eonstor Make Your Publiations Visible. A Servie of Wirtshaft Centre zbwleibniz-informationszentrum Eonomis Görg, Holger et al. Working Paper Firm size distribution and employment flutuations: Theory and evidene Kiel Working Paper, No. 2064 Provided in Cooperation with: Kiel Institute for the World Eonomy (IfW) Suggested Citation: Görg, Holger et al. (2016) : Firm size distribution and employment flutuations: Theory and evidene, Kiel Working Paper, No. 2064 This Version is available at: http://hdl.handle.net/10419/148047 Standard-Nutzungsbedingungen: Die Dokumente auf EonStor dürfen zu eigenen wissenshaftlihen Zweken und zum Privatgebrauh gespeihert und kopiert werden. Sie dürfen die Dokumente niht für öffentlihe oder kommerzielle Zweke vervielfältigen, öffentlih ausstellen, öffentlih zugänglih mahen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweihend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrehte. Terms of use: Douments in EonStor may be saved and opied for your personal and sholarly purposes. You are not to opy douments for publi or ommerial purposes, to exhibit the douments publily, to make them publily available on the internet, or to distribute or otherwise use the douments in publi. If the douments have been made available under an Open Content Liene (espeially Creative Commons Lienes), you may exerise further usage rights as speified in the indiated liene. www.eonstor.eu
KIEL WORKING PAPER Firm Size Distribution and Employment Flutuations: Theory and Evidene No. 2064 Novmber 2016 Holger Görg, Philipp Henze, Viroj Jienwatharamongkhol, Daniel Kopasker, Hassan Molana, Catia Montagna, Fredrik Sjöholm Kiel Institute for the World Eonomy ISSN 2195 7525
ABSTRACT FIRM SIZE DISTRIBUTION AND EMPLOYMENT FLUCTUATIONS: THEORY AND EVIDENCE* Holger Görg, Philipp Henze, Viroj Jienwatharamongkhol, Daniel Kopasker, Hassan Molana, Catia Montagna, Fredrik Sjöholm This paper studies the effet of the firm-size distribution on the relationship between employment and output. We onstrut a theoretial model, whih predits that hanges in demand for industry output have larger effets on employment in industries haraterised by a distribution that is more skewed towards smaller firms. Industry-speifi shape parameters of the firm size distributions are estimated using firmlevel data from Germany, Sweden and the UK, and used to augment a relationship between industry-level employment and output. Our empirial results align with the preditions of the theory and onfirm that the size distribution of firms is an important determinant of the relationship between hanges in output and employment. Keywords: Firm distribution, Firm size, Employment, Flutuations JEL lassifiation: : E20, E23, L20 *This researh was supported by the NORFACE ERA-NET (New Opportunities for Researh Funding Ageny Co-operation in Europe Network) Welfare State Futures Programme, Grant Number 462-14-120. We gratefully aknowledge the professional assistane of UK Data Servie, http://do.ukdataservie.a.uk/do/6644/mrdo/ UKDA/UKDA_Study_6644_Information.htm. The usual dislaimer applies. Holger Görg Kiel Institute for the World Eonomy Viroj Jienwatharamongkhol Nottingham University (Ningbo) Hassan Molana University of Dundee and the Sottish Institute for Researh in Eonomis Fredrik Sjöholm Lund University and the Researh Institute of Industrial Eonomis, Stokholm Philipp Henze University of Kiel Daniel Kopasker University of Aberdeen and the Sottish Institute for Researh in Eonomis Catia Montagna University of Aberdeen and the Sottish Institute for Researh in Eonomis The responsibility for the ontents of this publiation rests with the author, not the Institute. Sine working papers are of a preliminary nature, it may be useful to ontat the author of a working paper about results or aveats before referring to, or quoting, a paper. Any omments should be sent diretly to the author. 1
1. Introdution Extensive empirial evidene douments differenes in the relationship between employment and output aross ountries and industries. The large variability in how muh a given hange in output affets employment (e.g. Perman and Stephan, 2015; Hoffman and Lemiueux, 2014) reflets ountry-speifi produtivity responses to output hanges. The differenes in these responses have typially been explained by the existene of differenes in labour market institutions, suh as work-sharing agreements and employment protetion laws, that affet the ease and time it takes to, e.g., lay off workers. While these ountry speifi fators are important in explaining flutuations in the aggregate employment/output ratio, they annot aount for the observed variations aross different industries within ountries. In this paper we argue that variations in the size distribution of firms aross industries and ountries an help to explain the differenes in the response of aggregate employment to output hange. There is ample evidene on the existene of signifiant intra-industry heterogeneity, with sharp variations in firm harateristis and performane both within narrowly defined industries, and aross ountries (e.g., Syverson, 2011). A key impliation in the existing literature is that resoure alloation aross different firms matters. Speifially, hanges in aggregate performane (total fator produtivity, employment, trade and foreign diret investment flows) result not only from hanges within firms, but also from ompositional hanges of firms within and aross industries via seletion and realloation effets. 1 It is then oneivable that differenes in the distribution of firms aross industries and ountries will result in different aggregate responses to shoks. We provide a theoretial speifiation of the employment-output relationship at the industry level, whih aptures the role of firm heterogeneity by onsidering an industry haraterised by firm-speifi produtivity. We show that exogenous hanges in output have larger effets on employment in industries where the produtivity distribution is more skewed towards less effiient firms, i.e. in industries that exhibit a lower degree of produtivity heterogeneity. This suggests that a higher average industry produtivity offers a greater insulation of aggregate employment from output shoks. At the ore of this result lies the fat that aggregate employment responses do not simply reflet hanges in employment at the firm level, but also intra-industry realloations ensuing from entry and exit of firms into the industry as a result of the output shoks. Thus, whilst larger and more produtive firms might exhibit larger employment responses to aggregate output flutuations (onsistent with the findings in Mosarini and Postel-Vinay, 2012), the hange in the mass of firms in the 1 See e.g. Olley and Pakes (1996) and Caves (1998) for some early ontributions to this literature. More reently, several ontributions have shown how misalloations aross heterogeneous prodution units an affet aggregate produtivity and the transmission of shoks (see, e.g. Hopenhayn et al., 1993; Restuia and Rogerson, 2008; Foster et al. 2008; Bartelsman et al., 2013). 2
industry is larger in industries haraterised by lower heterogeneity and this underpins the greater employment response to output flutuation. We then propose that, onsistent with the theory, the aggregate industry-level effets of firm-level adjustments and realloations an be aptured empirially using a measure of the shape of the firms size distribution. On the basis of existing evidene (e.g., Bernard et al., 2014), we approximate an industry s firm size distribution by the Pareto distribution. Using detailed firm-level data over the period 1999-2007, we proeed to estimate industry-level Pareto shape parameters for size distributions of firms within industries in three ountries: Germany, Sweden and the UK. Our theoretial predition is then examined by using the industry-level data to estimate an employment-output relationship augmented with the estimated Pareto shape parameters as well as with additional variables to ontrol for observable ountry differenes. One advantage with our sample is that these three ountries are haraterised by different firm-size distributions, different setoral strutures, and different welfare state models and labour market institutions. The inlusion of ountries with different harateristis strengthens the robustness of our results and enables us to draw more general onlusions. Data suggests that there is a large variability between industries and ountries in the distribution of firms. For instane, we show that the UK has a distribution whih is skewed towards smaller firms in omparison to the distributions in Germany and Sweden. More importantly, we find that the distribution of firms plays a signifiant role in determining the effet of output hanges on hanges in employment at the industry level. As predited by our theoretial model, employment responses are found to be larger in industries with higher shares of smaller firms. This result has impliations for poliy. To the extent that governments have in plae employment reation and/or unemployment protetion poliies, suh industries might require a greater intensity of intervention in reessions. Although a number of reent ontributions fous on the relationship between intra-industry realloations and employment dynamis, the role of firms distribution in determining flutuations in employment remains relatively unexplored. Hene, as far as we are aware, the issue we address in this paper has not been dealt with in the existing literature. A number of studies highlight the impat of firm harateristis on employment reation, but their firmlevel fous makes it diffiult to draw inferenes about the onsequenes of realloation aross firms for aggregate employment, and about the relationship between employment and output, as we do in this paper. A strand of this literature fouses on the relationship between firm-level adjustments and employment dynamis and shows how different firms exhibit different ylial patterns of net job reation. 2 Using US private setor firm-level data, Neumark et al. (2011) find an inverse relationship between net job growth rates and firm size, 2 For an earlier theoretial ontribution see Hopenhayn and Rogerson (1993). 3
with small firms ontributing disproportionately to net job reation. 3 However, Haltiwanger et al. (2013) find that these results do not hold when firms age is taken into aount. Mosarini and Postel-Vinay (2012) study the effet of firm harateristis on firm-level job reation. They show that large employers are more ylially sensitive than smaller ones, shedding proportionally more jobs in reessions and reating more jobs during booms. Our findings that aggregate employment is more responsive to output hanges when industries are dominated by smaller firms might appear, at first glane, to ontradit those of Mosarini and Postel-Vinay (2012). However, their ontribution has a different fous: they show that the size of a firm an affet its growth in a manner that depends on labour market onditions. Instead, we onsider how the size distribution of firms within an industry affets the industry-level (as opposed to firm-level) employment flutuations. That we find employment to be more responsive to output hanges in industries whose firm-size distribution is more skewed towards smaller firms needs not be inonsistent with the evidene that larger firms are more ylially sensitive than smaller ones for a given industry distribution. As we shall explain below, this is beause aggregate employment responses to an output shok reflet the effet of intra-industry realloations on employment adjustments at both the intensive and the extensive margin. Another strand of the literature explores the so-alled granular hypotheses of aggregate flutuations. Gabaix (2011) argues that beause firms size distributions are very fat-tailed, idiosynrati shoks to individual firms will not average out and will therefore be refleted in aggregate GDP flutuations. Di Giovanni and Levhenko (2012, 2014) highlight the role of firm-to-firm linkages in aggregate flutuations and show that the size omposition of firms in industries interats with trade openness in determining aggregate output volatility. 4 These papers fous on the effet of firm size distributions on output volatility. Finally, our paper is related to the large literature on Okun s law (Okun, 1962), whih fouses on the impat of output growth on the unemployment rate. A large number of papers onfirm Okun s onjeture but also find that the impat varies aross ountries beause of differenes in their labour market regulations and other institutional features (e.g. Nikell and Layard; 1999; Ball et al. 2013; De Serres and Murtin, 2014). In this ontext too our finding is pertinent in that we show that the link between output and employment depends on ountry and industry differenes aptured by the distribution of firms. The rest of the paper is organised as follows. Setion 2 develops a theoretial model whih highlights the role of the firm distribution. Setion 3 arries out the empirial analysis and Setion 4 onludes the paper. 3 New firms tend to be small and, although they are likely to experiene higher job destrution rates, grow more rapidly, whih aounts for their signifiant ontribution on job reation. 4 However, Stella (2015) finds that after ontrolling for aggregate shoks, idiosynrati shoks have little role in explaining aggregate flutuations. 4
2. The model Consider an industry onsisting of an upstream and a downstream setor. The latter is perfetly ompetitive and produes a final good by using as intermediate inputs horizontally differentiated varieties produed by the upstream setor. We postulate a onstant elastiity of substitution tehnology, 1 λ 1 1 1/ σ 1 1/ σ σ Y = M ( y ( i) ) di, 0 λ 1, σ > 1, (1) i M where Y is the quantity of the final good, y( i ) is the quantity of input of variety i, M is the mass of available varieties, σ is the onstant elastiity of substitution between any two varieties and λ aptures the extent of variety effet : the larger is λ the larger is the inrease in output resulting from a given inrease in the mass of varieties, i.e. the stronger are industry-wide sale eonomies; thus, λ=0 and λ=1 orrespond to the two extreme ases of no variety effet and maximum variety effet, respetively. 5 Choosing y( i ) to maximise the aggregate profit of the setor, PY ( ) ( ) varieties, ( ) λ 1 p i y( i) = M Y P σ i M p i y i di, subjet to (1) yields the demand funtion for individual, i M, (2) where p( i ) and P are the prie of variety i and the aggregate prie of the input basket, respetively. The zero profit ondition, together with (2), then ensures that P is in fat the prie index dual to the input basket in (1), hene 1 λ 1 ( 1 σ ( )) 1 σ. (3) i M P = M p i di The upstream setor onsists of a ontinuum mass M of firms where eah variety i M of the differentiated input is produed by one firm using a linear tehnology with inreasing returns to sale that utilises a omposite Cobb-Douglas basket of labour and the homogeneous final good. We denote the quantities of the latter inputs and the resulting omposite input by l, z and v, respetively, and assume 5 See Montagna (2001) for details. 5
( ) v i 1 γ ( ) z( i) γ l i =, (4) 1 γ γ where γ [0,1] measures the strength of vertial industry linkage in the industry. Firms in the upstream setor are assumed to differ in their produtivity. Heneforth, we drop the variety indiator i and distinguish firms by their produtivity parameter ϕ [ 1, ). To produe a quantity y ( ϕ ), a firm with produtivity ϕ requires the omposite input level of v ( ϕ) y ( ϕ ) = α +, (5) ϕ where α is the fixed input requirement while the marginal input requirement is given by the inverse of the produtivity parameter, 1/ϕ. Denoting by P v the unit omposite input prie, the input ost is v ( ϕ) ( ϕ) ( ϕ) P v = Wl + Pz, (6) whih, upon minimisation subjet to (4), yields the optimal unit ost 1 Pv W γ P γ =. (7) Applying Shepperd s lemma to Pv v ( ϕ ) then yields the firm s demand for the two inputs whih an be shown to imply Wl Pz ( ϕ) ( γ) P v( ϕ) =, (8) 1 v ( ϕ) γp v( ϕ) =. (9) v The firm hooses p ( ϕ ) to maximise its profit, p ( ϕ) p( ϕ) y( ϕ) Pv( ϕ) =, subjet to its demand, input requirement and input prie given by (2), (5) and (7) respetively. This yields the prie setting rule p ( ϕ ) = σ P v ( σ 1), (10) ϕ whih, together with the definition of revenue, r( ϕ) p( ϕ) y( ϕ) ( ) r( ) / Pv v =, an be used to rewrite profit as π ϕ = ϕ σ α. (11) Following Melitz (2003), we assume that there is a ompetitive pool F of firms that an enter the upstream setor by paying a sunk ost f measured in terms of the final good. This investment enables entrants to draw 6
their tehnology as embodied in the speifi value of the produtivity parameter ϕ. The draw is from a ommon population with a known p.d.f. ( ) g ϕ defined over the support [ ) 1, with a ontinuous umulative distribution G ( ϕ ). A potential entrant s onsequent deision to enter the industry depends on the magnitude of its ϕ [ 1, ) in relation to the threshold produtivity π ( ϕ ) < 0 for all ϕ 1, ϕ ) while ( ) 0 marginal firm therefore is ( ϕ ) π ϕ > for all ϕ ( ϕ, ) π ϕ = ; ϕ whih yields ( ) 0 ϕ ats as a ut-off in that. Given (11), the zero profit ondition for the r = σαp v. (12) ( ) It is known, prior to entry, that only a fration 1 ( ϕ ) M = G F of potential entrants will sueed to survive where, ex-post, M is the mass of varieties available in the market. We therefore redefine the p.d.f. of the surviving (inumbent) firms over ϕ [ ϕ, ) by µ ( ϕ) ( ϕ ) g =, whih an then be used to obtain a 1 G ( ϕ ) measure of the aggregate produtivity of the surviving firms, denoted by ϕ, as the weighted average of their produtivity levels (see Melitz, 2003, for details), σ 1 ϕ ϕ µϕdϕ 1 σ 1 = ( ). (13) ϕ The demand funtion in (2) and the prie rule in (10) respetively imply ( ) 1 ( ) ( ) / ( σ ϕ ϕ ϕ ) ( ϕ ) = ( ϕ) / ( ϕ ) and p( ) p( ) p y p y p p definition of revenue, yield r r ( ϕ ) ( ϕ ) ϕ = ϕ σ 1 ϕ / ϕ = ϕ / ϕ whih, together with the. (14) Using this result, all the relevant aggregate variables an then be expressed in terms of ϕ. To larify the notation used in the rest of the paper, we denote the average value of a variable x by x( ϕ ) whose orresponding aggregate values an be shown to be given by Mx( ϕ ). The average produtivity ϕ an then be defined in terms of the ut-off produtivity distribution, we have G κ (1 + κ) ( ϕ ) ϕ g( ϕ ) κϕ ϕ [ ) ϕ using an appropriate speifi p.d.f. for ϕ. Postulating a Pareto = 1 and =, 1,, (15) 7
where the shape parameter κ provides an inverse measure of dispersion: the higher is κ the more homogeneous are the firms. 6 Then, (15) implies M ( ) = F, (16) ϕ κ and using (13) we obtain 1/( σ 1) κ ϕ = ϕ. (17) 1+ κ σ We assume that the entry proess ontinues until the expeted net profit of entry is zero at the industry level, hene, ( ) PF f 0 Mπ ϕ =. (18) Finally, the industry-level labour demand is ( ) L = Ml ϕ. (19) 2.1. The relationship between employment and output Our main purpose in this paper is to examine how the relationship between industry-level labour demand and output is affeted by the shape of the distribution of firms aptured by κ. To this end, we redue the model to the following 3 equations (see Appendix A.i) that determine l ( ϕ ), W/P and M whih, for onveniene, are written in logarithmi form as, ln l ( ϕ) η γ ln W =, (20) P ( 1 γ)( σ 1)( κ 1) W ln M ln = µ u, (21) lκ P W ln M + ( 1 γ ) ln = µ d + lny, (22) P 6 In the Pareto distribution, both mean and variane are negatively related to the shape parameter κ. The smaller is κ, the higher is the average firm effiieny and the higher is the produtivity dispersion (i.e. the lower is the density of firms at lower produtivity levels). It is in this sense that we argue that the value of κ aptures the effiieny of the distribution: a more effiient distribution of firms is one with a higher average produtivity and a higher dispersion i.e. one with a smaller κ. To obtain meaningful results we impose κ > σ 1. 8
where η, µ d and u µ are onstant parameters that depend on ( α, f,,,, ) γ λσκ. Equation (20) gives the labour demand for the firm with average produtivity. Equations (21) and (22) are respetively derived from the zero-profit onditions for the upstream and downstream industries and represent the loi of ombinations of lnw/p and lnm whih ensure these equilibrium onditions hold. As an be seen from these, a rise in Y shifts up, in (lnw/p, lnm) spae, the zero profit lous for the downstream industry while a higher κ makes the zero profit lous for the upstream industry steeper. The solution for these is given by W ln = ω + P lκ ( 1 γ )( lκ + ( σ 1)( κ 1) ) lny (23) and ln M ( σ 1)( κ 1) + ( 1)( 1) = µ + lκ σ κ lny (24) where ω and µ are onstant parameters that depend on ( α, f,,,, ) γ λσκ. As the above equations show, both W/P and M are inreasing in Y. However, the impat of Y on the two variables differs and depends on the distribution parameter κ ; speifially, the larger is κ, the smaller is the impat of Y on W/P whereas the larger is the impat of Y on M. Hene, a hange in Y affets the firm-level employment via its impat on W/P and this impat will be smaller the more homogenous are the firms. In other words, the response of the firm-level labour demand to a hange in the industry-level output demand in an industry whih is populated with relatively bigger number of smaller (or less produtive) firms is smaller. This is in line with the evidene provided by Mosarini and Postel-Vinay (2012) as shown in Appendix A.ii and reflets employment adjustments at the intensive margin. As is evident from equation (24), however, κ has an opposite effet at the extensive margin: the larger is κ, the larger is the impat of Y on M. As a result, unless the effets at intensive and extensive margins anel eah other out, κ will influene the impat of Y on industry employment, L, and the influene will be positive if the extensive margin effet dominates. To see this, we substitute from (20), (23) and (24) into the industry-level labour demand given by equation (19) to obtain our main result (see Appendix A.i), namely ( ) ln L= β κ lny, (25) where β( κ) = 1 λκ ( 1 γ ) λκ + ( σ 1)( κ 1) ( )( ). It follows that β( κ) 0< < 1 provided that 1 0 γ < and 0< λ 1 hold. In other words, as long as the extent of vertial linkages in 1 + λκ / κ 1 σ 1 the upstream setor (aptured by γ) is not too large and there are some industry-wide sale eonomies 9
(aptured by a positive value of λ), the model predits a positive relationship between employment and output hanges at the industry level, akin to that implied by Okun s law for the aggregate level. What makes our result more interesting is the predition that the effet of a hange in output on employment depends on the produtivity distribution of firms in the industry, aptured by the shape parameter κ : the more skewed is the distribution towards low produtivity firms, the larger is κ and the bigger is the effet of an exogenous hange in the industry output on its employment. As explained above, this reflets the dominane of adjustments of employment at the extensive margin over those at the intensive margin. In sum, the model outlined in this setion provides theoretial support for the onjeture that interindustry differenes in produtivity distributions affet the responsiveness of employment to output hanges. Speifially, it suggests that in industries haraterised by, on average, larger and more produtive firms and by a higher degree of firm heterogeneity, aggregate employment is more insulated from output shoks. This is the main predition of the model whih we aim to test empirially in the next setion. 3. Empirial Estimations 3.1 Data and desriptive statistis Firm-level data are required to investigate the effets of the firm size distribution empirially. We are able to use firm data for three ountries, Germany, Sweden and the UK, whih inlude information on employment and on the industry of the establishment. German firm-level data is available from the Establishment History Panel (EHP). It provides information on the population of establishments in Germany. We have aess to a randomly drawn sample overing 50 perent of the population, yielding information for about 800,000 plants per year over the period 1997-2011. The EHP is made available by the Institute for Employment Researh (IAB). Swedish data is provided by the Statistis Sweden and overs the population of all registered firms. From 1997-2012, around 170,000 unique ompanies are inluded in the data. Unlike data from Germany and the UK, the Swedish data is on firms rather than on plants. However, 78 perent of Swedish firms are single-plant firms. Firm-level data for the UK is from the Annual Respondents Database (ARD) and inludes data from the Inter-Departmental Business Register (IDBR), whih is the key sampling frame for UK business statistis used by the Offie for National Statistis (ONS). As the German EHP, the ARD is essentially a ensus of UK businesses, it ontains about 70 thousand enterprises. 7 With the addition of data from the IDBR, the dataset ontains around 3.7 million enterprises. The sample used overs the period 1997-2007. 7 The ARDis desribed by Barnes (2002). 10
Firm-level data from Germany, Sweden and the UK are used to onstrut a measure of the size distribution of firms within industries. The unit of observations is ountry speifi 3-digit NACE manufaturing industries over the period 1999-2007. 8 We have onsidered these three ountries beause they are haraterised by different welfare state regimes and labour market institutional settings, as well as by different setoral strutures. All of these fators might affet the relationship between output flutuations and employment. One aspet of the ountry differenes an be seen in Figure 1, whih illustrates the relative size of different aggregated 2-digit industries in the three ountries. 9 Food, Beverage, and Tobao (DA) is the largest industry in the UK aounting for around 17 perent of total manufaturing employment, substantially more than the shares in Germany and Sweden. Another large industry in the UK is Paper produts (DE), whih is large also in Sweden but not in Germany. Germany and Sweden have both their largest employment shares in Mahinery (DK) with around 18 perent of total manufaturing employment. -- Figure 1 around here -- Another differene between these ountries is in the type of welfare states and labour market regulations, whih are prominent among the explanations advaned for the existing inter-ountry differenes in employment performane (e.g., Perman and Stephan, 2015; Hoffman and Lemiueux, 2014). The three ountries in our sample orrespond to three types of soial models within the European Union: the Anglo-Saxon (UK), the Central European (Germany) and the Sandinavian (Sweden). These soial models substantially differ in terms of labour market institutions and legislation, partiularly with respet to employment protetion, unemployment benefits, minimum wages or the role of unions. Another key differene is their reliane on ative labour market poliies. For instane, expenditures on ative labour market poliies during 1997 to 2007 averaged 3.1 perent of GDP in Germany, 2.6 perent in Sweden and 0.6 perent in the UK. 10 For eah industry, in eah ountry, and for eah year, we estimate a Pareto shape parameter for firm size distribution whih we then use as a proxy for κ that features in the above theoretial analysis. 11 We obtain the 8 There are 97 industries inluded in our sample. See the appendix for more information on the data and variables. Sine the available firm level data for the UK urrently overs only up to 2008 (data for 2008 is inomplete), a onsistent sample for the three ountries annot be extended beyond 2007. 9 Again, our eonometri analysis is onduted at the more disaggreaged 3-digit level of NACE. 10 OECD Employment and Labour Markets. Key Tables from OECD: http://www.oed-ilibrary.org/employment/ publiexpenditure-on-ative-labour-market-poliies-2009_20752342-2009-table9# 11 We use firm size as a proxy for produtivity, onsistent with both the one-to-one orrespondene between size (in terms of number of employees) and produtivity emerging from the theory see A.ii in the Appendix and the high orrelation observed empirially between firm size and produtivity. It is observed in the literature that firms distributions of employees and sales an be losely approximated by a Pareto distribution, exept in the region of very small firms. Aordingly, the Pareto distribution of firm size is subjet to bias if entrants are disproportionately small and their share is large. Bernard et al. (2015) show that the Pareto fit beomes more robust one the data are orreted for the partial year effet, as this dereases the share of small firms. 11
maximum likelihood estimates of κ based on the C.D.F. ( ) 0 firm size (number of employees) and s 0 is the lower bound. We define L κ, s = κs x = κ s x κ (1 + κ) N Nκ (1 + κ) likelihood funtion ( ) κ s F s =1, 0 < s s, where s denotes the s0 x s i i = and use it to write the joint s0 N N 0 0 i 0 i whih yields the log-likelihood funtion i= 1 i= 1 ( κ ) = κ + κ + κ It follows that s ( x ) ln L, s Nln N ln s (1 ) ln x. 0 0 N i= 1 i ˆ0 min i N ln L N N x order ondition, N ln s 0 ln x i = + i = 0, yields ˆ κ = N ln κ κ i= 1 i= 1 x1 errors for ŝ 0 and ˆκ are obtained using a standard bootstrapping approah. = and the solution to the first 1. The asymptoti standard The distribution of firms is more homogenous and more skewed towards small firms if the shape parameter is larger. Aordingly, a smaller shape parameter implies a relatively more heterogeneous distribution of firms, i.e. with a thiker tail of large firms. In Figure 2 we show the aggregated annual Pareto shape parameter estimates for our three ountries over the period 2000-2007. The series are normalized with the Pareto distribution in the UK in 2000 set to unity. A few onlusions an be drawn. Firstly, there is a large differene between the UK on the one hand, and Sweden and Germany on the other: the Pareto shape parameter is substantially higher in the UK. This means that the UK firms are relatively more homogeneous with a relatively large presene of small firms. The distributions in Sweden and Germany are similar in the first years of observations but there is a divergene over time with the German distribution shifting towards larger firms (i.e. its Pareto parameter beomes smaller). Moreover, the distributions are relatively stable over time with only a modest hange towards less heterogeneity in the UK, and the above mentioned hange towards more heterogeneity in Germany. There is pratially no hange in the aggregate distribution for Sweden. -- Figure 2 about here -- Figure 3 highlights the differenes for three industries, seleted on the basis that they represent different types of ativities. The jewellery industry involves very diverse firms inluding ones with mining ativities at one end of the spetrum and small retailers at the other. The medial equipment industry onsists primarily of high preision manufaturing firms with diverse tehnologial features. Paper is a more onventional apital intensive industry that omprises firms with large forestry ativities, whih are speialised in the prodution of pulp, as well as smaller firms whih fous on produing highly speifi types of paper, e.g. for utting or 12
pakaging. We inlude two measures in Figure 3: the Employment/Output ratios and the Pareto parameters (reall that a high value of the Pareto parameter means a distribution of firms skewed towards small firms). A few onlusions an be drawn. Firstly, the Employment/Output ratios differ between ountries: it tends to be lowest in Germany and highest in the UK. It also differs between industries with the apital-intensive paper industry having the lowest ratio. Seondly, the Employment/Output ratios are relatively stable in Germany and relatively volatile in the UK, with Sweden as an intermediate ase. The size distributions differ substantially aross industries and ountries, with the highest value of κ (i.e., most skewed towards small firms) in the jewellery industry. Germany has the least skewed distribution of firms in two out of three industries. The distributions are relatively stable over time in most industries and ountries. One exeption is the jewellery industry in the UK and Sweden where we see a distribution more skewed towards small firms in later years. -- Figure 3 about here -- 3.2 Testing the theoretial predition The theoretial model s key predition, as summarised in equation (25), is that the impat of output on employment depends on the shape of the size distribution, with the employment elastiity of output being larger the larger is κ. In its most basi form, this relationship an be represented by the redued form panel regression equation where ( ) ln L = + +, (26) ˆ ln it β1 βκ 2 it Yit εit L it and Y it are employment and output in industry i, ountry, in year t, ˆit κ is an estimate of the Pareto shape parameter for firm size distribution, and ε it is an idiosynrati disturbane term one it is orreted for the industry, ountry and time speifi fixed effets. As a generalisation, we add a vetor of regressors to ontrol for ountry-speifi fators. Speifially, to apture the effets of labour market institutional fators and the role of government in the eonomy, we inlude measures of: stritness of employment protetion poliies; union density; ative and passive labour market poliies; and government size. We also inlude trade openness, sine existing evidene suggests that it affets ompetitive fores and has seletion and realloation effets. 12 Finally, we also inlude ˆit κ as an additional regressor to apture the independent effet of any shifts in firm heterogeneity beyond that exerted via its interation with lny it. We therefore estimate the more general regression equation 12 See, e.g., Tybout (2003) for a survey and Coros et al. (2012) among others. 13
ln L = β + β lny + β ˆ κ lny + β ˆ κ + β z + µ + µ + µ + ε, (27) F F F it 0 1 it 2 it it 3 it 4+ j jt i t it j where F F F z refers to the jth ountry-speifi ontrol variable and µ, µ and µ are industry, ountry and jt i t time fixed effets to ontrol for unobservable along these dimensions. We expet to find ˆ β 1 > 0 and ˆ β 2 > 0. The oeffiient β 3, whih aptures any diret and independent effet that the firms size distribution might exert on employment, annot be analytially signed in our model. Nevertheless, it would not be implausible to expet a priori to find β 3 <0 sine, as the literature suggests, an industry with a higher degree of heterogeneity is haraterised eteris paribus by higher entry and a larger mass of surviving firms, and hene higher aggregate employment. 3.3 Results The variables and datasets we use in our regressions are explained in detail in Appendix A.iii. Our estimation results are reported in Table 1. The first olumn of Table 1 inludes output growth as the only explanatory variable together with the fixed effet (industry, time and ountry) dummies, and shows that the elastiity of employment with respet to output is 0.39: a ten perent inrease in industry-level output inreases employment by about 4 perent. The Pareto shape parameter is added as an independent regressor in olumn 2 and the negative and signifiant sign of its oeffiient estimate onfirms our onjeture that industries populated by more homogenous (and smaller) firms exhibit lower employment growth. Column 3 adds our main explanatory variable of interest, the interation term between output growth and the firm-size distributions parameter ˆ κ lny. Its positive and statistially signifiant effet onfirms our main theoretial onjeture it it that a hange in output has a larger effet on employment in industries with a more homogenous distribution of firms. Moreover, while inluding the interation term does not alter the independent impat of ˆκ, it redues the size of the diret effet of output growth; when measured diretly, the elastiity of employment now falls from 0.38 to 0.25. The total elastiity, however, is given by 0.25 + 0.21κˆ, where ˆκ is a sample-based measure of the shape parameter. Using the sample mean of ˆ κ = 0.556 implies the total elastiity of around 0.367 whih is of the same magnitude as the estimates in the first and seond olumns of Table 1. The sub-sample means for Germany, Sweden and the UK respetively are ˆ κ G = 0.425, ˆ κ S = 0.628 and ˆ κ U = 0.628 whih indiate that German industries are likely to show, on average, a smaller response of employment to output ompared with their Swedish and British ounterparts. Finally, we inlude as additional regressors the lagged values of ountry-speifi ontrol variables in the last olumn. We have inluded the lagged, rather than the urrent, values of ountry-speifi ontrol variables sine it is likely that it takes time for the poliies to have an impat on employment. In addition, albeit in a rude 14
way, it helps avoiding the simultaneity bias problem. The main results do not hange, exept for a drop in the statistial signifiane of the oeffiient apturing the diret impat of the Pareto shape parameter whose point estimate remains the same but beomes statistially insignifiant. Most of the ontrol variables have statistially signifiant effets with the expeted signs. More preisely, labour protetion regulations and ative labour market poliies are assoiated with higher employment growth, and passive labour market poliies and large publi setor with dereases in employment. However, trade openness and the degree of unionisation of the labour fore do not signifiantly affeting employment growth. Finally, the regressions on the whole have reasonable fits with the adjusted goodness of fit measure between 27% and 29% and both the log-likelihood values and the AIC support the most general speifiation as proposed by equation (27). -- Table 1 about here -- We ontinue with some robustness heks by estimating alternative speifiations of equation (27). These are reported in Table 2. In the first olumn we use the urrent instead of the lagged values of the ontrol variables and find these not to alter the main results; the estimates and statistial signifiane of β 1, β 2 and β 3 are almost idential to the ones reported in the last olumn of Table 1. Next, we experiment with a different measure of trade openness. As previously disussed, openness has been suggested to affet ompetitive fores and employment but in the results reported in Table 1 our ountry-level measure on trade openness has no statistially signifiant effet. We therefore re-examine the role of openness further in the last two olumns by inluding an industry-speifi share of trade in prodution in the seond olumn of Table 2, and inluding both industry-speifi and aggregate openness in the last olumn. While neither of the openness variables have a statistially signifiant effet, inluding the industry-speifi measure eliminates the diret effet of output growth while inflating the effet output exerts via its interation with the Pareto shape parameter. On the grounds that output is likely to be the most ruial determinant of employment, we an only interpret this as a spurious result. 4. Summary and Conlusions In this paper we have onjetured that firm heterogeneity is a hannel that an ontribute to explaining the observed differenes in the output-employment relationship at the industry level. To examine this onjeture, we have developed a theoretial model to shows how the intra-industry realloations resulting from firm heterogeneity lead to employment adjustments at both the intensive and extensive margins. The effet of output hanges on employment hanges are shown to depend negatively on the extent of firm-dispersion in the industry. Capturing firms produtivity density funtion by the Pareto distribution, we have found that the larger is the shape parameter of the produtivity distribution of firms in an industry, i.e. the more homogenous is the distribution of firms, the larger is the impat of output hanges on employment hanges. Aordingly, 15
employment is pereived to be more insulated from output shoks in those industries that have (on average) larger and more produtive firms. We have then used data from Germany, Sweden and the UK to examine the empirial validity of these theoretial priors. Speifially, we have estimated industry-speifi shape parameters of the firm size distributions using firm-level data from Germany, Sweden and the UK, and then used these estimates to augment a relationship between industry-level employment and output. Estimates based on the available rossountry ross-industry data support our theoretial onjeture and onfirm that the firm-size distribution provides a hannel for the transmission of output shoks and that intra-industry realloations. Previous literature has pointed to ross-ountry differenes in labour market institutions as an important reason for differenes in employment volatility. This paper omplements this literature by highlighting the role of one partiular industry harateristi: the size distribution of firms. Our results suggest that a deeper understanding of employment volatility needs to take both ountry and industry speifi fators into aount; in so doing, they point to the importane of making a more nuaned distintion between labour market and industrial poliies. Our paper provides a first step in this diretion and hopefully offers important insights for further researh and to poliymakers alike. 16
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Mosarini, G. and F. Postel-Vinay (2012). The Contribution of Large and Small Employers to Job Creation in Times of High and Low Unemployment, Amerian Eonomi Review, 102, 2509-2539. Neumark, D., B. Wall, and J. Zhang (2011). Do Small Businesses Create More Jobs? New Evidene for the United States from the National Establishment Time Series, The Review of Eonomis and Statistis, 93, 16-29. Nikell, S., & Layard, R. (1999), Labor market institutions and eonomi performane, Handbook of labor eonomis, 3, 3029-3084. Okun, Arthur M. (1962), Potential GNP: its measurement and signifiane, Amerian Statistial Assoiation, Proeedings of the Business and Eonomis Setion, 98 104. Olley, S. and A. Pakes (1996), The Dynamis of Produtivity in the Teleommuniations Equipment Industry, Eonometria, Vol.64, pp.1263 97. Perman, R., Stephan, G., & Tavéra, C. (2015). Okun s Law a Meta analysis, The Manhester Shool, vol. 83(1): 101-126. Restuia, D., and R. Rogerson (2008). Poliy Distortions and Aggregate Produtivity with Heterogeneous Establishments, Review of Eonomi Dynamis, vol. 11, Issue 4, 707-720. Stella, A. (2015). Firm Dynamis and the Origins of Aggregate Flutuations, Journal of Eonomi Dynamis and Control, 55, 71-88. Syverson, C. (2011), What determines produtivity?, Journal of Eonomi Literature, 49, 326-365 Tybout, J.R. (2003). Plant and Firm Level Evidene on the New Trade Theories, in E.K. Choi and J. Harrigan, eds. Handbook of International Trade, Blakwell, Malden, 388-415. 18
Appendix A.i Equations of the model and derivation of employment-output relationship The equations below are repeated for onveniene and the numbers in square brakets after an equation s desription refers to the orresponding number in the main text. ( ϕ) = ( ϕ) ( ϕ) r p y definition of revenue of firms with average produtivity (A1) Mr ( ) ϕ = PY zero profit ondition in downstream setor (A2) λ σ 1 P M p ( ϕ ) = aggregate CES prie index [3] (A3) v ( ϕ) = α + y ( ϕ ) ϕ input requirement of firms with average produtivity [5] (A4) Pv Wl PW γ 1 = γ unit input ost [7] (A5) ( ϕ) = ( γ) P v( ϕ) labour demand of firms with average produtivity [8] (A6) 1 v p ( ϕ ) = σ P v ( σ 1) ϕ prie-markup rule of firms with average produtivity [10] (A7) ( ) = r( ) / Pv π ϕ ϕ σ α profit of firms with average produtivity [11] (A8) ( ϕ ) r = σαp v revenue of marginal firms [12] (A9) r r M ( ϕ ) ( ϕ ) ϕ = ϕ ( ) σ 1 relationship between the marginal and average firms revenue [14] (A10) = F mass of suessful entrants [16] (A11) ϕ κ 1/( σ 1) κ ϕ = ϕ relationship between the marginal and average produtivities [17] (A12) 1+ κ σ ( ) Mπ ϕ = PFf zero profits ondition in upstream setor [18] (A13) ( ) L = Ml ϕ aggregate labour demand [19] (A14) For any given value of Y and the parameters (, f,,,, ) α γ λσκ, equations (A1)-(A14) determine the values of 14 l ϕ, v ϕ, y ϕ, p ϕ, p ϕ, r ϕ, r ϕ, ϕ, ϕ, P v. It is however endogenous variables: L, W/P, F, M, ( ) ( ) ( ) ( ) ( ) ( ) ( ) more informative to redue the above equations to the following 4 equations determining l ( ϕ ), W/P, M and L 19
as follows. First, we use (A1), (A4), (A5), (A7), (A9) and (A11) to eliminate r ( ϕ ), v( ϕ ), and F. Then, we use (A12) to substitute out P v, ( ) p ϕ, r ( ϕ ) ϕ. The resulting substitutions in (A3), (A6), (A8) and (A10) then an be shown to yield the solutions for ϕ, y ( ϕ ), π ( ϕ ) and l ( ϕ ) in terms of W/P and M: λ 1 γ σ W σ 1 ϕ σ = M (A15) 1 P y ( ϕ ) 1 γ λ ασκ W σ 1 M = (A16) κ + 1 σ P ( 1) 1 γ α σ W π ( ϕ) = (A17) κ + 1 σ P l ( ϕ ) ( 1 )( 1 ) γ α γ κσ + σ W = (A18) κ + 1 σ P Equation (18) is the firm-level labour demand whih is written in terms of the industry-level real wage. This is beause we are ultimately interested in analysing the industry-level employment-output relationship. However, it is worthwhile noting that the more onventional firm-level labour demand, written in terms of the firm-level real wage, is given by, l ( ϕ ) ( 1 )( + 1 ) γl α γ κσ σ W σ 1 = M κ + 1 σ p ( ϕ) γ, (A19) whih, for any given number of firms in the industry M, has exatly the same form as (A18) but shows that firm-level employment is less affeted by the firm-level real wage the larger is number of firms in the industry. Equation (20) in the paper is derived from (A18). To obtain equations (21) and (22) in the paper, we substitute from the above solutions in the two remaining equations, A(2) and (A13), whih are the zero profit onditions in the downstream and upstream setors respetively, to obtain two equations in terms of W/P and M: ( 1 ) γ W M= MY d P ( 1 )( 1)( 1) λκ γ σ κ W M = Mu P (A20) (A21) where 1 M κ + σ u ασκ σ 1 1 σ 1 κ+ 1 σ 1 κ+ σ 1 λ λ λκ λκ λκ = and M = ( κ) ( σ) ( σ 1) ( )( ) ( κ + 1 σ) determines W/P and M d f α. Solving the above 20
W P MY d = Mu λκ ( 1 γ ) λκ + ( σ 1)( κ 1) (A22) ( σ 1)( κ 1) M M 1 1 M ( 1)( 1 λκ + ) ( σ 1)( κ 1) Y λκ ( σ 1)( κ 1) λκ + ( ) ( σ )( κ ) u ( d ) λκ + σ κ = (A23) from whih equations (23) and (24) in the paper are obtained. We then use (A18), (A22) and (A23) to eliminate and l ( ϕ ), W/P and M from (A14) to obtain λκ λκ ( )( ) ( ) ( ) ( )( ) ( ) 1 λκ 1 1 + 1 ( ) ( )( ) ( 1 γ ) λκ + ( σ 1 )( κ 1 ) α γ κσ σ L= M 1 γ λκ σ 1 κ 1 1 1 1 u + M γ λκ + σ κ d Y κ + 1 σ (A24) from whih equation (25) in the paper is derived. A.ii The relationship between employment of firms with average and marginal produtivity In the absene of data on firm-level produtivity, in our empirial investigation we have approximated firms produtivity distribution by their size distribution. We have justified this on the basis of the evidene in the literature that larger firms are found to be more produtive. To see that this in fat holds in our model, we ompare the employment of firms with average and marginal produtivity. Given that in general a firm s W = P employment in the model is given by l( ϕ) ( 1 γ) v( ϕ) (7) and (8) in the paper) we an write, l l p ( ) ( ) γ where v( ϕ) ( ϕ ) γ y( ϕ) W y( ϕ) ϕ y W ϕ = 1 γ α + = ( 1 γ) α + ϕ P y ( ϕ ) ϕ ϕ P ( ϕ) / p( ϕ ) = ϕ / ϕ and v( ϕ ) ( ) ( 1 ) ( ϕ ) y = α +, an be rewritten as ϕ ϕ γ α ϕ α κ ( σ 1) P γ κ W = + ( v( ) ). Next, l( ϕ ) ( 1 γ) v( ϕ ) obtain l( ) κ κ W ϕ = l( ϕ ) α 1 ( 1 γ) κ ( σ 1) κ ( σ 1) P zero profit ondition, the marginal firms input requirement is onstant, i.e., ( ) ( ϕ ) ( ϕ ) ( ϕ ) ϕ ϕ p ( ϕ ) γ y ( ϕ ) W = α + (see equations (5), ϕ, whih, using (A10), (A12), = P γ γ an be used to. However, we also know that, due to y p y v ϕ = α + = α + whih, upon substitution from (A9) and taking into aount 21
p ( ϕ ) = σ P v ( σ 1) ϕ implies v( ϕ ) equation, we have the required result, namely, l l ( ϕ) ( ϕ ) 2 ( σ 1) ( ( σ 1) ) W = ασ and thus l ( ϕ ) = ασ ( 1 γ ) P γ. Using this and the previous = 1+ > 1. (A25) σ κ The above result, whih implies dl ( ϕ) > dl ( ϕ ), is onsistent with the evidene reported in Mosarini and Postel-Vinay (2012), that the response over the business yle of employment to shoks in larger firms is relatively higher. This result also holds for the variable input requirement. To see this, we ompare the variations in employment of firms with average and marginal produtivity resulting from flutuations in their variable input requirement. Denoting the employment assoiated with the variable input requirement of a firm γ VC VC y ( ϕ ) W by l ( ϕ ), (A4) and (A6) imply l ( ϕ) = ( 1 γ), whih an be written in terms of the ϕ P employment assoiated with the variable input requirement of the marginal frim by noting that γ VC y ( ϕ ) ϕ y ( ϕ ) W l ( ϕ) = ( 1 γ). As above, equations (A10), (A12) and p( ϕ) / p( ϕ ) = ϕ / ϕ y ( ϕ ) ϕ ϕ P y ( ϕ ) ϕ κ an be used to write = whih, when used together with y ϕ ϕ κ σ 1 l VC l l VC VC ( ϕ ) ( 1 γ) ( ϕ ) ( ) ( ) γ ( ϕ ) W y ϕ P = ( ) κ ( σ 1), yields κ 1 ϕ = >, (A26) whih implies showing that dl VC ( ϕ) > dl VC ( ϕ ) aggregate output shok., i.e.: a larger firm has a larger response to an exogenous A.iii Data: definitions and soures Data on the main variables are as follows: Y: Measure of industry output For eah ountry, the observations were onstruted by deflating the nominal annual prodution values (sbs_na_2a_dade) from Eurostat for industry aggregates by the Eurostat GDP (Euro) deflator (nama_05_gdp_p). 22
L: Measure of employment, total industry employment For Sweden and the UK, this was obtained by aggregating the firm-level employment for eah industry. For Germany, this was obtained by aggregating full-time equivalent employees for eah industry. The minimum firm size is 1 employee, and the minimum industry size is 10 firms. UK soure: Offie for National Statistis. (2012). Annual Respondents Database, 1973-2008: Seure Aess. [data olletion]. 3rd Edition. UK Data Servie. SN: 6644. Sweden soure: Statistis Sweden. (2015). Business Statistis Database, 1986-2012: Seure Aess. [data olletion]. Mirodata Online Aess. Germany soure: Institute for Employment Researh, http://fdz.iab.de/en/fdz_establishment_data/establishment_history_panel.aspx κ : Measure of firms size distribution Approximated by the Pareto shape parameter and estimated using the annual firm-level employment for eah industry. The definition, measurement and data soure for the additional explanatory variables are as follows: Employment Protetion Poliies: Measure of overall stritness of employment protetion. Sale 0 to 6 representing least to most stringent (soure: OECD). Union Density: Measure of union density. Ratio of wage and salary earners that are trade union members, divided by the total number of wage and salary earners (soure: OECD). Ative Labour Market Poliies: Measure of expenditure on ative labour market poliies. Total annual expenditure as a perentage of GDP (soure: OECD). Passive Labour Market Poliies: Measure of expenditure on passive labour market poliies. Total annual expenditure as a perentage of GDP (soure: OECD). Government Size: Measure of size of the publi setor. Total annual government expenditure as a perentage of GDP (soure: OECD). Trade Openness: Measure of trade openness. Total annual value of imports and export as a perentage of GDP (soure: OECD). Trade Openness at the Industry Level: Measure of trade openness. Total annual value of industry-level imports and exports as a perentage of total industry-level prodution (soure: Eurostat PRODCOM). 23
FIGURES AND TABLES Figure 1. Average Share of Total Employment by Country and NACE rev.1 Manufaturing Subsetions (2000-2007) Note: Eah share is alulated by dividing the 2-digit industry total employment by the total manufaturing setor employment. The sample is balaned within ountries and shares for eah ountry add one. DA: Manufature of food produts, beverages and tobao DB: Manufature of textiles and textile produts DC: Manufature of leather and leather produts DD: Manufature of wood and wood produts DE: Manufature of pulp, paper and paper produts; publishing and printing DF: Manufature of oke, refined petroleum produts and nulear fuel DG: Manufature of hemials, hemial produts and man-made fibres DH: Manufature of rubber and plasti produts DI: Manufature of other non-metalli mineral produts DJ: Manufature of basi metals and fabriated metal produts DK: Manufature of mahinery and equipment n.e.. DL: Manufature of eletrial and optial equipment DM: Manufature of transport equipment DN: Manufaturing n.e.. 24