nurses wanted: is the job too harsh or is the wage too low?
TRANSCRIPT
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Journal of Health Economics 28 (2009) 748–757
Contents lists available at ScienceDirect
Journal of Health Economics
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urses wanted Is the job too harsh or is the wage too low?
.L. Di Tommasoa, S. Strømb,c,∗,1, E.M. Sætherd,2
Dept. of Economics and CHILD, University of Turin, via Po 53, Torino 10124, ItalyDept. of Economics, University of Turin, via Po 53, Torino 10124, ItalyDept. of Economics, University of Oslo, Blindern, PO Box 1095, Blindern 0317, Oslo, NorwayPricewaterhouse Coopers, N-0245 Oslo, Norway
r t i c l e i n f o
rticle history:eceived 30 March 2007eceived in revised form 17 January 2009ccepted 22 January 2009vailable online 3 February 2009
EL classification:2233
a b s t r a c t
When entering the job market, nurses choose among different kind of jobs. Each of these jobs is char-acterized by wage, sector (primary care or hospital) and shift (daytime work or shift). This paperestimates a multi-sector-job-type random utility model of labor supply on data for Norwegian reg-istered nurses (RNs) in 2000. The empirical model implies that labor supply is rather inelastic; 10%increase in the wage rates for all nurses is estimated to yield 3.3% increase in overall labor supply.This modest response shadows for much stronger inter-job-type responses. Our approach differs fromprevious studies in two ways: First, to our knowledge, it is the first time that a model of labor sup-ply for nurses is estimated taking explicitly into account the choices that RN’s have regarding work
11
eywords:urse labor supplyulti-sector
hift-work
place and type of job. Second, it differs from previous studies with respect to the measurement of thecompensations for different types of work. So far, it has been focused on wage differentials. But thereare more attributes of a job than the wage. Based on the estimated random utility model we there-fore calculate the expected value of compensation that makes a utility maximizing agent indifferentbetween types of jobs, here between shift work and daytime work. It turns out that Norwegian nursesworking shifts may be willing to work shift relative to daytime work for a lower wage than the current
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. Introduction
The motivation for this paper is that the ageing of the popu-ation in most Western countries combined with new treatmentpportunities is expected to increase the demand for health ser-ices both in primary care and at the hospital level. Example theumber of people in care in Norwegian institutions is predicted to
ncrease by 70% from 2005 to 2040 (Torsvik, 2000). Nurse labor is arimary input to the production of health services and the currentnd expected future shortages of nurses’ labor is a problem of great
oncern for healthcare policy makers. Moreover, even though morehan 90% of the trained registered nurses (RNs) work as nurses inorway, many of them work part-time. The Norwegian union forNs has argued that if wages were increased nurses would work∗ Corresponding author at: Dept. of Economics, University of Turin, via Po 53,orino 10124, Italy. Tel.: +39 011 6704038; fax: +39 011 6703895.
E-mail addresses: [email protected] (M.L. Di Tommaso),[email protected] (S. Strøm), [email protected]. Sæther).
1 Tel.: +39 011 6704411.2 Tel.: +47 95 26 05 38; fax: +47 24 06 25 38.
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167-6296/$ – see front matter © 2009 Elsevier B.V. All rights reserved.oi:10.1016/j.jhealeco.2009.01.003
© 2009 Elsevier B.V. All rights reserved.
onger hours. If labor supply among RNs is highly wage elastic, theemand for the services of RNs can to some extent be accommo-ated by the existing stock of RNs with only moderate increases inN wages. If, on the contrary, wage elasticity are rather low, thenhe increasing demand for nursing services will have to be matchedy the supply of new RNs.
Our first concern here is to estimate the labor supply of RNs.he novelties of our approach are the following. First, we model thehoice of four types of jobs (hospitals and primary care, shift worknd daytime work) together with hours of work in each type of jobs.he choice of the nurse is assumed to follow from utility maximiza-ion, given her job opportunities with respect to type of institutionsnd types of work available in the area where she lives and given theousehold budget constraint. In the latter we fully account for howpouse income, government benefits and taxes affects the house-old budget. Our econometric framework is a random utility model.he deterministic part of the utility function depends on observedariables and unknown deep structural parameters that we esti-
ate on data. The random part of the utility function is alternativepecific which means that it varies across types of jobs and hoursf work. The reason for this variation is that the random part cap-ures unobserved attributes related to the types of job, for instance,tress and burdensome work loads. To our knowledge, this is the
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M.L. Di Tommaso et al. / Journal o
rst time that such a model of labour supply for nurses is esti-ated. It should be noted that the random utility choice model
utomatically accounts for the possible selection in data.Second, in order to calculate a compensation for working shifts,
e apply a new methodology originally developed by Dagsvik andarlstrøm (2005). Because the random part of the utility functionaries across the alternatives, the measure of compensated vari-tion becomes random, the reason being that the realization of aandom variable related to one alternative, say working daytime, isot equal to the realization of the random part of working shifts. Inur model the utility function is a non-linear function of disposableousehold income. This implies that the calculation of the expectedalue of the compensating variation is not straightforward.
We find that the overall labor supply is rather inelastic. A 10%ncrease in the wage level for all nurses is estimated to yield a 3.3%ncrease in the unconditional expectation of hours supplied in theN population, which is a result in the range of what others have
ound for other countries; see for instance Shields (2004). Thus, thenion’s argument of a rather elastic labor supply is not confirmed.age increases, however, have an impact on the choice of job type.We have calculated the expected value of the compensation
or working shifts relative to daytime, and we find that the RNsould be willing to work shifts at a lower wage. The reasons for
his result and for the attractiveness of shift work are apparentlyhat shift work is compensated with both an hourly wage premiumnd shorter mandated hours. For many RNs shift work may alsoffer flexibility with respect to combining work, family life andhild-care.
Moreover we find that the RNs respond strongly to changes inob-type specific wages, which means that health authorities areble to use wage policies to move the nurses around in the healthare system. This policy conclusion is similar to Elliott et al. (2007)or UK nurses labour market in so far as they also stress the impor-ance of wage policies to make the job more attractive.
. Relevant literature and the model
The labor supply of RNs has been extensively investigated dur-ng the last decades. Most of the studies concern the nurse laborupply in the US, but recently there have been an increasing num-er of studies based on European data. Shields (2004) providesn excellent review of the studies and he shows that with someew exceptions RNs labor supply is rather inelastic. Most of thether studies have estimated participation and hours of work intwo-step procedure; Phillips (1995) is a good example of that
pproach in which participation as well as hours of work are driveny gross wage rates and household/individual characteristics. Theserevious models, which are reviewed in Shields (2004), tend toe reduced form models with varying close ties to a structuralousehold decision model. Taxes are entirely ignored. Contractualrrangements are not explicitly accounted for, with one exception,skildsen et al. (2003). These arrangements are important featuresf jobs within health care. RNs have the options to choose betweenaytime and shift work, and to choose between to work in hos-itals, and primary care. Shift work is compensated with a wageremium and shorter mandated hours and in Norway also over-ime work is regulated. It seems important to account for thesenstitutional aspects when estimating RNs labor supply.
Shields and Ward (2001), analyzing the impact of UK nurses’ job
atisfaction on intentions to quit, find that nurses who report over-ll dissatisfaction with their jobs, have a 65% higher probability touit than those reporting to be satisfied. In particular dissatisfac-ion with promotion and training opportunities are found to havestronger impact than workload or pay.ttash
h Economics 28 (2009) 748–757 749
As mentioned Askildsen et al. (2003) took into account somenstitutional aspects in estimating nurses’ labour supply, but onlyy including shift work bonuses in a linear hours of work equa-ion. They did not model the decision of the RNs to work shiftr daytime only. The shift bonuses stem from the nurses work-ng shifts, and the bonuses may thus be endogenous in the sensehat they are correlated with unobserved characteristics of jobype and hence with the error term in the hours equation. Theyeport that shift bonuses are estimated to have a negative impactn supply of labor and interpret this to represent the burden ofhift work on labor supply. However, the interpretation could sim-ly be that the mandated hours of work is lower in shift workhan in daytime work and this can explain the negative coef-cient for shift bonuses. To our knowledge, no one has so farodeled the choices that the RNs are able to make with respect
o choice of work place and type of job when labor supply is esti-ated.In a duration-analysis of nurses’ decision to quit the Norwegian
ublic sector, Holmås (2002) identifies that RNs working shifts haveslighter higher probability to quit than daytime workers. This may
ndicate that shift work is considered to be less attractive than day-ime work, but it may also be the result of higher mobility for thoseorking shift work as the observation of the nurse in a new (shift)
ob is censored in primary health care or at a hospital not affili-ted with Norwegian Association of Local and Regional AuthoritiesNALRA).
In our model the RNs derive utility from leisure, household dis-osable income and “job type”. The marginal utility of leisure isllowed to vary with respect to the age of the RN, whether she isarried or not, how many small children she has and whether she
s born in Norway or not.We assume utility maximizing RNs, given their choice sets and
heir budget constraints. Because we do not observe all details ofhe preferences, the utility functions are random to us as econome-ricians. The utility function has, thus, two parts, a deterministicne and a random one. The random part is meant to reflect thathe RN may derive utility from unobserved attributes related tohe different job types. What we observe regarding job type isype of institution (hospitals and primary care) and type of jobdaytime and shift work). Type of job and type of work placend other non-pecuniary job attributes may matter for the cho-en labor market affiliation of the RN. Some jobs may be morenteresting, flexible and challenging than other jobs. Jobs mayary with respect to promotion and training offered and maylso vary with respect to working hours and hourly wage. Whate thus derive from the model are choice probabilities related
o type of institution, type of job and hours of work. To accountxplicitly for the RNs’ choice of institution and job type may be con-idered as accounting for observed heterogeneity affecting laborupply.
In our model, realized and observed hours of work are equalo job-specific hours of the chosen job. This seems to be con-istent with labor markets throughout the industrialized world,here it is typically found that hours of work are fixed for many
ypes of jobs. In health care, this seems to be particularly the cases the working hours of all RNs must fit with the needs of theard of 24 h capacity. Of course, RNs sometimes are offered over-
ime work to cover vacancies, but the contracted working hoursust fit into the rotation scheme puzzle. Thus to change hours ofork one has to change job, either within the institution or move
o another institution; see Altonji and Paxon (1988) for findingshat support this view. To represent the fact that working hoursre offered in the market, we introduce institution and job-typepecific number of jobs with certain hours. In our model the likeli-ood of choices is the choice probabilities derived from the random
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tility model weighted with the opportunity densities of offeredours.3
Benefits, such as child allowances, spouse income and taxes haveo be accounted for in constructing the budget constraint. Note thathe tax structure, including marginal taxes on all types of incomere exogenous to the individual, but the observed taxes are endoge-ous and depend on the decisions of the individual. This is fullyccounted for in the model. The tax and benefit structure is avail-ble upon request to the authors, but they can also be downloadedrom the homepage of Statistics Norway.
The sectoral dimension of the model allows us to go beyondverall labor supply responses to changes in wages and tax rates.ur hypothesis is that although overall labor supply may be rather
nelastic, these modest labor supply responses shadow for strongeresponses with respect to choice of health care institution and jobype.
We report the calculations of the compensation (compensatingariation, CV) that the RN needs in order to be indifferent betweenorking daytime and working shifts. Most often compensationsave been calculated in terms of compensating wage differen-ials; see Kostiuk (1990) and Lanfranchi et al. (2002). Becausehere are more attributes to a job than wages, the calculation ofompensating variation yields a more comprehensive measure ofompensations. Because the utility is random and with a tastehifter that reflects the RN’s preferences for unobserved attributesf the different jobs, the CV measure is random. To calculatehe expected value of CV in random utility models where util-ty is a non-linear function of income is not straightforward. Weave applied a new random utility methodology; see Dagsvik andarlstrøm (2005) and Dagsvik et al. (2006). We have used this newethodology to calculate the expected value of CV and its distribu-
ion in the considered population of RNs.
. The model
Let U(Cjn, Ljn) be the utility for nurse n, working in institution j,nd working hjn annual hours.
Here j = 1 if working daytime hospital, j = 2 if working shift hos-ital, j = 3 if working daytime primary care, and j = 4 if working shiftrimary care.4
Cjn is disposable household annual income and Ljn is annualeisure:
jn = f (wjnhjn) + In, (1)
here wjn is the hourly wage rate and In is non-labor income,ncluding the after-tax income of a spouse. The functional form of(.) depends on the characteristics of tax and benefit functions.
Because we do not observe all variables that affect preferencesRNs may derive utility from unobserved attributes related to dif-erent job types), we assume the utility function to be random,hus:
(Cjn, Ljn) = vjn(Cjn, Ljn)ε(Cjn, Ljn), (2)
here vjn(Cjn, Ljn) is the deterministic part of the utility functionnd
(Cjn, Ljn) ≡ εjn (3)
3 For a review of discrete choice approaches and the use of weighted choice prob-bilities, see Creedy and Kalb (2005), Aaberge et al. (1999) and Dagsvik and Strøm2006).
4 The categories are mutually exclusive. In the empirical specification, we selectednly nurses who did not change their type of job during the year (see Table A4 forhe sample selection).
h Economics 28 (2009) 748–757
s a random variable assumed to be IID extreme value distributedith probability distribution function:
r(εjn ≤ x) = exp(−1/x) for any number x > 0. (4)
We will assume that the nurse will choose the job that max-mizes utility, which means that she will work in job type i and
orking hin hours if:
(Cin, Lin) ≥ U(Cjn, Ljn) for all{j /= i} ∈Bn. (5)
n is the choice set of the nurse n.Given the job type, the nurse is assumed to choose between 9
ifferent loads of working hours in each of the job types, with 37.5 her week in a fulltime job when working daytime, and with 35.5 her week in a fulltime job when working shifts. To get annual hourse multiply by 48. The exact hours categories are given in the data
ection below.To us as econometricians, the choice set, Bn, is random. To this
nd, let �jn, be the total number of jobs available in the differentob type category for nurse n and let gj(hjn) be the relative numberf feasible jobs with hours of work hjn, j = 1,2,3,4; Then, �jngj(hjn)epresents the frequency of different job types within the choiceet of nurse n.
Because preferences and choice sets are not completely knowno the econometricians, the best we can do in simulating the behav-or of a nurse is to calculate the probability of choosing a job and
orking certain hours, given the characteristics of the choice set.or more details about this type of modeling we refer to Dagsvik andtrøm (2006). Let ϕin denote the probability that nurse n choosesob type i and work hi hours, given her choice set. Thus,
in = Pr(U(Cin, Lin) = max{j∈Bn}U(Cjn, Ljn)) (6)
With the assumed probability distribution for εin (see Train,003) we get:
in = in(win, hi, In)�ingi(hi)∑4j=1
∑x>0 jn(wjn, xj, In)�jngj(xj)
; i = 1,2,3,4, (7)
here xj is equal to hours of work in category j and
jn(win, hi, In) = vjn(f (winhin) + In, Ljn). (8)
The weighted choice probabilities in Eq. (7) are the contributiono the likelihood when the model is estimated in a maximum like-ihood program. Let ϕin(win, hi, In) be brief for the probability in Eq.7).
We note that:
˚1n =∑h1>0
ϕ1n(w1n, h1, In) = choice probability of working daytime in hospitals
˚2n =∑h2>0
ϕ2n(w2n, h2, In) = choice probability of working shift in hospitals
˚3n =∑h3>0
ϕ3n(w3n, h3, In) = choice probability of working daytime in primary care
˚4n =∑h4>0
ϕ4n(w4n, h4, In) = choice probability of working shift in primary care
(9)
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Moreover, the expected hours of work in the different jobs, con-itional on job type, are:
E[H1n] =∑
h1>0ϕ1n(w1n, h1, In)h1
˚1n= expected hours conditional to
E[H2n] =∑
h2>0ϕ2n(w2n, h2, In)h2
˚2n= expected hours conditional to
E[H3n] =∑
h3>0ϕ3n(w3n, h3, In)h3
˚3n= expected hours conditional to
E[H4n] =∑
h4>0ϕ4n(w4n, h4, In)h4
˚4n= expected hours conditional to
he unconditional expectation over all job types, E[Hn], is given by
[Hn] =4∑j=1
∑hj>0
ϕjn(wjn, hjn, In)hjn. (11)
. Empirical specification
The deterministic part of the utility function is specified as aox-Cox function in disposable income and leisure; see Dagsviknd Strøm (2006) for an axiomatic justification for this functionalorm of the deterministic part of the utility function:5
og in = a (Cin10−5)� − 1
�+(bi +
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bsXsn
)(Lin − L0)� − 1
�(11)
ere X1: number of children ≤6; X2: number of children {>6, ≤11};3: 1 if Norwegian, =0 otherwise; X4: 1 if married or cohabiting,0 otherwise; X5: age; X6: age squared; bi = bH when job i is in aospital and bi = bP when the job is in primary care.
The deterministic part of the utility function is quasi-concave if�,�}≤ 1, it is linear in C and L if {�,�}= 1 and log-linear in thesewo variables if {�,�}= 0.
Wage rates are assumed to be lognormal distributed, they arellowed to vary across the four different job-types and they dependn human capital characteristics such as age, experience and inhat country the nurse is born. Moreover, the wage rates depend
n the region the nurse lives in and on the centrality of the locationf the institution. In estimating the wage equation, the log normallyistributed wage rates have been estimated on the mentionedovariates, together with selection variables, before we estimatehe rest of the model. Thus, we have applied the Heckman two-stepstimation procedure in the estimation of the wage rates, in whichhe selection variables, the probabilities of being observed in theour job types, are based on a reduced form of the model. The exactpecification of the wage equations and the estimates are given inppendix A, Table A1.
In most labor supply studies, also related to nurse labor sup-ly, it is assumed that offered hours in the market are uniformlyistributed. This is not in accordance with how at least a union-
zed labor market is and also not with the “technology and working
nvironment” in health care. Full-time hours are 37.5 and 35.5 foraytime work and shift-work, respectively, in line with the standardublic sector employment contract. Part-time work is commonith hours of work as a percentage of full-time employment. The5 Note that the deterministic part of the utility function is the argument in thehoice probability. The intuition behind the axioms is that if the fraction of nursesho prefer jobs with one specific outcome relative to jobs with other specific out-
omes, then the relationship between the fraction stays the same if the 2 consideredutcomes is multiplied by a scalar. This implies a Box-Cox utility function; see alsoalmagne (1985).
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h Economics 28 (2009) 748–757 751
time hospitals
t hospitals
time primary care
t primary care
(10)
mployers often prefer RNs to work part-time as this makes it easiero compose the 24-h work-schedule.
Analyzing the observed hours distribution,6 we have identifiedine concentrations of hours of work around the following num-ers:
Daytime: {12.2, 18.9, 22.8, 27.8, 29.8, 32.3, 37.5, 38.6, 42.9}Shift-work: {11.5, 17.9, 21.6, 26.3, 28.2, 30.6, 35.5, 36.6, 40.7}
We thus assume that offered hours are available according tohese concentrations. The full time job, 35.5 h per week in shiftork and 37.5 h per week in daytime work, has the highest fre-
uency. Therefore, we attach to the full time jobs the coefficientsH and �P in hospitals and primary care, respectively. That is,2j(hj) = exp (Zj�j), where Zj = 1 if the hours category is a full timeategory, and zero otherwise.
Annual leisure is given as net leisure after subtracting 12 h a dayor sleep and rest and hours of work, relative to total hours in a year:
jn = 8760 − (12 × 365) − 48hjn8760
(12)
Unobservable factors, like access to child-care (which is gener-lly highly accessible in Norway), may influence the RN’s choice ofhift work or not, and thus the shift variable effect may reflect omit-ed variables. If child-care is scarce, the nurse may need to choosehift work rather than daytime work.7 On the other hand, there areany nurses with a preference for shorter hours for their children
t the day-care facility or who wants to be present when their chil-ren finish school in the early afternoon. It is possible to combinehift work with a professional career, if your spouse works regularours. Normally, he also will have a considerably higher incomeaking it possible for the wife to work part-time.
. Sample selection and data
In Norway, by the beginning of 2000, there were 66,238 peo-le below retirement age, with registered nurse as their highestducation (see Table A4 in Appendix A). 6% of them were on mater-ity leave and 14.9% were not participating in the labor market ashey were undertaking further education or enrolled in one of theocial security programs, such as disability pension, medical andocational rehabilitation and early retirement. Of the 52,376 RNsorking in 2000, there were 35,411 female RNs employed by local
r regional municipalities. We selected only nurses employed byocal or regional municipalities because for the others we did not
ave information on wages, working hours and shift work. Theseata were collected in the month of October 2000 by the NALRA.he NALRA register data is matched with annual labor income andther administrative data registers delivered by Statistics Norway.6 Available from the authors upon request.7 In 2008 the child-care facility coverage is very high in Norway, while in 2000
he coverage was somewhat lower, in particular in the big cities.
7 f Health Economics 28 (2009) 748–757
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Table 1Maximum likelihood estimates.
Variable Coefficients Estimates t-Values
Disposable household incomeConstant a 7.6123 36.0Shape � 0.8707 53.9
LeisureConstant, hospital bH 1.3786 4.3Constant, prim. care bP 1.4435 4.4#Children, ≤6 b1 0.4814 8.96 < #Children ≤ 11 b2 0.4504 9.5Norwegian b3 0.2197 4.7Married b4 0.2817 7.2Age b5 0.9783 0.9Age2 b6 0.0999 0.8Shape � −2.0228 −21.1
Opportunity densityFull-time, hospital �H 0.9213 15.4Full-time, prim. care �P 1.1901 20.2
Number of observations: 8471. McFaddens rho: 0.11.
Table 2Predicted and observed aggregates.
Name Variables inthe model
Predictedvalues
Observedvalues
Shares hospitalDaytime ˚1 0.086 0.077Shift ˚2 0.408 0.388
Shares primary careDaytime ˚3 0.110 0.060Shift ˚4 0.396 0.476
Conditional weekly hours, hospitalDaytime E[H1]/˚1 25.2 30.4Shift E[H2]/˚2 27.5 27.1
Conditional weekly hours: primary care
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52 M.L. Di Tommaso et al. / Journal o
o focus on the shift premium, we focus on “ordinary RNs” avoid-ng nurses with other tasks or responsibilities such as specialistNs and ward administrators (excluding 45% of the NALRA sample)ecause their tasks are very different from regular nurses. More-ver, to improve the quality of the matched data, we also excludeome individuals, e.g. those not employed all 12 months of the year,hose with several job-contracts during the year and RNs with dis-osable household income less than NOK 100 000 and above NOK000 000 (as of Nov 2008 1 Euro = 8.9 NOK). In this paper, theata set, thus, consists of 8.471 female registered nurses. Summarytatistics are presented in Table A3 in Appendix A.
For a general overview of the Norwegian health care system, seean den Noord et al. (1998) and European Observatory on Healthare Systems (2000). A brief description of Norwegian nursing sec-or is provided in Appendix B.
The alternatives available for NALRA nurses are hospital jobsith shift work, hospital jobs with daytime hours, primary care
obs with shift work and primary care jobs with daytime hours.he sample is almost equally divided between hospital and primaryare jobs. Shift work is by far more common than daytime. Seeable A2 (Appendix A) for an overview of observed choices andourly wages and Table A3 (Appendix A) for a summary statistics
or the variables used in the analysis.Hourly wage is the applied earnings measure, calculated by
ividing annual earnings reported to the tax authorities by theeported hours from the NALRA register.8 The observed mean wages higher in shift work (NOK 151–157) than daytime work (NOK39–140). These wages are not yet corrected for individual char-cteristics. Hospital nurses are generally younger than nurses inrimary care; they work in more urban areas and have fewer chil-ren. Similarly, the shift workers are younger than the daytimeorkers. Corrections for these observed variables are accounted
or in the wage equations.Because there are reasons to believe that the alternative specific
andom part of the utility function could be correlated with theage rate, we have instrumented the wage when we estimate the
tructural model. As an instrument we have used the estimatedage equation where the wage rate is dependent on some observed
nd unobserved variables. The reason for the correlation could behat different types of work are compensated by the wage.
. Estimates and predictions
The unknown coefficients are estimated by maximizing the logikelihood (the log of the joint a priori probabilities of the observedhoices). The estimates are given in Table 1.
Except for the coefficients related to age, all coefficients areharply determined and with expected signs. The shape coefficients� and �) are both significantly below 1. The deterministic part ofhe utility function is thus strictly quasi-concave. Marginal utility ofeisure is increasing with number of small children, which implieshat female nurses with small children tend to supply less labor
han other females. Marginal utility of leisure is estimated to beigher among Norwegians than among non-natives, which implieshat non-natives tend to supply more labor than native Norwegians.arried women are estimated to have higher marginal utility of
8 The reason why we do not apply the reported NALRA hourly wage, but insteadonstruct the wages from annual income reports, is that only a small share of theALRA institutions reports the wage completely. Moreover, shift compensation andther benefits are often not accounted for. Pay rates are set at national level but theres room for some local adjustments. For example the pay rate in the capital, Oslo, isigher than in other parts of the country. The way we have constructed the hourlyage implies that these local adjustments have been taken care of in the wage rate.
n fact the wage rate is equal to annual income divided by hours of work.
7
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Daytime E[H3]/˚3 26.6 30.0Shift E[H4]/˚4 28.1 26.9Total weekly hours, unconditional E[H] 27.4 27.5
eisure than non-married. Marriage then seems to have a nega-ive impact on the supply of labor (in addition to the impact ofpouse income on labor supply). The estimates indicate that fullime jobs are significantly more available than other working loads,nd slightly more so in primary care than in hospitals.9
Table 2 gives the predicted and observed averages. It is not easyo predict many shares and hours. Table 2 demonstrates that the
odel performs rather well, in particular in hospitals and for totalours in the total population of nurses. Our multi-sector-job typeodel can be interpreted as a labor supply model in which observed
eterogeneity like work-place and job-type is explicitly accountedor. We then observe that the unconditional expectation of hoursupplied per week in the population is predicted on target (27.4ersus 27.5 weekly hours)!
. Labor supply elasticities
In Table 3 we give the elasticities of aggregate labor supply withespect to an overall increase in wage rates in all four different
ategories of job-types. First, labor supply is aggregated across indi-iduals and then the elasticities are calculated for this aggregateum with respect to the wage rate in all job types. This aggregatelasticity is equivalent to taking the elasticity of the labor supply9 The base category includes all other offered hours.
M.L. Di Tommaso et al. / Journal of Health Economics 28 (2009) 748–757 753
Table 3Elasticity of RNs’ labor supply with respect to an overall wage increase.
Job-type Choice probabilities Expected hours, conditional on job type Unconditional expectation of hours
Daytime hospital −0.988 0.432 −0.556S .300 0.522D .417 −0.348S .301 0.497W 0.331
ft
iwteb0qA0snwnftcttoDSo
irrwt0
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iwsw
Table 4Elasticities.
Job-type Choice probabilities Unconditionalexpectation ofhours
Elasticity of RNs’ labor supply with respect to a wage increasein daytime work hospital
Daytime hospital 8.859 9.291Shift-work hospital −0.846 −0.546Daytime primary care −0.862 −0.445Shift-work primary care −0.814 −0.513Weighted average across job types – 0.324
Elasticity of RNs’ labor supply with respect to a wage increasein shift-work hospital
Daytime hospital −3.545 −3.113Shift-work hospital 5.112 5.412Daytime primary care −3.511 −3.094Shift-work primary care −3.538 −3.237Weighted average across job types – 0.318
Elasticity of RNs’ labor supply with respect to a wage increasein daytime work primary care
Daytime hospital −1.112 −0.682Shift-work hospital −1.077 −0.777Daytime primary care 8.791 9.208Shift-work primary care −1.069 −0.768Weighted average across job types – 0.333
Elasticity of RNs’ labor supply with respect to a wage increasein shift-work primary care
Daytime hospital −3.343 −2.911
tgthe differences in the choice probabilities and expected hours ofwork are minor.
The extended model can be used to derive wage elasticities; nowwe also can calculate the elasticity of not working with respectto an overall wage increase. The results are given in Table 6. We
Table 5Predicted aggregates when not working is an option.
Name Variables in the model Predicted values
Not working ˚0 0.01Hospital
Daytime ˚1 0.09Shift ˚2 0.40
Primary careDaytime ˚3 0.11Shift ˚4 0.39
HospitalDaytime E[H1]/˚1 25.2
hift-work hospital 0.222 0aytime primary care −0.765 0hift-work primary care 0.196 0eighted average across job types – –
or every individual, and then calculating the weighted sum usinghe predicted choice probabilities for each individual as weights.
The results show that an overall wage increase gives the RNs anncentive to change their job-type away from daytime work towards
orking shifts. Thus shift-work is indicated to be the most attrac-ive type of work. Taking this into account we find that the totallasticity of aggregate labor supply, given that the RNs can chooseetween daytime work and shifts in hospital and primary care, is.331. This is in the range of what others have obtained based onuite different approaches and for other countries, Shields (2004).skildsen et al. (2003) estimated the overall elasticity to be around.25 before they instrumented the wage rate in the hours’ regres-ion for RNs. As instruments they used the mean wages of auxiliaryurses working in the same institutions as the RNs, together withorking experience of the RNs. But the wage level of auxiliaryurses is much lower than the wage level of RNs and hence this may
orce the coefficient attached to wage rates to increase to matchhe behavior and working hours of RNs. This and their treatment ofontractual arrangements in the hours’ equation may have biasedheir IV-results (an elasticity of around 0.8). It should also be notedhat all other estimates of female labor supply in general basedn Norwegian data report elasticities in the range of 0.2–0.3; seeagsvik and Strøm (2006) for some recent estimates and Røed andtrøm (2002) for a survey. Shields (2004) reports the 0.25 estimatef Askildsen et al. (2003), and not their much higher estimate.
In order to fully assess the impact of job-specific wage ratencreases on labor supply we have to account for how these wageate changes may affect the choice probabilities of job-types. Theesults are reported in Table 4 and they show that one is able to useage policies to move the RNs around in the health care system, but
he impact on overall supply is the same (the elasticity is around.33).
The impact of a 10% increase in non-wage income on over-ll labor supply (unconditional expectation of hours), taking intoccount the choice structure, is negative, but numerically small−0.046).
As mentioned above, our data covers RNs who are working asNs. Our justification for not including nurses who do not work asNs is that those who do not work are out of the labor market forery special reasons (on disability, early retired, etc). But in ordero check how our labor supply elasticities would be affected if notorking were an option, we have used the estimated model to sim-late a new choice probability structure in which not working is anption.
In this case, when the woman is not working, the deterministicart of the utility function is given by 0n(0,0,In) and �0g0(0) = 1.
The choice probabilities are now given by
in = in(win, hi, In))�ingin(hi)∑4j=0
∑xj>0 jn(wjn, xj, In)�jngjn(xj)
; i = 0,1,2,3,4, (13)
This extended model can also be interpreted as an innovation isntroduced into the market, where the innovation is such that the
oman has the option of not working. The model can be used toimulate the new choice probability structure for each nurse ande can thus obtain new aggregate choice probabilities similar to
P
Shift-work hospital −3.426 −3.126Daytime primary care −3.386 −2.969Shift-work primary care 5.195 5.496Weighted average across job types – 0.324
hose given in Table 2 above. These new aggregate probabilities areiven in Table 5. When comparing Tables 2 and 5 we observe that
Shift E[H2]/˚2 27.6
rimary careDaytime E[H3]/˚4 26.1Shift E[H4]/˚5 28.0Total hours, unconditional E[H] 27.2
754 M.L. Di Tommaso et al. / Journal of Health Economics 28 (2009) 748–757
Table 6Elasticity of RNs’ labor supply with respect to an overall wage increase, when non-working is an option.
Job-type Choice probabilities Expected hours, conditional on job type Unconditional expectation of hours
Not working −5.290 – –Daytime hospital −0.937 0.432 −0.505S .300 0.572D .418 −0.295S .302 0.548W 0.378
oaTmm
8m
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hw
bttE
9
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idfs
hift-work hospital 0.272 0aytime primary care −0.713 0hift-work primary care 0.246 0eighted average across job types – –
bserve that the elasticity of not working with respect to an over-ll wage increase is negative and sizeable as expected. Comparingables 3 and 6 we see that to include the option of not workingake the overall labor supply more elastic, but the difference isinor (0.331 versus 0.378).
. Compensating differentials within a random utilityodel
Let CVn denote the compensation that nurse n needs in order toe indifferent between working daytime and working shifts. ThusVn is determined by
in(Cin, Lin) = Ujn(Cjn + CVn, Ljn). (14)
To simplify exposition, we have now organized the job-types sohat i denote categories of hours working daytime (18 categories)nd j denotes categories of working shifts (18 categories). To cal-ulate CVn is not straightforward because the utility function isandom and the random part depends on nurses choices. We havewo ways of dealing with this problem. We can either compute CVn
hrough Monte Carlo simulations or try to find a closed form solu-ion for the expected value of CVn. We choose the second option ande apply a new methodology developed by Dagsvik and Karlstrøm
2005).We consider individuals observed to work daytime and calculate
hat would they have demanded to work shifts; then we calculatehe same for those observed to work shifts; what they would haveemanded to work daytime.
Let vDin(Cin, Lin), vDin for short, denote the deterministic part ofhe utility function when the nurse works daytime, either in hos-ital or primary care, thus i ∈ {1,2„9;19„27}. Hence there are 18 hategories in this daytime option, the first 9 being in hospital andhe next 9 being in primary care. And let vSin(Cin, Lin) denote theeterministic part of the utility function when working shifts, either
n hospital or primary care, thus i ∈ {10„18;28„36}. Hence there are8 categories in this shift option, the first 9 being in hospital andhe next 9 being in primary care.
Then the expected compensating variation, E[CVn], is given by
[CVn] = I −18∑i=1
vDin�ingi(hi)
∫ y∗i
0
× dy∑18i=1max[(vDin�ingi(hi), (vSin(y)�ingi(hi)]
(15)
here I = after-tax non-labor income, including spouse income, and∗i
is determined by vDin(CDin, LDin) = vSin(y∗i, LSin).
The calculations yield the following result:
1N∑E[CV ] = −NOK 19,885.
Nn=1
n
The compensating variation equals around 6% of the annualousehold disposable income. Thus the average nurse benefits fromorking shifts relative to working daytime and would thus have
pvSmq
Fig. 1. Expected compensating variation.
een willing to work shifts with a lower wage. As much as 85% ofhe nurses benefit from working shifts (E[CVn] < 0). It thus seemshat RNs working shifts are overcompensated. The distribution of[CVn] is given in Fig. 1.
. Conclusions
We have estimated a multi-sector-job-type model on Norwe-ian data covering a representative sample of RNs who work asrained registered nurses in 2000. Our approach differs from previ-us studies in two ways: First, to our knowledge, it is the first timehat a model of labour supply for nurses is estimated taking explic-tly into account the choices that RN’s have regarding work placend type of job. Second, it differs from previous studies with respecto the measurement of the compensations for different types ofork. So far, it has been focused on wage differentials. But there
re more attributes of a job than the wage. Based on the estimatedandom utility model, we therefore calculate the expected valuef compensation that makes a utility maximizing agent indifferentetween types of jobs, here between shift and daytime work.
We find that labor supply is rather inelastic; 10% increase in theage rate for all nurses is estimated to yield 3.3% increase in over-
ll labor supply. This modest response shadows for much strongernter-job-type responses. It turns out that Norwegian nurses work-ng shifts may be willing to work shifts for lower wage than theurrent one.
Our study, therefore, suggests that a generic increase in wagesn this sector does not increase RN’s labour supply while wagesifferentials among sectors and types of job can create incentivesor an increase in job-type-specific labour supply. Our conclusionstress the importance of sector/type job characteristics respect to
ecuniary characteristics of the job and support results from pre-ious work by Shields and Ward (2001) and Elliott et al. (2007).hields and Ward (2001) find that job satisfaction measures areore important than monetary variables to prevent nurse fromuitting the job. Elliott et al. (2007) find that wage differentials
M.L. Di Tommaso et al. / Journal of Health Economics 28 (2009) 748–757 755
Table A1Predicted hourly wages, Norway 2000.
Heckman selection model two-step estimates hourly wage Hospital RNs shift Day Primary care RNs shift Day
Coef. S.E. t-Value Coef. S.E. t-Value Coef. S.E. t-Value Coef. S.E. t-Value
Age −0.039 0.091 −0.440 −0.261 0.127 −2.060 0.140 0.081 1.720 −0.070 0.120 −0.580Age2̂/100 0.198 0.337 0.590 0.926 0.439 2.110 −0.476 0.293 −1.630 0.311 0.419 0.740Age3̂/1000 −0.376 0.541 −0.690 −1.410 0.658 −2.140 0.707 0.460 1.540 −0.571 0.635 −0.900Age4̂/10,000 0.246 0.318 0.770 0.778 0.363 2.140 −0.385 0.264 −1.460 0.366 0.353 1.040Experience 0.012 0.012 0.990 −0.006 0.022 −0.260 0.004 0.011 0.400 −0.010 0.019 −0.530Experience2̂/100 −0.083 0.201 −0.410 0.260 0.311 0.840 0.058 0.175 0.330 0.109 0.281 0.390Experience3̂/1000 0.321 1.292 0.250 −2.053 1.743 −1.180 −0.617 1.090 −0.570 −0.270 1.616 −0.170Experience4̂/10,000 −0.606 2.733 −0.220 4.750 3.354 1.420 1.484 2.254 0.660 −0.013 3.163 0.000Born in a Nordic country excl. Norway −0.005 0.019 −0.250 0.001 0.016 0.040 0.003 0.018 0.170 −0.003 0.021 −0.120Born in a OECD country excl. Nordic −0.009 0.025 −0.360 0.035 0.029 1.210 −0.018 0.021 −0.830 0.022 0.023 0.940Born in a non-OECD country 0.009 0.023 0.390 0.053 0.031 1.690 −0.001 0.021 −0.070 0.022 0.037 0.600County 1 Østfold −0.021 0.022 −0.940 −0.033 0.023 −1.450 0.138 0.119 1.160 −0.073 0.109 −0.670County 2 Akershus −0.026 0.018 −1.420 −0.026 0.016 −1.560 0.171 0.125 1.370 −0.029 0.109 −0.260County 4 Hedmark −0.014 0.026 −0.560 −0.041 0.029 −1.410 0.151 0.126 1.200 −0.065 0.107 −0.610County 5 Oppland −0.028 0.025 −1.110 −0.015 0.032 −0.480 0.158 0.128 1.230 −0.091 0.109 −0.830County 6 Buskerud 0.017 0.019 0.890 −0.097 0.022 −4.380 0.192 0.123 1.560 −0.076 0.111 −0.690County 7 Vestfold −0.043 0.022 −1.980 −0.046 0.025 −1.840 0.142 0.120 1.190 −0.045 0.109 −0.410County 8 Telemark −0.010 0.024 −0.420 −0.048 0.028 −1.700 0.166 0.124 1.330 −0.056 0.103 −0.540County 9 Aust-Agder −0.035 0.025 −1.420 −0.071 0.026 −2.700 0.140 0.123 1.140 −0.070 0.113 −0.620County 10 Vest-Agder −0.028 0.017 −1.660 −0.051 0.018 −2.750 0.167 0.124 1.340 −0.086 0.113 −0.770County 11 Rogaland 0.002 0.018 0.130 −0.023 0.018 −1.320 0.179 0.123 1.460 −0.048 0.107 −0.450County 12 Hordaland −0.025 0.016 −1.570 −0.066 0.014 −4.840 0.155 0.124 1.250 −0.051 0.108 −0.480County 13 Sogn og Fjordane 0.001 0.032 0.020 −0.073 0.034 −2.120 0.169 0.125 1.350 −0.084 0.115 −0.730County 14 Møre og Romsdal −0.019 0.022 −0.860 −0.036 0.026 −1.360 0.159 0.124 1.280 −0.091 0.115 −0.790County 15 Sør-Trøndelag −0.033 0.015 −2.250 −0.011 0.017 −0.660 0.146 0.130 1.120 −0.069 0.113 −0.610County 16 Nord-Trøndelag −0.023 0.020 −1.110 −0.037 0.026 −1.430 0.159 0.127 1.250 −0.100 0.110 −0.910County 17 Nordland −0.042 0.023 −1.820 −0.063 0.028 −2.250 0.164 0.126 1.300 −0.055 0.112 −0.500County 18 Troms −0.022 0.039 −0.570 −0.027 0.038 −0.730 0.156 0.128 1.220 −0.058 0.111 −0.530County 19 Finnmark −0.076 0.038 −2.000 −0.037 0.054 −0.700 0.181 0.131 1.380 −0.099 0.116 −0.850Municipal Centrality 1 −0.006 0.017 −0.370 −0.028 0.033 −0.850 −0.011 0.011 −1.010 0.007 0.013 0.530Municipal Centrality 2 0.017 0.020 0.830 −0.002 0.025 −0.090 0.004 0.016 0.250 −0.022 0.026 −0.830Municipal Centrality 3 −0.009 0.018 −0.520 0.008 0.024 0.350 −0.005 0.014 −0.330 0.023 0.021 1.110M 30 −M 40 −M 40 −C 30
bon
nistptW
ou
A
Piwfc
A
A
fiNNe
iansformal qualifications and different tasks. The decision to omit thespecialized nurses and the health administrators makes it possibleto focus on the shift premium. The inclusion of other personnelcategories is left for future research. RNs dominate the hospitalnursing services whereas the lower paid auxiliary nurses play a
Table A2Number of nurses according to chosen job and wage rates.
Number of nurses (%) Mean hourly wage, NOK
unicipal Centrality 4 0.004 0.032 0.1unicipal Centrality 5 0.011 0.018 0.6unicipal Centrality 6 0.004 0.013 0.3
onstant 5.288 0.877 6.0
etween the nursing sector and other sectors have a strong impactn the ability of the National Health System to attract and retainurses.
To reply to our initial question, we conclude that the lack ofurses labour supply in Norway cannot be solved with a generic
ncrease in wages. Our results suggest that possible policies in thisector should aim at improving non-monetary characteristics ofhe job and/or increasing the quota of non-Norwegian nurses. Aromising field of research would extend the previous work andake into account some aspect of job satisfaction as in Shields and
ard (2001).In future work we will extend the model to deal with transitions
ver time and hence estimate the multi-sector-job-type randomtility model on panel data.
cknowledgements
The project has been financed by the Health Economics Researchrogramme at the University of Oslo (HERO), with a funding com-ng from the Norwegian Research Council. In preparing the data
e received a generous help from Tao Zhang at the Frisch Centre
or Economic Research. We are grateful for helpful comments andonstructive criticism from the referees and the editor.ppendix A
See Tables A1–A4.
HHPP
T
N
0.145 0.059 −2.460 −0.002 0.015 −0.110 0.002 0.020 0.1100.015 0.022 −0.700 0.013 0.015 0.850 0.024 0.017 1.4500.001 0.018 −0.080 −0.002 0.012 −0.170 0.015 0.014 1.0207.630 1.325 5.760 3.419 0.857 3.990 5.598 1.250 4.480
ppendix B. Structure of the Norwegian nursing sector
The public health care providers are the dominant employersor Norwegian registered nurses. In 2002, 91.4% of those work-ng within health and social services were public employees. TheALRA, organize employers in municipalities and counties. TheALRA institutions employ most public health personnel, with thexception of two national hospitals.
The occupational sub-category specified as “Registered Nurses”n the NALRA register is a group that normally has not undertakenny postgraduate training. We have excluded nurses working asursing specialists or ward administrators. By restricting the analy-is to staff nurses we avoid the comparisons of groups with different
ospital day 649 (7.7) 140.1ospital shift 3276 (38.7) 157.6rimary day 509 (6.0) 139.1rimary shift 4037 (47.6) 151.8
otal 8471 (100)
orway 2000.
756 M.L. Di Tommaso et al. / Journal of Health Economics 28 (2009) 748–757
Table A3Summary statistics. Norway 2000.
All staff nurses (NALRA) Study sample
Mean S.D. Min Max Mean S.D. Min Max
Age 39.3 10.0 22 66 42.7 0.9 23 66Born in Norway = 1 0.92 0.28 0 1 0.92 0.27 0 1Single 0.30 0.46 0 1 0.08 0.27 0 1Married 0.59 0.49 0 1 0.79 0.41 0 1No. of children, age < 6 0.54 0.60 0 3 0.4 0.60 0 3No. of children, 6 < age < 11 0.44 0.71 0 4 0.51 0.75 0 4Live in central area 0.67 0.47 0 1 0.65 0.47 0 1Household dispsoable income, NOK 381,320 274,505 53,572 1.50E + 07 417,147 119,990 108,560 949,110Leisure, Eq. (13) – – – 0.35 0.04 0.26 0.44
No. of observations 19,424 8471
Table A4Sample selection.
Subtracted Sample
All registered nurses licenced in 2000 with a permanent residence code 87,532
SubstractingForeign personnel without income in 2000 (never arrived or have left the country) 6,277 81,255Reached retirement age (age 67 or older) 11,809 69,446Undertaken further education (not nursing related)—changed profession 659 68,787Authorized during year 2000 or with temporary licence (summer intern) 2,549 66,238Early retirement, disability pension, rehabilitation program, not working more than 1 G 9,869 56,369Maternity leave during 2000 3,993 52,376
Substracting for subsample in this studyMale RNs 5,246 47,130Not working for NALRA institution (no data on working hours) 11,719 35,411Not working as an staff nurse—“ordinary” registered nurse (other title and responsibility) 15,987 19,424More than one job or not employed whole year 6,336 13,088Constructed hourly wage (annual income/(monthly hours × 12)) > S.D. limit 1,304 11,784Censored in regression 242 11,542Excluded nurses with disposable household income less than NOK 100 000 and above NOK 1 000 000 3,071 8,471
Total sample in this study 8,471
Of whichHospital daytime 649Hospital shift work 3,276Primary care daytime 509
mliatytahfp
Nwiwemstwbo
cdapsws
R
A
A
A
C
D
Primary care shift work
ore important role in nursing homes and in home nursing. At theocal health centers and municipal casualty clinics the nursing staffs mostly RNs. The RNs in hospitals generally face more complicatednd acute cases than in the primary care level. On the other handhey normally work in teams with other RNs, and the patients areounger and with better prospects than in the nursing homes. Inhe nursing homes the RNs are leaders of a team of auxiliary nursesnd nurse assistants. Nurse assistants are personnel without anyealth qualification. In home nursing, the quality of the job is dif-
erent: nurses work more independently but deals with more trivialroblems related to ageing.
Shift work is regulated by law and through agreements betweenALRA and the RNs’ union. A registered nurse works 37.5 h pereek in a full-time position with daytime hours. Having a job that
ncludes shift work will reduce this to 35.5 h per week. Part-timeork is common and expressed as a percentage of full-time, how-
ver, it is not straight forward to change workload as other nursesust cover the reduction in hours to cover the 24 h ward shift
chedule. As a consequence the RNs quite often must change wardo achieve their preferred hours of work. The character of the shiftork varies, from a combination of daytime and evenings, to a com-ination of days, evenings and nights. Weekend work, every thirdr fourth week, is also common. Due to aggregation of the different
D
D
4,037
8,471
ompensation payments, we are unable to separate between theifferent shift forms. Kostiuk (1990) and Lanfranchi et al. (2002)pply a similar shift measure. Compared to other professions andhysicians in particular, the amount of overtime work is limited. Inhorter time periods some institutions are dependent on overtimeork, but it is generally accepted to supplement with temporary
taff from a recruitment agency.
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