information technology and establishment size in america: rybczynski redivivus☆

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Information Technology andEstablishment Size in America:Rybczynski RedivivusMartin Campbell-Kelly a , Daniel D. Garcia-Swartz b & Dhiren Patkic

a Department of Computer Science , Warwick University , CV4,7AL , UKb Daniel Garcia-Swartz, Compass Lexecon, 332 S. MichiganAvenue, Chicago , IL , 60604 , USAc Center at The University of Chicago , 5807 S Woodlawn Avenue,Chicago , IL , 60637 , USAPublished online: 30 May 2012.

To cite this article: Martin Campbell-Kelly , Daniel D. Garcia-Swartz & Dhiren Patki (2012)Information Technology and Establishment Size in America: Rybczynski Redivivus , InternationalJournal of the Economics of Business, 19:2, 337-357, DOI: 10.1080/13571516.2012.684930

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Information Technology and Establishment Size in

America: Rybczynski Redivivus?

MARTIN CAMPBELL-KELLY, DANIEL D. GARCIA-SWARTZ andDHIREN PATKI

ABSTRACT The Rybczynski Theorem is one of the staples of international trade the-ory. In their article in this issue of the journal, J.J. Rosa and J. Hanoteau apply thetheorem to a two-by-two world in which the two “industries” are small firms andlarge firms, and the two inputs are information and all other. The assumption thatsmall firms are more information intensive, coupled with the fact that information hasbecome pervasive in recent decades, allows them to derive the prediction that smallfirms will account for increasingly larger proportions of total output and employmentin the economy. We highlight a couple of issues that we find problematic in the Rosa–Hanoteau study, and then develop two different empirical strategies to probe the con-nections between IT and the size distribution of establishments. First, we combineCounty Business Patterns with input–output data to explore whether the share ofsmall plants has grown at a faster pace among industries that demand IT more heav-ily. Second, we explore, on an industry-by-industry basis and taking into account thepotential endogeneity of IT location, whether clustering of IT firms in specific UScounties is associated with a relatively large share of small establishments, on average,in those counties.

Key Words: Rybczynski Theorem; IT Industry; Size Distribution ofEstablishments.

JEL classifications: L25, L63, L86.

The opinions expressed in this paper are exclusively our own and do not necessarily coincide withthose of the institutions with which we are affiliated. We received very helpful comments in theanonymous refereeing process and from the Journal’s North American editor. Florencia Garcia-Vicente provided outstanding research assistance. All errors are ours.

Martin Campbell-Kelly, Department of Computer Science, Warwick University, CV4, 7AL, UK; e-mail:[email protected]. Daniel Garcia-Swartz, Compass Lexecon, 332 S. Michigan Avenue,Chicago, IL 60604, USA; e-mail: [email protected]. Dhiren Patki, Becker Center at TheUniversity of Chicago, 5807 S. Woodlawn Avenue, Chicago, IL 60637, USA; e-mail: [email protected].

Int. J. of the Economics of Business,Vol. 19, No. 2, July 2012, pp. 337–357

1357-1516 Print/1466-1829 Online/12/020337–21� 2012 International Journal of the Economics of Business

http://dx.doi.org/10.1080/13571516.2012.684930

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1. Introduction

In their article in the current issue of this journal, J.J. Rosa and J. Hanoteauapply the Rybczynski theorem to a world with two “industries” – small firmsand large firms – and two inputs – information and everything else. Theyobserve that, in recent decades, there has been an increase in the relative abun-dance of the information input. They combine this fact with the assumptionthat small firms use information more intensively than large firms to derive afundamental prediction: over time, small firms will account for increasinglylarger proportions of total output and employment in the economy.

With data for four to six non-consecutive years and three or four countries(France, Germany, the UK, and sometimes the United States), they test the pre-diction that the rising availability of information should lead to a decline infirm size for a variety of manufacturing industries. They estimate variousregression models in which the outcome variable is average firm size (amongfirms with at least 20 employees) in each one of 27 industrial sectors. Amongthe right-hand-side variables, they include the number of telephones lines per100 inhabitants, the price of ICT equipment, and the price of computers toproxy for the increasing availability of information in the economy. They finda negative association between the number of telephone lines and average firmsize: an increase in lines is correlated with a decrease in firm size. They alsofind a positive association between ICT (or computer) prices and average firmsize: a decrease in prices is correlated with a decrease in firm size. They con-clude that the estimated models lend support to their “shrinking hand” theory.

In our view, the Rosa–Hanoteau reinterpretation of Rybczynski is extre-mely thought-provoking. We, however, raise a couple of issues that we findproblematic in their study, one of them theoretical and the other one empirical.Even though we express these caveats regarding the Rosa–Hanoteau theory,we nonetheless proceed to probe the association between the intensity of ITuse and the size distribution of establishments in US manufacturing industries.

Rather than studying average firm size among firms with at least 20employees, we focus on the share of small plants in the US economy.1 Morespecifically, we estimate a number of models in which the outcome variablesare the share of establishments with 1–4 workers and the share of those with1–19 workers. We rely on the electronic version of the County Business Pat-terns and the input–output coefficients data sets, and thus are able to base ourconclusions on time series and, especially, cross-section variation across hun-dreds of industrial sectors (in our strategy #1) and hundreds of US counties (inour strategy #2) over a period of 10 years.

Our first empirical strategy focuses on changes in the share of small plantsamong manufacturing industries at the four-digit SIC level between 1988 and1997. We estimate models that address two questions. First, at the most basiclevel, has the share of small manufacturing plants increased over time, onaverage? Second, and more fundamentally, has it increased at a faster rate inthose industrial sectors that demand IT more heavily? In the identification ofthe effects that matter, we take advantage not only of changes over time in therelevant variables, but also of the cross-sectional variation in the intensity of ITdemand across hundreds of industrial sectors in the US economy.

Our second empirical strategy follows a different approach. Rather thanfocusing on differential intensity of demand across industrial sectors, we

338 M. Campbell-Kelly et al.

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concentrate on differential intensity of IT location across US counties. Relyingon a “knowledge spillover” kind of story, we pose the question: For any givenindustrial sector, is it the case that the clustering of IT firms in specific countiesleads to the presence of relatively large shares of small establishments in thosecounties, on average? This strategy explores a hypothesis according to which,for a given manufacturing industry, proximity to IT clusters leads industrialplants located in those counties to use IT more heavily than plants located incounties where the IT presence is light or non-existent. If this hypothesis istrue, and if it really is IT that is driving the “shrinking hand” effect, then,within any given industry, we should observe a larger share of small plants incounties where IT tends to cluster. Of course, even if we did find an associa-tion, an alternative interpretation would still be possible: it could well be thecase that unobservable features of a county lead both IT firms and small plantswithin a given manufacturing sector to locate heavily in that county. Thus weestimate dynamic panel data models that use instrumental variables to accountfor the potentially endogenous nature of IT location.

Our paper is organized as follows. Section 2 summarizes the Rosa–Hanoteau reinterpretation of Rybczynski and our caveats regarding theirstudy. Section 3 explains the foundations of our empirical strategy # 1 and theresults derived from it. Section 4 does the same with our empirical strategy #2. Section 5 summarizes our conclusions and suggests directions for furtherresearch.

2. The Rosa–Hanoteau Theory and a Couple of Caveats

In the current issue of the journal, Rosa and Hanoteau present the two-by-two –that is, two goods and two factors – version of the Rybczynski theorem.2 Here,we summarize the Rosa–Hanoteau theory and raise a couple of issues that wefind problematic in their reinterpretation of Rybczynski.

2.1. The Rosa–Hanoteau Version of Rybczynski

In the two-by-two world, the essence of the Rybczynski theorem can be sum-marized in a fairly straightforward fashion: an increase in the endowment of afactor will increase the output of the industry that uses that factor intensively,and will decrease the output of the other industry (Feenstra, 2004, p. 18). Intheir statement of the theorem, Rosa and Hanoteau assume that modern Wes-tern economies can be understood in terms of two industries – the small-firmsector and the large-firm sector – and two factors – information and all other.Their next key assumption is that small firms use the information input moreintensively than large firms. Since all firms in a sector need roughly the sameamount of information on the variables that matter to them, smaller firms useinformation more intensively, since they spread the information cost on smalleroutputs. Put differently, the information/output ratio is higher for smallerfirms.3

With these assumptions, the Rybczynski result follows: the informationrevolution that has taken place over the last few decades – which Rosa andHanoteau equate to an exogenous increase in the endowment of the informa-tion input – has led to the growth of the small-firm sector and the decline of

Information Technology and Establishment Size In America: Rybczynski Redivivus? 339

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the large-firm sector. That is, the sector that uses information more intensivelyhas expanded, and the one that uses it less intensively has contracted.

They use data on 27 industrial sectors for France, Germany, the UK, and(sometimes) the United States to explore whether their theory has empiricalsupport. In essence, their empirical investigation relies on a panel of industriesfor three or four countries over four to six non-consecutive years, roughlybetween 1967 and 2004. They use the number of telephone lines and the priceof ICT equipment as proxies for the diffusion of IT. Among other control vari-ables, they also include market size, trade openness, and the level of humancapital. They find a negative and statistically significant association betweenthe number of telephone lines and average firm size. They also find a positiveand significant association between the price of ICT equipment – or the com-puter price – and average firm size. They interpret these findings as providingempirical support for their theory.

2.2. A Theoretical Caveat

Our first caveat is theoretical: Rosa and Hanoteau rely on the (strong) assump-tion that the world of the Western economies they study can be interpreted ina two-by-two framework (i.e., two inputs and two sectors). Although thismight seem inconsequential, the fact is that the predictions that can be derivedfrom the Rybczynski theorem in higher dimensions are much less exciting thanthose that constitute the core of the Rosa–Hanoteau theory.

Consider the higher-dimensional version of Rybczynski as presented inFeenstra (2004, ch. 3). Assume an economy with i ¼ 1; :::;N goods and j ¼1; :::;M factors. The production functions are yi ¼ f ðviÞ, where vi ¼ ðvi1; :::; viM Þis the vector of factor inputs for the inputs that are required in the productionof good i. The usual assumptions about the nature of production functionsapply. If w represents the vector of factor prices, then unit-cost functions canbe expressed as ciðwÞ ¼ minviP0fw0vjfiðviÞ P 1g, and they have the usual proper-ties of cost functions.

The zero-profit conditions constitute the first set of equilibrium conditionsand they can be expressed as

pi ¼ ciðwÞ i ¼ 1; . . . ;N ð1Þ

The assumption of full employment of factors provides the second set ofequilibrium conditions. If we write @ci=@w ¼ aiðwÞ to represent the amount ofinputs required for the production of one unit of good i, then the total inputsused in industry i are given by vi ¼ yi aiðwÞ. If the elements of the vector aiðwÞare written as ai jðwÞ; j ¼ 1; :::;M ; and we let Vj; j ¼ 1; :::;M ; denote the econ-omy’s endowment of factor j, then the full-employment conditions can be writ-ten as

XN

i¼1

aijðwÞyi ¼ Vj j ¼ 1; :::;M ð2Þ

In matrix form, if we let A ¼ ½a1ðwÞ0; :::; aN ðwÞ0� represent the M � N matrixof factors required to produce one unit of output for each one of the N indus-tries, then the full-employment conditions can be expressed as


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AY ¼ V ð3Þ

From this point on, the derivation of the Rybczynski theorem is straightfor-ward. Assume that the number of goods equals the number of factors. Wedifferentiate the full-employment conditions relative to factor endowments,holding prices (and thus factor prices) constant, and we obtain

XN

i¼1

@yi@Vk

ai jðwÞ ¼ 0; j ¼ 1; :::;M ; j–k ð4aÞ

XN

i¼1

@yi@Vk

ai kðwÞ ¼ 1 ð4bÞ

Under certain assumptions about the matrix A, we can use these conditionsto derive the fundamental Rybczynski results in higher dimensions. From con-dition (4b), it must be the case that @yi=@Vk[0 for some good i. Then we canuse this result in condition (4a) to show that there must exist some other good,call it i’ for which @yi0=@Vk\0. That is, for an increase in the endowment ofeach factor, there must be a good whose output increases and another goodwhose output falls (Feenstra, 2004, p. 70). This prediction is, of course, consid-erably weaker than the one Rosa and Hanoteau derive from the two-by-twoversion of the theorem. This is not an indictment of their interpretation of thetheorem, but rather a reminder that their interpretation hinges strongly on theassumptions they make about the dimensionality of the problem.

2.3. An Empirical Caveat

Our empirical caveat focuses on the way in which Rosa and Hanoteau testtheir theory. The fundamental limitation of their empirical strategy is not thatthey rely on a few countries and a few years of data – after all, many empiricalstudies rely on a few hundred observations. It resides in the fact that they havevery little, if any, cross-sectional variation for the IT-related variables that mat-ter.

For the computer price – or more generally, for the price of ICT equipment– they have none: they use one price for all countries. This may make sense fora number of reasons, including the fact that, as we know by experience, it isremarkably difficult to find systematic historical information on computerprices for countries other than the United States. On theoretical grounds, some-body could argue that the market for ICT equipment should be viewed as justone (world) market, although the empirical implications of this view are opento interpretation once we take into account the complexities of the real world(and the long period of time that Rosa and Hanoteau cover with their data). Inany case, since they have one price only, identification of the relevant effect iscoming fully from inter-temporal changes in computer prices and their correla-tion with changes in the size distribution of firms. That is, the coefficient oncomputer prices picks up a purely time-series effect, and it is telling us that,over time, both prices of computers and the average size of firms have movedin the same direction – they have declined. This is true even if they normalize


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the price of ICT equipment by dividing it by the GDP price in each one of thethree or four countries they study, which they appear to do.

In the case of the number of telephone lines, the other variable they use toproxy for the diffusion of information technology, they have a small amount ofcross-sectional variation, since they have information for three countries(France, the UK, and Germany). Our best guess, however, is that here too iden-tification is arising from an inter-temporal correlation between the growth inthe number of telephone lines (in all countries) and the decline in the averagesize of firms. In other words, it is likely the case that the negative coefficienton the number of telephone lines picks up fundamentally a time-series effect.

None of this means, of course, that Rosa and Hanoteau have failed to findthe “true” effect of IT. It does mean, however, that the effects that they haveuncovered arise, in our view, mainly from time-series correlations, which wehave learned to interpret with a certain degree of caution, at least sinceGranger and Newbold (1974) did their pioneering work on time-series regres-sions.4 Since we believe, nonetheless, that the Rosa–Hanoteau reinterpretationof Rybczynski should be taken seriously, we next develop two empirical strate-gies that take advantage not only of time series but also of (strong) cross-sectional variation.

3. Empirical Strategy #1: Intensity of Demand for IT and Rateof Establishment Shrinkage

In order to test whether the proliferation of IT has had an impact on establish-ment size, we implement two different approaches. The first one uses a differ-ence-in-differences methodology to pose two questions. First, has the share ofsmall firms increased, on average, in US manufacturing industries? Second,has this share increased at a faster rate for those industrial sectors that demandIT more heavily?

Put differently, our first approach relies on the potential connection betweenthe intensity with which an industry demands IT services and products and thedistribution of firm size (establishment size, in our case) in that industry. At avery general level, our first empirical strategy is somewhat related to that ofBrynjolfsson et al. (1994), who used County Business Patterns data and informa-tion on IT investments by six industrial sectors to explore a similar, but certainlynot identical, hypothesis. If, in fact, it is the pervasiveness of IT (as opposed tosome other factor) that is causing companies (establishments) to shrink, then weshould observe that industries that demand IT more heavily undergo firm – orestablishment – shrinkage at a faster rate. Put differently, if industries thatdemand IT very lightly, or not at all, experience establishment shrinkage at thesame rate as the heavy demanders of IT, then we should probably conclude thatthere is some other, potentially unobserved or overlooked, force that is causingthe decline in average establishment size in the economy.

How do we identify the heavy demanders of IT? Input–output (IO) coeffi-cients provide a natural way to think about intensity of demand. Two types ofIO tables are available from the Bureau of Economic Analysis. Annual IOaccounts are updated once a year, are available for 1998–2008, and includeinformation on 65 industries. Benchmark IO tables contain information on sev-eral hundred industrial sectors, are updated once every five years, and are


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based on detailed data from the Economic Census conducted by the CensusBureau (Streitwieser, 2010, p. 3). We rely on benchmark IO data, which theBureau of Economic Analysis of the Department of Commerce has made avail-able going back to 1947.

IO coefficients are derived from two fundamental tables. The “make table”shows the value of each commodity produced by each industry in the USeconomy for each year. The “use table” shows the uses of commodities byindustries as intermediate inputs and by final users in any given year(Streitwieser, 2010, pp. 3–6). These two tables serve as the foundation for four“requirements” tables. One of them, the commodity-by-industry direct require-ments table, focuses on the direct effects, that is, the amount of commodityinputs required by an industry to produce a dollar of the industry’s output (atproducers’ prices). The other three present the total effects and are called totalrequirement tables: they capture the total impact of a change in final demand –not only the direct effect in terms of intermediate inputs in the production of afinal good, but also the production requirements of all other industries thatsupport the additional demand for intermediate inputs. An increase in thedemand for motor vehicles, for example, will have a direct effect on thedemand for tires, which will be captured in the direct requirements table. Itwill also have an indirect effect on the demand for rubber, which will only becaptured in the total requirements table (Streitwieser, 2010, pp. 7–11). We relyon the industry-by-industry total-requirements table to identify the heavydemanders of IT products and services.

In order to implement this empirical strategy, we combine the IO data pre-pared by the Bureau of Economic Analysis with County Business Patterns(CBP) data collected by the US Census Bureau, which capture the distributionof establishment size within an industry. CBP electronic files are available onan annual basis going back to 1987, and sporadically for prior years. IO bench-mark data in electronic format are available going back to 1947 and every fiveyears thereafter. However, only from 1962 onwards do these data provide anindustry breakdown that is fine enough to identify the heavy demanders of ITin a precise way.

We start by estimating a pooled OLS, difference-in-differences model(Wooldridge, 2002, pp. 128–30) for all US manufacturing industries during theperiod 1988–1997.5 (The difference-in-differences terminology comes from thepolicy-evaluation literature, and we retain the terminology even though we donot have a policy intervention in between our relevant periods.) We focus on1988–1997 because the CBP data are available for these years on the basis of aconsistent SIC classification.6 Our model takes the following form:

SSi t ¼ aþ bDHi þ cDT þ k ðDHi � DTÞ þ pXi t þ qi t ð5Þ

In this model, SSi t is the share of small establishments in industry i at timet; DHi is a binary variable that takes on the value 1 if industry i ranks amongthe top 50 industries in terms of its input–output coefficient for IT at the start-ing point (1988) and 0 otherwise; DT takes on the value 1 if year t is among thelast five years in the data set; ðDHi � DT Þ simply reflects the interactionbetween both binary variables; and Xi t is a collection of other variables thatmay have an impact on the size distribution of establishments for a givenindustry at a given point in time.7


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If we do not include other covariates on the right-hand side of the estimat-ing equation, the OLS estimator k has the following, difference-in-differencesinterpretation. Define SSL; 1 to be the sample average of the share of smallplants among industries that do not belong to the heavy demanders of IT inperiod 1 (the first five years of data) and SSL; 2 to be the sample average of theshare of small plants for those industries in period 2 (the last five years).Define SSH ; 1 and SSH ; 2 analogously for the industries that are among the topdemanders of IT in periods 1 and 2, respectively. Then k can be interpreted asfollows:

ðSSH ;2 � SSH ;1 Þ � ðSSL;2 � SSL;1Þ ð50Þ

The model thus captures how much more the share of small establishmentsgrows, on average, between periods 1 and 2 among industries that are heavydemanders of IT than among industries that are not. The model is usefulbecause it controls for both time-specific and group-specific effects.

We estimate this model for the share of small establishments defined bothas the proportion of plants with 1–4 employees and as the proportion of estab-lishments with 1–19 employees. In some versions of this model, we include, ascontrol variables, the total number of establishments in the industry (dividedby 1,000) – a proxy for the size of the industry – and the first difference in thetotal number of establishments – a proxy for the pace of change of the indus-try. (In addition, in some versions of the model, we also include the interactionof these proxies with the binary variable representing the heavy demanders ofIT.) Although, strictly speaking, when including additional covariates thekcoefficient can no longer be represented as in (5´), its interpretation remainsbasically unchanged.

Table 1. Difference-in-differences model for the share of plants with betweenone and four workers, 1988–1997

(1) (2) (3) (4) (5)

HIGH_IT �0.000 0.005 0.001 0.005 0.002

(0.986) (0.721) (0.950) (0.704) (0.904)

PERIOD_2 0.032⁄⁄⁄ 0.032⁄⁄⁄ 0.032⁄⁄⁄ 0.031⁄⁄⁄ 0.031⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

PERIOD_2 � HIGH_IT 0.012⁄ 0.012⁄ 0.011⁄ 0.011⁄ 0.011⁄

(0.027) (0.027) (0.032) (0.024) (0.030)

PLANTS 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄

(0.000) (0.000) (0.000) (0.000)

PLANTS � HIGH_IT 0.004⁄ 0.003⁄

(0.017) (0.015)

FD_PLANTS 0.036⁄⁄ 0.034⁄⁄

(0.002) (0.004)

FD_PLANTS � HIGH_IT 0.007

(0.825)

CONSTANT 0.232⁄⁄⁄ 0.222⁄⁄⁄ 0.222⁄⁄⁄ 0.223⁄⁄⁄ 0.224⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

N 5,759 5,759 5,759 5,183 5,183

p-values in parentheses. ⁄p < 0.05; ⁄⁄p < 0.01; ⁄⁄⁄p < 0.001.


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Table 1 reports the results from estimating various versions of this modelwith the share of establishments having between one and four workers as thedependent variable.8

The coefficient on the PERIOD_2 variable, which is statistically significantregardless of model specification, shows that the share of plants with betweenone and four workers grew by about 3.2 percentage points between 1988 and1992 and 1993 and 1997. Furthermore, as evidenced by the coefficient on PER-IOD_2 interacted with the binary variable for the heavy demanders of IT(HIGH_IT), the share of small plants grew by about 1.2 percentage points moreamong industries that demanded IT very heavily. Including the number ofplants and its first difference in the model does not alter the fundamental find-ings: the share of plants with between one and four workers grew, and it greweven more among the heavy demanders of IT.

Table 2 reports the results for the same model estimated with the share ofestablishments having 1–19 workers as the dependent variable.

The PERIOD_2 coefficient, which is statistically significant no matter thespecification, reveals that the share of plants with 1–19 workers grew by about2.6 percentage points between 1988 and 1992 and 1993 and 1997. In addition,that share grew by about 2.5 percentage points more among industries thatdemanded IT very heavily. In other words, the growth in the share of smallplants was almost twice as large among the heavy demanders of IT. Again,including the number of plants and its first difference in the model does notmodify the results: the share of plants with 1–19 workers increased, and itincreased considerably more among the heavy demanders of IT.

A model closely related to this one takes the following form:

Table 2. Difference-in-differences model for the share of plants with 1–19workers, 1988–1997

(1) (2) (3) (4) (5)

HIGH_IT �0.013 �0.004 �0.012 �0.003 �0.010

(0.556) (0.829) (0.585) (0.862) (0.637)

PERIOD_2 0.027⁄⁄⁄ 0.026⁄⁄⁄ 0.026⁄⁄⁄ 0.026⁄⁄⁄ 0.026⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

PERIOD_2 � HIGH_IT 0.025⁄⁄ 0.025⁄⁄ 0.024⁄⁄ 0.024⁄⁄ 0.023⁄⁄

(0.003) (0.003) (0.003) (0.002) (0.004)

PLANTS 0.009⁄⁄⁄ 0.009⁄⁄⁄ 0.009⁄⁄⁄ 0.008⁄⁄⁄

(0.000) (0.000) (0.000) (0.000)

PLANTS � HIGH_IT 0.008⁄⁄ 0.007⁄⁄

(0.009) (0.006)

FD_PLANTS 0.040⁄⁄ 0.038⁄⁄

(0.004) (0.008)

FD_PLANTS � HIGH_IT �0.007

(0.820)

CONSTANT 0.513⁄⁄⁄ 0.497⁄⁄⁄ 0.497⁄⁄⁄ 0.497⁄⁄⁄ 0.498⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

N 5,759 5,759 5,759 5,183 5,183



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SSi t ¼ aþ bDHi þ c t þ k ðDHi � tÞ þ pXi t þ qi t ð6Þ

The only difference between this model and the previous one is that herewe have replaced the DT binary variable with the linear trend t, and we havealso replaced the interaction term ðDHi � DT Þ with a new interaction term thatinvolves the linear trend, namely ðDHi � tÞ. In a model like this one, the c esti-mated coefficient captures the absolute annual change (increase) in the share ofsmall plants among industries that are not heavy demanders of IT, and the kcoefficient tells us by how much more that share changed (rose) annuallyamong industries that were among the top demanders of IT at the startingpoint. Table 3 reports the results from estimating the model with the share ofestablishments having between one and four workers as the dependent vari-able.

As evidenced by the coefficient on the TREND variable, which is statisti-cally significant in all specifications, the share of plants with between one andfour workers grew roughly by 0.6 percentage points each year between 1988and 1997, on average. The coefficient on TREND interacted with the HIGH_ITbinary variable also shows that, among the heavy demanders of IT, the shareof small plants grew by 0.2 percentage points more every year, on average.Including the number of plants and its first difference in the model does notalter these results in any meaningful way.

Table 4 reports the results from estimating this model with the share ofestablishments having 1–19 workers as the dependent variable.

The coefficient on the TREND variable, which is statistically significant inall specifications, shows that the share of plants with 1–19 workers grew byabout half of one percentage point each year, on average, between 1988 and1997. In addition, among the heavy demanders of IT, that share grew by an

Table 3. Trend and differential trend model for the share of plants withbetween one and four workers, 1988–1997

(1) (2) (3) (4) (5)

HIGH_IT �0.008 �0.003 �0.007 �0.005 �0.008

(0.585) (0.825) (0.646) (0.710) (0.569)

TREND 0.006⁄⁄⁄ 0.006⁄⁄⁄ 0.006⁄⁄⁄ 0.006⁄⁄⁄ 0.006⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

TREND � HIGH_IT 0.002⁄ 0.002⁄ 0.002⁄ 0.003⁄ 0.003⁄

(0.016) (0.016) (0.020) (0.011) (0.012)

PLANTS 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄

(0.000) (0.000) (0.000) (0.000)

PLANTS � HIGH_IT 0.004⁄ 0.004⁄

(0.017) (0.011)

FD_PLANTS 0.029⁄⁄ 0.029⁄

(0.007) (0.013)


(0.896)

CONSTANT 0.214⁄⁄⁄ 0.204⁄⁄⁄ 0.205⁄⁄⁄ 0.202⁄⁄⁄ 0.202⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

N 5,759 5,759 5,759 5,183 5,183



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additional half of one percentage point each year, on average. The differentialeffect is statistically significant regardless of model specification. That is, theshare of establishments with 1–19 workers grew twice as fast among the heavydemanders of IT. Including the number of plants and its first difference in themodel does not modify these findings.9

All these models present a consistent picture. First, between the late 1980sand the late 1990s, the share of small manufacturing establishments (definedas either those with 1–4 or those with 1–19 workers) grew in the UnitedStates. Second, this share grew at a faster pace in those industries thatdemanded IT products and services more heavily. This evidence could beinterpreted as lending some support to the Rosa–Hanoteau “shrinking hand”hypothesis.

The main caveat that should be raised in connection with these modelsis that the intensity of demand for IT products and services may not be trulyexogenous. Brynjolfsson et al. (1994) correctly point out that endogeneity ofIT demand may arise for a number of reasons. First, the optimal levels ofvarious production inputs, including IT capital, are functions of one another,as well as of other exogenous variables that are observable to managers butpotentially not to the econometrician. Second, in the process of minimizingcoordination costs, managers may choose both firm (or plant) size and theoptimal level of the IT input in an interrelated fashion, giving rise to stan-dard simultaneity problems. They use lagged levels of the relevant variablesto correct for the potential endogeneity of IT capital (and other forms of capi-tal).

We would like to address this problem by estimating the model in adynamic panel data framework with instrumental variables for IT intensity.However, we do not have repeated observations on IO coefficients by industry

Table 4. Trend and differential trend model for the share of plants with 1–19workers, 1988–1997

(1) (2) (3) (4) (5)

HIGH_IT �0.026 �0.018 �0.025 �0.021 �0.027

(0.276) (0.435) (0.297) (0.378) (0.263)

TREND 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄ 0.005⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

TREND � HIGH_IT 0.005⁄⁄ 0.005⁄⁄ 0.005⁄⁄ 0.005⁄⁄ 0.005⁄⁄

(0.002) (0.002) (0.003) (0.002) (0.002)

PLANTS 0.009⁄⁄⁄ 0.009⁄⁄⁄ 0.009⁄⁄⁄ 0.008⁄⁄⁄

(0.000) (0.000) (0.000) (0.000)

PLANTS � HIGH_IT 0.007⁄⁄ 0.007⁄⁄

(0.009) (0.006)

FD_PLANTS 0.034⁄ 0.033⁄

(0.011) (0.018)


(0.395)

CONSTANT 0.498⁄⁄⁄ 0.482⁄⁄⁄ 0.482⁄⁄⁄ 0.479⁄⁄⁄ 0.479⁄⁄⁄

(0.000) (0.000) (0.000) (0.000) (0.000)

N 5,759 5,759 5,759 5,183 5,183



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over time – we have relied on IO coefficients for IT at the starting point to mea-sure differential intensity of IT demand.10 In any case, this in itself may ame-liorate the endogeneity problem, since it could perhaps be argued thatintensity of IT demand in year t is exogenous relative to choices regardinginput mix and establishment size made in year ðt þ kÞ.

4. Empirical Strategy #2: Proximity to IT Clusters and Pervasiveness of SmallEstablishments

Whereas our first approach relies on the differential intensity of IT demandacross industries for identification, our second approach rests on the potentialimpact of IT clustering on establishments within a given industry. Put differ-ently, in our first approach identification is derived from the variability of IOcoefficients for IT across industries. In our second approach, on the contrary,we hold industry constant and ask the following question: Is it in fact the casethat, for a given industry, counties in which IT firms tend to cluster have largerproportions of small establishments, on average, than counties where the ITpresence is light or non-existent?

Here, we explore an “osmosis,” or knowledge spillover, kind of story: if ITknow-how and influence are truly “in the air,” then it should be the case that,for any given industry, establishments located in areas with strong presence ofIT firms tend to use IT more heavily, and thus tend to suffer the (potentiallyplant-shrinking) impact of IT more strongly, than establishments located inareas with little or no IT clustering. Thus, within a given industry, we shouldobserve larger shares of small establishments, on average, in areas with heavyIT concentration than in areas with little or no IT.

How do we measure IT clustering? The “location quotient” concept fromthe economic-geography literature provides a good approach (McCann, 2001,pp. 144–6). The location quotient for industry i at time t in county c is definedin the following way:

Li t c ¼ ðNi t c=Nt cÞðNi t=NtÞ ð7Þ

The location quotient for industry i at time t is a ratio of ratios, let us callthem ratio A and ratio B. Ratio A is that between the number of employees ofindustry i located in county c at time t and the county’s labour force at thattime. Ratio B is that between the number of employees of industry i at time tin the whole economy and the economy’s labour force. The location quotientfor the IT industry in a county for a given year thus tells us how intense thegeographic concentration of IT is in that county relative to its concentration inthe economy as a whole. A location quotient that is greater than one indicatesrelative concentration.

For this exercise, we rely exclusively on CBP data, but this time at thecounty level. For each industrial sector, we calculate, by county, the share ofsmall establishments, defined as the share of plants having 1–19 workersamong all plants (for that industry) in that county. We also compute, for eachcounty, the location quotient for the IT industry and the total employmentlevel (which proxies for the size of the market in that specific county). Thenwe estimate, industry by industry, a wide variety of models in which the share


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of small establishments in each county for the period 1988–1997 is a functionof the location quotient for IT in that county and the county’s overall marketsize plus year-specific fixed effects. More specifically, for each industry the esti-mated model is of the following form:

SSt c ¼ aþ ct þ bLQITt c þ rMct þ /c t ð8Þ

In this model, SSt c denotes the share of small establishments in county c attime t for the industry in question, ct is a year-specific fixed-effect, LQIT

t c is thelocation quotient for the IT industry (including both computer hardware andsoftware/services) in that county and year, and Mc t is the county’s total marketsize (measured as total employment) in that year. In a fixed-effects specifica-tion, we add county-specific fixed effects.

This model has one fundamental weakness, however: even if we were tofind a cross-county association between the degree of IT clustering and theshare of small plants in a given industry, in a simple OLS context we wouldnot be able to tell whether it is really IT clustering that is “causing” this plantshrinkage. An alternative interpretation is possible: think of a world in whichcertain counties, for reasons unobserved to the econometrician, attract both adisproportionately large share of small plants for a given industry and a dis-proportionately large share of all IT companies in the nation. Then, a simpleOLS regression of the share of small establishments (for that industry) on thelocation quotient for the IT industry (plus some other controls) would likelyproduce a positive (and perhaps even significant) coefficient on the IT locationquotient, even when IT clustering may not really be having any impact on thesize distribution of firms in that industrial sector.11

We would like to have a truly exogenous instrument for IT location.Although we do not, we have a panel of counties, and dynamic-panel-data(DPD) models have been designed precisely for situations in which truly exog-enous instruments are scarce or non-existent. More generally, these models areparticularly useful when researchers have panels with a few time periods andmany individuals (as we do), the process under study is dynamic, individual-specific fixed effects should be taken into consideration, some of the right-hand-side variables may be endogenous, and most, if not all, of the availableinstruments are “internal” (i.e., are based on lags of the potentially endogenousvariables; Bond, 2002; Roodman, 2006).

Two general versions of DPD models have been developed: the “differenceDPD” model and the “system DPD” model. In both cases, instrumental vari-ables for potentially endogenous variables are constructed via a GeneralizedMethod of Moments (GMM) approach. The Arellano–Bond (1991) differenceDPD model relies on a first-difference transformation (as opposed to a withintransformation) to purge the fixed effects, and then uses lagged levels of theendogenous variables as instruments for the contemporaneous first differences.In other words, it instruments current first differences with past levels. TheBlundell–Bond (1998) system DPD model takes the difference equation as apoint of departure but adds an equation in which current levels of the poten-tially endogenous variables are instrumented with past differences.12 Trulyexogenous instruments can still be included in the model as IV-style instru-ments (as opposed to GMM-style instruments; Bond, 2002; Roodman, 2006;Wooldridge, 2002, ch. 11).


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Table

5a.Theim

pactofIT

clusteringonthesh

areofsm

allplants,byindustry,allUScounties

1988–199

7,SIC

codes

2000–240

0

(1)

(2)

(3)

(4)

(5)

(6)

OLS

FE

IV_N

LD

DPD_3

DPD_5

DPD_7

SIC

=20

00(foodandkindred

products)

locq

_it

�0.010

⁄⁄⁄

�0.007

�0.017

⁄⁄⁄

�0.008

⁄⁄⁄

�0.007

⁄⁄⁄

�0.006

⁄⁄⁄

(0.000)

(0.121)

(0.000

)(0.000)

(0.000)

(0.000

)

SIC

=21

00(tobacco

products)

locq

_it

0.071⁄

�0.002

0.08

8⁄⁄⁄

0.052

0.039

0.035

(0.011)

(0.972)

(0.000

)(0.342)

(0.427)

(0.449

)

SIC

=22

00(textile

millproducts)

locq

_it

0.076⁄

⁄⁄0.009

0.09

4⁄⁄⁄

0.025⁄

0.022⁄

⁄0.019⁄

(0.000)

(0.322)

(0.000

)(0.014)

(0.009)

(0.014

)

SIC

=23

00(apparel

andothertextileproducts)

locq

_it

0.087⁄

⁄⁄0.005

0.09

8⁄⁄⁄

0.023⁄

⁄⁄0.023⁄

⁄⁄0.022⁄⁄

⁄

(0.000)

(0.463)

(0.000

)(0.000)

(0.000)

(0.000

)

SIC

=24

00(lumberandwoodproducts)

locq

_it

0.004⁄

0.001

�0.009

⁄⁄⁄

0.001

0.001

0.002

(0.026)

(0.619)

(0.000

)(0.572)

(0.280)

(0.168

)

p-values

inparen

theses.⁄ p

<0.05;⁄⁄p<0.01;⁄⁄

⁄ p<0.00

1.


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Table

5b.Theim

pactofIT

clusteringonthesh

areofsm


1988–199

7,SIC

codes

2500–2900

(1)

(2)

(3)

(4)

(5)

(6)

OLS

FE

IV_N

LD

DPD_3

DPD_5

DPD_7

SIC

=25

00(furniture

andfixtures)

locq

_it

0.035⁄

⁄⁄�0

.003

0.011

0.007

0.010

0.011⁄

(0.000)

(0.639

)(0.077)

(0.130)

(0.053)

(0.030

)

SIC

=26

00(paper

andallied

products)

locq

_it

0.028⁄

⁄⁄0.00

70.010

0.021⁄

⁄0.011

0.013⁄

(0.000)

(0.411

)(0.129)

(0.010)

(0.118)

(0.043

)

SIC

=27

00(printingandpu

blishing)

locq

_it

�0.003

0.00

3�0

.000

�0.001

0.000

�0.000

(0.061)

(0.227

)(0.837)

(0.580)

(0.867)

(0.946

)

SIC

=28

00(chemicalsandallied

products)

locq

_it

0.007

0.00

6�0

.011

�0.000

0.001

0.005

(0.071)

(0.383

)(0.077)

(0.951)

(0.839)

(0.378

)

SIC

=29

00(petroleum

andcoal

products)

locq

_it

0.017⁄

⁄⁄�0

.005

�0.028

⁄⁄⁄

�0.022

⁄�0

.014

�0.010

(0.001)

(0.678

)(0.000)

(0.024)

(0.076)

(0.117

)

p-values

inparen

theses.⁄ p

<0.05;⁄⁄p<0.01

;⁄⁄

⁄ p<0.001.


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Table

5c.

Theim

pactofIT

clusteringonthesh

areofsm


1988–1997,

SIC

codes

3000–3400

(1)

(2)

(3)

(4)

(5)

(6)

OLS

FE

IV_N

LD

DPD_3

DPD_5

DPD_7

SIC

=30

00(rubber

andmiscellaneousplasticproducts)

locq

_it

0.034⁄

⁄⁄0.007

0.044⁄⁄

⁄0.020⁄

⁄0.019⁄

⁄0.01

8⁄⁄

(0.000)

(0.281

)(0.000

)(0.006)

(0.002)

(0.002)

SIC

=31

00(leather

andleatherproducts)

locq

_it

0.052⁄

⁄⁄�0

.007

0.066⁄⁄

⁄0.008

0.005

0.00

3

(0.000)

(0.504

)(0.000

)(0.420)

(0.470)

(0.590)

SIC

=32

00(stone,clay,andglassproducts)

locq

_it

�0.028

⁄⁄⁄

�0.003

�0.060

⁄⁄⁄

�0.012

�0.014

⁄⁄�0

.014

⁄⁄

(0.000)

(0.755

)(0.000

)(0.053)

(0.010)

(0.009)

SIC

=33

00(primarymetal

indu

stries)

locq

_it

0.024⁄

⁄⁄0.012

0.014⁄⁄

0.006

0.004

0.00

4

(0.000)

(0.294

)(0.002

)(0.361)

(0.383)

(0.399)

SIC

=34

00(fabricatedmetal

products)

locq

_it

0.017⁄

⁄⁄�0

.012

0.003

0.012⁄

0.007

0.00

7

(0.000)

(0.101

)(0.554

)(0.041)

(0.143)

(0.166)

p-values

inparen

theses.⁄ p

<0.05

;⁄⁄p<0.01;⁄⁄

⁄ p<0.001.


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Table

5d.Theim

pactofIT

clusteringonthesh

areofsm


1988–199

7,SIC

codes

3500–3900

(1)

(2)

(3)

(4)

(5)

(6)

OLS

FE

IV_N

LD

DPD_3

DPD_5

DPD_7

SIC

=35

00(indu

strial

machineryandequipment)

locq

_it

0.002

�0.000

0.008⁄

⁄0.003⁄

0.003

0.00

2

(0.380)

(0.982)

(0.001)

(0.035)

(0.052

)(0.150

)

SIC

=36

00(electronic

andotherelectric

equipment)

locq

_it

0.031⁄

⁄⁄�0

.004

0.019⁄

⁄⁄0.017⁄

⁄0.016⁄⁄

0.01

7⁄⁄

(0.000)

(0.642)

(0.000)

(0.003)

(0.007

)(0.009

)

SIC

=3700

(transportation

equipment)

locq

_it

0.023⁄

⁄⁄�0

.005

0.008

0.009

0.001

0.00

1

(0.000)

(0.449)

(0.160)

(0.147)

(0.780

)(0.881

)

SIC

=38

00(instruments

andrelatedproducts)

locq

_it

0.007⁄

0.005

0.013⁄

⁄0.004

0.000

0.00

1

(0.047)

(0.406)

(0.008)

(0.261)

(0.996

)(0.844

)

SIC

=39

00(m

iscellaneousmanufacturingindu

stries)

locq

_it

0.014⁄

⁄⁄�0

.003

�0.001

0.002

�0.000

0.00

0

(0.000)

(0.594)

(0.895)

(0.637)

(0.963

)(0.970

)

p-values

inparen

theses.⁄ p

<0.05

;⁄⁄p<0.01;⁄⁄

⁄ p<0.001.


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Table 5a–d summarizes the key results from estimating model (8) in a vari-ety of specifications for a variety of industries. Column 1 presents the OLS esti-mate, column 2 the “within” estimate (i.e., the model with county fixedeffects), column 3 the estimate for a model with GMM instrumental variablesbut no lagged dependent variable, and columns 4–6 various versions of a sys-tem DPD model (with three lags, five lags, and seven lags used in the con-struction of the GMM instruments).13 Modelling the problem as dynamic (andthus introducing lags of the dependent variable as right-hand-side variables)allows us to consider a situation in which there are adjustment costs – that is,a world in which the process of adjustment to the optimal establishment sizedepends on the difference between the optimal size and last year’s actual size.In the version that we report in the table, all the variables on the right-handside, other than the year fixed effects, were considered endogenous and wereinstrumented, including the county’s market size. (Considering market size astruly exogenous did not change the results in any substantial way.) Thesemodels generally pass a battery of tests, including the standard AR(1) and AR(2) tests in first differences and the Sargan and Hansen tests of over-identifyingrestrictions.14 For space reasons, we report only the coefficient on the locationquotient for IT.

In 15 out of 20 industrial sectors, the OLS coefficient on the location quo-tient for IT is positive and statistically significant. If we were to interpret thiscorrelation as causality, we would say that an increase of one unit in the ITlocation quotient generates an increase in the share of small plants of between0.7 percentage points (for instruments and related products) and 8.7 percentagepoints (for apparel and other textile products). Only two sectors (food and kin-dred products, and stone, clay, and glass products) have OLS coefficients thatare negative and significant for the IT location quotient.

Perhaps more interestingly, the effect does not vanish when we use instru-mental variables to address the issues posed by the potentially endogenousnature of IT location. In 12 out of 20 industrial sectors the (instrumented) loca-tion quotient for IT still has a positive and significant coefficient in at least one(and often several) of the models reflected in columns 3 through 6. If webelieve that these models are truly accounting for the potential endogeneity ofIT location, then we should conclude that at least in these sectors there appearsto be some evidence of a plant-shrinking effect derived from proximity to ITclusters. The DPD coefficients in these sectors (models 4 through 6), it shouldbe noted, tend to be considerably smaller than the OLS coefficients. Thatshould come as no surprise, however, since (leaving aside the use of instru-mental variables) the DPD models include the lagged dependent variable onthe right-hand side. The coefficient on the location quotient for IT (the b coeffi-cient), therefore, can be interpreted as capturing the short-term impact of ITproximity on the size distribution of establishments.15

Interestingly enough, one of the sectors in which the coefficients on the ITlocation quotient are consistently positive and significant (regardless of modelspecification) is electronic and other electric equipment, a sector that containedmany of the industrial sub-sectors that demanded IT most heavily – that is,that had the highest IO coefficients for IT – in the period under study. Thismakes sense: if proximity to IT clusters is to have any effect at all in terms ofshrinking plant size in an industry or group of industries, it should happen inthose industries where IT plays a key role as an input.


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Among the industrial sectors that had positive and significant DPD coeffi-cients for the IT location quotient, the short-term effect of proximity to IT clus-ters was non-trivial: an increase of one unit in the location quotient for IT ledto an increase in the share of small plants that could be as small as 0.3 percent-age points (industrial machinery and equipment) but could also be as large as2.5 percentage points (textile mill products). The long-term effects were consid-erably larger.

This evidence, again, could be interpreted as consistent with the Rosa–Hanoteau “shrinking hand” theory. The key question in a model like this oneis whether we have truly succeeded at addressing the potentially endogenousnature of IT location. If the instrumental-variable methodology has taken careof the problem, then one possible interpretation of our results is that IT cluster-ing generates, via some sort of knowledge-spillover effect and for a wide vari-ety of industrial sectors, larger shares of small plants than those prevailing ingeographic units with little IT presence.

5. Conclusions and Directions for Further Research

We have implemented two empirical strategies to explore the connectionsbetween IT use and the size distribution of plants in US manufacturing indus-tries between the late 1980s and the late 1990s. Rather than focusing on theaverage firm size, we have concentrated on the share of small plants (definedhere as establishments with 1–4 and 1–19 workers). Both approaches rely notonly on changes in the relevant variables over time but also on heavy cross-sectional variation. Strategy # 1 uses variation in IT use across hundreds ofindustrial sectors, whereas strategy # 2 relies on variation in the intensity of ITlocation across hundreds of US counties for identification purposes. Both strat-egies produce results that could be interpreted as broadly consistent with theRosa–Hanoteau “shrinking hand” hypothesis. The share of small manufactur-ing plants grows, on average, between the late 1980s and the late 1990s, but itgrows considerably faster in industries that demand IT products and servicesmore heavily. In addition, and for a wide variety of industrial sectors, itappears that proximity to IT clusters generates larger shares of small manufac-turing plants.

It is worth reflecting further on what our results mean in practice. That is,if a plant-shrinking effect arising from IT use really exists, how should weinterpret it? One possible interpretation of our findings is that heavy IT useleads to higher shares of small plants because IT, by lowering the minimumefficient scale of operation, makes it easier for new (and small) companies (orplants) to enter various industrial sectors (see, e.g., Varian et al., p. 26). Thiseffect would be particularly visible in sectors that are heavy demanders of IT,that is, in sectors where the IT input plays a key role.

This is a hypothesis that deserves further exploration, and that we cannottruly probe with our data. The number of small plants (say, with 1–19 workers)in an industry at time t, let us call it nst , equals the number of small plants inthe previous period, nst�1, plus the number of new small establishments thatenter the industry at t, minus the number of small establishments that exit theindustry at t, plus the number of larger establishments that downsize andbecome small (1–19 workers) at t, minus the number of small establishments


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that become larger (20 workers or more) at t. Since we do not have repeatedobservations on the same companies (or plants) over time, we do not observeany of these flows into, and out of, the state of being a small establishment,and thus we cannot conclude that (net) entry of new small plants into specificindustries is driving our results. A panel of firms (or establishments) wouldallow us, or others, to truly explore whether intense IT use facilitates entry bynew players into an industry at a very small scale.

More generally, our empirical strategies could be applied to other countriesand time periods. As far as the US is concerned, CBP data are available after1998, although on the basis of the NAICS industrial classification. SinceNAICS-SIC mappings exist, it would be possible to extend our analysis all theway to almost the present time. This would allow us to understand whetherthe trends that we have identified in this study persisted after the late 1990s.

Notes

1. We are aware that there is a terminology already in place for referring to small firms. In Eur-ope, for example, micro-firms are those with 1–9 employees, small firms have 10–49, and med-ium-sized firms have 50–249. We focus on establishments with 1–4 and with 1–19 workers, andrefer to both as “small plants” or “small establishments.”

2. The original reference for the Rybczynski theorem is Rybczynki (1955). For a discussion, seeFeenstra (2004, pp. 16–21).

3. For a survey article on entrepreneurial firms, see Van Praag and Versloot (2007).4. In general, the time-series literature suggests that we should proceed in the following way. (1)

Use Dickey–Fuller or Augmented Dickey–Fuller tests to determine whether the series involvedin the regression are stationary. If the series have trends, determine whether the trends aredeterministic or stochastic. (2) If the series contain stochastic trends, test whether they are co-integrated. (3) If the time-series are co-integrated, then the regression may be estimated viaOLS. Preferably, however, it should be estimated via the Stock–Watson Dynamic OLS (DOLS)model or an error-correction model. For more details, see Heij et al. (2004, pp. 667–81) andStock and Watson (2003, pp. 545–61).

5. Service industries tend to have much larger proportions of small firms, on average, than manu-facturing industries. We plan to analyze service industries separately in the future.

6. NAICS codes replaced SIC codes in 1998. Although mappings from NAICS to SIC codes, andvice versa, do exist, they raise some issues at the time of implementation.

7. The two-period and two-group model we estimate here is a simplified version of a more gen-eral model that is usually estimated in the policy-intervention literature; see Bertrand et al.(2002). The authors point out that difference-in-differences estimation relies on many years ofdata and focuses on serially correlated outcomes, but usually disregards the fact that the errorsare inconsistent. They suggest that collapsing the time-series information into two periods – the“before” and “after” in the intervention literature – may be an effective approach for address-ing this problem.

8. We have estimated all of our models with clustered standard errors. In this case, the errors areclustered by industry. In our second empirical strategy, they are clustered by county.

9. It is worth noting, by the way, that the number of plants and the first difference of the numberof plants enter all models with positive and significant coefficients, which suggests that theshare of small plants grew at a faster rate in “large” industries (or more specifically, industrieswith many establishments) and in rapidly growing industries (or more precisely, industries thatadded many establishments on net).

10. The industrial classification in the IO data sets, which is radically different from the SIC indus-trial classification, experienced several changes over time. We had to invest substantialresources to match IO industries to CBP industries, and we chose to do that carefully in oneyear (i.e., at the starting point of the data). Matching IO industries to CBP industries over manyyears of data would be an extremely costly undertaking.

11. For a study in which IT location is treated as an endogenous outcome, see Campbell-Kelly et al.(2010).


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12. In practice, the system DPD estimator involves constructing an expanded data set with the dif-ference and the level equations stacked on top of one another (and twice the observations). TheGMM formulas and the software still approach system DPD models as a single-equation esti-mation problem.

13. It is well known that difference DPD models perform poorly if the dependent variable isclose to a random walk, since in those situations past levels convey little information on, andthus are weak instrumental variables for, current differences. See, for example, Roodman(2006, pp. 26–7).

14. The exception is the model in column 3, which tends to reject the null hypothesis in the Sargantest.

15. The long-term impact can be obtained by focusing on the long-run equilibrium of the model,and can be computed as the coefficient on the IT location quotient divided by (1 minus thecoefficient on the lagged dependent variable).

References

Arellano, Manuel, and Bond, Stephen (1991) Some tests of specification for panel data: Monte Carloevidence and an application to employment equations, Review of Economic Studies, 58, pp. 277–97.

Bertrand, Marianne, Duflo, Esther, and Mullainathan, Sendhil (2002) How much should we trustdifferences-in-differences estimates? NBER Working Paper # 8841.

Blundell, Richard, and Bond, Stephen (1998) Initial conditions and moment restrictions in dynamicpanel data models, Journal of Econometrics, 87, pp. 115–43.

Bond, Stephen (2002) Dynamic panel data models: a guide to micro data methods and practice.CEMMAP Working Paper CWP09/02.

Brynjolfsson, Eric, Malone, Thomas, Gurbaxani, Vijay, and Kambil, Ajit (1994) Does informationtechnology lead to smaller firms? Management Science, 40, pp. 1628–44.

Campbell-Kelly, Martin, Danilevsky, Marina, Garcia-Swartz, Daniel, and Pederson, Shane (2010)Clustering in the creative industries: insights from the origins of computer software, Industry andInnovation, 17, pp. 309–29.

Feenstra, Robert (2004) Advanced International Trade – Theory and Evidence (Princeton, NJ: PrincetonUniversity Press).

Granger, Clive, and Newbold, Paul (1974) Spurious regressions in econometrics, Journal of Econo-metrics, 2, pp. 111–20.

Heij, Christiaan, de Boer, Paul, Franses, Philip, Kloek, Teun, and van Dijk, Herman (2004) Economet-ric Methods with Applications in Business and Economics (Oxford: Oxford University Press).

McCann, Philip (2001) Urban and Regional Economics (Oxford: Oxford University Press).Roodman, David (2006) How to do xtabond2: An introduction to “difference” and “system” GMMin STATA. Center for Global Development Working Paper 103.

Rosa, Jean-Jacques, and Hanoteau, Julien (2012) The shrinking hand: why information technologyleads to smaller firms, International Journal of the Economics of Business, this issue.

Rybczynski, Tadeusz (1955) Factor endowments and relative commodity prices, Economica, 22,pp. 336–41.

Stock, James, and Watson, Mark (2003) Introduction to Econometrics (Boston, MA: Addison-Wesley).Streitwieser, Mary (2010) Measuring the nation’s economy: an industry perspective – a primer onBEA’s industry accounts. Available at: http://www.bea.gov/papers/pdf/an_industry_perspec-tive_a_primer_on_beas_industry_accounts.pdf

Van Praag, Mirjam, and Versloot, Peter (2007) What is the value of entrepreneurship? A review ofrecent research, Small Business Economics, 29, pp. 351–82.

Varian, Hal, Farrell, Joseph, and Shapiro, Carl (2005) The Economics of Information Technology – AnIntroduction (Cambridge: Cambridge University Press).

Wooldridge, Jeffrey (2002) Econometric Analysis of Cross Section and Panel Data (Cambridge: MITPress).


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http://www.bea.gov/papers/pdf/an_industry_perspective_a_primer_on_beas_industry_accounts.pdf

http://www.bea.gov/papers/pdf/an_industry_perspective_a_primer_on_beas_industry_accounts.pdf

information technology and establishment size in america: rybczynski redivivus☆

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