Decomposing Wage Distributions Using Reweighing and Recentered ...

Decomposing Wage Distributions Using Reweighing and Recentered Influence Function Regressions: A New Look at Labor Market Institutions and the Polarization of Male Earnings

Sergio Firpo, PUC – Rio, Nicole M. Fortin, UBC and Thomas Lemieux, UBC UCLA, March 2007

1

Related Papers

Firpo, Fortin and Lemieux, “Decomposing Wage Distributions using Influence Function Projections and Reweighing,” December 2005. (FFL)

Firpo, Fortin and Lemieux, “Unconditional Quantile Regressions”, November, 2006. (UQR)

2

Motivation

The Polarization of Income

Recently there has been a renewed interest for changes in wage inequality.

These changes have been characterized as the “polarization” of the U.S. labor market into high-wage and low-wage jobs at the expense of middle-skill jobs (Autor, Katz and Kearney, 2006).

These changes have also been called the “war on the middle-class” in the popular press.

The stagnation of the average worker’ wages is in sharp contrast with the extremely high CEO’s pay which have made the headlines. 3

Motivation

The Polarization of Income

4

Motivation

The Polarization of Income Using Current Population Survey data, the recent changes in men’s wages look like this

0

Log Wage Change .05 .1

.15

Change in Log Wages 2003/05-1988/90

-.05

0

.2

.4

Quantile

.6

.8

1

5

Motivation

The Polarization of Income or like this 1

United States -- Men

.2

Density .4 .6

.8

1988-90 2003-05

0

1

1.5

2

2.5

3

3.5

4

4.5

Log Wages in 2005 dollars 6

Motivation

Explanations for Increasing Wage Inequality To the extent that different explanations for these changes may provoke different policy responses, it is important to better understand the explanations or the sources of these changes.

The consensus explanation of the early 1990s was that of skillbiased technological change (SBTC) (Krueger 1993; Bound, Berman, and Griliches 1994); but it is being challenged by recent trends and cross-country comparisons.

The alternative explanation of international trade and globalization, has been found to play a relatively minor role [Feenstra and Hanson (2003) offer an explanation]. 7

Motivation

A Role for the Labor Market Institutions?

DiNardo, Fortin and Lemieux (1996), Lee (1999), DiNardo and Card (2002) have argued for a substantial role played by labor market institutions in increasing wage inequality.

It is now generally accepted, even by proponents of the SBTC (Autor, Katz and Kearney, 2005), that changes in minimum wages explain a large portion of the increase in lower tail inequality, especially for women.

For men, the decline of unionization remains a potentially attractive explanation for the “declining middle”.

8

Motivation

The Role of Other Factors

For men, there is a consensus that growth in the upper tail of the wage distribution is associated with higher returns to education, especially post-graduate education (Lemieux, 2006)

The goal of the paper will be to assess the role of various factors Unionization Education Occupations (including high-wage occupations) Industry (including high-tech sectors) Other factors (including experience, non-white) on the changes in male wage inequality between 1988-90 and 2003-05 at various quantiles of the wage distribution

9

Motivation

Wage Structure or Composition Effects?

Yet different factors have different impacts at different points of the wage distribution.

Moreover, some factors are thought to have an impact through the “wage structure” or “price effects”, e.g. increasing returns to education.

While other factors are thought to have an impact through “composition effects” or “quantity effects”, e.g. decline in union density.

10

Motivation

What explains what happens where?

There exists no methodology that permits the decomposition of changes in wages at each quantile of the distribution into “composition” and “wage structure” effects, as in the OaxacaBlinder decomposition, for each explanatory variable.

The DFL reweighing procedure can be used to divide an overall change into a composition and a wage structure effect, but not to into components attributable to each explanatory variable.

Main contribution of the paper is to show how our UQR regressions can be used to perform such a decomposition at different quantiles of the wage distribution.

11

Outline of the presentation 1.

Methodological Issues: a. Beyond Oaxaca-Blinder b. Some Notation c. Step 1: Reweighing d. Step 2: RIF-regressions e. The Case of the Mean f. The Case of the Median

2.

Decomposing Changes on US Male Wages 2003-05/1988-90 a. Data b. Unconditional Quantile Regression Estimates c. Decomposition Results

3.

Conclusion 12

Methodological Issues Beyond Oaxaca-Blinder

Oaxaca-Blinder decompositions are a popular tool of policy analysis.

It assumes two groups, T=0,1, and a simple linear model, for T=0, Y0i=Xiβ0+εi and for T=1, Y1i=Xi β1+εi

The overall average wage gap can be written as E(Y1|T=1)− E(Y0|T=0)= E(X|T=1) β1− E(X|T=0) β0 = E(X|T=1) [β1−β0 ] + [E(X|T=1)− E(X|T=0)]β0 or

∆o

overall gap

=

∆s

+

∆x

wage structure effect + composition effect

These effects can then subdivided into the contribution of each of the explanatory variable or a subset thereof. 13


The Oaxaca-Blinder has its shortcomings.

If the linear model is misspecified, this leads to misleading classification into wage structure or composition effects (Barsky et al. 2002).

The focus only on the mean is limited to address complex changes in wage distributions (e.g. glass ceiling effects).

There has been increasing interest in looking at what happens at different quantiles of the wage distribution.

14


For example, Autor, Katz and Kearney, 2005 use the Machado-Mata methodology of numerically integrating conditional quantile regressions to reassess current explanations for rising wage inequality.

An important disadvantage of the Machado-Mata methodology is that, unlike the classic Oaxaca-Blinder decomposition, it cannot be used to separate the composition effects into the contribution of each variable.

It is also computationally intensive simulation method.

15


We generalize the Oaxaca-Blinder method of decomposing wage differentials into wage structure and composition effects in several important ways.

1) We apply this type of decomposition to any distributional features (and not only the mean) such as quantiles, the variance of log wages or the Gini. 2) We estimate directly the elements of the decomposition instead of first estimating a structural wage-setting model. 3) We break down the wage structure and composition effects into the contribution of each explanatory variable.

We implement this decomposition in two steps. 16


In Step 1, we divide the overall wage gap into a wage structure effect and a composition effect using a reweighing method. Change in Log Wages 2003/05-1988/90

-.05

0


.15

Total Change Wage Structure Composition

0

.2

.4

Quantile

.6

.8

1

17


In Step 2, we break down these terms⎯overall, composition and wage structure effects ⎯ into the contribution of the explanatory variables using the RIF-OLS regression. Total Effects

-.05

0


.15

Union Education Occupations Industries Other

0

.2

.4

Quantile

.6

.8

1

18

Methodological Issues Some Notation

In DFL, we used reweighing to construct counterfactual wage distributions; here, we appeal to the treatment effect literature to clarify the assumptions required for identification.

Using the notation of the treatment effects (potential outcomes) literature, where Ti = 1 if individual i is observed in group 1 and Ti = 0, if in group 1.

Let Y1,i be the wage that worker i would be paid in group 1 and Y0,i be the wage that would be paid in group 0.

Wage determination depends on X and on some unobserved components ε Є Rm, through Y1,i = g1(Xi, εi) and Y0,i = g0(Xi, εi), where the gT(·, ·) are some unknown wage structures.

19

Methodological Issues Some Notation

To simplify notation, let Z1,i =[Y1,i,Xi’]’, Z0,i =[Y0,i,Xi’]’, Zi =[Yi,Xi’]’

Denote the corresponding distribution Z1|T = 1 ~d F1,

Z0|T = 0 ~d F0,

and Z0|T = 1 ~d FC, be the counterfactual distribution that would have prevailed with the wage structure of group 0 but with individuals with observed and unobserved characteristics as of group 1, that is, the with distribution of (X, ε)|T = 1.

20

Methodological Issues Step 1: Reweighing

Let ν1 , ν0 and νC be some functional of those distributions (variance, median, quantile, Gini, etc.) We write the difference in the ν’s between the two groups theνoverall wage gap, which is basically the difference in wages measured in terms of : ∆νO = ν1 − ν0

21


The two key assumptions that we need to impose are

1) that the error terms in the wage equation are ignorable, that is, conditional on X the distributions of the ε are the same across groups;

2) there is overlapping or common support of the observable characteristics, that is, no one value of a characteristic can perfectly predict belonging to one group.

22


Under these assumptions, we can decompose ∆νO in two parts: ∆νO = [ν1 - νC ]− [νC - ν0 ]= ∆νS + ∆νX

The first term ∆νS represent the effect of changes in the “wage structure”. It corresponds to the effect on of a change from g0(·, ·) to g1(·, ·) keeping the distribution (X, ε)|T = 1.

The second term ∆νX is the composition effect and corresponds to changes in the distribution of (X, "), keeping the “wage structure” g0(·, ·).

23


We show that the distributions F1, Fo and FC can be estimated nonparametrically using the weights ω1(T) = T/p,

ω0(T)= (1-T)/(1-p)

and ωC(x,T) = p(x) · 1-p · 1-T 1-p(x) p 1-p where p(x) = Pr[T = 1|X = x] is the proportion of people in the combined population of two groups that is in group 1, given that those people have X = x, and p is that unconditional probability.

24

Methodological Issues Step 1: Reweighing Theorem 1 [Inverse Probability Weighing]: Under Assumptions 1 and 2, for all x in X: r

(i) Ft (z) = E[ω1(T) · 1{Y ≤ y}· Π l=11{Xl ≤ xl}],

t = 0, 1

r

(ii) FC (z) = E[ωC(x,T) · 1{Y ≤ y}· Π l=11{Xl ≤ xl}],

Theorem 2 [Identification of Wage Structure and Composition

Effects]: Under Assumptions 1 and 2, for all x in X:

(i) ∆νS, ∆νX are identifiable from data on (Y, T,X); (ii) if g1 (·, ·) = g0 (·, ·) then ∆νS = 0; (iii) if FX|T=1 ~ FX|T=0, then ∆νX = 0 25

Methodological Issues

Step 2: Application of the UQR methodology

Here, we use a recently developed methodology (UQR) to obtain quantile regression estimates from the unconditional distribution of wages the general concept used (recentered influence function) applies to any distributional functional ν, such as quantiles, the variance or the Gini. these can be integrated up as easily as in the case of the mean

The RIF is simply a recentered IF, which is a well-known tool used in robust estimation and in computation of standard errors.

Intuitively, the influence function (IF) represents to “contribution” of a given observation to the statistic (means, quantile, etc.) of interest. 26


Step 2: Application of the UQR methodology

It is always the case that for any distributional functional ν ν=

:

∫ RIF(y; ν) · dFY (y) = ∫ E [RIF(Y ; ν |X = x] · dFX(x)

= EX(E [RIF(Y ; ν |X = x]) where RIF(Y ; ν) is the recentered influence function.

The RIF(Y ; ν ), besides having an expected value equal to functional v, corresponds to the leading term of a von Mises type expansion.

The RIF regression, E[RIF(Y ; qτ )|X] = X’γτ, is called the UQR in the case of quantiles and γτ (called UQPE) is simply the regression parameter of RIF(Y; qτ ) on X 27


Step 2: Application of the new UQR methodology

Then ∆νO = EX(E[RIF(Y1;ν1|X,T=1]) – EX(E[RIF(Y0;ν0|X,T=0]) ∆νS = EX(E[RIF(Y1;ν1|X,T=1]) – EX(E[RIF(Y0;νC|X,T=1]) ∆νX = EX(E[RIF(Y0;νC|X,T=1]) – EX(E[RIF(Y0;ν0|X,T=0])

28

Methodological Issues Step 2: Application of the new UQR methodology

Then in the case where the conditional expectation is linear, letting γν is the parameter of the RIF-regression E[RIF(Y;ν)|X] = X’γν.

and

∆νS = EX(X|T=1)γ1 – EX(X|T=1)γC = EX(X|T=1)[γ1 –γC] ∆νX = EX(X|T=1)γC – EX(X|T=0)γ0 = EX(X|T=1)γC – EX(X|T=0)γ0 + EX(X|T=1)γ0 –EX(X|T=1)γ0 = [EX(X|T=1) – EX(X|T=0)] γ0 + EX(X|T=1)[γC – γ0] main effect specification error

As in the Oaxaca-Blinder, these effects can then subdivided into the contribution of each of the explanatory variable. 29

Methodological Issues: The Case of the Mean

Assume two groups, T=0,1 and a simplified model For T=0, Y0i=Xiβ0+εi and for T=1, Y1i=Xi β1+εi

The overall average wage gap can be written as E(Y1|T=1)− E(Y0|T=0)= E(X|T=1) β1− E(X|T=0) β0 or

∆µo

overall gap

= E(X|T=1) [β1−βC ] + [E(X|T=1)βc − E(X|T=0)β0 ] = ∆µs + ∆µx wage structure effect + composition effect

where βc is a counterfactual wage structure

30

Methodological Issues The Case of the Mean We define the counterfactual wage structure βc , such that E(Y0|T=1,X)= X’i βc

That is, we propose to estimate βc by OLS (linear projection) on the T = 0 sample reweighed to have the same distribution of X as in period T = 1. In practice, the reweighing uses an estimate of the “propensityscore” p(x) = Pr[T = 1|X = x] the proportion of people in the combined population of two groups that is in group 1, given that those people have X = x.

31

Methodological Issues The Case of the Mean

In the case of the mean, we have RIFµ=Yi since the influence function of the mean is Yi- µ

The RIF-regression (conditional expectation of the RIF) corresponds to the OLS regression because E[RIF(Y;µ|X])= E(Y|X)

Here the expected (over X) value of conditional mean is simply the unconditional mean by the Law of Iterated Expectations: µ= E(Y)=EX [E(Y |X=x)]=E(X)βOLS

The usual OLS regression is both a model for conditional mean and the unconditional mean because fitted values average out to the unconditional mean. 32

Methodological Issues The Case of the Median

In the case of quantiles, because in general, Qτ(Y) ≠ EX[Qτ(Y|X)], we cannot use conditional quantile regressions

So even if quantile regressions yield estimates of Qτ(Y|X)=X'ατ, we would have Q τ(Y) ≠ EX[Qτ(Y|X)]=EX[X]ατ

That is, quantile regression coefficients cannot be used to decompose the corresponding unconditional quantile.

By contrast, the method we propose here refers to the effects of changes in X on unconditional quantiles of Y. 33

Methodological Issues: The Case of the Median

In the case of the quantile (median τ=0.5), we have RIF(Yi; qτ )= qτ +[τ –1(Yi≤ qτ) ]/fy(qτ) = [1(Yi>qτ) ]/fy(qτ) + qτ –(1- τ)/ fy(qτ)

= c1,τ [1(Yi >qτ) ] + c2,τ where c1,τ = 1/ fy(qτ) and c2,τ =qτ - c1,τ (1- τ) It follows that E[RIF(Y ; qτ )|X]= c1,τ E [1(Yi >qτ) |X] + c2,τ = c1,τ Pr [Yi >qτ |X] + c2,τ

The scaling factor, 1/fy(qτ ), translates this probability impact into a Y impact since the relationship between Y and probability is the inverse CDF and its slope is the inverse of the density (1/f) 34

Methodological Issues The Case of the Median

35

Decomposition

Data: US Men 2003-05/1988-90

Data is from the MORG-Current Population Survey for 1988-19891990 and 2003-2004-2005

This results in large sample size: 226,078 obs. in 1988-90, and 170,693 obs. in 2003-05

The dependent variable is log hourly wages.

Observations with allocated wages are deleted; top-coding applies to a small percentage and is left alone.

The specification is used for the UQR wage regressions includes covered by a union, non-white, non-married, 6 education classes, 9 experience classes, 17 occupations classes and 14 industry classes. 36

Decomposition

Data: Table 1. Sample means Log wages Std of log wages Union covered Non-white Non-Married Education Primary Some HS High School Some College College Post-grad Age

1988-90 2.179 0.576 0.223 0.127 0.386

2003-05 2.237 0.595 0.152 0.133 0.408

∆ 0.058 0.019 -0.072 0.006 0.022

0.060 0.121 0.379 0.203 0.137 0.100 35.766

0.046 0.082 0.308 0.271 0.193 0.099 38.249

-0.014 -0.038 -0.070 0.068 0.056 -0.001 2.483

37

Decomposition

Unionization and the “Declining Middle”

For men, a potentially attractive explanation for the “declining middle” phenomena remains the decline of unionization

US Men 1988-90

0

0

.2

.2

.4

.4

Density .6 .8

Density .6 .8

1

1

1.2

1.2

US Men 2003-05

1

1.5

2

2.5

3

3.5

4

4.5

1

1.5

Log Wages in 2005 dollars Overall Non-Union

Union Normal Density

2

2.5

3

3.5

4

4.5

Log Wages in 2005 dollars Overall Non-Union

Union Normal Density

38

Decomposition

Data: Table 1. Sample means Occupations 1988-90 Upper Management 0.080 0.039 Lower Management 0.074 Scientists 0.052 Social Support Occ Lawyers & Judges 0.006 Doctors & Dentists 0.004 Health Treatment Occ 0.010 Clerical Occ 0.066 Sales Occ 0.084 Insurance Sales 0.004 Real Estate Sales 0.003 Financial Sales 0.003 0.108 Service Occ 0.028 Primary Occ 0.163 Construction & Repair Oc 0.144 Production Occ 0.133 Transportation Occ

2003-05 0.079 0.058 0.085 0.064 0.006 0.006 0.014 0.071 0.090 0.003 0.002 0.003 0.133 0.012 0.172 0.100 0.101

∆ -0.001 0.019 0.011 0.012 0.001 0.002 0.004 0.005 0.006 -0.001 0.000 0.000 0.025 -0.016 0.009 -0.044 -0.032

39

Decomposition

Data: Table 1. Sample means Industries Agriculture, Mining Construction Hi-Tech Manufac Low-Tech Manufac Wholesale Trade Retail Trade Transportation & Utilities Information except Hi-Tech Financial Activities Hi-Tech Services Business Services Education & Health Services Personal Services Public Admin

1988-90 0.035 0.096 0.101 0.139 0.051 0.106 0.085 0.018 0.045 0.035 0.069 0.097 0.103 0.058

2003-05 0.022 0.115 0.075 0.104 0.045 0.116 0.072 0.015 0.054 0.054 0.057 0.105 0.115 0.052

∆ -0.013 0.019 -0.026 -0.036 -0.006 0.010 -0.013 -0.002 0.009 0.019 -0.012 0.008 0.012 -0.006 40

Decomposition

Data: Union coverage by industry Industries Agriculture, Mining Construction Hi-Tech Manufac Low-Tech Manufac Wholesale Trade Retail Trade Transportation & Utilities Information except Hi-Tech Financial Activities Hi-Tech Services Business Services Education & Health Services Personal Services Public Admin

1988-90 0.094 0.256 0.273 0.277 0.102 0.103 0.454 0.178 0.054 0.182 0.080 0.298 0.055 0.422

2003-05 0.060 0.178 0.149 0.156 0.071 0.070 0.353 0.123 0.041 0.074 0.057 0.261 0.049 0.412

∆ -0.034 -0.078 -0.124 -0.122 -0.032 -0.033 -0.101 -0.055 -0.013 -0.108 -0.023 -0.037 -0.006 -0.010 41

Decomposition

Unconditional Quantile Regression Results

RIF-OLS regressions are estimated at every 5th quantile

Base group is composed of married white individuals with some college, and between 20 and 25 years of experience

The occupations and industries are normalized so that they are neutral for the base group in 2003-05

In all types of Oaxaca decompositions, part of the “unexplained” gap or the “wage structure effect” depends on the base group

This problem is exacerbated here when there is a lack of support of the base group in some parts of the wage distribution 42

Decomposition

Unconditional Quantile Regression Results 1988-90 Quantile Union covered Non-white Non-Married Primary Some HS High School College Post-grad

10 0.154 (0.004) -0.069 (0.005) -0.132 (0.004) -0.376 (0.008) -0.384 (0.006) -0.049 (0.004) 0.085 (0.006) 0.031 (0.007)

50 0.394 (0.003) -0.140 (0.004) -0.120 (0.003) -0.479 (0.006) -0.257 (0.005) -0.132 (0.004) 0.226 (0.005) 0.292 (0.006)

2003-05 90 -0.032 (0.005) -0.079 (0.005) -0.032 (0.004) -0.230 (0.009) -0.106 (0.007) -0.110 (0.005) 0.342 (0.006) 0.712 (0.008)

10 0.101 (0.004) -0.039 (0.004) -0.094 (0.003) -0.417 (0.008) -0.419 (0.006) -0.064 (0.004) 0.064 (0.005) 0.028 (0.006)

50 0.401 (0.005) -0.121 (0.004) -0.144 (0.003) -0.539 (0.008) -0.301 (0.006) -0.154 (0.004) 0.225 (0.005) 0.329 (0.007)

90 -0.007 (0.007) -0.065 (0.007) -0.068 (0.005) -0.119 (0.013) -0.015 (0.01) -0.059 (0.006) 0.415 (0.008) 0.983 (0.01) 43

Decomposition

UQR Results: Union, Education, etc. Non-Married 1 0

.25

-.05 -.1

.8

1

.2

.4 .6 Quantile

.8

1

.8

1

-.75 .4 .6 Quantile

.8

1

.2

.4 .6 Quantile

.2

.8

1

.4 .6 Quantile

.8

1

.8

1

1 0

.25

.5

.75

1 .5 .25 0 -.25 -.5 -.75 0

0

Post-Graduate

.75

1 .75 .25 0 -.25 -.5 -.75 .4 .6 Quantile

.2

College

.5

.75 .5 .25 0 -.25 -.5 -.75

.2

0

High School

1

Drop-Out

0

-.5

-.15 0

-.25

.4 .6 Quantile

-.5

.2

-.75

0

-.2

-.2

2003-05 1988-90

-.2

-.15

-.25

0

-.1

-.05

.2

.5

0

0

.75

.4

Elementary

.05

Non-White .05

Union

0

.2

.4 .6 Quantile

.8

1

0

.2

.4 .6 Quantile

44

Decomposition

UQR Results: Sensitivity Analysis Union

.2

.4

0

0

.2

.4

Union

0

.2

Bandwidth 0.06 Bandwidth 0.04 Bandwidth 0.02 OLS

- .2

- .2

Unconditional Q(t) 95% Confidence Int. Conditional Q(t) 95% Confidence Int. OLS .4

Quantile

.6

.8

1

0

.2

.4

.6

.8

1

.6

.8

1

Union

0

0

.2

.2

.4

.4

Union

Quantile

The impact of unionization on male log wages 1983-85 Comparison with other estimates OLS (---) Conditional Quantile (− )

0

.2

RIF-OLS UCQ(t) 95% CI NP UCQ(t) Bootstrap 95% CI OLS

- .2

- .2

RIF-OLS UCQ(t) NP UCQ(t) Flexible NP UCQ(t) OLS .4

Quantile

.6

.8

1

0

.2

.4

Quantile

45

Decomposition

UQR Results: Selected Occupations

1

.2

.4 .6 Quantile

.8

1

1.25 1.5 1.75 1 .5 .25 0 -.5 -.25

.2

.4 .6 Quantile

.8

1

Transportation Occ.

0

.2

.4 .6 Quantile

.8

1

0

.2

.4 .6 Quantile

.8

1

.8

1

Service Occ.

.75 .5

.75 .5 .25 -.5 -.25

0

.25

.5

.75

1

1.25 1.5 1.75

Production Occ.

0

1.25 1.5 1.75

.8

1

.4 .6 Quantile

0 0

.75

1 .2

-.5 -.25

-.5 -.25

0

.25

.5

.75

1

1.25 1.5 1.75

Health Treatment Occ.

0

.25

1

0

.8

Scientists

-.5 -.25

.4 .6 Quantile

1.25 1.5 1.75

.2

1

0

-.5 -.25

0

.25

.5

.75

1 .75 .5 .25 0 -.5 -.25

-.5 -.25

0

.25

.5

.75

1

2003-05 1988-90

Financial Sales

1.25 1.5 1.75

Doctors & Dentists

1.25 1.5 1.75

1.25 1.5 1.75

Upper Management

0

.2

.4 .6 Quantile

.8

1

0

.2

.4 .6 Quantile

46

Decomposition

UQR Results: Selected Industries

.8

1

.2

.4 .6 Quantile

.8

1

.8

1

.3 0 -.1 -.3 -.5 .4 .6 Quantile

.8

1

.2

.4 .6 Quantile

.8

1

.2

.4 .6 Quantile

.8

1

.5 -.1

0

.1

.3

.5 .1 0 -.1 -.3 -.5 0

0

Transportation & Utilities

.3

.5 .3 0 -.1 -.3 -.5 .4 .6 Quantile

.2

Personal Services

.1

.3 .1 0 -.1 -.3 -.5

.2

0

Education & Health Services

.5

Hi-Tech Services

0

.1

.3 0

-.3

.4 .6 Quantile

-.5

.2

-.5

-.3

-.1

0

.1

.3 -.5

-.3

-.1

0

.1

.3 .1 0 -.1 -.3 -.5 0

Retail Trade .5

Low-Tech Manufac. .5

Hi-Tech Manufac. .5

.5

Construction 2003-05 1988-90

0

.2

.4 .6 Quantile

.8

1

0

.2

.4 .6 Quantile

.8

1

47

Decomposition Results Total Effects:

∆νO = [ν1 - νC ]− [νC - ν0 ]= ∆νS + ∆νX

90-10 Total Change 0.059 Wage Structure -0.013 Composition 0.072

Change in Log Wages 2003/05-1988/90

90-50 0.125 0.078 0.047

-.05

0


.15

Total Change Wage Structure Composition

50-10 -0.066 -0.091 0.025

0

.2

.4

Quantile

.6

.8

1

48

Decomposition Results Total Effects Total Effects

Total Effects: Union Occupation Industry Education Other Residual Total

50-10

90-50

0.025 -0.009 0.004 0.083 -0.015 -0.030 0.059

-0.015 0.004 0.005 0.022 -0.009 -0.074 -0.066

0.040 -0.013 -0.001 0.061 -0.006 0.045 0.125

-.05

0


.15


90-10

0

.2

.4

Quantile

.6

.8

1

49

Decomposition Results: Composition Effects:

∆νX = [EX(X|T=1) – EX(X|T=0)] γ0 + EX(X|T=1)[γC – γ0] 90-10 Composition Effects: Explained 0.064 Spec. error 0.008 Total 0.072

Composition Effects

0.032 0.032 -0.007 0.015 0.025 0.047

-.05

0


.15

Total Explained Spec. Error

50-10 90-50

0

.2

.4

Quantile

.6

.8

1

50

Decomposition Results: Composition Effects

90-10

50-10

90-50

Composition Effects

Composition Effects: Union 0.014 -0.018 0.031 Occupation 0.010 0.017 -0.007 Industry 0.016 0.009 0.007 Education 0.006 0.010 -0.005 Other 0.018 0.013 0.005 Spec. error 0.008 -0.007 0.015 Total 0.072 0.025 0.047

-.05

0


.15


0

.2

.4

Quantile

.6

.8

1

51

Decomposition Results

Wage Structure Effects: ∆νS = EX(X|T=1)[γ1 –γC] 90-10 Wage Structure Effects: Explained 0.025 Residual -0.038 Total -0.013

Wage Structure Effects

-0.024 0.049 -0.067 0.029 -0.091 0.078

-.05

0


.15

Total Explained Residual

50-10 90-50

0

.2

.4

Quantile

.6

.8

1

52

Decomposition Results: Wage Structure Effects

90-10 50-10 Wage Structure Effects: Union 0.011 0.003 Occupation -0.019 -0.013 Industry -0.012 -0.003 Education 0.078 0.012 Other -0.033 -0.022 Residual -0.038 -0.067 Total -0.013 -0.091

Wage Structure Effects

-.05

0


.15


0

.2

.4

Quantile

.6

.8

90-50 0.009 -0.006 -0.008 0.066 -0.012 0.029 0.078

1

53

Decomposition Results: Summary

Increases in top-end wage inequality are best accounted for by Wage structure effects associated with education (postgraduate) Composition effects associated with de-unionization

Decreases in low-end wage inequality are best accounted for by Wage structure effects associated with occupations and “other” factors Composition effects associated with de-unionization

Increases in total wage inequality are best accounted for by Composition effects associated with other factors, industry, unionization, and occupation by order of importance. 54

Decomposition Results: Discussion

We show that de-unionization and changes in returns to education remain the dominant factors accounting for changes in wage inequality in the 1990s.

We find that the role of occupation and industry are also found to play a role, but it is difficult to assign these changes to SBTC.

Our results are suggestive that Social norms may also be at play to explain changes in returns to occupations such as financial analysts, doctors and dentists, as argued by Piketty and Saez (2003).

55

Conclusion:

In this paper, we propose a new methodology to perform Oaxaca-Blinder type decomposition for any distributional measure (for which an influence function can be computed) the methodology can also be used to analyze changes in Gini and other measures we implement this methodology to study changes in male earnings inequality from 1988-90 to 2003-05

56

Appendix

Issues Associated with Choice of Base Group

Base group are married, white individual with between 20 and 25 years of experience and indicated education level US Men 2003-05

0

0

.2

.2

Density .4 .6

Density .4 .6

.8

.8

1

1

US Men 1988-90

1

1.5

2

2.5

3

3.5

Log Wages in 2005 dollars Overall Base: Some Coll

Base: HS

4

4.5

1

1.5

2

2.5

3

3.5

4

4.5

Log Wages in 2005 dollars Overall Base: Some Coll

Base: HS

57

Appendix

Minimum Wages and Wage Inequality Minimum Wage 1988

1979

Minimum Wage

1979

1988

1.25

1979

.75 1 .5

1979

.75 .5

.25

1988

1988

.25

0

0 ln(2)

ln(5)

ln(10)

ln(2)

ln(25)

a) Men

ln(5)

ln(10)

ln(25)

b) Women Minimum Wage 1988

1979

1979

.75

.5

.25

1988

0 ln(2)

ln(5)

ln(10)

ln(25)

c) All Workers

Figure 1. Kernel Density Estimates of Real Log Wages ($1979)

Source: Fortin and Lemieux, JEP (1997)

58

Appendix

Basic Concepts

59

Appendix

Basic Concepts

60

Appendix

Basic Concepts

61

Appendix

Basic Concepts

62