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31E00700 Labor Economics:Lecture 4Matti Sarvimäki8 Nov 2012

IntroductionShort-RunLong-RunDoes Work-Sharing Work?First Part of the Course: Outline1Supply of labor1static labor supply: basics2static labor supply: bene ts and taxes3intertemporal labor supply2Demand for labor3Labor market equilibrium31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?IntroductionLabor demand is derived demand Firms hire workers and buy capital to produce goods andservices that consumers want31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?IntroductionLabor demand is derived demand Firms hire workers and buy capital to produce goods andservices that consumers wantLabor demand is importantstrong demand leads to high wages and low unemployment. and subject to a lot of regulationminimum wages, maximum hours, safety regulation,anti-discrimination laws etc.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?IntroductionLabor demand is derived demand Firms hire workers and buy capital to produce goods andservices that consumers wantLabor demand is importantstrong demand leads to high wages and low unemployment. and subject to a lot of regulationminimum wages, maximum hours, safety regulation,anti-discrimination laws etc.Today we will study demand for labor in theshort-runlong-run( rms can adjust only labor inputs)( rms can adjust all inputs)and the impact of maximum hours policy on employment31E00700 Labor Economics: Lecture 4Matti Sarvimäki

Labor and Capital

Decreasing Marginal Product of Labor(aka André must go )

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Marginal and average productThe total product curve gives the relationship between output and the numberof workers hired by the rm (holding capital xed). The marginal product curveshows the output produced by each additional worker, and the average productcurve shows output per worker.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

Labor Demand in the Short-RunFirm's problemmax{E }pf E , K wE rKp the price of the output, f E , K is the production function, Eemployee-hours, K the ( xed) capital stock, w wage rate and r rentalwhererate of capital is

Labor Demand in the Short-RunFirm's problemmax{E }pf E , K wE rKp the price of the output, f E , K is the production function, Eemployee-hours, K the ( xed) capital stock, w wage rate and r rental whererate of capitalFirst-Order-ConditionpfE E , K wi.e. value of the marginal product of labor,price of the unit of labor.VMPE pfe ( ), equals theis

Labor Demand in the Short-RunFirm's problemmax{E }pf E , K wE rKp the price of the output, f E , K is the production function, Eemployee-hours, K the ( xed) capital stock, w wage rate and r rental whererate of capitalFirst-Order-ConditionpfE E , K wi.e. value of the marginal product of labor,VMPE pfe ( ), equals theprice of the unit of labor.This yields the short-run labor demand curve for the rmEsrd Ew , p, K is

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Labor Demand in the Short-Run38VAPE22VMPE148Number of WorkersA pro t-maximizing rm hires workers up to the point where the wage rateequals the value of marginal product of labor (left panel). This corresponds tothe marginal cost of production being equal to the output price (right panel).31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Labor Demand in the Short-Run38VAPE22VMPE148Number of WorkersA pro t-maximizing rm hires workers up to the point where the wage rateequals the value of marginal product of labor (left panel). This corresponds tothe marginal cost of production being equal to the output price (right panel).For example, if the wage is 22, the rm hires eight workers. However, if thewage is 38, the value of average product of labor would be less than the wage the rm does not hire anyone31E00700 Labor Economics: Lecture 4Matti Sarvimäki

Firm-level short-run labor demand curve123dδ Esrδwdδ Esrδpdδ EsrδK 0 (downward sloping due to decreasing marginal cost) 0 (increase in output price higher value of marginal product) 0 (more capital higher marginal product)

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Short-run labor demand curve 60EmploymentIf the wage rate falls, all the rms in the industry will increase their output. As aresult, the price of the output will decrease and labor demand will adjust downwards31E00700 Labor Economics: Lecture 4Matti Sarvimäki

Labor Demand in the Long-RunFirm's problemmax{E ,K }pf (E , K ) wE rK[as before, but now the rm chooses the level of laborand capital]

Labor Demand in the Long-RunFirm's problemmax{E ,K }pf (E , K ) wE rK[as before, but now the rm chooses the level of laborand capital]EquilibriumThe FOCs are pfE (E , K ) w and pfK (E , K ) r , hencefE (E , K )fK (E , K ) wri.e. the slope of the isoquant curve equals the slope of the isocost line

Labor Demand in the Long-RunFirm's problemmax{E ,K }pf (E , K ) wE rK[as before, but now the rm chooses the level of laborand capital]EquilibriumThe FOCs are pfE (E , K ) w and pfK (E , K ) r , hencefE (E , K )fK (E , K ) wri.e. the slope of the isoquant curve equals the slope of the isocost lineDuality: We get the same result from solvingmin{E ,K }wE rKs.t.fk (E , K ) q0

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Isoquant CurvesCapitalXΔKYq1q0ΔEEmploymentAll capital-labor combinations that lie on a single isoquant produce the samelevel of output. The input combinations at points X and Y produce q9 units ofoutput. Combinations of input bundles that lie on higher isoquants mustproduce more output. The slope of the isoquant curve corresponds to themarginal rate of technical substitution31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Isocost LinesCapitalC1/rC0/rIsocost with Cost Outlay C1Isocost with Cost Outlay C0C0/wC1/wEmploymentAll capital-labor combinations that lie on a single isocost curve are equallycostly. Capital-labor combinations that lie on a higher isocost curve are morecostly. The slope of an isoquant equals the ratio of input prices wr .31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?The Firm's Optimal Combination of InputsCapitalC1/rAC0/rP175Bq0100EmploymentA rm minimizes the cost of producing q0 units of output by using thecapital-labor combination at point P, where the isoquant is tangent to theisocost. All other capital-labor combinations (such as those given by points Aand B) lie on a higher isocost curve.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Impact of Wage Decreas on the Long RunDemand for Labor1Scale e ect:The rm takes advantage of the lower price oflabor by expanding production2Substitution e ect:The rm takes advantage of the wagechange by rearranging its mix of inputs31E00700 Labor Economics: Lecture 4Matti Sarvimäki

The Impact of a Wage Reduction(Holding Costs Constant)CapitalC0/rRP75ʹ′q0Wage is w025Wage is w140A wage reduction attens the isocost curve. If the rm were to hold the initialcost outlay constant at C0 , the isocost would rotate around C0 and the rmwould move from point P to point R. A pro t-maximizing rm, however, willnot generally want to hold the cost outlay constant when the wage changes.

IntroductionShort-RunLong-RunDoes Work-Sharing Work?The Impact of a Wage Reduction on the Outputand Employment of a Pro t-Maximizing mploymentA wage cut reduces the marginal cost of production and encourages the rm toexpand (from producing 100 to 150 units). The rm moves from point P topoint R, increasing the number of workers hired from 25 to 50.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Substitution and Scale E ectsCapitalDC1/rQC0/rRP200D100Wage is w1Wage is w0254050EmploymentA wage cut generates substitution and scale e ects. The scale e ect (from Pto Q) encourages the rm to expand, increasing the rm's employment. Thesubstitution e ect (from Q to R) encourages the rm to use a morelabor-intensive method of production, further increasing employment.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Short- and Long-Run Demand CurvesDollarsShort-RunDemand CurveLong-RunDemand CurveEmploymentIn the long run, the rm can take full advantage of the economic opportunitiesintroduced by a change in the wage. As a result, the long-run demand curve ismore elastic than the short-run demand curve.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Elasticity of SubstitutionThe elasticity of substitution (K /E ) (w /r )σ /K /Ew /ri.e. the percentage change in the capital to labor ratio given a percentagechange in the price ratio (wages to real interest).31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Elasticity of SubstitutionThe elasticity of substitution (K /E ) (w /r )σ /K /Ew /ri.e. the percentage change in the capital to labor ratio given a percentagechange in the price ratio (wages to real interest).Interpret as the percentage change in the capital labor ratiogiven a 1% change in the relative price of labor to capitalExample: If the elasticity of substitution is 5, then a 10%increase in the ratio of wages to the price of capital wouldresult in the rm increasing its capital-to-labor ratio by 50%.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Elasticity of Substitution: The Extreme CasesCapital and labor are perfect substitutes (σ ) if the isoquant is linear (twoworkers can always be substituted for one machine). The two inputs are perfectcomplements (σ 0) if the isoquant is right-angled (the rm then gets thesame output when it hires 5 machines and 20 workers as when it hires 5machines and 25 workers)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Marshall's Rules of Derived DemandLong-run elasticity of labor demand ELR ELR /ELR δLR w /w w31E00700 Labor Economics: Lecture 4 wELRMatti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Marshall's Rules of Derived DemandLong-run elasticity of labor demand ELR ELR /ELR δLR w /w w wELRMarshall's Rules: Labor Demand is more elastic (δLR larger) whenelasticity of substitution is greater(see above)elasticity of demand for rm's output is greater(higher wages lead to higher prices elastic demand means large cut inoutput rms cut employment heavily)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Marshall's Rules of Derived DemandLong-run elasticity of labor demand ELR ELR /ELR δLR w /w w wELRMarshall's Rules: Labor Demand is more elastic (δLR larger) whenelasticity of substitution is greater(see above)elasticity of demand for rm's output is greater(higher wages lead to higher prices elastic demand means large cut inoutput rms cut employment heavily)the labor's share in total costs of production is greater(if production is labor intensive, even a small increase in wagessubstantially increases marginal cost of production)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Marshall's Rules of Derived DemandLong-run elasticity of labor demand ELR ELR /ELR δLR w /w w wELRMarshall's Rules: Labor Demand is more elastic (δLR larger) whenelasticity of substitution is greater(see above)elasticity of demand for rm's output is greater(higher wages lead to higher prices elastic demand means large cut inoutput rms cut employment heavily)the labor's share in total costs of production is greater(if production is labor intensive, even a small increase in wagessubstantially increases marginal cost of production)the supply elasticity of other factors of production is greater(more expensive to substitute workers to capital if the price of capital isvery responsive to demand for capital)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Factor Demand with Many InputsMany di erent inputsSkilled and unskilled labor, old and young workers, old andnew machines.31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Factor Demand with Many InputsMany di erent inputsSkilled and unskilled labor, old and young workers, old andnew machines.Cross-elasticity of factor demand xi /xi w j /w ji.e. the percent change in the demand for input i given a percentage change inthe price of input jSubstitutes: cross-elasticity positiveComplements: cross-elasticity negative31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?The Demand Curve for a Factor of Production isA ected by the Prices of Other InputsPrice ofinput iPrice ofinput iD0D1D0Employment ofinput iD1Employment ofinput iThe labor demand curve for input i shifts up if the price of a substitutable inputrises (left panel) and down if the price of a complement rises (right panel)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Work-SharingMany people believe that the amount of work is xedIf so, unemployment follows from not sharing this work equally decreasing working hours will help the unemployed31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Work-SharingMany people believe that the amount of work is xedIf so, unemployment follows from not sharing this work equally decreasing working hours will help the unemployedHunt (1999) examines the issue empirically by focusing on areduction of standard hours in GermanyIdenti cation problem: Many things can happen simultaneouslywith the working hours reform (e.g. business cycle)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Work-SharingMany people believe that the amount of work is xedIf so, unemployment follows from not sharing this work equally decreasing working hours will help the unemployedHunt (1999) examines the issue empirically by focusing on areduction of standard hours in GermanyIdenti cation problem: Many things can happen simultaneouslywith the working hours reform (e.g. business cycle)Solution: Exploit the fact that cuts in regulard hours weremade on industy-by-industry basis31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Work-SharingMany people believe that the amount of work is xedIf so, unemployment follows from not sharing this work equally decreasing working hours will help the unemployedHunt (1999) examines the issue empirically by focusing on areduction of standard hours in GermanyIdenti cation problem: Many things can happen simultaneouslywith the working hours reform (e.g. business cycle)Solution: Exploit the fact that cuts in regulard hours weremade on industy-by-industry basisTakeaway: (a) hours ,(b) wages ,(c) statisticallyinsigni cant estimates for employment e ect31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?BackgroundGerman unions negotiate industry level minimum wages,regular hours, vacations.(agreements also bind non-union members)After a IG Metall strike in 1984 regular hours for metalworkersreduced from 40 to 38.5 starting from 1985Other unions followed(and IG Metall pushed metalworkers hours to 35 by 1995)Hours cuts accompanied with full wage compenstation (not clear what this means)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

ModelFirm's problemmax g (h, N , K ) whN fN pw (h hs ) N rK{h,N ,K }where g ( ) is the production funtion, h hours per worker, N number of workers, Kcapital, w wages, f a xed-cost of hiring a worker, p overtime premium, hs standardhours (anything above this is overtime) and r rental rate of capital.

ModelFirm's problemmax g (h, N , K ) whN fN pw (h hs ) N rK{h,N ,K }where g ( ) is the production funtion, h hours per worker, N number of workers, Kcapital, w wages, f a xed-cost of hiring a worker, p overtime premium, hs standardhours (anything above this is overtime) and r rental rate of capital.Marginal costs of an extra worker and hourMCNMCH wh f pw (h hs )(1 p ) wh

ModelFirm's problemmax g (h, N , K ) whN fN pw (h hs ) N rK{h,N ,K }where g ( ) is the production funtion, h hours per worker, N number of workers, Kcapital, w wages, f a xed-cost of hiring a worker, p overtime premium, hs standardhours (anything above this is overtime) and r rental rate of capital.Marginal costs of an extra worker and hourMCNMCH wh f pw (h hs )(1 p ) wh The impact of an reduction in12hs(Fig. 1)h hs : N (substitution from workers to hours, scale e ect,substitution from labor to capital) h hs : N (substitution from hours to workers, scale e ect,substitution from capital to workers)

Identi cationThree estimation equations (Sect VI)yln yitln yitln it β2 hsit β3 hsit 1 ui vt it β2 hsit β3 hsit 1 ui vt β1 t it β2 hsit β3 hsit 1 ui vt β1 t β4 wit 1 itwhere yit is employment or hours at industry i at period t , , hs is standardhours hours at this industry at period t , ui is a set of industry-level xed-e ect,vt is a set of time e ects, β1 t captures industry-speci c trends and wit 1 is theitnominal bargained wage in the previous quarterIdentifying assumptions (dif-in-dif )timing of standard hours reduction independent of time-speci c deviations from common time-e ects (after conditioning ontime-invariant industry-e ects) caused by the treatmentunobservablesSpec. as , but allowing for industry-speci c trendsSpec. : as , but also conditioning on industry-level bargained wages(probably should not do this as wages likely a ected by standard hours)

Identi cationThree estimation equations (Sect VI)yln yitln yitln it β2 hsit β3 hsit 1 ui vt it β2 hsit β3 hsit 1 ui vt β1 t it(1)(2) β2 hsit β3 hsit 1 ui vt β1 t β4 wit 1 it(3)where yit is employment or hours at industry i at period t , , hs is standardhours hours at this industry at period t , ui is a set of industry-level xed-e ect,vt is a set of time e ects, β1 t captures industry-speci c trends and wit 1 is thenominal bargained wage in the previous quarteritIdentifying assumptions (dif-in-dif )timingSpec. 1:of standard hours reduction independent oftime-speci c unobservables deviations from common time-e ectsconditioning on time-invariant industry-e ects) caused by the treatment(afterSpec. 2: as 1, but allowing for industry-speci c trendsSpec. 3: as 2, but also conditioning on industry-level bargainedwages (probably should not do this as wages likely a ected by standard hours)

Impact on Employment (Table V)Col 1, last rowpoint estimate: one hour decrease in standard hours decreasesemployment by 3.8 percenthowever, standard error is 3.6 percent no statistically signi cante ectCols 2 and 3: similar resultsIV is used here to correct for attenuation bias due to measurementerror (not selection)note that measurement error always leads to a bias towards zerobut this can be corrected if one has two independent measures ofthe same thing (one measure used as an instrument for the other)Cols 4 and 5: weighting by industry size reduces the estimatesnot clear why to weight (treatment is at industry-level)the di erence between unweighted and weighted results simply tellsyou that less was going on in larger industries. and the di erence between the results from alternativespeci cations are not statistically signi cant anyways

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Impact on Employment (Table VI)Point estimates on col 1 2 suggest that one hour reduction instandard hours decreases employment by 5 6 percent amongmen (statistically signi cant)Hunt: this is too large to be plausibleAs we discussed in the rst lecture, underpowered studiesproduce either insigni cant or very large estimates (see Gelman,Weakliem (2009): Of Beauty, Sex and Power, American Scientist 97)Some point estimates for women (col 5 6) suggest positiveemployment e ects, but these are not signi cant31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Impact on Actual Hours (Table VII)Benchmarksone hour reduction from 40 hours is 2.5 percent acoe cient of 0.025 for standard hours implies one-for-onereduction in actual hoursa coe cient of zero would imply no e ect on actual hours (i.e.full shifting to overtime)Results (cols 1 3): 0.024 (s.e. 0.003)Estimates for men smaller implying some shifting to overtime(consistent with employment results)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Impact on Actual Hours (Tables I and II)These estimates based on individual-level panel datay actual hours or overtime dummies, D standard hoursCols 1 3:overtime);β 0 implies no e ect on actual hours (full shiftingβ 1 complete pass-through to actual hourstoCol 1: Cross-sectional variationCol 2: Within-individual variationCol 3: Within-individual variation IV to correct formeasurement error in reported standard hoursCol 4:β 0 implies an increased likelihoodβ 0 implies no e ectto work overtime ashsdecreases,Col 5:hsβ 0decreases,implies an increased likelihood to work undertime asβ 0implies no e ectTakeaway: One hour reduction in standard hours reduces actualhours by 0.88 1 hours31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?Impact on Wages (Table III)Here no claims for causalityWages and hours jointly determinedFuture reductions in standard hours may be anticipated inbargaining processStill informative about correlation between standard hours andwagesResults: One hour reduction in standard hours associated with2 2.4 percent increase in hourly wage monthly pay remainsroughly constant (for a person not working overtime)31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?ConclusionsHoursmost/all reduction in standard hours transfered to actual hoursWageshourly wages increase when standard hours decrease31E00700 Labor Economics: Lecture 4Matti Sarvimäki

IntroductionShort-RunLong-RunDoes Work-Sharing Work?ConclusionsHoursmost/all reduction in standard hours transfered to actual hoursWageshourly wages increase when standard hours decreaseEmploymentThis study does not have enough data to really tell whathappensNevertheless, a reasonable working hypothesis is thatwork-sharing does not increase employmentAdditional evidence: Crépon, Kramarz (2002, JPE) concludethat an one-hour reduction of the workweek decreasesemployment by 2 4%31E00700 Labor Economics: Lecture 4Matti Sarvimäki

31E00700 Labor Economics: Lecture 4 Matti Sarvimäki 8 Nov 2012. IntroductionShrt-RunoLong-RunDoes Wrk-Shaoring Wrk?o First Part of the Course: Outline 1 Supply of labor 1 static labor supply: basics 2 static labor supply: bene ts and taxes 3 intertemporal labor supply 2 File Size: 1MB

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