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Wages, hours, earnings and employment under unionism Kim, Woo-Yung 1995-12-31

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WAGES, HOURS, EARNINGSAND EMPLOYMENTUNDERUNIONISMByWoo-Yung KimB.Admin.(Business Administration)Kookmin University, 1982M.A.(Economics) LakeheadUniversity, 1988A THESIS SUBMITTEDIN PARTIAL FULFILLMENTOFTHE REQUIREMENTSFOR THE DEGREEOFDOCTOR OF PHILOSOPYinTHE FACULTYOF GRADUATE STUDIESDEPARTMENTOF ECONOMICSWe accept this thesisas conformingto the required standardTHE UNIVERSITYOF BRITISHCOLUMBIAAPRIL 1995©Woo-Yung Kim,1995In presenting this thesis in partialfulfilment of the requirements foran advanceddegree at the University of BritishColumbia, I agree that the Libraryshall make itfreely available for reference andstudy. I further agree that permissionfor extensivecopying of this thesis for scholarlypurposes may be grantedby the head of mydepartment or by his or herrepresentatives. It is understoodthat copying orpublication of this thesis forfinancial gain shall not be allowedwithout my writtenpermission.(Signature)Department of________________The University of BritishColumbiaVancouver, CanadaDate_________________DE-6 (2/88)AbstractMost studies on unions have concentratedon examining the union impact onwages.This thesis, in two essays, examinesthe union impact on wages, hours, earningsandemployment, particularly focussing on theunion impact on hours of work.The first essay summarizes previous theoreticalunion models which normally assumefixed hours of work and extends themso that hours as well as wages andemploymentcan be determined by collective bargaining.Three kinds of union models areemployedto examine union impacts on hours as wellas union impacts on wages andemployment:the monopoly union model (Oswald[1982]), the right to manage model(Nickell [1981];Nickell and Andrews [1983]) andthe efficient contractsmodel (McDonald and Solow[1980]). The predicted union impacton hours and employment is foundto be ambiguouswhile the union impacton wages is found to be positive.The second essay is concerned with estimatingunion-nonunion wage, hoursand earnings differentials. Using the 1990 LabourMarket Activity Survey,this essay finds that(1) union-nonunion hours differentialsare ambiguous for males, but theyare positive forfemales,(2) employers in the union sectorextract more hours frommore able workers and thiscontributes greatly tothe positive union-nonunion hoursdifferential and(3) union-nonunion hours differentialsare smaller for malesthan for females and asaresult, union-nonunion earningsdifferentials are largerfor females than for males.11Table of ContentsAbstractiiList of TablesviList of FiguresviiiAcknowledgementix1 Introduction12 The Effects of Unionization on Wages,Employment and Hours52.1 Introduction52.2 A Simple Model Without Unions72.3 Effects of Unionization on Wages,Hours and Employment112.3.1 The Right to Manage Model122.3.2 The Efficient ContractsModel152.4 Extensions202.4.1 Featherbedding202.4.2 Sequential Bargaining212.5 Conclusion233 Union-Nonunion Wage, Hoursand Earnings Differentials253.1 Introduction251113.2 A Brief Review of Previous Studies on theUnion-Nonunion Hours Differential293.3 The Econometric Model313.4 Data373.4.1 General Description373.4.2 Descriptive Statistics on Variables393.5 Selectivity-Unadjusted Estimates433.5.1 Union Status Dummy Models433.5.2 Selectivity-Unadjusted Estimates of HourlyEarnings and WeeklyHours Equations443.5.3 Alternative Methods on Union-NonunionDifferentials483.5.4 Hourly Earnings, Weekly Hoursand Weekly Earnings Differentials503.6 Selectivity-Adjusted Estimates543.6.1 Selectivity-AdjustedEstimatesofHourlyEarnings andWeeklyHoursEquations553.6.2 Hourly Earnings, Weekly Hoursand Weekly Earnings Differentials573.7 Maximum Likelihood Estimates. . . 613.7.1 Variance-Covariance Matrix623.7.2 Participation and UnionStatus Equations653.7.3 Hourly Earnings Equations673.7.4 Weekly Hours Equations673.7.5 Hourly Earnings,Weekly Hours and Weekly EarningsDifferentials693.8 Applications763.8.1 Male-Female EarningsDifferentials763.8.2 The Impact of An Increasein Female Union Densityon MaleFemale Earnings Differentials79iv3.8.3 Union Effects on Wage and Hours Dispersion813.9 Conclusion844 Conclusion87Appendices92A Proofto Chapter 292B Figures for Chapter 295C The Specification of the LikelihoodFunction in Chapter 3100D Variances of Error Terms in theExtended H-L Model in Chapter3 102E Variances of Union-NonunionDifferentials in Chapter3 104F Appendix Tables for Chapter 3105Bibliography118VList of Tables3.1 Estimates ofthe Union-Nonunion Hours Differentialin Previous EmpiricalStudies323.2 DescriptiveStatisticson HourlyEarnings, WeeklyHours and WeeklyEarnings by Sector for Males in 1990413.3 DescriptiveStatisticson HourlyEarnings, Weekly Hours andWeeklyEarnings by Sector for Females in 1990423.4 Union-Nonunion Hours Differentials Estimatedfrom Equations (3.1)-(3.3)433.5 Union-Nonunion Hourly Earnings, Weekly Hoursand Weekly EarningsDifferentials by Sector for Malesin 1990, Selectivity-Unadjusted503.6 Union-Nonunion Hourly Earnings, Weekly Hoursand Weekly EarningsDifferentials by Sector for Femalesin 1990, Selectivity-Unadjusted . . .533.7 Union-Nonunion Hourly Earnings,Weekly Hours and Weekly EarningsDifferentials by Sectorfor Males in 1990, Selectivity-Adjusted593.8 Union-Nonunion Hourly Earnings, WeeklyHours and Weekly EarningsDifferentials by Sector for Femalesin 1990, Selectivity-Adjusted603.9 Estimates of the Variance-CovarianceMatrix643.10 Union-Nonunion HourlyEarnings, Weekly Hours andWeekly EarningsDifferentials by Sector for Malesin 1990, Maximum LikelihoodEstimates 713.11 Union-Nonunion Hourly Earnings,Weekly Hours and WeeklyEarningsDifferentials by Sector forFemales in 1990, Maximum LikelihoodEstimates 743.12 Estimates of DecompositionTerms of the Male-Female WageDifferential 78vi3.13 The Changes of the Male-Female Wageand Earnings Differentials WithOne Percentage Point Increase of FemaleUnion Density803.14 Differences in Variances ofLog of Hourly Earnings and WeeklyHoursBetween Union and NonunionMales and Females813.15 Estimates of the DecompositionTerms in the Differencesin Variances ofHourly Earnings and WeeklyHours between Union and NonunionSectors 83F.1 Definitions of the Variables106F.2 Sample Means of The Variables107F.3 Construction of the SampleData Set108F.4 Sample Sizes by Sexand Sector108F.5 The OLS Estimates of HourlyEarnings Equations109F.6 The Selectivity-UnadjustedEstimates of Weekly HoursEquations, Males110F.7 The Selectivity-UnadjustedEstimates of Weekly HoursEquations, Females111F.8 The Probit Estimatesof Participation and Union StatusEquations . 112F.9 The Selectivity-AdjustedEstimates of Hourly EarningsEquations . . 113F.10 The Selectivity-AdjustedEstimates of Weekly HoursEquations114F.11 The ML Estimatesof Participation and UnionStatus Equations115F.12 The ML Estimatesof Hourly Earnings Equations116F.13 The ML Estimatesof Weekly Hours Equations117viiList of FiguresB.1 Indifference Curves and The AssociatedLabour Supply Curve95B.2 Possible Equilibrium Outcomes under theMonopoly Union Model . . .. 96B.3 A Representation of the Contract Curve inWage-Hours-Employment Space97B.4 Optimal Outcomes under the Efficient ContractsModel98B.5 Compensating Wage Differentials for UnionWorkers99viiiAcknowledgementI am most grateful to the members of my supervisorycommittee, Denise Doiron, DavidGreen and Craig Riddell, for their intellectualand emotional support providedto me atevery important stage of this thesis. Theirquestions and comments have ledme to thinkmore deeply about the subject and helpedme improve upon my arguments.I thankthem for their guidance.This thesis has been also benefitedfrom comments made by PaulBeaudry, KenWhite and my colleagues, GarryBarrett, Nicholas Gravel, HisafumiKusuda and ChayunTantivasadakarn. I am especially gratefulto Garry Barrett for helpingme write severalcomputer programs at early stage ofthis thesis.I also wish to express my thanks toa number of individuals who have,directly orindirectly, helped me completethis thesis. My wife, Sun-Bee,has givenmeevery supportand encouragement for my studyin Canada. I thank her for everythingshe has done forme. Some of my family members are inKorea and Germany. Eventhough we have beenapart for several years,they have never stopped providingme with emotional support.I would like to take this opportunityto express my gratitude. Aboveall, I am mostgrateful to my uncle, Dr.See-Ho Shin, for his supportin numerous ways. Last butnotleast, I would like to thankmy mother who alwayssacrifices herself for others,includingme. She has been my friend andteacher in my life. Withouther, this thesis would neverhave been completed.ixChapter 1IntroductionUnions are a distinct featnreof all industrial societies. As an economicor politicalorganization, unions tryto improve the employment conditionsof their members. Thisgoal is normally achieved byraising wages, improving workingconditions, protectingthe workers from arbitrary dismissalby employers, and so forth. Theeffects of unions,however, are not only limitedto their members butalso spill over to the restof society(see, for example, Freeman andMedoff [1979,1984]).During the past several decades,a large volume of empirical andtheoretical workhas been carried out inan attempt to understand unionimpacts on various economicvariables. Most of thesestudies have concentratedon examining the unionimpact onwages and, to a lesser extent,employment.’ In particular,only a few economistshaveformally analyzed the unionimpact on hours of work.It is important to recognizethedifferences in mechanismsby which hours are determinedin the union and nonunionsectors for at least two reasons.The first reasonis to do with the effectivenessof labourmarket policies. For instance,let us assume that hoursin the nonunion sectorare mainlydetermined accordingto the worker’s labour supplyschedule, but hoursin the union sector are determined bycollective bargaining. Now,suppose that the governmentprovidesa wage subsidy to low incomeworkers to induce morehours. This policymay be effectivein the nonunion sectorsince the low incomeworkers will tend tosubstitute additionalhours as the priceof leisure increases. But, theeffectiveness of suchpolicy is less clear‘For example, Lewis’s1986 survey contains almost 200studies on the union wage effectsbut containsonly 21 studies on the unionhours effects in the U.S.IChapter 1. Introduction2in the union sector if the union’s decision depends onthe median voter’s preferences orif the union cares relatively more about the levelof employment than hours and henceis unwilling to bargain for more hours at the expenseof employment. Therefore, it isin the interest of policy makers to understand thedifferences between the two sectorsin determining hours. Second, if one of the reasonswe care about the union impactonwages is the income inequality betweenthe workers in the two sectors,it may be moreappropriate to look at the union impacton earnings rather than the union impactonwages. Since the union impact on earningsdepends on the union impact onhours as wellas the union impact on wages, we needto study the union impact onhours.Evidence on the union impact on hoursis rather mixed (see table 1 in chapter3for a summary of previous findings).Although a majority of researchersin this areadetect a statistically significant union-nonunionhours differential, they do not agreeonthe sign of the hours differentialor its magnitude. Unfortunately, mostempirical studieson this topic adopt very restrictivespecifications for the hoursequation. Furthermore,their models often treat union statusas exogenous. Given the restrictivenessof theirspecifications, it is questionable whethertheir estimates on the union-nonunionhoursdifferential are robust to a moregeneral specification of the hoursequation.Theoretical studies in this areaare also unsatisfactory. Most theoreticalunion models have focused on how wagesand employment are determinedunder unionism withassumptions that either workinghours per employeeare fixed or they are determinedaccording to the laboursupply schedule (see, for example,Oswald [1982]). If it ispossible that unions can achievea higher goal by influencinghours of work, i.e., shorteningstandard workweek or extensivelyusing overtime, both assumptionsseem unrealistic.Recent evidence indicates thatunions quite often negotiateover hours of workper week(Clark and Oswald [1993]).In view ofthe limitationsoftheearlier studies, it is clearthat we need a moregeneralChapter 1. Introduction3theoretical and empirical frameworkto examine the union impact onhours. It is theprimary goal of this thesis to providesuch a framework and to criticallyevaluate theprevious empirical findings in this area.The two essays of this thesis constitutean attempt to overcome the limitationsofprevious analyses in measuring theunion impact on hours. Althoughthe two essays aremostly concerned with the union impacton hours, they also examine theunion impactson wages, earnings and employmentsince they are closely relatedto each other. Inaddition, both essays show howthe obtained results may he appliedto other relatedissues such as male-female wageand earnings differentialsand union impacts on hoursdispersion.The first essay examines previoustheoretical union models whichnormally assumefixed hours of work andshows how the predictions obtainedfrom those modelsmightchange ifhours as well as wagesand employment are allowedto be determined by collective bargaining. Three kindsof union models are employedto examinethe union impacton hours as well as the union impactson wages and employment:the monopoly unionmodel (Oswald [1982]), theright to manage model (Nickell[1981]; Nickell and Andrews[1983]) and the efficient contractsmodel (McDonald andSolow [1980]). Ingeneral, theunion impacts on hours andemployment are foundto be ambiguous anddepend uponthe firm’s production technologyand the union’s objectivefunction. However, undercertain assumptionson the bargaining process, thefirm’s production technologyand theunion’s objectivefunctionit is shown that unionizationleads to a higher wagerate, lowerhours and increasedemployment if the unioncares relatively moreabout employmentthan wages and hours,but otherwise, unionizationleads to a higherwage rate, but mayor may not increasehours and employment.It seems that the onlyrobust predictionobtained from the threeunion models is thatwages are higherin the union sector,whichChapter 1. Introduction4coincides with the main conclusiondrawn by Manning (1994). Therefore,it is an empirical matter to determine the unionimpact on hours.The second essay is concernedwith estimating union-nonunionwage, hours and earnings differentials. The dataused in this essay is drawnfrom the 1990 LabourMarketActivity Survey. The modeldeveloped in this paperis more general than othersin thearea. More importantly, the hoursequations are specified as structuralequations ratherthan specified as reduced forms.The advantage of this specificationis that pure unionhours effects can be separatedout from union effectson hours which arise becauseofthe union wage effects. Thisessay presents several interestingresults. First, thereismixed evidence for union-nonunionhours differentials formales. The estimates oftheunion-nonunion hours differentialfor males vary considerablydepending on the estimation methods used. Onthe other hand, union-nonunionhours differentials for femalesare found to be positiveno matter what estimationtechnique is used andfound to bestatistically significantin many cases. Second, relativeto the nonunion sector,employersin the union sector seemto extract more hoursfrom better educatedand more experienced workers. Evidencefor this is shown by largercoefficients on educationand tenurein the union hours equationand positive and significantcorrelations betweenunion hoursand union wages for bothmales and females. Thisresult is interestingsince returns toeducation and experienceare usually lower inthe union sector. Third,union-nonunionwage differentialsare found to be similarbetweenmales and females,but union-nonunionhours differentialsare found to be muchsmaller for males thanfor females. Asa result,union-nonunion earningsdifferentials are foundto be larger for femalesthan for males.In addition, thisessay discusses howthe size of male-femalewage differentialsmightchange if maximumlikelihoodestimates insteadof least squares estimatesare used, howan increase in femaleunion density affectsmale-femaleearningsdifferentials and whetheror not unions reducethe dispersions of wagesand hours.Chapter 2The Effects of Unionizationon Wages, Employmentand Hours2.1 IntroductionMost theoretical union modelshave focused on how wagesand employment are determined under unionism.An implicit or explicit assumptionunderlying those modelsiseither that working hoursper employee are fixedor that they are determinedaccordingto the labour supplyschedule.’ Both assumptionsare unrealistic. First,one of the important roles of trade unionshas been to influence thelength of workday and workweek(see, for example, Hannicutt[1984] and Rees [1989]).Recent evidence that unionsquiteoften negotiate over hoursof work is presentedin Clark and Oswald(1993).2Second,from the theoretical pointof view it may be suboptimalfor unions to chooseonly wagesand let hours to bedetermined according totheir members’ laboursupply curves whenunions can influenceboth wages and hours.Recently, a few researchersincluding Earle andPencavel (1990), Pencavel(1991), Dinardo (1991) and Johnson(1990) have extendedthe existing unionmodels by allowingemployersand unionsto negotiate over hoursas well as wages andemploymentin thecollective bargaining process.Focussing on the efficientcontracts model,these researchershave obtained several valuableresults. For example,Earle and Pencavel(1990) showed‘For example, the assumptionthat hours per employeeare determinedaccording to the worker’slabour supply curve isused by Oswald(1982).21n their survey ofunion leaders’ views inGreat Britain, 53out of 57 union leaderssay yes to thequestion, “Doesyour union usually negotiateover hours of workper week?” Onthe other hand, veryfew union leaderssaid that unions negotiateover employment.5Chapter 2. The Effects of Unionization on Wages, Employment and Hours6that under a “rent-max” form oftheunion’s objectivefunction theoptimalhoursandemployment are independent of the wage rate, which canbe interpreted as a contract curvebeing verticalin both wage-employment and wage-hours spaces.3Pencavel (1991) generalized the “rent-max” union objective function and characterizedthe optimal outcomesof the efficient contract model. Dinardo (1991)showed that under a union’s objectivefunction in which the worker’s preferences are representedby the Cobb-Douglas utilityfunction, unions decrease hours of work. With a similarunion’s objective function Johnson (1990) showed that the negotiated hours lie tothe left of the each union member’slabour supply curve. In other words, each unionmember would like to work more hoursat the negotiated wage rate.What is not fully addressed in the literature, however,is the shape of the contractcurve in the three variable case in whichthe two parties bargain over wages, employment and hours.4Is the slope of the contract curvein wage-employment space positive,negative or vertical? What about theslope of the contract curvein wage-hours space?Under what circumstances can we determinethese slopes of the contract curve?Anotherrelated issue not fully examinedin the literature is the effects of unionizationon wages,hours and employment. If hoursare fixed, we expect that thewage rate is higher, butthe level of employment can be higeror lower or even unaffected under unionism.In thecase where hours are determined by collectivebargaining, we know littleabout the unioneffects on those variables.In this chapter we show how onecan characterize the contractcurve when wage,hours and employment arejointly determinedby collectivebargaining.Although it is notpossible to determinethe shapeofthe contract curve under themostgeneral specification3The “rent-max” union objective functionis shown in section 2.3.2.4Pencevel (1991) showedthat the slope of the contract curvein wage-employment space canbepositive, negative or vertical,holding hours constant at theequilibrium. This is not a desirableway tofind out the slope of the contractcurve since the optimal hoursshoald adjust along the contractcurvein wage-employment space.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 7of the union’s objective function, we are able to show, in some specialcases, whether thecontract curve is downward-sloping or upward-sloping or verticalin wage-employmentspace and wage-hours space respectively. For example,if the union is utilitarian, it ispossible to show that the contract curve is downward-slopingin wage-hours space andupward-sloping inwage-employment space. Thismayin turnimplythat as thebargainingpower of the union increases, wages and employmentrise, but hours fall.In order to examine the effects of unionization onwages, hours and employment,we first characterize nonunion outcomesand compare them with the union outcomesobtained under the monopoly union,right to manage and efficient contractsmodels.In general, we find that unionizationleads to a higher wage rate, but the effectsofunionization on hours and employment are ambiguousand depend on the specificationsof the union’s objective function.The organization of this chapter is as follows.Section 2.2 sets up the basicmodelwithout unions and describesoptimal nonunion outcomes. In section2.3, we introduceunions in the economy and examinetheeffects of unionization on wages,employment andhours under three different unionmodels, i.e., the monopoly union, rightto manage andefficient contracts models. Section 2.4discusses two possible extensionsof our results.Section 2.5 summarizes the main resultsof this chapter. Finally, proofsand figures arepresented in Appendices A andB.2.2 A Simple Model WithoutUnionsThe model presented in thissection is a special case ofthe model in Donaldson andEaton (1984). Workers areassumed to be homogeneous.5Firms are assumed to he5The assumption of homogeneousworkers is not necessary here, butit is almost inevitable inthemodel with unions. The reasonis that when union members votefor more than two subjects aunion’sutility function is bound tobe ill-defined. Oswald (1982) showsthat a well-behaved utilitarianunionutility function can be constructed evenwhen workers are heterogeneous inthe two variable case (wageChapter 2. The Effects of Unionization on Wages, Employmentand Hours 8competitive in the product market and assumedto produce a single consumption good.More importantly, firms are assumed to be utilitytakers in this model. That is, a firmhas to meet its workers’ ongoing or reservation utilitylevel when choosing wages andhours. Finally, I assume that workers and hoursare perfect substitutes in productionand there are no person-specific costs or quasi-fixedcosts of employment.6Given the assumptions above, a firm’s problemcan be written asmax II(W,H,N) = G(HN) — WHN(2.1)W,H,Ns.t. U(WH,T — H)U (2.2)where W is wage rate, H hours perworker, N number of workers andT total availabletime for work. The production functionC is assumed to be strongly concave intotallabour (HN) and theutilityfunctionU is assumed to be strongly quasi-concavein income(WH) and leisure (T — H). Finally, theoutput price is normalized to beunity.The constraint (2.2) impliesthat the firm has to meet the worker’songoing utilitylevel U. At the equilibrium, (2.2)will hold with equality. Hence, itmay be rewritten asY=WH=y(T—H,U)(2.3)Since y is strongly convex in leisure,it is true thatYi= dy/8(T — H)< 0, y =c92y/c9(T — H)2>0 andY2= dy/DU> 0, assumingy to be twice differentiable. Substituting (2.3) into the profitequation (2.1) and maximizingthe substituted profitequationand employment). One of the assumptionshe made is that workersare equally productive and hencereceive the same wage despiteof heterogeneity. Unfortunately,having this kind of heterogeneitydoesnot add much to the model withhomogeneous workers. For this reason,we simply assume that workersare homogeneous.6The assumption of perfect substitutionbetween workers and hoursis used to simplify our analyses.Donalsonand Eaton(1984) allow the case where the totallabour takes aformofA(H)N,where A(H) canbe a strongly concave functionofH. Also, we can allow somekind of quasi-fixed costsofemployment inthe model. Having fixed costs inthe model will affect theoptimalwage rate, hoursand employment. Forexample, the employer will increasethe number ofhoursper worker but reduce the numberofworkers inthe presence offixed costs. However,having fixed costs in themodel willnot change themainpredictionson union effects as long as the size offixed costs in the union sectoris similar to that in thenonunionsector. The role of fixed costsin measuring union impactis discussed in the next sectionin detail.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 9with respect to H and N yield the followingtwo first order conditionsy,H+y=O(2.4)G’(HN)+ y, = 0 (2.5)Using (2.3), equations (2.4) and(2.5) can be rewritten asW = G’(HN)(2.6)14/= Yi (2.7)Equation (2.6) looks very familiar.It states that the optimal wage rateshould be equalto thevalue of marginalproduct oftotallabour (HN). On theother hand, equation(2.7)states the optimal wage rateshould also be equalto the marginal rate of substitutionofincome for leisure at the utilitylevel Li. The above twoequations and (2.3) determinethe optimal W, H and N.In order to understandwhy equation (2.7) musthold at the equilibrium,we needsome preliminary results.Note that equation (2.3)can be rewritten asW = W(H, U)(2.8)Equation (2.8) is nothingbut the expression for anindifference curvein wage-hours spaceat U = (I. This indifferencecurve has the same featuresas appeared in AltonjiandPaxson (1988). That is,the indiffernece curve(2.8) has a U-shapeand the associatedlabour supply curve goesthrough the bottomof the indifference curve.Figure 1 inAppendix B depictsa family of the indifferencecurves (U’ >U°) and the associated71fwe replace hoursper worker with work intensityin our problem and specifyU = U(W, B) whereB measures the intensityof work, then our problembecomes similar to theone considered byJohnson(1990), and our solution conceptsare still valid. Johnson showedthat= 4Inat the equilibrium.In our case, combining(2.6) and (2.7) yieldsfIu =Inat the equilibrium.Therefore, there are noqualitative differencesbetween the two models.Chapter 2. The Effects of Unionization on Wages, Employment and Hours 10labour supply curve (LS). Note that at the bottoms of indifference curves, i.e., where= 0, wage rates are minimized while maintaining certain utility levels and also thewage rates are equal to the marginal rate of substitution of the income for leisure.8Withtheseresults, we can now explain whyequation (2.7) mustbe trueinequilibrium.Since hours and employment are perfect substitutes in production, any combination ofH and N such that the product of H and N is a constant will yield the same revenueto the firm. Therefore, the whole problem is reduced to minimizing the labourcosts,W(H, LJ)HN, while keeping HN an optimal level. It is then obvious thatin order tominimize the labour costs, H has to be chosen such that W is minimizedkeeping theutility level at U since N can be always adjusted to maintain HN to be a constant.Weknow from the properties of the indifference curve, the minimum W is achievedat thebottom of the indifference curve U and at that point it must be truethat the wage rateis equal to the marginal rate of substitution of the income for leisure.Therefore, theoptimal W and H will satisfy equation (2.7).In sum, if hours and employment are perfect substitutes in productionand if thereare no quasi-fixed costs for employment, the optimalhours per worker for the firm arethe hours that each worker would have supplied at the chosen wagerate ifthe worker hadmaximized his or her utility at that wage rate. Put differently,the optimal combinationof the wage rate and hours for the firm is in accordancewith the worker’s labour supplycurve. The optimal level of employment forthe firm is then determined by the totallabour demand curve, equation (2.6).8The slope of an indifference curve can be shown as=U2uWU1 H 0. Hence,= 0 if andonly if W =Chapter 2. The Effects of Unionization on Wages, Employment and Hours 112.3 Effects of Unionization on Wages, Hours and EmploymentIn this section we consider the monopoly union, right to manage and efficientcontractsmodels to see how unionization might affect the wage rate, hoursper worker and thelevel ofemployment of a firm. However, since the right to manage modelis more generalthan the monopoly union model, we focus on analyzingthe right to manage model andexamine the monopoly union model as a specialcase. We also compare the resultsobtained from this three variable bargaining problemwith those obtained from the twovariable bargaining problem in which the firmand the union bargain over just the wagerate and employment.There is no general agreement on the specificationof a union’s objective function.Therefore, the most general specification may take theformV=V(Y,H,N;U)(2.9)whereYt-_WH,Vi—_OV/OY>O,V2=ÔV/OH<O,V3=ÔV/ÔN>O,andUisa worker’s non-union utility level.9We use theunion’s objective function (2.9)whenwe characterize the outcomes of the monopoly,right to manage and efficient contractsmodels. However, it is very difficult to predictunion effects on the wage rate,hoursand employment with the union’s objectivefunction (2.9). Therefore, in orderto obtainpossible predictions we consider aspecial caseV(WH, H, N; U) = N{U(WH,T— H)- Ulk(2.10)where k > 0 and U is a concaveutility function of a worker. Notethat the parameter/c measures the relative weightput on each union member’s utilitygain. The union’sobjective function (2.10) has beenused by Johnson (1990) and DiNardo(1991) and it is9This union’s objective function is usedby Earle and Pencavel (1990).Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 12more general than the special union’s objectivefunction considered by Pencavel(1991).b0Finally, the firm’s objective function is asssumedto be the same as before.2.3.1 The Right to Manage ModelThe right to manage model (Nickell[1981]; Nickell and Andrews[1983]) in the twovariable case (wage and employment)assumes that a union and a firmbargain over awage rate and giventhenegotiated wagerate, thefirm determinesthe levelofemploymentunilaterally. In the three variable case,there can he several possible situations.”In ourproblem, the firm is indifferent betweenhours and employment, so it is not possibleto distinguish between the cases wherethe two parties negotiate overwages and hoursand where they negotiate over wagesand employment. However, asmentioned in theintroduction, unions and firms seemto frequently negotiate over hoursbut not overemployment. Therefore, it is morereasonable to thinkthat the unionand firm negotiatethe wage rate and hours and thefirm determines the level of employmentunilaterally inthe right to manage model. FollowingManning (1987), this problemcan be writtenas12max OlnV(WH, H, N;U)+(1 — O)lnll(W H,N) (2.11).s.t. G’(HN) — W = 0(2.12)‘°Thespecial unionobjectivefunctionconsideredby Pencavel (1991) takes the form,N[Y+f(H)Y]’,where Y = WH,f’< 0 andf”< 0. Our union’s objective function (2.10)is not totally different fromhis. If U = Y+ ln(T — H) with f(H) = ln(T — H) and if U is replacedby Y, then our union’sutilityfunction (2.10) becomes Pencavel’s.11For example, the union and the firmnegotiate over the wage rate andthe firm unilaterally chooseshours and employment, or the two partiesnegotiateover the wagerate and hours and thefirmunilaterallychooses the employment, orthe two parties bargain over the wagerate and employmentand the firmchooses hours unilaterally.-‘2An alternative approach is to maximize0 = V(WH, H, N; U)+i311(W, H, N) subject to G’(HN) —W = 0, where /3 is nonnegative. I followthe specification used by Manning(1987) simply because hisspecification is more commonlyseen in the bargaining models.The results ofthe twospecifications donot differ qualitatively.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 13Note that if 0 = 1 in (2.11),the right to manage model degenerates tothe monopolyunion model where, in this case, theunion chooses the wage rate and hours,and the firmchooses the level of employment atthe negotiated wage rate and hours.From the firstorder conditions for for (2.11) and(2.12) one can show thatdW 1= G N1(ie),(2.13)= G”H•1+(12(2.14)whereG”HN2V21a(V,W+V2)ll5)G”H2N”a2=(2.16)It is straightforward to show fromthe first order conditionsthata1 and a2 are positive.Thus, G”N andIvG”H. This implies thatin general, the indifferencecurves are flatter than the demandcurves at the equilibriumin wage-hours and wage-employment spaces respectively.Note that if 0 = 1, theslopes of the indifferencesareequal to the slopes ofthe demand curves, which isthe equilibrium conditionsfor themonopoly union model.The solutions (2.13)-(2.16) aretoo general to predictthe effects of unionizationonthe wage rate, hours and employment.Thus, we consider aspecial case wheretheunion’sobjective function takesthe form of (2.10). Wealso impose 0 =1 to make our pointsclear.’3Under these assmuptions,the first order conditionsare summarized as follows:WU1— U2 = —NHU,G”> 0(2.17)U — U = —kNH2(J,G”> 0(2.18)13This, of course, is the monopolyunion case. The main predictionson union effects are not affectedeven if0< 1.Chapter 2. The Effects of Unionization on Wages, Employment and Hours14W = C’(2.19)The above three equations determine the optimal wage,hours and employment. Themain implication of (2.17) is that hours are not determinedby a worker’s labour supplydecision.14Therefore, the assumption used by Oswald(1982) that hours are determinedby a worker’slabour supply decisionmaynot be appropriate in unionized establishments.Furthermore, at the equilibrium, union workerswork fewer hours than they wouldliketo work at the equilibrium wage rate since W>.Equation (2.18) states that unionworkers attain ahigher utilitylevelthan nonunionworkers and equation (2.19)representsthe total labour demand curve.15From equations (2.17)-(2.19) one can show that thewage rate will increase as a resultof unionization. However, union effects onhours and employment are ambiguous.Figure2 in Appendix B depicts some possibleeqilibrium outcomes. Note thatany equilibriumwage rate and hours must lie on the lefthand side of the labour supplycurve (LS) sinceW > ‘. Since the nonunion equilibriumis at the bottom of U (point b),it is obviousthat at any point on U whereU > U the union wage rate is greater thanthe nonunionwage rate. However, the hourscan increase (pointa3),decrease (pointai) or remain atthe same level (pointa2). Theunion effects on hours dependon the shape of the laboursupply curve. For example, ifthe labour supply curve isstrongly backward bending,then hours will decrease asa result of unionization. SinceC is strongly concave and thewage rate increases afterunionization, what is not possibleis the situation in whichbothhours and employment increaseafter unionization. Otherwise,any other combinationsof hours and employment arepossible as long as they satisfyequations (2.17)-(2.l9).14Remember that the laboursupply curve is representedby WU1— U2 = 0.‘5Tosee how an increase ofIc affects the optimal wage rate,hours and employment, I deriveddW/dk,dN/dk and dH/dk from equations(2.17)-(2.19). The signsof the derivatives depend on thecurvatureof the total labour demandcurve, i.e., G”, theshape of the labour supply curveand the value of Icitself. Therefore, in general, we cannot determine the effects ofIc on the optimal wage rate, hoursandemployment.Chapter 2. The Effects of Unionization on Wages, Employment and Hours 15Finally, it is worthwhile to note that if k = 1 in (2.10), i.e., the unioncares equallyabout employment and each member’sutilitygain from unionization, and ifan additionalconstraint is added to (2.11) and (2.12) that hours are determinedby the worker’s laboursupply decision, i.e., H = H(W), then our monopoly union’s problem becomes exactlythe same problem that is in Oswald(1982).16Notice, however, that his assumption(H = H(W) or WU1—0) is adhoc andthe solution ofthe monopoly union’s problemis suboptimalbecause the union can attain ahigher utilitylevelby setting WU, — U2 > 0.In addition, the union effects on hours and employment obtainedfrom his results aredifferent from ours. In our case, those effects are ambiguousif the labour supply curvehas a positive slope. But, in his case, hours must increase if thelabour supply curve isupward-sloping, and employment must decreasedue to the strongly concave productionfunction, given that the wage rate rises after unionization.This result also seems to betoo strong because at least in early years unions moved towardsthe reduction of hoursof work.’72.3.2 The Efficient Contracts ModelIn the efficient contracts model it is assumedthat the union and the firm bargain overwages, employment and hours and therefore, unlikethe monopoly union and righttomanage models, the outcomes of the efficient contractsmodel are pareto optimal. Formally, the optimal wage rate, hours andemployment in this bargaining problemare the‘6The union utility function in Oswald (1982)has the same ordering as our union utilityfunction(2.10) when k=1. In addition, Oswald alsoassumed that hours and employmentare perfect substitutesin production. Therefore, if we assume, ashe did, that hours are determinedby the worker’s laboursupply decision, our problem becomesexactly the same as his.17See, for example, Hannicutt(1984) fora brief history of labour movement towardsshorter workinghours in the early 20th century.Chapter 2. The Effects of Unionization on Wages, Employment and Hours16solution of the following problem:’8max = OlrtV(WH,H, N; U)+(1 — O)lnll(W,H,N) (2.20)where 0 (0 < 0 < 1) represents the union’s bargainingpower.Fromthefirst order conditions of (2.20), we can obtainthe followingtwo relationships:0’jrIv In (2.21)WV1+V2 W-G’Hv,Iv= H(2.22)where V1 = BV/OY, V2 = ÔV/OHand V3 = OV/dN. Equations (2.21) and(2.22) areobtained by equating the slopesof the indifference cnrve with the slopes ofthe isoprofitcurve in wage-employment space andwage-hours space respectively. Notethat equations(2.21) and (2.22) determine optimal combinationsof wage, hours and employment,andwe will refer them as a contract curve in wage-hours-employmentspace. Like McDonaldand Solow (1981) and many others, onecan find the slopes of the contractcurve bytaking total differentials of (2.21) and(2.22) and sloving for andØsimultaneously.Under themostgeneral specificationoftheunion’s objectivefunction(2.9), we cannotsignfand In other words, thecontract curve can take any shape.Also, it isimpossible for us to predict theunion effects on the wage rate,hours and employmentsince the relationship betweenthe union’s objective function andthe worker’s utilityfunction is unclear. Thus,we adopt (2.10) as the union’s objectivefunction in order toobtain possible qualitative results.Under the union’s objective function(2.10), equations (2.21) and(2.22) becomeu-U _w-G’kHNU, — N> 0 (2.23)18Again, I employ the specificationused by Manning (1987) forthe similar reason presented earlier.19This is true even in the two variable(wage and employment) case.See, for example, GundersonandRiddell (1988).Chapter 2. The Effects of Unionization on Wages, Employment and Hours 17WU1—U2W—G’0 224HU1 - H>.)Equations (2.33) and (2.34) characterizepareto optimal combinationsof wage, hours andemployment on the contract curve. Taking total differentialsof the above two equations,we obtain the following results (see Appendix A for derivations):20dW — (1—k)(WU1--U2)—kH(U11W—2U12W+U22)25dH — (1—k)HU,+kH(U21—U,W)—+kH(WU—U)(U,,U)—(1—k)(UU—2U,+U26dH — H U12G”H[kH(U21—U11W)+(1—k)U,The signs of (2.25) and (2.26) depend on the value of k. Ifk 1, it can be shownthat < 0 and%<0, and hence >0.21On the other hand, if k> 1, we cannotdetermine the signs of the slopes.The intuition for theresults is as follows. Suppose thatthe union cares relativelymoreabout employmentthan each member’sutilitygain,i.e., k < 1. Without loss ofgenerality,assume that the wage rate increases. Since thefirm is indifferent between hours andemployment, the union can determine hours.As the wage rate rises, each union membermay want to work less or more hoursdepending on whether income effects dominatesubstitution effects. However, since theunion puts more weight on employment,it willtry to substitute employment for hours wheneverpossible.22 If k = 1, the union willstill try to substitute employment for hours becauseof the diminishing marginal utility20Theslope ofthe contract curve in (W,N) space,i.e.,%,can be easily inferred from taking the ratioçdW.idN0dHan21See Appendix A for the proof.“In general, this argument will depend uponwhether or not there are fixed costsof employment. Ifthere are fixed costs ofemployment, theunion may not successfully substitute employmentfor hours. Ihave somewhat generalized thefirm’s objective function as 11 = G[A(H)N]— WHN— CN, where A(H)is a concave function of H and C is fixedcosts of employment per worker.In this case the slope ofdW/dH includes A(H) and C terms, butthe predictions are not so different from those obtainedfromthesimpler model. Ifthe fixed costs,C, is higher in the unionized firm than it isin the nonunionized sector,then the predictions will change.In this case the unionized firm will havean incentive to substitutehours for workers and hence the signofdW/dH will depend on the sizeofthe fixed costs. Iffixed costsincreases by a large amount after unionization,it is possible that dW/dH can even bepositive.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 18of income and leisure.23Put differently, the union’sutility increases with a diminishingrate when income increases but decreases with an increasing ratewhen leisure decreases.Therefore, the return to an increase in hours,i.e., the return to an increase in incomebut a decrease in leisure, will be relatively smallerthan the return to an increase inemployment. In sum, in both cases weexpect to be positive but to be negative.Ifthe union cares more about each member’sutilitygain than employment,i.e., k>1,the signs of and-are ambiguous.Here, the union has no strong preference overemployment, so union members can attaina higher utility level either through a higherwage rate with more hours or througha higher wage rate with less hours dependingonincome and substitution effects.24Sincehours may or may not increase as the wagerateincreases, it is also not clear whether employmentwill increaseor decrease with the wagerate. Therefore, the sign of the two slopesis ambiguous.Assuming that k 1, i.e.,< 0 andft< 0, we can draw the contract curvein(W-H-N) space. Figure 3 in AppendixB depicts the contract curve (CC).Note that thecurves represented by CwCh, CwCn andChCn are the projections of the contractcurveCC in (W-H), (W-N) and (H-N) spaces respectively.Union impacts on the wage rate, employmentand hours are depicted infigure 4 inAppendix B when k 1. Point b represents“before unionization”and point a represents“after unionization”. In (W-H) space,point b must be at the bottom of theindifferencecurve U since that pointrepresents the optimal outcomes ofthe firm’s maximizationproblem without unions. Pointa, however, must be on thedecreasing portion of theindifference curve U sinceWU1— U2 > 0. Finally, movementfrom b to a implies thatboth the wage rateand employment increase, buthours decrease after unionization.Finally, consider a specialcase where the unionworker is risk-neutral inincome. In23Notethat jfk = 1, our unionobjectivefunction is ordinally equivalentto autilitarianutilityfunction.24When k> 1, the denomonatorof (2.25) may be seen as thesum of substitution effects andincomeeffects. Also note that if kapproaches infinity, WU1— U2= 0.Chapter 2. The Effects of Unionization on Wages, Employment and Hours19particular, let us assume the uniou’s objective function to beV(WH, H, N) = N[WH+f(H)— Y]k(2.27)wheref’< 0,f”< 0 and k > 0. The union’s objective function (2.27) appears inPencavel (1991). With this union’s objective functionand our firm’s objective function,we obtain the following two conditions for au efficient bargaining:G’H = (1 — )WH+(f—1) (2.28)G’N = —f’N (2.29)Pencavel refers equation (2.28) as an efficient contractsemployment condition and equation (2.29) as an efficient contracts hours condition.The employment condition statesthat the maginal revenue product of employmentis the weighted sum of income and opportunity costs(f— Y) and the hours condition states that the marginalrevenue productofhours is equal to the disutility of work of unionmembers. The way that Pencavelfindsthe slope of the contract curve in wage-employmentspace is to obtain%from (2.28)holding hours constant.25In this case, it can be shown thatdW G”HdN = (1 — k)(2.30)From (2.30), we can say that if the union caresrelatively more about income thanemployment (k > 1), the contract curve hasa negative slope and if the union caresmoreabout employment than income (k< 1), the contract curve has a positive slope.Ifk —+ 1, the contract curve becomes vertical.This case is equivalent to the“rent-max”union’s objective function.Obviously, equation (2.30) cannotrepresent the true slope of thecontract curve inwage-employment space sincehours will not be held constant alongthe contract curve.25 d(WH) . dWIn fact, Pencavel (1991) findsdNinstead of-ag.For fixed hours, the two derivatives wouldgenerate the same sign.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 20The correct slopes of the contract curve can be found by solving(2.28) and (2.29) simultaneously. Using the method described earlier, we obtaindW(1—k)(W+f’)—kHf”(231)clii (1—k)HdW (1 — k)(W+ f’)G” kHf”G”2 32dN (l—k)(NG”+f”)We know that C” < 0 andf”< 0 from our assumptions. Also, it can be shownthatW+f’ > 0 from (2.28) and(2.29).26With these signs, we can show that jfk< 1,%> 0andJ< 0, if k —‘ 1, both and -- approach infinity,and if k > 1, both%andare indeterminate. Note that if k> 1, we have%< 0 from (2.30), whereas it isambiguous in (2.32). Also, even thoughthe signs of are same in bothequations (2.30)and (2.32) when k< 1, their magnitudes may be quite different. Sinceunion effects onwage rate and employment dependnot only on the sign of butalso on its magnitude,it is important to recognize the differencebetween the two methods.2.4 ExtensionsIn this section we briefly discusshow one can extend our resultsto related areas. Thefirst extension deals with workrules or featherbedding (Johnson[1990]) and the secondextension is concerned with thesequential bargaining (Manning[1987]).2.4.1 FeatherbeddingIt is well known that althoughthe outcomes ofa bargaining over both wageand employment are pareto optimal forthe union and firm, the firmhas an incentive to reducethelevel of employmentat the negotiated wage.A suggested and practiced wayto prevent26This condition is analogousto WU1— U2> 0 in our earlier results.Chapter 2. The Effects of Unionization on Wages, Employment and Hours 21the firm from cheating is to adopt “featherbedding” which usually specifiesthe numberof workers required per machine.In our model the firm also has an incentive to reduce hoursat the negotiated wageand level ofemployment.27Therefore, it is not sufficientto specify the number ofworkersrequired per machine in the contract to preventthe firm from cheating. There are twoways to prevent the firm from doing so. First, ifhours and employment are not perfectsubstitutes, the contract must specify both numbersof hours and number of workersrequired per machine. Second, if hours and employmentare perfect substitutes as in ourcase, the contract only needs to specify total manhoursrequired per machine. Johnson(1991) recognized the possibility of the second casewhere the union and the firm mightbargain over the wage rate, manhours/capital ratioand hours. In our model we can alsoallow this case if the firm’s objective function is specifiedas11= G(Z) — WHN — rK(2.33)where Z=and K and r are capital and rentalprice respectively. The methoddescribedin the previous sectionto obtain the slopes ofthecontract curvemay directlybeappliedto this case as well. However,as Johnson (1990) pointedout,theoutcomes of thiskind of bargaining willnot be as efficientas theoutcomes obtained by bargainingdirectlyover wage, hours and employmentsince the union has to considerhow the bargainingoutcomes may influence capitalin negotiation.2.4.2 Sequential BargainingManning (1987) considersa bargaining situation wherethe union and firm negotiate overwages and employmentsequentially. In particular,he shows that conventionalunion27This is clear from the fact thatat the solution of the efficientbargaining the value of marginalproduct is strictly less than the wagerate.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 22models such as the monopoly union, right to manage and efficientcontracts models arespecial cases of the sequential bargaining model, by assigninga particular value to thebargaining power ofthe union at each stage ofthe bargaining process. For example, iftheunion has all the power in negotiating wages and thefirm has all the power in negotiatingemployment, the sequential bargainingmodel is reduced to the monopoly union model.On the other hand, if both parties have the same bargainingpower in negotiating wagesand employment, the sequential bargaining modelis reduced to the efficient contractsmodel.The sequential bargaining model canbe also employed in our case wherethe unionand firm negotiate over wages, hours and employment.For example, let us assume thatunion and firm bargain over a wagerate at the first stage, hours at the secondstage andemployment at the third stage.28Underthis scenario the sequential bargainingproblemcan be written as the following:max03lnV(WH,H,N)+(1 —03)lnll(W H, N)(2.34)max02lriV[WH,H,N(W, H)]+(1 —02)lnll[W H,N(WH)] (2.35)max 0ilnV[WH(W),H(W),N(W)+(1 — 0i)lnll[W,H(W),N(W)](2.36)Using the definition for II itis straightforward to show that(1) if01 = 1, 0 < 02 1,and 03 = 0, the solutionsof (2.34)-(2.36) are identicalto those of the monopolyunionmodel, (2) if 0 <01 < 1, 0 < 02 1 and 03 = 0, the solutions areidentical to those ofthe right to managemodel, and (3) if01 = 02 = 03 = 0, the solutions are identicaltothose of the efficient contractsmodel. The main differencebetween the monopoly unionmodel and right to managemodel is that in the rightto manage model unionshave nolonger monopoly powerin setting wages. This isreflected by01 < 1.251t is important to assumethat both parties negotiatea wage rate first, but it is notimportant toassume that hours are negotiatedbefore employment in ourmodel since they are perfectsubstitutes inproduction. Our results willbe unaffected even ifemployment is negotiated beforehours.Chapter 2. The Effects of Unionization on Wages, Employmentand Hours 23Finally, following Manning (1987), it may be possibleto show how the optimal wagerate, hours and employment change in responseto the changes of the bargaining powerswhich are measured by Os. This remainsto be a usuful exercise in futureresearch.2.5 ConclusionThis main purpose of this chapter wasto examine the effects of unionizationon wages,employment and hours. To do that, wehave characterized the nonunionoutcomes andcompared them with the outcomes obtainedunder the monopoly union, rightto manageand efficient contracts models withoutassuming fixed hours of work.In general, unionimpacts on hours and employment arefound to be ambiguouswhile the union impactonwages is found to be positive.However, if some structuresare imposed on the union’sobjectivefunction - for example,ifautilitarianunion’s objectivefunction is assumed - wehave been able to show thatunder the efficient contracts modelthe wage rate increases,hours decrease, and employmentincreases as a result of unionization.Since the theoretical union modelsdo not provide us witha solid prediction on unionimpact on hours of work,it remains to be an empiricalmatterto determineunion impacton hours of work. The shapesof labour supply, labourdemand and contractcurvesare some of the important factorsdetermining union impacton hours of work. In themonopoly union model,the employer in theunion sector can haveall the power inchoosing hours of work.Therefore, in this worldunion impact on hoursof work dependsupon how employersintheunionsectorbehave differentlyfromemployersinthenonunionsector. On the other hand,in the efficient contractsmodel, hours of workare jointlydetermined by the employerand the union.Therefore, union impacton hours of workwill depend upon the worker’staste for work aswell as the employer’s selectionof hoursof work. We will lookinto these issues in thenext chapter.Chapter 2. The Effects of Unionization on Wages, Employment andHours 24In this chapter we have also shown how one can find the slope of thecontract curvein wage-employment space without assuming fixed hours.The slope obtained in thischapter is quite different from the one obtained byfixing hours. In particular, if theunion cares relatively less about employment thanthe utility gains of its members, wehave shown that the contract curve does not necessarilyhave a negative slope in contrastto the one shown in Pencavel (1991).Like Johnson (1990) and DiNardo (1991), we havealso obtained the result that at theequlibriumunion workers would liketo work morehours at the negotiated wage rate.Theimplication of this finding is twofold. First,it means that the usual assumptionof fixedworking hours or the assumptionthat workerscan choose thenumberofhours they wouldliketo work may be inappropriatein the union sector. Second, it also meansthat some ofthe higher wages that union workers receivecould be “compensating wagedifferentials”for the unsatisfactory hours setby unions and firms. Figure5 in Appendix B depicts anequilibrim under the efficient contractsmodel. Under the contract curve(CC) the totalunion-nonunion wage differentialis denoted by (a — b). It can be decomposedas the sumof the compensating differential (a —c) and the pure union-nonunionwage differential(c — b). This notion that unionworkers might recieve compensatingwage differentialsfor their restrictive work wasempiricallytested by Duncan andStafford (1980).A more challenging task in this areais to analyze union effects onwages, hoursand employment in a general equilibriumsetting. Some researchers like Diewert(1974)and Khun (1988) haveexamined union effects on wagesand employment in generalequilibrium models. However,to my knowledge, no one hasshown how wages, hoursand employment are determinedin a unionized economy in ageneral equilibrium model.This remains an importantfuture research agenda amonglabour economists.Chapter 3Union-Nonunion Wage, Hours and EarningsDifferentials3.1 IntroductionUnderstanding what unions do has been animportant research agenda amongsocialscientists. Unions affect society in manyways. They not only affect workers’wealth butalso affect work rules, absenteeism andmany other aspects of work life. Furthermore,unions alter the distribution of incomein society.In Canada, unions are especially important. Althoughunion density has declined inthe last decade, it is still the casethat approximately 40% of the malelabour force and30% of the female labour force are unionized. Therefore,it is important to understandwhat unions do and how they affectthe economy if any labour marketpolicies are to beeffective. Nonetheless, research onunions is quite scarce in Canadain terms of volumeand also in terms of variety. Thereare a handful of studies on the unionwage effects,but very few studies deal with otheraspects of unions. For thisreason, this studyexamines the union effectson hours of work and earnings, witha hope to obtainingamore comprehensive understandingof the union effectson the Canadian economy.Quite recently, several researchersin the U.S. have attemptedto measure the unionnonunion hours differentialusing models which areanalogous to the ones oftenused instudies of the union-nonunionwage differential. Althoughmost studies detect a statistically significant union-nonunionhours differential, theydo not agree on the signof thehours differential orits magnitude. For example, Raisian(1983) found that unionmale25Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials26heads of households work 1.5% more thau nonunionmale heads per year. Earle andPencavel (1990) in their cross-sectional analysisalso found that union workers generallywork more than nonunion workers, althoughtheir estimates differ by gender, colour,industry and occupation.1On the other hand, inan analysis of union wage, hours, andearnings differentials in the construction industry,Perloff and Sickles (1987) report thatmale union workers work 4% less than male nonunion workersper week. DiNardo (1991)also reports that male union workers work3% to 10% less than male nonunion workersannually.Unfortunately, most empirical studieson this topic adopt very restrictivespecifications for the hours equationin that their models do not allow completeinteractionsbetweenthe union status dummy and exogenousvariables. More importantly,theirmodels often treat union status as exogenous. Giventhat there is increasing agreementonthe likelihood that the selection of workersinto the union sector is endogenous,theirleast-squares estimates for the union-nonunionhours differential could be biased.Perloff and Sickles (1987) allow for themost general structure amongstudies in thisarea to date. Allowing wages, hoursand union status to be jointlydetermined, theyestimate a system of three equationsusing full-information maximumlikelihood. Eventhough their analysis is certainlymore general than others, theirassumption of a singlewage equation and a singlehours equation for both union andnonunion workers is stillrestrictive.2Furthermore, theirhours equations are specifiedas reduced forms ratherthan structural equations. As Earleand Pencavel (1990) noted,reduced-form hours1Their estimates for union-nonunionannual hours differentials rangefrom 0.2% to 1.8% for whitemen, 18.3% to 18.4% for whitewomen, 5.3% to 7% for nonwhitemen, and 4.2% to6.6% for nonwhitewomen. These estimatesare further broken down byindustry and occupation. Seetable 4 in their paper(pI65) for details.2Even though Perloff andSickles (1987) include completeinteraction terms between explanatoryvariables and union statusin the wage equation, theirspecification of a single wageequation for bothunion and nonunion workersis still restrictive in that theyassume the error termin the union wageequation to have the samevariance as the error term inthe norn.mion wage equation.This is inconsistentwith what Freeman(1980,1982) and others have found previously.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials27equations make it difficult to separate the pureunion hours effects from the unionhourseffects resulting from union wage effects.The model developed in this chapter is moregeneral than others in the area.Thegeneralization is achieved in three mainways. First, separate wage and hours equationsare specified for union and nonunion sectors.Hence, our model allows for differentmechanisms in determining wages and hours betweenthe two sectors and also allows fordifferences in the distributions ofunion andnonunion wages and hours.Second, thehoursequations are specified as structuralequationsratherthan specified asreducedforms. Theadvantage of this specificationis that pure union hours effectscan be separated out fromunion effects on hours which arisebecause of the union wage effects.Finally, a separateparticipation equationis used to take account of the censoringon wages and hours. Thisspecification is more general thanthe Tobit specification used byPerloff and Sickles.This chapter also presents a newway of decomposing union-nonunionhours differentials. In previous studies union-nonunionhours differentials are calculatedeither fromestimates of reduced-formhours equations or from estimatesof structural hours equations. The first type of hoursdifferentials can be thoughtof as total hours differentialssince the hours differentials includeunion wage effects on hours,and the second typecan be thought of as pure hoursdifferentials. Unfortunately,these two types of hoursdifferentials have not been linkedin a systematic way. This chaptershows how one candecompose total hours differentialsas the sum of pure hoursdifferentials and derivedhours differentials which resultfrom the union and/or employer’shours adjustment tounion-nonunion wage differentials.By doing this, we will havea better understanding ofthe nature of union-nonunionhours differentials.This chapter presentsseveral interesting empiricalfindings. First, thereis mixedevidence for union-nonunionhours differentials for males.The selectivity-unadjustedestimates for union hoursdifferentials for males are foundto be negative and statisticallyChapter 3. Union-Nonunion Wage, Hours andEarnings Differentials28significant as most of theU.S. research has found. However, the differentialsbecomestatistically insignificant when the extendedHeckman-Lee 25L5 estimationmethod is usedand become even positive and statisticallysignificant when full informationmaximumlikelihood is used. Therefore, negativeestimates for union hoursdifferentials for malesobtained by previous studiesare not robust to more general estimationmethods. Onthe other hand, union-nonunion hoursdifferentials for females arefound to be positivein all three methods and statisticallysignificant except for the extendedHeckman-Lee25L5 method. Our obtainedpositive union-nonunionhours differentials for femalesareconsistent with Earle and Pencavel’s(1990) findings for females in theUnited States.The second main result presentedin this chapter is that additionalhours worked bybetter educated and more experiencedworkers are larger inthe union sector than inthenonunion sector. Specifically,education and experienceaccount for51% of the positiveunion-nonunion hours differentialfor malesand33% ofthe positivepure hours differentialfor females.3This resultis interesting since returnsto education and experienceareusually lower in the unionsector. This phenomenonmay occur ifemployersin the unionsector favour better educatedand more experiencedworkers because theypay less foreducation and experience thantheir counterpartsin the nonunion sector.The third new finding presentedin this chapter is positiveand statistically significantcorrelations between theerror terms in union wageequations and theerror terms inunion hours equationsfor both males and females.To the extent that the errortermsin wage equations reflectunmeasured workers’abilities, the positivecorrelation in theunion sector impliesthat more able workers workmore hours in theunion sector. Thisfinding is also consistentwith the hypothesisthat employers in theunion sector haveanincentive to extractmore hours from moreable workers.In addition, this chapterdiscusses how thesize ofmale-femalewage differentialsmight3The figures are obtainedfrom maximum likelihoodestimates. See section3.7.5 for the details.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials29change if maximumlikelihood estimates insteadof least squares estimates are used, howan increase in femaleunion density affects male-femaleearnings differentials and whetheror not unions reduce the dispersions of wages and hours.The organization of this chapter is as follows. InSection 3.2, I briefly review previousstudies of the union-nonunion hours differential. Section3.3 lays out the econometricmodel. The data, variables and descriptive statisticsare described in Section 3.4. Section3.5 presents union-nonunion wage, hours and earnings differentialsbased on selectivity-unadjusted estimates. Here, I also proposealternative ways to measure union-nonunionhours differentials. Section 3.6 reportsthe results obtained from selectivity-adjustedestimates. Section 3.7 discusses the full informationmaximum likelihood estimatesofthe system of six equations. Union-nonuniondifferentials in wages, hours andearningsobtainedfrommaximumlikelihoodare alsopresentedin this section.Section 3.8 discussesthree related issues to whichour results may be applied. Section3.9 briefly summarizesthe results and contains concluding remarks.Finally, the specification ofthe likelihoodfunction, derivation of variancesand tables are presented in AppendicesC-F.3.2 A Brief Review of PreviousStudies on the Union-NonunionHours DifferentialAs discussed in the introduction,empirical studies of the impactof unions on hours ofwork present quite differentestimates for the union- nonunionhours differential, mainlydue to differences in both modelspecification and data. Table3.1 illustrates the range ofestimates of the hours differentialfound in previous studies (Note:WH denotes weeklyhours, AH annual hoursand AW annual weeks).4Column 3 in table 3.1 indicatesthe4Study 3 in table 3.1estimated an hours equationsimilar to specification (3.2),but the union variablewas measured as the fractionof unionized workers to thetotal number of employeesin a city. Thenthe union-nonunion hours gap wascalculated as the hoursgap resulting from one standarddeviationincrease in the union variable.The union-nonunion hours differentialsfor study 1 and 4 are obtainedChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials30specification of the hours equation which takes oneof the following forms:(3.1)lnH1=X11X+ crU1+e (3.2)lnH1= XzS.+ctU1+7lnW1+ e (3.3)where X1 is a lxK row vector of exogenous variables,Li a Kxl column vector of parameters, U1 the uuion status dummy(U1=0,1), W1 the hourly earnings, a and thecoefficients of U1 and W1respectively, ande the error term.Although estimates of the union-nonunionhours differential vary considerablyfromstudyto study, it seemsthatunionizationreduces hours ofworkat least for maleworkers,5In table 3.1, 7 out of 9 studies show that unionizationhas a negative impact on hours ofwork for males.For males, estimated union-nonunion annualhours differentials (AR) rangefrom -10% to 7% with an average of -2%, estimated union-nonunionweekly hours differentials(XVR) range from -7% to 2.4% withan average of -3.2%, and estimated union-nonunionannual weeks differentials (AW) rangefrom 1.1% to 4.6% with anaverage of 2.9%. Study2 is the only study I am awareof measuring the union-nonunionhours differential forfemales. Estimated femaleunion-nonunion hours differentialsin study 2 are positiveinall categories and quite large,especially for white females.Although equations (3.1)-(3.3)are the specifications commonly usedin the literatureto measure the union-nonunionhours differential, least-squaresestimates of the unionstatus dummy (U1)in equations(3.1)-(3.3) may be biased dueto endogeneity of theby evaluating the hoursdifferentials at the average hoursof nonunion workers.Union-nonunion hoursdifferentials for specifications(3.2) and (3.3) are approximatelyequalto the coefficient ofthe unionstatusdummy, so I used the estimatedcoefficient of the union statusvariable to compute theunion-nonunionhours differential for studies2, 5, 6, 7, 8 and 9.the survey on the union-nonunionhours differential, Lewis(1986) also claims that the typicalestimate of the union hours differentialfor male workers is about-1.8%.Chapter 3. Union-Nonunion Wage, Hours andEarnings Differentials 31determination of union status. Manystudies have been concerned withthe effects ofendogeneity of union statuson estimates of union-nonunion wage differentialsand havetried to produce consistent estimatesby applying sample selection bias procedures(forexample, see Lee [1978] and Heckman[1976]). In addition, having the hourly earningsvariable (W1)in the hours equation(3.3) can cause a severe endogeneity problembecause(i) the hourly earnings variable islikely to be correlated with the hoursof work and (ii)the hourly earnings also depends onunion status which is likely to be endogenous.63.3 The Econometric ModelThe econometric model developedin this section has a system of sixequations - hourlyearnings and weekly hours equationsfor union and nonunion workers,union status equation and participation equation.The six equations are formallypresented below.The hourly earnings of individuali in the union and nonunionsector is assumed tobe determined according tolnW=Z,,Ft+e11 (3.4)=+e21 (3.5)where1nWis thelatent valuefor thenaturallog ofusualhourly earnings,Z31 isavectorof exogenous variables andI” is a vector of correspondingparameters where s=u,n.It isassumed thate1j‘—‘ N(O,u21)and e2r-.N(O,o-2).The vectorsZand Z,,.j includeage, education, tenure, province,occupation, industryand firm size variables.7Therefore, our specificationsfor union and nonunionwage6There is also a problemof constructing the hourly earningsvariable by dividing weeklyor annualearnings by the dependent variable(H1).This problem is well discussedin I3orjas (1980).7Several authors (Banal[1973]; Moffitt [1984]; Altonziand Paxson [1988]; Biddleand Zarkin [1989])argue that wages shoulddepend on hours of work for thereason that individualsface some kinds ofconstrants in choosing hourssuch as a market earnings locuswhich is determined by individuals’tastesand firms’ production technologyand costs. We assumethat hours do not enterthe wage equations fortwo reasons. First, thestandard specifications for the wageequations in the literatureare based on theChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 32Table 3.1: Estimates of the Union-Nonunion Hours Differentialin Previous EmpiricalStudiesEstimated Gap(%) Equation Worker Coverage1. Dinardo (1991) -3’--’-lO (AH)(3.1) Male-4--’-7 (WH) Male2. Earle and 0.2’-4.8 (AR)(3.3) White malePencavel (1990) -1.li---’-2.1 (WH)2.3’3_(AW)18.3-.’18.4 (AR) (3.3) White female9.4’-.4O.7 (WH)7.6—.8.9_(AW)5.3-.’7 (AR) (3.3) Nonwhite male1.6’-.’2.4 (WR)3.7—4.6_(AW)4.2t-.i6.6 (AH)(3.3) Nonwhite female3.9-.4.8 (WH)0.3.4.8_(AW)3. Montgomery (1989) -6 (WH)(3.2) Workers in SMSAs4. Perloff and -4 (WH)(3.1) Male construction workersSickles_(1987)5. Raisian (1983) 0.4 (WH)(3.2) Male heads of households1.1 (AW) Male headsof households6. Olson (1981) -5 (WH)(3.2) Full-time workers7. Ichniowski (1980) -1 (WH)(3.2) Fire fighters8. Ehrenberg (1973) -2-9 (AR)(3.2) Fire fighters9. Ashenfelter (1971) -7 (WH)(3.2) Fire fightersChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 33equations are based on the theory of human capital as well as industrial, occupationaland regional wage differentials. Wages in the union sector are known to bedeterminedby job characteristics rather than personal characteristics. Therfore, it isparticularlyimportant to include industrial and occupational dummies in the unionwage equation.We also include firm size variables in order to allow for threatseffects.8The fact thatwages in the union sector are determined by collective bargainingis reflected in differentcoefficients between the union and nonunion wageequations.Following Earle and Pencavel (1990), hours equationsinclude the hourly earnings inorder to control for the union wage effects on hours:iflH*=X11t\”+7lfl1V*u+e3 (3.6)lriH*=X,S+7tt1nW,+e4j (3.7)wherelnH*81is the latent value for the natural log of usual hoursworked per week9,X81is a vector of exogenous variables, & is acorresponding vector of parameters and78is acoefficient of the hourly earnings, where s=u,n. Similarly,I assume thate3 N(0,a23)ande4 N(0,a24).The vectors and include variables relatedto family backgrounds and all thevariables appearing in the wage equationsexcept firm size dummies. Weexclude firmsize dummies in the hours equationsfor identification.’° If hours equationsrepresentlabour supply curves, excluding firmsize dummies seems to be a natural choicesincehuman capital theory, and we wantto compare the union wage differentials obtainedfrom the standardspecifications with those obtainedfrom our joint estimation. Second, it is difficultto think that unionworkers also face those kinds ofconstraintssince wages and hours in the union sectorare determined bycollective bargaining. For this reason we choosenot to include the hours in the wageequations.51t is generally believed that employers in largernonunionized firms have higherprobability of beingunionized and hence, maypay higher wages to their employees to preventunionization.9jchose hours per week as a dependent variablesince unions and firms quite oftennegotiate overhours per week in collective bargaining (seefor example Clark and Oswald[1993]).10Firm size dummies measure the numberof employees in all locations in Canada.See AppendixTable F.1 for definition.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials34they are demand side variables. However, ifhonrs eqnations representthe contract curveor possibly the demand curve, which might be truein the union sector, the firm sizedummies could enter the hours equations if one wants tocontrol for employment in thehours equations. In this case we expect the sign of firmsize dummies to be negativesince hours and employment are generally consideredto be substitutes in production.The problem is that our data set does not provideinformation on employment at thelocations where individuals work. Therefore,it is difficult to think that having the firmsize variables will capture the possible substitutabilltybetween hours and employment.To test this, we have run (3.6) and(3.7) with the firm size variables and also haverunthe reduced-form hours equations. We foundthat all the coefficients on the firm sizevariables are statistically insignificantfor both male union and nonunion workersandpositive for female union and nonunionworkers which contradicts our expectations.”Therefore, we choose not to include thefirm size dummies in the hours equations.We assume the hours in the nonunion sector aremainly determined according to theworker’s labour supply schedule. The coefficienton the wage rate(7n)in the nonunionhours equation can be positive, negative,or zero depending on the magnitudes betweenincome and substitution effects.On the other hand, hours in the unionsector may bedetermined by the employer’s responseto the union’s wage increase (monopolyunionmodel) or by a joint agreementon wages and hours between the two parties(efficientcontracts model) which may reflect bothsupply and demand sides of hours.In the firstcase the union hours equation will representthe demand for hours and inthe second caseit will representa contract curve. Since we are unableto distinguish between thetwo,the union hours equation is assumedto include both possibilities.The coefficient on thewage rate (-yj in the unionhours equation may also be positive,negative, or zero. Inparticular, the negative coefficienton the wage rate does not necessarilyindicate that“Actual estimates are available uponrequest.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials35the union hours equation represents the demand forhours since the contract curvemaywell have a negative slope. This possibility hasbeen shown in the previous chapter.It is desirable to include fixed costs inhours equations. Unfortunately, the data setwe use does not provide information onsuch costs. One way to circumvent this problemis to think that some of the fixed costs canbe captured by occupation and industry.Forexample, employers in the service sectormay face small fixed costs relativeto those inthe manufacturing sector and hence, workersin the service sector may work lessthantheir counterparts in the manufacturingsector. In such a case, we canindirectly controlfor fixed costs in hours equations.Let U be an indicator variable which equalsone if individual i is in theunion sectorand zero otherwise, then thedetermination of union statusmay be put in a standardprobit form:IiifUj*>O,U1= —(3.8)10 otherwise.andU =Q1A+e5(3.9)whereQis a vector ofexogenous variablesand A is a vector ofcorrespondingparameters.Note that the latent variableUj captures theutilitygain fromjoining the union and alsothe firm’s selection based on productivity.Since the utility gain fromjoining the unionis likely to depend on the union-nonunionwage and hours differentials,Qis assumed toinclude all the variables inZ and X1.Equations(3.8)-(3.9) are a typical probitmodel.After normalizingthe varianceofe5,a25,to be unity,we can obtain consistentestimatesfor A by probit estimation.Finally, since hourly earningsand weekly hours are observedonly for the employed,Chapter 3. Union-Nonunion Wage, Hoursand Earnings Differentials36we specify a participation equationto correct for censoring.Iiifpi*>oFi= —(MO)I..0 otherwise.and=+e6 (3.11)where1*is the latent variable which measuresthe utility gain from enteringlabourforce. In other representations,P$cmaymeasurethe differencebetweendesiredhoursandreservation hoursor the difference between desired hoursand minimum hours requiredby firms.12 S is a vectorof exogenous variables whichinclude personal characteristicsand is a vector of parameters.Equations (3.10) and(3.11) are also a typicalprobitmodel. We will normalize thevariance ofe6,a26,tobe unity for identification.The likelihood functionis based on equations (3.4)-(3.11)and on the assumptionof joint normality ofthe error terms (ci,e2,e3,e4,e5,e6). To estimateequations (3.4)-(3.11), the observations arepartitioned into threegroups: nonworkers, unionworkersand nonunion workers. Thus,the likelihood functionof any individual i canbe writtenasL = (1 — F)Fr(ee1< —S)+P1UFr(ei,e3,> —Q1A,G6j>—S)+P(1 —U)Pr((e2,64j, < —QA,66j > —S)(3.12)Note that the likelihoodfunction (3.12) assumesthat participation andunion statusare jointly determined.In other words,it allows for a possibilitythat some individualsdo not participatein the labour marketbecause they havelow probability ofgetting at2Zabel (1993) tests severalparticipation specificationsand concludes thatthe general form like equations (3.1O)-(3.11) performsbetter than othersin explaining labour supplydecisions.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials37job in the union sector. One can constrnct a more restrictedlikelihood fnnction in whichunion status is realized only after individuals participate. However,such a model shouldbe tested rather than assumed. Our specification allowsfor testing such a model.The specification of the likelihood functionis done by rewriting a four variate normaldensityfunction as theproduct ofabivariatenormal distribution functionand abivariatenormal densityfunction.’3A completespecificationofthelikelihoodfunctionis presentedin Appendix C. The variance-covariance matrixfor the estimated parametersis formedusing the outer product of first partial derivativematrix.The specifications of the hourly earningsand weekly hours equations are commonlyseen in the labour supply literature.The identification of parameters inthe systemrequires either (1) independence betweenwages and hours or (2) having atleast onevariable in the hourly earnings equationsthat is not in the hours equations.In ourspecification firm size variables areincluded in the hourly earnings equationsbut not inthe weekly hours equations, so correlationcoefficients between theerror terms as wellas the parameter vectors in equations(3.4)-(3.ll) can be estimated by maximizingthelikelihood function (3.12).3.4 Data3.4.1 General DescriptionThe basic sample of individualsused to estimate our modelis drawn from the1990Labour Market Activity Survey(LMAS) which isa supplement to the January1991Labour Force Survey(LFS). The 1990 LMAS providesdemographic informationfor allindividuals interviewedat the reference week(the first week of 1991)and weekly retrospectiveinformationonup to 5 jobs that individuals heldin 1990. For the cross-sectional13Even ifour model is basedon a six variate normal distribution,estimation ofthe likelihoodfunctionrequires only a four variatenormal distribution. This is evidentftom equation (3.12).Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials38analysis I use the information on the jobs heldby individuals at the last week of April1990. This choice is made to reduce seasonality andto make my data set comparablewith other cross-sectional data sets such as theU.S. Current Population Survey (CPS).’4In cases where individuals have more than onejob at that week, I use the informationon the job with most hours worked per week (mainjob).’5The initial sample consists of observationson 63,007 individuals with 30921 malesand 32086 females. However, I make the followingdeletions for estimation. First,Iexclude people who are younger thanage 20 and older than age 65, full-time studentsand disabled people. Second, I exclude thepeople whose main jobs are classifiedas self-employed, unpaid family workersor farmers.’6Third, I delete individualswith missingdata on firm size variables.A detailed table showing the selection criteriaemployed isgiven in Appendix Table F.3.After the deletions the total sampleconsists of 13374 male workers,2586 male non-workers, 11904 female workers and7197 female non-workers. For estimationI extract a25% random sampleofeach group, so there are3344 male workers, 647 male non-workers,2976 female workers and 1799 femalenon-workers in the random sample.17The public use 1990 LMAS doesnot have a class of workervariable, i.e., the publicsector dummy.18This couldbe a drawback since thepublic sector dummyis known tobe a very important variable inboth earnings and union statusequations.’9Fortunately,14For example, Earle and Pencavel(1990) used the May 1979 CPS.150utof 63007 individuals,2824 people (4.5%) had more thanonejob at the last week ofApril 1990.A similar sample selection is madein Earle and Pencavel (1990)and DiNardo (1991).16Here, farmers are the peoplein the agricultural industryor people reporting their occupationasfarmers.17Using the whole sample is nota problem for least squares estimation.However, it is verytime-consuming and expensive formaximum likelihood estimation.For this reason, I was forced touse arandom sample.15Thedefinition ofpublic sectoris based on whether theemployingenterprise is ownedby government.This includes various publicservices and crown corporationsas well as federal, provincialand municipaladministrations.19Forexample, Robinson andTomes (1984), Gyourkoand Tracy (1988) and morerecently GundersonChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials39the class of worker variable has been added in the pnblic use 1990 LMASby the specialrequest to Statistics Canada. Hence, the dataset used in this chapterhas this additionalinformation.Appendix Table F.1 provides definitionsof the variables and Appendix Table F.2provides sample means by gender,union status and participation. The data onunemployment rates by sex and provincefor April1990 are extracted from the CANSIM. Thetenure variable is constructed using informationon “When did...start working on thisjob?”. Thus, the tenure variable is intended to measureexperience on the current job.The firm size variables measure the number of employeesin all locations in Canada.3.4.2 Descriptive Statistics on VariablesExamination of Appendix Table F.2 indicates thatfor both male and female workersdifferences in personal characteristics donot appear to be significant between theunionand nonunion sectors, exceptthat a greater portion of females have universitydegreesin the union sector. However, thereappear to be sizable differences in tenure,industry,type of employment and the size of thefirm. For example, a greaterportion of unionworkers have longer tenure, workin non-service industries, are employedin the publicsector and work in larger firms.The differences in personal characteristicsbetween workers andnonworkers comefrom age, education and the numberof children of age under5. Both male and femalenonworkers are relativelyolderand have lower education. Also,as expected,thepresenceof young children is correlatedwith female participation andprovincial unemploymentrates affect both male andfemale participation.Table 3.2 reports descriptive statisticson hourly earnings, weeklyhours and weeklyand Riddell (1993) have shown thatthere is a significant wage differentialbetween the privateandpublic sectors. They have also detecteda significant and positive correlationbetween union status andthe employment in the public sector.Chapter 3. Union-Nonunion Wage, Hours andEarnings Differentials40earnings for males in several key sectors.2°Theaverage union-nonunion hourlyearnings differential is about15%. As expected, the hourly earnings differential is largerfor males in the construction industry,for blue collar workers and for part-timeworkers. The average union-nonunion hoursdifferential is about-5%. Apart from part-timeworkers, union workers workfewer hours than nonunion workers.Finally, the averageunion-nonunion weekly earnings differentialis about 9%, which is smaller thanthe average union-nonunion hourly earnings differential.Therefore, uncontrolled union-nonunionearnings differentials for males becomesmaller if one uses weekly earningsinstead ofhourly earnings as a measureof the differential. In addition,hours as well as earningsare less dispersed in the unionsector than in the nonunionsector. This indicates thatthe earnings inequality withinthe union sector is smaller thanthe earnings inequalitywithin the nonunion sector.2’The means and standard deviationsof the earnings and hours forfemales are presented in Table 3.3. Theaverage union-nonunion hourlyearnings differentialis about35% for females. Like males, the part-timeworkers gain a lot fromunionization. Theaverage union-nonunion weeklyhours differential is small butpositive, so the averageunion-nonunionweeklyearnings differentialbecomesabit greaterthan the averagehourlyearnings differential. Thismeans that the uncontrolledunion-nonunion earningsdifferential increases if union effectson hours are taken into account.Lastly, for females,thedispersion of hours is smaller,but the dispersion ofearnings is larger in theunion sector20Sample sizes by gender andsector are reported in AppendixTable F.4. Also, notethat the measuresfor hourly earnings and weeklyhours are the “usual hourlyearnings ($)“ and “usualhours worked perweek” respectively. The weeklyearnings is the product ofthe two. The figures inparentheses are samplestandard deviations.The columns “Ye” denote union-nonuniondifferentials.21For approximation we havecalculated four Lorenzordinates. In the unionsector, the bottom25% of the total workers earn15.4% of total earnings,50% earn 39.4%, and 75% earn65.4%. In thenonunion sector, the bottom25% earn 11.7% ofthe total earnings,50% earn 34.9%, and75% earn 59.2%.Therefore, it is reasonable to concludethat earnings inequalityis smaller in the unionsector than in thenonunion sector.Chapter 3. Union-Nonunion Wage, Hours and EarningsDifferentials 41Table 3.2: Descriptive Statistics on HourlyEarnings, Weekly Hours and WeeklyEarningsby Sector for Males in 1990Hourly Earnings WeeklyHours Weekly EarningsSector Union Nonunion% Union Nonunion % Union Nonunion%Manufact 16.04 16.12-0.55 40.44 41.55-2.67 642.65 669.45 -4.00(4.4) (8.3)(5.3) (6.5) (173.0)(356.6)Construct 19.52 13.89 40.5641.71 45.45 -8.24811.64 638.49 27.12(6.4) (5.5)(8.9) (12.2) (314.8)(334.9)Otherlnd 18.00 15.09 19.2239.97 42.38 -5.69716.84 629.77 13.83(6.3) (8.4) (8.1)(12.4) (278.9)(391.6)BlueCoir 16.8613.00 29.71 40.98 42.95-4.57 687.69557.28 23.40(5.4) (5.5) (7.4)(9.7) (247.8) (263.9)Mgr/Prof 20.1719.51 3.40 39.51 42.72-7.51 793.22 826.74-4.05(6.8) (9.4) (8.2)(11.7) (303.4)(453.5)OtherOcc 16.78 13.0228.87 39.78 42.29-5.94 666.23 535.1024.51(5.6) (7.3)(7.9) (13.0)(231.5) (314.0)FuilTime 17.61 15.3814.49 41.01 43.59-5.91 718.24662.69 8.38(5.9) (8.1)(6.7) (10.3) (256.0)(374.0)PartTime 17.7913.39 32.88 23.4416.78 39.74 425.87202.17 110.65(7.5) (8.8)(13.5) (8.9)(292.8) (140.6)Private 16.73 15.0910.90 40.72 42.82-4.89 680.56 641.176.14(5.6) (8.1)(7.8) (10.8)(261.7) (378.7)Public 19.06 18.691.96 39.85 41.01-2.84 752.17739.52 1.71(6.1) (8.3)(7.5) (17.4)(259.1) (352.4)Total 17.6215.31 15.03 40.3942.70 -5.41707.84 647.39 9.34(5.9) (8.2)(7.7) (11.3)(262.9)(377.8)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials42Table 3.3: Descriptive Statistics on Hourly Earnings, Weekly Hoursand Weekly Earningsby Sector for Females in 1990Hourly Earnings Weekly HoursWeekly EarningsSector Union Nonunion% Union Nonunion % Union Nonunion%Manufact 10.76 10.57 1.78 37.1938.34 -3.01 403.98 405.57 -0.39(4.1) (4.6) (6.6)(8.7) (174.4) (203.5)Construct 12.96 10.60 22.21 47.30 33.6440.58 699.52 359.83 94.40(4.4) (3.6) (30.7)(9.3) (569.7) (169.1)Otherlnd 15.38 10.93 40.72 34.2834.23 0.14 531.61 372.00 42.91(5.9) (5.8) (9.3) (11.2) (257.0) (221.6)BlueCoir 10.56 8.65 22.06 37.9239.42 -3.79 406.87 345.30 17.83(3.8) (3.1) (8.3) (10.4)(178.7) (172.8)Mgr/Prof 17.61 13.6229.27 34.43 36.74 -6.29 609.82492.00 23.95(6.3) (6.4) (10.0)(9.3) (279.5) (248.7)OtherOcc 12.60 9.82 28.37 34.2033.10 3.32 435.11322.80 34.79(4.1) (4.9) (8.1)(11.5) (187.7) (184.1)FuliTime 14.94 11.0635.16 38.55 39.18 -1.62575.04 431.21 33.36(5.6) (5.1) (5.0)(7.0) (229.5) (207.9)PartTime 13.94 10.2835.55 21.68 18.87 14.91 303.63181.11 67.66(6.7) (7.1) (8.1)(7.4) (206.3) (125.7)Private 13.10 10.66 22.9634.57 34.78 -0.62455.94 370.04 23.21(5.2) (5.3) (9.1)(10.9) (230.7)(209.8)Public 16.60 14.12 17.5834.98 33.24 5.24 582.08458.65 26.91(6.1) (8.5) (9.2)(12.9) (257.8)(312.1)Total 14.72 10.8835.21 34.76 34.68 0.22514.06 375.81 36.79(5.9) (5.6) (9.1)(11.0) (251.5) (218.9)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 43Table 3.4: Union-Nonunion Hours Differentials Estimated from Equations (3.1)-(3.3)Equation Male Workers(%) Female Workers (%)(3.1) -3.65(-3.81) -0.33(-0.23)(3.2) -3.56(-2.93) 3.15(1.65)(3.3) -2.90(-2.38) 3.05(1.53)than in the nonunion sector.223.5 Selectivity-Unadjusted Estimates3.5.1 Union Status Dummy ModelsFor comparison withunion-nonunion hours differentials obtainedbyprevious U.S. studiesI begin by estimating the hours equations (3.1)-(3.3) describedin section2.23Table 3.4reports the estimated union-nonunion hours differentials.24The estimates for males intable 3.4 are quite consistent with the previous estimatespresented in table 3.1: malesin the union sector work fewer hours per weekthan males in the nonunion sector. Forfemales, the union-nonunion hours differentialis positive and significant at betterthan0.2 level when specifications (3.2) and(3.3) are used, but it becomes insignificantwhenspecification (3.1) is used. For females,only specification (3.3) has been usedpreviously,i.e., by Earle and Pencavel (1990). Therefore,we can only compare ourestimate fromspecification (3.3) with Earle andPencavel’s. Although our estimatefrom specification221am not aware of any study which examinesthe difference of wage dispersions between femalesinunion and nonunion sectors. Therefore,at this point, I am unable to compare my findingwith others.23TheX variables used in the regressions aresimilar to those employed by Earle andPencavel (1990)except I include provincial unemploymentrates as Perloff and Sickles (1987)do. The omission ofunemployment rates does not change qualitative results.The actual regressors (X) are shownin AppendixTable F.6.24Union-nonunion hours differentialsobtained from equation(3.1) are calculated evaluating atmeanhours of nonunion workers. Union-nonunionhours differentials obtainedfrom equations (3.2) and(3.3)are obtained by(ea— 1) . 100. The figures in parenthesesare t-ratios.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials44(3.3) is a bit smaller than the average estimate of Earle and Pencavel, bothestimatesindicate that females in the union sector work more hoursper week than their nonunioncounterparts.As mentioned earlier, specifications (3.l)-(3.3) aretoo restrictive and may be subjectto the endogeneity problems since union staus and wagesare possibly correlated withthe error terms in the hours equations. We will correct these problemsone by one in thesubsequent sections.3.5.2 Selectivity-UnadjustedEstimatesofHourlyEarnings andWeeklyHoursEquationsIn this section we turn to more general specificationsof the hours equations where hoursequations are specified separately for theunion and nonunion sectors. ThsOLS and 2SLSestimates of equations(3.6)-(3.7) for males are presented in AppendixTable F.6.25 Themost significant difference between thetwo sets of estimates is on the coefficientof thehourly earnings. In the OLS case, thecoefficient on the hourly earningsis negative andsignificant for nonunion workerswhereas in the 2SLS case it is negativeand significantfor union workers.26Provided that the selectionbias is not serious, the 2SLSestimatesare consistent but the OLS estimatesare not, especially in the union sectorwhere wageand hours might be determinedjointly.The positive coefficient on the hourlyearningsfor nonunion workers indicatesan upward-sloping labour supplycurve. This result seemsto contradict the backward bendinglabour supply curve often foundin the literature onthe male labour supply. Note howeverthat previous studies on laboursupply have notdistinguished between union andnonunion sectors. Tocompare with previous estimates25The predicted wage, lnFV,is used as an instrument for iriWin 2SLS estimation.261t is not uncommon to see thatthe sign of the estimated coefficienton the wage variable in hoursequations changes when the predictedvalue is used. Forexample, Vella (1993) obtainsa negativecoefficient on the wage variablein hours equations when actualwage rates are used but obtainsapositive coefficient when thepredicted values are used instead.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 45of labour supply elasticities, I pooled the two sectors aud estimated the hours equation.The estimated labour supply elasticity with respect to the wage was found to be-0.065but it was not significant at the 0.1 level. The positive and statistically significantelasticity obtained for the nonunion sector disappears when we donot separate the twosectors. On the other hand, the coefficient on the hourly earningsfor nnion workers isfound to be -0.008 and significant at the 0.2 level. One should not however interpretthefigure as a labour supply elasticity since one of the results in the previouschapter is thathours in the union sector are not determined by the worker’s laboursupply schedule.27The negative coefficient for union workers may imply that employersin the union sectorreact to a wage increase by reducing the number ofhours of work or mayjust depict anegative sloping contract curve between wages and hours.In sum, the previous estimatesof the labour supply elasticity are misleading since the differencesin determining hoursbetween union and nonunion sectors are not takeninto account in estimation.One unexpectedresult seen in AppendixTable F.6 isthat the coefficienton maleheadsin the union sector is negative and significant. Tothe extent that being a head reflectsafamilyresponsibility, we expect the sign ofthehead variable to be nonnegative. However,the unexpected sign may well be due to the non-ramdomnessof sample selection. In fact,as we will see later, this coefficient becomesinsignificant when sample selection problemsare corrected.28First, personal tastes and incentivescan affect the coefficients forboth union andnonunion males. Second, the coefficientson education and tenure in theunion sector canbe determined by the firm’s selectionas well as taste factors. The2SLS estimates onhigh education for nonunionmales are all negative while the correspondingestimates for271nchapter 2 we showed that the wagerate is greater than the marginalrate ofsubstitution ofincomefor leisure at the equilibrium in theunion sector.28Theinsignificant coefficient on themale union heads may be due to the factthat a large portion ofthe male union workers are headoffamily so that hours are insensitive tobeing a head.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 46union males are all positive.29Although this pattern is not so evident for tenure, the2SLS estimate on tenure 11 to 20 years is negative and significant for nonunionmales.From these estimates, we can say that maleswith high education andlonger tenure in thenonunion sector work less, but those in the union sector work more.More importantly,we can see that the coefficients on high education and longer tenurefor the union malesare consistently larger than those for nonunion males. There are twopossible reasons forwhy union workers with high education and longer tenuremight work more. Ifeducationand tenure measure the worker’s productivity, both the demandand contract curves willshift to the right as the level of education and/or tenurerise. Therefore, we would expectthat hours increase with education and tenure at thesame wage rate. Another possibilityis that employers in the union sector may have anincentive to extract more hours frombetter educated and more experienced workerssince return to education and tenureisgenerally lower in the union sector than in the nonunionsector.3°These two factors canalso explain why the coefficients on education and tenureare larger for union males thannonunion males.Concerning industry and occupation, there appearsto be no significant pattern between union and nonunion males. In both sectors,workers in the service industrytendto work fewer hours than those in themanufacturing industry.31This result providessome evidencefor that fixed costs ofemploymentmay be smallerin the service sectorandhence, workers in that sector work less holdingother things constant. The publicsectoremployees are seen as working ashorter workweek than the privatesector employees inboth union and nonunion sectors.29This pattern is also true in theOLS estimates.30This explanation make sense more in themonopoly union model thanin the efficient contractsmodel. The coefficients on the wage ratein the hours equations are negativefor both males and females.However, we cannot say that thehours equations represent demand forhours since the contract cuvemay also have a negative slope. Weneed more information to reacha solid conculsion.31Note that manufacturing sector is theomitted sector. See Appendix F fordetailed information onour base person.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 47Next, the OLS and 2SLS estimates of the honrs equations for females are presentedin Appendix Table F.7. Like males, the coefficients on the hourly earnings change significantly and the sign of the coefficients is reversed when the 2SLS estimation is used. Inthe 2SLS case, the coefficient on the hourly earnings is 0.036 and significant at the 0.01level for nonunion females. This result is consistent with previous estimates oflaboursupply elasticity for females when sample selection bias is not corrected. However, someresearchers (for example, Nakamura, Nakamura and Cullen [1979], Robinsonand Tomes[1985] and Smith and Stelcner [1988]) found that the positively sloped laboursupplyschedule for females disappears when sample selection bias is corrected. We willtesttheir argument in the subsequent sections. For females in the union sector the coefficienton the hourly earnings is -0.001 but insignificant. This pattern is very similar tothat ofmales.Like males, the coefficients on education and tenurefor union femalesare considerablylarger than those for nonunion females. This result is alsoconsistent with the hypothesisthat employers in the union sector tend to extract more effort from bettereducated andmore experienced workers.Finally, the estimates of hourly earnings equations(3.4)-(3.5) are presented in Appendix Table F.5. Since the estimation resultsare quite familiar to researchers in thisarea, I just point out that the coefficients onfirm size variables are generally larger fornonunion workers than for union workers. Thisis consistent with the hypothesisthatnonunion workers in larger establishmentsare paid some premium by their employerswho try to prevent unionization.3.5.3 Alternative Methodson Union-Nonunion DifferentialsThe coefficients obtained from the hourly earningsand hours equations are then usedtocompute union-nonunion wage and hours differentialsfor various groups. We computeChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 48the wage and hours differentials for group k as:32WDk = Zk(I’t— F”) (3.13)HDk = Xk(At— A”) + lnWkQ5”— ‘5”')(3.14)whereZk, Xkand lrlWk are the vectors of average values for group k, and theestimatedcoefficients are obtained by the OLS or 2SLS.33Equations (3.13) and (3.14) are the conventional way of measuringunion-nonuniondifferentials. Note that equation (3.14) calculates the union-nonunionhours differentialholding the wage rate constant between the two sectors.I will refer to this differentialas the pure hours differential since this differential does not includethe union effects onhours which rise because of the union wage effects.It willbe also interestingto knowtheunion-nonunion hours differentialwhichincludesboth the union-nonunion hours differentialresultingfromunion wage effects and the purehours differential. I will refer this differentialas the total hours differential and refer thehours differential resulting from union wage effectsas the derived hours differential.In order to see how the total hours differential maybe decomposed as the sum of thepure hours differential and the derived hours differental,we first replace mW in (3.14)with the predicted value, lnW(Z). Now, thepredicted hours for union and nonunionworkers with characteristics X and Z, but not W,arelnf[(X”,Zj= 7umnWu(Zu)+XtLAU(3 15)lnf[”(X”,Z”)= .IumnWht(Zn)+ X”A” (3.16)Thetotal union-nonunion hours differential forgroup k evaluated at mean characteristics32Another way to measure the union-nonunionwage (hours) differentials is to calculatethe differencein predicted union and nonunion wages(hours), which was used by Lee (1978).I also applied thismethod, but results are not significantlydifferent from those obtained by our presentmethod.53The variance ofWDk is then calculated as follows: Var(WDk) = ZIcVC(Iu— T”)Zk’ where VC(x)is the variance-covariance matrixofx. Similarly, Var(HDk)= XWkVC(t’— 492)XWk’whereXWk =(Xk,lnVVk),e= (A,tu)ande=Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials49is thenHDk= lrifIt(Xk,Zk) — inE(Xk, Zk)=7uzkFU + XjAu— — XkZX’t= uZkFU+XkS+7UZkV — UZkJ’fl— 7ZkI’ — XkATh=Xk(Au-A)+(-+Z(f- (3.17)The sum of the first two terms of the last line isanother measnre of the pure union-nonunion hours differential. The main differencebetween the pure hours differentialmeasured by (3.14) and that measured by (3.17) isthat the former uses the average wagerate of all workers in group lv while the latteruses the average wage rate of nonunionworkers in group lv in calculation. The lastterm of (3.17) represents the derivedunion-nonunionhours differential. As mentionedearlier,this derivedhours differentialmeasuresthe employer and union’s hours adjustmentto wage increases in the union sector.34Union-nonunion earnings differentialsis defined by the sum of the union-nonunionwage differentials andtheunion-nonunionhours differentials. Inprinciple,union-nonunionearnings differentials can be obtainedeither by the sum of (3.13) and(3.14) or by thesum of (3.13) and (3.17). However, we prefer thelatter since it seems more sensible totreat wages as endogenous in calculatingearnings differentials. Finally,the parametersin equation (3.13) are obtainedby OLS and the parameters in equations(3.14)-(3.17)are obtained by 2SLS. The variancesof the pure, derived and totalhours differentialsmeasured by (3.17) are obtained by theS-method.34Notethat equation (3.17) can be alternativelyexpressed asHDk=Xk(/SY— A2)+Q” —7th +-Zh(f— F2). In this case, the derived differentialis the average nonunion worker’s laboursupplyresponse to theunion-nonunionwage differential. Equation (3.17) is adoptedhere since the interpretationofthe derived differential is more natural.In both specifications, the derived differentialis very sensitivesince the sign of the derived differentialtotally depends on the sign of (orta).This may be ashortcoming ofthe decompositionmethod used in equation (3.17).Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials50Table 3.5: Union-Nonunion Hourly Earnings,Weekly Hours and Weekly EarningsDifferentials by Sector for Malesin 1990, Selectivity-UnadjustedWHSector HE Purel Pure2 Derv.Total WEManufact 0.121 -0.008-0.007 -0.001 -0.008 0.113(0.026) (0.020) (0.021) (.0008)(0.021) (0.033)Construct 0.281 -0.055-0.053 -0.002 -0.055 0.226(0.041) (0.033) (0.033) (0.002)(0.033) (0.052)Otherlnd 0.130 -0.013-0.012 -0.001 -0.0130.116(0.022) (0.018) (0.019) (.0008)(0.019) (0.029)BlueCoir 0.178 -0.008-0.006 -0.001 -0.007 0.170(0.021) (0.017) (0.016)(.0007) (0.015) (0.027)Mgr/Prof 0.006 -0.027-0.027 -.0001 -0.027-0.020(0.026) (0.024) (0.024)(.0004) (0.024) (0.036)OtherOcc 0.228 -0.029-0.027 -0.002 -0.029 0.199(0.029) (0.025) (0.025)(0.004) (0.025) (0.038)FullTime 0.136 -0.018-0.016 -0.001 -0.0180.118(0.017) (0.015) (0.014)(.0007) (0.015) (0.022)PartTime 0.206-0.035 -0.033 -0.002-0.035 0.172(0.020) (0.017) (0.017)(0.002) (0.017) (0.026)Private 0.145-0.043 -0.042 -0.001-0.043 0.102(0.017) (0.015) (0.016)(.0007) (0.015) (0.023)Public 0.110 0.0770.079 -0.001 0.0780.188(0.044) (0.031) (0.031) (.0008)(0.031) (0.054)Total 0.138-0.018 -0.017 -0.001-0.018 0.120(0.016) (0.014) (0.015)(.0007) (0.014) (0.022)3.5.4 Hourly Earnings,Weekly Hours and WeeklyEarnings DifferentialsTable 3.5 reports the union-nonuniondifferentials for males.35The union-nonunionhourly earnings differentialsreported in table 3.5 reflectstandard findings. Thatis,a larger earnings gainin the union sector fallsto workers in the constructionindustry,35jtable 3.5, HE=HourlyEarnings, WH=Weekly Hours,WE=Weekly Earnings.Purel and Pure2 are obtained by equations(3.14) and (3.17) respectively.Derv. and Total arethe derived and totalhours differentials respectively.The standard errors forthe hours and earnings differentialsare obtainedusing the s-method and reportedin parentheses.Chapter 3. Union-Nonunion Wage, Hoursand Earnings Differentials51blue collar workers and part-timeworkerswhile workers with high-paidjobs such as managers or professionals gain little in theunion sector. This result providessome evidencefor the hypothesis that earnings inequalityamong workers is smallerin the union sectorthan in the nonunion sector.Pure union-nonunion hours differentialsmeasured by equation(3.14), i.e., Purel, aregenerally negative, whichmeans unionized male workerswork less than nonunionizedmale workers if they have thesame characteristics andreceive the samewage rate. Thehours gap is about-2% on average. Two interesting resultsare shown with thepurehours differential. First,unionization reduces weeklyhours for part-time workersas wellas for full-time workers. Thefact from raw data thatpart-time male workersin theunion sector work40% more than their counterpartsis not due to unionismbut due todifferences in characteristicsof the workers betweenthe two sectors. Second,there is asignificant difference betweenunions in the private sectorand unions in thepublic sectorin terms of their effectson hours. Unionizationhas a negative impacton hours in theprivate sector while ithas a positive impact inthe public sector.Pure2 in table 3.5 reportspure union-nonunion hoursdifferentials obtained fromusing a decompositionterm in equation (3.17).Comparing Purel estimateswith thePure2 estimates, one canimmediately notice thatthe two sets offigures are very close,although Pure2 estimatesare generally less preciselyestimated in the sensethat Pure2estimatesareobtainedusingfittedvaluesofwagerates. Ourproposedmeasureofthepureunion hours differential(Pure2) appears tobe a good approximationfor the conventionalmeasure of the pureunion hours differential(Purel).On average, the derivedunion-nonunionhours differentialis -0.1% and significantatthe 0.2 level. Hence, thereis some evidencethatapart ofthe unionhours differentialsaredue to union effectson wages. Total union-nonunionhours differentialsstill indicate thatunion workers in the privatesector work less thantheir counterpartswhile the oppositeChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials52is true in the public sector. As for the economy, total union-nonunionhours differentialis -2%.Finally, union-nonunion weekly earnings differentials are positiveand significant.However, theunion-nonunionweekly earnings differentialsare systematicallysmallerthanunion-nonunion hourly earnings differentials exceptfor the public sector. This is a newfinding which previous literature has not addressed.An implication of this result is thatthe earnings inequality between union and nonunionworkers is in fact smaller if we lookat weekly earnings rather than hourly earnings.Next, the union-nonunion hourly earnings, weeklyhours and weekly earnings differentials for females are reported in table 3.6. Fromthe estimates in the table, one cansee striking differences between males andfemales. Unlike males, female union workerswork more than their counterparts. Furthermore,pure union-nonunion hours differentials are positive and significant at the0.05 level whereas derived union-nonunion hoursdifferentials are not significant. As a result, averagetotal hours differential is about6%and significant at the 0.05 level.Union-nonunion earnings differentials are nowbiggerthan union-nonunion wage differentials, whichindicates an increase in inequalitybetween union and nonunion femalesif inequality is measured by weeklyearnings ratherthan hourly earnings.One may think that females witha strong attachment to the labourmarket andhigh taste for work may prefer employmentin the union sector sincejobs in the unionsector are usually “full-time” jobsand protected by unions fromarbitrary dismissal byemployers. If this is true, eventhe 2SLS estimates will notbe consistent dueto theproblem of a non-random sample.For this reason, we now turnto selectivity-adjustedestimates.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 53Table 3.6: Union-Nonunion Hourly Earnings, Weekly Hours and Weekly Earnings Differentials by Sector for Females in 1990, Selectivity-UnadjustedWHSector HE Purel Pure2 Derv. Total WEManufact 0.085 -0.018 -0.016 -.0001 -0.0160.069(0.039) (0.044) (0.044) (.0008) (0.044) (0.059)Construct 0.420 0.009 0.009 -.0004 0.009 0.429(0.228) (0.300) (0.225) (0.003) (0.300) (0.343)Otherlnd 0.120 0.068 0.070 -.0001 0.070 0.190(0.019) (0.023) (0.023) (.0008) (0.023) (0.030)BlueColr 0.170 -0.009 -0.006 -.0002-0.006 0.164(0.044) (0.050) (0.046) (.0002) (0.046) (0.067)Mgr/Prof 0.112 0.025 0.028 -.0001 0.028 0.140(0.026) (0.029) (0.030) (.0008) (0.030) (0.039)OtherOcc 0.116 0.093 0.094 -.0001 0.094 0.210(0.022) (0.026) (0.026) (.0008) (0.026) (0.034)FuilTime 0.113 0.049 0.052 -.0001 0.0520.165(0.018) (0.022) (0.022) (.0008) (0.021) (0.028)PartTime 0.141 0.090 0.091 -.00010.090 0.231(0.019) (0.022) (0.023) (.0008) (0.022)(0.029)Private 0.115 0.027 0.028-.0001 0.028 0.143(0.020) (0.024) (0.023) (.0008) (0.023) (0.030)Public 0.135 0.167 0.172-.0001 0.171 0.306(0.040) (0.044) (0.044) (.0008) (0.044)(0.060)Total 0.119 0.0580.060 -.0001 0.060 0.180(0.018) (0.021) (0.022) (.0008) (0.021)(0.028)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials543.6 Selectivity-Adjusted EstimatesIf we assume that the error term in the participation equationand the error term inthe union status equation are uncorrelated, we can writeselectivity-corrected wage andhours equations as follows:36lrIW=Z1I+ +lG2:)+ uli (3.18)lnW =—+ +u2 (3.19)= X.jY+7’flnW1+ + +u3 (3.20)lnH1= X,,tS.Th+7’1lnWj—+J46F(s)+U4 (3.21)whereais the covariance between ej ande,fis the standard normal densityfunctionand F is the standard normal distributionfunction.One can easily show that the conditional meansof Uki are zero. The conditional variances ofUki are, however, not so obvious. Appendix D presents derivations of conditionalvariances ofUki.The parameters in equations(3.18) and (3.19) are estimated by the Heckman-Lee’stwo stage method. The parametersin equations (3.20) and (3.21) are thenestimated byreplacing actual union and nonunion wageswith predicted union and nonunionwagesin the Heckman-Lee two stage method.37A similar estimation methodwas also usedby Nakamura, Nakamura andCullen (1979). As is clear fromequations (C10)-(C13) inAppendix D, the variance-covariancematrix of the OLS estimateswill not be consistentdue to heteroscadastic errorterms. This problem is thenfurther complicated by the361fthe two error terms are correlated,equations (3.18)-(3.21) are misspecified.In this case, we mustincludeE[eiIU = 1,P = 1],E[e2U= O,P= 1],E[eaIU= 1,F = 1] andE[e41U = O,P = 1] insteadof the two inversed Mill’s ratiosin equations (3.18)-(3.21). Estimationofthis model is not mucheasierthan estimation by maximumlikelihood. Hence, in this section weestimate a special case wherethe twoerror terms (es ande) are uncorrelated. We will relax this assumptionwhen we estimate the modelbymaximum likelihood.37The predicted wages do not includethe two inversed Mill’s ratios. LikeVella (1993), we wish toremove the effect ofselection bias operatingthrough wages when estimatinghours equations. Inclusionof the two inverse Mill’s ratios, however, doesnot change the estimates significantly.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials55fact that A, and 1nW are used in place of A, 4) and lriW1.Thecorrect asymptoticvariance-covariance matrix of the parameter estimatesin equations (3.18)-(3.21) is verycomplex and computationally difficult to obtain. Therefore,I use White (1980)’s methodto correct the problem of heteroscadasticity. Asymptoticallyefficient estimates and theassociated variance-covariance matrix are obtainedin the next section when thefull-information maximum likelihood is employed.3.6.1 Selectivity-AdjustedEstimatesof Hourly Earnings and Weekly HoursEquationsAppendix Table F.9 presents the selectivity-adjustedestimates of the hourly earningsequations for males and females. The coefficientson education and tenure are generallysmaller for union workers than for nonunion workers.Male construction workersearnmore in the union sector than in thenonunion sector. The significant coefficienton firmsize variables for nonunion females supportsa hypothesis that employersin the nonunionsector pay more as the size of firm getsbigger in order to prevent unionization.Thsesfindings are generally consistent with previousfindings.For males, the covariance betweennonunionwage and union status(a25)is -0.224 andsignificant at the 0.05 level. The negativeestimate ofa25 means thatmales who enterthe nonunion sector are the ones who arebetter in terms of generating higherwages atthe nonunion jobs. In other words,males selected into the nonunionsector earn morethan average nonunion workerswith the same characteristics andworking conditions.38The negative and significantcovariance between unionwage and participation(a16)ispuzzling. One would expectthis covariance to be positiveif individuals who workinthe union sector are drawn froman upper section of unionwage distribution. Wewill38See Green (1991) for detailed explanationon how to interpret covariances betweenwage and unionstatus.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials56see whether this negative covariance persists even when the full-informationmaximumlikelihood is used in the next section.For females, the covariance between nonunion wage and participation(a26)is 0.252and significant at the 0.05 level. This implies thatfemales who enter the labour marketthrough finding jobs in the nonunion sector obtainhigher wages than average nonunionfemales with similar characteristics. This resultis often seen in the labour supply literature. The rest of covariances are found to be statisticallyinsignificant.The selectivity-adjustedestimates ofweeklyhoursequations are reportedin AppendixTable F.lO. The estimated coefficients on logarithmof hourly earnings are now generally larger in absolute value than those inthe selectivity-unadjusted estimates(2SLS),especially for union workers. Note that the positiveand significant coefficientson Log-wage in the selectivity-unadjusted estimates(2SLS) for both males and females inthenonunion sector now becomenegativewhile insignificant.This provides some support forthe Nakamuras’ and Robinson and Tomes’ conclusion.The estimatedcoefficient on unionmale head, which was negative and significant before,is now positive but insignificant.Again, larger coefficients on educationand tenure variables for union workers,especiallyfor union males, provide some evidencefor that employers in the union sectorextractmore hours from more able workers,possibly due to union’s wage standardizationpractice. The coefficients on industry andoccupation variables are found tobe very similarbetween the selectivity-unadjustedestimates and the selectivity-adjustedestimates.For males, the covariance betweenunion hours and participation(a36)is 0.693 andsignificant at the 0.1 level. Thispositive truncation means thatmales who participatein the union sector are the oneswho have a strong tendencyto work more hours thanthe average male worker in thatsector. Therefore, onlythe upper section of thehoursdistribution is observed for union males.For females, the covariance betweennonunion hours and union status(a46)is -0.270Chapter 3. Union-NonunionWage, Hours and Earnings Differentials57and significant at the 0.1 level.The negative a46 meansthat females who enterthelabour force through gettinga nonunion job are the oneswho tend to work morehoursthan the averagefemalenonunionworker. In sum, estimatesof covariances betweenerrorterms for males and femalesindicate that the sampleselection problem shouldnot beoverlooked.Before we compute theselectivity-adjusted union-nonuniondifferentials, we brieflydiscuss what determinesthe probabilitythatan individualwill workand what determinesthe union status of an individual.39Appendix Table F.8presents the probitestimates ofthe participation and unionstatus equations formales and females.For both males andfemales, being headof family and being bettereducated increase theprobability thatanindividual will workwhile being single, beingold and having youngchildren reduce theprobability. Coefficientson the union statusequation reflect bothan individual’s tastefor unionization andan employer’s selection.For instance, the negativecoefficients onuniversity educationmay indicate thata lower demand forunionizationamong university graduates overwhelmsa higher demand forthose workersfrom an employer.Oneinterestingobservationfrom the estimatesofthe femaleunionstatus equationis therelatively significantcoefficients on headof family and youngchildren. Sincethose variablesenterthe hoursequations but not thewage equations, thesignificant coefficientson thosevariables provide someevidence thatunion status dependsnot only on union-nonunionwage gap butalso union-nonunionhours gap.3.6.2 HourlyEarnings, WeeklyHours and WeeklyEarnings DifferentialsNext, the union-nonunionhourly earnings, weeklyhours and weeklyearnings differentialsare calculated usingthe same methodas before. The variancesof the differentialsarecomputed fromthe variancesof underlying coefficientsobtained by White’smethod.more detailed discussionwill be provided in section3.7.2.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials58Table 3.7 presents the results.4°For males, the average union-nonunion hourly earningsdifferential obtained fromselectivity-adjusted estimates is about34% and significant at the 0.05 level, and largerthan that obtained from the OLS estimates. As Robinson(1989) noted, most researcherswho used economy wide samples of workers havefound larger wage differentials whentheyused selectivity-adjustedestimates. Therefore,our estimatesfor males are consistentwith previous findings.As before, union-nonunion hourly earnings are largerfor construction, blue collar andpart-time workers. However, the hourly earningsdifferential is found to be larger in thepublic sector than in the private sectorwhile the reverse was true in the OLScase.Pure, derived and total union-nonunionhours differentials for males are negativeinall cases. However, pure and derived hours differentialsare found to be statistically insignificant although total hours differentialsshow some significance. Negative totalhoursdifferentials reduce the magnitudes ofweekly earnings differentials somuch that the average weekly earnings differential becomesonly about 4% and even becomes statisticallyinsignificant.The results for females are presentedin table 3.8. Hourly earningsdifferentials forfemales are all positive but insignificant.At this point, it is hard to saywhether union-nonunion hourly earnings differentialsdo not really exist or the differentialsare foundto be statistically insignificantbecause inefficient variance-covariancematrix of the estimates is used to calculate the variancesof the differentials or becausea lot of variabilityis introduced by using so manyfitted terms in regression. Wewill come back to checkthe second possibility in the nextsection when we use maximumlikelihood method.40As before, wage, hours and earningsdifferentials are obtained byequations (3.13)-(3.17). Thestandard errors for the hours and earningsdifferentials are obtained using the6-method. Figures inparentheses are standard errors.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials59Table 3.7: Union-Nonunion Hourly Earnings, WeeklyHours and Weekly Earnings Differentials by Sector for Males in 1990, Selectivity-AdjustedWHSector HE Purel Pure2 Derv.Total WEManufact 0.314 -0.226 -0.176 -0.137-0.313 0.0008(0.141) (0.245) (0.261) (0.203)(0.171) (0.211)Construct 0.448 -0.202 -0.147 -0.196-0.342 0.106(0.153) (0.301) (0.335) (0.285) (0.177)(0.222)Otherlnd 0.339 -0.197 -0.141 -0.148 -0.2890.050(0.148) (0.269) (0.278) (0.219) (0.187)(0.236)BlueCoir 0.398 -0.212 -0.144 -0.174-0.318 0.080(0.147) (0.292) (0.303) (0.254)(0.175) (0.232)Mgr/Prof 0.181 -0.214 -0.186-0.079 -0.265 -0.084(0.145) (0.200) (0.208) (0.128)(0.176) (0.215)OtherOcc 0.420 -0.192 -0.133-0.183 -0.317 0.103(0.153) (0.299) (0.317) (0.261)(0.208) (0.244)FuilTime 0.336 -0.207-0.153 -0.147 -0.300 0.035(0.145) (0.260) (0.274) (0.221) (0.178)(0.224)PartTime 0.404 -0.227-0.166 -0.176 -0.342 0.062(0.150) (0.298) (0.320) (0.257) (0.200)(0.247)Private 0.306 -0.227-0.195 -0.134 -0.329 -0.023(0.144) (0.245) (0.267) (0.199)(0.189) (0.226)Public 0.460 -0.1340.002 -0.201 -0.1990.261(0.187) (0.454) (0.333) (0.294)(0.179) (0.299)Total 0.338-0.208 -0.154 -0.147-0.302 0.036(0.143) (0.262) (0.275)(0.218) (0.179) (0.225)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 60Table 3.8: Union-Nonunion Hourly Earnings, Weekly Hours and Weekly Earnings Differentials by Sector for Females in 1990, Selectivity-AdjustedWHSector HE Pure Derv. Total WEManufact 0.128 0.220 0.137 0.104 0.2410.369(0.219) (0.373) (0.409) (0.191) (0.400)(0.474)Construct 0.475 -0.423 -0.532 0.386 -0.1450.330(0.441) (0.550) (0.814) (0.439) (0.747) (1.026)Otherlnd 0.124 0.210 0.149 0.101 0.250 0.374(0.228) (0.356) (0.391) (0.197) (0.382)(0.483)BlueColr 0.212 0.242 0.142 0.172 0.3140.526(0.228) (0.417) (0.461) (0.218) (0.429)(0.491)Mgr/Prof 0.070 0.223 0.192 0.057 0.2490.318(0.219) (0.306) (0.343) (0.184) (0.345)(0.405)OtherOcc 0.157 0.181 0.010 0.1280.228 0.385(0.246) (0.393) (0.428) (0.217) (0.421)(0.551)FullTime 0.121 0.204 0.132 0.0980.231 0.352(0.227) (0.349) (0.384) (0.195) (0.379)(0.478)PartTime 0.161 0.197 0.157 0.1310.288 0.449(0.232) (0.404) (0.429) (0.208)(0.414) (0.516)Private 0.1610.079 -0.008 0.131 0.123 0.284(0.243) (0.382) (0.389) (0.216)(0.407) (0.544)Public 0.021 0.631 0.6460.017 0.664 0.685(0.273) (0.332) (0.411) (0.224)(0.401) (0.361)Total 0.130 0.2020.138 0.106 0.244 0.374(0.229) (0.360) (0.395) (0.199)(0.388) (0.486)Like the selectivity-unadjusted case,pure union-nonunion hours differentialsare positive but statistically insignificantin almost all cases except for the publicsector. However, the average total hoursdifferential increases dramaticallyfrom about 6% in theselectivity-unadjusted case to about25%. As a result, the average weeklyearningsdifferential increases by about20 percentage point from the correspondingselectivityunadjusted estimate. As before, the derivedhours differentials arefound to be statistically insignificant.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials613.7 Maximum Likelihood EstimatesAlthough the selectivity-adjusted estimates obtaiued in the previous sectionmay beconsistent, they are inefficient.41Inefficiencyoccurs because(i) wage aud hours equationsare estimated independently of participation and union statnsequations and (ii) wageand hours equations themselves are estimated separately. Furthermore,the variancecovariance matrixof parameter estimates obtained by White’s methodis also inefficient.In this section theparticipation,union status, wageand hours equations areestimatedjointlyby maximizingthe likelihoodfunction(3.12).42The obtained maximumlikelihoodestimates are efficient conditional on distribution assumptions.The maximum likelihood estimates of participationand nnion status equations arepresented in Appendix Table F.11, and the maximum likelihoodestimates of hourlyearnings and weekly hours equations are presentedin Appendix Table F.12 and AppendixTable F.13 respectively. The maximum likelihoodestimates of the variauce-covariancematrix of the error terms are presented in the nextsection.41As memtioned earlier, the consistency oftheselectivity-adjusted estimates depends on theassumption that the participation decision and union status decisionare independent.42The estimation is done by mainly three steps. Startingfrom the least squares estimates obtainedin the previous section, I first used the complementaryDavidon-Fletcher-Powell (DFP) algorithmuntilthe estimates do not change much and then switched toNewton-Raphson algorithm until convergence.Finally, I again used DFP algorithm to makesure that the value of log-likelihood function doesnotincrease. Both algorithms require thefirst derivatives and Newton-Raphsonalgorithm requires thesecond derivatives in addition. If possible,I calculated the first derivatives analyticallybut in somecases I calculated them numerically.For example, consider OF[a(x), 6(x), e(x)J/bx= F1 . ba(x)/bx+F2 86(x)/Ox+F3 . bc(x)/8x, where F is the bivariate normal distribution function witha(x) and 6(x),c(x) is the conditional correlation coefficient,x is an unconditional correlationcoefficient, F1 = OF/baand F2 and F3 are similarly defined. Numericalmethod is used to computeF1,P’2 andP’3in the aboveexample. That is, F1 is obtained byF[a(x)+6b(x)c(r)J—F[aOr)b(v)c(r)]where 6 is assumed tobe10—6.Finally, the second derivatives are obtainedusing outer product of the first derivatives.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials623.7.1 Variance-Covariance MatrixThe estimates of the variance-covariance matrix of the error terms inthe system ofequations are shown in table 3.9 (Note: T-statistics are in parentheses).The estimatesprovide important information in several aspects.First, note that standard errors ofresiduals in union hourlyearnings and weeklyhours equations(ai anda3)are significantlysmaller than those in nonunion hourly earnings and weekly hoursequations (a2anda4)respectively. Since the standard errors of theresiduals can explain some of union effectson wage and hours dispersions, smaller standard errorsin the union sector provide someevidence for the negative impact of unionson dispersions of wages and hours.Second, the correlation between participation andunion status(P56)is -0.080 formales and -0.123 for females. Although these estimates arestatistically insignificant,they are not negligible, especially for females.The presence of these correlations mayaffect the selectivity-adjusted estimatesof union-nonunion wage, hours and earningsdifferentials obtained in the previous sectionsince they are obtained under theassumptionthat this correlation is zero. The negativecorrelation between participationand unionstatus indicatesthat workers participatein thelabour market throughemploymentin thenonunion sector. This situation is plausibleif union jobs are rationed amongnonunionworkers to a large extent.Third, the most interesting findingfrom the estimates of the variance-covariancematrix is the significant positive correlationsbetween union hourly earningsand unionweekly hours(P13),but insignificant correlations betweennonunion hourlyearnings andnonunion weekly hours(p24).This phenomenon is seen for bothgenders. To the extentthat the error terms in hourlyearnings equations reflectunmeasured workers’ abilities,the positive correlation inthe union sector indicatesthat more able workers workmorehours in the union sector. If more ableunion workers can earn relatively morein theChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials63nonunion sector, like highly educated or highly skilled union workers, then employersinthe union sector have incentives to extract more hours from those workerssince the costsof using additional ability is small relative to the costs to beincurred in the nonunionsector. Under this circumstances, a positiveP13is expected in the union sector but notin the nonunion sector. This is a new finding which has not been discoveredin previousstudies.An important consequence of significant correlation betweenunion hourly earningsand weekly hours(p13)is that the maximum likelihood estimatesof the two equationswill be quite different from the selectivity-unadjustedand -adjusted estimates. As wewill see later, the estimates of the union weekly hoursequations are most affected by thesignificant correlation. More importantly, these resultsprovide a good reason for whythe maximumlikelihood method is preferred to theother methods.Some ofthe correlation coefficients related toparticipation and union status are alsoshown to be statistically significant.For males, the correlation betweenunion hours andunion status(ps)is negatve (-0.380) and significant at the0.05 level, which indicatesthatwe only observe the lower section of theunion hours distribution. Like the selectivity-adjusted estimates, the correlations between unionwage and participation(p16)andnonunion wage and participation(p26)are negative and significant. One wouldnormallyexpect these correlations to be positive.This unexpected result is maybe due toa failureto control nonlabour income. Since the nonlabourincome is not controlled in regression,it is possible that people withhigh ability accumulate more assetsand hence less likelyto participate in the labour market.43In such a case,P16andP26could be negative.For females, the correlation betweennonunion wage and participation(p26)is positive43This explanation is maybe consistent withthe early retirement phenomenon in thepast decades.Also, it is not totally unusual tofind the negative correlations in the literature.For example, Zabel(1993), who used other earnings instead ofnonlabourincome, also found a negative correlation betweenthe error term in participation equation andthe error term in wage equation.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials64Table9 Estimates of the Van anre-Covaniance MafniCorrelation Male FemaleUnion Sectorstandard dev. ofwage(1)0.313(40.02)0.307(58.70)standard dev. ofhour(a3)0.294(4.40) 0.404(14.51)union status-wage(p15)0.005(0.04)0.030(0.21)participation-wage(p16 -0.589(-4.20)-0.047(-0.20)union-status-hour(p35 -0.380(-3.77)-0.656(-9.86)participation-hour(p36)-0.322(-1.11) 0.060(0.08)wage-hour(p13 0.601(2.50) 0.282(1.47)Nonunion Sectorstandard dev. of wage(u2)0.449(47.36) 0.392(34.28)standard dev. of hour(cr4 0.326(86.77)0.485(28.84)union status-wage(p25)-0.183(-1.00)0.009(0.03)participation-wage(p26 -0.512(-4.62)0.273(1.64)union status-hour(p45)-0.079(-0.29)-0.161(-0.61)participation-hour(p46 -0.204(-0.59)-0.020(-0.05)wage-hour(p24) -0.029(-0.06)-0.119(-0.32)Participation and Union StatusP56-0.080(-0.25) -0.123(-0.19)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials65(0.273) and significant at the 0.1 level, while the correlationbetween union wage andparticipation is insignificant. Like males, we also observea negative and significantcorrelation between union hours and union status(p)for females which indicates thatfemales observed in the union sector are the oneswho work less than average femaleunion workers with similar characteristics.In sum, there seems to be a differencein mechanismsby which individuals are selectedinto union and nonunion sectors, and the differenceis most apparent in the correlationbetweenunion status andhours. For both males andfemales,individuals who enterunionsector are the ones who work less than the averageunion worker while those who enternonunion sector are the ones who workmore than the average nonunion worker.To theextent that the error terms in the hoursequations reflect taste for work, thedifference inthe correlations between union and nonunionworkers may imply that individuals withlower taste for work enter the unionsector while individuals with highertaste for workenter the nonunion sector.3.7.2 Participation and UnionStatus EquationsThe estimates ofparticipation equationspresented in AppendixTable F.11 are not significantly different from the probit estimatespresented in Appendix Table F.8.Being headof family and being better educatedincrease the probability of enteringlabour forcewhile being old reduces theprobability. The coefficients onprovincial unemploymentrates are negative and significantfor males. Having young childrensignificantly reducesthe probability of participatingin labour market for females only.There are also regionalvariations in participationrates, especially for females,which may reflect regionaldifferences in job opportunitiesor income assistance programs.Overall, the results are quiteexpected.The estimates of union statusequations presented in Appendix TableF.ll are againChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials66quite similar to the probit estimates previously obtaiued.The positive coefficients onUnemployment Rate imply that workers who live in regionswith high unemploymentrates are more likely to be union members. These findingsare consistent with Perloffand Sickles (1989)’s. However, as Perloff and Sickles pointedout, the causality may runin the other direction. That is, unemployment ratesmay by higher in regions that arehighly unionized.The union status equations are ofthe reducedform,so the coefficients on the variablesshould be interpreted as the net effects onunion status. Bettereducated individualsmaynot like unions for personal reasons or dueto the lower return on educationin the unionsector, but employersmay like to hirethem on productivity grounds. As aresult,theneteffects of education on union status dependon these two offsetting forces. Our estimatesshow that the net effects of educationare not significant except formale universitygraduates. The net effect of educationfor university graduates is negative(-0.201) SOthat they are less likelyto be inthe union sector. Coefficients on tenurevariables can beinterpreted in a similar way. Our estimatesindicate that individuals withlonger tenureare more likely to be union members.As expected, individuals in the servicesector have a lower probabilityof being unionized than those in the manufacturingsector while individuals in health,education andpublic administration sectors havea higher probability. White collarworkers also havelower probability to be unionmembersthan blue collar workers.The firm size variablesare intended to measure costsof unionization. Being employedin larger establishmentsreduces the costs of unionizationand hence increase the probabilityof unionization.Significant and positivecoefficients on these variablesprovide some evidence forthishypothesis.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 673.7.3 Hourly Earnings EquationsMaximum likelihood estimates of hourly earnings equations are presented in AppendixTable F.12. For both males and females, hourly earnings increase significantly witheducation and tenure, and the return to education and tenure are generally smallerin theunion sector for both sexes. This result has been quite robust regardlessof estimationmethods. There are also significant provincial, industry and occupationalwage differentials. Except B.C. residents, people who live outside Ontario generally earnless thanthose who live in Ontario. Male workers in the construction andprimary industries earnmore than those in manufacturing industry while bothmale and female workers in theservice industry earn significantly less. Professionals and managers earnconsiderablymore than blue collar workers, especially for females. Being employed inthe the public sector has a positive effect on hourly earningsbut its effect is significant only forunion females. Firm size variables are in general positive andsignificant and the sizes ofcoefficients are smaller in the union sector.Although maximum likelihood estimates ofthe hourly earnings equations are notso much different from the OLS and selectivity-adjustedestimates, there are still somenoticeable changes of coefficients on certain variables.For example, the maximum likelihood estimates for the coefficient on the publicsector dummy are quite differentfromthe corresponding selectivity-adjustedestimatesfor both sexes. The differences betweenthe two sets of estimates may lead to differentconclusions with regard to the impactofpublic sector employment on hourly earnings.3.7.4 Weekly Hours EquationsFrom the maximum likelihood estimatespresented in Appendix Table F.13,one cannotice that the constant terms and the coefficientson log of hourly earnings in the unionChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials68sector are generally larger than those in the 2SLS estimates in absoluteterm. On theother hand, less significant changes are seen with regard to the correspondingcoefficientsin the nonunion hours equations. This phenomenon is possibly dueto the positive andsignificant correlation between hourly earnings and weeklyhours in the union sectorbut the insignificant correlation in the nonunion sector. Sincethe relationship betweenthe error term in the hourly earnings equation and the errorterm in the weekly hoursequation is more explicitly captured in the maximumlikelihood estimation than in the25L5 estimations, we would expect that a significantcorrelation between the two errorterm will have more impact on the coefficient on logof hourly earnings in the maximumlikelihood estimation.The negative and significant coefficients on the hourly earningsfor both male andfemaleunion workers indicatethat hours decreaseas the wage rate increases inthe unionsector. This result may come from theemployer’s hours adjustment to anincrease inwage or from a joint bargaining betweenthe union and the employer.The coefficientson the hourly earnings are insignificantfor both male and female nonunion workers,which indicates that substitution andincomeeffects offset each other whenthe wage rateincrease for nonunion workers. This resultis very similarto the corresponding selectivity-adjusted estimates. The presenceofyoungchildrenis a moreimportant factorfor femalesthan for males in explaininghoursdetermination. Provincial unemploymentrates do notappear to be a significant factor.From the coefficients on educationand tenure variables, one can clearlysee that coefficients on high education(post-secondary and university education)and longer tenure(more than 6 years) in the union weeklyhours equations are uniformlylarger than thecorresponding coefficients inthe nonunion weekly hoursequations for both genders.4444This does not mean that better educatedand more experienced union workers workmore hours thantheir nonunion counterparts. The averagehours per week for university graduatesin the union sector,for instance, are smaller than the averagehours per week for those in the nonunion sector.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 69This pattern is much more distinct in maximum likelihood estimates than it is in theleast squares estimates. Let us examine the explanation provided earlier that employersin the union sector have an incentive to extract more hours from better educated andmore experienced workers because they pay less for education and experience when compared to employers in the nonunion sector. This explanation is reasonableif employersin the union sector have all the power in choosing hours, i.e., the monopoly union model.If the employer and the union determine the hours together, theexplanation is less clearsince the hours are determined by the worker’s taste for work as wellas the employer’sselection of hours. One of the important findings in section 3.7.1is that workers withlower taste for work enter the union sector. Therefore,it is difficult to think that better educated and more experienced union workers wantto work more hours than theirnonunion counterparts. As a result, the explanation that employersin the union sectorextract more hours from the able workers seems reasonablein both monopoly union andefficient contracts models. This result and the positivecorrelation between hourly earnings and weekly hours in the union sector together providestrong evidence that ability,measured or unmeasured, is positively correlatedwith hours of work in the union sector.Concerning industry and occupation, there appearsto be no significant differences inthe coefficients between union and nonunion workersexcept that females with service occupations (Wcolr2) work significantlyfewer hoursthan blue collar femalesinthe nonunionsector while this pattern is not seenin the union sector. The maximum likelihoodestimates for these variables are however quitedifferent from the previous least-squaresestimates.3.7.5 Hourly Earnings, WeeklyHours and Weekly Earnings DifferentialsUsing the full-information maximum likelihoodestimates of the hourly earningsandweekly hours equations, union-nonunion differentialsfor males are calculated by theChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 70methods (3.13)-(3.17) and reported in Table 3.10. In most cases, the variances of thedifferentials are obtained by the 6-method. Appendix E describesthe derivations of thevariances of varions differentials.The estimates presented in table 3.10 are clearly different from the previous leastsquares estimates. Not only the pure hours differentials are positive butalso they arestatistically significant at better than the 0.1 level. Since we knowthat employers in theunion sector extract more hours from better educated and moreexperienced workers,we calculate how much of the average pure union-nonunion hours differentialis dueto the differences in coefficients on education and tenure betweenunion and nonunionworkers.45 The result is striking. Education and tenure canexplain about 51% of theaverage pure union-nonunion hours differential. Therefore,it is reasonable to concludethat the positive union-nonunion hours differentialfor males is largely due to the largeimpact of education and tenure on hours in theunion sector.4°The average pure union-nonunion hours differentialsrange from about 16% to 20%and are significant at betterthan 0.1 level.The average derivedhours differential is about-10% and also significant at the 0.1 level. These two differentialsare most significant forconstruction workers. The pure hours differentialsfor this group range from about 21%to even 30% and the derived hours differential isabout -18%.As for the economy, the total hours differentialis about 9% and significant at the 0.2level. The average total hours differentialis found to be large for construction workers,part-time workers and public sector employees.45The hours differential resulted from differencein coefficients on education and tenureis calculatedby X(A” — A’) where X is a vector ofeducationand tenure variables and A is the corresponding vectorof coefficients46The large impact ofeducation and tenure onhours of work may be due to larger fixedemploymentcosts, such as training costs, for skilled unionworkers than for skilled nonunion workers.The argumentthat fixed employment costs increase hoursofwork can be found in Ehrenberg (1970)and the argumentthat nonwage benefits, some of which are fixed employmentcosts, for union workers are Iarger thanthose for nonunion workers can be found in Freeman (1981).Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 71Table 3.10: Union-Nonunion Hourly Earnings, Weekly Hoursand Weekly Earnings Differentials by Sector for Males in 1990, MaximumLikelihood EstimatesWHSector HE Purel Pure2 Derv. Total WEManufact 0.163 0.116 0.147 -0.0950.052 0.215(0.080) (0.096) (0.102) (0.059) (0.071) (0.096)Construct 0.312 0.213 0.304 -0.182 0.1220.434(0.082) (0.116) (0.138) (0.097) (0.058)(0.091)Otherlnd 0.174 0.176 0.213-0.101 0.112 0.286(0.083) (0.096) (0.102) (0.062)(0.065) (0.095)BlueCoir 0.195 0.144 0.180 -0.114 0.0660.261(0.083) (0.099) (0.106) (0.072) (0.067) (0.095)Mgr/Prof 0.097 0.162 0.188 -0.0570.131 0.228(0.079) (0.081) (0.084) (0.042) (0.063) (0.091)OtherOcc 0.262 0.197 0.252 -0.1520.100 0.362(0.082) (0.115) (0.129) (0.081)(0.063) (0.096)FuliTime 0.180 0.160 0.197 -0.1040.093 0.272(0.078) (0.094) (0.100) (0.061) (0.062) (0.087)PartTime 0.230 0.198 0.243 -0.1340.109 0.339(0.079) (0.104) (0.114) (0.073) (0.061)(0.089)Private 0.193 0.1590.191 -0.112 0.079 0.272(0.071) (0.093) (0.102) (0.055)(0.053) (0.081)Public 0.138 0.172 0.227-0.080 0.147 0.285(0.131) (0.130) (0.124) (0.092)(0.105) (0.149)Total 0.181 0.162 0.198-0.105 0.093 0.275(0.077) (0.094) (0.101) (0.061) (0.062)(0.089)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 72One may wonder why the maximum likelihood estimates ofpure hours differentialsare so different from the corresponding selectivity-adjusted estimates.There are several reasons why they may differ. First, as mentioned before, the selectivity-adjustedestimates are obtained under the assumption that the correlation betweenparticipationdecision and union status(p56)is zero whereas the maximum likelihood estimates areobtained without such an assumption. Second, distributionalassumptions are differentbetween the two estimationmethods. Thatis, unlike the Reckman-Lee 2SLS estimation,maximum likelihood requires an assumption of the joint normalityof the error terms inthe system of equations. Besides, maximum likelihoodis a nonlinear estimation.Even though the two estimates are quite different,it does not mean that they areincompatible. Because the standard errorsof the selectivity-adjusted estimates of purehours differentials are very large, we can not rejectthehypothesis that the pure hours differential is positive. In fact, the maximumlikelihoodestimates of pure hours differentials(Purel and Pure2) lie within the two standarderror of the selectivity-adjustedestimatesof pure hours differentials. Therefore, we cannoteven reject the hypothesis that purehours differentials are 0.162 and0.192, which are the maximum likelihood estimatesofPurel and Pure2, from the selectivity-adjusted estimates.Union-nonunionhourly earnings differentials are positiveas expected and statisticallysignificant at the 0.05 levelfor mostgroups. On average, the union-nonunionhourly earnings differential is about 18% and significantat the 0.05 level. Note that this differentialis larger than the one obtained from theOLS estimatesbut smallerthan theone obtainedfrom the selectivity-adjusted estimates.As before, part-time workers andconstructionworkers gain most from joining theunion whereas professionals and managersgain leastfrom doing that.Finally, union-nonunion weekly earnings differentialsare also positive and significantat the 0.05 levelin most cases. Noticethat unlikepreviouscases, theearnings differentialsChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials73are now larger than the wage differentials dueto the positive hours differentials.Next, union-nonunion hourly earnings, weekly hours and weeklyearnings differentials for females are calculated and presented in Table 3.11.Unlike the statistically insignificant hourly earnings differentials for femalesobtained from the selectivity-adjustedestimates, most of the union-nonunion hourly earningsdifferentials are not only positive but also statistically significantat better than the 0.1 level. This result mayimplythat greater efficiency is obtained byfull information maximum likelihood thanby theextended Heckman-Lee 2SLS estimationmethod. The estimated hourly earningsdifferentials are generally larger than those obtained fromthe OLS and selectivity-adjustedestimates. However, the patterns ofthedifferentials are similar: a largerearnings gain inthe union sector falls to blue collar andpart-time workers while workers withhigh-paidjobs such as managers or professionalsgain relatively less. The union hourly earningsdifferential in the public sector is smallerthan that in the private sectorand statisticallyinsignificant. This result seemsmore reasonable than the OLS resultthat the hourlyearnings differential is greater inthe public sector than in the privatesector.47Estimates in table 3.11 provide strong evidencefor the positive union-nonunion hoursdifferentials for females. Likethe selectivity-adjustedestimates,the maximumlikelihoodestimates of pure union-nonunionhours differentials are foundto be positive. Furthermore, they are generally statistically significant.On average, the pure hours differentialis about 37% when evaluatedat the averages of actual hourlyearnings and characteristicsand about 44% when evaluatedat the averages of predictedhourly earnings and characteristics of nonunion females.Like before, we calculate thecontribution of educationand tenure to the positiveunion-nonunion hours differential.We find that about33%of the average pure union-nonunionhours differential comesfrom the differences in the47Robinson and Tomes (1984) also reportthat union-nonunion hourly earningsdifferentials are greaterin the private sector than in the publicsector for both males andfemalesalthough their sample selectioncriteria are different from mine.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials74Table 3.11: Union-Nonunion Hourly Earnings,Weekly Hours and Weekly Earnings Differentials by Sector for Females in1990, Maximum Likelihood EstimatesWHSector HE Purel Pure2 Derv.Total WEManufact 0.184 0.2460.305 -0.074 0.231 0.414(0.109) (0.265) (0.250) (0.047) (0.241)(0.267)Construct 0.491 0.514 0.620-0.198 0.422 0.913(0.284) (0.272) (0.278) (0.124) (0.245)(0.337)Otherlnd 0.194 0.385 0.454-0.078 0.376 0.569(0.106) (0.229) (0.206) (0.048)(0.195) (0.232)BlueCo].r 0.229 0.260 0.327-0.093 0.234 0.463(0.118) (0.286) (0.270) (0.059)(0.260) (0.286)Mgr/Prof 0.174 0.2970.366 -0.072 0.295 0.469(0.115) (0.227) (0.196) (0.053) (0.184)(0.217)OtherOcc 0.205 0.442 0.508-0.083 0.425 0.630(0.104) (0.235) (0.221) (0.043) (0.208)(0.234)FuliTime 0.1890.351 0.424 -0.076 0.347 0.536(0.104) (0.229) (0.205)(0.463) (0.194) (0.221)PartTime 0.220 0.440 0.489-0.089 0.400 0.621(0.106) (0.249) (0.227)(0.050) (0.215) (0.241)Private 0.2050.374 0.439 -0.083 0.3570.562(0.098) (0.223) (0.209)(0.041) (0.197) (0.221)Public 0.1630.361 0.434 -0.066 0.3680.531(0.173) (0.296) (0.257)(0.079) (0.247) (0.298)Total 0.196 0.3710.438 -0.079 0.3590.555(0.105) (0.230) (0.210)(0.047) (0.198) (0.225)Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials75coefficients on education and tenure. Even though this figureis lower than 51% obtainedfor males, education and tenure are still an important factorin explaining the positivehours differential for females.Maximum likelihood estimates for the pure unionhours differentials are larger forpart-time workers than for full-time workers whilethere is no significant difference between private and public sector females.The pure hours differentials for females withprofessional occupations and working in manufacturingand public sectors are found tobe statistically insignificant.Maximum likelihood estimates for derived hoursdifferentials are found to be quitelarge. This is mainlydue tothe large coefficient onthe hourly earnings intheunion hoursequation and the relatively large union-nonunionwage differential. The derived hoursdifferentials obtained by maximumlikelihood arenegative and significant at better thanthe 0.1 level whereas the corresponding selectivity-unadjustedand -adjusted estimatesare not statistically insignificant. The derived hoursdifferential is the largest in absolutevaluefor part-timefemalessincetheseworkers gain the largesthourlyearningsdifferentialwhen they enter the union sector.Due to the negative derived hours differentials,total union-nonunion hours differentials are smaller than the pure hours differentials.However, total hours differentials arestill positive and significant at the 0.1 levelin most groups. On average, thetotal hoursdifferential is about36%.Finally, the union-nonunion weeklyearnings differentials are positive andsignificantat the 0.05 level. The average earningsdifferential is about 56%. As before,the earningsdifferential is larger than the wagedifferentials, so it is reasonable toconclude thatunionization increases earningsdifferentials more than wage differentials.This result isconsistent with our earlier findings.Chapter 3. Union-Nonunion Wage, Hours and EarningsDifferentials 763.8 ApplicationsIn this section, we examinethree related issuesto which our results may be applied.Thefirst part ofthis section deals with the male-femaleearnings differentials, the second partdeals with the impact of unionization on male-femaleearnings differentials, and thelastpart deals with the union effects on hoursdispersion.3.8.1 Male-Female Earnings DifferentialsMost studies dealing with male-female earningsdifferentials base their analyses onestimates of wage equations that areestimated independently fromhours equations. However, as we have seen in the previoussections, the estimates of wage equationschange alot depending on whether thewage equations are estimatedjointly withhours equationsor they are estimated independently fromhours equations. This is especiallytrue in theunion sector since wage and hours mightbe determinedjointly by collectivebargaining.As a result, we expect that the sizesof the standard decomposition termsmight changedepending on different sets ofestimates used. We examinethis possibilty in this section.Consider an economy segmentedin two sectors, union andnonunion sectors. Theexpected wages for an averagemale and an average female maybe written asET47 = Frob(U = i)Wy+ Frob(U = O)W$(j= in,f)(3.22)where and W’ arethe average union and nonunionwages for genderj measuredin logarithm and U is the dummyindicating union status of genderj.For notationalsimplicity, let Frob(U= 1)=ctj. The male-femalewage differential is then writtenasEWncEWf = (am—aj)(W,---T’T/)+ (af)(W, — Wy)+(1 — af)(W, — Wy) (3.23)The first line of (3.23) measuresthe contribution of the differencein union densitiesChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials77betweenmales and femalesto the male-femalewagedifferential. The second lineof (3.23)represents the sum of weighted male-female wagedifferentials in union and nonunionsectors. Although it is possible thatthe difference in union densities betweentwo genderscan be decomposed as the differencein characteristicsand the differencein coefficients,weonly focus on decomposing male-femalewage differentialsin union and nonunion sectorsbecause our purpose is to compare the sizesof decomposition terms obtainedfrom theestimates of wage equations that are estimatedindependentlyfrom hours equationswiththose obtained from theestimates of wageequations that are estimatedjointlywithhoursequations.48Following Oaxaca (1973), the male-femalewage differentials in unionand nonunionsectors are decomposed intotwo parts:Difference in Characteristics= (Z — Z)I’(3.24)Difference in Coefficients =(I — I)Z(3.25)These two terms are then obtainedusing the OLS estimates, selectivity-adjustedestimates and maximumlikelihoodestimates respectively. The results arepresented in tableThe three sets of estimates showsignificant differences, especiallyfor the termdue to difference in coefficients, althoughthe proportions of the decompositionterms areroughly the same in each case.For the union sector, the maximumlikelihood estimatefor the difference in coefficients(=0.209) is larger than theOLS estimate (=0.179) butsmallerthan the selectivity-adjustedestimate (=0.279). For thenonunion sector, the corresponding maximum likelihoodestimate (=0.292) is thelargest and the OLS estimate(=0.229) is the smallest. On average,the corresponding maximum likelihoodestimate45To decompose the differencein union densities betweenmales and females, one can linearizetheprobability of becoming aunion member using the Taylor approximation.For details, see Doiron andRiddell (1993).491ntable 3.12, OLS=OrdinaryLeast Squares, Sel-Adj=SelectivityAdjusted and ML=MaximumLikelihood. Figures in (3a)-(3c)are obtained using female union densityas a weight. A complete decomposition will include the term due to differencein male-female union density.The size ofthe term is 0.013.All differences are measured in logarithm.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials78Table 3.12: Estimates of Decomposition Termsof the Male-Female Wage Differential.OLS Sel-Adj MLUnion Sector(la) Due to Differences in Characteristics0.022 0.032 0.025(ib) Due to Differences in Coefficients0.179 0.279 0.209(ic) Due to Both0.201 0.311 0.233Nonunion Sector(2a) Due to Differences in Characteristics0.091 0.096 0.104(2b) Due to Differences in Coefficients0.229 0.272 0.292(2c) Due to Both0.320 0.368 0.396Both Sectors(3a) Due to Differences in Characteristics0.064 0.071 0.072(3b) Due to Differences in Coefficients0.209 0.275 0.259(3c) Due to Both0.273 0.345 0.331(=0.259) is betweenthe OLS estimate(=0.209) and selectivity-adjustedestimate(0.275).Among the three sets of the estimates,selectivity-adjusted estimatesappear to beleast convincing. Unlike the OLS andML estimates, male-female wagedifferentials arelarger in the union sector thanin the nonunion sector. This resultcontradicts our expectations that femalesin the union sector are less discriminatedagainst than femalesin the nonunion sector.One of the important implicationsof results presented intable 3.12 is that the OLSestimate of the differencein coefficients, often called thediscriminatory or unexplainedpart, is not reducedeven whenwage equations arejointlyestimatedwith hours equations.Therefore, the large discriminatorypart in male-female wagedifferential appears to bepersistent regardless of differentestimation techniques used.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials793.8.2 The Impact of An Increase in Female Union Densityon Male-FemaleEarnings DifferentialsA recent study by Doiron and Riddell (1993) explores a possibility thatan increase inunion density offemales relativeto a small declinein that of males may have contributedto the narrowing of the male-femalewage differentialin Canada. Because union workerson average earn more than nonunion workers perhour, an average wage for femaleswould increase as the union density of femalesincreases, and hence would reduce themale-female wage differential.In this section we examine how an increasein female union density affects the male-female earnings differential. Our earlierresults suggest that unionization leadsto anincrease in hours of work for females in additionto an increase in wages. Therefore, ashift of female workers from the nonunionsector to the union sector will increasetheiraverage earnings morethan their averagewage. As a result, it will reducethe male-femaleearnings differential more than themale-female wage differential.To truly tackle this issue, we need morethan one data set. For example. DoironandRiddell used three different data sets(1981, 1984 and 1988) to capture thechanges inmaleandfemaleunion densities overtime. Sincethis is not possible here,wefocus on howa small increase in female union densitywould affect the male-female wage andearningsdifferentials. Specifically, we computethe changes in male-femalewage and earningsdifferentials when female union densityincreases by one percentagepoint holding maleunion density constant. During thelast two decades, female uniondensity has graduallyincreased, but male union densityhas not changed much.Thus, our assumption ofconstant male union density is notso unrealistic.The male-female earnings differentialcan be expressed like equation(3.23) in theprevious section except forthat union and nonunion wages arereplaced by union andChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials80Table 3.13: The Changes of the Male-Female Wage and Earnings DifferentialsWith OnePercentage Point Increase of Female Union DensityWage Differential Earnings DifFerentialDne to Differences in Union Densities -.0022-.0017Dne to Differences in Characteristics -.0008-.0010Dne to Differences in Coefficients -.0008-.0027Total -0.46%-0.79%nonunion earnings respectively. The standard decompositionmethods can also be applied to the earnings differential in a straightforwardway. Like the male-female wagedifferential, the male-female earnings differentialcan be written asEYm — EY1 = (am — Qf)(Y — i)+(a.i)(i— yU)+ (1 — af)(Y,—(3.26)where Y denotes weekly earnings (wage rate timestimes hours of work).Using maximumlikelhood estimates, we obtainthe changes of male-femalewage andearnings differentials when femaleunion densityincreases by one percentagepoint. Thesechanges are also decomposedby (3.24) and (3.25). Table 3.13 presentsthe results.5°Theresults indicatethat one percentagepoint increaseinfemaleunion densityreducesthe male-female earnings differential by0.79% and the male-female wage differential by0.46%. Thereduction oftheearnings differentialis mainlyachievedthroughthereductionof differences in coefficientswhereas the reduction ofthe wage differential is mainlyachieved through the reductionof the gap between male and femaleunion densities.The upshot of the results presentedin table 3.13 is that an increase in femalenniondensity reduces the earningsdifferential more than the wagedifferential. The differencebetween the total changes(-0.33%=-0.79%-i-0.46%) comes fromthe reduction in the50The changes of the decomposition termsin the table are measured in logarithm, but totalchangesare converted into percentage.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials81Table 3.14: Differences in Variances of Log ofHourlyEarningsand Weekly Hours BetweenUnion and Nonunion Males and Fempiies______ ________Males FemalesHourly EarningsUnion 0.117 0.161Nonunion 0.284 0.217Difference -0.167 -0.056F-Statistics 2.43 1.35Weekly HoursUnion 0.074 0.124Nonunion 0.086 0.201Difference -0.012 -0.077F-Statistics 1.161.62male-female hours differentials as a resultof an increase in female union density.Thisresult suggests that some ofthe decreasein male-femalehours differential during thepasttwo to three decades may be attributedto an increase in female uniondensity as well.3.8.3 Union Effects on Wageand Hours DispersionIt is well known that wages are less dispersedin the union sector than in the nonunionsector. The evidence for theU.S. can be found in Freeman (1980,1982),and the evidencefor Canada can be found in Meng(1990) and Lemieux (1993). Table3.14 presentsthe variances of the log of hourlyearnings and weekly hoursfor males and females byunion status calculated from ourdata set. As expected, forboth males and females, thevariances of log of hourly earningsare smaller in the union sector.By the F test, thedifferences are significant atthe 0.01 level for malesand at the 0.05 level for females.Inaddition, weekly hours arealso less dispersed in theunion sector. The F statisticsforthe differences are significantat better than the 0.10 level formales and at better thanthe 0.05 level for females.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials82There are several reasons why the variances of wages and hours mightbe smallerin the union sector. First, the smaller variances may be due tomore homogeneouscharacteristics among union workers. Second, unions may tryto standardize wages andhours for workers with similar charactersitics. Finally,unions may reduce employers’subjectivity in determining wages and hours fortheir members.This section uses maximumlikelihood estimatesto identify which of the three factorsis most responsible for smaller variances of wages and hours inthe union sector. Recallthe weekly hours equations (3.6) and (3.7) presentedin section 3.3. Following Freeman(1980)’s methodology, the difference in the varianceof log of hourly earnings in the twosectors is decomposed asFU[VC(ZU) — VC(Z)]I” (3.27)andFVC(Z)I”— FVC(Z)I”7,(3.28)where VC denotes a variance-covariance matrixof a vector Z, where Z is a vectorofall variables appeared in the hours equation of sectorj. The difference in the variance oflog of weekly hours is similarly decomposed.Note that all the union coefficientsin (3.27)can be replaced by nonunion coefficients, and allthe variance and covariance matrixesofnonunion characteristics in (3.28) canbe replaced by those of union characteristics.Thedecompositionterm (3.27) is thedifference invariances attributableto differences in characteristics and the decompositionterm(3.28) is the difference in variancesattributable todifferences in coefficients. The decompositionterm (3.28) provides one possiblemeasureof union effects on wage dispersion. Holdingthe variances and covariancesof characteristics constant, unions can affectthe distribution of wages andhours through influencingthe coefficients in wage andhours equations.Remaining differencesin wages and hours dispersions can be attributedto differencesChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials83Table 3.15: Estimates of the Decomposition Terms in the Differencesin Variances ofHourly Earnings and Weekly Hours between Union and NonunionSectorsMales FemalesWagesDue to Differences in Characteristics -0.011(-0.025)0.012(0.013)Due to Differences in Coefficients-0.040(-0.026) -0.015(-0.016)Due to Difference in Variances of Residuals-0.104 -0.060Total Difference -0.155-0.063HoursDue to Differences in Characteristics-0.041(0.014) -0.004(0.016)Due to Differences in Coefficients0.070(0.015) 0.004(-0.016)Due to Difference in Variances of Residuals-0.020 -0.072Total Difference0.009 -0.072in variances of error terms in wage andhours equations. The difference in variancesoferror termsmay reflect some ofthe differencesin determining wages and hours betweenthetwo sectors that are not capturedby regression coefficients. Therefore,these differencesprovide another measure of unionimpacts on wages and hours dispersions.Table 3.15 presents maximum likelihoodestimates of the decompositionterms formales and females respectively.5’Concerning the wage dispersion formales, our resultsare consistent with those obtainedby previous studies where least squareestimates aregenerally used.52 For example,Freeman (1980) and Meng(1990) found that some ofthe lower dispersion of wagefor males in the union sectoris due to more homogeneouscharacteristics in that sector.They also found that moresignificant sources of the lowerdispersion ofwages in theunion sector are due to smallercoefficients and smallervariance51Note: The first estimates in thetable are obtained using methods(3.27) and (3.28). The secondestimates in parentheses areobtained using alternative methodswhere union coefficientsin (3.27) arereplaced by nonunion coefficientsand the variances and covariancesmatrixes ofnonunion characteristicsin (3.28) are replaced by thoseofunion characteristics. All differencesare measured in logarithm.52Unfortunately, most studies I amaware of in this area focus on males.Therefore, I am unable tocompare my results for femaleswith others.Chapter 3. Union-Nonunion Wage, Hours and Earnings Differentials 84of the residual in the union wage equation. The same pattern is observed in table 3.15.Concerning thehours dispersion, there is no strong evidencethat the smallervarianceof hours in the union sector is due to more homogeneous characteristicsin that sector.The sign of the estimate of the difference in characteristics varies as thedifferent weightsare used. Moreover, the estimate of the difference in coefficientsis positive for males,which means that if male union workers have the same characteristics as male nonunionworkers, they in fact work longer hours. This resultmay suggest that although unionsdo standardize wages among their members, they donot standardize hours. Finally, themost significant source of a narrower dispersion ofhours in the union sector is a smallervariance of residual in the union hours equation.This may indicate that unions aresuccessful in reducing the degree of employers’ arbitrarydetermination of hours.In sum, there is strong evidence that unions reduce wagedispersion, but a ratherweak evidence that unions reduce hoursdispersion.3.9 ConclusionIn this chapter we examined union-nonunion wage,hours and earnings differentials inCanada. We particularly focussed on union-nonunionhours and earnings differentialssince this subject has not received much attentionin Canada. In estimating the union-nonunion differentials, we used three differentestimation techniques in orderto test therobustness ofthe estimates. The mainestimates ofunion-nonunion differentials for malesand females are summarized here.1) Union-nonunion hours differentialsfor males are ambiguous. The averagepureunion hours differential for malesis about -2% and statistically significant whenobtainedfrom the selectivity-unadjustedestimates. But, the differential becomesstatistically insignificant when obtained from the extendedHeckman-Lee 2SLS estimation methodandChapter 3. Union-Nonunion Wage, Hoursand Earnings Differentials85becomes even positive (16%) and statisticallysignificant when calculatedfrom maximumlikelihood estimates.2) Union-nonunion pure hours differentialsfor females are found tobe positive inall the estimation methods used and generallyfound to be statisticallysignificant. Theaverage pure union hours differentialsrange from 6% to56% depending on estimationmethods. Maximum likelihoodestimates for this differentialare found to be larger thanleast squares estimates.Total union hours differentialsfor females range from7% to 56%and are statistically significantas well.3) As expected,union-nonunion wage andearnings differentialsarepositiveandstatistically significant for both malesand females. The average wageand earnings differentialsfor males range from14% to 34% and 4% to28% respectively. The average wageandearnings differentialsfor females range from10% to 20% and 18% to56 % respectively.The larger union earnings differentialfor females are due tolarger positive unionhoursdifferentials.The implications ofthe largerunion earnings differentialsfor females on male-femaleearnings differentials are discussedin section 3.8.2. Themain finding of thatsectionis that an increase infemale union density reducesthe male-female weeklyearningsdifferential more than themale-female hourly earningsdifferential. Thisresult makessense since an increasein female union densitywould reduce the male-femalehoursdifferential due to positiveunion hours effectsfor females, and hencewould reduce themale-female weeklyearnings differential more.This chapter also finds aninteresting resultthat employers in theunion sector tendto extract more hoursfrom able workers. Thisresult is consistent witha hypothesis thatemployers in the unionsector have an incentiveto do that becausereturns to moreableworker are lower in the unionsector.One can argue thatthe positive union-nonunionhours differentials weobtained inChapter 3. Union-Nonunion Wage, Hours and Earnings Differentials86this study, especially for females, may be due to omitted variablessuch as abseuteeismrates, fringe benefits and work schedulesin the hours equations. Allen (1984) found thatabsenteeism rates are higher in the union sectorthan in the nonunion sector and Freeman (1981) found that union workers receive larger fringebenefits than their nonunioncounterparts do. Since both absenteeism and fringe benefitsare known to be positivelycorrelated with hours of work, at leastin theory, a failure to control for absenteeismrates and fringe benefits in the hoursequations may lead to positiveunion-nonunionhours differentials.53Thepositiveunion-nonunionhours differentialsmayalso comefrom afailureto controlfor work schedules in the hours equations.A recent study by Kostiuk (1990) reportsthata larger percentage of union workers than nonunionworkers are working onshift workschedules in the United States.A study by Northrup (1989) also reportsthat twelve-hour shift work schedules havebeensuccessfully adopted in the chemicalindustries in theUnited States that are highly unionized.So far, the effects of absenteeism, fringebenefitsand work schedules on the union-nonunionhours differential are unknown.These issuescertainly deserve more attentionin the future.53Alarge portion of fringe benefits canbe thought of as fixed costs of employment.The theoreticalprediction that absenteeismand fixed costs increase hours of workis shown in Ehrenberg (1970).Chapter 4ConclusionThe economic impact of the union has been animportant subject for economists.Weare interested in unions for various reasons.Do unions distort the efficiency ofthelabour market? If so, how much? Dounions increase or reduce inequality betweenindividuals in our society? Dounions have a positive or negativeimpact on productivityand profitability? Are quit rates higheror lowerintheunion sector? Do unions encourageor discourage absenteeism? These are thesomeof questions that economiststry to answerand policy makers are also interestedin.However, despite the considerableamount of research doneon unionism, not manypeoplehave raised the question,“Do unions increase or reducehours ofwork?” In generalperception, unions are believedto reduce hours of work. However,whether the hoursof work are in fact lower in the union sectordepends also on the firm’sreaction to theunion demand for shorter hours.If unionized firms face highemployment costs (suchas high recruiting and trainingcosts), and hence have an incentiveto substitute hoursfor employment, it is not clearthat we should expectthe hours of work to be lowerinthe union sector. Also,as we have seen in chapter 2, ifthe union cares more aboutemployment than eachmember’s utility, the union impacton hours is ambiguous evenin the absence of such fixedcosts of employment. As Pencavel(1991) pointed out, weknow very little about unionimpact on hours of work.The purpose of this thesisis twofold. First, it summarizesprevious theoretical union87Chapter 4. Conclusion88models which normally assnme fixed honrs of work and extends themto allow the possibility that both the nnion and the firm can bargain overhonrs as well as wages andemployment. By doing so, it obtains some predictionson union impacts on wages, honrsand employment. Second, this thesis develops an empiricalframework which allows oneto examine the nnion wage, honrs and earningseffects simultaneously. The empiricalresnlts obtained in this thesis are very diverse.There are considerable variations in thennion-nonnnion honrs differential betweengender, indnstry and occnpation.In conclusion, we briefly snmmarize themain resnlts of this thesis:1. The three union models (monopolynnion, right to manage and efficient contractsmodels), incorporated with hoursof work, predict that nnion effects on hours andemployment are generally ambiguous,but union effect on wages is positive. However, in some special cases, itis possible to determine the union effectson hoursand employment. For example, if theunion’s objective function is assumedto beutilitarian and if the unionand the firm bargain over the threevariables jointly,both wage rates and employment rise,but hours decrease in the union sector.2. In the efficient contracts model the slopeof the contract curve in wage-employmentspaceobtained without assumingfixedhours is quite differentfromtheone obtainedwith assuming fixed hours.In particular, if the unioncares relatively less aboutemployment than the utilitygains of its members, it is shownthat the contractcurve does not necessarily have anegative slope in contrast tothe one shown inPeucavel (1991).3. Like severalothers, we showthat at thebargainingequilibriumunion workers wouldlike to work more hours at thenegotiated wage rate. Thishas two implications.First, it means that a usual assumptionof fixed working hours or the assumptionthat workers can choose the numberof hours they would like to workmay beChapter 4. Conclusion89inappropriate in the unionized sector. Second,it also means that some of thehigher wages that union workers receive could bethe compensating wages for theunsatisfactory hours set by unions and firms.4. Empirically, union-nonunion hours differentials formales are ambiguous. Althoughthe selectivity-unadjusted estimates indicate thatunion workers work less thannonunion workers with similarcharacteristics, maximumlikelihood estimatesindicate the opposite.5. However, union-nonunion hours differentials for femalesare found to be positive inall cases and generally found to be statisticallysignificant.6. The positive union-nonunion hours differentialsfor both males and females arelargely dueto larger coefficientson educationandtenurein theunionhours equationand the positive correlation betweenthe union wage and hoursequations. Thisprovides some evidencefor that employers in the unionsector extract more hoursfrom more able workerssince they pay less for educationand experiencethan theircounterparts in the nonunion sector.7. As expected, union-nonunion wage andearnings differentials are positiveand statistically significant for bothmales and females. However, dueto smaller unionnonunion hours differentialsfor males, the average union-nonunionearnings differentialfor females is larger thanthe average union-nonunionearnings differential formales.8. An increase in female uniondensity reduces the male-femaleearnings differentialmore than the male-femalewage differential. Thisresult makes sense sinceanincrease in female uniondensity would reduce themale-female hours differentialChapter 4. Conclusion90due to larger positive union hours effectsfor females, and hence would reducethemale-female earnings differentialmore.9. There is strongevidencethat unions reducewagedispersion, but only weak evidencethat unions reduce hours dispersion.There are several ways to extendthis thesis both theoreticallyand empirically. First,one could possibly examine unioneffects on wages, hoursand employment in a generalequilibrium model in orderto obtain a more completepicture of the union impactson economy. Second, empirically,it may be desirable to controlfor absenteeism, workschedules and nonwagebenefitsin hours equationsin order to obtaintrueunion-nonunionhours differential. Since workersin the union sector aremore likely to work on theshiftwork schedules, have higherabsence rates, and receivelarger nonwage benefits,all ofwhich are believed tolead to longer hours ofwork, it could bedue to the omissionof such variables in the hoursequations that we obtain positiveunion-nonunion hoursdifferentials.Differentials in wage, hours,earnings and employmentbetween union andnonunionsectors indicate thatunions change the use ofproduction factorsin order to create wageand earnings premiumsfor their members. Thosedifferentials may beconsidered as ameasure of inefficiency,technicalor allocative, causedby unions. On the otherhand, theunion-nonunion differentialsmay lead to greater equalityin the income distribution.Asis seen in chapter4 in this thesis, low incomegroups such as part-timeworkers gain mostfrom unionization in termsof wage and earnings.Also, the male-femaledifferential inearnings is reduced becauseof the larger union-nonunionhours differentialfor females.The overall impacts of unionson our society are thereforenot clear-cut.What unions representis an issue that hasnot been settled to date.Some peopleargue that the unionrepresents its members’opinions while othersargue that the unionChapter 4. Conclusion91simply represents its leader’s opinions. Both viewsseem too extreme. If we take thefirst view, the union should not care about the sizeof membership and if we accept thesecond view, the union should only act in order to maximizeits leader’s pecuniary andnon-pecuniary benefits. We do not observethese twoextremecases in thereal world. Onething we do know, however, is that unionscan effectively alter employment conditionsof workers and their impacts on our societyare hardly negligible. This leads usto studywhat unions do, but also leadsus to think about what unions can do to improvethewelfare of our society.Appendix AProofto Chapter 2Proofof<O and <OWhenklFirst, we show how to obtain.Equations(2.23) and (2.24) can be simplifiedasfollows:G’=(Al)U-U =kU1H(W- G’)(A2)Substituting (Al) into (A2), weobtainU- U =k(U1WH-HU2)>0(A3)The inequality of the righthand side of (A3) is very importantto determine the signs ofand.Let F be the function such thatF(H; U) = U(WH,T-H)- U-kU1(WH,T-H)WH+kU2(WH,T-H)H (A4)Using the implicit function theorem,we can computeA5dHFwwhereFH = (1 — k)(WU1— U2)— kH(U11W2— 2U12W+U22) (A6)and= (1 — k)HU1+kH2(U12 — WU11)(A7)Hence,dW — (1—k)(WU—U2)—kH(U11W—2U12W+U22)225dH— (1—k)HU1-j-kH(U21—U11W)92Appendix A. Proof to Chapter293With the results above, itis straightforward to obtainSince actual calculationis long and tedious, but straightforward,we are not presenting the stepsof calculation.Instead, we focus on howto calculate%.(Please contact the authorfor detailed calculations.)Taking total differentialof equation (Al) yieldsG”HdN= [(W2— G”N]dH+H(U1Un_U2U11)dw(A8)Then, after dividing (A8)by dH and rearrangingterms, we obtaindN — G”N U,(WU,2—U22)—U(WU,,---U,)H(U,U,2—UU,,)dw1A9G”U,2H+G”U,2H dHBy substituting the resultsfor%into (A7) and rearrangingthe terms, we obtaindN — N kH(WU,—U)(U,1U22—U,)—(1—k)(UU,—2U12U,U+UnU2 26dH — — H+U,2G”H[kH(U22—U,,W)-f-(1—k)U,Now, we prove<0 and <0when k 1.Fromthe assumptionofthe concavityof U we know thatU1122— U2120, and since a concave functionis a quasi-concavefunction it is true thatU2212— 2U12U12+U112 0. The production functionG isassumedto be stronglyconcave, so G”< 0. We also knowthatWU1— U2 > 0 from (2.24).Therefore, we onlyneed to know the signsofU11W2— 2U12W+U22 and U21 — U11Wtodetermine the signsof andft.Recall that theworker’s labour supplycurve is characterizedbyWU1(WH,T— H) — U2(WH,T —H) =0(Al0)Applying the implicitfunction theormto (AlO), one canshowU, H(U,2-WU,,)AlldW— W2U,,_2WU,2+U,,W2U,,_2WU,+U22Equation (All) isnothing but theSlutsky equation.The first part ofthe right handside of (All) isthe substitutioneffect and the secondpart is the incomeeffect. Thedenominationofthe right hand sideof (All) is the secondorder condition ofthe worker’sutility maximizationproblem, so it is negative.Hence, the substitutioneffect is positiveAppendix A. Proof to Chapter 294as expected. We also know that if leisure is a normalgood (hours are an inferior good),the income effect is negative. Therefore,U12— WU11must be positive. Withthese resultsand k 1, we obtain that%<0 andØ<0.Appendix BFigure B.1: Indifference Curvesand The Associated Labour SupplyCurveFigures for Chapter 2LwU’U0SH95Appendix B. Figures for Chapter 296wLal/aJI‘I!‘I,‘I,II,bSHFigure B.2: Possible Equilibrium Outcomes under theMonopoly Union ModelAppendix B. Figures forChapter 297w___CnNFigure B.3: A Representation of the Contract Curvein Wage-Hours-Employment SpaceAppendix B. Figures for Ghapter 2 98w___________HHFigure B.4: Optimal Outcomesunder the Efficient ContractsModelAppendix B. Figures forChapter 2 99wcL*Ua-CUCSHFigure B.5: CompensatingWage Differentials for UnionWorkersAppendix CThe Specification of the LikelihoodFunction in Chapter3Under the joint normality assnmptionof the error terms in thesix equations describedin section 3.3, I specify the likelihoodfunction as follows.The contribution to the likelihoodfunction of a nonworkerisF(—S)(B1)where F is the standard univariatenormal distribution.The contribution to the likelihoodfunction of a union workerisF(S+po,is)P56 13] (B2)ala3a5,13where f is the standard bivariatenormal densityfunction with the correlationcoefficientrq and F is the standard bivariatenormal distributionfunction with thecorrelationcoefficientPij,km isthe mean of e conditionalon e andi,jkis the standarddeviation of e conditionalon e andek andPij,kmis the correlation coefficientbetweene and e conditional one andem.Finally, the contributionof the likelihood functionof a nonunion worker is(€3€4NF(QAp5,24)(S4+pe,24)B3a5,24 C624P56,24where[tj,jk, i,jkandPij,kmare defined asabove.The formulas forthe conditional means, standarddeviations and correlationcoefficients are obtainedusing the propertiesof conditional normal densities.For all i,j, kand in,[i,jk = r1,ke +rI6,ek= (1—100Appendix C. The Specification ofthe LikelihoodFunction in Chapter 3101— rjkr,,kmuk — rjmri,mkomPij,km0i,km’j,kmwhere— — rjJrj— 2(1 — r2r23—2rrkrk+r2kRi,jk= 1—r2Note that the above formulas are obtainedwith the assumption that u5=a6= 1.Appendix DVariances of Error Termsin the Extended H-L Modelin Chapter 3Since the derivation procedures forobtaining the variances ofUkj in equations (3.18)-(3.21) are similar, I oniy presenthow the variance of uiis obtained. Readers can verifythe variances of otherZtkj by following the procedure presented below.Let W1=W2= Suppressingthe subscript i, we canwrite= e1 — 15W1— a16W2(Cl)Note thatE(uiIP= 1,U = 1) = 0. Hence,Var(ttiIP = 1,U = 1)=E(ui2IP= 1,1 = 1)(C2)By substituting (Cl)into (C2), obtainE(ui2jF= 1,U = 1) = E[(ei — oW1— cri6W2)1P= 1, U = 1](C3)The right hand sideof (C3) involves E(eiP= 1,U = 1) andE(ei2IP= 1,U = 1).SinceE(eijP 1,U= 1) =oi5Wi+ui6W2,weon1yneedtofindoutE(eiP= 1,U = 1).Let=E(ei2IP= l,U = 1), a QA and b=S.+00= jei2f(eiIF=l,U=l)deiJjf.jfjei2f(ei,e5,6)dede1F(a)F(b)— jbff(es,e6)L,elf(elIes,e)delde5deC4F(a)F(b)(wheref(.)and F(.) are appropriatenormal density anddistribution functions.Fromtheproperties of conditionnormal density functions,we knowVar(eiIes,e6)=u12(l— R21,56)=u12(l— — r216)(C5)102Appendix D. Variances ofError Terms in the ExtendedH-L Model in Chapter 3 103E(e1e5,e6)=(a15e5+a16e6)(C6)whereris the correlation coefficient betweene3 and ek. Using (C5) and (C6),E(ei2Ies,e6)=a12(1— r215 — r216)+ (aise5+cri6e)2 (C7)By substituting (C7) into(C4), we obtain= u2(1— r215 — r216)+a152ji°e5f(e)f(e6)dedeF(a)F(b)+00 +002u15u16f_b f—aesef(es)f(e)desde+ F(a)F(b)+a252 e62f(es)f(e)sdeC8F(a)F(b)Applying integration by partto (C8) and using the definitionsof W1 and W2,(C8) canbe simplified as=a12— aa215W1— ba216W+2a15a16W12(C9)Finally, by substituting(C9) into (C3) and simplifyingthe terms, the varianceof u1can be found asVar(ujIU=1,P=1)=u12— a152W1(QA+W1)— a162W2(S+W2) (ClO)Now, let W3= F(QA)1and Wi and W2be definedas same as before. Then,Var(u2IU=0,P=1)=a— a252W3(QA+W3)— a262W2(S+ W2)(Cli)Var(u3jU=1,P=1)=a2— a352W1(QA+W1)— a362W2(S4+ W2) (C12)Var(v4IU=0,P=1)=a2— a452W3(QAH- W3)— a462W2(SH-W2)(C13)Appendix EVariances of Union-NonunionDifferentials in Chapter3The variances of the union-nonunionhourly earnings and weekly hoursdifferentials presented in columns (1) and(2) in Table 3.5 are obtainedby the methods shown in thefootnote of section3.5.3. The variances of the rest ofunion-nonuniondifferentials areobtained by the 6-method. Since thederivation proceduresof these differentials are similar,I will only demonstrate how thevariance of the pureweekly hours differential presentedin column (3) is obtained. Thefollowing procedure can bedirectly applied to derivingthe variances of the remainingdifferentials.Denote the union-nonunionpure weekly hours differentialas PWHD. Then, fromequation (3.17) in section3.5.3,FWHD= Zf1(—+ X(Au— A).(Dl)Applying the 6-method,the variance of PWHD canbe shown asSPWHD 8PWHD’80 80where 0 is the vector of(fm,7t,:,A’4’),8P7J-TDis a row vector offirst partialderivatives of PWHD withrespect to 0 and VC(0)is the variance-covariancematrix ofaNote that the variance-covariancematrix of 0 involvescovariances betweenthe estimates of nonunion hourlyearnings equations(fm)and the estimates ofnonunion weeklyhours equations(-f,A”). This is not the casewhen the variance ofthe pure weeklyhours differential isobtained using theOLS and selectivity-adjustedestimates, becausesuch covariances arenot available from thoseestimates.104Appendix FAppendix Tables for Chapter3Note 1: Excluded variables iuestimation are: Age 34-54years, Non-Single, HighSchoolEducation, Ontario, Tenure1-5 years, Manufacturing Industry,Blue Collar Occupation,Private Sector and Small FirmSize.Note: In Tables9 and 10 Select1 is the inverseof Mill’s ratio obtainedfrom the participation equation, i.e.,Select2 is the inverseof Mill’s ratio obtainedfrom theunion status equation. Itis defined as for unionworkers and fornonunionworkers.Note 3: T-statistics arepresented in parentheses.105Appendix F. Appendix Tablesfor Chapter 3106_________Table F.l: Definitions of the VariablesVariable DefinitionsUnioncov Covered bycollective bargaining or memberof a union =1; other =0Head Head of a family=1; other =0ChdOS Number of own childrenof age between 0 an5Unempl Provincial unemploymentrates by sex in April1990A2024 Age 20 to 24=1; other =0A2534 Age 25 to 34=1; other =0A5564 Age 55 to 64=1; other =0Single Single =1; other=0Highschl Some secondaryeducation or graduatedfrom highschool =1;other=0Postsecd Some post-secondary,post-secondary cert. ordiplomaor trades cert. or diploma=1; other =0Univgrad University degree=1; other =0Atlantic Residedin P.E.I., Newfoundland, NovaScotia orNew Brunswick=1; other =0Quebec Residedin Quebec =1; other =0Ontario Resided in Ontario=1; other =0Prairie Resided inManitoba or Saskatchewan=1; other =0Alberta Residedin Alberta =1; other=0TenOl Tenureless than 1 year =1; other=0Ten6lO Tenure6 to 10 years =1; other=0Tenll2O Tenure11 to 20 years =1; other=0Ten20ov Tenure 20 yearsover =1; other=0Primind Forestryor Mining =1; other=0Constrct Construction=1; other =0Service Trade, Financeor Service =1; other=0Trcmut Transportation,Communicationor Utilities =1; other=0Healeduc Healthor Education =1;other =0Pubadm PublicAdministration=1; other =0Wcolrl Managerialor Professional=1; other =0Wcolr2 Clerical,sales or service =1;other =0Public Public sector=1; other =0Medfirm Numberof employees between100 and 499 =1; other=0Bigfirm Numberof employees more than500 =1; other=0Appendix F. Appendix Tables for Chapter3107Table F.2: Sample Means of TheVariablesMaleFemaleVariable UnionNonunion Nonworker UnionNonunion NonworkerHead 0.8460.803 0.751 0.2980.284 0.196ChdO5 0.294 0.3050.279 0.251 0.2060.406Unempl 8.231 7.9978.950 7.453 7.1637.796A2024 0.0500.107 0.1020.051 0.114 0.073A2534 0.3020.350 0.274 0.3340.335 0.266A5564 0.1080.085 0.302 0.0790.084 0.279Single 0.1760.235 0.2860.146 0.1970.114Element0.076 0.067 0.1700.050 0.049 0.169Postsecd0.339 0.329 0.2370.382 0.377 0.229Univgrad 0.1610.187 0.126 0.2360.122 0.077Atlantic0.070 0.075 0.1050.070 0.0700.100Quebec0.301 0.2360.383 0.306 0.2230.332Prairie0.059 0.0690.057 0.071 0.0670.059Alberta0.063 0.1050.065 0.082 0.0930.073BC 0.1280.105 0.105 0.1160.125 0.125TenOl 0.2080.3220.248 0.333Ten6lO 0.1340.1340.141 0.118Tenll2O 0.2330.127 0.2020.099Ten20ov0.144 0.0720.070 0.029Primind0.037 0.0380.006 0.005Constrct 0.0820.108 0.0020.031Service 0.1010.4580.122 0.633Trcmut0.173 0.0790.078 0.031Healeduc0.167 0.0320.512 0.166Pubadm0.170 0.0340.146 0.024Wcolrl0.233 0.3550.471 0.303Wcolr20.208 0.2480.408 0.621Public0.381 0.0630.461 0.065Medfirm0.170 0.1270.212 0.122Bigfirm0.632 0.3290.593 0.341Union Membership0.4580.398Participation Rate0.8410.643NO. of Observations1547 1797647 12361740 1799Appendix F. Appendix Tables for Chapter3108SectorManufactConstructOtherlndBlueCoirMgr/ProfOtherOccFuilTimePartTimePrivatePublicTotalUnion41110110359063752661488599126351547Nonunion389220118885657336817118616511461797Male40594971665225139033842202149613092115960Female41333592059245017733121899129853208619101Table F.3: Construction of theSample Data SetReason for Exclusion1. Full-Time Student at Any Time Duringthe Sample Year2. Age 16-193. Age 64 Over4. Disabled5. Self-Employed or Non-Paid Family Members6. Agricultural Sector Workers7. Workers Who Don’t Know theSize of Their Company9. Total Excluded10. Original Sample11. Final Sample (10.- 9.12. 25% Random Sample of the)Final Sample:a) Workers3344 2976b) Non-Workers647 1799c) Total3991 4775Table F.4: Sample SizesMaleby Sex and SectorFemaleUnion Nonunion121 1844 501111 1506126 153625 455485 1132933 1276303 464598 1601638 1391236 1740Appendix F. Appendix Tables for Chapter3109Table F.5: The OLS Estimatesof Hourly Earnings EquationsMale FemaleVariable UnionNonunion Union NonunionA2024 -0.224(-5.88) -0.203(-4.95)-0.201(-4.61) -0.119(-3.46)A2534 -0.063(-3.33) -0.047(-1.92)0.030(1.42) 0.052(2.26)A5564 0.033(1.26) -0.117(-2.94)-0.033(-0.96) -0.005(-0.15)Single -0.027(-1.22)-0.191(-6.93) -0.066(-2.50)0.029(1.11)Element -0.127(-4.17) -0.045(-0.99) 0.026(0.60)-0.190(-4.02)Postsecd 0.120(6.80)0.121(4.90) 0.127(5.55)0.098(4.47)Univgrad 0.320(11.37)0.275(8.59) 0.337(11.54)0.283(8.45)Atlantic -0.241(-7.84)-0.349(-8.55) -0.181(-5.05)-0.276(-6.94)Quebec -0.096(-5.15)-0.066(-2.49) -0.024(-1.12)-0.049(4.89)Prairie -0.097(-2.92)-0.142(-3.33) -0.119(-3.31)-0.193(-4.80)Alberta -0.075(-2.33)0.003(0.09) -0.062(-1.83)—0.042(-1.19)BC 0.023(0.95)-0.018(-0.49) 0.074(2.52)-0.006(-0.18)TenOl 0.028(1.30)-0.098(-3.83) -0.046(-1.99)-0.049(-2.19)Ten6lO 0.032(1.28)0.086(2.56) 0.072(2.58)0.069(2.16)Tenll2O 0.089(4.08)0.182(5.19) 0.137(5.33)0.151(4.29)Ten20ov 0.135(5.09)0.259(5.71) 0.130(3.40)0.264(4.43)Primind 0.109(2.63)0.205(3.58) -0.092(-0.83)0.206(1.46)Constrct 0.209(6.54)0.155(3.94) 0.415(1.85)-0.002(-0.04)Service -0.079(-2.59)-0.085(-3.00) -0.031(-0.63)-0.131(-3.74)Trcmut -0.001(-0.04)0.074(1.69) 0.194(3.71)0.121(1.95)Healeduc -0.086(-2.73)-0.121(-1.95) 0.076(1.66)-0.076(-1.78)Pubadm -0.042(-1.21)-0.045(-0.51) 0.107(2.01)0.022(0.26)Wcolrl0.021(0.77) 0.199(6.66)0.199(4.11) 0.321(7.10)Wcolr2 0.011(0.50)-0.022(-0.71)0.040(0.87) 0.136(3.22)Public 0.065(2.68)0.013(0.19)0.069(2.98) 0.049(0.93)Medflrm 0.056(2.19)0.095(2.88) 0.099(3.55)0.051(1.62)Bigfirm 0.052(2.43)0.106(4.16) 0.133(5.51)0.141(6.35)Constant 2.698(91.89)2.534(68.54) 2.176(56.72)2.090(45.69)R2 0.2990.361 0.4490.284No of Ohs1547 17971236 1740Appendix F. Appendix Tables for Chapter3 110Table F.6: The Selectivity-UnadjustedEstimates of Weekly Hours Equations,MalesOLS 2SLSVariable Union NonunionUnion NonunionLogwage -0.005(-O.20) -O.042(-2.64)-O.008(-l.36) 0.014(2.29)Head -0.045(-2.17) -O.006(-O.31)-0.047(-2.27) -0.005(-O.26)ChdO5 -O.006(-O.49) -O.005(-0.41)-O.006(-O.50) -0.006(-O.44)Unempl -0.047(-0.69)0.027(0.40) -0.050(-0.73)0.027(0.40)A2024 0.020(0.55)0.016(0.57) 0.013(0.36)0.033(1.16)A2534 -0.018(-0.98)-0.004(-0.20) -0.018(-1.00)-0.001(-0.03)A5564 -0.037(-1.53) -0.047(-1.75) -0.036(-1.48)-0.042(-1.54)Single -0.121(-5.61)-0.042(-2.02) -0.116(-5.30)-0.037(-1.80)Element 0.012(0.43)-0.058(-1.91) 0.011(0.40)-0.060(-1.98)Postsecd 0.010(0.61)-0.010(-0.62) 0.011(0.69)-0.017(-1.03)Univgrad 0.101(3.75)0.005(0.25) 0.104(4.01)-0.015(-0.67)Atlantic 0.100(1.42)-0.029(-0.43) 0.084(1.18)0.022(0.32)Quebec 0.052(1.46)-0.006(-0.16) 0.052(1.46)-0.001(-0.02)Prairie 0.052(1.50)-0.052(-1.57) 0.035(0.97)-0.016(-0.45)Alberta0.098(3.17) -0.005(-0.20)0.085(2.62) 0.017(0.60)BC 0.027(0.95)-0.033(-1.11) 0.023(0.81)-0.024(-0.81)TenOl -0.033(-1.65)0.002(0.14) -0.032(-1.63)0.008(0.45)Ten6lO 0.009(0.42)0.015(0.67) 0.010(0.45)0.007(0.31)Tenll2O 0.001(0.05)-0.046(-1.93) -0.001(-0.03)-0.058(-2.43)Ten20ov -0.003(-0.11)0.009(0.30) -0.002(-0.09)-0.007(-0.23)Primind 0.042(1.11)0.106(2.75)0.038(1.00) 0.104(2.68)Constrct 0.018(0.65)0.058(2.22) 0.022(0.79)0.050(1.89)Service -0.081(-2.95)-0.003(-0.16) -0.076(-2.72)0.002(0.11)Trcmut 0.051(2.09)0.007(0.23) 0.055(2.22)-0.001(-0.02)Healeduc -0.017(-0.59)-0.098(-2.34) -0.016(-0.55)-0.087(-2.07)Pubadm 0.052(1.64)0.109(1.85) 0.055(1.74)0.113(1.92)Wcolrl -0.069(-2.86)0.021(1.02) -0.071(-2.93)0.001(0.04)Wcolr2 -0.024(-1.17)-0.016(-0.79) -0.023(-1.12)-0.021(-1.02)Public-0.063(-2.83) -0.137(-3.09)-0.063(-2.86) -0.134(-3.01)Constant 3.781(47.88)3.842(63.32) 3.800(71.32)3.681(70.26)0.073 0.0400.074 0.039No of Obs 15471797 15471797Appendix F. Appendix Tables for Chapter3111Table F.7: The Selectivity-Unadjusted Estimatesof Weekly Hours Equations, FemalesOLS 2SLSVariable Union NonunionUnion NonunionLogwage 0.075(2.34) -0.029(-1.13)-0.001(-0.13) 0.036(4.48)Head 0.061(2.64)0.076(3.13) 0.068(2.96)0.091(3.73)ChdO5 -0.039(-2.00)-0.137(-6.32) -O.037(-1.89)-0.133(-6.17)Unempi 0.051(0.35)0.205(1.32) 0.053(0.36)0.237(1.53)A2024 -0.036(-0.73)0.076(2.03) -0.051(-1.03)0.098(2.65)A2534 0.062(2.53)0.106(4.10) 0.065(2.61)0.107(4.16)A5564 -0.121(-3.16)-0.022(-0.57) -0.125(-3.25)-0.024(-0.62)Single 0.079(2.49)0.053(1.76) 0.072(2.28)0.023(0.75)Element 0.024(0.50)-0.105(-2.08) 0.025(0.51)-0.089(-1.77)Postsecd 0.045(1.72)0.002(0.11) 0.056(2.15)-0.010(-0.42)Univgrad 0.018(0.51)-0.047(-1.29) 0.045(1.35)-0.077(-2.14)Atlantic -0.006(-0.04)-0.176(-1.33) -0.024(-0.19)-0.110(-0.83)Quebec -0.085(-1.31)-0.071(-1.02) -0.089(-1.37)-0.072(-1.05)Prairie 0.013(0.30)-0.147(-3.02) 0.001(0.02)-0.071(-1.41)Alberta 0.005(0.09)-0.042(-0.83) -0.003(-0.06)0.010(0.20)BC -0.035(-0.62) -0.147(-2.51)-0.031(-0.55) -0.157(-2.68)TenOl -0.005(-0.20)0.006(0.23) -0.009(-0.35)0.009(0.39)Ten6lO 0.059(1.88)0.030(0.87) 0.065(2.06)0.028(0.81)Tenll2O 0.111(3.84)0.045(1.21) 0.123(4.24)0.034(0.91)Ten2Oov 0.137(3.19)0.048(0.75) 0.148(3.47)0.023(0.36)Primind 0.257(2.06)-0.071(-0.47)0.250(2.00) -0.056(-0.37)Constrct -0.182(-0.73)-0.155(-2.31)-0.157(-0.63) -0.159(-2.38)Service -0.098(-1.79) -0.095(-2.53) -0.100(-1.82)-0.090(-2.43)Trcmut -0.037(-0.62)-0.226(-3.39) -0.019(-0.33)-0.223(-3.37)Healeduc -0.108(-2.09)-0.193(-4.25) -0.101(-1.95)-0.182(-4.03)Pubadm -0.002(-0.03)0.172(1.84) 0.009(0.15)0.180(1.95)Wcolrl -0.125(-2.26)-0.021(-0.42) -0.113(-2.04)-0.049(-1.02)Wcolr2 -0.086(-1.66)-0.181(-4.00) -0.084(-1.63)-0.191(-4.27)Public -0.023(-0.90)-0.175(-3.14) -0.017(-0.67)-0.181(-3.27)Constant 3.377(30.66)3.634(34.02) 3.549(39.57)3.433(35.37)0.103 0.1190.099 0.129No of Obs 12361740 12361740Appendix F. Appendix Tables forChapter 3112Table F.8: The Probit Estimates of Participationand Union Status EquationsParticipationUnion StatusVariable Male FemaleMale FemaleHead 0.258(3.81)0.340(6.80) -0.052(-0.70)0.087(1.30)ChdO5 -0.190(-4.12) -0.479(-13.77)-0.041(-0.88) 0.087(1.55)Unempi -0.300(-1.41)0.003(0.01) 0.298(1.18)0.349(0.82)A2024 0.035(0.34)0.164(2.03) -0.192(-1.65)-0.110(-0.92)A2534 0.057(0.86)0.161(3.14) 0.066(0.99)0.065(0.91)A5564 -0.957(-13.07) -0.923(-15.75)0.005(0.05) -0.153(-1.47)Single -0.413(-5.62)-0.175(-2.68)0.080(0.99) -0.171(-1.95)Element -0.157(4.83)-0.456(-6.37) -0.198(-1.87) 0.171(1.32)Postsecd 0.238(3.94)0.419(9.09) 0.014(-0.24)0.046(0.68)Univgrad 0.196(2.56)0.606(9.16) -0.245(-2.66)-0.087(-0.93)Atlantic -0.107(-0.47)-0.350(-1.51) -0.166(-0.64)-0.226(-0.63)Quebec -0.260(-2.24)-0.281(-2.29) 0.289(2.19)0.225(1.19)Prairie -0.016(-0.13)0.035(0.37) -0.057(-0.45)0.077(0.58)Alberta -0.050(-0.46)-0.036(-0.37) -0.342(-3.12)-0.202(-1.40)BC -0.090(-0.86)-0.190(-3.59) 0.321(2.87)0.224(1.39)TenOl-0.178(-2.57) -0.177(-2.52)Ten6lO0.125(1.49) 0.093(1.01)Tenll2O0.170(2.09) 0.269(3.01)Ten20ov0.191(1.91) 0.252(1.79)Primind-0.0002(-0.001) 0.281(0.81)Constrct0.196(2.05) -1.400(-4.13)Service-0.454(-5.66) -0.708(-6.62)Trcmut0.087(0.91) 0.255(1.72)Healeduc1.358(11.66) 0.602(5.24)Pubadm0.367(2.48) 0.285(1.71)Wcolrl-1.150(-13.92)-0.629(-4.91)Wcolr2-0.516(-6.69) -0.653(-5.58)Public1.056(9.56) 0.937(10.15)Medfirm0.707(8.70) 0.611(7.39)Bigfirm0.959(14.75)0.666(9.92)Constant1.376(9.39)0.519(3.59) -0.766(-4.23)-0.625(-2.55)Log-Likelihood-1582-2682-1557 -1298No of Obs3991 477533442976Appendix F. AppendixTables for Chapter3113Table F.9: TheSelectivity-Adjusted Estimatesof Hourly EarningsEquationsMaleFemaleVariable UnionNonunionUnion NonunionA2024 -0.206(-4.03)-0.177(-3.30)-0.199(-2.46) -0.119(-2.26)A2534 -0.059(-2.33)-0.047(-L34) 0.033(1.19)0.051(1.33)A5564 0.184(1.86)0.017(0.15) -O.011(-0.17)-0.137(-2.03)Single0.025(0.62) -O.152(-2.91)-0.072(-1.84)0.033(0.72)Element -0.088(-2.02)0.004(0.04) 0.045(0.69)-0.246(-4.79)Postsecd 0.091(2.63)0.095(2.67) 0.116(3.38)0.150(4.05)Univgrad 0.300(7.27)0.275(5.19) 0.322(7.07)0.343(5.35)Atlantic -0.189(-5.01)-0.313(-4.75) -0.171(-4.80)-0.321(-8.93)Quebec -0.045(-1.21)-0.061(-1.15) -0.013(-0.32)-0.060(-1.16)Prairie -0.085(-2.46)-0.134(-3.27) -0.115(-3.13)-0.187(-5.01)Alberta -0.061(-1.66)0.031(0.79) -0.062(-1.68)-0.054(-1.36)BC 0.038(1.17)-0.041(-0.72)0.085(1.88)-0.009(-0.20)TenOl 0.030(0.84)-0.082(-2.38)-0.049(-1.30) -0.061(-1.79)Ten6lO0.030(0.82)0.075(1.35) 0.072(2.29)0.078(1.76)Teni1200.088(2.93)0.162(3.38)0.139(3.85) 0.172(3.02)Ten2Oov 0.131(3.34)0.234(4.02) 0.134(2.16)0.288(3.66)Primind0.105(2.95) 0.207(4.28)-0.087(-0.64) 0.209(2.08)Constrct0.212(4.08) 0.146(3.42)0.374(1.42) -0.070(-0.64)Service -0.070(-1.13) -0.046(-1.13)-0.045(-0.44)-0.175(-2.63)Trcmut-0.008(-0.21)0.060(0.82)0.202(2.72)0.132(1.81)Healeduc -0.098(-1.52)-0.293(-2.81)0.090(1.27)-0.038(-0.56)Pubadm-0.049(-1.04)-0.091(-0.82)0.115(1.55)0.021(0.18)Wcolrl 0.029(0.50)0.306(4.76)0.185(2.41) 0.286(3.98)Wcolr20.014(0.34)0.028(0.54)0.025(0.32)0.094(1.26)Public 0.059(1.22)-0.120(-1.17)0.081(1.13)0.169(1.16)Medfirm0.050(1.00)0.030(0.55)0.110(1.67)0.097(1.30)Bigfirm0.046(0.85)0.017(0.27)0.145(2.12)0.175(3.25)Selecti-0.408(-1.81) -0.361(-1.45) -0.053(-0.64)0.252(3.16)Select2-0.016(-0.17)-0.224(-2.15)0.031(0.19)0.158(0.81)Constant2.784(23.42)2.483(31.77) 2.173(11.27)2.056(15.01)R20.3030.3640.449 0.290No of Obs1547 179712361740Appendix F. Appendix Tablesfor Chapter 3114Table F.10: The Selectivity-AdjustedEstimates of Weekly HoursEquationsMale FemaleVariable UnionNonunion UnionNonunionLogwage -0.437(-0.71) -0.041(-0.04)0.813(1.52) -0.088(-0.33)Head 0.021(0.69) -0.053(-1.11)0.048(0.79) 0.105(1.35)ChdO5 -0.047(-2.24)0.024(0.80) 0.011(0.13) -0.210(-1.78)Unempi -0.131(-2.19)0.081(1.25) 0.091(1.04)0.166(1.39)A2024 -0.058(-0.48)0.012(0.06) 0.083(0.87)0.093(1.68)A2534 -0.032(-0.64)-0.014(-0.25) 0.026(0.67)0.121(2.72)A5564 -0.267(-1.42)0.148(0.93) -0.039(-0.20)-0.141(-0.52)Single -0.209(-2.35)0.025(0.16) 0.133(2.79)0.045(0.88)Element -0.080(-1.29)-0.016(-0.21) 0.066(0.62) -0.213(-1.39)Postsecd 0.104(1.37)-0.047(-0.47) -0.077(-0.82)0.050(0.35)Univgrad 0.278(1.37)-0.024(-0.82) -0.028(-1.32)0.041(0.49)Atlantic 0.005(0.04)-0.013(-0.39) 0.127(1.12)-0.206(0.27)Quebec -0.031(-0.65)0.033(0.45) -0.041(-0.64)-0.126(-1.26)Prairie 0.014(0.26)-0.051(-0.36) 0.104(1.29)-0.150(-2.08)Alberta 0.067(1.71)0.003(0.01) 0.040(0.77)-0.031(-0.66)BC 0.023(0.43)-0.025(-0.43) -0.067(-1.00)-0.186(-2.60)TenOl -0.015(-0.27)0.005(0.05) 0.019(0.55)0.018(0.55)Ten6lO 0.022(0.69)0.010(0.13) 0.012(0.24)0.030(0.62)Tenll2O 0.037(0.66)-0.052(-0.28) 0.020(0.26)0.010(0.17)Ten20ov 0.051(0.62)0.002(0.01) 0.044(0.49)0.007(0.07)Primind 0.089(1.22)0.105(0.48) 0.035(3.33)-0.081(-0.47)Constrct 0.108(0.89)0.055(0.37) -0.601(-0.10)-0.027(-0.35)Service -0.098(-0.95)-0.001(-0.01) -0.131(-1.40)-0.021(-0.47)Trcmut 0.049(1.75)0.002(0.03) -0.172(-1.52)-0.253(-2.73)Healeduc -0.080(-0.97)-0.116(-0.33) -0.124(-2.11)-0.256(-3.52)Pubadm 0.026(0.48)0.107(0.81) -0.060(-0.71)0.154(1.06)Wcolrl -0.039(-0.68)0.026(0.07) -0.315(-2.00)0.064(0.50)Wcolr2 -0.007(-0.18)-0.016(-0.29) -0.162(-1.93)-0.102(-1.30)Public -0.053(-1.14)-0.147(-0.64) -0.025(-0.50)-0.362(-2.88)Selecti 0.693(2.09)-0.483(-1.15) -0.172(-0.53)0.233(0.53)Select2 -0.039(-0.73)-0.009(-0.15) 0.140(0.90)-0.270(-1.78)Constant 4.911(2.78)3.919(1.47)1.661(1.23)3.470(6.55)R2 0.0780.040 0.1010.132No of Obs 15471797 12361740Appendix F. Appendix Tablesfor Chapter 3115Table F.11: The ML Estimatesof Participation and Union StatusEquationsParticipationUnion StatusVariable MaleFemale MaleFemaleHead 0.268(3.71)0.223(4.22) -0.051(-0.57)0.011(0.12)ChdO5 -0.169(-3.78) -0.429(-12.55)0.043(0.91) 0.155(0.97)Unempi -0.324(-2.68)0.053(0.36) 0.384(2.54)0.338(1.45)A2024 0.092(0.89)0.106(1.23) -0.201(-1.58)-0.030(-0.23)A2534 0.031(0.46)0.091(1.72) -0.044(-0.63)-0.014(-0.17)A5564 -0.980(-13.78)-0.974(-16.24) -0.038(-0.22)0.098(0.25)Single -0.419(-5.38)-O.0O1(-0.02) 0.094(0.92)-0.138(-1.36)Element -0.165(-2.07)-0.472(-6.72) -0.070(-0.64)0.187(0.78)Postsecd 0.179(2.96)0.441(9.60) -0.027(-0.41)0.065(0.39)Univgrad 0.472(5.11)0.772(10.57) -0.201(-2.06)-0.063(-0.25)Atlantic -0.039(-0.26)-0.355(-2.52) -0.254(-1.48)-0.212(-0.83)Quebec -0.255(-2.55)-0.307(-3.45) 0.275(2.45)0.226(1.37)Prairie 0.062(0.61)0.026(0.36) -0.057(-0.57)0.035(0.36)Alberta -0.069(-0.69)-0.081(-1.03) -0.364(-3.63)-0.200(-1.68)BC -0.106(-1.00)-0.226(-2.52) 0.268(2.35)0.155(1.04)TenO1-0.200(-2.73) -0.230(-3.29)Ten6lO0.030(0.34) 0.102(1.05)Tenll2O0.146(1.75) 0.227(2.34)Ten20ov0.174(1.67) 0.202(1.22)Primind-0.043(-0.38) 0.233(0.90)Constrct0.056(0.54) -0.652(-1.86)Service-0.522(-5.86) -0.472(-3.76)Trcmut0.087(0.85) 0.230(1.37)Healeduc1.228(10.85) 0.763(5.61)Pubadm0.241(1.67)0.294(1.65)Wcolrl-1.054(-13.14) -0.548(-3.84)Wcolr2-0.489(-5.85) -0.633(-4.79)Public0.986(9.16) 0.894(9.61)Medfirm0.800(9.73) 0.683(7.56)Bigfirm1.018(15.47)0.784(10.78)Constant 1.372(11.16)0.488(5.26)-0.770(-4.64) -0.733(4.79)No of Obs 399147753344 2976Appendix F. Appendix Tables for Chapter3116Table F.12: The ML Estimatesof Hourly Earnings EquationsMale FemaleVariable UnionNonunion UnionNonunionA2024 -0.245(-6.03)-0.199(-4.22) -0.155(-3.32)-0.097(-2.37)A2534 -0.084(-4.07)-0.043(-1.49) -0.009(-0.38)0.038(1.55)A5564 0.050(1.61)-0.030(-0.72) -0.080(-1.61)-0.087(-1.59)Single -0.009(-0.30)-0.115(-3.32) -0.040(-1.32)0.014(0.43)Element -0.101(-3.05)-0.041(-0.85) -0.056(-1.12)-0.192(-3.39)Postsecd 0.073(3.67)0.096(3.27) 0.088(2.81)0.113(4.22)Univgrad 0.281(9.24)0.239(6.49) 0.315(7.81)0.337(8.29)Atlantic -0.186(-6.93)-0.257(-7.33) -0.137(-4.39)-0.266(-7.68)Quebec -0.046(-1.49)-0.056(-1.27) 0.038(1.14)-0.089(-2.30)Prairie -0.065(-2.16)-0.137(-3.43) -0.091(-3.04)-0.172(-5.08)Alberta -0.040(-1.22)0.009(0.24) -0.043(-1.31)-0.048(-1.39)BC 0.041(1.17)0.032(0.69) 0.111(2.58)-0.050(-1.28)TenOl -0.004(-0J8)-0.082(-2.91) -0.029(-1.13)-0.043(-1.74)Ten6lO 0.028(1.02)0.105(2.64) 0.067(1.89)0.105(3.21)Tenll2O 0.084(3.42)0.123(3.48) 0.110(3.70)0.190(5.19)Ten2Oov 0.115(3.75)0.198(3.78) 0.165(4.44)0.194(2.97)Primind 0.085(2.29)0.146(3.03) -0.165(-1.95)0.262(2.17)Constrct 0.196(5.25)0.112(2.06) 0.340(1.34)-0.034(-0.49)Service -0.095(-2.36)-0.058(-1.55) -0.093(-1.62)-0.142(-2.97)Trcmut 0.002(0.05)-0.018(-0.39) 0.117(1.95)0.034(0.60)Healeduc-0.097(-2.22) -0.197(-2.15)0.017(0.34) -0.073(-1.13)Pubadm -0.023(-0.59)-0.089(-0.96) 0.045(0.76)0.058(0.67)Wcolrl0.065(1.77) 0.152(3.06)0.232(4.98) 0.275(4.91)Wcolr20.008(0.29) -0.082(-2.03)0.064(1.37) 0.091(1.74)Public0.032(1.02) 0.105(1.22)0.073(2.20) 0.085(0.90)Medfirm0.046(1.56) 0.084(1.83)0.108(3.01) 0.062(1.42)Bigfirm0.062(2.08) 0.125(2.69)0.124(3.58) 0.123(2.76)Constant 2.741(49.57)2.530(40.35) 2.212(26.59)2.065(27.39)Log-Likelihood-39671-49326No of Obs1547 17971236 1740Appendix F. Appendix Tables forChapter 3117Table F.13: The ML Estimatesof Weekly Hours EquationsMaleFemaleVariable UnionNonunion UnionNonunionLogwage -0.582(-1.68) -0.019(-0.06) -0.404(-1.61)0.128(0.27)Head -0.004(-0.14)0.001(0.05) 0.061(1.33)0.105(2.65)ChdO5 -0.007(-0.44)0.002(0.11) -0.067(-0.91)-0.125(-2.73)Unempl -0.016(-0.46)0.003(0.05) 0.065(0.61)0.149(1.65)A2024 -0.152(4.60)0.013(0.17) -0.042(-0.56)0.117(1.59)A2534 -0.041(-1.04) 0.009(0.32)0.050(1.44) 0.100(2.42)A5564 0.009(0.21)-0.056(-1.71) -0.107(-0.56)-0.088(-0.80)Single -0.092(-2.78)-0.029(-0.60) 0.070(1.22)0.041(0.73)Element-0.016(-0.32) 0.029(0.80)-0.011(-0.09) -0.077(-0.65)Postsecd0.039(1.10) -0.033(-0.78)0.067(0.81) 0.013(0.19)Univgrad 0.198(1.84)-0.025(-0.28) 0.162(1.05)-0.146(-0.87)Atlantic-0.051(-0.60) 0.012(0.11)-0.100(-0.81) -0.061(-0.42)Quebec -0.042(-0.96)-0.009(-0.17) -0.095(4.24)-0.053(-0.64)Prairie -0.021(-0.48)-0.041(-0.67) -0.040(-0.80)-0.125(-1.32)Alberta0.073(1.83) 0.026(0.74)-0.017(-0.33) -0.014(-0.29)BC 0.011(0.32)-0.008(-0.20) -0.010(-0.14)-0.154(-2.54)TenOl0.023(0.89) 0.001(0.04)0.009(0.30) 0.037(1.20)Ten6lO 0.022(0.68)0.000(-0.01) 0.050(1.15)-0.007(-0.12)Tenll2O 0.040(0.91)-0.002(-0.04) 0.145(2.86)0.044(0.45)Ten2Oov 0.054(0.95)0.019(0.24) 0.166(2.37)0.048(0.37)Primind0.141(3.12) 0.090(1.31)0.171(0.80) -0.012(-0.06)Constrct 0.178(2.52)0.039(0.67) 0.073(0.51)-0.163(-1.58)Service -0.034(-0.63)-0.007(-0.19) -0.020(-0.26)-0.074(-0.85)Trcmut0.036(1.02) 0.072(1.70)-0.044(-0.48) -0.274(-3.21)Healeduc-0.131(-2.01) -0.170(-1.32)-0.210(-2.92) -0.258(-2.30)Pubadm-0.013(-0.26) 0.141(1.77)-0.058(-0.68) 0.035(0.30)Wcolrl 0.070(1.47)0.025(0.30) 0.071(0.77)-0.043(-0.24)Wcolr20.013(0.35) -0.015(-0.41)-0.005(-0.07) -0.192(-1.79)Public-0.076(-2.32) -0.224(-4.49)-0.080(-2.20) -0.217(-2.49)Constant5.405(5.55) 3.782(4.57)4.684(7.71) 3.268(3.46)Log-Likelihood-39671-49326No of Ohs154717971236 1740Bibliography[1] Abowd, J.M. and Farber,H.S (1982), “Job Queuesand the Union Statusof Workers.” Industrial and Labor RelationsReview Vol. 67,354-76.[2] Allen, S.G. 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