NBER WORKING PAPER SERIES THE MARGINAL PRODUCTS OF RESIDENTIAL AND NON-RESIDENTIAL CAPITAL THROUGH Casey B. Mulligan Luke Threinen

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1 NBER WORKING PAPER SERIES THE MARGINAL PRODUCTS OF RESIDENTIAL AND NON-RESIDENTIAL CAPITAL THROUGH 2009 Casey B. Mulligan Luke Threinen Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachuses Avenue Cambridge, MA April 2010 The auhors appreciae commens on relaed work from economiss a he Federal Reserve Board. Updaes of hese esimaes will be provided on Mulligan s blog The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions by Casey B. Mulligan and Luke Threinen. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 The Marginal Producs of Residenial and Non-Residenial Capial Through 2009 Casey B. Mulligan and Luke Threinen NBER Working Paper No April 2010 JEL No. E22,O47 ABSTRACT Esimaes of he marginal produc of capial can help forecas economic growh, es compeing business cycle heories, and perform cos-benefi analysis. This paper presens annual and quarerly esimaes of he marginal produc of capial in he U.S. separaely for he residenial and non-residenial secors. The wo secors had posiively correlaed marginal producs unil he 2000s, when he residenial marginal produc fell during he housing boom, and rose during he housing bus. By he end of 2009, he residenial MPK was back o he level of he 1990s. The Grea Recession and recovery sawhe non-residenial MPK fall from hisorically high values o hisorically low ones, and hen increase much of he way back. Casey B. Mulligan Universiy of Chicago Deparmen of Economics 1126 Eas 59h Sree Chicago, IL and NBER c-mulligan@uchicago.edu Luke Threinen Universiy of Chicago Deparmen of Economics 1126 Eas 59h Sree Chicago, IL hreinen@uchicago.edu An online appendix is available a: hp://

3 I. Inroducion Economic heory suggess ha marginal produc of capial series migh help predic economic growh forward one or wo years, even under abnormal condiions such as warime or depression. In some siuaions, he marginal produc of capial is an essenial ingredien in cos-benefi analyses (Harberger 1968; Bya, e al., 2006; Miyakov and Ruehl, 2009). Evidence on he marginal produc of capial can also help es various explanaions for business cycles, help idenify causes and consequences of he recen housing bubble, and help quanify he economic burdens of business axes. The purpose of his paper is o produce annual and quarerly esimaes of he marginal produc of capial (ne of depreciaion), one each for he residenial and nonresidenial secors of he U.S. economy. By definiion, he marginal produc of capial ne of depreciaion is he change in ne domesic produc (NDP) during he accouning period (e.g., one quarer) ha would resul from an increase in he beginning-of-period capial sock of $1 worh of capial, holding consan he oal supply of all oher facors. The addiional $1 of capial is assumed o have he same composiion as he res of he capial sock. For example, if he economy s capial consised of 400 idenical srucures and 100 idenical vehicles, each of which cos $2 o acquire, hen he marginal produc of capial would be he exra NDP aained by saring he quarer wih idenical srucures and idenical vehicles (ha is, $0.80 worh of srucures and $0.20 worh of vehicles). Suppose ha origins of he curren recession could be raced back o limis on he supply of aggregae invesmen due o a credi crunch. (Real invesmen did fall hrough he firs year and a half of his recession.) The credi crunch heory says ha he marginal produc of capial would rise over his period as a consequence of he increased cos of capial faced by hose wih new capial projecs. Alernaively, a financial crisis or somehing else could reduce labor usage more direcly, and, given he 1

4 complemenariy of labor and non-residenial capial in producion, a fall in nonresidenial invesmen would merely resul from low marginal producs of capial, hereby puing he non-residenial capial sock on a pah ha is consisen wih a lesser amoun of labor usage (Mulligan, 2010). The marginal produc of capial is also ineresing as an aggregae leading indicaor of business condiions, which is he moivaion for is use in a number of sudies (e.g., Feldsein and Summers (1977), Auerbach (1983)). This relaionship alone may make i a predicor of subsequen economic growh. Addiionally, Fisherian consumpion-saving heory suggess ha he marginal produc of capial, or variaions of i, should predic consumpion growh. In a Robinson Crusoe economy, he consumer would save for he fuure by reducing curren consumpion and using he proceeds o build capial asses. She would hen use he marginal produc and capial gains from hose asses o add o consumpion in he fuure. Because he saving decision is made in he presen while he principal and ineres are spen in an uncerain fuure, he incenive o save depends on, among oher hings, he expeced marginal produc and expeced capial gains. The curren marginal produc iself helps predic he incenive o save only o he exen ha i is closely relaed o he expeced sum of fuure marginal produc and capial gains. For his reason, we presen measures of he marginal produc ha migh be more indicaive of hose expeced gains, and (consisen wih naional accouning pracices: see Fraumeni, 1997) measures of depreciaion ha reflec expeced depreciaion and obsolescence, raher han acual depreciaion and obsolescence. I is helpful o examine he marginal produc of residenial capial separaely from he marginal produc of non-residenial capial for a leas wo reasons. For one, he aggregae demand for labor is expeced o have a closer relaionship wih he sock of non-residenial capial han he sock of houses, because workers use non-residenial capial in doing heir jobs. Addiionally, some imporan capial marke disorions such as business axes and he housing bubble are expeced o have opposie effecs on he socks of residenial and non-residenial capial, and hereby opposie effecs on heir marginal producs. 2

5 Secion II presens our mehods for calculaing annual marginal producs, and discusses he findings for The marginal produc of capial is very differen in he residenial and non-residenial secors, boh in erms of levels and flucuaions. Secion III examines he imporance of axes in explaining he gap beween marginal producs in he wo secors. The mehods and resuls for quarerly poswar marginal producs hrough 2009-IV are presened in Secion IV. In order o isolae some of he possible deerminans of measured marginal producs, Secion V compares hem wih average producs. Secion VI concludes, and Appendices record he ime series values discussed in he body of he paper. II. Aggregae Annual Marginal Producs In a compeiive capial marke wih consan reurns o scale, he marginal produc of capial is simply he income accruing o domesically employed capial divided by he amoun of capial employed a he beginning of he accouning period, valued a replacemen cos. Compuing his measure enails a couple of minor hurdles. Firs, he locaion of capial income may no mach he locaion of capial. For example, naional income is he income of ciizens, while he capial sock, measured as accumulaed domesic invesmen, comprises he capial locaed on home soil, regardless of he naionaliy of is owners. We accoun for his by focusing on domesic measures of boh he income and sock of capial, or esimaing hem when necessary. Second, naional accouns do no disaggregae non-corporae business incomes ino labor and capial income. We accoun for his by assuming ha he capial income share for non-corporae business is he same as for corporae business. Third, neiher governmen capial income nor governmen nonresidenial capial is recorded in he naional accouns. Thus, our non-residenial esimaes consider privae secor socks and flows only. A final hurdle arises because capial income is a flow, he price level of which changes hroughou he accouning period. To accoun for his in our calculaion of 3

6 annual real capial income, we discoun ime flows back o he -1 price level using he annual PCE deflaor. The period ne-of-depreciaion marginal produc of residenial capial MPH is calculaed using hree enries from he NIPAs (he PCE deflaor, nominal ne housing value added 2, and nominal compensaion of employees in housing) and one enry from he fixed asse ables (curren-cos sock of residenial srucures): MPH (ne housing value added) (compensaion of HH secor employees) = (residenial srucures, curren cos) 1 (ne housing value added) (PCE housing services) (housing inermediaes) (residenial srucures depreciaion) 1 P (PCE deflaor) where ne housing value added is PCE housing services minus housing inermediaes and depreciaion. 3 The period ne-of-depreciaion marginal produc of privae nonresidenial capial is calculaed using one enry from he fixed asse ables and en enries from he NIPAs: P P 2 Ne housing value added is no available for he mos recen year. We esimae i by aking he average of he quarerly values ha we esimae for he quarerly series see Secion III. 3 Following Feldsein, Dicks-Mireaux, and Poerba (1983), our concep of he marginal produc of capial is gross of all axes (alhough, in pracice, hey did no aemp o add back any porion of sae and local axes or business ransfer paymens, oher han propery axes): he concep is he effec of a uni of capial on naional income or oupu, even he par accruing o ax auhoriies. Since we have calculaed ne marginal produc of residenial (non-residenial) capial by making subracions from oupu (naional income), raher han addiions o capial income, we do no have o add business ransfer paymens or sae and local axes back in. 4

7 MPK [ + ] 1/ 1 α NI NFI Egov P P H MPH = (privae non-residenial capial, curren cos) 1 α Tpr (Compensaion of Privae Secor Employees) 1 NI Egov Tou NI Egov Tou Tpr (Proprieor's Income) NI (Naional Income) NFI (Ne Facor Income paid o he res of he world) Egov (Compensaion of Governmen Employees) H (residenial srucures, curren cos) Tpr (propery ax paymens) Tpr + Tou (axes on producion & impors) + (business curren ransfer paymens) (subsidies) + (surplus of governmen enerprises) α is capial s share of facor income, so α imes privae naional domesic income (NDI Egov) is privae domesic capial s income. 4 The erm in square brackes is he income accruing o domesically and privaely employed nonresidenial capial. Figure 1 displays boh he residenial and nonresidenial ne-of-depreciaion marginal producs of capial (MPKs), calculaed as oulined above. From he lae 1950s hrough he lae 1970s, he wo series display srong posiive correlaion, wih a smaller degree of correlaion during he 1980s and 1990s. However, saring in 2001, he series display srong negaive correlaion. The non-residenial MPK has many ups and downs. In conras, prior o he mos recen cycle, he poswar residenial MPK series seems o have only five phases in 70 years: a downward rend in he 1930s and 1940s, an up rend , a downrend , an up rend , and a fla period during he 1990s. 4 Proprieor s income and Tou (Tou is essenially indirec axes and business fees paid o governmen) are assumed o be divided among capial and labor in he same proporions as he res of privae domesic income. Propery axes are assigned o pre-ax capial income, and allocaed o he proprieor s secor in proporion o he res of privae domesic naional income. 5

8 As shown in more deail in Figure 2, he residenial MPK shows a seep decline, 5 while he nonresidenial MPK rises, during he period of buildup in housing generally associaed wih he housing bubble ( ). Then, afer he housing cycle peak, boh series change direcion, wih he nonresidenial MPK falling in 2007 for he firs ime since 2001 and he residenial MPK haling is seep four-year decline. These changes coincide wih a sharp fall in consrucion of new housing and a corresponding pickup in invesmen in nonresidenial srucures (Mulligan and Threinen, 2008). III. Tax Policy and Disorions beween Residenial and Nonresidenial Capial The axes scales in Figure 1 show a dramaic difference beween he measured marginal producs of residenial and nonresidenial capial in a ypical year. On average from , he marginal produc of residenial capial was only 5.8 percen per year, whereas he marginal produc of non-residenial capial was more han double abou 13.9 percen per year. Mismeasuremen could cause he wo measured marginal producs o be differen, alhough he direcion of he measuremen bias is ambiguous. For example, inangible capial (Griliches, 1981) is excluded from our capial sock measures and may be differenially imporan in he non-residenial secor. On he oher hand, land values are also excluded from our capial sock measures, and residenial capial may be especially land inensive. 5 The fall in marginal produc of residenial capial in 2005 is parly explained by Hurricanes Karina and Ria, he effecs of which should ideally be excluded from esimaes of expeced marginal produc. For his reason, values for he quarerly series below will be inerpolaed for he year

9 Indirec axes (such as sales and excise axes) and income axes are expeced o cause he gross-of-ax marginal produc of non-residenial capial o significanly exceed he marginal produc of residenial capial, because invesors are presumed o require similar afer-ax reurns from heir invesmens in he wo secors. 6 In order o calculae he magniude of hese effecs, we calculae an average afer-ax reurn for non-residenial capial by adjusing for indirec and income axes ha do no apply o housing, and compare he ax-adjused MPK o MPH. New homes owe essenially zero sales and excise axes, and he impued services o owner-occupied housing are no subjec o sales, excise, or income ax. Landlords ypically do no owe sales or excise ax on he rens hey receive, as long as he renal period is more han a few monhs. Indirec axes are paid by non-residenial businesses, so we subrac capial s share of hose axes from gross-of-ax non-residenial capial income, 7 and make no subracion from residenial oupu. Figure 3 s solid and dashed blue series shows he gap beween MPK and MPK gross of axes (ha is, as shown in Figures 1 and 2) and adjused for indirec axes, respecively. On average from , he indirec-ax-adjused gap is 6.9 percen per year, as compared o 8.1 percen per year for he gross-of-ax gap. 6 Propery axes are levied on boh residenial and non-residenial propery, and naional accouns daa show ha owner-occupied housing s share of propery axes paid is similar o is share of he oal capial sock (residenial and non-residenial). 7 If capial could be freely moved beween he residenial and non-residenial secors o equalize afer ax reurns, hen sales axes on non-residenial oupu would creae a wedge beween MPH and MPK equal o he produc of he sales ax rae and capial s share of income in he non-residenial secor. We measure indirec axes as he difference beween axes on producion and impors less subsidies plus business curren ransfer paymens and propery axes, so our measure includes excise axes, cusoms axes, business license fees, and some even smaller iems. 7

10 We consider hree alernaive adjusmens for federal and sae individual and corporae income axes. Two of hem assume a marginal income ax rae (35 and 50 percen, respecively), and calculae marginal non-residenial capial income axes as he produc of ha rae and he MPK adjused for indirec axes. 8 The assumed rae is inended o represen he combinaion of corporae axes and he individual income axes owed by business owners on heir business income. A larger assumed rae is appropriae o he exen ha capial is owned by axable corporaions and/or he business owners are in relaively high personal income ax brackes. Figure 3 shows wo of he income ax adjusmens, and how he combined adjusmen leaves a gap ha is closer o zero han o he gross-of-ax gap. On average from , he gaps using he 35 and 50 percen marginal income ax raes are 2.7 and 0.7 percen per year, 9 respecively. Given ha he gross-of-ax gap was 8.1 percen per year, i seems ha mos of ha gap can be explained by he collecion of various axes on non-residenial business aciviy ha are no colleced in he residenial secor. 10 IV. Quarerly Marginal Producs Pars of he gross-of-ax calculaions described above can be duplicaed direcly o produce quarerly series. However, because he BEA esimaes capial socks and cerain oher series only on an annual basis, quarerly measuremen of he marginal producs of capial require esimaes of he quarerly evoluion of hose series. 8 Some housing oupu is axed by he personal income ax because some of he housing (less han a quarer) is owner by businesses, so in principle he MPH should be income ax adjused oo. However, he adjusmen may be small because businesses own so lile of he housing and because business may use renal housing o sheler oher income from axes. 9 A hird aleraive assumes ha he combined corporae and individual income ax burden is he same in he corporae and noncorporae non-residenial secors, and ha each dollar of corporae income ax colleced on corporae income is associaed wih a dollar of individual income ax colleced on disribuions o corporae equiy and deb holders, hereby subracing wice he raio of corporae income ax revenue o corporae capial from he sales-ax adjused MPK. The resul is gap of -0.4 percen per year. 10 Feldsein, Dicks-Mireaux, and Poerba (1983) calculaed a marginal produc of capial ha was gross of propery axes bu ne of all indirec axes and business ransfer paymens (no jus labor s share of hem). Their ax reamen amouns o wha we have considered he MPK ne of indirec ax (see he dashed blue series in our Figure 3). They also included measured capial o include he value of land, which would furher reduce he measured MPK by abou 20 percen. 8

11 III.A. Residenial Capial Our firs sep in producing he quarerly residenial marginal produc of capial series (gross of ax) was o esimae he evoluion of he ne real residenial capial sock by quarer. This was done by allocaing he annual change in he real ne sock in a given year across quarers in he same proporions as real gross residenial invesmen during he same year. The second sep was o inflae his real series o creae a scaled nominal series, which was done using he residenial invesmen price index. Finally, he annual change in he curren cos residenial capial sock was allocaed across he quarers of a given year in he same proporions as changes in he scaled nominal series (produced in sep wo) over he quarers of ha year. Furhermore, he annual series lack published values for he mos recen year. In order o esimae he real capial sock for he mos recen year, i was assumed ha a given gross real residenial invesmen in a quarer affeced he real ne capial sock in he same way during he mos recen year as i was esimaed o have done in he las published year. Tha is, for he mos recen year, RealResCapSock = RealResCapSock -1 + (GrRealResInv /GrRealResInv -4 ) * (GrRealResInv -4 /ToalResInv) * (ΔRealResCapSock) where RealResCapSock is he real residenial capial sock in quarer, GrRealResInv is he gross real residenial invesmen in quarer, ToalResInv is he oal real gross residenial invesmen during he mos recen published year, and ΔRealResCapSock is he change in he ne real residenial capial sock beween he wo mos recenly published years. This real series was hen inflaed using he residenial invesmen price index. Finally, he scaled nominal series was convered o he final esimae by assuming ha changes in he scaled series and corresponding changes in he final series occurred in he same proporion during he las published year and he mos recen year. Similar issues affeced esimaion of he income series. The ne housing value added series, which was used in he calculaion of annual residenial capial income, also 9

12 appears only on an annual basis. Quarerly housing value added was esimaed by allocaing he annual ne housing value added, less compensaion of employees, across he four quarers of a given year in he same proporions as nominal personal consumpion expendiures on housing during ha year. For quarers of he final year of he series, i was assumed ha year-over-year residenial capial income increased a he same rae as year-over-year nominal personal consumpion expendiures on housing. Tha is, for he mos recen year, ResCapInc = ResCapInc -4 *(PCEHousing /PCEHousing -4 ) where ResCapInc is he esimaed residenial capial income in quarer and PCEHousing is nominal personal consumpion expendiures on housing in quarer. Finally, ne capial income in 2005 (in paricular, depreciaion) was srongly affeced by Hurricanes Karina and Ria, so esimaes produced by he above mehod would no be a suiable measure of expeced capial income for ha year. As a resul, he marginal producs of capial for he four quarers of 2005 are linearly inerpolaed beween 2004:Q4 and 2006:Q1. III.B. Nonresidenial Capial The quarerly series for he nonresidenial marginal produc of capial was consruced using he same basic formula as he annual series given above. The numeraor of ha formula can be applied direcly because each of he needed series is available on a quarerly basis. As a resul, only he quarerly evoluion he nonresidenial capial sock series required any modificaion from he original formula. This esimaion of he quarerly evoluion of he ne nonresidenial capial sock was done in a manner analogous o he approach oulined above for he quarerly residenial series. The annual change in he real ne sock in a given year was allocaed across quarers in he same proporions as real gross nonresidenial invesmen during he same year. Nex, his real series was inflaed o creae a scaled nominal series, which was done using he nonresidenial invesmen price index. Finally, he annual change in he curren cos nonresidenial capial sock was allocaed across he quarers of a given year 10

13 in he same proporions as changes in he scaled nominal series over he quarers of ha year. As was he case wih he residenial daa, he annual series lack published values for he mos recen year. In order o esimae he real capial sock for he mos recen year, i was assumed ha a given gross real nonresidenial invesmen in a quarer affeced he real ne capial sock in he same way during he mos recen year as i was esimaed o have done in he las published year. Finally, he scaled nominal series was convered o he final esimae by assuming ha changes in he scaled series and corresponding changes in he final series occurred in he same proporion during he las published year and he mos recen year. This is exacly he approach aken wih he residenial daa. Finally, as wih he residenial daa, capial income in 2005 was srongly affeced by exraordinary depreciaion associaed wih Hurricanes Karina and Ria, so he marginal producs of capial for he four quarers of 2005 are linearly inerpolaed beween 2004:Q4 and 2006:Q1. III.C. Resuls Figure 4 displays boh he residenial and nonresidenial ne-of-depreciaion marginal producs of capial on a quarerly basis, calculaed as oulined above, since 1947-I. In order o make some of he deails more visible, Figure 5 shows he same series for he quarers 1990-I hrough 2009-IV. As expeced, he same general rends ha were eviden in he annual series appear here. Figure 4 suggess ha, wih he excepion of he mos recen cycle, he residenial MPK does no change as significanly over he business cycle as does he non-residenial MPK, bu has more significan decade-o-decade changes. 11 The main facs of noe in he quarerly series are, firs, ha he rends in boh series since 2001 have been basically smooh across quarers, wih a seady decline in he residenial MPK followed by an increase saring in 2006 and he reverse rend in nonresidenial MPK. Second, he increase in he residenial MPK and he coinciden 11 The relaive cyclicaliy of he wo series may be due o a greaer complemenariy of labor wih businesssecor capial, as opposed o housing. 11

14 decrease in he nonresidenial MPK coninued hrough 2009, alhough he non-residenial MPK has reversed is rend in he wo mos recenly available quarers (2009-III and -IV). The mos recen residenial MPK is also a leas as high as is hisorical average, and near he highs of he 1990s, which suggess ha residenial invesmen may have hi is lows. V. Quarerly Average Producs A secor s marginal produc of capial is ha secor s capial income per dollar of capial, which can be decomposed ino he produc of he secor s capial share of income imes he secor s income per dollar of capial. Tha is, he marginal produc of capial is he produc of capial s share and he average produc of capial. The average produc of capial would be a beer indicaor of he marginal produc of capial when measured capial share flucuaes mainly due o measuremen error raher han genuine changes in he reurns o labor and capial. For example, a high frequencies here may be lags in he recording of capial or labor income, as wih severance paymens ha are made o a worker afer he sops conribuing o producion. A low frequencies, labor unions may rise or fall, and labor unions may exercise heir power by having some of he reurns o capial reallocaed oward hemselves (Leonief, 1946). These are some of he reasons o examine measures of average producs in addiion o marginal producs. Wih he quarerly marginal produc series already esimaed, i is sraighforward o compue he ne average producs of capial (APKs) in he wo secors. For he residenial secor, he quarerly ne value of housing services (including labor) was esimaed using a formula analogous o he one used o esimae he quarerly ne value added of housing services from residenial capial. The ne residenial APK is hen calculaed by dividing his series by he already esimaed quarerly residenial capial sock. For he nonresidenial secor, we have APK = (PNDI ResVA ) / (privae nonresidenial fixed asse sock, curren cos) 12

15 where APK is he period ne average produc of nonresidenial capial, PNDI is he period privae ne domesic income, and ResVA is he ne residenial value added (which was produced for he esimaion of residenial APK as oulined above). Figure 6 displays boh he residenial and nonresidenial ne-of-depreciaion average producs of capial on a quarerly basis, calculaed as oulined above. These series have a sronger correlaion han he marginal series during he period from However, hey show he same divergence from and parial reconvergence since 2006 ha he MPK series suggess should have occurred. Addiionally, as wih he MPK series, he nonresidenial APK is presenly wihin is average range, while he residenial APK remains below is average from he pas wo decades. VI. Conclusions The marginal produc of non-residenial capial, ne of depreciaion, is more han double he marginal produc of residenial capial. Mos of he marginal produciviy gap beween he wo secors can be explained by he fac ha so much residenial oupu escapes income and indirec business axaion. Over he las en years, he marginal and average producs of residenial capial fell, and hen increased, as housing consrucion was booming and busing. In his sense, he residenial daa sugges ha he supply of residenial capial shifed along a relaively sable demand for he services of ha capial. As indicaed by he marginal produc of residenial capial a he end of 2009, curren housing supply seems resriced by comparison wih he housing boom (when he residenial MPK was low), bu fairly normal by comparison wih he 1990s when he residenial MPK was similar o wha is was a he end of These paerns are consisen wih he findings of Davis, Lehner, and Marin (2008) and ohers ha housing ren-price raios were low during he 12 Conversely, a marginal produc of residenial capial ha significanly exceeded he levels of he 1990s would indicae housing supply condiions ha are more resricive han hey were in he 1990s. 13

16 housing boom, and wih he conclusions ha he housing boom was fueled by opimisic expecaions, or by easy credi. The marginal produc of non-residenial capial was much higher during he housing boom han i was during he recession, when raes of invesmen in nonresidenial equipmen and sofware were low. In his sense, he supply of non-residenial capial seems less resriced during he recession han i was before. In oher words, he recession s invesmen raes may have been low because of a slack labor marke, raher han he oher way around (Mulligan, 2010). In any case, he esing of various heories of his recession, and he prior housing cycle, can be enhanced wih marginal producs daa like hose shown in his paper. 14

17 Fig 1. The Marginal Produc of Capial, % 20% Nonresidenial (lef axis) Residenial (righ axis) 8% 7% 6% annual rae 15% 10% 5% 4% 3% annual rae 5% 2% 1% 0% 0%

18 17% Fig 2. The Marginal Produc of Capial, % 16% Residenial (righ axis) 6.5% annual rae 15% 14% 6.0% annual rae 13% Nonresidenial (lef axis) 5.5% 12% 5.0%

19 non-residenial minus residenial, annual rae 20% 15% 10% 5% 0% Fig 3. The Secoral Marginal Produc of Capial Gap, gross of axes ne of indirec business axes ne of indirec ax & income ax (MITR = 35%) ne of indirec ax & income ax (MITR = 50%) -5%

20 Fig 4. The Marginal Produc of Capial, 1948-I hrough 2009-IV 25% 8% 20% Residenial (righ axis) 7% 6% annual rae 15% 10% Nonresidenial (lef axis) 5% 4% 3% annual rae 2% 5% 0% Noe: all 2005 values inerpolaed beween 2004:Q4 and 2006:Q1 1% 0%

21 Fig 5. The Marginal Produc of Capial, 1990-I hrough 2009-IV 17% 7.0% Residenial (righ axis) 16% 6.5% 15% annual rae 14% 13% Nonresidenial (lef axis) 6.0% 5.5% annual rae 12% 5.0% 11% Noe: all 2005 values inerpolaed beween 2004:Q4 and 2006:Q1 4.5%

22 Fig 6. The Average Produc of Capial, 1947-I hrough 2009-IV 90% 8% 80% 7% 70% 6% 60% 5% annual rae 50% 40% Nonresidenial (lef axis) Residenial (righ axis) 4% annual rae 30% 3% 20% 2% 10% 0% Noe: all 2005 values inerpolaed beween 2004:Q4 and 2006:Q1 1% 0%

23 Table 1. Annual MPK and Socks, by secor, Residenial Nonresidenial Residenial Nonresidenial Period MPK Cap. Sock MPK Cap. Sock Period MPK Cap. Sock MPK Cap. Sock % $ % $ % $1, % $1, % $ % $ % $1, % $1, % $93 7.6% $ % $1, % $1, % $84 7.0% $ % $1, % $1, % $92 9.7% $ % $1, % $1, % $ % $ % $1, % $1, % $ % $ % $1, % $2, % $ % $ % $2, % $2, % $ % $ % $2, % $2, % $ % $ % $3, % $3, % $ % $ % $3, % $3, % $ % $ % $3, % $4, % $ % $ % $3, % $4, % $ % $ % $4, % $4, % $ % $ % $4, % $4, % $ % $ % $4, % $5, % $ % $ % $4, % $5, % $ % $ % $5, % $5, % $ % $ % $5, % $5, % $ % $ % $5, % $6, % $ % $ % $6, % $6, % $ % $ % $6, % $6, % $ % $ % $6, % $6, % $ % $ % $6, % $7, % $ % $ % $7, % $7, % $ % $ % $7, % $8, % $ % $ % $8, % $8, % $ % $ % $8, % $8, % $ % $ % $9, % $9, % $ % $ % $9, % $9, % $ % $ % $10, % $10, % $ % $ % $11, % $11, % $ % $ % $12, % $11, % $ % $ % $13, % $11, % $ % $ % $14, % $12, % $ % $ % $16, % $14, % $ % $ % $17, % $15, % $ % $ % $17, % $16, % $ % $ % $17, % $17, % $ % $ % $ % $990 Noe: socks in billions, a replacemen cos, beginning of period

24 Table 2. Quarerly MPK and Socks, by secor, 1948 I hrough 2009 IV Residenial Nonresidenial Residenial Nonresidenial Period MPK Cap. Sock MPK Cap. Sock Period MPK Cap. Sock MPK Cap. Sock 1948 I 3.41% $ % $ I 5.51% $ % $ II 3.41% $ % $ II 5.54% $ % $ III 3.43% $ % $ III 5.61% $ % $ IV 3.42% $ % $ IV 5.67% $ % $ I 3.54% $ % $ I 5.80% $ % $ II 3.47% $ % $ II 5.81% $ % $ III 3.48% $ % $ III 5.83% $ % $ IV 3.70% $ % $ IV 5.91% $ % $ I 3.72% $ % $ I 5.99% $ % $ II 3.78% $ % $ II 6.08% $ % $ III 3.74% $ % $ III 6.06% $ % $ IV 3.64% $ % $ IV 6.13% $ % $ I 3.70% $ % $ I 6.24% $ % $ II 3.68% $ % $ II 6.28% $ % $ III 3.72% $ % $ III 6.32% $ % $ IV 3.78% $ % $ IV 6.39% $ % $ I 3.96% $ % $ I 6.47% $ % $ II 4.01% $ % $ II 6.45% $ % $ III 4.02% $ % $ III 6.55% $ % $ IV 4.07% $ % $ IV 6.64% $ % $ I 4.27% $ % $ I 6.66% $ % $ II 4.33% $ % $ II 6.73% $ % $ III 4.42% $ % $ III 6.64% $ % $ IV 4.44% $ % $ IV 6.67% $ % $ I 4.64% $ % $ I 6.53% $ % $ II 4.70% $ % $ II 6.60% $ % $ III 4.69% $ % $ III 6.63% $ % $ IV 4.65% $ % $ IV 6.68% $ % $ I 4.71% $ % $ I 6.53% $ % $ II 4.71% $ % $ II 6.67% $ % $ III 4.68% $ % $ III 6.43% $ % $ IV 4.65% $ % $ IV 6.53% $ % $ I 4.68% $ % $ I 6.41% $ % $ II 4.69% $ % $ II 6.47% $ % $ III 4.67% $ % $ III 6.49% $ % $ IV 4.70% $ % $ IV 6.54% $ % $ I 4.88% $ % $ I 6.35% $ % $ II 4.93% $ % $ II 6.26% $ % $ III 4.99% $ % $ III 6.29% $ % $ IV 5.00% $ % $ IV 6.38% $ % $ I 5.19% $ % $ I 6.12% $ % $ II 5.25% $ % $ II 6.10% $ % $ III 5.28% $ % $ III 6.15% $ % $ IV 5.31% $ % $ IV 6.23% $ % $962

25 Residenial Nonresidenial Residenial Nonresidenial Period MPK Cap. Sock MPK Cap. Sock Period MPK Cap. Sock MPK Cap. Sock 1970 I 6.19% $ % $ I 4.61% $3, % $3, II 6.24% $ % $1, II 4.70% $3, % $3, III 6.04% $1, % $1, III 4.74% $3, % $3, IV 6.35% $ % $1, IV 4.81% $3, % $3, I 6.37% $1, % $1, I 5.01% $3, % $4, II 6.30% $1, % $1, II 4.99% $3, % $4, III 6.25% $1, % $1, III 5.01% $3, % $4, IV 6.22% $1, % $1, IV 5.10% $3, % $4, I 6.12% $1, % $1, I 5.20% $3, % $4, II 6.10% $1, % $1, II 5.29% $3, % $4, III 6.13% $1, % $1, III 5.39% $3, % $4, IV 6.13% $1, % $1, IV 5.46% $4, % $4, I 5.84% $1, % $1, I 5.47% $4, % $4, II 5.82% $1, % $1, II 5.56% $4, % $4, III 5.75% $1, % $1, III 5.60% $4, % $4, IV 5.61% $1, % $1, IV 5.63% $4, % $4, I 5.39% $1, % $1, I 5.87% $4, % $4, II 5.41% $1, % $1, II 5.85% $4, % $4, III 5.40% $1, % $1, III 5.96% $4, % $4, IV 5.35% $1, % $1, IV 6.03% $4, % $4, I 5.21% $1, % $1, I 6.03% $4, % $5, II 5.21% $1, % $1, II 6.03% $4, % $5, III 5.22% $1, % $1, III 6.03% $4, % $5, IV 5.26% $1, % $1, IV 5.99% $4, % $5, I 5.16% $1, % $1, I 5.97% $4, % $5, II 5.19% $1, % $2, II 5.99% $4, % $5, III 5.14% $1, % $2, III 6.01% $5, % $5, IV 5.21% $1, % $2, IV 6.03% $5, % $5, I 5.14% $1, % $2, I 6.09% $5, % $5, II 5.05% $2, % $2, II 6.07% $5, % $5, III 5.04% $2, % $2, III 6.10% $5, % $5, IV 4.95% $2, % $2, IV 6.13% $5, % $5, I 4.78% $2, % $2, I 6.13% $5, % $5, II 4.74% $2, % $2, II 6.12% $5, % $5, III 4.67% $2, % $2, III 6.11% $5, % $6, IV 4.66% $2, % $2, IV 6.22% $5, % $6, I 4.55% $2, % $2, I 6.26% $5, % $6, II 4.51% $2, % $2, II 6.34% $5, % $6, III 4.44% $2, % $2, III 6.41% $5, % $6, IV 4.43% $2, % $3, IV 6.40% $6, % $6, I 4.50% $3, % $3, I 6.52% $6, % $6, II 4.49% $3, % $3, II 6.61% $6, % $6, III 4.53% $3, % $3, III 6.62% $6, % $6, IV 4.56% $3, % $3, IV 6.63% $6, % $6,690

26 Residenial Nonresidenial Residenial Nonresidenial Period MPK Cap. Sock MPK Cap. Sock Period MPK Cap. Sock MPK Cap. Sock 1992 I 6.78% $6, % $6, I 5.93% $12, % $11, II 6.87% $6, % $6, II 5.80% $12, % $11, III 6.83% $6, % $6, III 5.79% $12, % $11, IV 6.85% $6, % $6, IV 5.77% $12, % $11, I 6.69% $6, % $6, I 5.62% $13, % $11, II 6.65% $6, % $7, II 5.52% $13, % $12, III 6.68% $6, % $7, III 5.44% $14, % $12, IV 6.67% $6, % $7, IV 5.40% $14, % $12, I 6.79% $6, % $7, I 5.33% $14, % $12, II 6.77% $7, % $7, II 5.27% $15, % $13, III 6.75% $7, % $7, III 5.20% $15, % $13, IV 6.70% $7, % $7, IV 5.13% $16, % $13, I 6.70% $7, % $7, I 5.07% $16, % $14, II 6.72% $7, % $7, II 5.03% $16, % $14, III 6.77% $7, % $7, III 5.03% $17, % $14, IV 6.77% $7, % $7, IV 5.01% $17, % $14, I 6.80% $7, % $7, I 5.12% $17, % $15, II 6.79% $7, % $8, II 5.12% $17, % $15, III 6.74% $7, % $8, III 5.15% $17, % $15, IV 6.71% $8, % $8, IV 5.18% $17, % $15, I 6.74% $8, % $8, I 5.56% $17, % $15, II 6.75% $8, % $8, II 5.64% $17, % $16, III 6.76% $8, % $8, III 5.68% $17, % $16, IV 6.79% $8, % $8, IV 5.78% $17, % $16, I 6.70% $8, % $8, I 5.93% $17, % $17, II 6.75% $8, % $8, II 5.98% $17, % $16, III 6.74% $8, % $8, III 6.13% $17, % $16, IV 6.66% $9, % $9, IV 6.22% $16, % $16, I 6.75% $9, % $9, II 6.72% $9, % $9,490 Noe: see Noes o Table III 6.70% $9, % $9, IV 6.63% $9, % $9, I 6.59% $9, % $9, II 6.58% $10, % $10, III 6.61% $10, % $10, IV 6.70% $10, % $10, I 6.69% $10, % $10, II 6.61% $10, % $10, III 6.57% $11, % $10, IV 6.46% $11, % $11, I 6.36% $11, % $11, II 6.40% $11, % $11, III 6.35% $11, % $11, IV 6.36% $11, % $11,342

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28 Mulligan, Casey B. and Luke Threinen. Marke Responses o he Panic of NBER working paper no , Ocober Whie, Michelle J. and Lawrence J. Whie. The Tax Subsidy o Owner-Occupied Housing: Who Benefis? Journal of Public Economics. 7(1), February 1977: