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Unformatted text preview: Unions II
Lecture 10, March 20, 2012 Announcements
• Final Exam:
– A-LI TUE 17 APR AM 9-11 SEEL
– LL-Z TUE 17 APR AM 9-11 SHER • Final Exam Structure: Three Questions
– “Define and explain the significance”
– Two theoretical/quantitative problems • Tutorials continue this Friday
– Alfia will be taking up selected problem set questions
– Every Friday for the remainder of the semester
– Alfia’s Office Hours • Q&A Session (by me)
– Monday, April 16th, 3:00 to 5:00, SS2106 1 Review: Unions I
• Institutional background on unions
– What is a union?
– How prevalent are unions?
• In 2010, 25.3% of LF (30.8% of non-agricultural workers).
• Private Sector is 13.5%; Public Sector is 64.7% • Models of union behaviour, and firm-union interaction
– Employment and wage determination in unionized settings • Monopoly union
– Pareto inefficient • Efficient contracts
• Introduction to bargaining
– Nash bargain
– Rubinstein bargaining & “strikes”
2 Review: The Monopoly Union
• In this setting, the union sets the wage, and the firm chooses employment.
• The firm will choose the employment level that maximizes profits given
the union wage.
– This will be on the labour demand function • The union, knowing this rule, chooses its favorite combination of E, W:
– Maximize utility subject to employment and wages being on the labour demand
function. • Other considerations of the “bargaining range”:
– Minimum profits for firms
– Minimum wage (the alternative wage) for the union 3 CHAPTER 14: Unions and Collective Bargaining Review Employment: Monopoly Union F IGURE 14.5 The Firm’s and Union’s Preferred Wage-Employment Outcomes
and the Bargaining Range The preferre
the firm and
in which the
come Iu corr
the labour d
The firm’s pr
profits that c
subject to th
that the wag
equal the alt
set of wage
and Wu. W W0
• lu 0 =0 Bargaining
Wf = Wa • U* lf DL *
4 corresponds to a different level of profits. The higher the wage rate, the lower the maximum
attainable level of profits. Review: Pareto Efficiency?
• Recall the definition of Pareto Efficiency
• No outcome is efficient if one party can be made better off without making
the other worse off.
• We can show that the arrangement above (the monopoly union) is
inefficient, in the sense that there are contracts available to the parties that
will make both better off.
– This requires allowing joint determination of employment and wages. • Mutually beneficial trades are available at the monopoly union outcome.
• In the following figure, we can see:
– The monopoly outcome is given by A;
– The point A’ is feasible, and yields higher utility for the union, and higher
profits for the firm;
– By contrast, the point A’’ is Pareto Efficient.
5 “gains from trade” and thus are inefficient in the Pareto sense. (Recall that an outcome is said
to be Pareto-efficient or Pareto-optimal if no individual or group of individuals can be made
better off without making some individual or group of individuals worse off.)
This is illustrated in Figure 14.6. Starting at points on the labour demand curve such as
A and B, it is possible to make one or both parties better off by moving to outcomes in the Review: The inefficiency of
F IGURE 14.6 onopoly employment Contracts
m Efficient and Inefficient Wage-Employment Wage-employment contract
on the labour demand curve
are inefficient. For example,
compared to the point A on
the labour demand curve,
both parties are better off a
point A9, which yields higher
union utility and higher firm
profits. The set of Paretoefficient wage-employment
contracts, called the contrac
curve and shown as CC9, is
the locus of points at which
a union indifference curve
is tangent to a firm isoprofit
curve. Because the union
indifference curves are
downward sloping, this set
of tangencies must occur
to the right of the labour
demand curve, where the
firm isoprofit curves are also
downward sloping. W C
A′ A″ •
B Wa C′ DL
6 Review: Efficient Contracts
• What types of contracts are efficient?
– Connect all tangencies between the union indifference curves and iso-profit curves. • This locus of points is called the “contract curve.”
– It lies to the right of the labour demand curve
– At any given wage rate, more employment would make both parties better off. • Clearly, unions and firms have an incentive to move to the contract curve.
– Firms and workers have an incentive to constrain themselves to the contract curve
– “kills” the labour demand relationship in the data • Obstacles:
– Information problems, mistrust – demand curve may be only credible alternative
– Difficult to enforce contracts (shifts in product demand, asymmetric information) 7 Review: The contract curve
W u0 Connect the tangencies between
Iso-profit curves and
indifference curves à༎ CC’ C π0
8 The impact of unions
• So far, we focused on models of union behaviour and their potential impact
on employment and wages.
– But is there any evidence that unions can successfully raise the wages of their
workers? • In order for this to be the case, there must be:
– “Rents” to divide
– Effective monopoly power exerted by unions • We now move to a traditional “labour economics” question: how much do
unions raise the wages of their members?
– H. Gregg Lewis 9 How much do unions raise wages?
• Ideal Question: What is the average effect of unionization on a worker’s
• What is the appropriate counterfactual:
– What would happen if the union did not exist?
– What would happen to an individual worker if he/she switched to an otherwise
identical non-union job?
– An important matter of understanding the “thought experiment” that we wish to
conduct. • Define the wage GAP as: D= WU − WN
≈ ln WU − ln WN
WN • i.e., the percentage difference in wages between union and non-union
10 Wage GAIN
• The wage GAP is not necessarily the same as the wage GAIN: D′ = WU − W0
W0 • Where W0 is the wage that workers would have received in the absence of
• The wage “gain” measures the impact of unions on wages in the unionized
sector of the labour market.
• We need to account for spillovers, whereby the unionized sector may affect
the non-union sector.
– “General Equilibrium” effects • Typically analyze two-sector models that allow spillovers of workers from
the unionized sector who lose their jobs after unionization (depending on
the impact of the union in the unionized sector).
11 PART 5: Unions URE 15.1 Case 1: Conventional spillovers Two-Sector Model of General Equilibrium (a) Union wage impact in a two-sector model
Sector A (Union) Sector B (Nonunion) Wage Wage SB SA S B WU
a W0 W0
DA a EA
0 Employment b E B EB
E Both sectors start off with the competitive wage W0. Unions raise wages from W0 to WU in the union sector, creating a reduction in employment of a. These displaced workers go to the nonunion sector, shifting out the nonunion supply schedule by a,
and reducing wages from W0 to WN. This induces some individuals in the nonunion sector to leave that sector (i.e., there is a
movement down the supply curve given the lower wage), presumably to leave the labour force altogether. (b) Union wage impact with a threat effect 12 Spillovers
• In Case 1, the union increases the wage from W0 (the competitive wage) to
• Employment falls (moves along the demand function): E0A → E1A
• The additional workers must move to the non-union sector, shifting the
labour supply schedule outwards, and depressing wages from: W0 → WN
• Non-union wages are therefore lower than W0, and the wage “GAIN” is
exaggerated by the wage “GAP.” WU − WN > WU − W0
13 DA a EA
1 Employment EA
0 DB b E B EB
1 E Both sectors start off with the competitive wage W0. Unions raise wages from W0 to WU in the union sector, creating a reduction in employment of a. These displaced workers go to the nonunion sector, shifting out the nonunion supply schedule by a,
and reducing wages from W0 to WN. This induces some individuals in the nonunion sector to leave that sector (i.e., there is a
movement down the supply curve given the lower wage), presumably to leave the labour force altogether. Case 2: Union “Threat” Effect (b) Union wage impact with a threat effect
Sector A (Union) Sector B (Threatened
WU S B S C S B
WN W0 Sector C (Unthreatened
SC a W0 a C b W0
N a EA E A
E b EB EB
1 DB DC
EC EC E
B The nonunion sector is broken into two subsectors. In sector B, the nonunion firm raises its wage to W N to reduce the threat
of being unionized. The displaced workers b go to the nonunion sector C, which does not respond with a threat effect, further
augmenting the increased labour supply of a who already came from the union sector.
14 Union threat effects, and other cases
• In many settings, the threat of a union may lead some non-unionized firms to
raise their wages to pre-empt unionization.
– Classic example: DOFASCO and STELCO • In this case, the wage difference between unionized workers and non-unionized
workers in the “threatened” sector may be very small.
• But the unthreatened, non-union (“residual”) sector might have even lower
• In Case 3, we consider the possibility that employment is determined by
“efficient contracts” where employment is the same as in the competitive case.
– No effect on the other sector; • In Case 4, we simply allow for unemployment in the union sector (which
reduces pressure on the non-union sector).
• The bottom line: general equilibrium spillovers make it difficult to imagine
what wages would be like in the absence of unions.
15 CHAPTER 15: Union Impact on Wage and Nonwage Outcomes F IGURE 15.1 Two-Sector Model of General Equilibrium Case 3: Efficient Union Employment (c) Union wage impact with a vertical contract curve
Sector A (Union)
W Sector B (Nonunion)
SB SA WU
W0 d WN = W0 DA
0 E DB
E With a vertical contract curve Cd, the union bargains for retaining the same level of employment, in spite of the higher wage.
There is no adverse employment effect and, hence, no augmentation of labour supply in the nonunion sector.
16 (d) Union wage impact with wait unemployment DA
0 DB E E Case 4: Wait Unemployment With a vertical contract curve Cd, the union bargains for retaining the same level of employment, in spite of the higher wage.
There is no adverse employment effect and, hence, no augmentation of labour supply in the nonunion sector. (d) Union wage impact with wait unemployment W Sector A (Union)
c Sector B (Nonunion)
A SA W SB S WU W0
WN W0 EA
0 E S B a
b c DB DA
1 B EB EB
1 E This is the same as panel (a) except that some of the displaced workers (the horizontal distance c) prefer to engage
in “wait” unemployment, looking for jobs in the union sector. The net increase in employment in the nonunion sector B
thereby is only b 5 a 2 c. 17 Estimating the wage gap
• Let’s set aside the distinction between the wage “gain” and the wage “gap.”
• How much does union membership raise the wages for a “marginal”
– What would happen if a person switched union status, all else equal. • The easiest way to to begin is to place the union effect in the context of the
human capital earnings function: ln Wi = α + β DU ,i + ε i
• Where DU is a dummy variable for union status: ⎧1
DU = ⎨
⎩ 0 if non-union 18 Interpreting the coefficient on union dummy
• More generally, of course we can include some covariates:
K ln Wi = α + β DU + ∑ γ j Xi + ε i
j =1 • As an aside, note that we can link the wage gap to our regression
W − WN
Wi = (1 + β DU )WN , β = U
• If DU = 0: Wi = (1 + β × 0 )WN = WN • If DU = 1: ⎛ WU − WN ⎞
Wi = (1 + β × 1)WN = ⎜ 1 +
⎟ WN = WU
N • Taking logs: ln Wi = ln WN + ln(1 + β DU ) ≈ ln WN + β DU
19 Constructing a counterfactual:
Human Capital Earnings Function
• Rather than just adding the covariates “ad hoc”, we can use our human
capital model as a way to construct a counterfactual.
– Predict wages for individual if he/she not in a union. • Wages in the absence of a union:
K ln Wi = α + ∑ γ j Xi + ε i
N j =1 • Wages with a union:
K ln W = ln Wi + β = α + β + ∑ γ j Xi + ε i
i N j =1 • Giving us our suggested framework:
K ln Wi = α + β DU + ∑ γ j Xi + ε i
j =1 20 Is OLS informative?
• We can then collect data on wages, covariates and union status, and
estimate the regression by OLS (as usual).
– The Labour Force Survey has the required variables; • But there are several potential econometric problems.
– The quality of workers in union firms may be higher if firms “cherry pick”
from queue of applicants;
– Unobserved differences in industry technology
– Simultaneity: unions are attracted to high wages (i.e., high wages and rents
induce unionization). • All of these biases might lead to an overstatement of the union wage effect 21 Unobserved Heterogenity (Fixed Effects)
• For unobserved worker characteristics, at least, the use of longitudinal
(panel) data can be very helpful.
• We augment the base model with an assumption about the structure of the
ln Wit = α + β Dit + ∑ γ j Xit + ε it
j =1 ε it = λi + uit
• Our empirical concern with OLS is that: E ⎡ λi DiU ⎤ ≠ 0
• And that OLS is biased by (omitted variables bias, or “selection bias”): ˆ
E ⎡ β ⎤ = β + ρλ , DU
22 Exploiting Longitudinal Data
• In this case, if we have repeated observations on an individual, we can use
a “fixed effects” or “first differenced” estimator to purge the fixed
heterogeneity from the error term: ln Wit − ln Wit −1 = (α − α ) + β ( D − D
it −1 K ) + ∑ γ j ( X jit − X jit −1 )
j =1 + ε it − ε it −1 ε it − ε it −1 = λi + uit − λi − uit −1 = uit − uit −1 ≡ Δuit
• But since:
• The fixed heterogeneity (λi) falls out, and is no longer in the error term.
• We just estimate:
Δ ln Wit = βΔDit + ∑ γΔXit + Δuit
j =1 23 How “Fixed Effects” works
• The “fixed effects” estimator purges the regression of unobserved fixed
heterogeneity of individuals that may be correlated with their propensity to
be a union member.
• It rests on changes in union status for individuals: ΔDiU
• Those who do not change union status do not contribute to the estimation.
– Just those individuals that switch into, or out of, union jobs. • It therefore relies on observing the same people before and after they
switch union status.
– How much of a raise do union joiners get?
– How much of a wage cut do union leavers incur? 24 Shortcomings of “Fixed Effects”
• While this estimation strategy is promising, it also has problems:
• Measurement error of union status.
– Many apparent switchers are just coding errors, and this “noise” biases OLS
towards zero (i.e., attenuates the effect of union status). • Endogeneity of status changes.
– What if switching union status is correlated with the error term in the fixedeffects specification?
– This just moves the problem of unobserved heterogeneity from levels to
changes. • Bottom line:
– When employed, longitudinal data yield slightly lower estimated union wage
effects (15% versus 18% for OLS). 25 Variation of the Union Wage Effect
• The union wage gap is higher in sectors where there is a higher proportion
of unionized workers;
• The wage gap is smaller in large firms;
– The firm-size effect is positive for both union and non-union workers, but
especially for non-union. • The wage gap increases during recessions:
– Union wages are less sensitive to business cycle conditions • Union wage effect is higher for women than men (in Canada)
– Not much difference by gender in the US • Differential is even higher if we include benefits (i.e., total compensation
as opposed to just wages). 26 sibly zero for high-skill workers. For example, Lemieux estimates a wage gap of 21 percent
for the lowest-skill group, and less than 1 percent for the top-skill group. Card estimates a
wage gap of 28 percent for the bottom fifth of the skill distribution, but 0 and 11 percent for
the top 2 quintiles of the skill distribution. Blackburn (2008) also shows that the union wage
premium is much lower for college graduates than for nongraduates in the U.S. The union premium varies by skill F IGURE 15.2 The Relationship between Union and Nonunion Wages
and Personal Characteristics • Union wage effect is higher for low skilled workers:
wage rates WU
WN • Is this selection? Wages increase with skill
levels in both union and nonunion sectors but more so
in the nonunion sector. The
union wage premium is the
vertical distance between the
two lines—larger at low-skill
levels and smaller at highskill levels. In effect, unions
obtain larger base increases
(intercept) but they tend not
to negotiate skill premiums
(slope). Skill level 27 ben40208_ch15_456-492.indd 469 10/21/11
10/21/11 workers, unions also increase the variability of earnings relative to a hypothetical economy,
without collective bargaining. Because of these offsetting factors—lower wage dispersion
within the union sector but greater inequality between union and nonunion workers—the
direction of the overall impact of unionism on the wage distribution is indeterminate.
Studies by Hyclak (1979, 1980), Freeman (1980a), and Quan (1984) indicate that in the
United States the net effect of unionism is to reduce wage dispersion. In a detailed analysis of
the impact of labour market institutions on the distribution of wages, DiNardo, Fortin, and
Lemieux (1996) confirm the significant equalizing effect of unions. In fact, they attribute an
important role to the decline in unions for contributing to the increasing wage inequality in
the United States (see Chapter 14). They note that the decline in unions is associated especially with a drop in middle-level-paying jobs—better-paying blue-collar jobs traditionally The effect of unions on wage inequality
• Combined, these effects suggest that union wages are less disperse than
FIGURE 15.3 Wage Dispersion in the Union and Nonunion Sectors
In the union sector the
wage distribution is more
compressed (less dispersed)
with fewer workers receiving
low wages and few receiving
very high wages. In effect,
the tails of the distribution
are compressed into the
higher spike at the middle
of the wage distribution in
the union sector. The union
distribution also tends to be
to the right of the nonunion
distribution, reflecting the
higher wages generally
received in the union sector. Number of
workers Union • Overall effect on wage inequality? Nonunion
Wage rate – Unions lower wage inequality
ben40208_ch15_456-492.indd 474 10/21/11 1:19 PM 28 Allocative Inefficiency
• If we take as a given that unions raise wages in the union sector, and also
reduce overall employment,
– Then output will be lower in the unionized sector
– And higher in the non-union sector. • This will lead to allocative inefficiency:
– Labour is inefficiently allocated across the union and non-union sectors, and output
could be increased without using any more total labour. • We can readily show this graphically:
– Recall that the labour demand curve gives the VMPL of labour;
– The area below the labour demand curve integrates to total output (VMPL times L). • Compare the loss of output in the union sector to the gain of output in the nonunion sector.
• The competitive wage in both sectors is the same: W0, and employment starts
at: E0 , E0
29 magnitude of this allocative inefficiency can be illustrated using the fact that, because the
labour demand curve is the marginal revenue product curve, the area under the labour
demand curve equals the total value of the output produced. Thus, the value of the output
produced by the union sector declines by E 1 a b E 0 as a result of the union wage impact, while Allocative Inefficiency of Unions
). The Union Wage Impact and Allocative Inefficiency
Union sector Nonunion sector Wage Wage
W0 c b WN O EU
1 d W0 EU
E0 g f EN
30 Comparing the change in output across
• Lost output in the union sector:
– Employment falls:
E0 → E1
– The loss of output is given by: E1 cabE0 • Increased output in the non-union sector:
– Employment increases E0N → E1N
– The increase of output is given by: E0 edfE1N • Because the VMPL is lower in the non-union sector (as employment
expands beyond E0 ), the new output is lower than the lost output in the
union sector. 31 Deadweight Loss
• If we assume that labour supply is inelastic, then we can be even more precise.
– The increase of employment in the non-union sector exactly equals the decrease of
employment in the union sector. • The difference in lost output is given by the sum of two triangles:
– acb (in the union sector)
– dgf (in the non-union sector). • If the labour demand curve is linear, then the triangle dgf equals the triangle
def, as shaded in the figure.
• We can also see that the lost triangle in the union sector is deadweight loss –
the value of lost output in excess of the cost of producing it (the labour costs).
• This combines with the lost “wages” in the non-union sector of dgf, and both
triangles sum to the total deadweight loss.
• Note also that employers gain in the non-union sector as wages are reduced. 32 But does this matter?
• How large is the deadweight loss that can be attributed to unions?
• It depends on:
– The labour supply elasticity;
The shape of the demand curve;
The level of union wages in excess of the competitive wage;
The extent to which employment is not “efficient.” • It also depends on the extent to which the competitive allocation is the
appropriate “counterfactual” benchmark.
– What if there is imperfect competition in the product market?
– Theory of the Second-Best • Most estimates are very low.
– Difficult to estimate anyway. • Compelling evidence that unions have small effect on firms.
33 Next week
• Unemployment (Chapter 17)
• Recommended problems:
• 16.1, 16.2, 16.4 34 ...
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