The Structural Transformation Between Manufacturing and Services and the Decline in the U.S. GDP Volatility

Transcription

1 The Structural Transforation Between Manufacturing and Services and the Decline in the U.S. GDP Volatility Alessio Moro y First Version: Septeber 2008 This Version: October 2009 Abstract In this paper I construct a two-sector, input-output growth odel to quantify the role of the structural transforation between anufacturing and services in reducing the U.S. GDP volatility. For a sector with a given gross output TFP volatility, value added TFP volatility is an increasing function of the share of interediate goods in gross output. In the U.S. this share has been around 0.6 in anufacturing and 0.38 in services during the period. Thus, the sae level of gross output TFP volatility in the two sectors iplies a 55% larger value added TFP volatility in anufacturing. In the odel, this iplies that when the services share in GDP increases, the volatility of TFP in the iplied aggregate production function is reduced and GDP volatility declines. Nuerical results for the calibrated odel econoy suggest that the increase in the share of services in GDP can account for 32% of the U.S. GDP volatility reduction between the and the periods. JEL Classi cation: C67, C68, E25, E32. Keywords: Volatility Decline, Structural Change, Real Business Cycle, Total Factor Productivity. I would like to thank Michele Boldrin, Javier Díaz Giénez and Nezih Guner for their guidance and Vasco Carvalho, Antonia Diaz, Huberto Ennis, Esteban Jaiovich, Matthias Kredler, Paolo Mattana, Vincenzo Merella and seinar participants at Carlos III, Cagliari, Uppsala, the SMYE 2009 in Istanbul, the XIV Workshop on Dynaic Macroeconoics in Vigo, and the EEA-ESEM Meeting 2009 in Barcelona for the useful coents. The Region of Sardinia is kindly acknowledged for nancial support. The usual disclaiers apply. y Departent of Econoics, Universidad Carlos III de Madrid, aoro@eco.uc3.es.

2 Introduction There is a large literature docuenting the decline over tie in the U.S. GDP volatility. Aong the various explanations advocated to explain this process are: iproved inventory anageent techniques (Davis and Kahn, 2008), better onetary policy (Leduc and Sill, 2007), better nancial instruents (Jerann and Quadrini, 2006), a decline in aggregate total factor productivity (TFP) volatility (Arias et al., 2007), and the structural transforation between anufacturing and services. This last explanation is based on the observation that services represents the least volatile coponent of GDP and that the share of services in GDP increased in the U.S. between the and the periods. Table reports the volatility of real value added in anufacturing and services during the period and the average shares of anufacturing and services in GDP in the and the periods. 2 Table Volatility and Relative Size of Manufacturing and Services in the US SD% GDP share GDP share Manufacturing 4.26% Services.68% In the literature, the structural transforation hypothesis has been ainly tested through xed weights counterfactual experients. These experients x the shares in GDP of broad categories of goods to those of a given period. Next, a counterfactual GDP series is constructed using these shares together with the actual series of the broad categories real value added. The volatility of the counterfactual GDP series is then copared with the volatility of the actual GDP series. With this procedure, Davis and Kahn (2008) nd that the structural See McConnell and Perez-Quiros (2000), Blanchard and Sion (200), Stock and Watson (2002) and Dalsgaard et al. (2002), aong others. In this paper, the ter "structural transforation" refers to the transforation of the aggregate production function of the econoy that occurs when the share of services in GDP increases relative to that of anufacturing. 2 Figures are coputed using Jorgenson Dataset, Manufacturing includes all non-services sectors. 2

3 transforation can account for 2% of the GDP volatility reduction in the U.S. between the pre and the post 984 periods. However, this ethodology raises two issues. First, by xing the shares of each broad category in GDP, the volatility iplied by uctuations in these shares vanishes in the counterfactual GDP series. Alcala and Sancho (2003) show that when appropriate chain-weighted index nubers are used instead of the xed categories shares, the increase in the share of services in GDP can account for 30% of the reduction in output volatility in the U.S. over the period. 3 Second, these experients do not take into account general equilibriu e ects on aggregate volatility that can arise when the services sector expands with respect to anufacturing. For instance, it ight be the case that the correlation between real value added in anufacturing and services changes after an expansion of the services sector relative to anufacturing. This, in turn, a ects GDP volatility. In this paper I present a two-sector, input-output growth odel to study the link between the share of services in GDP and GDP volatility. The two sectors, anufacturing and services, produce gross output using a Cobb-Douglas production function in capital, labor and interediate goods purchased fro the sector itself and fro the other sector. Household s preferences are non-hoothetic in that the incoe elasticity of services is greater than one and that of anufacturing saller than one. Fro the input-output structure it is possible to derive a Cobb-Douglas aggregate production function in capital, labor and a total factor productivity (TFP) ter, siilar to the standard neoclassical aggregate production function. The ain di erence is that the TFP ter is now a function of gross output TFP of the two sectors. Assuing that gross output TFP follows a coon process in the two sectors, and paraetrizing the production function using U.S. data, the resulting aggregate TFP volatility is 32% larger when the econoy produces only anufacturing than when it 3 See also Black and Dowd (2009) for a siilar result for regional, state and aggregate data in the U.S. 3

4 produces only services. This suggests that, even if the underlying TFP process is the sae at the gross output level in anufacturing and services, aggregate TFP volatility depends on the relative size of the two sectors in GDP. In this situation, a larger share of services in GDP iplies a saller aggregate TFP volatility and, in turn, a saller GDP volatility. The previous result is driven by the following echanis. For a sector with a given gross output TFP, value added TFP is an increasing function of the share of interediate goods in gross output in that sector. 4 This relationship extends to TFP volatility: for a given volatility of gross output TFP, the share of interediate goods in gross output provides a ultiplier on value added TFP volatility. Using U.S. data fro Jorgenson dataset, 2007, I docuent that anufacturing displays a larger average share of interediate goods in gross output with respect to services during the period, 0.6 versus This di erence iplies that the sae gross output TFP volatility in the two sectors results in a TFP volatility at the value added level 55% larger in anufacturing than in services. As GDP is a function of sectorial value added and the share of each sector in GDP, it follows that a larger share of services in GDP iplies a saller aggregate TFP volatility when gross output TFP is the sae in the two sectors. In the data, gross output TFP volatility is larger in anufacturing than in services during both the and the periods. Furtherore, gross output TFP volatility declines in both sectors between the two periods. It follows that three e ects on aggregate TFP volatility can be identi ed over tie. The rst e ect is due to the decline in gross output TFP volatility in both sectors. The second e ect is due to the fact that the sector with the largest gross output TFP volatility (anufacturing) shrinks with respect to the other sector. Finally, the sector with the largest interediate goods ultiplier on value added TFP volatility (again anufacturing) shrinks with respect to the other sector. The 4 This theoretical issue was rst shown in Hulten (978). 4

5 odel presented in this paper allows to separate the rst e ect fro the other two. In this way, it is possible to quantify the e ect that the structural transforation between anufacturing and services had on the GDP volatility decline in the U.S. The strategy is to use the odel to construct two steady states. The only structural di erence between the two steady states is the level of gross output TFP in each sector. The di erence in gross output TFP levels in the two sectors between the two steady states atches the di erence easured in the data between 960 and As incoe in the second steady state is higher, because of higher gross output TFP levels, the non-hootheticity of preferences iplies that the services share of GDP is also larger. The odel is calibrated so that the iplied share of services in the rst steady state is equal to the average share observed in the data during the period, 0.55, and that iplied in the second steady state is equal to the average share observed in the data during the period, I then calibrate stochastic processes for gross output TFP shocks in anufacturing and services for the period. Using these processes I perfor siulations of linear quadratic approxiations of the odel around the two steady states. In this way, di erences in GDP volatility across steady states can be attributed to the di erent shares of the two sectors in GDP. The odel displays a GDP volatility 8% larger in the rst with respect to the second steady state. This iplies that the structural transforation alone is able to explain 32% of the di erence in GDP volatility observed in the data between the and the periods. In addition, the odel replicates other features of the decline in GDP volatility observed in the literature. As described above, without any change in the stochastic process of gross output shocks, when the share of services in GDP is larger, the odel endogenously generates a saller aggregate TFP volatility. This suggests that at least a part of the "good luck" explanation of the GDP volatility decline is due to a change in the transission echanis 5

6 of sectorial shocks to the aggregate econoy, rather than to a change in the stochastic processes of the shocks. Indeed, Giannone et al. (2008) argue in favor of the change in the transission echanis as the explanation of the observed reduction in aggregate TFP volatility. Davis and Kahn (2008) show that the volatility of each broad coponent of GDP declined over tie in the U.S. The broad coponents considered in their paper are durables, non-durables, services and structures. In the odel presented here, coponents of GDP are services consuption, anufacturing consuption and investent, where the latter is a anufactured good. Other conditions equal, the volatility of each of these coponents of GDP is saller in the steady state with the largest share of services in GDP. Finally, it is worth noting that the decline in GDP volatility occurred in ost G7 countries (Stock and Watson, 2003). This fact suggests that changes in the characteristics of a single country, such as changes in onetary policy, cannot represent a coon explanation of the volatility decline across countries. Instead, the share of services in GDP increased over tie in all industrialized countries. 5 The reaining of the paper is organized as follows: section 2 discusses the relationship between gross output TFP and value added TFP, both at the theoretical and at the epirical level for the U.S.; section 3 presents the odel; section 4 discusses the quantitative analysis; nally, section 5 concludes. 2 Fro sectorial TFP to value added TFP Consider a generic sector in which the representative r produces gross output using a Cobb-Douglas production function in interediate goods M and a function of capital and labor f(k; N). 6 Markets are copetitive so the r takes the price of capital r, of labor 5 As shown in Blanchard and Sion (200), the reduction in GDP volatility in the U.S. does not occur suddenly between the pre-84 and the post-84 periods, but it is a process that started at least in 950 and was interrupted in the seventies and id-eighties. Interestingly, Buera and Kaboski (2009) show that the rise in the services sector in the U.S. is also a phenoenon that started around Assue f(k; N) to be hoogeneous of degree one in capital and labor. 6

7 w, of gross output p g and of interediate goods p as given. The proble of the r is to axiize the value of gross output inus the cost of inputs: ax pg Bf(K; N) M rk wn p M. () K;N;M Here Bf(K; N) M is the gross output production function, 0 < < and B is gross output TFP. I refer to B as sectorial TFP. The rst order condition of () with respect to interediate goods iplies that M = ( ) pg p B f(k; N). (2) Using (2) in () the following reduced for proble is obtained o ax np v B f(k; N) rk wn. (3) K;N Proble (3) is a standard pro t axiization proble in which the representative r axiizes the di erence between value added and the cost of priary inputs capital and labor. In (3), B f(k; N) is the real value added production function of the sector considered and p v = ( ) p g p the price of real value added. 7 It follows that TFP at the value added level is given by B. I refer to B as value added TFP. 7 Here real value added is de ned, as in Sato (976), as the contribution to gross output growth of priary inputs (capital and labor) and technical change. Sato (976) shows that when the gross output production function is separable into interediate goods and a function of priary inputs and technical change, the real value added index is unique and given by a Divisia index that satis es dv V = dg G ( ) dm M. where V is the real value added index, G the gross output index, M the interediate goods index and is the share of value added in gross output. Applying this forula to the gross output production function in (), Bf(K; N) M, I obtain the Divisia index for real value added dv V = db B + df (K; N) f (K; N), which is the rate of change of B f(k; N) over tie. Thus, B f(k; N) represents the real value added production function and p v = ( ) p g p its price. 7

8 Figure : Noinal share of interediate goods in anufacturing (continuous line) and in services (dashed line) in the U.S. Source: Jorgenson Dataset, 2007, and own calculations. In the real business cycle literature, before coputing volatility statistics, each variable is logged and detrended using the Hodrick-Prescott (HP) lter. For a variable log(b t ) and its HP lter log( B t ), the deviation ^b t at tie t is given by ^b t = log(b t ) log( B t ). Instead, for the variable log(b t ) the deviation ~ b t at t is given by ~ b t = (=)[log(b t ) log( B t )]. As a result, the value of a ects value added TFP volatility through its e ect on sectorial TFP B. 8 In equilibriu, is equal to the share of capital and labor and to the share of interediates in gross output in the sector considered. Figure reports the share of interediate goods in gross output in the anufacturing and in the services sectors fro 960 to 2005 in the U.S. The average share of interediate goods is 0.6 in anufacturing and 0.38 in services. These nubers iply that if the volatility of B were the sae in the two sectors, the di erence in would deliver a value added TFP volatility 55% larger in anufacturing than in services. 9 8 Note that the result extends to the case in which volatility is coputed as the standard deviation of the variable s growth rate. In that case, for a given growth rate of B t, ^b t =log(b t ) log(b t ), the growth rate of B t is ~ b t = (=)[log(b t ) log(b t )]. 9 Note that the Cobb-Douglas assuption on the gross output production function is not needed for the result. The relationship between sectorial TFP and value added TFP is obtained in any growth accounting exercise à la Solow (957), as long as the gross output production function is constant returns to scale and separable in value added and interediate goods. Separability is an iplicit assuption in all acroeconoic 8

9 Aggregate TFP is coputed using GDP as a easure of output, where GDP coincides with aggregate real value added. This suggests that even if the volatility of B were constant across sectors and countries, an econoy producing only anufacturing would experience a volatility of aggregate TFP 55% larger than an econoy producing only services. Table 2 reports volatility of sectorial TFP and value added TFP in anufacturing and services in the U.S. The series are logged and detrended using the Hodrick-Prescott lter before coputing statistics. Table 2 TFP volatility in Manufacturing and Services in the U.S. (SD%) Sectorial TFP B t Value Added TFP B t Subperiod Manufacturing.7%.35% 0.92% 2.93% 3.38% 2.30% Services 0.74% 0.9% 0.5%.9%.47% 0.82% Ratio The rst colun of Table 2 reports sectorial TFP volatility in the two sectors over the period. Sectorial TFP in anufacturing is 58% ore volatile than in services during the whole saple period In the second and third coluns of Table 2 I report easures for two sub-periods which are usually considered in the literature to copare GDP volatility, before and after 984. For both sectors sectorial TFP volatility declines between the two periods, although the services sector displays a larger decline, 44% copared to 32% in anufacturing. Furtherore, in both subperiods anufacturing displays a larger volatility than services. When value added TFP is analyzed, the di erence between the two sectors enlarges because of the larger in services with respect to anufacturing. Value added TFP volatility is 46% larger in anufacturing than in services during the whole saple, 30% larger in the rst subperiod and 80% larger in the second one. odels that disregard interediate goods utilization. See also the EU KLEMS Growth and Productivity Accounts, (2007). 9

10 To suarize, three e ects potentially able to ipact the volatility of the econoy can be identi ed over tie. The rst one is the reduction in sectorial TFP volatility in anufacturing and services occurred between the and the periods. The second e ect derives fro the fact that the sector with the highest TFP volatility at the sectorial level (anufacturing) shrinks with respect to the other (services). The third e ect is due to the shrinking of the sector with the largest ultiplier on value added TFP due to interediate goods (again anufacturing) with respect to the other sector (again services). In the next section I construct a odel that perits to separate the rst e ect fro the other two. In this way, it is possible to assess the contribution of the structural transforation to the GDP volatility reduction. 3 The Model 3. Firs There are two sectors in the econoy, anufacturing and services. The representative r in each sector produces gross output using a Cobb-Douglas production function in capital, labor, anufactured interediate goods and interediate services. The anufacturing production function is G = B KN M " S ", (4) and that of services is G s = B s Ks Ns s M " s s S s "s s, (5) where 0 < <, 0 < j <, 0 < " j <, K j and N j are the aounts of capital and labor, M j is the anufactured interediate good, S j is interediate services and B j is sectorial TFP, with j = ; s. 0 Sectorial TFP B j is assued to follow soe stochastic process, 0 The literature provides estiates for the anufacturing sector that report an elasticity of substitution between value added and interediate goods saller than one (see Bruno, 984, for instance). However, 0

11 unspeci ed for the tie being. The anufacturing producing r solves ax [p G rk wn p M p s S ] (6) K ;N ;M ;S subject to (4), where p is the price of anufacturing, p s is the price of services, r is the rental price of capital and w the wage rate. The services producing r solves ax [p s G s rk s wn s p M s p s S s ] (7) K s;n s;m s;s s subject to (5): Given the structure of the supply side of the econoy, copetitive arkets iply that the relative price of services with respect to anufacturing, p s =p, is independent of the quantities produced of the two goods. This is given by p s B s [ "s( s)]+s[ "( )] s = ( ; s ; " ; " s ). (8) p Bs Details of the derivation are given in Appendix B. In (8), is a function of the paraeters, s, " and " s. The relative price of the two goods is technologically deterined, that is, it depends only on the paraeters of the production functions and on sectorial TFP, B and B s. This result is due to the input-output structure of the odel together with the assuption that the capital and labor aggregator is the sae for the two rs, K j N with j = ; s. 2 j, gure shows that the share of interediates goods in gross output reains roughly constant in the long run in both sectors. This observation supports the unit elasticity of substitution between value added and interediate goods assued in (4) and (5). In Appendix A I show how to derive the representative r proble (6) fro a ore general proble with a continuu of rs in anufacturing and services. The sae derivation applies to proble (7) below in the text. 2 That is, the non-substitution theore applies (Sauelson, 95).

12 3.2 Households The odel econoy is inhabited by a easure one of households indexed in the interval i 2 [0; ]. Households in this econoy have preferences over anufacturing and services and are endowed with one unit of labor tie each period which they supply inelastically. The consuption index at date t is given by c t = bc ;t + ( b) (c s;t + s), (9) with s > 0, < and 0 < b <, where c ;t and c s;t are the per capita consuption levels of anufacturing and services. As households are identical I avoid the use of the index i for the tie being. The paraeter s is interpreted as hoe production of services. 3 The utility function (9) displays an incoe elasticity of deand saller than one for anufacturing and larger than one for services. Households solve the following proble subject to P ax E t [log c t ] (0) c t t=0 p s;t c s;t + p ;t c ;t + p ;t [k t+ ( )k t ] = r t k t + w t. where E is the expectations operator, the subjective discount factor and the depreciation rate of the capital stock. Each period t, the household decides services consuption, c s;t, anufacturing consuption, c ;t, and investent, k t+ ( )k t, given the rent fro the capital stock owned, r t k t, and the wage fro the unit aount of labor services o ered, w t. The capital stock is produced in the anufacturing sector. This iplies that the price of capital is p. 4 3 See, for instance, Kongsaut, Rebelo and Xie (200) for this interpretation. 4 This is the sae assuption as in Echevarria (997) and Kongsaut, Rebelo and Xie (200) and nds support in the data. Kongsaut, Rebelo and Xie (200) nd that anufacturing and construction produced between 90% and 93% of investent during the period

13 3.3 Two Aggregate Production Functions In this section I show that fro the input-output structure of the odel it is possible to derive a Cobb-Douglas aggregate production function in capital, labor and a TFP ter, siilar to the standard neoclassical aggregate production function. As in the latter case, the aggregate production function for this econoy relates the aggregate resources available for consuption and investent purposes to the aount of capital and labor used in production in the econoy. An aggregate production function for this econoy can be obtained by solving the following static axiization proble h ax B K K ;N ;M ;S ;M s N M " i S " M M s () subject to B s [(K K ) (N N ) ] s Ms "s S s "s s = S + S s, where B (KN ) (M " S " ) and B s [(K K ) (N N ) ] s (M "s s S s "s ) s are the gross output production functions de ned in (4) and (5) and K and N are the aounts of capital and labor available in the econoy in the period considered. The solution to proble () deterines the axiu aount of anufacturing that can be consued - or invested - in the econoy when c s = 0 for all households, that is, when the services sector serves only as an interediate sector. 5 The solution to proble () at tie t is V ;t = ( ; s ; " ; " s )B f ( ; s;" ;" s) ;t B f 2( ; s;" ;" s) s;t K t N t, (2) 5 In other words, the solution to () deterines the point in which the production possibility frontier of this econoy crosses the anufacturing axis. The entire production possibility frontier can be found by solving () with constraint B s [(K K ) (N N ) ] s M s "s S s "s s = S + S s + c s. In this case, the solution to () gives the aount of anufacturing that can be consued - or invested - when the aount of services consuption is c s. 3

14 where, f and f 2 are functions of ; s ; " and " s. By dividing (2) by (8) it is possible to derive the axiu aount of services that can be consued when the anufacturing sector produces only interediate goods V s;t = s ( ; s ; " ; " s )B f 3( ; s;" ;" s) ;t B f 4( ; s;" ;" s) s;t K t N t, (3) where s, f 3 and f 4 are also functions of ; s ; " and " s. Details of the derivation and the explicit functional for of, s, f, f 2, f 3 and f 4 are given in Appendix B. As a standard neoclassical aggregate production function, (2) and (3) represent the econoy s resources in two extree cases, one in which only anufacturing is consued - or invested - and services is just an interediate sector, and another in which the opposite situation holds. Note that TFP is di erent in the two cases and TFP volatility also, because of the di erent exponents of B ;t and B s;t in (2) and (3). Using Jorgenson it is possible to copute f = :8, f 2 = 0:43, f 3 = 0:27 and f 4 = :44 for the U.S. Assue that at each date sectorial productivity is the sae in anufacturing and services, that is B ;t = B s;t = B t at any t. In this case, the exponent of B t is f + f 2 = 2:24 in (2) and f 3 + f 4 = :7 in (3), with a di erence between the two cases of 3%. Thus, TFP volatility is also 3% larger in the rst case. The functions (2) and (3) represent the points in which the production possibility frontier of this econoy intersects the anufacturing and services axes. This suggests that, in this econoy, the volatility of aggregate output is reduced oving along the production possibility frontier, that is, reducing anufacturing consuption - or investent - and increasing services consuption. In U.S. data, GDP coposition changes over tie becoing ore intensive in services and less in anufacturing. As GDP coposition changes, the transission of sectorial shocks to the aggregate econoy changes and this iplies a change in easured aggregate TFP volatility. This result is consistent with the view expressed in Giannone et al. (2008), who argue that the decline in aggregate TFP volatility is not due 4

15 to a change in the stochastic processes of shocks, but rather to a change in the propagation echanis of those shocks The Copetitive Equilibriu A copetitive equilibriu for the econoy under study is a set of prices fp ;t ; p s;t ; r t ; w t g t=0 and allocations fc ;t ; c s;t ; k t+ ; K ;t ; N ;t ; K s;t ; N s;t ; M ;t ; M s;t ; S ;t ; S s;t g t=0 such that: each t; a) Given prices, c ;t ; c s;t and k t+ solve the representative household s proble (0) at b) Given prices, K ;t, N ;t M ;t and S ;t solve the anufacturing representative r proble (6) and K s;t, N s;t M s;t and S s;t solve the services representative r proble (7) at each t; and c) Markets clear: R 0 k tdi = k t = K ;t + K s;t, N ;t + N s;t =, R 0 c ;tdi = c ;t, R 0 c s;tdi = c s;t, G ;t = c ;t + k t+ ( )k t + M ;t + M s;t, G s;t = c s;t + S ;t + S s;t. 6 The di erent functions f, f 2, f 3 and f 4 also iply that aggregate TFP growth is di erent in (2) and (3). Thus, even if sectorial TFP growth is the sae in anufacturing and services, an econoy producing only anufacturing will experience a growth rate of aggregate TFP larger than an econoy producing only services. This echanis is potentially able to explain the larger growth rates of developing with respect to developed econoies. I address this issue in a parallel research. 5

16 3.5 The Planner s Proble In the odel presented there are no distortions so an equal-weight Pareto proble delivers the copetitive equilibriu solution. A benevolent social planner in this econoy solves the following dynaic prograing proble subject to and V (k; z ; z s ) = ax c ;c s;k0 flog(c) + E [V (k0 ; z 0 ; z 0 s)jz ; z s ]g, (4) B s = ( ; s ; " ; " s ) Bs c = [bc + ( b) (c s + s) ], c s + c + k 0 ( )k = V, [ "s( s)]+s[ "( )] s, B = B e z, B s = B s e zs, z 0 = z z + 0, with N(0; 2 ), z 0 s = z z s + 0 s, with s N(0; 2 s), where the prie indicates the value of a variable in the next period, V (k; z ; z s ) is the value function, and E is the expectations operator. Manufacturing is the nueraire of the econoy, c s, c, and k 0 ( )k are consuption in the services sector, consuption in the anufacturing sector and investent - which is a anufactured good - all in per capita ters. The arginal rate of transforation between anufacturing and services,, is given by (8). 7 As services can be transfored into anufacturing at the rate, it is possible to write a unique resource constraint where the aggregate production function, V, is given by (2). As population in the econoy is constant over tie and equal to one, the aggregate 7 As the rst and the second welfare theores hold, the relative price of services with respect to anufacturing in the copetitive equilibriu, p s =p, is equal to the arginal rate of transforation between services and anufacturing in the centralized econoy,. 6

17 and the per-capita production functions coincide. Sectorial TFP in each sector, B and B s, is the product of a level coponent, B and B s respectively, and a cycle coponent, e z and e zs, respectively. Each period, a shock a ects the cycle coponent of each sector s total factor productivity. The process for this shock is z 0 = z z + 0 for anufacturing and zs 0 = z z s + 0 s for services. The shocks and s are i.i.d. over tie and extracted fro noral distributions with zero ean and variances 2 and 2 s. Finally, note that the sectorial real value added concept, needed to construct aggregate value added requires the existence of the appropriate price index to de ate sectorial noinal value added. In the planner s econoy there are no prices by construction but the correspondence with the copetitive equilibriu can be used to resort to the real value added concept. In Appendix C, I show how the value added price indices in the two sectors are obtained in the copetitive equilibriu. Once the equilibriu is found in the planned econoy, these prices can be used to obtain real value added in the two sectors. Once real value added in the two sectors is obtained, aggregate real value added is coputed as a chain-weighted Fisher quantity index. 8 Aggregate real value added is the odel s counterpart of real GDP in the data, which is also coputed as a chain-weighted Fisher quantity index. 9 4 Strategy and Results In this section I use the planner s proble presented in section 3.5 to quantify the role of the structural transforation in reducing GDP volatility in the U.S. To do this, I perfor siulations of linear quadratic approxiations of the odel around two steady states that di er in the size of the services sector in the econoy. 20 The idea is that, when the services 8 The quantitative results of the paper do not change when a Tornqvist index is used. 9 See the Bureau of Econoic Analysis (2006). 20 See Appendix D for the derivation of the non-stochastic steady state of the econoy. Note also, that the two-sector odel presented in this paper does not display a balanced growth path (BGP). In general, ulti-sector growth odels do not display a BGP, unless under restrictive assuptions on the utility or the production functions, as in Kongsaut, Rebelo and Xie (200) and Ngai and Pissarides (2007). Ngai and 7

18 sector displays a larger share in GDP, the volatility of GDP is in uenced to a larger extent by the volatility of the service sector and to a saller extent by anufacturing volatility. As the services sector displays a saller value added TFP volatility, as discussed above, GDP volatility is expected to decline when the relative size of services in the econoy increases. To paraetrize the odel I use Jorgenson dataset, The Data Appendix provides details on the dataset. One odel period corresponds to one year in the data. The paraeters de ning the elasticity of output with respect to inputs in the production functions (4) and (5) are directly coputed fro the data given the Cobb-Douglas assuption. The depreciation rate = 0:05, the subjective discount factor = 0:96, and the autoregressive paraeter z = 0:95 are taken fro Cooley and Prescott (995). 2 The paraeter governing the elasticity of substitution between anufacturing and services, = :5, is consistent with the values used in Rogerson (2008) and Duarte and Restuccia (2008). Finally, the deterinistic part of sectorial TFP in anufacturing, and in services, B and B s, is noralized to one. Apart fro the standard deviations of productivity shocks in the two sectors, and s, that will be discussed later, there are two paraeters left, s and b. The two targets of the calibration are the average share of services in GDP in the period and that in the period. Thus, with the calibrated s and b, the share of services in GDP in the rst steady state atches the average share of services in GDP observed during the period, I label this the steady state. In the second steady state, labelled , the only structural di erence - i.e., di erence in the paraeters - with respect to the rst steady state is the deterinistic part of sectorial TFP in the two sectors: Pissarides (2007) provide conditions for BGP existence in a odel with structural change and interediate goods. In the class of odels they consider, all sectors use the sae Cobb-Douglas technology in capital, labor and interediate goods, with di erent TFP levels. The odel presented here does not possess these characteristics, as the production functions of the two sectors di er both in the elasticity paraeters and in the TFP levels. 2 Note that Cooley and Prescott (995) use quarterly data while here I use yearly data. The paraeters are then accordingly coputed. 8

19 in the steady state B is ( + ' ) and B s is ( + ' s ), where ' = 0:30 and ' s = 0:27 are the growth rates of sectorial TFP easured in the two sectors between 960 and As incoe in the second steady state is larger, because of higher sectorial TFP levels, the non-hootheticity of preferences iplies that the services share in GDP is also larger. With the calibrated s and b, the odel atches a share of services in GDP equal to 0.67 in the steady state, which is the average share easured in the data during the period. Table 3 reports paraeters values. 22 Table 3: Paraeter Values Paraeter De nition Value Source Share of capital in value added 0.34 Data Share of K and N in G 0.40 Data " Share of M in anufacturing interediates 0.7 Data s Share of K s and N s in G s 0.62 Data " s Share of S s in services interediates 0.72 Data ' Growth rate of sectorial anu. TFP 60/ Data ' s Growth rate of sectorial serv. TFP 60/ Data Subjective discount rate 0.96 Literature Depreciation rate 0.05 Literature Elasticity paraeter in preferences -.5 Literature z Autoregressive paraeter 0.95 Literature B s Initial sectorial TFP level in services Noraliz. B Initial sectorial TFP level in anufacturing Noraliz. s Hoe production of services 0.4 Calibrated b Weight of anufacturing in preferences Calibrated To interpret the value of the paraeter s, note that the calibration iplies a consuption of arket services c s in total services consuption, c s + s, of 5% in the steady state and of 30% in the one. This is consistent with the large shift fro hoe to 22 In general, non-hoothetic preferences are not crucial to generate an increase in the share of services in GDP. As value added TFP growth in services is lower than in anufacturing, this can be accoplished through CES preferences with a low elasticity of substitution (as in Ngai and Pissarides, 2007 for instance). However, in the U.S., both the relative price and the relative quantity of services with respect to anufacturing increase over tie. For the odel to generate both an increase in the relative quantity and in the relative price of services with respect to anufacturing, an incoe e ect coing fro non-hoothetic preferences is needed. Without being a target of calibration, the ratio of real value added in services over real value added in anufacturing increases by 30% in the odel between the two steady states. In the data, the increase between the corresponding periods is 26%. 9

20 arket production observed over tie in the U.S. 23 Furtherore, note that the sall value of the paraeter b is due to the fact that the capital good is produced in the anufacturing sector only. This iplies that, to atch the share of anufacturing in GDP observed in the data, the weight of anufacturing in preferences ust be sall. The calibration iplies that in the steady state, the proportion of anufacturing consuption is 0.27 of noinal aggregate value added while in the it is 0.5. The investent rate (investent/total value added) is 0.8 in both steady states. Furtherore, anufacturing consuption over total anufacturing is 0.59 in the steady state and 0.44 in the steady state. Table 4: Volatility of US GDP Period Percentage SD % % % In table 4, I report the volatility of GDP in the U.S. econoy for the whole period and for the sub-periods and The standard deviation in the rst sub-period is 57% larger than in the second sub-period. This con rs the general result encountered in the literature of a large decline in GDP volatility between the two sub-periods. I now turn to perfor siulations of linear quadratic approxiations of the odel around the two steady states. 25 Results in the following tables are averages of 000 siulations of the odel econoy, each 20 years long. The Hodrick-Prescott paraeter used to lter the series is = 00, consistent with yearly data. I rst calibrate the standard deviations of the error ters in the two sectors, and s, for the periods and I then 23 See Freean and Shettkatt (200, 2005). 24 Standard deviations are coputed as in standard business cycle exercises. The Hodrick-Prescott paraeter used to lter the series is = 00, consistent with annual data. The series used is the yearly real GDP series fro the St. Louis FED. 25 For the ethodology to perfor linear quadratic approxiations I follow Diaz-Gienez (999). 20

21 perfor siulations of the steady state by using the calibrated values of and s for the period and of the steady state by using the calibrated values of and s for the period. The values are = :2% and s = 0:85% for the rst period and = 0:84% and s = 0:69% for the second period. Table 5 reports the Table 5: Volatility across steady states Siga Manufact. Siga Services Services Share in GDP Percentage S.D. of GDP Ratio S.D. ( )/( ) Model Data Model Data Model Data % 0.85% % 2.28% % 0.69% %.45% results. The standard deviation of GDP is.55% in the steady state, copared to a 2.28% easured in the data during the corresponding tie period. In the steady state GDP volatility becoes 0.97%, copared to.45% in the data. Although the odel is not able to generate as uch volatility as in the data, the ratio of the standard deviations of GDP in the two subperiods in the odel,.60, is close to the ratio in the data,.57. The odel is able to replicate the entire reduction in GDP volatility observed in the data between the two subperiods. The result in table 5 derives fro two e ects. One e ect coes fro the reduction in sectorial TFP volatility in anufacturing and services between the two periods and The second e ect is due to the increase in the share of services in GDP between the two steady states. To quantify the e ect of the structural transforation alone I perfor a decoposition experient. I run siulations of the two steady states using the and s calibrated for the entire period, :% and 0:78%, in both siulations. In this way, the di erence in GDP volatility observed between steady states derives fro the di erent size of the services sector across steady states, and not fro a reduction in sectorial TFP volatility. The rst row of table 6 reports results for the steady state in the decoposition 2

22 Table 6: The decoposition experient Siga Manufact. Siga Services Services Share in GDP Percentage S.D. of GDP Ratio S.D. ( )/( ) Model Data Model Data Model Data % 2.28%.% 0.78% %.45%.8.57 experient. GDP volatility is.42% in the odel, copared to 2.28% in the data. The second row reports the steady state. The volatility of GDP is.20%. The ratio of volatility in the over the steady state is.8. Thus, volatility in the steady state is 8% larger than in the steady state. This iplies that the structural transforation alone is able to explain around 32% of the di erence in GDP volatility between the two periods. 26 The results encountered con r that the structural change contributes substantially to the decline in GDP volatility in the U.S. Consider now the change in volatility in the coponents of GDP in the odel, anufacturing consuption, services consuption, and investent, between the two steady states. 27 This is reported in Table 7. The volatility of each coponent of GDP is larger in the rst steady state with respect to the second. This is consistent with Davis and Kahn (2008), who show that the volatility of each coponent of GDP declines over tie in the U.S. As in the standard one sector growth odel, investent displays a larger volatility with respect to consuption in both steady states. The large volatility of services with respect to anufacturing consuption is due to the non-hootheticity of preferences that ake the elasticity of services consuption with respect to incoe larger than that of anufacturing consuption. Finally, consider the standard experient perfored in the literature to assess the contribution of the structural transforation to the decline in GDP volatility. In this experient 26 (8%)=(56%) ' 32%: 27 Each of these coponents is expressed in real value added units of the relevant sector before coputing volatility. 22

23 Table 7: Volatility of single GDP coponents Services Perc. S.D. of Perc. S.D. of Siga Manufact. Siga Services Share in GDP Manu. Consup. Services. Consup. Perc. S.D. of Investent % 4.8% 7.47%.% 0.78% % 2.65% 2.76% Ratio ( )/( ) the shares of anufacturing and services in GDP are xed to the values observed at the beginning of the saple period, and a counterfactual GDP series is constructed using the actual series of anufacturing and services real value added. The volatility of this counterfactual series is then copared with that of the actual GDP series and the di erence between the two is attributed to the contribution of the structural transforation to the GDP volatility decline. 28 I perfor this experient using the data on anufacturing and services real value added generated by the odel in the two steady states reported in table 5. That is, I x the share of services in GDP to 0.55 and construct counterfactual GDP series for the and the steady states in table 5. Table 8 reports the results. 29 Although the standard deviations of anufacturing and services decline across steady states, the volatility of the counterfactual GDP series does not change. Thus, this ethodology does not capture the contribution of the structural transforation on the GDP volatility decline encountered in the decoposition experient of table 6. This is because the volatility of GDP does not depend only on the volatility of the single coponents of GDP, but also on their correlation. In the odel, the correlation between anufacturing and services is negative and declines in absolute value in the with respect to the steady state. This is a general equilibriu e ect that is not accounted for by the xed weights experient, which iplicitly assues that GDP volatility is a siple weighted average of the volatilities of the 28 See Blanchard and Sion (200), Stock and Watson (2002), and Davis and Kahn (2008). McConnell and Perez-Quiros (2000) use saple averages as weights. 29 In practice, the growth rate of the counterfactual GDP series is a Tornqvist index where single coponents are anufacturing and services. In this index the weight of services is xed to 0.55 and that of anufacturing to

24 Siga Manufact. Table 8: The counterfactual experient Siga Services S.D. of Manufact. S.D. of Services S.D. of the Counterfactual GDP Fixed Services Share= % 0.85% 8.4% 5.0% % 0.69% 5.26% 2.07%.58%.57% single coponents of GDP. 5 Conclusions The structural transforation between anufacturing and services in odern econoies is a well established fact. At the sae tie, the reduction in GDP volatility appears to be a coon process across industrialized countries. In this paper I show that in the U.S., the sae TFP volatility at the sectorial level in anufacturing and services delivers a di erence in TFP volatility at the value added level of 55% between the two sectors because of the di erent share of interediate goods in the two sectors. The quantitative analysis suggests that the sectorial transforation can account for up to 32% of the di erence observed in GDP volatility between the and the periods. The di erent share of interediate goods in the production of anufacturing and services has also iportant iplications for the growth rate of an econoy. Echevarria (997) shows that the sectorial transforation between anufacturing and services iplies a decline in aggregate TFP growth because services display a lower valued added TFP growth with respect to anufacturing. In Moro (2009), I show that around 2/3 of the di erence in value added TFP growth rates between anufacturing and services is due to the di erent share of interediate goods in the two sectors, rather than to a di erent TFP growth rate at the gross output level. This fact iplies that, even when sectorial TFP grows at the sae rate in the two sectors, aggregate TFP growth is not uniquely deterined but depends on the weights of the two sectors in GDP. It follows that the deand side (internal or external to 24

25 the econoy), which deterines the size of the two sectors in GDP through preferences, a ects both aggregate TFP volatility and aggregate TFP growth. I study the iplications of the structural transforation on growth in a parallel research. 25

26 Data Appendix All data except the GDP series are fro Jorgenson Dataset, The series for GDP is the annual Real GDP series fro the Federal Reserve Bank of St. Louis. 3 Jorgenson dataset, 2007, provides data for 35 sectors fro 960 to 2005 that cover U.S. GDP. It reports, for each sector, the value and the price of output and the value and the price of capital, labor and 35 interediate goods coing fro each of the 35 sectors. Values are in illions of current dollars and prices are noralized to in 996. Variables are de ned as: q k = quantity of capital services, p k = price of capital services, q l = quantity of labor inputs, p l = price of labor inputs, q ;j = quantity of interediate goods inputs fro sector j and p ;j = price of interediate goods inputs fro sector j. For gross output, p p = price of output that producers receive, and q = quantity of gross output. Thus, q = (q k p k + q l p l + q p )=p p, where q is an index of individual q ;j and p is an index of individual p ;j. I use the rst 27 sectors to construct the anufacturing sector and the last 8 to construct the services sector. The anufacturing sector includes ) Agriculture, forestry and sheries, 2) Metal ining, 3) Coal ining, 4) Crude oil and gas extraction, 5) Non-etallic ineral ining, 6) Construction, 7) Food and kindred products, 8) Tobacco anufactures, 9) Textile ill products, 0) Apparel and other textile products, ) Luber and wood products, 2) Furniture and xtures, 3) Paper and allied products, 4) Printing and publishing, 5) Cheicals and allied products, 6) Petroleu re ning, 7) Rubber and plastic products, 8) Leather and leather products, 9) Stone, clay and glass products, 20) Priary etals, 2) Fabricated etal products, 22) Non-electrical achinery, 23) Electrical achinery, 24) Motor vehicles, 25) Other transportation equipent, 26) Instruents, 27) Miscellaneous anufacturing. Services include 28) Transportation and warehousing, 29) Counications, 30 Downloadable at 3 Downloadable at 26

27 30) Electric utilities (services), 3) Gas utilities (services), 32) Wholesale and retail trade, 33) Finance, insurance and real estate, 34) Personal and business services, 35) Governent enterprises. Using individual sectors, I construct indices of gross output, capital, labor and interediate goods for the two broad sectors, anufacturing and services. Gross output for each broad sector is constructed using chain-weighted Fisher indices. 32 The aggregate labor series in each broad sector, anufacturing and services, is coputed as P ln N t = I n jt ln N jt, (5) j= where each ln N jt is the growth rate of the labor index in sector j at t. I = 27 for anufacturing and I = 8 for services. The weight n jt represents the average of the previous and current period share of labor copensation of sector j in total labor copensation of the broad sector - anufacturing or services. 33 as The aggregate capital series in each broad sector, anufacturing and services, is coputed P ln K t = I k jt ln K jt, (6) where each ln K jt is the growth rate of the capital index in sector j at t. j= I = 27 for anufacturing and I = 8 for services. The weight k jt represents the average of the previous and current period share of capital copensation of sector j in total capital copensation of the broad sector - anufacturing or services. The index of anufactured interediate goods used in the broad anufacturing sector is constructed as a chain-weighted Fisher quantity index of inputs fro the 27 anufacturing sectors going to the 27 anufacturing sectors. The index of interediate services used in 32 This type of index is suggested by the U.S. National Product and Incoe Accounts (NIPA) to construct real value added. See Bureau of Econoic Analysis (2006) for details. 33 For a description of the ethodology used to constructed sectorial labor and capital series, see Jorgenson, Gollop, and Fraueni (987). 27