Allocative Efficiency,Plant Dynamics and Regional Productivity: Evidence from Germany

Abstract

The productivity gap between East and West Germany is a long ongoing discussion among the public and policy makers. Regional disparities still appear to be substantial. In this paper, we shed light on the role of allocative efficiency as a region’s driver of productivity disparities. We show that over 50 percent of the East-West productivity gap is associated with a less efficient labor allocation in former East Germany. Controlling for the heterogeneity among German federal states, we perform spatial regression on official firm-level data (AFiD), revealing that the regional differences in allocative efficiency are significantly associated with trade openness, competitive intensity, economies of scale and labor mobility.

Keywords

regional productivity gap productivity decomposition allocative efficiency labor allocation E24 J24 L11 L25 O47

Introduction

Productivity growth is vital for the general improvement of real incomes and living standards (Schreyer and Pilat 2001). Achieving equal living standards and opportunities across Germany is a central socio-political goal of the German government. This is also institutionally reflected in the commission for ‘equal living conditions’, founded in 2018 (see e.g., Röhl 2020). For this reason, reducing the persistent productivity disparities across German regions, as for instance between East and West Germany, constitutes one of the major challenges for German policy makers. Given the importance of this objective, it is unsurprising that there is abundant literature regarding possible reasons for the productivity differences and how to overcome them (see e.g., Belitz, Gornig, and Schiersch 2020; Brunow and Hirte 2009; Eckey, Kosfeld, and Türck 2007; Görzig et al. 2010; Niebuhr 2000).

What has so far not been addressed in the literature is the role of allocative efficiency in explaining these regional productivity differences. According to Farrell (1957)’s notion, the allocation of inputs is efficient if the production of outputs is maximized. This implies that firms with an above-average productivity should also experience an above-average employment of inputs as inputs should always follow their most productive use. In our study, we use the decomposition method by Olley and Pakes (1996) to investigate this correlation, that is, the relationship between plant productivity and (labor) input share on the regional level using German plant-level data (AFiD) from 2004 to 2018.

Our results are threefold. First, we show that regional productivity disparities can be significantly attributed to differences in allocative efficiency. In fact, more than 50 percent of the aggregate productivity gap between East and West Germany can be explained by the less efficient labor allocation between plants. Second, we detect a general decline in allocative efficiency between 2004 and 2018, which is more pronounced for East than for West German states, leading to a further widening of the observed discrepancies in allocative efficiency. Third, we show empirically that the regional disparities are associated significantly with trade openness, competitive intensity, economies of scale and labor mobility.

The remainder of this paper is structured as follows. In Section 2, we motivate our hypothesis that allocative efficiency plays a major role in explaining regional productivity disparities in Germany. Section 3 presents the data used. In Section 4, we lay out the decomposition method deployed in our analysis. Section 5 offers a descriptive analysis of allocative efficiency and labor productivity in German regions. In Section 6, we conduct a spatial regression to derive policy implications on how to narrow regional discrepancies in allocative efficiency. Section 7 concludes.

Allocative Efficiency and Regional Productivity Differences

Regional productivity disparities are prevalent in many countries and there is a large and growing body of literature that investigates potential causes. Marrocu and Paci (2013), for instance, shed light on the potential causes of the differences in productivity growth of EU regions. They identify education, the endowment of creative graduates, differences in physical, technological, and social capital as well as in cultural, industrial, and geographical characteristics as drivers of regional productivity growth. For the case of Italian NUTS-3 regions, Kang et al. (2022) demonstrate how local knowledge capabilities, moderated by entrepreneurial activity, affect regional productivity in Italy. Another group of studies shows how university activities can influence regional productivity and innovativeness, as well as the creation of new firms (see, e.g., Drucker and Goldstein 2007). For the case of Germany, there are numerous studies trying to explain regional productivity differences. A couple of studies investigate productivity convergence in German regions and its underlying forces such as spatial differences in technology spillovers or infrastructure (see e.g., Eckey, Kosfeld, and Türck 2007; Niebuhr 2000). Other studies provide a more general view on the determinants of regional productivity differences in Germany such as human capital, capital intensity, product policy, or firm size (Belitz, Gornig, and Schiersch 2020; Brunow and Hirte 2009; Görzig et al. 2010). With regard to allocative efficiency, i.e., the efficient allocation of input factors, such as labor, and its impact on regional productivity in Germany, the existing literature does not provide much insight.

The hypothesis that the (re)allocation of resources between firms plays a central role in explaining productivity developments has been widely documented in the literature. By now, it is well established that, even within narrowly defined industries, firm-level productivity is highly dispersed (see e.g., Bartelsman, Haltiwanger, and Scarpetta 2013; Dosi et al. 2021). There is a considerable body of literature using micro-level data to show the prevalence of resource reallocation processes between heterogeneous firms, typically by using so-called productivity decomposition methods (see e.g., Baily, Hulten, and Campbell 1992; Bartelsman, Haltiwanger, and Scarpetta 2013; Brown et al. 2018; Decker et al. 2017; Disney, Haskel, and Heden 2003; Foster, Haltiwanger, and Krizan 2001; Griliches and Regev 1995; Olley and Pakes 1996). With respect to the impact of resource allocation on regional productivity, the number of studies is rather limited. Still, it is evident from these studies that the allocation and reallocation of market shares between firms and industries are key drivers of regional productivity developments. For example, Rigby and Essletzbichler (2000) show large discrepancies among states within the U.S. regarding the impact of resource reallocation on productivity growth, while Le Gallo and Kamarianakis (2011) perform a similar analysis on regions within the European Union. Moreover, Böckerman and Maliranta (2007) conduct a decomposition study on Finnish regions, revealing significant differences in resource allocation among firms with different levels of productivity.

Taking a stance similar to these regional decomposition studies, we investigate the role of allocative efficiency in explaining regional productivity differences in Germany. We expect to see large differences in the role allocative efficiency plays for regional productivity, which, for example, could be attributed to institutional differences of regions as induced by the former division of Germany until 1990. The market economy in West Germany and the planned economy in East Germany rested on very different mechanisms for (re)allocating resources among companies. Hence, it is conceivable that traces of these two different economic systems are still visible today. Apart from this Germany-specific institutional shift, the literature offers a wide list of potential drivers of firm productivity dispersion and allocative efficiency. For instance, Foster, Haltiwanger, and Krizan (2001) include the uncertainty of the business environment, plant-level differences (such as managerial ability, capital vintage, location, and disturbances), and the diffusion of knowledge among firms as essential drivers of firm-level heterogeneity. With respect to the drivers of reallocation processes, Melitz (2003) shows that trade exposure fosters reallocation, as only the most productive firms self-select and benefit from trade. He argues that trade exposure makes it more difficult for less productive firms to be profitable, which causes them to exit the market. Similarly, Syverson (2011) argues that an increase in competition both from domestic and foreign competition reinforces the market selection process. He also emphasizes that flexible production factor markets (labor and capital) facilitate the reallocation of resources towards their most productive use. In a more recent study, Brown et al. (2018) underline that product market, education, and financial market reforms play an important role in the dynamics of resource allocation.

With this in mind, we hypothesize that these drivers vary not only across industries and countries, but also across regions within the same country. Therefore, we investigate whether they can be associated with regional allocative efficiency in Germany. This exercise can be a first step towards deriving specific policies apt to reduce regional productivity disparities.

Data

Our analysis is based on an official dataset of German manufacturing plants covering the period from 2004 to 2018. The data is provided by the German statistical office (AFiD panel).¹ We deliberately rely on plant-level rather than firm-level data as it better reflects the regional manufacturing landscape, given that many large firms have plant subsidiaries in different German regions that would not appear in a firm-level database which only registers firm headquarters (Leibnitz IWH 2019). Using plants instead of firms almost triples the number of establishments that we can use for our decomposition analysis. This also allows us to cover more sectors and regions as well as to provide a more comprehensive picture of the manufacturing industry.

For measuring productivity, we use the number of employees as input and sales as output measure. We deflate plant-level sales using industry-specific gross output deflators from Eurostat’s database of national accounts aggregates. Unfortunately, the dataset does not provide information on value-added which would take the use of intermediate goods into consideration and would thus represent a more accurate output measure when comparing plants with different production processes. However, previous studies have shown that there is a high correlation between value-added and gross output within narrowly defined industries, as the pattern of intermediate goods is similar within the same industry (see e.g., Bartelsman, Haltiwanger, and Scarpetta 2013; Foster, Haltiwanger, and Krizan 2001).

With respect to the industry classification chosen for our analysis, we faced a trade-off between the reliability of decomposition results, mostly determined by the granularity of the industry classification and the number of plants per industry, and the desire to provide an all-encompassing analysis by covering as many manufacturing plants as possible. We therefore decided to set the minimum number of plants per sector at 20 plants and to use the intermediate SNA/ISIC aggregation A38 as industry classification. This procedure aggregates similar ISIC two-digit divisions to 13 sectors (Eurostat 2008).² The list of industries included in our dataset can be found in Table A1 in Appendix A.³ Except for the states of Bremen and Saarland, our choice for the industry classification and the minimum number of plants allows us to cover six intermediate sectors in each state and year, comprising 14 out of the 24 ISIC two-digit manufacturing industries. With these 14 ISIC divisions in each of the 14 states, our analysis includes an annual number of more than 30 000 plants, which equals around 75 percent of all plants registered in the plant-level database.

Table 1 reports the corresponding summary statistics. We focus on three different periods: 2004–2006, 2010–2012, and 2016–2018. Thus, we do not only compare allocative efficiency and productivity between different states within each of these periods but also track their development over time. Moreover, the selected periods cover the time just before the Great Recession from 2007 to 2009 and the subsequent periods which allows us to investigate potential changes caused by the disruption. To reduce the impact of extreme values, we truncated the data for each industry and year at the 1^st and 99^th productivity percentile and additionally eliminated plants with suspiciously large changes in productivity.⁴

Table 1.

Summary Statistics for German Manufacturing Plants Between 2004 and 2018.

	Count	Mean	SD	p5	p95
2004–2006
Sales	92 042	19 743.8	65 762.6	1003.7	75 249.1
Employment	92 042	98.6	212.4	12.4	334.2
Labor productivity	92 042	162.5	142.8	40.7	404.5
2010–2012
Sales	91 410	21 211.9	77 770.6	1103.1	80 655.3
Employment	91 410	104.3	245.6	14.0	345.5
Labor productivity	91 410	166.4	156.6	41.5	427.3
2016–2018
Sales	95 199	22 017.6	75 891.8	1184.1	84 548.2
Employment	95 199	108.8	254.3	15.0	364.6
Labor productivity	95 199	167.7	153.9	42.6	423.5

Note. The table depicts summary statistics for plants within the manufacturing sector during the three time periods considered in our study. All values are reported for the cleaned sample as documented in Section 3. Sales are reported in thousand deflated euros, productivity is measured in thousand deflated euros in sales per employee. SD is the standard deviation, p5 and p95 describe the 5th and 95th percentile of the distribution, respectively.

Note further that the data provided by the German statistical office is an unbalanced panel with new plants entering and incumbents exiting. Unfortunately, it does not reliably distinguish ‘real’ entries and exits from events with no consequences for industry churning, such as changes in ownership or name, changes in the plant or firm ID or simple gaps in reporting. This is a common issue of many micro-level databases (Haltiwanger, Jarmin, and Miranda 2013), which becomes a particular problem in decomposition studies that aim to shed light on the dynamics of an industry where entries and exits make up a significant portion. One option to deal with this lack of information would be to simply drop all entries and exits and to consider only those plants that are constantly in the market, thereby creating a balanced panel of plants that can be consistently tracked over time. However, for the purposes of our study, this is not a viable option because we would lose a substantial part of plants and could thus make only very limited statements regarding the state of the manufacturing sector in German regions. We therefore conduct our analysis using the unbalanced panel and address the lack of plant traceability by applying the cross-sectional decomposition method by Olley and Pakes (1996) instead of a time-series approach.

Methodology

Productivity Decomposition by Olley and Pakes (1996)

For our empirical analysis, we use the productivity decomposition method by Olley and Pakes (1996) (OP). It is widely applied to measure the contribution of resource allocation across firms to aggregate productivity (see e.g., Bartelsman, Haltiwanger, and Scarpetta 2004, 2009 2013; Brown et al. 2018; Hyytinen, Ilmakunnas, and Maliranta 2016; Maliranta and Määttänen 2015). In contrast to the various ‘dynamic’ time-series approaches in the literature, which investigate productivity growth (Foster, Haltiwanger, and Krizan 2001; Griliches and Regev 1995; Melitz and Polanec 2015), the OP method follows a cross-sectional logic and provides a snapshot of industries' (economies') allocative efficiency at a given point in time. It may therefore be considered a ‘static’ productivity decomposition (Brown et al. 2018).

The starting point for the decomposition method proposed by Olley and Pakes (1996) is the definition of industry aggregate productivity as a share-weighted sum of plant-level productivity:

P_{j t} = \sum_{i} s_{i j t} p_{i j t}

(1)

where p_ijt denotes the productivity level and s_ijt the share of plant i in industry j at time t. As explained in Section 3, we use sales per employee as our productivity measure. For input shares, we use the number of employees relative to the industry aggregate within the respective federal state. Contrary to the common practice in decomposition studies to measure productivity in logs, we represent productivity in levels due to the potential pitfalls associated with using logs, as pointed out by Dias and Marques (2021) and Bruhn, Grebel, and Nesta (2023).

The OP decomposition method decomposes aggregate productivity into two components which we term within-plant and between-plant component. The within-plant component is represented by the unweighted mean of plant-level productivity, whereas the between-plant component is expressed by the covariance between plant productivity and input share:

\begin{array}{l} P_{j t} = {\bar{p}}_{j t} + \sum_{i} (s_{i j t} - {\bar{s}}_{j t}) (p_{i j t} - {\bar{p}}_{j t}) \\ = {\bar{p}}_{j t} + cov (s_{i j t}, p_{i j t}) \end{array}

(2)

with

{\bar{p}}_{j t}

and

{\bar{s}}_{j t}

representing unweighted means. We follow the ‘abuse of notation’ for the cov operator suggested by Melitz and Polanec (2015), omitting the division of the sum by the number of firms as this is already included in the market shares.

It follows from the above equation that the covariance term represents the gap between the unweighted and the weighted mean of plant-level productivity. To make this gap comparable across years, states and industries, we present it as a share of the corresponding aggregate industry productivity, that is, cov(s_ijt, p_ijt)/P_jt. In what follows, we refer to this share as ‘Allocative Efficiency’ (AE). It can be interpreted as the part of aggregate productivity that is explained by the efficient allocation of resources among plants. In other words, it is a measure for the market’s capability of channeling resources away from the less towards the more productive plants. Consequently, we can interpret an increase of the share of the covariance term as a more efficient allocation of employees between plants. It is the magnitude and development of this covariance share which we will focus on in our analyses in Sections 5 and 6.

Decomposing Aggregate Productivity on the Industry-State Level

To facilitate cross-state comparisons, we aggregate the annual industry-level results for productivity and allocative efficiency derived from equations (2) to a weighted average industry for each state and year. Following the example of Bartelsman, Haltiwanger, and Scarpetta (2013), we use state- and time-invariant industry employment as weights to aggregate annual industry-level results; more precisely, we use the average of Germany-wide employment per industry over all years as weights for the individual industries.⁵ Thus, we remove the impact of state-individual industry compositions and changes thereof. For instance, if a highly productive industry is particularly large in one federal state, it will impair our objective to draw cross-state comparisons of allocative efficiency within industries. The following equations summarize the overall procedure for computing productivity and allocative efficiency in the weighted average industry:

Φ_{k t} = \sum_{j} {\bar{s}}_{j} \cdot P_{j k t} = \sum_{j} {\bar{s}}_{j} \cdot \sum_{i} s_{i j k t} \cdot p_{i j k t}

(3)

A E_{k t} = \sum_{j} {\bar{s}}_{j} \cdot A E_{j k t} = \sum_{j} {\bar{s}}_{j} \cdot \frac{\sum_{i} cov (s_{i j k t}, p_{i j k t})}{P_{j k t}}

(4)

with

{\bar{s}}_{j}

as the Germany-wide (time-invariant) average share of industry j in the total employment of Germany’s manufacturing sector, P_jkt as the share-weighted productivity, and AE_jkt as allocative efficiency of industry j in state k at time t. The plant-level share s_ijkt represents the labor share of plant i in total employment of industry j in state k.

Allocative Efficiency and Regional Productivity in Germany

In this section, we examine the level and progression of allocative efficiency and productivity over three distinct time periods: 2004–2006, 2010–2012, and 2016–2018. To this end, we apply Equations (3) and (4) to each state and year and create averages over the three mentioned periods. Note our focus on the manufacturing sector only. We report productivity and allocative efficiency distributions of the underlying, more fine-grained industries in Appendix B.

Allocative Efficiency and Labor Productivity in East and West Germany

Table 2 shows allocative efficiency and labor productivity of the German regions on an aggregate level. On average, allocative efficiency in Germany has experienced a notable and steady decrease from 17.8 percent in the 2004–2006 period to 15.8 percent between 2016 and 2018. Conversely, labor productivity has undergone only minor changes, hovering at a level of roughly 200 000 euros in sales per employee. Because allocative efficiency has decreased, this roughly constant aggregate labor productivity implies that the unweighted average of plant-level productivity has increased, compensating the less efficient distribution of labor.

Table 2.

Allocative Efficiency and Labor Productivity in East and West Germany.

	Allocative Efficiency			Labor Productivity
	2004–2006	2010–2012	2016–2018	2004–2006	2010–2012	2016–2018
Germany	17.8	17.0	15.8	197.5	200.6	199.2
Former West Germany	18.3	17.8	16.6	202.3	204.9	202.7
Former East Germany	15.0	12.2	10.6	167.3	175.2	177.3
Former East ex Berlin	14.3	12.2	10.4	163.1	171.7	174.7

Note. The table depicts average allocative efficiency (in percent of aggregate productivity) and labor productivity (in thousand deflated euros in sales per employee) for the three time periods. The values for each of the four regional boundaries listed in the left column are employment-weighted averages of the respective state-level results.

Dividing overall values into former East and West Germany reveals a clear gap, with the West outperforming the East in both allocative efficiency and labor productivity. Excluding Berlin, as it may distort the overall impression of former East Germany, does not change the general pattern (see Table 2). While the East-West productivity gap was to be expected, its concurrence with a gap in allocative efficiency has not, to the best of our knowledge, been documented in the literature. The gap has increased over the three periods under investigation. Whereas East Germany’s allocative efficiency was still at roughly 82 percent of the West German level between 2004 and 2006, it was only at about 64 percent in the last period from 2016 to 2018. The reason for this widening gap is that the overall decline in allocative efficiency is significantly more pronounced for East Germany, decreasing by about 30 percent from the first to the last period, compared to only a 10 percent decrease in the West.

On the contrary, a decline in labor productivity has not been observed. In East Germany, labor productivity notably increased between the first and the last period by about 6 percent, in spite of the sharp decrease in allocative efficiency. Conversely, productivity in West Germany remained more or less constant, showing a minor increase of only 0.2 percent. Hence, the overall slump in the efficiency of resource allocation is evidently compensated for by an increase in average plant-level productivity, especially in East Germany. This strong productivity growth in East Germany is the main reason for the narrowing of the East-West productivity gap. While, between 2004 and 2006, the West’s productivity was around 21 percent larger relative to East German productivity, this gap shrank to only 14 percent in the 2016–2018 period.

As to allocative efficiency, the convergence in productivity could have been more pronounced if allocative efficiency in East Germany had not experienced such a substantial deterioration. In fact, when controlling for the gap in allocative efficiency between East and West in 2016–2018 by comparing their unweighted averages of plant-level productivity (158.4 and 169.0, respectively), the actual productivity gap (14 percent) is more than halved (less than 7 percent). In other words, over 50 percent of the 2016–2018 gap between aggregate productivity in East and West Germany are associated with a less efficient labor allocation between plants.

Allocative Efficiency and Labor Productivity in the German States

In Table 3, we report the regional figures on the dispersion of allocative efficiency and productivity. As explained in Section 3, we do not report any data for Bremen and Saarland due to their small number of plants. The former East German states comprise Brandenburg, Mecklenburg-West Pomerania, Saxony, Saxony-Anhalt, Thuringia and the Eastern part of Berlin. Allocative efficiency varies substantially between states, ranging from a minimum of 4.2 percent in Mecklenburg-West Pomerania to as much as 24.7 percent in Rhineland-Palatinate. There are also considerable changes in allocative efficiency within states across periods. Overall, the changes in allocative efficiency follow a negative trend. In contrast to West Germany with only few exceptions, all the states in East Germany have recorded a sharp decline in allocative efficiency, especially Berlin, Brandenburg and Mecklenburg-West Pomerania. These states almost halved their allocative efficiency in the last two periods compared to the first. This decline is primarily caused by the industry for rubber, plastics and other non-metallic mineral products (ISIC 22–23); moreover, in Berlin and Mecklenburg-West Pomerania, we detect a significant decrease in the industry comprising repair and installation of machinery and equipment as well as other manufacturing activities (ISIC 31–33).

Table 3.

Allocative Efficiency and Labor Productivity in the German Federal States.

State	Allocative Efficiency			Labor Productivity
State	2004–2006	2010–2012	2016–2018	2004–2006	2010–2012	2016–2018
Schleswig-Holstein	13.6	10.5	10.7	189.4	186.8	194.3
Hamburg	18.4	20.0	13.6	237.7	266.6	277.2
Lower Saxony	19.9	20.4	16.9	215.5	223.3	213.6
North Rhine-Westphalia	18.4	18.0	16.4	215.2	220.8	211.5
Hesse	19.5	20.7	20.2	191.7	197.1	192.3
Rhineland-Palatinate	22.6	24.7	23.5	201.6	210.4	219.8
Baden-Württemberg	17.5	18.0	19.2	191.5	193.4	201.2
Bavaria	17.4	14.2	12.2	194.9	189.8	185.2
Berlin	21.7	11.9	13.1	205.9	212.3	204.8
Brandenburg	18.3	12.9	12.1	197.4	192.2	196.4
Mecklenburg-West Pomerania	8.3	4.2	4.3	161.3	158.9	166.1
Saxony	14.2	12.7	11.2	155.4	164.1	163.8
Saxony-Anhalt	11.8	11.9	10.9	173.3	188.7	188.0
Thuringia	16.6	14.3	10.0	149.2	163.4	171.5

Note. The table depicts average allocative efficiency (in percent of aggregate productivity) and labor productivity (in thousand deflated euros in sales per employee) for the three time periods.

Overall, the regional patterns appear consistent over time. For example, the East German state of Mecklenburg-West Pomerania consistently shows the lowest values for allocative efficiency, ranging from 4.2 percent to 8.3 percent. In the Western state of Rhineland-Palatinate, values are persistently higher, varying between 22.6 percent and 24.7 percent. Figure 1 illustrates the regional pattern. As depicted, West German states tend to have a higher allocative efficiency than East German states, indicating that the East-West gap is evidently not caused by single outliers but reflects a regional pattern.

Figure 1.

Allocative efficiency in the German federal states 2004–2018.

A similar picture appears with respect to labor productivity as reported in Table 3 and visualized in Figure 2. Comparing Figures 1 and 2 shows that the more productive states also tend to have a higher allocative efficiency, and vice versa (Pearson correlation of 0.6). This is in line with the findings from our East-West comparison above and suggests that there is a large potential to boost regional productivity convergence by improving regions' allocative efficiency.

Figure 2.

Labor productivity in the German federal states 2004–2018.

To get an impression of the magnitude of this potential, consider the productivity levels in 2016–2018 for the most and least efficient states. As reported in Table 3, labor productivity in Rhineland-Palatinate (219.8) is about 32 percent higher than in Mecklenburg-West Pomerania (166.1); Rhineland-Palatinate’s share of allocative efficiency in aggregate productivity is almost a quarter (23.5 percent), in Mecklenburg-West Pomerania, it is only minor (4.3 percent). Hence, allocative efficiency accounts only for a small fraction of aggregate productivity. If we assume no difference in allocative efficiency between the two states and just compare the unweighted averages (168.2 and 159.1, respectively), the productivity gap is reduced by a striking 26% points from 32 percent to less than 6 percent. Hence, the lagging state, Mecklenburg-West Pomerania, has great potential to catch up in its productivity level by improving allocative efficiency, that is, by improving the reallocation of labor towards more productive plants.

Allocative Efficiency and Regional Industry Characteristics

We perform spatial regressions to analyze the extent to which the observed patterns in allocative efficiency may be associated with regional industry characteristics and we reflect on policy implications that could narrow the productivity disparities. For the variables in our regression, we use annual industry-state level values between 2004 and 2018. Due to data constraints, we lack the years 2007–2009.

Before we look at our regressions, we briefly address two important macroeconomic events that may affect the patterns observed in our data. First, it is likely that the Great Recession from 2007 to 2009 has affected the allocation of labor among German manufacturing plants, as the abundant literature on the impact of financial and economic crises on resource (re)allocation shows. However, the findings are ambiguous. There is the wide-spread view that economic crises enhance the reallocation of resources from the least towards the most productive firms. The underlying idea is the so-called ‘cleansing effect’, which describes that an economic downturn makes it more difficult for less productive firms to maintain their market shares, eventually forcing them out of the market (see e.g., Caballero and Hammour 1994; Foster, Grim, and Haltiwanger 2016; Kozeniauskas, Moreira, and Santos 2022). On the other hand, several studies show that such crises, in particular in credit markets, can also affect reallocation dynamics negatively (see e.g., Foster, Grim, and Haltiwanger 2016; Osotimehin and Pappadà 2017). In addition, economic crises are often accompanied by government intervention aimed at mitigating the effects of the crisis on companies, for example by means of favorable loan agreements or subsidized furlough programs. As these policies disproportionately benefit less productive firms, they inhibit the reallocation of employees towards their most productive use (see e.g., Kozeniauskas, Moreira, and Santos 2022).

It is likely that the aftermath of the Great Recession affects our results during 2010–2012, and possibly 2016–2018. Compared to 2004–2006, we identified a general decrease in allocative efficiency in many states, which may be partly caused by the described negative effects of financial and economic crises. The study by Grebel, Napoletano, and Nesta (2022) corroborates this explanation. They find evidence for factor misallocation in German manufacturing after the Great Recession, which they link to, among other aspects, significant labor hoarding in German establishments. Yet, several West German states experience an increase in allocative efficiency after the Great Recession. Hence, assuming that the Great Recession actually did have a significant impact on reallocation dynamics in Germany, it seems that this impact differs across regions. To explain this phenomenon and, more generally, the heterogeneous development of allocative efficiency in the federal states requires an examination of regional characteristics, as done in the regression analysis below.

The second macro level aspect is the former East-West division that may have affected the observed pattern in allocative efficiency. As a centrally planned economy until 1990, the lower values in allocative efficiency of the East German states may still persist and have not yet been fully overcome. Bartelsman, Haltiwanger, and Scarpetta (2013) show, in this context, that centrally planned economies in Central and Eastern Europe catch-up in allocative efficiency when transforming into a market economy. Yet, this explanation is not satisfactory for the German case. The likely gains in allocative efficiency of East German states after reunification were followed by a notable decrease starting in 2004, as we report in Section 5. Hence, apart from (former) institutional differences between Western and Eastern states in Germany, there must be further drivers apt to explain the gaps in allocative efficiency. In the following, we investigate further determinants at a more fine-grained, regional level in order to shed more light on this discrepancy.

Regression Model

Regions cannot be considered isolated entities. They interact across boarders and thus the reallocation of production factors of a region is affected by neighboring regions. To take such spatial autocorrelation into account, we use a spatial regression model. More precisely, we use the spatial autoregressive (SAR) model, also called the spatial lag model (Elhorst 2003).⁶ Since we assume that spatial effects occur primarily within an industry and not between different industries, we specified the spatial weighting matrix so that an industry in a given state is only affected by the characteristics of the same industry in its neighboring state(s).⁷

We include three different regional industry characteristics as explanatory variables, computed annually for each state and industry: export intensity (ExpInt: exports per sales in %), the Herfindahl index (HHI: sum of squared sales market shares) and the mean plant size (MPS: log of plant size in employees per plant). To control for time-specific effects that occurred in all states during the period of observation (e.g., changes in labor market policy), as well as industry-specific characteristics (e.g., differences in required worker skills) and state-specific characteristics (e.g., local infrastructure or historical economic developments), we include time and industry-state fixed effects.⁸ Hence, our econometric specification to explain allocative efficiency (AE) is:

\begin{array}{l} A E_{j k t} = ρ (W \times A E_{j l t}) + α ι_{N} + E x p I n t_{j k t} β_{1} + H H I_{j k t} β_{2} + H H I_{j k t}^{2} β_{3} \\ + M P S_{j k t} β_{4} + M P S_{j k t}^{2} β_{5} + θ_{t} + u_{j k} + ε_{t} \end{array}

(5)

with subscript j for industries, subscript k for states, subscript l for neighboring states, and subscript t for years. The scalar parameter ρ measures the magnitude of the endogenous spatial interaction effects of allocative efficiency; ι_N is a vector of ones associated with the constant α; β₁ to β₅ are parameter vectors for the explanatory variables; θ_t and u_jk represent vectors for time and industry-state fixed effects, respectively, and ϵ_t is a vector of disturbance terms.

We use export intensity as a proxy for trade openness. Melitz (2003) shows that exposure to trade is positively correlated with inter-firm resource reallocation, that is, allocative efficiency, due to two types of selection effects. First, only the most productive firms self-select into and thereby benefit from export markets as the entry into export markets entails costs which only they can afford. Second, trade exposure prohibits the least productive firms to earn positive profits and eventually forces them to exit the market. In our regression exercise, we expect a positive relationship between export intensity and allocative efficiency.

As the second independent variable, we deploy the Herfindahl index as a measure of market concentration and a proxy for (the inverse of) competitive intensity. Despite certain drawbacks of using the Herfindahl index as a proxy for competition, it is a widely applied practice, particularly when no data is available on plant-level profits that would allow for an arguably more appropriate measure (see e.g., Aghion et al. 2005; Boone 2008).

Our hypothesis regarding the relationship between market concentration and allocative efficiency can be divided into two lines of arguments. On the one hand, there are aspects pointing towards a positive correlation between market concentration and allocative efficiency. One may argue that higher market concentration leads to more innovation driven by the largest players due to higher expected rents, sometimes referred to as the ‘Schumpeterian effect’ (Aghion et al. 2005; Schumpeter 1942). According to Mohnen and Hall (2013), more innovation tends to translate into higher productivity. Hence, if the largest plants become more productive, allocative efficiency should increase. A second argument that supports a positive correlation between market concentration and allocative efficiency is the presence of economies of scale. As a consequence, plants with the highest market share should possess the highest productivity levels. If market concentration increases, it is conceivable that these largest plants will benefit from even higher economies of scale relative to their competitors. This would further widen the gap between the largest, most productive and the smallest, least productive plants, which is tantamount to a higher allocative efficiency.

On the other hand, a high degree of market concentration, that is, weak competitive intensity may also decrease innovation and thereby productivity growth. Arrow (1962) argued that the incentive to innovate is higher in a less concentrated, more competitive industry than under monopolistic conditions. The idea is that a monopolist, who already enjoys high profits, has only little incentive to replace these profits by innovating, compared to new entrants (Bloom, Van Reenen, and Williams 2019). If we follow this line of argument, an increase in market concentration can be linked to a decrease in allocative efficiency, as it weakens the incentive for the dominating players with high market shares to innovate and increase their productivity. Moreover, lower competition intensity is typically associated with a less stringent market selection process, making it easier for the least productive plants to maintain their market shares and stay in the market (Brown et al. 2018; Syverson 2011). Therefore, low competitive intensity may weaken the reallocation of workers towards the most productive plants and thereby decrease allocative efficiency.

Overall, the relationship between market concentration and allocative efficiency is ambiguous. A positive as well as the negative association may prevail. However, an outcome that reconciles the two opposing perspectives is also conceivable, which could, for instance, translate into an inverse U shape relationship. To test for such a relationship, we include a squared term for the HHI in our regression (see Equation (5)). The ambiguity may not come as a surprise, given that our above reasoning is significantly inspired by the debate on the relationship between competition or market concentration and innovation, where, both theoretically and empirically, this ambiguity remains unresolved (see e.g., Aghion et al. 2005; Bloom, Van Reenen, and Williams 2019; Cohen and Levin 1989; Scherer 1967). We further comment on this below when discussing our regression results.

As a third industry characteristic, we include mean plant size. A higher mean plant size can be associated with increased economies of scale. The largest plants within an industry will presumably benefit in particular from economies of scale, which increases their productivity. This widens the gap to the less productive and smaller plants within the industry, which contributes positively to allocative efficiency. Furthermore, plant size may facilitate the reallocation of jobs (labor), as many empirical studies suggest (see, e.g., Baldwin and Picot 1995; Klette and Mathiassen 1996; Davis, Haltiwanger, and Schuh 1996). Wagner (1995) and Fuchs and Weyh (2010) corroborate this finding for the German case. There are several reasons for the higher job reallocation rates in smaller establishments. For instance, Contini and Revelli (1997) point out that smaller firms have shorter lifespans which increases the frequency of firm births and deaths, thus contributing positively to job dynamism. Conversely, larger firms or plants tend to reshuffle workers within ‘internal labor markets’ rather than openly on the labor market, which inhibits the reallocation of labor. In addition, Stiglbauer et al. (2003) point out that larger firms are more diverse in terms of product lines and sales regions, which makes it easier for them to accommodate external shocks. Last not least, a high average plant size typically implies high entry barriers. This, in turn, may reduce competitive pressure for incumbents, which eventually may have negative repercussions on allocative efficiency, as explained above.

Against this background, we hypothesize that industries with increasing average plant size are characterized by a more efficient reallocation of labor. After passing a certain threshold, however, a higher average plant size leads to a deterioration in allocative efficiency. To allow for this ambiguity econometrically, analogous to the Herfindahl index, we include a squared term of the mean plant size in our regression model.

Results

The regression results are reported in Table 4, whereas Table 5 documents the direct and indirect (or spillover) effects. For ease of comparison and to gauge the relevance of spatial effects, we report OLS results next to the results of the SAR model. In model (1) we include export intensity (ExpInt), the Herfindahl index (HHI) and mean plant size (MPS), to give a first impression on the partial correlations. The association of ExpInt and HHI is positive with allocative efficiency, MPS is significantly negative. Model (2) adds the quadratic terms of HHI and MPS. The results show that HHI and MPS, as hypothesized, are inverted U-shaped. Taking spatial autocorrelation into account leads us to the two SAR models. Model (3) repeats model (1) but with spatial correlations as indicated by allocative efficiency interacted with the spatial weights matrix W, i.e., W × AE. The coefficient is positive and highly significant, which suggests significant spillovers from neighboring states. Including the squared terms as in model (2) delivers model (4) with spatial autocorrelation taken into account. As shown, the coefficients keep their sign and significance, which underlines the robustness of the results. The adjusted R² of the OLS model is fairly low with 26 percent. Despite the modest explanatory power of our model, the results remain relevant as all documented associations are highly significant, providing an important indication for the drivers of regional allocative efficiency.

Table 4.

Allocative Efficiency and Industry Characteristics.

	OLS		SAR
	(1)	(2)	(3)	(4)
ExpInt	0.397***	0.326***	0.382***	0.314***
ExpInt	(0.043)	(0.043)	(0.041)	(0.040)
HHI	102.8***	237.2***	104.8***	233.5***
HHI	(9.136)	(23.41)	(8.576)	(21.97)
HHI²		−361.4***		−346.5***
HHI²		(59.24)		(55.67)
MPS	−4.558***	69.72***	−5.064***	69.86***
MPS	(1.623)	(19.15)	(1.526)	(17.94)
MPS²		−8.371***		−8.429***
MPS²		(2.082)		(1.950)
W × AE			0.169***	0.158***
W × AE			(0.038)	(0.037)
Observations	1,008	1,008	1,008	1,008
Industry-state combinations	84	84	84	84
R² (adj)	0.209	0.261
McFadden R² (adj)			0.093	0.103
Log-likelihood			−2,957.5	−2,923.6

Note. Standard errors in parentheses. *** p < 0.01, ** p < 0.05, * p < 0.1. Time and industry-state fixed effects are included in every model.

Table 5.

Direct and Indirect Effects of Industry Characteristics on Allocative Efficiency.

	OLS		SAR
	(1)	(2)	(3)	(4)
Direct effects
ExpInt	0.397***	0.326***	0.385***	0.316***
ExpInt	(0.043)	(0.043)	(0.041)	(0.041)
HHI	102.8***	237.2***	105.6***	235.1***
HHI	(9.136)	(23.413)	(8.669)	(22.10)
HHI²		−361.4***		−348.8***
HHI²		(59.240)		(55.97)
MPS	−4.558***	69.72***	−5.103***	70.32***
MPS	(1.623)	(19.146)	(1.539)	(18.06)
MPS²		−8.371***		−8.485***
MPS²		(2.082)		(1.963)
Indirect effects
ExpInt			0.075***	0.057***
ExpInt			(0.020)	(0.017)
HHI			20.53***	42.24***
HHI			(5.689)	(11.99)
HHI²				−62.67***
HHI²				(19.21)
MPS			−0.992**	12.64***
MPS			(0.409)	(4.725)
MPS²				−1.525***
MPS²				(0.546)

Note: See Table 4.

The highly significant positive association between export intensity and allocative efficiency was to be expected and confirms that trade openness can be linked to the reallocation of resources towards the most productive firms. Let us now take a closer look at HHI and MPS. For better understanding, Figure 3 depicts the respective inverse U shape relationships of HHI and MPS with allocative efficiency. With respect to market concentration (HHI, panel a), starting from a low level in HHI, an increasing market concentration is associated with an increase in allocative efficiency. This supports the hypothesis of the prevalence of a Schumpeterian effect. The positive correlation only holds until a threshold of market concentration is reached, beyond which a further increase in market concentration is associated with a decrease in allocative efficiency, which we attribute to the very low competitive intensity in such industries. In fact, computing the HHI that maximizes the inverse U-shaped function results in an HHI of 0.337 which represents the 99^th percentile.⁹

Figure 3.

Effects of HHI and MPS on allocative efficiency. (a) Effect of HHI and (b) Effect of MPS. Note: These two panels show the absolute effect (= integrated marginal effect) of HHI and MPS on allocative efficiency. Both have an inverted U-shape; assuming all remaining variables equal to zero, the two lines indicate the absolute effect of the respective variable on allocative efficiency.

With regard to the correlation of mean plant size (MPS) and allocative efficiency, we also observe an inverse U-shape relationship. Note that for better comprehensibility, we exponentiated the logged values of MPS in Figure 3(b). For industries with a small mean plant size, an increase in the mean plant size corresponds to an improvement in allocative efficiency which can be explained by an increase in economies of scale and the Schumpeterian effect on innovation. Surprisingly, we only observe this positive marginal effect up to a mean plant size of around 63 employees, which represents the 14^th percentile in the mean plant size distribution. Hence, the majority of the industry-state combinations in the German manufacturing sector is above the threshold, beyond which a further increase in the mean plant size is associated with a decrease in allocative efficiency. We trace this back to a combination of the competition-reducing impact of heightened entry barriers and the decrease in job reallocation rates. Overall, our data show a significant negative correlation between plant size and job reallocation rates.¹⁰

Regarding the occurrence of spatial effects, Table 5 indicates that allocative efficiency within a specific state is affected by industry characteristics in neighboring states in a very similar manner as is the case for direct effects. It is positively affected by a high degree of trade openness (ExpInt) in neighboring states, and for HHI and MPS, respectively, we observe inverse U shape relationships. We interpret this as affirmation of our expectation that the economies of neighboring states are closely interconnected. Assuming that plants compete across states, it seems logical that an increase in trade openness, market concentration or mean plant size in neighboring states will exert similar, yet less pronounced, effects as the direct effects.

Discussion and Policy Implications

Our regression analysis has shown that regional discrepancies in allocative efficiency are significantly associated with regional differences in export intensity, market concentration and plant size. Note that we document associations between these variables, not making any causal claims. Hence, our ensuing reflections on potential policy implications are to be seen against this background.

First, we have detected a positive relationship between export intensity and allocative efficiency, which is in line with the literature (see e.g., Melitz 2003). This finding suggests that policies aimed at the intensification and liberalization of trade, such as trade agreements or export promotion programs, could have a positive impact on allocative efficiency. When looking at the general distribution of export intensity across the German federal states in Table 6, it becomes apparent that, despite evident variations between industries, the average export intensity in East German states is consistently below the export intensity in the West. This East-West gap in export intensity is corroborated by several previous firm-level studies conducted in Germany (see, e.g., Arnold and Hussinger 2005; Kirbach and Schmiedeberg 2008; Wagner 2008). Hence, it would be in particular the former East German states that could benefit from policies that promote exports.

Second, our regression has revealed an inverse U shape relationship between market concentration and allocative efficiency. Competition policies are typically aimed at preventing high levels of market concentration. With respect to its impact on allocative efficiency, our results indicate that an increase in market concentration up to a certain threshold can in fact be beneficial. Only for the most concentrated industries in our data, the marginal effect of further concentration declines. For this limited number of industries, policies aimed at reducing market concentration or fostering competition, such as anti-trust laws or merger and acquisition regulations, may lead to higher allocative efficiency. Looking at the Herfindahl index of the German federal states, as done in Table 6, a heterogeneous picture emerges, which, unlike for export intensity, does not reveal an East-West gap. In fact, the three states with the lowest average market concentration are the West German states of North Rhine-Westfalia, Baden-Württemberg and Bavaria. Hence, even though market concentration represents a significant lever for reducing regional differences in allocative efficiency, it does not serve as an explanation for the East-West gap.

Third, we have identified an inverse U shape relationship between mean plant size and allocative efficiency. In industries with a small average plant size, policies aimed at facilitating plant growth may induce an increase in allocative efficiency as it enables the benefiting from economies of scale and higher expected returns for innovators. However, the relationship is reversed for larger mean plant sizes, because an (established) industry with a high mean plant size generates entry barriers and affects job reallocation rates, negatively. As reported above, the threshold is already reached at around 63 employees per plant. When comparing the mean plant size across states, it becomes evident that all states surpass the threshold of 63 employees (see Table 6). The mean plant size also differs notably between Eastern and Western states (Schleswig-Holstein as the only exception) with West German states outperforming East German states in this respect, an observation in line with many previous studies (see, e.g., Fuchs and Weyh 2010; Bachmann et al. 2022). Hence, for most industries in West German states, allocative efficiency could presumably be enhanced by policies aimed at lowering entry barriers, for instance, by reducing regulations and bureaucratic burdens or facilitating capital access for start-up companies. Moreover, labor mobility may be fostered directly through measures such as more flexible labor market regulations or state programs to support job transitions. This policy recommendation partly also applies to East German states. Yet, taking the standard deviation into account, there are several industries in the East whose allocative efficiency can be expected to benefit from an increase in mean plant size. Fostering the emergence of large-scale firms could be achieved by attracting such type of firms from elsewhere or by implementing polices that facilitate growth of small and medium-sized plants, such as tax incentives, easy capital access and the promotion of investments in innovation.

Table 6.

Selected Industry Characteristics in the German Federal States.

State	Export intensity		Herfindahl index		Mean Plant Size
State	Mean	SD	Mean	SD	Mean	SD
Schleswig-Holstein	34.0	14.2	0.045	0.034	87.2	18.8
Hamburg	33.6	23.7	0.158	0.098	119.5	60.2
Lower Saxony	35.6	12.2	0.026	0.020	103.2	15.1
North Rhine-Westfalia	34.1	13.5	0.009	0.004	102.1	17.4
Hesse	34.0	12.6	0.035	0.024	106.5	19.8
Rhineland-Palatinate	36.8	15.2	0.032	0.012	104.3	19.7
Baden-Württemberg	36.9	13.5	0.010	0.003	108.3	36.4
Bavaria	36.8	13.1	0.015	0.019	128.2	49.2
Berlin	32.3	18.7	0.102	0.070	91.1	35.8
Brandenburg	29.7	10.3	0.073	0.056	70.8	15.5
Mecklenburg-West Pomerania	20.3	8.3	0.058	0.037	73.4	25.6
Saxony	24.5	12.4	0.017	0.009	70.6	14.9
Saxony-Anhalt	21.5	10.2	0.032	0.011	78.7	21.2
Thuringia	25.9	8.7	0.029	0.012	92.7	33.6
Mean	31.1	13.3	0.046	0.029	95.5	27.4

Note. The table depicts unweighted means and standard deviations of industry-state level characteristics for each state from 2004 to 2018. Export intensity is computed as exports per sales in %, the Herfindahl index is the sum of squared sales market shares and the mean plant size measures the average number of employees per plant.

Although our study is not dynamic, one aspect stands out that calls for a dynamic answer. High allocative efficiency requires that an industry has (a few) highly productive large firms that benefit from economies of scale and have a high labor input share. For late entrants, and these are all former Eastern firms that entered the market after reunification, it was and is more difficult to compete in a well-established (Western) market with already large incumbents. It is more difficult for them to exploit economies of scale because the incumbents already hold these advantages as first movers; accordingly, the average size of operations is high and the reallocation of labor is low. Consequently, the opportunities for new entrants to grow decrease. This interpretation is in line with Schumpeter’s ideas on entrepreneurship. The most promising ecosystem for improving allocative efficiency seems to be a (young) emerging entrepreneurial industry where all players find a level playing field, a hypothesis that is closest to Schumpeter’s Mark 1 hypothesis, which attributes entrepreneurial behavior and innovation to rather small firms (see e.g., Kamien and Schwartz 1982; Malerba and Orsenigo 1995; Nelson and Winter 1982; Schumpeter 1934). Due to the globalized world (see the role of export intensity and spatial spillovers above) and the history of East German states, having adopted a (free) market economy only recently, they have to deal with a Schumpeter Mark II environment, that is, an environment in which large-scale firms from other regions dominate the market.

Conclusion

In this study, we have shown that regional variation in the efficiency of labor allocation among manufacturing plants plays a major role in explaining regional productivity disparities in Germany. The market selection process that steers employees towards the most productive plants appears to work less efficiently in eastern than in western Germany. Yet, our results also reveal that the mere focus on East-West comparisons hides partially large differences between German states. We show that these regional productivity differences could be substantially narrowed by fostering labor reallocation processes. With respect to the causes of the observed variation in allocative efficiency, our regression results indicate that the variation is significantly associated with regional differences in trade openness, competitive intensity, economies of scale and labor mobility. For export intensity, we find that policies aimed at the intensification and liberalization of trade can increase allocative efficiency. Such policies are a promising avenue for narrowing regional productivity differences given that the less productive East German states have particularly low export rates. Regarding the impact of market concentration and plant size on allocative efficiency, we find an inverse U shape relationship. Therefore, policy implications with respect to these industry characteristics depend on the circumstances of the individual region and industry.

The regression results presented in this study can be an important step towards explaining the observed regional differences in allocative efficiency. Future research in this field should attempt to extend this analysis. For instance, it would be insightful to include a measure for competitive intensity that is not based on market concentration (as is the Herfindahl index), because a highly concentrated industry does not necessarily entail low competition. Therefore, including measures such as the price cost margin (see e.g., Aghion et al. 2005) could help distinguish between the impact of market concentration and competitive intensity. Apart form investigating industry characteristics, it could be interesting to extend our analysis by investigating the effects of metropolitan areas on regional allocative efficiency. Larger cities typically exhibit higher levels of productivity, driven by, among others, agglomeration effects (such as enhanced labor market pooling) and increased market selection mechanisms (see e.g., Combes et al. 2012). With respect to agglomeration effects and geographic proximity, Porter (1996) further emphasizes its importance for the flow of highly applied knowledge across firms, which could also affect allocative efficiency. Including such agglomeration effects in our regression exercise would certainly strengthen the robustness of our results. Yet, an analysis of these effects in Germany would require a more fine-grained, regional analysis (e.g., NUTS2), which will reduce the available number of plants per region. This also implies that fewer industries and fewer regions could be covered in such an analysis as they do not reach the minimum number of plants necessary for reliably computing allocative efficiency. Nonetheless, even for a limited sample, such an analysis could reveal interesting insights.

To conclude, this study demonstrates that the improvement of allocative efficiency is a promising, so far neglected, avenue for narrowing regional disparities in Germany. However, even though we focus on Germany, we expect other countries to show similar regional variations in allocative efficiency. Evidently, given its history as a divided country with two different economic systems, regional analyses in Germany have certain idiosyncrasies. Nonetheless, the identified drivers of allocative efficiency, such as differences in export intensity, market concentration, or plant size, can be expected to also apply to other countries. Therefore, studying regional variations in allocative efficiency in other countries may be a fruitful area for future work.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Simon Bruhn

Data Availability Statement

The dataset used during in this study is not publicly available as it contains proprietary information that the authors acquired through a license. Information on how to obtain it and reproduce the analysis is available from the authors on request.

Notes

Appendix A

Appendix B

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