# «by Christian Pfeifer University of Lüneburg Working Paper Series in Economics No. 152 November 2009 ...»

**Effective Working Hours and Wages:**

The Case of Downward Adjustment via Paid

Absenteeism

by

Christian Pfeifer

University of Lüneburg

Working Paper Series in Economics

No. 152

November 2009

www.leuphana.de/institute/ivwl/publikationen/working-papers.html

ISSN 1860 - 5508

**Effective Working Hours and Wages:**

The Case of Downward Adjustment via Paid Absenteeism

Christian Pfeifer

Leuphana University Lüneburg and IZA

(30.11.2009) Abstract This paper compares contractual with effective working hours and wages, respectively.

Effective working hours are defined as contractual working hours minus absent working hours. This approach takes into account workers' downward adjustment of working time via paid absenteeism if working time constraints are present, which induce workers to accept contracts with larger than their optimal choice of working hours. A German personnel data set, which contains precise information on wages as well as working and absence hours, is used to assess the impact of such downward adjustment on wage inequality and wage differentials (gender, schooling, age).

JEL Classification: J22, J31 Keywords: absenteeism, earnings, inequality, wage differentials, working hours Corresponding author: Christian Pfeifer, Institute of Economics, Leuphana University Lüneburg, Scharnhorststr. 1, 21335 Lüneburg, Germany; phone: +49-4131-6772301; e-mail: pfeifer@leuphana.de.

Acknowledgements: This work was financially supported by the VolkswagenStiftung. I thank Nils Braakmann, Olaf Hübler, and participants of a research seminar in Lüneburg for their comments.

1. Introduction One of the most frequently used application in econometrics is the estimation of earnings functions to assess wage differentials. The dependent variable is usually the log of earnings and measured on the basis of year, month, week, day, or hour. Most economic models rely on the hourly wage rate. In empirical practice, however, several hourly wage measures can be computed from the data and the question is which one is preferable. Contractual hourly wages (total income divided by contractual working hours) are normally used since they can be easily computed in most data sets. This might be problematic in an economic interpretation because a worker's utility does not depend on contractual working hours but on effective working hours and his perceived wage rate is not the contractual but the effective hourly wage (total income divided by effective working hours). Moreover, firms are interested in effective wages and not in contractual wages when making employment decisions. Thus, it is of central importance to define effective working hours and to assess the empirical importance of different hourly wage measures.

Some studies take into account overtime work when defining effective working hours and computing hourly wages (e.g., Bell and Hart, 1999; Bell et al., 2000; Hübler, 2002;

Wolf, 2002; Anger, 2007). Overtime is however only one form of working time adjustment, which is upward orientated. In the presence of fixed contractual working hours, a worker might choose overtime work if his utility maximizing working hours are larger than contractual working hours. The important case of downward adjustment of working time via paid absenteeism is on the other hand largely ignored.1 If working Absenteeism refers to reported sickness related work absence of employees. Such sickness reports need not to be true. Even if an employee is really sick, he can choose to some degree how long he stays from time constraints are present that induce a worker to accept a contract with larger than his optimal working hours, a worker can use absence to approach his optimal level of working hours (Allen, 1981; Brown and Sessions, 1996; Dunn and Youngblood, 1986).

This paper uses a personnel data set of a German company that is perfectly suitable to study the above issue because it comprises exact information about contractual, absent, and effective working hours as well as about wages. Moreover, the German case is of special interest for a first study due to its very generous institutional sickness benefits (Osterkamp and Röhn, 2007; Frick and Malo, 2008). Sick pay in Germany is regulated in the Act on Continued Payment of Remuneration (“Lohnfortzahlungsgesetz”). An employee who is sick for more than three days has to present a medical certificate of sickness from his physician. Sick employees have a legitimate claim of 100 percent wage replacement paid by the firm from the first absent day and for a period up to six weeks. In case of longer sickness absence due to the same disease, the wage replacement rate decreases to 70 percent and is paid by the health insurance up to 78 weeks. The issue of effective wages is, however, not only relevant for Germany but to some degree for every institutional setting in which workers receive sickness benefits when absent from work.

The next section illustrates the basic theoretical context, which is based on the static labour supply and demand models, and the relevance of effective hourly wages. Section 3 informs about the data set, basic descriptive statistics for hours and earnings, and work to recover from a disease or injury. Worker absenteeism is hence often used as a proxy for work effort, which is justified because absenteeism can be interpreted as shirking behaviour as well as a signal for work attachment (Barmby et al. 1994; Brown and Sessions, 1996; Ichino and Moretti 2009).

different inequality measures for contractual and effective wages. The regression results for hours and wages are presented in Section 4. The paper concludes with a summary and discussion of the results.

2. Theoretical framework A worker's decision to be absent from work can be modelled in the framework of the static neo-classical labour supply model (Allen, 1981; Brown and Sessions, 1996). Let a worker's utility U in equation (1) depend positively on total consumption and total leisure. Leisure L is a fixed amount of time T minus the time spend at work H as depicted in equation (2). Consumption is generated from total income, which is for simplicity only labour income. Total labour income Y in equation (3) is constrained by the product of hourly wages w and the total number of working hours H.

The worker's problem is to maximize his utility in equation (1) under the time constraint in equation (2) and the budget constraint in equation (3). The standard textbook solution is that a worker chooses to work as many hours until his marginal rate of substitution

the graphical solution in Figure 1, the worker's optimal working hours choice H* is the tangential point of the indifference curve (U*) and the budget constraint with the slope

In the next step, the distinction between contractual and effective working hours and wages is made and illustrated in Figure 1. If the worker has to decide about accepting a job, firms offer him a fixed contractual numbers of working hours HC and fixed contractual hourly wages wC (e.g., due to collective contracts or inflexible work and pay schedules). The worker might have to accept a contract with larger than his optimal working hours ( H C H * and U C U * ) because of such working hours constraints and a lack of better job opportunities. As a worker cares only about the working hours actually being at work, which are effective working hours HE, he might deviate from contractual working hours. The difference between HC and HE can in principle be negative, i.e., the worker makes an upward adjustment of working time via overtime hours (Bell and Hart, 1999) which is not subject of this analysis, or positive, i.e., the worker makes a downward adjustment of working time via (fully) paid absent working hours HA, which are valued by the worker as leisure hours.2 The latter is possible as workers in Germany receive a 100 percent wage replacement rate in case of - sickness related - absenteeism. As total income YC is, at least if long-term aspects are not taken into account (Brown, 1994), independent of effective working hours, the worker perceives his effective hourly wage wE as different from the contractual wage wC. The The assumption that all reported sickness absence is leisure increasing shirking behaviour of workers is quite strong. But it is useful to illustrate the issues of interested.

new time and budget constraints are as in equations (4) and (5) and the effective hourly wage is then calculated following equation (6).

The new budget constraint is a horizontal line at YC = wC H C due to the 100 percent wage replacement (see equation (5)). The worker has therefore an incentive to be as much absent as possible. In the extreme case, the worker would choose not to appear at work at all (HE=0 and L=T). Such an behaviour is however unlikely to be tolerated by firms and likely to have negative career consequences (e.g., layoff, training, wage growth, promotion). Fairness and work group norms can also restrict such an extreme behaviour (e.g., unfair towards colleagues as they have to work more) (Bradley et al., 2007). Thus, a worker might choose reference points to determine his amount of absent and effective working hours (Munro and Sugden, 2003). He could for example choose his original optimal working hours (HE=H*) or his original optimal utility level ( U* = U( YC,H C H E H*) ) as reference points. The former example with HE=H* is used to briefly illustrate the effect of absenteeism on effective hourly wages and utility.

The perceived effective hourly wage is total contractual income divided by effective working hours (see equation (6)) which results into a steeper hypothetical budget constraint because wE wC. Further, utility in case of absenteeism is larger than to

Differences between workers in absence behaviour and consequently in effective wages can arise from heterogeneous preferences for leisure and consumption. Workers who defer in their optimal working hours are also likely to have different reference levels for effective working hours. A worker with lower optimal working hours is then likely to have more absent working hours and a higher effective wage compared to a worker whose optimal working hours do not deviate much from contractual working hours.

Moreover, workers might be offered different contractual wages which also leads to different optimal working hours and reference levels. If workers with low contractual wages are more absent than workers with high contractual wages, the differences in effective wages between both groups would be lower than the differences in contractual wages.

Effective wages are furthermore crucial in the determination of labour demand, which is illustrated again in the static neo-classical model. A competitive firm maximizes its profits (∏) in equation (7) if the difference between the value of total output (pQ) and costs is maximised. We assume market output prices (p), a fixed production technology (Q), constant capital (K), market capital prices (r), and market contractual wages (wC).

Moreover, total labour input consists of the number of workers (N) times effective working hours (HE), which are contractual working hours (HC) minus absent working hours (HA≤HC). As the firm has to pay the contractual wage regardless of absent working hours (100 percent wage replacement), total labour costs are independent of absent working hours. Following the above computation of effective wages in equations (5) and (6), contractual labour costs can be reformulated into effective labour costs.

Because workers are homogenous, all workers provide the same number of working hours. Furthermore, absent working hours are exogenously chosen by workers. Thus, the firm’s only choice variable is total labour input. The standard first order condition in (8) yields that a firm hires workers up to the point in which effective wages equal the value of marginal product.

The discrepancy between contractual and effective wages arises quite obviously, because effective wages are larger than contractual wages in case of workers' downward adjustment of working time via paid absenteeism. Thus, labour demand would be too high if falsely contractual instead of effective wages are taken into account, which would result into a loss of profits. Furthermore, a firm might statistical discriminate against worker groups with higher absenteeism, which would result into lower employment chances for these workers (Aigner and Cain, 1977; Pfeifer and Sohr, 2008).

3. Data set and descriptive statistics The data set was extracted directly from computerized personnel records of a large German limited liability company that produces innovative products for the world market. The company has a works council and is subject to an industry wide collective contract. The personnel records contain information on all employees in the company’s headquarter on a monthly basis from January 1999 to December 2005. The subsequent empirical analysis includes all blue-collar and white-collar workers, who are neither apprentices nor trainees, who are not in early retirement schemes, and who are not absent on a permanent basis (e.g., parental leave, sabbaticals). Moreover, monthly observations are aggregated on the basis of calendar years because individual absenteeism is very volatile over the year. Therefore, workers who are not observed for all twelve months in a calendar year are excluded from the sample. In sum, the sample contains 9633 yearly observations of 1790 workers in an unbalanced panel design.

Table 1 presents descriptive statistics about working hours and earnings. Workers have on average 1815.5 contractual working hours per year. Because workers also have on average 58.4 absent working hours per year, which are officially sickness related and fully paid, effective working hours are only 1757.1 and hence significantly lower.3 Workers are on average 3.25 percent of their contractual working time absent. The average probability that a worker reports absence in a year is larger than 70 percent.

Nominal yearly gross income is on average 36727.6 Euros. The contractual hourly wage is computed by dividing yearly income by contractual working hours, whereas the effective hourly wage takes into account effective working hours in the denominator.