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Absenteeism, seasonality, and the business cycle
Journal of Economics and Business 53 (2001) 405– 419
Absenteeism, seasonality, and the business cycle Rick Audasa,*, John Goddardb a
Faculty of Administration and Canadian Research Institute for Social Policy, University of New Brunswick, New Brunswick, Canada b Department of Economics, University of Wales Swansea, UK Received 22 June 1999; received in revised form 26 April 2000; accepted 11 July 2000
Abstract Previous theoretical literature on malfeasance provides the basis for a theoretical model of absenteeism that incorporates both labor demand and supply side influences. This paper uses this theoretical framework as the basis for an analysis of the link between absenteeism, aggregate production and unemployment, using monthly US data for 1979 –93. Tests are carried out for unit roots at seasonal and nonseasonal frequencies. Cointegration tests suggest a long run relationship consistent with the theoretical model. © 2001 Elsevier Science Inc. All rights reserved. JEL classification: C22; J22; J41 Keywords: Absenteeism; Efficiency wages; Seasonal integration
1. Introduction This paper uses US monthly time series data to investigate the empirical relationship between fluctuations in the business cycle and the rate of worker absenteeism at the macroeconomic level. Early empirical studies viewed absenteeism principally as a labor market supply side phenomenon (Doherty, 1979; Markham, 1985; Leigh, 1985). This paper attempts to model both supply and demand side influences on the rate of absenteeism. Although it is widely assumed that absenteeism is influenced by cyclical factors, to our
* Corresponding author. Tel.: ⫹506-458-7314. E-mail address: [email protected] (R. Audas). 0148-6195/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 8 - 6 1 9 5 ( 0 1 ) 0 0 0 3 8 - 8
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knowledge no attempt has been made to verify or quantify this relationship using recent time series econometrics techniques. This paper is an attempt to fill this gap. Discussion of the implications of fluctuations in the business cycle for workplace discipline dates back at least as far as Kalecki’s (1943) observation that “. . . under a regime of permanent full employment, the ‘sack’ would cease to play its role as a disciplinary tool.” In their landmark paper, Steers and Rhodes (1978) develop a theoretical model of employee absenteeism, arguing that “economic and market conditions” play a prominent role in determining the individual’s motivation to attend work. As the economy enters recession, the consequences of losing one’s job become more serious as the opportunities to find alternative employment are reduced. To reduce the probability of dismissal, workers will attend more frequently. Barmby et al. (1995) argue that some portion of absence is malfeasant and can be explained using incentive models. Absenteeism can be explained along similar lines with the phenomenon of shirking in the efficiency wage literature: the risk of incurring dismissal and a spell of unemployment provides a disincentive to shirk (Calvo, 1979; Salop, 1979; Diamond, 1981; Shapiro and Stiglitz, 1984). The strength of this disincentive varies (countercyclically) with the business cycle. Most previous empirical studies also view absenteeism primarily as a labor supply phenomenon. Doherty (1979) and Kenyon and Dawkins (1989) implicitly assume that the demand for reliable labor is constant. Leigh (1985) argues informally that firms’ demand for reliable labor may be highest when economic conditions are at their worst. This suggests that labor demand influences tend to operate on absenteeism in the same direction as unemployment. Similarly, Markham (1985) suggests that firms may be less concerned about absence when economic conditions are strong, as “their attention is turned to meeting increasing consumer demands”. Weiss (1985) and Coles and Treble (1993, 1996) argue on different grounds that labor demand impacts on absenteeism, at the micro level. The firm’s monitoring effort should reflect the shadow cost of absence, and may also depend on production technologies. Consider a firm which operates an assembly line production process, in which workers are complements in production and the absence of one worker reduces the productivity of others. In a simple case, output might be zero if n ⬍ k, and constant for n ⱖ k, where n is the number of workers who attend, and k is the number needed for the assembly line to be operational. The firm has an incentive to pay higher agency costs to induce more reliable attendance by its workers than would be the case if its workers were perfect substitutes and if returns to scale were constant. In this paper, we argue that product and labor demand also influence absenteeism at the macro level, because firms’ shadow costs of absence vary over the business cycle. The returns to monitoring are high when product demand is buoyant, and low when product demand is slack. If hiring and firing workers is not costless, it may be efficient for the firm to hoard workers across anticipated cyclical (or seasonal) variation in demand. This would result in firms treating malfeasant absenteeism less leniently when product demand and therefore labor demand are high. An important implication is that different influences operating primarily on the demand and the supply side of the labor market may tend to pull on the rate of absenteeism in
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opposite directions during the same phase of the business cycle. On the one hand, during an upswing, firms under pressure to meet orders will monitor absence stringently, increasing the risks of detection for the malfeasant employee. On the other hand, when unemployment is low, the costs of dismissal as a result of malfeasance are reduced, since the employee knows he can easily find another job elsewhere. In the empirical literature, Doherty (1979) finds consistent evidence of an inverse relationship between unemployment and a variety of absenteeism measures, by applying ordinary least squares (OLS) to an annual UK data set covering the period 1954 –74. The benefit/earnings ratio is also found to be a significant influence, lending further support to the hypothesis of incentive effects on absenteeism. Leigh (1985) finds a significant negative correlation between the annual change in absenteeism and unemployment, using aggregated data from the US Panel Study of Income Dynamics (PSID) for the period 1967–78. He also finds a similar effect in a cross-sectional analysis at the industry level for 1976 –77. Markham (1985) uses monthly US Bureau of National Affairs (BNA) absenteeism data at national, regional and plant levels for the period 1976 – 82. Using OLS, a significant relationship between absenteeism and both unemployment and an index of employment opportunities is obtained. Finally, Kenyon and Dawkins (1989) use OLS on quarterly Australian data for the period 1966 – 84 to demonstrate an inverse relationship between unemployment and absenteeism. Absenteeism is also found to be positively related to the percentage of days lost through industrial disputes. In this paper, an empirical examination of variation in absenteeism over the business cycle provides an opportunity to exploit recent developments in the econometric analysis of economic time series data, which were unavailable to the authors of the studies reviewed above. Specifically, we are able to test and correct for the presence of stochastic trends in the data. The empirical link between the business cycle and absenteeism is established by investigating the effects of two main business cycle indicators: an aggregate industrial production measure and the rate of unemployment. Monthly, US data are used for the period 1979 –93. The availability of monthly data also allows us to investigate the nature of seasonality. Although the nonmalfeasant component of absenteeism (attributable to morbidity) is likely to account for some part of any seasonal variation, there are at least two reasons why malfeasant absence may also be seasonal. First, the perceived benefit of a day away from work may be higher in summer than in winter, or during (rather than outside) school holidays. Second, the firm’s monitoring effort might vary through the seasons within the year due to the effects of labor hoarding.1 An important part of our empirical analysis is the application of methods developed by Hylleberg et al. (1990) and Beaulieu and Miron (1993) to test for unit roots in the presence of seasonality, which may be either deterministic or stochastic. The rest of the paper is structured as follows: In section 2, a theoretical model is developed which captures the essence of the arguments outlined above. The model considers the employee’s decision whether to be a malfeasant absentee, or whether to be nonmalfeasant. The link between the business cycle and the rate of absenteeism is established through the influence on this decision of two transition probabilities: the probability that a malfeasant employee loses his job as a result of his malfeasance being detected, and the probability that
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an involuntarily unemployed worker finds a job and re-enters employment. In section 3, the results of the empirical analysis are presented including a cointegration analysis of the long run relationship between the business cycle indicators and the rate of absenteeism. There is evidence of a cointegrating relationship consistent with the theoretical model. Finally, section 4 concludes.
2. Modeling malfeasant absenteeism In the theoretical model, we describe a worker who does not voluntarily take spells of absence as nonmalfeasant, and one who does as malfeasant. The model allows for both types of worker to be employed in some time periods, and to be involuntarily unemployed in others. The following symbols are used:
t
⫽ probability that a nonmalfeasant worker employed between time t and t ⫹ 1 is dismissed at t ⫹ 1; t ⫹ t ⫽ probability that a malfeasant worker employed between time t and t ⫹ 1 is dismissed at t ⫹ 1; t ⫽ probability that a worker who is involuntarily unemployed between time t and t ⫹ 1, or who is employed but dismissed at t ⫹ 1, regains employment at t ⫹ 1 and therefore becomes employed between t ⫹ 1 and t ⫹ 2; w ⫽ wage paid to all employed workers per period; b ⫽ benefit paid to all involuntarily and voluntarily unemployed workers per period; vi ⫽ income equivalent of leisure time enjoyed by unemployed workers. vi is assumed to vary between workers. kvi ⫽ income equivalent of leisure time per period enjoyed by malfeasant employed worker i. k (0⬍k⬍1) is the proportion of work time spent absent.2 We begin by defining the arrays of transition probabilities between employment and involuntary unemployment. Initially, we do so under the steady state condition that workers assume the transition probabilities will remain the same in all future periods, or t ⫽ , t ⫽ and t ⫽ for all t. If the worker is employed at time t and chooses to be nonmalfeasant, he either retains his job at t ⫹ 1 with probability 1 ⫺ , or loses it with probability . If the job is lost, there is a probability of of re-entering employment immediately at t ⫹ 1. The transition probabilities from employment at t to employment and unemployment at t ⫹ 1 are therefore 1 ⫺ (1 ⫺ ) and (1 ⫺ ), respectively. Similarly, if the worker chooses to be malfeasant, he faces transition probabilities of 1 ⫺ ( ⫹ ) (1 ⫺ ) and ( ⫹ ) (1 ⫺ ) from employment at t to employment and unemployment respectively at t ⫹ 1. Any worker who is involuntarily unemployed at t faces transition probabilities of and 1 ⫺ to employment and unemployment respectively at t ⫹ 1. To determine the conditions under which nonmalfeasant employment is preferred to malfeasant employment and vice versa, it is necessary to compare the present value of expected lifetime income in each case. For simplicity, infinite time horizons are assumed. Let
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x*1 denote the present value of expected lifetime income for a worker who, if currently employed will choose to be nonmalfeasant. Let x*2 denote the present value of lifetime income for the same worker if he is currently involuntarily unemployed. Similarly, let y*1 and y*2 denote the present values of expected lifetime income for malfeasant workers who are currently employed and involuntarily unemployed respectively. Finally, let d denote the discount rate. Because the transition probabilities are constant through time, x*1, x*2, y*1 and y*2 evaluated at time t ⫹ 1 (and at all future times) are the same as at time t. This means that in steady state, a worker who chooses to be nonmalfeasant at t will always be nonmalfeasant, and one who chooses malfeasance will always be malfeasant. The steady state equations for x*1, x*2, y*1 and y*2 are X*⫽ Z 1 ⫹ A 1X*
Y* ⫽ (Z 1 ⫹ Z 2) ⫹ A 2Y*
f X* ⫽ (I ⫺ A 1) ⫺1Z 1
Y* ⫽ (I ⫺ A 2)⫺1(Z 1 ⫹ Z 2)
where X* ⫽
冉 xx**冊 1 2
Y* ⫽
A 1 ⫽ (1 ⫹ d)⫺1 A 2 ⫽ (1 ⫹ d)⫺1
冉 冉
冉 yy**冊 1 2
1 ⫺ (1 ⫺ )
冉 b ⫹w v 冊 (1 ⫺ 1⫺ 冊
Z1 ⫽
1 ⫺ ( ⫹ )(1 ⫺ )
1
Z2 ⫽
冉 kv0 冊 i
冊
( ⫹ )(1 ⫺ ) 1⫺
Z1 and Z1 ⫹ Z2 are vectors containing the payoffs per period from employment and unemployment for nonmalfeasant and malfeasant workers respectively. A1 and A2 are matrices of (discounted) transition probabilities. These equations can be used to establish the range of values for vi (the income equivalent of leisure) over which malfeasant employment is preferred to nonmalfeasant employment and vice versa. Malfeasant employment is preferred if Z 2 ⬎ CZ 1 where C ⫽ ((I ⫺ A 2)(I ⫺ A 1)⫺1 ⫺ I) ⫽
冉 c0 c0 冊 11
12
f vi ⬎ vCRIT ⫽ (c11w ⫹ c12b)/(k ⫺ c12) where c11 and c12 are functions of , and , and vCRIT is the critical value of vi at which the employee is indifferent between malfeasance and nonmalfeasance. Workers who place a low value on leisure (vi ⬍ vCRIT) find that in the long term, the gains from malfeasance are insufficient to compensate for the costs in wages foregone as a result of being unemployed for a higher proportion of the time. Workers who place a high value on leisure (vi ⬎ vCRIT) find the opposite. To determine the conditions under which voluntary unemployment is preferred to malfeasant employment, we note that the former produces an income equivalent of b ⫹ vi per
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period, while the latter produces b ⫹ vi in some periods and w ⫹ kvi in others. Expected income from involuntary unemployment therefore exceeds that from malfeasant employment whenever vi ⬎ (1 ⫺ k)-1(w ⫺ b). Together with the previous results, this establishes that with steady state transition probabilities, malfeasant employment is the preferred choice for all workers with vCRIT ⬍ vi ⬍ (1 ⫺ k)-1(w ⫺ b). This condition is therefore sufficient to determine the rate of absenteeism which corresponds to the steady state transition probabilities defined above. We now consider the effect on the rate of absenteeism of short term variations in the transition probabilities. Suppose that t, t and t may be above or below their steady state values for the period t to t ⫹ 1, but are expected (at time t) to return to their steady state values for all periods from t ⫹ 1 to t ⫹ 2 and beyond. We define x1t and y1t to be the present values of expected lifetime income at t for workers who are employed at t and who will be nonmalfeasant and malfeasant respectively between t and t ⫹ 1. x2t and y2t are the present values for nonmalfeasant and malfeasant workers who are involuntarily unemployed at t. These present values can be written as: X t ⫽ Z 1 ⫹ A 1tX*
Y t ⫽ Z 1 ⫹ Z 2 ⫹ A 2tX*
if vi ⬍ vCRIT
X t ⫽ Z 1 ⫹ A 1tY*
Y t ⫽ Z 1 ⫹ Z 2 ⫹ A 2tY*
if vi ⬎ vCRIT
and
where Xt ⫽
冉 xx 冊 1t
2t
Yt ⫽
A 2t ⫽ (1 ⫹ d)⫺1
冉 yy 冊 A ⫽ (1 ⫹ d) 冉 1 ⫺ (1 ⫺ ) 冉 1 ⫺ ( ⫹ )(1 ⫺ ) ( ⫹1⫺)(1 ⫺ )冊 ⫺1
1t
1t
2t
t
t
t
1
t
t
t
t
t
冊
t(1 ⫺ t) 1 ⫺ t
t
t
If vi ⬍ vCRIT, then in steady state, the worker prefers nonmalfeasance. The condition for malfeasance to be preferred between t and t ⫹ 1 is Z 2 ⬎ (A 1t ⫺ A 2t)X* f vi ⬎ vLOW ⫽ {k(1 ⫹ d)}⫺1t(1 ⫺ t)(x*1 ⫺ x*2) vLOW is the minimum value of vi at which malfeasance is preferred between t and t ⫹ 1 by workers who would normally be nonmalfeasant. If t ⫽ and t ⫽ , vLOW ⫽ vCRIT (the steady state solution). However, if t ⬍ or t ⬎ , vLOW ⬍ vCRIT. Some workers with vLOW ⬍ vi ⬍ vCRIT, who in steady state would be nonmalfeasant, choose to be malfeasant for the period t to t ⫹ 1, so the rate of absenteeism rises above its steady state value. Similarly, if vi ⬎ vCRIT, then in steady state, the worker prefers malfeasance. The condition for nonmalfeasance to be preferred between t and t ⫹ 1 is Z 2 ⬎ (A 1t ⫺ A 2t)Y* f vi ⬎ vHIGH ⫽ {k(1 ⫹ d)}⫺1t(1 ⫺ t)(y*1 ⫺ y*2) vHIGH is the minimum value of vi at which malfeasance is preferred between t and t ⫹ 1 by workers who would normally be malfeasant. If t ⫽ and t ⫽ , vHIGH ⫽ vCRIT (the steady state solution). However, if t ⬎ or t ⬍ , vHIGH ⬎ vCRIT. Some workers with
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vCRIT ⬍ vi ⬍ vHIGH, who in steady state would be malfeasant, choose to be nonmalfeasant for the period t to t ⫹ 1, so the rate of absenteeism drops below its steady state value. Short-term fluctuations in the rate of absenteeism are therefore driven by fluctuations in the parameters which govern the probabilities of transition between employment and unemployment and vice versa, t and t. In order to develop an empirical model, it is necessary to establish a link between these transition probabilities and appropriate macroeconomic business cycle indicators. First, t is expected to vary directly with aggregate production. As argued above, when output is high, firms may attempt to satisfy their increased demand for labor by hiring more workers, or by monitoring malfeasance among their existing workers more stringently. Conversely when output is low, firms may lay off some workers, or may monitor malfeasance less stringently. Varying the stringency of monitoring malfeasance allows adjustments to be made to the (effective) labor force without incurring the transactions costs associated with hiring and firing. Relaxing monitoring during slack periods therefore constitutes a form of labor hoarding. Second, t is assumed to vary inversely with the rate of unemployment. The higher the latter, the lower the probability that an involuntarily unemployed worker will re-enter employment at any particular point in time, and vice versa. Overall, there is no clear expectation as to whether absenteeism should be pro- or countercyclical. During peaks in the cycle, pressure to increase output which leads to more stringent monitoring will tend to reduce absenteeism. At the same time, by reducing the costs to the individual of dismissal, low unemployment tends to encourage malfeasance. During recessions, the same factors tend to operate in the opposite directions. The fact that fluctuations in production and unemployment are not perfectly synchronised, however, should make it possible to identify their individual effects on the rate of absenteeism. This is investigated in the following empirical section.
3. Absence and business cycle indicators: unit root and cointegration tests The data set consists of 180 monthly observations for the 15 year sample period 1979 to 1993 (inclusive). The US monthly Current Population Survey (CPS) was used to obtain series for at and ut, the rates of absence and unemployment respectively. The CPS contains information on approximately 17,000 individuals across a wide demographic and geographic base. Respondents are asked to state the number of hours normally worked and the number of hours actually worked in each week, and to explain any difference between the two by selecting one of a number of listed causes of absence. The rate of absenteeism is calculated by dividing the total number of hours absent attributed to “own illness”, “too busy with home or school” or “other reasons,” by the total number of hours normally worked. Absences attributed to factors such as “slack work,” “job terminated,” “materials shortage,” “strike” or “holiday” are not included in the numerator. The unemployment rate is the number of unemployed divided by the sum of the unemployed, those who worked, and those who did not work but held jobs. Real monthly industrial production (adjusted for the number of calendar days in the month but otherwise seasonally unadjusted) was obtained from
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Datastream and is used to measure yt.3 In the estimations, all variables are in natural logarithms. The empirical analysis begins with investigation of the univariate time series properties of at, yt and ut, taking into account any seasonality which is present in the monthly versions of these series. There are three possibilities as to the nature of the seasonality: deterministic; stationary stochastic; and nonstationary stochastic seasonality. With deterministic seasonality (zt ⫽ ␦0 ⫹ ⌺sj ⫽ 2 ␦jsjt ⫹ ⑀t, where s is the number of seasons and sjt are seasonal dummies, assuming for simplicity no deterministic or stochastic trend components) the underlying seasonal pattern is regular throughout the series. Stationary stochastic seasonality (zt ⫽ zt-s ⫹ ⑀t, with 兩兩 ⬍ 1) implies that the seasonal pattern tends to change over time, although there is no tendency for the magnitude of the seasonal variation (between consecutive observations) to increase. With nonstationary stochastic seasonality (zt ⫽ zt-s ⫹ ⑀t), there is one zero frequency unit root and s-1 unit roots at nonzero frequencies. The seasonal pattern again changes over time, and the typical magnitude of the variation between consecutive observations also tends to increase. Miron (1990) argues that before the recent development of the literature on seasonal integration, econometricians tended to handle seasonality in an ad hoc (and possibly incorrect) manner. Abeysinghe (1994) demonstrates more formally that the use of seasonal dummies to model a process whose seasonality is actually nonstationary creates a spurious regression problem (in much the same way as the incorrect substitution of a deterministic for a stochastic trend). Therefore, a correct diagnosis of the nature of the seasonal component is as important as for the trend component, although most empirical evidence suggests that unit roots at nonzero frequencies (which produce nonstationary seasonality) are less common than unit roots at zero frequency (which produce stochastic trends). For quarterly series, Hylleberg et al. (1990) develop a method (the HEGY procedure) which uses a single auxiliary regression to test for unit roots at zero and nonzero frequencies, against alternatives which may incorporate a deterministic trend, deterministic seasonality or both. Beaulieu and Miron (1993) adapt the HEGY procedure to allow equivalent tests on monthly series. The main focus of the HEGY procedure is testing for stochastic nonstationary versus deterministic seasonality, because stochastic stationary seasonality can always be modelled by selecting an appropriate lag structure. The Beaulieu-Miron adaptation of the HEGY procedure to test a monthly series xt for nonseasonal and seasonal unit roots involves running the following auxiliary regression:
冘 ␥s
12
z13t ⫽ ␥0 ⫹ ␥1t ⫹
j jt
j⫽2
冘z
12
⫹
k kt⫺1
k⫽1
冘␦ z H
⫹
h 13t⫺h
⫹ ⑀t
(1)
h⫽1
In (1), z13t ⫽ (1 ⫺ B12)xt where B is the lag operator. The intercept, deterministic trend and/or seasonal dummies are optional. H is the number of lags of z13t required to whiten the residuals; in practice, we augment only with lags of z13t which test significant. z1t ⫽ ((1 ⫺ B12)/(1 ⫺ B))xt is interpreted as xt adjusted for the 11 seasonal unit roots. Failure to reject H0 : 1 ⫽ 0 against H1: 1⬍0 therefore indicates the presence of a nonseasonal unit root at zero frequency (i.e. a stochastic trend). Similarly, each of z2t . . . z12t is xt adjusted for the nonseasonal and 10 of the seasonal unit roots.4 To reject seasonal unit roots at all frequen-
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413
Table 1 Tests for seasonal integration
冘 ␥s ⫹ 冘 z 12
Auxiliary regression: z13t ⫽ ␥0 ⫹ ␥1t ⫹
12
j jt
j⫽2
Series IT
t(1) t(2) t(3) t(4) t(5) t(6) t(7) t(8) t(9) t(10) t(11) t(12) F(3艚4) F(5艚6) F(7艚8) F(9艚10) F(1112) F(1艚␥1)
⫺2.37 ⫺2.96* ⫺3.12* ⫺0.98 ⫺3.93* 2.53* ⫺3.53* 1.20 ⫺3.25* ⫺1.75 ⫺1.77 0.00 5.37* 11.37* 7.05* 6.98* 1.57 4.54
12
IS
⫹
k⫽1
at
Deterministic component Augmentation
冘␦z 12
k kt⫺1
h 13t⫺h
⫹ ⑀t
h⫽1
yt ITS
IT
—
—
1,5,7,12,13
⫺2.62 ⫺3.80* ⫺5.27* ⫺0.85 ⫺5.50* 2.78* ⫺6.21* 1.25 ⫺4.01* ⫺1.42 ⫺4.67* 1.13 14.48* 19.67* 20.55* 9.29* 11.84* —
⫺2.15 ⫺3.80* ⫺5.27* ⫺0.86 ⫺5.50* 2.47* ⫺6.21* 1.21 ⫺4.01* ⫺1.41 ⫺4.68* 1.07 14.48* 19.65* 20.50* 9.25* 11.79* 3.53
⫺2.51 ⫺0.54 ⫺1.98* ⫺0.10 ⫺1.74 0.81 ⫺2.37* ⫺1.00 ⫺0.59 ⫺0.73 ⫺0.72 ⫺1.82 1.97 1.84 3.35* 0.45 1.92 3.16
ut
IS
ITS
IT
—
—
2,3,12,14
⫺0.39 ⫺3.87* ⫺4.04* ⫺3.43* ⫺4.02* 2.65* ⫺2.29 ⫺4.80* ⫺6.15* 0.57 ⫺0.98 ⫺5.14* 15.29* 12.51* 15.03* 19.19* 13.87* —
⫺2.88 ⫺3.95* ⫺4.23* ⫺3.26* ⫺4.20* 2.56* ⫺2.75 ⫺4.59* ⫺6.28* 0.55 ⫺1.75 ⫺4.96* 15.56* 13.04* 15.54* 19.95* 14.42* 4.24
⫺2.79 ⫺3.52* ⫺1.34 ⫺0.01 ⫺3.24 2.15* ⫺1.05 ⫺1.83 ⫺4.39* 1.07 ⫺1.44 ⫺1.76 0.97 9.07* 2.21 10.01* 2.55 3.89
IS
ITS —
—
⫺1.48 ⫺4.32* ⫺5.22* 0.68 ⫺5.43* 1.30 ⫺3.73* ⫺3.26* ⫺5.01* 0.34 ⫺2.50* ⫺6.33* 13.98* 15.88* 13.36* 12.64* 25.12* —
⫺2.70 ⫺4.32* ⫺5.24* 0.69 ⫺5.46* 1.21 ⫺3.94* ⫺3.13* ⫺5.06* 0.32 ⫺3.02* ⫺6.06* 14.09* 15.90* 13.88* 12.85* 25.83* 3.88
Critical values: 5% significance level IT IS ITS
t(1) ⫺3.29 ⫺2.74 ⫺3.23
t(2) ⫺1.86 ⫺2.71 ⫺2.73
t(k) ⫺1.87 ⫺3.18 ⫺3.17
t(k⫹1) ⫾1.92 ⫾2.18 ⫾2.17
F(k艚k⫹1) 2.97 5.99 5.99
F(1艚y1) 5.91 — 5.67
* Denotes significant at the 5% level. Critical values are shown for t(k), t(k⫹1) and F(k艚k⫹1) for k ⫽ 3,5,7,9,11.
cies, k must not equal zero for k ⫽ 2 and for at least one element of each of the sets {3,4}, {5,6}, {7,8}, {9,10} and {11,12}. All of these hypotheses can be tested using t or F statistics obtained from OLS estimation of (1).5 The critical values, which depend on the number of observations and on whether an intercept, trend and/or seasonal dummies are included in (1), are generated from large numbers of replications of (1 ⫺ B12)xt ⫽ ⑀t. Table 1 shows the results of the nonseasonal and seasonal unit root tests on at, yt and ut using three alternative specifications of (1): with intercept and trend (IT); with intercept and seasonals (IS); and with intercept, trend and seasonals (ITS). For at, failure to reject H0:1艚␥1 ⫽ 0 in both IT and ITS and H0:1 ⫽ 0 in IS suggests that IS is the correct specification, and that there is a nonseasonal unit root. No seasonal unit roots are detected from the t or F tests on 2 . . . 12. The seasonal dummies test significant, indicating that seasonality in the absenteeism series is deterministic. In line with the earlier discussion, we assume that the dummies may be capturing regularities in both the nonmalfeasant and
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malfeasant components of seasonal absenteeism.6 The diagnoses for both yt and ut are the same as for at. Therefore, we can now use the cointegration tests developed by Johansen (1988, 1991) to investigate whether there is empirical evidence of a long run, cointegrating relationship between at, yt and ut. For a system comprising three nonstationary I(1) series each with a deterministic seasonal component, the Johansen method is based on the following vector autoregression (VAR) which represents the most general specification of the data generating process:
冘⌽ 3
z t ⫽ ␣ ⫹ ⌫s t ⫹
m
z tⴚm ⫹ ⑀ t
(2)
m⫽1
where in our case, zt’ ⫽ (at yt ut), ␣ ⫽ {␣i} is a 3 ⫻ 1 vector of intercepts, ⌫ ⫽ {␥ij} is a 3 ⫻ 11 matrix of coefficients, st ⫽ {sjt} is an 11 ⫻ 1 vector of seasonal dummies, ⌽m ⫽ {(m) ij } for i, j ⫽ 1.3 and m ⫽ 1. . . M where M is the maximum lag length, and ⑀t’ ⫽ (⑀1t ⑀2t ⑀3t). Before any cointegration tests can be carried out, it is necessary to establish the lag structure, eliminating the M0’th set of lags from (2) if the quality of the model is not significantly reduced by moving to M0 -1 lags, and so on. On this criterion, we find that M ⫽ 4 is the appropriate lag length.7 For the purposes of the cointegration tests, (2) with M ⫽ 4 can be reparameterised as follows:
冘⌿ 3
⌬z t ⫽ ␣ ⫹ ⌫s t ⫹
m⌬z tⴚm
⫹ ⌰z tⴚ1 ⫹ ⑀ t
(3)
m⫽1
where ⌿m ⫽ {(m) ij } and ⌰ ⫽ {ij} are 3 ⫻ 3 matrices of coefficients. The question whether there is one or more cointegrating vector linking at, yt and ut depends whether restrictions on r ⫽ rank(⌰) can be imposed in (3); one cointegrating vector, say et ⫽ at ⫺ 0 ⫺ 1yt ⫺ 2ut, requires r ⫽ 1. The results of Johansen’s two alternative tests for r, based on the maximal eigenvalue and trace statistics, are shown in section 1 of Table 2. H0:r ⫽ 0 is rejected in favor of H1:r⬎0 at the 5% level with the trace statistic, and at just above the 5% level with the maximal eigenvalue statistic. Tests of H0:rⱕ1 then fail to reject in favor of H1:r⬎1. As expected, the tests also fail to reject H0:rⱕ2 against H1:r⬎2. Overall, the tests provide strong evidence of a single cointegrating vector. Section 2 of Table 2 shows the estimated coefficients of the single cointegrating vector, together with likelihood ratio tests for the significance of ˆ 1 and ˆ 2. Both coefficients are signed in accordance with the theoretical discussion in section 2, and both are highly significant. These results enable us to assess the relative impact of the demand and supply side influences on absenteeism during an upturn (or downturn) in the business cycle. For a 1% increase in the level of real output to have zero impact on absenteeism, the results suggest it would have to be accompanied by a reduction in unemployment equivalent to just over 3% of the current unemployment rate (so if the unemployment rate were 10%, the necessary reduction in this figure would be just over 0.3%). If the percentage fall in the rate of unemployment is more than three times the percentage increase in real output, absenteeism
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Table 2 Tests for cointegration 1. Tests for r ⫽ rank (⌰) in (2) H0 r⫽0 rⱕ1 rⱕ2
H1 r⬎0 r⬎1 r⬎2
Maximal eigenvalue statistic 20.91** 7.97 1.09
Trace statistic 29.98* 9.07 1.10
2. Estimated cointegrating relationship: at ⫽ ˆ 0 ⫹ ˆ 1yt ⫹ ˆ 2ut ⫹ e1 ˆ 0 ⫽ ⫺1.8657 ˆ 1 ⫽ ⫺0.7537 ˆ 2 ⫽ ⫺0.2309 Likelihood ratio tests: (i) H0:1 ⫽ 0 2(1) ⫽ 7.82** (ii) H0:2 ⫽ 0 2(1) ⫽ 4.97* 3. Maximum likelihood estimation of equation for ⌬at in (2) ⌬at ⫽ ␣ˆ 1 ⫹ ␥ˆ 12jsjt
冘 j
⫺0.47*et⫺1 ⫺ 0.30*⌬a t⫺1 ⫺ 0.28*⌬at⫺2 ⫺ 0.27*⌬at⫺3 (0.11) (0.10) (0.09) (0.07) ⫹0.37 ⌬yt⫺1 ⫹ 0.88** ⌬yt⫺2 ⫺ 0.61 ⌬yt⫺3 (0.48) (0.49) (0.47) ⫺0.04 ⌬ut⫺1 ⫹ 0.08 ⌬ut⫺2 ⫹ 0.15**⌬ut⫺3 ⫹ ˆ 1t (0.09) (0.10) (0.09) 2 ⫽ 0.48 s.e. regression ⫽ 0.0586 n ⫽ 175 R2 ⫽ 0.54 R serial correlation: 2(1) ⫽ 0.38 2(2) ⫽ 0.63 2(3) ⫽ 0.80 2(12) ⫽ 13.71 heteroscedasticity: 2(1) ⫽ 0.01 Standard errors of estimated coefficients are in parentheses. * Denotes significant at 5% level; ** Denotes significant at 10% level. Estimates of the constant and seasonal dummy coefficients are not reported. Serial correlation tests are Ljung-Box statistics, based on the autocorrelation function of the residuals. Heteroscedasticity test is a Lagrange Multiplier test based on an auxiliary regression of squared residuals on squared fitted values.
should be rising. If unemployment is falling at less than this rate, absenteeism should be falling. The estimated equation for ⌬at obtained from maximum likelihood estimation of (3) as a VAR, with the cointegrating restriction r ⫽ 1 imposed, is shown in section 3 of Table 2. With the exception of the lags of the dependent variable, the model does not reveal any strong short run dynamic effects.8 However, the coefficient on the error correction term et-1 is correctly signed and highly significant, and the diagnostics suggest that the specification is satisfactory.9 The empirical results therefore support the hypothesis that variations in both production and unemployment are important in explaining absenteeism. Firms alter their monitoring intensity in response to changes in product demand, and individuals change their propensity to attend work as labor market conditions vary.
4. Conclusion In this paper, we have investigated the determinants of malfeasant employee absenteeism at the macro level. The paper not only adds to the limited quantity of previous work
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examining absenteeism specifically, but also contributes to the wider and more extensive literature on malfeasance. We regard absenteeism as a phenomenon with a significant malfeasant component. Because absenteeism (in contrast to most other types of malfeasance) is readily observable, we are able to sidestep the data problems that often prevent researchers from subjecting theoretical models of malfeasance to empirical scrutiny. The theoretical model views malfeasant absenteeism in a manner similar to the treatment of on-the-job shirking in the efficiency wage literature. The incentive to be an absentee depends on the transition probabilities from employment to unemployment as a result of detection as a malfeasant absentee, and from unemployment back to employment. If hiring and firing labor is expensive, it may be efficient for the firm to hoard workers across cyclical fluctuations in demand, treating malfeasant absenteeism less leniently when product demand and labor demand are buoyant than when demand is slack. When unemployment is low, however, the costs of dismissal as a result of being detected as a malfeasant absentee are reduced, since the employee knows he can find another job easily. An implication of these arguments is that different influences operating principally on the demand and supply side of the labor market may tend to pull in opposite directions on the rate of absenteeism during the same phase of the business cycle. Monthly US time series data for the period 1979 –93 is used to test for macro relationships between absenteeism, production and unemployment. These series each appear to contain one nonseasonal unit root and no seasonal unit roots. Evidence of a cointegrating relationship between absenteeism, production and unemployment is presented. The finding that absenteeism varies inversely with unemployment is consistent with the previous empirical literature (Doherty, 1979; Leigh, 1985; Markham, 1985; and Kenyon and Dawkins, 1989). The findings that absenteeism also varies inversely with production, and that absenteeism, unemployment and production are cointegrated are new. These empirical results help extend our previous understanding of the causes of absenteeism at the aggregate level.
Notes 1. Testing. for seasonality in a variety of aggregate US series, Barsky and Miron (1989) find limited evidence of production smoothing, and significant seasonal variation in labour productivity, which they attribute to labour hoarding. 2. In. common with other malfeasance literature, we simplify by assuming that the choice between malfeasance and non-malfeasance is discrete, and that there are no ‘degrees’ of malfeasance, which in this case would correspond to varying proportions of time spent absent. 3. The Stata 6.0 code used to generate the rate of absenteeism, using the NBER CPS data dictionary (Current Population Survey, 1994; StataCorp, 1999) is as follows: keep if activlw ⫽⫽ 1 兩 activlw ⫽⫽ 2 兩 activlw ⫽⫽ 4 兩 activlw ⫽⫽ 5 keep if uhourse ⬎ 0 mvencode hourslw, mv(0) gen timelost ⫽ uhourse – hourslw replace timelost ⫽ 0 if timelost ⬍ 0
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gen absence ⫽ timelost if reasonlw ⫽⫽ 10 兩 reasonlw ⫽⫽ 12 兩 reasonlw ⫽⫽ 15 兩 absentlw ⫽⫽ 1 兩 absentlw ⫽⫽ 8 gen validtl ⫽ timelost if timelost ⬎ 0 & absence ⫽⫽ 0 mvencode validtl, mv(0) mvdecode absence, mv(0) mvencode absence, mv(0) gen worktime ⫽ uhourse –validtl gen abrate ⫽ absence/worktime Unemployment is generated from the CPS as follows: gen unemp ⫽ 1 if esr ⫽⫽ 3 gen labforce ⫽ 1 if esr ⬍ ⫽ 3 mvencode unemp labforce, mv(0) sum unemp if labforce ⫽⫽ 1 The Datastream code for the industrial production series is USIPTOT.G 4. Full definitions are: z1t ⫽ (1 ⫹ B ⫹ B2 ⫹ B3 ⫹ B4 ⫹ B5 ⫹ B6 ⫹ B7 ⫹ B8 ⫹ B9 ⫹ B10 ⫹ B11) xt; z2t ⫽ (1 ⫺ B ⫹ B2 ⫺ B3 ⫹ B4 ⫺ B5 ⫹ B6 ⫺ B7 ⫹ B8 ⫺ B9 ⫹ B10 ⫺ B11) xt; z3t ⫽ ⫺(B ⫺ B3 ⫹ B5 ⫺ B7 ⫹ B9 ⫺ B11) xt; z4t ⫽ ⫺(1 ⫺ B2 ⫹ B4 ⫺ B6 ⫹ B8 ⫺ B10) xt; z5t ⫽ ⫺(1/2)(1 ⫹ B ⫺ 2B2 ⫹ B3 ⫹ B4 ⫺ 2B5 ⫹ B6 ⫹ B7 ⫺ 2B8 ⫹ B9 ⫹ B10 ⫺ 2B11) xt; z6t ⫽ (公3/2)(1 ⫺ B ⫹ B3 ⫺ B4 ⫹ B6 ⫺ B7 ⫹ B9 ⫺ B10) xt; z7t ⫽ (1/2)(1 –B ⫺ 2B2 ⫺ B3 ⫹ B4 ⫹ 2B5 ⫹ B6 ⫺ B7 ⫺ 2B8 ⫺ B9 ⫹ B10 ⫹ 2B11) xt; z8t ⫽ –(公3/2)(1 ⫹ B – B3 – B4 ⫹ B6 ⫹ B7 ⫺ B9 – B10) xt; z9t ⫽ ⫺(1/2)(公3 ⫺ B ⫹ B3 ⫺ 公3B4 ⫹ 2B5 ⫺ 公3B6 ⫹ B7 ⫺ 2B8 ⫺ B9 ⫹ 公3B10 ⫺ 2B11) xt; z10t ⫽ (1/2)(1 ⫺ 公3B ⫹ 2B2 ⫺ 公3B3 ⫹ B4 ⫺ B6 ⫹ 公3B7 ⫺ 2B8 ⫹ 公3B9 ⫺ B10) xt; z11t ⫽ (1/2)(公3 ⫹ B – B3 ⫺ 公3B4 ⫺ 2B5 ⫺ 公3B6 ⫺ B7 ⫹ B9 ⫹ 公3B10 ⫹ 2B11) xt; z12t ⫽ ⫺ (1/2)(1 ⫹ 公3B ⫹ 2B2 ⫹ 公3B3 ⫹ B4 ⫺ B6 ⫺ 公3B7 ⫺ 2B8 ⫺ 公3B9 ⫺ B10) xt; 5. H0: 2 ⫽ 0 (tested against H1:2⬍0) should be rejected using a t-test. At least one of H0:k ⫽ 0 (tested against H1:k⬍0) or H0:k⫹1 ⫽ 0 (tested against H1:k⫹1⫽0) should be rejected using t-tests, or alternatively H0:k艚k⫹1 ⫽ 0 should be rejected using an F-test, for k ⫽ 3,5,7,9,11. See Hylleberg et al. (1990) and Beaulieu and Miron (1993) for full details of these procedures. 6. The seasonal peak occurs in February with a mean absence rate of 0.030868 across the 15-year period under consideration. Over the same period, the seasonal trough occurs in July with an average absence rate of 0.023693. 7. The likelihood ratio test statistic for the significance of the coefficients on the M0’th ˆ M 兩⫺ ln兩⍀ ˆ M 兩}, where the VAR is estimated as lagged terms is 2 ⫽ (T ⫺ M0){ln兩⍀ 0⫺1 0 a system of three seemingly unrelated regressions. T is the total number of observaˆ M ⫽ {ˆ ij} is the error covariance matrix from the VAR with M0 lags estimated tions; ⍀ 0 using the observations for t ⫽ M0 ⫹ 1 . . . T, i.e. ˆ ij ⫽ ⌺t ⑀ˆ it⑀ˆ jt/(T - M0) for ij ⫽ 1, 2, ˆ 3; and ⍀ M0⫺1 is the covariance matrix with M0⫺1 lags also estimated using the same
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observations. The distribution of 2 under the null is 2(9) in this case. For M0 ⫽ 5,4,3,2 and 1, this test produces 2 ⫽ 7.38, 25.59, 41.51, 43.63 and 1055.42 respectively. The critical value at the 5% significance level is 16.92. Further tests with M0⬎5 did not show any sets of lags of order higher than 5 to be significant. 8. Following the earlier discussion of the pro- and counter-cyclical influences on absenteeism, the failure to identify significant short run effects is unexpected. This could reflect inadequacies in the theoretical model, or it could simply be due to shortcomings in the data set. 9. We have also carried out a similar analysis using absence and unemployment rates disaggregated by sex, with the same production series. For reasons of space, the results are not reported in full. For absence, all seasonal unit roots are rejected for both males and females. A non-seasonal unit root is diagnosed for females but rejected for males. For unemployment, all seasonal unit roots are rejected, and non-seasonal unit roots are detected in both cases. If these results are accepted, a cointegration analysis is appropriate for females but not for males, whose absence is diagnosed as stationary. For females, the cointegration tests are successful in diagnosing a single cointegrating vector with correctly signed and significant coefficients. If we proceed with the same analysis for males, there is ambiguity as to the number of cointegrating vectors.
Acknowledgment We would like to thank John Treble for comments on an earlier draft of this paper.
References Abeysinghe, T. (1994). Deterministic seasonal models and spurious regressions. Journal of Econometrics 61, 259 –272. Barmby, T. A., C. D. Orme & J. G. Treble (1995). Work absence histories: a panel data study. Labour Economics 2, 53– 66. Barsky, R. B., & J. A. Miron (1989). The seasonal cycle and the business cycle. Journal of Political Economy 97, 503–534. Beaulieu, J. J., & J. A. Miron (1993). Seasonal unit roots in aggregate US data. Journal of Econometrics 55, 305–328. Calvo, G. A. (1979). Quasi-Walrasian theories of unemployment. American Economic Review Proceedings 69, 102–106. Coles, M. G., & J. G. Treble (1993). The price of worker reliability. Economics Letters 41, 149 –155. Coles, M. G., & J. G. Treble (1996). Calculating the cost of absenteeism. Labour Economics 3, 169 –188. Current Population Survey. (1994). CPS Labour Extracts (2nd edition), NBER 50 Variable Uniform Extract 1979 –1993, CD-ROM Documentation, September 1994. Diamond, P. A. (1981). Mobility Costs, Frictional Unemployment and Efficiency. Journal of Political Economy 89, 798 – 812. Doherty, N. A. (1979). National Insurance and absence from work. Economic Journal 89, 50 – 65. Hylleberg, S., R. F. Engle, C. W. J. Granger & B. S. Yoo (1990). Seasonal integration and cointegration. Journal of Econometrics 44, 215–238.
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Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12, 215–238. Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregression models. Econometrica 59, 1551–1580. Kalecki, M. (1943). The political aspects of full employment, Lecture to the Marshall Society. Kenyon, P., & P. Dawkins (1989). A time series analysis of labour absence in Australia. Review of Economics and Statistics 71, 232–239. Leigh, J. P. (1985). The effects of unemployment and the business cycle on absenteeism. Journal of Economics and Business 37, 159 –170. Markham, S. E. (1985). An investigation of the relationship between unemployment and the absenteeism: a multi level approach. Academy of Management Journal 28, 229 –234. Miron, J. A. (1990). The economics of seasonal cycles, NBER Working paper 3522. Salop, S. C. (1979). A model of the natural rate of unemployment. American Economic Review 69, 117–125. Shapiro, C., & J. E. Stiglitz (1984). Equilibrium unemployment as a worker discipline device. American Economic Review 74, 433– 444. StataCorp (1999). Stata Statistical Software: Release 6.0 College Station, TX: Stata Corporation. Steers, R. M., & S. R. Rhodes (1978). Major influences on employee attendance: a process model. Journal of Applied Psychology, 63, 391– 407. Weiss, A. (1985). Absenteeism and wages. Economics Letters, 19, 277–279.
Absenteeism, seasonality, and the business cycle Rick Audasa,*, John Goddardb a
Faculty of Administration and Canadian Research Institute for Social Policy, University of New Brunswick, New Brunswick, Canada b Department of Economics, University of Wales Swansea, UK Received 22 June 1999; received in revised form 26 April 2000; accepted 11 July 2000
Abstract Previous theoretical literature on malfeasance provides the basis for a theoretical model of absenteeism that incorporates both labor demand and supply side influences. This paper uses this theoretical framework as the basis for an analysis of the link between absenteeism, aggregate production and unemployment, using monthly US data for 1979 –93. Tests are carried out for unit roots at seasonal and nonseasonal frequencies. Cointegration tests suggest a long run relationship consistent with the theoretical model. © 2001 Elsevier Science Inc. All rights reserved. JEL classification: C22; J22; J41 Keywords: Absenteeism; Efficiency wages; Seasonal integration
1. Introduction This paper uses US monthly time series data to investigate the empirical relationship between fluctuations in the business cycle and the rate of worker absenteeism at the macroeconomic level. Early empirical studies viewed absenteeism principally as a labor market supply side phenomenon (Doherty, 1979; Markham, 1985; Leigh, 1985). This paper attempts to model both supply and demand side influences on the rate of absenteeism. Although it is widely assumed that absenteeism is influenced by cyclical factors, to our
* Corresponding author. Tel.: ⫹506-458-7314. E-mail address: [email protected] (R. Audas). 0148-6195/01/$ – see front matter © 2001 Elsevier Science Inc. All rights reserved. PII: S 0 1 4 8 - 6 1 9 5 ( 0 1 ) 0 0 0 3 8 - 8
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knowledge no attempt has been made to verify or quantify this relationship using recent time series econometrics techniques. This paper is an attempt to fill this gap. Discussion of the implications of fluctuations in the business cycle for workplace discipline dates back at least as far as Kalecki’s (1943) observation that “. . . under a regime of permanent full employment, the ‘sack’ would cease to play its role as a disciplinary tool.” In their landmark paper, Steers and Rhodes (1978) develop a theoretical model of employee absenteeism, arguing that “economic and market conditions” play a prominent role in determining the individual’s motivation to attend work. As the economy enters recession, the consequences of losing one’s job become more serious as the opportunities to find alternative employment are reduced. To reduce the probability of dismissal, workers will attend more frequently. Barmby et al. (1995) argue that some portion of absence is malfeasant and can be explained using incentive models. Absenteeism can be explained along similar lines with the phenomenon of shirking in the efficiency wage literature: the risk of incurring dismissal and a spell of unemployment provides a disincentive to shirk (Calvo, 1979; Salop, 1979; Diamond, 1981; Shapiro and Stiglitz, 1984). The strength of this disincentive varies (countercyclically) with the business cycle. Most previous empirical studies also view absenteeism primarily as a labor supply phenomenon. Doherty (1979) and Kenyon and Dawkins (1989) implicitly assume that the demand for reliable labor is constant. Leigh (1985) argues informally that firms’ demand for reliable labor may be highest when economic conditions are at their worst. This suggests that labor demand influences tend to operate on absenteeism in the same direction as unemployment. Similarly, Markham (1985) suggests that firms may be less concerned about absence when economic conditions are strong, as “their attention is turned to meeting increasing consumer demands”. Weiss (1985) and Coles and Treble (1993, 1996) argue on different grounds that labor demand impacts on absenteeism, at the micro level. The firm’s monitoring effort should reflect the shadow cost of absence, and may also depend on production technologies. Consider a firm which operates an assembly line production process, in which workers are complements in production and the absence of one worker reduces the productivity of others. In a simple case, output might be zero if n ⬍ k, and constant for n ⱖ k, where n is the number of workers who attend, and k is the number needed for the assembly line to be operational. The firm has an incentive to pay higher agency costs to induce more reliable attendance by its workers than would be the case if its workers were perfect substitutes and if returns to scale were constant. In this paper, we argue that product and labor demand also influence absenteeism at the macro level, because firms’ shadow costs of absence vary over the business cycle. The returns to monitoring are high when product demand is buoyant, and low when product demand is slack. If hiring and firing workers is not costless, it may be efficient for the firm to hoard workers across anticipated cyclical (or seasonal) variation in demand. This would result in firms treating malfeasant absenteeism less leniently when product demand and therefore labor demand are high. An important implication is that different influences operating primarily on the demand and the supply side of the labor market may tend to pull on the rate of absenteeism in
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opposite directions during the same phase of the business cycle. On the one hand, during an upswing, firms under pressure to meet orders will monitor absence stringently, increasing the risks of detection for the malfeasant employee. On the other hand, when unemployment is low, the costs of dismissal as a result of malfeasance are reduced, since the employee knows he can easily find another job elsewhere. In the empirical literature, Doherty (1979) finds consistent evidence of an inverse relationship between unemployment and a variety of absenteeism measures, by applying ordinary least squares (OLS) to an annual UK data set covering the period 1954 –74. The benefit/earnings ratio is also found to be a significant influence, lending further support to the hypothesis of incentive effects on absenteeism. Leigh (1985) finds a significant negative correlation between the annual change in absenteeism and unemployment, using aggregated data from the US Panel Study of Income Dynamics (PSID) for the period 1967–78. He also finds a similar effect in a cross-sectional analysis at the industry level for 1976 –77. Markham (1985) uses monthly US Bureau of National Affairs (BNA) absenteeism data at national, regional and plant levels for the period 1976 – 82. Using OLS, a significant relationship between absenteeism and both unemployment and an index of employment opportunities is obtained. Finally, Kenyon and Dawkins (1989) use OLS on quarterly Australian data for the period 1966 – 84 to demonstrate an inverse relationship between unemployment and absenteeism. Absenteeism is also found to be positively related to the percentage of days lost through industrial disputes. In this paper, an empirical examination of variation in absenteeism over the business cycle provides an opportunity to exploit recent developments in the econometric analysis of economic time series data, which were unavailable to the authors of the studies reviewed above. Specifically, we are able to test and correct for the presence of stochastic trends in the data. The empirical link between the business cycle and absenteeism is established by investigating the effects of two main business cycle indicators: an aggregate industrial production measure and the rate of unemployment. Monthly, US data are used for the period 1979 –93. The availability of monthly data also allows us to investigate the nature of seasonality. Although the nonmalfeasant component of absenteeism (attributable to morbidity) is likely to account for some part of any seasonal variation, there are at least two reasons why malfeasant absence may also be seasonal. First, the perceived benefit of a day away from work may be higher in summer than in winter, or during (rather than outside) school holidays. Second, the firm’s monitoring effort might vary through the seasons within the year due to the effects of labor hoarding.1 An important part of our empirical analysis is the application of methods developed by Hylleberg et al. (1990) and Beaulieu and Miron (1993) to test for unit roots in the presence of seasonality, which may be either deterministic or stochastic. The rest of the paper is structured as follows: In section 2, a theoretical model is developed which captures the essence of the arguments outlined above. The model considers the employee’s decision whether to be a malfeasant absentee, or whether to be nonmalfeasant. The link between the business cycle and the rate of absenteeism is established through the influence on this decision of two transition probabilities: the probability that a malfeasant employee loses his job as a result of his malfeasance being detected, and the probability that
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an involuntarily unemployed worker finds a job and re-enters employment. In section 3, the results of the empirical analysis are presented including a cointegration analysis of the long run relationship between the business cycle indicators and the rate of absenteeism. There is evidence of a cointegrating relationship consistent with the theoretical model. Finally, section 4 concludes.
2. Modeling malfeasant absenteeism In the theoretical model, we describe a worker who does not voluntarily take spells of absence as nonmalfeasant, and one who does as malfeasant. The model allows for both types of worker to be employed in some time periods, and to be involuntarily unemployed in others. The following symbols are used:
t
⫽ probability that a nonmalfeasant worker employed between time t and t ⫹ 1 is dismissed at t ⫹ 1; t ⫹ t ⫽ probability that a malfeasant worker employed between time t and t ⫹ 1 is dismissed at t ⫹ 1; t ⫽ probability that a worker who is involuntarily unemployed between time t and t ⫹ 1, or who is employed but dismissed at t ⫹ 1, regains employment at t ⫹ 1 and therefore becomes employed between t ⫹ 1 and t ⫹ 2; w ⫽ wage paid to all employed workers per period; b ⫽ benefit paid to all involuntarily and voluntarily unemployed workers per period; vi ⫽ income equivalent of leisure time enjoyed by unemployed workers. vi is assumed to vary between workers. kvi ⫽ income equivalent of leisure time per period enjoyed by malfeasant employed worker i. k (0⬍k⬍1) is the proportion of work time spent absent.2 We begin by defining the arrays of transition probabilities between employment and involuntary unemployment. Initially, we do so under the steady state condition that workers assume the transition probabilities will remain the same in all future periods, or t ⫽ , t ⫽ and t ⫽ for all t. If the worker is employed at time t and chooses to be nonmalfeasant, he either retains his job at t ⫹ 1 with probability 1 ⫺ , or loses it with probability . If the job is lost, there is a probability of of re-entering employment immediately at t ⫹ 1. The transition probabilities from employment at t to employment and unemployment at t ⫹ 1 are therefore 1 ⫺ (1 ⫺ ) and (1 ⫺ ), respectively. Similarly, if the worker chooses to be malfeasant, he faces transition probabilities of 1 ⫺ ( ⫹ ) (1 ⫺ ) and ( ⫹ ) (1 ⫺ ) from employment at t to employment and unemployment respectively at t ⫹ 1. Any worker who is involuntarily unemployed at t faces transition probabilities of and 1 ⫺ to employment and unemployment respectively at t ⫹ 1. To determine the conditions under which nonmalfeasant employment is preferred to malfeasant employment and vice versa, it is necessary to compare the present value of expected lifetime income in each case. For simplicity, infinite time horizons are assumed. Let
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x*1 denote the present value of expected lifetime income for a worker who, if currently employed will choose to be nonmalfeasant. Let x*2 denote the present value of lifetime income for the same worker if he is currently involuntarily unemployed. Similarly, let y*1 and y*2 denote the present values of expected lifetime income for malfeasant workers who are currently employed and involuntarily unemployed respectively. Finally, let d denote the discount rate. Because the transition probabilities are constant through time, x*1, x*2, y*1 and y*2 evaluated at time t ⫹ 1 (and at all future times) are the same as at time t. This means that in steady state, a worker who chooses to be nonmalfeasant at t will always be nonmalfeasant, and one who chooses malfeasance will always be malfeasant. The steady state equations for x*1, x*2, y*1 and y*2 are X*⫽ Z 1 ⫹ A 1X*
Y* ⫽ (Z 1 ⫹ Z 2) ⫹ A 2Y*
f X* ⫽ (I ⫺ A 1) ⫺1Z 1
Y* ⫽ (I ⫺ A 2)⫺1(Z 1 ⫹ Z 2)
where X* ⫽
冉 xx**冊 1 2
Y* ⫽
A 1 ⫽ (1 ⫹ d)⫺1 A 2 ⫽ (1 ⫹ d)⫺1
冉 冉
冉 yy**冊 1 2
1 ⫺ (1 ⫺ )
冉 b ⫹w v 冊 (1 ⫺ 1⫺ 冊
Z1 ⫽
1 ⫺ ( ⫹ )(1 ⫺ )
1
Z2 ⫽
冉 kv0 冊 i
冊
( ⫹ )(1 ⫺ ) 1⫺
Z1 and Z1 ⫹ Z2 are vectors containing the payoffs per period from employment and unemployment for nonmalfeasant and malfeasant workers respectively. A1 and A2 are matrices of (discounted) transition probabilities. These equations can be used to establish the range of values for vi (the income equivalent of leisure) over which malfeasant employment is preferred to nonmalfeasant employment and vice versa. Malfeasant employment is preferred if Z 2 ⬎ CZ 1 where C ⫽ ((I ⫺ A 2)(I ⫺ A 1)⫺1 ⫺ I) ⫽
冉 c0 c0 冊 11
12
f vi ⬎ vCRIT ⫽ (c11w ⫹ c12b)/(k ⫺ c12) where c11 and c12 are functions of , and , and vCRIT is the critical value of vi at which the employee is indifferent between malfeasance and nonmalfeasance. Workers who place a low value on leisure (vi ⬍ vCRIT) find that in the long term, the gains from malfeasance are insufficient to compensate for the costs in wages foregone as a result of being unemployed for a higher proportion of the time. Workers who place a high value on leisure (vi ⬎ vCRIT) find the opposite. To determine the conditions under which voluntary unemployment is preferred to malfeasant employment, we note that the former produces an income equivalent of b ⫹ vi per
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period, while the latter produces b ⫹ vi in some periods and w ⫹ kvi in others. Expected income from involuntary unemployment therefore exceeds that from malfeasant employment whenever vi ⬎ (1 ⫺ k)-1(w ⫺ b). Together with the previous results, this establishes that with steady state transition probabilities, malfeasant employment is the preferred choice for all workers with vCRIT ⬍ vi ⬍ (1 ⫺ k)-1(w ⫺ b). This condition is therefore sufficient to determine the rate of absenteeism which corresponds to the steady state transition probabilities defined above. We now consider the effect on the rate of absenteeism of short term variations in the transition probabilities. Suppose that t, t and t may be above or below their steady state values for the period t to t ⫹ 1, but are expected (at time t) to return to their steady state values for all periods from t ⫹ 1 to t ⫹ 2 and beyond. We define x1t and y1t to be the present values of expected lifetime income at t for workers who are employed at t and who will be nonmalfeasant and malfeasant respectively between t and t ⫹ 1. x2t and y2t are the present values for nonmalfeasant and malfeasant workers who are involuntarily unemployed at t. These present values can be written as: X t ⫽ Z 1 ⫹ A 1tX*
Y t ⫽ Z 1 ⫹ Z 2 ⫹ A 2tX*
if vi ⬍ vCRIT
X t ⫽ Z 1 ⫹ A 1tY*
Y t ⫽ Z 1 ⫹ Z 2 ⫹ A 2tY*
if vi ⬎ vCRIT
and
where Xt ⫽
冉 xx 冊 1t
2t
Yt ⫽
A 2t ⫽ (1 ⫹ d)⫺1
冉 yy 冊 A ⫽ (1 ⫹ d) 冉 1 ⫺ (1 ⫺ ) 冉 1 ⫺ ( ⫹ )(1 ⫺ ) ( ⫹1⫺)(1 ⫺ )冊 ⫺1
1t
1t
2t
t
t
t
1
t
t
t
t
t
冊
t(1 ⫺ t) 1 ⫺ t
t
t
If vi ⬍ vCRIT, then in steady state, the worker prefers nonmalfeasance. The condition for malfeasance to be preferred between t and t ⫹ 1 is Z 2 ⬎ (A 1t ⫺ A 2t)X* f vi ⬎ vLOW ⫽ {k(1 ⫹ d)}⫺1t(1 ⫺ t)(x*1 ⫺ x*2) vLOW is the minimum value of vi at which malfeasance is preferred between t and t ⫹ 1 by workers who would normally be nonmalfeasant. If t ⫽ and t ⫽ , vLOW ⫽ vCRIT (the steady state solution). However, if t ⬍ or t ⬎ , vLOW ⬍ vCRIT. Some workers with vLOW ⬍ vi ⬍ vCRIT, who in steady state would be nonmalfeasant, choose to be malfeasant for the period t to t ⫹ 1, so the rate of absenteeism rises above its steady state value. Similarly, if vi ⬎ vCRIT, then in steady state, the worker prefers malfeasance. The condition for nonmalfeasance to be preferred between t and t ⫹ 1 is Z 2 ⬎ (A 1t ⫺ A 2t)Y* f vi ⬎ vHIGH ⫽ {k(1 ⫹ d)}⫺1t(1 ⫺ t)(y*1 ⫺ y*2) vHIGH is the minimum value of vi at which malfeasance is preferred between t and t ⫹ 1 by workers who would normally be malfeasant. If t ⫽ and t ⫽ , vHIGH ⫽ vCRIT (the steady state solution). However, if t ⬎ or t ⬍ , vHIGH ⬎ vCRIT. Some workers with
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vCRIT ⬍ vi ⬍ vHIGH, who in steady state would be malfeasant, choose to be nonmalfeasant for the period t to t ⫹ 1, so the rate of absenteeism drops below its steady state value. Short-term fluctuations in the rate of absenteeism are therefore driven by fluctuations in the parameters which govern the probabilities of transition between employment and unemployment and vice versa, t and t. In order to develop an empirical model, it is necessary to establish a link between these transition probabilities and appropriate macroeconomic business cycle indicators. First, t is expected to vary directly with aggregate production. As argued above, when output is high, firms may attempt to satisfy their increased demand for labor by hiring more workers, or by monitoring malfeasance among their existing workers more stringently. Conversely when output is low, firms may lay off some workers, or may monitor malfeasance less stringently. Varying the stringency of monitoring malfeasance allows adjustments to be made to the (effective) labor force without incurring the transactions costs associated with hiring and firing. Relaxing monitoring during slack periods therefore constitutes a form of labor hoarding. Second, t is assumed to vary inversely with the rate of unemployment. The higher the latter, the lower the probability that an involuntarily unemployed worker will re-enter employment at any particular point in time, and vice versa. Overall, there is no clear expectation as to whether absenteeism should be pro- or countercyclical. During peaks in the cycle, pressure to increase output which leads to more stringent monitoring will tend to reduce absenteeism. At the same time, by reducing the costs to the individual of dismissal, low unemployment tends to encourage malfeasance. During recessions, the same factors tend to operate in the opposite directions. The fact that fluctuations in production and unemployment are not perfectly synchronised, however, should make it possible to identify their individual effects on the rate of absenteeism. This is investigated in the following empirical section.
3. Absence and business cycle indicators: unit root and cointegration tests The data set consists of 180 monthly observations for the 15 year sample period 1979 to 1993 (inclusive). The US monthly Current Population Survey (CPS) was used to obtain series for at and ut, the rates of absence and unemployment respectively. The CPS contains information on approximately 17,000 individuals across a wide demographic and geographic base. Respondents are asked to state the number of hours normally worked and the number of hours actually worked in each week, and to explain any difference between the two by selecting one of a number of listed causes of absence. The rate of absenteeism is calculated by dividing the total number of hours absent attributed to “own illness”, “too busy with home or school” or “other reasons,” by the total number of hours normally worked. Absences attributed to factors such as “slack work,” “job terminated,” “materials shortage,” “strike” or “holiday” are not included in the numerator. The unemployment rate is the number of unemployed divided by the sum of the unemployed, those who worked, and those who did not work but held jobs. Real monthly industrial production (adjusted for the number of calendar days in the month but otherwise seasonally unadjusted) was obtained from
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Datastream and is used to measure yt.3 In the estimations, all variables are in natural logarithms. The empirical analysis begins with investigation of the univariate time series properties of at, yt and ut, taking into account any seasonality which is present in the monthly versions of these series. There are three possibilities as to the nature of the seasonality: deterministic; stationary stochastic; and nonstationary stochastic seasonality. With deterministic seasonality (zt ⫽ ␦0 ⫹ ⌺sj ⫽ 2 ␦jsjt ⫹ ⑀t, where s is the number of seasons and sjt are seasonal dummies, assuming for simplicity no deterministic or stochastic trend components) the underlying seasonal pattern is regular throughout the series. Stationary stochastic seasonality (zt ⫽ zt-s ⫹ ⑀t, with 兩兩 ⬍ 1) implies that the seasonal pattern tends to change over time, although there is no tendency for the magnitude of the seasonal variation (between consecutive observations) to increase. With nonstationary stochastic seasonality (zt ⫽ zt-s ⫹ ⑀t), there is one zero frequency unit root and s-1 unit roots at nonzero frequencies. The seasonal pattern again changes over time, and the typical magnitude of the variation between consecutive observations also tends to increase. Miron (1990) argues that before the recent development of the literature on seasonal integration, econometricians tended to handle seasonality in an ad hoc (and possibly incorrect) manner. Abeysinghe (1994) demonstrates more formally that the use of seasonal dummies to model a process whose seasonality is actually nonstationary creates a spurious regression problem (in much the same way as the incorrect substitution of a deterministic for a stochastic trend). Therefore, a correct diagnosis of the nature of the seasonal component is as important as for the trend component, although most empirical evidence suggests that unit roots at nonzero frequencies (which produce nonstationary seasonality) are less common than unit roots at zero frequency (which produce stochastic trends). For quarterly series, Hylleberg et al. (1990) develop a method (the HEGY procedure) which uses a single auxiliary regression to test for unit roots at zero and nonzero frequencies, against alternatives which may incorporate a deterministic trend, deterministic seasonality or both. Beaulieu and Miron (1993) adapt the HEGY procedure to allow equivalent tests on monthly series. The main focus of the HEGY procedure is testing for stochastic nonstationary versus deterministic seasonality, because stochastic stationary seasonality can always be modelled by selecting an appropriate lag structure. The Beaulieu-Miron adaptation of the HEGY procedure to test a monthly series xt for nonseasonal and seasonal unit roots involves running the following auxiliary regression:
冘 ␥s
12
z13t ⫽ ␥0 ⫹ ␥1t ⫹
j jt
j⫽2
冘z
12
⫹
k kt⫺1
k⫽1
冘␦ z H
⫹
h 13t⫺h
⫹ ⑀t
(1)
h⫽1
In (1), z13t ⫽ (1 ⫺ B12)xt where B is the lag operator. The intercept, deterministic trend and/or seasonal dummies are optional. H is the number of lags of z13t required to whiten the residuals; in practice, we augment only with lags of z13t which test significant. z1t ⫽ ((1 ⫺ B12)/(1 ⫺ B))xt is interpreted as xt adjusted for the 11 seasonal unit roots. Failure to reject H0 : 1 ⫽ 0 against H1: 1⬍0 therefore indicates the presence of a nonseasonal unit root at zero frequency (i.e. a stochastic trend). Similarly, each of z2t . . . z12t is xt adjusted for the nonseasonal and 10 of the seasonal unit roots.4 To reject seasonal unit roots at all frequen-
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Table 1 Tests for seasonal integration
冘 ␥s ⫹ 冘 z 12
Auxiliary regression: z13t ⫽ ␥0 ⫹ ␥1t ⫹
12
j jt
j⫽2
Series IT
t(1) t(2) t(3) t(4) t(5) t(6) t(7) t(8) t(9) t(10) t(11) t(12) F(3艚4) F(5艚6) F(7艚8) F(9艚10) F(1112) F(1艚␥1)
⫺2.37 ⫺2.96* ⫺3.12* ⫺0.98 ⫺3.93* 2.53* ⫺3.53* 1.20 ⫺3.25* ⫺1.75 ⫺1.77 0.00 5.37* 11.37* 7.05* 6.98* 1.57 4.54
12
IS
⫹
k⫽1
at
Deterministic component Augmentation
冘␦z 12
k kt⫺1
h 13t⫺h
⫹ ⑀t
h⫽1
yt ITS
IT
—
—
1,5,7,12,13
⫺2.62 ⫺3.80* ⫺5.27* ⫺0.85 ⫺5.50* 2.78* ⫺6.21* 1.25 ⫺4.01* ⫺1.42 ⫺4.67* 1.13 14.48* 19.67* 20.55* 9.29* 11.84* —
⫺2.15 ⫺3.80* ⫺5.27* ⫺0.86 ⫺5.50* 2.47* ⫺6.21* 1.21 ⫺4.01* ⫺1.41 ⫺4.68* 1.07 14.48* 19.65* 20.50* 9.25* 11.79* 3.53
⫺2.51 ⫺0.54 ⫺1.98* ⫺0.10 ⫺1.74 0.81 ⫺2.37* ⫺1.00 ⫺0.59 ⫺0.73 ⫺0.72 ⫺1.82 1.97 1.84 3.35* 0.45 1.92 3.16
ut
IS
ITS
IT
—
—
2,3,12,14
⫺0.39 ⫺3.87* ⫺4.04* ⫺3.43* ⫺4.02* 2.65* ⫺2.29 ⫺4.80* ⫺6.15* 0.57 ⫺0.98 ⫺5.14* 15.29* 12.51* 15.03* 19.19* 13.87* —
⫺2.88 ⫺3.95* ⫺4.23* ⫺3.26* ⫺4.20* 2.56* ⫺2.75 ⫺4.59* ⫺6.28* 0.55 ⫺1.75 ⫺4.96* 15.56* 13.04* 15.54* 19.95* 14.42* 4.24
⫺2.79 ⫺3.52* ⫺1.34 ⫺0.01 ⫺3.24 2.15* ⫺1.05 ⫺1.83 ⫺4.39* 1.07 ⫺1.44 ⫺1.76 0.97 9.07* 2.21 10.01* 2.55 3.89
IS
ITS —
—
⫺1.48 ⫺4.32* ⫺5.22* 0.68 ⫺5.43* 1.30 ⫺3.73* ⫺3.26* ⫺5.01* 0.34 ⫺2.50* ⫺6.33* 13.98* 15.88* 13.36* 12.64* 25.12* —
⫺2.70 ⫺4.32* ⫺5.24* 0.69 ⫺5.46* 1.21 ⫺3.94* ⫺3.13* ⫺5.06* 0.32 ⫺3.02* ⫺6.06* 14.09* 15.90* 13.88* 12.85* 25.83* 3.88
Critical values: 5% significance level IT IS ITS
t(1) ⫺3.29 ⫺2.74 ⫺3.23
t(2) ⫺1.86 ⫺2.71 ⫺2.73
t(k) ⫺1.87 ⫺3.18 ⫺3.17
t(k⫹1) ⫾1.92 ⫾2.18 ⫾2.17
F(k艚k⫹1) 2.97 5.99 5.99
F(1艚y1) 5.91 — 5.67
* Denotes significant at the 5% level. Critical values are shown for t(k), t(k⫹1) and F(k艚k⫹1) for k ⫽ 3,5,7,9,11.
cies, k must not equal zero for k ⫽ 2 and for at least one element of each of the sets {3,4}, {5,6}, {7,8}, {9,10} and {11,12}. All of these hypotheses can be tested using t or F statistics obtained from OLS estimation of (1).5 The critical values, which depend on the number of observations and on whether an intercept, trend and/or seasonal dummies are included in (1), are generated from large numbers of replications of (1 ⫺ B12)xt ⫽ ⑀t. Table 1 shows the results of the nonseasonal and seasonal unit root tests on at, yt and ut using three alternative specifications of (1): with intercept and trend (IT); with intercept and seasonals (IS); and with intercept, trend and seasonals (ITS). For at, failure to reject H0:1艚␥1 ⫽ 0 in both IT and ITS and H0:1 ⫽ 0 in IS suggests that IS is the correct specification, and that there is a nonseasonal unit root. No seasonal unit roots are detected from the t or F tests on 2 . . . 12. The seasonal dummies test significant, indicating that seasonality in the absenteeism series is deterministic. In line with the earlier discussion, we assume that the dummies may be capturing regularities in both the nonmalfeasant and
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malfeasant components of seasonal absenteeism.6 The diagnoses for both yt and ut are the same as for at. Therefore, we can now use the cointegration tests developed by Johansen (1988, 1991) to investigate whether there is empirical evidence of a long run, cointegrating relationship between at, yt and ut. For a system comprising three nonstationary I(1) series each with a deterministic seasonal component, the Johansen method is based on the following vector autoregression (VAR) which represents the most general specification of the data generating process:
冘⌽ 3
z t ⫽ ␣ ⫹ ⌫s t ⫹
m
z tⴚm ⫹ ⑀ t
(2)
m⫽1
where in our case, zt’ ⫽ (at yt ut), ␣ ⫽ {␣i} is a 3 ⫻ 1 vector of intercepts, ⌫ ⫽ {␥ij} is a 3 ⫻ 11 matrix of coefficients, st ⫽ {sjt} is an 11 ⫻ 1 vector of seasonal dummies, ⌽m ⫽ {(m) ij } for i, j ⫽ 1.3 and m ⫽ 1. . . M where M is the maximum lag length, and ⑀t’ ⫽ (⑀1t ⑀2t ⑀3t). Before any cointegration tests can be carried out, it is necessary to establish the lag structure, eliminating the M0’th set of lags from (2) if the quality of the model is not significantly reduced by moving to M0 -1 lags, and so on. On this criterion, we find that M ⫽ 4 is the appropriate lag length.7 For the purposes of the cointegration tests, (2) with M ⫽ 4 can be reparameterised as follows:
冘⌿ 3
⌬z t ⫽ ␣ ⫹ ⌫s t ⫹
m⌬z tⴚm
⫹ ⌰z tⴚ1 ⫹ ⑀ t
(3)
m⫽1
where ⌿m ⫽ {(m) ij } and ⌰ ⫽ {ij} are 3 ⫻ 3 matrices of coefficients. The question whether there is one or more cointegrating vector linking at, yt and ut depends whether restrictions on r ⫽ rank(⌰) can be imposed in (3); one cointegrating vector, say et ⫽ at ⫺ 0 ⫺ 1yt ⫺ 2ut, requires r ⫽ 1. The results of Johansen’s two alternative tests for r, based on the maximal eigenvalue and trace statistics, are shown in section 1 of Table 2. H0:r ⫽ 0 is rejected in favor of H1:r⬎0 at the 5% level with the trace statistic, and at just above the 5% level with the maximal eigenvalue statistic. Tests of H0:rⱕ1 then fail to reject in favor of H1:r⬎1. As expected, the tests also fail to reject H0:rⱕ2 against H1:r⬎2. Overall, the tests provide strong evidence of a single cointegrating vector. Section 2 of Table 2 shows the estimated coefficients of the single cointegrating vector, together with likelihood ratio tests for the significance of ˆ 1 and ˆ 2. Both coefficients are signed in accordance with the theoretical discussion in section 2, and both are highly significant. These results enable us to assess the relative impact of the demand and supply side influences on absenteeism during an upturn (or downturn) in the business cycle. For a 1% increase in the level of real output to have zero impact on absenteeism, the results suggest it would have to be accompanied by a reduction in unemployment equivalent to just over 3% of the current unemployment rate (so if the unemployment rate were 10%, the necessary reduction in this figure would be just over 0.3%). If the percentage fall in the rate of unemployment is more than three times the percentage increase in real output, absenteeism
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Table 2 Tests for cointegration 1. Tests for r ⫽ rank (⌰) in (2) H0 r⫽0 rⱕ1 rⱕ2
H1 r⬎0 r⬎1 r⬎2
Maximal eigenvalue statistic 20.91** 7.97 1.09
Trace statistic 29.98* 9.07 1.10
2. Estimated cointegrating relationship: at ⫽ ˆ 0 ⫹ ˆ 1yt ⫹ ˆ 2ut ⫹ e1 ˆ 0 ⫽ ⫺1.8657 ˆ 1 ⫽ ⫺0.7537 ˆ 2 ⫽ ⫺0.2309 Likelihood ratio tests: (i) H0:1 ⫽ 0 2(1) ⫽ 7.82** (ii) H0:2 ⫽ 0 2(1) ⫽ 4.97* 3. Maximum likelihood estimation of equation for ⌬at in (2) ⌬at ⫽ ␣ˆ 1 ⫹ ␥ˆ 12jsjt
冘 j
⫺0.47*et⫺1 ⫺ 0.30*⌬a t⫺1 ⫺ 0.28*⌬at⫺2 ⫺ 0.27*⌬at⫺3 (0.11) (0.10) (0.09) (0.07) ⫹0.37 ⌬yt⫺1 ⫹ 0.88** ⌬yt⫺2 ⫺ 0.61 ⌬yt⫺3 (0.48) (0.49) (0.47) ⫺0.04 ⌬ut⫺1 ⫹ 0.08 ⌬ut⫺2 ⫹ 0.15**⌬ut⫺3 ⫹ ˆ 1t (0.09) (0.10) (0.09) 2 ⫽ 0.48 s.e. regression ⫽ 0.0586 n ⫽ 175 R2 ⫽ 0.54 R serial correlation: 2(1) ⫽ 0.38 2(2) ⫽ 0.63 2(3) ⫽ 0.80 2(12) ⫽ 13.71 heteroscedasticity: 2(1) ⫽ 0.01 Standard errors of estimated coefficients are in parentheses. * Denotes significant at 5% level; ** Denotes significant at 10% level. Estimates of the constant and seasonal dummy coefficients are not reported. Serial correlation tests are Ljung-Box statistics, based on the autocorrelation function of the residuals. Heteroscedasticity test is a Lagrange Multiplier test based on an auxiliary regression of squared residuals on squared fitted values.
should be rising. If unemployment is falling at less than this rate, absenteeism should be falling. The estimated equation for ⌬at obtained from maximum likelihood estimation of (3) as a VAR, with the cointegrating restriction r ⫽ 1 imposed, is shown in section 3 of Table 2. With the exception of the lags of the dependent variable, the model does not reveal any strong short run dynamic effects.8 However, the coefficient on the error correction term et-1 is correctly signed and highly significant, and the diagnostics suggest that the specification is satisfactory.9 The empirical results therefore support the hypothesis that variations in both production and unemployment are important in explaining absenteeism. Firms alter their monitoring intensity in response to changes in product demand, and individuals change their propensity to attend work as labor market conditions vary.
4. Conclusion In this paper, we have investigated the determinants of malfeasant employee absenteeism at the macro level. The paper not only adds to the limited quantity of previous work
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examining absenteeism specifically, but also contributes to the wider and more extensive literature on malfeasance. We regard absenteeism as a phenomenon with a significant malfeasant component. Because absenteeism (in contrast to most other types of malfeasance) is readily observable, we are able to sidestep the data problems that often prevent researchers from subjecting theoretical models of malfeasance to empirical scrutiny. The theoretical model views malfeasant absenteeism in a manner similar to the treatment of on-the-job shirking in the efficiency wage literature. The incentive to be an absentee depends on the transition probabilities from employment to unemployment as a result of detection as a malfeasant absentee, and from unemployment back to employment. If hiring and firing labor is expensive, it may be efficient for the firm to hoard workers across cyclical fluctuations in demand, treating malfeasant absenteeism less leniently when product demand and labor demand are buoyant than when demand is slack. When unemployment is low, however, the costs of dismissal as a result of being detected as a malfeasant absentee are reduced, since the employee knows he can find another job easily. An implication of these arguments is that different influences operating principally on the demand and supply side of the labor market may tend to pull in opposite directions on the rate of absenteeism during the same phase of the business cycle. Monthly US time series data for the period 1979 –93 is used to test for macro relationships between absenteeism, production and unemployment. These series each appear to contain one nonseasonal unit root and no seasonal unit roots. Evidence of a cointegrating relationship between absenteeism, production and unemployment is presented. The finding that absenteeism varies inversely with unemployment is consistent with the previous empirical literature (Doherty, 1979; Leigh, 1985; Markham, 1985; and Kenyon and Dawkins, 1989). The findings that absenteeism also varies inversely with production, and that absenteeism, unemployment and production are cointegrated are new. These empirical results help extend our previous understanding of the causes of absenteeism at the aggregate level.
Notes 1. Testing. for seasonality in a variety of aggregate US series, Barsky and Miron (1989) find limited evidence of production smoothing, and significant seasonal variation in labour productivity, which they attribute to labour hoarding. 2. In. common with other malfeasance literature, we simplify by assuming that the choice between malfeasance and non-malfeasance is discrete, and that there are no ‘degrees’ of malfeasance, which in this case would correspond to varying proportions of time spent absent. 3. The Stata 6.0 code used to generate the rate of absenteeism, using the NBER CPS data dictionary (Current Population Survey, 1994; StataCorp, 1999) is as follows: keep if activlw ⫽⫽ 1 兩 activlw ⫽⫽ 2 兩 activlw ⫽⫽ 4 兩 activlw ⫽⫽ 5 keep if uhourse ⬎ 0 mvencode hourslw, mv(0) gen timelost ⫽ uhourse – hourslw replace timelost ⫽ 0 if timelost ⬍ 0
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gen absence ⫽ timelost if reasonlw ⫽⫽ 10 兩 reasonlw ⫽⫽ 12 兩 reasonlw ⫽⫽ 15 兩 absentlw ⫽⫽ 1 兩 absentlw ⫽⫽ 8 gen validtl ⫽ timelost if timelost ⬎ 0 & absence ⫽⫽ 0 mvencode validtl, mv(0) mvdecode absence, mv(0) mvencode absence, mv(0) gen worktime ⫽ uhourse –validtl gen abrate ⫽ absence/worktime Unemployment is generated from the CPS as follows: gen unemp ⫽ 1 if esr ⫽⫽ 3 gen labforce ⫽ 1 if esr ⬍ ⫽ 3 mvencode unemp labforce, mv(0) sum unemp if labforce ⫽⫽ 1 The Datastream code for the industrial production series is USIPTOT.G 4. Full definitions are: z1t ⫽ (1 ⫹ B ⫹ B2 ⫹ B3 ⫹ B4 ⫹ B5 ⫹ B6 ⫹ B7 ⫹ B8 ⫹ B9 ⫹ B10 ⫹ B11) xt; z2t ⫽ (1 ⫺ B ⫹ B2 ⫺ B3 ⫹ B4 ⫺ B5 ⫹ B6 ⫺ B7 ⫹ B8 ⫺ B9 ⫹ B10 ⫺ B11) xt; z3t ⫽ ⫺(B ⫺ B3 ⫹ B5 ⫺ B7 ⫹ B9 ⫺ B11) xt; z4t ⫽ ⫺(1 ⫺ B2 ⫹ B4 ⫺ B6 ⫹ B8 ⫺ B10) xt; z5t ⫽ ⫺(1/2)(1 ⫹ B ⫺ 2B2 ⫹ B3 ⫹ B4 ⫺ 2B5 ⫹ B6 ⫹ B7 ⫺ 2B8 ⫹ B9 ⫹ B10 ⫺ 2B11) xt; z6t ⫽ (公3/2)(1 ⫺ B ⫹ B3 ⫺ B4 ⫹ B6 ⫺ B7 ⫹ B9 ⫺ B10) xt; z7t ⫽ (1/2)(1 –B ⫺ 2B2 ⫺ B3 ⫹ B4 ⫹ 2B5 ⫹ B6 ⫺ B7 ⫺ 2B8 ⫺ B9 ⫹ B10 ⫹ 2B11) xt; z8t ⫽ –(公3/2)(1 ⫹ B – B3 – B4 ⫹ B6 ⫹ B7 ⫺ B9 – B10) xt; z9t ⫽ ⫺(1/2)(公3 ⫺ B ⫹ B3 ⫺ 公3B4 ⫹ 2B5 ⫺ 公3B6 ⫹ B7 ⫺ 2B8 ⫺ B9 ⫹ 公3B10 ⫺ 2B11) xt; z10t ⫽ (1/2)(1 ⫺ 公3B ⫹ 2B2 ⫺ 公3B3 ⫹ B4 ⫺ B6 ⫹ 公3B7 ⫺ 2B8 ⫹ 公3B9 ⫺ B10) xt; z11t ⫽ (1/2)(公3 ⫹ B – B3 ⫺ 公3B4 ⫺ 2B5 ⫺ 公3B6 ⫺ B7 ⫹ B9 ⫹ 公3B10 ⫹ 2B11) xt; z12t ⫽ ⫺ (1/2)(1 ⫹ 公3B ⫹ 2B2 ⫹ 公3B3 ⫹ B4 ⫺ B6 ⫺ 公3B7 ⫺ 2B8 ⫺ 公3B9 ⫺ B10) xt; 5. H0: 2 ⫽ 0 (tested against H1:2⬍0) should be rejected using a t-test. At least one of H0:k ⫽ 0 (tested against H1:k⬍0) or H0:k⫹1 ⫽ 0 (tested against H1:k⫹1⫽0) should be rejected using t-tests, or alternatively H0:k艚k⫹1 ⫽ 0 should be rejected using an F-test, for k ⫽ 3,5,7,9,11. See Hylleberg et al. (1990) and Beaulieu and Miron (1993) for full details of these procedures. 6. The seasonal peak occurs in February with a mean absence rate of 0.030868 across the 15-year period under consideration. Over the same period, the seasonal trough occurs in July with an average absence rate of 0.023693. 7. The likelihood ratio test statistic for the significance of the coefficients on the M0’th ˆ M 兩⫺ ln兩⍀ ˆ M 兩}, where the VAR is estimated as lagged terms is 2 ⫽ (T ⫺ M0){ln兩⍀ 0⫺1 0 a system of three seemingly unrelated regressions. T is the total number of observaˆ M ⫽ {ˆ ij} is the error covariance matrix from the VAR with M0 lags estimated tions; ⍀ 0 using the observations for t ⫽ M0 ⫹ 1 . . . T, i.e. ˆ ij ⫽ ⌺t ⑀ˆ it⑀ˆ jt/(T - M0) for ij ⫽ 1, 2, ˆ 3; and ⍀ M0⫺1 is the covariance matrix with M0⫺1 lags also estimated using the same
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observations. The distribution of 2 under the null is 2(9) in this case. For M0 ⫽ 5,4,3,2 and 1, this test produces 2 ⫽ 7.38, 25.59, 41.51, 43.63 and 1055.42 respectively. The critical value at the 5% significance level is 16.92. Further tests with M0⬎5 did not show any sets of lags of order higher than 5 to be significant. 8. Following the earlier discussion of the pro- and counter-cyclical influences on absenteeism, the failure to identify significant short run effects is unexpected. This could reflect inadequacies in the theoretical model, or it could simply be due to shortcomings in the data set. 9. We have also carried out a similar analysis using absence and unemployment rates disaggregated by sex, with the same production series. For reasons of space, the results are not reported in full. For absence, all seasonal unit roots are rejected for both males and females. A non-seasonal unit root is diagnosed for females but rejected for males. For unemployment, all seasonal unit roots are rejected, and non-seasonal unit roots are detected in both cases. If these results are accepted, a cointegration analysis is appropriate for females but not for males, whose absence is diagnosed as stationary. For females, the cointegration tests are successful in diagnosing a single cointegrating vector with correctly signed and significant coefficients. If we proceed with the same analysis for males, there is ambiguity as to the number of cointegrating vectors.
Acknowledgment We would like to thank John Treble for comments on an earlier draft of this paper.
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