than one viable employment opportunity available (that is, assuming more than one (cid:133)rm is able to o⁄er the highest job bene(cid:133)ts), how does the worker decide to allocate work hours between jobs? Third, how do short-run changes in work hours depend on job utility? 5.2.1 Implications for Long-Run Labor Supply Kimball and Shapiro (2008) argue that income e⁄ects on labor supply are likely to be substantial. They then look at what that would imply for the Frisch (marginal value of wealth held constant )labor supply elasticity if income and substitution e⁄ects on labor supply cancel out. But, our framework allows for work hours to remain relatively constant even if the income e⁄ect dominates the substitution e⁄ect. Consider the e⁄ects when consumption and real wages rise. Recall that B = (cid:21)W +J , and that as shown in the right panel of Figure 4, work hours i i are increasing in B. If the income e⁄ect dominates the substitution e⁄ect, then (cid:21)W is i decreasing (W is growing, but (cid:21) is declining in line with increases in consumption), which. i All else equal that makes B(cid:151)and therefore work hours(cid:151)decrease as well. But if job utility, J , is rising su¢ ciently, then the income e⁄ect can be counterbalanced i by the increase in J along with the increase in W that blunts the fall of (cid:21)W in (cid:21)W +J . i i i i i There is another surprising implication. Even if (cid:21)W 0 because the income e⁄ect i ! overwhelms the substitution e⁄ect (that is, because (cid:21) 0 more quickly than W ), work i ! (cid:22) hours will tend to some constant H > 0 as long as job utility J tends to some constant i (cid:22) J > (cid:8) (0). That is, even if people face quickly declining marginal utility for additional i 0 consumption, a positive asymptote for work hours can exist if there are jobs people enjoy as much as the marginal non-work activity they would otherwise (cid:133)ll out their days with. 5.2.2 Implications for Job Choices If two jobs have both the same wages and the same job utility, the division of time between them can only be pinned down by general equilibrium forces. But, when two jobs have the same net job bene(cid:133)ts but di⁄erent combinations of wages and job utility, the endogenous 14

determination of (cid:21) can lead to a determinate interior optimum based on worker optimization alone. Suppose B = B with J > J and W > W . That is, job 1 is higher paid than but 1 2 2 1 1 2 job 2 is more pleasant. Let (cid:31) be the fraction of total work hours that the worker devotes to working for (cid:133)rm 1. At an interior optimum for a worker B = (cid:21)W +J = (cid:21) W +J = B , 1 1 1 2 2 2 2 so(cid:21) = J2 J1 .Giventhelabor-hourssupplyfunction, theoptimallevelofworkhourssatis(cid:133)es W1 (cid:0)W2 (cid:0) H = T (cid:8)0(cid:0) 1(B). Substituting into the worker(cid:146)s budget constraint implies that (cid:0) C = T (cid:8)0(cid:0) 1(B) ((cid:31)W 1 +(1 (cid:31))W 2 )+rM +(cid:5), (cid:0) (cid:1) (cid:0) (cid:16) (cid:17) which after rearrangement yields 1 U ((cid:21)) rM (cid:5) 0 (cid:31) = (cid:0) (cid:0) W . W W T (cid:8) 1(B) (cid:0) 2 1 (cid:0) 2 (cid:18) (cid:0) 0(cid:0) (cid:19) It follows that for any given marginal value of wealth and job bene(cid:133)ts, higher exogenous wealth is associated with greater work hours being devoted to jobs with higher job utility and lower wages. Alternatively, at any given set of wages and equilibrium job bene(cid:133)ts, the higher (cid:21) is the more work hours are devoted to jobs with the highest wages. Also, note that in the event that more than two jobs have the same net job bene(cid:133)ts, any but the extreme of these set of jobs(cid:150)the one with the highest wage and lowest job utility and the one with the lowest wage and highest job utility(cid:150)is equivalent from the worker(cid:146)s perspective to a convex combination of time devoted to the extreme jobs. So, in the absence of (cid:133)xed costs of going to work the analysis for i > 2 jobs is essentially the same as for two jobs. (If there are (cid:133)xed small costs per job, the worker might slightly prefer an in-between job and would never choose three jobs). 5.2.3 Implications for Short-Run Labor Supply At any given level of job bene(cid:133)ts B, having a more pleasant, lower-paying job will result in a lower (Frisch) labor supply elasticity. To see this, rewrite B = (cid:21)W +J as (cid:21)(W (1 (cid:16) )), i i i i (cid:0) where (cid:16) J =(cid:21)W is the fraction of the wage that is a compensating di⁄erential. De(cid:133)ning i i i (cid:17) (cid:0) 15

the elasticity of work hours with respect to B by (cid:17)(cid:22) = (cid:8) 0 (T (cid:0) H) , then dlnH = (cid:17)(cid:22)dlnB so H(cid:8) (T H) 00 (cid:0) that holding everything constant except wages dlnB = dlnW =(1 (cid:16) ). So, with J and (cid:21) i i i (cid:0) held constant, dlnH dlnH dlnB (cid:17)(cid:22) i (cid:17) = = = i dlnW dlnB dlnW (1 (cid:16) ) i i i i (cid:0) is the Frisch elasticity of labor supply. Thus, the higher job utility is, the lower is labor supply elasticity with respect to temporary changes in the real wage. The results about multiple jobs in Section 5.2.2 suggested that as economies become richer, workers are likely to switch to jobs with higher job utility. Therefore, if (cid:17)(cid:22) as determined by the curvature of (cid:8) stays relatively constant as an economy gets richer, the volatility of work hours will fall relative to the volatility of temporary changes in the real wage. Cross-sectionally, and more speculatively, workers employed in jobs that they (cid:147)hate(cid:148) should have a higher Frisch labor supply elasticity if the relevant curvature of (cid:8) is similar across workers in these di⁄erent jobs. 6 Firms In the decentralized version of the optimization problem for (cid:133)rms, the (cid:133)rms are price takers in the product market. Each (cid:133)rm(cid:146)s production function takes as inputs capital and e⁄ective labor input (the product of hours, e⁄ort, and labor-augmenting technology). The (cid:133)rm rents capital at an exogenous rental rate (determined by the international real interest rate). The hourly cost of labor is captured by the inclusive wage: the sum of the real wage and the hourly cost of amenities. The solution to the (cid:133)rm(cid:146)s cost minimization problem implies that its cost function can be stated as a function of the rental rate of capital and the e⁄ective wage: the ratio of the inclusive wage to e⁄ective labor productivity (the product of e⁄ort and labor-augmenting technology). Minimization of the e⁄ective wage is the focus of the (cid:133)rm(cid:146)s optimization subproblems. 6.1 Cost Minimization Consider a representative providing a job with job-enjoyment technology (cid:9) . The (cid:133)rm(cid:146)s i production function is Y = K(cid:11)(Z E H )1 (cid:11), where capital(cid:146)s share (cid:11) (0;1) and other i i i i i (cid:0) 2 variables are as de(cid:133)ned earlier. Let R denote the rental rate of capital, which is exogenous 16

to the (cid:133)rm. (There are no adjustment costs, so R = r+(cid:14)). (cid:22) For any output level Y a (cid:133)rm(cid:146)s cost minimization problem involves choosing capital K , i i andtotalworkhoursH , tominimizetotalcostRK + H subjecttoK(cid:11)(Z E H )1 (cid:11) = Y (cid:22) . i i W i i i i i i (cid:0) i is the inclusive wage: i W = W +A . i i i W That is, in payment for their labor, workers receive the real wage W (which includes fringe i bene(cid:133)ts), and as indirect payment(cid:151)through job utility(cid:151)amenities A . i The solution to the (cid:133)rm(cid:146)s costs minimization problem is standard. The (cid:133)rm(cid:146)s total cost is a function of the desired level of output, Y , the rental rate of capital, R, and the i e⁄ective wage, ! . Thee⁄ectivewage! is equal totheinclusivewageperlabore⁄ectiveness: i i ! = =(Z E ). Thus, the (cid:133)rm(cid:146)s cost function is i i i i W (! ;R;Y ) = R(cid:11)=(((cid:11)(cid:11)(1 (cid:11))1 (cid:11))!1 (cid:11)Y ). (2) C i i (cid:0) (cid:0) i(cid:0) i 6.2 Optimization Subproblems for Firms The rental rate of capital is exogenous, but the e⁄ective wage is a function of the real wage, e⁄ort, and amenities, all of which are choice variables: How should the (cid:133)rm analyze its decision? First, unless the (cid:133)rm is going to shut down, the (cid:133)rm must choose the e⁄ective wage so that the (cid:133)rm o⁄ers are at least as high as equilibrium job bene(cid:133)ts. Then, two nested subproblems follow. The (cid:133)rst subproblem involves the choice of amenities. Then, given the optimal choice of amenities, the (cid:133)rm faces a decision about the real wage and e⁄ort. The solution to both of these nested subproblems can be summarized in terms of tangency conditions. 6.2.1 The Central Optimization Subproblem: Minimizing the E⁄ective Wage Given equation (2), any operating (cid:133)rm should minimize its e⁄ective wage subject to its constraints: min ! = =(Z E ) i i i i i,Ei W W s.t. (cid:21)( A )+J (E ;A ;(cid:9) ) B. i i i i i i W (cid:0) (cid:21) =Bi | {z } 17

In solving this optimization subproblem (cid:133)rms take the marginal value of wealth (cid:21), the rental rate of capital R, and equilibrium job bene(cid:133)ts B, as given. However, both the real wage W , i and amenities A , are choice variables. We will assume additive separability in job utility i between e⁄ort and amenities: J (E ;A ;(cid:9) ) = F E ; E +G A ; A;p , (3) i i i i i i i i i i i A (cid:0) (cid:1) (cid:0) (cid:1) where E captures innovations in the nature of work proper and A captures innovations in i i the nature of the work environment. We will write (cid:9) = ( E; A;p ). i i i i A 6.2.2 First Nested Subproblem: Choice of Amenities By the de(cid:133)nitions of the inclusive and e⁄ective wages (cid:21)W = (cid:21)( A ) i i i W (cid:0) so (cid:21)W = (cid:21)(! Z E A ). Substituting this last equation into the (cid:133)rm(cid:146)s problem of meeting i i i i i (cid:0) the market level of B so it can attract workers (which must bind at the optimal solution) it follows that (cid:21)! Z E + F (E ; E)+G (A ; A;p ) (cid:21)A = B. i i i i i i i i i A i (cid:0) i =Ji(Ei;Ai;(cid:9)i) This implies the nested subprob|lem: {z } max G(A ; A;p ) (cid:21)A . Ai i i A i (cid:0) i Thus, the choice of amenities should satisfy the tangency condition @G =@A = (cid:21). This i optimality condition is shown graphically in (A;G) space in the left panel of Figure 5. 18

G(A) J V B VZg’ G i i i J i VZg’’ VZ i g i i i A E A E i i J i Figure 5: Solution to a representative (cid:133)rm(cid:146)s optimization subproblems. It is helpful to de(cid:133)ne S (cid:21); A max G(A ; A;p ) (cid:21)A , i (cid:17) Ai i i A i (cid:0) i (cid:0) (cid:1) (cid:8) (cid:9) the individual surplus received from the (cid:133)rm(cid:146)s optimal choice of amenities. Note that S < 0 (cid:21) bytheenvelopetheorem. Thus, thelowerthemarginalvalueofwealth(intuitively, thericher a worker is), the greater the surplus from amenities. 6.2.3 Second Nested Subproblem: Choice of E⁄ort Given the optimal choice of amenities, the (cid:133)rm(cid:146)s problem of minimizing the e⁄ective wage reduces to a second nested subproblem: i min ! = W i Wi,Ei Z i E i s.t. (cid:21)! Z E +F(E ; E)+S (cid:21); A = B, (4) i i i i i i J(cid:22) i(Ei;(cid:21);(cid:9)i)(cid:0) (cid:1) where J (cid:22) is the net job utility functio|n (net of{tzhe costs o}f amenity provision measured in i utils). Rearranging, (cid:22) B (cid:21)Z ! E = J (E ;(cid:21);(cid:9) ) (5) i i i i i i (cid:0) (cid:22) (cid:22) and the objective is to (cid:133)nd a feasible value of J corresponding to the lowest ! . In E;J i i space the left-hand side of equation (5) traces out all e⁄ort and job-utility combination(cid:0)s tha(cid:1)t 19

are consistent with any given e⁄ective wage: the (cid:133)rm(cid:146)s isocost lines shown as downward sloping lines in the right panel of Figure 5. In that same panel the job utility function is shown as a concave curve. The (cid:133)rm(cid:146)s objective is to (cid:133)nd the tangency that yields an isocost line with the intercept at B and minimum downward (absolute value) slope that touches the job utility curve. In other words, given B, the solution to the (cid:133)rm(cid:146)s optimization subproblem is implicitly captured by the isocost line that has the (cid:135)attest (algebraically greatest) feasible slope. Feasibility is determined by the (cid:133)rm(cid:146)s net job utility function, which captures all net job utility and e⁄ort combinations that a (cid:133)rm is able to o⁄er. As seen in the right panel of Figure 5, ! > ! > ! and ! is the (cid:133)rm(cid:146)s optimal e⁄ective wage: it can do better than ! , 0i0 i 0i i 0i0 and although ! is preferred to ! , the former is not feasible given the (cid:133)rm(cid:146)s net job utility 0i i function. GivenA andS (cid:21); A , oncetheoptimalE and! arepinneddown, itisstraightforward i i i i to back out the opti(cid:0)mal W(cid:1) using the de(cid:133)nition of the e⁄ective wage and the value of J given i i the de(cid:133)nition of net job utility. 6.2.4 Why E⁄ort is Unpleasant at the Optimum Despite the fact that job utility can be increasing in e⁄ort for some part of the range, the tangency condition shown in the right panel of Figure 5 implies that e⁄ort will be unpleasant at the optimum. Indeed, at the optimum: (cid:22) @J @J @J i i i = (cid:21)Z ! = = E = (cid:21)(W +A ). i i i i i @E (cid:0) @E ) @E (cid:0) i i i Then, (cid:21) > 0 and E > 0 imply that for positive wages (and nonnegative amenities), at the i optimal choice of e⁄ort @J =@E < 0. That is, the optimal choice of e⁄ort occurs where job i i utility is decreasing in e⁄ort. In other words, since e⁄ort is productive it would make no sense to limit e⁄ort when additional e⁄ort is also pleasant. E⁄ort should be increased until additional e⁄ort is painful enough that it counterbalances the extra productivity. 20

7 Equilibrium The next question is: How are equilibrium job bene(cid:133)ts and the marginal value of wealth determined? 7.1 Job Bene(cid:133)ts From any (cid:133)rm(cid:146)s point of view the (cid:133)rm-speci(cid:133)c e⁄ective wage, ! , must equal the prevailing i market value of ! for the (cid:133)rm to have positive output. Perfect competition in the product market implies that, in equilibrium, each (cid:133)rm(cid:146)s marginal cost is equal to the price of (cid:133)nal output(cid:151)which is normalized to 1. Given the cost function in equation (2) that means (cid:133)rms with positive output must have 1 = R(cid:11)=((cid:11)(cid:11)(1 (cid:11))1 (cid:11)) !1 (cid:11), (cid:0) (cid:0) i(cid:0) (cid:0) (cid:1) which implies 1=(1 (cid:11)) W +A (cid:11)(cid:11)(1 (cid:11))1 (cid:11) (cid:0) i i (cid:0) = (cid:0) . Z E R(cid:11) i i ! =!i =! Figure6extendstheintu|iti{oznfr}omFi|gure5toth{iszcaseinwh}ich,asfarasarepresentative (cid:133)rm is concerned, the slope of an isocost line (cid:21)Z ! is exogenously determined. Because i (cid:0) cost minimization must hold, optimality continues to require being at a point of tangency between the net job utility function and an isocost line. Amenities A are determined as i earlier. Given the values of (cid:21), Z , and !, the (cid:133)rm faces, the left panel of Figure 6 shows optimal i (cid:22) e⁄ort requirements, E , and net job utility, J . These determine the optimal real wage i i W = !=Z E A , and job utility J . i i i i i (cid:0) 21

J B d(’T H) B J i VZg i E H E H T i J i Figure 6: Determination of total work hours under perfect competition. Theintersectionofthe(cid:133)rm(cid:146)sisocostlinewiththehorizontalaxisnowdeterminesequilibrium job bene(cid:133)ts B. Given this equilibrium level of B, the right panel of Figure 6 shows the determination of total work hours, H. This logic can be expressed by the functions E = i E (!(cid:21)Z ;(cid:9) ) and B = B (!(cid:21)Z ;(cid:9) ). Note that the (cid:133)rm that is able to o⁄er the highest job i i i i i i i bene(cid:133)ts is the (cid:133)rm that implicitly sets the economy(cid:146)s equilibrium level of job bene(cid:133)ts. 7.2 The Marginal Value of Wealth 7.2.1 The Labor Earnings Functions In general equilibrium, our open-economy framework has r = (cid:26), and C = rM + (cid:5) + H (cid:31) W , where (cid:31) is the fraction of total work hours that the individual devotes to (cid:133)rm i i i i i. P(Thus, i (cid:31) i = 1.). Let W = i (cid:31) i W i denote the wage averaged across jobs. Given the individual(cid:146)Ps (cid:133)rst-order condition fPor consumption, a labor-earnings demand function (LED) can be de(cid:133)ned as follows: WH = U 0(cid:0) 1((cid:21)) rM (cid:5) = LED. (6) (cid:0) (cid:0) Since W = Z !E A , a labor-earnings supply function (LES) can be de(cid:133)ned in this i i i i (cid:0) way: WH = i Z i ! (cid:1) E i (!(cid:21)Z i ;(cid:9) i ) (cid:0) A i (cid:21); A i ;p A i (cid:1) H i (B(!(cid:21)Z i ;(cid:9) i )) = LES, (7) P (cid:0) (cid:0) (cid:1)(cid:1) where once again we have made use of the de(cid:133)nition of the average wage. 22

7.2.2 Graphing Labor-Earnings Demand and Labor-Earnings Supply Labor-Earnings Demand U ( ) is decreasing in C. Therefore, equation (6) implies a 0 (cid:1) negative relationship between (cid:21) and labor-earnings demand as measured by WH. Thus, in (WH;(cid:21)) space the labor-earnings demand function is downward sloping. Labor-Earnings Supply For labor-earnings supply consider (cid:133)rst the case in which only clones of (cid:133)rm i exist. Then, LES is given by WH = Z i ! (cid:1) E i (!(cid:21)Z i ;(cid:9) i ) (cid:0) A i (cid:21); A i ;p A i (cid:1) H i (B(!(cid:21)Z i ;(cid:9) i )). (cid:2) (cid:0) (cid:1)(cid:3) Showingthatin(WH;(cid:21))spacelabor-earningssupplyisdownwardslopingrequiresanswering the following three questions. (a) What does a change in (cid:21) imply for amenities? Suppose that the marginal value of wealth (cid:21) rises to (cid:21). Then, as shown in the left panel of Figure 7, amenities decrease. This 0 means that the surplus from amenities received by individuals, S (cid:21); A , declines, which(cid:151) i as shown in the right panel of Figure 7(cid:151)induces a downward s(cid:0)hift in(cid:1)the net job utility (cid:22) function in E;J space. (cid:0) G(A)(cid:1) J B’ V’ V B VZ i g’ G i J i G’ i VZg i J’ i A E A’ i A i E i E’ i J i = F+S J = F+S’ i Figure 7: Derivation of labor-earnings supply curve. (b) What does a change in (cid:21) imply for the isocost lines? The right panel of Figure 7 shows that higher (cid:21) implies a steeper isocost line, which in turn leads to a decline in net job 0 utility and a rise in e⁄ort. Also, although the change can seem ambiguous, job bene(cid:133)ts rise to B 0 , which leads to higher work hours.11 dB=d(cid:21) > 0 means that the H in WH goes up. 11See the appendix for additional details. 23

(c) How do real wages factor in? If all (cid:133)rms are identical W is trivially equal to W i . The analysis behind Figure 7 showed that the result of higher marginal value of wealth includes lower amenities, A , and higher e⁄ort, E . ! is unchanged, and since W = Z !E A i i i i i i (cid:0) dW =d(cid:21) = Z !dE =d(cid:21) dA =d(cid:21) > 0. i i i i (cid:0) Taken together, the answers to these three questions imply that labor-earnings is increasing in (cid:21) so that LES is upward sloping in (WH;(cid:21)) space. Determination of the Marginal Value of Wealth Figure 8 shows LED and LES, and the determination of equilibrium (cid:21) and labor earnings WH when all (cid:133)rms are identical. V LED V LES WH WH Figure 8: Equilibrium labor earnings and the marginal value of wealth using labor-earnings supply and demand. What about the determination of the marginal value of wealth and labor earnings when (cid:133)rms with a range of wage/e⁄ort combinations are operational? For simplicity, consider the case of two types of (cid:133)rms indexed by i = 1;2, which, as noted in Section 5.2.2, can be thought of as the relevant extremes. Suppose these two types of (cid:133)rms have job utility functions given by J = and J = 1 1 2 2 J J as depicted in Figure 3. Then, what is relevant is the upper envelope of these job utility functions. For a su¢ ciently low marginal value of real wealth, say (cid:21), (cid:133)rm 1 is able to o⁄er 0 the highest marginal net job bene(cid:133)ts and type 2 (cid:133)rms do not operate. For a higher marginal value of real wealth, say, (cid:21) > (cid:21) both type 1 and type 2 (cid:133)rms are able to o⁄er the same 00 0 marginal net job bene(cid:133)ts and workers allocate hours across (cid:133)rms according to the logic in Section 5.2.2. Finally for even higher marginal values of real wealth such as, say, (cid:21) > (cid:21) 000 00 type 2 (cid:133)rms are able to o⁄er the highest marginal net job bene(cid:133)ts, and type 1 (cid:133)rms are unable to operate. 24

Market equilibrium can be shown in the labor-earnings supply and demand diagram. LED is a simple extension what we derived above. In particular, labor-earnings demand is described by (cid:21) = U (rM +(cid:5)+((cid:31) W +(1 (cid:31) )W )H), 0 1 1 1 2 (cid:0) where (cid:31) is the fraction of total work hours devoted to (cid:133)rms of type 1. The appropriate 1 version of labor-earnings supply is slightly di⁄erent than that considered earlier. For su¢ ciently low values of (cid:21) only (cid:133)rms of type 1 operate and the associated real wages, marginal net job bene(cid:133)ts, and work hours are relatively low. Therefore, in terms of labor-earnings supply, low values of (cid:21) are associated with low labor earnings. Atthecriticalvalue(cid:21) notedabovebothtypesof(cid:133)rmsareoperational. Figure9showsan 00 equilibrium in which both types of (cid:133)rms are operational. Wages, marginal net job bene(cid:133)ts, and hours are higher than under (cid:21)(cid:150)and therefore so are labor earnings. However at (cid:21) any 0 00 level of labor earnings within a certain range is an equilibrium, implying a perfectly elastic portion of the labor-earnings supply curve. In this region, an increase in non-labor income that shifts LED out leads to allocations of more hours toward the more pleasant job without changing (cid:21). Finally, for higher values of (cid:21) only (cid:133)rms of type 2 are operational. This is associated with higher wages, marginal net job bene(cid:133)ts, and hours. Thus, in terms of labor-earnings supply high values of (cid:21) are associated with high values of labor earnings. V LED LES V WH WH Figure 9: Labor earnings supply and demand with two (cid:133)rms. 7.3 Implications Our framework allows us to address several interesting questions. For instance: How does a (cid:133)rm(cid:146)s overall technology matter for its competitiveness? What are the e⁄ects of changes in 25

technology (whether changes in labor-augmenting technology or job-enjoyment technology) on labor earnings and the marginal value of wealth? Which changes in technology are consistent with higher real wages and trendless labor hours if the income e⁄ect outweighs the substitution e⁄ect? In the Appendix, we show the following. First, within our framework, di⁄erences in job-enjoyment technology between (cid:133)rms can counterbalance di⁄erences in labor-augmenting technology, and vice versa. In particular, a (cid:133)rm falling behind in labor-augmenting technological progress can keep up its ability to attract workers even with lower wages if its job enjoyability technology advances su¢ ciently. Second, within our framework, a permanent increase in labor augmenting technology, a permanent positive innovation in the nature of work proper, or a permanent positive innovation in the nature of the work environment can each lead simultaneously to higher labor earnings, a lower marginal value of real wealth, and trendless or nearly trendless work hours. In essence, then, anything that (cid:147)regular(cid:148)technology can do, job enjoyability technology can do as well. To the extent that higher job utility matters for competitiveness, it is even plausible that (cid:133)rms might set what would otherwise be above-optimal e⁄ort requirements in order to induce workers themselves to think of ways to increase job utility. This amounts to a low cost form of research and development in job enjoyment technology. 8 Welfare We argue above that and upward trend in job utility make it possible for work hours to remain approximately constant over time even if the income e⁄ect of higher real wages on labor supply exceeds the substitution e⁄ect of higher real wages. The question that immediately follows is: What are the welfare e⁄ects of such changes? In this section, we elaborate on the relationship between job utility and welfare, suggest ways in which theoretical relationships can be operationalized and give a numerical example for the potential welfare gains associated with secular changes in job utility. Under straightforward though far from certain assumptions, given constant work hours, an observed increase in consumption of 1% might be associated with an increase in welfare of 2%. In this case, at least half of these welfare gains are coming from increases in job utility. 26

8.1 Measuring Welfare In our framework, changes in welfare induced by changes in exogenous parameters are well assessed via comparative steady-state analysis. In steady state, given r = (cid:26), an individual(cid:146)s problem is equivalent to the static optimization problem max U(C)+(cid:8)(T H)+ H J C,H,Hi 0 (cid:0) i i i (cid:21) P s.t C = rM +(cid:5)+ W H i i i P and H = H . i i P Given the multipliers (cid:21) and b, let = max U(C)+(cid:8)(T H)+ H J +b(H H )+(cid:21)(rM +(cid:5)+ W H C) . L (cid:3) C,H,Hi 0 f (cid:0) i i i (cid:0) i i i i i (cid:0) g (cid:21) P P P Recall that the optimal choice of H yields two cases: H = 0 and J +(cid:21)W < b, or H > 0 i i i i i and J +(cid:21)W = b. Therefore, b = B, where, B denotes the economy(cid:146)s level of equilibrium i i marginal net job bene(cid:133)ts. Using the envelope theorem, d =(cid:21) = H dJ =(cid:21)+ H dW +d((cid:5)+rM). (8) L (cid:3) i i i i i i P P Above, each of the three terms on the right-hand side highlight distinct ways in which the economy(cid:146)s opportunity set becomes larger. Changes in welfare from changes in job utility are captured by the (cid:133)rst term; changes in welfare from higher wages are re(cid:135)ected in the second term; and changes in welfare from changes in exogenous wealth appear in the last term. The (cid:133)rst term ( H )dJ =(cid:21) can be interpreted as the portion of the change in the i i i maximized value of utilPity that answers the question of how much the worker would have to be paid per year in order to be willing to go back to working in yesterday(cid:146)s conditions. 27

8.2 Toward Pinning Down the Implied Increase in Welfare To better understand the implications of the envelope theorem as laid out in equation (8) note that the second term on the right-hand side is the change in wages for narrowly de(cid:133)ned job categories (for which, empirically, it should be possible to obtain a direct measure) and satis(cid:133)es H dW = d( H W ) W dH . i i i i i i (cid:0) i i i P P P Therefore, to gauge this component of welfare, we need to adjust the change in overall labor earnings by subtracting not only extra earnings from people working longer hours overall, but also extra earnings coming from people switching towards jobs that are more highly paid and have lower job utility. If (cid:21)W is moving down, then the overall trend should involve compositional shifts towards jobs with higher job utility and relatively lower pay than other available jobs. This means that the increase in labor earnings will tend to understate the true increase in welfare (leaving aside changes in overall hours, which obviously need to be adjusted for). In terms of understanding the remaining terms for the change in welfare, note that B = J +(cid:21)W i i which implies dJ dB d(cid:21) i = W dW . i i (cid:21) (cid:21) (cid:0) (cid:21) (cid:0) Thus, pinning down the (cid:133)rst term in the right-hand side of equation (8) calls for looking at labor hours, consumption, and hourly wages. Substituting into equation (8) and rearranging yields d H dB d(cid:21) d((cid:5)+rM) (cid:3) L = + . (9) (cid:21) H W H W (cid:21) (cid:0) (cid:21) H W i i i i i i i i i The last term on the rigPht-hand sideP(cid:150)the value of extra nonP-labor income(cid:150)is easy to understand. Hence, we will focus on getting measures for the (cid:133)rst two terms on the right-hand side of equation (9). De(cid:133)ne (cid:13) = CU =U . (That is, 1=(cid:13) is the elasticity of intertemporal substitution.). CC C (cid:0) Then d(cid:21)=(cid:21) = (cid:13)dC=C. Moreover, as discussed earlier, for any job i the Frisch elasticity (cid:0) of labor supply (cid:17) and the fraction (cid:16) of the wage that is a compensating di⁄erential, (cid:17) = i i i 28

(cid:17)(cid:22)=(1 (cid:16) ), where (cid:17)(cid:22) = (cid:8) (T H)=(H(cid:30) (T H)), it follows tat i 0 00 (cid:0) (cid:0) (cid:0) ((1 (cid:16) )(cid:21)W ) dB=B = (1=(cid:17)(cid:22))dH=H = dB = (cid:0) i i dH=H = dB=(cid:21) = (W =(cid:17) )dH=H. (10) ) (cid:17)(cid:22) ) i i Substituting the appropriate expressions into equation (9) and simplifying yields d (W =(cid:17) )dH (cid:13)dC d((cid:5)+rM) L (cid:3) = i i + + . (11) (cid:21) H W H W C H W i i i i i i i i i P P P The intuition for equation (11) is that in the additively separable case (cid:13) tells how many times bigger the income e⁄ect is than the substitution e⁄ect. If hours are relatively constant despite increasing wages, then there must be substantial increases in job utility to counteract the income e⁄ects associated with increases in consumption. On the other hand, if hours H move in the direction indicated by the income e⁄ect it gives less hint of improvements in job utility. (If (cid:13) = 1, income and substitution e⁄ects cancel, but increases in consumption still have the usual e⁄ect on welfare.). 8.3 Calibrating (cid:13) from job choices In addition to evidence from the e⁄ects of interest rates on the path of consumption, in principle evidence about (cid:13) can be found from workers(cid:146)job choices. Consider an individual working two jobs satisfying J > J . Then, (cid:21)W +J = (cid:21)W +J , meaning that 2 1 1 1 2 2 J J d(cid:21) dJ dJ dW dW 2 1 1 2 1 2 (cid:21) = (cid:0) = = (cid:0) (cid:0) . W W ) (cid:21) J J (cid:0) W W 2 1 1 2 1 2 (cid:0) (cid:0) (cid:0) For any individual with dJ dJ = 0, for example, dJ ;dJ = 0, then 1 2 1 2 (cid:0) d(cid:21)=(cid:21) = (dW dW )=(W W ), 1 2 1 2 (cid:0) (cid:0) (cid:0) and using d(cid:21)=(cid:21) = (cid:13)dC=C it follows that (cid:0) (cid:13) = [(dW dW )=(W W )]=(dC=C). 1 2 1 2 (cid:0) (cid:0) 29

8.4 Illustrating the Calculation of Welfare Gains The short-run elasticity of intertemporal substitution has been suggested by Hall (1988) to be approximately zero, and by Kimball, Sahm, and Shapiro (2011) to be 0.08. However, there are reasons to think the long-run elasticity of intertemporal substitution should be higher than its short-run counterpart. This includes taking account of full adjustment, new goods, habit formation, and (cid:147)keeping up with the Joneses.(cid:148)In the context of our analysis, it is the long-run elasticity of intertemporal substitution that should be used. Suppose the long-run elasticity of intertemporal substitution is 0.5, in which case (cid:13) = 2. Using this value for (cid:13) along with equation (11) implies that for d(cid:5) = 0, dM = 0, and dH = 0, a 1% increase in consumption would be associated with a welfare increase of at least 2%. Anatural questionthatfollowsiswhatfractionof welfaregainsareattributabletohigher job utility. To see this, note that dividing equation (8) by H W and combining it with i i i equation (11) yields P H dJ H dW (W =(cid:17) )dH (cid:13)dC i i i + i i i = i i + , (cid:21) H W H W H W C P i i i P i i i i i i P P P or H dJ d H W W dH (W =(cid:17) )dH (cid:13)dC i i i + i i i i i i = i i + , (12) (cid:21) H W H W (cid:0) H W H W C P i i i (cid:18) Pi i i P i i i (cid:19) i i i P P =1% 1%P P =0 =(cid:13)% (cid:0) where the second term on |the left-hand{zside re(cid:135)ects }switc|hing{zfrom}rela|t{ivze}ly higher paid jobs to relatively lower paid jobs. If there were no changes in job utility or hours then a 1% increase in consumption is just a 1% increase in consumption. But, if consumption increases 1%, (cid:13) = 2, dH = 0 endogenously despite the income e⁄ect exceeding the substitution e⁄ect, then this equation implies an increase in welfare equivalent to the direct e⁄ect of a 2% increase in consumption. So, the di⁄erence, 1%, must be due to improvements in job utility from the two terms on the left of equation (12). 9 Conclusions The paradox of hard work is this: for decades, work hours per capita among adults have remained roughly trendless, despite strong trends in macroeconomic variables, such as real 30

consumption and real wages. In principle, the paradox of hard work can be rationalized in several di⁄erent ways. Of these alternatives, we focus on the general equilibrium e⁄ects of secular changes that make work more pleasant. Economists have long understood that crosssectional di⁄erences in job utility at a particular time give rise to compensating di⁄erentials. In this paper, we develop a theory that focuses on the less-studied long-run macroeconomic consequences of trends in job utility. Our theory allows for the interaction of work hours (which stands in for all aspects of the job that interfere with leisure and home production) and e⁄ort (which stands in for all aspects of a job whose cost is in terms of proportionate changes in e⁄ective productive input from labor). We also consider the role of amenities (which we de(cid:133)ne to be job characteristics whosecostisintermsofgoods)andtheroleofsecularincreasesinjobutility(thatis, secular declines in drudgery, which can stemfromchanges in standard notions of technology, such as labor-augmenting technology, and also from changes in job-enjoyment technology). General equilibrium can be analyzed through two new theoretical objects: labor-earnings supply and labor-earnings demand. Two main implications emerge. First, secular improvements in job utility imply that work hours can remain approximately constant over time even if the income e⁄ect of higher wages on labor supply exceeds the substitution e⁄ect of higher wages. Second, secular improvements in job utility can themselves be a substantial component of the welfare gains from technological progress. These two implications are connected by an equation (cid:135)owing from optimal hours choices: improvements in job utility that have a signi(cid:133)cant e⁄ect on labor supply tend to have large welfare e⁄ects. References [1] Abel, Andrew B. 1990. (cid:147)Asset Prices Under Habit Formation and Catching Up With the Joneses.(cid:148)American Economic Review, 80(2): 38-42. [2] Alesina, Alberto F., Edward L. Glaeser and Bruce Sacerdote. 2006. (cid:147)Work and Leisure in the U.S. and Europe: Why So Di⁄erent?(cid:148)In NBER Macroeconomics Annual 2005, Volume 20, edited by Mark Gertler and Kenneth Rogo⁄. MIT Press. [3] Altonji, Joseph G. 1982. (cid:147)The Intertemporal Substitution Model of Labour Market Fluctuations: AnEmpiricalAnalysis.(cid:148)Review of Economic Studies, 49(5): 783-824. [4] Barsky, Robert B., F. Thomas Juster, Miles S. Kimball, and Matthew D. 31

Shapiro. 1997. (cid:147)Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study.(cid:148)Quarterly Journal of Economics 112(2): 537-579. [5] Basu, Susanto, and Miles S. Kimball. 2002. (cid:147)Long-Run Labor Supply and the Elasticity of Intertemporal Substitution for Consumption.(cid:148)Boston College and University of Michigan: unpublished manuscript. [6] Blundell, Richard, Pierre-Andre Chiappori, Thierry Magnac and Costas Meghir. 2001. (cid:147)Collective Labor Supply: Heterogeneity and Nonparticipation.(cid:148) Institute for Fiscal Studies, London Working Paper 01/19. [7] Blundell, Richard and Thomas MaCurdy. 1999. (cid:147)Labor Supply: A Review of Alternative Approaches.(cid:148)In Orley Ashenfelter and David Card, eds. Handbook of Labor Economics Vol. 3A. Amsterdam: North-Holland. [8] Blundell, Richard, Costas Meghir and Pedro Neves. 1993. (cid:147)Labor Supply and Intertemporal Substitution.(cid:148)Journal of Econometrics 59: 197-160. [9] Coulibaly, Brahima. 2006. (cid:147)Changes in Job Quality and Trends in Labor Hours.(cid:148) International Finance Discussion Papers 882. Washington: Board of Governors of the Federal Reserve System. [10] Epstein, Brendan and Ryan Nunn. 2013. (cid:147)Taxation, Match Quality, and Social Welfare.(cid:148) International Finance Discussion Papers 1079. Washington: Board of Governors of the Federal Reserve System. [11] Epstein, Brendan and Shanthi P. Ramnath. 2014. (cid:147)Taxes and Long-Run Changes inOECDWorkHoursRevisited.(cid:148)BoardofGovernorsoftheFederalReserveSystem and United States Treasury Department: unpublished manuscript. [12] Faggio, Giulia and Stephen Nickell. 2007. (cid:147)Patterns of Work Across the OECD.(cid:148) The Economic Journal, 117 (521): F416-F440. [13] Fang, Lei and Cara McDaniel. 2011. (cid:147)Trends in Home Hours in the U.S. and Europe.(cid:148)Unpublished manuscript available at www.caramcdaniel.com [14] Francis, Neville and Valerie Ramey. 2009. (cid:147)A Century of Work and Leisure.(cid:148) American Economic Journal: Macroeconomics, 1 (2): 189-224. [15] Fuhrer, Je⁄rey C. 2000. (cid:147)Habit Formation in Consumption and its Implications for Monetary Policy Models.(cid:148)American Economic Review, 90 (3): 367-390. [16] Guner, Nezih, Remzi Kaygusuz and Gustavo Ventura. 2012. (cid:147)Taxation and Household Labor Supply.(cid:148)Review of Economic Studies, 79 (3): 1113-1149. [17] Hall, Robert E. 1988. (cid:147)Intertemporal Substitution in Consumption.(cid:148)The Journal of Political Economy, 96: 339-357. 32

[18] Hansen, Gary D. 1985. (cid:147)Indivisible Labor and the Business Cycle.(cid:148)Journal of Monetary Economics, 16 (3): 309-327. [19] Heston, Alan, Robert Summers and Bettina Aten. Penn World Table, Center for International Comparisons of Production, Income and Prices at the University of Pennsylvania. [20] Keynes, John Maynard. 1930. (cid:147)Economic Possibilities for Our Grandchildren.(cid:148) Printed in Vol. IX of The Collected Writings of JM Keynes, 1973. London: Macmillan for The Royal Economic Society. [21] Kimball, Miles S., Claudia Sahm and Matthew D. Shapiro. 2011. (cid:147)Measuring Time Preference and the Elasticity of Intertemporal Substitution Using Web Surveys.(cid:148)BoardofGovernorsoftheFederalReserveSystemandUniversityofMichigan: unpublished manuscript. [22] Kimball, Miles S., and Matthew D. Shapiro. 2008. (cid:147)Labor Supply: Are the Income E⁄ects Both Large or Both Small?(cid:148)NBER Working Paper No. 14208. [23] King, Robert G., Charles I. Plosser, and Sergio R. Rebelo. 1988. (cid:147)Production, GrowthandBusinessCycles: I.TheBasicNeoclassicalModel.(cid:148)Journal of Monetary Economics 21: 195-232. [24] Krusell, Per, Toshihiko Mukoyama, Richard Rogerson and Aysegul Sahin. 2008. (cid:147)Aggregate Implications of Indivisible Labor, Incomplete Markets, and Labor Market Frictions.(cid:148)Journal of Monetary Economics, 55 (5): 961-979. [25] Ljungqvist, Lars and Thomas J. Sargent. 2007. (cid:147)Do Taxes Explain European Employment? Indivisible Labor, Human Capital, Lotteries, and Personal Savings.(cid:148) In NBER Macroeconomics Annual 2006, Volume 21, edited by D. Acemoglu, K. Rogo⁄, and M. Woodford, 181-246. The MIT Press. [26] Luttmer, Erzo F.P. 2005. (cid:147)Neighbors as Negatives: Relative Earnings and Well- Being.(cid:148)The Quarterly Journal of Economics, 120 (3): 963-1002. [27] MaCurdy, Thomas E. 1981. (cid:147)An Empirical Model of Labor Supply in a Life-Cycle Setting.(cid:148)Journal of Political Economy, 89: 1059-1085. [28] Mankiw, Gregory N., Julio J. Rotemberg and Lawrence H. Summers. 1985. (cid:147)Intertemporal Substitution in Macroeconomics.(cid:148)The Quarterly Journal of Economics, 100 (1): 225-251. [29] McDaniel, Cara. 2011. (cid:147)Forces Shaping Hours Worked in the OECD, 1960-2004.(cid:148) American Economic Journal: Macroeconomics, 3 (4): 27-52. [30] Mulligan, Casey B. 1998. (cid:147)Substitution Over Time: Another Look at Life-Cycle Labor Supply.(cid:148)In Ben S. Bernanke and Julio Rotemberg, eds. NBER Macroeconomics 33

Annual 1998. Cambridge: MIT Press. [31] Mulligan, Casey B. 2001. (cid:147)Aggregate Implications of Indivisible Labor.(cid:148) NBER Working Paper No. 8159. [32] Ohanian, Lee, Andrea Ra⁄o and Richard Rogerson. 2008. (cid:147)Long-Term Changes in Labor Supply and Taxes: Evidence from OECD Countries, 1956-2004.(cid:148)Journal of Monetary Economics, 55 (8): 1353-1362. [33] Patterson, Kerry D. and Bahram Pesaran. 1992. (cid:147)The Intertemporal Elasticity of Substitution in Consumption in the United States and the United Kingdom.(cid:148)The Review of Economics and Statistics, 74 (4): 573-584. [34] Prescott, Edward C. 2004. (cid:147)Why do Americans Work so Much More than Europeans?(cid:148)NBER Working Paper No. 10316. [35] Prescott, Edward C., Richard Rogerson and Johanna Wallenius. 2009. (cid:147)Lifetime Aggregate Labor Supply with Endogenous Workweek Length.(cid:148)Review of Economic Dynamics, 12 (1): 23-36. [36] Prescott, Edward C. and Johanna Wallenius. 2011. (cid:147)Aggregate Labor Supply.(cid:148) Sta⁄Report 457, Federal Reserve Bank of Minneapolis. [37] Rayo, Luis, and Gary S. Becker. 2007. (cid:147)Habits, Peers, and Happiness: An Evolutionary Perspective.(cid:148)American Economic Review, 97 (2): 487-491. [38] Rogerson, Richard. 1988. (cid:147)Indivisible Labor, Lotteries, and Equilibrium.(cid:148)Journal of Monetary Economics, 21 (1): 3-16. [39] Rogerson, Richard. 2006. (cid:147)Understanding Di⁄erences in Hours Worked.(cid:148)Review of Economic Dynamics, 9 (3): 365-409. [40] Rogerson, Richard. 2007. (cid:147)Taxation and Market Work: Is Scandinavia an outlier?(cid:148) Economic Theory, 32 (1): 59-85. [41] Rogerson, Richard. 2009. (cid:147)Market Work, Home Work and Taxes: A Cross-Country Analysis.(cid:148)Review of International Economics, 17 (3): 588-601. [42] Rosen, Sherwin. (cid:147)The Theory of Equalizing Di⁄erences.(cid:148)1986. Handbook of Labor Economics, 1: 641-692. [43] Shimer, Robert. 2009. (cid:147)Convergence in Macroeconomics: The Labor Wedge.(cid:148)American Economic Journal: Macroeconomics. 1 (1): 280-297. [44] Smith, Adam. 1776. (cid:147)An Inquiry Into the Nature and Causes of The Wealth of Nations.(cid:148)Chicago: University of Chicago Press, 1976. Edwin Cannan, Ed. [45] Struck, Clemens C. 2013. (cid:147)Habit Persistence and the Long-Run Labor Supply.(cid:148) Trinity College, Dublin: unpublished manuscript. 34

[46] Vissing-Jorgensen, Annette. 2002. (cid:147)Limited Asset Market Participation and the Elasticity of Intertemporal Substitution(cid:148) Journal of Political Economy, 110 (4): 825-853. [47] Yogo, Motohiro.2004.(cid:147)EstimatingtheElasticityofIntertemporalSubstitutionWhen Instruments are Weak.(cid:148)The Review of Economics and Statistics, 86 (3): 797-810. A Details for the Labor-Earnings Supply Derivation Firms maximize net job bene(cid:133)ts given the constraints they face. In particular, B = max (cid:21)!Z E +F E ; E + A ; A (cid:21)A . i Ei;Ai i i i i i i (cid:0) i (cid:8) (cid:0) (cid:1) (cid:0) (cid:1) (cid:9) The envelope theorem implies that when (cid:21) changes dB = (!Z E A )d(cid:21) = ( A )d(cid:21) = W d(cid:21) > 0 i i i i i i i (cid:0) W (cid:0) wheneverW > 0. Sincethisistrueforalljobs, themaximumB overallimustalsoincrease. i i The fact that dB=d(cid:21) > 0 highlights an interesting role for amenities. Consider a decline (cid:22) in the marginal value of wealth. In the absence of amenities, in E;J space the job utility function would remain (cid:133)xed while isocost curves became less steep and job bene(cid:133)ts declined. (cid:0) (cid:1) Yet, once amenities are considered, a lower marginal value of wealth shifts the net job (cid:22) utility function shifts up in E;J space. Because of the logic of the envelope theorem job bene(cid:133)ts must still decline, but not as much as they would in the absence of amenities. Thus, (cid:0) (cid:1) endogenous provision of amenities blunts the e⁄ect of lower (cid:21). In other words, changes in amenities serve as endogenous bu⁄ers to income e⁄ects on labor supply. B The Role of Technology B.1 Competitiveness Across(cid:133)rms, di⁄erencesinjob-enjoymenttechnologycancounterbalancedi⁄erencesinlaboraugmentingtechnology, andviceversa. Toseethis, consider(cid:133)rms1and2asshowninFigure A1, where (cid:9) < (cid:9) , Z > Z , and (cid:133)rms di⁄er in their net job utility curves. As depicted, 2 1 2 1 although (cid:133)rm 1 has lower labor-augmenting technology, given its higher job-enjoyment technology it is the one that would implicitly set the economy(cid:146)s equilibrium level of job bene(cid:133)ts (recall that, all else equal, higher (cid:9) shifts the job utility curve up). Because workers take i jobs with the highest B, (cid:133)rm 2 is unable to attract workers(cid:151)and therefore must shut down. (cid:22) For a higher value of (cid:9) (which would shift J su¢ ciently high up) or a higher Z (which 2 2 2 35

would make (cid:133)rm 2(cid:146)s isocost lines su¢ ciently steep) (cid:133)rm 2 could o⁄er the exact same level of job bene(cid:133)ts as (cid:133)rm 1(cid:151)in which case both (cid:133)rms would be able to operate(cid:151)or even higher job bene(cid:133)ts(cid:151)in which case (cid:133)rm 2 would be the one to implicitly establish economy-wide equilibrium B, and (cid:133)rm 1 would be unable to attract workers. J B 1 B 2 VZ g 1 VZ g J 2 1 E J 2 Figure A1: A di⁄erence in job utility overwhelming a di⁄erence in labor-augmenting technology. B.2 Labor Earnings and the Marginal Value of Wealth For the sake of intuition, throughout the remainder of this section we make four simplifying assumptions. 1) We revert to assuming that there is only one (cid:133)rm and therefore avoid i indexes. 2) For the e⁄ects of changes in the nature of work proper, E, three possibilities emerge depending on whether @F =@ E = 0, @F =@ E < 0, or @F =@ E > 0. @F =@ E = E E E E 0 means that changes in E do not a⁄ect how onerous extra e⁄ort is. @F =@ E < 0 means E that higher E makes extra e⁄ort more onerous. @F =@ E > 0 means that higher E makes E increases in e⁄ort less onerous. We focus on @F =@ E 0 since it is the most intuitively E (cid:21) appealing possibility. 3) Base on another bit of intuition, we only consider cases in which @G =@ A 0. 4) We continue to assume the additively separable case J = F+G. Relaxing A (cid:21) these assumption leads to interesting analysis but not quite interesting enough to include here. B.2.1 The E⁄ect of a Rise in Z on (cid:21) and WH ~ Suppose labor-augmenting technology increases from Z to Z > Z. The left panel of Figure A2 shows that, all else equal, higher Z leads to higher job bene(cid:133)ts (meaning higher work hours) and higher e⁄ort, which leads to higher real wages because the e⁄ective wage is constant. These changes jointly imply higher WH. Now, consider the implications of higher 36

WH. LES shiftsoutbecauseatanygiven(cid:21)higherZ isconsistentwithhigherlaborearnings. This outward shift in LES implies a decrease in equilibrium (cid:21) and an increase in equilibrium WH (the lower (cid:21) induces changes exactly opposite to those in the left panel of Figure 8 in the main text). J J B’ B’ VZ’g B B J’ J’ VZg J J VZg J’ E E E E’ E E’ J J VZg Figure A2: E⁄ects of increase in labor-augmenting technology (left) and e⁄ects of positive innovation in the nature of work proper (right). B.2.2 E⁄ect of a Rise in E on (cid:21) and WH Consider an increase in E to ~E > E (that is, a positive innovation in the nature of work proper). Start from the right panel of Figure A2, where @F =@ E > 0 is assumed: all else E equal, higher E is consistent with higher job bene(cid:133)ts (meaning higher work hours) and higher e⁄ort (meaning(cid:151)because the e⁄ective wage is an exogenous constant(cid:151) higher real wages). If @F =@ E = 0 the new E e⁄ort remains unchanged but job bene(cid:133)ts rise. In E either case, labor earnings rise. All other changes are then analogous to those in Section B.2.1. B.2.3 E⁄ect of a Rise in A on (cid:21) and WH If @G =@ A > 0 and A rises (that is, a positive innovation in the nature of the work A environment occurs), the optimal level of amenities rises as shown in the left panel of Figure A3. This induces an upward shift in the net job utility function akin to that shown in the right panel of Figure 8 in the main text, but without any accompanying change in the slope of isocost lines. Therefore, e⁄ort remains (cid:133)xed. Because the e⁄ective wage is an exogenously determined constant, all else equal, higher amenities imply that real wages must decline. So, although job bene(cid:133)ts are higher, the net e⁄ect on labor earnings, WH, is ambiguous. 37

If instead @G =@ A = 0 and E rises, as shown in the right panel of Figure A3 the level A of amenities remains (cid:133)xed, but the surplus from amenities rises. This induces an upward shift in the net job utility function, which is consistent with e⁄ort remaining (cid:133)xed and job bene(cid:133)ts rising. Because the e⁄ective wage must remain constant, real wages rise, and all other change are analogous to those in Section B.2.1. G(A) G(A) V V G’ G’ G G A A’ A A A i Figure A3: E⁄ect of positive innovation in the nature of the work environment with @G =@ A >0 (left) and @G =@ A =0 (right). A A B.3 Real Wages and Trendless Work Hours B.3.1 Unaltered Slope of Net Job Utility Consider an initial equilibrium such as point A in the left panel of Figure A4, which corresponds to an isocost line with slope (cid:21)Z!. Then, if labor-augmenting technology rises, or (cid:0) there is a positive innovation in the nature of work proper and @F =@ E = 0, or there is a E positive innovation in the nature of the work environment and @G =@ A = 0, as shown in A Section B.2 labor earnings rise and the marginal value of wealth decreases. And, at lower (cid:21) amenities are optimally higher, and the surplus from amenities is also higher(cid:151)which is consistent with an upward shift in the net job utility function (with no change in its slope) and less steep isocost lines. If there is no change in labor hours, then the new equilibrium must be at a point such as A(cid:146)in the left panel of Figure A4. There, e⁄ort is lower but the e⁄ective wage ! = (W +A)=(EZ) is unchanged.12 12Note that W A dln!+dlnE+dlnZ = dlnW + dlnA W +A W +A 38

J J B B A’ A’ A A E E VZg VZg Figure A4: Impact of technological changes. Increase in Labor-Augmenting Technology In the case in which Z rises, because e⁄ort declines and amenities rise, the real wage can only be higher after the increase in labor-augmenting technology if the product EZ is higher and proportionally greater than the increase in amenities. In mathematical terms, because the e⁄ective wage must remain constant, then a rise in Z triggers a rise in real wages only if A dlnZ > dlnA dlnE. W +A (cid:0) In such case, because after the rise in Z real wages are higher and so is job utility, then work hours remain constant as a result of the rise in job utility countervailing the income e⁄ect(cid:146)s outweighing of the substitution e⁄ect. So, an increase in labor-augmenting technology can indeed be consistent with higher real wages and trendless labor hours (and higher e⁄ective labor productivity). Positive Innovations in Job-Enjoyment Technology If labor-augmenting technology rises, or there is a positive innovation in the nature of work proper and @F =@ E = 0, or E there is a positive innovation in the nature of the work environment and @G =@ A = 0, A then, again, at point A(cid:146)e⁄ort is lower. Because amenities are higher and the e⁄ective wage must remain constant, then given that the product EZ is lower real wages must decline. And this decline must exactly satisfy W +A dlnW = dlnE A dlnA. W (cid:0) (cid:1) 39

So, allelseequal, neitherapositiveinnovationinthenatureofworkproperwith@F =@ E = E 0 nor a positive innovation in the nature of the work environment with @G =@ A = 0 are A consistent with both trendless work hours and higher real wages. B.3.2 Altered Slope of Net Job Utility Consider an initial equilibrium such as point A in the right panel of Figure A5, which corresponds to an isocost line with slope (cid:21)Z!. Then, given a positive innovation in the (cid:0) nature of work proper with @F =@ E > 0, as shown in Section B.2.2 labor earnings rise E and the marginal value of real wealth decreases. And, at lower (cid:21) amenities are optimally higher, and the surplus from amenities is also higher(cid:151)which is consistent with an upward shift in the net job utility function (with change in slope as implied by @F =@ E > 0) and E less steep isocost lines. If there is no change in labor hours but the income e⁄ect outweighs the substitution e⁄ect, then the new equilibrium must be at a point such as A(cid:146)in the left panel of Figure A4(cid:151)job utility must be higher. At point A e⁄ort is higher but the e⁄ective 0 wage ! = (W +A)=(EZ) must remain unchanged. Because amenities are also higher, real wages are higher only if W dlnE > dlnA. W +A So, when positive innovations in the nature of work proper make e⁄ort less taxing, a rise in E can indeed be consistent with higher real wages and trendless labor hours (and higher e⁄ective labor productivity). B.3.3 Technological Equivalence Comparison of the left and right panels of Figure A4 along with results from Sections B.3.1 and B.3.2 imply that, in principle, the impact of an increase in labor-augmenting technology can be exactly equal to the impact of a positive innovation in the nature of work proper. 40