Open Access

Employment adjustment in German firms

Journal for Labour Market ResearchZeitschrift für ArbeitsmarktForschung201447:159

https://doi.org/10.1007/s12651-014-0159-0

Published: 31 January 2014

Abstract

Using a representative establishment data set for Germany, I show that, in line with the existing literature for several countries, firms’ adjustment costs for employment are characterized by a fixed and convex functional form. Furthermore, they are asymmetric with dismissal costs exceeding hiring costs. An analysis of firms’ adjustment in the period 1996–2010 also indicates that adjustment behavior has changed over time. Comparing the employment adjustment in the two observed business cycles comprising the years 1996–2003 and 2004–2010, I find that the adjustment speed was higher in the second business cycle indicating that adjustment costs have fallen in recent years.

Keywords

Adjustment costsDynamic labor demandEmployment adjustmentGermany

Betriebliche Beschäftigungsanpassung in Deutschland

Zusammenfassung

Anhand von repräsentativen Daten des IAB-Betriebspanels wird gezeigt, dass die Kosten der betrieblichen Beschäftigungsanpassung in Deutschland eine funktionale Form mit fixer und konvexer Komponente aufweisen, wie es auch frühere Studien für andere Länder feststellen. Des Weiteren ist die Struktur der Anpassungskosten asymmetrisch, wobei die Entlassungskosten größer als die Einstellungskosten sind. Bei der Analyse des betrieblichen Anpassungsverhaltens für den Zeitraum 1996–2010 wird zudem deutlich, dass sich das Verhalten über die Zeit geändert hat. Ein Vergleich der betrieblichen Beschäftigungsanpassung in den zwei beobachteten Konjunkturzyklen 1996–2003 und 2004–2010 zeigt eine schnellere Anpassung im zweiten Konjunkturzyklus, was auf gesunkene Anpassungskosten hinweist.

JEL Classification

C24D22E24J23

1 Introduction

Following the 2008/2009 economic crisis, the adjustment of firms’ labor volume has again moved into the focus of economic analysis. Across countries, firms have shown different reactions to this crisis, but also within countries firms’ behavior has differed from previous reactions. For example, German firms predominantly adjusted working hours, while less adjustment of the number of employees was visible (see Burda and Hunt, 2011). This points to a fundamental change in firms’ adjustment processes. Several studies for Germany indicate that firms’ employment adjustment has indeed changed over time (see, e.g., Gartner and Klinger, 2010; Herzog-Stein and Seifert, 2010). However, these studies are mostly based on descriptive analyses of aggregated data. In contrast, the present study provides a more detailed econometric analysis based on data at the establishment level. Using a representative panel data set on German establishments, I estimate a dynamic labor demand model for the period 1996 to 2010. This allows us to compare employment adjustment in the two business cycles occurring between 1996 and 2010 and to investigate econometrically whether firms’ adjustment behavior has changed over time. Moreover, I analyze labor demand separately for Western and Eastern Germany, thus extending the sparse empirical evidence on dynamic labor demand in Eastern Germany.

I also provide new insights concerning the functional form of firms’ adjustment costs. Adjustment costs are an important component of dynamic labor demand theory. Firms’ adjustment behavior depends on the functional form of the adjustment costs they face. Although empirical evidence so far indicates a fixed and convex specification (see Vermeulen, 2006, p. 11), this has not been established for Germany yet. In the only studies for (Western) Germany which contain an intensive analysis of the functional form, Kölling (1998) prefers a convex and Yaman (2011) a linear functional form of adjustment costs, making the empirical evidence for Germany ambiguous. I will use a different switching regression approach than Kölling (1998) and will show that for Germany in addition to the convex specification a fixed component of adjustment costs is also relevant. Thus, I provide empirical support for the assumption of fixed and convex adjustment costs in Germany. Furthermore, the existing studies do not contain separate results for Western and Eastern Germany, which I provide.

The paper proceeds as follows: Sect. 2 sketches the main aspects of adjustment costs and presents the relevant empirical evidence on the functional form of adjustment costs. Section 3 provides a description of our data. Section 4 shows the empirical model, while Sect. 5 presents and discusses the results of a basic dynamic labor demand model. I investigate the change of firms’ adjustment behavior over time in Sect. 6, and Sect. 7 concludes.

2 Adjustment costs: theoretical considerations and empirical evidence

The underlying theory for our analysis is the dynamic labor demand theory. While the static labor demand theory focuses on firms’ optimal employment level, the dynamic counterpart analyzes firms’ adjustment toward the optimum and the time it takes to reach the optimal employment level which is not possible within the static theory (see Cahuc and Zylberberg, 2004, p. 212). Adjustment costs are an essential component of dynamic labor demand theory because they play an important role in firms’ adjustment behavior. These costs are the reason that a plant does not dismiss all employees before the weekend and re-hire them on Monday (see Franz, 2013, p. 146; Nickell, 1986, p. 473). Labor is not a completely variable production factor because adjustment costs form a fixed component of total labor costs. Therefore Oi (1962) calls labor a ‘quasi-fix’ factor. Adjustment costs arise from an employment change and consist of hiring costs (e.g., search, selection, first training, administrative expenses of the Human Resources Department) and costs of dismissals (e.g., severance pay, consideration of dismissal protection, administrative expenses of the Human Resources Department). Ehrenberg and Smith (2012, p. 145) consider hiring costs as investments and so they point out the ‘sunk’ character of these costs.

Several criteria can be used for distinguishing adjustment costs (see, e.g., Hamermesh, 1993a, p. 207; Kölling, 1998, p. 8; Nickell, 1986, p. 475). Besides internal/external and implicit/explicit, one can distinguish between a gross and a net perspective in the analysis of adjustment costs. Net adjustment costs incur if the number of employees changes. In contrast, each hiring and dismissal decision affects gross adjustment costs, even if the employment level does not change. But there is no clear tendency in previous studies for a certain concept. In this study, I use a net approach due to the underlying empirical model which is based on previous studies using the net approach (see Sect. 4).

The basic theory of dynamic labor demand assumes labor to be a homogeneous production factor, which is a restrictive assumption in the context of adjustment costs (see Kölling, 1998, p. 61). Different kinds of jobs and different qualification levels of employees can lead to different sizes of adjustment cost meaning that the firm would not adjust separate groups of employees in the same manner. Yet, following earlier studies, I assume labor to be homogeneous for the sake of analytical simplicity. Nevertheless, this allows us to draw some interesting conclusions about the adjustment procedures of labor demand (see Kölling, 1998, p. 61).

Another simplifying assumption concerns the two dimensions of labor demand. Firms can adjust their total labor volume by changing the number of employees and by changing working hours. Adjustment of working time gives more flexibility compared to an adjustment of just the number of employees. It can be done faster (see Sargent, 1978, p. 1015) and cheaper (see Shapiro, 1986, p. 516) than the adjustment of the number of employees. Therefore, in periods when the adjustment of the number of employees is no longer optimal, a firm can still get closer to the optimal labor volume by changing the number of hours worked (see, e.g., Nickell, 1978, pp. 332–335; Santamäki, 1988, pp. 101–102). Yet, the consideration of both dimensions leads to complex adjustment models. In order to simplify the model, working hours are ignored in the following analysis. The data set used (see Sect. 3), which does not provide clear information about working hours, is another reason for disregarding the working time. However, basic conclusions about adjustment procedures of labor demand are still possible (see Hamermesh, 1993a, p. 209).

Furthermore, adjustment costs differ in functional form. One can classify fixed, linear, and convex adjustment costs. Fixed adjustment costs incur from firms’ decision to adjust employment independently of the amount of employment adjustment.1 An example is a job advertisement for two or four employees, which costs the same in both cases (see Hamermesh, 1989, p. 675; Kölling, 1998, p. 44). If the firm faces a new optimal employment level due to a shock or a changing economic situation, it must make a decision about an adjustment to the new optimum. Fixed adjustment costs and their relative magnitude to the profits resulting from an employment level closer to the optimal one are essential for this decision. If profits exceed costs, the firm will adjust employment. Because of the fixed specification, firms’ adjustment is then done instantly and completely towards the new optimal employment level (see Hamermesh, 1993a, p. 214).2

Linear adjustment costs, which increase proportionally in the amount of adjustment, result in a different adjustment behavior. Again, firms adjust instantly while taking into account the costs-profits relation. But with a linear structure, the employment level is not adjusted completely towards the optimal level (see, e.g., Kölling, 1998, p. 30; Nickell, 1986, p. 491). Instead, firms keep employment constant near the optimum because of costs exceeding profits (see, e.g., Anderson, 1993, p. 1018; Kölling, 1998, p. 30; Nickell, 1978, p. 332; Nickell, 1986, p. 495). Examples for a linear cost structure, such as hiring from an agency (see Nickell, 1986, p. 477) or severance pay, show that linear adjustment costs are not unrealistic.

Convex adjustment costs, mostly used in a quadratic specification, are the third functional form. This specification was the one first used in the literature and goes back to Holt et al. (1960). Convex costs increase disproportionately with the amount of adjustment. Although a convex specification might be suitable for a specific part of adjustment (see Nickell, 1986, p. 477), it should not be considered as the only existing functional form (see, e.g., Bentolila and Bertola, 1990, p. 382; Hamermesh, 1989, p. 475; Nickell, 1986, p. 477; Rothschild, 1971, p. 605). A convex cost structure is a very restrictive assumption and difficult to justify. The reason for the common use of convex adjustment costs in the literature was the simple analytical handling in the models (see, e.g., Kölling, 1998, p. 9; Pfann and Verspagen, 1989, p. 365). But already Holt et al. (1960, p. 52) mentioned that the quadratic form is just a ‘…suitable first approximation.’ Adjustment costs can have different forms in reality (see Nickell, 1986, p. 519). Assuming convex adjustment costs rather than fixed or linear costs, firms spread adjustment of employment over several periods (see, e.g., Cahuc and Zylberberg, 2004, p. 218; Hamermesh, 1993a, p. 211; Nickell, 1986, p. 483). Because of the convexity, marginal costs increase with the amount of employment adjustment. Therefore, it is optimal to spread the adjustment over several periods. Furthermore, the optimal employment level will not be reached in finite time (see, e.g., Kölling, 1998, p. 21; Nickell, 1986, p. 483), although there is long-run convergence to the optimum (see Kölling, 1998, p. 60).

Considering the functional form also raises the question whether adjustment costs are symmetric or asymmetric, thus whether hiring costs and firing costs are equal. A symmetric cost structure simplifies the econometric model but there is no reason to expect an upward employment adjustment to generate the same costs as a downward employment adjustment (see Schiantarelli and Sembenelli, 1993, p. 149). Therefore, asymmetric adjustment costs are a much less restrictive assumption. The costs of hiring and firing result from different sources so that asymmetry is a reasonable assumption.

In case of a fixed specification, increasing adjustment costs lead to a longer period with no adjustment and a greater amount of employment change if an adjustment is optimal (see Gorter et al., 2003, p. 100). Assuming a linear structure instead, higher adjustment costs also cause a longer period of inaction. Furthermore, the difference between the optimal employment level and the actual level when the firm stops adjustment is larger (see, e.g., Anderson, 1993, p. 1018; Nickell, 1978, p. 337; Nickell, 1986, p. 495). Finally, the result of higher convex adjustment costs is a slower adjustment which is spread over many more periods (see, e.g., Cahuc and Zylberberg, 2004, p. 218; Sargent, 1978, p. 1018).

There is a large body of empirical evidence on the significant role of firms’ adjustment costs (see, e.g., Burgess, 1988; Dolfin, 2006, p. 870; Gavosto and Sestito, 1993, p. 447; Nissim, 1984, p. 433; Oi, 1962; Rosen, 1968, p. 337; Rota, 2004, p. 43) showing that these costs actually have an effect on adjustment behavior. In contrast, Hall (2004) as well as Pindyck and Rotemberg (1983a, 1983b) find that adjustment costs are just marginal. Regarding the functional form, the studies by Holt et al. (1960) and Nickell (1984, p. 546) show that a convex structure is appropriate.3 However, their evidence it not entirely persuasive as they assume pure convexity in their empirical models and make no comparison with other functional forms in these analyses. In addition, given the not convincing theoretical justification it is not surprising that there are many empirical objections to pure convex costs.

Hamermesh (1989, p. 687) presents first evidence against a pure convex structure. He shows that a fixed cost specification suits the data better than convex adjustment costs. The results of Anderson (1993), Caballero et al. (1997), Cooper and Willis (2009), Gavosto and Sestito (1993), Holtz-Eakin and Rosen (1991), Rota (2004), and Varejão and Portugal (2007a) are also inconsistent with the assumption of pure convex adjustment costs. Instead, they find that firms’ adjustment behavior is better represented by an assumption of a combination of various functional forms, for example, a fixed and convex specification (see, e.g., Abowd and Kramarz, 2003; Cooper et al., 2004; Hamermesh, 1992; Kramarz and Michaud, 2010; Lapatinas, 2009; Nilsen et al., 2007; Pfann and Verspagen, 1989).4 For Germany, however, the studies by Kölling (1998) and Yaman (2011), which are the only two analyses investigating intensively the functional form of the adjustment costs I am aware of, find that a model with combined fixed and convex adjustment costs components provides no further insights compared with a pure convex specification (see Kölling, 1998, p. 153) or respectively that a model with linear adjustment costs fits better the data (see Yaman, 2011, p. 25).5 Therefore, the predominance of the combination structure for adjustment cost has not been shown to extend to Germany yet.

Regarding the symmetry or rather asymmetry of adjustment costs the empirical evidence clearly favors asymmetry. However, there is no clarity concerning the relation of hiring costs to dismissal costs (see Hunt, 2000, p. 181). Based on data from the production sector in Italy, Jaramillo et al. (1993) find higher dismissal costs compared to hiring costs. This relation also has been confirmed for Germany (see Burda, 1991, p. 73; Kölling, 1998, p. 151), for France (see Abowd and Kramarz, 2003; Goux et al., 2001; Kramarz and Michaud, 2010) as well as for Norway (see Nilsen et al., 2007, p. 597). In addition, based upon British and Dutch data, Pfann and Palm (1993) show higher dismissal costs for non-production workers, whereas they find higher hiring costs for production workers. Other evidence for hiring costs exceeding dismissal costs is described in Pfann and Verspagen (1989) for the Netherlands and in Chang and Stefanou (1988), Hamermesh (1993a, p. 208) as well as in Hamermesh and Pfann (1996) for the US.

Our study investigates firms’ adjustment behavior of labor in Germany. I assume a combined cost structure and asymmetry with dismissal costs exceeding hiring costs that I will test in the following analysis. Our hypothesis regarding the relation of hiring and dismissal costs is based on the labor market institutions in Germany. Germany, like other countries in continental Europe, has a more regulated labor market with higher dismissal protection than, for instance, the US (see, e.g., Abraham and Houseman, 1994, p. 59; Burda, 1991, p. 62; Emerson, 1988, p. 776). This in turn leads to less flexibility for firms and results in higher adjustment costs, especially higher dismissal costs in Europe compared to the US (see, e.g., Hunt, 2000, p. 177; Merkl and Wesselbaum, 2011, p. 805).

3 Data and descriptive evidence

The data used for the analysis come from the IAB Establishment Panel, which is a representative annual survey of German establishments.6 The establishments interviewed are drawn from a stratified sample of plants, which are included in the German employment statistics. The strata are defined over plant sizes and industries; however, sampling within each cell is random. The panel oversamples large establishments, but weighting for representative results is possible. The panel started in 1993 with Western German plants and was extended to Eastern German plants in 1996. Nowadays, almost 16,000 establishments are interviewed each year. Information about, for example, plant characteristics, wages, profitability, management policy and especially about the workforce composition and its development over time is provided by the panel with the reference date June 30th.

I use the waves 1996 until 2010. It is important to note that the IAB Establishment Panel is an annual survey. This temporal aggregation makes an analysis of firms’ employment adjustment difficult so that one would prefer quarterly or monthly data (see Hamermesh, 1993b, pp. 97–106; Kölling, 1998, pp. 112–113). When using annual data I implicitly assume that the firms’ decision are taken at intervals of one year which is mostly not given in reality (see Hamermesh, 1993b, pp. 97–98). Thus, observation time and timing of firms’ decision are not the same and results may be biased. Previous studies show that a higher level of temporal aggregation leads to a lower adjustment speed (see, e.g., Hamermesh, 1993b, p. 99; Kölling, 1998, p. 124; Varejão and Portugal, 2007b, p. 13). However, Kölling (1998, p. 113) does not interpret the explanation by Hamermesh (1993b, pp. 97–98) as a theoretical reason for this bias. Furthermore, Varejão and Portugal (2007b, p. 13) also argue that a ‘temporal aggregation does not imply a priori any bias’. Moreover, when using quarterly or monthly data seasonal fluctuations could lead to misleading results (see Kölling, 1998, p. 113). Therefore, Kölling (1998, p. 113) argues that an analysis of dynamic labor demand using the IAB Establishment Panel is possible if one looks critically at the results. This has to be considered in the analysis.

Although the IAB Establishment Panel contains information about the agreed weekly working time and overtime, this information is not available for all years. An exact calculation of working hours based on the numbers of employees in full-time and part-time jobs is also not viable. Therefore, our empirical investigation can only analyze the adjustment of the number of employees and has to neglect the working time dimension. In particular, I consider the number of employees covered by social security.7 The group of employees covered by social security is more homogenous regarding adjustment costs than the group of all employees. Therefore, the analysis of firms’ adjustment behavior (e.g., adjustment speed) should be more accurate. Furthermore, I only analyze the private sector because of differences in the adjustment behavior between the public and private sector (shown descriptively by Ellguth and Kohaut, 2011a). Another reason for this decision is the derivation of the empirical model, which is based on the assumption of profit maximization (see Sect. 4) that does not hold for the public sector.

Furthermore, I only consider firms’ adjustment of the core workforce. In the last few years, the use of temporary agency workers has increased, especially after the reform of the Temporary Employment Agencies Act (Arbeitnehmerüberlassungsgesetz) in 2003 (see, e.g., Antoni and Jahn, 2009; Spermann, 2011, pp. 5–11). The temporary agency workers can serve as an alternative instrument for employment adjustment. Therefore, one could also consider them in an analysis of firms’ adjustment behavior. However, I ignore temporary workers for two reasons. First, the IAB Establishment Panel does not contain the number of temporary agency workers in all years of the sample. Secondly, I am interested in the adjustment of the core workforce that does not include temporary agency workers. As mentioned before, there are stricter regulations in the German labor market than in the U.S. labor market. Dismissal protection plays an important role in Germany. Analyzing the core workforce, I focus on firms’ adjustment behavior with regard to employees affected by labor market regulations (e.g., dismissal protection).

Figure 1 illustrates the average number of employees covered by social security per plant from 1996 until 2010. The fluctuation over time expresses changing employment levels and thus the employment adjustment of the plants. Furthermore, it shows the phases of the business cycle (except for the first years). The average number of employees per plant is lower during the economic downturn 2002/2003 and increases again in the economic upturn after 2004. Figure 2 provides more detailed information on adjustment behavior. Every year plants increase, decrease or do not change employment, regardless of the business cycle phase.8 However, there is no clear pattern. Although a bigger share of plants reduced employment in the economic downturn 2002/2003, some plants also increased employment during that time. Another striking result is that more than 50 percent of the plants do not change their employment level over the year. This is a first evidence in favor of non-convex adjustment costs: no employment adjustment is only optimal for a plant in the presence of fixed or linear adjustment costs.9
Fig. 1

Average number of employees per plant

Notes: Weighted data, private sector only

Source: IAB Establishment Panel, waves 1996–2010, own calculations

Fig. 2

Share of the plants which decrease, do not change or increase employment (in percent)

Notes: Weighted data, private sector only

Source: IAB Establishment Panel, waves 1996–2010, own calculations

Table 1, which illustrates the varying adjustment decision of the plants from one year to another, further underlines the relevance of non-convexity. With convex adjustment costs plants should optimally spread employment adjustment over several time periods so that adjustment takes place in every period. But Table 1 indicates that many plants which adjust (increase or decrease) employment in one year do not further adjust it in the following year.10 Of course, I need econometric analysis to identify the functional form of adjustment costs more clearly.
Table 1

Share of the plants which decrease, do not change or increase their employment if their employment decreased, did not change or increased in the previous year (in percent)

Year

Plants whose employment decreased in the previous year

Plants whose employment did not change in the previous year

Plants whose employment increased in the previous year

thereof plants, whose employment decreased

thereof plants, whose employment not chang.

thereof plants, whose employment increased

thereof plants, whose employment decreased

thereof plants, whose employment not chang.

thereof plants, whose employment increased

thereof plants, whose employment decreased

thereof plants, whose employment not chang.

thereof plants, whose employment increased

1996

33.37

47.22

19.41

18.28

68.40

13.32

27.07

48.24

24.69

1997

31.26

40.93

27.81

17.40

66.67

15.93

29.70

41.83

28.47

1998

26.78

44.38

28.84

19.67

65.26

15.07

30.71

37.85

31.44

1999

32.27

39.66

28.07

20.06

58.27

21.67

29.80

39.86

30.33

2000

29.98

44.94

25.08

19.85

63.13

17.01

37.03

38.11

24.86

2001

30.93

45.81

23.26

20.46

64.55

14.99

31.16

43.05

25.80

2002

31.88

44.43

23.69

21.57

66.10

12.33

34.14

41.43

24.42

2003

31.08

46.75

22.17

21.41

66.48

12.11

38.52

40.69

20.79

2004

31.14

47.40

21.46

19.37

68.60

12.03

34.16

41.98

23.86

2005

31.64

43.34

25.03

19.47

66.64

13.89

33.99

42.25

23.77

2006

25.24

48.66

26.10

17.55

68.05

14.40

26.32

49.41

24.28

2007

25.30

46.26

28.44

15.23

69.26

15.51

25.58

42.37

32.05

2008

25.55

48.15

26.30

15.48

69.28

15.24

26.27

39.96

33.77

2009

30.11

41.87

28.02

17.83

67.70

14.48

30.60

44.90

24.50

2010

26.95

41.36

31.68

15.52

68.77

15.71

27.91

44.85

27.25

Notes: Weighted data, private sector only

Source: IAB Establishment Panel, waves 1996–2010, own calculations

4 Econometric model

As no direct data on firms’ adjustment costs is available for Germany, the analysis of the firms’ adjustment costs structure is based on a theoretical model of dynamic labor demand. I will compare a pure convex specification for adjustment costs with a combination of a fixed and a convex structure.11 First I derive the empirical model with convex adjustment costs which I will then compare to the empirical model with fixed and convex adjustment costs. For the model with pure convex costs, I follow the work of Kölling (1998, pp. 10–22), Nickell (1986), as well as Sargent (1978, 2010) and assume labor L t , which is the only existing production factor, to be homogeneous.

The starting point of the model is the following profit equation:12
$$ \varPi=\sum_{t=0}^{\infty}{ \rho^t\biggl(a_1L_t-\frac{1}{2}a_2L_t^2 - L_tw_t - \frac{c}{2}(L_t-L_{t-1})^2 \biggr)}. $$
(1)
Π is the present value of future differences between revenues (with output following from a quadratic production function with the positive and constant parameters a 1 und a 2 and prices normalized to unity) and the sum of labor costs and convex adjustment costs (with a constant parameter c).13 ρ (0<ρ<1) denotes the firm’s discount factor. Assuming rational expectations14 profit maximization leads to the following law of motion for the firm’s employment:
$$ L_t = \gamma_1L_{t-1} + \gamma_2L_t^* + \nu_t. $$
(2)
According to Eq. (2) the number of employees in period t is a function of the optimal employment level L in period t and the employment level in the previous period L t−1. γ 1 represents a measure of the adjustment speed as γ 1 indicates how strongly L t depends on L t−1 and thus how sluggishly L t is adjusted towards \(L_{t}^{*}\) (see Kölling, 1998, p. 21). Low adjustment costs cause a high adjustment speed and result in a low value for γ 1. Finally, ν t is the residual term when estimating Eq. (2).
Following the traditional approach in the literature, Eq. (2) will be expressed with employment levels in logarithmic form.15
$$ l_t = \lambda_1l_{t-1} + \lambda_2l_t^* + \nu_t, $$
(3)
where lower-case letters represents logarithms. Yet, I still cannot estimate Eq. (3) in its current form since the data does not contain information about the optimal employment level. To solve this problem, I follow Kölling (1998, p. 132). Assuming a Cobb-Douglas production function and using the implication that in the long-run optimum the real wage equals the marginal product of labor (see Breitung, 1992, p. 144) one can show that the logarithm of the optimal employment level depends on the logarithm of the output and the logarithm of the real wage rate. After another transformation, which is obligatory because the IAB Establishment Panel does not contain information about output and real wage rate, \(l_{t}^{*}\) can be expressed as a linear function of the logarithm of the turnover and the logarithm of the nominal wage bill per employee (see Breitung, 1992, p. 170).16 In addition, further controls are included in the empirical model which is given by:
$$ l_t = \alpha_1l_{t-1} + \beta_1\mathrm{log.turnover} + \beta_2\mathrm{log.wage} + \boldsymbol{\beta} \boldsymbol{x}_t + \nu_t. $$
(4)

The vector of controls x t , which are assumed to be strictly exogenous, includes several variables for employment structure like: the share of female employees in the workforce, the share of qualified employees, the share of part-time employees, the share of fixed-term employees and the share of employees covered by social security in the regression (see Bellmann and Pahnke, 2006, p. 207; Kölling, 1998, p. 134). Additionally, I consider a dummy variable whether the managers regarded the profit situation in the previous year as very good or good, a dummy reflecting modern production technology, a dummy reflecting the existence of a works council (lagged by one year to avoid endogeneity problems), a dummy reflecting the existence of a collective agreement (lagged by one year to avoid endogeneity problems), two dummies indicating whether the managers expect an increasing or decreasing turnover and a set of dummy variables for the industry and the year.

Regarding the share of female employees, two effects in the labor demand equation are possible. On the one hand, women in stereotyped occupations (e.g., secretary) are overrepresented in small plants, which would lead to a negative coefficient. On the other hand, women are rather concentrated in the production of bulk commodities or in simple services which are carried out in bigger plants. This in turn implies a positive coefficient. There are also ambiguous expectations regarding the sign of the share of qualified employees. As they are more productive than other employees, the plant is able to produce the same output with less workers (negative coefficient). However, the higher productivity can result in higher economic success and so in more labor demand (positive coefficient). The sign of the share of part-time employees is expected to be positive, as a plant needs more employees to produce same output. The share of fixed-term employees should also has a positive effect because for fixed-term employees adjustment costs are lower, especially dismissal costs (see Goux et al., 2001, p. 548; Varejão and Portugal, 2007a, p. 159). Thus, labor demand can be higher without adjustment costs increasing too much. Both signs are possible for the share of employees covered by social security. On the one hand, these employees show higher adjustment costs compared to marginal employees. If adjustment is mainly achieved by changing the number of employees covered by social security, a higher labor demand increases costs in case of adjustment (negative coefficient). On the other hand, the employees covered by social security could have higher productivity compared to other employees and so the same effects occur as with qualified employees (positive/negative coefficient).

The dummy variable whether the managers regarded the profit situation in the previous year as very good or good is expected to have a positive sign, as plants in a good economic situation are likely to show a higher labor demand (see Bellmann and Kölling, 1997, p. 98). The same should hold for the dummy variable reflecting modern production technology, as it leads to higher productivity and thus to more labor demand. No clear effect can also be predicted for the dummy variable reflecting the existence of a works council. Following the exit-voice-approach, a works council results in a better economic situation for the plant with less fluctuation and, hence, less adjustment (see, e.g., Freeman and Medoff, 1984; Hirsch et al., 2010; Jirjahn, 2010). Thus, more labor demand and a positive coefficient can be expected. However, the works council with its codetermination rights (e.g., in case of dismissal or social plans) and rent-seeking activities may increases labor costs, especially adjustment costs (see, e.g., Addison and Teixeira, 2006; Hirsch et al., 2010; Jirjahn, 2010; Müller-Jentsch, 1997, pp. 265–272). The result would be a lower labor demand and a negative coefficient. The dummy variable reflecting the existence of a collective agreement should have similar negative effects. Further, as a collective agreement indicates higher union power, it may also lead to higher adjustment costs (see Jaramillo et al., 1993).

If the plant expects a higher turnover in the future connected with a higher labor demand, it will start the upward employment adjustment in the present period because of the convex cost structure (see Bellmann and Pahnke, 2006, p. 207). The result is a positive coefficient for the dummy variable indicating whether the managers expect increasing turnover and a negative coefficient in the decreasing case.

For the analysis of the asymmetry I estimate the following model including interaction terms17 based on Jaramillo et al. (1993) as well as Schiantarelli and Sembenelli (1993):
$$\begin{aligned} l_t =& \alpha_1l_{t-1} + \varDelta \alpha_1\delta l_{t-1} + \beta_1\mathrm{log.turnover} \\ &{} + \varDelta \beta_1\delta\mathrm{log.turnover} + \beta_2\mathrm{log.wage} \\ &{} + \varDelta \beta_2\delta\mathrm{log.wage} + \boldsymbol{\beta} \boldsymbol{x}_{t} + \varDelta \boldsymbol{\beta} \delta \boldsymbol{x}_{t} + \nu_t \end{aligned}$$
(5)
with
$$\delta = \begin{cases} 1, & \mbox{if}\ L_t > L_{t-1}\\ 0, & \mbox{else}. \end{cases} $$
Different costs for upward and downward adjustment and thus different adjustment speeds are reflected in different values for α 1. A negative Δα 1 indicates a faster adjustment in the case of upward adjustment and so higher dismissal costs compared to the costs of hiring.

As Eq. (4) is a dynamic panel model, I use an system GMM estimator (GMM-SYS/Arellano-Bover estimator) (see Arellano and Bover, 1995).18 This estimator is an extension of the difference GMM estimator (GMM-DIFF/Arellano-Bond estimator) (see Arellano and Bond, 1991). The GMM-SYS estimator uses previous levels l t−2,…,l 1 as instruments for the first differences Δl t−1 like the GMM-DIFF estimator and additionally lagged first differences Δl t−1,…,Δl 2 as instruments for the levels. Comparing the two estimators, the GMM-SYS estimator is more efficient and yields better results (see, e.g., Bond and van Reenen, 2007, p. 4452; Blundell and Bond, 1998, p. 116; Blundell and Bond, 2000, p. 339; Blundell et al., 2000). Additionally, I use the more robust two-step version of the estimator, which leads to an additional efficiency increase if the standard errors are Windmeijer-corrected (see, e.g., Bond, 2002, p. 147; Roodman, 2009, p. 97; Windmeijer, 2005, pp. 44–46).

Every plant adjusts employment according to Eq. (4) or (5) if pure convex adjustment costs are assumed. But if a fixed and convex structure is assumed, these equations are just relevant for those plants which actually decide to adjust. And not every plant selects itself in the state of employment adjustment so that Eq. (4) or (5) is not relevant for every plant. The selection process, which leads to the sample of adjusting plants, is based on the fixed cost component. Depending on fixed adjustment costs, the plant will only adjust employment if the profit gained from adjustment exceeds costs or, put differently, if the difference to the optimal level L is big enough. Hence, adjustment only occurs and plants select themselves in the state of employment adjustment if
$$ k < \bigl| L_{t-1} - L_t^* \bigr| $$
(6)
with a threshold value k. Otherwise the plant will keep the employment level of the previous period (L t =L t−1+ν t ). For fixed and convex adjustment costs, I thus arrive at a switching-regression where the inequality (6) determines whether the employment level L t is changed according to Eqs. (4) or (5), respectively, or whether the employment level L t stays constant (L t =L t−1+ν t ).19 There are different approaches estimating a switching-regression (e.g., D-method). In my analysis I use a two-step procedure according to Maddala (1994, pp. 223–228). In a first step a probit model is estimated for the selection or switching. Afterwards, in a second step the current equation—in my case Eq. (4) or (5)—is estimated with a selection term à la Heckman estimated from the probit model.20 , 21 To obtain correct standard errors, the bootstrap is used. Note that the results of this second step can be interpret in the same way as in the dynamic panel without the selection term.
The basis for the probit model is inequality (6), which determines the latent variable. The firm’s decision about employment adjustment depends on the following inequality and thus L t L t−1 if:
$$\begin{aligned} &{\bigl| L_{t-1} - L_t^* \bigr| - k > 0}\\ &{\quad \Leftrightarrow \biggl| L_{t-1} - \sum_{i}{X_i} \biggr| - k > 0} \end{aligned}$$
in which ∑ i X i are the determinants of \(L_{t}^{*}\). The relation described by Eq. (2) is also given for L t−1 and so labor demand in t−1 depends on L t−2 as well as \(L_{t-1}^{*}\).22 This leads to the following condition for L t L t−1:
$$\begin{aligned} &{\Leftrightarrow \bigl| \gamma_1L_{t-2} + \gamma_2L_{t-1}^* - L_t^* \bigr| - k > 0} \\ &{\Leftrightarrow \biggl| \gamma_1L_{t-2} + \gamma_2\sum_{i}{\varDelta X_{it-1}} - \sum_{i}{\varDelta X_{it}} \biggr| - k > 0 .} \end{aligned}$$
Besides L t−2, the decision for adjustment depends on the change of L or its determinants from the previous to the current period. In the analysis the model for the latent variable in the probit model is given by:
$$ y_{t}^* = \rho l_{t-2} + \boldsymbol{\sigma} |\triangle \boldsymbol{x}_t| + \boldsymbol{\theta} \boldsymbol{z}_t + u_t. $$
(7)
In addition to l t−2, the vector |x t | in Eq. (7) contains the absolute value of the percentage change of turnover and wage bill per employee as well as the absolute values of changes in percentage points of the various employment shares. Furthermore, |x t | contains two dummy variables indicating whether managers’ valuation of the profit situation has increased or decreased and two dummy variables indicating whether the production technology has been upgraded or downgraded. I also include two dummy variables indicating whether managers are expecting a change of turnover in the current period after expecting no change in the previous period and whether managers are expecting no change of turnover in the current period after expecting a change in the previous period. These variables represent also the exclusion restrictions. Labor demand depends on the level-variables and is not determined by the changes. Finally, the vector z t includes some of the variables from Eq. (4), which I expect to show an impact on fixed adjustment costs, too. These variables affect the threshold value k in Eq. (6). The existence of a works council or a collective agreement, which leads to higher adjustment costs, results in a higher k. Therefore, the profit gained from adjustment and so the difference \(| L_{t-1} - L_{t}^{*} |\) has to be bigger. I also include dummy variables indicating whether the managers regarded the profit situation in the previous year as very good or good, reflecting a modern production technology, indicating whether managers expect an increasing or decreasing turnover and sets of industry and year dummies.23

5 Empirical results

First, I estimate the model with pure convex adjustment costs. In doing so, I also investigate a potential asymmetry in adjustment costs. Second, I estimate the model with fixed and convex costs in a switching-regression approach. This estimation is only done for plants which actually adjust employment. Afterwards, I compare the results of both models and decide which better suits the data.24

Table 2 reports the estimation results of the model with convex, symmetric adjustment costs (specification (4)).25 The coefficient α 1 for the lagged logarithmic number of employees covered by social security has the value 0.6746 in Western Germany. It represents a median adjustment of approximately 1.8 years, implying a lower adjustment speed compared to the result of Kölling (1998, p. 143), who, analyzing West German plants during 1993–1996, finds a median adjustment of around 0.7 years.26 However, our result is in line with results from other studies for Germany. The bulk of these studies show a median adjustment between 0.7 and 7.7 years.27 Furthermore, Table 5 contains the elasticities of labor demand regarding nominal wage rate and turnover, respectively: The long-run value for the wage rate is −0.27 and for turnover 0.10. These results are also in line with other studies for Germany, which not all use dynamic labor demand models for the analysis. The share of qualified employees has a negative sign and so their higher productivity enables the plant to produce the same output with fewer people. As expected, the coefficient of the share of part-time employees is greater than zero. The plant needs more employees for the same output. Furthermore, I find a positive effect for the share of fixed-term employees as well as for the share of employees covered by social security. Moreover, a good profit situation leads to higher labor demand which is also reflected by the signs of the dummy variables for the expected turnover. In contrast, the existence of a works council reduces labor demand.
Table 2

Estimation of the basic model of dynamic labor demand with convex adjustment costsa (only private sector; 1996–2010; two-step GMM-SYS estimator; dependent variable is log number of employees covered by social security)

Explanatory variables

Western Germany

Eastern Germany

coeff.

std.error

coeff.

std.error

Lagged employment l t−1

0.6746***

0.0252

0.6600***

0.0232

Turnover (log)

0.0310***

0.0099

0.0238**

0.0110

Nom. wage bill per employee (log)

−0.0867***

0.0082

−0.0783***

0.0101

Share of female employees (in percent)

0.0002

0.0003

−0.0003

0.0003

Share of qualified employees (in percent)

−0.0013***

0.0001

−0.0014***

0.0002

Share of part-time employees (in percent)

0.0006***

0.0002

0.0011***

0.0002

Share of fixed-term employees (in percent)

0.0020***

0.0004

0.0024***

0.0004

Share of employees covered by social security (in percent)

0.0164***

0.0005

0.0202***

0.0006

Profit situation ‡(dummy: very good/good = 1)

0.0258***

0.0031

0.0259***

0.0038

Modern production technology (dummy: 1 or 2 on 5-point scale = 1)

0.0055

0.0038

0.0122**

0.0048

Works council ‡(dummy: yes = 1)

−0.0299***

0.0100

−0.0105

0.0124

Covered by collective agreement ‡(dummy: yes = 1)

0.0035

0.0054

0.0021

0.0053

Firm expects turnover increase (dummy: yes = 1)

0.0233***

0.0029

0.0399***

0.0041

Firm expects turnover reduction (dummy: yes = 1)

−0.0366***

0.0033

−0.0586***

0.0040

Constant

−0.0838

0.1505

−0.5030***

0.1590

Industry dummies

yes

 

yes

 

Year dummies

yes***

 

yes***

 

Number of observations (plant-years)

49577

 

38141

 

Wald (37)

4248.20***

 

5602.03***

 

Hansen (103)

122.5397*

 

184.8406***

 

Arellano-Bond (m1 | m2)

−12.52***

−1.47

−14,66***

1.57

Theil U

0.1180

 

0.1367

 

aThe table presents coefficients and Windmeijer-corrected standard errors. Reference categories of the dummy variable groups: no turnover change expected, agriculture and forestry, 1996 and 1997. Significance levels: p<0.1; p<0.05; p<0.01. Arellano-Bond (m1 | m2) are tests for first- and second-order serial correlation in the first differenced residuals. For the Theil U statistics the years 2008 to 2010 are predicted based on an estimation of the years 1996 to 2007. ‡Indicates that the information refers to the previous year

Source: IAB Establishment Panel, waves 1996–2010

Table 3

Estimation of the basic model of dynamic labor demand with convex adjustment costs and an asymmetric cost structurea (only private sector; 1996–2010; two-step GMM-SYS estimator; dependent variable is log number of employees covered by social security)

Explanatory variables

Western Germany

Eastern Germany

coeff.

std.error

coeff.

std.error

Lagged employment l t−1

0.7280***

0.0225

0.7535***

0.0197

l t−1 ×dummy(1=L increased between t−1 and t)

−0.0747***

0.0054

−0.0793***

0.0075

Turnover (log)

0.0108

0.0090

0.0059

0.0116

Nom. wage bill per employee (log)

−0.0535***

0.0071

−0.0606***

0.0098

Share of female employees (in percent)

0.0001

0.0002

−0.0001

0.0003

Share of qualified employees (in percent)

−0.0009***

0.0001

−0.0010***

0.0002

Share of part-time employees (in percent)

0.0005***

0.0001

0.0008***

0.0002

Share of fixed-term employees (in percent)

0.0001

0.0004

0.0001

0.0004

Share of employees covered by social security (in percent)

0.0125***

0.0004

0.0155***

0.0006

Profit situation ‡(dummy: very good/good = 1)

0.0200***

0.0030

0.0252***

0.0042

Modern production technology (dummy: 1 or 2 on 5-point scale = 1)

0.0069*

0.0036

0.0147***

0.0053

Works council ‡(dummy: yes = 1)

−0.0131

0.0102

−0.0145

0.0131

Covered by collective agreement ‡(dummy: yes = 1)

−0.0011

0.0050

−0.0003

0.0058

Firm expects turnover increase (dummy: yes = 1)

−0.0006

0.0030

0.0020

0.0047

Firm expects turnover reduction (dummy: yes = 1)

−0.0377***

0.0032

−0.0539***

0.0043

Constant

0.0850

0.1337

−0.4445***

0.1592

Industry dummies

yes

 

yes

 

Year dummies

yes***

 

yes***

 

Other interactions with dummy(1=L increased between t−1 and t)

yes***

 

yes***

 

Number of observations (plant-years)

49423

 

30317

 

Wald (74/73)

8571.57***

 

10220.42***

 

Hansen (103/101)

109.3018

 

162.172***

 

Arellano-Bond (m1 | m2)

−10.94***

−0.03

−10.35***

0.76

Theil U

0.1080

 

0.0873

 

aThe table presents coefficients and Windmeijer-corrected standard errors. Reference categories of the dummy variable groups: no turnover change expected, agriculture and forestry, 1996 and 1997 (Eastern Germany: additional 1998). Significance levels: p<0.1; p<0.05; p<0.01. In order to avoid a correlation with the error term, I use l t−2 instead of l t−1 for the interaction. The model for Eastern Germany is estimated with two lags to get an Arellano-Bond-Test which does not indicate second-order serial correlation in the first-differenced residuals. Arellano-Bond (m1 | m2) are tests for first- and second-order serial correlation in the first differenced residuals. For the Theil U statistics the years 2008 to 2010 are predicted based on an estimation of the years 1996 to 2007. ‡Indicates that the information refers to the previous year

Source: IAB Establishment Panel, waves 1996–2010

Table 2 also contains various summary statistics to assess the quality of the models estimated. The value of the Hansen test indicates a misspecification.28 However, one has to consider that the Hansen test provides no unambiguous and strong statements (see Roodman, 2009, p. 98) and that even with a positive result it is possible that the model is biased (see Wooldridge, 2010, p. 135). I continue to rely on my model because an Arellano-Bond-Test does not indicate a second-order serial correlation in the first-differenced residuals.29 The table also shows the value of the Theil U statistic as a measure for the predictive power (see Greene, 2012, p. 128). The basis for the calculation is an estimation for the period 1996–2007 which is then used to predict the years 2008–2010. A higher value indicates a lower predictive power, but a single value is not meaningful. I use the Theil U statistic to compare the predictive power of different models.

For Eastern German plants the coefficient α 1 has the value 0.6600 which implies a median adjustment after approx. 1.7 years. Apparently, the adjustment process is faster and so adjustment costs are lower in Eastern Germany compared to Western Germany, which has also been found by Bellmann and Pahnke (2006, pp. 212–213) as well as Fuchs (2010, pp. 168–169). However, the difference to Western Germany is not statistically significant as the confidence intervals overlap. The long-run elasticities in Eastern Germany are 0.07 for turnover and −0.23 for wage rate. The other coefficients are not qualitatively different to Western Germany. Only the effect for the existence of a works council is statistically insignificant for Eastern German plants, and modern production technology has a statistically significant positive sign. Apparently, plants with modern technology have higher productivity and demand more employees. Since an Arellano-Bond-Test indicates no second-order serial correlation in the first-differenced residuals, I use the model although the Hansen test indicates a misspecification.

Next, I analyze a potential asymmetry of the adjustment costs by estimating model (5) including the interaction terms for the direction of adjustment (see Table 3).30 For Western and Eastern Germany the coefficient Δα 1 is less than zero, suggesting that employment adjustment proceeds faster in case of an employment increase. Besides, all the interaction terms together are statistically significant, indicating asymmetric adjustment costs with dismissal costs exceeding hiring costs.31 Furthermore, the Theil U statistics indicate that the model with asymmetric adjustment costs has a higher predictive power.

So far, the results indicate that adjustment costs are asymmetric with dismissal costs exceeding hiring costs.32 In a next step, Table 4 presents the results for the model with fixed and convex as well as asymmetric adjustment costs.33 The results of the probit model which is estimated in the first step to calculate the selection terms are given in Table 8 in the Appendix.34 In Western Germany the coefficient α 1 has the value 0.7877, which results in a median adjustment of approximately 2.9 years. As in the pure convex case, I have evidence for asymmetric adjustment costs in Western and Eastern Germany. Thus, the 2.9 years are the median adjustment for employment decrease in Western Germany. If employment increases, the plant adjusts approximately 0.7 years faster. The corresponding values are 2.4 years (employment decrease) and 1.8 years (employment increase) for Eastern German plants and hence the difference is 0.6 years. The long-run elasticity for the wage rate is −0.19/−0.43 (employment increase/decrease) in Western Germany and −0.12/−0.76 in Eastern Germany. As the effect of turnover is statistically insignificant, I report no long-run elasticities for turnover.35 The other coefficients are qualitatively similar to the previous models, as long as they are statistically significant. Along with turnover, the share of fixed-term employees, the existence of a works council and an expected turnover increase are statistically insignificant in Western Germany. With fixed and convex, asymmetric adjustment costs, the effect of modern technology is statistically significant for Western German plants. Apart from turnover, also the statistical significance of the share of fixed-term employees (now insignificant) and an expected turnover increase (now statistically significant) also change compared to the model with symmetric convex or asymmetric convex in Eastern Germany.
Table 4

Estimation of the basic model of dynamic labor demand with fix and convex adjustment costs and an asymmetric cost structurea (only private plants which adjust their level of employment; 1996–2010; two-step GMM-SYS estimator; dependent variable is log number of employees covered by social security)

Explanatory variables

Western Germany

Eastern Germany

coeff.

std.error

coeff.

std.error

Lagged employment l t−1

0.7877***

0.0457

0.7493***

0.0582

l t−1 ×dummy(1=L increased between t−1 and t)

0.0629***

0.0090

−0.0744***

0.0158

Turnover (log)

−0.0052

0.0190

0.0186

0.0393

Nom. wage bill per employee (log)

−0.0912***

0.0172

−0.1032***

0.0250

Share of female employees (in percent)

0.0002

0.0006

−0.0003

0.0010

Share of qualified employees (in percent)

−0.0016***

0.0003

−0.0015***

0.0005

Share of part-time employees (in percent)

0.0008*

0.0004

0.0013**

0.0006

Share of fixed-term employees (in percent)

0.0001

0.0008

0.0007

0.0008

Share of employees covered by social security (in percent)

0.0162***

0.0010

0.0194***

0.0021

Profit situation ‡(dummy: very good/good = 1)

0.0195***

0.0053

0.0411***

0.0098

Modern production technology (dummy: 1 or 2 on 5-point scale = 1)

0.0116**

0.0057

0.0276**

0.0140

Works council ‡(dummy: yes = 1)

−0.0155

0.0174

−0.0153

0.0280

Covered by collective agreement ‡(dummy: yes = 1)

−0.0053

0.0110

−0.0070

0.0129

Firm expects turnover increase (dummy: yes = 1)

0.0042

0.0051

0.0195*

0.0107

Firm expects turnover reduction (dummy: yes = 1)

−0.0341***

0.0049

−0.0494***

0.0098

Constant

0.2033

0.4267

−0.9315*

0.4873

Industry dummies

yes

 

yes

 

Year dummies

yes***

 

yes

 

Selection term

yes***

 

yes**

 

Other interactions with dummy(1=L increased between t−1 and t)

yes***

 

yes***

 

Number of observations (plant-years)

28824

 

17577

 

Wald (73/70)

4280.76***

 

9928.60***

 

Hansen (103/100)

380.1639***

 

422.321***

 

Arellano-Bond (m1 | m2)

−5.91***

0.45

−6.80***

1.13

Theil U

0.0794

 

0.0841

 

aThe table presents coefficients and standard errors that are calculated from a bootstrapping with 150 replications. Reference categories of the dummy variable groups: no turnover change expected, agriculture and forestry, 1996 and 1997 (Eastern Germany: additional 1998 and 1999). Significance levels: p<0.1; p<0.05; p<0.01. In order to avoid a correlation with the error term, I use l t−2 instead of l t−1 for the interaction. The model for Eastern Germany is estimated with two lags to get an Arellano-Bond-Test which does not indicate second-order serial correlation in the first-differenced residuals. Arellano-Bond (m1 | m2) are tests for first- and second-order serial correlation in the first differenced residuals. For the Theil U statistics the years 2008 to 2010 are predicted based on an estimation of the years 1996 to 2007. ‡Indicates that the information refers to the previous year

Source: IAB Establishment Panel, waves 1996–2010

Coming back to the question whether the adjustment costs are purely convex or fixed and convex, I have no straightforward test to answer this question. Yet, my analysis gives me some important hints in favor of a fixed and convex specification. First of all, the selection terms are statistically significant in Western and Eastern Germany meaning that selection in the state of employment adjustment plays a role. Furthermore, a model with fixed and convex costs has a higher predictive power (Theil U statistic).36 I also find a higher predictive power assuming pure convex costs if the model is estimated just for plants which actually adjust employment. However, if only these plants are considered, the selection term has to be included, resulting in my model with fixed and convex adjustment costs. Based on all this evidence I prefer a fixed and convex specification instead of a pure convex one. The result of asymmetric adjustment costs does not depend on the assumption of purely convex or fixed and convex cost structure.37 , 38

Table 5 summarizes the main results for the adjustment coefficient and elasticities of the several models in this study. As mentioned already, the values are in line with previous studies for Germany such as Addison and Teixeira (2005), Bellmann and Pahnke (2006), Bohachova et al. (2011), Breitung (1992), Buch and Lipponer (2010), Flaig and Rottmann (2001), Flaig and Steiner (1989), Franz and König (1986), Fuchs (2010), Koellreuter (1980), Kölling (1998), Pfeiffer (1999) as well as Rottmann and Ruschinski (1998). These studies differ in database, observation period, observed regions, analyzed sectors, estimation approaches and the specification of adjustment costs. While Flaig and Rottmann (2001), Flaig and Steiner (1989), Koellreuter (1980), as well as Pfeiffer (1999) use a static estimation approach, other studies employ a dynamic approach. My study is the only existing one apart from Kölling (1998) that allows for asymmetric adjustment costs. In addition, it extends the sparse literature analyzing dynamic labor demand models for eastern Germany by Fuchs (2010) and by Pfeiffer (1999).
Table 5

Overview of the main results of several models

Model

Data

Specification of the adjustment costs

Adjustment coefficient (α 1)

Wage elasticity (short-/long-term)

Turnover elasticity (short-/long-term)a

Table 2

Western Germany; 1996–2010

convex and symmetric

0.675

−0.09/−0.27

0.03/0.10

Eastern Germany; 1996–2010

convex and symmetric

0.660

−0.08/−0.23

0.02/0.07

Table 3

Western Germany; 1996–2010

convex and asymmetric

0.653b

−0.05/−0.15b

(0.04/0.12)b

0.728c

−0.05/-0.20c

(0.01/0.04)c

Eastern Germany; 1996–2010

convex and asymmetric

0.674b

−0.01/−0.04b

(0.03/0.11)b

0.754c

−0.06/−0.34c

(0.01/0.03)c

Table 4

Western Germany; 1996–2010

fix, convex and asymmetric

0.725b

−0.05/−0.19b

(0.02/0.06)b

0.787c

−0.09/−0.43c

(−0.01/−0.02)c

Eastern Germany; 1996–2010

fix, convex and asymmetric

0.675b

−0.03/–0.12b

(0.02/0.09)b

0.749c

−0.10/−0.76c

(0.02/0.14)c

aStatistically insignificant elasticities are in parenthesis

bPlants with an employment increase

cPlants with an employment decrease

Source: IAB Establishment Panel, waves 1996–2010; own calculations

6 Changing adjustment behavior over time

Our observation period from 1996 to 2010 contains two business cycles and thus several economic up- and downturns.39 The first cycle comprises the years 1996 to 2003 and the second one starts in 2004. With these two cycles it is possible to investigate whether firms’ adjustment behavior has changed over time. For such an analysis I need to compare entire business cycles instead of single years. If two single years are compared, these two years could originate from different economic phases of the business cycle. This may lead to a comparison of employment adjustment in economic upturn (predominantly hirings) with that in economic downturns (predominantly firings). This could result in a difference in the estimated effects caused by asymmetry and not just because of a changing over time.

I find evidence for a change in adjustment behavior of German plants in several studies. The German Council of Economic Experts compares firms’ adjustment behavior and the labor market reaction of three different economic upturns (1993II–1995II; 1999II–2001I; 2004IV–2007II). Their results indicate a change in the adjustment of employment. Especially in the last upturn the economic recovery was employment-intensive and many full-time jobs covered by social security were created (see GCEE, 2007, items 482–492). The flexibility and the dynamic of the labor market increased, which was—among other things—the result of labor market reforms in the years 2003 to 2005. This is also found by Gartner and Klinger (2010), who compare the economic upturns 1998II–2001I and 2004IV–2008I as well as the economic downturns 2001II–2004III and 2008II–2010II. Furthermore, they find a lower turnover rate of employment in the second business cycle (see Gartner and Klinger, 2010, p. 729). A change towards a lower fluctuation in the number of employees is also found by Burda and Hunt (2011) who compare the recession 2008–2009 with previous ones, Herzog-Stein and Seifert (2010) who compare the recession 2008–2009 with the recession 1973–1975, as well as Rothe (2009) who compares the upturns 1998I–2002IV, 2006I–2008II and the downturns in between. Apart from less adjustment activity with respect to the number of employees, a greater adjustment of working hours can be discovered due to better flexibility (see Burda and Hunt, 2011), although the instrument of working time adjustment was also used in previous recessions (see Herzog-Stein and Seifert, 2010, pp. 553–555).

All in all, there is clear evidence of changing adjustment behavior. But except for Burda and Hunt (2011) who also compare current employment levels with predicted ones, all the studies mentioned above use descriptive analyses of aggregated data. In contrast, I apply an econometric approach with establishment data. Using the dynamic labor demand model from Sect. 5 with fixed, convex, and asymmetric adjustment costs, I analyze a possible change in adjustment behavior. I do so by interacting the lagged logarithmic number of employees covered by social security with a dummy variable indicating whether the observation is from the first business cycle from 1996 to 2003. I restrict the interaction on the lagged logarithmic number of employees covered by social security and interact not all regressor variables because a possible change in firms’ labor demand, which would be analyzed in case of interacting all regressor variables, is not part of this analysis. This paper rather focuses on a possible change in adjustment behavior reflected by the adjustment speed.40

Table 6 reports the results of this estimation. The interaction term is significantly positive in both Western and Eastern Germany. Based on the coefficients, the median adjustment of Western German plants is approximately 0.14/0.22 years (employment increase/employment decrease) larger in the first business cycle compared with the second business cycle. The corresponding values are 0.22/0.34 years for Eastern Germany. Compared with the analysis without interaction term (see Table 4), a few differences can be found. The coefficients for adjustment, α 1, are lower if the interaction term is included. Furthermore, the short-run elasticity of labor demand with regard to wage rate has decreased in Western Germany. The statistical significance level for the coefficients has changed only marginally, except for the dummy variable for the modern production technology in Eastern Germany that is now insignificant.
Table 6

Estimation of the basic model of dynamic labor demand with fix, convex and asymmetric adjustment costs allowing for different adjustment behavior in different business cyclesa (only private plants which adjust their level of employment; 1996–2010; two-step GMM-SYS estimator; dependent variable is log number of employees covered by social security)

Explanatory variables

Western Germany

Eastern Germany

coeff.

std.error

coeff.

std.error

Lagged employment l t−1

0.7210***

0.0454

0.6831***

0.0585

l t−1 ×dummy(1=L increased between t−1 and t)

−0.0626***

0.0092

−0.0771***

0.0161

l t−1 ×dummy(1=obs. from 1996–2003)

0.0221***

0.0035

0.0424***

0.0090

Turnover (log)

0.0170

0.0190

0.0505

0.0402

Nom. wage bill per employee (log)

−0.0685***

0.0172

−0.1021***

0.0257

Share of female employees (in percent)

0.0003

0.0006

−0.0001

0.0011

Share of qualified employees (in percent)

−0.0014***

0.0003

−0.0013***

0.0005

Share of part-time employees (in percent)

0.0010**

0.0004

0.0015**

0.0006

Share of fixed-term employees (in percent)

0.0004

0.0008

0.0007

0.0008

Share of employees covered by social security (in percent)

0.0159***

0.0010

0.0182***

0.0021

Profit situation ‡(dummy: very good/good = 1)

0.0173***

0.0052

0.0380***

0.0095

Modern production technology (dummy: 1 or 2 on 5-point scale = 1)

0.0136**

0.0057

0.0201

0.0130

Works council ‡(dummy: yes = 1)

−0.0133

0.0172

−0.0242

0.0282

Covered by collective agreement ‡(dummy: yes = 1)

−0.0062

0.0113

−0.0005

0.0127

Firm expects turnover increase (dummy: yes = 1)

0.0050

0.0051

0.0200*

0.0106

Firm expects turnover reduction (dummy: yes = 1)

−0.0315***

0.0049

−0.0464***

0.0097

Constant

−0.0809

0.4241

−1.0865**

0.4894

Industry dummies

yes

 

yes

 

Year dummies

yes***

 

yes***

 

Selection term

yes***

 

yes**

 

Other interactions with dummy(1=L increased between t−1 and t)

yes***

 

yes***

 

Number of observations (plant-years)

28824

 

17577

 

Wald (74/71)

4568.55***

 

11215.95***

 

Hansen (103/100)

265.3168***

 

250.9633***

 

Arellano-Bond (m1 | m2)

−5.63***

0.43

−6.67***

1.22

aThe table presents coefficients and standard errors that are calculated from a bootstrapping with 150 replications. Reference categories of the dummy variable groups: no turnover change expected, agriculture and forestry, 1996 and 1997 (Eastern Germany: additional 1998 and 1999). Significance levels: p<0.1; p<0.05; p<0.01. In order to avoid a correlation with the error term, I use l t−2 instead of l t−1 for the interaction. The model for Eastern Germany is estimated with two lags to get an Arellano-Bond-Test which does not indicate second-order serial correlation in the first-differenced residuals. Arellano-Bond (m1 | m2) are tests for first- and second-order serial correlation in the first differenced residuals. ‡Indicates that the information refers to the previous year

Source: IAB Establishment Panel, waves 1996–2010

These differences in firms’ adjustment behavior between the business cycles can also be found in an analysis with pure convex, symmetric or asymmetric adjustment costs (results are available on request).41 Thus, the assumption on the functional form does not drive this result. The employment adjustment in the second business cycle proceeds at a higher speed.42 The plants spread the adjustment over a shorter period of time as it is indicated by the lower median adjustment. This might be evidence of lower adjustment costs. A higher flexibility in the adjustment of employment can be a reason for that. However, my results contrast with studies mentioned above based on a descriptive analysis of aggregated data. These studies find a lower fluctuation in recent years. An explanation might be that some plants adjust with a higher speed and at the same time fewer plants decide to adjust at all. But this explanation is not tenable in light of the analysis with assumed pure convex and asymmetric adjustment costs because all plants, adjusting or not, are included. Fewer plants with employment adjustment in the second cycle would lead to a negative interaction term which I do not observe. Still, there is an explanation for the differences between the results of my study and the results of the studies mentioned above. The opportunity of working time adjustment improved over time as a result, for example, of the increased use of working time accounts (see Burda and Hunt, 2011, p. 299). As this has made working time adjustment easier, less adjustment of the number of employees is needed. However, once plants have to adjust employment, they now adjust more quickly because the possibility of employment adjustment has also improved in the course of several labor market reforms (see Herzog-Stein and Seifert, 2010, p. 552).

In addition to better opportunities for working time adjustment43, there are also changes of other labor market institutions which affect firms’ adjustment behavior and therefore may explain the empirical result of a faster adjustment. In 2004 the firm-size threshold of the German dismissal protection law was increased from 5 to 10 employees (in the legal sense of the German dismissal protection law). The result was decreased dismissal protection for employees in firms with size of 10 and less, although incumbent employees in these firms still had their prior dismissal protection (see Bauernschuster, 2013, p. 296). Less dismissal protection results in decreased dismissal costs for these small firms which should lead to a faster adjustment of the number of employees. This can also explain the higher adjustment speed in the second business cycle. But it is not totally convincing. The dismissal protection just changed for firms with 6 to 10 employees whereas there were no changes for the bulk of firms. Furthermore, empirical evidence for Germany does not show unambiguously that less dismissal protection leads to more and faster employment adjustment (see, e.g., Abraham and Houseman, 1994; Bauer et al., 2007; Buechtemann, 1993; Schramm and Endemann, 2010). Moreover, a robustness check without small plants (less than 30 employees) shows that the change in adjustment speed is not due to small plants.44 If only bigger plants are considered in the analysis, the interaction term is also statistically significant and thus indicates a change in adjustment speed. Therefore, the change in dismissal protection cannot explain the increased adjustment speed.

Changes in collective bargaining might additionally explain the empirical results. Since the middle of the 1990s there is a decline in collective agreement coverage in Germany observable (see Ellguth and Kohaut, 2011b, p. 245). As some aspects of collective agreements (such as severance pay and specific employment protection) result in higher adjustment costs, the decline of collective agreement coverage leads to lower adjustment costs. This could explain the higher adjustment speed since the coverage rate of sectoral bargaining was on average 9 percentage points lower in the second business cycle. However, an empirical investigation whether plants without a collective agreement adjust their employment more quickly shows no statistical significant effect of a collective agreement on adjustment speed.45 Therefore, the decline of collective agreement coverage cannot explain the increased adjustment speed either.

Another change regarding collective bargaining in Germany is the increased use of collective opening clauses which relate to different aspects of the sectoral collective agreements (see Brändle et al., 2011; Kohaut and Schnabel, 2007). Some clauses lead to more flexibility in working time adjustment and have the same effects on firms’ adjustment behavior as improved opportunity of working time adjustment in general. But opening clauses also increase the flexibility of wages. Therefore, a firm can adjust wages instead of adjusting the number of employees to improve profits in a bad economic situation. Although this an explanation for the results of the mentioned studies using aggregated data, it does not lead to a faster adjustment of the number of employees. However, the increased use of opening clauses started in the middle of the 1990s and is thus not specific to the second business cycle.

Firms’ adjustment behavior is also affected by changes in temporary agency employment. Since the reform of the Temporary Employment Agencies Act (Arbeitnehmerüberlassungsgesetz) in 2003 the use of temporary agency employment is eased for plants and the number of temporary agency employees has increased (see, e.g., Antoni and Jahn, 2009; Hirsch and Müller, 2012). Temporary agency employment is an alternative instrument for the adjustment of firms’ labor volume. If it is easier to use temporary agency employment, less adjustment of the number of employees covered by social security is needed. This can also explain the aggregate results, but should not directly affect the adjustment speed.

These considerations suggest that some of the changes of labor market institutions in Germany can explain the aggregate picture of less adjustment of the number of employees but not directly the increased adjustment speed. However, the faster adjustment can indirectly be the result of the institutional changes. Most of these changes imply that less adjustment of the number of employees is needed so that the firms do not have to hire and dismiss so many people at once. The results are lower (convex) adjustment costs due to the convexity of adjustment costs. Moreover, if only a few employees are affected, the works council may not interfere strongly in the dismissal, which again decreases adjustment costs. These various kinds of lower costs result in a faster adjustment of the number of employees.

7 Conclusions

Using a large and representative establishment data set for Germany, I investigate firms’ labor adjustment behavior in terms of the number of employees covered by social security. The results of my empirical analysis indicate that adjustment costs are characterized by a convex structure including a fixed component. Thus firms do not adjust employment permanently, and there are periods with no employment adjustment. Furthermore, the cost structure is found to be asymmetric: In case of an employment increase, the adjustment runs faster compared with a decrease suggesting that dismissal costs exceed the costs of hiring. These results are in line with the existing literature. Based on my preferred baseline model the long-term wage elasticity is −0.19 in case of an employment increase and −0.43 in case of an employment decrease in Western Germany. The corresponding values are −0.12 and −0.76 for Eastern Germany. Thus the elasticities are higher (in absolute terms) in case of a reduction in employment.

Moreover, I identify a change in firms’ employment adjustment over time. The adjustment was spread over a longer period of time in the business cycle from 1996 to 2003 and thus the adjustment speed was lower compared to the following business cycle from 2004 to 2010. This indicates lower adjustment costs in the business cycle after 2003, which might be related to recent reforms and more flexibility in the labor market (e.g., better opportunities for working time adjustment, easier use of temporary agency employment). Nowadays, the plants seem to be able to adjust their employment covered by social security more quickly.

For a further investigation of labor adjustment, I would need information on working time to include this adjustment dimension in the analysis, thus providing a more complete picture of firms’ labor adjustment. Several studies have shown an intensified use of working time adjustment in the recent past, which may also affect the change in the adjustment of the number of employees. Because of recent reforms of temporary agency employment in Germany, this type of employment may have become more important for firms’ employment adjustment. The faster adjustment of the employment covered by social security in the second business cycle found in this study may reflect this, among other things. Future research should thus take temporary agency employment explicitly into account and analyze its role as an alternative adjustment instrument.

Executive summary

Over the business cycle, firms have to adjust their labor volume. This employment adjustment causes adjustment costs, which firms have to take into account. Their adjustment behavior depends on the functional form of these adjustment costs. One can distinguish three basic specifications: fixed, linear and convex. A combination of these specifications is also possible and in the existing literature there is a predominance of such a combined structure for adjustment costs. However, this has not been shown to extend to Germany yet. Furthermore, adjustment costs are asymmetric. Studies show for Germany that dismissal costs exceed hiring costs.

There are no direct data on firms’ adjustment costs available for Germany. Thus, I use a dynamic labor demand model for the analysis of the functional form of firms’ adjustment costs in Germany. I compare a pure convex specification for adjustment costs with a combination of a fixed and a convex structure. The data used for the analysis are the waves 1996 until 2010 of the IAB Establishment Panel. Because of limitations in data, the empirical investigation can only analyze the adjustment of the number of employees and has to neglect the working time dimension. Moreover, only the number of employees covered by social security are considered.

The descriptive results show that every year plants increase or decrease employment, regardless of the business cycle phase. However, more than 50 percent of the plants do not change their employment level over the year. Furthermore, there is a first evidence in favor of non-convex adjustment costs. Conducting a dynamic panel analysis and a switching regression, my empirical analysis provide further evidence in favor of non-convex adjustment costs. Although there is no straightforward test to answer the question whether the adjustment costs are purely convex or fixed and convex, my analysis gives me some important hints in favor of a fixed and convex specification. Moreover, the empirical results indicate asymmetric adjustment costs in Germany with dismissal costs exceeding the costs of hiring.

Furthermore, I investigate whether firms’ adjustment behavior has changed over time between 1996 and 2010. Several studies for Germany have shown that labor market flexibility increased and the turnover rate of employment decreased over time. Besides less adjustment activity with regard to the number of employees, a greater adjustment of working time can be discovered. There is a clear evidence of changing adjustment behavior, but the previous studies contain only descriptive analyses of aggregated data. In contrast, I use an econometric approach with establishment data. The results show that the adjustment speed increased over time. Plants adjust their employment covered by social security more quickly in the business cycle from 2004 to 2010 compared to the previous business cycle from 1996 to 2003. This indicates lower adjustment costs in the business cycle after 2003, which might be related to recent reforms and more flexibility in the labor market (e.g., better opportunities for working time adjustment, easier use of temporary agency employment).

Future research should take the working time dimension into account if data provide this information. This would result in a more complete picture of firms’ labor adjustment. One should also consider temporary agency employment explicitly and analyze its role as an alternative adjustment instrument.

Kurzfassung

Ein Betrieb muss im Konjunkturverlauf immer wieder seine Beschäftigung anpassen. Bei dieser Anpassung fallen Kosten an, die der Betrieb zu berücksichtigen hat. Dabei wird das genaue Anpassungsverhalten der Betriebe durch die funktionale Form der Anpassungskosten bestimmt. Es lassen sich drei Grundformen unterscheiden: fix, linear und konvex. Darüber hinaus ist auch eine Kombination der drei Grundformen möglich. Ergebnis früherer Studien ist, dass solch eine kombinierte Struktur für die betrieblichen Anpassungskosten zu präferieren ist. Dieses konnte jedoch noch nicht für Deutschland gezeigt werden. Des Weiteren sind die Anpassungskosten asymmetrisch, wobei sich für Deutschland zeigt, dass die Entlassungskosten größer sind als die Einstellungskosten.

Für Deutschland sind keine direkten Daten für die betrieblichen Anpassungskosten verfügbar. Aus diesem Grund erfolgt die Analyse auf Basis eines Modells der dynamischen Arbeitsnachfrage. Dazu werden zwei Modelle untersucht, das eine basiert auf der Annahme rein konvexer Anpassungskosten und für das andere wird ein fixe und konvexe Spezifikation angenommen. Dabei wird überprüft, welches Modell zu präferieren ist. Die Basis für die empirische Analyse ist das IAB-Betriebspanel, aus dem die Beobachtungen der Jahre 1996 bis 2010 verwendet werden. Der Datensatz enthält jedoch keine belastbaren Informationen zur Arbeitszeit, so dass nur eine Anpassung der Zahl der Beschäftigten berücksichtigt wird. Außerdem werden nur die sozialversicherungspflichtig Beschäftigten betrachtet.

Ein Ergebnis der deskriptiven Analyse ist, dass es in jedem Jahr unabhängig von der aktuellen konjunkturellen Lage Betriebe gibt, die ihre Beschäftigung erhöhen oder verringern. Darüber hinaus passen aber mehr als 50 Prozent der Betriebe jedes Jahr ihre Beschäftigungshöhe nicht an. Außerdem gibt es erste Hinweise für die Existenz nicht-konvexer Anpassungskosten. Die empirischen Ergebnisse, die von dynamischen Panelschätzungen und Switching-Regressionen stammen, beinhalten ebenfalls Indizien dafür, dass nicht-konvexe Anpassungskosten relevant sind. Für die Beantwortung der Frage, ob das Modell basierend auf der Annahme rein konvexer Anpassungskosten oder das Modell basierend auf einer kombinierten Kostenstruktur zu präferieren ist, existiert allerdings kein eindeutiger Test. Aber mehrere konkrete Hinweise deuten darauf hin, dass die funktionale Form der Anpassungskosten eher durch Kombination von einer fixen und einer quadratischen Komponente gegeben ist. Außerdem zeigen die Ergebnisse, dass die betrieblichen Anpassungskosten asymmetrisch sind mit Entlassungskosten, die die Einstellungskosten übersteigen.

Des Weiteren erfolgt eine Untersuchung, ob sich das betriebliche Anpassungsverhalten im Zeitverlauf von 1996 bis 2010 verändert hat. Frühere Studien für Deutschland zeigen, dass der Arbeitsmarkt in den letzten Jahren flexibler geworden ist. Die Fluktuation der Beschäftigung hat jedoch abgenommen. Während es in den letzen Jahren eine vermehrte Anpassung der Arbeitsstunden gab, wurde eine Anpassung der Zahl der Beschäftigten nur in einem geringeren Maße vorgenommen. Insgesamt deutet die bisherige empirische Evidenz auf unterschiedliche Anpassungsverhalten in den verschiedenen Konjunkturzyklen hin. Diese Evidenz beruht jedoch nur auf deskriptiven Analysen aggregierter Daten. Im Gegensatz dazu, werden in dieser Arbeit disaggregierte Betriebsdaten empirisch untersucht. Es zeigt sich eine Zunahme der Anpassungsgeschwindigkeit. Die Betriebe haben die Zahl ihrer sozialversicherungspflichtig Beschäftigten im zweiten beobachteten Konjunkturzyklus von 2004 bis 2010 schneller angepasst als im ersten Zyklus von 1996 bis 2003. Dieses deutet auf geringere betriebliche Anpassungskosten im Konjunkturzyklus nach 2003 hin. Als Begründung für diese Entwicklung kommen u.a. Reformen am deutschen Arbeitsmarkt in Betracht, die die Möglichkeiten zur Arbeitszeitanpassung und den Einsatz von Leiharbeit betreffen.

Gegenstand zukünftiger Forschung sollte die betriebliche Anpassung der Arbeitszeit sein, sofern es es die Datengrundlage ermöglicht. Damit wären konkrete Aussagen über die betriebliche Anpassung des gesamten Arbeitsvolumens möglich. Des Weiteren sollte man auch die Leiharbeit berücksichtigen und deren Rolle als alternative Möglichkeit zur Beschäftigungsanpassung untersuchen.

Footnotes
1

For details about fix adjustment costs I refer to Hamermesh (1989, 1990).

 
2

The result of fixed adjustment costs are periods with adjustment and periods with no adjustment. Therefore Hamermesh (1990, p. 96) calls this behavior ‘bang-bang adjustment’.

 
3

Nickell (1984, p. 546) finds that the adjustment has a lag, which is just the case in the presence of convex adjustment costs.

 
4

Vermeulen (2006, p. 11) confirms the dominance of a combination structure for adjustment costs in the existing literature, while only some of these studies use dynamic labor demand models for the analysis.

 
5

Muehlemann and Pfeifer (2013) also provide results for the functional form of adjustment costs in Germany, but their analysis focusses on hiring costs of skilled workers. They find a convex structure for these costs.

 
6

For a detailed description of this data set see Bellmann et al. (2002), Fischer et al. (2009), and Kölling (2000).

 
7

Bellmann and Pahnke (2006) also use the number of employees covered by social security only. Nevertheless as a robustness check (results are available on request) I also carry out the analysis with all employees, which does not change my insights.

 
8

Increase or decrease of the employment means a change of the number of employees covered by social security from the previous to the present year.

 
9

This evidence may be not completely convincing. One could think that no employment adjustment can also be optimal in the presence of convex adjustment costs if the optimum does not change. However, the optimum will not be reached in finite time. Furthermore, it is plausible that the optimal employment level changes at least within two years. Therefore, no employment adjustment two years in a row should not be observed in the presence of pure convex adjustment costs. Yet, Table 1 shows the opposite.

 
10

One could argue that results coming from annual data do not show permanent adjustment and thus cannot serve as evidence for pure convex costs because employment adjustment towards the optimum is already achieved within a year. However, the economic environment and thus the optimal employment level changes at least annually. Therefore, a plant might switch from increasing employment to decreasing, but should not stop adjustment.

 
11

A separate analysis of a linear form is not required because its effect on adjustment behavior is nested in the fixed and convex form (see Gavosto and Sestito, 1993, p. 437).

 
12

For the profit equation some restrictive assumptions are made regarding the production function: the production function is quadratic and uses homogeneous labor as the only input factor in the short-run. While a wide range of production functions have been used in the literature, a quadratic production function was used, e.g., by Bentolila and Saint-Paul (1994), Hamermesh (1995), Kölling (1998), Sargent (1978). Note that the exact specification of the production function does not play a role for general statements about firms’ adjustment behavior (see Kölling, 1998, pp. 11–12). Furthermore, the fact that capital is not considered (see Hamermesh, 1995, p. 624) and that labor is homogeneous (see Kölling, 1998, p. 61) does not bias the results regarding firms’ adjustment behavior.

 
13

The factor \(\frac{1}{2}\) in the formulas for production and adjustment costs simplifies optimization.

 
14

Equation (1) is maximized for the derivation of Eq. (2). The result of this profit maximization is an Euler equation, which contains expectations about future labor demand (not shown in this paper). In this context rational expectations are assumed, which is a suitable and often used assumption (see Kölling, 1998, p. 148; Bresson et al., 1992, p. 361).

 
15

Clearly, Eq. (3) does not follow directly from Eq. (2). I use the logarithmic expression in the tradition of the previous studies, e.g., Arellano and Bond (1991), Bellmann and Pahnke (2006), Bohachova et al. (2011), Breitung (1992, 1994), Buch and Lipponer (2010), Cooper and Willis (2009), FitzRoy and Funke (1998), Funke et al. (1998), Kölling (1998), Lapatinas (2009) and Rottmann and Ruschinski (1998).

 
16

For details about the algebraic transformation I refer to Kölling (1998, pp. 132–134).

 
17

In the empirical analysis and interpretation of the results it is important to note that the interaction terms might be affected by endogeneity since the dummy variable depends on firms’ employment adjustment, which determines also l t . Therefore, a new employment level l t after adjustment might also affects the dummy variable. But Jaramillo et al. (1993, p. 642) consider this with reference to Heckman (1978) not as a problem due to the use of a dynamic panel estimation according to Arellano and Bond (1991). I use a dynamic panel as well with a similar approach.

 
18

For details about the analysis of dynamic panel models I refer to (Baltagi, 2008, Chap. 8).

 
19

For details on switching-regressions see, e.g., Cameron and Trivedi (2005, pp. 555–557), Goldfeld and Quandt (1976) as well as Maddala (1986).

 
20

There are other studies which analyze fixed adjustment costs by using a Heckman approach (see, e.g., Nilsen et al., 2007). But Nilsen et al. (2007), for instance, do not use a dynamic panel model as the second step.

 
21

For details on sample selection and dynamic panel data models and applications see, e.g., Garcia et al. (2007), Jiménez-Martín (2006), Jiménez-Martín and Garcia (2010) as well as Lodigiani and Salomone (2012).

 
22

The reason for the use of Eq. (2) although L t−1 and X i are both observed separately is technical simplification. Note that the selection depends not on L t−1 and X i as single variables but on the difference of these two, which is not directly given in the data and not easy to generate.

 
23

The panel nature of the data is considered by using year dummies and clustering standard errors at establishment level.

 
24

Because of the existing general differences between the labor markets in Western and Eastern Germany I will conduct the econometric analysis separately for the two German regions.

 
25

Summary statistics are reported in Table 7 in the Appendix.

 
26

The median adjustment is the time span the plant needs to do half of the adjustment towards the optimum. It is based on the equation \(\alpha_{1}^{t} = 0.5\), which is solved for t (see Hamermesh, 1993a, p. 248) and which has the dimension ‘years’. For an alternative interpretation of α 1 see Funke et al. (1998, p. 231). (1−α 1) is the share of the adjustment towards the optimum, occurring between the previous and the current period.

 
27

The reasons for the wide range of results might be, among other things, a different observation period or a different estimation method.

 
28

In order to improve the Hansen test, I ran several alternative models. An estimation of the models with two lags still leads to a Hansen test which indicates a misspecification. Another reason for the indication of misspecification might be the assumption of strict exogeneity for all regressor variables, especially turnover, wage and the variables for the employment structure. But assuming endogeneity for turnover, wage and the variables for the employment structure still results in a Hansen test that indicates a misspecification.

 
29

Fuchs (2010, p. 123) uses the same argument for a further analysis of her (seemingly misspecified) model. All Arellano-Bond-Tests in my study indicate no second-order serial correlation in the first-differenced residuals unless otherwise mentioned.

 
30

The model for Eastern Germany is estimated with l t−1 and additional l t−2 such that the Arellano-Bond-Test does not indicate a second-order serial correlation in the first-differenced residuals.

 
31

Note that the analysis is not a clear comparison of plants increasing employment with plants decreasing employment because the reference category for the dummy variable are plants that decrease or do not change employment. Therefore as a robustness check, I also estimate the model with a dummy variable indicating whether the plant decreases employment (results are available on request). This also results in estimates indicating that dismissal costs exceeds hiring costs.

 
32

More precisely, as the analysis is based on all separations, it is not only dismissal costs but separation costs in total which exceed hiring costs.

 
33

Only plants which adjust their employment (change their number of employees covered by social security from the previous to the present year) are considered in this analysis. This sample selection is corrected by including a selection term in the model (see section 4).

 
34

As a robustness check, I estimated the probit model also with l t−1 instead of l t−2 as well as with the change of the employment shares from the pre-previous to the previous period instead of the change from the previous to the current one. But these variations lead to a lower predictive power in the probit model, do not really result in a different outcome for the second step and the Hansen test still indicates a misspecification. Using neither l t−1 nor l t−2 the Hansen test is getting even worse. I also estimated the probit model without the level-variables, although some of these are statistically significant (see Table 8 in the Appendix). Again, this does neither improve the Hansen test nor the predictive power of the probit model.

 
35

The insignificant results for turnover can be due to banks and insurances where turnover cannot be measured in the standard way. But a robustness check without this sector does not lead to a statistically significant effect of turnover (results are available on request).

 
36

Note that the Theil U statistic is used as a measure for the predictive power in the same way as in the analysis of the model with purely convex adjustment costs.

 
37

I also estimate the models separately for the production and the service sector (results are available on request). Both estimations indicate fixed and convex, asymmetric adjustment costs. Furthermore, the elasticities for turnover and wage in the production sector are in line with Flaig and Rottmann (2001) as well as Pfeiffer (1999).

 
38

The functional form of firms’ adjustment costs varies with plant size. While I also prefer a fixed and convex, asymmetric specification for smaller plants (less than 100 employees), the results of an empirical analysis for bigger plants (100 and more employees) indicate that adjustment costs are characterized by a purely convex, asymmetric structure (results are available on request). This is in line with the results of Del Boca and Rota (1998) for Italy.

 
39

In Germany, no clear definition and scheduling of economic phases exists. For that reason there is no comprehensive classification of the years 1996 to 2010. Based on the development of the GDP, the Ifo Business Climate Index and findings of the German Council of Economic Experts as well as the Federal Statistical Office I apply the following classification: 1996–2000, 2004–2007 and 2010 upturns; 2001–2003 and 2008–2009 downturns.

 
40

Although it is not in the focus of this analysis, I also estimated the model which contains interactions of all regressor variables with the dummy variable indicating whether the observation is from the first business cycle (results are available on request). However, these interactions are not jointly statistically significant. Thus, this result strengthens my decision to restrict the interaction on the lagged logarithmic number of employees covered by social security.

 
41

In Western Germany the interaction term is only statistically significant in the analysis with pure convex, symmetric adjustment costs if year dummies are not considered in the analysis.

 
42

Strictly speaking a third business cycle starts with the year 2010. Therefore, the analysis is repeated excluding the year 2010 (results are available on request). The results do not change. An analysis without the year 2010 also indicates a faster adjustment in the second business cycle.

 
43

The empirical relevance of this explanation cannot be checked because the data set does not provide clear information about working hours.

 
44

Results are available on request.

 
45

Results are available on request.

 

Notes

Declarations

Authors’ Affiliations

(1)
Lehrstuhl für Arbeitsmarkt- und Regionalpolitik, Friedrich-Alexander-Universität Erlangen-Nürnberg

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