Is There Evidence of Skill Biased Technological Change in CPS Residual Inequality?∗ Bok Hoong Young Hoon 16 July 2010

Abstract Skill biased technological change (SBTC) has generally been regarded as an important factor driving the increasing wage inequality in the US over the past three decades. Such an explanation is consistent with the increasing residual wage inequality, the inequality in wages between observably similar workers, in the commonly used March supplement of the Current Population Survey (CPS). A recent nding however, that residual inequality in the Merged Outgoing Rotation Group (MORG) supplement of the CPS has been relatively stable since the mid 1980s, is at odds with a SBTC theory of increasing wage inequality. In this paper I investigate whether the dierence in residual inequality between the March and MORG CPS samples is due to the inclusion of performance-based payments (bonuses, tips, or commissions) in wage measures of the March CPS. Using income information provided by the Medical Expenditure Panel Survey (MEPS) I show that including performance pay in wages leads to an increase in residual inequality that matches the discrepancy in residual inequality between the March and MORG CPS samples. Furthermore, using a matched sample constructed by combining all three samples, I nd that performance pay is positively related to the dierence in wages reported in the March and MORG CPS samples, and accounts for almost one-fth of the variation in this measure. ∗

I would like to thank Daniel Parent, Jennifer Hunt, David Card, and Jason Dean for their many

helpful discussions. I am also grateful for the insightful comments and suggestions oered by Samer Atallah, Carlene Belford, Helen Lim, Christos Ntantamis, Eesha Sen Choudhury, Shengzu Wang, and all other participants of McGill's weekly PhD student seminar and work-in-progress seminar.

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1 Introduction A large body of work in labour economics has been dedicated to documenting and explaining the sharp increase in wage inequality that has taken place in the US over

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the past three decades.

During this period, wages of workers at the upper end of the

wage distribution grew by about 50% more than the wages of those at the bottom, and wages of college educated workers grew by a similar amount relative those of high school educated workers.

Although multiple theories have been proposed for such

a large increase in wage inequality (for example, de-unionization, and the declining real value of the minimum wage), one of the more widely accepted explanations is based on a theory of skill biased technological change (SBTC). In a nutshell, SBTC refers to the favouring of skilled over unskilled workers brought about by a shift towards the greater use of technology in production. As a theory of increasing wage inequality, SBTC increases the relative demand of high skilled workers leading to an increase in the wage gap between the skill and unskilled. There has been general support for the main prediction of a SBTC theory of wage inequality, that wage inequality between dierent skill groups should have increased over the past three decades, both over dierent dimensions of skill and in a variety of datasets. For example, SBTC does a good job in accounting for the sharp increase in the college to high school wage gap that occurred in the 1980s in spite of an increasing supply of college educated workers. Similarly, the theory has traditionally been shown to be consistent with the steadily increasing trend in residual inequality, the inequality in wages between observably similar workers, as indicated by the commonly used March supplement of the Current Population Survey (CPS). However, recent work by Lemieux (2006) and Autor, Katz, and Kearney (2008), using the Merged Outgoing Rotation Group (MORG) supplement to the CPS, nd that residual inequality has been relatively stable since the mid to late 1980s, a nding which is at odds with a SBTC theory of wage inequality. Furthermore, it is inconsistent

1 Blackman, Bloom, Freeman (1989), Freeman (1991), Bound and Johnson (1992), Card (1992), Katz and Murphy (1992), Juhn, Murphy, Pierce (1993), DiNardo, Fortin, Lemieux (1996), DiNardo and Lemieux (1997), Lee (1999), Card (2001), Card and Lemieux (2001), Acemoglu (2002), Card and DiNardo (2002) , Beaudry and Green (2005).

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with not only the rate of growth of residual inequality indicated by the March CPS, but also the level of residual inequality: residual inequality in the March CPS is about 30% higher than that of the MORG CPS. This is puzzling since both samples are compositionally similar; in fact, many workers in the March CPS reappear in the MORG CPS. In light of these recent ndings, the main goal of this paper is to determine whether trends in residual wage inequality in the CPS is still supportive of a SBTC theory of wage inequality. Since residual inequality in the March and MORG CPS samples dier in their support for SBTC, one way to investigate this issue is by identifying which sample more accurately reects the inequality in wages between observably similar workers. I do this by examining whether the discrepancy between residual inequality in the two CPS samples is a result of more performance based payments (bonuses, tips, and commissions) in wage measures of the March CPS than in those of the MORG CPS. Since these types of payments are more likely to reward unobserved measures of skill. Showing that performance pay can account for some or all of the disagreement between the March and the MORG CPS samples would (1) suggest that residual inequality in the March CPS is a better indicator of wage inequality between observably similar workers, and (2), provide an explanation as to why residual inequality in the MORG CPS is inconsistent with a SBTC theory of wage inequality. I build on work by Lemieux, MacLeod, and Parent (2009) who use the Panel Study of Income Dynamics (PSID) to show that performance-based compensation systems are associated with higher wage inequality than non performance-based systems.

They show that workers in performance pay jobs enjoy higher returns to

both measurable and unmeasurable skills than do their counterparts working in non performance-based paying jobs. Since most datasets do not allow for the control of performance pay, the inequality-enhancing eect associated with this form of compensation will typically aect within-group (residual) rather than between-group wage inequality. I examine this issue by using a relatively new dataset, the Medical Expenditure Panel Survey (MEPS), to compare the residual inequality of two samples that dier only in the inclusion of performance pay. Consistent with Lemieux,

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MacLeod, and Parent (2009), who nd that performance pay compensation systems are primarily associated with higher levels of wage inequality at the upper end of the distribution, I nd that including components of performance pay not only increases within-group wage inequality, but that this increase occurs at the upper end of the distribution. Having shown that wage measures that include performance pay leads to higher levels of residual inequality I look for evidence of more performance pay in those of the March CPS so as to determine whether this is contributing to the discrepancy in residual inequality between the two CPS samples. There is reason to believe that this could be the case. Firstly, questions in the March survey explicitly asks respondents to include more performance pay based payments than those of the MORG survey.

Secondly, any received performance pay will always be included in wage

measures of the March CPS since the reporting of performance pay (and income in general) is independent of (calendar) time of receipt. This is not necessarily the case for the point-in-time administered MORG survey which may inadvertently omit measures of performance pay if such payments are received only occasionally (and in particular, late in the year). Using the rich income information contained in the MEPS, I show that it is possible to replicate the discrepancy in CPS residual inequality by constructing wage measures that approximate those reported in the CPS samples. Furthermore, note that if there are more components of performance pay in the March than in the MORG CPS, then hourly wages should be systematically higher in the March CPS, and a measure of the dierence in hourly wages should be increasing in the dierent predictors of performance pay. By matching all three samples (the March CPS, the MORG CPS, and the MEPS) across narrowly dened demographic groups I nd that the inclusion of performance pay in the March CPS can reasonably be expected to contribute to the disagreement in residual inequality between the March and MORG CPS samples. In particular I nd that the dierence between hourly wages in the March and MORG samples is increasing in the amount of performance pay received, and that measures of performance pay can account for about 18% of the variation in wage dierence between the March and MORG samples.

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The paper is as follows. In the next section I introduce and examine the CPS discrepancy between 1996 and 2005. In Section 3 I provide a brief discussion of how the eects of performance pay on residual wage inequality can be readily inferred from existing models. In section 4 I discuss the occurrence of performance pay in the CPS. In Section 5 I introduce the MEPS and use it to investigate the relationship between performance pay and residual wage inequality.

Based on the results of

Section 5, in Section 6 I examine whether performance pay can account for the CPS discrepancy. Section 7 concludes.

2 The March-MORG Current Population Survey Discrepancy As mentioned in the introduction, work by Lemieux (2006) and Autor, Katz, and Kearney (2008) shows that both the rate of growth and the level of residual wage inequality are higher in the March than in the MORG CPS. This results in a positive March-MORG dierence that has been increasing over the last three decades.

In

investigating this puzzling phenomenon Lemieux (2006) argues that this discrepancy is brought about by a greater degree of measurement error in the wages of hourly paid workers of the March sample compared to the MORG. In the March CPS hourly wages are derived for all workers (salaried and hourly paid) using the total amount earned, and the number of hours worked, in the previous year; in the MORG, this measure is derived in a similar manner only for salaried workers workers report directly their hourly wage rate.

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while hourly paid

Under the reasonable assumption

that directly reported hourly wages are less noisy than derived hourly wages, there is less measurement error in the MORG than in the March CPS, resulting in lower residual inequality. The fact that the share of the workforce being paid hourly has increased over this period means that the size of the discrepancy also increased. The above mentioned relationship applies to both samples of males and samples

2 Hourly wages for salaried workers in the MORG CPS are derived using  usual weekly earnings rather than the previous year's earnings as it is in the March CPS (see Section 4).

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of females. For the rest of the paper I focus only on males.

The March and MORG

CPS samples I use are constructed so as to match as closely as possible those used by Lemieux (2006). I restrict both samples to include only full-time (greater or equal to 35 hours a week) male workers between the ages 16 and 64 (inclusive), who have positive potential experience, are not self employed, and who earned hourly wages between $1 and $100 in 1979$.

Top-coded wages are taken to be 1.4 times their

assigned value. Sample statistics are provided in Tables 1 and 2. Table 1 shows that the ten-year pooled samples of the March and MORG are quite similar in terms of education and experience. There is a higher proportion of whites in the MORG but a lower proportion of workers who are unionized or who are paid hourly. Notice also that hourly wages in the March CPS are about 7% higher than in the MORG and exhibit greater dispersion.

Table 2 looks at these statistics broken down by year.

Both samples show similar trends - slight increases in education and experience, and two to three percentage point decreases in both the proportion of workers unionized and paid by the hour. In Figure 1 and the top panel of Table 3, I present the March-MORG residual variance relationship for the years 1996-2005; in the bottom panel of Table 3 I also

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present the 99-1 dierence measure of residual dispersion.

To maintain consistency

with previous wage inequality studies I construct the wage residuals by regressing log hourly wages on age, education, and the interactions of nine schooling dummies with a quartic in age. As noted by Lemieux (2006), any shift in sample composition towards more educated, more experienced workers will mechanically bring about an increase in residual inequality. To ensure that the small compositional changes indicated in Table 2 are not driving the increase in inequality over time I apply the sample reweighting technique introduced by DiNardo, Fortin, and Lemieux (1996), holding the composition at its 1996 level. Similarly, to ensure that the small dierences in experience and unionization between the samples are not responsible for the

3 I do this mainly to be consistent with the wage inequality literature which focuses more on male wage inequality.

4 Since the eect of performance pay that I investigate later in the paper is expected to be at

the extreme ends of the distribution I extend the 90-10 percentile dierence of residuals (Katz and Murphy, 1992; Katz and Autor, 1999) to consider the dierence between the 99

6

th and 1st percentile.

disagreement in level of residual inequality I apply the same reweighting procedure across samples, xing the composition of the March sample to be consistent with

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that of the MORG.

As indicated in Table 3, over this ten-year period residual wage inequality exhibited a three to ve percent increase when using either measure of residual dispersion. The trends illustrated in Figure 1 and Table 3 match reasonably well those presented by Lemieux (2006) in terms of both the change in, and level of, residual wage inequality during these ten years. From Figure 1 it appears that the size of the discrepancy has been roughly constant from 1996 to 2005. In Table 4 I break down changes in the 99-1 dierence into changes at dierent points of the distribution showing that such a conclusion is misleading. For both samples, the increase in residual inequality in the upper half of the distribution is responsible for the majority of its overall increase. In fact, for the March CPS, it can account for the entire increase in overall residual inequality over this period.

In the bottom panel I show that the top

quartile is driving the growth in dispersion, accounting for the entire increase (of overall dispersion) of the March CPS and for almost 70% of the entire increase in the MORG. The main point is that residual inequality has been growing primarily

th

above the 75

percentile, and that this growth has been higher in the March CPS

than in the MORG CPS.

3 Modeling the Eect of Performance Pay on Residual Wage Inequality As suggested by Lemieux, MacLeod, and Parent (2009), performance-based compensation is more likely to be tied to individual productivity while pay in non performance-based compensation systems is more likely to be tied to the produc-

5 A visual examination of the results produced after applying the reweighting technique over time and across samples indicates that composition eects are negligible  the levels of residual inequality for many years are unchanged to 4 decimal places.

This is not surprising given the

trivial dierence in demographic composition between samples, and the negligible change in sample composition during this period.

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tivity of the average worker.

As such, compensation systems that pay for perfor-

mance place greater emphasis on unobserved (to the econometrician) components of idiosyncratic skill, recognizing and rewarding these characteristics more accurately than other compensation systems. I illustrate this by adopting Acemoglu's (1998) two-index aggregate production function model in which the two measures of skill used as inputs, education and ability, are imperfect substitutes. Workers can either be college educated (referred to as  skilled ,

S)

or high-school educated (referred to as  unskilled ,

U ).

These

workers can also be classied as  high ability (H ) or  low ability (L). By combining these observed (education) and unobserved (ability) dimensions of skill we get four inputs to production: low ability, high-school workers (UL ); high ability, high-school workers (UH ); low ability, college workers (SL ); and high ability, college workers (SH ). Production takes place according to the CES production function: 1

Y = [(ALU UL )ρ + (AHU UH )ρ + (ALS SL )ρ + (AHS SH )ρ ] ρ where

Aij

represents the productivity associated with a worker in ability group

and education group

j

; and

ρ < 1.

i

Under standard neoclassical assumptions this

model represents precisely the features of an extreme form of performance-based compensation system: wages fully reect both observable and unobservable aspects of productivity. In this setting residual wage inequality is given by the wage dierence between high and low ability high-school educated workers (equation (1)), and the wage dierence between high and low ability college educated workers (equation (2)):

 

where



wH wL





wH wL



wH wL



= U,P P

 =

S,P P

AHU ALU

ρ 

AHS ALS

ρ 

UH UL

ρ−1

SH SL

ρ−1

(1)

;

(2)

is the wage gap between high ability and low ability high school

U,P P

educated workers in performance pay jobs, and

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wH wL



is the wage gap between

S,P P

high ability and low ability college educated workers in performance pay jobs. In a non performance-based setting I assume that compensation is less reective of dierences in individual unobservable ability and more representative of the average level of productivity of the worker's particular observable skill group. In this model this can be shown by simply augmenting individual productivity to better reect the average productivity associated with each worker's observable characteristic:

 

where

wH wL



wH wL



ρ−1 ρ  αAHU + (1 − α) AU UH = UL βALU + (1 − β) AU  ρ  ρ−1 δAHS + (1 − δ) AS SH = ; SL λALS + (1 − λ) AS 

U,N ON

S,N ON

the average productivity of high school and 0 < α, β, δ, λ < 1; AU , A S represent 

college workers respectively;

wH wL

represents the wage gap between high abil-

U,N ON

ity and low ability high school workers in non-performance pay jobs; and



wH wL



S,N ON represents that between high ability and low ability college workers in non-performance

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pay jobs. It is easy to see that this implies a lower level of residual inequality.

Econometrically this means that the reward to individual (unobserved) ability is dependent on the compensation system, leading to wage residuals which are compensation-system specic:

εji = bj αi + µi where

b

j

εji

j = pp, non − pp

are wage residuals associated with compensation system

j

for worker

is the return to unobserved worker ability in compensation system

unobserved worker ability of worker

i,

and

µi

j , αi

i,

is the

is an error term. Since the return to

ability is higher in performance pay jobs than in non-performance pay jobs (Lemieux, MacLeod, and Parent, 2009), the degree of residual inequality (given by 2 (bj ) var (αi ) + var (µi )) will also be higher in these jobs.7


var εji =

6 I show this in Appendix I. 7 Notice that this assumes that there are no dierences between compensation systems in the dispersions of ability and measurement error.

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4 Performance Pay and the Current Population Survey In this section I present descriptive evidence that suggests performance pay may be treated dierently in the March and MORG CPS supplements.

Firstly, even

though the CPS datasets do not provide an indicator of the receipt of performance pay, it is possible to get an idea of which forms of performance pay are likely to be included in each dataset by examining the wording of the questionnaires. According to documentation on the March supplement provided by the Minnesota Population Centre (MPC):

For 1962-1968, interviewers asked how much the individual earned in wages and salary. For 1969-1979, the survey asked about wages or salary before any deductions.

For later years, respondents were prompted to

include overtime pay, tips, bonuses, and commissions from their primary employer, as well as money from other employers.

On the other hand, documentation on the MORG supplement provided by the National Bureau of Economic Research (NBER) indicates the following:

Earnings per week. How much does...usually earn per week at this job before deductions? Include any overtime pay, commissions, or tips usually received. Hourly wage.  How much does ...earn per hour? . . . . . . .. . . ..Tips are not included.

In general then, the March CPS asks both salaried and hourly paid workers to report all forms of performance pay, whilst the MORG CPS asks about tips and commissions only for salaried workers, and does not include bonuses for either type of worker. This omission of bonuses for workers in the MORG CPS is potentially quite important

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because, as I show in the next section, there is reason to believe that these payments make up a large share of performance based payments. As further evidence that performance pay might be playing a larger role in the March CPS consider the relevant time period of each survey.

The retrospectively

administered March CPS collects information on the previous year's earnings and hours worked, while the point-in-time MORG CPS collects information on current earnings and hours worked.

This means that in any year that a worker receives

performance pay, it is less likely to be recorded in the MORG than in the March CPS. Finally, there may be more performance pay in wage measures of the March CPS than in the MORG CPS because, compared to directly reported hourly wages in the MORG CPS, hourly wages that are derived from a periodic measure of earnings (as done in the March CPS) tend to include forms of payment other than the basic hourly wage (Mellor and Haugen, 1986). As an initial check of the claim that there is more performance pay in the March CPS than in the MORG compare the coecients on education and age obtained from yearly wage equations for each CPS sample.

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I report these in Table 5. Notice

that during this period the coecients on 9 of the 10 education variables, and 9 of the 10 age variables, are all greater in the March CPS than in the MORG CPS. These larger returns to observable measures of skill in the March CPS are consistent with the inclusion of more performance pay if there is a positive correlation between these measures of skill and performance pay.

Indeed, supporting the theoretical

predictions of Lazear (1986) and Brown (1990), Parent (1999) and Lazear (2000) provide evidence of such positive selection into performance pay jobs. It is likely that performance pay is becoming increasingly important. Lemieux, MacLeod, and Parent (2009) show that, between the late 70s and the late 90s, the incidence of performance pay increased by roughly 10 percentage points. I show later in the paper that the total value of performance pay more than doubled between 1996 and 2005. The nding by Autor, Katz, Kearney (2008) that residual inequality has increased at the upper end of the residual distribution since the 1970s possibly

8 Wage equations control for age, education, and the interaction of nine schooling dummies with a quartic in age.

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provides further evidence supporting the importance of performance pay.

5 The Medical Expenditure Panel Survey The main problem in evaluating the contribution of performance pay to the CPS discrepancy is the CPS's lack of performance pay information.

I circumvent this

problem by using information from the Medical Expenditure Panel Survey (MEPS) Household Component. Published by the Agency for Healthcare Research and Quality (AHRQ) since 1996, the Medical Expenditure Panel Survey is a collection of information on individuals and their families, their employers, their medical providers, and medical expenditure across the United States. The Household Component (HC) of the MEPS used in this study contains detailed demographic, employment, and medical related information on a nationally representative subsample of those individuals surveyed the year before in the National Health Interview Survey.

The survey utilizes an

overlapping panel design in which a new sample is introduced each year. For each panel, information is collected in ve rounds of interviews administered over two full calendar years, after which the sample exits. As stated at the outset of this section, the MEPS provides much of the performance pay information that is lacking in the CPS. In particular it asks the amount of each type of performance pay (bonuses, tips, or commissions) a worker received and, for each type, the period over which this amount is based.

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5.1 MEPS Descriptive Statistics In constructing the MEPS sample I use the same restrictions that were applied to the CPS samples in Section 2.

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A benet to the present study is the MEPS' strong

9 See Appendix II for details on the way earnings information is collected in the MEPS.

10 It should be noted that the value applied to top-coding in the MEPS diered from that applied to the CPS and changed from year-to-year. Top-coded values applied to hourly wages in the MEPS

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similarity to the CPS; both in terms of the information it provides, and in terms of its demographic composition. In Table 6 I present summary statistics of the pooled MEPS sample and, for comparison, those reported earlier for the CPS samples. Apart from the slightly higher incidence of hourly paid workers in the MEPS, all three pooled samples appear to be compositionally quite similar. Table 6 also shows that even though 30 percent of workers received some form of performance pay in this ten-year span, the majority of these workers received bonuses (the component not mentioned in the MORG earnings questions) rather than tips or commissions. In Table 7 I present yearly demographic and employment related statistics, including those related to performance pay. Comparing these values to those of the CPS presented in Table 2 shows the similarity in trends between the MEPS and the CPS samples between 1996 and 2005. The bottom three panels of the table examine separately the trends traced out by the incidence and value of performance pay. Panel (b) of the table shows that the incidence of performance pay has been at or declining slightly during this ten-year period. Similarly, panel (c) indicates that the value of performance pay received, as represented by an hourly rate, has also been relatively at or even slightly decreasing.

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In the last panel I show the total value

of performance pay has increased substantially, in some years showing an almost threefold increase over its 1996 level, implying that the number of hours over which performance-based payments was earned must have also experienced a proportional increase. This will be an important point in Section 6 when I assess the ability of performance pay to explain the CPS discrepancy. In Table 8 I present conditional values related to the receipt of performancebased compensation. There is evidence in the performance pay literature that this form of compensation is more prevalent for workers at the upper end of the wage distribution - workers with higher productivity, and more education.

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Consistent

are as follows: $71.87 (1996); $67 (1997); $76 (1998); $96.15 (1999, 2000); $100.96 (2001); $100 (2002); $97.50 (2003); $65.63 (2004); $72.12 (2005).

11 This hourly rate is calculated using the amount of a given type of performance pay received

and the actual number of hours over which this payment was reported to have been received.

12 Abowd (1990), Jensen and Murphy (1990), Kahn and Sherer (1990), Garen (1994), Shaefer

(1998), Lazear (2000), Dohmen and Falk (2006), Lemieux, MacLeod, and Parent (2009).

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with this literature, column (1) shows that the incidence of performance pay is higher amongst more educated workers and salaried workers - in general workers more likely to occupy the upper end of the wage distribution. This last point is emphasized by the positive relationship between the incidence of performance pay and the base hourly wage.

13

Column (2) shows that this relationship also holds for the amount

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of performance pay received conditional on receiving performance pay.

Similar

to the relationship between the incidence of performance pay and experience, the role played by experience is not clear cut. However more educated and higher wage earners are associated with larger amounts of performance payments. In fact there are sharp increases in this measure for workers falling in the upper quintiles of both these categories. A nal point of interest is that salaried workers receive, on average, almost ten times the performance pay of hourly paid workers.

5.2 The Eect of Performance Pay on Residual Wage Inequality in the MEPS In this subsection I examine the eect that including performance-based payments in wage measures has on residual wage inequality. I exploit the rich earnings information of the MEPS to construct two measures of hourly wage - one that includes performance pay (referred to as the  ferred to as the 

base 

measure).

base+

measure), and one that does not (re-

In this way I get the equivalent of two samples

that are identical in ever respect other than performance pay.

The

base

measure

represents either the hourly wage reported directly by hourly paid workers or, for salaried workers, the hourly wage constructed using a periodic measure of earnings

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and number of hours worked.

I obtain the

base+ measure by simply adding the

13 Dened either as the derived hourly rate excluding performance pay components for salaried workers or the reported hourly wage for hourly paid workers.

14 Conditioning on receipt takes away the inuence of column (1) on values reported in column

E ($P P | X) = P rob (P P = 1 | X) · E ($P P | X, P P = 1) + P rob (P P = 0 | X) · E ($P P | X, P P = 0), I report E ($P P | X, P P = 1).

(2). Specically, instead of reporting:

15 Neither the salary nor the hourly wage reported in the MEPS includes performance-based

payments.

The questionnaire reads  How much {is/was} (PERSON)'s salary before taxes, not

including tips, commissions, or bonuses? for salaried workers; and  What {is/was} (PERSON)'s

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hourly rate of performance pay to the

base

measure.

This `hourly rate of perfor-

mance pay' is derived for each type of performance pay considered (bonuses, tips, or commissions) using the amount received and the number of employment hours with which this amount is associated. In Figure 2, I plot the residual variance from wage regressions for each hourly wage measure. From the residual variances it is clear that wages that include performance pay are associated with higher levels of residual wage inequality. Such a conclusion is also consistent with the gradual convergence of the residual variances of the two wage measures.

Recall from Table 6 that both the incidence of performance pay

and the hourly rate of performance pay were either at or even slightly declining during this ten-year period. In order to indicate which parts of the distribution are experiencing the inequality-enhancing eects of performance pay, I present in Table 9 the average (over the 10 years) 99-75 and 75-1 percentile dierences associated

16

with the residual distributions of each sample.

While the average 75-1 dierence is

roughly equivalent for both samples, the 99-75 dierence associated with the measure is more than 60 percent greater than that of the

base+

base measure, indicating th

that performance pay mainly aects residual inequality above the 75

percentile.

6 Performance Pay and the CPS Discrepancy Having shown in the last section that the inclusion of performance pay components of compensation brings about increased residual wage inequality, I investigate in this section whether it can also explain the greater residual inequality in the March CPS compared to the MORG CPS. I approach this investigation in two ways. The rst is a reapplication of the method introduced in Section 6 with the exception that hourly wage rate for (PERSON)'s regular work time,

not including

base+

tips, commissions, or bonuses

at (EMPLOYER)? for hourly paid workers. (bold in original)

16 I present only the 99-75 and 75-1 dierences to emphasize that the eect is occurring mainly th percentile. The 99-50 and 50-1 dierences give similar results  the 50-1 dierence above the 75 is roughly equivalent in both the the

base+ than the base measure.

base+ and base measure, while the 99-50 dierence is higher for

15

and

base

are tailored to more accurately reect the performance pay inclusions in

the March and MORG CPS samples. In the second approach I study directly the way in which workers report wages dierently in the March and MORG surveys by examining the manner in which this dierence is related to the various aspects of performance pay.

6.1 Can the CPS Discrepancy Be Reconstructed Using the MEPS? The setup for this approach is identical to that outlined in subsection 5.2 with the following exceptions:

base+ is renamed  March Proxy and remains unchanged; while

for salaried workers.

These  proxies are meant to reect the CPS performance

base is renamed  MORG Proxy and redened so as to include tips and commissions pay inclusions discussed in Section 4.

Using these newly dened wage measures I

re-examine the levels of residual wage inequality associated with each proxy. In Figure 3 I superimpose the trends in residual wage inequality found using the

17

MEPS proxies onto those found in Section 2 using the actual CPS samples.

We

see that the proxies, which dier only in performance pay, do a reasonable job in replicating the level of residual wage inequality found in both CPS samples, and thus in reproducing the observed CPS discrepancy. Two points to note: in general both proxies indicate a lower level of wage inequality than their respective CPS counterparts and, the MORG Proxy provides a better t than the March Proxy. It is possible that measurement error is responsible for both of these occurrences. While non-hourly paid respondents of the CPS report yearly earnings, those of the MEPS can choose between reporting yearly, monthly, biweekly, weekly, or daily earnings.

18

If measurement error associated with derived hourly wages increases

with the length of the earnings period, then there should be more measurement

17 To account for any compositional dierences between the MEPS and the CPS I apply the DiNardo, Fortin, and Lemieux (1996) reweighting technique across the MEPS and MORG CPS samples. This has no eect on the MEPS results.

18 Roughly 27% of non-hourly paid workers in the MEPS reported earnings for periods shorter

than one year.

16

error in the CPS samples, and thus higher levels of residual inequality compared to the proxies.

This line of reasoning may also explain the better t of the MORG

Proxy since the dierence in measurement error between the proxy and the CPS only occurs in the wages of salaried workers, while for the March Proxy and CPS it occurs in the wages of both hourly and salaried workers. I propose another, more subtle reason for the imperfect t between the March Proxy and March CPS based on the dierent manner in which performance pay enters the hourly wages of each of these samples. For all the workers in the March Proxy I have information on both the value of performance pay received and the number of hours over which this performance pay is based. This allows me to derive a measure of the true hourly rate of performance pay. Panel (c) of Table 6 shows

19

that this hourly rate was relatively at.

Combined with a decreasing incidence of

performance pay (panel (a) of Table 6), this implies that performance pay should have a diminishing eect on residual inequality over time. in the downward trending

base+

This is quite apparent

and March Proxy illustrated in Figures 2 and 3

respectively. For workers in the CPS however there is no explicit information on any aspect of performance pay and any implicit measure of hourly performance pay will be part of the derived hourly wage. I claim that if the total value of performance pay indicated in the MEPS also occurred in the CPS, then the unobserved hourly rate of performance pay in the CPS is increasing over time. This is because the number of hours used to derive hourly wages in the CPS is relatively stable.

20

Thus any

trend in hourly performance pay in the CPS is more accurately represented by the trend followed by total performance pay in the MEPS (Panel (d) of Table 7). The important point is that any eect of an hourly rate of performance pay in the March Proxy will be declining (hence the decreasing residual inequality over time in Figure 3), while any eect of this measure in the March CPS should be increasing (hence the increasing residual inequality over time in Figure 3). In Figures 4 and 5 I make further use of this reconstructive approach to examine

19 Note that because the hourly rate of performance pay, must have been a large increase in amount while

ppM EP S

HOU RSM EP S

remained relatively at.

since

OT AL P PM EP S ppM EP S = T HOU RSM EP S , T OT AL P PM EP S increased

then there by a large

20 Recall that the samples are restricted to workers with at least 35 hours of work a week.

17

separately salaried and hourly paid workers. This is done to show which group of workers is driving the discrepancy and to determine if the performance pay result of Figure 3 still holds. The previous paragraph's discussion on measurement error still holds for Figures 4 and 5 which provide additional indications.

Firstly, all

proxies continue to do a good job in replicating their CPS counterparts. Secondly, the March-MORG discrepancy is larger for hourly paid workers than for salaried workers. Even though this is consistent with a measurement error explanation for the discrepancy, the size of the discrepancy for salaried workers appears larger than would be expected based on pure measurement error, implying the need for another factor such as performance pay. Thirdly, all samples that are expected to be inuenced by the total value of performance pay - salaried and hourly paid workers in the March CPS, and salaried workers in the MORG CPS - exhibit residual inequality trends that are increasing and register a maximum corresponding to the year in which total value of performance pay was the highest, 2001.

6.1.1 Closeness of Distributions Analysis The usefulness of the reconstructive approach in conrming a performance pay explanation of the CPS discrepancy hinges on how well the residual distributions generated by the proxies replicate those of the actual CPS samples. The use of the residual variance in this approach as a measure of inequality can be misleading as it provides no indication of the level of inequality at dierent parts of the distribution. In this subsection I examine how close the distributions of residuals produced using the MEPS are to those derived from the CPS using a quantile-quantile plot (qqplot). Appendix III provides an overview of this analytical tool.

As a means of visually

assessing the closeness of two distributions, two features of the qqplot make it a suitable candidate. Firstly, it allows a comparison of the distributional shapes of each sample - if distributions are simply linear transformations of each other so that distributional shapes are identical, the qqplot will be a straight line, although o of the 45-degree reference line. Secondly, the qqplot aids in determining whether the two distributions have similar tail behaviour. As pointed out in Wilk and Gnanadesikan

18

(1968), when the distributions have very long tails, using a quantile approach puts greater emphasis on comparison at the tails (where the density is low) relative to the middle of the distributions (where the density is high). It is for this reason that the qqplot is preferred to other assessment methods like the Kolmorogov-Smirnov test and the percent-percent (p-p) plot, which are more sensitive at the centre of the distributions than at the tails. This is important for the present analysis since, as Table 9 shows, the eects of performance pay occurs at the very upper end of the distribution. For each of the ten years I construct qqplots showing the closeness of residual distributions between (a) the March CPS and the March Proxy; (b) the MORG CPS and the MORG Proxy; (c) the March CPS and the MORG CPS; and (d) the March Proxy and the MORG Proxy. There was little year-to-year variation in these plots so in Figure 6 (a), (b), (c), and (d) I present these qqplots only for 1997. These plots can be interpreted using the following rule: at the upper end of the qqplot, the axis towards which the qqplot diverges contains the distribution with the thicker upper tail; at the lower end of the qqplot, the axis towards which the qqplot

21

diverges contains the distribution with the thinner lower tail.

Based on this rule

the March Proxy appears to have a thicker upper tail but a thinner lower tail than the March CPS indicating that the proxy may not be accurately reproducing the residual wage inequality found in the CPS. According to Figure 6(a) it seems that excessive inequality generated at the uppermost end of the MEPS' residual distribution is being tempered by lower inequality at the bottom of the distribution, leading to an overall level of residual wage inequality that is not signicantly dierent from the CPS. While the qqplot in Figure 6(b) indicates that the MORG Proxy does a better job in tting the distribution of residuals found from the CPS there is still a divergence at the upper end towards the proxy axis suggesting, as with the March Proxy, a higher level of inequality in this part of the distribution of proxy residuals relative to that of the CPS.

21 An additional point on use of the qqplot: since it is used to evaluate how close two distributions are to each other it gives no indication of whether a tail is  thick or  thin , rather it indicates whether the tail of one distribution is thick or thin relative to the other distribution.

If we are

trying to show that two distributions are close, smaller divergences (from the 45-degree line) are preferred.

19

Comparing the qqplots between the dierent proxies (Figure 6(c)) to those between the dierent CPS samples (Figure 6(d)) may provide further insight regarding the usefulness of this approach in resolving the CPS divergence with a performance pay argument. Figure 6(c) provides strong evidence that performance pay only affects inequality at the upper end of the distribution since, by construction, the only dierence between these two samples is the treatment of performance pay. On the other hand, Figure 6(d) indicates that the role of performance pay does not seem nearly as extreme in the discrepancy in CPS samples as it is in the proxies. Nevertheless, divergence from the 45-degree reference line at the upper end of Figure 6(d) does indicate that, even though performance pay may not fully explain the March-MORG CPS discrepancy, it might account for some of it. We thus see that, while the analysis of this subsection has conrmed some important results - for example that performance pay aects residual inequality at the upper end of the distribution (Figure 6(c)) - it has fallen short of validating the results produced by the reconstructive approach. That is to say, the inability of the proxy residuals to suciently mimic the CPS residual distribution indicates that the results of the reconstructive examination of the role of performance pay in the CPS discrepancy might be overly optimistic.

6.2 The Matched Sample Approach Because much of the information used in Section 6.1 came from the MEPS, any resulting conclusions rely on the assumption that information in the MEPS and CPS samples are identical.

In this section I assume only that the conditional (on

observables) distribution of both the incidence and the value of performance pay is the same in the MEPS as in the CPS. Under this assumption, if there is more performance pay in the March than in the MORG CPS, then the dierence in hourly wages between the two samples should be increasing in measures of performance pay obtained from the MEPS. To test this relationship I construct a matched March-MORG-MEPS sample by

20

matching the three samples across 1400 mutually exclusive demographic groups, comprising of seven education classications, twenty experience classications, and the ten years between 1996 and 2005. For each education-experience-year cell I use information from the MEPS to calculate the probability of receiving performance pay and the average total amount of performance pay. These are the two measures of performance pay that I use in the analysis. Similarly, for each of the 1400 cells, I calculate the dierence in reported hourly wage between the March CPS and the MORG CPS. This measure represents dierences in hourly wages brought about by non-demographic factors, including measurement error, and possibly performance pay. Because some of the education-experience-year cells contain no observations I get a nal matched sample of 964 demographic groups. In Table 10 I present the average wage dierence by quintile of the hourly wage distribution showing not only that this dierence is greater at higher points of the wage distribution, but also the sharp increase (almost three times that of the 4th quintile) associated with the highest quintile of the wage distribution.

6.2.1 Weighted Least Squares To determine whether a positive relationship exists between the March-MORG CPS wage gap and measures of performance pay I rst use a weighted least squares regression of the March-MORG wage dierence on both measures of performance pay (including quadratics in these measures) and year dummies.

The results are pre-

sented in column (1) of Table 11. Coecients in rows (1) and (3) indicate that both the probability of receiving performance pay and the amount of performance pay received contribute positively to the discrepancy in wages between the CPS samples. The negative coecient of -.0002 (.0001) on the quadratic incidence term however implies incidence plays no role at levels higher than 25%. In particular, at its average value (28%), the eect of incidence is zero (and even slightly negative). On the other hand, the coecient on the quadratic  amount term (not shown in Table 11) is practically insignicant so that increases in the amount of performance pay received always increases the inconsistency between the March and MORG wage measures.

21

Standardizing the  amount coecient indicates that a one standard deviation increase in the amount of performance pay (714$) is associated with a .80 standard deviation increase (.43$) in the CPS wage gap.

6.2.2 Quantile Regressions While the linear regression results presented in column (1) provide some evidence that performance pay plays a part in the CPS wage dierence, it appears to point to a bigger role for the amount of performance pay. A problem with relying solely on conditional mean regression results is that they may not be representative of relationships that exist in more non-central locations of the response variable's conditional distribution; in particular the tails. If omitted performance pay is a primary contributor to the dierence in wages between the March and MORG CPS wage measures then the positive relationship described above should be stronger at points higher up in the conditional distribution of the CPS wage dierence. I examine this prediction

yi = Xi β (p) + ε(p) ; Q(p) (yi | Xi ) = Xi β (p) represents

using the quantile regression model (Koenker and Bassett, 1978): where the

p

th

0
indicates the quantile. Note that

conditional quantile given

Xi .22

th

Results for the 10

th

, 30

th

, 50

th

, 70

, and 90

th

quantiles are presented in columns (2)-(6) of Table 11. The quantile regression estimates of the overall eect of incidence presented in rows (1) and (2) do not dier substantially from those of the least squares estimation. Furthermore, while the impact of incidence does appear to be increasing up to the 70

th

quantile, tests of equality of these estimates across quantiles indicate no

statistical dierence at conventional levels.

22 In the quantile regression model, the

pth

23

I present p-values of these tests in the

quantile regression estimator is the solution to the

following minimization problem:

 

  X X min p yi − Xi β (p) + (1 − p) yi − Xi β (p) .  β  yi >Xi β

yi


23 Under the null hypothesis that

βˆk (p) = βˆk (q),

22

the Wald statistic

βˆk (p) − βˆk (q) σˆ 2βˆk (p)−βˆk (q)

2 is dis-

lower panel of Table 11. In contrast, the estimated eect of the value of performance pay in row (3) increases considerably across quantiles; a trend that is consistent with a performance pay explanation of the CPS wage dierence.

Increasing the value of performance

pay by one standard deviation brings about an increase in the wage dierence of .30 standard deviations (.16$) at the 10

th

deviations (.69$) at the 90

th

quantile, but an increase of 1.27 standard

quantile. Testing the equality of the estimated eects

between quantiles (p-values presented in the lower panel of Table 11) indicates also

2

that these dierences are statistically signicant. Finally, notice that the pseudo-R , a local measure of goodness of t, increases with quantile level.

24

Overall, results from the quantile regression analysis are suggestive of two things. Firstly, that performance pay can account for some of the disagreement in hourly wage measures between the March and the MORG CPS samples. This follows from the increasingly strong relationship between the amount of performance pay and the CPS wage dierence at higher quantiles and is shown graphically in Figure 7(a). Secondly, the quantile regression results suggest that the amount of performance pay plays a larger role in the CPS wage dierence than does the incidence of performance pay: a one standard deviation increase in the incidence of performance pay (12%) can account for dierence.

25

at most

a .22 standard deviation increase (.11$) in the CPS wage

It is of no surprise then that, unlike the eect of the amount of perfor-

mance pay, the eect of the incidence of performance pay is not signicantly dierent across quantiles (Figure 7(b) and the lower panel of Table 11).

tributed as

24 The

χ21 .

2 is determined by

26

1

D (p) 1 R2 (p) = 1 − D 0 (p) ; where D (p) is the sum of 0 weighted absolute deviations for the fully specied model and D (p) is the sum of weighted absolute

pth

quantile pseudo-R

deviations for the model with only a constant.

25 Estimated eect calculated at a one percent rate of incidence of performance pay. 26 To check the robustness of these results I redid the analysis of subsection 6.2 matching instead

across industry-occupation groups.

While the explanatory power of performance pay increased

by about 75%, coecients from this matched sample were very similar to those of the educationexperience matched sample. Additionally, experimenting with more or less narrowly dened groups made no signicant dierence.

23

7 Conclusion Explaining why wage inequality in the US has increased so much over the last four decades has been an important research area in labour economics.

Recent work

by Lemieux (2006) and Autor, Katz, and Kearney (2008) shows that, contrary to the March CPS, the MORG CPS indicates that growth in residual inequality has been relatively modest since the mid 1980s. Understanding why residual inequality in these samples dier is an important step in being able to condently evaluate theories of wage inequality.

Controlling for changes in sample composition over time, and

assuming that the conditional distribution of unobservable skill is the same across CPS samples, Lemieux argues that these ndings are due to the greater degree of measurement error incorporated into the hourly wage measure of the March CPS relative to the MORG. However, with only a limited understanding of what makes up the wage residual of each sample it is dicult to be fully convinced of such an argument. In this paper I examine if performance pay plays any role in the discrepancy between residual inequalities of the March and MORG CPS samples. By mechanically constructing samples that dier only in their incidence and value of performance pay I rst show that including performance pay in wages results in a greater level of residual inequality. Furthermore, this increase in inequality occurs primarily at the upper end of the distribution - coinciding with the part of the wage distribution most associated with measures of performance pay. Using this result I investigate whether performance pay contributes to the CPS discrepancy on the grounds that such forms of compensation are included in the March CPS and not in the MORG. Results appear to suggest a role for performance pay in explaining the CPS discrepancy.

Firstly, including the relevant forms of performance pay in each CPS wage

measure does a reasonably good job in replicating the CPS discrepancy. Secondly, the dierence in wages between the March and MORG CPS samples is increasing in measures of performance pay. Disentangling the eects of performance pay due to the incidence from those due to the amount received I nd that the amount received can account for a larger share of, and can explain more of the variation in,

24

the March-MORG CPS wage dierence than can the incidence.

25

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Directed Technical

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Assessing the Role of Skill

Premia in Inequality Trends." Canadian Journal of Economics 33, no. 4 (2000): 907-36. [7] Blackburn, McKinley L., David E. Bloom, and Richard B. Freeman. "The Declining Economic Position of Less-Skilled American Males." National Bureau of Economic Research, Inc, NBER Working Papers: 3186, 1989. [8] Bound, J., and G. Johnson. "Changes in the Structure of Wages in the 1980s - an Evaluation of Alternative Explanations." American Economic Review 82, no. 3 (1992): 371-92. [9] Brown, C. "Firms Choice of Method of Pay." Industrial & Labor Relations Review 43, no. 3 (1990): S165-S82. [10] Brown, C., and J. Medo. "The Employer Size Wage Eect." Journal of Political Economy 97, no. 5 (1989): 1027-59. [11] Card, David. "The Eect of Unions on the Distribution of Wages: Redistribution or Relabelling?": National Bureau of Economic Research, Inc, NBER Working Papers: 4195, 1992.

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[12] Card, D. "The Eect of Unions on Wage Inequality in the Us Labor Market." Industrial & Labor Relations Review 54, no. 2 (2001): 296-315. [13] Card, D., and J. E. DiNardo. "Skill-Biased Technological Change and Rising Wage Inequality: Some Problems and Puzzles." Journal of Labor Economics 20, no. 4 (2002): 733-83. [14] Card, D., and T. Lemieux. "Can Falling Supply Explain the Rising Return to College for Younger Men?

A Cohort-Based Analysis." Quarterly Journal of

Economics 116, no. 2 (2001): 705-46. [15] Chay, K. Y., and D. S. Lee. "Changes in Relative Wages in the 1980s: Returns to Observed and Unobserved Skills and Black-White Wage Dierentials." Journal of Econometrics 99, no. 1 (2000): 1-38. [16] Dickens, William T., and Lawrence F. Katz. "Inter-Industry Wage Dierences and Theories of Wage Determination." National Bureau of Economic Research, Inc, NBER Working Papers: 2271, 1987. [17] DiNardo, J., N. M. Fortin, and T. Lemieux. "Labor Market Institutions and the Distribution of Wages, 1973-1992: A Semiparametric Approach." Econometrica 64, no. 5 (1996): 1001-44. [18] Dinardo, J., and T. Lemieux. "Diverging Male Wage Inequality in the United States and Canada, 1981-1988: Do Institutions Explain the Dierence?" Industrial & Labor Relations Review 50, no. 4 (1997): 629-51. [19] Dohmen, Thomas, and Armin Falk.  Performance Pay and Multi-dimensional Sorting: Productivity, Preferences and Gender. IZA Discussion Paper No. 2001, March 2006. [20] Freeman, Richard B. "How Much Has De-Unionisation Contributed to the Rise in Male Earnings Inequality?":

National Bureau of Economic Research, Inc,

NBER Working Papers: 3826, 1991. [21] Garen, J. E. "Executive-Compensation and Principal-Agent Theory." Journal of Political Economy 102, no. 6 (1994): 1175-99. [22] Goldin, C., and R. A. Margo. "The Great Compression - the Wage Structure in the United-States at Mid-Century." Quarterly Journal of Economics 107, no. 1 (1992): 1-34.

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[23] Groshen, E. L. "Sources of Intra-industry Wage Dispersion - How Much Do Employers Matter." Quarterly Journal of Economics 106, no. 3 (1991): 869-84. [24] Hao, Lingxin, and Daniel Q. Naiman. Quantile Regression, Quantitative Applications in the Social Sciences. Thousand Oaks, Calif.: Sage Publications, 2007. [25] Jensen, M. C., and K. J. Murphy. "Performance Pay and Top-Management Incentives." Journal of Political Economy 98, no. 2 (1990): 225-64. [26] Juhn, C., K. M. Murphy, and B. Pierce. "Wage Inequality and the Rise in Returns to Skill." Journal of Political Economy 101, no. 3 (1993): 410-42. [27] Kahn, L. M., and P. D. Sherer. "Contingent Pay and Managerial Performance." Industrial & Labor Relations Review 43, no. 3 (1990): S107-S20. [28] Katz, Lawrence F., David H. Autor, Orley Ashenfelter, and David Card. "Changes in the Wage Structure and Earnings Inequality." In Handbook of Labor Economics. Volume 3a, 1463-555: Handbooks in Economics, vol. 5. Amsterdam; New York and Oxford: Elsevier Science, North-Holland, 1999. [29] Katz, L. F., and K. M. Murphy. "Changes in Relative Wages, 1963-1987 - Supply-and-Demand Factors." Quarterly Journal of Economics 107, no. 1 (1992): 35-78. [30] Koenker, R., and G. Bassett. "Regression Quantiles." Econometrica 46, no. 1 (1978): 33-50. [31] Lazear, E. P. "Performance Pay and Productivity." American Economic Review 90, no. 5 (2000): 1346-61. [32] . "Salaries and Piece Rates." Journal of Business 59, no. 3 (1986): 405-31. [33] Lee, D. S. "Wage Inequality in the United States During the 1980s:

Rising

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28

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Composition Eects, Noisy

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29

Tables Table 1: Current Population Survey Sample Statistics, 1996-2005 Pooled March Hourly Wage Age Education Experience

MORG

8.13

7.65

(5.98)

(5.27)

39.5

38.5

(10.9)

(11.0)

13.6

13.5

(2.6)

(2.9)

20.9

20.0

(11.0)

(11.0)

White

83.2

86.5

Union

16.0

15.0

Paid Hourly

51.1

50.3

Observations

72257

423551

Notes: Extracts of the March CPS were obtained from the Integrated Public Use Microdata Series provided by the Minnesota Population Centre (MPC). Extracts of the Merged Outgoing Rotation Group (MORG) CPS were obtained from the National Bureau of Economic Research (NBER).

30

31

Group (MORG) CPS were obtained from the National Bureau of Economic Research (NBER).

provided by the Minnesota Population Centre (MPC). Extracts of the Merged Outgoing Rotation

Notes: Extracts of the March CPS were obtained from the Integrated Public Use Microdata Series

Table 2: March and MORG Current Population Survey Demographic Trends, 1996-2005 1996 1997 1998 1999 2000 2001 2002 2003 March Education 13.4 13.4 13.5 13.5 13.5 13.5 13.7 13.7 Experience 20.1 20.4 20.6 20.6 20.7 20.9 21.1 21.2 Union 17.3 17.6 17.6 16.6 16.3 15.3 15.5 15.4 Paid 53.3 52.6 53.1 53.0 51.5 50.7 49.2 49.4 Hourly Observations 5770 5808 5997 6149 6239 6000 10014 9907 MORG Education 13.5 13.4 13.5 13.5 13.5 13.6 13.6 13.6 Experience 19.2 19.4 19.6 19.7 19.7 20.0 20.3 20.5 Union 16.3 16.2 15.9 15.6 15.1 14.6 14.4 14.4 Paid 52.3 52.4 51.5 50.8 50.0 49.4 49.2 48.7 Hourly Observations 42494 43797 42619 42152 41796 42596 46087 43925

44485

43348

6618

9755

13.6 20.8 13.5 49.3

13.6 21.7 14.7 51.4

13.7 21.3 14.9 49.2

13.6 20.7 14.0 49.1

2005

2004

Table 3: Change in Residual Wage Inequality, CPS, 1996-2005 March

MORG

1996

.2674

.1985

2005

.2788

.2113

1996

2.571

2.202

2005

2.642

2.304

Variance

4.3

%∆

6.4

99-1 Dierence %

2.7

∆

4.6

Notes: Based on a regression of log hourly wage on age, education, and the interaction of nine schooling dummies with a quartic in age. Regressions were weighted by the sample earnings weight along with hours worked. The 99-1 dierence represents simply the dierence between the residual at the 99th and 1st percentile of the residual distribution.

32

Table 4: Change in 99-1 and 99-50 Residual Dierence, CPS, 1996-2005

99-50

March

50-1

99-50

MORG

50-1

1996

1.159

1.412

1.074

1.128

2005

1.254

1.388

1.153

1.151

0.095

-0.024

0.079

0.023

99-75

75-50

99-75

75-50

1996

0.852

0.307

0.799

0.276

2005

0.933

0.322

0.867

0.286

∆

∆

0.081

0.015

0.068

Notes: Based on a regression of log hourly wage on age, education, and the interaction of nine schooling dummies with a quartic in age. Regressions were weighted by the sample earnings weight along with hours worked.

33

0.010

Table 5: Education and Age Coecients from March and MORG CPS Samples Education

Age

March

MORG

March

MORG

1996

.0763

.0762

.0836

.0727

1997

.0821

.0738

.0751

.0711

1998

.0712

.0698

.0711

.0657

1999

.0779

.0741

.0794

.0648

2000

.0657

.0728

.0770

.0660

2001

.0923

.0745

.0565

.0668

2002

.0787

.0736

.0770

.0667

2003

.0852

.0748

.0821

.0739

2004

.0872

.0748

.0804

.0746

2005

.0720

.0700

.0754

.0735

Notes: Based on a regression of log hourly wage on age, education, and the interaction of nine schooling dummies with a quartic in age. Regressions were weighted by the sample earnings weight along with hours worked. All estimates signicant at a 1% level.

34

Table 6: Comparison of MEPS and CPS Samples, 1996-2005 Pooled Samples MEPS

CPS March

Age Education Experience

MORG

39.3

39.5

38.5

(11.0)

(10.9)

(11.0)

13.3

13.6

13.5

(2.8)

(2.6)

(2.9)

21.1

20.9

20.0

(11.1)

(11.0)

(11.0)

White

85.8

83.2

86.5

Union

16.3

16.0

15.0

Paid Hourly

53.7

51.1

50.3

Received Performance Pay

30.1

Received Bonus

26.8

72257

423551

Received Commission

3.9

Received Tips

1.7

Observations

104251

Notes: Extracts of the MEPS were obtained from the Agency of Healthcare Research and Quality (AHRQ), an agency of the US Department of Health and Human Services. Extracts of the March CPS were obtained from the Integrated Public Use Microdata Series provided by the Minnesota Population Centre (MPC). Extracts of the Merged Outgoing Rotation Group (MORG) CPS were obtained from the National Bureau of Economic Research (NBER).

35

36

19.5 18.0 58.6

Experience

Union

Paid Hourly

3.1

Received

2.1 1.3

Hourly Commis

Hourly Tips

792 5907

Total PP

Observations

11656

1215

328

1995

1099

1.4

3.0

5.4

1.4

3.1

28.6

31.3

56.9

17.9

20.3

13.2

1997

8128

1470

509

2165

1361

0.7

2.4

5.0

1.6

3.1

28.6

31.6

55.6

18.1

20.7

13.3

1998

9081

1746

25

1799

1683

0.7

2.0

4.1

1.6

4.6

27.2

31.0

53.4

16.7

21.0

13.3

1999

8900

1853

55

1728

1833

1.2

2.0

4.7

1.8

4.3

25.9

29.6

52.2

15.8

21.1

13.4

2000

12280

2123

111

2636

1972

1.2

2.6

5.0

1.9

4.2

25.7

29.1

52.6

16.0

20.9

13.2

2001

13665

1993

48

2858

1823

1.2

2.9

5.3

2.1

3.9

25.9

29.4

52.2

15.2

21.4

13.2

2002

11553

1753

total value of performance pay received (1979$).

over which performance pay was based) is available in the MEPS but not in the CPS; (d) Average

the number of hours over which this payment was based. The latter value (the number of hours

This was constructed by dividing the total amount of each form of performance pay received by

forms of performance pay were received; (c) Average hourly value of performance pay (1979$).

26

2670

1583

1.2

2.6

5.8

1.9

4.1

26.3

29.9

51.0

14.6

21.5

13.3

2003

The dummy variable indicating receipt of performance pay took on a value of 1 if any of the three

variables indicating receipt of each of these components were constructed from this information.

bonus was received, whether commissions were received, and whether tips were received. Dummy

Notes: (a) Demographic variables; (b) Incidence of performance pay. The MEPS asks whether a

20

1708

Total Commis

Total Tips

685

Total Bonus

(d)

4.5

Hourly Bonus

(c)

Received Tips

1.6

28.5

Received Bonus

Commis

31.4

Received PP

(b)

13.0

1996

Education

(a)

Table 7: MEPS Demographic and Performance Pay Trends, 1996-2005

11722

1481

50

2175

1330

1.2

2.0

4.1

1.3

4.0

24.9

28.3

53.0

15.8

21.7

13.3

2004

11359

1459

35

978

1478

0.8

1.7

3.7

1.6

3.8

26.8

29.8

54.1

15.6

21.9

13.2

2005

Table 8: Incidence and Value of Performance pay, MEPS 1996-2005 Probability of

Value of Total

Performance

Performance

Pay

Pay

(1)

(2)

Less than 12 years

18.57

443.2

12 years

26.39

574.2

Education 13-15 years

31.78

1139.7

16 years

42.14

2460.2

17+ years

32.91

3942.5

1st Quintile (less than 11 years)

31.92

1138.4

2nd Quintile (11-17 years)

36.00

1817.4

3rd Quintile (18-24 years)

30.22

1808.5

4th Quintile (35-32 years)

27.71

1750.4

5th Quintile (33-59 years)

23.71

1525.3

6.12

1058.5

Experience

Base Hourly Wage 1st Quintile 2nd Quintile

14.08

544.5

3rd Quintile

21.00

716.0

4th Quintile

28.33

1198.6

5th Quintile

38.49

2991.6

Salaried

39.51

2604.1

Hourly

22.66

278.4

Paid

Note: The value of total performance pay is conditional on receiving performance pay. This removes the eect of dierences in the left hand column groups in the probability of receiving performance pay.

37

Table 9: Average 99-75 and 75-1 Residual Dierence, 99-75 75-1

base+

base+ and base

base

1.363

0.833

1.391

1.368

Notes: Based on a regression of log hourly wage on age, education, and the interaction of nine schooling dummies with a quartic in age using data from the MEPS. Regressions were weighted by the sample earnings weight along with hours worked.  base+ represents the hourly wage including the hourly rate of all forms of performance pay;  base represents the hourly wage excluding performance pay.

38

Table 10: Mean March-MORG CPS Wage Dierence, by Quintile of Hourly Wage Quintile (Hourly Wage)

Mean (March-MORG) Wage Dierence

st

1

-.0359503

2

.1673735

nd

3

rd

.2991691

th

4

.4276913

5

1.288095

th

Notes: Number of observations = 964

39

40

2 964

.1795

.6616 .9865 .9758

.8694 .4029 .5468

.2309 .4994

.9669

[q90] = [q50]

[q90] = [q30]

[q90] = [q10]

[q70] = [q50]

[q70] = [q30]

[q70] = [q10]

[q50] = [q30]

[q50] = [q10]

[q30] = [q10]

964

.1321

Yes

(.0061)

.0639***

(.0053)

-.0269***

(.0023)

.0107***

.5

.0029

.0000

.0000

.0000

.0008

.1720

.0000

.0003

.0162

.0490

Value of PP ($)

964

.1630

Yes

(.0099)

.0745***

(.0053)

-.0274***

(.0029)

.0111***

.7

(5)

regressions at the 10

th , 30th , 50th , 70th , and 90th quantiles. Bootstrapped standard errors in

standard errors are in parentheses. Columns (2)-(6) are based on similarly specied quantile

amount of performance pay as they were practically insignicant (smaller than 10e-08). Robust

received, quadratics in both these measures, and year controls. I omit results for the quartic in

dierence on the probability of receiving performance pay, the amount of performance pay

Notes: Column (1) is based on a weighted least squares regression of the March-MORG wage

.5942

[q90] = [q70]

964

.0912

Yes

(.0081)

.0453***

(.0037)

-.0198***

(.0018)

.0086***

Probability of PP (%)

964

.0476

Yes

(.0079)

Yes

.0224***

(.0067)

(.0058)

.0560***

(.0076)

-.0167***

(.0025)

(.0050) -.0239***

.0085***

.0101**

.3

.1

(4)

Tests of Equality Across Quantiles (p-values)

# observations

pseudo-R

2 R

YEAR

Value of PP ($)/100

PP) /100

2

(Probability of

Probability of PP (%)

Quantile

Quantile Regression (3)

(1)

(2)

WLS

Table 11: The Eect of Incidence and Value of Performance Pay

964

.1788

Yes

(.0133)

.0946***

(.0103)

.0281***

(.0055)

.0087

.9

(6)

Figures

Figure 1: Current Population Survey Residual Variance, 1996-2005

41

Figure 2: The Eect of Performance Pay on Residual Wage Inequality, 1996-2005

42

Figure 3: MEPS-CPS Comparison, 1996-2005

43

Figure 4: MEPS-CPS Comparison, Salaried Workers, 1996-2005

44

Figure 5: MEPS-CPS Comparison, Hourly Paid Workers, 1996-2005

45

(a) March Comparison

(b) MORG Comparison

(c) Proxy Comparison

(d) CPS Comparison

Figure 6: qqplots, 1997

46

Figure 7:

The Eect of Performance Pay on the March-MORG Wage Dierence

Across Quantiles

47

(a) Density Function

(b) Distribution Function

(c) qqplot of

X

Figure 8

48

vs.

Y

(a) Density function, March 2000

(b) Distribution Function, March 2000

(c) qqplot of CPS vs. Proxy, March 2000

Figure 9

49

Appendix I To show that wage inequality between high ability and low ability high school educated (unskilled) workers is higher in performance pay jobs than in non-performance ρ  ρ  αAHU +(1−α)AU AHU pay jobs, we have to show that > ALU βALU +(1−β)AU

∵ AU = µAHU + (1 − µ) ALU ⇒ ALU 6 AU 6 AHU

where µ > 0

If there is at least one worker of each type, the inequalities are strict:

µ >0

and

ALU < AU < AHU . Let AU = AHU − ε where ε > 0 ⇒ αAHU + (1 − α) AU = αAHU + (1 − α) (AHU − ε) = αAHU + (1 − α) AHU − (1 − α) ε = AHU − (1 − α) ε < AHU where ε > 0 Let AU = ALU + ε ⇒ βALU + (1 − β) AU = βALU + (1 − β) (ALU + ε) = βALU + (1 − β) ALU + (1 − β) ε = ALU + (1 − β) ε > ALU ρ  ρ  αAHU +(1−α)AU > ∴ AAHU βA +(1−β)A LU LU

U

An identical argument applies for a higher level of wage inequality between high ability and low ability college educated (skilled) workers in performance pay jobs than in non-performance pay jobs.

Appendix II The Medical Expenditure Panel Survey (MEPS) is a relatively new dataset.

As

such, in this appendix I provide details on the way information on all forms of earnings is collected in the MEPS. This information is collected in the Employment and Employment Wage sections of the Household Component questionnaire; in what follows, relevant question numbers in this questionnaire are given in brackets. First o, it is important to note (in particular for the present study) that earnings information in the MEPS pertain to the current reference period and are therefore more similar to the point in time earnings measures of the MORG CPS than then retrospective measures of the March CPS. Workers are rst asked whether they are paid a salary, by the hour, or some other way (for example, by the day or by job/mile). Workers that report being paid a salary are asked how much is their salary [EW11], and a series of questions aimed at identifying accurately the period over which this

50

salary applies [EW11OV1, EW11OV2, EW12, EW17].

Income information is col-

lected for workers paid by the day or by the job/mile using a similar sequence of questions [EW03, EW04, EW05, EW05OV1 EW05OV2, and EW06].

27

Hourly paid

workers are asked to report their hourly wage [EW18]. Note that hourly and nonhourly income information collected in this way does not include any measures of performance pay (see footnote 15). Having collected information on workers'  base income, the MEPS then uses a similar sequence of questions to collect information on performance-based forms of income: tips, bonuses, and commissions. For each type of performance pay, workers were asked whether or not they received it [EW23_01, EW23_02, and EW23_03 respectively], how much of each type was received [EW24A, EW24B, and EW24C], and over what period these payments apply [EW24AOV1, EW24AOV2, EW24BOV1, EW24BOV2, EW24COV1, and EW24COV2].

Workers were given the option of

reporting received these payments over periods of one hour, one day, one week, two weeks, one month, one year, or over some other specied time interval.

Appendix III The qqplot I use is a special case of a quantile probability plot applied to the analysis of two one-dimensional nite or innite samples as discussed in Wilk and Gnanadesikan (1968). In this application I examine the nite samples of residuals constructed from the wage equations for both the MEPS and CPS samples. The primary goal will be to determine whether the distribution of residuals associated with the MEPS proxy is suciently replicating its corresponding CPS residual distribution.

The

procedure involves examining the equivalence of points corresponding to the same quantile between two standardized distributions.

An example is helpful.

Figures

8a and 8b show the density and distribution functions of two randomly generated samples,

X ∼ N (0, 1.5)

and

Y ∼ N (0, 2),

each of size

n = 10000. Y relative

Both gures illustrate the higher level of inequality in

to

X.

The

cumulative distribution function (c.d.f ) (Figure 8b) shows explicitly what is meant by  comparing points corresponding to the same quantile of each distribution - for each distribution, the intersection of the horizontal line and the c.d.f. indicates the value at the 9th decile of the distribution. Figure 8b shows that this value is larger for

Y

(2.575566) than for

X

(1.924978). Figure 8c illustrates the qqplot of

X

against

27 Unfortunately information is collected using only one time interval for any given worker. Collection over multiple time frames would have made it possible to check how consistently income information was collected.

51

Y

and represents the matching of quantiles of the

X

and

Y

distributions. The 45-

degree (dashed) line represents the locus of the qqplot if the c.d.f.'s of identical. I plot a horizontal line at

x=1.924978

X

and a vertical line at

and Y were y =2.575566

corresponding to the 90th percentile of each distribution. The following relationship th can be seen. Consider quantiles q ∈ Q . For any i quantile, if y (q) > x (q) ∀q > i, then the qqplot lies below the 45-degree line for these quantiles, and the distribution th of Y has a thicker upper tail. For any i quantile, if y (q) 6 x (q) ∀q > i , then the qqplot lies above the 45-degree line for these quantiles, and the distribution of

X

has a thicker upper tail (and thus exhibits greater upper-tail inequality). The lower end of the distribution exhibits the opposite relationship. If

y (q) 6 x (q) ∀q > i,

then the qqplot lies above the 45-degree reference line (as in Figure 8c), and the distribution of

Y

has a thicker upper tail. The opposite holds if the qqplot lies below

the reference line. To show the direct relevance of such a diagnostic plot to the distribution of residuals I present the density function, the distribution function, and the qqplot comparing the March 2000 CPS to the constructed March 2000 Proxy in Figure 9. This year was chosen because, as Figure 3 shows, the Proxy appeared to do a good job in replicating residual inequality as represented by the residual variance. The density illustrated in Figure 9a shows that there does appear to be more inequality (in the proxy than in the CPS) at the upper end of the distribution that is being oset by less inequality (in the proxy than in the CPS) at the lower end of the distribution. This inability to mimic the CPS is reected in the high degree of non-linearity illustrated in the associated qqplot (Figure 9c).

52