the demand for hours of work

Scottish Journal of Polifical Economy, Vol. 34, No. 4, November 1987 0 1987 Scottish Economic Society

THE DEMAND FOR HOURS O F WORK

DEREK BOSWORTH A N D TONY WESTAWAY

Institute for Employment Research, University of Warwick and Department of Economics, University of Loughborough.

I

INTRODUCITON

The large literature on employment functions and factor demand models has tended to focus on employment, and, while hours of work have been discussed in a number of places, this has mainly been of incidental concern. Despite the wealth of literature in this area, several important questions have not been wholly resolved. The main focus of attention in this paper is whether average hours of work should be treated as a homogeneous entity, when they are in practice a weighted average of overtime, normal hours and short time working, a question which appears to have merited little if any discussion in the existing literature. The second question concerns the role played by quasi-fixed labour costs in the determination of hours of work. The third is whether changes in normal hours result in commensurate changes in average hours of work and, therefore, can be used as a policy instrument to create additional employment through worksharing.

While factor demand studies implicitly or explicitly treat hours as a homogeneous entity, it is clear from Figures 1 and 2 that the various components (i.e. the length and incidence of normal, short-time and overtime working) show significant differences in their patterns over time. Normal hours form a dominant part of average hours and it is perhaps none too surprising that the models which purport to explain average hours, with normal hours as an explanatory variable, give a good overall fit. A natural consequence of a disaggregated approach is to question whether the same model can explain all of the dimensions of the composite, average hours variable. The application of a traditional model to the various components of hours undertaken in this paper shows that this is not the case. The results indicate that existing models tend to be more closely tuned to the overtime than the short time end of the spectrum.

Recent interest in the influence of quasi-fixed labour costs (QFLCs) has been intensified for two reasons. First, there is the possibility that govern- ment taxes (such as employer National Insurance Contributions, NICs) may have stimulated longer hours of work at the expense of employment opportunities (Ehrenberg, 1971, Hart and Sharot, 1978), although this view is not unanimous (Bosworth and Westaway, 1985). Second, empirical tests of the role played by QFLCs in explaining hours have revealed inconsistencies

Date of receipt of final manuscript: 1 December 1986.

368

THE DEMAND FOR HOURS OF WORK 369

6 0

50 VI u > ._ c e

40 0 L

Shorl - l ime Hourr

4

Figure 1. Incidence of hours worked on short-time, normal and overtime working, 1963 to 1983.

25

20

u > .- c p 15 0) (5 0 I 0) a $ 10 0 I

5

0

Overlime Hours per Operative

, I I 2 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 I! 4

Figure 2. Overtime hours per operative on overtime and hours lost per operative on short-time, 1963 to 1983.

370 D. BOSWORTH AND T. WESTAWAY

between the micro and the industry level studies. Disaggregated work on the structure of labour costs suggests that QFLCs are unlikely to be sufficiently large to move the firm from normal hours to permanent overtime working (Garbarino, 1964; Bosworth, 1982). A second objective of this paper therefore is to examine the effect of employer NICs on the demand for hours of work. The disaggregation of hours to some extent helps to resolve the dilemma concerning the role of QFLCs.

Normal hours are institutionally determined and can be assumed to be exogenously given in the models of hours of work. However, we can examine whether changes in normal hours lead to commensurate changes in average hours of work and, therefore, can be used as a policy instrument to create additional employment through worksharing. Bod0 and Giannini (1985, p. 134) conclude that, “theoretical analysis does not enable us to say a priori what the effects of a generalized reduction of contractual working time on actual hours will be”. With regard to the empirical evidence, Hart (1984, pp. 172-2) argues that, on this point, the results contained in studies such as Brechling (1965), Ehrenberg (1971) and Hart and Sharot (1978) are “mixed”. Subsequent work, such as Bod0 and Giannini (1985) and Bosworth and Westaway (1985), does not wholly resolve the issue. All of these studies use an average hours of work measure in their empirical tests and some of the inconsistencies in the results may be traced to the different impact of changes in normal hours on the various elements that comprise the composite variable.

Section (11) therefore develops the theoretical framework. Section (111) discusses the sources of data and the empirical results. Finally, section (IV) outlines the main conclusions and makes a number of suggestions for future research.

I1

MODEL CONSTRUCTION

There are two principal methods of obtaining an expression for the desired demand for hours within a neoclassical framework: the short run employment function approach (SREF) found in Brechling (1965), Ball and St Cyr (1966), Hart and Sharot (1978) and the inter-related factor demand models (IRFDMs) found in Nadiri and Rosen (1969) and Briscoe and Peel (1975). However, the resulting specifications for optimal hours are generally very similar and, if anything, are made more so by the inclusion of lagged dependent variables to represent the costs of adjustment. Hence, we abstract from further discussion of the differences between the two approaches, and use an IRFDM framework.

The firm is assumed to minimise total costs,

C.= w(H)EH + qE + p ( r + G(U))KU (1) subject to an exogeneously given level of output, Y. The wage rate, w, is


taken to be a function of the number of hours worked, w = w(H); E is the number of employees; q denotes quasi-fixed labour costs per person. The user cost of capital, c, is a composite of the price of capital, p, the rate of interest, r, and the rate of depreciation, 6 (which is itself a function of the level of utilisation, 17). It is further assumed that (dS/dU) = 6' = constant and that (dw/dH)(H/w) = wl = constant.' Partial adjustment mechanisms are adopted to account for the costs of adjustment;' the steeper the adjustment cost function, other things being equal, the more slowly the firm moves towards its desired level. While the short-run employment functions tend to assume that there are adjustment costs for employment, but not for hours of work (Brechling, 1965, Ball and St Cyr, 1966, and Hart and Sharot, 1978), this is essentially an empirical question, and the model can be modified to test for non-negative adjustment costs on all inputs. The expression for desired hours is ~ r i t t e n , ~

H* =f (Y, T, HN, 4 , wo, ~ i , R, KL, E L , HL) (2) where: wo is the basic wage, so that wl/wo is the prevailing overtime premium; the subscript L denotes the lag structure. It has been argued that, (dH*/dH,) 5 0, (dH*/d(wl/wo)) S 0 (Brechling, 1965, p. 192, Hart and Sharot, 1978, p. 300, Bod0 and Giannani, 1985, pp. 133-6).

A variety of other explanatory variables have been suggested in the empirical literature and these are included in the vector, R. In this paper a stocks variable is included (Rossana, 1983 and 1985, Topel, 1982), where the firm is assumed to have some target level of stocks per unit of output in mind. Stocks can influence hours in several ways. First, they may simply reflect expectations about the future, with firms building up stocks in anticipation of increases in demand. In this case, stocks will move directly with hours of work. Second, they may be subject to changes, meeting the unanticipated differences between output and demand. In this instance, stocks would tend to move inversely with hours. A bankruptcy term is also

Similar assumptions can be found in Nadiri and Rosen (1969, p. 460), Neild, (1963, p. 64), Brechling, (1965, p. 200) Hart and Sharot, (1978, p. 301). The assumption that (H dw/w dH) = e = constant appears unrealistic over the whole range of values of hours. On the other hand, it may be acceptable for values of H > HN, expressed as,

w = wO(H/HN)'"i

where: w = w, at H = HN; for H > HN, (dwlw) = wl(d(H/HN)/(H/HN)) and e = w,, where wl reflects the steepness of the overtime premia ladder. In practice, the subject of the earlier studies has implicitly been overtime working, and an extension to short time working requires a modification of the underlying wage-hours equation.

'For an alternative approach to the costs of hiring and firing, see Hart (1984). However, this approach does not help greatly until the magnitudes of the quit and hire rates are endogenised, with per unit costs increasing functions of the size of change in each period.

There are several things worth noting. First, this specification implicitly assumes that variations in hours adequately represent analogous variations in capital utilisation. Second, the Nadiri and Rosen solution has w as a right hand side variable, but, w = w(H). In practice, however, for choices of w(H) corresponding with the authors' assumption that e = constant, it is possible to rearrange the Nadiri and Rosen solution in terms of purely exogenous variables.


included. Again, this may reflect the general economic climate and business expectations, in which case, it would be negatively related to hours of work. In addition, however, bankruptcies will tend to remove firms working at the short time end of the spectrum, thereby raising average hours of work.

The traditional neoclassical models developed above focus on average hours per person employed. This reveals something about overtime working, as H - H N is the average level of overtime hours per person employed (a negative value would presumably be interpreted as short time working). This may prove to be the most relevant concept where all firms face identical product and factor prices, output conditions, etc. In such a world, every employee would work for H hours in total and H - H N of these will be in the form of overtime working. By implication, average overtime hours per employee will be the same as average overtime hours per employee on overtime. In the real world, however, such conditions are not found and the average number of hours per employee is a weighted average of short time, normal hours and overtime working,

H = ( H S T E S , + H N E N + HoEo) /E = HsTIsT + H N I N + HoIo (3) where subscript: ST denotes short time, N, normal and 0 overtime working. 4 is defined as E,/E, the incidence of the jth type of hours working. Thus, each type of working has both a length, Hi, and an incidence, 4, dimension. Their variation over time is shown in Figures (1) and (2).

Equation (3) is not without interest, but, in practice, H N is a major component of H , and its use as an explanatory variable for H is somewhat problematic. However, the equation can be rewritten as:

H = H N + OHIO - S T H I S T (4)

where: OH = Ho - H N , denotes average overtime hours per operative on overtime; S T H = HN - HST, is interpreted as average hours lost through short time working per operative on short time. If we assume that any given micro production unit will either be in an overtime or a short time situation (but not both), then equation (4) can be separated into two analogous expressions: the overtime equation is obtained where ZST = 0; the short time equation is obtained where I. = 0. Equation (2) can now be replaced by an expression for overtime working,

(Vole)* = g ( H * ) - 1 = g ’ ( H * ) ( 5 )

Given that,

H = HSTIST + H N I N + HoIO = (HN - STH)IsT + HNIN + (HN + OH)lo = H N ( I S T + 1, + lo) + O H I O - S T H I S ,

and, given that,

1 = Is, + 1, + lo then,

H = HN + OHIO - STHIST

T H E DEMAND F O R H O U R S O F WORK 373

w”(H)

I I I I I I I I I

I I

I I - HN H H

Figure 3

or one for short time,

(V&-ZsT)* = h ( H * ) - 1 = h ’ ( H * ) (6) where: V, is the ratio of average overtime hours per operative on overtime to normal hours, V, = OH/HN; V,, is the analogous short time ratio, VsT = STHIHN.

Figure 3 illustrates the (approximately) quadratic wage-hours function of the Ball and St Cyr (1966) type: downward sloping section, w(G), is influenced by guaranteed pay; the upward sloping section, w ( H ) , is determined by overtime premia. Where there are no QFLCs, the curve reaches the minimum hourly wage rate, w,, at normal hours, HN. The introduction of QFLCs modifies the position somewhat, altering the downward sloping part of the curve to Q,. Unlike guaranteed pay, this influence does not terminate at HN and, for a smooth quadratic wage-hours function, it will alter the number of hours at which the minimum point occurs. In effect, at the margin, the reduction in QFLC from an increase in H above HN off-sets the overtime payment, and the minimum point of wage costs per hour moves to the right of HN. In the real world, however, the instantaneous (hourly) rates faced by the firm are not smooth, monotonically changing functions (see, for example, Bod0 and Giannini, 1985). In the case of overtime, they are discrete, stepped functions: overtime premia are often paid at a given (constant) mark-up for


succeeding hours. Thus, the instantaneous rates are represented by the stepped curve w ’ ( H ) . When the wage rate is calculated as an average over all of the hours worked, this is represented by the curve w“(H), which is approximated by w (H) in the neoclassical literature. Recognition of these “steps” in the overtime premia ladder throws some light on the potential influence of variations in QFLCs on hours of work. In particular, hours are likely to be insensitive to changes in QFLCs at the foot of each step: hence, sensitivity can be expected to be low at HN, but to increase towards H , the next step in the ladder. One implication of this appears to be that average hours, H, are less likely to be influenced by variations in QFLCs than overtime hours, as the former includes individuals on normal hours (e.g. at the step). This hypothesis can be tested directly, by comparing the results of the regressions explaining average hours with those explaining overtime working. If this hypothesis is correct, it could reconcile the potentially conflicting results outlined in section I above.

Given that premia are institutionally determined, in terms of wage and premia payments, it is equally costly to demand an extra hour of overtime from an employee on overtime (at least up to the next rung on the ladder) as it is to ask an employee to move from normal hours to working one hour of overtime. By implication, this effectively assumes a perfectly elastic supply of labour at each wage/premium combination. In such a world, the amount of overtime is rationed by the amount the firm chooses to demand, and its distribution across workers is indeterminate. It may be more realistic (and certainly more in keeping with the institutionalist’s view of the world-see Whybrew, 1968), to think in terms of an internal labour market for overtime. The internal supply may be induced not only by the premia offered, but also by other “side payments” to employees. Thus, the combined premia and side payments are the true price of overtime. This price seems likely to be an increasing function of both incidence and hours of overtime.

We could proceed by setting up cost and production functions that allow for the distinctions between components of hours. However, this optimal control theory problem is left for future research. Alternatively, as a first approximation, we could assume that the firm determines its total overtime (short time) requirements in a manner consistent with equation ( 5 ) (or (6)) , and then separates this into demands for incidence and length. One justification for this two-tier approach might be that different levels of management are involved in the two decisions (again see Whybrew, 1968). We could then ask under what restrictions this approach would lead to a general form for the hours equations that was identical for each of the separate components of hours. The justification for this type of approach is twofold. First, we must recognise that, while information exists about the two dimensions of hours, length and incidence, no data are available about their relative prices, PI and Po. Second, this approach allows us to explore whether the functional form traditionally used to examine average hours of work is also appropriate to the examination of its component parts. Differences in the time series behaviour of the components of hours may not

.

THE DEMAND FOR HOURS OF W O R K 375

have quite so fundamental implications for the existing empirical results if the traditional functional form is still appropriate at this more disaggregated level.

The same, general, functional form can be derived for the component parts of hours on the assumption that,

and, P, = i(Zo) s.t. (d&/dZo) > 0

Po=j(Vo) s.t. (dPo/dVo) > O (7) This is caused by the fact that overtime comes from workers already in the firm’s employment (i.e. from the internal labour market). Thus, higher rewards are needed as the firm demands higher amounts of overtime from (at the margin) an increasingly reluctant workforce. On the basis of this assumption, it is possible to establish a submodel which chooses between the incidence and length in a way which minimises the costs of providing any given amount of overtime, (VoZo)*. The result of this is two equations,’

zo = axy= k((ZOVO)*) = k’(H*)

v, = gxl = l((ZoV0)*) = I’(H*) and,

Analogous arguments can be applied to the firm’s allocation of short time working across its workforce. We can now proceed to investigate whether there is any empirical support for this set of restrictions which leads to the same general form of the function explaining the components of hours.

The cost minimisation problem can be written as the Lagrangian expression,

LG = PIfo + PoVo + A (X - foVo)

where X is total overtime hours as a percentage of total normal hours. X is determined by the first tier decision making process and is taken as given exogenously in the second tier. The first order conditions yield,

and

X = zovo

PI = af;

Po = cv;

a&l+ b ) - & CV$(l+ d) - I,

If the “price” equations are of the form,

and

where a, b, c and d are constants. Equation (i) then collapses to,

and, using equation (ii) we obtain (8), where a, p, y and n are constants.

(ii)

(iii)

(iv)


111.

ESTIMATION OF THE MODEL

1. Methodology, data and sources

The estimation of the model is separated into two primary stages; the first deals with the explanation of average hours of work per employee; the second decomposes hours into its component parts. The disaggregated work considers results for both overtime and short time working, distinguishing between the “length” and “incidence” dimensions. The list of explanatory variables, their definition and expected signs are summarised in Table 1 above. The expected response of each of these groups of dependent variables to changes in the explanatory variables is summarised in three columns under the appropriate sub-headings. We have argued that average hours and the components of overtime are inversely related to overtime premia, whereas the influence of HN is indeterminate. QFLCs, on the other hand, are expected to be positively related to average hours and overtime (incidence and length). Higher values of QFLCS, although not a major influence, may also lead to a fall in short time working. The QFLC variable is separated into its pre- and post-1975 constituents by means of a dummy variable. Thus, we

TABLE 1 Variables, notation, definitions and expected signs

Variable Definition Expected sign ~~~

(i) Dependent variable H 0,

ST,

10 ‘ST O H ST,

(ii) Independent variables

OP overtime premium FC

H N

D

K E Z B bankruptcies

average hours of work per employee incidence of overtime multiplied by overtime hours as

a proportion of normal hours (0, = l o ( O H / H N ) ) incidence of short time multiplied by short time hours as

a proportion of normal hours (ST, = I s T ( S T H / H N ) ) incidence of overtime working (lo = E,/E) incidence of short time working (IsT = Es,/E) average overtime hours per employee on overtime average short time hours lost per employee on short time

quasi-fixed labour costs (QnCs) (subscripts 1 and 2

normal hours of work per employee

seasonal dummies (subscripts 2, 3 and 4 denote the

capital stock (subscript L denotes lagged value) employment (subscript L denotes lagged value) stocks of finished and semi-finished goods

denote the pre- and post-1975 employer NIC systems)

Y output

associated quarter)

o V I O o H - - - + +(?) - -(?)


construct, FC(Z) = D . FC and FC(ZZ) = (1 - D ) . FC, where D takes a value of 1 before the 1975 change and 0 thereafter. Thus, if NICs are viewed as fixed costs prior to 1975 but variable costs after the change, then the coefficients of these two variables should be different. Higher levels of output are expected to increase overtime, reduce short time and increase average hours of work. The total numbers employed and capital installed are seen as substitutes for hours of work, and this is reflected in their a priori signs. Finally, as we discussed above, the effects of stocks and bankruptcies are not clear, as the components of hours respond to two conflicting influences. However, Table 1 presents the sign that reflects which of the influences is expected to dominate.

The equations are all estimated using a consistent functional form, although a number of variations in the methodology were tried, including, polynomial distributed lag functions for E, K and the dependent variable (Bosworth and Westaway, 1985) and more dynamic specifications of the underlying model. These variants are not reported in detail, but are discussed in the text. The principal aims are to test whether the traditional model is more suited to one aspect of hours than another, to examine the differences in the resulting parameter estimates, and to explore the associated econometric problems. It seems worth emphasising that, once the fact that H is an aggregate of a number of heterogeneous elements is recognised, it is probably unreasonable to expect a single specification to apply across the board without econometric problems arising in one or more of the equations estimated. The regressions are estimated using a consistent quarterly data base for UK manufacturing industry, running from 19631 to 1982IV inclusive, with one observation (19741) omitted due to data problems. All empirical results were estimated using TSP 4.OB (Hall and Hall, 1983).

The data on the primary dimensions of hours of work for the manufacturing sector are available from the Department of Employment surveys of overtime and short time working, published quarterly in the D E Gazette. This source gives information about the incidence of short time and overtime working (ZsT and Zo respectively) from which the incidence of normal hours (IN) can be constructed. In addition it provides data on the average hours lost on short time per operative on short time and average hours of overtime per operative on overtime (ST, and OH), from which the average hours of these two groups (HST and Ho) can be calculated, given the estimate of normal hours, HN, published separately in the DE Gazette. Thus, the incidence levels of each dimension of hours are used as relative weights to construct average actual hours of work, as shown in equation (3). Finally, the survey of short time and overtime working provides information about total numbers of operatives, which is used as the total employment of the sector, E.

Overtime premia were constructed as the ratio of earnings to basic pay, taken from the CSO, Monthly Digest. It was recognised that this simple ratio might include an element of shift pay and, hence, some experimentation was undertaken with deviations from trend earnings/basic on the grounds that


shift premia would exhibit a longer term variation than overtime premia.6 Output is the index of industrial production for manufacturing, taken from the CSO, Monthly Digest. Annual data on the capital stock are published in the “Blue Book” (CSO, National Income and Expenditure). These annual figures are broken down into quarterly estimates using the more frequent investment data published in the CSO, Monthly Digest. Quasi-fixed labour costs are the ratio of total employer NIC contributions to the total wage bill, both figures are from the CSO, Monthly Digest. Stocks of finished goods and work in progress are available on a year by year basis, published in the CSO, Annual Abstract of Statistics and are interpolated to provide quarterly estimates.

2. Average hours of work

The results of explaining average hours of work per person are illustrated using the regression equation reported in the first column of Table 2. Considerable experimentation was undertaken with both discrete lags and polynomial distributed lag functions. While the polynomial forms were of considerable interest, they did not add any great insights vis-a-vis the discrete lags shown in the estimated equation. The equation is estimated using the Cochrane-Orcutt (C-0) estimating technique, as the Durbin h statistic (Dh) and the first and fourth order Lagrange Multiplier (LM) tests (Bruesch, 1978, Godfrey , 1978) show the presence of autocorrelation when ordinary least squares (OLS) is used. The LM1 and LM14 tests on the revised results suggest that autocorrelation is slightly less of a problem for the C-0 results, although fourth order autocorrelation tends to persist. The R2 and F statistics appear to indicate that the overall fit is reasonably good and the majority of coefficients have the anticipated sign and are significant at the 95 percent level or higher. Replacing the level of output by deviation and trend output variables only alters the results marginally, and both cases are discussed below. A detailed examination of the individual coefficients reveals some interesting features.

Despite the problems of measurement, the overtime premium variable has the anticipated negative sign, although it is not even close to being significant at the 95 percent level. Experiments with the trend and deviation from trend values of the earnings to basic variable failed to yield any greater insights. The fixed cost variable has a positive coefficient, but proves insignificant in all of the equations tested. The separation of FC into FC(Z) and FC(ZZ) results

6 A n alternative method of separating overtime and shift premia was tried, using key collective agreement data on shift premia from the DE, Time Rates of Wages and Hours of Work. In practice, the lack of variation in the nationally negotiated rates of shift premia meant that the resulting series was a simple function of earnings to basic pay and normal hours. It therefore added little empirically to the approach described in the text. It is perhaps worth noting, however, that changes in normal hours do have a “cost penalty” effect, in much the same way as changes in output which are met from overtime or short time working (Bosworth and Westaway, 1985).

T H E DEMAND F O R H O U R S OF WORK 379

TABLE 2 Explanation of hours of work

Average hours Overtime working Short-time working

Combined Length Incidence Combined Length Incidence Variable: (1) (2) (3) (4) ( 5 ) (6) (7)

Constant

OPISP

FCU)

FC(II)

HN

Y

4

4

4 B

z/y

K - 6

E-4

LDEP

rho (r rho)

F SEE Dh

RZ

LM (1) LM(4) LM (1-4)

2.1203 (2.6678)

(0.9665) 0.0172

(0.7677) 0.0180

(0.7580) 0.7672

(3.5961) 0.3306

(4.6572) 0.0034

(1.5449) 0.0087

(3.8328) 0.0094

(5.0942)

(1.1585) 0.1328

(2.0651) -0.3187 (46071)

-0.2128

-0.0015

-0.0378

-0.0070

(3.8777)

(0.0135) 0.30

(2.60) 0.8641

04056 2.3548 2.7857

154606 126040

3240

20.6991 (4.0802)

-0.1477 (0.3772) 0.3219 (24055) 0.3198

(1.8278)

(2.27%) 1.7970

(3.1452) 0.0878

0.8740 (4.2686) 0.1146

(5.8550) -0.0767 (1.4578) 0.5335

-24371

(3.5067)

(1 ~0020) -2.0077 (3.5529)

-1.2614 (3.1459) 0.3137

(2.5302) -0.10

(-0.84) 04829

0.0515 -0.4274

1.1011 6.5383 2.2199

38.22

4.7952 (2.6561) 0.0763

(04623) 0.1529

(2.4586) 0.1573

(2.3058) -0.8665 (2.1394) 0.3644

(2.5035) 0.0241

(2.0603) 0.0567

(64930) 0.0248

(2.1762)

(0.9972) 0.1534

(0.9787)

(2.9475)

(2.4081) 0.3271

(2.5862)

-0.0193

-0.4576

-0.2988

-0.41 (-3.75)

0.7307 14.36

nc 7.7515 8.5375 5.9601

0.0224

15.6743 (3.9301)

-0.2368 (0.8841) 0.1741

(1.4139) 0.1700

(1.2850)

(1.7461) 1.4815

(3.2121) 0.0614

(3.6248) 0.0292

0.0886 (6.9615)

-04667 (1.7432) 0.4213

(1.0151)

(3.5824) -0.9820 (3.1391) 0.2860

(2.2636) 0.05

0.9033

0.0359 nc

0.1212 5.1825 4.4070

-1.5225

(2.0106)

-1.5916

(0.44)

47.16

-1274646 (2.2342) 5.4313

(2.0730) 0.2940

(0.1836) 0.2134

(0.1270) 5.1555

(0.3905)

(3.6240) 0.0556

-15.1551

(0.4466) -0.4810 (3.1164)

-0.3198

0.3604 (0.8551)

(0.0724) 14.6699 (3.6263) 12-4173

(2.2402)

-0.2797

(3.4997) -0.1722 (1.4141) 0.34

(3.02) 0.7453

15.42 0.3821 nc 1.0755 7.2897 7.3979

-36.4380 -95.2733 (24667) (1.8714) 1.5926 34%05

(1.1737) (1.9630)

(1.6535) (0.3773)

(1.6363) (0.3003) 3.9688 4.8533

(1.0731) (0.3969) 1.9072 -13.3201

(1.7417) (34430) 0.0193 0.0304

(0.2739) (0.3374)

(0.0556) (34302) 0.0016 -0.4947 (0.0237) (2.0348) 0.0569 0.4947 (0.3384) (1.5069) 1.7078 1.0196

(1.3214) (0.3028) 0.2633 11.0615 (0.2399) (3.1254) 0.0682 9.3304 (0.0650) (3.1045) 0.1383 -04450

(1.0659) (0.4013)

-0.9116 -0.5044

-0.9794 -0.4156

-0.0039 -0.2235

-0.15 0.48 (-1.22) (4.53)

0.4695 0.7689 5.33 17.40 0.1793 0.2873 nc 0.1499

4.5448 1.9497 12.5566 11.9161 9.2674 7.6126

Note: ( ) absolute t values given in parentheseethe critical value at 5% level, 60 degrees of freedom is 2.0; nc denotes that the value of Dh cannot be computed (e.g. standard error of the lagged dependent variable is too large); critical values of x2 for the LM test at the 1% and 5% levels are 3.84 and 6.64 (1 degree of freedom) and 9.49 and 13.28 (4 degrees of freedom).

in almost identical coefficients, which implies that the response of hours to NICs does not change following the 1975 alteration. Furthermore, restricting the coefficients to be identical, so that no account is taken of the change in employer NICs in 1975, has no significant impact on the significance of the associated coefficient or on the overall fit of the equation (as shown by the associated t and F tests).


Given that average hours include normal hours, it is perhaps none too surprising that the overall fit of the equation is good and that the coefficient on HN is significant at the 99 percent level. In this instance, the lagged dependent variable is insignificantly different from zero, and its exclusion from the regression does not affect the other parameter estimates or the overall fit. Thus, adjustment appears to be completed within the quarter, and the impact and full adjustment elasticities are approximately equal. The results therefore indicate that a one percent reduction in normal hours produces a decrease in average actual hours of slightly less than 0-8 percent, which from a policy point of view, implies that some of the potential for job creation is lost through higher overtime working. Similar conclusions are drawn from the other variants tested.

The coefficient on output is significant at the 99 percent level, and there is a seasonal effect which raises hours of work monotonically from the first through to the fourth quarter. Note that Y also appears in the stock effect term, and the overall impact of output must take account of both coefficients. The combined coefficient proves to be small (approximately 0.2). When included separately, the coefficients on the trend and deviation from trend output are both significantly different from zero at the 95 percent level or higher. The trend indicates a small positive effect on hours, and the coefficient on the deviation from trend term is just below 0.3 (compared with slightly over 0.3 in Table 2), although the overall effect of output on hours (i.e. taking into account the stock coefficient) is almost unchanged. Estima- tion of the equation with the absolute value of stocks and a single output term makes no difference to the remaining coefficients or significance levels. The signs on the stocks and bankruptcy variables suggest that they both appear to be acting as a proxy for business expectations, rather than in the alternative ways discussed in the theory outlined in section 11. The results proved most sensitive to the exclusion of the stocks variable. We return to the possible implications of this in the concluding section. ,

3. Overtime and short-time working

The next task is to obtain equivalent results for the various dimensions of hours. The initial decomposition divides average hours into overtime, V, ( = Zo(OH/HN)) and short-time working, V, , ( = ZsT(STH/HN)). The results are reported as columns (2) and ( 5 ) in Table 2. The first thing to note is that the results are quite different for the two dimensions of hours. In particular, the overtime equation appears to perform better than its short time counterpart in terms of overall fit and significance of the estimated coefficients. This finding is consistent with the view put forward in the theoretical section, that the traditional functions developed to explain hours of work are more suited to the overtime than the short-time end of the spectrum. In attempting to draw such conclusions, we should perhaps remind ourselves of the fact that short time hours vary considerably more than their overtime counterpart, as shown in Figure 2. The separation of these two


components appears to help reduce the problem of autocorrelation. The Dh test and the first and fourth order LM tests indicate that the composite overtime equation (e.g. explaining ZoVo) is free from autocorrelation in both its OLS and C - 0 forms. In the case of the composite short time working equation (ZsTVsT), the LM tests only indicate a first order autocorrelation problem in the OLS version, the C - 0 results appear to be free of both first and fourth order autocorrelation, although the test statistics are larger than in the case of overtime.

Examination of the overtime hours equation in more detail reveals a number of improvements over its average hours counterpart. In particular, while FC(Z) and FC(ZZ) still have almost identical coefficients, the coefficient on FC(Z) is significant at the 90 percent level and the coefficient on FC(ZZ) is close to being significant at that level. The overall, combined FC variable is in fact significant at the 95 percent level. This finding gives strong support for the argument presented in section 11), that overtime would be more sensitive than average hours of work to changes in QFLCs. The results indicate that, as we might expect, overtime working is much more sensitive than average hours of work to variations in output and, in addition, the results indicate the existence of distinct seasonal factors. The lagged independent variables are all significant at the 95 percent level or higher. In addition, the lagged dependent variable is now significant at the 95 percent level, although the associated coefficient still indicates a fairly rapid adjustment of overtime working to its desired level. However, by implication, the absolute values of the long run elasticities are now raised slightly above the impact elasticities. It should be added that the significant negative coefficient on normal hours might, in principle, be traced to the nature of the dependent variable (e.g. normal hours appears as the denominator of Vo), although the evidence presented in section 111.4 suggests that this is not the case. A general conclusion therefore is that reductions in normal hours tend to increase the level of overtime working.

A similar examination of column ( 5 ) in Table 2, reveals that the estimated equation is not capable of giving as great an insight about the causes of short time working, even though the results, as we might expect, are, to some extent, a mirror image of their overtime counterparts. There are, however, some differences compared with the overtime results. Short time working appears highly sensitive to variations in output, as well as to changes in lagged capital and labour. Firms appear particularly sensitive to downturns in the level of activity following an expansion of capital and labour in earlier periods. In addition, the seasonal dummies show a quite different pattern to those in the equivalent overtime equation. The coefficient on the overtime premium variable now takes a significant positive value. Thus, insofar as higher levels of premia discourage overtime working, they may leave the firm more susceptible to short time working during recession. Higher values of FC might be expected to encourage the firm to operate with a higher overtime regime and make the firm less susceptible to short time working during recession, other things being equal. However, this seems unlikely to be a


major influence. In practice, while neither of the coefficients on the FC variables is significant, they possess unanticipated positive signs, although (as the evidence from section 111.4 suggests) this may be the result of the failure to distinguish the length and incidence dimensions. The coefficient on H N is insignificantly different from zero, although it has the anticipated sign (with lower normal hours associated with lower levels of short time working). Despite the significance of a number of the coefficients, the results tend to give the impression that the specification is less adequate in the context of short time than overtime working.

4. Length and incidence dimensions

Following the arguments for disaggregating hours to their natural conclusion, it seems likely that further improvements might accrue from the decomposition of short-time and overtime working into their respective “length” and “incidence” components. Columns (3) and (4) of Table 2 therefore report on the length and incidence of overtime respectively, while columns (6) and (7) give the analogous results for short-time working. This sub-division provides further insights about the influences on hours of work and highlights where the current specification is weakest. Examination of the overtime results reported in columns (3) and (4) indicates that there is no significant autocorrelation problem in the incidence equation, but there is evidence of first order autocorrelation in the length equation. The LM tests for the OLS equations, which are not reported in the table, indicated that the incidence and length of overtime results are both free of fist and fourth order autocorrelation. However, we continue to report the results for the C-0 regressions throughout. Examination of columns (6) and (7) reveals a somewhat greater likelihood of an autocorrelation problem, with larger fourth order test statistics than in the case of overtime working.

The further disaggregation of overtime working has produced additional improvements in a number of respects. While there is still little difference in the sizes of the coefficients on FC(Z) and FC(ZZ), the elasticity with respect to changes in FC is higher in the length of overtime than in the incidence equation. In the length equation, the coefficients on FC(Z) and FC(ZZ) are both significant at the 95 percent level, and the combined coefficient is close to being significant at the 99 percent level. The incidence appears more sensitive than the length of overtime working to changes in normal hours, but the coefficient is significant at the 95 percent level or higher in the latter case (although it should be remembered that H N still appears as the denominator of the dependent variable in the length equation). Given the discussion in section 111.2, it is interesting to note that HN still plays some role in the incidence equation, where normal hours is not a component part of the dependent variable. The coefficient on the output term in the incidence equation takes a value approximately four times as large as in the length equation. The seasonal dummies also show major differences between the two equations. While the first quarter is the lowest in both, the dummies

THE DEMAND FOR HOURS OF W O R K 383

peak in period three in the length equation, other things being equal, while the dummies in the incidence equation reach a low point in this period vis-a-vis periods two and four. This phenomenon may well have to do with the way in which overtime is organized during the main holiday period. The lagged dependent variable is significant in both equations, although the associated coefficients indicate that adjustment is quite rapid. Our basic conclusion is that the results lend strong support for disaggregating overtime into its length and incidence dimensions in empirical work.

In the case of short time working, the length equation does not appear to fit particularly well and has surprisingly few coefficients significant at the 90 percent level or higher; the incidence equation appears to fit better, and a number of its coefficients are significantly different from zero at the 90 percent level or higher. Comparison of the two equations indicates that the differences in response to variations in output, lagged capital and lagged employment are particularly marked. In fact the coefficient on Y takes different signs in the two equations, and this may be indicative of a more fundamental specification problem. The first three seasonal dummies show broadly the same pattern in the two equations, but the fourth quarter results differ. The coefficients on FC now exhibit the anticipated negative signs in both equations, and they come closer to significance in the length than in the incidence equation (confirming the results found in columns 3 and 4). The coefficients on normal hours have a negative sign in the two equations, although neither is significantly different from zero at the 90 percent level or higher. As an overview, the principle finding is that, while the signs of the coefficients are generally the same in the two equations (output being the primary exception), there are systematic differences in the magnitudes of the coefficients which suggest that the incidence of short time working is much more sensitive than the length of short time working to changes in the explanatory variables. This should be seen against the background of a greater inherent variability of the length of short time working, illustrated in Figures 1 and 2. Similar to the earlier finding for overtime, the results provide strong support for the hypothesis that the length and incidence of short time working should be disaggregated in empirical work. On the other hand, there appear to be much more important problems with the specification of the model of short time working, which we comment on in more detail in section IV.

Finally, comparisons between the short time and overtime length equations, columns (3) and (6), and the corresponding incidence equations, columns (4) and (7), reveal a general reversal of signs associated with each of the explanatory variables. There are a number of exceptions to this general rule. The coefficients on the output and the overtime premium variables retain the same sign in both length equations. The output result again hints at some more fundamental problem with the short time, length equation. The stock variable retains a positive coefficient in all four equations, although it is not significantly different from zero at the 90 percent level or higher. It is interesting that the positive coefficients on the stock variables in the length


and incidence equations are consistent with the hypothesis that high stock levels tend to exacerbate short time working. In conclusion, it is probably fair to say that: both incidence equations tend to fit relatively well, but there are still some grounds for believing that the model is more appropriate to the explanation of overtime than short time working; on the other hand, the explanation of the length dimension is more obviously superior for the overtime than the short time dimensions (again, we return to this in section IV below).

IV

CONCLUSIONS

This paper argues that hours of work have not been accorded the attention they deserve, despite the fact that they have been the subject of considerable policy debate concerning unsocially long hours of work, the impact of long hours on the demand for employees and the associated role of quasi-fixed labour costs (e.g. lump sum National Insurance Contributions) on the choice between hours and employment. The work to date has invariably focussed on average actual hours and has drawn on the theoretical framework provided by short run employment functions or interrelated factor demand models. The results reported here indicate a key role for fluctuations in output, which we would interpret in the role of a capacity utilisation variable (see Bod0 and Giannini, 1985).

The major theme of this paper, however, is that hours are not a homogeneous entity, but a composite of overtime, normal and short time working, and each of these has both a length and incidence dimension. Thus, the explanation of the various components of hours offers a major new area of interest that has been barely touched on by the existing literature. Examination of the composition of average hours reveals the importance of the normal hours component, which has traditionally been used as an explanatory variable. It is perhaps not surprising that this variable tends to dominate the explanation of average hours and that, when it is included, the overall explanatory power of the equation is high, because around 70 percent of employees work normal hours. However, it is interesting to note that the normal hours variable still plays some role in the explanation of at least certain of the dimensions of the disaggregated hours variable (even, where it does not appear as a part of the dependent variable).

The theory generally adopted in modelling hours of work appears better suited to the explanation of overtime than short time working. Thus, the significant growth of short time working in the 1970s perhaps, in part, explains the statistical problems which exist in the explanation of average hours of work, where short time working forms an increasingly important and highly volatile component. Short time working seems to need a quite different treatment. In particular, it appears to require a model which takes


account of the interim nature of short time working, with some employees moving into unemployment, and others moving back to full time working.

Taken to its natural conclusion, the decomposition of hours leads to the separate examination of the length and incidence of overtime working. This gives rise to some interesting new problems, such as the measurement of the “prices” of these two dimensions, which cannot be wholly resolved at the current time. Nevertheless, the empirical results reported above indicate that this further disaggregation is rewarding in a number of respects. In particular, they highlight the fact that the various dimensions have different patterns over time. In addition, the results indicate that the length and incidence of short time and overtime working differ appreciably in their response to changes in the exogenous variables. The poorer performance of the short time equation is traced principally to the length dimension. One possibility is that the model should recognise that short time working is a composite variable in another, so far unexplored sense, as it includes both employees laid off for a part of the week and employees laid off for the whole week. This may require a different treatment of those employees wholly stood down (which may, in the length dimension, require logit or probit analysis) and those laid off for just a part of the week.

The results also seem to indicate that more careful consideration should be given to the role played by stocks. Experimentation with alternative specifications indicate that the resulting coefficients were quite sensitive to the omission of this variable. One explanation is that a more sophisticated treatment of stocks is required, where stocks are a substitute for current production (Topel, 1982). This change is, however, more radical than it first appears, requiring considerable modification to the theoretical framework, and the adoption of an explicitly dynamic specification (Berndt er al., 1979, McIntosh, 1981, White and Berndt, 1979).

One of the primary policy dimensions touched on in this study concerned the role played by quasi-fixed labour costs. Our interest was intensified by the apparent inconsistency between the results of the micro studies of the structure of labour costs (which suggest little, if any, role for QFLCs), and the more aggregate, econometric work (which provided some support for the fact that variations in QFLCs were a significant influence on average hours of work). The theoretical discussion arising from the decomposition of hours offers an explanation: at or around normal hours of work, the marginal costs of overtime are extremely high, and seem likely to overpower any increases in QFLCs; above normal hours, at least up to the next step in the overtime premium, the demand for hours can be expected to be much more sensitive to variations in QFLCs. By implication, QFLCs can be expected to play a more important role in the explanation of overtime working than average hours. This appears to be confirmed in the results reported, with a significant coefficient on FC in the length of overtime equation, but not in the explanation of average hours or short time working.

One rather puzzling aspect of these results concerns the continued role of the QFLC variable after 1975, when the employer NICs changed from a lump

386 D . BOSWORTH AND T. WESTAWAY

sum to a percentage of income basis. It is interesting to speculate that, after operating under the old NIC regime for many years, employers continue to treat the new percentage payments as if they are lump sum. However, this seems unlikely to have persisted for so long. An alternative explanation may lie in the existence of upper and lower limits to the employer contributions, which effectively mean that above the upper limit, the NICs still effectively take a lump sum form. It is interesting that, again, it is the workers whose income is augmented by overtime premia whose earnings are most likely to lie above the upper limit. This area requires further consideration, but it does seem to suggest that the existing structure of employment taxes may still be biased in favour of long hours of work and against employment.

Advocating a more positive policy stance, such as the imposition of a progressive tax on overtime payments, requires more detailed consideration. There are clearly potential dangers in such a move. One such danger arises because overtime is a buffer against transitory variations in output. If the cost of covering such fluctuations by means of overtime is increased, it might lead to unwanted side effects, such as an increase in transitory employment and the growth in the secondary labour market, higher costs at times of peak demands, longer delivery periods, etc. While the grounds for reducing permanent overtime working are probably stronger than for transitory overtime, there are still consequences. In particular, the potential increase in employment may be achieved at the cost of lower earnings amongst the groups of low paid workers, who use overtime to augment their incomes, and who can afford it least.

The question of normal hours has equally interesting policy implications. The results reported indicate that a reduction in normal hours tends to reduce short time working and increase overtime working. Indeed, the impact on overtime working continues even in the long run. Thus, at least some of the job creating effects of a move towards shorter normal hours are lost through existing employees working more overtime.

REFERENCES BALL, R. J. and ST. CYR, E. B. A., “Short Term Employment Functions in British

Manufacturing Industry”, Review of Economic Studies, Vol. 33, July 1966, pp. 1 w - 2 ~ . __.

BELL, D. N. F., “Labour Utilisation and Statutory Non-Wage Costs”, Economica, Vol. 49, 1982, pp. 335-43.

BERNDT, E: R., FUSS, M. A. and WAVERMAN, L. , “A Dynamic Model of Costs of Adjustment and Inter-related Factor Demands, with an Empirical Application to Energy Demand in U.S. Manufacturing”, Working Paper No. 7925, Institute for Policy Analysis, University of Toronto, November 1979 (Presented to the European Meeting of the Econometric Society, Athens, Greece, September 3-6th, 1979).

BODO, G. and GIANNINI, C., “Average Working Time and the Influence of Contractual Hours: An Empirical Investigation for Italian Industry (197O-81)”, Oxford Bulletin of Economics and Statistics, Vol. 47, 1985, pp. 131-52.

BOSWORTH, D. L., “The Wage Utilisation Relationship and the Structure of Labour Costs”, Occasional Paper No. 65, Department of Economics, Loughborough University, 1982.

T H E DEMAND F O R HOURS O F WORK 387

BOSWORTH, D. L. and WESTAWAY, A. J., “Hours of Work in U.K. Manufacturing Industry: an Empirical Analysis”, in Wilson, R., (ed.), Hours of Work, Research Report Series, Institute for Employment Research, University of Warwick, 1986.

BRECHLING, F. P. R., “The Relationship Between Output and Employment in British Manufacturing Industries”, Review of Economic Studies, Vol. 32, July 1965, pp.

BREUSCH, T. S., “Testing for Autocorrelation in Dynamic Linear Models”, Australian Economic Papers, Vol. 17, 1978, pp. 334-55.

BRISCOE, G. and PEEL, D., “The Specification of the Short Run Employment Function”, Oxford Bulletin p f Economics and Statistics, Vol. 37, 1975, pp. 115-42.

CRAINE, R., “On the Service Flow From Labour”, Review of Economic Studies, Vol. 40, January 1973, pp. 39-46.

EHRENBERG, R. G., Fringe Ben@ts and Overtime Behavior, Lexington Books, Mas- sachusetts, 1971.

FELDSTEIN, M. S., “Specification of the Labour Input in the Aggregate Production Function”, Review of Economic Studies, Vol. 34, October 1967, pp. 375-86.

GARBARINO, J., “Fringe Benefits and Overtime as Barriers to Expanding Employment”, Industrial and Labour Relations Review, Vol. 17, April 1964, pp. 426-42.

GODFREY, L. G., “Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables”, Econometrica,

HALL, B. H. and HALL, R. E., Time Series Processor, Version 4.0, User’s Manual, Stanford.

HART, R. A. and SHAROT, T., “The Short Run Demand for Workers and Hours: a Recursive Model”, Review of Economic Studies, Vol. 45, 1978, pp. 299-309.

HART, R. A., “Worksharing and Factor Prices”, European Economic Review, Vol. 24,

HAZLEDINE, T., “Employment Functions and the Demand for Labour in the Short Run”, in Hornstein, Z., Grice, J., and Webb, A., The Economics of the Labour Market, HMSO, London, 1979, pp. 149-81.

MCINTOSH, J., “Dynamic Inter-related Factor Demand Systems: the United Kingdom, 1950-78”, Discussion Paper, Economics Department, University of Essex, November 1981.

NADIRI, N. J. and ROSEN, S., “Inter-Related Factor Demand Functions”, American Economic Review, Vol. 59, September 1969, pp. 457-71.

NEILD, R. R., Pricing and Employment in the Trade Cycle: a Study of British Manufacturing Industry, 1950-61, Cambridge, 1963.

ROBERTS, C. J., “A Survey of Employment Models”, Centre for Industrial Economic and Business Research, Paper No. 30, University of Warwick, 1972.

ROSSANA, R. J., “Some Empirical Estimates of the Demand for Hours in U.S. Manufacturing Industries”, Review of Economics and Statistics, Vol. LXV, No. 4, 1983

ROSSANA, R. J., “Buffer Stocks and Labour Demand: Further Evidence”, Review of Economics and Statistics, Vol. LXVI, No. 1, 1985 pp. 16-26.

TOPEL, R. H., “Inventories, Layoffs, and the Short-Run Demand for Labour”, American Economic Review, Vol. 72, 1982, pp. 769-87.

WHITE, C. J. M. and BERNDT, E. R., “Short Run Labour Productivity in a Dynamic Model”, Dbcussion Paper, Department of Economics, University of British Columbia, June 1979.

WHYBREW, E. G., Overtime Working in Britain, Royal Commission on Trade Unions and Employee Associations, Research Paper No. 9, HMSO, London, 1968.

187-216.

Vol. 46, 1978, pp. 1293-1302.

1984, pp. 165-88.

pp. 560-69.

the demand for hours of work

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