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Published in: Social Indicators Research 2/2017

11-06-2016

Estimating Income-Dependent Relative Income Effects in the UK

Author: Langchuan Peng

Published in: Social Indicators Research | Issue 2/2017

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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.

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Footnotes
1
Until now, the literature has not agreed on whether the paradox exists for most countries or how large it is (for example, Kahneman and Deaton 2010; Easterlin et al. 2010; Stevenson and Wolfers 2013; Oishi and Kesebir 2015).
 
2
Mayraz et al. (2009) and Ferrer-i-Carbonell (2005) find different results using the same dataset (GSOEP). The former let subjects choose the reference group themselves while the latter defines the reference group as all agents at the similar education level, inside the same age bracket, and living in the same region.
 
3
It should be noted that like most studies in this area, we don’t consider the endogenous reference group, although some studies already show that people choose their reference groups in reality (e.g., Clark and Senik 2010; Falk and Knell 2004).
 
4
Respondents choose this answer based on their own perceived quality of life. To help them better perceive, before this key question, the survey asks a couple of questions concerning different areas of life. The Subjective Well-being (SWB) question in BHPS refers to “life evaluation”, not “emotional well-being”, based on the two different definitions regarding SWB discussed in Kahneman and Deaton (2010).
 
5
The life satisfaction question appeared since wave 6 but paused on wave 11. To have a series of continuing years, we choose all waves after wave 11.
 
6
Lepper (1998) and Sandvik et al. (1993) also adopt this view.
 
7
In BHPS, annual total household income is the sum of annual labor and non-labor income.
 
8
This scale “assigns a value of 1 to the household head, of 0.5 to each additional adult member and of 0.3 to each child”. (http://​www.​oecd.​org/​eco/​growth/​OECD-Note-EquivalenceScale​s.​pdf).
 
9
In the BHPS survey, respondents are classified into 19 demographic areas, such as inner London, outer London, east Anglia, east midlands, greater Manchester, and Wales.
 
10
We test an alternative estimation function which includes age-squared and find that the coefficients on other variables don’t vary much and the coefficient on age-squared is not significantly different from zero.
 
11
From now on, “married” means this marriage status indicator is equal to one; “not married” means this indicator is equal to zero.
 
12
Gender and race are not included because they are constant over time.
 
13
Very satisfied is defined as answering 5, 6 or 7.
 
14
Several studies are exceptions. They regress the actual income on a list of determinants and use the predicted income level to represent a person’s reference income level (see for example, Luttmer 2005).
 
15
For an individual experiencing a 10 % increase of the average income of his reference group (from \(Y_{1}\) to \(Y_{2}\)), his utility level will decrease (in absolute value) by (\(\beta_{2} + \beta_{3} \log y_{i} ) \times \left( {\log \left( {Y_{2} } \right) - \log \left( {Y_{1} } \right)} \right) = \left( {\beta_{2} + \beta_{3} \log y_{i} } \right) \times \log \frac{{Y_{2} }}{{Y_{1} }} = \left( {\beta_{2} + \beta_{3} \log y_{i} } \right) \times \log \left( {1.1} \right) \approx \left( {\beta_{2} + \beta_{3} \log y_{i} } \right)/10.\)
 
16
Because relative income effects are jointly determined by the coefficients of reference income and interaction term, we run the joint significance test on own income with interaction term and reference income with interaction term. The results of the joint significance test rejects the null hypothesis that the coefficients are jointly equal to zero.
 
17
0.02386/0.285 = 8.37 %.
 
18
This is consistent with previous columns. In column 3, we force the insignificant coefficient of own income into two parts: a positive part and a negative part. As a whole, it is still insignificant.
 
19
Recall that the health indicator is from a question asking the survey respondents to evaluate his or her own health status. To avoid any potential bias caused the by endogeneity issue from subjective evaluation, we start by following Distante (2013) and using an alternative control variable ‘Limits in Activities of Daily Life (ADL)’. This alternative choice is a binary indicating whether the respondents think a certain list of daily activities is limited by their health conditions. The estimation results show that replacing the subjective health status indicator with an objective one neither affects the coefficient nor significance level.
 
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Metadata
Title
Estimating Income-Dependent Relative Income Effects in the UK
Author
Langchuan Peng
Publication date
11-06-2016
Publisher
Springer Netherlands
Published in
Social Indicators Research / Issue 2/2017
Print ISSN: 0303-8300
Electronic ISSN: 1573-0921
DOI
https://doi.org/10.1007/s11205-016-1385-3

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