Within-Establishment Wage Inequality and Satisfaction

The aim of this paper is to provide fresh empirical evidence on the mechanisms through which wage inequality affects worker satisfaction.Theoretically, the wages of others may affect workers' utility for two main reasons: Workers may derive well-being from their social status (the comparison effect) and/or they may use others' wages to help predict their own future wage (the information effect). The author tests both hypotheses. To do this, she models individual utility from pay as a function of a workers own wage and the earnings of all other workers within the same establishment, and she estimates the model using matched British employeremployee data. The author assumes incomplete information about others' wages. She finds that the comparison effect matters. Interestingly, she also provides some evidence on a positive relation between well-being and inequality. Her results are robust to different specifications and different definitions of the reference group. JEL C25 J28 J31 J33


Introduction
Since the early work of Hammermesh (1977) and Freeman (1978) many authors have analyzed the determinants of individuals' subjective assessment of the utility gained from their work environment. A significant amount of empirical work in recent economic literature has focused on the role of income comparisons in determining job satisfaction: the idea is that job satisfaction is not determined by absolute wages only, but rather by relative wages (for detailed reviews see Frey and Stutzer, 2002;Senik, 2004;Easterlin, R., 2006;Clark et al., 2008). This literature has generally concluded that income comparisons are important in determining workers' job or pay satisfaction.
Theoretically, the wages of others may affect workers' utility for two main reasons.
Firstly, workers preferences may depend directly on their salary relative to their reference groups. We have comparison effects: workers derive well-being from their social status. In the well know model of Fehr and Schmidt (1999) utility depends positively on one's own income, but negatively on the differences between one's own income and that of others suggesting a dislike of others having more and a compassion of others having less. Thus, the model predicts a negative relation between well-being and inequality. But if, contrary to Fehr and Schmidt's hypotheses, we suppose that lower incomes for others raise individual's utility (prestige effect), we could in principle also predict a positive relation between well-being and inequality.
Secondly, workers may use others wages to help to predict their own future wage, as in the "tunnel effect" of Hirschman and Rothschild (1973). Thus, the more others earn, the happier the worker is, as others good fortune provides information about the workers' future prospects.
We observe information effects. Workers may appreciate inequality if this signals future potential career improvements (at least in the short term).
The role of wage inequality in predicting subjective well-being is therefore controversial. In this article, we provide fresh empirical evidence of the mechanisms through which wage inequality may affect worker satisfaction. Both comparison and information effects are tested. To achieve our aims, we model individual utility from pay as a function of a worker's own wage and the earnings of all other workers within the same establishment, and we estimate the model using British employer-employee data. Contrary to previous literature, we assume incomplete information about others wages. We find that the comparison effects matter. Of most interest, we provide some initial evidence regarding a positive relationship between wellbeing and inequality. The opposite finding is generically suggested by the literature. Therefore, we check for the robustness of our results to different specifications and different definitions of the reference group.
This article is organized as follows. In section 2, we review the relevant literature.
Section 3 presents our empirical strategy. Section 4 describes data and illustrates some descriptive statistics. Section 5 reports the main set of results. Section 6 discusses the robustness of our findings, whereas the last section concludes.

Literature review of the models of relative concerns
Neoclassical approaches to utility suggest that it will vary positively with the absolute wage level and negatively with the number of hours worked. Put simply, workers like income and dislike effort. However, recent years have seen the formulation of models intending to highlight that relative wages will be an important determinant of utility. The very broad idea is the existence of externalities emanating from the wages of others. In other words, we observe preference interactions (as termed by Manski, 2000), where what others do, or what happens to them, directly affects my own utility. Therefore, utility is allowed to depend on "relative concerns". There are several ways in which this can be done.
Models of mean-dependence assume that utility is increasing one's own absolute income but there is also a relative component where one's own income is compared with the average income of others. Individuals care about how their income compares with the norm, or reference income, of a socially constructed comparison group. Thus, individuals gain utility to the extent that their income exceeds the average or reference income of people in their comparison set and lose utility to the extent that their income falls below the reference level (Clark and Oswald, 1996). Many authors find that comparison income (i.e. average income of others) is negatively correlated with satisfaction (among the others, Pfeffer and Langton, 1993;Clark and Oswald, 1996;Sloane and Williams, 2000;McBride, 2001;Bygren, 2004;Blanchflower and Oswald, 2004;Luttmer, 2005). Ferrer-i-Carbonell (2005) finds that income comparisons are "upwards": poorer individuals' satisfaction is negatively influenced by the fact that their income is lower than the reference group, while richer individuals do not get happier from having an income above the average. Wunder and Schwarze (2006) Card at al (2011) also shows empirical evidence supporting upward income comparisons.
More recently, a significant amount of work has focused on the discrepancies between current and desired or aspiration states (e.g. Gilboa and Schmeidler, 2001;Solber, Diener, Wirtz andLucas, 2002, Stutzer, 2004). At the interface between economics and psychology, the idea that losses and gains are assessed not in absolute terms but in terms of the change they represent from a reference point (such as the current state) has received wide currency in prospect theory (Kahneman and Tversky, 1979) and related accounts (e.g. Vendrik and Woltjer, 2007). The implications for economic models of relative concerns have received much attention.
Among others, Layard (1980), Frank (1985a and Robson (1992) show that individuals care about their rank. Brown et al. (2007) offer empirical evidence that one's utility not only increases one's own income but also the rank one holds in income. In particular, allowing for multiple reference point impacts on inequality (e.g. Frank 1985 a,b;Van de Stadt, Kapteyn and Van de Geer, 1985;Quiggin, 1993;Wilkinson, 1996;Hopkins and Kornienko, 2004). The main idea is based on psychophysical models of contextual effects on judgments. It states that judgments of a wage are made relative to the wage distribution. Thus, judgments can be made with regard to the endpoints of a contextual distribution and/or the variance of the distribution (e.g. Volkmann, 1951;Janiszewski and Lichtenstein, 1999;Steward at al., 2003). The skewness of a distribution can also be relevant. The "range frequency theory" captures this idea as follow: the ordinal position of own wage within a ranked list of contextual wages (a comparison set) is important in determining judgment (e.g. Parducci, 1695;Parducci and Perrett, 1971;Mellers 1982Mellers , 1986Hagerty, 2000;Highhouse at al, 2003;Brown et al., 2008;Boyce at al, 2010;Wood et al, in press). For example, feelings of satisfaction will depend on the position of the rated wage within an ordered set of comparison wages and with respect to the highest and lowest values in the comparison set (Seidl et al, 2002).
Judgments may also depend on perceived unfairness, in such cases models of inequity perception could be applied (see Hopkins, 2008, for a review). A good example is the well known Fehr and Schmidt (1999) model where utilities depends positively on one's own income, but negatively on the differences between one's own income and that of others suggesting a dislike of others having more and a compassion of others having less. Thus, the model predicts a negative relation between well-being and inequality. But if, contrary to Fehr and Schmidt's hypotheses, we suppose that lower incomes for others raises an individual's utility (prestige effect), we could in principle also predict a positive relation between well-being and inequality.
The model predicts returns to increased inequality if the benefits of prestige outweigh the cost of envy (see Hopkins, 2008). 1 Finally, tournament theories are based on the "tunnel effect" of Hirschman and Rothschild (1973). Workers may use others wages to help predict their own future wage: the more others earn, the happier the worker is as the success of others provides information about workers' future prospects (information effects). Therefore, workers may appreciate inequality if it signals future potential career improvements, at least in the short term (for empirical evidence see, for example, Cark et al., 2009). 2

Empirical strategy
We empirically test a model of relative concerns (an adapted version of the model proposed by Fehr and Schmidt, 1999) that assumes that individual utility from pay, U*, depends not only on an individual's own wage but also on the wage of others: (1) U ik * = U*(w ik , w -ik ) = w ik + (α /n-1) ∑ wjk>wik (w jk -w ik ) + (β/n-1) ∑ wjk<wik (w ik -w jk ) where w ik is the wage of individual i in establishment k, and w -ik are the wages other people in the reference group (with w 1k <w 2k < … <w i-1 k <w i+1 k <…<w nk ). The reference group is defined as the n-1 other people working in the same establishment. The first sum on the right hand side of equation 1 represents the comparisons with better paid workers (upward comparisons). It can also give information about worker future prospects. The second sum represents the comparisons with worse paid workers (downward comparisons).
The effect of one's own wage on utility from pay is assumed to be positive. The parameters of interest are α and β, weighs respectively on the upward and downward comparisons. If α<0, we have so called envy, a dislike of others having more (Friedman and Ostrov, 2005). If α>0, we observe a tunnel effect (Hirschman and Rothschild, 1973): others good fortune provides information about my own future prospects. If β is negative, we have compassion, improvements for others impact positively on satisfaction (Fehr and Schmidt, 1999). If β is positive we have pride, a person perceives the approval of others for her own performance (Friedman, 2005). 3 In a large population with wage distribution F(.), Eq. 1 can be written as: where µ wk is the average wage in establishment k and R(w ik )=∫ zik (1-F(y))dy is the measure of relative deprivation introduced by Yitzahaki (1979). See Deaton (2003) for details. Looking at Eq. 2, we can immediately notice a link between utility from pay and wage equality/inequality.
As pointed out in Hopkins (2008), it can be shown that if there are two distributions F(w) and G(w) that have the same mean and the same support and if F is more equal in the sense of second order of stochastic dominance (equivalently generalized Lorenz dominance) then R(w) is lower at all wage levels under F than under G. Actually, if the means are the same, generalized Lorenz dominance is the same as Lorenz dominance; if F Lorenz dominates G then the Lorenz curve associated with F is always closer to the line of complete equality than of G, implying a lower Gini coefficient (see Thistle, 1989, Shaked andShanthikumar, 2007). Thus, in Eq. 2, if (α+β)<0, then an individual will have higher utility in more equal establishments (even keeping their own wage constant). If (α+β)>0, then great intra-establishment wage inequality leads, on average, to high utility. The signs and the sizes of the parameters α and β are empirical questions.
To empirically test the signs of the parameter α and β in Eq. 1, we estimate a random effects ordered probit model. Utility from the pay of worker i in establishment j is unobservable, what we observe is only the response to a question on satisfaction with pay, U (that is a categorical ordered response variable). We assume U* jk to be a linear function of the worker and job characteristics, X ik , i.e. the latter vector includes the worker's wage, w ik (logarithmically transformed), and the variables upwards comparisons, ((∑ wjk>wik (w jk -w ik ))/(n-1)), and downward comparisons, ((∑ wjk<wik (w ik -w jk ))/(n-1)). The model can be written as where ε is the i.i.d. error term, µ k represents the random establishment effect, J is the number of response categories and τ j are threshold levels. 4 Note that the random effects estimator (RE) assumes orthogonality between the effects and all covariates: if this assumption fails, then RE is not consistent. In the latter case, we can follow two possible approaches. First, we can use the Mundlak correction term (as in ): we decompose the establishment effect, µ k , into a random effect, µ 0k , that is uncorrelated with the covariates and a mean value of some of the establishment varying covariates (i.e. average establishment wage) that are allowed to be correlated with the random effects. Second, we can follow the approach proposed by Ferrer-i- (2004) that considers satisfaction as a cardinal variable and applies linear techniques, producing within regression. As a robustness check, we apply both approaches.  Table 1 for descriptive statistics about employees' characteristics.

Data and descriptive statistics
Our dependent variable is "satisfaction with the amount of pay" that is measured on a scale from 1, "very dissatisfied" to 5, "very satisfied". The frequency distribution of the responses to the job satisfaction question shows that 34% of the workers in our sample are at least "satisfied" (only about 4% are "very satisfied"), while nearly 42% are "dissatisfied" or "very dissatisfied" (about 13.5% are "very dissatisfied").
Employees are asked how much they are paid each week (before tax and other deductions were taken out). They responded by ticking one of 14 boxes corresponding to bands of weekly gross pay. Figure 1 gives a graphical representation of the density function of the wage distribution. The height of the curve indicates the concentration of people at different points along the wage scale while the area under the curve between two wages levels shows the share of the population with wages between those two levels. The location, spread and mode of the wage distribution indicate respectively the real wage levels, wage inequality and wage clumping. The median wage is in the range £310-£360. The curve is asymmetrical towards the left, thus implying that the proportion of employees earning less than the modal wage is larger than those earning more. Using this information, the workers' weekly wage is defined as the mean value of the band to which they belong. Moreover, managers are asked about the wage distribution at establishment level: that is, the number of employees in each of the four bands of hourly gross pay defined in the management questionnaire. The latter bands are defined as follows: £180 or less; £181-£200; £201-£599; £600 or more. This information allows us to define the variables upward comparisons and downward comparisons. Having only a limited number of wage bands, as well as having only categorical wage data, indeed represents limitations of the data. However, this is not really a problem in our framework as we assume incomplete information about others wages. In other words, workers knowing the wage bands of the co-workers, but they do not know their exact wages. By construction, individuals do not feel envy, pride and compassion for others in the same band, but they exhibit envy, pride and compassion (as appropriate) for workers belonging to different bands of wages. In other words, individuals belonging to the same band have equal social status. No information about future career prospects is obtained from other workers in the same band. Figure 2 gives information about the levels of wage inequality (measured by Gini index) and relative deprivation existing in the establishments included in our sample. Even if the number of bands is limited, there is enough variability to perform our analysis.

Estimation results
Three specifications are estimated: (i) the random effects ordered probit model; (ii) the random effects ordered probit model with the Mundlak correction; (iii) the linear fixed effect model.
We find similar results across all specifications. The estimated coefficient of one's own wage is positive and significant indicating a positive relationship between one's own wage and satisfaction (conditional to the other covariates). This relationship is expected and consistent with most results in the literature.
Of most interest, we focus on the comparison and information mechanisms determining satisfaction. We find that the estimated coefficient on upward comparisons is negative and significant (α<0): there is evidence of envy, a dislike of others having more. Workers prefer a distribution of wages in which they are not paid worse compared to other workers in the same firm. This can be also due to the fact that workers believe that their performance or productivity is not inferior to that of better paid workers and, therefore, their wages are inappropriate.
The estimated coefficient on downward comparisons is positive and significant (β>0): there is evidence of pride: the larger the average differences in wage is, with respect to workers paid worse in the same establishment, the higher the contentment with one's own achievement. In other words, workers perceive the approval of others for their own performance (prestige effect), which leads to a higher well-being.
Evidence of upward and downward comparisons is consistent with results in the literature (e.g. Ferrer-i-Carbonell, 2005;Wunder and Schwarze, 2006). But, our results are different from the findings of previous literature because we find that downward comparisons dominate upward comparisons. In other words, prestige seems to be more important than the cost of envy (α+β>0). This implies that great within-establishment wage inequality leads, on average, to high satisfaction. These results may depend on the realistic assumption of incomplete information about others wages. In fact, assuming incomplete information allows us to reduce noises due to small variations of wages across all workers and, therefore, impacts on the size of the mechanisms (envy, pride, satisfaction and information effects) determining satisfaction.
The above empirical evidence suggests that comparison effects matter. However, we also find some evidence of information effects. But, focusing on the second specification, the estimated coefficient of the average establishment wage (Mundlak term) is positive and significant suggesting that workers are more satisfied in establishments able to pay on average better wages. In fact, high average wages can be seen as signals about the worker's own future wage. This result is consistent with the findings of .
In all specifications, we have also included a set of controls for personal characteristics and job attributes. These controls have significant (and expected) influences on satisfaction with pay. Women, workers with children, older workers and those with lower educational levels are more satisfied. Individuals experiencing good working conditions (security, autonomy, no stress, flexi-time, good relations with managers and training) are also more satisfied. Instead, individuals working long hours, workers with tenure longer than three years and employed in the public sector are less satisfied.

Discussion
The results of this study indicate that there is a positive relation between satisfaction and wage inequality at the workplace. The opposite finding is generically suggested by the literature. Therefore, the reader could argue that our result depends on the specification and/or the definition of the reference group. The following robustness checks show that this is not the case.
First, we estimate a slightly different specification. We use the one proposed by Ferrer-i-Carbonell (2005) that includes the set of explanatory variables, own wage and the following two variables 5 If w ik >w rk then richer = ln(w ik )-ln(w rk )

poorer=0
If w ik <w rk then richer = 0 poorer= ln(w rk )-ln(w ik ) If w ik =w rk then richer = 0 poorer= 0 The idea is illustrated the same in our model: satisfaction is affected differently by a wage below that of the reference group and by a wage above the reference group. The average wage for the reference group is w rk . Four definitions of reference group are used: (i) co-workers; (ii) same individual characteristics (age, gender and education); (iii) same job attributes (gender, tenure and occupation); (iv) co-workers in the same occupation. Estimates are presented in Second, we estimate a specification including the set of explanatory variables, own wage and a dummy for whether the individual's wage is less than the median in their pay unit and occupation as in Card et al (2011). We also include a dummy for whether the individual's wage is more than the 25 percentile wage in their establishment and occupation (see Model E).
Once again we find that both upwards and downwards comparisons matter. Moreover, the latter outweighs the former.

Conclusion
In this paper, we model individual utility from pay as a function of a worker's own wage and the earnings of all other workers within the same establishment. We assume incomplete information about other wages. This realistic assumption leads to the following interesting results. Comparison effects matter in determining utility from pay. But, social status (that is, having a wage above the wages of others) matters more than the dislike of others having more.
This leads to the conclusion that great within-establishment wage inequality implies, on average, high satisfaction. We also find some evidence of information effects: workers are more satisfied in establishments able to pay on average better wages as the latter can be seen as indications of the worker's own future wage.
Our results are important because satisfaction is potentially associated with the subsequent behavior in the labour market (measured by variables as job performance, worker turnover, absenteeism and endorsement of collective action strategies; see i.e. Harder, 1992;Levine, 1993;Leicht and Shapelak, 1994;Curtin, 1977;Weiner, 1980;Pattersson et al., 2004), therefore it is important to understand how wage inequality impacts on job performance through satisfaction. In particular, personnel economics has underlined the incentive role played by the earnings that certain others within the same establishment may receive. In particular, in the tournament model (Lazear and Rosen, 1981), relative worker performance determines social status (the winner) and, therefore, the level of individual effort increases with the earnings difference between winning and losing the tournament. Wage inequality appears to be an incentive. In parallel, the literature has highlighted the potential importance of wage compression (Akerlof and Yellen, 1990). The latter is seen pre-condition for fairness and cooperation among the workforce, and then better firm performance.
Our results can be interpreted as broadly supportive of the tournament model. In particular, the findings are supportive about the positive influence of wage inequality within a firm on the worker's effort through satisfaction. Thus, firms should implement a differentiated prize structure.   Co-workers in the same occupation Co-workers in the same occupation ** means statistically significant at 1% level; * means statistically significant at 5% level; for a list of covariates see Table 2. £51