Estimation of Wage Equations in Australia: Allowing for Censored Observations of Labour Supply *

Transcription

1 Estmaton of Wage Equatons n Australa: Allowng for Censored Observatons of Labour Supply * Guyonne Kalb and Rosanna Scutella* Melbourne Insttute of Appled Economc and Socal Research The Unversty of Melbourne Melbourne Insttute Workng Paper No. 8/02 ISSN ISBN May 2002 * Thanks to the Department of Famly and Communty Servces for fundng ths research. The vews expressed n ths paper are those of the authors and do not represent the vews of the Mnster for Famly and Communty Servces, the Department of Famly and Communty Servces or the Commonwealth Government. We should also lke to thank John Creedy, Mark Harrs and members from the Department of Famly and Communty Servces for helpful dscussons and suggestons. Melbourne Insttute of Appled Economc and Socal Research The Unversty of Melbourne Vctora 3010 Australa Telephone (03) Fax (03) Emal melb-nst@unmelb.edu.au WWW Address

2 Abstract Ths paper presents results for fve separately estmated sets of partcpaton and wage equatons. The Australan workng-age populaton s dvded nto sole parents, sngle men, sngle women, marred men and marred women. The approach n ths paper takes the censorng of labour supply observatons at 50 hours per week nto account. The results for the wage equatons are as antcpated wth educaton, work experence and age ncreasng the expected wage. As expected, allowng for the censorng of labour supply reduces the predcted wage levels, partcularly for marred men who are most lkely to work 50 hours or more.

3 1 1 Introducton Ths paper reports estmates of wage functons for a number of demographc groups n Australa, usng pooled nformaton from the 1994/95, 1995/96, 1996/97 and 1997/98 Surveys of Income and Housng Costs (SIHC). Ths s an extenson from a prevous paper usng 1995 and 1996 SIHC data (Creedy et al., 2001). More mportantly, n addton to the extra years of data, the model used n ths paper accounts for the censorng of labour supply nformaton at 50 hours that occurs n the SIHC data. The am of estmatng wage equatons often s to mpute wage rates for those who are not currently workng, so that they can be used n labour supply models. 1 In ths paper the wage equaton s estmated separately, but a smlar approach to the one taken n ths paper could be followed when estmatng wage and labour supply smultaneously. The mputaton of wage rates s complcated by the fact that wage equatons should deally contan varables, such as ndustry and occupaton, whch are not observed for non-workers (for the same reason that wage rates are not avalable). These varables are major determnng factors of wage rates. Ths paper therefore follows the same approach as a prevous paper on ths topc (Creedy et al., 2001). As n other artcles, the estmaton procedure corrects for the sample selecton bas that would arse from the fact that only the wage rates of those currently workng are observed usng the standard Heckman procedures (Heckman, 1979). Earler Australan wage functons were dscussed for example by Mller and Rummery (1991), Murray (1996), Kalb (2000), and Creedy et al. (2001). The results show that after accountng for censorng, lower wage rates are predcted. Ths may, for example, be mportant when these wage equatons are used to mpute wage rates n labour supply models. In addton, the equaton could be used to mpute wages for those workng 50 hours or more, allowng for the uncertanty of hours worked but ncorporatng the avalable nformaton. In the latter case the predcton of the wage 1 Many tax polces are specally desgned n an attempt to stmulate an ncrease n labour supply. There would therefore be lttle value n restrctng analyses to those currently workng, thereby excludng nonpartcpants whose partcpaton decson may be nfluenced by taxes and transfers. Labour supply analyses requre an ndvdual-specfc budget constrant, so a wage rate must be assgned to non-workers.

4 2 would be condtonal on t lyng n the observed range. The standard selecton model s descrbed brefly n secton 2. The data are descrbed n secton 3. Estmates of the wage equatons are reported n secton 4. The problem of assgnng wage rates to non-workers and the predcton of wage rates for some hypothetcal ndvduals are dscussed n secton 5. Bref conclusons are n secton 6. 2 The Statstcal Model The estmaton of wage equatons nvolves a system of two correlated equatons, the frst of whch determnes selecton (employment) usng a probt equaton, whle the second determnes wage rates, condtonal on employment. The correlaton between the two equatons accounts for the possble selecton nto work of those wth hgher wage rates. The wages of workers may therefore not represent the wages of non-workers. However, the ncluson of an addtonal term n the wage equaton ndcatng the tendency to partcpate can correct for ths. Each ndvdual's observed employment outcome s regarded as beng the result of an * unobservable ndex of tendency to partcpate n the labour force and employablty,, whch vares wth observed personal characterstcs, z. The varables ncluded n z may nclude both supply and demand sde varables. Hence: E * = z γ + u (1) ' where u s assumed to be ndependently dstrbuted as N(0, 1) 2. The realsaton of * E determnes whether the ndvdual s employed (E = 1), or unemployed or out of the labour force (E = 0), such that: E 1f E = 0 f E * * where ( z ' γ) > 0 wth prob. Φ 0 wth prob. 1- ' ( z γ) Φ( z γ) ' Φ s the standard normal dstrbuton functon evaluated at z ' γ. The assocated normal densty functon s denoted E (2) φ ( z ' γ). The parameters of (2) can be consstently estmated by a standard probt model; see Maddala (1983). Havng 2 As there s no nformaton about the scale of E the varance of u cannot be dentfed and s therefore set equal to unty.

5 3 estmated (2), an estmate, λˆ, of the nverse Mll s rato for a workng ndvdual s obtaned usng: λˆ ' ( γˆ ) ' ( z γˆ ) φ z = (3) Φ Let w denote the logarthm of the wage rate and x a vector of characterstcs of ndvdual. The regresson model s wrtten as: w ' E = 1 = xβ + ε (4) The u from equaton (1) and ε are assumed to be jontly normally dstrbuted as N(0, 0, 2 ε 1, σ, ρ) 3. In order to avod selectvty bas, a correcton term s added to (4): ' E = 1 = xβ + ρσε υ (5) w λˆ + Equaton (5) takes nto account the correlaton between u and ε. It can be seen that the varance of υ, σ 2 2 ε 2 ( 1 ρ δ ) 2 σ, s heteroscedastc, snce: = σ (6) where: ' ( λ + z γ) δ = λ (7) Effcent estmaton of ths model s carred out usng the convenent two-step procedure of frst estmatng the probt model for the employment probablty and calculatng the predcted value for the nverse Mll s rato. The predcted Mll s rato s then used n the wage equaton. Greene (1981) shows how to calculate the corrected standard errors. In the SIHC, descrbed below, for ndvduals workng 50 hours per week or more, the exact hours worked are not observed. In these cases only the maxmum possble value s known of the dependent varable w, that s, the wage rate has to be smaller than the total ncome from wages and salares dvded by 50. Gven that people are extremely unlkely to work more than 100 hours per week, the total ncome from wages and 3 The covarance between u and ε s thus ρσ ε.

6 4 salares dvded by 100 s used as a lower boundary for the wage rate. Estmatng the wage equaton by the Maxmum Lkelhood method, nstead of the usual contrbuton of an observaton to the lkelhood functon of: ln L = ln Pr(υ = w ' x β ρσ λˆ) = 0.5ln(2π) ln σ ε (w ' x β ρσ 2σ the contrbuton, when only the range of the wage s known, becomes: ln L = ln Pr( w = ln,mn ' w,max xβ ρσελˆ ' x β ρσ λˆ υ w,max l ( t) exp σ 2π 2 ' w xβ ρσ λˆ 2, mn ε σ ε 2 ' x β ρσ λˆ) dt where w,max s the maxmum possble value for the wage rate, and w,mn s the mnmum possble value for the wage rate. ε 2 ε λˆ) 2 (8) (9) By usng nterval regresson n these cases (and ncludng a range rather than one value for the dependent varable), overestmaton of the wage rate s avoded and the uncertanty assocated wth the wage rate for people workng more than 49 hours s ncluded n the estmaton. 3 The Data The data used n ths analyss are taken from the 1994/95, 1995/96, 1996/97 and 1997/98 Surveys of Income and Housng Costs, avalable from the ABS n the form of confdental unt record fles (CURFs). The survey collects nformaton on the sources and amounts of ncome receved by persons resdent n prvate dwellngs throughout Australa, along wth data on a range of characterstcs of ncome unts and ndvduals. The survey s contnuous wth around 650 households ntervewed every month durng the fnancal year. In the surveys from 1994/95 to 1997/98, nformaton s avalable respectvely for 13827, 14017, and ndvduals over the age of 15. Earler Surveys of Income and Housng Costs (or Income Dstrbuton Surveys as they were called then) were carred out, but the 1994/95 survey s the frst to provde publshed data on the precse hours worked (up to 50 hours per week) by each ndvdual worker n the sample; earler surveys contan only grouped nformaton on labour supply, dvded nto broad hours groups. The detals of hours worked are

7 5 requred for the calculaton of wage rates, obtaned for each ndvdual as the rato of total earnngs to hours worked. Hence the followng analyss gnores the possblty that ndvduals may obtan overtme premums, or may work n more than one job. Where ndvduals worked 50 hours or more 4, the exact wage rate s unknown. It s only known that the wage must be lower or equal to the total earnngs dvded by 50. The estmaton procedure takes ths nto account by usng an nterval regresson when the recorded hours worked equals 50. In ths nterval regresson, we assume that the maxmum number of hours of labour supply s 100 per week. As a result the wage must be hgher than the total earnngs dvded by 100. The majorty of the data used as explanatory varables were recoded as zero-one dummy varables. To keep all the varables to a smlar scale all of the non-wage ncome varables were dvded by 1000 whle age was dvded by 10. Any ndvduals wth nconsstent observatons on ncome from wages or salares and hours worked, that s postve earnngs for zero hours or zero earnngs for postve hours, are excluded from the wage equaton (as sensble wage rates cannot be calculated for them). However these observatons do reman n the partcpaton equaton assumng that we correctly observe whether or not they are n the work force. As the emphass of the analyss s on obtanng results to be used n labour supply analyss for people of workng age, ndvduals over 65 years are excluded from the sample. Furthermore, groups such as the dsabled and those n full-tme educaton are excluded, because they are unlkely to partcpate n the labour force and the factors determnng ther partcpaton decson would be qute dfferent from other people of workng age. Fnally, the self employed are omtted from the sample, because ther decson to work an addtonal hour cannot be lnked to the wage rate for that addtonal hour, whch s crucal n the labour supply estmaton for the wage and salary earners 5. 4 Table A.1 shows the proporton of people n the dfferent demographc groups, who work 50 hours or more. Except for sole parents, a substantal number of people fall nto ths category. 5 In the four surveys used, there were 1035 people ether at school or studyng full-tme. There were 18 unpad voluntary workers and 283 ndvduals permanently unavalable for work. Also, there were 8141 ndvduals over the age of sxty-fve. There were 4978 self-employed persons.

8 6 The four surveys were pooled 6 and the sample was dvded nto fve demographc groups. These are: sole parents; sngle females wthout dependents; sngle males wthout dependents; marred females; and marred males. Summary tables of sample characterstcs are provded for each demographc group n the Appendx. It was not possble to estmate separate equatons for sole mothers and sole fathers, gven the small number of sole fathers n the sample 7. Table 1 presents the average real wage rates across the four years for the fve demographc groups. Here t can be seen that, once wage nflaton has been accounted for, average wages do not seem to change systematcally between the varous survey years. In estmaton, we nclude year dummes n the wage equaton to check more formally for systematc dfferences over tme. Table 1: Average real wage rates for 1994/95 to 1997/98, nflated to May 1998 level 1994/ / / /98 Sole parents Sngle females Sngle males Marred females Marred males Examples of dstrbutons of the logarthms of observed hourly wage rates for the fve demographc groups are shown n Fgures 1 to 5. These are based on May 1998 wages and the censorng of labour supply at 50 hours per week s not taken nto account 8. The hstograms suggest that these dstrbutons are approxmately lognormal, although they are slghtly more peaked than the correspondng normal dstrbutons wth the same mean and varance. Indvduals reportng wage rates lower than $4 an hour or greater than $100 an hour are consdered outlers and are omtted from the wage equaton. 6 All wage rates are ncreased to the values they would have had n 1998 usng ndces derved from average weekly earnngs for males and females respectvely and all ncome from other sources s nflated wth the approprate consumer prce ndex to obtan the value t would have had n There were 194 male sole parents, compared wth 1593 females. 8 That s, when the wage rate s calculated from weekly earnngs and the weekly hours worked no account s taken of the fact that for people workng 50 hours or more the exact weekly hours are unknown. Instead, wages for ths group are calculated by dvdng earnngs by 50.

9 7 These observatons reman n the partcpaton equaton. As expected, the graphs show that the modal wage rate s hgher for men than for women. Fgure 1: Log hourly wage rates for sole parents, May 1998 wages.15 Proporton of sole parents Log wage rate Fgure 2: Log hourly wage rates for sngle females wthout dependents, May 1998 wages.15 Proporton of sngle females Log wage rate

10 8 Fgure 3: Log hourly wage rates for sngle males wthout dependents, May 1998 wages.15 Proporton of sngle males Log wage rate Fgure 4: Log hourly wage rates for marred females, May 1998 wages Proporton of marred females Log wage rate

11 9 Fgure 5: Log hourly wage rates for marred males, May 1998 wages.15 Proporton of marred males Log wage rate 4 Emprcal Results Ths secton presents the man emprcal results. The results for the selecton equatons are presented n the Appendx. The estmated wage equatons, condtonal on beng n employment, are reported for each demographc group n Tables 2, 3 and 4. The results here look qute smlar to the results n Creedy et al. (2001). The man dfference between the two models s that, n the verson presented here, some addtonal explanatory varables on recent work experence are ncluded. The sample szes are, for marred women, marred men, sngle women, sngle men and sole parents respectvely 7434, 9513, 3398, 4459 and 836. The nverse Mll s rato has the expected sgn for marred women and sole parents only, that s for these two groups the parameter s sgnfcant and postve. The nverse Mll s rato s nsgnfcant for marred men and sngle women and sgnfcantly negatve for sngle men. The nterpretaton of negatve nverse Mll s ratos n ths context was dscussed by Ermsch and Wrght (1994) 9. The results on ths coeffcent are not comparable to the results n Creedy et al. (2001) snce a dfferent selecton equaton was estmated. 9 Mller and Rummery (1991) found a postve value for women and a negatve value for men. They also revew results found n prevous Australan studes. They do not dstngush between sngle and marred men and women. Murray (1996) found a postve value for mothers (sngle and marred) and Kalb (2000) found a postve value for marred women and a negatve (nsgnfcant) value for marred men.

12 10 Here all models are presented wth the Mll s rato ncluded. However to mpute wages for non-workers, the equatons for marred men and sngles are re-estmated usng the nterval regresson specfcaton wthout the selecton correcton. For these groups the Mll s rato s not sgnfcant at the 5-per cent level. Table 2: Wage Equatons: Marred Women and Men Women Men coeffcents std.err. coeffcents std.err. constant ** ** Age/ ** ** Age squared/ ** ** # months worked n last ** Work exp (last fnancal year) ** ** Tradesperson/labourer (reference) Professonal ** ** Paraprofessonal ** ** Clercal/sales ** ** Agrculture/forestry (reference) Mnng ** ** Manufacturng ** ** Constructon ** ** Utltes ** ** Trade * ** Transport ** ** Communcaton ** ** Fnancal/busness servces ** ** Other servces ** ** Australa (reference) Europe/Mddle East * Asa ** ** Amerca/Afrca ** No qualfcatons (reference) postgraduate ** * undergraduate * dploma ** ** vocatonal ** ** NSW (reference) Vctora ** ** Queensland ** ** South Australa ** ** Western Australa ** ** Tasmana ** * ACT/Northern Terrtory ** ** Captal cty ** ** Age * unversty degree * ** Mll s rato ** σ ε Number of observatons Notes: ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. These standard errors are not corrected for usng the predcted Mll s rato.

13 11 Table 3: Wage Equatons, Sngle Women and Men Women Men coeffcents std.err. coeffcents std.err. constant ** ** Age/ ** ** Age squared/ ** ** # months worked n last ** ** Work exp (last fnancal year) ** ** Tradesperson/labourer (reference) Professonal ** ** Paraprofessonal ** ** Clercal/sales ** ** Agrculture/forestry (reference) Mnng ** Manufacturng ** Constructon ** Utltes ** ** Trade ** Transport ** ** Communcaton ** ** Fnancal/busness servces ** Other servces ** Australa (reference) Europe/Mddle East Asa Amerca/Afrca No qualfcatons (reference) postgraduate ** undergraduate dploma ** ** vocatonal ** ** NSW (reference) Vctora Queensland ** South Australa Western Australa ** Tasmana ACT/Northern Terrtory ** Captal cty ** ** Age * unversty degree ** Mll s rato * σ ε Number of observatons Notes: ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. These standard errors are not corrected for usng the predcted Mll s rato.

14 12 Table 4: Wage Equaton: Sole Parents coeffcent Standard error Constant ** Female ** Age/ Age squared/ # months worked n last ** Work exp (last fnancal year) Tradesperson/labourer (reference) Professonal ** Paraprofessonal ** Clercal/sales ** Agrculture/forestry (reference) Mnng ** Manufacturng Constructon Utltes ** Trade Transport * Communcaton * Fnancal/busness servces Other servces Australa (reference) Europe/Mddle East Asa Amerca/Afrca No qualfcatons (reference) postgraduate ** undergraduate ** dploma ** vocatonal NSW (reference) Vctora Queensland South Australa Western Australa Tasmana ACT/Northern Terrtory ** Captal cty ** Mll s rato ** σ ε Number of observatons 830 Notes: ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. These standard errors are not corrected for usng the predcted Mll s rato. To ensure that changes over tme n the proporton of people not workng (whch combnes those n unemployment and out of the labour force) and the proporton n employment 10 dd not affect the estmated results, a wage equaton ncludng year 10 See Table A.1 for the proporton of respondents n the dfferent labour market states n each of the survey years.

15 13 dummes for each of the survey years has been estmated. These dummes turned out to be nsgnfcant, ndcatng that after takng nto account the changes n average wage rates for men and women separately, wages do not appear to dffer sgnfcantly over the years. The coeffcents more or less dsplay the expected varaton of wage wth age, that s wage rates generally ncrease wth age up to people s early fortes, after whch they declne agan wth age. The excepton s the sole parents group, where no effect from age s found. The age effect s more mportant for sngles than for couples. There s a consderable amount of dfference n wage rates between occupatons and educatonal qualfcatons. Wage rates of professonals, paraprofessonals, and clercal or salespersons are sgnfcantly hgher than for trades persons or labourers across all groups. As expected, the wage level s hghest for professonals, followed by paraprofessonals and then clercal or salespersons. Wage rates also tend to ncrease wth the level of educatonal qualfcaton across all groups. Generally, people educated at unversty level have the hghest wages, although for sngle men a vocatonal educaton seems just as benefcal. Sole parents wth a dploma receve consderably lower wages compared to sole parents wth a postgraduate or undergraduate degree, followed by sole parents wth a vocatonal qualfcaton. The sgnfcance of the nteracton term between age and educaton level (dstngushng between unversty level or less) ndcates that the effects of age and educaton are not completely ndependent of each other. For sngle women and marred couples the coeffcent ndcates that people wth a unversty degree, have wages that ncrease more wth age than people wthout a unversty degree. Ths mght ndcate that work experence results n more wage growth for people wth a hgher educaton level. Work experence n the prevous fnancal year has a postve effect on current wage rates. However, the number of months n employment out of the last seven has lttle, and sometmes even a negatve, effect; only for marred women and sole parents s the effect postve and sgnfcant. The latter group, n partcular, has a wage premum for recent work experence, but on the other hand, the effect of work experence n the last fnancal year s smaller than for other groups (and nsgnfcant).

16 14 Couples lvng n NSW experence hgher wage rates than those lvng n the other states, wth the excepton of those resdng n the Terrtores who receve even hgher wages; resdents of the ACT form the larger part of ths category. People lvng n captal ctes are pad hgher wage rates than ther counterparts lvng n other areas of the country. Wage rates of marred women and marred or sngle men are hgher n all ndustres compared wth the agrculture/forestry ndustry (the reference ndustry). For sngle women and sole parents only the wage rates n mnng, utltes, transport and communcaton are sgnfcantly hgher. People n the mnng and utltes ndustres generally have the hghest wages, for men and sole parents the dfference between these and other ndustres s partcularly hgh. The dfferences n wage rates between ndustres are smallest for marred women. There seems to be lttle effect on wages dependng on the country of orgn. Only mmgrants from Asa earn sgnfcantly lower wages f they are n the groups of sole parents or marred men or women. Marred men from Amerca and Afrca earn less than those born n Australa. The effects for sngles are nsgnfcant and smaller n sze. Ths perhaps reflects a dfference n the effect of beng an mmgrant between younger (who are more lkely to be sngle) and older age groups. Female sole parents earn sgnfcantly less than male sole parents. Comparng the sze of the coeffcent wth the dfference n the constant terms n the wage equatons for marred men and women and n the equatons for sngle men and women, t appears that the gender dfference n wages for sole parents s smlar to the gender dfference for the other groups. Fnally, the estmated standard error (σ ε ) has a smlar sze over all the demographc groups. It s largest for marred men, ndcatng that for ths group a larger proporton of the dfferences n wage rates has not been explaned by the varables ncluded n the equaton. The standard error s smallest for sngle women, however, the dfferences between groups are rather small.

17 15 5 Wage Predctons Ths secton consders the queston of how a wage rate may be assgned to unemployed ndvduals. In the smple case where the selecton and wage equatons contan a common set of varables, consder frst the condtonal mean log-wage rate, for an ndvdual wth gven characterstcs. For those who are employed, ths s gven by: ' 2 ( ) = x βˆ + ρˆσˆ λˆ E w E 1 = (10) ε Imputed wage rates for those who are unemployed can be obtaned usng the expresson: ' ' 2 φ ( ) ( zγˆ ) E 0 = x βˆ - ρˆσˆ ε ' 1 Φ( z γˆ ) E w = (11) The use of the condtonal mean log-wage s perhaps the most obvous choce for the predcted wage. It s also possble, for example, to take a random draw, for each ndvdual, from the relevant condtonal dstrbuton. Indeed, n labour supply analyses there s no necessty to be restrcted to usng observed wage rates for those employed n the sample perod: t would also be possble to take random draws from the relevant condtonal dstrbutons. In the present context, the expresson n (11) cannot be used wthout modfcaton because some varables used n the estmaton of the wage functons are not avalable for non-workers. In addton to the wage rate, nether the occupaton nor the ndustry of non-workers s known. Although these varables could not be ncluded n the selecton equatons, they were ncluded n the wage equatons because of ther demonstrated mportance n wage determnaton. An alternatve predctor for non-workers s smply (11) wth the dummy varables for occupaton and ndustry replaced by the sample proportons n the dfferent categores. Snce t s lkely, that the dstrbuton across occupatons dffers between the employed and the unemployed workers, extraneous nformaton on unemployment rates wthn the varous occupaton and ndustry groups are used to assgn proportons wthn occupaton and ndustry groups to the non-workers (see Table A.4). For a complete dscusson of ths approach see Creedy et al. (2001).

18 Margnal effects Ths subsecton provdes selected examples of the extent to whch a person s wage rate may change gven a change n ther observable characterstcs. Consder frst what the mpact of postgraduate qualfcatons s on the wage rates of ndvduals. A typcal sole parent or marred female wth a postgraduate degree s expected to be offered a wage rate whch s about 31 per cent hgher than for those wthout post secondary qualfcatons 11. Sngle females wthout dependents and marred men can expect a return from postgraduate qualfcatons of about 12 per cent, whle sngle males wthout dependents exhbt the lowest (and nsgnfcant) wage premum for a postgraduate qualfcaton wth wage rates only 11 per cent hgher. Second, lets consder what mpact lvng n a captal cty has on the wage rate of ndvduals. Wage rates are hgher across all fve demographc groups for ndvduals resdng n the captal cty of ther State. Sngle males experence the smallest effect on ther wage rates wth less than a three per cent ncrease by lvng n a captal cty. Sole parents, sngle females and marred males and females all have wage rates whch are between four and sx per cent hgher n captal ctes. Fnally, consder what the mpact of age s on the wage rates of ndvduals. To calculate the age effect, we need to take nto account the coeffcents of age and age squared. In addton the effect depends on the startng age. The effect for marred men s an ncrease of per cent for a ten-year ncrease n age from 25 to 35 years and a 3.0 per cent ncrease for a ten-year ncrease from 35 to 45 years. Ths reflects the turnaround pont n people s early fortes, from an ncreasng wage rate wth age to a decreasng wage rate wth age. 11 Ths value s calculated by usng the followng formula: [exp(relevant coeffcent) 1] 100%. In ths example that s: [exp(0.268)-1] 100% =30.7%. 12 The formula used n ths calculaton s [exp(coeffcent of age + coeffcent of age squared+2*(age at start/10)*(coeffcent of age squared)) 1] 100%. In ths example that s: [exp( *0.022)-1] 100% =7.7%.

19 Selected Examples of Predcted Wages Ths subsecton provdes selected examples of predcted wages obtaned when unemployed ndvduals are assgned the sample occupaton and ndustry characterstcs. Consder frst a female unemployed sole parent wth the followng characterstcs: aged 32 years; vocatonal qualfcaton; no recent work experence; separated/wdowed from a prevous relatonshp; European born; resdng n ACT/NT; wth no other ncome unt ncome; wth two dependent chldren, one aged between 5 and 9 years and the other between 10 and 15 years; lvng n other tenure. The predcted or mputed wage obtaned usng (employed) sample averages for ndustry and occupaton groups s found to be $9.87 per hour. We can also calculate a predcted wage usng the model, whch does not account for the censored labour supply observaton 13. Ths s $10.17, whch s only slghtly hgher than the specfcaton accountng for the censorng of labour supply over 49 hours. There are relatvely few sole parents workng long hours, so one would not expect a large dfference n the outcomes from the two specfcatons. Second, consder a sngle female wthout chldren; never marred; aged 22 years; Australan born; resdng outsde the Sydney metropoltan regon n NSW; wth a vocatonal qualfcaton; no recent work experence; lvng n other tenure wth no other ncome. The mputed hourly wage s found to be $10.48 ($10.63 n the model whch does not account for censorng n labour supply). Thrd, consder an unemployed sngle male wthout chldren; never marred; aged 22 years; vocatonal qualfcaton; no recent work experence; Australan born resdng outsde the Brsbane metropoltan regon n Queensland; n rented accommodaton. The mputed wage s $11.06 ($11.56 n the model whch does not account for censorng n labour supply). 13 The coeffcents for the models not accountng for the censorng of labour supply at 50 hours can be found n Tables A.8 to A10.

20 18 Fourth, consder an unemployed marred female: aged 42 years; wth one dependent chld aged over 15 years; European born; resdng n Perth; wthout formal educatonal qualfcatons; no recent work experence, but worked durng last fnancal year; partner has vocatonal qualfcaton but s currently not employed; other ncome s $25 per week; owns home outrght. The basc mputed wage s $12.32 per hour ($12.70 n the model whch does not account for censorng n labour supply). Fnally, consder an unemployed marred male: aged 47 years wth fve dependent chldren (three of whch are aged 5 to 9 years, two are aged 10 to 15 years); European born; resdng n Melbourne; wth a dploma; no recent work experence, but worked durng last fnancal year; partner has no formal qualfcatons and s currently not employed; no other ncome; owns home outrght. The basc hourly rate s $21.44 per hour. In a model not takng nto account the censorng of labour supply over 49 hours per week ths would have been $ The dfference for marred men between the two specfcatons s much larger than for the other groups, because a large proporton of the group of marred men falls n the category, whch works 50 hours or more. Thus accountng for censorng of labour supply s more mportant n ths group. To explore the senstvty of the results to the choce of upper boundary for the range of possble labour supply, the wage equatons have been re-estmated wth the maxmum labour supply set to 75 hours nstead of 100 hours. 14 These alternatve models have been used to predct the wage for the same hypothetcal persons as above. We fnd that changng the upper bound from 100 to 75 hours ncreases the expected wage somewhat but the dfference between these two specfcatons s much smaller than between the uncensored specfcaton and the 75 hours upper bound specfcaton. For example for sole parents the predcted wage becomes $9.97, whch s 10 cents hgher than the predcted wage when usng an upper bound of 100 hours and 20 cents lower than n the model where no allowance s made for the censorng. The effect s smallest for sngle women at $10.52, whch s only 4 cents hgher than for the alternatve upper bound and 11 cents lower than n the model not allowng for censorng. As expected the effect s hghest for marred men. At $ 22.74, t s $1.30 hgher than for the alternatve upper bound and $2.48 lower than the results from the model not allowng for censorng. 14 The tables wth re-estmated parameters are avalable from the authors on request.

21 19 From the above we conclude that t s mportant to allow for censorng. Although the choce of the upper boundary for labour supply s more or less arbtrary, the varatons n predcted wages as a result of alternatve upper boundares are relatvely small for varatons between 75 and 100 hours. It could be argued that a labour supply of 100 hours per week (an average of 14 hours per day for seven days per week) can safely be taken as an upper lmt on the possble hours of labour supply. The estmated model can be used to mpute wages for those who work 50 hours or more, by calculatng the expected wage condtonal on t beng n between the ncome from wages and salares dvded by the upper bound of labour supply and the ncome from wages and salares dvded by 50 (the lower bound of labour supply). Ths would be an mprovement over choosng 50 as the hours of labour supply, whch would systematcally overstate the wage level at hgher hours of labour supply. 6 Concluson Ths paper has reported estmates of wage equatons for Australan workers, usng pooled data from the Surveys of Income and Housng Costs for 1994/95, 1995/96, 1996/97 and 1997/98, the most recent four years for whch contnuous hours nformaton s avalable for each ndvdual. The results for the wage equatons are as expected, wth educaton, work experence and age ncreasng the expected wage. The process of assgnng a wage rate to non-workers, as necessary n the context of labour supply analyss, was examned wth specal attenton gven to dealng wth the stuaton where the wage equaton ncludes varables that are not avalable for the unemployed (such as occupaton and ndustry). Addtonally, wage nformaton on ndvduals, who work more than 49 hours per week and for whom the exact number of hours s therefore unknown n the SIHC, s ncluded as a range rather than approxmated by an exact value. Creedy et al. (2001) choose 50 hours as the labour supply for those who worked more than 49 hours. Ths results n an overestmaton of the wage rates.

22 20 Allowng for the censorng of labour supply makes a clear dfference n the predcted wage partcularly for marred men, who are the group most often observed to work long hours. The approach taken here could easly be ncorporated n a smultaneous wage and labour supply model. For labour supply models where the wage equaton s estmated separately, the approach set out n ths paper can be used to mpute wages for the nonworkers and for those who work 50 hours or more. The expected wage for the latter group s calculated by condtonng on the observed range of wage rates, whch can be attaned.

23 21 Appendx: Summary Statstcs Summary statstcs for the varous demographc groups are shown n Tables A.2 and A.3. Many varables are dummy varables takng (0,1) values, the tables show the proportons n each category for these varables. The samples used n the selecton equatons and the wage equatons are dfferent, so the summary statstcs for each are reported n a separate table. Informaton about the last full-tme job of those unemployed n June 1995, taken from the Labour Force Survey (ABS Catalogue, number 6203, Table 28), were used to construct the proportons gven n Table A.4.

24 22 Table A.1 Dstrbuton of labour market status over the survey years Sole parents 1994/ / / /98 Total Unemployed % NILF % Workng < 50 hours % Workng 50 hours plus % Total Sngle females Unemployed % NILF % Workng < 50 hours % Workng 50 hours plus % Total Sngle males Unemployed % NILF % Workng < 50 hours % Workng 50 hours plus % Total Marred females Unemployed % NILF % Workng < 50 hours % Workng 50 hours plus % Total Marred males Unemployed % NILF % Workng < 50 hours % Workng 50 hours plus % Total

25 23 Table A.2: Sample Proportons: Selecton Equatons varable Sole parents Sngle females Sngle males Marred females Marred males Age 15 to 19 years Age 20 to 24 years Age 25 to 29 years Age 30 to 34 years Age 35 to 39 years Age 40 to 44 years Age 45 to 49 years Age 50 to 54 years Age 55 to 59 years Age 60 to 64 years Number of months worked n last Work experence (last fnancal year) Separated/wdowed Australa (reference) Europe/Mddle East Asa Amerca/Afrca Postgraduate Undergraduate Dploma Vocatonal qualfcaton No post secondary qualfcaton (reference) Other ncome/ Chld support ncome/ NSW (reference) Vctora Queensland South Australa Western Australa Tasmana ACT/Northern Terrtory Captal cty Number of dependents Youngest chld aged 0 to 2 years Youngest chld aged 3 to 4 years Youngest chld aged 5 to 9 years Youngest chld aged 10 to 15 years Own home (reference) Mortgage Rented Other tenure Partner employed Partner has postgraduate qualfcaton Partner has undergraduate qualfcaton "Older" than partner "Younger" than partner

26 24 Table A.3: Sample Proportons: Wage Equatons Sole parents Sngle females Sngle males Marred females Marred males Age 15 to 19 years Age 20 to 24 years Age 25 to 29 years Age 30 to 34 years Age 35 to 39 years Age 40 to 44 years Age 45 to 49 years Age 50 to 54 years Age 55 to 59 years Age 60 to 64 years Number of months worked n last Work experence (last fnancal year) Professonal Paraprofessonal Clercal or sales person Tradesperson or labourer Agrculture/Forestry Mnng Manufacturng Constructon Utlty Retal/Wholesale Sales Transport Communcatons Fnancal/Busness Servces Other Servces Australan born Europe/Mddle East Asa Amerca/Afrca Postgraduate Undergraduate Dploma Vocatonal qualfcaton No post secondary qualfcatons NSW (reference) Vctora Queensland South Australa Western Australa Tasmana ACT/Northern Terrtory Captal cty

27 25 Table A.3: Contnued Sole parents Sngle females Sngle males Marred females Marred males Unversty qualfcaton x (age 20 to 24 years) Unversty qualfcaton x (age 25 to 29 years) Unversty qualfcaton x (age 30 to 34 years) Unversty qualfcaton x (age 35 to 39 years) Unversty qualfcaton x (age 40 to 44 years) Unversty qualfcaton x (age 45 to 49 years) Unversty qualfcaton x (age 50 to 54 years) Unversty qualfcaton x (age 55 to 59 years) Unversty qualfcaton x (age 60 to 64 years) Table A.4: Occupaton and Industry Proportons: Unemployed June 1995 Category Males Females Industry Dvson Agrculture, Forestry and Fshng Manufacturng Constructon Wholesale Trade Retal Trade Accommodaton, Cafes and Restaurants Transport and Storage Property and Busness Servces Government Admnstraton and Defence Educaton Health and Communty Servces Cultural and Recreatonal Servces Personal and Other Servces Other ndustres Occupatonal Group Managers and admnstrators Professonals Paraprofessonals Tradespersons Clerks Sales and personal servce Plant and machne operators and drvers Labourers and related

28 26 Table A.5: Selecton Equatons: Marred Women and Men a Women Men partcpaton Margnal effect b Std. Err. Margnal effect b Std. Err. Age ** ** Age squared ** ** # months worked n last ** ** Work exp (last fnancal year) ** ** Australa (reference) Europe/Mddle East Asa Amerca/Afrca No qualfcatons (reference) postgraduate ** ** undergraduate ** ** dploma ** ** vocatonal * Other ncome n ncome unt/ * Chld support NSW (reference) Vctora Queensland * South Australa ** Western Australa ** Tasmana ACT/Northern Terrtory Captal cty Number of chldren ** Youngest chld: 0 to ** * Youngest chld: 3 to ** Youngest chld: 5 to ** Youngest chld: 10 to * Owned (reference) mortgage * ** rented ** ** Other tenure ** Partner s employed ** ** Partner postgraduate Partner undergraduate Older than partner Younger than partner observed probablty predcted probablty (at mean of x) actual actual predcted not workng workng not workng workng not workng workng Number of observatons Notes: a ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. b the margnal effects on the probablty of beng employed are evaluated at the sample means and by changng the relevant varable by one unt (n most cases these margnal effects are the effects of a dscrete change from 0 to 1 n a dummy varable).

29 27 Table A.6: Selecton Terms, Sngle Men and Women a Sngle females Sngle males partcpaton Margnal effect b Std. Err. Margnal effect b Std. Err. Age ** Age squared ** ** # months worked n last ** ** Work exp (last fnancal year) ** ** Separated/wdowed ** Australa (reference) Europe/Mddle East ** Asa ** Amercas/Afrca No qualfcatons (reference) postgraduate ** undergraduate ** ** dploma ** ** vocatonal Other ncome n ncome unt/ ** ** NSW (reference) Vctora ** Queensland South Australa ** ** Western Australa Tasmana ** ACT/Northern Terrtory Captal cty Owned (reference) mortgage ** ** rented * Other tenure ** Observed probablty Predcted probablty (at the mean of all x) actual actual predcted not workng workng not workng workng not workng workng Number of observatons Notes: a ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. b the margnal effects on the probablty of beng employed are evaluated at the sample means and by changng the relevant varable by one unt (n most cases these margnal effects are the effects of a dscrete change from 0 to 1 n a dummy varable).

30 28 Table A.7: Selecton Terms: Sole Parents a partcpaton Margnal effect b Standard Error female * Age Age squared # months worked n last ** Work exp (last fnancal year) ** Separated/wdowed Australa (reference) Europe/Mddle East Asa ** Amerca/Afrca No qualfcatons (reference) undergraduate dploma vocatonal * Other ncome n ncome unt/ ** Chld support * NSW (reference) Vctora Queensland * South Australa Western Australa ** Tasmana ** ACT/Northern Terrtory Captal cty Number of Chldren Youngest chld: 0 to ** Youngest chld: 3 to ** Youngest chld: 5 to Youngest chld: 10 to Owned (reference) mortgage rented ** Other tenure Observed probablty Predcted probablty 0.501(at the mean of all x) actual predcted not workng workng not workng workng Number of observatons 1787 Notes: a ** coeffcent s sgnfcant at the 5 per cent level, * coeffcent s sgnfcant at the 10 per cent level. b the margnal effects on the probablty of beng employed are evaluated at the sample means and by changng the relevant varable by one unt (n most cases these margnal effects are the effects of a dscrete change from 0 to 1 n a dummy varable).