Economics Letters 121 (2013) 263–266

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Economics Letters

journal homepage: www.elsevier.com/locate/ecolet

Public employment and earnings inequality: An analysis based onconditional and unconditional quantile regressionsJean-Marc Fournier ∗, Isabell KoskeOECD Economics Department, 2 rue André Pascal, F-75775 Paris Cedex 16, France

h i g h l i g h t s

• The link between public employment and inequality is studied using quantile regressions.• The complementary nature of conditional and unconditional quantile regressions is shown.• Empirical results show that the two methods focus on different inequality concepts.• The inequality effect of cutting public employment varies across countries.

a r t i c l e i n f o

Article history:Received 12 July 2012Received in revised form3 May 2013Accepted 10 August 2013Available online 19 August 2013

JEL classification:C21D31J45

Keywords:Quantile regressionIncome inequalityPublic employment

a b s t r a c t

Studies investigating the link between public employment and earnings inequality based on micro datatypicallymake use of conditional quantile regressions. Such analysis revealswhy earningsmay bemore orless dispersed among public-sector than private-sector workers, but does not allow drawing conclusionsabout its impact on overall earnings inequality. The unconditional quantile regression technique proposedby Firpo et al. (2009) overcomes this deficiency, and this technique is applied here to show that a fallin public employment may raise or reduce earnings inequality, depending on country specificities. Thepaper also highlights the complementary roles of conditional and unconditional quantile regressions ininvestigating the determinants of earnings inequality.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In many countries, earnings have become more dispersed overthe past decades. This has given rise to a revived interest among re-searchers and policy makers in understanding the determinants ofearnings inequality. The existing literature typically relies on con-ditional quantile regression (CQR),which allows estimating the im-pact of an explanatory variable not only on the mean but also ondifferent parts of the distribution (Koenker and Basset, 1978). Themethod focuses on the conditional quantile of an individual, whichis his/her position in a virtual distribution in which all individu-als are assumed to have the same observed characteristics. It canthus answer questions such as: what is the impact on the earn-ings of the median individual in that virtual distribution of mov-ing from a private-sector to a public-sector job? Firpo et al. (2009)

∗ Corresponding author. Tel.: +33 1 45 24 92 03.E-mail addresses: jean-marc.fournier@oecd.org,

jean-marc.fournier@polytechnique.org (J.-M. Fournier).

0165-1765/$ – see front matter© 2013 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.econlet.2013.08.015

have recently proposed a new method that focuses on an individ-ual’s unconditional quantile, which is his/her position in the actualearnings distribution. The method allows answering questionssuch as: what is the impact on median earnings of changing theshare of public-sector employment by one per cent?

This paper uses the new unconditional quantile regression(UQR) methodology to explore the role of public employment inshaping the earnings distribution. The share of the public sectorin total employment is likely to have an important influence onearnings inequality. For example, unions might be more power-ful in the public sector (Grimshaw, 2000; Checchi and Lucifora,2002), performance-related pay may be less prevalent, earningsmight be set based on redistribution rather efficiency considera-tions (Alesina et al., 2000), and the labour supply might be lesselastic (Müller, 1998). Moreover, in light of mounting pressures onpublic budgets, many countries are considering cuts in public em-ployment, making an analysis of the potential inequality effects avery topical issue.

Despite its importance, the topic has received little attentionin the empirical literature. García et al. (2001) and Müller (1998)

264 J.-M. Fournier, I. Koske / Economics Letters 121 (2013) 263–266

investigate the role of public employment using household surveydata, but — due to the reliance on CQRs — cannot draw conclusionsabout its impact on overall earnings inequality. While the country-level analyses by Caldéron et al. (2005) and Koeniger et al. (2007)make this link, the papers rely on broad information at the macrolevel and, due to the panel approach, do not allow for cross-countrydifferences in the effects. The present paper fills this gap in theliterature by applying the UQR technique to household survey datafrom Australia, Canada, Korea, Switzerland, and the United States.CQR results are also reported for comparison and to illustrate thecomplementarities between the two techniques.

2. Theoretical considerations

Inequality can be decomposed into within-group and between-group inequality (Robinson, 1976). To illustrate this, consider apopulation divided into two groups, group 0 and group 1. Measur-ing inequality by the log variance of earnings in the total popula-tion Var, it can be expressed as

Var = Var0 + W1 ∗ (Var1 − Var0) within

+W1 ∗ W0 (Y1 − Y0)2

between

, (1)

where Y0 and Y1 denote the log mean earnings in the two groups,W0 andW1 the employment shares, and Var0 and Var1 the log vari-ances of earnings in the two groups (Freeman, 1980). If the meanearnings are the same in the two groups, a rise in the employmentshare W1 raises the economy-wide earnings inequality if and onlyif the variance in group 1 is larger than that in group 0 (within ef-fect). If the variances are the same in both groups, the economy-wide earnings inequality increases in the employment share W1until this share reaches exactly one half (between effect). More gen-erally (i.e., with non-equal variances), the economy-wide inequal-ity peaks when the share of group 1 is equal to

W1 =Var1 − Var02(Y1 − Y0)2

+12. (2)

While this analysis provides descriptive insights that help to un-derstandhow the overall inequality is related to the public employ-ment share, it ignores alternative income determinants. UQRs andCQRs allow including covariates and thus help to overcome thisdeficiency. CQRs assume the τ th conditional quantile of a randomvariable Y to be a linear function of randomly distributed exoge-nous factors X:

qY |X (τ )[Y ] = Xβ(τ), (3)

where this conditional quantile is the relative position of an indi-vidual among a (virtual) population of individuals who share ex-actly the same observed characteristics. The estimates capture thecorrelation between public employment and unobserved charac-teristics such as ability (Arias et al., 2001). If the estimated co-efficient on the public employment dummy decreases along thedistribution of conditional quantiles, this means that the part ofthe within-group inequality that cannot be explained by the con-trol variables is lower among public employees. In this sense, CQRsare amore sophisticated version of a simple variance calculation ofthe within-group inequality effect, controlling for other observedcharacteristics.

While CQRs only yield the within-group inequality effect, UQRsyield the total effect, i.e., the sumof the between-group andwithin-group inequality effects. Specifically, UQRs provide an estimateof the marginal effect on the unconditional quantile of a smallincrease in a certain characteristic:

γ (t) = limt→0

qY (τ ) [h(X + t, ε)] − qY (τ ) [h(X, ε)]t

, (4)

where earnings Y are a function h of observed characteristics Xand unobserved characteristics ε, and qY (τ )[Y ] is the τ th quantileof the unconditional distribution of Y . Individuals are assumed to

Fig. 1. Variance of log earnings as a function of the share of public sector (Freeman’sformula).

Table 1Variance effect: descriptive statistics and RIF-variance estimates.

Country Year W1 Y0 Y1 VAR0 VAR1 RIF-variance

Australia 2009 0.215 7.988 8.340 1.112 0.475 −0.294* (−2.05)Canada 2008 0.195 7.745 8.158 1.077 0.739 −0.256** (−6.04)Korea 2007 0.153 7.434 7.952 0.523 0.456 0.009 (0.18)Switzerland 2008 0.362 8.607 8.573 0.490 0.490 −0.102* (−2.03)United States 2007 0.220 8.096 8.147 0.821 0.609 −0.244** (−3.23)

Note: The last column indicates the RIF-variance coefficient together with itsT -statistic (in brackets). RIF-variance estimates refer to UQR estimates with therecentered influence function (RIF) of the variance.

* Indicate the significance level 5% of the RIF-variance coefficient.** Indicate the significance level 1% of the RIF-variance coefficient.

be independent; the function h is not altered by a change in otherindividuals’ characteristics. UQRs thus provide an estimate of thepartial equilibrium effect of the variable of interest. It is furtherassumed that the unobserved heterogeneity is independent fromobserved characteristics and that there is no reverse causality.Similarly to CQRs, UQRs go beyond Robinson’s analysis in that theyallow controlling for other determinants of inequality. As discussedby Firpo et al. (2009), the UQR method extends to other statisticssuch as the variance. In the presence of outliers in the tails of thedistribution, the results may depend on the statistic used, with alog earnings differentials (e.g., the 90–10 log earnings differential)being more robust.

3. Empirical analysis

The quantile regression techniques are applied to five differentcountries: Australia (Household Income and Labour Dynamics inAustralia Survey), Canada (Survey of Labour and Income Dynam-ics), Korea (Korean Labour and Income Panel), Switzerland (SwissHousehold Panel), and the United States (Panel Study of IncomeDynamics). The regressions relate the logarithm of an individual’sgross monthly labour earnings to a dummy variable that is equalto unity if the individual works for the local or central governmentor a public enterprise and a set of control variables. These are thelogarithm of working hours, gender, age and age squared, and thehighest education level attained (differentiating between lower-secondary education or less, upper-secondary education, and ter-tiary education), inspired by thework ofMincer (1958). The sampleis restricted to individuals aged 15 to 64whowork part time or fulltime and have positive labour earnings during the reference year.All data manipulations follow closely Fournier and Koske (2012).Descriptive statistics on mean earnings and the variance of earn-ings in the two sectors are provided in Table 1.

As a preliminary step, the impact of a rise in public-sector em-ployment on the variance of economy-wide earnings is calculatedusing Freeman’s formula. The results suggest that, for Australia,Canada, and the United States, a rise in the share of public-sectoremployment is associated with a decline in the variance of earn-ings, irrespective of the current size of the public sector (the linesin Fig. 1 are downward sloping). Earnings are less dispersed among

J.-M. Fournier, I. Koske / Economics Letters 121 (2013) 263–266 265

Fig. 2. Effect on log earnings of working in the public sector.

public-sectorworkers and thewithin-group inequality effect dom-inates. For Switzerland, Eq. (1) predicts that a change in public-sector employment has no discernible effect on the variance ofearnings, because both sectors are similar in terms of average earn-ings and the dispersion of earnings. For Korea, the implied profileis humped shaped, whereby the dispersion of economy-wide earn-ings rises in the share of public-sector employment until this sectorhas reached about 40% of total employment (which is well aboveits current share). Since the average earnings are higher amongpublic-sector employees while the within-group inequality is sim-ilar in the two sectors, the between effect dominates.

Turning to the CQR results, the earnings effect of working inthe public sector is equal to zero for most parts of the conditionalearnings distribution for Switzerland (Fig. 2). For the other fourcountries, there is an earnings premium, which declines along theconditional earnings distribution and, for the United States, eventurns into a penalty at very high quantiles. The downward-slopingCQR lines mean that the fraction of earnings that cannot be ex-plained by the control variables is less dispersed among public-sector workers. Potential explanations include less powerfulunions in the private sector or a higher reliance on performance-related pay.

Whether the lower dispersion of public-sector earnings in thesefour countries translates into a negative link between the share ofpublic-sector employment and earnings inequality is a priori un-clear, since this depends on the initial size of the public sector and

the relative level of earnings. The UQR technique allows answeringthis question. It indicates that a cut in public-sector employmentwould raise inequality in Australia and the United States by low-ering earnings at the bottom and raising earnings at the top of theearnings distribution (Fig. 2). In Canada, middle-income workerswould suffer the most from a cut in public-sector employment. InKorea, a cut in public-sector employmentwould be associatedwitha decline in inequality since the earnings of low-income workerswould fall less than the earnings of high-income workers (thoughthe effect is significant only at the 10% level). While this is surpris-ing in light of the more compressed earnings distribution in thepublic sector, the reason is that (average) earnings differ widelybetween sectors. Combined with the rather low share of the pub-lic sector in total employment, this means that the between-groupinequality effect dominates the within effect.

Focusing on the variance of earnings as a measure of inequalityleads to slightly different conclusions. Here, the UQR regressionssuggest that a rise in public-sector employment not only lowersinequality in Australia, Canada, and the United States, but also inSwitzerland. While the positive coefficient for Korea is in line withthe other approach, the coefficient is not significant at conven-tional levels of significance. As flagged above, the reason for thedifferent results might be outliers in the tails of the two countries’earnings distributions which are ignored when looking at earn-ings quantiles in the 10–90 range. The conclusions drawn from thequantile approach are thus considered as more robust than thoseof the variance approach.

266 J.-M. Fournier, I. Koske / Economics Letters 121 (2013) 263–266

Acknowledgement

The authors would like to thank the anonymous referee, whosecomments have helped improve the content of this paper.

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