Firm Organization with Multiple Establishments^*

Abstract

We show theoretically and empirically that the managerial organization of multiestablishment firms is interdependent across establishments. To derive our result, we study the effect of geographic frictions on firm organization. In our model, we assume that a CEO’s time is a resource in limited supply, shared across headquarters and establishments. Geographic frictions increase the costs of accessing the CEO. Hiring middle managers at one establishment substitutes for CEO time, which is reallocated across all establishments. Consequently, geographic frictions between the headquarters and one establishment affect the organization of all establishments of a firm. Our model is consistent with novel facts about multiestablishment firm organization that we document using administrative data from Germany. We exploit the opening of high-speed railway routes to show that not only the establishments directly affected by faster travel times but also the other establishments of the firm adjust their organization. Our findings imply that local conditions propagate across space through firm organization.

I. Introduction

Firm performance depends on firm organization, and firm organization crucially depends on firm characteristics. Most notably, it is well known that large firms have more layers of middle managers than do small firms. However, firm size alone fails to capture the complexity of large corporations. Large corporations often operate multiple establishments in different locations. The decision to maintain multiple establishments likely affects the managerial organization, as the establishments share managerial resources of the headquarters and at the same time often encounter diverse conditions in their respective locations. Yet the effects of operating multiple establishments on managerial organization are only poorly understood.

This article studies the managerial organization of firms with multiple establishments. We show that the managerial organization of an establishment does not only depend on the characteristics and local conditions of the establishment but also on those of the other establishments of the firm. In multiestablishment firms, organization should therefore not be studied at the establishment level but by considering the firm as a whole. A key implication of our study is that local economic conditions propagate across space through firm organization, because local conditions affect not only the organization of the local establishment, but also the organization of the headquarters and other establishments of a multiestablishment firm.

Specifically, we study the effect of geographic frictions on the managerial organization of a firm and its establishments. We use new data from administrative sources in Germany to document that distance between the establishments and the headquarters increases the number of managerial layers both at the establishments and the headquarters. We develop a model to show that geographic frictions increase the optimal number of managerial layers of multiestablishment firms. Importantly, the model predicts that geographic frictions between the headquarters and one establishment affect not only the optimal managerial organization of this particular establishment but also the organization of the headquarters and other potential establishments of a firm. We use our data to show that this prediction is reflected in the organizational response of multiestablishment firms to an exogenous reduction in travel times following the opening of high-speed railway routes.

We motivate our study by documenting three facts that, taken together, suggest that the managerial organization of multiestablishment firms is interdependent across establishments. First, the probability that a firm operates an establishment at a location decreases with distance from the headquarters. Distance also correlates negatively with establishment size (in line with Giroud 2013; Kalnins and Lafontaine 2013).

Second, the number of managerial layers of a multiestablishment firm correlates positively with the distance of its establishments from the headquarters (see Figure I). Quantitatively, doubling the distance is associated with the same increase in number of layers as increasing sales by a third. The correlation is not driven by larger firms investing in more distant locations. Distance correlates positively with the number of managerial layers both at the establishments and the headquarters.

Figure I

Distance to HQ Correlates Positively with Number of Managerial Layers of ME Firms

Bin scatterplot of the relation between the maximum distance of establishments to headquarters (HQ) and the number of managerial layers in a multiestablishment (ME) firm. 2012 cross section, no. firms: 8,217. Firms with establishments only in the HQ county are excluded for consistency with Table IV.

Third, multiestablishment firms typically add or drop managerial layers either at the headquarters or the establishments. Only rarely do they alter the number of layers simultaneously at the headquarters and the establishments. This pattern is independent of the distance of establishments.

We propose a model to understand how geographic frictions affect the optimal managerial organization. We model firms as knowledge hierarchies (Garicano 2000; Caliendo and Rossi-Hansberg 2012). We select this framework because recent evidence suggests that the efficient transfer of intangible inputs such as managerial knowledge is an important motive for integrating multiple establishments (Atalay, Hortaçsu, and Syverson 2014) and that spatial frictions impede knowledge flows within and between the sites of an organization (Keller and Yeaple 2013; Battiston, Blanes i Vidal, and Kirchmaier 2021). Furthermore, the notion of a layer in this framework is closely in line with our measure of layers in the data. We assume that a firm consists of a headquarters and possibly an additional establishment. The production workers at the headquarters and the establishment share a chief executive officer (CEO), who is located at the headquarters. Production is a problem-solving process. Workers input labor and generate problems that must be solved to produce output. The CEO helps the workers solve the problems that they cannot solve using their knowledge. The firm may choose to hire a layer of local middle managers, who solve some of the problems that would otherwise need to be solved by the CEO but entail a quasi-fixed cost for the firm.

Helping workers costs CEO time. The driving forces of the model are that the CEO has only one unit of time, and that geographic frictions between the establishment and the headquarters increase the amount of time that the CEO needs to help the workers at the establishment.

Through straining CEO time, geographic frictions reduce the probability that a firm operates an establishment. For the same reason, establishments tend to be smaller than the headquarters. This result is consistent with the lower investment probability and the lower size of establishments at distant locations documented in Fact 1.

The firm adjusts the establishment’s organization in response to more severe geographic frictions so that fewer problems need to be solved by the CEO. In particular, geographic frictions render it desirable to hire middle managers. Given that the CEO is shared between the headquarters and the establishment, the firm additionally adjusts the organization at the headquarters. The model thus explains Fact 2: the number of layers increases with geographic frictions, and the managerial organization responds both at the establishments and the headquarters.

As the middle managers entail a quasi-fixed cost, a firm only hires them if firm size is sufficiently large. Importantly, hiring middle managers at the establishment also increases efficiency at the headquarters (and vice versa). This is because middle managers release CEO time, hence middle managers at the establishment increase the amount of CEO time available for the headquarters and reduce the need to hire middle managers there. This result explains Fact 3: multiestablishment firms do not add layers at the headquarters and the establishments at the same time. Both the successive reorganization and the effect of geographic frictions reflect how multiestablishment firm organization is interdependent across establishments.

In the final part of our article, we utilize the opening of high-speed railway routes in Germany to study the response of firm organization to exogenous variation in geographic frictions. The routes reduce travel time between establishments and headquarters. We focus on the model prediction that geographic frictions between the headquarters and one establishment have repercussions for the managerial organization of the headquarters and other potential establishments of the firm. Importantly, geographic frictions affect establishment size in the model. Size changes lead to changes in the number of layers. Travel times therefore have an indirect effect through size on the managerial organization, in addition to their direct effect. Only the total—direct and indirect—effect of lower travel times is identified.

We find that establishments that benefit from lower travel times grow faster than those that do not. The number of managerial layers is constant. This is consistent with the direct negative effect of lower travel times on the number of layers and the indirect positive effect through larger size compensating each other. Importantly, we find that lower travel times increase the wages and number of managerial layers at the headquarters. This finding supports the interdependence of the managerial organization predicted by the model. The interdependence goes beyond the headquarters: if a firm has at least one establishment affected and one unaffected by lower travel times, the wages and share of employees in managerial occupations in the unaffected establishment increase faster than in establishments of firms that do not benefit at all from lower travel times.

Through the lens of the model, lower travel times between the headquarters and the establishment affect the managerial organization because they decrease the costs of accessing CEO knowledge at the establishment. In supplementary regressions, we exploit the model’s implication that changes in the helping costs have a more pronounced effect in sectors with a less predictable production process to explore this channel. We construct a sector-level measure of predictability using survey data on the tasks and workplace environment of employees. We find that the estimated effects are driven by establishments and headquarters in sectors with below-median predictability of the production process. In additional analyses, we find that the education and experience of employees change concomitantly with wages. This evidence supports the mechanism proposed by the model.

Our article contributes to several strands of the literature. To develop our model, we build on the literature of firms as knowledge hierarchies (for an overview, see Garicano and Rossi-Hansberg 2015). This study is closest to that of Antràs, Garicano, and Rossi-Hansberg (2008), which shows that middle managers facilitate the transmission of knowledge in the context of offshoring. Our model goes beyond their theory by incorporating simultaneous production at the headquarters and the establishment of a firm. This enables us to study the effect of local shocks on the organization of the local and nonlocal units of a firm. The broader literature focuses on firm size as a determinant of organization (Caliendo and Rossi-Hansberg 2012, henceforth CRH; Caliendo, Monte, and Rossi-Hansberg 2015; Caliendo et al. 2020; Friedrich 2020).¹ The possibility of multiestablishment production is largely neglected, although multiestablishment firms account for a substantial share of aggregate employment in developed economies.²

Our main result is that the managerial organization of multiestablishment firms is interdependent across establishments. The key driver of this result is that the establishments share the CEO. Hence, our result is more general than our specific model of firm organization, in line with prior findings on structural similarities of different hierarchy models (Chen 2017; Chen and Suen 2019).

The interdependence of establishment organization is particularly relevant for recent literature documenting how multiestablishment firms propagate local shocks through their internal networks (Seetharam 2018; Giroud and Mueller 2019; Giroud et al. 2021). This body of research discusses managerial and financial constraints as potential drivers of the empirical findings. However, although CEOs are considered decisive for firm performance (Bertrand 2009), managerial constraints have received very little systematic attention. Our contribution is to provide both a formal analysis and empirical evidence regarding the role of managerial constraints for multiestablishment firm organization.

Our empirical strategy builds on literature using the opening of high-speed railway routes to identify the effect of geographic frictions on firms (e.g., Bernard, Moxnes, and Saito 2019). Our approach is particularly close to Charnoz, Lelarge, and Trevien (2018), who study the effect of new routes on the functional specialization and hierarchical organization of business groups. Their results are consistent with the predictions of our model, although they use different outcome variables to capture both aspects of firm organization. Our contribution is to provide a unified theoretical and empirical analysis. Our outcome variables neatly map firm organization in our model. Our model explains why the effect of geographic frictions goes beyond a particular establishment and cleanly disentangles the direct effects of geographic frictions on organization and the indirect effects through size.

Our article also relates to the literature on multinational firms. Keller and Yeaple (2013) back out the costs to transfer knowledge across space from multinational operations. Their results support our assumption that geographic frictions hamper access to headquarter knowledge. In the broader literature, headquarter inputs are often considered public goods in the firm (e.g., Helpman, Melitz, and Yeaple 2004; Irarrazabal, Moxnes, and Opromolla 2013; Antràs and Yeaple 2014, for a survey). Our results caution that this assumption may apply to patents or trademarks, but not necessarily to managerial inputs.

Finally, our article offers a novel perspective on the recent management literature. Bloom et al. (2019) document that half of the total variation in management practices between U.S. establishments owes to variations between establishments in the same firm. Implementing managerial practices requires managerial time. The heterogeneity of management practices may reflect asymmetries in the number of layers and the amount of CEO time allocated to an establishment.

The article is structured as follows. Section II describes the data. Section III presents the facts on multiestablishment firm organization. Section IV develops the model. Section V presents the evidence from the opening of high-speed railway routes. The final section concludes.

II. Data

II.A. Data Sources

We use a linked firm-establishment-employee data set for Germany that is uniquely suited to the study of multiestablishment firms. The data contain information on the sales and legal form of firms, as well as the county and the sector of their establishments. For each establishment, we observe all employees subject to social security contributions on June 30, and their occupation and wage. The data cover firms in all sectors during the period 2000–2012. Each employee, establishment, and firm has a unique identifier that makes it possible to follow them over time.

We assemble the data set from two sources. The universe of social security records provides the data on employees and establishments. The Research Data Centre of the German Federal Employment Agency at the Institute for Employment Research makes these data available for research. We use the employee history, the Establishment History Panel, and the extension files on entries and exits of establishments. The Orbis database of Bureau van Dijk contains the balance sheet information of firms. We use a linkage table between the social security records and the Orbis database. The headquarters of a firm is identified as the establishment with the same postal code or locality as the firm.³Online Appendix A.1 contains details on the components of our data set and the record linkage procedure.

The data set is an unbalanced panel. We exclude 2011 due to changes in the occupational classification in that year (see Online Appendix A.2). Our main analyses use the 2000–2010 panel. We use 2012 for cross-sectional analyses, because it contains the maximum number of establishments, exhibits relatively few missing values for sales, and uses the new, finer occupational classification. Consistent with the literature, we restrict our sample to full-time employees (e.g., Card, Heining, and Kline 2013). We focus on firms with at least 10 employees in all years.

Multiestablishment (ME) firms comprise the headquarter establishment and at least one other establishment. For clarity, we use the term “headquarters” for the former and “establishment” to denote the latter. Single-establishment (SE) firms only consist of the headquarters.

II.B. Measures for Managerial Organization

We use the occupation of the employees to construct three measures of the managerial organization of firms. Our preferred measure is the number of managerial layers. We assign employees to four layers (following Caliendo, Monte, and Rossi-Hansberg 2015; see Online Appendix A.3 for details):

Level	Designation	Occupations
3	CEO	CEOs, managing directors
2	Middle managers	Senior experts, middle managers
1	Supervisors	Supervisors, engineers, technicians, professionals
0	Production workers	Clerks, operators, production workers

We treat the layer at the lowest level in the firm as nonmanagerial and count the number of layers above the lowest layer per firm.

Alternatively, we use shares of managerial occupations in the wage sum. The establishments report the occupations of employees in the social security data. In ME firms, establishments may assign different occupations to similar employees. Cross-checking the results regarding the number of layers with the managerial share ensures that our results are robust to this possibility. We determine managerial occupations in two ways. On the one hand, we use the assignment of employees to layers and treat all employees above the lowest level as managerial. On the other hand, we use the Blossfeld (1983, 1987) occupational categories, which build on research from sociology and are part of the Establishment History Panel.

Online Appendix A.4 illustrates the plausibility of the assignment of employees to layers. We replicate Caliendo, Monte, and Rossi-Hansberg (2015) and show how the tasks of employees systematically differ between layers in ways that plausibly reflect the different roles of employees within firms using survey data.

II.C. Descriptive Statistics

Table I provides descriptive statistics of the 2012 cross-section (see Online Appendix Table A.17 for the 2000–2010 data). Our sample comprises 109,000 firms. We only observe sales for the larger firms owing to missing values in the Orbis data. The firms consist of 144,000 establishments (including headquarters) and employ 6.4 million individuals. Nine percent of firms are ME firms. They make up a disproportionate share of establishments and employment: 31% of establishments belong to them, and 34% of employees work for them. This pattern is similar across sectors (see Online Appendix Table A.16). ME firms are substantially larger than SE firms in terms of employment and sales. ME firms also have a higher number of managerial layers and higher managerial shares. Online Appendix A.5.2 shows that this difference does not only reflect differences in firm size.

TABLE I

Descriptive Statistics, SE versus ME firms

Units of observation	N	of which ME firms (% share)
Firms	109,357	9.0
with nonmissing sales	57,811	9.2
Establishments (incl. HQ)	144,437	31.1
Employees	6,356,072	34.2
Descriptive statistics	N	ME	Mean	Std. dev.	p25	p50	p75	p95
No. employees	99,545	0	42	92	13	21	39	133
	9,812	1	222	1,980	22	50	127	650
Sales (M €)	52,524	0	28	694	2	4	9	67
	5,287	1	358	4,111	4	15	74	608
No. managerial layers	99,545	0	1.4	1.0	1	1	2	3
	9,812	1	2.0	1.0	1	2	3	3
Managerial share	99,545	0	28	28	5	19	43	88
(%, layers)	9,812	1	36	29	11	29	58	90
Managerial share	99,545	0	6	11	0	0	9	27
(%, Blossfeld)	9,812	1	9	12	0	5	12	33

Notes. 2012 cross section. HQ: headquarters; ME: multiestablishment firm; No. employees: number of full-time employees; Sales (M €): sales in million €; No. Managerial layers: number of managerial layers; Managerial share (%, layers/Blossfeld): share of wage sum earned by employees in managerial occupations (according to layers/Blossfeld occupational categories).

Table II illustrates the complexity of ME firms (see Online Appendix Table A.18 for the 2000–2010 data). On average, ME firms have five establishments (including headquarters). Half of them have two, and the largest 5% have 10 or more establishments. The establishments tend to be geographically dispersed. At the top of the distribution, the air-line distance between headquarters and establishments exceeds 540 km, about two-thirds of the maximum possible distance within Germany. Headquarters are substantially larger than establishments. Management is concentrated in the headquarters that have a higher number of layers and higher managerial shares than establishments. Online Appendix A.5.3 describes the organization of headquarters and establishments in detail.

TABLE II

Descriptive Statistics, ME Firms

Descriptive statistics, firm	N		Mean	Std. dev.	p50	p75	p95
No. establishments (incl. HQ)	9,812		4.6	19.6	2	3	10
Maximum distance to HQ, km	9,812		218	189	167	376	547
Minimum area covered, km2	3,579		30,117	41,725	7,025	49,915	125,253
Descriptive statistics, HQ/ establishment	N	HQ	Mean	Std. dev.	p25	p50	p75
No. employees	35,080	0	32	333	2	5	16
	9,812	1	107	669	11	27	76
No. managerial layers	35,080	0	1.0	0.8	0	1	2
	9,812	1	1.7	1.1	1	2	3
Managerial share	35,080	0	37	38	0	24	70
(%, layers)	9,812	1	38	32	11	32	64
Managerial share	35,080	0	8	19	0	0	5
(%, Blossfeld)	9,812	1	10	16	0	4	14

Notes. 2012 cross section. No. establishments (incl. HQ): number of establishments (including headquarters); Maximum distance to HQ, km: maximum distance between establishments and HQ in kilometers, where distance is computed as the population-weighted average of the distances between all municipalities in the establishment county and the HQ county; Minimum area covered, km²: minimum area covered by establishments and HQ in square kilometers, only available for firms with at least two establishments in addition to HQ.

III. Facts

III.A. Distance to Headquarters Decreases Location Probability

Table III describes the geographic organization of ME firms. Columns (1)–(3) show that firms are less likely to locate an establishment in a county that is distant from their headquarters. According to columns (4)–(6), establishment size also decreases with distance. Larger market potential increases location probability and establishment size. Higher wages and land prices in the county relative to the headquarters are negatively associated with location probability. Although higher wages also relate negatively to establishment size, higher land prices relate positively.

TABLE III

Distance to HQ Correlates Negatively with Location Probability and Establishment Size

	Location probability			Log no. est. employees
	(1)	(2)	(3)	(4)	(5)	(6)
Log distance to HQ	−0.315***	−0.303***	−0.368***	−0.106***	−0.112***	−0.137***
	(0.021)	(0.023)	(0.020)	(0.018)	(0.019)	(0.017)
Log market potential	0.745***	0.780***		0.485***	0.465***
	(0.026)	(0.031)		(0.044)	(0.046)
Relative wages	−0.942***	−0.887***		−0.330**	−0.433***
	(0.062)	(0.063)		(0.108)	(0.109)
Relative land prices		−0.021***			0.020***
		(0.005)			(0.005)
No. observations	3,715,666	3,222,108	3,715,666	21,496	19,203	21,496
No. firms	9,266	8,732	9,266	3,006	2,773	3,006
HQ sector FE	Y	Y	Y	N	N	N
HQ county FE	Y	Y	Y	N	N	N
Legal form FE	Y	Y	Y	N	N	N
County FE	N	N	Y	N	N	Y
Firm FE	N	N	N	Y	Y	Y
Model	Probit			OLS

Notes. 2012 cross section. The table presents the coefficient estimates of a probit model in columns (1)–(3) (a constant is included; standard errors clustered by HQ county are in parentheses) and a linear model in columns (4)–(6) (standard errors clustered by firm and county are in parentheses). The regressions in columns (4)–(6) control for firm fixed effects, hence they only include ME firms with establishments in at least two counties. ^**p < .01, ^***p < .001. Dependent variable: columns (1)–(3): indicator for whether firm i owns at least one establishment in county c; columns (4)–(6): log number of employees of establishment(s) in county c. Independent variables: Log distance to HQ: log distance between county c and HQ county of firm i in km; Log market potential: log of average of GDP of county c and surrounding counties weighted by distance; Relative wages/land prices: average wages/land prices in county c relative to wages/land prices in HQ county of firm i. We compute average wages in a county excluding firm i. Distance, market potential, and relative land prices are computed using data of the German Federal Statistical Office. The number of firms is lower than the number of ME firms due to missing values for the legal form. FE = fixed effects.

The results are consistent with a negative effect of geographic frictions between the headquarters and an establishment on establishment performance. The effects of market potential and wages indicate market-seeking and cost-cutting motives for having establishments. The different effects of land prices on location decision and size are in line with the cost of land being a fixed cost, so it is worth maintaining only larger establishments at locations with higher land prices.

Fact 1 summarizes our findings:

 

Fact 1.

Distance of a county from the headquarters is negatively related to the probability that a ME firm locates an establishment there as well as the size of the establishment conditional on location.

Online Appendix B.1 presents the results graphically and in the 2000–2010 panel.

III.B. Distance to Headquarters Increases the Number of Layers

Figure I shows that the number of managerial layers relates positively to the distance between the headquarters and the establishments. Table IV documents that the relationship is robust to controlling for size to capture the positive effect of size on the number of layers (e.g., Caliendo, Monte, and Rossi-Hansberg 2015) and the possibility of larger firms investing in more distant locations. We estimate Poisson regressions:

$$\begin{eqnarray*} {\rm no.} \ \rm {managerial\,\, layers}_{i} &=& \exp (\beta _{0} + \beta _{1} \rm {geographic\,\, frictions}_i + \beta _{2} \rm {size}_i\\ &&\qquad +\, \alpha _{l} + \alpha _{n} + \alpha _{s}). \end{eqnarray*}$$

i refers to the firm, l to its legal form, n to the county of the headquarters, s to the headquarter sector, and α denotes fixed effects. To account for the fractional nature of the managerial share, we follow Papke and Wooldridge (1996) and estimate a generalized linear model.

TABLE IV

Distance to HQ Correlates Positively with the Number of Managerial Layers of ME Firms

	No. managerial layers				Mg. share ∈ [0, 1]		Mg. share ∈ [0, 1]
					Layers		Blossfeld
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Maximum log	0.039***		0.050***		0.152***		0.131***
distance to HQ	(0.007)		(0.006)		(0.014)		(0.019)
Log area		0.025***		0.027***		0.070***		0.072***
		(0.005)		(0.004)		(0.011)		(0.013)
Log sales	0.115***	0.082***
	(0.004)	(0.006)
Log no. non-mg.			0.109***	0.088***
employees			(0.004)	(0.005)
No. firms	4,323	1,661	7,742	2,768	7,742	2,768	7,742	2,768
HQ sector FE	Y	Y	Y	Y	Y	Y	Y	Y
HQ county FE	Y	Y	Y	Y	Y	Y	Y	Y
Legal form FE	Y	Y	Y	Y	Y	Y	Y	Y
Model	Poisson				GLM

Notes. 2012 cross section. The table presents the coefficient estimates. A constant is included. Robust standard errors are in parentheses. ^***p < .001. Even columns include only ME firms active in at least three counties. The generalized linear model (GLM) assumes a logit link function and the binomial distributional family. Dependent variable: columns (1)–(4) number of managerial layers, columns (5)–(6) managerial share in wage sum, according to layers, columns (7)–(8) managerial share in wage sum, according to Blossfeld occupational categories. Independent variables: Maximum log distance to HQ: log of maximum distance between establishment and headquarters in km; Log area spanned by firm: log of minimum area covered by establishments and HQ in square kilometers; Log sales: log annual sales; Log no. non-mg. employees: log number of employees at lowest layer. FE = fixed effects, mg. = managerial.

We approximate geographic frictions with the maximum distance of establishments to the headquarters or the minimum area spanned by the establishments and the headquarters. The distance is defined for all ME firms, whereas the area is only defined for firms active in at least three counties. We use sales and the number of nonmanagerial employees as measures of firm size.

The regression results show that both distance and area correlate positively with the number of managerial layers in a firm. According to column (3), doubling the maximum distance of establishments to the headquarters is associated with the same increase in the number of layers as 46% more nonmanagerial employees. Moving from the lower to the upper quartile of the distribution of distance and the number of nonmanagerial employees is associated with 0.2 and 0.6 more layers, respectively. Taken together, this accounts for about half of the interquartile range of the number of layers. The managerial share also relates positively to the distance and the area.

The firm-level results may disguise different responses of headquarter and establishment organization. The managerial organization of the establishments does not copy the headquarters’: 71% of establishments have fewer managerial layers than the headquarters. We therefore complement the firm-level results with establishment and headquarter level analyses. Figure II shows that the number of managerial layers in both the headquarters and the establishments relates positively to distance. According to Table V, doubling the (maximum) distance is associated with the same increase in the number of layers as 22% more nonmanagerial employees in the establishments and 35% more nonmanagerial employees in the headquarters.

Figure II

Distance to HQ Correlates Positively with Number of Managerial Layers of HQ and Establishments

Bin scatterplot of the relation between (A) the distance of an establishment to the headquarters (HQ) and the number of managerial layers of the establishment, and (B) the maximum distance of the establishment(s) to the HQ and the number of managerial layers of the HQ. 2012 cross section, no. establishments: 31,718, no. HQ: 8,217. Establishments located in the HQ county and HQ of ME firms with establishments only in the HQ county are excluded for consistency with Table V.

TABLE V

Distance to HQ Correlates Positively with the Number of Managerial Layers of the HQ and Establishments

	Establishment			Headquarters
	No. layers	Mg. share ∈ [0, 1]		No. layers	Mg. share ∈ [0, 1]
		Layers	Blossfeld		Layers	Blossfeld
	(1)	(2)	(3)	(4)	(5)	(6)
Log distance	0.056***	0.191***	0.236***
to HQ	(0.011)	(0.032)	(0.053)
Maximum log				0.057***	0.166***	0.157***
distance to HQ				(0.007)	(0.016)	(0.022)
Log no. non-mg.	0.256***			0.162***
employees	(0.010)			(0.004)
No. est./HQ	26,409	31,717	31,717	7,999	8,217	8,217
Sector FE	Y	Y	Y	Y	Y	Y
County FE	Y	Y	Y	Y	Y	Y
Model	Poisson	GLM		Poisson	GLM

Notes. 2012 cross section. The table presents the coefficient estimates. A constant is included. Standard errors are in parentheses (clustered by firm in columns (1)–(3), robust in columns (4)–(6)). ^***p < .001. The generalized linear model (GLM) assumes a logit link function and the binomial distributional family. Dependent variable: columns (1) and (4) number of managerial layers, columns (2) and (5) managerial share in wage sum, according to layers, columns (3) and (6) managerial share in wage sum, according to Blossfeld occupational categories. Independent variables: Log distance to HQ: log of distance between establishment and headquarters in km; Maximum log distance to HQ: log of maximum distance between establishment and HQ in km; Log no. of non-mg. employees: log number of employees at lowest layer in establishment/HQ. FE = fixed effects, mg. = managerial.

Fact 2 summarizes our findings:

 

Fact 2.

The number of managerial layers of ME firms correlates positively with the distance between headquarters and establishments and the area they span, conditional on firm characteristics. The number of managerial layers of both the establishments and the headquarters increases with distance.

Online Appendix B.2 documents that the results are robust to modifications of the main variables, to alternative econometric specifications, in the 2000–2010 panel, and in sample splits.

III.C. Reorganization of Headquarters or Establishments

To complement the cross-sectional evidence on managerial organization, we study the reorganization dynamics of firms over time. The upper panel of Table VI displays the share of ME firms that transition from a number of managerial layers in year t to a potentially different number of layers in year t + 1. At least 80% of firms keep the number of layers constant. If they alter the number of layers, firms usually add or drop one layer. These dynamics are similar to those of French and Danish firms (Caliendo, Monte, and Rossi-Hansberg 2015; Friedrich 2020) and SE firms (Online Appendix Table B.18).

TABLE VI

Transition Dynamics of the Managerial Organization

Panel A: No. managerial layers of firm
No. layers in t/t + 1	0	1		2		3		SE	No. firms
0	85	8		1				6	10,778
1	5	81		8		1		6	18,274
2		7		79		8		5	18,754
3				6		90		4	22,391
Panel B: No. managerial layers at headquarters (HQ)/establishments (est.)
No. layers in t/t + 1	0/0	1/0	1/1	2/<2	2/2	3/<3	3/3	SE	No. firms
HQ 0/ est. 0	85	5						6	10,778
HQ 1/ est. 0	6	75	4	6				8	8,340
HQ 1/ est. 1	1	5	76	7		1		4	8,052
HQ 2/ est. 0,1		4	4	76	2	6		7	12,046
HQ 2/ est. 2			1	10	69	9	1	2	3,410
HQ 3/ est. 0,1,2				5	2	84	3	5	13,365
HQ 3/ est. 3						9	86	1	4,625

Notes. 2000–2010 data. Panel A displays the percentage share of firms that transition from a number of managerial layers in year t (given in the rows) to a potentially different number of layers or to SE firm status in year t + 1 (given in the columns). Panel B displays the percentage share of firms that transition from a managerial organization in year t (given in the rows) to a potentially different managerial organization or to SE firm status in year t + 1 (given in the columns). The figure in front of the slash denotes the number of layers of the HQ. The figure behind the slash denotes the maximum number of layers of the establishments. Firms with a higher number of layers at the establishments than at the HQ are dropped for readability. Empty cells contain fewer than 0.5% of firms. Fewer than 0.5% of firms exit. The diagonal is in bold.

The lower panel displays the reorganization dynamics at the level of the headquarters and establishments. We count the maximum number of layers at the establishments to account for the potentially different number of establishments across firms. Over time, the managerial organization at the unit level is less stable than the managerial organization at the firm level as reflected by less mass on the diagonal of the lower panel than on the diagonal of the upper panel. Notably, if ME firms change their organization, they typically add or drop layers at either the headquarters or the establishment(s), but not both. For example, among ME firms with two layers at the headquarters and the establishments, 9% add one layer at the headquarters and 10% drop one layer at the establishments. Only 2% choose a lower or higher number of layers at both.

Overall, among the firms that change the number of layers, 49% change it only at the headquarters, 42% change it only at the establishments, and just 9% change it at both.⁴

Fact 3 summarizes our finding:

 

Fact 3.

ME firms that reorganize typically add or drop layers either at the headquarters or at the establishments and rarely change layers simultaneously at the headquarters and the establishments.

Online Appendix B.3 documents that changes in the number of layers are related to changes in firm size (consistent with Caliendo, Monte, and Rossi-Hansberg 2015; Friedrich 2020), and shows that our results are robust to different ways of counting managerial layers, longer time lags, and in sample splits.

IV. Model

IV.A. Set-up

We use Facts 1–3 to inform a model in which firms endogenously choose whether to operate an establishment and the managerial organization. We consider an economy with two locations, j = {H, E}. N_j agents each supply one unit of time to the labor market in location j. Agents work in two sectors and can move between sectors, but not between locations. In the differentiated-goods sector, each firm i produces one product. The homogeneous-good sector produces a freely tradeable good under perfect competition using a constant-returns-to-scale technology, so wages w are equal across locations.⁵ The agents consume the homogeneous good and the differentiated products.

1. Production. Production in the differentiated-goods sector is a problem-solving process based on labor and knowledge (Garicano 2000; CRH). One unit of labor generates a unit mass of problems that have to be solved using knowledge to produce output. Mathematically, knowledge is an interval ranging from zero to an upper bound. We denote the length of the interval by z. A problem is solved if it is realized within the interval. The problems follow a distribution with the exponential density f(z) = λe^−λz, where z ∈ [0, ∞) refers to the domain of possible problems and λ denotes the predictability of the production process. A higher value of λ implies that a given amount of knowledge solves more problems. Combining n units of labor and knowledge |$\bar{z}$| yields |$q = n(1-e^{-\lambda \bar{z}})$| units of output, where |$1-e^{-\lambda \bar{z}}$| is the value of the cumulative distribution function.

A firm hires agents for production. The firm’s employees supply labor by spending their time generating problems. To supply knowledge, employees must learn. They spend wcz to learn knowledge z, where c denotes the learning cost. The firm remunerates the employees for their time and learning expenses, so they receive remuneration w(1 + cz) (as in CRH).

The employees of the firm can share problems among themselves, and hence can leverage differences in knowledge. This is costly: an employee in location j spends θ_kj units of time helping an employee in location k. Helping is more costly across than within locations: 1 > θ_{|${\mathit {EH}}$|} ≥ θ_{|${\mathit {HH}}$|} > 0. The helping costs are symmetric: θ_{|${\mathit {EH}}$|} = θ_HE, θ_EE = θ_{|${\mathit {HH}}$|}. If an employee does not know how to solve a problem, he cannot tell who knows, but must find a competent fellow employee.

2. Organization. Firms organize their employees in hierarchical layers. We call the employees at the lowest layer ℓ = 0 production workers. They supply labor and solve the problems realized in their knowledge interval. We call the employees at the higher layers ℓ ≥ 1 managers. They supply only knowledge and spend their time helping the employees at the next lowest layer. The CEO constitutes the highest managerial layer. All firms consist at least of production workers and a CEO; they may also have one or more layers of middle managers. The knowledge levels of the employees are overlapping, so employees at layer ℓ know the knowledge of employees at layer ℓ − 1 and more.⁶ The CEO is the most knowledgeable employee of the firm. A crucial assumption is that each firm has exactly one CEO, who is thus a resource in limited supply for a firm.

The helping costs θ_{|${\mathit{jk}}$|}, learning costs c, and the predictability of the production process λ are exogenous parameters, with values restricted by Assumption 1 (Online Appendix C.1.1). The homogeneous-good sector pins down wages w. To simplify the exposition, Sections IV.B and IV.C examine the organization of a firm in location H taking output as given. Section IV.D endogenizes output.

IV.B. Single-Establishment Firm Organization

We first determine the optimal organization of a SE firm as a benchmark for the analysis of ME firm organization. The organization consists of the number of below-CEO layers of middle managers L, the number |$n_{H,L}^\ell$| and knowledge |$z_{H,L}^\ell$| of employees per layer ℓ, and the knowledge of the CEO |$\bar{z}_{H,L}$|⁠. The indices H, L refer to the location of the firm and the number of below-CEO layers, reflecting that these variables affect the other choices. We focus on the decision to hire one layer of middle managers and study the decision to hire additional layers in Online Appendix C.2.1.

The optimal organization yields minimal production costs:

$$\begin{eqnarray} C (\tilde{q}) = \min _{L} \tilde{C}_{H,L} (\tilde{q}), & \end{eqnarray}$$

(1)

$$\begin{eqnarray} \rm {where} \quad \tilde{C}_{H,L}(\tilde{q}) &=& \min _{\lbrace n_{H,L}^\ell , z_{H,L}^\ell \rbrace _{\ell =0}^{L}, \bar{z}_{H,L} \ge 0} \left[\sum _{\ell =0}^{L} n_{H,L}^\ell w \left(1+c z_{H,L}^\ell\right)\right]\nonumber\\ && +\, w (1+c \bar{z}_{H,L}) \end{eqnarray} $$

(2)

 

$$\begin{eqnarray} \rm {s.t.} \quad n_{H,L}^0 (1-e^{-\lambda \bar{z}_{H,L}}) &\ge \tilde{q} \end{eqnarray}$$

(3)

$$\begin{eqnarray} 1 &\ge n_{H,L}^0 \theta _{\mathit {HH}} e^{-\lambda z_{H,L}^{L}} \end{eqnarray}$$

(4)

$$\begin{eqnarray} n_{H,L}^\ell &\ge n_{H,L}^0 \theta _{\mathit {HH}} e^{-\lambda z_{H,L}^{\ell -1}} \quad \rm {for\,\, } \ell >0 \end{eqnarray}$$

(5)

$$\begin{eqnarray} \bar{z}_{H,L} &\ge z_{H,L}^{L}, \quad z_{H,L}^\ell \ge z_{H,L}^{\ell -1} \quad \rm {for\,\, } \ell >0. \end{eqnarray}$$

(6)

The production costs consist of the costs for the employees and the CEO. Constraint (3) specifies that the number of production workers and CEO knowledge must suffice to produce output. Constraints (4) and (5) reflect that the CEO and the middle managers have only limited time to help production workers solve problems. Knowledge levels are overlapping (constraint (6)).

Online Appendix C.2.2 contains the Lagrangian equation and the first-order conditions. Two multipliers from the Lagrangian equation help characterize the organization. The multiplier for constraint (3), ξ_H,L, denotes the marginal production costs. The multiplier for constraint (4), ϕ_H,L, denotes the marginal benefit of CEO time that reflects how costly the CEO time constraint is for the firm.

CEO knowledge is optimal if the marginal increase of CEO remuneration equals the marginal decrease of production costs:

$$\begin{equation} w c = \xi _{H,L} n_{H,L}^0 \lambda e^{-\lambda \bar{z}_{H,L}}. \end{equation} $$

(7)

Constraints (3)–(5) determine the number of production workers, the knowledge at the highest below-CEO layer, and the number of middle managers (if any). If the firm hires middle managers, the knowledge of the production workers is a function of the managerial knowledge:

$$\begin{equation} e^{\lambda z_{H,L}^0} =\big(1+c z_{H,L}^1\big)\frac{\lambda \theta _{\mathit {HH}}}{c}. \end{equation} $$

(8)

The marginal production costs ξ_H,L and the marginal benefit of CEO time ϕ_H,L are:

$$\begin{eqnarray*} \xi _{H,L} &= \frac{w \left(1+c z_{H,L}^0 + \frac{c}{\lambda } + {{\mathbb {1}}(L=1)}\frac{c}{\lambda } \theta _{\mathit {HH}} e^{-\lambda z_{H,L}^0}\right)}{1-e^{-\lambda \bar{z}_{H,L}}} \\ \varphi _{H,1} &= \frac{w c}{\lambda } e^{\lambda \left(z_{H,1}^1-z_{H,1}^0\right)} \quad \rm {for\,\, } L = 1, \quad \varphi _{H,0} = \frac{w c}{\lambda \theta _{\mathit {HH}}} e^{\lambda z_{H,0}^0} \quad \rm {for\,\, } L = 0 \end{eqnarray*}$$

Understanding how output |$\tilde{q}$| affects firm choices is useful for the analysis of ME firms.

 

Proposition 1.

Given the number of below-CEO managerial layers L of the firm,

• the knowledge of the CEO |$\bar{z}_{H,L}$|⁠, the number |$n_{H,L}^\ell$| and the knowledge |$z_{H,L}^\ell$| of the employees at all below-CEO layers ℓ ≤ L, the managerial span of control |$\frac{n_{H,L}^{\ell -1}}{n_{H,L}^\ell }$| at all managerial layers 1 ≤ ℓ ≤ L + 1, and the marginal benefit of CEO time ϕ_H,L increase with output |$\tilde{q}$|⁠.

• The cost function strictly increases with output |$\tilde{q}$|⁠. The marginal costs increase with output for |$\tilde{q}\ge \hat{q}^{L}$|⁠, with |$\hat{q}^{0}=0$|⁠. The average-cost function is U-shaped. It reaches a minimum at |$\tilde{q}^{*_L}$| where it crosses the marginal cost function, and converges to infinity for |$\tilde{q}\rightarrow 0$| and |$\tilde{q}\rightarrow \infty$|⁠.

 

Proof. See Online Appendix C.2.3.

Our results align with those in CRH for nonoverlapping knowledge. We consider an additional outcome, the marginal benefit of CEO time. It increases with output, because higher output makes it more beneficial to increase CEO time and avoid the increase in below-CEO knowledge.

Regarding the decision to hire middle managers, the firm faces a trade-off. On the one hand, middle managers entail a quasi-fixed cost because they are remunerated but do not generate problems. On the other hand, middle managers reduce the number of problems sent to the CEO and thus allow decreasing the knowledge of the production workers and the marginal production costs. Consequently, hiring middle managers is only worthwhile if the firm is sufficiently large.

Figure III, Panel A illustrates the choice of hiring middle managers. The minimum efficient scale |$\tilde{q}^{*_L}$| increases with the number of below-CEO layers, reflecting the higher quasi-fixed costs. The cost function becomes flatter with the number of layers, because the marginal production costs increase less strongly with output. The firm adds a layer at the crossing |$\tilde{q}^{0\rightarrow 1}$| (see Online Appendix C.2.4).

Figure III

Illustration of the Average-Cost Function, no Transport Frictions

The figure plots the average-cost functions of a SE and a ME firm for τ = 1, θ_{|${\mathit {HH}}$|} = θ_{|${\mathit {EH}}$|}. Parameter values: |$\frac{c}{\lambda }=0.225$|⁠, θ_{|${\mathit {HH}}$|} = 0.26 (from CRH), w = 1. Panel A: The average-cost function of a SE firm is U-shaped given L. The firm adds a layer at |$\tilde{q}^{0\rightarrow 1}$|⁠. Panel B: The average-cost function of a ME firm with a symmetric number of below-CEO layers is U-shaped. The firm adds a layer at the establishment at |$\tilde{q}^{*_{(0,0)}}$| and at the headquarters at |$\tilde{q}^{(0,1)\rightarrow (1,1)}> \tilde{q}^{(0,0)\rightarrow (1,1)}$| (or vice versa, as the (0,1) and the (1,0)-organization have the same costs).

IV.C. Multiestablishment Firm Organization

The firm incurs iceberg-type transport costs τ ≥ 1 to ship output produced in one location to the other location,⁷ so it may maintain an establishment at location E to avoid these costs. We take as given the potentially different amounts of output |$\tilde{q}_j$| that the firm supplies at each location.

The CEO is located at the headquarters in location H. The firm chooses whether to produce in the headquarters, in the establishment, or both, as well as the number of below-CEO layers of middle managers L_j per location. We use the term “organizational structure” and the variable ω to denote the combination of the below-CEO layers (L_H, L_E). All other endogenous variables depend on the location and the organizational structure, so we index them by j, ω.

We split the optimization problem into three steps. First, the firm chooses the organizational structure ω, similarly to choosing the number of layers in Section IV.B:⁸

$$\begin{equation} C (\tilde{q}_H,\tilde{q}_E) = \min _{\omega } \tilde{C}_{H,\omega } (\tilde{q}_H,\tilde{q}_E). \end{equation} $$

(9)

Second, the firm chooses how much production q_j,ω and which share s_j,ω of CEO time to allocate to the headquarters and the establishment as well as CEO knowledge |$\bar{z}_{H,\omega }$|⁠:

$$\begin{eqnarray} \tilde{C}_{H,\omega } (\tilde{q}_H,\tilde{q}_E) &=& \displaystyle \min _{\lbrace q_{j,\omega }, s_{j,\omega } \rbrace _{j=H,E}, \bar{z}_{H,\omega } \ge 0} \sum _{j=H,E} C_{j,\omega } (q_{j,\omega }, s_{j,\omega }, \bar{z}_{H,\omega })\nonumber\\ && +\, \left[1-\sum _{j=H,E} s_{j,\omega }\right] w (1+c \bar{z}_{H,\omega }), \end{eqnarray} $$

(10)

$$\begin{eqnarray} \rm {s.t.} \quad s_{H,\omega } + s_{E,\omega } & \le 1 \end{eqnarray}$$

(11)

$$\begin{eqnarray} q_{H,\omega } + q_{E,\omega } & \ge \tilde{q}_H + \tilde{q}_E \end{eqnarray}$$

(12)

$$\begin{eqnarray} q_{j,\omega } & \ge \tilde{q}_j + \tau (\tilde{q}_k-q_{k,\omega }) \quad \rm {if\,\, } q_{k,\omega } \le \tilde{q}_k, \, k\ne j. \end{eqnarray}$$

(13)

The costs consist of the costs per location and the remuneration of the CEO time that is not used in production. Equation (11) reflects the CEO’s time constraint. Equation (12) states that total production has to cover total output. Local production may be lower than local output. Equation (13) states that if production is lower than output at one location, production at the other location has to compensate the shortfall plus transport costs.

Third, the firm chooses the number |$n_{j,\omega }^\ell$| and knowledge |$z_{j,\omega }^{\ell }$| of the employees in each layer ℓ.

$$\begin{eqnarray} &&C_{j,\omega } (q_{j,\omega }, s_{j,\omega }, \bar{z}_{H,\omega })\nonumber\\ &&\!\!\!\!\!\!\times \!\! \left\lbrace \begin{array}{@{}l@{\quad }l@{}}\stackrel{q_{j,\omega } > 0}{=} \displaystyle \min _{\lbrace n_{j,\omega }^\ell , z_{j,\omega }^\ell \rbrace _{\ell =0}^{L_j} \ge 0} \left[\sum _{\ell =0}^{L_j} n_{j,\omega }^\ell w \left(1+c z_{j,\omega }^\ell \right)\right] + s_{j,\omega } w (1+c \bar{z}_{H,\omega }) \\ \stackrel{q_{j,\omega } = 0}{=} 0 \end{array}\right.\!\!\!\!\!\!\!\!\!, \end{eqnarray} $$

(14)

$$\begin{eqnarray} \rm {s.t.} \quad n_{j,\omega }^0 \left(1-e^{-\lambda \bar{z}_{H,\omega }}\right) &\ge q_{j,\omega } \end{eqnarray}$$

(15)

$$\begin{eqnarray} s_{j,\omega } &\ge n_{j,\omega }^0 \theta _{jH} e^{-\lambda z_{j,\omega }^{L_j}} \end{eqnarray}$$

(16)

$$\begin{eqnarray} n_{j,\omega }^\ell &\ge n_{j,\omega }^0 \theta _{jj} e^{-\lambda z_{j,\omega }^{\ell -1}} \quad \rm {for\,\, } \ell >0 \end{eqnarray}$$

(17)

$$\begin{eqnarray} \bar{z}_{H,\omega } &\ge z_{j,\omega }^{L_j}, \quad z_{j,\omega }^\ell \ge z_{j,\omega }^{\ell -1} \quad \rm {for\,\, } \ell >0. \end{eqnarray}$$

(18)

The production costs consist of the below-CEO personnel costs and the remuneration for the CEO time allocated to the location. Constraints (15)–(18) are analogous to the constraints (3)–(6).

We solve the problem backward. We determine the number and knowledge of the employees per layer, taking as given the firm-level choices and the organizational structure. We then solve for the firm-level choices given the organizational structure, which we determine last. Online Appendix C.3.2 contains the Lagrangian equations and the first-order conditions.

1. Establishment-Level Choices. Constraints (15)–(17) determine the number of production workers and middle managers as well as the knowledge of the highest below-CEO layer. The knowledge of the production workers is a function of the managerial knowledge. The formal expressions are variants of those in Section IV.B, so we state them in Online Appendix C.3.2. The Lagrangian multipliers ξ_j,ω and ϕ_j,ω denote the marginal production costs and the marginal benefit of CEO time at location j.

2. Firm-Level Choices. The firm uses the full unit of CEO time and produces only the given output, that is, the constraints (11), and (12) or (13) are binding. The firm balances the marginal benefit and marginal cost of CEO knowledge, as in Section IV.B:

$$\begin{equation} w c = \sum _{j=H,E} \xi _{j,\omega } n_{j,\omega }^0 \lambda e^{-\lambda \bar{z}_{H,\omega }}. \end{equation} $$

(19)

Proposition 2 shows how the transport costs affect ME firm organization.

 

Proposition 2.

Suppose the firm produces in the headquarters and the establishment. The firm allocates CEO time to equalize the marginal benefit of CEO time across locations. Formally, in the optimum:

$$\begin{equation} \varphi _{H,\omega } = \varphi _{E,\omega }. \end{equation} $$

(20)

The firm either sets the production quantities equal to local output or chooses them to equalize the marginal production costs adjusted by the transport costs across locations. Formally, in the optimum,

$$\begin{eqnarray} \xi _{H,\omega } & \le \tau \xi _{E,\omega } \, \wedge \, \xi _{E,\omega } \le \tau \xi _{H,\omega } && \rm {if\,\, }q_{E,\omega } = \tilde{q}_E \wedge q_{H,\omega } = \tilde{q}_H, \end{eqnarray}$$

(21)

$$\begin{eqnarray} \tau \xi _{H,\omega } &= \xi _{E,\omega } && \rm {if\,\, } \tilde{q}_E>q_{E,\omega } \wedge q_{H,\omega } = \tilde{q}_H + \tau (\tilde{q}_E-q_{E,\omega }), \rm {\,\, and\,\, } \end{eqnarray}$$

(22)

$$\begin{eqnarray} \xi _{H,\omega } &= \tau \xi _{E,\omega } && \rm {if\,\, } \tilde{q}_H>q_{H,\omega } \wedge q_{E,\omega } = \tilde{q}_E + \tau (\tilde{q}_H-q_{H,\omega }). \end{eqnarray}$$

(23)

In the special case of no transport frictions, τ = 1, the firm chooses the production quantities to equalize the marginal production costs across locations:

$$\begin{equation} \xi _{H,\omega } = \xi _{E,\omega } \quad \rm {if\,\, } \tau = 1, \rm {\,\, i.e.,\,\, } q_{E,\omega }=\tilde{q}_H+\tilde{q}_E-q_{H,\omega }. \end{equation} $$

(24)

 

Proof. See Online Appendix C.3.3.

The firm can flexibly allocate CEO time, so it reallocates CEO time until its marginal benefit is equal across locations.⁹ The transport costs limit the flexibility of the allocation of production. The firm has three options: produce output locally, ship it from the other location, or do both. The firm produces output locally if local production has lower marginal costs than shipping output from the other location (equation (21)). If local production and shipping output from the other location have the same marginal costs, the firm produces part of the output locally and ships part of it from the other locations (equation (22) and (23)). Finally, if shipping output from the headquarters is cheaper than production at the establishment (or vice versa), the firm produces total output in the headquarters (establishment). In the special case of no transport frictions, the firm reallocates quantities until the marginal costs at the headquarters and the establishment are equal (equation (24)).

3. Comparative Statics. To derive the optimal organizational structure ω, it is useful to understand how choices depend on the output |$\tilde{q}_j$| and the helping costs θ_{|${\mathit {EH}}$|}. The comparative statics depend on which of equations (21)–(23) holds. Parameter changes easily lead to a violation of equations (22) and (23). We therefore assume that equation (21) holds. Online Appendix C.3.9 contains the results for the other cases (including equation (24)).

 

Proposition 3.

Suppose the firm produces in the headquarters and the establishment. Suppose that the firm incurs transport costs τ > 1 to ship output between locations, and that ξ_j,ω ≠ τξ_k,ω,  j ≠ k. Given the organizational structure ω,

• CEO knowledge |$\bar{z}_{H,\omega }$| increases with output |$\tilde{q}_j$|⁠. Higher output |$\tilde{q}_j$| increases the number of production workers |$n_{j,\omega }^0$| and the share of CEO time s_j,ω at location j and decreases the number of workers |$n_{k,\omega }^0$| and the share of CEO time s_k,ω at location k ≠ j.

• The knowledge of the employees at all below-CEO layers |$z_{k,\omega }^\ell ,\, \ell \le L_k, \, k=H,E$|⁠, the below-CEO managerial span of control |$\frac{n_{k,\omega }^{\ell -1}}{n_{k,\omega }^{\ell }}, \, 1\le \ell \le L_k,$| and the marginal benefit of CEO time ϕ_H,ω increase with local output |$\tilde{q}_j$| if the CEO spends a sufficient share of time on location j. The marginal production costs ξ_k,ω increase with output |$\tilde{q}_j$| if CEO knowledge is sufficiently high.

 

Proof. See Online Appendix C.3.4.

Changes of output |$\tilde{q}_j$| have a similar effect on endogenous outcomes at location j as in a SE firm. They also affect outcomes at the other location, where the firm hires fewer production workers due to the common CEO and higher CEO knowledge. The CEO allocates his time accordingly. If the CEO spends a sufficiently high share of time at location j, the increase in the number of production workers and thus problems there outweighs the decrease at the other location. Due to the CEO time constraint, below-CEO knowledge levels increase at both locations. Correspondingly, the marginal benefit of CEO time and the below-CEO managerial span of control rise. The effect on the CEO span of control is ambiguous: the higher number of production workers at location j increases the CEO span of control, but the lower number of production workers at the other location and the higher below-CEO knowledge may outweigh this effect. The marginal production costs increase with output if the firm is large enough, as reflected by sufficiently high CEO knowledge.

 

Proposition 4.

Suppose the firm produces in the headquarters and the establishment. Suppose that the firm incurs transport costs τ > 1 to ship output between locations, that ξ_j,ω ≠ τξ_k,ω, j ≠ k, and that the helping costs are higher across than within locations, θ_{|${\mathit {EH}}$|} > θ_{|${\mathit {HH}}$|}. Given the organizational structure ω,

• CEO knowledge |$\bar{z}_{H,\omega }$|⁠, the knowledge of the employees at all below-CEO layers |$z_{E,\omega }^\ell ,\, \ell \le L_E,$| the managerial span of control |$\frac{n_{E,\omega }^{\ell -1}}{n_{E,\omega }^\ell }, \, 1 \le \ell \le L_E$|⁠, and the marginal production costs ξ_E,ω at the establishment increase with the helping costs θ_{|${\mathit {EH}}$|}. The total number of production workers |$\sum _{j=H,E} n_{j,\omega }^0$| as well as the number of production workers |$n_{E,\omega }^0$| at the establishment decrease. The share of CEO time s_E,ω decreases if ∃j s.t. L_j > 0; it is constant otherwise.

• The knowledge of the employees at all below-CEO layers |$z_{H,\omega }^\ell ,\, \ell \le L_H,$| the managerial span of control |$\frac{n_{H,\omega }^{\ell -1}}{n_{H,\omega }^\ell }, \, 1 \le \ell \le L_H$|⁠, the number of production workers |$n_{H,\omega }^0$|⁠, and the marginal production costs ξ_H,ω at the headquarters as well as the CEO span of control |$\sum _{j=H,E} n_{j,\omega }^{L_j}$| and the marginal benefit of CEO time ϕ_H,ω decrease with the helping costs θ_{|${\mathit {EH}}$|}. The headquarter share of CEO time s_H,ω increases if ∃j s.t. L_j > 0; it is constant otherwise.

 

Proof. See Online Appendix C.3.5.

Higher helping costs θ_{|${\mathit {EH}}$|} make it more costly to generate problems at the establishment, because they may have to be sent to the CEO. The firm therefore adjusts establishment organization to generate fewer problems and send them to the CEO less frequently. To achieve the former, the firm decreases the number of production workers and increases CEO knowledge. To achieve the latter, the firm increases the knowledge of the employees and thus the below-CEO managerial span of control in the establishment. This allows the CEO to reallocate his time from the establishment to the headquarters, but increases the marginal production costs at the establishment.

The reorganization of the establishment has repercussions for the headquarters. Higher CEO knowledge decreases the number of production workers at the headquarters and thus the total number. Fewer problems are generated, so the knowledge of the employees at the below-CEO layers decreases, as do the below-CEO managerial span of control and the marginal production costs. The CEO span of control decreases due to the lower total number of production workers and the higher knowledge at the establishment, two factors that the lower knowledge at the headquarters does not outweigh. Correspondingly, the marginal benefit of CEO time decreases.

Unlike higher helping costs, higher transport costs do not affect the number or knowledge of the employees at all layers, the CEO or the below-CEO managerial span of control, the marginal production costs, or the marginal benefit and allocation of CEO time. Changes of the transport costs only affect the allocation of production quantities, as described in Proposition 2.

The key implication of Propositions 3 and 4 is that the organization of the ME firm is interdependent across the headquarters and the establishment. Changes in output or helping costs at the establishment result in organizational adjustments at the establishment and the headquarters owing to the shared CEO.

4. Organizational Structure. To render transparent the distinct effects of ME production and location characteristics on organizational structure, we first consider the special case of ME production in two identical locations without transport or helping cost frictions. We then add transport and helping costs frictions. Finally, we study differences in local output.

i. Special Case: No Geographic Frictions, θ_{|${\mathit {EH}}$|} = θ_{|${\mathit {HH}}$|}, τ = 1. Without transport costs, only total output |$\tilde{q}$| matters for the managerial organization. The marginal production costs are equal across locations. This holds mechanically if the number of below-CEO managerial layers is equal. In this case, ME production is equivalent to SE production. If the numbers of below-CEO managerial layers differ, the firm effectively produces with two distinct production technologies, albeit with the same marginal costs. The efficiency of a certain number of layers depends on output for a SE firm. The ME firm can choose the optimal combination of layers for its output by allocating CEO time and production quantities. This affects the choice of optimal organizational structure.

 

Proposition 5.

Suppose that there are no transport or helping cost frictions: τ = 1, θ_{|${\mathit {HH}}$|} = θ_{|${\mathit {EH}}$|}. Let (L_H, L_E)-organization denote the organizational structure of an ME firm with L_H below-CEO layers at the headquarters and L_E below-CEO layers at the establishment.

• The average-cost function of the (L_H, L_H)-organization is U-shaped in output and reaches a minimum at |$\tilde{q}^{*_{(L_H,L_H)}}$|⁠.

• The average-cost functions of the (L_H, L_H + 1)-organization and the (L_H + 1, L_H)-organization coincide. The average cost of the (L_H, L_H + 1)-organization is equal to the average cost of the (L_H, L_H)-organization at |$\tilde{q}^{*_{(L_H,L_H)}}$|⁠, and decreases with output |$\tilde{q} \in (\tilde{q}^{*_{(L_H,L_H)}}, \tilde{q}^{*_{(L_H+1,L_H+1)}})$|⁠.

• The average-cost function of the (L_H, L_H)-organization crosses the average-cost function of the (L_H + 1, L_H + 1)-organization at the output |$\tilde{q}^{(L_H,L_H)\rightarrow (L_H+1,L_H+1)}$| between the minimum efficient scales. The average-cost function of the (L_H, L_H + 1)-organization crosses the average-cost function of the (L_H + 1, L_H + 1)-organization at a higher level of output |$\tilde{q}^{(L_H,L_H+1)\rightarrow (L_H+1,L_H+1)}>\tilde{q}^{(L_H,L_H)\rightarrow (L_H+1,L_H+1)}$|⁠.

As a result, the ME firm with an (L_H, L_H)-organization adds a layer of middle managers at the headquarters or the establishment at the output |$\tilde{q}^{*_{(L_H,L_H)}}$| and a layer at the other unit at output |$\tilde{q}^{(L_H,L_H+1)\rightarrow (L_H+1,L_H+1)} \in (\tilde{q}^{(L_H,L_H)\rightarrow (L_H+1,L_H+1)}, \tilde{q}^{*_{(L_H+1,L_H+1)}})$|⁠.

 

Proof. See Online Appendix C.3.7.

Proposition 5 is a key result of the model. It states that the ME firm successively reorganizes the headquarters and the establishment as it grows. A firm with (L_H, L_H + 1)-organization optimally combines two production technologies. At the output |$\tilde{q}^{*_{(L_H,L_H)}}$|⁠, the (L_H, L_H)-organization has the minimum average costs. The firm allocates total output and CEO time to the headquarters. For higher output |$\tilde{q}>\tilde{q}^{*_{(L_H,L_H)}}$|⁠, the average costs of the (L_H, L_H)-organization increase. The average costs of the (L_H, L_H + 1)-organization decrease up to the minimum efficient scale of the (L_H + 1, L_H + 1)-organization, because the firm allocates an increasing share of output to the establishment. Figure III, Panel B illustrates this result.¹⁰

The managerial layer at the establishment releases CEO time: relative to output, the CEO spends a larger share of time at the headquarters than at the establishment. This keeps below-CEO knowledge low. The layer thus increases efficiency both at the establishment and the headquarters. It decreases the need to add a managerial layer at the headquarters. As in Propositions 3 and 4, the organization of a ME firm is interdependent: the optimal number of layers at the headquarters depends on the number of layers at the establishment (and vice versa).

ii. Transport and Helping-Cost Frictions, τ > 1, θ_{|${\mathit {EH}}$|} ≥ θ_{|${\mathit {HH}}$|}, |$\tilde{q}_E=\tilde{q}_H$|⁠.Figure IV, Panel A illustrates the average production costs of different organizational structures if local output and helping costs are equal across locations, but there are transport frictions. The average production costs are U-shaped, like those of a SE firm. This reflects how reallocating output is efficient only under certain conditions, and that higher output has a similar effect on firm organization as in a SE firm. Although the transport frictions affect the shape of the average-cost function of the (0,1)-organization, they do not affect the pattern of reorganization. The ME firm first adds a layer at one unit and then the other.

Figure IV

Illustration of the Average-Cost Functions, Transport Frictions

The figure plots average-cost functions of a ME firm. Parameter values: |$\frac{c}{\lambda }\!=0.225$|⁠, θ_{|${\mathit {HH}}$|} = 0.26 (from CRH), w = 1, τ = 1.1, |$\tilde{q}_H=\tilde{q}_E$|⁠. Panel A: at each kink, the ME firm adds a layer at one unit. The (0,1) and (1,0)-organization have the same costs. Panel B: higher helping costs θ_{|${\mathit {EH}}$|} decrease the output at which the firm reorganizes.

Figure IV, Panel B illustrates how the helping costs across space θ_{|${\mathit {EH}}$|} affect the number of managerial layers of the firm. Higher helping costs increase the knowledge levels of employees and thus the marginal production costs at the establishment. Adding a layer helps the firm mitigate the cost increase, because it allows decreasing production worker knowledge. The higher the helping costs, the smaller the level of output at which the firm adds a layer at the establishment.

In addition to their effect on the number of layers, higher helping costs affect ME production per se. Higher helping costs reduce the desirability of maintaining an establishment relative to shipping output from the headquarters, as they increase the marginal production costs at the establishment. Conversely, higher transport costs increase the desirability of local production in the establishment, because they increase the costs of shipping output from the headquarters.

iii. Output Differences, |$\tilde{q}_E \ne \tilde{q}_H$|⁠.Online Appendix C.3.8 shows how output differences between locations affect the optimal number and location of managerial layers. Most notably, lower output at the establishment than at the headquarters can make it optimal to hire middle managers at the headquarters but not the establishment. Output and the helping costs across space jointly determine at which level of output it is optimal to hire middle managers at the headquarters, the establishment, or both units. The level decreases with higher helping costs.

IV.D. The Optimal Output

We return to the setting with many firms i outlined at the beginning of Section IV.A. We assume that each firm faces a downward-sloping demand curve for its product. Firms compete monopolistically, so there is no strategic interaction between firms. Firms choose output levels |$\tilde{q}_j$| to maximize profits:

$$\begin{equation} \max _{\tilde{q}_H,\tilde{q}_E\ge 0} \pi _i = \sum _{j=H,E} p_j (\tilde{q}_j) \tilde{q}_j - C(\tilde{q}_H,\tilde{q}_E). \end{equation} $$

(25)

 

Proposition 6.

Suppose that the firm produces at the headquarters and the establishment. Suppose that the local production quantities are equal to local output (i.e., ξ_j,ω ≠ τξ_k,ω) and that they are sufficiently large. Higher helping costs across space θ_{|${\mathit {EH}}$|} decrease the optimal output at the establishment |$\tilde{q}_E$| and increase the optimal output at the headquarters |$\tilde{q}_H$|⁠.

 

Proof. See Online Appendix C.4.¹¹

Higher helping costs across space decrease the establishment output and increase the headquarters output due to their effect on the marginal production costs. Consequently, the helping costs have a direct effect on the managerial organization and an indirect effect through endogenous output. Thus, higher helping costs can increase the number of managerial layers both at the establishment and the headquarters due to the changes in output, as Online Appendix Figure C.3 illustrates.

IV.E. Comparison of Facts and Model

The helping costs θ_{|${\mathit {EH}}$|} reflect distance and other geographic frictions. Higher helping costs increase the marginal production costs of an establishment and decrease its optimal size and the attractiveness of a location for an establishment, consistent with Fact 1. Distance and geographic frictions also affect the transport costs. Higher transport costs mitigate the negative effect of higher helping costs on the probability to maintain an establishment.

In line with Fact 2, the higher marginal costs at the establishment increase the use of middle managers there. Depending on local output, higher helping costs also increase the use of middle managers at the headquarters due to the common CEO.

Hiring middle managers at the establishment (or the headquarters) releases CEO time that is reallocated across locations and reduces the need for middle managers at the headquarters (or establishment). Firms thus successively add middle managers at the headquarters or the establishment as they grow, consistent with Fact 3.

V. Reorganization due to High-Speed Railway Routes

V.A. Model Predictions

We use the opening of high-speed railway routes (HSRs) to provide evidence on the prediction that geographic frictions between an establishment and the headquarters affect not only the organization of the establishment but also the organization of the headquarters and possible other establishments. Figure V illustrates the model predictions using a directed graph. Solid circles denote observable variables, hollow circles denote unobservable variables, and the arrows denote causal links between variables. To keep the graph simple, we group firm- and establishment-level variables and use semi-solid circles if only part of the group is observable.

Figure V

Model Predictions Regarding the Effects of a Change in the Travel Times

The graph illustrates the predictions of the model regarding the effects of a change in travel times. The arrows denote causal relationships between the variables at the nodes. The node symbol • (●) denotes that a variable is (un)observable. ◐ denotes that a group of variables contains observable and unobservable variables.

The HSRs exogenously reduce the travel times between an establishment k and the headquarters. In the terms of the model, lower travel times decrease the helping costs θ_kH. Lower helping costs increase establishment output |$\tilde{q}_k$| and decrease headquarter output |$\tilde{q}_H$|⁠. They thus have direct and indirect effects on firm organization. The effects often point in different directions. Lower helping costs directly affect the organizational structure ω by decreasing the optimal number of layers and increasing the attractiveness of maintaining an establishment. They indirectly affect the organizational structure because higher output increases the optimal number of layers.

Similarly, CEO knowledge |$\bar{z}_{H,\omega }$|⁠, the allocation of CEO time s_j,ω, and the allocation of production q_j,ω depend directly on θ_kH, but also indirectly through |$\tilde{q}_j$| and ω. The number and knowledge of employees per layer |$n_{j,\omega }^\ell ,z_{j,\omega }^\ell$| depend directly on θ_kH and indirectly through |$\bar{z}_{H,\omega }, s_{j,\omega }, q_{j,\omega }$|⁠, and ω. Given the organizational structure ω, lower helping costs unambiguously increase the number of production workers and the share of CEO time at the establishment, but the effect on most other variables is ambiguous (see Online Appendix Table D.1). Endogenous changes of ω increase ambiguity, because knowledge changes discontinuously if firms change layers (as in CRH; for a proof, see Online Appendix C.3.7).

The complexity of the relationship between the helping costs θ_kH and firm organization has implications for the interpretation of the empirical estimates. The results in Proposition 4 hold conditional on output and the organizational structure. These variables do not vary exogenously, but depend on the helping costs, and we do not have instruments for them. If we conditioned on output or organizational structure in an establishment-level regression, the estimation would entail a “bad control” problem (Angrist and Pischke 2008, 64–68). Our empirical exercise therefore estimates the total—direct and indirect—effect of changes in helping costs using reduced-form regression equations.

V.B. Travel Time Data

We use data on the travel times between the 115 German train stations connected to the long-distance railway network from Deutsche Bahn AG, the state-owned railway firm. Travel times changed substantially due to the opening of three HSRs during our sample period.¹²Figure VI displays a map of the new HSRs and how they connect to the existing long-distance network. Trains on these routes exclusively transport people. Except for route 2, the high-speed trains run at up to 300 km/h, which is around 100 km/h faster than on the other routes of the German long-distance network. Online Appendix D.2 provides details on the routes and their construction.

Figure VI

The New High-Speed Railway Routes and the German Long-Distance Network

The map shows the German long-distance rail network (light) and the new high-speed railway routes (bold). Data from Deutsche Bahn AG (http://data.deutschebahn.com/dataset/geo-strecke).

As Figure VI shows, the German railway network is highly interconnected compared with that of other countries. For instance, the French railway network approximately has a “star” structure with Paris as the center. The German network features several hubs. The HSRs therefore affect more cities than merely those at the immediate ends. For example, route 1 between Cologne and Frankfurt reduced travel times from cities in the Ruhr area to those in east and south Germany, such as Leipzig, Stuttgart, and Würzburg.

We use data on the minimum net travel times and the number of changes between cities in 2000, 2004, and 2008. We follow Deutsche Bahn AG and compute travel times as time on the train plus 30 minutes per change. We merge the travel times and the firm data based on the county where the establishment and the station is located. We restrict the sample to firms that have headquarters and at least one establishment connected to the long-distance network to avoid unobservable differences between connected and unconnected firms driving the results. Online Appendix Table D.3 displays summary statistics for our sample.

A possible concern is that trains are not an attractive means of transportation for business travelers. However, this is not true of the high-speed trains. According to information from Deutsche Bahn AG for 2017, the share of business travelers on the new routes was about double their average share.¹³ This is unsurprising given that the HSRs render the train the fastest means of transportation between the connected cities. It is faster to travel by train than by car—it takes almost twice as long to drive from Frankfurt to Cologne, for example—or even plane. In addition, the high-speed trains are a flexible means of travel as regular tickets are valid on all trains that service a connection.

V.C. Empirical Specification

To gauge the effect of lower travel times on directly affected establishments, we estimate:¹⁴

$$\begin{equation} y_{ijt} = \beta _0 + \beta _1 \mathbf {1}\lbrace \textit{Lower travel times to HQ} \rbrace _{ijt} + \alpha _j + \alpha _{ct} + \epsilon _{ijt}. \end{equation} $$

(26)

i refers to a ME firm, j to an establishment, c to the county where an establishment is located and t indexes time. α denotes fixed effects. The variable of interest is an indicator variable for a travel time reduction between the establishment and its headquarters of at least 30 minutes.

To understand the effect on the headquarters, we estimate:

$$\begin{eqnarray} y_{iht} &=& \beta _0 + \beta _1 \mathbf {1} \lbrace \exists j\,\, \textit{with lower travel times to HQ}\rbrace _{iht} \nonumber\\ &&+\, \alpha _h + \alpha _{dt} + \epsilon _{iht}. \end{eqnarray} $$

(27)

h denotes the headquarters and d the headquarter county. The variable of interest indicates if travel times to at least one establishment decrease by at least 30 minutes.

To assess the effect on indirectly affected establishments of affected firms, we estimate:

$$\begin{eqnarray} y_{ikt} = \beta _0 + \beta _1 \mathbf {1} \lbrace {\it No\ lower\ travel\ times\ to\ HQ} & \nonumber\\ \wedge \exists j\ne k {\it\ with\ lower\ travel\ times\ to\ HQ}&\rbrace _{ikt} \nonumber\\ +\, \alpha _{k}+ \alpha _{ct} + \alpha _{dt}\nonumber\\ +\, \epsilon _{ikt}, \quad k \ne j. \end{eqnarray}$$

(28)

k refers to an indirectly affected establishment. The indicator variable is equal to 1 if the travel time between establishment k and the headquarters does not decrease by at least 30 minutes, but the travel time between one of the other establishments of the firm and the headquarters does. As outcome variables y_i.t, we use the number of nonmanagerial employees to measure size, the wages of nonmanagerial employees to approximate knowledge, and the number of managerial layers, complemented with the managerial share, to measure organization.

We set the indicators equal to 1 if the travel time between an establishment and the headquarters decreases by at least 30 minutes because the HSRs decrease the travel times by at least 30 minutes. The threshold thus helps us ensure that the reduction is driven by the exogenous new HSRs instead of potentially endogenous demand-driven adjustments to the time-table.¹⁵

The specifications mimic difference-in-differences estimation. The “treatment” is lower travel times between the directly affected establishment and the headquarters (equation (26)), or between at least one establishment and the headquarters (equations (27) and (28)). Its baseline effect is captured by the establishment or headquarter fixed effects. The (headquarter) county × year fixed effects capture the “after” dummy. The indicator variables |$\mathbf {1}\lbrace \cdot \rbrace$| correspond to the interaction of the “treatment” and “after” dummies. We implement the estimation using the reghdfe command by Correia (2014).

Lower travel times may affect other model parameters, such as local wages because employees commute longer distances (Heuermann and Schmieder 2019). Firms may also benefit from better suppliers (Bernard, Moxnes, and Saito 2019). The (headquarter) county × year fixed effects isolate the effect of lower geographic frictions on firm organization from other forces. Specifically, the regressions for directly affected establishments compare establishments with travel time reductions and establishments in the same county and year without reductions. Lower local wages or better suppliers benefit all establishments, so our estimation strategy accounts for their effect. Similarly, the regressions for the headquarters compare headquarters with travel time reductions to at least one establishment to headquarters in the same county and year without reductions. The specification for indirectly affected establishments compares establishments that belong to firms with treated establishments to establishments in the same county and year that belong to firms without treated establishments, additionally accounting for shocks at the headquarter location.¹⁶ Being treated in this set-up presupposes that firms have at least two establishments, so we restrict the sample accordingly. Due to the fixed effects, only establishments and headquarters in counties with at least one affected unit identify the coefficient β₁. We drop counties without affected units.

If the effects of possible omitted variables vary nonlinearly with unit size, the (headquarter) county × year fixed effects fully absorb them only if treated and control units have common support with respect to size. We hence match treated and control units by size before treatment, using the average number of employees in 2000/2001 as the size measure. We employ the Coarsened Exact Matching (CEM) algorithm (Iacus, King, and Porro 2012). For each (headquarters) county × year combination, we assign observations to quartiles based on their initial size. We keep only county × year × size quartile cells that contain treated and control units.¹⁷ Finally, we use the weights recommended by Iacus, King, and Porro (2012) to estimate the average treatment effect on the treated.¹⁸

We address several possible concerns with respect to our identification strategy. Importantly, we hypothesize based on the model that lower travel times have an effect on indirectly affected establishments of affected firms. If these establishments are located in the same counties as directly affected establishments, they may contaminate the control group in equation (26). We rerun regressions for firms with only one establishment and, alternatively, exclude indirectly affected establishments of affected firms from the sample to account for this possibility.

A second important concern is that firms may strategically locate their establishments close to the HSRs in anticipation of their opening. To address this possibility, we rerun regressions for establishments set up before 2000, the first year of the sample, and before 1995, when construction of route 1 started. A few establishments and headquarters move from one county to another during the sample period. We use their original location for the main analyses and drop them from the sample in robustness checks (Online Appendix Table D.22).

Finally, we document that the outcomes of treated and control units follow similar trends before the opening of the routes. This supports our assumption that the two groups differ only with respect to the travel time changes.

V.D. Regression Results

Table VII presents the regression results for the 2000–2010 panel. Columns (1)–(4) contain results for all firms. Columns (5)–(8) restrict the sample to firms with at least two establishments.

TABLE VII

Lower Travel Times Affect All Units of ME Firms

	All firms				Firms with ≥ 2 establishments
	No. em.	Wages	No. lay.	Mg.sh.	No. em.	Wages	No. lay.	Mg.sh.
	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
Directly affected establishment
Est. treated	0.084***	0.002	0.009	0.059	0.083***	0.004	0.016	0.049
	(0.019)	(0.004)	(0.016)	(0.253)	(0.021)	(0.005)	(0.018)	(0.273)
No. observations	47,732	47,732	47,732	47,732	40,143	40,143	40,143	40,143
No. est.	5,609	5,609	5,609	5,609	4,791	4,791	4,791	4,791
R-squared	0.901	0.931	0.875	0.890	0.899	0.932	0.878	0.902
Est. FE	Y	Y	Y	Y	Y	Y	Y	Y
County-year FE	Y	Y	Y	Y	Y	Y	Y	Y
Headquarters
Firm treated	−0.013	0.004	0.019	0.103	0.023	0.018*	0.065**	0.994+
	(0.019)	(0.005)	(0.022)	(0.338)	(0.033)	(0.008)	(0.022)	(0.504)
No. observations	13,393	13,393	13,393	13,393	6,261	6,261	6,261	6,261
No. HQ	1,469	1,469	1,469	1,469	683	683	683	683
R-squared	0.951	0.951	0.875	0.913	0.951	0.945	0.872	0.919
HQ FE	Y	Y	Y	Y	Y	Y	Y	Y
HQ c.-year FE	Y	Y	Y	Y	Y	Y	Y	Y
Indirectly affected establishment
Firm treated					−0.017	0.019***	0.020	0.521*
					(0.020)	(0.004)	(0.017)	(0.209)
No. observations					45,508	45,508	45,508	45,508
No. est.					5,508	5,508	5,508	5,508
R-squared					0.917	0.926	0.890	0.887
Est. FE					Y	Y	Y	Y
County-year FE					Y	Y	Y	Y
HQ c.-year FE					Y	Y	Y	Y

Notes. 2000–2010 panel. Standard errors clustered by (headquarter) county are in parentheses. ⁺p < .10, ^*p < .05, ^**p < .01, ^***p < .001. Dependent variables: No. em.: log number of nonmanagerial employees; Wages: average log wages of nonmanagerial employees; No. lay.: number of managerial layers; Mg.sh.: share of managerial occupations in wage sum in percent, where managerial occupations are determined according to Blossfeld occupational categories. Treated and control units are matched by size quartile, (headquarters) county, and year, except for the indirectly affected establishments that are matched by size quartile and year. We use the weights of Iacus, King, and Porro (2012) to estimate the average treatment effect on the treated. All variables are winsorized at the first and 99th percentiles. The p-value for the managerial share of the headquarters in column (8) is 5.4%.

As the top panel shows, lower travel times increase the size of the directly affected establishments. The number of nonmanagerial employees increases by 8%. This increase in size is not accompanied by an increase in wages, the number of layers or the managerial share. The middle panel shows that lower travel times lead to organizational adjustments at the headquarters of firms with at least two establishments. Average wages of nonmanagerial employees increase by 2%. The number of managerial layers and the managerial share also increase significantly. The coefficient estimate is equivalent to an increase of the managerial share by 9% in the average firm. As the bottom panel shows, the effect of lower travel times goes beyond the headquarters and the directly affected establishment. Both wages and the managerial share increase at establishments that do not themselves benefit from lower travel times, but belong to firms that do.

Overall, the results strongly support the prediction of the model that geographic frictions between an establishment and the headquarters affect the organization of not only the establishment, but also the headquarters and possible other establishments of the firm. The results are consistent with the interpretation that lower helping costs due to faster travel times improve the establishment’s access to the CEO or, more generally, managerial resources of the headquarters. This allows the establishment to grow without local organizational adjustments. Instead, the firm increases managerial capacity at the headquarters. Through the lens of the model, both the higher nonmanagerial wages, reflecting higher knowledge, and the higher number of layers at the headquarters reflect adjustments to release CEO time. The adjustments at the indirectly affected establishments support the interpretation that the firm reallocates managerial resources of the headquarters from the indirectly affected to the directly affected establishments.

1. Evidence Supporting the Validity of the Identification Strategy.Figure VII shows that the effect of lower travel times on the size of directly affected establishments is similar when we exclude possibly indirectly affected establishments from the sample and account for possible strategic location of establishments. The coefficients vary but are not significantly different from the baseline effect. The larger coefficient for firms with one establishment possibly reflects that these establishments are smaller than those in the baseline sample. The smaller coefficient for the sample without indirectly affected establishments may reflect that those grow more slowly than establishments of unaffected firms. Online Appendix Table D.4 displays the complete set of regression results.

Figure VII

Robustness to Alternative Control Groups and Strategic Location of Establishments

The figure plots the coefficients and 95% confidence intervals for the size of directly affected establishments from Table VII and from regressions on the sample of firms with one establishment, the sample excluding indirectly affected establishments, and samples varying the entry year. Treated and control establishments are matched on size quartile and year for the samples of firms with one establishment and without indirectly affected establishments and on size quartile, county, and year in the other cases. Standard errors are clustered by county. Online Appendix Table D.4 displays the regression results.

Figure VIII documents that the outcomes of treated and control units follow similar trends before the opening of the HSRs. This supports the assumption that the control units provide a valid counterfactual for the treated units after treatment. Online Appendix Table D.5 contains the results for all outcomes and samples as well as the indirectly affected establishments.

Figure VIII

The Effect of the Opening of High-Speed Railway Routes

The figure plots coefficients and 95% confidence intervals for regressions similar to equations (26) and (27). The dependent variable is (Panel A) the log number of nonmanagerial employees of an establishment and (Panel B) the number of managerial layers of the HQ. The explanatory variables are indicator variables for (Panel A) lower travel times to the HQ and (Panel B) lower travel times between the HQ and at least one establishment, interacted with biannual fixed effects. The excluded interaction is the year of the opening of the HSRs. We control for establishment (HQ) fixed effects and (HQ) county × year fixed effects. We consider a shorter time period for HQ because of a low number of observations. The sample is restricted to firms with at least two establishments. Standard errors are clustered by (HQ) county. Online Appendix Table D.5 displays the regression results.

2. Robustness.Online Appendix D.5 documents that the results are robust to alternative approaches to statistical inference, alternative variable definitions, and alternative sample restrictions. Notably, we find that the education and experience of employees change concomitantly with wages, in line with our knowledge hierarchy model. The model proposes that lower travel times affect firm organization via the specific channel of lower helping costs. To support this channel, Online Appendix D.6 documents that the effects are stronger in sectors with a less predictable production process.

VI. Conclusion

This article showed that the managerial organization of ME firms is interdependent across establishments. Specifically, we showed empirically and theoretically that geographic frictions between an establishment and the headquarters not only affect the organization of this particular establishment, but also the organization of the headquarters and other establishments of the firm.

Our study opens up several avenues for future research. In one direction, future work could study the productivity effects of reorganization in ME firms (as done for SE firms by Caliendo et al. 2020). Quantifying the local and nonlocal productivity effects of establishment reorganization would improve our understanding of firm performance. It would also lay the foundation for work on the propagation of shocks across space through firm organization and a comparison of the importance of managerial and financial constraints as propagation mechanisms.

In another direction, future work could exploit ME firms as a setting that opens up new angles on within-firm processes and frictions. For example, it has been difficult to empirically differentiate the knowledge and the monitoring hierarchy models, because they yield very similar predictions for SE firm organization (Chen and Suen 2019). The ME firm setting may provide an opportunity to shed light on the nuances between the two frameworks. Our preliminary analyses suggest that a monitoring hierarchy model, where geographic frictions make it more difficult to monitor workers at the establishment, yields predictions that are similar to those of our model for establishment organization but differ with respect to headquarter organization. Testing these differences is unfortunately beyond the scope of our data but would be very valuable for our understanding of firm organization with one and multiple establishments.

Data Availability

Code replicating the tables and figures in this article can be found in Gumpert, Steimer, and Antoni (2022) in the Harvard Dataverse, https://doi.org/10.7910/DVN/A4YMA9.

Footnotes

^*We are deeply grateful to Lorenzo Caliendo for in-depth comments and to Monika Schnitzer for her invaluable support. We are thankful to the editor, Pol Antràs, and four anonymous referees, who offered many constructive suggestions that are incorporated in this article. We thank Pol Antràs, Wolfgang Dauth, and Alexandra Roulet for very helpful discussions of the article, and Andrew Bernard, Damian Clarke, Florian Englmaier, Robert Gibbons, Andreas Steinmayr, Martin Watzinger, Jens Wrona, as well as seminar participants at Harvard, LSE, LMU Munich, MIT, Oxford, Regensburg, and the Graduate Institute, Geneva, and participants at various conferences for their comments. Amelie Grosenick and Christopher König provided outstanding research assistance. We thank Stefan Seth for his support with assembling the social security data. We gratefully acknowledge access to the ORBIS database via the LMU-ifo Economics & Business Data Center. We thank DB Fernverkehr AG for providing the data on the travel times between cities in the German long-distance railway network. The article was partly written while Anna Gumpert was a visitor at the Yale School of Management (SOM). She thanks the SOM for its hospitality and Lorenzo Caliendo for making the visit possible. The project has benefited from financial support through the German Research Foundation (DFG) under CRC TRR 190 (project number 280092119) and GRK 1928 and through a travel grant of the Fritz Thyssen Foundation.

1.

Mariscal (2018) shows how optimal information technology (IT) adoption affects firm organization and studies firm reorganization as IT prices fall. Spanos (2019) shows that firm organization explains part of the differences in productivity across locations. In the empirical literature on firm hierarchies, Rajan and Wulf (2006) document the flattening of corporate hierarchies over time. Guadalupe and Wulf (2010) examine the effect of competition on corporate hierarchies. Sforza (2020) compares the organizational responses to a credit supply and a trade shock.

2.

Gumpert (2018) develops a knowledge hierarchy model with multiple establishments, but a fixed number of layers. Crèmer, Garicano, and Prat (2007) study firm language in a setting with multiple divisions. McElheran (2014) presents facts about the allocation of decision-making authority in multiestablishment firms based on team-theoretic considerations.

3.

The social security data contain the address of an establishment. We are not allowed to use the address for our empirical analyses because of data confidentiality.

4.

These figures refer to all firms, that is, they include firms that have a higher number of layers at the establishment than at the headquarters and are excluded from Table VI.

5.

In Gumpert, Steimer, and Antoni (2019), we show that our results hold if wages differ across locations.

6.

We assume overlapping knowledge levels to simplify the analysis. A model with nonoverlapping knowledge levels yields qualitatively very similar results (for details, see Online Appendix C.1.2).

7.

That is, τ ≥ 1 units of a good need to be shipped for one unit to arrive at destination.

8.

As in Section IV.B, we focus on the decision to hire the first managerial layer and study hiring additional layers in Online Appendix C.3.1.

9.

As ϕ_H,ω = ϕ_E,ω, we state results only for ϕ_H,ω in the following.

10.

The average-cost function of the (0, 1)-organization coincides with the average-cost functions of the (0, 0)-organization and the (1, 1)-organization for quantities below and above the minimum efficient scales respectively, because for those levels of output, SE production with 0 and 1 below-CEO layers is more efficient than production with the (0, 1)-organization.

11.

The Online Appendix includes the results for the case that ξ_j,ω = τξ_k,ω, j ≠ k not considered in Proposition 6.

12.

A fourth route between Leipzig and Berlin opened in 2006. However, the travel time between these cities decreased only gradually according to the data, so the route is not used in the estimation.

13.

The statistics are computed based on the fraction of tickets sold with a corporate discount.

14.

This specification is similar to Charnoz, Lelarge, and Trevien (2018).

15.

One may worry that a possibly endogenous reduction in the number of changes triggers the treatment dummy. In the data, the number of changes decreases either due to the new HSRs, or if a station is connected to the long-distance network. Our results are robust to restricting the sample to stations connected to the long-distance network in all years (see Online Appendix Table D.23).

16.

The strictest specification would condition on county × headquarter county × year fixed effects, i.e., compare indirectly affected and unaffected establishments in the same county with headquarters in the same county. However, there are too few such pairs in the sample to run these regressions.

17.

In a few robustness checks, matching by county makes the size of treated and control units less similar due to the uneven spatial distribution of units. In these cases, we match units only by size quartile and year. We would ideally like to match indirectly affected establishments by headquarter county, county, and year, but there are too few pairs in the sample to do so. We match establishments by size quartile and year in Table VII and report results for matching on size quartile, (headquarters) county, and year in Online Appendix Table D.14.

18.

Online Appendix Tables D.8 and D.9 document that results are similar if we do not match observations.