Transition dynamics in aggregate models of innovative investment

Transcription

1 Transiion dynamics in aggregae models of innovaive invesmen Andrew Akeson Ariel Bursein Manolis Chazikonsaninou June 2018 Absrac Wha quaniaive impac do changes in economic policies and oher changes in he economic environmen have on he dynamics of aggregae produciviy in he shor, medium, and long run, hrough heir effec on firms incenives o inves in innovaion? We presen a unifying model ha ness a number of canonical models in he lieraure and characerize he ransiion dynamics of aggregae produciviy following a variey of changes in policies and he economic environmen in erms of wo sufficien saisics. We review he exen o which hese wo sufficien saisics can be disciplined by daa and discuss some uncerainies ha arise wih policy changes o which our sufficien saisics approach does no apply. UCLA and Federal Reserve Bank of Minneapolis UCLA UCLA

2 1 Inroducion Much of he growh in aggregae produciviy in our economy is driven by he invesmens by enering and incumben firms in innovaion. Wha is he quaniaive impac of changes in ax policies and/or changes in he economic environmen such as an increase in monopoly power or a decrease in he populaion growh rae on he growh of aggregae produciviy in he shor, medium, and long erm hrough heir impac on innovaive invesmens by firms. Despie several decades of imporan work on models of he impac of innovaive invesmen by firms on aggregae produciviy, 1 here are no widely acceped se of assumpions o use in specifying hese models nor any widely acceped procedure for disciplining he parameers of hese models wih daa. 2 Moreover, he ransiion dynamics implied by hese models have no received much aenion. In his paper, we build on our work in Akeson and Bursein (2018) (henceforh AB2018) o presen a model ha ness many of he canonical models of he ineracion of firms innovaive invesmens and aggregae produciviy and oupu. We look o inspec he mechanism underlying our model s posiive implicaions for he impac of a range of changes in he economic environmen, including changes in uniform subsidies o innovaive invesmen, changes in equilibrium markups for incumben firms, changes in corporae profis axes, and changes in he growh rae of populaion. 3 To do so, we develop an approximae analyical soluion o he ransiion dynamics of aggregae produciviy implied by hese models. 4 We use his approximae soluion o highligh wo sufficien saisics ha are key for deermining he model s quaniaive implicaions for he shor, medium, and long run ransiion dynamics of aggregae produciviy in response o a variey of changes in he economic environmen and we discuss wha daa migh be useful in disciplining hese wo key saisics. 1 See he excellen reviews in Jones (2005), Acemoglu (2009), Aghion e al. (2014), Aghion e al. (2015), and Akcigi (2017). 2 The Bureau of Economic Analysis has begun o incorporae measures of firms invesmens in inangible capial ino he Naional Income and Produc Accouns saring in The framework hey use for doing so (see e.g. Corrado e al. 2009) is an exension of he sandard neo-classical growh model ha absracs from knowledge spillovers from innovaion, which are cenral o he class of models ha we consider in his paper. 3 Imporan conribuions in he Public Finance Lieraure on he impac of ax policy on business enry (enrepreneurship) include Genry and Hubbard (2005), Cullen and Gordon (2006) and Giroud and Rauh (2015). For examples of analyses of he impac of ax policies on aggregae produciviy hrough heir impac on firms invesmens in innovaion in Schumpeerian models, see Pereo (2007), Jaimovich and Rebelo (2017), and Ferraro e al. (2017). Karahan e al. (2016) sudy he impac of changes in he growh rae of he labor force on firm enry, and De Loecker and Eeckhou (2017) and Edmond e al. (2018) sudy he macroeconomic implicaions of changes in markups. 4 Our approach is similar o ha used in Campbell (1994) o sudy he implicaions of he sochasic growh model. 1

3 Our model, which exends he model of firm dynamics in Garcia-Macia e al. (2016), feaures innovaive invesmens by enering and incumben firms ha may be direced eiher a acquiring producs new o ha firm or a improving he produciviy wih which a firm produces one of is curren producs. Enering and incumben firms acquire new producs eiher by invening producs ha are new o sociey as a whole (as in models of growh hrough expanding varieies) or by invening a beer echnology for produing a produc currenly produced by some oher incumben firm (as in Schumpeerian models of growh hrough business sealing). We nes a wider class of models of he spillovers from innovaive invesmen in he lieraure han in AB2018. Specifically, in addiion o he Semi-Endogenous Growh framework of Jones (2002), we nes models ha use wha is ermed Second Generaion Endogenous Growh echnologies governing he exen o which pas discoveries impac he produciviy of labor currenly allocaed o research. 5 To develop our sufficien saisics, we solve analyically for a firs order approximaion o he model implied pah of aggregae produciviy following a one-ime, exogenous, perurbaion o he aggregae allocaion of labor o innovaive invesmen. The firs of our sufficien saisics, which we erm he impac elasiciy of he model, is he elasiciy of he growh of aggregae produciviy beween his period and he nex wih respec o a given change in he log of he labor inpu allocaed o research. The second of our sufficien saisics is he persisence of his impulse o aggregae produciviy, i.e. i is he rae a which he level of aggregae produciviy reurns o is baseline growh pah. We show how hese sufficien saisics shape he model s quaniaive implicaions for he ransiion dynamics of aggregae produciviy following long-erm uniform changes in innovaion subsidies, long-erm changes in markups, and long-erm changes in corporae axes wih equal expensing of innovaive invesmen by enering and incumben firms. We also show ha hese wo sufficien saisics shape he long response of he aggregae produciviy growh o permanen changes in populaion growh. Furhermore, we show ha hese sufficien saisics also shape our model s normaive implicaions for he welfare consequences of hese changes in he economic environmen. Wha daa can be used o discipline hese wo sufficien saisics? The impac elasiciy of he model is disciplined by daa on firms dynamics. Our second sufficien saisic, he persisence of he response of aggregae produciviy, is much harder o measure. This second saisic is shaped by assumpions made abou ineremporal knowl- 5 See, for example, Pereo (1998), Segersrom (1998), Young (1998), Dinopoulos and Thompson (1998), and Howi (1999). As discussed in he surveys by Jones (2005), Ha and Howi (2007), and Akcigi (2017), hese Second Generaion Endogenous Growh models embed a mechanism hrough which, in equilibrium, he invenion of new varieies has an independen effec of increasing he amoun of labor devoed o research required o mainain a given aggregae produciviy growh rae. 2

4 edge spillovers in research ha were cenral o he debae in he lieraure weny years ago abou scale effecs in endogenous growh models. 6 This sufficien saisic is much harder o pin down wih daa because i requires one o idenify wheher he half-life of a shock o aggregae produciviy is a decade, a cenury, or a millenia. We show ha his model uncerainy is less imporan for posiive quaniaive analysis of he medium erm dynamics (e.g. 20 years) of aggregae produciviy in respose o he changes in he economic environmen ha we consider. In conras, his uncerany regarding ineremporal knowledge spillovers is much more imporan for he normaive implicaions of our model since hese normaive implicaions are driven by he longer erm responses of aggregae produciviy. We finish he paper wih analysis of he impac of a change in corporae profi axes when he expensing of innovaive invesmen for ax purposes is no he same for incumben and enering firms. We discuss how addiional effecs beyond hose summarized by our wo sufficien saisics impac he ransiion dynamics of aggregae produciviy. These addiional effecs arise from a policy-induced reallocaion of innovaive invesmen beween enering and incumben firms ha may raise or lower he ransiion pah of aggregae produciviy relaive o ha implied by our sufficien saisics, depending on he exen of business sealing and he specific form of ineremporal knowledge spillovers. The remainder of he paper is organized as follows. In Secion 2 we presen our model and discuss he models in he lieraure ha are nesed in our framework. In Secion 3, we derive resuls regarding he growh raes and levels of variables on he balanced growh pah of he model as a funcion of policies and he growh rae of populaion. In Secion 4, we compue analyically he ransiion dynamics of aggregae produciviy implied by he model o a firs order approximaion in he case in which we ake he dynamics of he allocaion of labor beween producion and research as given. We use hese formulas for he model s ransiion dynamics o highligh which feaures of daa on firm dynamics and he aggregae economy are criical for idenifying he parameers of he model ha are key o is dynamic implicaions. In Secion 5, we describe he counerfacual experimens ha we conduc wih he model and he resuls we obain regarding he shor and long erm responses of aggregae produciviy and welfare induced by hese various experimens. We presen proofs of our proposiions, he calibraion of he model parameers, and a wide range of supporing echnical maerial in a supplemenal appendix. 6 While ineres in his debae in he lieraure has diminished in he las decade, we find ha he issues raised here are sill cenral o undersanding he normaive implicaions of he models we consider. See Bloom e al. (2017) for a recen empirical conribuion o he measuremen of ineremporal knowledge spillovers. 3

5 2 The Model Our model of he impac of innovaive invesmen by heerogeneous firms on aggregae produciviy ness several of he canonical models in he lieraure. The model is specified so as o allow for sufficien aggregaion o make analysis of is ransiion dynamics racable. We presen he key elemens of he model here. Furher deails are provided in he Appendix. We presen he model in discree ime. There are hree ypes of goods: a final good used for consumpion and invesmen in physical capial, a final good ha we erm he research good ha is he inpu ino innovaive invesmen by firms, and differeniaed inermediae goods produced by innovaing firms. The Final Consumpion Good We le Y and C denoe oupu and consumpion of he final consumpion good, and le K denoe he sock of physical capial available for producion in period. The resource consrain for he final consumpion good is Y = C + K +1 exp( δ k )K (1) where (1 exp( δ k )) represens he depreciaion rae of physical capial. The represenaive agen has sandard preferences given by =0 β 1 γ L (C /L ) 1 γ (2) wih β < 1 and γ > 0. Populaion L grows a he exogenous rae exp(g L ) = L +1 /L. The final consumpion good Y is produced as a consan elasiciy of subsiuion (CES) aggregae of he oupu of a coninuum of differeniaed inermediae goods. A each dae, he echnology wih which any paricular inermediae good can be produced is summarized by is produciviy index z. Producion of an inermediae good wih produciviy index z is carried ou wih physical capial, k, and labor, l, according o y (z) = zk (z) α l (z) 1 α, (3) where 0 < α < 1. To simplify our noaion, we assume ha he suppor of z is a grid wih counable elemens z n for inegers n wih log z n+1 log z n equally spaced. For each inermediae good ha can be produced a ime, we refer o he echnology wih he highes value of z on his grid available for producing his good as he fronier echnology for his good. An inermediae goods producing firm is an organizaion ha owns he 4

6 exclusive righs o use he fronier echnology for producing one or more inermediae goods. The producive capaciy of he economy is deermined by is populaion, L, is curren sock of physical capial K, and he measure M (z) which denoes he measure of inermediae goods wih fronier echnology indexed by z a ime. Aggregae oupu of he final consumpion good is hen given by he CES aggregaor Y = [ ρ/(ρ 1) y (z) (ρ 1)/ρ M (z)], (4) z wih ρ > 1 and oupu levels y (z) of he inermediae goods given in equaion (3). Toal labor hours employed in producion of inermediae goods is denoed by l p L, wih l p [0, 1] represening he fracion of he populaion engaged in curren producion. The consrains on producion labor and physical capial require ha l p L = z l (z)m (z) and K = z k (z)m (z). In each period, physical capial and labor are freely mobile across inermediae goods producing firms and he markup µ 1 of price over marginal cos charged by inermediae goods producers is consan across inermediae goods and over ime. 7 As is sandard, cos minimizaion by inermediae goods producers implies ha k (z)/l (z) = K / ( l p L ) for all inermediae goods. Facor marke clearing and equaion (4) hen imply ha, in equilibrium, aggregae oupu can be wrien as Y = Z (K ) α ( L p ) 1 α, (5) where Z is given by Z = [ 1/(ρ 1) z ρ 1 M (z)]. (6) z Throughou his paper, we refer o Z as aggregae produciviy a ime. 8 7 As is sandard, wih Berrand compeiion and limi pricing, he gross markup µ charged by he incumben producer of each produc is he minimum of he monopoly markup, ρ/ (ρ 1), and he echnology gap beween he fronier echnology wih produciviy index z and any poenial second mos producive producer of he good, wih { produciviy index z/ µ (wih µ > 1), which poenially depends on he paen sysem. Tha is µ = ρ min ρ 1 }., µ Changes in he paen sysem can resul in changes in he equilibrium markup. 8 This model-based measure of aggregae produciviy, ( Z, does ) no correspond o measured oal facor produciviy (TFP), which is given by TFP = GDP /, where he definiion of GDP depends on K α L1 α he measuremen sandard for expendiures on innovaive invesmen being used (e.g., he definiion of oupu of he final consumpion good Y in equaion (1) corresponds o he Bureau of Economic Analysis 5

7 We refer o M = z M (z) as he oal measure of producs available, and o he raio Z ρ 1 /M as he average produciviy index of exising inermediae goods (specifically, he average of z ρ 1 across inermediae goods). We refer o s (z) = z ρ 1 /Z ρ 1 as he size of a produc wih fronier echnology z. This is because he revenue and employmen a associaed wih his produc in equilibrium is proporional o s (z). The Research Good The second final good in his economy, which we call he research good, is he inpu used for innovaive invesmen by firms. Producion of he research good is carried ou using research labor hours l r L, wih l p + l r research good is given by = 1. Oupu of he Y r = A r Z φ 1 l r L. (7) Here, A r represens he sock of freely available scienific progress, which grows a an exogenous rae g A = ḡ A. 9 The erm Z φ 1 wih φ 1 reflecs ineremporal knowledge spillovers in he producion of he research good, as in he model of Jones (2002). Using he language of Bloom e al. (2017), A r Z φ 1 denoes he produciviy wih which research labor L r ranslaes ino a real flow of ideas" Y r available o be applied o innovaive invesmen. Exogenous scienific progress (growh in A r ) drives up research produciviy over ime. If φ < 1, hen increases in he level of aggregae produciviy Z reduce research produciviy in he sense ha ideas become harder o find." Because he impac of advances in Z on research produciviy is exernal o any paricular firm, we call i a spillover. The parameer φ indexes he exen of his spillover. Innovaive invesmen is underaken by inermediae goods producing firms. Aggregae produciviy grows as a resul of innovaions by inermediae goods producing firms ha eiher increase he average produciviy index z of fronier echnologies available for exising inermediae goods or increase he oal measure of inermediae goods available. These innovaions arrive a raes deermined by he invesmens in innovaion underaken by hese firms. We refer o hose firms producing inermediae goods a ha pre-2013 measuremen of GDP, which did no include expendiures on innovaive invesmen), and 1 α denoes he share of labor compensaion in measured GDP. Our analyic comparaive saics can be used o consruc alernaive measures of TFP and GDP. 9 Some papers in he heoreical lieraure on economic growh wih innovaing firms assume ha all produciviy growh is driven enirely by firms expendiures on R&D (Griliches 1979, p. 93). As noed in Corrado e al. (2011) and Akcigi (2017) his view ignores he produciviy-enhancing effecs of invesmens by acors oher han business firms. We capure all of hese oher produciviy-enhancing effecs wih A r. Akcigi e al. (2013) consider a growh model ha disinguishes beween basic and applied research and inroduce a public research secor. As we discuss below, he only role served by he exogenous growh of scienific progress A r in our analysis is ha, by adjusing he parameer ḡ A, we can arge a given baseline growh rae of oupu in he balanced growh pah as we vary he parameer φ and ψ (for a given growh rae of populaion, ḡ L ). 6

8 also produced a 1 as incumben firms. We refer o hose firms a ha are new (and hence did no produce inermediae goods a 1) as enering firms. We now describe he echnologies for innovaive invesmen by enering and incumben firms. Innovaive invesmen by enering firms Le x e M denoe he measure of enering firms a, where x e denoes he measure of enering firms relaive o he measure of exising producs a. Each of hese enering firms invess unis of he research good o acquire he fronier echnology z o produce an inermediae good new o ha firm a he sar of period + 1. This newly acquired fronier echnology may apply o an inermediae good ha was previously produced by an incumben firm or may apply o a good ha is new o sociey. Specifically, wih probabiliy δ e, his produciviy index z drawn by he enran a + 1 is associaed wih an inermediae good ha was already being produced by an incumben firm a, bu wih a lower produciviy index. Since idenical inermediae goods are perfec subsiues in he producion of he final consumpion good, compeiion in he produc marke beween he enering firm and he previous incumben producer of his inermediae good implies ha he previous incumben producer ceases producion of he good. In his case, he innovaive invesmen by he enering firm does no resul in a ne increase in he oal measure of producs available M +1. Insead, i only resuls in a posiive incremen o he average produciviy index across exising producs. As is common in he lieraure, we say ha his inermediae good ha is new o he enering firm represens business sealing from an incumben firm. Wih he complemenary probabiliy 1 δ e, his newly acquired fronier echnology allows his enering firm o produce an inermediae good ha is new o sociey as a whole. In his case, he innovaive invesmen by he enering firm resuls in a ne increase in he oal measure of producs available M +1. As is common in he lieraure, we say ha his inermediae good ha is new o his enering firm represens a conribuion o produciviy hrough expanding varieies. The produciviy index z for solen producs in enering firms is drawn in a manner similar o ha in Klee and Korum (2004) and oher sandard qualiy ladder models. The produciviy index z for producs ha are new o sociey in enering firms is drawn in a manner similar o ha in Lumer (2007). The average value of z ρ 1 across all producs obained by enering firms a + 1 is given by Ez ρ 1 = η e Z ρ 1 /M. As we discuss below, he parameer η e conrols he average size (in erms of sales and employmen) of producs produced by enering firms relaive o he average size of all producs. 7

9 Each enering firm a mus inves M ψ unis of he research good. Thus, he oal use of he research good by enering firms is hus x e M 1 ψ, wih ψ 1. As we discuss below, in he lieraure, wo values of ψ are ypically considered. The firs value is ψ = 1. In his case, he resources required o creae one new produc fall wih he number of exising producs. The second value is ψ = 0. In his case, he invesmen of he research good required o inves in a new produc is independen of he number of exising producs. Incumben firms have he opporuniy o inves in acquiring new producs o heir firm and o improve heir exising producs. We describe hese invesmen echnologies nex. Innovaive invesmen by incumben firms o acquire new producs An incumben firm ha owns he fronier echnology z for producing a paricular inermediae good possesses he capaciy o acquire he fronier echnology on addiional goods new o ha firm hrough innovaive invesmen. This invesmen echnology is specified so ha o aain any given probabiliy of acquiring a new produc a + 1, a firm mus inves a rae x m (z) in proporion o s (z)m 1 ψ which is he size of is curren produc wih index z a ime imes M 1 ψ. When ψ = 1, hen invesmen o aain a given probabiliy of gaining a new produc mus be proporional o he size of he produc s (z). If ψ = 0, hen invesmen mus be proporional o he raio of z ρ 1 o Z ρ 1 /M, which is he average value of z ρ 1 across incumben producs. In equilibrium, incumben firms inves in proporion o s (z)m 1 ψ. Thus, if x m M 1 ψ is aggregae invesmen by incumben firms in obaining new goods, hen he probabiliy ha incumben firms gain a new produc per produc ha hey currenly produce is given by 1 exp ( h (x m )), where h( ) is a sricly increasing and concave funcion wih h(0) = 0 and h(x) < 1 for all x. As is he case wih enering firms, new producs acquired by incumben firms may be solen from oher incumben firms (wih probabiliy δ m ) or new o sociey (wih probabiliy 1 δ m ). The average value of (z ) ρ 1 of he new producs acquired by an incumben firm invesing based on a curren produc wih fronier produciviy z is Ez ρ 1 = η m z ρ 1. This assumpion implies ha he average value of z ρ 1 across all new producs obained by incumben firms a + 1 is given by Ez ρ 1 = η m Z ρ 1 /M. We nex consider invesmen by incumben firms in improving coninuing producs. Invesmen in coninuing producs by incumben firms An incumben firm ha owns he fronier echnology for producing a paricular inermediae good wih fronier echnology z can also inves o improve he echnology on ha produc. This invesmen echnology is specified so ha o aain any given percenage growh in his fronier ech- 8

10 nology, he firm mus inves a a rae x c (z) in proporion o s (z)m 1 ψ. The inerpreaion of he parameer ψ is he same as above. In equilibrium, incumben firms inves in proporion o s (z)m 1 ψ. Thus, if x m M 1 ψ is aggregae invesmen by incumben firms in improving heir producs, he expeced growh rae of he fronier echnology for producs reained by incumben firms is Ez ρ 1 = exp (ζ (x c )) z ρ 1. We assume ha ζ( ) is a sricly increasing and concave funcion, wih ζ(x) > 0 for all x 0. Wih hese definiions, we can wrie he resource consrain for he research good as Dynamics of M and Z (x c + x m + x e ) M 1 ψ = Y r (8) We now characerize he dynamics of he measure of inermediae goods M and aggregae produciviy Z as funcions of innovaive invesmen by enering and incumben firms. We have specified he model so ha, in equilibrium, he aggregaion of innovaive invesmen is highly racable. As a resul he equilibrium evoluion of he variables M and Z can be described as funcions only of aggregae innovaive invesmen of each ype per produc. The evoluion of he oal measure of producs M is deermined by he rae a which incumben firms lose he fronier echnologies for producs ha hey produced a and he raes a which incumben and enering firms gain he fronier echnologies for producs new o hese firms. Consider firs he rae a which incumben firms lose producs. For each produc ha hey produce a, incumben firms can lose is fronier echnology a + 1 eiher due o exogenous exi (wih probabiliy (1 exp ( δ 0 ))), or due o business sealing. Le exp( δ c ) denoe he probabiliy ha a produc remains in he same incumben firm a + 1, where δ c = δ c (x m, x e ) is defined by he equaion exp( δ c (x m, x e )) = exp ( δ 0 ) δ m (1 exp ( h (x m ))) δ e x e. (9) The corresponding evoluion of he oal measure of inermediae producs M is given by log M +1 log M = H(x m, x e ) where H(x m, x e ) log (exp ( δ c ) + 1 exp ( h (x m )) + x e ). (10) Using a similar logic, he evoluion of aggregae produciviy is given by log Z +1 log Z = G(x c, x m, x e ) where G(x c, x m, x e ) (11) 1 ρ 1 log (exp ( δ c) exp (ζ (x c )) + η m (1 exp ( h (x m ))) + η e x e ). 9

11 Equilibrium We now describe he marke srucure, policies, and equilibrium in our model economy. Policies and Firm Profi Maximizaion Problems We now describe he profi maximizaion problems of he various ypes of firms in his economy. We sar wih he firms ha purchase inermediae goods o produce he final consumpion good using he echnology in equaion (4). These firms are compeiive. They choose oupu and inpus o maximize profis aking he price of he final consumpion good (which we normalize o one) and he prices of inermediae goods as given, and receive a producion subsidy τ y per uni sold. 10 The prices of inermediae goods are denoed by p (z). Profi maximizaion by hese firms implies sandard CES inpu demands for each inermediae good wih demand elasiciies deermined by ρ. Because he echnology in equaion (4) is consan reurns o scale, hese final consumpion good producing firms have no profis in equilibrium. The physical capial sock is managed by compeiive firms ha ren ou physical capial o inermediae goods producing firms and inves in physical capial. Each firm akes he price of he final consumpion good, he renal rae for physical capial R k, and ineremporal prices for he final consumpion good {Q } as given, and are subjec o a corporae profis ax τ corp wih expensing for invesmen in physical capial of λ k. These firms seek o maximize he discouned presen value of afer ax dividends wih dividends given by D k = ( 1 τ corp ) Rk K ( 1 τ corp λ k ) (K+1 exp( δ k )K ) (12) Inermediae goods producing firms ren physical capial a rae R k and hire producion labor a wage W o produce inermediae goods according o he echnology in equaion (3). They se prices p (z) a a markup of µ > 1 over heir marginal cos of producion. Sandard argumens give ha, in equilibrium, hese firms expend a fracion (1 α)/µ of revenue p (z)y (z) on wages for producion labor and a fracion α/µ of revenue on renal paymens for physical capial. A fracion (µ 1)/µ of revenue is lef over as variable profis. These same argumens imply ha aggregae oupu inclusive of he producion subsidy is spli ino wage paymens o producion labor, renal paymens for physical 10 We inroduce his producion subsidy o allow us o undo he disorion in incenives for physical capial accumulaion arising from markups and he corporae profis ax in some of our counerfacual experimens. This will allow us o focus aenion on he impac of policies on welfare hrough heir impac on he dynamics of aggregae produciviy and no hrough heir impac on he incenives o accumulae capial relaive o an iniially disored equilibrium. 10

12 capial, and aggregae variable profis in he same manner. The research good is produced by compeiive firms (or in-house by inermediae good producing firms) using he echnology in equaion (7). These firms ake he produciviy of research labor as deermined by A r and Z φ 1 as given. They hire research labor a wage W and sell he research good a price P r. In equilibrium, P r = W /A r Z φ 1. Because he echnology in equaion (7) is consan reurns o scale, he wage bill for research exhauss revenues, so hese research good producing firms have no axable earnings. Tha is, P r Y r = W l r L in all periods. These resuls regarding facor shares imply a simple relaionship beween he innovaion inensiy of he economy as measured by he raio of spending on he research good o oupu inclusive of he producion subsidy, i r beween research and curren producion given by P ry r (1+τ y )Y and he allocaion of labor l r = µ l p 1 α i r. (13) Inermediae goods firms also choose innovaive invesmen for each produc ha hey manage. The dividend a ime per uni of ime associaed wih a produc wih fronier echnology z is given by D (z) = D s (z), where D = (1 τ corp ) µ 1 µ ( 1 + τy ) Y ( 1 τ corp λ I ) Pr M 1 ψ [(1 τ c ) x c + (1 τ m ) x m ], where τ c and τ m are raes a which incumben firms innovaive invesmens are subsidized and λ I is he rae a which incumben firms can expense heir innovaive invesmen for ax purposes. Each exising produc remains in he same incumben firm a + 1 wih probabiliy exp( δ c ) and has expeced size condiional on survival in he same firm equal o exp(ζ(x c ))s (z)z ρ 1 (14) /Z ρ In addiion, his firm anicipaes acquiring a /Z ρ 1 +1 wih probabiliy 1 exp( h(x m)). new produc wih expeced size of η m s (z)z ρ 1 Thus, he expeced discouned presen value of dividends associaed wih a produc of size s (z) a inclusive of he dividend a is direcly proporional o he size of he produc, i.e. i can be wrien as V s (z), where he facors of proporionaliy {V } saisfy he recursion Z ρ 1 V = D + exp( R )V +1 Z ρ 1 [exp ( δ c ) exp (ζ (x c )) + η m (1 exp ( h (x m )))] (15) +1 where he ineres rae R is defined by exp( R ) Q +1 /Q. 11

13 In equilibrium, enering firms mus earn non-posiive profis, so we mus have ( 1 τcorp λ E ) (1 τe ) P r M 1 ψ Z ρ 1 exp ( R ) V +1 Z ρ 1 +1 η e (16) where his expression is an equaliy if here is posiive invesmen in enry in period. In any period wih posiive enry, we can combine he firs order condiion for he opimal choice of x m o maximize he righ hand side of equaion (15) and (16) o obain a saic equaion deermining x m given by ( ) 1 τcorp λ I (1 τm ) η ( ) e = exp ( h (x m )) h (x m ). (17) 1 τcorp λ E (1 τe ) η m This condiion implies ha x m is consan in any periods in which enry is posiive. Likewise, in any period wih posiive enry, we can he firs order condiion for he opimal choice of x c o maximize he righ hand side of (15) and (16) o obain a saic equaion relaing x e, x m and x c given by ( 1 τcorp λ I ) (1 τc ) ( 1 τcorp λ E ) (1 τe ) η e = exp ( δ c (x m, x e )) exp (ζ (x c )) ζ (x c ) (18) Since x m is consan in all periods in which enry is posiive, equaion (18) defines an implici funcion x c (x e ) ha deermines x c as a funcion of x e in every period in which enry is posiive. In he Appendix, we show ha he derivaive dx c /dx e approaches zero in he limi as he lengh of a ime period in he model approaches zero. In his case, in he coninuous ime limi, equaion (18) implies ha x c is also consan in any periods in which enry is posiive. Household and governmen budge consrains Each period, he household collecs wage paymens W L, dividends from he physical capial firms, D k, and dividends from he incumben inermediae goods firms, D. The household also finances invesmen in enry ne of subsidies and axes (1 τ corp λ E )(1 τ e )P r M ψ x e and pays lump sum axes T. The governmen ses lump sum axes o finance he gap beween corporae ax receips and expendiures on subsidies for oupu and innovaive invesmen. Definiion of Equilibrium The economy sars wih iniial condiions for K 0, Z 0, and M 0 as given. The pahs for {L } and {A r } are given exogenously as well. An allocaion in his model is a sequence of variables { K +1, l p, l r, C, Y, Y r, Z +1, M +1, δ c } 12

14 and innovaive invesmens {x c, x m, x e }. An allocaion is feasible if i saisfies equaions (1)-(11). The vecor of prices and values in his economy are {Q, W, R k, P r, V, D k, D } ogeher wih a markup of price over marginal cos µ. The policies in his economy are he corporae ax rae τ corp, subsidy raes for innovaive invesmen τ c,τ m, and τ e, a subsidy rae for oupu of he final consumpion good τ y, and expensing allowances for physical invesmen λ K, innovaive invesmen by incumbens λ I, and innovaive invesmen in enry λ E. An equilibrium given policies is a feasible allocaion ogeher wih a vecor of prices and values and a markup such ha firms producing he final consumpion good, inermediae goods, and he research good, as well as he holding company for physical capial maximize profis, households maximize uiliy given heir budge consrain, he he governmen budge consrain is saisfied. Nesed Models Our model ness several commonly used models in he lieraure and has wo imporan feaures. The firs imporan feaure of our model is ha i permis sufficien aggregaion in equilibrium so ha he evoluion of aggregae produciviy and he oal measure of producs is a simple funcion of a few ypes of aggregae innovaive expendiure per produc (x c, x m, x e ) as in equaions (10) and (11). Noe ha we do no need o record oher aribues of he measure of fronier echnologies across producs M (z) as sae variables. This aggregaion dramaically simplifies he compuaion of ransiions relaive o models in which one mus keep rack of he full measure M (z) as a sae variable. Five commonly used models in he lieraure share his aggregaion propery: hree ypes of expanding varieies models and wo ypes of Neo-Schumpeerian models. We now discuss hese models. If δ e = δ m = 0, hen here is no business sealing and hence all new producs acquired by incumben and enering firms are new producs for sociey, expanding he measure of producs M. This is he assumpion ypically made in an expanding varieies model. Lumer (2007) is an example of an expanding varieies model in which here is only innovaive invesmen in enry. (Noe ha we do no consider he endogenous exi of producs due o fixed operaing coss feaured in ha paper.) Akeson and Bursein (2010) is an example of an expanding varieies model in which here is innovaive invesmen in enry and by incumben firms in coninuing producs. Lumer (2011) is an example of an expanding varieies model in which here is innovaive invesmen in enry and in he 13

15 acquisiion of new producs by incumben firms. Neo-Schumpeerian models based on he qualiy ladder framework ypically assume δ e = δ m = 1 and δ 0 = 0. The simples versions of hese models do no accommodae growh in he measure of varieies M. Grossman and Helpman (1991) and Aghion and Howi (1992) are examples of Neo-Schumpeerian models in which here is only innovaive invesmen in enry. Klee and Korum (2004) is an example of a Neo-Schumpeerian model in which here is innovaive invesmen in enry and by incumben firms in acquiring new producs (new o he firm, no o sociey). Acemoglu and Cao (2015) is an example of a Neo-Schumpeerian model in which here is innovaive invesmen in enry and by incumben firms in improving heir own producs. The second imporan feaure of our model is ha i allows for a simple and flexible reduced form specificaion of he echnology for producing real innovaive invesmen per produc (wha we call he echnology for research) ha ness hree specificaions of his echnology ha have played an imporan role in he lieraure. Specifically, from equaions (7) and (8), we can wrie a single consrain on real innovaive invesmen per produc x c + x m + x e = A r Z φ 1 M ψ 1 l r L. (19) We focus on hree specificaions of his echnology for research ha have played an imporan role in he lieraure (see Jones (2005) and Ha and Howi (2007) for a more exensive discussion). The firs specificaion of he echnology for research ha we consider has φ = 0.96 and ψ = 1. We refer o his firs specificaion as he Firs Generaion Endogenous Growh specificaion of he echnology for research. As we show below and as discussed in Jones (2005), wih φ close o one and ψ = 1, he economic implicaions of our model wih his echnology for research for he firs several cenuries of a ransiion o a new balanced growh pah resemble he ransiion dynamics of a fully endogenous growh model wih a research echnology wih φ = 1 and ψ = 1. The second specificaion of he echnology for research has φ = 1.67 and ψ = 1. This specificaion is similar o ha in Jones (2002), Korum (1997), or Segersrom (1998). In his specificaion of he echnology for research, ideas become harder o find in he sense ha increases in aggregae produciviy Z relaive o he pace of scienific progress A r lead o a reducion in he produciviy of labor allocaed o research in producing real innovaive invesmen per produc. Bloom e al. (2017) offer evidence for his specificaion of he echnology for research. We refer o his specificaion as Jones/Korum/Segersrom or J/K/S semi-endogenous growh specificaion of he research echnology. 14

16 The hird specificaion of he echnology for research has φ = 0.96 and ψ = 0. This specificaion is similar o ha in Pereo (1998), Segersrom (1998), Young (1998), Dinopoulos and Thompson (1998), Howi (1999), and Ha and Howi (2007). 11 In his specificaion, increases in he mass of producs M relaive o he pace of scienific progress A r lead o a reducion in he produciviy of labor allocaed o research in producing real innovaive invesmen per produc. We refer o his as he Second Generaion Endogenous Growh specificaion of he echnology for research. 3 Balanced Growh Pah We now describe how o solve for a balanced growh pah (BGP) of his economy given policies and model parameers. On a BGP, policies raes are consan, and he exogenous sequences for A r and L grow a consan raes ḡ A and ḡ L. Oupu Y, physical capial K +1, and consumpion C grow a a common rae ḡ Y. Aggregae produciviy Z +1 and he measure of producs M grow a raes ḡ Z and ḡ M. Innovaive invesmen raes per produc remain consan over ime a x c, x m, and x e. This las assumpion implies from equaion (8) ha he erm Y r M ψ 1 remains consan over ime as well. We firs discuss how o solve for he BGP growh raes. We hen disuss how o solve for he levels of variables on he BGP. BGP growh raes To solve for BGP growh raes, i is useful o consider he variable J Z 1 φ M 1 ψ ogeher wih he physical capial sock K as he endogenous sae variables of he economy. Since he erm Y r M ψ 1 is consan over ime on a BGP, equaions (7) and (8) imply ha he growh rae of J on a BGP depends only on he sum he growh of scienific progress and populaion and no on policies: ḡ J = (1 φ)ḡ Z + (1 ψ)ḡ M = ḡ A + ḡ L (20) Noe ha if ψ = 1, hen he growh rae of produciviy along he BGP, ḡ Z, is independen of policies. More generally, he division of he growh of J ino componens due o growh in aggregae produciviy Z and growh in he number of producs M depends on he parameers φ and ψ and on policies and he corrsponding mix of innovaive invesmen on a BGP as follows. 11 In he lieraure, i is ypical o parameerize he research echnology in his case wih φ = 1 and ψ = 0. Again, he implicaions of he model are no subsanially alered wih φ =

17 The value of x m on a BGP wih posiive enry is deermined from equaion (17) while he implici funcion x c (x e ) is deermined from equaion (18). The BGP level of x e is hen deermined from he equaion ḡ J = (1 φ) G ( x c ( x e ), x m, x e ) + (1 ψ) H ( x m, x e ) (21) In he appendix we presen condiions under which he righ hand side of his expression is sricly increasing in x e so a mos one posiive soluion o his equaion exiss. Once one solves for innovaive invesmens x c, x m,and x e, he growh raes of aggregae produciviy and he measure of producs are given by ḡ Z = G( x c ( x e ), x m, x e ) (22) and ḡ M = H( x m, x e ). (23) We hen have he sandard resul for he growh model ha ḡ Y = ḡ Z /(1 α) + ḡ L. BGP levels We now describe how o solve for he equilibrium levels of variables on a BGP given levels of A r and L r. The level of J Z 1 φ M 1 ψ is deermined on a BGP, bu he levels of Z and M individually on he BGP are no pinned down by BGP equaions alone. As discussed below, hese are deermined by he iniial condiions of he economy and he ransiion pah o he new BGP. We use he following equaions o solve for he level of variables on a BGP. The consumer s ineremporal Euler equaion gives he equilibrium BGP ineres rae R. From equaion (14), dividends from inermediae goods firms relaive o oupu inclusive of producion subsidies, d D / (( 1 + τ y ) Y ), are d = (1 τ corp ) µ 1 (1 τ corp λ I ) p r [(1 τ c ) x c + (1 τ m ) x m ] (24) µ where p r P rm 1 ψ ( 1 + τy ) Y. (25) 16

18 From equaion (15), he value of a produc relaive o oupu, v V /Y, is v = d 1 exp ( ( R ḡ Y )) (1 S e ), (26) where S e represens he share of labor employed in new firms wihin he period on a BGP, given by S e = η e x e exp ( (ρ 1) ḡ Z ). The BGP value of p r can be found as he soluion o he BGP version of he free enry condiion ( 1 τcorp λ E ) (1 τe ) p r x e = exp ( ( R ḡ Y )) v S e (27) in combinaion wih equaions (24) and (26). The BGP value of he research inensiy of he economy is ī r = p r ( x c + x m + x e ), and he allocaion of labor l r / ( 1 l r ) is obained from equaion (13). The raio of physical capial o oupu is given by he sandard Euler equaion from he profi maximizaion problem of he physical capial holding company exp( R) = ( ) 1 τcorp ( ) α ( ) 1 + τ y 1 τcorp λ K µ Ȳ +1 K +1 + exp ( δ K ) (28) Noe ha we canno solve for he levels of K +1 and Ȳ +1 unil we solve for he level of aggregae produciviy Z +1 as described below. Finally, from equaions (7) and (8) ogeher wih he definiion of J, we ge ha he level of J on a BGP is given by x c + x m + x e = A r lr L / J. (29) When ψ = 1, his equaion is sufficien o pin down he BGP level of produciviy Z. More generally, wih ψ < 1, here is a coninuum of pairs of Z and M each consisen wih he same value of J ha are candidae values of aggregae produciviy and he measure of producs on a BGP. The paricular values of Z and M ha arise on a paricular BGP depend upon he iniial condiions of he economy Z 0 and M 0 and he ransiion pah ha he economy akes o converge o BGP. Specifically, an equilibrium sequence of innovaive invesmens {x c, x m, x e } implies, hrough he funcions H and G defined above in equaions (10) and (11), a sequence of growh raes of M and Z. This sequence of growh raes can hen be used o race ou he pahs for he levels of M +1 and Z +1 from heir iniial condiions o heir levels on he BGP. We use a firs order approximaion of hese dynamics o solve for he levels of Z and M on a BGP as follows. 17

19 BGP level of aggregae produciviy To consruc our firs order approximaion o he dynamics of {J +1, Z +1, M +1 } we need o compue he elasiciies of he growh raes of hese variables wih respec o changes in invesmen in enry around he BGP. In compuing hese elasiciies, we make use of he resul ha x m = x m in every period of an equilibrium wih posiive enry. Thus, he resuls we develop below are condiional on he assumpion ha he ransiion pah of he equilibrium o BGP has posiive enry in every period. Define he elasiciy of he growh of aggregae produciviy wih respec o enry from equaion (22) as Θ G = [ G ( x c ( x e ), x m, x e ) d x c ( x e ) + ] G ( x c ( x e ), x m, x e ) x e (30) x c dx e x e where dx d e x c ( x e ) is compued from equaion (18). Similarly, define he elasiciy of he growh in he number of producs wih respec o enry from equaion (23) by Θ H = x e H ( x m, x e ) x e. (31) From he definiion of J we can define he elasiciy Θ J of he growh rae of J wih respec o changes in enry as Θ J = (1 φ) Θ G + (1 ψ) Θ H (32) We hen have he following proposiion ha allows us o pin down he BGP levels of aggregae produciviy and he measure of producs, Z 0 and M 0, from iniial condiions Z 0 and M 0 as follows. Proposiion 1. Given iniial values for Z 0, M 0, and J 0 = Z 1 φ 0 M 1 ψ 0 and he BGP level of J 0 from equaion (29), he BGP values of Z 0 and M 0 are, o a firs order approximaion given by log Z 0 = log Z 0 + Θ G Θ J (log J 0 log J 0 ) (33) where Θ G, Θ H and Θ J are evaluaed a he BGP. log M 0 = log M 0 + Θ H Θ J (log J 0 log J 0 ) (34) Wih hese soluions for he BGP levels of aggregae produciviy and he measure of producs, i is sraighforward o solve for he BGP levels of he physical capial sock and oupu given he BGP allocaion of labor o curren producion obained from equaion 18

20 (13) evaluaed a he BGP levels of p r and innovaive invesmen, he BGP physical capial o oupu raio obained from equaion (28), and he aggregae producion funcion (5). 4 Dynamics of Aggregae Produciviy We now consider he dynamics of aggregae produciviy implied by our model when he pah of research labor {l r L } is aken as exogenous. Our aim is o sudy which parameers of our model deermine he implicaions of he model for he shor and long erm responses of aggregae produciviy o a policy or demographically induced change in research labor as we discuss in he nex secion. Consider he pahs of quaniies Z = {Y r, x e, x m, x c, J +1, Z +1, M +1 } given iniial condiions for J 0, Z 0, M 0 and a pah of research labor {l r L }. Here we consider pahs for research labor {l r L } such ha he fracion of labor allocaed o research converges o is BGP value l r and populaion, L converges o is BGP pah { L r } and we consruc a firs order approximaion o he pahs for he variables in Z relaive he he BGP values of hese variables ha he economy is converging o. Here we assume ha, along he ransiion o he BGP, he raios (1 τ corpλ I)(1 τ m ) (1 τ corp λ E)(1 τ e ) and (1 τ corpλ I)(1 τ c ) remain consan. (1 τ corp λ E)(1 τ e ) This firs order approximaion is obained from he following equaions. As discussed above, equaion (17) implies ha wih posiive enry, x m = x m. Thus, equaions (7), (8), and (18) imply ha, o a firs order approximaion A (log x e log x e ) = ( log l r log l r ) + (log L log L ) (log J log J ) (35) where [ d ] A dxe x c ( x e ) + 1 x e, (36) x c + x m + x e and d dx e x c ( x e ) is compued from equaion (18) evaluaed a he BGP values of invesmen. Define Θ Θ J A. (37) Then, from he firs order approximaion around equaion (21), we have log J +1 log J +1 = Θ [( log l r log l r ) + (log L log L ) ] + (1 Θ) (log J log J ). The iniial condiion of his AR1 process, log J 0 log J 0, is given. We now develop he following analog of Proposiion 6 from AB2018 regarding he (38) 19

21 dynamics of he variable J. Proposiion 2. From he AR1 represenaion (38), we have ha o a firs order approximaion, he dynamics of log J in he ransiion o a BGP wih posiive enry are given by log J +1 log J +1 = Θ (1 Θ) j [( log l r j log l ) ( )] r + log L j log L + (39) j=0 + (1 Θ) +1 (log J 0 log J 0 ) The proof is by direc calculaion. Once we solve for he dynamics of J, he dynamics of aggregae produciviy Z and he measure of producs are given by he ime version of equaions (33) and (34), log Z log Z = Θ G Θ J (log J log J ) (40) log M log M = Θ H Θ J (log J log J ) (41) For many of our policy experimens, we make use of he following corollary o Proposiion 2. Corollary 1. Suppose he economy sars a = 0 on some iniial BGP, and here is a change in he economic environmen ha leaves he growh raes {g A } and {g L } unchanged, and he allocaion of innovaive invesmen x c, x m, x e is unchanged across BGPs. Then, o a firs order approximaion, he dynamics of aggregae produciviy relaive o is iniial BGP pah are given by log Z +1 log Z 0 ḡ Z = Θ G A (1 Θ) j ( ) log l r j log l r0 j=0 We see here from equaion (42) ha, under he condiions of Corollary 1, he dynamics of aggregae produciviy relaive o is rend on he iniial BGP can be summarized by wo sufficien saisics. We refer o he firs of hese saisics, Θ G /A, as he impac elasiciy of a change in research labor a on he level of aggregae produciviy a + 1 relaive o is iniial level. We refer o he second of hese saisics, 1 Θ as he persisence of he response of aggregae produciviy o an exogenous reallocaion of labor o research. Observe ha he impac elasiciy of an increase in labor devoed o research on aggregae produciviy relaive o is new BGP level is independen of he specificaion of he research good echnology indexed by φ and ψ. Insead, i is deermined by he parameers (42) 20

22 ha shape our model s implicaions for firm dynamics and he allocaion of innovaive invesmen across incumben and enering firms. Specifically, he elasiciy Θ G is bounded above by he conribuion of enry o aggregae produciviy growh, i.e. Θ G 1 G( x c, x m, x e ) ρ 1 G( x c, x m, 0) ρ 1 ρ 1 exp ((ρ 1)ḡ Z ) = 1 ( 1 δ ) e ρ 1 η e S e, (43) where S e denoed he share of producion employmen in enering firms on he BGP. The parameer A is bounded above by he share of innovaive invesmen by enering firms in oal innovaive invesmen. As we show in he appendix, boh Θ G and A converge o hese upper bounds as he lengh a ime period in calendar ime shrinks o zero. Likewise, he elasiciy Θ H is given by he conribuion of enry o he growh in he measure of producs, ha is Θ H = H( x m, x e ) H( x m, 0) exp(ḡ M ) = (1 δ e ) F e, where F e denoes he fracion of producs produced by newly enered firms. In conras, he persisence of his impac, which is deermined by he parameer 1 Θ in equaion (37), is highly sensiive o he he parameers φ and ψ of he research good echnology. This is because he elasiciy Θ J, defined in equaion (32), depends on hese parameers. We discuss he quaniaive implicaions of hese observaions when we consider he ransiion dynamics for aggregae produciviy implied by various specificaions of our model nex. Quaniaive implicaions of analyic resuls We now conduc experimens o explore he quaniaive implicaions of differen specificaions of our model for he dynamics of aggregae produciviy a shor, medium, and long erm horizons. We calibrae all specificaions of our model as described in greaer deail in he appendix. We se he elasiciy of subsiuion beween inermediae goods in producion o ρ = 4. As discussed above, he elasiciies Θ G and Θ H on he iniial BGP can be idenified by calibraing our model o mach daa on firm dynamics. We consider wo specificaions of hese parameers. In he firs, we assume ha here is no business sealing by enrans, i.e. δ e = 0. This specificaion is of ineres because i delivers he maximum values of Θ G and Θ H consisen wih daa on he shares of employmen and producs in enering firms. In our second specificaion, we se he business sealing parameer δ e so ha he conribuion of enrans o aggregae produciviy growh in equaion (43) is equal o 21

23 ha esimaed in Akcigi and Kerr (2018). As described in our calibraion appendix, o calibrae he parameer A on he iniial BGP we measure expendiures on innovaion by incumben firms using NIPA daa and infer expendiure on innovaion by enering firms from equaion (16). We consider he hree specificaions of he echnology for research described in subsecion 2. This gives us a oal of six model specificaions o consider. We consider a change in he allocaion of labor o research a ime = 0 of 10% (specifically of magniude log l r0 log l r = 0.10) saring from an iniial BGP calibraed as above, and assume ha he allocaion of labor o research remains a his elevaed level permanenly. We assume ha he allocaion of real innovaive invesmen x c, x m, x e is he same a = 0 as i is on he BGP o which he economy is converging. These assumpions saisfy he condiions in Corollary 1, so we can use equaion (42) o characerize he dynamics of aggregae produciviy and daa from he economy a = 0 o measure he elasiciies required o use his equaion. Given he impac elasiciy Θ G /A implied by daa on firm dynamics and our measuremen of he share of innovaive invesmen underaken by enering firms, he response on impac of aggregae produciviy growh a an annual frequency relaive o he iniial BGP rend wih respec o a reallocaion of labor o research of size log l r0 log l r = 0.10 is (ha is, aggregae produciviy would be 0.28 percen higher afer he firs year) if here is no business sealing and wih business sealing. As discussed above, hese implicaions of our model are independen of he specificaion of he echnology for research. In conras, he specificaion of he research echnologies as indexed by φ and ψ has a remendous impac on he implicaions of he model for he persisence of any impluse o aggregae produciviy. In Table 1, we repor he level of aggregae produciviy relaive o is prior rend a horizons of 20 and 100 years ha resuls from a hundred year long reallocaion of labor o research of magniude log l r log l r = As a heoreical maer, his cumulaive impac over various horizons of a long-lasing reallocaion of labor o research are he manifesaion of he model s implied persisence of an impulse o aggregae produciviy from a one-ime reallocaion of labor. Hence, in Table 1 we also repor he half-life of a one-ime impulse o aggregae produciviy. We see ha for he Firs Generaion Endogenous Growh specificaion of he research echnology, an impulse o aggregae produciviy from a one-ime reallocaion of labor o research is essenially permanen. This implies ha he cumulaive response of aggregae produciviy relaive o is iniial rend afer 20 and 100 years is equal o 20 and 100 imes he response of aggregae produciviy growh on impac respecively. For he J/K/S and Second Generaion Endogenous Growh specificaions of he research echnology, his is 22