Abstract
We study how life satisfaction among adult Swedes is influenced by having access to a cash margin, i.e. a moderate amount of money that could be acquired on short notice either through own savings, by loan from family or friends, or by other means. We find that cash margin is a strong and robust predictor of life satisfaction, also when controlling for individual fixed-effects and socio-economic conditions, including income. Since it shows not to matter whether cash margin comes from own savings or with help from family members, this measure captures something beyond wealth.
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Notes
We drop 327 individuals living with their parents in either 1991 and 2000. These are mostly youths that move out from their parents’ home between 1991 and 2000. The motivation for this sample restriction is that income comparisons between this group, mainly supported by their parents’ income, and others are hard to interpret. The attrition rate (of those eligible for re-interview in 2000) between the two waves is 22.0 %.
Both of our satisfaction measures can be considered mostly cognitive and evaluative in nature, in comparison to more specific measures of positive and negative affect which are also encompassed in the concept of SWB (Diener et al. 1999). Different measures that can broadly be classified as evaluative can still vary along an evaluative-affective continuum, however, and more evaluative measures have been found to correlate more strongly with material circumstances (Diener et al. 2010).
Respondents are only able to choose one alternative for this question. Although this is not clear from the survey documentation, we interpret the responses as hierarchical, in the sense that responses higher up in the order of response categories (as we list them) are chosen first when possible. This interpretation implies, for example, that those who have a cash margin through a bank loan are not able to borrow from family members or friends.
Given \(K\) discrete outcomes, the BUC estimator creates \(K-1\) new observations from each original one by transforming the dependent variable to one of the \(K-1\) possible dichotomisations, thus giving rise to a \(K-1\) times larger data set. Since the expanded data set has a binary outcome variable we can use the Chamberlain fixed-effects model. Finally, to account for the dilution of observations, standard errors are made cluster-robust with respect to individuals. Hence the acronym BUC, ‘Blow-Up and Cluster’. Since this estimator is of fairly recent origin there are, as of yet, few applied papers that use it. To our knowledge it has only been applied in Rudolf and Kang (2011). The BUC estimator is similar to the methods of Das and Soest (1999) and Ferrer-i-Carbonell and Frijters (2004), but is argued to be more robust for small samples (Baetschmann et al. 2011).
Letting \(\mathbf {x}\) denote the vector of all covariates, the latent variable variance follows from Eq. 1: \(\mathrm Var (y^*) = \varvec{\beta }^{\prime }\mathrm Var (\mathbf {x})\varvec{\beta }+ \mathrm Var (\varepsilon )\), where \(\mathrm Var (\varepsilon )=\frac{\pi ^2}{3}\) is imposed in the logit model and \(\mathrm Var (\widehat{y^*})=\varvec{\beta }^{\prime }\mathrm Var (\mathbf {x})\varvec{\beta }\) is estimated from the sample. \(\overline{R^2}= \mathrm Var (\widehat{y^*})/\mathrm Var (y^*)\) is now straightforwardly obtained from the above expressions. The normalisation procedure as well as the idea for measuring goodness of fit was first suggested by McKelvey and Zavoina (1975).
An alternative specification is to contrast lack of cash margin with a single category of having a cash margin, thus adding all cases under “Has cash margin” in Tables 4 and 5 to the reference category. This would slightly reduce the coefficient for lack of cash margin, to (−0.76, −0.5, −0.54, −0.41) for SLC and (−0.48, −0.29, −0.27, −0.23) for SDL.
Since the effect of an \(n\)-fold increase in income is \(\gamma \log n=c\), we find the equivalent income increase by solving for \(n\), giving \(n=e^{0.58/0.35}=5.2\).
Social relations have been found to be important for SWB (see e.g. Powdthavee 2008), and it is possible that our cash margin variable to some extent reflects this. The fact that those who lack a cash margin have a lower life satisfaction than those who have it by means of a bank loan suggests the importance of something beyond social relations alone, however (see also footnote 6).
As a comparison, Sacks et al. (2010) find coefficients in the range 0.22–0.28 for the log-income impact on standard deviations of life satisfaction. One reason for the lack of income effects in the long run may be that we use a very long panel, with 9 years between the two waves. This is in line with the literature on adaptation of well-being, stating that many factors correlated with well-being have a diminishing impact over time (Clark et al. 2008).
A related explanation is that the lack of a cash margin could capture differences in living expenses across regions. To test this hypothesis, we have run regressions where we include regional dummies and their interaction with income, but with no substantial results: the income interactions are generally not significant and lack of cash margin remains equally strong. Hence, we reject this explanation.
These results are consistent with Layard et al. (2008) who examine the functional relationship between happiness and income in a number of countries. They find that across most specifications, the relationship is logarithmic.
For single-person households without children all three measures coincide, for single person households with children the first two measures coincide, and for two-spouse households with two children the household measures coincide. As regards scaling, the per-spouse household measure can be considered a filtered version of the individual measure, reducing within-couple variation (noise) but maintaining the order of magnitude. The equivalised income, on the other hand, is anchored at singles without children and couples with two children, i.e. it coincides with the per-spouse measure at these points. At other points, however, equivalised income is scaled differently: for example, singles with children have their income adjusted downwards while couples without children have their income adjusted upwards.
When it comes to explanatory power, \(\overline{R^2}\) is consistently higher with both household measures than when using individual income. Per-spouse household income is the most robust measure; for the two other measures, including control variables tends to push estimates towards the per-spouse estimate.
This could happen if, e.g. unhappy individuals would tend to experience higher fluctuations in well-being than happy individuals. In fact, from examining the correlation between \(\bar{y}_i\) and \(|\Delta y_i|\) it turns out that such an interrelationship does exist in our data. The correlation is stronger for satisfaction with daily life (−0.39) than for satisfaction with life circumstances (−0.28). This correlation could, of course, be the result either of larger coefficient magnitudes or higher error variance for these individuals (or both).
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Acknowledgments
This paper has benefitted greatly from suggestions for improvements by Markus Jäntti and Anders Björklund. The authors also wish to express their gratitude towards Johan Egebark, Louise Johannesson, Maria Perrotta Berlin, and seminar participants at SOFI and at the Department of Economics at Stockholm University for valuable comments. Niklas Kaunitz gratefully acknowledges financial support from the Jan Wallander and Tom Hedelius Foundation. Finally, the authors wish to thank an anonymous referee for drawing our attention to the suitable Dickens quote.
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Appendices
Appendix 1: Control Variables Definitions
Income
Average of spouses’ combined monthly disposable income, i.e. net of taxes and transfers, based on tax register data contemporaneous with the survey year. (Equals individual income when the respondent is neither married nor cohabiting.)
Age Group
Five categories: 18–26, 27–36, 37–50, 51–64 and 65–75. Age is approximated by subtracting birth year from the survey year.
Highest Completed Education
Three categories: basic school (education level is junior high school or lower, includes no schooling), high school (highest completed education level is high school, gymnasium, or a short vocational training), higher education (has completed some higher level education, i.e. a university diploma or a longer vocational education).
Symptom Index
Numeric variable based on the summation of 44 separate symptom scores that take the values 0, 1 or 2, if the respondent has no, mild, or severe symptoms, respectively. Hence, an index score of zero indicates perfect health.
Marital Status
Three categories: not married, cohabiting (including married), divorced or widowed.
Children in Household
Three categories: indicates whether there are any children currently living in the respondent’s household, regardless of how many: no children, cohabiting parent (children living in household together with married or cohabiting respondent), single parent (children living in household, respondent is neither married nor cohabiting).
Employment Status
Five categories: respondents in LNU may hold multiple employment statuses, e.g. working full-time while searching for a job. We define mutually exclusive employment indicators in the following lexicographic order, meant to capture main activity: full-time, part-time, self-employed (works either in a firm partly or fully owned by him or herself, or in a free profession), unemployed (is currently searching for a job), retired (at least 65 years old and receiving pension) and other. The last category includes all respondents not falling into any other category, e.g. students.
Appendix 2: Sensitivity Analysis
1.1 Functional Form of Income
In line with most of the previous literature on life satisfaction we have imposed a logarithmic functional form upon the relationship between income and well-being. To assess the plausibility of this assumption, we have also estimated the model
where \(Q\) represents a partitioning of [0, 100] into quantiles and \(I_q(\cdot )\) is the indicator function for quantile \(q\). That is, we here estimate the mean impact of income on life satisfaction separately for each quantile.
Our results indicate that SLC does indeed display an approximately logarithmic association with income, while for SDL the relationship is somewhat weaker. The case for choosing a logarithmic functional form is strengthened further by the fact that \(\overline{R^2}\)-values for the cross-section regressions are virtually unaffected by changing to the less restrictive income specification, for both outcome measures.Footnote 16
Most importantly, the cash margin estimates are unaffected by changing the income specification, for satisfaction with both circumstances and daily life. The results from the flexible income specification are, thus, in accordance with our previous results.
1.2 Choice of Income Measure
Above we argued that erroneous functional form of income in the regressions cannot explain the large estimates of the impact of cash margin. However, in theory it is possible that the income measure itself is flawed, and that this biases the estimates of cash margin.
We have tested the results using three different income measures: individual disposable income, per-spouse household disposable income (our preferred income measure) and equivalised household disposable income. The latter is defined as total household disposable income, excluding earnings by children, divided by the square root of the number of family members in the household. The idea behind this measure is to include the economic cost of children, but also capture household economies of scale.Footnote 17
While there are some differences in how these measures interact with well-being (although they tend to converge as control variables are included), the cash margin estimates are largely unaffected by the choice of income measure.Footnote 18 Thus, while choosing the correct income measure is important for estimating the impact of income on life satisfaction, the cash margin estimates are robust in this regard.
1.3 Consistency of the Ordered Logit Fixed-Effects Model
The BUC estimator first expands the data set by using all possible dichotomisations of the dependent variable, thus deriving a binary dependent variable. At the next stage, the Chamberlain fixed-effects model for binary logit eliminates all observations where the, now binary, outcome variable is constant across all time periods. Taken together, this implies that the BUC estimator weights each original observation \((y_{i,t},\mathbf {x}_{i,t})\) proportionally to the span that \(y_{i,t}\) covers within that individual. Individuals with constant \(y_{i,t}\) over time will, consequently, not influence \(\hat{\varvec{\beta }}\) at all.
Under the identifying assumptions of the BUC estimator, this ‘sample reweighting’ does not threaten consistency. However, if, for example, \((\varvec{\beta }\mid y,i)\) should vary across outcomes or individuals, the BUC estimator would give the mean impact of the covariates for the weighted subsample, rather than for the original representative sample.Footnote 19 In such a case, it would be difficult to compare the cross-section estimates with those from the fixed-effects specifications.
As an informal test we have run all cross-section regressions also for the reduced sample used in the fixed-effects estimations (i.e. dropping individuals with constant satisfaction levels over time, separately for each outcome measure). For the SLC specifications the sample reduction leads to the cash margin coefficients being mildly attenuated, but in no case significantly different from earlier. For SDL the attenuation is somewhat stronger, at most a decrease in magnitude of around a third. The attenuation is generally a bigger problem for the income estimates than for the cash margin estimates. Consequently, the sample reduction associated with the BUC estimator is not a likely source of bias for our results on cash margin.
We have also estimated all models with OLS rather than ordered logit. In addition to simply using consecutive integer values for the outcome variables (1–5 for SLC, 1–3 for SDL), we have also estimated all specifications with the outcome variables transformed to binary outcomes in a linear probability model (with the cutoff between the top category and those below, in both cases). In neither case is the overall picture different from that described below: the variables of interest have the same relative magnitudes and statistical significance. These results can be obtained from the authors at request.
Appendix 3: Detailed Regression Results
See Table 6.
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Berlin, M., Kaunitz, N. Beyond Income: The Importance for Life Satisfaction of Having Access to a Cash Margin. J Happiness Stud 16, 1557–1573 (2015). https://doi.org/10.1007/s10902-014-9575-7
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DOI: https://doi.org/10.1007/s10902-014-9575-7