DEPARTMENT OF ECONOMICS

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1 ISSN ISBN THE UNIVERSITY OF MELBOURNE DEPARTMENT OF ECONOMICS RESEARCH PAPER NUMBER 1022 December 2007 Hours of Work: A Demand Perspective by Robert Dixon & Jon Freebairn Department of Economics Te University of Melbourne Melbourne Victoria 3010 Australia.

2 Hours of Work: A Demand Perspective * Robert Dixon and Jon Freebairn Te University of Melbourne Abstract : In Australia, and in oter countries, we observe at any one time a wide distribution of ours worked per week. We develop a cost-minimising model to explain employer coices over te number of employees and teir ours of work. An important finding is tat ours of work and te number of employees are not perfect substitutes. We sow tat tis as important implications for te way economists model labour demand and measure productivity. We sow tat estimates using total ours worked as te measure of labour input implicitly assumes perfect substitution of persons and ours and results, inter alia, in an overestimation of te rate of labour and multifactor productivity growt in Australia and especially in te period prior to te so called productivity slow-down. Keywords: Employment, Hours, Production Function, Total Factor Productivity JEL codes: J23 O47 E24 Corresponding autor: Professor Jon Freebairn Department of Economics University of Melbourne VIC j.freebairn@unimelb.edu.au Pone: (03) * We are grateful to Emayenes Seyoum-Tegegn for researc assistance.

3 2 I Introduction In Australia, and in oter countries, we observe at any one time a wide distribution of ours worked per week, including part time employment, full time employment and overtime, tese distributions vary by gender, industry and occupation, and tey vary over time. In May 2007 in Australia, 30 per cent of persons were part time workers, just 45 per cent worked around standard ours of 35 to 40 ours per week, and 17 per cent worked long ours of more tan 50 ours a week (ABS, 2007a). Among OECD countries, Australia lies in te upper one-tird in terms of te sare of employees working part time or long ours, but in neiter case is it at te extreme (OECD, 2004). Witin Australia, te distribution of ours of work varies markedly from industry to industry (wit, for example, 50 per cent of employees in accommodation, cafes and restaurants work part time down to a negligible level for electricity, gas and water) and between occupations (wit, for example, 63 per cent of elementary clerical, sales and service workers part time down to 10 per cent for managers) (ABS, 2007a). Over time, te distributions of ours of work ave varied bot in a trend sense and over te business cycle. For example, te proportion of part time employees increased from 10 per cent in 1970 to nearly 30 per cent by te mid-1990s and since ten as been relatively stable (ABS, 2007a and various years). Tis paper seeks to provide a demand side explanation of differences in employer demands for labour by ours of work. We develop a labour services cost minimising model to explain employer coices over te number of employees and teir ours of work. Te model explicitly recognises tat labour costs involve a mixture of fixed costs of iring, training and firing as well as variable costs of wages (and oter labour on costs suc as superannuation and payroll tax), and tat overtime wages involve a premium beyond a legislated normal working week. Employee labour productivity depends on te ours of work, and in particular ultimately decreasing productivity sets in. Differences in te employer desired mix of number of employees and te ours tey work vary wit te mix of fixed and variable labour costs, te overtime premium, te statutory normal ours, and te productivity relationsip wit ours worked. It is argued tat tese factors elp to explain differences in te observed patterns of ours worked across industries and occupations, and over time.

4 3 An important finding from our model is tat ours of work per employee and te number of employees are not perfect substitutes. Yet, in many important economic studies it is assumed tat te number of employees and ours of work are perfect substitutes in providing labour services. At its simplest, te perfect substitution argument says labour services L can be expressed as te product of te number of employees N times te average ours worked per employee H to give L = NH. Ten, for example, many labour demand studies seek to explain te determinants of L, and studies of labour and total factor productivity use L as a labour input measure. Given te imperfect substitutability of te number of employees and te ours tey work, it is argued tat demand and productivity studies using a total ours worked series, tat is L = NH wit te implicit assumption of perfect substitutability of N and H, are likely to incur undesirable biases. An explicit focus of tis paper to explain te pattern of ours worked, and some of its implications, is on te demand side of te labour market. Of course, labour supply factors also may be important, but tey are not considered in tis paper. Apart from te need to contain te size of te analysis, our focus on te demand side is justified on te tenable assumption tat because of te pervasiveness of unemployment in recorded data over te last 30 years, te data we observe on ours worked is on te demand side rater tan te supply side of te labour market model. Furter support for a demand side focus is provided by te observation by Wooden and Drago (2007) from analysis of te Houseold Income and Labour Dynamics for Australia survey tat at any one time about 40 per cent of employees, including tose working part time, normal ours and long ours, would prefer to work different ours to tose offered to tem. Te rest of te paper is organised as follows. Section II provides some statistical facts on te variation of ours of work per employee for Australia wic we seek to explain. Section III provides a microeconomic employer labour services cost minimising model for te long run equilibrium to explain te reasons for different coices of ours of employment. Section IV uses te Section III model to ypotesise reasons for te variation in observed ours of work by occupation and industry in Australia. A summary of earlier literature on differences in te time series properties of ours of work over te business cycle, or sort run responses, relative to number of employees and output, and in turn ow tese patterns vary across skill levels, is provided in Section V. Section VI illustrates te desirability in many economic studies

5 4 of labour demand and of productivity growt to recognise te imperfect substitutability of number of employees and ours, rater tan to use total ours worked wit its implicit assumption of perfect substitutability. A final Section VII provides some conclusions. II Some Statistical Facts An overview picture of te wide range of normal ours worked per week in May 2007 by males, females and persons is provided in Table 1. At te aggregate level, 30 per cent would be classified as part time working less tan 35 ours a week, 42 per cent work te standard working week of 35 to 40 ours, and 25 per cent work more tan 45 ours a week, wit 17 per cent working 50 and more ours wic often is used as te measure of long ours. Females, relative to males, are more likely to be part time and not to work long ours, and tey are sligtly more likely to work standard ours. [TABLE 1 NEAR HERE] Table 2 describes large differences in te pattern of ours worked across different occupations and industries wit te proportion of te workforce wo are part time workers and tose wo work long ours. Industries and occupations are ranked in ascending order by te sare of part time employees at May At te industry level, compared to te economy average of 28 per cent part time employment, four industries (accommodation, cafes and restaurants, retail trade, culture and recreational services, and ealt and community services) ave more tan 40 per cent part time employees, and four industries (construction, manufacturing, mining, and electricity, gas and water) ave less tan 15 per cent part time employees. Industries wit a relatively ig proportion of long-ours employees (more tan 20 per cent) are agriculture, transport, wolesale trade, mining and electricity, wile ealt and government ave a relatively low proportion (less tan 10 per cent) of long-ours employees. Te correlation between te sares of industry employees wit part time and long ours is low at [TABLE 2 NEAR HERE] Turning to occupations, te clerical, sales and services occupations (elementary especially but also intermediate and advanced clerical, sales and services occupations) ave more tan 40 per cent part time, and a relatively low sare of long ours employees. By contrast, less tan 20 per cent of associate professionals, tradespersons

6 5 and managers & administrators are part time, and te occupations wit relatively ig sares of long-ours workers are managers & administrators, intermediate production workers and associate professionals. In te case of te occupations, unlike te industries, tere is a relatively ig correlation of between occupations wit part time and long-ours employees. A picture of canges over time in te distribution of ours worked is given in Table 3 for te period 1980 to 2006 for men and women. From 1980 to about te turn of te century, te sare of part time employment increased from 50 to 58 per cent for women and from 25 to 31 per cent for men, and since ten te part time sare as stabilised. Te sare of employees working long ours increased from 18 to 26 per cent for men and from 5 to 9 per cent for women up to about 2002, and in recent years te sare working long ours as fallen. Tere as been a trend decline in te sare of employees working te normal or statutory working week, and primarily because of te expansion of part time employment. [TABLE 3 NEAR HERE] A long term picture of canges in te make-up of te workforce in terms of persons employed and average ours worked per employee is provided in Figure 1. Te two series run from to and are sown in index form wit = 100. Over te period, te number of employees as almost doubled, wit cyclical downfalls, particularly in 1983 and By contrast, te series for average ours worked as trended downwards by about 10 per cent, wit te largest falls in te late 1970s, and again wit some cyclical variation. [FIGURE 1 NEAR HERE] III Teoretical Model: Long Run Equilibrium We build a simple labour cost minimising model for a representative competitive firm. Te firm as to coose te number of employees N and te ours worked per employee H to minimise te cost of providing a quantum of labour services L. Consider a labour services production function of te form L= f( N, H) (1)

7 6 = ghn ( ) (1 ) Te general form is given by (1). We will use a more specific function (1 ) wic was proposed by Erenberg (1971), and as been used by Bell (1980), Calmfors and Hoel (1988 & 1989), Boot and Ravallion (1993), Kapteyn et al. (2004) and oters. It imposes constant returns to scale and marginal productivity for te number of employees N, and in essence assumes an infinite supply of clone workers available for ire, but it attaces a more general production function to ours of work per employee H. Te function gh ( ) may initially ave an increasing marginal productivity pase to reflect, say, learning by doing and skill acquisition, but ultimately a pase of declining productivity sets in to reflect, for example, tiredness or boredom. Declining productivity per our worked also may reflect te inability of te employer to provide suitable work given te importance of timeliness in te supply of some products, and in particular services wic cannot be stored. More formally, on in (1 ), we impose te conditions g (0) = 0, and beyond a particular level of H > H*, g, ( H ) > 0, and g,, ( H ) < 0. 1 gh ( ) Te labour services production function (1 ) can be sown as an isoquant map in number of employees, ours of work, or N-H, space. Te isoquant as a marginal rate of tecnical substitution, MRTS MRTS N H Ng H g H, = / = ( ( )/ ( )) (2) Given te assumed properties of gh ( ) and g, ( H) in (1 ), te isoquant will ave nice convex to te origin properties. More informative tan te MRTS is te elasticity of substitution of ours for employees in te provision of labour services, σ L : σ L = N H H N = g H H g H, ( )( ) ( ) ( ) = MP AP (3) 1 A particular example of (1 ) wit tese properties often used in te literature is L = NH α wit α < 1, or tis could be generalised to allow a set of ours H # # before decreasing returns set in as L = N( H H ) α. In general, economic efficiency means we would coose a set of ours were te MP is declining, ie te,, condition g ( H ) < 0, and te MP < AP.

8 7 were, MP = g, ( H) is te marginal product per our worked, and AP = g( H ) H is te average product per our worked. Ten, as we substitute ours for employees in providing labour services, te elasticity of substitution is < 1 wen MP > AP if skill acquisition requires at least a minimal set of ours, but ultimately wen decreasing returns set in and MP < AP te elasticity of substitution is > 1 and approaces zero. A special case of (1) often used in studies of labour demand and productivity assumes perfect substitution of te number of employees and ours of work labour services giving te specific special case production function L = NH (1 ) Tis function implicitly assumes a constant marginal product per our of work regardless of te number of ours worked, and in tis case te marginal and average products are equal. In tis special case, te elasticity of substitution, σ = 1, is constant and always equal to minus unity. Te total cost of labour services, C, is given by L O C = ( WH + W ( H HS) + F) N (4) were, H and N as before refer to ours per employee and number of employees, W is te variable labour cost per our up to standard ours HS, W O is te overtime wage premium, and F is te fixed cost per worker. From (4) we can form an isocost function in N-H space wit a marginal rate of transformation, MRT, MRT = N H = ( N H )(( WH ( WH + F)) for H < HS and (5) O O = ( N H )((( WH + W ( H HS)) ( WH + W ( H HS) + F), for H > HS. (5 ) Note from (5) and (5 ) tat te isocost function for labour services as two convex segments wit a discontinuity at te standard ours HS, wit te MRT increasing in absolute value at te HS kink. Te MRT depends on te ratio of variable costs to total labour costs, for example in (5) ( WH ( WH F) ) 1 + < by definition.

9 8 As wit te isoquant for labour services, also for te isocost function, it will be convenient to consider te elasticity of substitution rater tan te slope or MRT. Te elasticity of substitution of ours for employees along te cost function ( σ C ) is: O O ( ) ( ) ( ( )) ( ( ) σ C = N H H N = WH + W H HS WH + W H HS + F) (6) We note tat σ C is just minus te sare of variable wage costs in total labour costs. Ten, σ C > 1, it declines to 1 as te number of ours increase and spread te fixed costs, and it initially becomes steeper for ours in excess of te standard ours wen te overtime premium is payable. A labour cost minimising firm will coose te combination of number of employees (N) and ours per employee (H) were te MRTS = MRT, or were σ L = σ C. Using te latter, and substituting from (3) and (6), te least-cost combination of N and H is given were ( ) O O ( WH + W ( H HS)) ( WH + W ( H HS) + F) = MP AP (7) Tat is, employers will coose te N and H combination were te ratio of variable to total labour costs, te LHS of (7), equals te ratio of te marginal and average products of te production function for ours worked, te RHS of (7). As we explore in more detail in Figures 2, 3 and 4 below, from (7) we can picture te circumstances were employers demand part time, regular ours, and long ours (including overtime pay), respectively. Figures 2, 3 and 4 sow te employer decision coice problem over ours per worker (H) and number of employees (N) to minimise te cost of providing a given set of labour services (L). A convex isoquant represents te production function (1 ) wit te marginal rate of tecnical substitution and elasticity of substitution defined in (2) and (3), respectively. Te cost function information of (4) is represented by te isocost function, wit two convex segments joined at te point of standard ours HS, and te marginal rate of transformation and elasticity of substitution are defined in (5) and (6), respectively. Te cost minimising combination of H and N is given were te isoquant and isocost curves are tangent to eac oter at te H and N combination defined by (7).

10 9 Figure 2 describes te coice of part time employment. Here, employers minimise labour costs by coosing H < HS at E PT were ( ) WH ( WH + F) = MP / AP 1 (8) A necessary condition for part time employment is eiter tat te marginal productivity per our worked be declining for H < HS, or tat te fixed costs of employment be zero. Tat F = 0 seems unlikely, altoug F may be small, so (8) is strictly less tan unity and terefore MP < AP and marginal productivity per our is falling. If marginal productivity per our is not falling, full time employment, or H HS, to spread te fixed costs would be a dominant cost minimising coice. From (8), and Figure 2, part time employment is an employer cost minimising decision for employees wit te combinations of low fixed employment costs and wit declining marginal productivity per our setting in before te standard working week ours. [FIGURE 2 NEAR HERE] Figure 3 sows te case of an employer coice of overtime ours of work to minimise labour costs. Here te equilibrium condition at E O is given by ( ) O O O O (( W + W ) H W HS) (( W + W ) H W HS + F) = MP AP < 1 (9) Ten, a cost minimising coice of overtime ours will be positively related to te importance of fixed costs in total labour costs, to sorter and binding standard ours, and to te ours production function aving an extended period of ours worked before declining marginal productivity per our sets in, and ten only at a very gradual rate; and te coice will be negatively related to te wage premium paid for overtime relative to te standard wage rate. [FIGURE 3 NEAR HERE] Employer coice of a standard working week wit H 4. Here, at E F te equilibrium condition is ( ) = HS is illustrated in Figure O O WHS /( WHS + F) < MP AP < (( W + W ) HS) (( W + W ) HS + F) <1 (10) Te standard working week before te overtime wage premium is triggered clearly is a dominant determining variable. Te relative importance of fixed costs in total labour costs, te relative mark up of te overtime wage premium, and te point and rate

11 10 at wic te marginal productivity per our worked affect employer coices for a part time or an overtime appointment are also important explanatory variables. [FIGURE 4 NEAR HERE] An important result from our model of employer cost-minimising decisions over te coice of ours and number of employees is te unsuitability of te implicit assumption in (1 ) tat ours and employees are perfect substitutes, or tat te elasticity of te isoquant is minus one. Brecling (1965), Feldstein (1967) and oters ave raised tese concerns, but wit little recognition in subsequent empirical work on, for example, studies of productivity and te demand for labour, bot of wic we explore furter in section 6 below. Under te perfect substitutability assumption, so long as tere is a fixed cost element in te labour cost, it clearly is inefficient for an employer to ire any part time workers. Unless te fixed cost component is a very large sare of labour costs, it is inefficient to ire overtime workers, and ten if you cose overtime te cost effective coice becomes an infinite level of overtime ours. Put anoter way, te observed importance of part time employment and of a few ours per week of above standard ours of work requires te more general assumption tat at some point te marginal product per our falls (and is falling furter). A number of writers, including Hart (1984) and Hamermes (1993) provide empirical evidence to support te ypotesis tat te number of employees and ours worked per employee are imperfect substitutes. IV Differences in Hours Worked Across Occupations and Industries Te different patterns of ours worked by occupation and industry observed in Table 2 and over time observed in Table 3 and Figure 1 can be explained in part using te model of Section III above by focusing on differences in te relative importance of fixed costs in total labour costs, and ypoteses about differences in te marginal productivity functions per our of work. Differences in standard ours of work, especially over time, and institutional and social differences affecting te rigor wit wic standard ours are imposed in initiating payment of an overtime premium, also are likely to be important in some cases. Limited evidence of systematic variation in te overtime premium, bot over time and across industries and occupations, from te

12 11 general time and a alf make it difficult to attribute a significant explanatory role for tis term for Australian data. Wile tere are few, if any, compreensive empirical studies for Australia on te relative importance of te fixed and variable costs for labour, our guess is tat te ratio is similar as for oter OECD countries. Hart (1984) suggests for bot te US and te UK it is reasonable to put fixed labour costs at rougly 20 per cent of total variable (labour) costs (p 19), and Martins (2004) suggests tat te ratio of variable costs in total costs is around 75 per cent for Portugal. A number of empirical studies provide support for te argument tat an increase in te sare of fixed costs in te total labour cost does induce longer ours. Cutler and Madrian (1998) found tat increases in ealt insurance costs in te US resulted in longer ours of work by workers covered by ealt insurance, and Dolfin (2006) found tat iger costs of iring, training and firing were associated wit longer employee ours. It seems reasonable to ypotesise important differences in te relative importance of fixed costs across occupations and industries. Rosen (1968) for example argues tat te fixed cost sare rises wit te occupational skill level, and is empirical work wit data for te US railroad industry supports tis contention. Some of te connections between more skilled occupations and a iger sare of fixed costs in total labour costs include more time and effort required in te job searc and matcing process for iring managers and professionals, more staff investment in training and provision of firm specific uman capital, and iger costs of monitoring, and if required firing, skilled workers. More capital intensive industries, relative to labour intensive industries, are likely to invest more in te training and monitoring of teir workforce to protect te ongoing value of teir more expensive capital assets per employee. In te case of te production function for ours of work, we ave no ard evidence, but it seems reasonable to ypotesise variations across occupations and industries. Declining marginal productivity per our worked associated wit employee boredom, lack of interest and motivation, and from te monotony of repetition is likely to set in at a smaller number of ours for te less skilled occupations. It also seems likely tat declining marginal productivity will set in at a smaller number of ours for te labour intensive service industries due to te employer peak/off-peak product and derived labour demand fluctuations, wereas te goods industries can smoot production and sales to a greater extent troug te olding of inventories.

13 12 A number of institutional factors are likely to influence te employer costminimising coice of ours per employee via te effect of tese factors on te labour cost and productivity variables in (8), (9) and (10). Te way in wic te standard our binds becomes important. For example, a rater loose restriction applies in te case of most managers and professional occupations on salaries, at least relative to more tigtly enforced restrictions for te more unionised blue collar trades and for oters on wages. Te relative importance of fixed costs in labour costs is influenced by te industrial relations system, including te conditions for and costs of firing workers, bot absolutely but also relatively between part time and full time employees. Different caracteristics of different occupations and industries sown in Table 2 can be related to te conditions in wic employers are likely to coose part time, normal or long ours. Occupations and industries wit a ig proportion of low skill and repetitive jobs are more likely to see an early productivity decline per our worked tan tose wit a ig proportion of ig skilled and callenging jobs, and ence involve part time ours. In many service industries, wen compared wit goods production industries, te variability of labour demand by time of day and by day effectively means relatively low productivity of ours outside te peak periods, and favouring a part time coice for some employees. Industries and occupations wic are skill intensive, or capital intensive, or bot, are likely to incur ig investment costs in training and familiarisation, and ten employers want to old employees in secure full time employment, and sometimes on long ours, to capitalise on te investments made. A relatively low sare of fixed costs in total labour costs favouring part time employment seems to be te case in te low skill and labour intensive occupations and industries, relative to ig skilled and capital intensive industries and occupations were full time and overtime ours dominate. V Sort Term Adjustments to Hours of Work Wile te model of Section III and its application in Section IV was addressed primarily at long run equilibrium decisions on te number of employees and te ours of work to minimise te cost of providing labour services, an early strand of te labour economics literature, including Becker (1962), Oi (1962) and Rosen (1968), focussed on te sort run response of employment numbers and ours worked to canges in

14 13 output, including te responses of employment and ours worked over te business cycle. In tese models, quasi-fixed labour costs of employment resulted in ours following a cyclical pattern, and in employment being a lagging indicator and less volatile tan ours and output. Furter disaggregation of labour by skill and te relative importance of fixed costs in total labour costs, and ypotesising tat te more skilled labour was less substitutable wit te (sort term) fixed capital stock, was used to explain differences in te time series properties of output, and ours and employment by skill level. Consider in more detail te model and supporting empirical results provided by Rosen, especially for comparing te time series properties for labour wit different skill levels 2. His simplest model of sort term labour services ire decisions as a fixed capital stock and two categories of labour inputs, namely ig skilled and low skilled. Te ig skilled ave a relatively iger sare of fixed costs in total labour costs, and teir elasticity of substitution wit capital is relatively lower. A sort run fall in output is sown to induce labour services cost minimising decisions involving a smaller percentage reduction in labour services, and ten initially most of te reduction in ours per worker rater tan in fewer employees, wit employee numbers falling only wit a lag. Tese effects are driven by te quasi-fixed labour costs wic, once incurred (especially for recruitment and training), are sunk costs. In terms of te composition of labour services by skill level, te greater reduction in labour input falls on te lower skilled, in part because te lower sare of fixed costs means a relatively smaller fall in te (sort run relevant) relative labour cost for te low skilled, and in part because of te greater elasticity of substitution of low skilled labour wit te fixed capital input. Tat is, compared wit te time series for output, te time series for labour services is less variable, and ten te time series for number of employees is less variable again and a lagging indicator, and tis reduction in volatility and magnitude of te lag is greater for te more skilled relative to te low skilled labour types. Rosen finds tese implications to be consistent wit actual data for te US railways. Aggregate time series data on number of employees and average ours of work, suc as in Figure 1, include tese industry effects discussed by Rosen, and in addition tere are likely to be industry composition effects. For example, over te business 2 Compared wit te model of Section III were declining marginal productivity per our was important, te Rosen model assumes constant marginal productivity at around current ours of work.

15 14 cycle, different product demands are affected differently, including necessities versus discretion purcase products, and some sectors are better able to smoot production wit fluctuating demands, for example storable goods versus many consumer services. VI Some Implications A key finding of te preceding analysis is tat te ours of work per employee and te number of employees are imperfect substitutes. Rejection of te simplified production function for labour services (1 ), or L function (1 ), or ( ) L= Ng H marginal productivity per our ( g = NH, in favour of te more general, were beyond a basic number of ours worked te '( ) H ) declines, is required to explain te mix of observed part time, standard ours and overtime ours in employer cost minimising decisions. In tis section we raise some model specification issues and te interpretation of estimates of productivity and labour demand functions using time series data prepared under te simplifying assumption tat N and H are perfect substitutes, and in particular tat '( H) providing labour services. (i) Productivity Growt g is a constant for all ours worked, in Many estimates of indexes of labour productivity and of multifactor productivity, and te derived rates of growt of productivity, use a measure of total ours worked, tat is L = HN, as te labour input measure. Te Australian Bureau of Statistics (1999 and 2000, and te regular publication in Catalogue ) is just one of many examples. Here we consider only te measure of te labour input, and we ignore oter important issues often raised wit te measures of output and te capital input. To illustrate te potential biases in estimates of productivity growt using tis simplified measure rater tan te more general function of (1 ), consider te labour productivity index LP LP = Y L (11) were, Y is output and L is labour services measured as ours worked, namely L = NH.

16 15 Te labour productivity growt rate, dlp LP can be expressed as te difference in te growt rates of output and te labour services input dlp LP = dy Y dl L (12) Under te simplifying assumption tat te number of employees and ours of work are perfect substitutes, tat is (1 ), we can expand (12) as dlp LP = dy / Y dn / N dh / H (12 ) But, if we use te more general labour services function L= g( H) N of (1 ), ten (12) becomes were ( ) dlp LP = dy Y dn N α dh H (12 ) α = MP AP < 1 (13) and in equilibrium, as sown in (7), α equals te sare of variable labour costs in total labour costs and, as before, MP = g, ( H) is te marginal product per our worked, and AP = g( H ) H is te average product per our worked. Comparing (12 ) and (12 ), wen ours and employees are not perfect substitutes, and wen tere as been a decline in ours worked over time, as observed in Australia and sown in Figure 1, and in many oter countries, te use of (12 ) rater tan (12 ) over-estimates te growt of labour productivity. Te over-estimate given by ( ( α 1) dh H ), will be greater te larger te reduction over te time period of average ours worked and te smaller is te term α in (13) wic in turn depends primarily on te relative importance of variable labour costs in total costs (see te employer cost minimising condition (7)). A similar story can be told for te multifactor productivity (MFP) measure. For multifactor productivity, te bias in estimation will be given by s( 1) ( dh ) α H, were s is te sare of labour costs in total factor costs, and, as before, α is te sare of variable labour costs in total labour costs and dh H is te rate of cange in average ours worked. Again, wit declining (increasing) average ours worked per employee, te conventional MFP measure based on te assumption of perfect substitutability of

17 16 persons overestimates (underestimates) te rate of MFP growt wen compared wit a measure based on te more realistic assumption of imperfect substitution, or of declining productivity per our worked. Te simplified measure attributes some of te productivity cange to te employer coice of different working ours. Pictures of te pattern and magnitude of differences in time series estimates of labour productivity (LP) and multifactor productivity (MFP) assuming ours and persons are perfect substitutes (te conventional ABS estimates) and allowing tat tey are imperfect substitutes wit α = 0.83 are sown in Figures 5 and 6. Te Figures sow te difference between te two series for LP and MFP growt per annum for te market sector of Australia over te period troug Given tat ours per worker ave fallen over tis time period, te perfect substitution assumption estimate as on average exceeded te estimates based on te assumption tat ours and persons are imperfect substitutes. Te overestimate was relatively large in te 1970s wen te fall in average ours was most marked (Figure 1), and as muc as 0.3 percentage points per year in te case of LP and 0.2 percentage points for MFP, wit anoter blip in [FIGURES 5 AND 6 NEAR HERE] A disaggregated by industry comparison of productivity estimates prepared under different assumptions on te substitutability of ours and employees is sown in Table 4. 3 Here te compound average annual percentage canges in LP and MFP over te period troug are reported. Given tat tis is a period of relative stability of ours worked, it is not surprising tat te differences, or te bias, are small. Wat owever is of particular interest is tat a more disaggregated level, in tis case different industries, te bias varies in sign. Over te last twenty years average ours 3 Source of data is Australian Bureau of Statistics (2007b and c). Te data provided includes indices of total ours worked in eac industry wic we ave decomposed into its average ours worked and number of persons employed by comparing te total ours worked series wit figures for te numbers employed in eac industry obtained from te Labour Force Survey. Data on fixed costs of employment across industries (especially industries oter tan manufacturing) are extremely difficult to come by. Te only estimates we ave found are in Hart and Kawasaki (1999, p 67, Table 4.4). Based on te figures given tere we estimate te ratio of variable costs to total costs (and tus our estimate of α for eac industry) to be: 3 Mining, 0.91; Manufacturing, 0.94; Electricity, gas & water, 0.90; Construction, 0.96; Wolesale trade, 0.95; Retail trade, 0.95; Accommodation, cafes & restaurants, 0.95; Transport & storage, 0.95; Communication services, 0.95 ; Finance & insurance, 0.93, and; Cultural & recreation services, It will be seen tat tese figures are all quite ig and sow very little variation across industries.

18 17 worked per employee rose in te mining, electricity, gas and water, wolesale trade and finance and insurance industries, wile tey were constant in te construction, transport and storage industries, and fell in te oter four industries. Ten, depending on te industry experience wit average ours worked, productivity estimates based on te assumption of perfect substitutability of persons and ours can underestimate or overestimate productivity growt based on te more plausible assumption of imperfect substitution. [TABLE 4 NEAR HERE] In effect, wen te number of employees and te ours worked per employee are not perfect substitutes, as we argue is reality, and ours worked per employee vary, te conventional measures of labour productivity and of multifactor productivity confound two sources of gains in productivity in te conventional estimates based on te assumption of perfect substitutability. Tese two sources are on te on and tecnical canges, better work and management practices, increases in worker effort and intensity and so fort generally regarded as efficiency improvements, and on te oter and canges in productivity due to canges in ours worked. Of course, for some questions te distinction between te two sets of productivity gain may be of little merit or policy interest, and in oter cases te magnitudes of differences may be small and of no consequence. But for oter questions, and particular sample periods, including te 1970s, te distinction will be important. Furter, using (12 ) for LP, and an analogous formulae for MFP, it is easy to disentangle te two sets of sources of productivity gains. (ii) Aggregate Labour Demand Wen te number of employees and te ours tey work can be regarded as perfect substitutes, it is appropriate to derive and estimate labour demand functions wit labour ours, L= NH, as te demand dependent variable. But, if te dependent variable instead is specified to be te number of employees N, ten H sould be included as an explanatory variable, and under te perfect substitution assumption, wit a restricted elasticity of minus unity. Tis approac is adopted in te labour demand equation in te TRYM model for example (Taplin and Parameswaran (1993), Stacey and Downes ( 1995) and Downes and Bernie (1999)). Once we allow for imperfect substitutability of N and H for te reasons argued in tis paper, te elasticity parameter on te H explanatory variable is given by minus te sare of variable labour costs in total labour

19 18 costs (or te ratio of te marginal and average products per our worked), wic is less tan unity. Alternatively, in oter studies H is omitted as an explanatory variable (or wit an implied elasticity of zero), for example in te labour demand studies of Russell and Tease (1991), Debelle and Vickery (1998) and Lewis and MacDonald (2002). For suc specified models, if H varies over te sample period and is correlated wit included explanatory variables, estimates of te parameters on te included explanatory variables will be biased. Using a more general model specification of te demand for te number of employees wit H as an explanatory variable were te parameter on te variable H is estimated, for example in Dixon et al. (2005), te estimated elasticity of te number of employees N wit respect to average ours worked H is found to be about -0.75, a number wic closely corresponds to te estimated sare of variable costs in total labour costs reported for te US and UK by Hart (1984) and Martins (2004) for Portugal. A furter specification and estimation issue for a labour demand function wen te number of employees and ours worked per employee are imperfect substitutes is te issue of simultaneity. Since bot N and H are decision variables, bot N and H are jointly endogenous variables. Tis requires a simultaneous equation model wit bot N and H as endogenous variables, and te use of an appropriate estimator. VII Conclusions A model of firm labour services cost minimisation is used to explain te observed diverse range of ours of work from part time, normal ours and long ours. Te model explicitly recognises an important fixed cost component in total labour costs and a premium for overtime ours, and it allows labour productivity per our worked to decline after a number of ours. At te cost minimising mix of number of employees and ours per employee, te employer equates te sare of variable labour costs in total labour costs, around 0.8 but varying wit occupations and industries, wit te ratio of te marginal and average products per our worked, wic also varies wit circumstances. Part time employment is more common in tose occupations and industries were fixed costs are a relatively small sare of total labour costs, and were marginal

20 19 productivity per our worked declines before normal working ours. Tese include te lower skilled occupations and te service industries. Long ours of work employment is more prevalent were fixed costs are a relatively large sare of total labour costs, were productivity per our starts to fall only after many ours, and were institutional restraints triggering te overtime premium are weak. Tese conditions are found wit te managerial and professional occupations and in te capital intensive industries. Quasi-fixed labour costs, and difference across labour categories in te relative importance of fixed costs in total labour costs and in te substitutability of te different labour categories wit te fixed capital stock, result in different time series properties for te number of employees and ours relative to sort term product output canges, including over te business cycle. In general, as a consequence of output canges, ours respond earlier and wit greater volatility tan do te number of employees. Te different time series properties are more marked for te relatively more skilled workers and for tose wit iger fixed cost sares. A key implication of te paper is tat te number of employees and ours worked per employee cannot be treated as perfect substitutes in te supply of labour services. Recognition of imperfect substitution, and in particular te declining marginal productivity per our of work around te cost minimising labour services coice by employers, as important implications for te way economists model, estimate and interpret labour demand studies and measures of productivity. Measures of labour and multifactor productivity using total ours worked as te labour input, and implicitly assuming perfect substitution of persons and ours, confound te effects of efficiency gains wit, for example tecnology and better practices, and canges in ours worked. In a trend istorical sense, te efficiency gains ave been over estimated. Labour demand studies using total ours worked as te dependent variable are found wanting. A more desirable model involves a simultaneous equation model to explain bot ours and number of employees, and te elasticity parameter on te ours explanatory variable in te number employed equation will ave a value less tan unity and equal to te sare of variable costs in total labour costs.

21 20 REFERENCES Australian Bureau of Statistics (1990), Occasional Paper: Estimates of Multifactor Productivity, Cat. No , Canberra. Australian Bureau of Statistics (2000), Australian National Accounts: Concepts, Sources and Metods, Cat. No , Canberra. Australian Bureau of Statistics (2007a), Australian Labour Market Statistics, May 2007, Cat No , Canberra. Australian Bureau of Statistics (2007b), Information paper: Experimental Estimates of Industry Multifactor Productivity, Cat No , Canberra. Australian Bureau of Statistics (2007c), Experimental Estimates of Industry Multifactor Productivity- Data Cube, No Becker, G. (1962), Investment in Human Capital: A Teoretical Analysis, Journal of Political Economy, 52, Bell, D. (1982), Labour Utilization and Statutory Non-Wage Costs, Economica, 49, Brecling, F. (1965) Te Relationsip Between Output and Employment in Britis Manufacturing Industries, Review of Economic Studies, 32, Boot, A. and Ravallion, M. (1993), Employment and lengt of te working week in a unionized economy in wic ours of work influence productivity, Economic Record, 69, Calmfors, L. and Hoel, M. (1988), Work Saring and Overtime, Scandinavian Journal of Economics, 90, Calmfors, L. and Hoel, M. (1989), Work Saring, Employment and Siftwork, Oxford Economic Papers, 41, Commonwealt Treasury (1996) Documentation of te Treasury Macroeconomic (TRYM) Model of te Australian Economy, Canberra. Craine, R. (1973), On te Service Flow from Labour, Review of Economic Studies, 40,

22 21 Cutler, D. and Madrian, B. (1998), Labor Market Responses to Rising Healt Insurance Costs: Evidence on Hours Worked, RAND Journal of Economics, 29, Debelle, G. and Vickery, J. (1998), Te Macroeconomics of Australian Unemployment, in G. Debelle and J. Borland (eds), Unemployment and te Australian Labour Market, Reserve Bank of Australia, Sydney, Dixon, R., Freebairn, J. and Lim G. C. (2005), An Employment Equation for Australia, Economic Record, 81, Dolfin, S. (2006), An Examination of Firms Employment Costs, Applied Economics, 38, Downes, P. and Bernie, K. (1999), Te Macroeconomics of Unemployment in te Treasury Macroeconomic (TRYM) Model, TYRM Related Paper No. 20, Commonwealt Treasury, Canberra. Erenberg, R. (1971), Fringe Benefits and Overtime Beavior, Lexington Books, Lexington, Mass. Feldstein, M. (1967), Specification of te Labour Input in te Aggregate Production Function, Review of Economic Studies, 34, Hamermes, D. (1993), Labor Demand, Princeton University Press, Princeton. Hart, R. (1984), Te Economics of Non-Wage Labour Costs, Allen & Unwin, London. Hart, R. and Kawasaki, S. (1999), Work and Pay in Japan, Cambridge, Cambridge University Press. Kapteyn, A., Kalwij, A. and Zaidi, A. (2004), Te Myt of Worksaring, Labour Economics, 11, Lewis, P. and MacDonald, G. (2002), Te Elasticity of Demand for Labour in Australia, Economic Record, 78, Martins, A. (2004), Te Employment-Hours Trade-off: Teory and an Application to te Portuguese Case, Labour, 18, OECD, (2004), OECD Employment Outlook 2004, Organisation for Economic Cooperation and Development, Paris.

23 22 Oi, W. (1962), Labor as a Quasi-Fixed Factor, Journal of Political Economy, 70, Param, D. (2004), Sources of Australia s Productivity Revival, Economic Record, 80, Rosen, S. (1968), Sort-Run Employment Variation on Class-I Railroads in te U.S., , Econometrica, 36, Russell, B. and Tease, W. (1991) Employment, Output and Real Wages, Economic Record, 67, Stacey, G. and Downes, P. (1995) Wage Determination and te Labour Market in te Treasury Macroeconomic (TRYM) Model, TYRM Related Paper No. 13, Commonwealt Treasury, Canberra. Taplin, B. and Parameswaran, P. (1993), Employment, Investment, Inflation and Productivity: Decisions by te Firm, TYRM Related Paper No. 3, Commonwealt Treasury, Canberra. Wooden, M. and Drago, R. (2007), Te Canging Distribution of Working Hours in Australia, Melbourne Institute Working Paper Series, Working Paper No. 19/07, Te University of Melbourne.

24 23 TABLE 1 Percentage Distribution of Usual Hours Worked per Week by Gender, May 2007 Usual Hours Males Females Persons Worked per week and over Source: Compiled from ABS, Australian Labour Market Statistics, May 2007, , Table 2.8.

25 24 TABLE 2 Relative Importance of Part Time Employees and Long Hours Employees as a Percentage of te Workforce by Industry and Occupation, May 2007 Industry or Occupation Percentage of Employees Part Time Percentage of Employees Long Hours All Industry: Accommodation, cafes and restaurants Retail trade Culture and recreational services Healt and community services Education Personal and oter services Property and business services Agriculture, forestry and fising Finance and insurance Transport and storage Wolesale trade Government administration and defence Communication services Construction Manufacturing Mining Electricity, gas and water Occupation: Elementary clerical, sales and service Advanced clerical and service

26 25 Intermediate clerical, sales and service Intermediate production and transport Professionals Labour and related Associate professionals Tradespersons and related Managers and administrators Source: Compiled from ABS, , Labour Force, Australia, Detailed, Quarterly, Table 11 Employed persons by Actual ours worked, Industry and Sex and Table 12 Employed Persons and Actual Hours Worked, Occupation and Sex.

27 26 TABLE 3 Percentage Distribution of Employed Persons by Actual Hours Worked per Week by Gender, 1980 to 2006 Actual Weekly Hours Worked Zero Males Females Source: From Wooden and Drago (2007), Table 1, in turn from ABS, Labour Force, Australia, Detailed Electronic Delivery, ABS Catalogue No (Table 09: Employed persons and actual ours worked by sex).

28 27 TABLE 4 Compound Annual Percentage Canges in Labour Productivity (LP) and Multifactor Productivity (MFP) by Industry, Industry LP Bias LP * MFP Bias MFP * Mining Manufacturing Electricity, gas & water Construction Wolesale trade Retail trade Accommodation, cafes & restaurants Transport & storage Communication services Finance & insurance Cultural & recreation services Notes: LP is labour productivity wile MFP is multifactor productivity estimated by ABS on te assumption tat ours per employee and number of employees are perfect substitutes. LP * is labour productivity wile MFP * is multifactor productivity estimated assuming ours and employees are imperfect substitutes wit α = 0.83 as described in te text. Bias = LP LP * and MFP MFP *, wit more details in te text.