Public Sector Compensation: An Application of Robust and Quantile Regression

Abstract

This study assesses whether the theoretical compensation framework used to explain differences in public sector pay among full-time federal and state employees may also explain differences in pay at a local government level. In doing so, this study uses ordinary least squares (OLS) regression to test the application of the theoretical framework to a specific local government. Robust and quantile regression models are used subsequently to validate the findings obtained by the OLS model. The findings reveal that the covariates used to explain differences in compensation among full-time federal and state employees have similar effects at a local governmental level. While the OLS statistical model explains 26% (R² = .26) of the variance, the robust regression model explains 39% (R² = .39) of the variance. The percentage of variation explained by the quantile statistical models ranges from 14% (pseudo-R² = .14) to 50% (pseudo-R² = .50).

Keywords

compensation ordinary least squares regression public sector robust regression quantile regression

Introduction

The number of academic articles that have assessed public sector compensation has increased greatly since 2000. A number of articles have examined compensation at the federal level.^1-5 Numerous articles have examined compensation at the state level as well.^6-15 The number of studies focused on compensation at the local level has increased concomitantly.^16-19 Despite the increase in the extant literature, little attention has been given to the factors that influence compensation in local governments.^20-22

Concomitant with the growth of articles addressing compensation at the federal, state, and local levels, some studies have examined compensation among public sector careers, such as chief procurement officers,²³ city managers,²⁴ and local school superintendents.²⁵ Other studies have compared differences in compensation among private and public organizations^26-28 or among public and nonprofit institutions.²⁹ Although the extant literature has addressed important issues regarding compensation in the public sector, such as merit pay, performance-based pay, skill-based pay, and pay inequality, the number of studies that have examined the factors that influence pay in the public sector remains relatively small.^30-39

Due to the paucity of research focused on compensation in local governments, this study applies the theoretical compensation framework, developed in previous studies, to Montgomery County, Maryland, in order to assess whether similar covariates are significant predictors of the rate of pay among full-time employees. Thus, this study assesses whether covariates used in previous studies help explain differences in compensation among men and women, and among white and minority full-time employees. This study’s secondary purpose is to supplement the ordinary least squares (OLS) regression statistical model with competing models to assess whether the direction and magnitude of the statistical relationships among the covariates and the rate of compensation change or remain constant. Specifically, robust and quantile regression are used to validate the OLS regression model. In particular, quantile regression is used to validate the OLS regression model at different rates of compensation across the conditional distribution of the dependent variable. This is accomplished statistically by evaluating the relationship of the covariates and the rate of compensation at different quantiles such as the 10th, 25th, or 50th percentiles, which represent low to high levels of pay. By applying different statistical models to the same compensation data, the findings should estimate the extent to which the theoretical framework helps explain differences in compensation among public sector employees at a local governmental level.

In examining the rate of compensation among full-time employees in a specific local county government, this study addresses the following research questions:

Do the covariates found to be significant predictors of public sector compensation in previous studies have similar statistical relationships with the rate of pay of full-time employees in a particular local government?

Does the application of different statistical tests to the same data produce similar findings for each covariate of the theoretical framework?

Does the theoretical model used to explain differences in compensation among public sector employees at a macro governmental level help explain differences in pay at a micro level?

How well does the theoretical model explain differences in the rate of compensation among full-time public sector employees with low to high levels of pay?

In addressing the research questions above, this study aims to contribute to the extant literature by analyzing the compensation data with several statistical methods and by assessing the robustness of the theoretical compensation framework in explaining differences in the rate of pay among full-time county employees in a specific local government.

Previous Research

Academicians, elected officials, journalists, and researchers have made public sector compensation an important human resource management and public policy issue.^40,41 Journalists have made public sector compensation an important policy issue by placing media attention and scrutiny on salaries and wages earned by government employees.^42-45 Kaatz and Morris⁴⁶ observe that public employee compensation was moved to the forefront of the public agenda due to political and media attention. Similarly, Reilly⁴⁷ notes that the debate regarding whether private sector employees earn more in comparison with their public sector counterparts increased due to increased public scrutiny. Reilly et al.^48(p40) state that it is “difficult to pick up a local newspaper without reading about concerns regarding public sector wages, benefits, and/or pension programs.” One positive outcome of the increased media attention on public sector compensation is that new research has spawned. Hyde and Zeemering,⁴⁹ for example, examined the compensation of California city managers, based partially on increased media coverage, by comparing the pay of city managers to that of other professions.

Academicians and researchers have contributed to making public sector compensation an important human resource management issue by focusing on persistent disparities in pay between men and women and between white and minority employees.^50-54 When examining the compensation of public sector chief procurement officers, Alkadry and Tower⁵⁵ found that men earn more than women on average. They also found that the gap in pay between men and women increases when authority-based variables are considered. However, when Lewis et al.⁵⁶ examined the compensation for state and local government employees, they found that women benefitted more than men from public sector employment. They also found that the gender differences in the public–private wage gap had narrowed substantially. Meier and Wilkins⁵⁷ examined whether gender differences in pay existed between men and women school superintendents in Texas and found that women superintendents were paid higher than men, ceteris paribus. Briefly, research conducted by Reese and Warner⁵⁸ indicated that women employed by state governments in the United States have higher wages in comparison with men and women in the private sector.

Differences in pay between white and minority government employees also contributed to the study of compensation in the public sector.^59-61 Lewis et al.^62(p320) concluded that Blacks and Latinos gained more from the state and local government employment than whites. They also noted that Blacks and Latinos had higher levels of compensation in state and local governments than private firms. Llorens et al.⁶³ hypothesized that Blacks, Latinos, and women would choose employment in the public sector instead of employment in the private sector if wage penalties were greater in the private sector. They found that Blacks, Latinos, and women faced greater wage penalties in the private sector than in the public sector from 1998 to 2002. The authors also found that similarly skilled women experienced higher wage penalties in the private sector than in the public sector during the same time period. The regression analysis indicated that the public/private wage differential was statistically significant for Blacks, Latinos, and women. Last, Reese⁶⁴ found that American Indian, Black, and Latino women obtained gains in compensation in states with pay equity policies. Reese also found that the compensation of Asian women was higher than that of the average male in some states.

Research on public sector compensation also persists because the rate of pay affects recruitment, retention, and turnover.^65-70 For instance, Bowman⁷¹ noted that compensation is used most effectively in recruitment. In addition, Llorens⁷² observes that the ability of the public sector to attract and retain a high-quality workforce depends on having competitive compensation. However, Llorens and Stazyk⁷³ observe that the extant research has shown that compensation is a significant covariate of the public employee turnover. While compensation may attract qualified employees to the public sector initially, the inability or unwillingness of public organizations to offer competitive wages to employees during their public sector careers leads to the turnover.

Theoretical Framework

The extant research has found that public sector compensation is related statistically to several demographic and work-related covariates (see Figure 1). For example, Alkadry and Tower,⁷⁴ Bolitzer and Godtland,⁷⁵ and Meier and Wilkins⁷⁶ used age as a covariate to assess differences in public sector compensation. The extant research has obtained inconsistent findings for age. Alkadry and Tower⁷⁷ obtained statistically nonsignificant results for age when examining compensation among public sector chief procurement officers. However, Bolitzer and Godtland⁷⁸ found a negative association between age and the total, explained, and unexplained gender pay gap in the federal workforce for 1988, 1998, and 2007. Meier and Wilkins⁷⁹ found that age was related positively with the compensation of school superintendents in Texas. In this study, age is hypothesized to be related positively with the rate of compensation among full-time employees of Montgomery County, Maryland.

Figure 1.

Theoretical framework for public sector compensation.

As illustrated in Figure 1, ethnicity is another demographic covariate that has been used to assess differences in public sector compensation.^80-83 When ethnicity was measured as white or other, Alkadry and Tower⁸⁴ obtained a statistically negative relationship between ethnicity and the compensation of public sector chief procurement officers. However, Bolitzer and Godtland⁸⁵ obtained positive and negative associations between ethnicity and the gender pay gap in the federal workforce for 1988, 1998, and 2007. Specifically, they found that ethnicity contributed negatively to the explained pay gap between men and women federal employees and positively to the unexplained pay gap between men and women in the federal workforce. Meier and Wilkins⁸⁶ also obtained inconsistent results for ethnicity when examining the compensation of school superintendents in Texas. For instance, they found a positive relationship between Black and the compensation of superintendents; however, they obtained a negative relationship between Latino and the compensation of superintendents. In this study, it is hypothesized that the covariate for white employees will be related positively with the compensation of full-time employees of Montgomery County, Maryland. It is also hypothesized that the covariates for Blacks and Hispanics will be related negatively with the compensation of full-time employees of Montgomery County, Maryland.

Gender has also served as a covariate for assessing differences in public sector compensation (see Figure 1).^87-89 Alkadry and Tower,⁹⁰ for instance, used a covariate for male when examining the compensation of public sector chief procurement officers. In doing so, however, they obtained a statistically nonsignificant result between the covariate and the compensation of the chief procurement officers. On the other hand, when Meier and Wilkins⁹¹ examined the compensation of school superintendents in Texas, they obtained a positive relationship between the covariate coded as female and compensation. Reese and Warner⁹² coded the governors of U.S. state governments as “woman” and “other” when they analyzed the gender pay gap of state employees. They obtained a negative relationship between the covariate and the gender pay gap among state employees. In this study, it is expected that men will have higher rates of pay than women with full-time employment in Montgomery County, Maryland.

Another covariate used to assess differences among public sector employees is years of experience or service (see Figure 1).^93-95 The extant research shows inconsistent results for years of experience or service. For instance, Alkadry and Tower⁹⁶ found a positive relationship between years of service in the federal workforce and the salary of chief procurement officers; however, a statistically nonsignificant relationship was obtained between years of experience in procurement and salary. Research conducted by Bolitzer and Godtland⁹⁷ shows that experience in the federal government contributed negatively to the gender pay gap in the federal workforce in 1988 and 1998 but contributed positively to the gender pay gap in 2007. Last, Meier and Wilkins⁹⁸ obtained a positive relationship between experience and the compensation of school superintendents in Texas. With respect to this study, it is hypothesized that years or length of service (LOS) will be related positively with the compensation of full-time employees of Montgomery County, Maryland.

Scope of authority is another covariate used in previous studies to assess differences in compensation (see Figure 1).⁹⁹ When examining the rate of pay among chief procurement officers in the federal workforce, Alkadry and Tower¹⁰⁰ examined whether the scope of authority was related statistically with compensation. They found a positive relationship between the number of subordinates that the chief procurement officers supervised and the level of compensation. They also obtained a positive relationship between the volume of procurement handled by the chief procurement officers and compensation. In this study, a positive relationship is expected between employment in Montgomery County’s management leadership service (MLS) and the compensation of full-time employees.

Research Method

Montgomery County, Maryland, conducts annual workforce surveys on compensation. The 2019 compensation survey contains demographic, occupational, and salary-related data for approximately 8400 full-time employees. The demographic data include age, ethnic, and gender information for each employee. In addition, the survey collects occupational information for each employee, which includes LOS, type of position (i.e., managerial or nonmanagerial), and employee salary schedule. The data facilitate the assessment of whether demographic and occupational factors are statistically significant covariates of the rate of compensation among full-time employees of Montgomery County. With respect to addressing the research questions guiding this study, the data allow for assessing whether the covariates used in previous studies are significant predicators of the rate of compensation at the local level within a particular county government.

Montgomery County has a full-time workforce of approximately 8400 employees. Men compose 63% of the workforce. Whites represent 49% of the workforce. Of this ethnic cohort, men compose 69% of the workforce. Twenty-seven percent of the full-time workforce is Black. Among the Black full-time employees, men compose 60%. Hispanics compose 10% of the workforce. Similar to the white and Black cohorts, Hispanic men hold the majority of the full-time positions. Last, Asians hold less than 7% of the full-time positions. In contrast to the other ethnic cohorts, the percentage of Asian men and women in full-time positions is similar.

Covariates

The full-time employees of Montgomery County are the unit of analysis in this study. Three demographic variables are used as covariates. The first demographic covariate is age, which is measured by the number of years. Gender is the second demographic covariate and is coded as 1 for male and 0 for female. The third demographic covariate is ethnicity and is coded as follows: Asian = 1, other = 0; Black = 1, other = 0; Hispanic = 1, other = 0; and white = 1, other = 0.

The occupation-based covariates are LOS and MLS. LOS is measured in years from the year when the employee began his or her employment with Montgomery County to the present. With respect to measuring the MLS covariate, a full-time employee in the MLS workforce is assigned 1 and those not in the MLS are assigned 0.

Although the survey collects demographic and occupational data pertaining to Montgomery County’s full-time employees, the survey omits data related to education. The extant research on compensation shows that education is related positively with salaries and total compensation.^101-104 Chahyadi and Abusalim,¹⁰⁵ Cheng,¹⁰⁶ and Jalbert et al.¹⁰⁷ found that employees with higher levels of education earn more than less-educated employees in similar positions. While the covariates and the dependent variable used in this study are consistent with those of previous studies, the statistical model being tested is incomplete due to the absence of education-based explanatory variables.

Dependent Variable

The rate of compensation is the dependent variable in this study. This variable is measured by the annual pay obtained by each full-time employee. The average level of annual pay for all full-time employees of Montgomery County is approximately US$110,400. For men in full-time employment, the average annual compensation is about US$111,500. The average annual compensation for women in full-time employment is roughly US$108,600.

Statistical Models

Three statistical models are used to test the null hypotheses and to assess the relationships among the covariates and the rate of compensation. The OLS statistical model is as follows^108-110:

\hat{Compensation} = α + β_{1} Age + β_{2} White + β_{3} Asian + β_{4} Black + β_{5} Hispanic + β_{6} Male + β_{7} LOS + β_{8} MLS + ε_{ij}

where

\hat{Compensation}

is the predicted value of compensation for each full-time employee. Age is the covariate associated with the actual age of each full-time employee, white is the dichotomously coded covariate for white (1) and non-white (0) full-time employees, Asian is the dichotomously coded covariate for Asian (1) and non-Asian (0) full-time employees, Black is the dichotomously coded covariate for Black (1) and non-Black (0) full-time employees, Hispanic is the dichotomously coded covariate for Hispanic (1) and non-Hispanic (0) full-time employees, male is the dichotomously coded covariate for gender where men are assigned 1 and women 0, LOS is the covariate associated with the actual years of service of each full-time employee, MLS is the dichotomously coded covariate for full-time employees who have management-related (1) positions and those who do not have management-related (0) positions, and ε_ij represents the measurement error.

Each regression coefficient is tested a priori at α = .05. The OLS statistical model is used because the dependent variable is measured at the ratio level of measurement. Statistically, the OLS model would produce findings consistent with those of the extant research.

As a compliment to the OLS statistical model above, robust regression is used to validate the findings and the theoretical framework guiding this study. Robust regression is also used due to the detection of outliers with extreme low and high rates of compensation and due to the skewness of the data.^111,112 The robust statistical model is as follows:

\hat{Compensation} = α + θ_{1} Age + θ_{2} White + θ_{3} Asian + θ_{4} Black + θ_{5} Hispanic + θ_{6} Male + θ_{7} LOS + θ_{8} MLS + ε_{ij}

To be consistent with the OLS model above, each regression coefficient is tested a priori at α = .05.

Quantile regression is used to assess the relationships of the covariates on the rate of compensation across the conditional distribution of the dependent variable.^113-121 In so doing, the quantile statistical models supplement the findings of the OLS and robust models and validate the theoretical model in detecting differences in the rate of compensation at low, moderate, and high levels of pay. Specifically, the quantile regression models assess the statistical relationship of the covariates and the dependent variable at the 10th (US$54,500), 25th (US$64,500), 50th (US$74,500), 75th (94,500), and 90th (US$140,500) percentiles. The generic quantile statistical model is as follows:

\hat{Compensation} (θ) = β_{0} (θ) + β_{1} (θ) Age + β_{2} (θ) White + β_{3} (θ) Asian + β_{4} (θ) Black + β_{5} (θ) Hispanic + β_{6} (θ) Male + β_{7} (θ) LOS + β_{8} (θ) MLS + ε {(θ)}_{ij}

Similar to the OLS and robust regression models above, each regression coefficient is tested a priori at α = .05.

Findings

Table 1 summarizes the findings of the OLS and robust regression analyses. Although inconsistent results were obtained for some of the covariates, the results for several of the covariates are consistent. The findings for the covariate associated with age are consistent for the OLS and robust regression analyses. For the OLS regression, the findings for the unstandardized beta coefficient show that a unit increase in age increases compensation by .54 points (βAge_OLS = 0.542, p < .01). The findings for the robust regression reveal that a unit increase in age increases the rate of compensation by .14 points (βAge_R = .138, p < .001). With respect to the findings for whites versus nonwhites, the OLS regression indicates that whites and nonwhites have similar rates of compensation (βWhite_OLS = 8.69, p > .05). However, the robust regression analysis shows that compensation is related positively with the white cohort, where the movement from the nonwhite to the white cohort increases the rate of compensation by 8.42 points (βWhite_R = 8.421, p < .001). Similar findings were obtained for the comparison of Asian versus non-Asian full-time employees. While the OLS regression analysis reveals statistically nonsignificant findings for the comparison between Asians and non-Asians (βAsian_OLS = 11.50, p > .05), the robust regression analysis shows a positive relationship between Asians and the rate of compensation (βAsian_R = 6.68, p < .001), where moving from the non-Asian to the Asian cohort increases the rate of compensation by 6.68 points. Inconsistent findings were obtained for the comparison between Blacks and nonBlacks. Specifically, the OLS regression analysis reveals that the rate of compensation for Black and nonBlack full-time employees is similar (βBlack_OLS = −9.21, p > .05); by contrast, the robust regression analysis indicates that the rate of compensation is negatively associated with Black full-time employees (βBlack_R = −4.33, p < .001). Similar inconsistent findings were obtained for Hispanic versus non-Hispanic full-time employees.

Table 1.

OLS and Robust Regression Results for Full-Time Employee Compensation.

Covariate	OLS regression		Robust regression
Covariate	Unstandardized beta coefficient	Standardized beta coefficient	Beta coefficient
Age (years)	.542 (.208)	.031**	.138*** (.020)
White (=1)	8.691 (8.098)	.021	8.421*** (.792)
Asian (=1)	11.503 (10.784)	.014	6.679*** (1.055)
Black (=1)	−9.210 (8.417)	−.020	−4.325*** (.823)
Hispanic (=1)	−8.416 (9.624)	−.012	−2.434* (.941)
Male (=1)	14.274 (4.141)	.033***	−1.742*** (.405)
Length of service (years)	2.385 (.262)	.107***	1.275*** (.026)
MLS (=1)	455.964 (9.312)	.471***	46.150*** (.911)
Intercept	21.220 (11.133)		52.553*** (1.089)
N	8350		8350
F _(8,8341)	358.49		1194.82
Prob. > F	.001		.001
R-squared	.256		.391
Adj. R-squared	.255

Note. Standard errors are in parentheses. OLSs = ordinary least squares; MLS = management leadership service; Prob. = probability; Adj. = adjusted.

^*p < .05. **p < .01. ***p < .002.

With respect to gender differences in terms of the rate of compensation, the OLS regression analysis indicates that men in full-time employment have a higher rate of compensation than women in full-time employment (βMale_OLS = 14.27, p < .001). In contrast, the robust regression analysis reveals a statistically significant inverse relationship where men in full-time employment have a lower rate of compensation than women in similar positions (βMale_R = −1.28, p < .001). Similar findings were obtained for the covariate assessing LOS in the Montgomery County workforce. The OLS regression analysis shows a statistically positive relationship between LOS and the rate of compensation (βLOS_OLS = 2.39, p < .001), where a unit increase in LOS increases the rate of compensation by 2.39 points. The robust regression analysis reveals a statistically significant positive relationship between LOS and the rate of compensation (βLOS_R = 1.28, p < .001). In addition, a positive relationship exists between belonging to the county government’s MLS and the rate of compensation. The OLS regression indicates that membership into the county’s MLS program increases the rate of compensation by 445.96 points (βMLS_OLS = 455.964, p < .001). Despite obtaining a similar positive relationship between the management-based covariate and the rate of compensation, the robust regression analysis shows that membership into the county’s MLS increases the rate of compensation by 46.15 points (βMLS_R = 46.15, p < .001). Last, the findings show that the OLS regression model explains 26% ( $R_{OLS}^{2} = .256$ ) of the explained variance, while the robust regression model explains 39% ( $R_{R}^{2} = .391$ ).

The findings of the quantile regression analyses are consistent with those obtained by the robust regression analysis (see Table 2). As summarized in Table 2, the pseudo-R² coefficients obtained by the quantile statistical models range from 14% to 50% (

.140 \leq R_{θ}^{2} \leq .497

). The statistical model for the robust regression explains 39% (

R_{R}^{2} = .391

) of the variance. With few exceptions, the directions of statistically significant findings of the quantile regression models are consistent with those obtained by the robust regression model. The sizes of the beta coefficients obtained by the quantile regression analyses are relatively similar to those obtained by the robust regression model, with few exceptions.

Table 2.

Robust and Quantile Regression Results for Montgomery County Full-Time Employee Compensation.

Covariate	Robust regression	Quantile regression
	Beta coefficient	10th Q = US$54,500	25th Q = US$64,500	50th Q = US$74,500	75th Q = US$94,500	90th Q = US$114,500
	Beta coefficient	Coefficient	Coefficient	Coefficient	Coefficient	Coefficient
Age (years)	.138*** (.020)	−.0893*** (.023)	−.085** (.032)	.099** (.034)	.507*** (.030)	.663*** (.048)
White (=1)	8.421*** (.792)	7.143*** (.596)	8.051*** (1.792)	7.630*** (.821)	7.717*** (1.031)	6.069** (1.992)
Asian (=1)	6.679*** (1.055)	1.875* (.936)	3.983* (1.940)	6.272*** (1.639)	11.416*** (1.846)	14.865*** (3.768)
Black (=1)	−4.325*** (.823)	−.893 (.566)	−5.339** (1.887)	−5.877*** (.891)	−4.440*** (1.061)	−6.781** (2.027)
Hispanic (=1)	−2.434* (.941)	−1.429 (.832)	−3.729 (1.930)	−2.148* (.845)	−1.586 (1.188)	−5.332* (2.283)
Male (=1)	−1.742*** (.405)	−1.071** (.363)	−.763 (.399)	−1.457** (.538)	−2.262*** (.573)	−1.990* (.899)
Length of service (years)	1.275*** (.026)	1.071*** (.044)	1.356*** (.041)	1.506*** (.052)	1.311*** (.054)	1.278*** (.068)
MLS (=1)	46.150*** (.911)	51.250*** (2.347)	52.712*** (1.469)	58.296*** (2.114)	1380.00*** (131.305)	1390.00*** (2.832)
Intercept	52.553*** (1.089)	45.750*** (.877)	50.517*** (1.913)	51.414*** (1.147)	47.270*** (1.575)	54.230*** (2.990)
N	8350	8350	8350	8350	8350	8350
F _{(8, 8341)}	1194.82
Prob. > F	.001
R-squared	.391	.162	.162	.140	.230	.497

Note. Standard and bootstrap standard errors are in parentheses. Q = quantile; MLS = management leadership service; Prob. = probability; Adj. = adjusted.

*p < .05. **p < .01. ***p < .001.

For the covariate associated with age, the quantile regression models produced inconsistent findings; however, the findings are relatively consistent with those obtained by the OLS and robust regression models, with the exception of the findings for the 10th and 25th quantiles (see Table 2). At the 10th quantile, a unit increase in age decreases the rate of compensation by .089 points (βθ_.10Age = −.0892, p < .001). A similar inverse relationship exists at the 25th quantile, where a unit increase in age decreases the rate of compensation by .085 points (βθ_.25Age = −.085, p < .01). In contrast, the findings show positive relationships between age and the rate of compensation at the 50th, 75th, and 90th quantiles. At the 50th quantile, a unit increase in age increases the rate of compensation by .099 points (βθ_.50Age = .099, p < .01). The findings for the 75th quantile show that a unit increase in age increases the rate of compensation by .51 points (βθ_.75Age = .507, p < .001). At the 90th quantile, a unit increase in age increases the rate of compensation by 1.66 points (βθ_.90Age = .663, p < .001).

The findings for the ethnicity-based covariates are consistent for the robust and quantile regression models (see Table 2). At the 10th quantile, when moving from the nonwhite to the white cohort, the rate of compensation increases by 7.14 points (βθ_.10White = 7.142, p < .001). A similar positive relationship is present at the 25th quantile, where moving from the nonwhite to the white cohort increases the rate of compensation by 8.05 points (βθ_.25White = 8.051, p < .001). At the 50th quantile, moving from the nonwhite to the white cohort increases the rate of compensation by 7.63 points (βθ_.50White = 7.629, p < .001). Similarly, the rate of compensation increases by 7.72 points (βθ_.75White = 7.716, p < .001) when moving from the nonwhite to the white cohort at the 75th quantile. At the 90th quantile, the rate of compensation increases by 6.07 points (βθ_.90White = 6.069, p < .01) when moving from the nonwhite to the white cohort. Although these findings are consistent for the robust and quantile regression models, they differ from the OLS regression model, which obtained a statistically nonsignificant finding between the nonwhite and white cohorts and the rate of compensation (see Table 1).

With respect to the findings for Asians and non-Asians, the findings for the quantile regression models are consistent with those obtained by the robust regression model where positive relationships exist between the covariate and the rate of compensation (see Table 2). However, the findings differ from those produced by the OLS regression model (see Table 1). At the 10th quantile, moving from the non-Asian to the Asian cohort increases the rate of compensation by 1.88 points (βθ_.10Aisan = 1.875, p < .05). The finding for the 25th quantile shows that moving from the non-Asian to the Asian cohort increases the rate of compensation by 3.98 points (βθ_.25Asian = 3.98, p < .05). In addition, moving from the non-Asian to Asian cohort increases the rate of compensation by 6.27 points (βθ_.50Asian = 6.272, p < .001) at the 50th quantile. At the 75th quantile, the rate of compensation increases by 11.42 points (βθ_.75Asian = 11.416, p < .001) when moving from the non-Asian to the Asian cohort. Last, at the 90th quantile, the rate of compensation increases by 14.87 points (βθ_.90Asian = 14.865, p < .001) when moving from the non-Asian to the Asian cohort.

For the covariate associated with Blacks and nonBlacks, the findings of the quantile regression models are generally consistent with those produced by the robust regression model (see Table 2). Specifically, both the robust and the quantile regression models show an inverse relationship between the covariate and the rate of compensation. While a statistically nonsignificant relationship exists at the 10th quantile, the rate of compensation decreases by 5.34 points (βθ_.25Black = −5.339, p < .01) when moving from the nonBlack to the Black cohort at the 25th quantile. A similar inverse relationship is present at the 50th quantile where moving from the nonBlack to the Black cohort decreases the rate of compensation by 5.88 points (βθ_.50Black = −5.877, p < .001). At the 75th quantile, the rate of compensation decreases by 4.44 points (βθ_.75Black = −4.440, p < .001) when moving from the nonBlack to the Black cohort. In addition, moving from the nonBlack to the Black cohort decreases the rate of compensation by 6.78 points (βθ_.90Black = −6.781, p < .01) at the 90th quantile.

As Table 2 summarizes, inconsistent findings were obtained by the quantile regression models for the covariate associated with Hispanics and non-Hispanics. In general, the statistically nonsignificant and significant inverse relationships obtained by the quantile regression models are consistent with the findings produced by the robust regression analysis. The inverse relationships, however, are inconsistent with the finding obtained by the OLS regression model. Statistically nonsignificant findings were obtained at the 10th quantile (βθ_.10Hispanic = −1.429, p > .05) and at the 25th quantile (βθ_.25Hispanic = −3.729, p > .05), indicating that Hispanics and non-Hispanics have similar rates of compensation. However, at the 50th quantile, moving from the non-Hispanic to the Hispanic cohort decreases the rate of compensation by 2.15 points (βθ_.50Hispanic = −2.148, p < .05). The rate of compensation is similar for Hispanics and non-Hispanics at the 75th quantile (βθ_.75Hispanic = −1.586, p > .05), where a statistically nonsignificant inverse relationship exists. At the 90th quantile, the rate of compensation decreases by 5.33 points (βθ_.90Hispanic = −5.332, p < .05).

In contrast to the findings obtained by the OLS regression model, the quantile regression models show that the rate of compensation is related negatively with gender (see Table 2), which is consistent with the findings produced by the robust regression model (see Tables 1 and 2). At the 10th quantile, moving from the women to the men cohort decreases the rate of compensation by 1.07 points (βθ_.10Male = −1.071, p < .01). A statistically nonsignificant relationship exists at the 25th quantile (βθ_.25Male = −.763, p > .05). However, at the 50th quantile, the rate of compensation decreases by 1.46 points (βθ_.50Male = −1.457, p < .01) when moving from the women to the men cohort. At the 75th quantile, moving from the women to the men cohort decreases the rate of compensation by 2.26 points (βθ_.75Male = −2.262, p < .001). In addition, the rate of compensation decreases by 1.99 points (βθ_.90Male = −1.990, p < .05) when moving from the women to men cohort at the 90th quantile.

The findings for LOS are consistent for the OLS, robust, and quantile regression models (see Tables 1 and 2). Each analysis shows a positive relationship between LOS and the rate of compensation. For example, the quantile regression model for the 10th percentile shows that a unit increase in LOS increases the rate of compensation by 1.07 points (βθ_.10LOS = 1.071, p < .001). At the 25th quantile, a unit increase in LOS increases the rate of compensation by 1.36 points (βθ_.25LOS = 1.356, p < .001). A unit increase in LOS also increases the rate of compensation by 1.501 points (βθ_.50LOS = 1.506, p < .001) at the 50th quantile. At the 75th quantile, a unit increase in LOS increases the rate of compensation by 1.31 points (βθ_.75LOS = 1.311, p < .001). Similarly, at the 90th quantile, a unit increase in LOS increases the rate of compensation by 1.28 points (βθ_.90LOS = 1.278, p < .001).

Finally, the OLS, robust, and quantile regression models show consistent findings for the rate of compensation and whether a full-time employee belongs to Montgomery County’s MLS or not (see Tables 1 and 2). As Table 2 summarizes, the quantile regression models indicate positive relationships between the rate of compensation and MLS membership. At the 10th quantile, the rate of compensation increases by 51.25 points (βθ_.10MLS = 51.25, p < .001) when moving from non-MLS to MLS positions. Similarly, moving from non-MLS to MLS positions increases the rate of compensation by 52.71 points (βθ_.25MLS = 52.712, p < .001) at the 25th quantile. The rate of compensation also increases at the 50th quantile where moving from non-MLS to MLS positions produces a positive change in pay of 58.30 points (βθ_.50MLS = 58.296, p < .001). At the 75th quantile, moving from non-MLS to MLS positions increases the rate of compensation by 1380 points (βθ_.75MLS = 1380.00, p < .001). A similar rate of increase occurs at the 90th quantile where moving from non-MLS to MLS positions increases the rate of compensation by 1390 points (βθ_.90MLS = 1390.00, p < .001).

Discussion

When compared with the findings of previous studies, the OLS, robust, and quantile models produced lower coefficients of determination (R²). For instance, the OLS regression model produced R² of .26, while the robust regression model produced R² of .39. The quantile regression models obtained pseudo-R² values ranging from .14 to .50. In contrast, when assessing the salaries of public sector chief procurement officers, Alkadry and Tower¹²² used linear regression and obtained R² of .572 when salary was used as the dependent variable. Similarly, Kearney¹²³ used a linear regression model when examining the salaries of state employees and obtained R² of .512. In addition, Meier and Wilkins¹²⁴ obtained R² values of .79 and .80 when examining the salaries of school superintendents in Texas. Although the R² values of this study are lower than those reported in previous studies, the same covariates affect the rate of compensation of full-time employees in Montgomery County, Maryland.

The findings obtained by the robust and quantile models are inconsistent with those of Alkadry and Tower,¹²⁵ who obtained a statistically nonsignificant finding for age and the compensation of public sector chief procurement officers. However, the positive relationship between age and compensation is generally consistent for each regression analysis. Specifically, the rate of compensation increases with the age of full-time employees, which is consistent with the findings of Meier and Wilkins,¹²⁶ who found that age was related positively with the compensation of school superintendents in Texas. However, at the 10th and 25th percentiles, the quantile regression models indicate that age is inversely related to the rate of compensation, which is inconsistent with the findings of Meier and Wilkins. One plausible explanation for the inverse relationship is that a significant percentage of the individuals at the lower rates of compensation obtain county employment later in life. In general, the rate of compensation increases with an increase in the age of full-time employees.

Although the OLS regression obtained statistically nonsignificant findings for the ethnicity-based covariates, the robust and quantile regression models indicate the rate of compensation varies based on ethnicity. For example, whites who are employed full-time have higher rates of compensation than nonwhites in similar positions, which is inconsistent with the findings of Alkadry and Tower,¹²⁷ who found a negative relationship between ethnicity and the compensation of public sector chief procurement officers when ethnicity was categorized as white and other. The negative relationships for Blacks and the rate of compensation are inconsistent with the findings of Meier and Wilkins,¹²⁸ who found a positive relationship between Blacks and the compensation of school superintendents in Texas. However, the negative relationships for Hispanics and the rate of compensation are consistent with the findings of Meier and Wilkins, who found a similar finding when assessing the pay of school superintendents in Texas. These findings indicate that nonwhite employees earn less than white employees in similar full-time positions in Montgomery County, Maryland. More importantly, the findings obtained by the robust and quantile models indicate that ethnicity influences the rate of compensation among full-time employees.

The robust and quantile regression models obtained negative relationships for gender when categorized as 1 for men and 0 for women. In contrast, the OLS regression model produced a positive relationship between gender and the rate of compensation. The findings obtained by the robust and quantile regression models are consistent with the findings of Meier and Wilkins,¹²⁹ who found that women school superintendents in Texas earned higher salaries in than men in similar positions. In addition, the findings suggest that women who work full-time in county government tend to have higher rates of compensation than men, which is consistent with the findings of Lewis et al.,¹³⁰ who observed that women benefit from public sector employment. However, the findings are inconsistent with the findings of Alkadry and Tower,¹³¹ who obtained statistically nonsignificant results when assessing the compensation of public sector chief procurement officers. The findings are also inconsistent with the findings of Reese and Warner,¹³² who obtained a negative relationship between gender and the gender pay gap in state governments. When comparing the compensation of men and women in full-time employment in Montgomery County, Maryland, however, the robust and quantile regression models show that women have higher rates of compensation than men in similar positions all things being equal. As Lewis et al.¹³³ have asserted, women employed in the public sector benefit more than men.

Each regression model shows that LOS is related positively with the rate of compensation. These findings are consistent with the findings of Alkadry and Tower,¹³⁴ who obtained a positive relationship between years of service in the federal government and the compensation of public sector chief procurement officers. In addition, the findings are consistent with the findings of Meier and Wilkins,¹³⁵ who found that experience is related positively with the compensation of school superintendents in Texas. LOS is an important covariate of public sector compensation at the macro and micro governmental levels.

The regression models obtained positive relationships between scope of authority and the rate of compensation. These findings are consistent with the findings of Alkadry and Tower,¹³⁶ who found a positive relationship between the number of subordinates which chief procurement officers supervised and the rate of compensation. At macro and micro levels of government, differences in the rate of compensation between those in full-time management-based and nonmanagement-based positions are due to the additional responsibilities which supervisors and managers perform.

While the OLS statistical model detected some significant relationships between the covariates and the rate of compensation, the robust and quantile regression models detected significant relationship between the covariates and the dependent variable that the OLS statistical model failed to observe. Additionally, the robust and quantile models indicated that the direction of the statistical relationships were opposite of those obtained by the OLS model in some instances. One plausible explanation for the inconsistent findings between the OLS and the robust and quantile regression models is that the OLS model was negatively affected by the presence of outliers and issues of nonnormality in contrast with the robust and quantile regression models. Statistically, the robust and quantile statistical models adjusted for the nonnormality of the data and produced results where the relationships between the covariates and dependent variable were consistent.

Conclusion

The findings show that the theoretical framework used to explain differences in compensation between men and women, between whites and nonwhites, and between managers and nonmanagers in federal and state employment also helps explain differences in pay at the local level. Stated differently, the covariates used in previous federal and state compensation studies support disparities in compensation among local government employees. With respect to the use of multiple statistical methods to analyze the compensation data, the findings obtained by the statistical models validate the use of the covariates used in previous compensation studies. The simultaneous use of different statistical models helps confirm the findings of previous studies and validate the theoretical framework developed by the extant research.

While the findings of this study are important in terms of assessing the effect of demographic- and occupation-based factors on public sector compensation, the theoretical framework guiding the research is incomplete due to the exclusion of education-based covariates. The statistical models are also incomplete because surveys on public sector compensation neglect to obtain data related to educational attainment and training. By obtaining education-based data, future research on public sector compensation will be able to assess fixed and interaction effects of education on compensation.

Footnotes

Acknowledgments

I wishes to thank Professor Megan Topham, Department of Public Administration and Real Estate Development, Huizenga College of Business and Entrepreneurship, Nova Southeastern University, and the anonymous reviewers for providing their comments and insights which improved the quality of the article greatly.

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Salomon Alcocer Guajardo

Notes

Author Biography

Salomon Alcocer Guajardo, PhD, is an associate professor of public administration in the Department of Public Administration and Real Estate Development at the H. Wayne Huizenga College of Business and Entrepreneurship, Nova Southeastern University. His research centers on human resource management, on nonprofit and public organizational performance, and on organizational diversity.