WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE?


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1 MŰHELYTANULMÁNYOK DISCUSSION PAPERS MT DP. 2005/19 WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE? BERTHOLD HERRENDORF ÁKOS VALENTINYI Magyar Tudományos Akadéma Közgazdaságtudomány Intézet Budapest
2 KTI/IE Dscusson Papers 2005/19 Insttute of Economcs Hungaran Academy of Scences KTI/IE Dscusson Papers are crculated to promote dscusson and provoque comments. Any references to dscusson papers should clearly state that the paper s prelmnary. Materals publshed n ths seres may subject to further publcaton. Whch Sectors Make the Poor Countres so Unproductve? Authors: Berthold HERRENDORF, Arzona State Unversty, W.P. Carey School of Busness, Department of Economcs Emal: Ákos VALENTINYI, Unversty of Southampton; Insttute of Economcs, Hungaran Academy of Scences; CEPR Emal: We thank Edward Prescott, Rchard Rogerson, and Arlton Texera for ther help and for many useful dscussons about ths paper. We have profted from the comments of Mchele Boldrn, Gueorgu Kambourov, István Kónya, Dego Restucca, James Schmtz and the semnar partcpants at ASU, Budapest, Carlos III, Kentucky, Madmac Cemf), Mnnesota FED, the 2005 CEPR Summer Symposum n Internatonal Macro, the 2005 SED Conference, Smon Fraser, Toronto, and Western Ontaro. Herrendorf acknowledges research fundng from the Spansh Dreccón General de Investgacón Grant BEC ) and Valentny acknowledges research fundng from the Hungaran Scentfc Research Fund OTKA) project T/16 T ISSN X ISBN Publshed by the Insttute of Economcs Hungaran Academy of Scences Budapest, 2005
3 MŰHELYTANULMÁNYOK DISCUSSION PAPERS MT DP. 2005/19. BERTHOLD HERRENDORF VALENTINYI ÁKOS MELY SZEKTOROK MAGYARÁZZÁK SZEGÉNY ORSZÁGOK ALA CSONY TERMELÉKENYSÉGÉT? Összefoglaló A növekedés elszámolások standard eredménye szernt jelentősek az országok között az aggregált teljes tényezőtermelékenységben TFP) mutatkozó különbségek. Ebben a munkában arra keressük a választ, hogy vajon ezek az aggregált TFPben mutatkozó különbségek meghatározott szektorok TFPjében levő különbségekre vezethetőke vssza, és ha gen, akkor melyek ezek a problémás szektorok. Ennek a kérdésnek a megválaszolásához a gazdaságot négy szektorra bontjuk, ellentétben a korább hasonló elemzésekkel, amelyek a gazdaságot két szektorra bontották. Az általunk választott négy szektor szolgáltatásokat külkereskedelembe be nem kerülő fogyasztás jószág), fogyasztása jószágokat külkereskedelembe bekerülő fogyasztás jószág), építés beruházás javakat külkereskedelembe be nem kerülő beruházás jószág) és gépberuházás javakat külkereskedelembe bekerülő beruházás jószág) állít elő. Modellünknek a Penn World Tables referenca évre vonatkozó adatbázsához valókalbrálása révén arra a megállapításra jutottunk, hogy a külkereskedelembe bekerülő jószágokat termelő szektorok TFPjében sokkal nagyobbak az országok között különbségek, mnt a külkereskedelembe be nem kerülő jószágokat termelő szektorokéban. Ez konzsztens a BalassaSamuelson hpotézssel. Ezenkívül eredményünk azt s mutatja, hogy a külkereskedelembe bekerülő jószágokat termelő szektorok közül a gépberuházás javakat előállító szektor TFPjében nagyobbak az országok között különbségek, mnt a fogyasztás javakat előállító szektoréban. Eredményenk egyfelől képesek a korább kétszektoros elemzések egymásnak ellentmondó eredményet értelmezn, másfelől megmutatják, hogy mlyen krtérumnak kell megfelelne a gazdaság fejlődés egy skeres elméletének. Kulcsszavak: gazdaság fejlettség tényező, szektor TFP; relatív árak.
4 MŰHELYTANULMÁNYOK DISCUSSION PAPERS MT DP. 2005/19. BERTHOLD HERRENDORF  ÁKOS VALENTINYI WHICH SECTORS MAKE THE POOR COUNTRIES SO UNPRODUCTIVE? Abstract Standard growth accountng exercses fnd large cross country dfferences n aggregate TFP. Here we ask whether specfc sectors are drvng these dfferences, and, f ths s the case, whch these problem sectors are. We argue that to answer these questons we need to consder four sectors. In contrast, the lterature typcally consders only two sectors. Our four sectors produce servces nontradable consumpton), consumpton goods tradable consumpton), constructon nontradable nvestment), and machnery and equpment tradable nvestment). Interactng the data from the 1996 benchmark study of the Penn World Tables wth economc theory, we fnd that the TFP dfferences across countres are much larger n the two tradable sectors than n the two nontradable sectors. Ths s consstent wth the Balassa Samuelson hypothess. We also fnd that wthn the tradable sectors the TFP dfferences are much larger n machnery and equpment than n consumpton goods. We llustrate the usefulness of our fndngs by accountng for the conflctng results of the exstng two sector analyses and by developng crtera for a successful theory of aggregate TFP. Keywords: development accountng; sector TFPs; relatve prces. JEL classfcaton: O14, O41, O47.
5 1 Introducton One of the major challenges n economcs s to account for the huge nternatonal dsparty n ncome. Standard growth accountng exercses fnd that cross country dfferences n aggregate total factor productvty TFP henceforth) cause a szeable part of the dfferences n GDP per capta. 1 Ths suggests that we need to understand where the TFP dfferences come from. A growng lterature addresses ths ssue and shows that cross country dfferences n the nsttutonal envronment or n polces can cause dfferences n TFP. 2 In ths paper, we argue that nformaton about the sectoral patterns of TFP dfferences can help to dscrmnate among the exstng theores. We therefore ask whether specfc sectors are drvng the aggregate TFP dfferences, and, f ths s the case, whch these problem sectors are. A key challenge n measurng sector TFPs comes from the lmted avalable data. Unfortunately, dsaggregate and comparable data on sector nputs and outputs does not exst for a wde range of rch and poor countres. 3 The only broad source of comparable and dsaggregate cross country data s the Penn World Tables as provded by Heston et al. 2002). We wll work wth the largest and most recent benchmark study from 1996 PWT96 henceforth), whch provdes nformaton about expendtures, purchase prces, and quanttes. We wll nteract ths nformaton wth economc theory so as to nfer the sector nputs and outputs needed to calculate sector TFPs. Our approach follows Hseh and Klenow 2003) n that t utlzes that dfferences between sector TFPs lead to dfferences n the observable correspondng relatve prces. Our approach extends Hseh and Klenow 2003) n that we dsaggregate further and pay closer attenton to factors other than TFP dfferences that can cause observable relatve prces to dffer. Moreover, Hseh and Klenow 2003) asked the dfferent queston what can account for the fact that across countres nvestment quanttes are strongly postvely correlated wth 1 See, for example, Klenow and RodrguezClare 1997), Prescott 1998), Hall and Jones 1999), Hendrcks 2002), and Casell 2004). 2 See, for example, Holmes and Schmtz 1995), Parente and Prescott 1999), Acemoglu et al. 2001), Amaral and Quntn 2004), Erosa and Hdalgo 2004), Casell and Coleman 2005), Herrendorf and Texera 2005a,b) and Cole et al. 2005). 3 The McKnsey Global Insttute collected frm level data for a small number of countres, but that data s not publcly avalable. The OECD has sector data for many of ts members, but poorer countres are not OECD members. 1
6 ncome. 4 We argue that n order to understand sectoral TFP patterns, t s mportant to dsaggregate to four sectors. In contrast, the lterature typcally consders only two sectors: growth theorsts dstngush between consumpton and nvestment whle trade theorsts dstngush between tradables and nontradables. We come to our vew because both consumpton and nvestment have szeable tradable and nontradable components and the prces of the tradable relatve to the nontradable components vary systematcally wth GDP. To the extent that these prce varatons reflect varatons n sector TFPs, we can gan mportant nformaton from dsaggregatng consumpton and nvestment nto ther nontradable and tradable components. We therefore buld a model wth the followng four sectors: servces nontradable consumpton), consumpton goods tradable consumpton), constructon nontradable nvestment), and equpment nvestment tradable nvestment). Snce we consder constructon and equpment nvestment separately, another novelty of our model s that t has two dfferent captal stocks, namely the stocks of buldngs and equpment. Our model also pays close attenton to two factors other than sector TFP dfferences that can cause relatve purchase prces to dffer across countres: taxes broadly defned and dstrbuton servces. Examples of taxes nclude value added taxes, tarffs, brbes, and rents from monopoly power. Dstrbuton servces are retal, wholesale, and transport servces. Both affect the purchases prce but not the producer prces. Our man fndng s that there are huge crosscountry dfferences n the TFPs of the two tradable sectors and consderably smaller crosscountry dfferences n the TFPs of the two nontradable sectors. We also fnd that wthn the tradable sectors, the nternatonal TFP dspartes are larger n machnery and equpment nvestment than n consumpton goods. A successful theory of aggregate TFP ought to be consstent wth these fndngs. At ths stage, t s not clear to us how well the exstng theores do n ths respect. They attrbute the cross country dfferences n TFP to exogenous cross country dfferences n nsttutons or polces. Ths rases the queston why these exogenous dfferences do so much more damage n the tradable sectors than n the nontradable ones. 4 Casell and Coleman 2005) s also related to our approach n that they use nformaton about relatve wages to learn about the elastcty of substtuton between sklled and unsklled labor. 2
7 Here we have abstracted from human captal. It s well known that unmeasured cross country dfferences n human captal show up as cross country dfferences n TFP, but t s stll hotly debated for how much human captal can account. 5 Be that as t may, our dsaggregate four sector analyss has the testable mplcaton that unmeasured dfferences n human captal should cause the largest TFP dfferences n the sectors that have the largest labor shares. Carefully measurng the captal shares of our four sectors for the U.S., t turns out that the labor share n the nontradables s larger than n tradables. Whle ths speaks aganst smple theores of human captal, t stll leaves room for more sophstcated ones. For example, Acemoglu and Zlbott 2001) argued that poorer countres fnd t hard to adopt new technologes because sklled workers that can operate them are scarce. 6 If ths matters more n the tradable than n the nontradable sectors for example because the technologes there are more skll ntensve), then unmeasured dfferences n human captal can cause sector TFP dfferences that lne up wth our fndngs. Another possblty s that bad nsttutons n poorer countres allow rent extracton manly n the nontradable sectors, as nternatonal competton lmts t n the tradable ones. Ths could dstort the allocaton of sklled workers towards the nontradable sectors, n whch case unmeasured dfferences n human captal would lead to larger sector TFP dfferences n the tradables. We leave explorng these deas to future research. The mportance of our four sector approach s llustrated by comparng our results to the exstng ones. Whle the lterature has produced sound evdence suggestng that there are problem sectors, t has not produced conclusve evdence as to whch these problem sectors are. For example, many years ago Balassa 1964) and Samuelson 1964) conjectured that the cross country dfferences n labor productvty are much larger n the tradable sectors than n the nontradable ones. 7 In sharp contrast, Lews 2004) has argued recently that the frm level evdence collected by the McKnsey Global Insttute ponts to the nontradable sectors as the problem sectors. 8 If we use our results and compute the labor productvtes of the aggregate 5 See for example Barro 1991), Barro and Lee 1994) Mankw et al. 1992), Bls and Klenow 2000), Hendrcks 2002), Erosa et al. 2005), and Manuell and Seshadr 2005). 6 Ths s a verson of the approprate technology hypothess; see also Basu and Wel 1998). 7 Rogoff 1996) offers a revew of the lterature on the Balassa Samuelson hypothess. He concludes that the supportng evdence s surprsngly scant and mostly ndrect. 8 See also Baley and Solow 2001). 3
8 tradables and nontradables categores, then we confrm the conjecture of Balassa 1964) and Samuelson 1964). Ths suggests that the results of the McKnsey Studes, whch comprse only a relatvely small number of countres, do not generalze to a broad cross secton. 9 A second group of two sector analyses dentfed completely dfferent problem sectors. On the one hand, Kuznets 1971) found that cross country dfferences n labor productvty are much larger n agrculture than n the aggregate of the other goods. 10 On the other hand, Hseh and Klenow 2003) found that cross country dfferences n TFP are much larger n nvestment than n consumpton. Snce agrculture s a part of consumpton, these two fndngs seem opposte of each other. Our more dsaggregate four sector explans why they coexst nonetheless. If we aggregate the nontradable consumpton and tradable and nontradable nvestment and compute the labor productvtes of consumpton goods and the other goods, we fnd that consumpton goods are the problem sector. In contrast, f we aggregate nontradable and tradable components and compute the sector TFPs of aggregate consumpton and nvestment, we fnd that nvestment s the problem sector. In other words, the explanaton for the very dfferent results from two sector analyses s that sector TFPs dffer across countres at a more dsaggregate level. The next secton lays out the economc envronment. Secton 3 defnes the compettve equlbrum. Secton 4 descrbes our measurement and the calbraton of our model. We report our fndngs n Secton 5 and conclude n Secton 6. An appendx contans all proofs and a detaled descrpton of our data work. 2 Envronment There s a fnte set J of small open economes. Tme s dscrete and runs forever. All fnal goods are tradable wthn each country, but they may or may not be tradable across countres. We call a fnal good tradable f t s tradable across countres and nontradable f t s not. In 9 To be precse, McKnsey have frm level data on 10 countres. The only developng countres n ths data set are Inda and Brazl. 10 More recent related studes nclude Restucca et al. 2003), Córdoba and Rpoll 2004), and Golln et al. 2004). 4
9 each perod, there are four fnal goods: nontradable and tradable consumpton and nontradable and tradable nvestment. For concreteness we call them servces x s, constructon of buldng x b, consumpton goods x g, and equpment nvestment x e. We denote the set of goods ndces by I {s, b, g, e}. Constructon and equpment nvestment augment the stocks of buldngs k b and equpment k e, whch deprecate at the rates δ b, δ e 0, 1). 11 Each economy j J s populated by a representatve household, whose preferences are descrbed by the utlty functon: 12 β t u xst, j xgt) j. 1) t=0 β 0, 1) s the dscount factor and u has the standard regularty propertes. The representatve household s endowed wth one unt of labor n each perod and wth postve stocks of buldngs k j b0 and equpment k j e0 n the ntal perod. All technologes have constant returns to scale. There s no technologcal progress. Ths s wthout loss of generalty here, as we are nterested n ratos that along balanced growth paths are constant and ndependent of growth rates. Country j J produces fnal good I accordng to y j = F j k j b, k j e, l j ). 2) k b and k e are the stocks of buldngs and equpment and l s the labor allocated to the producton of y. F j has the usual regularty propertes. Note that F j dffers across goods and countres. We wll be more specfc on the nature of these dfferences n Subsecton 4.1 below when we specfy functonal forms. Tradable output s sold n the world market and delverng t from there to household requres dstrbuton servces. Bursten et al. 2003, 2004) document that the share of dstrbuton servces n the purchase prce of tradable goods the so called dstrbuton margn) can be large quanttatvely. 13 To capture ths, we assume that the producton functon for delverng x unts 11 Note that some authors use the terms structures and resdental housng and machnery and equpment nstead. 12 We wll specfy functonal forms below when we do our quanttatve exercse. 13 We do not consder a dstrbuton margn for constructon because the IO tables do not report t. We do not 5
10 of tradable good {g, e} to the representatve household n country j s gven by x j = G y j, y j s ), 3) where y j s the quantty of good that s purchased n the world market and y j s are the dstrbuton servces. G has the standard regularty propertes of a producton functon. Agan we wll be more specfc Subsecton 4.1 below. 3 Compettve Equlbrum We abstract from the possblty that assets are traded across countres. Ths s wthout loss of generalty because we wll restrct our attenton to balanced growth path comparsons. In each perod there are markets for each fnal good and each factor of producton. The market clearng condtons are: p gy j g y j g) + y j e y j e) = 0 4a) xs j + ysg j + yse j = ys, j x j b = y j b, 4b) k j b = k j b, k e j = k j e, 1 = l j, j J. 4c) I I I The frst condton says that trade must be balanced n each country. 14 The second condton says that the purchases of servces by the household and the dstrbuton sector must equal the producton of servces. Note that ths mplctly assumes that consumed servces and dstrbuton servces are perfect substtutes. The reason for ths assumpton s that we do not have nformaton about the relatve prces of the two n our data set. The thrd condton says that the purchases of new buldngs must equal the constructon of buldngs. The last three condtons say that the three factors owned by the household must equal the sums of the quanttes rented by the four sectors. consder a dstrbuton margn for servces because dstrbuton servces are servces. 14 Recall that we don t have borrowng and lendng across countres. Recall too that we consder small open economes, so we do not need to mpose world market clearng for the tradable goods. 6
11 We take nto account that taxes can be a source of crosscountry dfferences n observable relatve prces, as suggested by Char et al. 1996) and Restucca and Urruta 2001). We defne taxes broadly as any dstorton that ncreases the purchase prce and gets rebated to the households. Examples nclude value added taxes, tarffs, brbes, and monopoly rents. The tax rates are denoted by τ j t where I and j J. The tax revenues are rebated to the households through lumpsum transfers Λ j t. The fact that they are rebated dstngush taxes from sector TFPs: a decrease n a sector s TFP has the same effect on the relatve prce as an ncrease n the tax, but only the tax revenue gets rebated to the representatve household. We choose equpment n the world market as the numerare: p e = 1. We denote the relatve world market prce of consumpton goods before delvery by p g, the relatve producer prces by p j j, the relatve purchase prces after delvery and taxes by P, and the rental rates by r j b, r e, j and w j where, j) I J. For convenence, we defne the followng column vectors: τ τ s, τ b, τ g, τ e ), r r b, r e ), x x s, x b, x g, x e ), 5a) P P s, P b, P g, P e ), p p s, p b, p g, p e ), 5b) k k b, k e ), k k b, k e ), 5c) k b k bs, k bb, k bg, k be ), k e k es, k eb, k eg, k ee ), 5d) y y s, y b, y g, y e ), l l s, l b, l g, l e ). 5e) Defnton 1 Compettve Equlbrum) Gven sequences of taxes and rebates {τ j t, Λ j t } t=0 where j J, a compettve equlbrum conssts of sequences of relatve prces {P j t, p g, p j t, r j t, w j t } j t=0, household allocatons {xt, k j t+1 } t=0, frm allocatons {y j t, k j t, l j t } t=0, {x j t, y j t, y j st } t=0 for {g, e} such that: 1. p j g = p g and p j e = 1; 7
12 2. gven prces, {x j t, k j t+1 } t=0 solve the problem of the household n country j:15 s.t. max {x j t,k j t+1 } t=0 β t uxst, j xgt) j t=0 p j t ) x j t = r j t ) k j t + w j t + Λ j t, 6a) k j t+1 = 1 δ )k j t + x j t {b, e}, x j t, k j t+1 0, k j 0 > 0 gven; 3. gven prces, {y j t, k j t, l j t } t=0 solve the problem of the frm n sector I: max p j {y j t,k j t,l j t } t y j t r j t ) k j t w j t l j t s.t. 2); 6b) 4. gven prces, {x j t, y j t, y j st } t=0 for {g, e} solve the problems of the frms n the dstrbuton sector: max {x j gt,y j gt,y j sgt } max {x j et,y j et,y j set } j Pgt 1 + τ j gt j Pet 1 + τ j et x j gt p gty j gt + p j sty j sgt) s.t. 3), x j et y j et + p j sty j set) s.t. 3); 6c) 6d) 5. markets clear, that s, 4) hold. 4 Data and Measurement 4.1 Defntons We work wth the PWT96, that s, the 1996 Benchmark Study of the Penn World Tables. The PWT96 s a farly dsaggregate cross secton for 1996, whch s collected wthn the Internatonal Comparsons Program. It contans nformaton about expendtures, purchased quanttes, 15 Note that profts are zero n compettve equlbrum, so we suppress them. 8
13 Fgure 1: The composton of consumpton and nvestment Share of servces n consumpton expendture at nternatonal $ Log of per capta GDP at nternatonal $s Share of constructon n nvestment expendture at nternatonal $ Log of per capta GDP at nternatonal $s and purchase prces for 30 categores n 98 countres wth more than 1 mllon nhabtants. 16 We are gong to apply our model to three economes: the U.S., Latn Amerca, and the 20 poorest countres n our sample. 17 We represent them by the superscrpts US, LA, and PC, so j J {US, LA, PC}. Two remarks about our choce of countres are at order. Frst, our small economy assumpton s somewhat questonable for the U.S. We make t nonetheless because the alternatve would be to assume that the world market clears among our three economes. Ths s more questonable, as most of U.S. trade s wth countres outsde of the set consdered here. Second, we calculate the relevant statstcs for Latn Amerca and the Poorest Countres as the averages of the member countres statstcs. Snce we have data only for 1996, we hope that takng averages across broad sets of countres wll elmnate the devatons that ndvdual countres may experence from ther balanced growth paths. Because of ths concern, we do not consder countres such as Inda and Chna, who are typcally vewed as beng n a transton. We now aggregate the 30 expendture categores of the PWT96 to our four sectors. To do ths, we make a judgment about each categores as to whether t s manly nontradable or tradable and manly nvestment or consumpton. The detals are descrbed n Appendx B.1.1. The resultng assgnment s very smlar to that typcally used n other studes; see for example de Gregoro et al. 1994). Havng formed our four sectors, we can provde the 16 We restrct our attenton to benchmark years and countres, because only for those the Internatonal Comparsons Program actually collects the data. 17 The dentty of the Latn Amercan countres and the twenty poorest countres of our sample can be found n Appendx B.1. 9
14 Fgure 2: Prces of nontradables relatve to tradables Prce of servces over prce of consumpton good Log of per capta GDP at nternatonal $s Prce of constructon over prce of equpment Log of per capta GDP at nternatonal $s evdence that made us dsaggregate to our four, nstead of two, sectors. 18 Fgure 1 shows that both consumpton and nvestment have large nontradable and tradable parts. Fgure 2 shows that for both consumpton and nvestment the prces of the tradable relatve to the nontradable component ncrease systematcally wth ncome. To the extent that relatve prces reflect relatve sector TFPs, mportant nformaton should be obtaned from dsaggregatng consumpton and nvestment nto ther nontradable and tradable components. For completeness, Fgure 3 n Appendx C also shows the usual way of reportng relatve prce varatons across countres, namely by lookng at the prce of nontradables relatve to tradables or by lookng at the prce of consumpton relatve to nvestment. Both ncrease systematcally wth ncome too. Next, we need to dscuss what happens when countres specalze. A country that specalzes produces only one of the two tradable goods and replaces the domestc technology for the other tradable good by the world market technology, so t can obtan the other tradable good at the world market prce. We can avod dealng wth the dfferent possble specalzaton patterns f we endow each country wth the world market technology of exchangng the two tradable goods, that s, f we restrct the domestc technologes such that the margnal rate of transformaton between the two tradables equals p g n all countres. Gven ths restrcton, we can wthout loss of generalty restrct our attenton to the equlbrum n whch all countres produce everythng themselves, so exports and mports are zero. Whle ths may seem restrctve, t s easy to show that n any equlbrum wth or wthout specalzaton) the margnal rates 18 Appendx B.1 explans n detal how to compute the prces and quanttes of our four categores. 10
15 of transformaton for the operated technologes equal p g anyways and the followng varables are the same: the relatve prces, the consumed and produced quanttes of nontradables, the consumed quanttes of tradables and the world productons of tradables, and welfare. In other words, equlbra wth dfferent specalzaton patters only dffer wth respect to the quanttes of tradables that the dfferent countres produce. Snce we the PWT96 has no nformaton about the quanttes produced, we do not have nothng to say about them here anyways. To compute our model, we also need to adopt functonal forms. We work wth the followng ones: ux j s, x j g) log x j s) α x j g x g ) 1 α) j J, I, 7a) F j k j b, k j e, l j ) A j k j )θ l j )1 θ, k j [ µ 1 σ k j b ) σ 1 σ + 1 µ) 1 G y j, y j s ) mn { y j, ψ y j s } σ k j e ) σ 1 σ j J, {g, e}. 7b) ] σ σ 1 j J, I, 7c) 7d) α 0, 1) and x g 0, ) are constants that determne the expendture share of servces. Snce our consumpton goods nclude food and beverages, we nterpret x g as the subsstence level of consumpton goods. Havng x g > 0 allows us to match the fact that both the relatve prce of servces and the expendture share of servce are much lower n the poorer countres than n the U.S.. For the same reason, several recent studes, ncludng Kongsamut et al. 2001) and Golln et al. 2004), assumed subsstence terms. The producton functon has the standard Cobb Douglas form n captal and labor, but here captal s a CES aggregator of the stocks of buldngs and equpment. Specfcally, A j s the TFP of producng y n country j, θ 0, 1) s the captal share whch possbly dffers across sectors but s restrcted to be the same across countres), σ [0, ) s the elastcty of substtuton between buldngs and equpment, µ 0, 1) determnes the share of buldngs n output. The producton functon of the dstrbuton sector s Leontef. ψ 0, ) determnes the dstrbuton servces requred to delver one unt of x, {g, e}. 11
16 4.2 Measurement We now explan how we choose the model parameters and how we measure the taxes and the sector TFPs. We normalze A US e = 1. We assume that all taxes are zero n the U.S.: τ US = 0 for I. Ths leaves us wth 32 parameters. Specfcally, there are 21 technology parameters: the 11 remanng sectoral TFPs; the 4 captal shares; the 2 parameters n the CES aggregator of buldngs and equpment; the 2 parameters of the dstrbuton technologes; the 2 deprecaton rates. Moreover, we have the 3 preference parameters namely β, α, and x g and 8 taxes for Latn Amerca and the Poorest Countres. We wll calbrate 8 of these parameter values to the U.S. economy. These are the two deprecaton rates, the four sector captal shares, and the two parameters of the dstrbuton technology. Gven these 8 values, we wll choose the remanng 24 parameter values so as to match as closely as possble 28 dfferent statstcs from the PWT96. Among these 24 parameters are the 11 sectoral TFPs, so what we are dong here really s an exercse n measurement. We start by explanng how we calbrate to the U.S. economy. We calculate the sector captal shares from the U.S. nput output tables of 1997 as reported by the Bureau of Economc Analyss 4 statstcs). 19 Ths s less straghtforward than t mght seem at frst sght. To begn wth, propretor s ncome contans a labor component whch needs to be ncluded n the labor share. Moreover, snce our data has no nformaton about ntermedate nputs, we have not modeled them here. Ths mples that the captal shares n the model contan the payments to captal that accrue when ntermedate nputs are produced whereas the captal shares n the data shares do not contan these. Appendx B.1 reports the detaled steps requred to take care of ths. Followng these steps, we fnd the followng captal shares: 0.32 for servces, 0.20 for constructon, 0.39 for consumpton goods, and 0.31 for equpment. Once we have our 19 The data of BEA do not allow us to compute the captal shares for 1996, the year of our cross secton n the PWTs s the closest year for whch data s avalable. Note that for each sector n the PWT96 we needed to make a call as to whch of our four model sectors t should go. In contrast, we do not need to make that call n the nput output tables, as they provde more detaled nformaton. In partcular, the counterparts of our four sectors n the nput output tables are as follows: servces equal the sale to fnal expendture by all sectors except agrculture, mnng, manufacturng, personal transportaton equpment, and constructon; constructon equals the constructon commodtes delvered to fnal expendture fxed nvestment; consumpton goods equal the agrculture, mnng, and manufacturng commodtes not delvered to fnal expendture fxed nvestment; equpment nvestment equals the agrculture, mnng, and manufacturng commodtes delvered to fnal expendture fxed nvestment plus the fnal expendture on personal transportaton equpment. 12
17 methodology n place, t s straghtforward to calculate the captal shares for larger aggregates. Ths gves: 0.35 for tradables, 0.30 for nontradables, 0.33 for consumpton, 0.27 for nvestment and 0.31 for the whole economy. Note that we fnd that tradables are more captal ntensve than nontradables. Whle Bhagwat 1982) and Kravs and Lspsey 1988) suggested that ths s the case, there has been qute some confuson about ths. For example, Stockman and Tesar 1995) clamed that the captal share n non tradables s hgher than n tradables. We calculate the deprecaton rates from the fxed asset and nvestment data from the Bureau of Economc Analyss by settng the deprecaton rate equal to the average of [x t +k t k t+1 ]/k t between statstcs). We fnd that the average deprecaton rates were δ b = 0.02 and δ e = These numbers are somewhat dfferent from those of Greenwood et al. 1997), who had δ b = 0.06 and δ e = The lkely reasons for the dfferences are that these authors consdered structures but not buldngs and that durng the 1990s the BEA changed ts way of calculatng captal stocks. We calculate the two dstrbuton margns usng the 1997 benchmark IO tables at producer prces and at purchase prces. One dfference between these two tables s that the output of the dstrbuton ndustres retal and wholesale trade and transportaton) s reported at producer prces whereas at purchase prces t s ncluded n the output of ndustres that use them. Usng ths, we calculate the dstrbuton margns as follows: we dvde the dfference between the shares of fnal expendtures at purchase prces and at producer prces by fnal expendture at purchase prces. We fnd that the dstrbuton margn for consumpton goods s 0.46 and for equpment In equlbrum the two dstrbuton margns equal P US s P US s /P US g ψ g ) and /P US e ψ g ). Usng the values for the dstrbuton margns just calculated and the observed values for P US s /P US g and P US s /P US e, we can solve for ψ g, ψ e. Gven these eght parameter values, we choose the remanng 24 parameter values so as to match 28 statstcs from the PWT These are: the ratos of U.S. per capta GDP n nter 20 To put these numbers nto perspectve, Bursten et al. 2003) calculated 0.42 and Our dstrbuton margn for equpment nvestment s sgnfcantly lower than ther number. Ths s due to the fact that they focus on the most tradable part of equpment nvestment agrculture, mnng, and manufacturng). To be consstent wth the way n whch we construct equpment nvestment n the PWT96, our equpment nvestment s all nvestment other than constructon. 21 Appendx B.1.2 explans how we compute these statstcs. Appendx B.3 explans our mnmzaton proce 13
18 natonal prces over Latn Amercan and the Poorest Countres per capta GDP n nternatonal prces 2 statstcs); the three relatve prces n each country 9 statstcs); the expendture shares of servces n each country, whch we have plotted aganst ncome n Fgure 6 n Appendx C 3 statstcs); the nvestment shares of buldngs and equpment n domestc and nternatonal prces n each country, whch we have plotted aganst ncome n Fgures 4 5 n Appendx C 12 statstcs). We also use the fact that when multpled wth the $ market exchange rate as reported by the IMF, the prces of equpment across countres are unrelated to ncome. Ths has been noted by Eaton and Kortum 2001) and used by Hseh and Klenow 2003). It can be seen n Fgure 7 n Appendx C. Gven P US e = 1 we therefore mpose P LA e = P PC e = 1 2 statstcs). Table 1: Statstcs n the Data and the Model US LA PC Data Model Data Model Data Model Income relatve to the US Equp nvest share dom prces) Constr nvest share dom prces) Equp nvest share nt $s) Constr nvest share nt $s) Servces expendture share Relatve prce servces Relatve prce constructon Relatve prce consumpton goods Dstrbuton margn cons goods Dstrbuton margn equpment Table 1 summarzes our target statstcs n the data and the model. We match all relatve prces by constructon. We do a reasonable job at matchng the other target statstcs. The only excepton are the shares of servces n total consumpton, whch we mss by as much as 27%. The reason s that as countres develop the share of consumpton goods remans roughly constant whle the shares of servces ncrease and of agrcultural goods decrease. Our model wth just two consumpton goods s not dsaggregate enough to capture ths. To be sure that dure. 14
19 ths does not crtcally affect our measurement of sector TFPs, we have also expermented wth more complcated utlty functons that allow us to match the three servce shares much more closely. It turns out that ths does not mportantly change our measurement of the sector TFPs. Snce our current utlty functon s smpler and commonly used n the development lterature, we stck to t. Table 2: Parameter values θ s = 0.32 θ b = 0.20 θ g = 0.39 θ e = 0.31 δ b = 0.02 δ e = 0.14 ψ g = ψ e = 4.07 σ = 1.55 µ = 0.46 β = 0.98 α = 0.79 x g = 0.02 Table 2 summarzes the resultng parameter values. They are farly standard. Note that x g = 0.02 mples that n the U.S. 4% the consumed quanttes of goods are for subsstence, whle n Latn Amerca and the Poorest Countres these numbers are 17% and 70%, respectvely. There s one somewhat unexpected problem left: our procedure does not allow us to dentfy τs, j τ j b, A s, j A j b ). More precsely, for each country j {LA, PC}, we can match all targets equally well for a one dmensonal set of lnear combnatons of the four parameters τs, j τ j b, A s, j A j b ). We wll therefore wrte τ j b τ j s), A j sτ j s), A j b τ j s)), vary τ j s, and report the results under the constrant that both τs j and τ j b be non negatve.22 5 Fndngs Our man fndngs are summarzed n Table 3. To calculate the TFPs of tradables and nontradables, we aggregate our two tradable goods and our two nontradable goods usng nternatonal 22 Note that related studes do not experence ths ndetermnacy because they mpose addtonal restrcton. For example, Hseh and Klenow 2003) study consumpton versus nvestment and set the tax on consumpton goods to zero. 15
20 Table 3: Relatve aggregate, tradable, and nontradable TFPs for dfferent servce taxes τ LA s A US /A LA A US T /ALA T A US N /ALA N τ PC s A US /A PC A US T /APC T A US N /APC N prces. 23 We then fnd that there are much larger dfferences n the TFPs of tradables than of the nontradables. Specfcally, between the U.S. and Latn Amerca the TFP dfferences n the tradables are roughly twce the TFP dfferences n the nontradables. Between the U.S. and the Poorest Countres ths number goes up to four. Table 4 breaks the tradables and nontradables nto consumpton and nvestment. We can see that wthn the tradables the TFP dfferences n equpment are larger than the TFP dfferences n consumpton goods. The results for nontradables are too senstve to the choce of τ s to be able to make robust statements. To understand why for dfferent values of τ s, we match all observable statstcs equally well, consder how the other parameters adjust when τ j s ncreases. Table 4 reports that τ j b and AUS s /As j go down whle A US b /A j b goes up. The ntuton s as follows. As τ s j ncreases, purchase prces and produced quanttes need to reman the same f no observable statstcs are to change. For the relatve prce of servce to reman the same, the prce effect of the ncrease n τ j s must be 23 For example, gven π = 1, 1, 1, 1) the TFP of tradables s: A j T A gk j g) j θ g lg) j 1 θ g + Aek j e) j θ e le) j 1 θ e kg) j. 8a) θ g l j g ) 1 θ g + k j e ) θ e l j e ) 1 θ e We compute labor productvty n a smlar way. For example, the labor productvty of nontradables s:. LP j N A sk j s) j θ s ls) j 1 θ s + A j b k j b )θ b l j b )1 θ b ls j + l j. 8b) b 16
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