Estimating Income-Dependent Relative Income Effects in the UK

Abstract

Duesenberry’s (Income, saving, and the theory of consumer behavior. Harvard University Press, Cambridge, 1949) relative income hypothesis says that the utility of an individual depends not only on his absolute income level, but also on his relative income position in society. An individual gains utility if his income exceeds the income of most members in his comparison group and loses utility if his income falls below the income of most members in the group. Many empirical studies already show that these relative income effects have a significant role in determining well-being. However, most of them consider a symmetric case where the relative effects are homogenous among the population, or a simple version of an asymmetric case in which the population is categorized into two groups, conditioning on whether one’s income level is higher or lower than the income level of his reference group. The nature of relative income effects may be much more complicated, however, as two similarly-situated individuals may feel differently about their relative positions. The current analysis uses the British Household Panel Survey to depict a broader heterogeneity—income-dependent relative income effects. To explore the empirical possibility of income-dependent relative income effects, we regress a utility proxy on own income, the average income of the reference group, and an interaction of the two. Results suggest that one’s relative income effect indeed depends on one’s current income level.

1 Introduction

Contrary to the claims of neoclassical economics who describe humans as self-interested individuals, researchers in the social sciences recently show that personal preferences not only depend on their own material goods, but also on material goods of others (for example, Ferrer-i-Carbonell 2005; McBride 2001; Distante 2013). They question the traditional view of a utility function that only considers one’s own consumption or income levels. These relative effects assume that people derive utility not only from their own status, but also from comparing their status with others.

The relative income hypothesis was first proposed by Duesenberry (1949). As demonstrated by Clark et al. (2008), it can be a persuasive argument to explain the “Easterlin Paradox” (Easterlin 1974). The paradox is, “at a point in time both among and within nations, happiness varies directly with income, but over time, happiness does not increase when a country’s income increases” (Easterlin et al. 2010).¹ Clark et al. (2008) shows that this paradox points to the impact of relative income, instead of absolute income, on reported well-being.

The present study fits within the large literature pioneered by Easterlin (1974). It attempts to investigate the paradox through Duesenberry’s relative income effects. These effects create negative externalities because an increase in one’s income level reduces another’s well-being. Some scholars have considered a policy answer for correcting these relative income effects through government intervention, such as taxation (see, for example, Kanbur and Tuomala 2013).

Many studies in this area focus on symmetric relative income effects (for example, Clark and Oswald 1996; Luttmer 2005; Liu and Shang 2012). They argue that the magnitude of relative income effects is homogenous within the population. Generally, they conclude that others’ income has a substantial and negative impact on own well-being level. Holding everything else constant, an increase of the income level of one person’s reference group makes him worse off.

Duesenberry’s relative income hypothesis is not symmetric. Instead, he states that relatively poor people derive disutility from comparisons with more wealthy individuals while the wealthy do not derive utility from comparisons with poorer individuals. These relative income effects are referred to as upwards-asymmetric. Many papers have tested the idea, and the results have generally been mixed. Some studies agree with Duesenberry. For example, Ferrer-i-Carbonell (2005) finds that West Germans have upwards-asymmetric relative income effects. Poor agents’ well-being is negatively influenced by comparing with the income level of their reference group; rich agents do not feel happier from knowing their income is higher. Boyce et al. (2010) reports similar results using the British Household Panel Survey (BHPS), except that they find rich agents do feel happier from having higher income, but the magnitude of this utility from being ahead is smaller than that of the disutility from being behind.

On the contrary, McBride (2001), using the (US) General Social Survey (GSS) data, reveals that the relative income concerns are in fact asymmetric downwards; the impact is higher for the rich than for the poor. In addition, Mayraz et al. (2009) evaluates German Socio-Economic Panel (GSOEP) and finds that the relative income effects are symmetric, implying that there is a homogenous relative income effect within the population. The magnitude of utility of being ahead is no difference from that of the disutility of being behind.²

Also, some studies investigate comparisons across countries. Corazzini et al. (2012) conduct a cross-country experiment using students and find that well-being is perceived more in relative terms for students in high-income countries than low-income countries. This implies that the relative income effects are stronger when own income level is higher. However, they also find that personal characteristics such as gender and discipline of study contribute a lot to determining well-being. A similar example is Friehe and Mechtel (2014). Taking the division of Germany into the communist GDR and the democratic FRG and its reunification in 1990 as a natural experiment, they find that the relative income effects are much higher for East Germans than West Germans.

It is reasonable to assume that a high income earner cares differently about his reference group than a low income earner. In the literature of studying relative income effects, some studies support the idea that the wealthy should have stronger relative income effects than the poor because the poor will devote a large portion of their income to satisfy their basic needs, thus not much income is left to make luxury purchases and comparisons with others (Corazzini et al. 2012). However, other scholars emphasize the importance of “aspirations”, which suggests that the poor have stronger relative income effects because they have aspirations that tend to be far above their current socioeconomic level (Stutzer 2004). These upward aspirations are less prevalent for the wealthy, causing them to have weaker effects. These often opposing results motivate the current study that explores the potential heterogeneity of the relative income effects.

There are two main contributions of the current study. First, we use an interaction term to explore the possibility of income-dependent relative income effects. Most of the studies listed above explore homogenous relative income effects. Some investigate uniformly asymmetric relative income effects by categorizing the population into two groups, conditioning on, for example, whether one person’s income level is higher or lower than his reference group. The current study builds upon the consideration of asymmetric relative income effects. We relax the assumption of uniform asymmetry by allowing the relative income effect to be a function of one’s position on the income scale. It is a more general form of heterogeneity—income-dependent relative income effects. We estimate these effects by regressing a measure of utility on own income, others’ income and an interaction term between the two. The interaction term is widely used in economic studies (for example, Spilimbergo 2009). In the current analysis, it can measure whether relative income effect depends on the subject’s own income level.

Second, Layard (1980) shows that the definition of reference group matters a lot in this area. Most previous analyses divide the whole population into different cohorts based on one or two demographic variables such as age (e.g., aged 20 and under, 21–25, 26–30, etc.) and region. However, one disadvantage is that constructing reference groups using that method may cause two agents with similar ages living in the same region to not compare with each other only because their ages are just separated by one of the age thresholds. As a result, in the current study, we derive a cohort for every individual in the sample. We believe that in the real world, it should be the case that every person chooses a reference group, probably consisting of individuals with similar demographic variables, instead of being assigned one. Therefore, instead of assigning individuals to any age group, we consider the subject’s age group to include all others of the same age group plus or minus 5 years.³

The estimation results show significant heterogeneity of relative income effects. Specifically, we find that the relative income effects for the poor (in absolute value) are larger than those of the wealthy. Exploring the form of relative income effects is important. The literature already shows the impact of including homogenous relative income effects on optimal income taxation. The present study shows that allowing heterogeneous relative income effects can help us better understand the force behind well-being and build a more efficient income tax system to better take account of people’s actions.

2 Data and Descriptive Statistics

2.1 The Life Satisfaction Variable

We estimate relative income effects from a longitudinal panel survey of households in Great Britain, the British Household Panel Survey (BHPS). The first wave of data, including 10,000 people living in 5500 households in 250 areas, was collected in 1991. The most important advantage of a panel dataset is that it can mitigate the bias from the unobserved individual-specific factors. For example, “very satisfied” for person A may be equal to “fairly satisfied” for person B. Using a panel dataset and fixed effects estimation model, we can rule out that bias.

Starting in 1996, a general question was included, “How satisfied are you with life overall?” The answer serves as a proxy for individual utility level, u. Respondents choose from 1 to 7, where 1 means “not satisfied at all” and 7 “completely satisfied”.⁴

The current study uses wave 12 to wave 18 (from 2002 to 2008), a sub-sample across 7 years.⁵ The original BHPS was designed to be a representative of Great Britain, so it had a nearly equal probability sampling design. Since wave 7, there is oversampling of people from Wales, Scotland, and Northern Irelands, so now the proportions of households coming from those three areas are generally much higher than in reality. Following Distante (2013), we drop those “over-sampling” and keep only observations belonging to the original sample to maintain random sampling. In total, the panel gives us 51,194 individual-year observations.

The self-reported subjective well-being (SWB) level is treated as a legitimate and qualifying proxy of utility. Clark et al. (2008) argues that self-rated happiness and satisfaction scores are reasonable measures of the economic notion of utility.⁶ Economists tend to be skeptical about the use of SWB level. Nevertheless, it seems unlikely that human happiness can be interpreted without considering what human beings say.

2.2 Own Income and Relative Income

Because we are interested in how others’ income affects own satisfaction and how that magnitude depends on own income, own income and relative income are the two most important regressors in this analysis.

BHPS provides annual income for each household. In the current study, all income variables take the form of natural log and are deflated with 2005 as the base year.

In the large literature exploring the relative income hypothesis, there is no agreement on the definition of own income. Generally, studies use adjusted average household income (for example, Layard et al. 2008). In the current study, we use weighted average household income as the benchmark scenario.⁷ The weighted average household income is constructed using the total household annual income divided by the household’s OECD-modified equivalence scale.⁸ Within each household, the weighted average household income is equally distributed on each member. We also run another robustness check using the household income instead of weighted average household income.

Layard (1980) suggests people can have different reference groups. They can either choose individuals with whom they are locally close, people with similar demographic characteristics, or they may just compare with everyone else at a similar income level. How to define the reference income is a contentious issue, and several approaches exist in the literature. Specifically, there is no consensus on the definition of the reference group. Some simply select residents based on the geographical area of their primary residence (Easterlin 1995); some at first select residents based on geographical area, then refine by interacting geographical proximity with other dimensions (Ferrer-i-Carbonell 2005). Most previous studies divide the population into a number of different cohorts based on, age, region, and some other demographic variables. Once the cohorts are established, each person’s relative income is the average income of the cohort. In the current analysis, we choose a reference group for each individual in the sample that is the group of individuals within the same region⁹ and of similar ages, resulting in thousands of reference groups across the sample. Finally, consistent with previous studies, the reference group is assumed to be exogenous.

2.3 Control Variables

Dolan et al. (2008) gives a nice summary of factors associated with subjective well-being. Based on their results and recent literature, we choose a number of variables as regressors.

Age is found to be consistently related to SWB. Some studies show quadratic age may matter (for example, Blanchflower and Oswald 2004). In the current analysis, however, we consider only linear age.¹⁰

Health status is also confirmed to substantially affect SWB (Distante 2013). In BHPS, respondents are asked about their health status through the following question “How would you define your health status over the last 12 months?” The answer varies from 1 to 5 where 1 means excellent and 5 means very poor. Following Distante (2013), to construct a binary variable, we create a health status indicator equal to 1 when respondents choose 1 or 2, and 0 otherwise.

Marriage is another control variable in this analysis. Studies show that being alone appears to negatively affect SWB, so we create a dummy to separate those who live by themselves from others. Specifically, this binary variable equals one if the respondent chooses “married” or “living as couple” and equals zero if he chooses “widowed”, “divorced”, “separated”, or “never married”.¹¹

Employment status is another control variable that affects life satisfaction. The binary variable equals one if the respondent has a job with payment when interviewed, and equals zero otherwise.

Education levels are also important determinants of satisfaction, but the dataset limits our ability to control for them due to a high rate of missing data.¹² Finally, we also include year and region dummies.

2.4 Descriptive Statistics

Table 1 provides descriptive statistics and the distribution of the responses for the dependent variable. Table 1 shows that among the respondents, few choose the extreme values when asking about their life satisfaction level overall. During the 7 years from wave 12 to wave 18, the distribution of all seven difference levels of life satisfaction is fairly stable. For each year, at least 64 % chose 5 and 6 combined, and between 75 and 79 % of the people surveyed define themselves as very satisfied.¹³ Consistent with the Easterlin Paradox, there is little change in the reported life satisfaction as the average income level increases.

Table 1 Dependent variable: descriptive statistics and percentage of responses by year

Table 2 provides descriptive statistics for different income definitions we use in the regressions. We primarily focus on two types of income definitions: the household income and weighted average household income with OECD-modified equivalence scale. As for the reference group, we use two different construction methods. First, we construct individual-specific cohorts for every observation in this sample. This allows every observation in the dataset to have his own reference group. To be selected in one person’s reference group, the candidate must satisfy three conditions: (1) the data come from the same year; (2) they come from the same region, and (3) the age difference between them is less than or equal to 5 years. The income level of the reference group is the average income of all qualified candidates. Second, we also follow most previous studies and define reference groups by dividing the whole population into a number of cohorts based on region and age.¹⁴ The disadvantage of this method is that two agents who have similar ages that are close to any age threshold will not necessarily compare with each other. However, in real life, they probably should. That is why we prefer building a reference group for everyone. This is a process simulation in which every individual compares their income to all qualified individuals.

Table 2 BHPS descriptive statistics: income variables

Generally, Table 2 shows that those standing at a relatively more advantageous position in society have moderately higher life satisfaction, regardless of how we construct the reference group and how we define the income variable. We also perform t tests and under different settings, and for all situations we can reject the null hypothesis that the conditional means of life satisfaction are equal without regard to where the individual’s income compares to the average income of the reference group.

Table 3 provides descriptive statistics for the control variables we use in the regression. More importantly, it also provides the conditional mean life satisfaction level based on each binary control variable and results of t tests which test whether the mean of life satisfaction for the two groups is significantly different separately for each binary variable. It shows that all three control variables, health status, employment status, and marriage status, have positive and significant correlations with life satisfaction, as expected. The mean life satisfaction is significantly higher when healthy, employed, and/or married.

Table 3 BHPS descriptive statistics: control variables

3 The Econometric Framework

To estimate income-dependent relative income effects, I regress a utility proxy on own income, the average income of the individual’s reference group, and the interaction of the two.

Following Layard et al. (2008), individual i has a level of experienced utility u _i which is cardinal and comparable across individuals. Every respondent will report their level of happiness, h _i , based on their experienced utility. Reported happiness for individual i, h _i , is given by

$$h_{i} = u_{i} + v_{i}$$

(1)

Equation (1) shows that in order to generate an answer to a happiness question, individual i applies an idiosyncratic, strictly increasing and linear transformation v _i to u _i .

Following Clark and Oswald (1996), the estimation function is the following:

$$h_{i} = \beta_{o} + \beta_{1} \log y_{i} + \beta_{2} \log \mu_{i} + \beta_{3} \log y_{i} *\log \mu_{i} + \rho X_{i} + \in_{i}$$

(2)

$$\in_{i}\,=\,\varepsilon_{i} + v_{i}$$

(3)

where y _i is individual-level reported annual income. μ _i is the average level of annual income of the reference group for individual i. X _i is a set of control variables for individual i. $\in_{i}$ is the usual error term, which is assumed not to be correlated with explanatory variables.

It is straightforward to derive the relative income effects,

$$MUR_{i} = \frac{{\partial h_{i} }}{{\partial \log \mu_{i} }} = \beta_{2} + \beta_{3} \log y_{i}$$

(4)

Equation (2) is estimated using fixed effects to control for unobserved heterogeneity. Ferrer-i-Carbonell and Frijters (2004) show that estimation results using OLS or ordered probit will not be significantly different from each other. To give a more comprehensive result, ordered probit estimations will also be provided as one robustness check. To interpret the results, when the average of others’ income increases by 10 %, individual i’s own utility level will fall by—(β ₂ + β ₃logy _i )/10 point(s).¹⁵

The coefficient of interest is β ₃, which is the coefficient on the interaction term of own income and reference income. If the relative income effects do depend on own income, then β ₃ will be statistically significantly different from zero. Otherwise, it concludes that the relative income effects are homogeneous. Further, if β ₃ is negative, the relative income effects are downwards asymmetric, implying high income earners have higher relative income effects than low income earners. If β ₃ is positive, then the effects are upwards asymmetric, implying the poor have stronger relative income effects.

4 Estimation Results

The benchmark scenario adopts the weighted average household income using OECD-modified scale. The result of the benchmark scenario is shown in Table 4. Column 1 is the estimation results when we only include the absolute income level. In column 2 we also add the reference income as an additional explanatory variable. In column 3 we also add the interaction between own income and reference income. The first column clearly illustrates that the own income level has no effect on satisfaction. This is consistent with some studies (for example, Easterlin 1974; Boyce et al. 2010; Distante 2013). Column 2 shows that after we include reference income, the effect of absolute income is still zero. However, there is a significant and negative effect of reference income on life satisfaction. This suggests that others’ income is a much more important factor in determining one’s own happiness level than own income. The results can be interpreted as whenever the average income level of one person’s reference group increases by 10 %, his life satisfaction level will go down by 0.021 point on the 7-point scale.

Table 4 Life satisfaction estimation results: the benchmark case

Next, in column 3, the coefficient on the interaction term is significant and positive. As own income rises, the effect of reference income on satisfaction is decreasing (in absolute value). This implies that the relative income effect is heterogeneous within the population: generally, the wealthy have smaller relative income effects than the poor.¹⁶

Figure 1 depicts the relative income effects at various levels of own income. It demonstrates the heterogeneity of relative income effects across the population. It varies significantly depending on an individual’s own income level. The individual at the 5th percentile of the income distribution has a relative income effect roughly three times as large as that of the individual at the 95th percentile. Formally, $MUR = \left( { - 1.141 + \ln \left( y \right) \times 0.097} \right)/10$. If a person is at the 25th percentile of the income distribution (10,976.1), then when the income level of his reference group decreases by 10 %, his life satisfaction level rises by 0.02386 point on the 7-point scale. This effect is roughly 8 % as strong as having a good health.¹⁷ However, if he is at the 75th percentile of the income distribution (24656.1), that rise shrinks by one-third to only 0.01601 point on the 7-point scale. Recall that the relative income effect is 0.0211 when no interaction term is included. In conclusion, with the interaction term, the relative income effect ranges from −1.1233 to 0.1602 when there is a 10 % change of relative income. It clearly shows that without the interaction term, we cannot capture the true form of relative income effects, but only an average level.

Fig. 1

Relative income effects as a function of own income. *Relative income effects are interpreted as the numerical decrease (increase) of utility on the 1–7 scale when one’s reference income increases (decreases) by 10 %

We are also interested in the coefficient on own income. Column 3 shows that after adding the interaction term, the coefficient on own income becomes significant. However, own income has a negative effect on satisfaction and that effect is lower (in absolute value) as reference income rises. It suggests that as income of the reference group surrounding that person goes up, he is more likely to report higher satisfaction. Specifically, the effect of own income on satisfaction becomes zero when reference income equals 17,556.86. For two-thirds of the total observations studied in the present analysis, their reference income is above that threshold and an additional dollar of own income translates to more happiness for them.¹⁸

Finally, across three columns, the control variables show consistent findings. As age rises, people become less happy. The coefficients on health status, marriage status and employment status are as expected. Respondents tend to be happier if they are healthy, married, or employed.¹⁹

4.1 Robustness Check

In this section, we evaluate the robustness of our estimation results through several alternative ways.

The first column of Table 5 is the estimation results from the benchmark scenario. First, we replace weighted average household income with household income and show the estimation results in column 2 of Table 5. Given the highly intensive correlation between household members, we believe that it is possible that it is the whole family income that matters, instead of individually weighted average household income. All control variables remain constant for comparison. Correspondingly, the reference group is constructed the same as above, except that we use household income instead.

Table 5 Life satisfaction estimation results: alternative income definition and reference group construction method

The results reported in column 2 of Table 5 are consistent with those discussed above. The reference income has significant and negative effect on satisfaction. More importantly, the interaction term is significant and positive, which again illustrates that relative income effects are heterogeneous within the population.

Second, we test whether the result of the benchmark scenario is also valid when using the traditional way to construct the reference group. Compared with the benchmark case, in the current scenario, we still use the weighted average household income with OECD modified scale. However, now we divide the whole population into several dozens of cohorts. Specifically, we divide the population into different cohorts based on region × age. There are 18 different regions in this dataset, and agents within each region are divided into the following age groups 15–25, 26–35, 36–45, 46–55, and all above 55 years old. This generates 18 × 5 = 90 different cohorts. Each person will take the average income level of the cohort he belongs to as the reference income level. Column 3 of Table 5 reports the estimation findings. The results are mostly consistent. The coefficient on reference income alone is slightly less significant than previous scenarios. This can be explained by the poor construction of the reference groups: some reference groups leave out some individuals who should belong there, such as those whose ages are near any age threshold. Finally, after adding the interaction term, the reference income has a significant and negative influence. Meanwhile, the interaction term is positive and significant, indicating that the relative income effects are heterogeneous and decreasing as own income increases.

Third, we use 1 year’s data to perform a cross-section analysis. This is to test whether using an ordered probit model yields similar findings. Table 6 shows the results of ordered probit using each year’s data. Consistent with the benchmark case, the income variable is the weighted average household income with OECD-modified scale and we also use the individual-specific cohorts constructed using the same criteria as before. The interaction term between own income and reference income is not significant in some waves, although the sign of the coefficient is usually consistent with the benchmark results (expect for wave 14). This shows that by regressing the whole sample with all the years, we obtain an average effect of relative income effects across 7 years, which significantly depend on the own income level. Treating the utility proxy as ordinal or cardinal does not significantly affect the results.

Table 6 Life satisfaction ordered probit estimation results: by wave

5 Conclusions

Since the “Easterlin Paradox” was discovered, a lot of studies interested in the relationship between income and happiness find that it is not, at least primarily, our own income that determines our reported well-being. Our study contributes to this growing literature and we find that compared with absolute income, relative income plays a much more important role in determining people’s well-being levels.

Further, different from previous studies in this area which focus on either homogenous or uniformly asymmetric relative income effects, we use the interaction term to explore the dependence between own income and reference income. We find that consistent with previous work, reference income has a negative effect on life satisfaction. Further, our results show that absolute income affects reported life satisfaction indirectly through reference income: it changes the magnitude of the relative income effect. As the absolute income level increases, the magnitude of relative income effect decreases (in absolute value). This result that the wealthy are not as competitive as the poor is consistent with some studies in this literature which support Duesenberry’s claim that relative income effects are upwards-asymmetric. However, this income-dependent relative income effect is more general.

The field of relative income hypothesis is a young and growing field. Relative income effects are gradually accepted in many areas and generate non-negligible impacts, such as the optimal income taxation literature. Relative income effects create negative externalities since each individual suffers from growth in others’ income. As a result, exploring the true correlation between income and happiness can help us derive a more efficient optimal income tax system to adjust for the negative externalities.

In the current study, we make a first step and find that own income affects the magnitude of the relative income effect. Future research can explore the potential of nonlinearity, such as quadratic-income-dependent relative income effects. Also, this study adopts the income variable as the aggregation of labor and non-labor income. It is, however, reasonable to expect agents may have different responses between relative labor income and non-labor income. It could be intriguing to explore this potential heterogeneity. Further, the heterogeneity of relative income effects may not only depend on our own income level, but also some other variables such as marriage status or health status. That suggests that two individuals with the exact income level may still have distinct relative income effects. There are myriad avenues for pursuing the true form of heterogeneity.