Does Home Production Drive Structural Transformation?

Transcription

1 Crawford School of Public Policy CAMA Cenre for Applied Macroeconomic Analysis Does Home Producion Drive Srucural Transformaion? CAMA Working Paper 19/2016 April 2016 Alessio Moro Universiy of Cagliari Solmaz Moslehi Monash Universiy Saoshi Tanaka Universiy of Queensland and Cenre for Applied Macroeconomic Analysis, ANU Absrac Using new home producion daa for he U.S., we esimae a model of srucural ransformaion wih a home producion secor, allowing for boh non-homoheiciy of preferences and differenial produciviy growh in each secor. We repor wo main findings. Firs, he esimaion resuls show ha home services have a lower income elasiciy han marke services. Second, he slowdown in home labor produciviy, sared in he lae 70s, is a key deerminan of he rise of marke services. Our counerfacual experimen shows ha, wihou he slowdown, he share of marke services would be lower by 5.8% in THE AUSTRALIAN NATIONAL UNIVERSITY

2 Keywords Srucural Change, Home Producion, Services Secor. JEL Classificaion E20, E21, L16 Address for correspondence: (E) ISSN The Cenre for Applied Macroeconomic Analysis in he Crawford School of Public Policy has been esablished o build srong links beween professional macroeconomiss. I provides a forum for qualiy macroeconomic research and discussion of policy issues beween academia, governmen and he privae secor. The Crawford School of Public Policy is he Ausralian Naional Universiy s public policy school, serving and influencing Ausralia, Asia and he Pacific hrough advanced policy research, graduae and execuive educaion, and policy impac. THE AUSTRALIAN NATIONAL UNIVERSITY

3 Does Home Producion Drive Srucural Transformaion? Alessio Moro Universiy of Cagliari Solmaz Moslehi Monash Universiy Saoshi Tanaka Universiy of Queensland CAMA April 7, 2016 Absrac Using new home producion daa for he U.S., we esimae a model of srucural ransformaion wih a home producion secor, allowing for boh non-homoheiciy of preferences and differenial produciviy growh in each secor. We repor wo main findings. Firs, he esimaion resuls show ha home services have a lower income elasiciy han marke services. Second, he slowdown in home labor produciviy, sared in he lae 70s, is a key deerminan of he rise of marke services. Our counerfacual experimen shows ha, wihou he slowdown, he share of marke services would be lower by 5.8% in JEL Classificaion: E20, E21, L16. Keywords: Srucural Change, Home Producion, Services Secor. We hank Benjamin Bridgman for providing he home producion daa for he U.S. We also hank Timo Boppar, Fabio Cerina, Horag Choi, Begoña Domínguez, Chris Edmond, Miguel León-Ledesma, Sephorah Mangin, Rachel Ngai, Michelle Rendall, Akos Valeninyi, Yuichiro Waki, and oher seminar paricipans a Carlos III, Indiana Universiy, Kansas Ciy Fed, IMF, Universiy of Melbourne, Monash Universiy, Universiy of Queensland, Universiy of Tokyo, Keio Universiy, Kyoo Universiy, Hiosubashi Universiy, Universiy of Warwick, Sociey for Economic Dynamics (Warsaw), Conference on Urbanizaion, Srucural Change, and Employmen (Hong Kong), Midwes Macro Meeings Fall 2015 (Rocheser), Public Economic Theory (Luxembourg), and Workshop of Ausralasian Macroeconomics Sociey (Sydney) for heir helpful commens and suggesions. The usual disclaimers apply. Conac: amoro@unica.i. Conac: solmaz.moslehi@monash.edu.au. Conac: s.anaka@uq.edu.au. 1

4 1 Inroducion Since he early 1990s, a number of sudies have incorporaed household home producion in a neoclassical framework in order o explain several macroeconomic phenomena. 1 Srucural ransformaion is one of he fields in which researchers have recenly been discussing he role of home producion. 2 While previous sudies in his field have successfully derived rich implicaions by modeling home producion, empirical works ha assess he model s abiliy o explain he daa have been limied. Therefore, an imporan quesion o be addressed in his lieraure is wheher a srucural ransformaion model wih a home producion secor is able o accoun for he acual home producion daa. In his paper, we propose and esimae a model of srucural ransformaion wih a home producion secor ha can accoun for he movemens of he home and marke secor shares in exended oal consumpion in he U.S. 3 In order o consruc he home producion daa for he esimaion, we follow he income approach recenly developed in he lieraure, and compue he value added of home producion from is inpu facors and heir prices. 4 We hen use he esimaed model o sudy he role of a home producion secor in he process of srucural ransformaion. In paricular, we run a couner-facual experimen o quanify he effecs of he slowdown in home labor produciviy growh in he U.S. afer he lae 1970s, which is documened in Bridgman (2013). Our framework is based on a muli-secor growh model in which srucural ransformaion is generaed hrough non-homoheic preferences and differenial produciviy growh across secors, as in Buera and Kaboski (2009). We exend his model o include a home producion secor operaed by he household. Since he iner-emporal and he inra-emporal problems can be solved independenly in his class of growh models wih srucural ransformaion, we can re-wrie he laer as a saic, consumpion choice problem of he household, which depends on he prices for he hree marke goods, he implici price for home produced services, and he exended oal consumpion. This las version of he model allows us o esimae he implied share equaions, using he home producion daa ogeher wih he value added consumpion daa for he marke secors. In he esimaion, we explore differen household preferences specificaions. In paricular, 1 These sudies include issues on business cycles (Benhabib, Rogerson, and Wrigh (1991); Greenwood and Hercowiz (1991)), life-cycle labor supply decisions (Ríos-Rull (1993)), and fiscal policy (McGraan, Rogerson, and Wrigh (1997)), among ohers. 2 The srucural ransformaion lieraure sared discussing home producion following he wo seminal papers, Rogerson (2008) andngai and Pissarides (2008). 3 We define exended oal consumpion as he value of marke consumpion plus he value added of home producion. 4 Our income approach is similar o hose in Landefeld, Fraumeni, and Vojech (2009) andbridgman (2013). 2

5 Figure 1 Home and Marke Secor Shares (Lef) and Home Labor Produciviy (Righ) Home and Marke Secor Shares Home Labor Produciviy Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Labor Produciviy (Uni: 2005 USD per Hour) Year Year Noe: The consumpion value added of he marke secors is calculaed based on he daa of Herrendorf, Rogerson, and Valeninyi (2013). The consumpion value added of he home secor is calculaed by using he income approach similar o Bridgman (2013). The home labor produciviy is obained by deflaing he value added of home producion wih he price index for he home secor and hen dividing i by hours worked a home. The deails of he daa used here are discussed in Secion 4. we allow for differen income elasiciies of home and marke services in he household consumpion demand, somehing ha has no been considered in he previous lieraure. 5 This is moivaed by he empirical evidence documened in Eichengreen and Gupa (2013), which suggess ha marke services wih a home counerpar could have a differen income elasiciy from he oher services. In our resuls, i urns ou ha his feaure of he model is crucial o accoun for he daa. We highligh wo main resuls. Firs, we find ha home services have a lower income elasiciy han marke services. The esimaion resuls indicae ha, if he income elasiciies are he same beween marke and home services, he model canno generae he secular decline of he home service share since he lae 1940s (see he lef panel in Figure 1). This resul conrass wih previous sudies in he lieraure, which explain he movemen of marke and home service shares only hrough differences in he raes of echnological progress across secors. 6 Our esimaes sugges ha he changes in echnologies are no enough o accoun for he movemen of he home and marke shares observed in he daa. The second resul is obained by running a couner-facual experimen, in which we le home labor produciviy grow afer 1978 a he same average pace before he slowdown (see he righ panel in Figure 1). We find ha in he couner-facual he share of marke 5 A common assumpion in previous works is o assume he same income elasiciy for home and marke services. See for insance Rogerson (2008), Ngai and Perongolo (2013) and Rendall (2015). 6 See Ngai and Pissarides (2008) andbuera and Kaboski (2012b) for example. 3

6 services in he oal consumpion expendiure is 0.86 in 2010, compared o 0.81 wihou he slowdown, which shows a 5.8% decrease. Tha is, if here were no slowdown in home labor produciviy, he exen of srucural change would be considerably lower han he acual daa indicaes. This experimen herefore suggess ha he home producion secor can have quaniaively imporan implicaions for he srucural change observed in marke secors. Our paper relaes o he lieraure, sared by Rogerson (2008) and Ngai and Pissarides (2008), ha considers home producion as a key deerminan in he process of srucural ransformaion. More recen sudies in his lieraure include Buera and Kaboski (2012a), who focus on differences in skill inensiies beween home and marke, Buera and Kaboski (2012b), who model differences in producion scale beween home and marke, Ngai and Perongolo (2013), who sudy he rise of female labor force paricipaion in he U.S., and Rendall (2015), who analyzes he implicaions of he difference in he ax sysem for female labor force paricipaion beween he U.S. and Germany. As emphasized above, while hese sudies have derived rich implicaions of srucural ransformaion models wih a home producion secor, hey do no esimae hese models using acual home producion daa. There are wo recen conribuions which esimae a model of srucural ransformaion wihou a home producion secor using he U.S. daa. Buera and Kaboski (2009) esimae a hree-secor model using he U.S. daa in a general equilibrium framework. Herrendorf, Rogerson, and Valeninyi (2013), on he oher hand, consider a parial equilibrium seup, and esimae a hree-secor model using final consumpion expendiure and consumpion value-added daa since Our mehodology is close o ha of Herrendorf, Rogerson, and Valeninyi (2013). However, we consider a srucural ransformaion model wih a home producion secor, and esimae he model using he value added of home producion ogeher wih consumpion value added daa for he marke secors. Finally, our paper is also relaed o he lieraure which has developed he income approach o impue he value of non-marke aciviies from inpu facors and heir marke prices. This idea goes back o as far as Kendrick (1979). In recen years, researchers a he BEA have furher developed his approach o consruc heir Saellie Accoun for Household Producion (Landefeld and McCulla (2000); Landefeld, Fraumeni, and Vojech (2009); Bridgman, Dugan, Lal, Osborne, and Villones (2012); Bridgman (2013)). This paper s sraegy o consruc he home value added closely follows hese works. The reminder of he paper is as follows. Secion 2 presens he model; Secion 3 discusses he esimaion procedure; Secion 4 explains he daa; Secion 5 repors he esimaion resuls, while Secion 6 runs he couner-facual experimen. In Secion 7, we consider an exension by disaggregaing he service secor. In Secion 8, we discuss he implicaions of he model for hours worked. In Secion 9, we conclude. 4

7 2 Model This secion presens a model of srucural ransformaion wih a home producion secor. 2.1 Seup Time is discree. There is a represenaive household, whose objecive is o maximize her uiliy. There are five ypes of goods produced in his economy: four consumpion goods (agriculure, manufacuring, marke services, and home services) and one invesmen good. The household s preferences is given by u = β ln C, =0 where β is he subjecive discoun facor. The composie consumpion index C is defined as C = i=a,m,s ( ω i ) 1 σ ( c i + c σ 1 i) σ σ σ 1. (1) where c i denoes consumpion of good i {a, m, s}. In (1), he parameer ω i deermines he weigh on each good in he household s preferences; he parameer c i conrols nonhomoheiciy in preferences; and he parameer σ governs he elasiciy of subsiuion among he hree goods. Service consumpion is a composie of marke services, c sm, and home produced services, c sh,as [ c s = ψ(c sm ) γ 1 γ +(1 ψ)(c sh ] γ + c sh ) γ 1 γ 1 γ. (2) In (2), he parameer γ governs he elasiciy of subsiuion beween marke and home services and ψ is he share parameer in he service aggregaor. Noe ha we allow for a differen income elasiciy beween marke and home services hrough he parameer c sh. We provide a discussion of his parameer in Secion 2.4 and in he esimaion secion. In our seup, for each period, he household is endowed wih l = 1 uni of labor ha she splis ino working ime in he marke, l mk, paid a wage w and working ime a home, l sh. Also, he household holds he capial sock k in he economy, and decides how much o ren in he marke, k mk, a rae r, and how much o use in home producion, k sh. Then, he household s consrains are given by p a c a + p m c m + p sm c sm + k+1 mk (1 δ) k mk + k+1 sh (1 δ) k sh = r k mk + w l mk, (3) 5

8 l mk + l sh = l, where p j is he price of good j {a, m, sm} and δ is he depreciaion rae. We normalize he price of he invesmen goods o be equal o one. The oal amoun of capial is defined as k k mk + k sh. The household produces home services hrough he following echnology, c sh = A sh ( ) k sh α ( ) l sh 1 α. On he marke producion side, here is a perfecly compeiive firm in each marke secor j {a, m, sm} wih echnology, Y j = A j ( ) K j α ( ) L j 1 α. Finally, here is also a perfecly compeiive firm operaing in he invesmen good secor wih echnology, Y x = A x (K x ) α (L x ) 1 α. 2.2 Household s Problem Nex, we re-wrie he previous seup by reaing he home producion secor as being operaed by a perfecly compeiive firm. This allows us o consider he home producion secor as an addiional marke secor, which helps us o simplify he problem. Assuming perfec compeiion in he home secor, we can define an implici price index for he home good as p sh r α w 1 α A sh α α 1 α. (4) (1 α) Using he above price, we can show ha p sh c sh = w l sh + r k sh. (5) We now add up (5) o he budge consrain of he household, (3), and obain p a c a + p m c m + p sm c sm + p sh c sh + k +1 (1 δ) k = r k + w l. 6

9 Thus, we can rewrie he household problem as max β ln C =0 (P1) subjec o [ c s = C = ψ(c sm i=a,m,s ) γ 1 γ ( ω i ) 1 σ ( c i + c +(1 ψ)(c sh σ 1 i) σ σ σ 1 ] γ + c sh ) γ 1 γ 1 γ,, p a c a + p m c m + p sm c sm + p sh c sh + k +1 (1 δ) k = r k + w l. Given he definiion of he implici price for home services (4), i is sraigh-forward o show ha problem (P1) is equivalen o he original seup in Secion Separaing Iner- and Inra-Temporal Problems As he final sep oward he esimaion, we show ha he household s problem (P1) can be decomposed ino he following wo problems Iner-Temporal Problem: The household solves: max β ln C {C,k +1 } =0 (P2) subjec o P C + k +1 (1 δ) k = r k + w l + p sh c sh + where P [ i=a,m,s ω i (p i ) 1 σ] 1 1 σ 2. Inra-Temporal Problem: The household solves: i=a,m,s p i c i, [ and p s ψ γ (p sm ) 1 γ +(1 ψ) ( γ p sh ) 1 γ ] 1 1 γ. max {c a,cm,csm,c sh } i=a,m,s ( ω i ) 1 σ ( c i + c σ 1 i) σ σ σ 1 (P3) subjec o [ c s = ψ(c sm ) γ 1 γ +(1 ψ)(c sh ] γ + c sh ) γ 1 γ 1 γ, 7 See Online Appendix A for deails. 7

10 and p a c a + p m c m + p sm c sm + p sh c sh = P C p i c i p sh c sh E, i=a,m,s where E sands for he exended oal expendiure on consumpion - ha is, oal consumpion plus home producion. The above decomposiion indicaes ha he iner-emporal problem (P2) and he inraemporal problem (P3) can be solved separaely. Also, noe ha he inra-emporal problem (P3) is he one ha causes secoral ransformaion among four consumpion good secors. In Secion 3, we esimae he inra-emporal problem (P3) using ime series daa for prices { } p a,p m,p sm,p sh and exended oal consumpion E. 8 We choose o esimae (P3) insead of he full model (P1) for wo reasons. Firs, we are ineresed in esimaing preference parameers in he model. Given he separaion of he wo problems shown in his secion, i is sufficien o esimae (P3) o obain consisen esimaors of he relevan preference parameers. Second, o esimae he full model (P1), we would need o ake a sand on how o bring he invesmen secor o he daa. We know ha, in he daa, aggregae invesmen comes from he hree marke secors (agriculure, manufacuring, and services) and ha he composiion has been changing over ime. Given his feaure of invesmen, one needs o make some simplificaion assumpions o model he invesmen secor. However, depending on he modeling choice, esimaes could be differen. Wih his in mind, we avoid making his choice in he iner-emporal problem, and focus only on he esimaion of he inra-emporal problem (P3). 2.4 Preference Specificaions The model presened in he previous subsecions encompasses he sandard models of srucural ransformaion, namely hose of Kongsamu, Rebelo, and Xie (2001) and Ngai and Pissarides (2007), wih he addiion of home producion. Since our purpose is o sudy he effec of home producion on srucural ransformaion, we esimae he following four differen specificaions, which imply differen ineracion mechanisms of he home and he marke secors. 9 Model 1: We firs impose c s = c sh = 0. As discussed in Kongsamu, Rebelo, and Xie (2001), he parameer c s > 0 can be inerpreed as home producion of services. Thus, when adding an explici home producion secor o he model, a naural resricion is o impose 8 Regarding he implici price of home good, p sh, we discuss which daa we use for i in Secion Noe ha in all specificaions we resric c m o be zero, as sandard in he lieraure. 8

11 c s = 0. In his way we can asses wheher he home secor can replicae he role played by he non-homoheic parameer in he sandard model. Model 2: In he second specificaion, we only impose c sh = 0. This implies ha we are allowing for boh an explici home producion secor and he sandard non-homoheiciy effec for services. Thus, he parameer c s simply reflecs a non-homoheic naure of services, which is no fully explained by home producion. Model 3: Third, we esimae he specificaion in which we only impose c s = 0. In his case, we allow he non-homoheiciy o be differen beween marke and home services hrough c sh, while we keep he non-homoheic erm for he composie service c s a zero. 10 By doing so, we can assess how much he non-homoheiciy in home services c sh improves he model s fi o he daa by iself. Model 4: Finally, we esimae he fully unresriced model. By esimaing he firs hree models we obain insighs ino he role of each non-homoheic componen. Here, we have all non-homoheic effecs working ogeher. In he above preference specificaions, he parameer c sh is moivaed by he empirical evidence which suggess ha services caegories can have differen income elasiciies. For insance, Eichengreen and Gupa (2013) show ha he share of modern marke services rises faser wih income compared o ha of he more radiional marke services, which can also be produced a home. Alhough his evidence does no provide insighs ino he income elasiciy of home services, i is reasonable o suppose ha home and marke services have differen income elasiciies. If he laer have a larger elasiciy, we should expec a parameer c sh < 0. In his case, he parameer can be inerpreed as a minimum requiremen of home producion ha he household has o provide (for insance mainenance and cleaning) before enjoying he res of home services produced. 3 Esimaion This secion describes he esimaion. We ake a wo-sep procedure: firs, we fix he value of he elasiciy of subsiuion parameer beween home and marke services by using a 10 Noe ha in a CES aggregaor wih wo goods, he presence of a non-homoheic erm associaed wih one of he goods implies ha he oher good will also display a non-homoheic behavior. This is he case here for home services and marke services. On his poin, see Moro (2015). 9

12 priori informaion from he lieraure; second, we esimae he res of he parameer values from he daa. 11 We explain hese seps in deail here. Firs Sep In his sep, we fix he value of he parameer γ, which governs he elasiciy of subsiuion beween home and marke services. 12 In he lieraure, one se of sudies esimaes he parameer γ by using flucuaions of aggregae home hours over he business cycles (McGraan, Rogerson, and Wrigh (1997); Chang and Schorfheide (2003)). Anoher se of sudies, insead, uses household micro daa for home hours (Ruper, Rogerson, and Wrigh (1995); Aguiar and Hurs (2007)). The esimaed value of he parameer γ ranges beween 1.49 and One imporan noe here is ha all of hese esimaes correspond o he elasiciy of subsiuion beween all marke and non-marke ypes of consumpion. Insead, in our model he parameer only refers o he subsiuabiliy beween marke services and home producion. As i seems reasonable o consider ha marke services are more subsiuable wih home producion han oher goods, we se he value of γ equal o 2.3, he highes one esimaed in previous sudies. 13 Second Sep To esimae he res of he parameers, we firs derive equaions for he share of each secor in he exended oal consumpion. Given he he se of (pre-deermined) variables, given γ, and given he res of he parameers, x ( ) p a,p m,p sm,p sh,e, θ ( σ, c a, c s, c sh,ω a,ω m,ω s,ψ ), { p problem (P3) can be solved for four shares, j cj E }, where j {a, m, sm, sh}. Since secoral shares sum up o one, he error covariance marix becomes singular wih four share equaions. Thus, we drop one share equaion, and finally have he hree non-linear equaions o be 11 In Online Appendix B, we esimae γ ogeher wih he res of he parameers. 12 Noe ha γ does no coincide wih he elasiciy of subsiuion when non-homoheic parameers appear in he uiliy funcion. However, in our esimaions we find ha he difference beween γ and he rue elasiciy of subsiuion is quaniaively very small. Therefore, we consider γ as a measure of he elasiciy of subsiuion. 13 Our sraegy for he choice of he elasiciy parameer is he same as he one in Rogerson (2008). In Online Appendix B, we run esimaions insead by assuming γ equal o 1.5, he lowes value esimaed in he lieraure. We show ha our main resuls don change even in ha case. 10

13 esimaed: p a c a = f 1 (x ; θ, ˆγ)+ɛ 1, E p m c m = f 2 (x ; θ, ˆγ)+ɛ 2, E p sm c sm E = f 3 (x ; θ, ˆγ)+ɛ 3, where ˆγ is he value of he parameer γ from he firs sep. In Appendix B, we show he derivaion of (f 1,f 2,f 3 ). 14 To esimae our demand sysem we closely follow previous works in he lieraure: Deaon (1986) and Herrendorf, Rogerson, and Valeninyi (2013). Specifically, we employ ieraed feasible generalized nonlinear leas square o esimae he share equaions. 15 For he parameers wih consrains (σ 0, ω a + ω m + ω s =1,ω i 0, 0 ψ 1), we ransform hem ino unconsrained parameers as follows; σ = e b 1,ω a = 1 1+e b 2 + e b 3,ω m = e b 2 1+e b 2 + e b 3,ω s = e b 3 1+e b 2 + e b 3,ψ= eb4 1+e b 4. Afer esimaing he unconsrained parameers, we ransform hese back o compue poin esimaes and sandard errors for he original parameers. 4 Daa One of he conribuions of his paper is o esimae a srucural ransformaion model wih a home secor by using acual home producion daa for he U.S. We follow he income approach recenly developed in he lieraure o consruc home producion daa. Since he approach is based on he value-added mehod, we focus on consumpion value added shares for our esimaion. We explain below how we consruc he daa for our esimaion. 4.1 Home Producion Daa The basic idea of he income approach is o compue he value of home producion from he marke value of inpu facors: here home labor L sh and home capial K sh. Formally, home 14 See Equaions (8) hrough (10) in he appendix. 15 This mehodology has also been recenly used in he esimaion of supply sysems. See León-Ledesma, McAdam, and Willman (2010). 11

14 value added of he household secor is given by where r sh and δ sh (r sh + δ sh )K sh + w sh L sh, are, respecively, he rae of reurn and he depreciaion rae of home capial, and w sh is he reurn on home labor. For he home capial K sh, we use he nominal sock of consumer durables (BEA, FA Table 8.1). Unlike Bridgman (2013), we don include gross housing value added in home capial, because he value of housing services also shows up in he household s consumpion expendiure. 16 For he rae of reurn on home capial r sh, we use he personal income receips from asses (BEA, NIPA Table 2.1) divided by oal financial asses of he household (Board of Governors, FL ) ne of equiy in non-corporae business (Board of Governors, FL ). For δ sh we use he depreciaion of durables (BEA, FA Table 1.3). For home labor L sh, we use hours spen in home producion consruced by Landefeld, Fraumeni, and Vojech (2009) and Bridgman, Dugan, Lal, Osborne, and Villones (2012). These sudies use muliple ime use survey daa and exrapolae hem using CPS daa on populaion and labor force saus. For he reurn on home labor w sh, we calculae hourly wage by using compensaion for employees in he privae households secor (BEA, NIPA Table 6.2) and he number of employees in ha secor (BEA, NIPA Table 6.5), assuming ha hose workers spend 40 hours in working per week. 17 Finally, Bridgman (2013) deflaes nominal home value added wih he price index of gross value added for household secor (BEA, NIPA Table 1.3.4), o obain real home value added. We use his as he price for home value added { } p sh in our esimaions below. Thus, excep for he consrucion of home capial K sh, we closely follow he mehodology in Bridgman (2013). 4.2 Oher Daa Value Added Consumpion and Price Index The daa for value-added consumpion and he corresponding price indices for agriculure, manufacuring, and services are from Herrendorf, Rogerson, and Valeninyi (2013). The advanage of using hese daa is ha value-added consumpion is compued from final con- 16 This is he same approach aken for insance in Bridgman, Duernecker, and Herrendorf (2015). 17 Duernecker and Herrendorf (2015) also use compensaion for employees in he privae households secor o compue he hourly wage rae for home labor. As hey noe, he main assumpion here is ha he marginal produc of household workers is he same as he marginal produc of a non-household worker who is doing household work. 12

15 sumpion expendiure by using he U.S. inpu-oupu marix, in order o avoid invesmen componens being included in consumpion value-added daa. 18 Durable Goods As menioned above, we consider all durable goods as inpus for home producion. Therefore, i is reasonable o remove he value of durables from he value-added consumpion daa, because oherwise households have durables boh as consumpion goods and as capial inpus for home producion. Since he value of durables in consumpion expendiure daa consiss of he value added from he hree marke secors, we again follow he approach in Herrendorf, Rogerson, and Valeninyi (2013) o remove he value of durables from value added consumpion. Tha is, we firs decompose he value of final-expendiure durables ino he value added of each secor using an inpu-oupu marix, and hen subrac hose values from he consumpion value added of each secor. In he robusness Secion 5.2, we relax he assumpion ha all durables are used as invesmen in home capial. Tha is, we consider he case in which some durables are reaed as consumpion goods, and he res are invesmen goods for home capial. For example, we consider goods like jewelry and waches as direcly consumed by households, while goods like home appliances form par of home capial. As we will show laer, our esimaion resuls are no affeced by he relaxaion of his assumpion. In he esimaion, we focus on he ime period beween 1947 and 2010, due o he availabiliy of consumpion value added daa. In order o calculae four secor shares (agriculure, manufacuring, services, and home) in exended consumpion value added, we combine consumpion value added daa wih value added of he home secor. One imporan assumpion made here is ha goods produced a home are no used for invesmens. 5 Esimaion Resuls In his secion, we describe our esimaion resuls. 5.1 Benchmark Resuls Table 1 summarizes esimaion resuls for our benchmark case. In Columns (1) hrough (4), we repor he esimaion resuls of Models 1 o 4, which we described in Secion 2.4. In 18 Several papers in his lieraure assume ha all invesmen is produced in he manufacuring secor. However, he oal value of invesmens exceeds he oal value of manufacuring goods from 1999 onward in BEA s daa. 13

16 Column (5), we also repor he resuls when we impose he consrain σ = 0 on Model 4. We name he model wihou he consrain as Model 4a, and he one wih he consrain, Model 4b. From he perspecives of he Akaike and Bayesian Informaion Crieria (AIC and BIC) repored in Table 1, i is eviden ha neiher of Models 1 or 2 (Columns (1) and (2)) displays a beer performance han Model 3 or 4a (Columns (3) and (4)). The poor fi of Models 1 and 2 is also visually presened in Figure 2, indicaing ha neiher of hem can correcly capure he increasing rend of marke services and he decreasing rend of home services. These facs imply ha he common specificaion in he lieraure, which assumes he same income elasiciy of marke and home services (i.e. c sh = 0), canno explain why he demand for marke services has increased relaive o home services over he period. Also, from he esimaion resul of Model 2, i is clear ha he non-homoheiciy erm on aggregae services c s doesn help o solve he issue by iself. 19 We now urn o discuss Model 3 and Model 4a. There are hree poins which are worh emphasizing here. Firs, as discussed above, Models 3 and 4a display a beer fi han Models 1 and 2, suggesing ha he non-homoheic erm c sh is key o accoun for he rends in boh marke and home service shares. 20 Second, by comparing he performances of Model 3 and Model 4a, we noe ha he non-homoheic erm on aggregae services c s plays an imporan role once he non-homoheic erm on home services c sh is inroduced. This is also visually shown in Figure 3. When c s is consrained a zero (Model 3), he model is no able o produce enough divergence in he paerns of home and marke service shares. Insead, when c s is unconsrained (Model 4a), he model s performance improves. This is because, in he former case, here is only one non-homoheiciy parameer conrolling he relaive rends of wo share series, bu in he laer case, here are wo parameers shaping hose rends. Third, when boh he non-homoheiciy erm for aggregae services c s and he one for home services c sh are inroduced, he value of σ is no longer saisically significanly differen from zero. The poin esimaor of σ is , and he value of he heeroscedasiciy-robus sandard error is This implies ha he uiliy funcion akes a Leonief specificaion in erms of agriculural, manufacuring, and aggregae services. Noably, his resul for σ is similar o hose in Buera and Kaboski (2009) and Herrendorf, Rogerson, and Valeninyi (2013). Given ha he poin esimaor of σ is no saisically significanly differen from zero, we resric he value of σ o zero, and run he esimaion of Model 4b (Column (5) 19 In fac, he AIC and BIC sugges ha Model 1 performs beer han Model Ngai and Pissarides (2008) generae a rise of he marke services share in a model wih home producion hrough homoheic preferences and differenial TFP growh across secors. Our resuls insead sugges ha a non-homoheic componen on home producion is key o quaniaively accoun for he acual rise of he marke services share in he U.S. in a model wih a home secor. 14

17 in Table 1). The resul shows ha, while he roo mean squared errors are unchanged, he AIC and he BIC decrease, implying ha his specificaion is he mos preferred in erms of hose measures. Therefore, we use Model 4b for our couner-facual experimens in he following subsecions. 21 Table 1 Secoral Share Esimaion Resuls (1) (2) (3) (4) (5) a 4b σ (0.0291) (0.0202) ( ) ( ) c a (3.603) (3.856) (9.276) (15.51) (13.65) c s (31.22) (368.1) (323.0) c sh (121.3) (133.8) (182.8) ω a ( ) ( ) ( ) ( ) ( ) ω m ( ) ( ) ( ) ( ) ( ) ω s ( ) ( ) ( ) ( ) ( ) ψ ( ) ( ) ( ) ( ) ( ) N AIC BIC RMSE a RMSE m RMSE sm RMSE sh Robus sandard errors in parenheses p<0.10, p<0.05, p<0.01 Noe: N sands for he number of he sample in he esimaion. AIC is Akaike Informaion Crierion. BIC is Bayesian Informaion Crierion. RMSE j is he Roo Mean Squared Error for j-secor s share equaion. 21 To inerpre he esimaed non-homoheic erms c a, c s and c sh for Model 4b, we compue heir values relaive o he consumpion level of each good in These are 0.81 for ( c a /c a ), 0.85 for ( c s /c s ), and 0.73 for ( c sh /c sh ). 15

18 Figure 2 Fied Secoral Shares for Model 1 ( c s = c sh = 0) and Model 2 ( c sh =0) Model 1 Model 2 Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Year Year Daa Model Daa Model Figure 3 Fied Secoral Shares for Model 3 ( c s = 0) and Model 4a (no resricions) Model 3 Model 4a Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Year Year Daa Model Daa Model Figure 4 Fied Secoral Shares for Model 4b (σ =0) Model 4b Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Year Daa Model 16

19 Table 2 Durable Good Caegories Consumpion Goods Invesmen Goods Moor Vehicles Good Caegories in NIPA Table video, audio, phoographic, and informaion processing equipmen and media, sporing equipmen, supplies, guns, and ammuniion, spors and recreaional vehicles, recreaional books, musical insrumens, jewelry and waches, luggage and similar personal iems, elephone and facsimile equipmen furniure and furnishings, household appliances, glassware, ableware, and household uensils, ools and equipmen for house and garden, herapeuic appliances and equipmen, educaion books new moor vehicles, ne purchases of used moor vehicles, moor vehicle pars and accessories 5.2 Robusness Here, we discuss he robusness of he benchmark resuls. For breviy, we repor all esimaes in Appendix A. Spliing Durable Goods As we discussed in Secion 4, we consider all durable goods as invesmen in home capial in he benchmark case. However, while some ypes of goods are more likely o be used for home producion (e.g. home appliances), some ohers are more naurally assigned o consumpion (e.g. jewelry and waches). Therefore, i seems reasonable o check wheher our esimaion resuls are robus when we relax he assumpion ha all durables are used as capial inpus for home producion. For his purpose, we firs classify he final durable good expendiure in wo caegories: direc consumpion goods and capial inpus for home producion. Then, we calculae consumpion value added from he former, and use he laer o compue home value added. We refer o BEA s NIPA Table when dividing final durable good expendiures ino he wo caegories. We hen apply he inpu-oupu marices in Herrendorf, Rogerson, and Valeninyi (2013) o hose which we classified as consumpion goods in order o conver consumpion expendiure ino consumpion value added. The creaed consumpion value-added daa are hen added o he consumpion value added of each marke secor. We also refer o BEA s FA Table 8.1 when consrucing he sock of durable goods, which is consisen wih he way we spli hem in consumpion expendiure daa. 22 The daa of he sock are hen 22 NIPA Table and FA Table 8.1 have almos he same srucure in erms of he classificaion of durable goods. Therefore, i is possible o consruc he sock of durable goods consisen wih he way we spli durable goods in he consumpion expendiure daa. 17

20 used o consruc home capial. Table 2 shows our classificaion of durable goods ino he wo caegories. One ype of good ha is likely o be used exensively boh for consumpion and for home capial is moor vehicles. Therefore, for moor vehicles, we consider wo cases: firs we include hem in consumpion goods (Case 1); and second we consider hem as home capial invesmen (Case 2). Table A.1 and Table A.2 in Appendix A presen he resuls for each case. As shown in he ables, none of he findings in our benchmark esimaion change significanly in boh cases. Noably, our finding ha he non-homoheiciy parameer c sh significanly improves he model s performance is fairly robus even afer we inroduce he new definiions for home capial goods. Excluding Governmen Consumpion Governmen consumpion is exernally imposed on he household, and here is no a price a which households opimally decide he quaniy o purchase. Therefore, i doesn seem o be fully appropriae o sudy srucural ransformaion by considering consumpion purchased by he governmen secor. For his reason, we remove governmen spending from consumpion value added daa, and re-esimae our model o check he robusness of our benchmark resuls. In his exercise, we are implicily assuming ha households are axed by he governmen o run a balanced budge, and ha governmen spending does no provide uiliy o he households. Table A.3 in Appendix A presens esimaion resuls when we exclude governmen s spending from he consumpion value-added daa. Again, none of he findings in our benchmark esimaion change significanly even when we conrol for he governmen s spending. 6 Couner-Facual Experimen As documened in Bridgman (2013), home labor produciviy grows roughly a he same pace as labor produciviy in he marke economy during he period 1947 o 1978 (2.0% versus 2.1%). Afer ha period, however, he growh rae sagnaes around zero (see Figure 5, lef panel). To precisely dae he slowdown, we es for muliple srucural breaks using he approach proposed in Bai and Perron (1998, 2003). We find ha, a 1% significance level, here is a break beween 1978 and 1979, afer which he mean growh rae of home labor produciviy decreases by 2.8%. 23 Given is magniude and long lasing duraion, i is reasonable o ask how large he quaniaive effec of his slowdown is for he process of 23 See Online Appendix D for deails. 18

21 Figure 5 Couner-Facual Experimen: No Slow-Down in Home Labor Produciviy Couner Facual Home Labor Produciviy Couner Facual Share Movemen Labor Produciviy (Uni: 2005 USD per Hour) Share in Exended Toal Consumpion Service Home Manufacuring Agriculure Year Year Daa Couner Facual Model 4b Fied Value Couner Facual srucural ransformaion. In his secion, we address his quesion by running a counerfacual experimen in which, oher condiions being equal, here is no slow-down in labor produciviy during he period 1979 o More precisely, we assume ha in he household problem, all marke prices and oal expendiure evolve as observed in he daa, while he price of he home good evolves differenly from he daa due o a couner-facual evoluion of home labor produciviy A sh.by using he firs order condiions of he firm in he home secor, we can derive Δp sh p sh = Δw w ΔA sh, (6) A sh which defines he relaionship beween he growh rae of he home price and ha of home labor produciviy. 24 Using Equaion (6) we can calculae he couner-facual price of he home good from he couner-facual home labor produciviy. 25 To run he experimen, we use Model 4b, which provides he bes fi of he daa. The oucome of he exercise is displayed in he righ panel of Figure 5. Wihou he slowdown in home labor produciviy, he divergence beween he share of marke services and he home share over he period is subsanially reduced. This experimen hus suggess ha, holding oher condiions equal, he slowdown in home labor produciviy 24 Using he firs order condiions of he firm in he home secor we can derive p sh = w (1 α) A sh ( ) K sh α = L sh (1 α) w ( Y sh L sh ) = w (1 α) A sh By aking oal differeniaion on boh sides, we reach he equaion in he ex. 25 As he couner-facual home labor produciviy grows on average 2.8% higher han he acual growh rae, he growh rae of he couner-facual price from 1979 onwards will be lower han he acual growh rae by 2.8%. 19.

22 Table 3 Couner-Facual Experimen: No Slowdown in Home Labor Produciviy Ex. Consumpion Share Consumpion Share Consumpion per Capia Bench CF Δ% Bench CF Δ% Bench CF Δ% Agriculure Manufacuring Marke Services Home Services Noe: Consumpion per capia is in 2005 U.S. dollars. The numbers in Δ% columns are percen changes from he benchmark fied value (Model 4b). is crucial in accouning for he whole rise of he marke services share. Models ha do no have an explici home producion secor migh overlook an imporan facor which affecs he rise of marke services. The firs hree columns in Table 3 repor he exended consumpion shares in he benchmark esimaion (he fied values of Model 4b) and in he couner-facual for he year The marke services share is 0.60 in he benchmark and 0.50 in he couner-facual experimen. This difference is compensaed by he home share, which is 0.30 in he benchmark and 0.39 in he couner-facual. These numbers sugges a large subsiuion of marke services by home services wihou he slowdown in home labor produciviy. A similar resul holds for he services share when we look a he (marke) consumpion shares repored in he second hree columns in he able. Services is 0.86 in he benchmark and 0.81 in he couner-facual. This difference amouns o a 5.8% decrease of he marke service share. The las hree columns in he able repor consumpion per capia in 2005 U.S. dollars. As marke prices do no change in he couner-facual, he paerns are he same as hose of he exended consumpion shares excep for home services. To conclude, he resuls in he couner-facual experimen indicae ha he slowdown in he home labor produciviy has quaniaively a significan impac on he rise of he marke service secor over he period of he analysis. 20

23 7 Disaggregaing he Service Secor In our benchmark specificaion in Secion 2, we assume ha all marke services ener he aggregaor wih home services, hus implicily assuming ha hey are all subsiuable wih home services o he same exen. Alhough his is he specificaion mos commonly used in he lieraure (see for insance Rogerson (2008), Ngai and Perongolo (2013), Rendall (2015)), one migh hink ha some marke services do no have a home counerpar. For insance, finance, healh and educaional services don seem o be subsiuable wih home services. Therefore, i is imporan o furher disaggregae marke services ino home subsiuables and non-subsiuables, and o wrie and esimae a model which explicily considers hese wo secors. In his secion, we explore his possibiliy. 7.1 Model We assume he same general srucure of he model as in Secion 2, and inroduce wo ypes of marke services. The consumpion index of he represenaive household in period becomes C = i=a,m,sn,sc ( ω i ) 1 σ ( c i + c σ 1 i) σ Here c a sands for he household s consumpion on agriculural goods, c m on manufacuring goods, c sn on modern services (i.e. marke services which are non-subsiuable o home), and c sc on radiional services. The laer is a composie of services in he marke c sm and home produced services c sh : σ σ 1. [ c sc = ψ(c sm ) γ 1 γ +(1 ψ)(c sh ] γ + c sh ) γ 1 γ 1 γ. The budge consrain of he household is p a c a + p m c m + p sn c sn + p sm c sm + p sh c sh = E, where now p sn marke and, as before, p sh of he model. 27 is he price of modern services, p sm is he price of radiional services in he is he implici price of he home good. 26 We esimae wo versions 26 Noe ha he separaion beween he iner-emporal problem and he inra-emporal problem also applies here. This is easily seen once noed ha he uiliy funcion akes he same form as in (1)-(2) bu wih an addiional ype of consumpion. 27 Again, in all specificaions, we assume c m equal o zero. 21

24 Table 4 Modern and Tradiional Marke Services in he Consumpion Expendiure Service Caegories in NIPA Table Modern Marke Services Housing and Uiliies (49), Healh Care (60) Transporaion Services (68), Recreaion Services (76) Financial Services and Insurance (86), Communicaion (96) Educaion Services (100), Professional and Oher Services (121) Social Services and Religious Aciviies (120) Tradiional Marke Services Food Services and Accommodaions (81) Personal Care and Clohing Services (105), Household Mainenance (107) Noe: The numbers in brackes in he above able correspond o he line numbers in NIPA Table Model 5 We impose c sh = 0, which implies he same income elasiciy for radiional marke services and home services, while we keep he differenial income elasiciy beween modern services and radiional services. Model 6 We esimae he fully unresriced model so ha income elasiciy is allowed o be differen for he hree ypes of services. 7.2 Daa In order o esimae he model presened in Secion 7.1, we need o consruc he consumpion value added and corresponding price daa for he modern and radiional marke service secors. To creae he consumpion value added daa, we follow he approach in Herrendorf, Rogerson, and Valeninyi (2013). Tha is, firs, wihin final consumpion expendiure daa, we define wo caegories, modern and radiional marke services. Second, we remove he disribuional coss from he final consumpion expendiure on goods and move hem ino expendiure on modern services. 28 Third, we creae he inpu-oupu marices which have he modern and radiional marke service secors. Finally, we apply he inpu-oupu marices o final consumpion expendiure o conver hem ino consumpion value added. Table 4 shows how we divide marke services ino he modern and radiional caegories in he consumpion expendiure daa. 29 In he daa, he services ha appear o have a clear home-counerpar are: food services and accommodaions, personal care and clohing services, and household mainenance. Thus, we consider hese as radiional marke services, and he res as modern marke services. In order o creae he inpu-oupu marices, we 28 This procedure convers final consumpion expendiure measured in purchaser s prices ino he one measured in producer s prices. We move disribuional coss o he modern service secor because our definiion of modern services includes ransporaion services as shown laer. 29 We use NIPA Table o creae he modern and radiional marke service expendiure daa. 22

25 apply a similar caegorizaion. The deails on how we consruc he inpu-oupu marices are documened in Online Appendix C. To creae he corresponding prices, we use nominal value added, chain-weighed valueadded quaniies, and chain-weighed value-added prices a indusry level from BEA s GDPby-Indusry Table. Since chain-weighed quaniies are no addiive, we apply he so called cyclical expansion procedure o aggregae quaniies ino he four caegories (agriculure, manufacuring, modern marke services, and radiional marke services). 30 We hen use hem o calculae he aggregae prices for he four caegories. In Online Appendix C, we describe how we consruc prices in deail. 7.3 Esimaion Resuls Columns (1) and (2) in Table 5 summarize he esimaion resuls for Models 5 and 6, respecively. Also, Figures 6 and 7 provide heir graphical fi o he daa. Firs, noe ha, in Column (2) in Table 5, he non-homoheiciy parameer c sh is esimaed o be negaive. Also, Model 6 ouperforms Model 5 in erms of he AIC and BIC saisics. These wo facs imply ha home services exhibi lower income elasiciy han radiional marke services, and ha he difference in income elasiciies sill plays an imporan role o accoun for he movemen of home service and oher shares. These resuls are consisen wih hose in he benchmark case. Second, noe ha when we disaggregae he marke service secor ino modern and radiional ones, he poin esimae of σ is no longer close o zero. The esimaed value is 1.48 in Model 5 and 1.24 in Model 6. This resul is due o he fac ha he elasiciy of subsiuion beween modern and radiional services is larger han ha among agriculural goods, manufacuring goods, and oal marke services. Therefore, he esimaed σ increases once he service secor is disaggregaed ino he wo secors. 30 For an explanaion of he cyclical expansion procedure, see Herrendorf, Rogerson, and Valeninyi (2013). 23

26 Table 5 Disaggregaed Service Secor: Esimaion Resuls (1) (2) Disagg. of Services 5 Disagg. of Services 6 σ (0.0549) (0.0182) c a (3.657) (3.693) c sn (620.3) (830.2) c sc (115.4) (426.5) c sh (154.3) ω a ( ) ( ) ω m ( ) ( ) ω sn ( ) ( ) ω sc ( ) ( ) ψ ( ) ( ) N AIC BIC RMSE a RMSE m RMSE sn RMSE sm RMSE sh Robus sandard errors in parenheses p<0.10, p<0.05, p<

27 Figure 6 Disaggregaed Service Secor: Model 5 ( c sh =0) Model 5: AG MA SN Model 5: SM SH Share in Exended Toal Consumpion Modern Marke Service Manufacuring Agriculure Share in Exended Toal Consumpion Home Tradiional Marke Service Year Year Figure 7 Disaggregaed Service Secor: Model 6 (no resricions) Model 6: AG MA SN Model 6: SM SH Share in Exended Toal Consumpion Modern Marke Service Manufacuring Agriculure Share in Exended Toal Consumpion Home Tradiional Marke Service Year Year 25