The Impact of Informative Producer Services on Economic ...itkandil/seminar/huang.pdf · The Impact...

The Impact of Informative Producer Services on Economic

Growth: Theory and Evidence from US Manufacturing Industries

Chien-Yu Huang

North Carolina State University

Abstract

Informative producer services such as consulting, advertising, technical support, repair and mainte-

nance services, etc. are formally introduced in to an endogenous growth model of variety-expansion.

The role of these services is to overcome the information friction generated in the process of technology

specialization. The model has three implications. First, Activities of these informative producer services

positively aect the steady state rate of growth. Second, the growth of variety leads to the growth of the

amount of informative producer services per rm. Third, subsidies to informative producer services can

stimulate economic growth rate. The paper provides empirical evidence by using industrial level data of

US manufacturing industries.

1 Introduction

The fact that service sectors among developed countries gradually become a major part of the economy overpast three decades have been drawn much attention and studies. Evidence shows that the growing of servicesectors are mainly driven by the sector of producer services. See STI 20001 and OECD Employment Outlook20002. In US, for example, the growth of the services sector mainly comes from the growth of informationservices, professional, scientic and technical services, nancial services, real estate services, whole sale andretail trade services etc, which are all producer services3. To explain the growing importance of producerservices, one strand of literature focuses to use static model to explore the role of producer services inthe linkage and coordination of specialized operations within rms. See Francois (1988, 1990), Deardor(2001), Debaere, P., H. Görg and H. Ra (2009). However, the role of producer services hasn't been guredprominently in the economic growth and development literature with a dynamic general equilibrium model,as noted by Francois (2010)4.

This paper formally introduces producer services into a R&D-driven endogenous growth model of varietyexpansion and evaluates the impact of those producer services on economic growth. Rather than emphasizingthe role of producer services stressed in Francois (1988, 1990)5 , this paper focuses to explore their role inthe vertical coordination of the market between upstream specialized intermediate input producers andthe downstream input users. This paper shows that the role of producer services are informative in the

1SCIENCE TECHNOLOGY INDUSTRY (STI) business and industry policy forum series, The Service Economy, 2000OECD, Paris, page 13.

2Producer services, in denition, are intermediate inputs to further production activities that are sold to other rms,although households are also important consumers in some cases. They typically have a high information content and oftenreect a contracting out of support services that could be provided in-house. (OECD Employment Outlook, June 2000, OECD,Paris. page 83.).

3Employment outlook: 200414, Monthly Labor Review November 2005, page 47 table 24In growth literature, there is one strand exploring the structure change of industries, trying to capture the transition of

employment from manufacturing to service sectors and the growing of output share in service industries, (e.g.: Kongsamut(2001) and Acemoglu and Guerrieri (2008)). In the literature, they treat services as part of the nal output or part of nalconsumption. They didn't distinguish services into consumer services and producer services. Therefore, unlike the pointshighlighted in this paper, they way they construct the model doesn't intend to explore the role of producer services as well asillustrates the interdependence of the producer service and manufacturing sectors.

5The role of the producer services, stressed by Francois (1990) and Jones and Kierzkwsky (1988), in the linkage betweenproduction operations within rms should more relate to the types of producer services such as auditing services, accountingservices, managerial and administrative services.

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sense that they are used to disclose the information embodied in a specialized intermediate input to itusers. They are used to reduce the information frictions generated by technology specialization while themanufacturing sector continue to expand (growing of the new varieties). Those informative producer servicesare supplementary to the specialized intermediate input in nal good production in the sense that theyfacilitates the intermediate input transactions among intermediate input producers and its users.

To illustrate the informative role of producer services, here gives an example. Imagine a specializedproduct designed by Microsoft, say Window 7, a high-tech operating system, is going to be sold to and usedby its end users. What services did Microsoft need to provide while selling its new operating system, Window7? First, before oering Windows 7 to the market, Microsoft needs to know more about its potential market,to comprehend the willingness of Window Vista and XP users to switch to Windows 7. In other words,Microsoft needs services for market research and survey. Once Microsoft decides to promote Windows 7, itwill start to disseminate the information of its product through all possible channels to reach its potentialusers. Microsoft needs advertising services. In addition, for the business enterprises and public institutionswho are interested in adopting Window 7, Microsoft would like to provide them with various types ofconsulting services, such as training, planning, deployment, and other initial technical supporting servicesabout Windows 7. Moreover, when these enterprises and institutions decide to purchase Windows 7, tradingpartners will need to look for external legal services to ensure the carry out of the business contract, enforcingboth Microsoft to obligate the subsequent repair and maintenance services and Window 7 users to respectintellectual property right hold by Microsoft. Finally, Microsoft will need to provide repair and maintenanceservices to Window 7 users for a period of time after sale.

The above example illustrates that an information gap between inventors and end-users will emergeafter the introduction of a specialized product. The gap arises simply because users either do not knowthe existence of the product or do not possess sucient knowledge about the product. More specically,The successive industrial R&D activities in manufacturing sector lead to technological specialization andfurther result in the division of knowledge domain to dierent specialized elds. Each group only holds itsown know-how and do not possess the knowledge of other elds, which therefore, endogenously creates asubstantial amount of information frictions within the economy. To overcome these information frictions,those producer services are regarded as the role of informative middlemen who undertake to enhance theunderstanding and availability of the specialized product and nally help to realize the bilateral trade ofthat specialized product. In general, those informative producer services include most of the professional,scientic and technical services in NAICS code 54 industries6, repair and maintenance services in NAICScode 81 industries, part of the service categories in information and nancial service in NAICS code 51 and52 industries7, and all similar type of services mentioned above that are provided in-house in the rms. Theinformative producer services, whatever provided internally or purchased externally, are classied as therm's xed operating cost, a period by period expenditure specied in John Sutton (1992). In terms of theterminology of business accounting, they are considered as overhead cost or business operating expense. Inthis model, they are endogenously determined.

I incorporate the above insight into Romer's simplied version lab equipment model by introducing theinformation frictions between intermediate good and nal good producers8. I assume that there is positiveprobability that a given potential intermediate input user (a nal good producer) learns of a particularintermediate input and decides to use it. When technology advances and becomes more specialized (that is,when new intermediate inputs are designed and introduced by new entrants), the information friction rises.Each nal good producer has less probability to learn of and use that particular intermediate input. In orderto secure the market of that input against shrinking, the intermediate rm would like to provide informativeproducer services to overcome the information frictions.

6One kind of service shouldn't be included in this category is scientic research and development service, these services innature generate information frictions within the economy, not reduce them.

7The particular services in nancial and information service (NAICS code 51 and 52) industries I notify are those supplementto promote and support the sales of specialized services and commodities designed (eg: the customer support, marketing andbroker agency) in these industries, but not include the designed services and commodities (eg: the services of designing nancialderivatives and computer software) themselves. In addition, it is also important to note that one should always distinguishthe producer services I suggest in nancial industries to those nancial intermediaries in general studied in the literature (eg:Cameron (1967), Diamond and Dybvig (1983), Greenwood and jovanovic (1989), Bencivenga and smith (1991), )

8Romer (1990) implicitly assumes that the whole transaction process of selling a specialized input does not involve anycostly intermediary activities. In other words, the specialized input is immediately available to the nal good producers afterinvention.

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First, my model implies that the activities of informative producer services positively contribute to long-run growth rate. These services, served to reduce information frictions, enlarge the market size for the inputproducers, increase rate of return of successive R&D activities, and consequently result in higher economicgrowth rate. The result justies informative view on some particular informative producer services, suchas advertising, in IO literature. In the literature, scholars hold controversial views against advertising. Someviews advertising as a tool to persuade consumers, regarding advertising as a waste of resource9. They arguethat advertising has no real value to the consumers and what's more, it induces an anti-competitive eect tothe economy and a reduction in welfare level. Others, however, believe that advertising is in nature informa-tive, used to deliver the product information, which may have pro-competitive consequences10. Empiricalndings by Telser (1964) suggest that advertising services facilitates entry and new-product introductions.My model adopts the later view and surprisingly, gives an even stronger prediction that these services havepositive impact on the rate of economic growth.

Second, in my model, successive entry of the new technologies leads to growing provision of the amountof informative producer services per rm. It basically captures the urgent demand for informative producerservices in the process of technology specialization in the modern economy. This implication may partiallyexplain why service sector and manufacturing sector11 tend to expand at the same time frame after IndustrialRevolution.

Moreover, this model also gives an interesting policy implication. Subsidy to produce informative pro-ducer services can stimulate economic growth rate. The detail of this subsidy scheme and its comparisonwith others are discussed in Huang (2010).

Finally, I test the rst two model implications discussed above by using the industrial level data ofexpenditure on informative producer services from US manufacturing industries. The empirical ndings areconsistent with the two implications.

The content is organized as follows: In section 2, I create a model to incorporate the informative producerservices into Romer's simplied variety-expansion model (Barro and Sala-i- Martin, 2004). In section 3, Idiscuss the empirical implications in the model. Section 4 discusses the dataset. Section 5 discusses theempirical methodology and specication. Section 6 and 7 give the empirical ndings. Finally, section 8 isconclusion.

2 The Variety Expansion Model with Informative Producer Ser-

vices

The model I construct is based on the structure of Romer's simplied version lab equipment model discussedin chapter 6 of Barro and Sala-i-Martin (2004). There are two sectors of activity in the production sideof the economy: a competitive sector producing a homogeneous nal good, and a non-competitive sectorproducing dierentiated intermediate good.

2.1 The producers of homogeneous nal good

Information friction within the economy is captured by an assumption that nal good producers do not havesucient knowledge about all the existing intermediate input designs. Each nal good producer only haveaccess to a subset of the existing intermediate inputs. Therefore the production technology for nal goodproducer i is:

Yi = l1−αi

∑j∈N(i)

xαij N(i) ⊂ N.

Yi is nal output, li is labor input, Xij is the employment of the jthe type of the specialized intermediatenondurable goods and services. N is the existing number of all intermediate input designs. α ∈ [0, 1]. I

9This view was hold by Chamberlin (1933), Robinson (1933), Bain (1949) Comanor and Wilson (1967, 1974)10This view was hold by Ozga (1960), Stigler (1961), Telser (1964) and Nelson (1970).11Strictly speaking, the manufacturing sector, I dened here, is the sector that produce all various specialized intermediate

goods and services. It means that the specialized services designed, for example, the services of designing nancial derivatives orthe services in designing computer software that are generally classied as the activities in service industries should be includedin the manufacturing sector.

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assume that each nal good producer will use a particular intermediate input once the producer acknowledgesthat input. Therefore, N(i), the subset of existing number of intermediate input designs, is the set ofintermediate inputs that is acknowledged and used by the nal good producer i. Furthermore, dierent nalgood producers possess knowledge of dierent sets of intermediate varieties. Therefore, N(i) is dierentamong nal good producers.

I further assume whether a specialized intermediate input is acknowledged or isn't acknowledged by aparticular nal good producer is random. It implies each nal good producer uses one particular intermediateinput with a probability. I propose the following production technology for the nal good producer i tocapture the above characteristics as well as to ensure the tractability of the model.

The production technology for the nal good producer i can be written as:

Yi = l1−αi

N∑j=1

Qijxαij , (1)

where Qij is dened as:

Qij =

1 with Probability Ωij

0 with Probability 1− Ωij

.

Qij is a random variable set to be the value of either zero or one, implying that each nal food producer i usesa particular specialized input j with probability Ωij . This specication basically keeps all the characteristicsof the production function proposed by Spence (1976), Dixit and Stiglitz (1977) and Ethier (1982). The onlydierence is the setup of random variable Qij . This setup captures the idea that economy exists informationfriction between nal good producers and intermediate good producers, indicating only a subset of theexisting intermediate inputs are available to the nal good producer.

This is a lab equipment model. It implies aggregate output Y =∑i Yi, can be used in a perfectly

substitutable manner for various purposes. Specically, this output can be used for either consumption,production of intermediates, the R&D needed to invent new types of intermediates, or informative producerservices. Other than the price of informative producer services, all prices are measured in units of thehomogeneous ow of goods, Y 12.

The prot for the nal good producer is

Yi − wli −N∑j=1

PjQijxij , (2)

where w is the wage rate, and Pj is the price of intermediate j. Since the nal good markets is assumedto be competitive, the producer takes w and Pj as given. Prot can be maximized by taking the derivativewith respect to xij and li. The demand function of specialized input xij can be specied as

xij =

li(

αPj

)1

1−α with Probability Ωij

0 with Probability 1− Ωij

(3)

The price elasticity of demand for each type of intermediate is the constant −1/(1 − α). Therefore, theaggregate demand of a specialized input j, denoted as xj , is

Xj =∑i

xij = Ωj L (α

Pj)

11−α , (4)

where Ωj is proposed by the following function13

Ωj =( 1kmj)

γ(N)1−γ

Nfor

mj

N< k

12I assume there exists the technology spillover in the informative producer service sector. Therefore, the quality adjustedprice for the informative producer services decreases as the technology advances.

13The probability function setup here makes the function of informative producer services in disseminating product informa-tion essential, which is a very strong assumption. The reason I adopt this setup is its convenience to deduce linear testableimplications for the model in section 3. In Huang (2010), I use a CES type setup for the probability function, which avoidsthe essentiality of informative producer service in the model and the results implied in the model are still hold given certainparameter restriction.

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The parameters k, γ satisfy the restrictions that k > 0,and 0 < γ < 1. mj is the level of informative producerservices used by intermediate rm j.

Ωj satises the following properties: (1) Ωj lies within the Interval (0, 1). Recall that Ωij is the probabilitythat nal good producer i uses a particular specialized input j. This implies that every nal good producerwill randomly employ a combination of specialized inputs in each period14. The symmetric assumption Iimpose among nal good producers implies Ωij = Ωj , Ωj can be regarded as the proportion of nal goodproducers who could use this particular input j. Also, this property signies that parameter k should alwayssatisfy the restriction, mj/N < k; (2) Ωj is a decreasing function of N . This property captures the insightthat technology advance leads to a diculty in the employment of a particular specialized input j; (3) Ωjis also a increasing function of mj . It captures the idea that the role of informative producer services is toreduce the information cost among two intermediate good trading partners. In addition, γ measures theeectiveness of informative producer services in overcoming information frictions.

In symmetric equilibrium where Ωj = Ω and mj = m, the aggregate nal output production can bewritten as

Y = AL1−α(NXj)α(ΩjN)1−α = L1−αXαA((

1

km)γ(N)1−γ)1−α, (5)

where X = NXj . The RH'S of equation(5) can be decomposed as two terms. One is L1−αXα, which is thecontribution of factor inputs L and X to output Y . The other is A(( 1

km)γ(N)1−γ)1−α, which is total factorproductivity. One should notice that the amount of informative producer services per rm m shows up inthe term of total factor productivity.

2.2 Intermediate Good Producers

The intermediate rm faces a two-stage decision process. In the rst stage, intermediate producer decideswhether or not to devote resources to invent a new design. In the second stage, the producer determinesthe optimal price for selling her newly invented goods and chooses the optimal quantity level of informativeproducer services, mj .

We assume inventor of good j retains a perpetual monopoly right to good xj . This ow of the monopolyrent provides incentive for invention. The present value of the returns for discovering the jthe intermediategood is given by

V (t) =

ˆ ∞t

πj · e−r(t,v)(v−t)dv (6)

where πj is the prot ow at date v, and r(t, v) = ( 1v−t ) ·

´ vtr(w)dw is the average interest rate between

time t and v . The interest rate r will be a constant in equilibrium.

Stage 2: Optimal Price and Optimal Quantity Level of Informative Producer Services

Once the specialized input xj is invented, it uses resource of nal output Y to produce it. The productionfunction for xj is

xj = Rxj ,

where Rxj is the resource measured in unit of nal output Y . It, therefore, implies the marginal and averagecost of producing xj are assumed to be constant and normalized to 1. In addition, informative producerservices are also produced by the resource of nal output Y , represented by the following production function

mj =N

φRmj

where Rmj is the resource measured in unit of nal output Y , φ is just a constant parameter. Here, Iassume there exists technology spillovers into the sector of informative producer services 15. Therefore, the

14This assumption implies that there is no long-term supply-demand relationship between particular nal good and interme-diate good producer. One example that the assumption can be rationalized while one thinks the informative producer servicein terms of technical and supporting services of a particular high-tech product. If intermediate rm doesn't provide sucientenough technical and supporting services, the buyer has higher probability to terminate the trading contract and searches toanother trading partner in next period.

15The common impression that the productivity of service sectors are stagnant during 1970 to 1990. However, the productivityof some producer services are actually growing over time and even faster after the introduction of ICT technology (e.g.Triplett,J.E. and B.B. Bosworth (2002), Fixler, D.J. and D. Siegel (1999) and Anita Wöl (2003))

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technology stock (number of intermediate varieties) N enters as the productivity of producing the services.It, hence implies the unit cost of production of mj is φ/N unit of nal output, which decreases with N .

The prot ow for intermediate good producer is given by

πj = Pjxj −Rxj −Rmj (7)

= [Pj − 1]xj − φN mj

wherexj = Ωj(

α

Pj)

11−αL. (8)

xj is the aggregate demand of specialized intermediate input j, facing producer j from equation(4). Thequantity L is the aggregate labor input and is assumed to be constant. The maximization problem forintermediate good producer is

maxPj ,Mjπj = Ωj [Pj − 1]L (α

Pj)

11−α − φ

Nmj (9)

= [Pj − 1]L (α

Pj)

11−α

( 1kmj)

γ(N)1−γ

N− φ

Nmj .

The solution for the monopoly price is

Pj = P =1

α. (10)

The price, Pj , is constant over time and the same for all intermediate good j.By substituting equation(10) into equation(9) and taking the derivative with respect to mj , one gets the

following rst order condition and the solution for mj :

γ1

kBL(

1

k

mj

N)γ−1 − φ = 0 (11)

mj = (φk

γBL)

1γ−1 kN, (12)

where

B = (1− αα

)α2

1−α .

From equation(12), it is obvious that the growth of N actually leads to the growth of mj and both growat the same rate. The probability Ωj is constant over time . This result brings the rst implication inmy model. The technological advancement (the growth of the specialized inputs) leads to growth of theamount of informative producer services per rm, which, to some extent, can explain why service sectorsand manufacturing sectors expanded at the same time frame after Industrial Revolution. The intuition isthat the technological advancement generates the information frictions between nal good producers andintermediate input producers, which makes market size of a particular specialized input shrinks. To securethe market size against shrinking, each intermediate input producer correspondingly increases the provisionof informative producer services.

By substituting the price Pj from equation(10) into equation(8), one determines the aggregate equilibriumquantity of each intermediate good:

xj = (γBL

φk)

γ1−γ α

21−αL, (13)

which is also constant over time and across j. The equilibrium aggregate quantity of intermediates, denotedby X , is given by

X = Nxj = (γBL

φk)

γ1−γ α

21−αLN. (14)

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By substituting for Pj from equation(10) into equation(9), one gets a formula for the prot ow as a functionof

mjN :

πj(v) = BL(1

k

mj

N)γ − φ mj

N.

If I further multiplymjN on both side of the rst order condition from equation(11). one gets

γBL(1

k

mj

N)γ = φ

mj

N(15)

and substitute equation(15) into above prot ow function, the prot ow becomes

πj(v) = (1− γ)BL(1

k

mj

N)γ . (16)

It shows that the prot ow is an increasing function of the ratiomjN . (It later shows the rate of return r

and the steady state growth rate g are also an increasing function of the ratiomjN ). This equation implies

that the activities of engaging in informative producer services positively by the intermediate good producerpositively aect its own prot ow given a technology level N unchanged. Specically, by engaging in moreamount of informative producer services at a given technology level, the intermediate rm enlarges its marketsize, which in turn creates itself a larger prot ow. On the other hand, given the amount of informativeproducer services m unchanged, the increase in technology level N , generates higher information frictionsin the input markets, and thus crowds out the existing rm's market size. This nally, leads to a lowerprot ow. Therefore, the two opposite eects make only the ratio m

N matters. Substituting formjN from

equation(12) into above, one gets the equilibrium prot ow:

πj(v) = (1− γ)γγ

1−γ

(BL

(φk)γ

) 11−γ

(17)

which is constant over time and across goods. Finally, by substituting the optimal values of Pj and xj intoequation(5), one gets the inventor's net present value of prot at time t:

V (t) = (1− γ)γγ

1−γ

(BL

(φk)γ

) 11−γˆ ∞t

e−r(t,v)(t−v)dv (18)

Stage 1:The Decision to Conduct R&D In this stage, a potential investor decides if they would liketo conduct R&D and enter the business. It is assumed that the cost to create a new type of product is ηunits of Y . Also, inventor has free entry into the business, so that anyone can pay for the R&D cost η tosecure the net present value, V (t) . Therefore, the free entry condition is given by

V (t) = η (19)

If one dierentiates the free entry-condition in equation(19) with respect to time, using the formula for V (t)from equation(18) and taking account the condition r(t, v) = 1

(v−t)´ vtr(w)dw, one gets

r(t) =π

V (t)+

·V

V(20)

where π is the constant prot ow given by equation(17). Since η is constant, the free entry condition in

equation(19) implies that·V = 0. It follows from equation(20) that interest rate is constant and equal to

r(t) = r = πη . Substituting for π from equation(16) yields

r =(1− γ)BL( 1

kmjN )γ

η, (21)

wheremj

N= (

φ

γBL)

1γ−1 k

γγ−1 .

7

We can see that interest rate r is an increasing function of the ratiomjN as mentioned above. The underlying

technology and the market structure peg the rate of return at the value shown in equation(21). Since freeentry requires V = η, η is the market value of a rm that possesses the blueprint to produce one of theintermediate goods, and the corresponding aggregate market value is ηN .

2.3 Households

The economy is populated by innitely lived agents. The population is constant and equal to L. Agents'preferences are represented by the following standard CRRA utility function:

U =

ˆ ∞0

(c1−σ

1− σ) · e−ρtdt (22)

They derive utility from consumption c and supply inelastic labor. The household's intertemporal budgetconstraint is,

·a = w + ra− c. (23)

Each household earn the rate of return r on the assets a and receive the wage rate w on one unit of thelabor. Savings are used to nance R&D investments and there is no capital. The standard Euler equationis,

·c

c= (1/σ)(r − ρ) (24)

The usual transversality condition implies r must exceed the long run growth rate of output Y .

2.4 General Equilibrium

In a closed economy, the total assets of households are equal to the market value of rms,

A = aL = ηN (25)

Since η is constant, the change in assets must be

·A = η

·N (26)

The wage rate is given by

w =1

η(1− α)(

Y

L) (27)

After some manipulation, the interest rate, given by equation(21), can be written as

r =1

η[(1− α)α (

Y

N)− φ

Nmj ] (28)

Substituting equation(27) and(28) into households' aggregate budget constraint(23), the households' budgetconstraint becomes

η·N = Y − C −X − φ

NM (29)

This condition states that, at every point in time, GDP, must be allocated to consumption C, the production

of intermediates X, the creation of·N new goods (each of which costs η), and also the aggregate level of

informative producer services M (which costs φ/N). Substitution for r from equation(21) into equation(24)leads to the steady growth rate as a function of the ratio m

N :

g =1

σ

[(1− γ)BL( 1

kmN )γ

η− ρ]. (30)

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Substituting formjN from equation(12)into above, one gets the equilibrium steady state growth rate:

g =1

σ

(1− γ)γγ

1−γ

(BL

(φk)γ

) 11−γ

η− ρ

(31)

One can see from equation(30) that steady growth rate is an increasing function of the ratio mN . This

suggests that the impact of the amount of informative producer services per rm m not only have leveleect, but could also have overall long-run growth eect on the economy. Specically, the services thrustedto reduce information friction by disseminating the product information can enlarge the market size of thespecialized product. It, therefore, increases the equilibrium prot ow and the incentive for the potentialrm to conduct R&D. As a result, it has positive impact on economic growth rate.

Moreover, from equation(31)the steady state growth rate depends not only on the parameters, suchas η, R&D unit cost, and the population scale Lin Romer's baseline variety expansion model, but alsodepends on the parameter φ, the unit cost of informative producer services at the early stage of developmentand γ the eectiveness of the informative producer services in overcoming information friction. This resultdelivers interesting policy implication. Compared to traditional variety expansion model without informativeproducer services, this model provides an additional channel for policy intervention to stimulate economicgrowth subsidies to reduce the unit cost of producer services φ

N . Besides, one can also nd that theparameter value γ shown in equation(31) governs the eectiveness of subsidy through such channel16. Ittherefore, implies that a precise calibration of the parameter γ can be instructive to help government todecide its eective subsidy allocation scheme. This model also provides a simple way to calibrate γ, as isshown in the appendix.

3 Two Empirical Implications

The rst implication in the model is that the activities of engaging in informative producer services contributeto the steady state rate of growth. This implication is directly shown in equation(30):

g =1

σ

[(1− γ)BL( 1

kmN )γ

η− ρ]. (32)

This implication can be rewrite to link the variable that can be measured and found in the dataset directly.First I multiply the rst term in RH'S of equation(32) with γ and 1

γ into above and substitute for γBL( 1kmN )γ

from equation(15) into equation(32). I get

g =1

σ

((1− γ) 1

γφmN

η− ρ

), (33)

Second, I rewrite equation(33):

g =1

σ

((1− γ) 1

γφNMN

η− ρ

)=

1

σ

((1− γ) 1

γRMN

η− ρ

)=

(1− γ) 1γ

ση

RMN− ρ

σ, (34)

where M = mN is the aggregate quantity of informative producer services and RM is the aggregate expen-diture of informative producer services. I can write down a simple linear regression model with dependentvariable g and independent variable RM

N to test if the coecient of the ratio RMN is positive. Practically,

equation(34) can be tested in either industry level or country level. In the following empirical sections, Iapply the theory directly to industry level. Therefore, the growth rate g is the mesasure of industrial growth,RM is the overall industrial expenditure on informative producer services and N is the knowledge stock ofthe industry. Later I use number of rms of the industry to be proxy for knowledge stock N . A detaildiscussion of the proxy is shown in subsection 5.3.

16Huang (2010) gives a more detail discussion about the parameter φ and γ.

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The second implication in the model is that the advancement of technology leads to the growth of theprovision of informative producer services per rm. This implication deduced directly from equation(22).

m = (φk

γBL)

1γ−1 kN.

This equation implies that when technology N increases, the amount informative producer services per rmincreases. I can rewrite the model by multiplying both sides with the term φ

NN . I get

RM =φ

NM = (

φk

γBL)

1γ−1 kφN, (35)

and I take logarithm on both sides, It becomes

lnRM = ln

(γBL

(φk)γ

) 11−γ

+ lnN. (36)

equation(36) rst, implies that the two variables lnRM and lnN are cointergrated. It can be tested if longenough time series data for aggregate expenditure of informative producer services RM and technology stockN are available. 17 . Second, if I further, divide both side of equation(35) by industrial nal output Y andtake logarithm scale. The equation becomes

lnRMY

=1

1− γln(

γB

(φk)γ) +

1

1− γlnL+ ln

N

Y. (37)

The model implies a positive correlation between variable lnRMY and lnNY . As discussed in detail below, ifboth series are stationary, a simple linear regression model can be applied to test this correlation by usinga panel or cross-sectional of industrial level datasets.

4 Choices of Datasets

Two datasets of expenditure of informative producer services were selected from BEA's (Bureau of EconomicAnalysis) industrial level data of US manufacturing sectors. One was collected from the Use table of AnnualIndustry Input Output Account in BEA, covering 19 3.5-digit NAICS level manufacturing industries from1997 to 2008. It is a annual panel with 11 years and 19 industries, totally 209 observations. The otherone was collected from Use table of Benchmark year Industry Input Output Account in BEA, covering 2516-digit NAICS level manufacturing industries of two benchmark years 1997 and 2002. By taking average ofthe two years, I got a cross-sectional data with 251 (industries) observations.

Both of the datasets started from year 1997, since the data for most of the industrial expenditure ofinformative producer services is not so common to acquired before 1997. One reason is that the importanceof producer service sectors had not been received serious attention until NAICS (North American IndustryClassication System) was adopted in 1997 in North America (Including US, Canada, Mexico). One maindierence of NAICS, in contrast to previous Standard Industry Classication System SIC, is its compre-hensive and detail classication of producer services. NAICS allows me to test the model implications byindividually looking into various type expenditure of associated informative producer services. In NAICS,I select six types of informative producer services that t appropriately with the denition of the functionof informative middleman I dened in the introduction. The categories include most of the professional,scientic and technical services in NAICS 5412 code industries 18 which ts the most strict denition inthe model and broadly the categories include publishing and broadcasting services in NAICS 511, 513 codeindustries, information services in NAICS 514 code industries, legal services in NAICS 511code industries,repair and maintenance services in NAICS code 81 industries. Besides, I also includes whole sale and retailtrade services in NAICS 41, 42 code industries into categories. Though the main function of whole sale and

17This paper didn't perform this test, since industrial level data I collected from BEA used in empirical analysis below onlylasts for eleven years, which is not an enough lone time series.

18One kind of service shouldn't be included in the selection is scientic research and development services in NAICS 5417code industries, these services in nature generate information frictions within the economy, not reduce them.

10

retail trade services shouldn't be regarded as delivering product information but, rather, delivering the phys-ical body of the products. However, the delivering process to some extent should be able to carry minimuminformation of the product to the customers. Therefore, I include whole sale and retail trade services intocategories that t the most loosen denition of informative middlemen.

Both of the datasets were collected from Use table of Industry Input Out Account of BEA. In the absenceof the permission to have access into detail rm level data19, the second best choice is the industrial levelexpenditure data from Industry Account of BEA20. In addition, the data was collected from Use table. Alongthe column of Use table, the data are the services payment to those informative producer service industriesout of manufacturing industries. It implies that those services are served as intermediate inputs used bymanufacturing industries. It excludes the part of the services that was purchased as nal consumptionexpenditure by households 21. The data in Use Table, separating services as intermediate inputs use fromnal consumption, precisely ts the need to test the implications of the theory.

Other data, including industrial output, industrial full time employment, industrial number of rms,industrial TFP percentage change are collected individually from dierent database. Industrial output andfull time employment, are also collected from both Annual Industry Account of BEA with 3.5 digit NAICSlevel manufacturing industries from 1997 to 2008, and Benchmark Industry Account of BEA with 6 digitNAICS level manufacturing industries of the years 1997 and 2002. The data for number of rms, for bothdatasets, was collected from SUSB (Survey of US Business) in Census Bureau. Industrial TFP growth rateof 3.5 digit NAICS manufacturing industries from 1998 to 2008 was collected from BLS (Bureau of LaborStatistics). Industrial TFP growth rate of 6 digit NAICS manufacturing industries from year 1997 to 2002are collected and aggregated with appropriate aggregation rule from database of NBER-CES ManufacturingIndustry. The detail construction of those data series is shown at the appendix.

5 The Empirical Methodology and Model Specication:

5.1 Empirical Methodology

In the empirical growth literature, cross-section studies generally focus on average growth rates measuredover long periods of time, and relate these to average associated independent variables measured over thesame period. Panel studies use repeated observations over shorter time periods, commonly ve-year averages,while with large cross sections. Comparing to the datasets studied in the literature however, my rst datasetof annual panel uses the data of 19 3.5 digit NAICS level US manufacturing industries from 1998 to 2008 withonly 11 years and 19 industries, which, though has enough time series as a panel, has extremely small crosssections. The second dataset, though has 251 industries as its cross sections, doesn't have enough time series22. The limitation of both datasets, in contrast to the datasets studied in the literature, do not allow meto extract information to form a rm statistical inference for the theory by resorting to advanced empiricaltechniques and complicated econometric methods. Therefore, the econometrics methodology I adopt here isto focus on discovering some basic statistical correlations implied in the theory by using the basic and simpleeconometric approach.

First, my strategy is to only include the main regressors of interests, but not try to include as manyregressors as possible in the regressions to control other eects 23. Besides, I impose the assumption ofequality of slope parameter coecients across industries and over times in estimation with both of thedatasets.

19The public database of Compustat has rm level data. However, it only includes samples with big rm size in the industries.The rm level data from Compustat is not appropriate to be used as industrial level data by simply aggregating them.

20The industrial level service expenditure data in BEA is not the rst best choice because the use table in BEA only countsthe service inputs purchased externally from other service industries, but doesn't counts the service inputs provided in house.Therefore, the data of service expenditure in BEA is underestimated.

21Recall that in some cases informative producer services are also purchased by household as nal consumption (OECDEmployment Outlook, June 2000, OECD, Paris. page 83.).

22Data with two benchmark years 1997 and 2002 are too short to form a valid panel dataset. Besides, the dataset can onlygenerate one year industrial output growth rate which is the main dependent variable in the following estimation. Therefore,an appropriate solution is to treat the dataset as cross-sectional data by taking average the data across these two years.

23Including many regressors in regression is at the expense of losing too much degree of freedom in estimation which is notallowed in a dataset with small sample size

11

Secondly, I focus on dealing with the standard Fixed Eect and OLS linear regression models. For therst dataset of annual panel, I simply pooled the data across industries and apply standard Fixed Eectestimation to the rst dataset of annual panel from 1998 to 2008. However, In testing the long run eectof informative producer service expenditure per rm on measures of industrial growth, One disadvantage ofusing annual panel is that much of the annual variation in measure of industrial output growth rates mayreect short run business cycle uctuations or adjustments to occasional shocks. I can only rely on a simpledynamic econometric specication to implicitly lter out these short run transitional eects corresponding toshocks, while acknowledging the limitations of this approach. The richer dynamic econometric specicationsinvolved with many lagged dependent variables and independent variables suggested in Bond, Leblebiciogluand Schiantarelli (2009) to control high frequency business cycle uctuation is at the expense of sacricingtoo many observations over several periods of time, which is not aordable by a small panel dataset likemine. For the second dataset with only two benchmark years 1997 and 2002. I take average for all variablesrelevant to the estimation in these two years to get a cross-sectional data. Then I apply OLS estimationto this dataset. However, the similar concern with the limitation of the dataset to rigorously reect thelong run growth eect of the service expenditure per rm should be kept in mind, while performing thetests. Finally, the estimated standard errors in OLS and standard xed eect model here are both robustto heteroscadasticity 24.

Moreover, like most regular growth empirical literature, I don't tend to investigate the potential endo-genity problems. To solve endogenity problems should involved with looking for external instruments andinternal instruments. Appropriate external instruments for estimation are not easily found. The internalinstruments (using lagged independent variables) suggested by Arelino and Bond (1991) needs to sacriceobservations for several periods of times which is not allowed for this small dataset of annual panel 25.

Again, the econometrics methodology I adopt is to focus on discovering some basic statistics correlationsthat are implied in the theory. People might question the reliability of the results. However, A morecomplete and detailed empirical research couldn't be conducted until a more complete dataset with enoughcross sections and long time series can be established.

5.2 Specication for the First Model Implication.

The model, as discussed in section 7, predicts that there is a positive correlation between expenditure ofinformative producer service per rm and industrial growth. Therefore, by log-linearizing the RH'S ofequation (34) I get the following common linear regression model. 26

git = β0 + β1lnASit + β2lnLit + εit, (38)

where εit is a mean zero, serially uncorrelated shock which I assume to be independent across industries.The dependent variable git is a measure of growth in industry i. In the empirical tests below both totalfactor productivity growth and real per worker industrial output growth are used as dependent variables.An alternative choice of dependent variable between total factor productivity growth and real per workerindustrial output growth is directly implied in the model 27 . Moreover, The model also implies that industrialtotal R&D expenditure is the resource used to design new intermediate varieties, which in turn implies thatthe growth of new variety (TFP growth) is equal to R&D expenditure per rm. It further implies thatI can use R&D expenditure per rm as third dependent variable. The regression analysis of using R&Dexpenditure per rm as third dependent variable will be discussed when applying it in the second dataset ofcross-section.

For independent variables, rst, recall that this model provides an easy way to calibrate the parameterγ. I therefore, incorporate this additional information into regression estimation. I combine the calibrated

24In Stata, The robust standard errors in two model estimations can be respectively implemented by the option command ro added after the command reg in OLS estimation and by the option command cluster in standard xed eect estimation.

25This paper actually tries to solve the endogenity problem by instrumenting suspected endogenous regressors. I obtain theinstruments by lagging at least three periods from t− 2 , using ivreg2 in Stata, However, the empirical results didn't pass bothStock-Yogo weak identication test and Kleibergen-Paap underidenticantion test provided by implementing ivreg2 in Stata.These results can be obtain upon request.

26The derivation detail is shown in the appendix.27Romer's type R&D-based endogenous growth theory implies that the source of output growth comes directly from produc-

tivity growth. Therefore, the nal industrial output growth rate equals industrial TFP growth rate in the model.

12

value γ with the service expenditure per rmRmiNi

to get this adjusted service expenditure ASit, where

ASit = ( 1−γγ )

RmitNit

is an adjusted value of service expenditure per rm of industry i at time t 28. Lt is thefull time industrial employment, which represents the scale for this industries. Including scale variable Li totest scale eect on economic growth rate is very common in endogenous growth theory (e.g. Backus, Kehoeand Kehoe (1992), Jones (1995), Peretto and Laincz (2007)). Finally, the test of the theory boils down towhether β1 > 1.

This regression model also extends to include additional regressors to control other eects subject todierent econometric approaches applied in either cross -sectional data or annual panel data under theregular growth empirical framework. In the following subsections, I will discuss each of these additionalregressors.

5.2.1 The additional regressors included in standard xed eect estimation while dealing

with the annual panel

Based on the above model structure, the regression model, extended to include additional regressors subjectto standard xed eect estimation of annual panel, can be written as:

git = β0 + β1lnASit + β2lnLit + β3lnyit−1 + vi + et + εit, (39)

where vi allows for time-invariant unobserved heterogeneity in industrial measure of growth without requiringexplicit measurement of these factors 29. et allows fro controlling common shocks to all industries. Thiscan be done by including a full set of year dummies in the regression model 30. Finally, I include a simplerdynamic specication the logarithm of industry output per worker lag for one period lnyit−1, to allow someindustrial output to deviate from their long-run growth paths during the sample periods. The specicationis consistent with transitional growth in the Solow model See Mankiw, Romer and Weil (1992).

5.2.2 The additional regressors included in standard OLS estimation while dealing with data

of cross-section

The regression model under OLS estimation while dealing cross-sectional data can be written as the following:

gi = β0 + β1lnASi + β2lnLi + β3lnyi97 + εi, (40)

The only additional regressor included in the model is the logarithm of industrial output per worker inbenchmark year 1997. This setup is also similar to the setup in Mankiw, Romer and Weil (1992). Theyinclude an initial income level into regression estimation to conrm the convergence predicted in neoclassicalgrowth framework.

5.2.3 Time series property for this annual panel

For this annual panel I also conduct a test to see if the series contain the unit root. By subtracting thecross-sectional average from original series 31, I run a test of stationarity in panel dataset proposed byLevin-Lin-Chu (2002) for dependent and independent variables 32. For the dependent variable, the growthrate of industrial output g, the test rejects the null of non-stationarity when allowing a time trend. For theother dependent variable, the growth rate of industrial TFP, the test rejects the unit root with or withouta trend. For the main independent variable, the logarithm of each kind of adjusted informative producer

28Some may argue that including calibrated values into estimation may generate the empirical results that are more robust ifthere are industry specic parameters in the model. It is probably true to some extent. However, I still would like to retain theassumption of equality of parameters across industries and over times. The reason is that a serious treatment of heterogeneouscoecients across industries involves an overall calibration and estimation of all parameters that are industry specic. Forexample, not until I can estimate the other industry specic parameter η. These empirical results under the heterogeneouscoecient assumption are not precise either.

29The standard xed eect model by implementing the command xtreg in Stata automatically eliminate this xed eectfactor vij

30In Bond, Leblebicioglu and Schiantarelli (2009), they include time dummies rather than a simple linear trend in the modelto allow for a more general evolution of total factor productivity (TFP).

31Levin, Lin, and Chu (2002) suggest this procedure to mitigate the impact of cross-sectional dependence.323 lags of the series are used in ADF regressions

13

service expenditure per rm lnASit, the test rejects the null hypothesis of unit root while allowing a timetrend 33. For the regressor, logarithm of industrial employee lnLit, the test rejects the null hypothesis ofunit roots without a time trend and nally, for logarithm of industry output per worker lag for one periodlnyit−1, the test rejects the null hypothesis of unit roots with or without a time trend. These test ensurethat all series do not have empirical evidence that they are I(1) series.

5.3 Specication for The Second Model Implication

The second implication of the model indicates that the expenditure of informative producer service is anincreasing function of number of existing product varieties. This captures the urgent demand of growingamount of informative producer services in a process of technology specialization. By dividing both side ofequation(36) by industrial output Yit and taking logarithmic scale. I get the following basic econometricmodel specication:

lnRMit

Yit= ξ0 + ξ1ln

NitYit

+ ξ2lnLit + δt. (41)

The dependent variable RMitYit

is the ratio of industrial informative producer service expenditure to industrial

nal output in industry i. NitYit

is the ratio of number of intermediate product varieties to industrial naloutput in industry i. Lit is the full time employment of industry i. By dividing both sides of equation(36)with the industrial output Yit, I rescale variables of dierent industries to make them comparable. Otherwise,the results of estimation will bias toward industries with larger size.

Nit is the number of intermediate product varieties. In my dataset, however, there is no exact data seriescorresponding to number of intermediate varieties. The question then becomes how to evaluate a substitutemeasure of product variety empirically. In the strands of R&D growth theory with variety expansion, It iscustomary to posit that each product variety i is manufactured by a local monopolist so that there is a one-for-one correspondence between product variety and the number of rms. This feature is not an assumptionbut a consequence of the fact that entry is costly. If the entrepreneur's entry target existing product lines,it will lead to losses due to direct price competition with existing incumbent. One-for-one correspondencebetween product variety and the number of rms is also justied empirically, Dunne, Roberts, and Samuelson(1988) report that single-plant rms constituted 93% of all rms in manufacturing industries between 1963and 1982. Multiplant rms only constituted 7% of all rms with average 2.5 plants per rm. The report ofCensus Bureau nds that more than 90% of each establishment's shipments classied within its designated4-digit industry, implying that the vast majority of plants produce one product 34. Combining the twoarguments above, It directly implies that vast majority rms are single-product rms. Moreover, evidencefrom the gure 6 of Laniz and Peretto, percentage of single-plant rms out of the total and the averagenumber of plants per multiplant rm hardly changed over the decades preceding the data in Fig. 6 of theirpaper. This tells us that manufacturing is mostly populated by single-plant, single product rms.

Due to above justications in both theoretical and empirical manner, One-for-one correspondence betweenproduct variety and the number of rms raises two natural candidates to proximate product variety numberof rms and number of establishments 35. Here I adopt the former. The test of the theory boils down towhether ξ1 > 0.

This specication directly apply to OLS estimation when dealing with the cross sectional dataset.

5.3.1 The additional regressors included while dealing with the annual panel

When dealing with annual panel under xed eect estimation, this specication then can be extended to thefollowing:

lnRMit

Yit= ξ0 + ξ1ln

NitYit

+ ξ2lnLit + µi + λt + δt. (42)

33Among those series, logarithm of adjusted information service expenditure per rm, logarithm of adjusted legal serviceexpenditure per rm and logarithm of adjusted miscellaneous professional, scientic, and technical service expenditure per rmreject the unit root at the level less than 5% with or without considering the time trend.

34The above argument is cited directly from Laincz and Peretto (2007)35Lancz and Peretto (2007) adopts number of establishment as the proximate to product variety

14

For the similar reason, µi allows for time-invariant unobserved industrial heterogeneity and λt controls forthe common shock eect.

5.3.2 Time series property for the annual panel

By subtracting the cross-sectional average from original series. The dependent variable, lnRMitYitfor each

type of informative producer service passes Levin-Lin-Chu (2002) unit root test, rejecting null hypothesis ofunit root with or without time trend except that of whole sale and retail trade service 36. The independentvariable, logarithm of the ratio of number of intermediate product varieties to in industrial nal output lnNitYitalso passes the test, rejecting null hypothesis of unit root with or without a time trend.

6 The Empirical Results of First Implication Positive Correlation

between Expenditure of Informative Producer Service per Firm

and Measure of Industrial Growth

The following are the arrangement of the regression models. First, I test the contribution of each individ-ual type of informative producer service expenditure per rm to industrial growth. Each regression modelcontains the same dependent variable. The dependent variable is the measure of industrial growth. Eachregression also contains one main independent variable log of adjusted informative producer service ex-penditure per rm subject to one particular type of informative producer services. There are six typesof informative producer services corresponding to six independent variables. They are respectively: log ofadjusted wholesale and retail trade service expenditure per rm denoted as ln(wr_adj), log of adjustedpublication and broadcasting service expenditure per rm denoted as ln(pb_adj), log of adjusted informa-tion service expenditure per rm denoted as ln(info_adj), log of adjusted legal service expenditure per rmdenoted as ln(legal_adj), log of adjusted miscellaneous professional, scientic, and technical service expen-diture per rm denoted as ln(ms_adj) and log of adjusted repair and maintenance service expenditure perrm denoted as ln(rm_adj).

Second, I test the contribution of total informative producer service expenditure per rm to industrialgrowth. In the regression, I use the same dependent variable as above measure of industrial growth. For theindependent variable, I sum up various types of informative producer service expenditure per rm, combiningthis total expenditure per rm with its corresponding calibrated parameter γ and taking logarithm scale.I get my independent variable log of total informative producer services expenditure per rm denoted asln(total_adj). In addition, I also run another regression with the same dependent variable but replace theindependent variable with another independent variable log of the adjusted subtotal service expenditureper rm denoted as ln(subtotal_adj). Subtotal service expenditure per rm sums up all types of serviceexpenditure per rm except that of whole sale and retail services 37. Other regressors subject to dierenteconometric approaches toward dierent datasets discussed in section 5.2 and 5.3 are included into estimation.The tables below show only the constant term and the results of interest: the estimated coecients of logof the adjusted informative producer service expenditure per rm and log of labor scale denoted as ln(L).

The content is organized as follows: (1) Section 6.1 and 6.2 are the empirical results of xed eectestimation of the annual panel across 19 industries over 11 years. Section 6.1 shows the empirical results ofthe contribution of service expenditure per rm to growth rate per worker. Section 6.2 shows the empiricalresults of the contribution of service expenditure per rm to TFP growth rate. (2) Section 6.3 and 6.5 arethe empirical results of OLS estimation of the cross sectional dataset across 251 industries. Section 6.3 showsthe empirical results of the contribution of service expenditure per rm to growth rate per worker. Section6.4 shows the empirical results of the contribution of service expenditure per rm to TFP growth rate. (3)Section 6.5 shows the robust testing with R&D per rm as third dependent variable 38.

36Even though the the series of whole sale and retail rate service expenditure to industrial output cannot reject unit root atstandard 10% level, the p-value is 0.1482 which is still small.

37Recall that whole sale and retail trade service just ts the most loosen denition of informative middleman services. I,therefore, have motivation to remove them from the total service expenditure to see the estimated results.

38These R&D expenditure data is also collected from use table of BEA benchmark year Industry Account, which is theexpenditure of US manufacturing industries used in purchase of NAICS 5417 R&D services. In average, the R&D activities inNAICS 5417 industries counts for one-quarter of the total R&D expenditure in US industries (Source: Measuring the Price of

15

6.1 Industrial Output Growth per Worker versus Adjusted Informative Pro-

ducer Service Expenditure per Firm: Fixed Eect Estimation under The

Panel Data

Table 1 shows the empirical results of individual regressions corresponding to six type of informative producerservice expenditure. The dependent variable is industrial growth rate per worker, The main independentvariable in each model is log of one particular type of adjusted informative producer service expenditure perrm. We can see that the estimated results, in most cases, are consistent with predictions of the theory. Theestimated coecients of the main independent variables ,corresponding to six regressions, are all positiveand signicant at 5 % level except that of wholesale and retail trade services, ln(wr_adj).

Table 2 shows the empirical results of the regressions corresponding to total and subtotal service expen-diture. The dependent variable is the same as above. The main independent variables in two regressions arelog of adjusted total informative producer service expenditure per rm, ln(total_adj) and log of adjustedsubtotal informative producer service expenditure per rm, ln(subtotal_adj) respectively. We can see that,in the rst regression, the estimated coecient of the independent variable ln(total_adj) is positive but notsignicant. One possible explanation of its insignicance is its inclusion of the expenditure of whole sale andretail trade services. Therefore, I also run another regression with the independent variable ln(total_adj)replaced by ln(subtotal_adj). It turns out the estimated coecient becomes positive and signicant at 10% level. This estimated coecient implies, in general without distinguishing various type of informativeproducer services, one percentage increase in the service expenditure per rm contributes 0.11 percentagepoint increase in industrial growth rate per worker.

In addition, in table 1, the eect of the scale lnLi on industrial output growth rate is not signicantin most cases except in the regression with wholesale and retail trade services. In table 2, once I excludeexpenditure of wholesale and retail trade service from the total expenditure, the eect of the scale lnLibecomes insignicant as well. These results are consistent with most of the empirical ndings. See Jones(1995) and Peretto and Laincz (2007) 39.

6.2 Industrial TFP growth rate versus Adjusted Informative Producer Service

Expenditure per Firm: Fixed Eect Estimation under The Panel Data

Table 3 shows the empirical results of individual regressions corresponding to six type of informative producerservice expenditure. The dependent variable here is replaced by industrial TFP growth rate, The mainindependent variable for each regression is the same as shown in Table 1. Similar to what I found in section6.1, we can see from table 3 that the estimated results, in most cases, are consistent with predictions of thetheory. The estimated coecients of the main independent variables, corresponding to six regressions, areall positive and signicant at 10 % level except that of the independent variable, ln(wr_adj).

Table 4 shows the empirical results of the regressions corresponding to total service expenditure andsubtotal service expenditure. The dependent variable is still industrial TFP growth rate. The main indepen-dent variable in each regression is the same as shown in Table 2. In table 4. the estimated coecients of themain independent variables, ln(total_adj) and ln(subtotal_adj), are all positive, but, again, the estimatedcoecient is only signicant for the second case. It shows that, in general, one percentage increase in theservice expenditure per rm contributes 0.0556 percentage point increase in industrial TFP growth rate.These ndings are consistent with the model predictions.

Moreover, the eects of the scale lnLi on industrial TFP growth rate are also similar to what I found inSection 6.1. It shows no signicance in most cases once I control dierent type of service expenditure perrm. One exception is in the model with wholesale and retail trade service. In the model, the eects of thescale lnLi on industrial TFP growth rate is still signicant. In table 4, once I exclude the expenditure ofwholesale and retail trade services from total service expenditure, the eect of the scale lnLi again becomesinsignicant.

Interestingly, the above empirical results show that correlation between measure of industrial growth andthe independent variable, ln(wr_adj) are insignicant. One possible explanation is that the role of wholesale

Research and Development Output BEA working paper 2009, page 20).39One exception is Backus kehoe and kehoe (1992). Their paper shows that scale eects are signicant in manufacturing

industries

16

Table 1: Industrial output growth per worker and log of each adjusted individual type of informative producerservice expenditure per rm Fixed eect

(1) (2) (3) (4) (5) (6)g_per g_per g_per g_per g_per g_per

lnL 0.140*** -0.0225 -0.0324 -0.0351 0.0581 -0.0267(0.001) (0.703) (0.627) (0.596) (0.354) (0.681)

ln(wr_adj) 0.00929(0.349)

ln(pb_adj) 0.236**(0.013)

ln(info_adj) 0.250**(0.015)

ln(legal_adj) 0.251**(0.016)

ln(ms_adj) 0.149**(0.046)

ln(rm_adj) 0.241**(0.016)

Constant -0.564** 1.504* 1.631* 1.676* 0.711 1.600*(0.019) (0.073) (0.075) (0.070) (0.359) (0.078)

Observations 209 209 209 209 209 209

p-values in parentheses

* p < .1, ** p < .05, *** p < .01

Dependent variable:

g_per: industrial output growth per worker

Regressors (shown in the table):

ln(wr_adj): log of adjusted whole sale and retail trade service expenditure per rm

ln(pb_adj): log of adjusted publishing and bracasting service expenditure per rm

ln(info_adj): log of adjusted information service expenditure per rm

ln(legal_adj): log of adjusted legal service expenditure per rm

ln(ms_adj): log of adjusted miscellaneous professional and technical support service per rm

ln(rm_adj): log of adjusted repair and maintenance service expenditure per rm

ln(L): log of industrial employment

Regressors (not shown in the table):

year dummies and log of lagged income per worker for one period

Notes: Data cover the years 1998 - 2008, 19 3.5 NAIC level manufacturing industries

17

Table 2: Industrial output growth per worker and log of adjusted total informative producer services expen-diture per rm Fixed eect

(1) (2)g_per g_per

ln(L) 0.145*** 0.0802(0.002) (0.113)

ln(total_adj) 0.0114(0.227)

ln(subtotal_adj) 0.110*(0.054)

Constant -0.384 0.433(0.200) (0.481)

Observations 207 209


* p < .1, ** p < .05, *** p < .01

Dependent variable:



ln(total_adj): log of adjusted total informative prodcer service expenditure per rm

ln(subtotal_adj): log of adjusted subtotal informative producer service expenditure per rm

(excluding whole sale and retail trade service expenditure)





18

and retail trade services probably shouldn't be regarded as informative middlemen in delivering productinformation but, rather, delivering the physical body of the products, as suggested in section 4. Therefore, itdoesn't contribute signicantly to industrial TFP growth rate. However, later in the cross sectional dataset, Ind a positive and signicant correlation between industrial TFP growth rate and the independent variable,ln(wr_adj). Therefore, not until a careful examination through a better dataset, one still couldn't give clearargument about the contribution of wholesale and retail trade services to industrial growth.

Furthermore, when we examine in more detail, we can see that the estimated of the main independentvariables in table 1 and 2 are all much larger than those obtained in table 3 and 4. It is a consequence ofthe fact that the increase of informative producer services not only contributes to TFP growth rate but alsocontributes to the growth of intermediate inputs. Recall the aggregate nal output production function:

Y = AL1−αXα(ΩN)1−α = AL1−α(NXj)α(ΩjN)1−α = AL1−α(NIΩjxij)

α(ΩjN)1−α.

Therefore, the growth of nal output can be decomposed as:

g = (1−α)((1−γ)

·N

N+γ

·m

m)+(1−α)

·L

L+α

·X

X= (1−α)((1−γ)

·N

N+γ

·m

m)+(1−α)

·L

L+α((1−γ)

·N

N+γ

·m

m). (43)

We know that·NN =

·mm holds at all times. Therefore, the growth of nal output can be rewritten as:

g = (1− α)

·N

N+ (1− α)

·L

L+ α

·N

N, (44)

where the rst term (1−α)·NN and third term α

·NN in the RH'S of equation(44) are TFP growth rate and growth

rate of total intermediate inputs X respectively. As a result, the increase in the expenditure of informative

producer services per rm, RmN increases the growth of technology,·NN which increases TFP growth rate as

well as growth rate of total intermediate inputs X. Both increase in TFP growth and intermediate inputsgrowth contributes to industrial growth rate per worker g.

6.3 Industrial Output Growth per Worker versus Adjusted Informative Pro-

ducer Service Expenditure per Firm: OLS Estimation under The Cross

Sectional Data.

For this dataset, by taking average of all independent variables over time across two benchmark year 1997and 2002, I test the same model implication by applying OLS estimation to this dataset.

Table 5 shows the empirical results of individual regressions corresponding to six type of informativeproducer service expenditure. The dependent variable is averaged industrial output growth rate per workerbetween the years of 1997 and 2002. The main independent variable in each model is log of one particulartype of adjusted informative producer service expenditure per rm averaged between the years of 1997 and2002. Similar to the what I found in section 6.1, we can see that the estimated coecients of the mainindependent variables, corresponding to six regressions, are all positive and signicant at 1 % level exceptthat of the independent variable, (lnwr_adj). These ndings are consistent with the predictions of thetheory.

Table 6 shows the empirical results of the regressions corresponding to total service expenditure andsubtotal service expenditure. The dependent variable is still averaged industrial output growth rate perworker. The main independent variables in two regressions are log of adjusted total informative producerservice expenditure per rm, ln(total_adj) and log of adjusted subtotal informative producer service ex-penditure per rm, ln(subtotal_adj) respectively. In the rst regression, we can see that the correlationbetween industrial output growth rate per worker and the independent variable, (lntotal_adj) is positivebut not signicant. Again, The estimated coecient in the second regression becomes signicant once Iexclude the expenditure of whole sale and retail trade services from the total service expenditure. It shows,in general, one percentage increase in service expenditure per rm contributes to 0.0144 percentage pointincrease in industrial output growth rate per worker.

Besides, the eect of the scale lnLi on industrial output growth rate is not signicant in all cases once Icontrol the expenditure of various type services.

19

Table 3: Industrial TFP growth and log of each adjusted individual type of informative producer serviceexpenditure per rm Fixed eect

(1) (2) (3) (4) (5) (6)tfp_g tfp_g tfp_g tfp_g tfp_g tfp_g

ln(L) 0.0902*** -0.000435 -0.00678 -0.00526 0.0200 -0.00232(0.001) (0.992) (0.878) (0.905) (0.550) (0.957)

ln(wr_adj) 0.0105(0.289)

ln(pb_adj) 0.0871*(0.065)

ln(info_adj) 0.0926*(0.072)

ln(legal_adj) 0.0902*(0.074)

ln(ms_adj) 0.0733*(0.084)

ln(rm_adj) 0.0875*(0.074)

_cons -0.581*** -0.0439 -0.00775 -0.0150 -0.158 -0.0306(0.001) (0.857) (0.976) (0.954) (0.431) (0.904)

N 198 198 198 198 198 198


* p < .1, ** p < .05, *** p < .01

Dependent variable:

tfp_g: industrial TFP growth


ln(wr_adj): log of adjusted whole sale and retail trade service expenditure per rm

ln(pb_adj): log of adjusted publishing and bracasting service expenditure per rm

ln(info_adj): log of adjusted information service expenditure per rm

ln(legal_adj): log of adjusted legal service expenditure per rm

ln(ms_adj): log of adjusted miscellaneous professional and technical support service per rm

ln(rm_adj): log of adjusted repair and maintenance service expenditure per rm





20

Table 4: Industrial TFP growth and log of adjusted total informative producer services expenditure per rm Fixed eect

(1) (2)tfp_g tfp_g

ln(L) 0.0888*** 0.0356(0.000) (0.234)

ln(total_adj) 0.00480(0.566)

ln(subtotal_adj) 0.0556*(0.069)

_cons -0.566*** -0.242(0.001) (0.196)

N 196 198


* p < .1, ** p < .05, *** p < .01

Dependent variable:

tfp_g: industrial TFP growth


ln(total_adj): log of adjusted total informative prodcer service expenditure per rm

ln(subtotal_adj): log of adjusted subtotal informative producer service expenditure per rm






21

Table 5: Averaged Industrial output growth per worker and log of each averaged adjusted individual type ofinformative producer service expenditure per rm OLS

(1) (2) (3) (4) (5) (6)g_per g_per g_per g_per g_per g_per

ln(L_av) 0.00305 0.00724 0.00441 0.00349 0.00479 0.00519(0.619) (0.359) (0.471) (0.560) (0.439) (0.409)

ln(wr_adj_av) 0.00504(0.433)

ln(pb_adj_av) 0.0183**(0.012)

ln(info_adj_av) 0.0227***(0.000)

ln(legal_adj_av) 0.0289***(0.000)

ln(ms_adj_av) 0.0190***(0.002)

ln(rm_adj_av) 0.0158***(0.008)

Constant -0.188*** -0.241*** -0.226*** -0.226*** -0.219*** -0.215***(0.004) (0.004) (0.000) (0.000) (0.001) (0.001)

Observations 240 157 251 251 251 251


* p < .1, ** p < .05, *** p < .01

Dependent variable:



ln(wr_adj_av): log of averaged adjusted whole sale and retail trade service expenditure per rm

ln(pb_adj_av): log of averaged adjusted publishing and bracasting service expenditure per rm

ln(info_adj_av): log of averaged adjusted information service expenditure per rm

ln(legal_adj_av): log of averaged adjusted legal service expenditure per rm

ln(ms_adj_av): log of averaged adjusted miscellaneous professional and technical support service per rm

ln(rm_adj_av): log of averaged adjusted repair and maintenance service expenditure per rm

ln(L_av): log of averaged industrial employment


log of lagged income per worker of year 1997

Notes: Data, by taken average of the raw data between the year 1997 and 2002

cover 251 six-digit NAIC level manufacturing industries

22

Table 6: Averaged Industrial output growth per worker and log of averaged adjusted total informativeproducer services expenditure per rm OLS

(1) (2)g_per g_per

ln(L_av) 0.00357 0.00354(0.553) (0.562)

ln(total_adj_av) 0.00503(0.341)

ln(subtotal_adj_av) 0.0144**(0.025)

Constant -0.204*** -0.196***(0.001) (0.002)



* p < .1, ** p < .05, *** p < .01

Dependent variable:



ln(total_adj_av): log of averaged adjusted total informative prodcer service expenditure per rm

ln(subtotal_adj_av): log of averaged adjusted subtotal informative producer service expenditure per rm


ln(L): log of averaged industrial employment





23

6.4 Industrial TFP growth versus Adjusted Informative Producer Service Ex-

penditure per Firm: OLS Estimation under The Cross Sectional Data.

Table 7 and table 8 show the empirical results of individual regressions corresponding to six type of infor-mative producer service expenditure. In table 7, the dependent variable is replaced by 4-factor industrialTFP growth rate, In table 8, the dependent variable is replaced by 5-factor industrial TFP growth rate40.The main independent variable for each regression in table 7 and table 8 are the same as shown in Table5. We can see from table 7 and 8 that the estimated results, in all cases, are consistent with predictionsof the theory. The estimated coecients of the main independent variables are all positive and signicanteven that of the independent variable, (lnwr_adj). The estimated coecient of the independent variable,ln(pb_adj) is signicant at 10% level. Others are all highly signicant at 1% level.

Table 9 shows the empirical results of the regressions corresponding to total informative producer serviceand subtotal service expenditure. The dependent variables are 4-factor and 5-factor industrial TFP growthrate respectively. The main independent variables in two regressions are the same as shown in Table 6.Table 9 shows that both the estimated coecients of the main independent variables in two regressions areall positive and signicant at 5 % and 1 % level respectively. The estimated coecient of the independentvariable, ln(subtotal_adj) shows that, in general, one percentage increase in informative producer serviceexpenditure per rm contributes to an average 0.00345 percentage point increase in 4-factor industrial TFPgrowth rate.

In addition, we can see from table 7 8 and 9, again, the scale variable lnLi has no signicant eect onindustrial TFP growth rate. Furthermore, when we examine in more detail, again, we can see that theestimated coecients of the main independent variables in table 5 and 6 are all much larger than thoseobtained in table 7, 8 and 9. These results are consistent with the ndings on section 6.1 and 6.2.

6.5 Industrial R&D Expenditure per Firm versus Adjusted Informative Pro-

ducer Service Expenditure per Firm: OLS Estimation under The Cross

Sectional Data.

The model predicts that the industrial growth rate per worker comes from technological growth rate·NN and

the R&D production function implies directly that technological growth rate·NN is equal to R&D expenditure

per rm RrdN . As a consequence, I can use industrial R&D expenditure per rm as third dependent variable

to take place industrial growth rate per worker and industrial TFP growth rate in the above regressions andkeep with the same the independent variables in each model:

RrdN

= β0 + β1lnASit + β2lnyit−1 + β3lnLit + εit. (45)

The test boils down to if β1 > 0.From table 10 and 11, still we can see that the estimated results, in all cases, are consistent with the

predictions of the theory. They all show a positive correlation between each indivdual type of adjustedinformative producer service expenditure per rm and industrial R&D expenditure per rm. The estimatedcoecients of the independent variable, ln(wr_adj) is signicant at 5%. Others are signicant at 1% level.In table 11, The estimated coecients of the independent variables, ln(total_adj) as well as ln(subtotal_adj)are all positive and signicant, respectively, at 5% and 1% level.

40The dierence between 4-factor TFP and 5-factor TFP measure is that 5-factor TFP measure distinguish worker hours toproduction workers hours and non production worker hours. Most of non production workers are those who engages in producerservices, rather than directly in product production (denition of non production workers from (Production and NonproductionWorkers in U.S. Manufacturing Industries, Industrial and Labor Relations Review Vol. 26, No. 1, Oct., 1972, Page 660 of660-669 )).

24

Table 7: Industrial 4-factor TFP growth and log of each adjusted individual type of informative producerservice expenditure per rm OLS

(1) (2) (3) (4) (5) (6)tfp_g4_av tfp_g4_av tfp_g4_av tfp_g4_av tfp_g4_av tfp_g4_av

ln(L_av) 0.00114 0.00329 0.00189 0.00184 0.00193 0.00195(0.537) (0.230) (0.378) (0.391) (0.373) (0.371)

ln(wr_adj_av) 0.00287**(0.017)

ln(pb_adj_av) 0.00322*(0.055)

ln(info_adj_av) 0.00444***(0.004)

ln(legal_adj_av) 0.00464***(0.004)

ln(ms_adj_av) 0.00434***(0.004)

ln(rm_adj_av) 0.00423***(0.005)

Constant -0.0232 -0.0484 -0.0326 -0.0315 -0.0322 -0.0323(0.237) (0.110) (0.158) (0.168) (0.163) (0.164)

Observations 240 157 251 251 251 251


* p < .1, ** p < .05, *** p < .01

Dependent variable:

tfp_g4_av: 4-factor averaged industrial TFP growth













25

Table 8: Industrial 5-facor TFP growth and log of each adjusted individual type of informative producerservice expenditure per rm OLS

(1) (2) (3) (4) (5) (6)tfp_g5_av tfp_g5_av tfp_g5_av tfp_g5_av tfp_g5_av tfp_g5_av

ln(L_av) 0.00116 0.00330 0.00191 0.00186 0.00195 0.00197(0.530) (0.227) (0.372) (0.385) (0.367) (0.366)

ln(wr_adj_av) 0.00285**(0.017)

ln(pb_adj_av) 0.00320*(0.056)

ln(info_adj_av) 0.00442***(0.004)

ln(legal_adj_av) 0.00462***(0.004)

ln(ms_adj_av) 0.00432***(0.004)

ln(rm_adj_av) 0.00421***(0.005)

Constant -0.0233 -0.0485 -0.0328 -0.0317 -0.0324 -0.0325(0.233) (0.109) (0.155) (0.165) (0.160) (0.161)

Observations 240 157 251 251 251 251


* p < .1, ** p < .05, *** p < .01

Dependent variable:

tfp_g5_av: 5 factor averaged industrial TFP growth













26

Table 9: 4-facor and 5-factor Industrial TFP growth and log of adjusted total informative producer servicesexpenditure per rm OLS

(1) (2) (3) (4)tfp_g4_av tfp_g5_av tfp_g4_av tfp_g5_av

ln(L_av) 0.00104 0.00106 0.000872 0.000890(0.593) (0.585) (0.650) (0.643)

ln(total_adj_av) 0.00293** 0.00291**(0.025) (0.026)

ln(subtotal_adj_av) 0.00365*** 0.00362***(0.004) (0.005)

Constant -0.0216 -0.0218 -0.0210 -0.0212(0.288) (0.283) (0.307) (0.303)

Observations 231 231 250 250


* p < .1, ** p < .05, *** p < .01

Dependent variable:












27

Table 10: Industrial RD expenditure per rm and log of each adjusted individual type of informative producerservice expenditure per rm OLS

(1) (2) (3) (4) (5) (6)rd_exp_av rd_exp_av rd_exp_av rd_exp_av rd_exp_av rd_exp_av

ln(L_av) 0.0780 0.0134 0.208 0.184 0.202 0.223(0.629) (0.969) (0.258) (0.308) (0.292) (0.238)

ln(wr_adj_av) 1.019**(0.011)

ln(pb_adj_av) 1.356***(0.004)

ln(info_adj_av) 1.302***(0.001)

ln(legal_adj_av) 1.334***(0.001)

ln(ms_adj_av) 1.223***(0.001)

ln(rm_adj_av) 1.242***(0.001)

Constant -0.490 -0.151 -2.641 -2.244 -2.327 -2.564(0.779) (0.969) (0.209) (0.273) (0.283) (0.229)

Observations 240 157 251 251 251 251


* p < .1, ** p < .05, *** p < .01

Dependent variable:

rd_exp_av: averaged industrial RD expenditure per rm













28

Table 11: Industrial RD expenditure per rm and log of adjusted total informative producer services expen-diture per rm OLS

(1) (2)rd_exp_av rd_exp_av

ln(L_av) 0.0360 0.150(0.817) (0.475)

ln(total_adj_av) 1.056**(0.018)

ln(subtotal_adj_av) 1.133***(0.004)

Constant 0.179 -1.564(0.913) (0.510)



* p < .1, ** p < .05, *** p < .01

Dependent variable:

rd_exp_av: averaged industrial RD expenditure










29

7 The Empirical Results of Second Implication Positive Correla-

tion between The Ratio of industrial Expenditure on Informative

Producer Services to Industrial Output and The Ratio of Number

of Intermediate Varieties to Industrial Output

The following are the arrangement of the regression models. First, I test the correlation between the ratioof each individual type of informative producer service expenditure to industrial output and the ratio ofnumber of intermediate varieties (number of rms) to the industrial output. On one hand, each regressionmodel contains the same independent variable log of the ratio of number of intermediate varieties (numberof rms) to the industrial output, denoted as ln(N_Y_av). On the other hand, each regression containsone dependent variable corresponding to one type of services log of the ratio of informative producerservice expenditure to industrial output subject to one particular type of informative producer services.There are six types of services corresponding to six dependent variables and therefore, six linear regressionmodels. Six dependent variables are respectively: log of the ratio of wholesale and retail trade serviceexpenditure to industrial output denoted as ln(wr_Y_av), log of the ratio of publication and brocastingservice expenditure to industrial output denoted as ln(pb_Y_av) , log of the ratio of information serviceexpenditure to industrial output denoted as ln(info_Y_av), log of the ratio of legal service expenditure toindustrial output denoted as ln(legal_Y_av), log of the ratio of miscellaneous professional, scientic, andtechnical service expenditure to industrial output denoted as ln(ms_Y_av), and log of the ratio of repairand maintenance service expenditure to industrial output denoted as ln(rm_Y_av).

Second, I test the correlation between the ratio of total informative producer service to industrial outputand the ratio of number of intermediate varieties (number of rms) to industrial output. In the regression,I use the same independent variable as above log of the ratio of number of intermediate varieties (numberof rms) to the industrial output, ln(N_Y_av). For the independent variable, I sum up various types ofinformative producer service expenditure and divide it by industrial output and take logarithm scale. Iget my dependent variable log of the ratio of total service expenditure to industrial output denoted asln(total_Y_av). I also run another regression by using the same independent variable as above but replacethe dependent variable with another log of the ratio of subtotal service expenditure to industrial outputln(subtotal_Y_av). Subtotal service expenditure sums up all types of service expenditure except that ofwhole sale and retail services. Other regressors subject to dierent econometric approaches toward dierentdatasets discussed in Sections 5.2 and 5.3 are also included into estimation. The tables below show only theconstant term and the results of interest: the estimated coecients corresponding to the ratio of dierenttype of service expenditure to industrial output and estimated coecients of log of labor scale denoted asln(L_av).

7.1 The Empirical Results from the First Dataset of Panel

Table 12 and 13 are the estimated results of annual panel under OLS estimation. Table 12 shows theempirical results of individual regressions corresponding to six type of informative producer services. Themain independent variable is log of the ratio of number of intermediate varieties (number of rms) to theindustrial output ln(N_Y_av), The dependent variable in each model is log of ratio of one particular typeof informative producer service expenditure to industrial output. The estimated coecients of the mainindependent variables, in all six regressions, are positive and signicant.

Table 13 shows the empirical results of the regressions corresponding to total and subtotal service ex-penditure. The dependent variable is the same as shown in table 12, The main independent varaibles intwo regressions are ln(total_Y_av) and ln(subtotal_Y_av). In both regressions, the estimated coecientsof the independent variables ln(total_Y_av) and ln(subtotal_Y_av) are all positive and signicant. Theseempirical ndings are consistent with predictions of the theory.

When we examine eect of the scale variable ln(L_av) in table 13, the estimated coecients are allpositive and shows signicant eect of employment scale on ln(wr_Y_av) and ln(pb_Y_av). When weexamine the results in table 14, The estimated coecients of the employment scale are positive and signicant.These ndings are also quiet consistent with predictions of the theory.

30

Table 12: Industrial output share of service expenditure and the ratio of intermediate varieties to industrialoutput Fixed eect

(1) (2) (3) (4) (5) (6)ln(wr_Y) ln(pb_Y) ln(info_Y) ln(legal_Y) ln(ms_Y) ln(rm_Y)

ln(N_Y) 0.245* 1.005*** 1.208** 0.864* 0.882** 0.685**(0.086) (0.006) (0.015) (0.077) (0.049) (0.047)

ln(L) 0.405** 0.100 0.486 0.333 1.096** 0.230(0.024) (0.790) (0.243) (0.451) (0.022) (0.490)

Constant -5.028*** -3.548* -6.139*** -5.543*** -8.616*** -4.775***(0.000) (0.075) (0.002) (0.008) (0.001) (0.008)

Observations 209 209 209 209 209 209


* p < .1, ** p < .05, *** p < .01

Dependent variables:

ln(wr_Y): log of industrial output share of whole and retail trade services

ln(pb_Y): log of industrial output share of publishing and brocasting services

ln(info_Y): log of industrial output share of information service

ln(legal_Y): log of industrial output share of legal service

ln(ms_Y): log of industrial output share of miscellaneous professional and technical support service

ln(rm_Y): log of industrial output share of repair and maintenance service


ln(N_Y): log of the ratio of number of rms to industrial output


year dummies


Table 13: Industrial output share of service expenditure and the ratio of intermediate varieties to industrialoutput Fixed eect

(1) (2)ln(total_Y) ln(subtotal_Y)

ln(N_Y) 0.289*** 0.863**(0.000) (0.040)

ln(L) 0.433*** 0.809**(0.004) (0.043)

Constant -4.478*** -6.224***(0.000) (0.002)



* p < .1, ** p < .05, *** p < .01


ln(total_Y): log of industrial output share of total informative prodcer service

ln(subtotal_Y): log of industrial output share of subtotal informative producer service



ln(N_Y): log of the ratio of number of rms to industrial output



year dummies


31

7.2 The Empirical Results from the Second Dataset

Table 14 and 15 are the estimated results of cross-sectional dataset under OLS estimation. Table 14 showsthe empirical results of individual regressions corresponding to six type of informative producer service.The main independent variable is still ln(N_Y_av), The dependent variable in each model is the same asshown in table 12. The estimated coecients of the independent variable, ln(N_Y_av), in half of the sixregressions, are positive and signicant except for the models with the dependent variable, ln(wr_Y_av) forwholesale and retail trade services, the dependent varaible, ln(pb_Y_av) for publishing and broadcastingservices, as well as the dependent variable, ln(rm_Y_av) for repair and maintenance services. Among theseexceptions, the estimated coecient of the independent variable, ln(N_Y_av) is negative but not signicantfor the model with the dependent variable, ln(wr_Y_av).

Table 15 shows the empirical results of the regressions corresponding to total and subtotal service ex-penditure. The main independent variable is ln(N_Y_av). The dependent variable in each model is alsothe same as in table 13. The estimated coecients of the independent variables, ln(N_Y_av) in two regres-sions, are positive but only signicant when the expenditure excludes wholesale and retail trade services.The empirical ndings above are still quiet consistent with the theory prediction.

When we examine the eect of scale variable ln(L_av) on the ratio of service expenditure to industrialoutput in table 14. The estimated coecient of the scale variable, ln(L_av) is positive and shows signicanceonly on the model with dependent variable, ln(info_Y_av). However, the estimated coecient is negativeand signicant on the model with dependent variable ln(wr_Y_av). This result is not consistent with thetheory prediction. This result raises the question again that if we should treat the role of whole sale andretail trade services as delivering product information. In table 15, it shows that estimated coecients arepositive and signicant at 10 % level while I excludes expenditure of whole sale and retail trade servicesfrom the total service expenditure.

Table 14: Industrial output share of individual service expenditure and the ratio of intermediate varieties toindustrial output OLS

(1) (2) (3) (4) (5) (6)ln(wr_Y_av) ln(pb_Y_av) ln(info_Y_av) ln(legal_Y_av) ln(ms_Y_av) ln(rm_Y_av)

ln(N_Y_av) -0.000890 0.122 0.257*** 0.138*** 0.105*** 0.000758(0.967) (0.215) (0.000) (0.002) (0.000) (0.984)

ln(L_av) -0.00394 -0.319** 0.103*** 0.0813 0.0189 0.00118(0.888) (0.024) (0.002) (0.125) (0.356) (0.980)

Constant -2.930*** -3.794** -6.367*** -6.463*** -4.638*** -5.196***(0.000) (0.025) (0.000) (0.000) (0.000) (0.000)

Observations 252 159 252 252 252 252


* p < .1, ** p < .05, *** p < .01


ln(wr_Y_av): log of averaged industrial output share of whole and retail trade services

ln(pb_Y_av): log of averaged industrial output share of publishing and brocasting services

ln(info_Y_av): log of averaged industrial output share of information service

ln(legal_Y_av): log of averaged industrial output share of legal service

ln(ms_Y_av): log of averaged industrial output share of miscellaneous professional and technical support service

ln(rm_Y_av): log of averaged industrial output share of repair and maintenance service


ln(N_Y_av): log of averaged ratio of number of rms to industrial output




32

Table 15: Industrial output share of total service expenditure and the ratio of intermediate varieties toindustrial output OLS

(1) (2)ln(total_Y_av) ln(subtotal_Y_av)

ln(N_Y_av) 0.0163 0.0568***(0.269) (0.002)

ln(L_av) 0.000604 0.0466*(0.977) (0.080)

Constant -2.517*** -4.096***(0.000) (0.000)



* p < .1, ** p < .05, *** p < .01


ln(total_Y_av): log of averaged industrial output share of total informative prodcer service

ln(subtotal_Y_av): log of averaged industrial output share of subtotal informative producer service



ln(N_Y_av): log of averaged ratio of number of rms to industrial output




8 Conclusion

This paper highlights the importance of informative producer services in reducing endogenous informationfrictions created by technological advancement in the economy. The insight is being incorporated into aR&D-based endogenous growth model and the impact of informative producer services on economic growthis analyzed.

There are three main results. First, the steady state economic growth rate is positively related to theprovision of informative producer services. Since economic role of these services is to overcome informationfrictions, which enlarges the market size of the specialized commodity, increases the incentive for potentialrms to conduct R&D and consequently contributes to the economic growth rate.

Second, informative producer service sectors would continue to grow as long as the level of industrialtechnology keeps rising, which may explain why service and manufacturing sectors tend to grow within thesame time frame after Industrial Revolution took place.

Third, subsidies to informative producer service can stimulate economic growth rate. I nd that steadystate growth rate negatively depends on the parameter φ, the unit cost of informative producer services at theearly stage of development and also depends on the parameter γ, the eectiveness of the informative producerservices in overcoming information friction. This result gives interesting policy implication. The parameterφ shown in the steady state growth rate implies a new channel to stimulate economic growth subsidiesin reducing unit cost of informative producer service. The parameter value γ shown there determines theeectiveness of subsidizing through such channel. This policy implication indicates that a precise calibrationof the parameter γ can be instructive to decide the eective subsidy allocation plan for the government.

Finally, I test the rst two model implications by using the data from US manufacturing industries.Empirical ndings are consistent with the two model implications.

33

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