This work is distributed as a Discussion Paper by the STANFORD INSTITUTE FOR ECONOMIC POLICY RESEARCH

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1 This work is disribued as a Discussion Paper by he STANFORD INSTITUTE FOR ECONOMIC POLICY RESEARCH SIEPR Discussion Paper No THE PRODUCTIVITY SURGE OF THE NINETIES AND FUTURE GROWTH By Rober M. Coen Norhwesern Universiy And Ber G. Hickman Sanford Universiy May 2002 Revised February 2003 Sanford Insiue for Economic Policy Research Sanford Universiy Sanford, CA (650) The Sanford Insiue for Economic Policy Research a Sanford Universiy suppors research bearing on economic and public policy issues. The SIEPR Discussion Paper Series repors on research and policy analysis conduced by researchers affiliaed wih he Insiue. Working papers in his series reflec he views of he auhors and no necessarily hose of he Sanford Insiue for Economic Policy Research or Sanford Universiy by Rober M. Coen and Ber G. Hickman. All righs reserved. Shor selecions 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 PRODUCTIVITY SURGE OF THE NINETIES AND FUTURE GROWTH Rober M. Coen and Ber G. Hickman Norhwesern Universiy and Sanford Universiy The srong performance of he U.S. economy during he lae 1990 s spawned boh popular visions of a ranscenden fuure for he New Economy and careful empirical sudies of key aspecs of ha experience. In paricular, he marked acceleraion of produciviy growh during he period has been exensively analyzed in a se of papers using disaggregaed growh accouning echniques o make a convincing case ha he spur in aggregae produciviy growh is largely raceable o he informaion echnology (IT) secor, which includes compuer hardware, sofware, and communicaions equipmen. The IT conribuion o he growh of oal labor produciviy is raced boh o he producion of informaion echnology capial a rapidly falling prices, which encouraged aggregae capial deepening, and o he direc conribuion of echnical progress in he producion of informaion capial o aggregae mulifacor produciviy (MFP). Jorgenson and Siroh (2000) and Oliner and Sichel (2000) find some acceleraion of MFP ouside he IT secor, whereas Gordon (2000) does no, owing o he fac ha he aribues par of he acceleraion of acual labor produciviy o cyclical gains. These findings naurally lead o he following quesions: wha does he recen surge of produciviy growh imply abou he fuure performance of he economy? Does he experience sugges ha he susainable growh pah of he economy he pah consisen wih full-employmen (F.E.) and low and sable inflaion will embody a corresponding acceleraion of produciviy growh in he coming years, or was he recen surge due mainly o ransiory or cyclical facors? Wha migh he fuure pah look like in quaniaive erms? We answer hese quesions using an updaed version of he supply side of he Hickman-Coen (HC) Annual Growh Model. 1 The model provides an inernally consisen framework for esimaing and projecing he naural rae of unemploymen, he F.E. labor force and hours of work, he F.E. produciviy growh rae, and he growh pah of poenial or F.E. oupu. Our daa is from official governmen sources in he Unied Saes, including he naional income accouns (NIA) from he Bureau of Economic Analysis (BEA) and labor force and produciviy daa from he Bureau of Labor Saisics (BLS). The BLS series on labor produciviy, oupu, hours, and relaed daa in he nonfarm business (NFB) secor are he mos widely cied produciviy measures and are feaured in our analysis. The sample period is and he projecions are for THE NATURAL RATE OF UNEMPLOYMENT We allow for demographic facors in modeling he naural rae. The aggregae naural rae is The auhors wish o hank Rober M. Solow for commens and suggesions, Paul Pino for research assisance, and he Sanford Insiue for Economic Policy Research for financial suppor. 1 See Coen and Hickman (1994, 1995) for he previous version.

3 2 calculaed as a weighed average of he raes for 16 age-sex groups, wih weighs proporional o he fullemploymen labor force in each group. This specificaion capures he influence of wo demographic facors. Firs, demographic changes can raise he aggregae rae insofar as hey shif he composiion of he labor force oward groups whose unemploymen raes are relaively high, especially hose aged Second, he growh in he supply of younger workers may raise heir normally high unemploymen raes furher as i leads o mismaches beween he skills and work experiences employers seek and hose offered by younger job applicans, leading o a high rae of job urnover and unemploymen spells for hese groups. The labor-force share of workers aged rose markedly during he 1960 s and 1970 s as baby-boomer cohors enered he labor force, and hen declined jus as markedly as hey maured in he 1980 s and 1990 s, as may be seen from Figure 1(he shaded areas in his and subsequen chars mark he cyclical expansions of he period as daed by he Naional Bureau of Economic Research). 2 The naural unemploymen rae is esimaed in wo seps. Firs, following Saiger, Sock and Wason (2001), we smooh he aggregae unemploymen rae wih he Hodrick-Presco (HP) filer o remove is high-frequency componens, as picured in Figure 2A. I can be shown ha compuing he separae HP rends for all 16 age-sex groups in our model and aggregaing hem wih he corresponding labor force weighs, yields virually he same aggregae HP rend as direcly compued from he aggregae unemploymen rae. The aggregae HP rend hus compued (no shown) is our provisional measure of he naural rae. Is i also a TV-NAIRU, wih he propery ha i represens a ime-varying unemploymen rae consisen wih seady inflaion? The answer is yes, according o Saiger, Sock and Wason, who compare heir TV-NAIRU esimaed from an acceleraionis specificaion of he Phillips Curve wih he same HP rend as picured in our Figure 2A, sressing ha for all pracical purposes he esimaed NAIRU is he same as he univariae HP rend. Second, we exend he scope of he demographic analysis by allowing for he influence of populaion shifs on he secoral unemploymen raes hemselves hrough he following regressions: (1) ( U /(1 U )) = c + c ( U ) + c ( N / N ) + v, ln i i 1 k 2 0 i where U k is he acual unemploymen rae of prime-age male workers aged fory-five o fify-four, U i is he acual unemploymen rae of age-sex group i, (N i /N) is he (noninsiuional) populaion raio for group i, and v is a sochasic disurbance. The populaion raios are included o allow for he influence of labor marke mismaches on he age-and-sex-specific raes, following Wacher (1976). The raionale for including he unemploymen rae of prime-age males as a regressor is ha his group s unemploymen experience is largely independen of demographic shifs and provides a good measure of he underlying changes in labor marke ighness. Nex, we subsiue he HP rend of he prime-age male unemploymen rae for is acual rae in equaions (1) and se he disurbance erms o zero in order o calculae naural 2 Perry (1970), Wacher (1976), and Gordon (1982) sudied he early impac of his demographic wave on he naural rae of unemploymen in seminal sudies, and Shimer (1998) and Kaz and Krueger (1999) have examined is influence in recen decades.

4 3 raes for he oher age-sex groups by purging hem of cyclical and random facors. Finally, he aggregae naural rae, UN, combines he age-sex specific raes wih weighs equal o each group s share of he naural or full-employmen (F.E.) civilian labor force. Figure 2B depics he esimaed naural rae including he direc and indirec effecs of demographic shifs. I will be seen ha he esimaed rae closely resembles he direc HP filer of acual unemploymen in he op panel, alhough i peaks a a slighly lower level and a year laer han he laer. To assess he imporance of demographic facors in he behavior of he naural rae during he eighies and nineies, we perform a counerfacual experimen o isolae he changes in he naural rae due o populaion shifs. The prime-age naural unemploymen rae is fixed a is 1982 level and he sysem of age-sex equaions is re-solved for he period The resuls indicae ha had no he naural rae of his key group declined afer 1982, he aggregae naural rae would noneheless have fallen from 7.38 in 1982 o 6.04 in 2000, or by 44 percen of he oal decline in he esimaed naural rae. However, mos of he demographic impac occurred before he expansion of he nineies. Beween he business cycle roughs of 1982 and 1992, he counerfacual simulaion accouns for 91 percen of he decline in he esimaed naural rae, whereas he corresponding figure for is only 16 percen. The small conribuion of demographic change o he reducion of he naural rae during he expansion of he 1990 s reflecs he fac ha he youh-age componen of populaion was nearly consan during hose years, as shown in Figure 1. THE PRODUCTION FUNCTION AND FACTOR DEMAND SYSTEM We assume a long run or planning producion funcion of Cobb-Douglas form and consan reurns o scale: e * α * 1 α = (2) X A ( K ) ( I H ). The e superscrip signifies he expeced value of oupu, and he * superscrip denoes desired levels of he inpus. The exponenial rae of echnical change in period is ln (A /A -1 ). Le H be hours employed and I an exogenous index of he effecs of changes in he composiion of labor-hours on he efficiency of curren employees. 3 The desired inpus are assumed o be chosen so as o minimize he cos of producing he expeced oupu in long-run equilibrium, which requires ha he raio of he marginal producs of labor and capial be equaed o he raio of heir expeced prices, so ha: (3) K / H = [ α /(1 α)]( W / Q), where Q is he renal price of capial and W he nominal wage rae. Subsiuing his condiion ino he producion funcion successively for capial and worker inpus and omiing inessenial consans, we derive he following long-run inpu expressions: 3 We use as our measure of I he labor composiion index published by BLS in is esimaes of mulifacor produciviy. This index accouns for changes in educaion, work experience, and gender. The index base is 1996=1.0.

5 4 * e e α e 1 (1 α ) (4) H ( W / Q ) X A I. = * e e (1 α ) e 1 (1 α ) (5) K ( W / Q ) X A I. = Firms do no adjus inpus immediaely o he desired levels, however, owing o adjusmen coss of changing inpu levels. 4 These coss are represened in he model by an adjusmen hypohesis in which he observed inpus are adjused parially each period a consan geomeric raes: * λ / 1 = 1 (6) H H ( H / H ). * κ / 1 = 1 (7) K K ( K / K ). Our shor-run inpu demand funcions are obained by combining equaions (4) and (6) and (5) and (7) o yield: e e α e 1 (1 α ) λ 1 λ (8) H [( W / Q ) X A I ] ( H ). = 1 e e ( 1 α ) e 1 (1 α ) κ 1 κ (9) K [( W / Q ) X A I ] ( K ). The expeced renal price of capial is: = 1 e (10) Q = PI ( r + δ ) TX, e where PI is he invesmen deflaor, r he discoun rae, δ he depreciaion rae, and TX capures he influence of business axaion and invesmen subsidies. 5 Expecaions of wages and prices are deermined by second-order auoregressions on curren values. Expeced oupu is se equal o acual oupu o enable our esimae of he Okun s Law gap beween acual and poenial oupu (equaions 14 and 15). 6 Our nex ask is o esimae he parameers of equaions (8) and (9) for he nonfarm business secor, combining he BLS produciviy daase wih BEA daa on capial sock and depreciaion. 7 The firs 4 Examples of hese coss for labor are searching, hiring, raining and layoff coss. In he case of capial, adjusmen coss may sem from purchase coss ha are exernal o he firm or from inernal insallaion coss. 5 The discoun rae is se a 6%, which is a rough esimae of he average ex pos real afer-ax reurn on capial and can be hough of as he arge reurn firms seek on new invesmen. This specificaion gives superior fis for he facor demand funcions o formulaions using nominal or real long-erm marke ineres raes before or afer axes. 6 As a check, a model simulaion subsiuing an auoregressive specificaion for expeced oupu differed only marginally from our presen findings. 7 The capial sock daa is he official BEA series measured in billions of chained 1996 dollars. Chain aggregaes are no addiive, however, so he corresponding depreciaion series canno be properly measured using he sandard ideniy for he perpeual invenory mehod o derive an implici aggregae depreciaion rae. As Whelan (2000) shows, such a derived series is biased oward a faser-han-acual pace of depreciaion. Raher, he appropriae measure is a weighed average of depreciaion raes of he underlying

6 5 problem is o specify he reamen of echnical progress or oal facor produciviy (TFP) growh. 8 We begin by calculaing he Solow residual S from he producion funcion as an approximae measure of he annual rae of echnical change for a given value of α: 9 (11) S ln( X / X 1 ) ˆ α ln( K 1 / K 2) ) (1 ˆ) α ln( L / L 1 ), = where labor inpu L = IH. S is an approximaion o ln (A /A -1 ), since i is affeced by varying uilizaion raes of measured inpus and by sochasic disurbances o aggregae demand and supply. To purge he esimaed echnical progress rend of hese ransiory elemens, he residual was firs cumulaed and hen smoohed wih an HP filer, providing a flexible, low-frequency esimae of ln A, which resuled in rend values ha accord well wih generally acceped views and our own previous esimaes based on piecewise rend breaks. 10 Nex, he same α value was imposed in he facor demand funcions, which were hen esimaed simulaneously by he mehod of seemingly unrelaed regressions o deermine heir consan erms and adjusmen speeds. This procedure ensures ha he imposed echnical progress rend is consisen wih he value of α in he esimaed facor demand sysem. Three values of α were ried: 0.36, 0.30, and The bes fi was aained for The fied facor demands for are (-values are shown in parenheses beneah esimaed parameers): (8A) ln(h / H -1 ) = *[ -0.25*ln(W e / Q e ) + ln( X /H -1 ) ln A 0.75*ln I ] *HRES -1 (-14.70) (14.85) (8.79) RSQBAR = Durbin-Wason = (9A) ln(k / K -1 ) = *[ 0.75*ln(W e / Q e ) + ln( X /K -1 ) ln A 0.75*ln I ] *KRES -1 (-4.93) (6.67) (17.25) RSQBAR=0.816 Durbin-Wason = In hese expressions, HRES and KRES are he uncondiional residuals in AR(1) processes. The esimaed adjusmen speed of labor is 0.697, indicaing ha 70 percen of he gap beween desired and acual labor caegories of equipmen and srucures. We use he depreciaion series Whelan calculaed in his manner in our renal price of capial variable. 8 TFP is more commonly used in heoreical exposiions and he macroeconomic lieraure han is synonym MFP. 9 Since he capial sock is daed a he end of he year, he curren capial inpu is based on lagged capial sock in he expression for he Solow residual. 10 We applied a smoohing parameer of 400, We noe, however, ha imposing less smoohing would yield a greaer acceleraion of echnical progress in he second half of he 1990 s. A smoohing parameer of 100, for example, yields rend esimaes for he Solow residual averaging 1.02 in and 1.29 in , as compared wih our preferred measures of 0.97 and 1.10.

7 6 inpu is closed each year. As expeced, he adjusmen speed for capial sock is a much slower 10 percen per year. The firs rial value for α of 0.36 was calculaed as one minus he mean labor share during he sample period. This procedure is frequenly used in sudies of he producion funcion, since under compeiive marke condiions and consan reurns o scale he facor shares measure heir marginal produciviies. However, under realisic, imperfecly compeiive marke condiions, he capial share will include monopoly rens, hereby oversaing he marginal produciviy of capial services, so ha here is no heoreical conradicion in favoring he beer fiing value of 0.25 in our esimaed producion funcion. The indexes of echnical progress and is HP rend during are graphed in Figure 3A. The lower panel, Figure 3B, shows he corresponding growh raes of he acual and rended Solow residuals. 11 As an aid o judging he relevance of our esimaes of he annual growh raes of echnical progress, we compare our measure o he mulifacor produciviy index of he BLS in Figure 4. The overall similariy beween he wo series is remarkable he correlaion coefficien is A subsanial gap did open beween hem during , however, when he Solow residual averaged an annual gain of 1.76 percen as compared wih 1.06 percen for he MFP measure. The gap is aribuable o he fac ha he inpu of capial services is assumed o be proporional o he aggregae capial sock in our model, whereas individual capial socks are weighed by renal prices in he aggregaion procedure underlying he aggregae capial-inpu measure used in he BLS mulifacor produciviy esimaes. The laer approach (originaed by Jorgenson and Griliches, 1967) is based on he idenificaion of renal prices wih marginal producs of differen ypes of capial, so ha capial qualiy is improved when asses wih higher marginal producs are subsiued for hose wih lower ones. The pace of such subsiuion was acceleraed in he lae nineies by he rapid decline in prices of IT capial, so ha he qualiy-adjused capial inpu measure accouned for relaively more of he growh of oupu in he BLS measures, reducing heir residual esimae of MFP relaive o our calculaed Solow residual. F.E. LABOR SUPPLY Labor supply, measured in hours, is he produc of annual hours per worker AH and he number of employed persons E, he laer depending on he unemploymen rae U and he size of he civilian labor force LC. The principal deerminans of he labor-force paricipaion rae LP are he employmenpopulaion raio E/N and he real afer-ax consumpion wage WRC. The E/N raio, an indicaor of he probabiliy of finding work, capures so-called discouraged-worker effecs, while WRC measures he opporuniy cos of leisure. The esimaed paricipaion equaions are disaggregaed ino 16 age-sex groups. Denoing F.E. levels of variables by he suffix F, he F.E. paricipaion rae for he i-h group in year is given implicily by: 11 Noe ha he series denoed TREND in Figure 3B is he firs difference of he HP rend hrough he cumulaed Solow residual index in Figure 3A, raher han one direcly calculaed by filering he acual Solow residual series ploed in Figure 3B.

8 7 (12) ln ( LPF /(1 LPF )) i + c 5, i i = c1, i + c2, i ( EF / N ) + c3, iwrcf TREND + c ln( LP /(1 LP )), 6, i i, 1 i, 1 + c 4, i ( LA / N ) where LPF i = (LCF i / N i ), TREND is a log-linear rend variable, and LA sands for he armed forces, appearing only in he equaions for males under age 45. The sub-sysem of labor supply equaions (1) and (12) and can be solved for he F.E. values of he naural rae of unemploymen UN, civilian labor force LCF, and civilian employmen EF, condiional on he real wage and exogenous variables. The volume of F.E. employmen in he nonfarm business secor, ENFBF, is hen obained from an ideniy relaing i o he difference beween EF and an exogenous esimae of employmen ouside he NFB secor, EFDIF. The average-hours equaion is a hybrid relaion combining boh supply and demand facors. An equaion explaining acual hours per worker AH in he NFB secor depends primarily on he real afer-ax consumpion wage WRC, which affecs workers labor supply decisions, and on cyclical variaions in labor demand as measured by he unemploymen rae U. Then F.E. average hours are given by he F.E. counerpar of he AH equaion: (13) AHF = c + c WRCF + c UF + c LCWF, where LCWF is he F.E. proporion of women in he labor force, reflecing he fac ha women end o work fewer hours han men do. Given AHF and ENFBF, he level of F.E. hours HF in he NFB secor is obained as heir produc. Assuming ha average hours ouside he NFB secor behave he same as hose wihin i, we calculae oal hours in he non-nfb secor as AHF*EFDIF. Finally, F.E. hours in he oal economy are obained by summing hose in he NFB and non-nfb secors. DETERMINATION OF F.E. OUTPUT Esimaes of F.E. oupu, he F.E. real wage, and he naural rae of unemploymen are obained by solving a simulaneous sysem of labor demand and supply equaions ha also deermines he F.E. levels of he labor force and labor hours. The primary calculaion is for he NFB secor, bu esimaes are also presened for he oal economy. We begin by solving he heoreical labor demand funcion, equaion (8), for acual oupu: (14) e e α 1 α 1/ λ (1 λ ) / λ = [( W / PI ) /( r + δ ) TX ] A I H H 1 X. Now le XF be F.E. oupu, HF be F.E. labor inpu, and WRIF be he F.E. real invesmen wage. Subsiuing for heir counerpars in equaion (14) yields he expression for F.E. oupu: α 1 α 1/ λ (1 λ ) / λ (15) XF [ WRIF /( r + δ ) TX ] A I HF H. = 1 Thus we define poenial or F.E. oupu as he oupu ha would have o be demanded o induce firms o hire he F.E. labor supply a he naural rae of unemploymen and wih he real wage a is (labor-marke clearing) F.E. level. Comparing equaions (14) and (15), we see ha he calculaed difference beween X and XF is a srucural descenden of Okun s (1962) seminal concep of poenial oupu as providing a

9 8 measure of he oupu gap, or he oupu increase ha would be necessary o reach full employmen of labor from he exising levels of employmen and oupu. Thus i is a policy-oriened concep depending on srucural facors raher han simply a rend hrough pas business cycles. The parameers in equaion (15) come, of course, from he esimaed labor demand equaion (8A). Noe ha XF is a funcion of boh he real invesmen wage and he real consumpion wage, he laer being a deerminan of LCF. To close he sysem, addiional equaions are needed o deermine hese F.E. real wage raes. The HC model assumes markup pricing on uni labor cos, which implies ha he real produc wage equals he reciprocal of he markup imes labor produciviy. The F.E. version of he equaion is: (16) WRXF = 1/ MUHP)( XF / HF ), ( in which MUHP refers o he smoohed HP-filered markup. Changes in he real consumpion and invesmen wages may differ from hose in he real produc wage for several reasons. Firs, here may be differenial raes of echnical progress in he wo secors. Second, consumpion and invesmen goods prices may respond differenly o exernal shocks, such as changes in energy prices. Finally, consumpion and invesmen prices may display differen paerns of cyclical behavior. Changes in acual relaive prices will, of course, be refleced in observed facor demands and supplies. To allow for heir influence on he F.E. pah, we express he F.E. real consumpion wage as he F.E. real produc wage muliplied by he acual raio of he oupu deflaor o he consumpion deflaor, and similarly for he F.E. real-invesmen wage. The F.E. pah for he NFB secor is generaed by solving he simulaneous sysem composed of equaions (1), deermining he naural unemploymen rae, (12) and (13), deermining he F.E. labor supply, and (15) and (16), which ogeher wih required ideniies, deermine poenial oupu. I is no he smooh pah of simple rend esimaes of F.E. oupu, since our concep responds endogenously o changes in he rae of echnical progress, demographic changes affecing he naural unemploymen rae and he labor supply, changes in axaion affecing he wage-renal raio and he labor supply, and variaions in he rae of change of labor hours (labor adjusmen facor). Technical progress and he naural rae of unemploymen of prime-age males have been smoohed in esimaing he F.E. pah, bu he remaining elemens are subjec o considerable variaion. To provide a corresponding series of F.E. GDP, we add as an exogenous componen he difference beween acual GDP and acual NFB oupu o he model-deermined esimae of poenial NFB oupu. 12 This procedure is subjec o some (probably small) error because he chained real GDP esimaes are nonaddiive in heir componens. In any even, he oupu gaps for NFB and GDP coincide closely (he correlaion coefficien is 0.999) excep for a slighly greaer ampliude for he nonfarm business secor. OUTPUT AND UNEMPLOYMENT GAPS Our esimaes of poenial oupu and he oupu gap for boh he NFB secor and real GDP are 12 The exogenous componen (abou 25 percen of GDP) includes he farm, household, housing, and governmen secors.

10 9 displayed in Figure 5. The profiles for he NFB secor exhibi faser oupu growh and larger oupu gaps han hose for GDP, bu he paerns of he oupu gaps are much he same. Of he hree long expansions during , ha of was he sronges, wih a poenial GDP growh rae of 4.70 percen, acual growh a 4.52 percen, and an oupu gap averaging 75 basis poins. During , acual GDP growh of 3.22 percen exceeded poenial growh of 2.83 percen and he oupu gap averaged 59 basis poins. The corresponding figures for he expansion of are respecively 3.32, 3.19 percen and 1.11 percenage poins. In remarkable conras o is predecessors, he long expansion of was a lae bloomer, nearing poenial only in 1998 and exceeding i only a is 2000 peak. 13 Mos of he expansion, hen, was spen caching up o poenial, and despie he sock marke bubble, i did no seriously overshoo on eiher oupu or inflaion. Our esimaes of he oupu and unemploymen gaps for real GDP are compared in Figure 6. The wo gaps are inversely correlaed as expeced, wih a correlaion coefficien of The slope of a regression of he GDP gap on he unemploymen gap is 1.9, close o he exbook value of 2.0 usually cied for Okun s Law. We conclude ha our esimaes of he naural rae of unemploymen and he level of poenial oupu are consisen wih one anoher and saisfy he relaionship prediced by acceped macroeconomic heory. ACTUAL AND F.E. OUTPUT GROWTH, The growh rae of acual oupu is decomposed ino he growh raes of labor hours and labor produciviy for boh he NFB secor and he oal economy in Table 1A. In order o provide an hisorical perspecive on he performance of he New Economy, he average annual growh raes of hese variables are shown for he hree long expansions of , , and and for he umuluous period , dominaed by he oil shocks and heir afermahs. We discuss he esimaes for he NFB secor firs, since hese are he basic produciviy measures available for he macro economy. For ha secor, he average growh raes of oupu, produciviy and hours over he enire period were respecively 3.69, 2.02, and 1.67 percen. The prize for bes real-secor performance in every caegory is decisively won by he expansion, wih produciviy growh exceeding ha of by 96 basis poins, hours growh by 21 basis poins, and oupu growh by 1.17 percenage poins. The expansion compares favorably wih ha of , however, wih an edge in produciviy growh of 49 and in oupu growh of 17 basis poins. A breakdown of he expansion beween is firs and second halves is included in he las wo rows of he able. This division highlighs he surge in produciviy growh in he lae 1990 s, when i increased from 1.51 percen in o 2.53 in , or by 1.02 percenage poins. A he same ime, labor inpu increased 92 basis poins, so ha oal oupu grew a a rae of 4.61 percen in 13 Afer narrowing slighly in 1992, he oupu gap plunged emporarily in 1993 as poenial oupaced acual growh. The growh rae of F.E. oupu more han doubled beween 1992 and 1993, largely because of a marked acceleraion in he growh rae of he F.E. labor supply.

11 , as compared wih only 2.68 in The corresponding decomposiion for F.E. oupu growh in he NFB secor is presened in Table 1B. Over he enire period , he average growh raes of esimaed F.E. oupu, produciviy and labor supply were slighly higher han heir acual counerpars in Table 1A a respecively 3.74, 2.06, and 1.69 percen. The margin of superioriy for he expansion is somewha higher for he F.E. esimaes han for he acual measures, wih F.E. produciviy growh exceeding ha of by 1.32 percenage poins and F.E. oupu growh by 1.23 poins. During acual and poenial produciviy grew respecively by 2.02 and 2.07 percen, or abou he same as heir raes for he enire sample period. Finally, i is noeworhy ha acual produciviy growh increased 1.02 percenage poins beween and , whereas he corresponding gain for F.E. produciviy was only 9 basis poins. Thus our srucural mehodology for separaing rend and cycle leads o he conclusion ha he grea bulk of he recen produciviy spur refleced cyclical gains as he NFB economy caugh up o is poenial pah. This is in sharp conras o he previous long expansions of and (Figure 5). The sory is much he same when he produciviy esimaes for he oal economy are examined in Tables 1A and 1B, alhough he acceleraion of produciviy growh is more pronounced for F.E. GDP (51 basis poins) han for is NFB counerpar (9 basis poins). Also, he growh raes of oupu, hours and produciviy for he oal economy are generally slower han in he NFB secor. Decomposiion of he F.E. Labor Supply The growh rae of F.E. hours in he NFB secor may be decomposed ino several deerminans as follows. Firs, express F.E. hours as he produc of average hours AHF and employmen ENFBF: * (17) HF = AHF ENFBF. Now rewrie (17) as: (18) HF = AHF EFRAT * EF. * where EFRAT = ENFBF/EF, he raio of NFB employmen o oal employmen. EF in urn may be decomposed as he produc of he naural employmen rae and he civilian labor force: (19) EF = 1 UN )* LCF. ( Finally, he civilian labor force can be expressed as he produc of he labor force paricipaion rae and he civilian noninsiuional populaion: * (20) LCF = LPF POP. Combining all of hese expressions, we obain he final decomposiion of he level of HF: (21) HF = AHF EFRAT *(1 UN )* LPF * POP. *

12 11 The decomposiion in Table 1C is based on he sub-period average growh raes of he variables in his expression. Hours in he NFB secor increased a virually he same rae in he firs hree subperiods, owing o offseing changes in he various componens. During , hours increased a a yearly rae of 1.67 percen despie a decline in average hours a a rae of 39 basis poins. Populaion growh explains mos of he increase in labor inpu, bu conribuions also came from increases in labor force paricipaion, he NFB employmen share, and he naural employmen rae. The average rae of populaion growh increased from 1.51 percen in o 1.97 percen in , and growh of he paricipaion rae also increased from 10 o 56 basis poins. Ye he growh rae of NFB hours decreased slighly beween he wo periods, as he rae of decline of average hours acceleraed, NFB employmen grew less rapidly relaive o oal employmen, and he naural employmen rae fell. Populaion growh fell sharply in , o 1.18 percen per year, bu hours coninued o grow a abou he same pace as in he previous sub-periods, because average hours sabilized, he naural employmen rae rose, and he paricipaion rae coninued is rise. The period wih he smalles populaion growh rae and lowes rae of growh of labor force paricipaion was , and his was also he period of smalles growh of hours (1.52 percen). The growh rae of F.E. hours rebounded o a peak of 2.02 percen in , largely due o a sharp increase in he growh of NFB employmen relaive o oal employmen and o furher increases in he naural employmen rae. Finally, he F.E. growh raes of NFB and oal employmen are displayed as an addendum in he las wo columns, as an aid o undersanding he relaive movemens underlying he evoluion of he EFRAT variable. Componens of F.E. Produciviy Growh A decomposiion of F.E. labor produciviy ino is principal sysemaic componens is obained by dividing equaion (15) by HF o obain: (22) XF / HF [ WRIF /( r + δ ) TX ] ( HF α 1 α (1 λ ) / λ (1 λ ) / λ = A I H 1 ). The firs erm measures he conribuion o F.E. produciviy of capial deepening, since he wage-renal raio deermines he capial-labor raio. The nex wo erms accoun for he levels of echnology and of labor qualiy as measured by he labor composiion index, whereas he final erm allows for he effecs of he lag in he adjusmen of labor inpu o is long-erm equilibrium. Taking logs and firs-differencing he equaion yields an expression for he decomposiion of he growh rae of F.E. labor produciviy as a funcion of he raes of capial deepening, echnical progress, increase in labor qualiy, and labor adjusmen. However, our esimaed labor demand funcion (equaion 8A) also includes an auoregressive error erm in addiion o he four srucural componens. The decomposiion presened in Table 1D includes a column labeled Labor Resid o accoun for he auoregressive erm. The decomposiion reveals ha he superior performance of F.E. produciviy growh in he sixies was due o subsanially higher raes of boh echnical progress and capial deepening han were subsequenly achieved. Produciviy growh averaged 1.32 percenage poins higher in he sixies han in he nineies, wih echnical progress conribuing 1.02 percenage poins and capial deepening anoher 38

13 12 basis poins. The expansion of was a disan hird in all respecs excep for an acceleraion of he labor composiion componen relaive o Finally, he modes acceleraion of F.E. produciviy growh in he second half of he expansion of basis poins reflecs increases of 18 basis poins in capial deepening and 13 basis poins in echnical progress, mosly offse by a reducion of 16 basis poins in labor composiion. Decomposiion of Facors Affecing Capial Deepening Furher insigh concerning he sources of variaions in capial deepening may be gained by decomposing is deerminans as follows. The conribuion of capial deepening o F.E. produciviy is deermined by he following expression from equaion (22): (23) [ WRIF /( r + δ ) TX ] α The F.E. real invesmen wage, WRIF, may be facored as WRXF*PXPI, or he real produc wage imes he raio of he oupu and invesmen deflaors. Making his subsiuion in (23), aking logs, and firs differencing yields he decomposiion of he growh rae of capial deepening: (24) DCAP = α [ DWRXF + DPXPI D( r + δ ) DTX ], * where he prefix D represens he logarihmic firs-difference operaor. An independen increase in he real produc wage decreases PX/W, and hence PI/W, inducing deepening. Similarly, an independen increase in PXPI reduces PI/PX, and hence PI/W, wih he same resul. The discoun rae is a consan in our model, bu changes in he depreciaion rae and in axes affecing invesmen decisions have inverse effecs on he deepening rae. Table 1E conains he breakdown of he componens of he growh raes of F.E. capial deepening during he sample period. Deepening occurred a 1.17 percen per annum in , declined o an average of 50 basis poins in , and rebounded o 70 basis poins in and 88 basis poins in Real wage growh was a subsanial simulus o capial deepening hroughou he sample period and was especially imporan during he expansion. Large decreases in he relaive price of invesmen goods dominaed he real wage effec beginning in he early eighies, however, owing principally o he rapid fall of semi-conducor and compuer prices during hose years. Increasing depreciaion raes depressed deepening moderaely beween 1961 and 1995, bu raher subsanially in Significan increases in deepening accompanied he liberalizaion of ax policy affecing invesmen decisions from he early sixies o he mid eighies, bu subsequen ighening of depreciaion rules and eliminaion of he ax credi for equipmen invesmen led o small negaive impacs hrough he mid-nineies. PROJECTIONS OF F.E. GROWTH IN We now uilize our model o projec he F.E. growh pah of he economy over he nex wo decades, condiional on alernaive rajecories of he principal exogenous variables. For our baseline projecion, we adop he Census Bureau s inermediae populaion series and assume ha raios of non-

14 13 insiuional o oal populaion remain consan a heir 2000 values for each age-sex group. The rae of echnical progress is assumed o coninue a is average of 1.1 percen per year, and he following exogenous elemens are incorporaed: Seady growh of he labor qualiy index a 0.39 percen per year, he rae observed in A consan naural unemploymen rae of year old males, he key labor force group, a 2.55 percen, is level in A consan markup of price over uni labor cos a is 2000 value. Afer rising from 1.57 o 1.61 in he 1990 s, he markup appeared o be leveling off in he las years of he decade. Reducions in federal income ax raes for and oher currenly legislaed changes in federal axaion ha affec our measure of he ax rae on labor income. The raes in effec in 2006 are assumed o remain unchanged hrough There are no scheduled changes in corporae axaion ha aler our esimaes of he implici renal cos of capial. Coninued reducions in he relaive price of invesmen goods a raes deermined by a secondorder auoregression fied o acual daa for A gradual rise in he rae of depreciaion of capial a he pace observed during A consan raio of armed forces o non-insiuional populaion a he 2000 level. A consan level of employmen ouside of he NFB secor a ha observed in 2000, which implies a coninuing decline in he raio of non-nfb o NFB employmen Growh in produciviy (oupu per hour) ouside of he NFB secor a a rae of 1.50 percen per year, which was he average rae of increase in Hours per worker ouside of he NFB secor are se equal o he soluion value for F.E. average hours in he secor. The F.E. pah is obained by solving he model dynamically over he period , using acual values of lagged endogenous variables for 1999 and earlier. The dynamic soluion yields a pah along which full employmen is coninuously mainained, in conras o he saic soluion over he sample period, for which each year s F.E. values are condiional on he acual pah of he economy up o ha ime. For he wo esimaed equaions ha were adjused for serially correlaed residuals he average hours equaion and he labor demand equaion he soluion incorporaes lagged residuals from he final year of he sample, so ha hese residuals affec only he levels of he soluion values of he variables, no heir changes over ime. As noed above, he esimaed labor force paricipaion equaions include rends o accoun for facors influencing paricipaion ha are no capured by oher variables in he equaions. When run ou mechanically over weny years, he rends someimes resul in implausible levels of paricipaion. In hese cases, we adjused he rend erms o keep he paricipaion raes wihin reasonable bounds. Table 2 summarizes he baseline projecion, showing average annual growh raes for each decade, and , ogeher wih a recap of our esimaes of F.E. growh raes for In panel A of he able, we see ha F.E. oupu in he NFB secor is projeced o rise a 3.41 percen per year in he firs decade, slowing o 2.74 percen in he second decade. The corresponding figures for F.E. GDP are

15 and These growh raes represen significan reducions from hose of he las half of he 1990 s and are largely raceable o significanly lower raes of labor supply growh. F.E. produciviy growh rises slighly in he NFB secor and remains roughly consan for he oal economy, relaive o he lae 1990 s. We see from panel B ha very lile of he decline of F.E. labor supply growh in he firs decade of he projecion is due o a reardaion in populaion growh; raher, changes in all of he oher facors impac labor supply growh negaively. We projec ha average hours will resume a downward rend, following a modes rise in he 1990 s. The share of NFB employmen in oal employmen is projeced o coninue is upward rend, bu a a slower pace han observed in The naural rae of employmen, whose increase in conribued abou one-quarer of a percenage poin o F.E. labor supply growh, declines very slighly in he firs decade of he projecion (he naural unemploymen rae rises from 4.29 percen in 2000 o 4.36 in 2010). And finally, we foresee only a sligh increase in he aggregae rae of labor force paricipaion in and a decline in , in conras o a modesly rising rend in he 1990 s. 14 Panel C shows he decomposiion of F.E. NFB produciviy growh. The small acceleraion in he projecion, relaive o , sems largely from smaller drag arising from labor adjusmen. By assumpion, he conribuion of echnical progress remains a 1.10 percen, and he conribuion of labor qualiy declines slighly o 0.29 (one minus he capial elasiciy imes 0.39), while he endogenous rae of capial deepening is unchanged. From panel D we see ha capial deepening is simulaed by higher growh of he real produc wage and by a somewha smaller rae of increase in he depreciaion rae (he discoun rae is held consan a 6 percen, as in he sample period). However, hese posiive influences are offse by a diminished rae of decline of he relaive price of capial goods. Viewed in he longer perspecive provided by panel B of Table 1, F.E. NFB oupu growh in he firs decade of he baseline rails he 1960 s by 1.65 percenage poins and he 1990 s by 0.42, bu exceeds ha in he 1980 s by The sronges resemblance is o he decade of he 1970 s; bu in comparison o he 1970 s, produciviy growh accouns for a larger porion, and labor supply growh for a smaller porion, of poenial growh. The second half of he projecion regisers he slowes decade of F.E. growh since 1960, due principally o a low rae of growh of F.E. labor supply. Our projecion may be compared wih ha recenly published by of he Congressional Budge Office for , which serves as he basis for CBO s assessmen of he federal budge oulook (CBO, 2002, Table E-1). CBO seeks o projec acual raher han F.E. oupu, bu only he firs wo or hree years of heir forecas is mean o incorporae business cycle consideraions; hereafer, hey essenially envisage a sable, high-employmen growh pah. For he period , hey forecas average growh of real GDP a 3.05 percen, which is virually he same as our F.E. esimae of 2.93 percen for he same period. 14 The paricipaion rae rises from 67.1 in 2000 o 67.4 in 2010, hen declines o 65.4 in If paricipaion raes by age and sex are held consan a heir 2001 F.E. levels, he aggregae paricipaion rae declines even more sharply o 66.0 in 2010 and 63.1 in Rising raes of female paricipaion coninue o counerbalance declines in male paricipaion and o parially or wholly offse he negaive impac of demographic changes on aggregae paricipaion.

16 15 Their unemploymen rae forecas rises o 6.1 percen in 2002, hen declines o 5.2 percen in 2005 and remains a ha level, which may be viewed as CBO s esimae of he naural rae of unemploymen. This considerably exceeds our projeced naural rae of 4.3 percen. CBO s published forecas does no include explici esimaes of produciviy and hours growh. However, he former migh be inferred from heir projeced growh of real wages, which ough o approximae he rae of produciviy growh on a seady growh pah (on he assumpion of consan price markups). The difference beween heir projeced growh of employmen coss and ha of consumer prices is abou 1.5 percenage poins on average. This is quie a bi below our esimae of F.E. produciviy growh for eiher he oal economy (2.1 percen) or he NFB secor (2.3 percen). Since CBO arrives a abou he same medium-erm GDP growh rae as we do, he implicaion is ha hey foresee more rapid growh of hours. Alernaive Populaion Pahs The Census Bureau prepares high and low esimaes of fuure populaion, in addiion o he middle series uilized in our baseline projecion. Table 3 compares soluions of our model for he hree varians. Since he growh decomposiions of produciviy and capial deepening for he hree varians are similar o hose shown for he baseline, he able repors growh raes only for F.E. oupu, produciviy and hours and he decomposiion of hours growh. For he low populaion varian, non-insiuional populaion grows 0.21 percenage poins more slowly in he firs decade and 0.27 more slowly in he second decade, compared o he baseline (middle varian). This ranslaes ino somewha larger differences in F.E. hours (0.28 and 0.35 for he firs and second decades, respecively) largely because of slower growh of NFB relaive o oal employmen. F.E. produciviy growh is abou he same as in he baseline, and so he lower growh raes of F.E. oupu are almos wholly due o lower growh of labor supply. For he high populaion varian, non-insiuional populaion growh is 0.29 percenage poins higher in he firs decade and 0.38 higher in he second. The increases in F.E. hours are larger (0.37 and 0.52, respecively), because of more rapid growh in he raio of NFB o oal employmen and smaller reducions in labor force paricipaion. F.E. produciviy growh is only very slighly higher han in he baseline, and so he difference in hours growh is he reason for higher growh of F.E. oupu. Even for he high populaion esimaes, he growh rae of F.E. hours in is percenage poins below ha in pas decades; in , i falls even furher shor of prior decades by percenage poins. Higher Technical Progress The baseline projecion mainains echnical progress a he rae of 1.10 percen observed in This rae is no exraordinarily high compared o prior decades and, in fac, falls well shor of he rae of 2.05 percen recorded in How would poenial growh differ if we added, say, 0.5 percenage poin o rae of echnical progress beginning in 2001? The answer is ha F.E. produciviy growh will be higher by abou 0.67 percenage poins. This resul can be obained analyically, as well as by model simulaion, and is consisen wih he sandard neoclassical growh model wih a consan-reurns, Cobb-

17 16 Douglas producion funcion. The relaionship beween produciviy growh and echnical progress in he sandard model and in our own can be derived as follows. Boh models begin wih he same producion funcion, equaion (2) above. Neglecing disincions beween desired or expeced and acual variables, denoing logarihmic ime derivaives of variables wih corresponding lower-case leers, and dropping ime subscrips, he producion funcion implies: (25) x = a + α k + ( 1 α)( i + h), The sandard model assumes a consan saving rae and herefore requires a consan capial-oupu raio for seady growh, i.e., k = x. Assuming ha a, i and h are consans, he seady sae growh of produciviy is: a (26) x h = + i, 1 α Our model does no specify a consan saving rae bu insead imposes he expansion-pah condiion on he capial-labor raio, as in equaion (3), which allows us o idenify explicily he relaive-price deerminans of capial deepening. Using he definiion of Q in equaion (10) and he markup pricing assumpion in equaion (16), wih M denoing he markup, equaion (3) can be wrien as: K α 1 X PX = H 1 α M H PI( r + δ ) TX (27), which implies, assuming consan M : (28) k = x p d x, where p is he growh rae of PI/PX, d is he growh rae of r+δ, and x is he growh rae of TX. Subsiuing from (28) ino (25), and assuming a, p, d, x, i and h are consan, our model generaes seady growh of produciviy a: a 1 α α 1 α (29) x h = + ( p d x) + i. If p and d are negaive and x is zero, as in our baseline projecion, he produciviy growh rae exceeds he value expeced in he sandard model (26) for given a and i; hus, Hicks-neural echnical progress a a rae of 1.10 ranslaes ino seady sae produciviy growh a a rae of 2.29 in our baseline (2.25 afer allowing for Labor Adj, as shown in Table 2). However, if we assume a higher value of echnical progress han in he baseline, bu mainain all oher baseline assumpions, we see from (29) ha he increase in produciviy growh, relaive o he baseline, is simply a/(1-α), as in he sandard model In he Cobb-Douglas case, Hicks-neural progress a rae a is equivalen o Harrod-neural progress a rae a/(1-α), so ha he simulaion resul could equally well be described as a shock o Harrod-neural progress of 0.67 percenage poins inducing an equal increase in produciviy growh, as in he sandard non-parameric growh model. Our use of Hicks-neural progress allows for he incorporaion of he Solow residual as an empirical measure of echnical progress and for direc comparison wih he growh-

18 17 In he neo-classical growh model, boh F.E. produciviy and F.E. oupu would rise by a/(1-α), since labor supply growh is exogenous and consan. However, in our model wih endogenous labor supply, faser growh of F.E. produciviy is parially offse by slower growh of F.E. labor supply, owing o declining labor force paricipaion caused by faser growh of real wages. Finally, we call aenion o he fac ha he deerminans of labor produciviy growh (equaion 29) are held consan or nearly consan (see p. 13) in he baseline projecion in Table 2, so ha i is reasonable o inerpre he resuls for F.E. produciviy growh in he NFB secor (a growh rae of abou 2.25 percen) as a seady-sae value for he enire period. SUMMARY AND CONCLUSIONS Our hisorical analysis indicaes ha he produciviy surge observed in he NFB secor during he second half of he 1990 s was largely a cyclical phenomenon as he economy caugh up o is poenial pah, wih acual produciviy growh increasing 1.02 percenage poins and F.E. produciviy growh only 9 basis poins from he firs half of he expansion. Even hough poenial produciviy growh did no accelerae much in he second half of he 1990 s, growh of poenial oupu did, owing o a 0.5 percenage poin rise in labor supply growh. Because he recovery in he early nineies sared from a low level of oupu uilizaion, and because poenial growh acceleraed moderaely in , he expansion ended wih oupu only slighly above poenial, for boh real GDP and NFB oupu. The experience differed markedly during he long expansions of he 1960 s and 1980 s, when oupu rose o levels 3 o 4 percen above poenial. The close balance beween acual and poenial oupu in he maure sage of he expansion of is consisen, of course, wih he modes level of inflaion of he period. Our baseline projecion for embodies an average annual growh rae of F.E. produciviy of 2.27 percen in he NFB secor, wih lile change in he subsequen decade. By way of comparison, acual average produciviy growh for he secor was 1.51 percen in and 2.53 in Thus he F.E. projecion is 26 basis poins lower han he growh rae of measured produciviy during he lae nineies, bu 16 basis poins higher han our esimae of 2.11 percen for F.E. produciviy growh for he same period. I is also 25 basis poins above he average rae of produciviy growh of 2.02 percen during , and 21 basis poins above he corresponding average of 2.06 for F.E. produciviy growh. Overall we regard i as a raher opimisic forecas. While our oulook for F.E. produciviy growh over he nex wo decades is reasonably brigh, we foresee reducions in he growh raes of F.E. oupu for boh he NFB secor and oal GDP, due o reduced raes of labor supply growh ha are below hose experienced in any decade since Growh of F.E. GDP along our baseline averages 2.99 in and 2.50 percen in , compared o 3.65 percen in and 3.42 percen for he enire period, Our GDP projecion is similar o CBO s laes forecas of abou 3 percen growh for he years ou o 2012, bu our esimae appears o res on higher produciviy growh and lower growh of hours han heirs. accouning approach o he measuremen of oal- or muli-facor produciviy.