Subjective wellbeing at different spatial scales for individuals satisfied and dissatisfied with life

Life satisfaction data

For this study, we aggregate overall individual level LS scores derived from waves 1–16 (collected in 2001–2016) of the Household, Income and Labour Dynamics in Australia (HILDA) Survey¹. LS is taken from responses to the question, “All things considered, how satisfied are you with your life?” Responses are given on an 11-point Likert scale where 0 means totally dissatisfied and 10 stands for totally satisfied.

We acknowledge that calculating the mean of Likert items can be problematic, especially not knowing whether increments in scale correspond to equal increments in the underlying latent variable. Treating LS as ordinal vs interpersonally cardinally comparable is a contentious issue in literature. Justifications for cardinality shows that treating LS data as cardinal yields similar results to treating it as ordinal, and both assumptions are compatible with LS scores (Ferrer-i-Carbonell & Frijters, 2004; Blanchflower & Oswald, 2011; Kristoffersen, 2017). Further, Kristoffersen shows that LS scores are equidistant (Kristoffersen, 2017). The purpose of this paper does not require us to take a strong standpoint in this debate. Rather, our aim is to examine the consequences of aggregation commonly used in subjective wellbeing studies.

Objective variables

The objective variables used in this study include eight related to human capital, four to social capital, and three to built capital (all based on data from the HILDA Survey discussed below). One natural capital proxy variable (normalized difference vegetation index (NDVI)) was included (discussed below) as no natural capital variables are collected as part of the HILDA Survey. Natural capital has been shown to have a significant impact on LS (Ambrey & Fleming, 2014; Tsurumi & Managi, 2015; Fleming, Manning & Ambrey, 2016; Larson, Jennings & Cloutier, 2016). However, many LS and wellbeing studies omit reference to the environmental domain entirely (Helliwell, Layard & Sachs, 2018). The choice of variables for inclusion within this study were identified based on outcomes from previously published literature, including a similar study (utilizing HILDA data) performed at the individual scale (Kubiszewski, Zakariyya & Costanza, 2018).

The objective variables were aggregated for individuals living within a given geographic area. We aggregated continuous variables by calculating the mean value per given area. For example, the mean household disposable income for a given area was calculated. Categorical variables were aggregated by obtaining the proportion of individuals of a specific category out of the total individuals within each respective area; for example, the proportion of men, the proportion of university graduates, and the proportion of those with a long-term health condition within each area.

Separating “satisfied” and “unsatisfied” individuals

We also divided our total sample into two subsamples. These subsamples separately considered individuals who responded as having a LS score between completely dissatisfied (0) to neutral (5) and individuals who responded as having a LS score between just above neutral (6) and completely satisfied (10). For brevity, we refer to the full sample as “All,” sample 2 as “Satisfied,” and sample 3 as “Unsatisfied.” Using LS subsamples as a means of understanding different portions of the population has been previously used in literature (Andreasson, 2018). In this paper, we use two sub-samples as our total sample is not large enough to split further.

Besides our current approach of separating “satisfied” and “unsatisfied” at a response of 5 and below and above 5, we also attempted to separate the total sample through other methods. In this respect, we attempted creating separation points using the median of LS and LS quartiles. Both of these separation points showed insufficient variation between the subsamples and the sample size were too small to make an informed analysis. Our two current subsamples provide a meaningful split in the population in determining what are the different contributions to the LS for each of the subsamples and why. Most importantly, it gives us additional information on the portion of the population that is most at risk.

Estimation strategy

We examine the relationship between average LS and objective variables using the following empirical model: (1) ${\text{Average LS}}_{i,t}={\text{β}}_0+{\text{β}}_1{X}_{i,t}+{\text{λ}}_t+u_{i,t}$ where Average LS_i,t is average LS of individuals in area i in year t, X_i,t are the objective variables for area i in year t, λ_t is the year fixed effect, and u_i,t is the area level idiosyncratic error.

Our regression model uses pooled ordinary least squares controlling for time fixed effects and using cluster-robust standard errors. Our choice of estimation method is based on a number of factors. The Hausman test indicates the possibility of unobserved characteristics being correlated with the objective variables included in the model, for all samples, (at 1% significance level for SA1–SA4 and at 5% level for state) thus the use of random effects estimation would be inappropriate.

We also ruled out extremely large time invariant area level fixed effects. Our unit of estimation is not the individual but an aggregate of individuals within a given statistical area. It is important to note that the composition of individuals being aggregated within a given area changes across the years. Table 1 shows the percentage of individuals who have moved to a new area in each year in our “All” sample. As expected, there is greater movement, or relocation, at smaller spatial scales compared to larger scales. In addition, 5,477 individuals were added to the HILDA Survey in wave 11 (2011).

We conducted Fisher-type Augmented Dickey Fuller tests under various assumptions on each of the SA levels to ensure that aggregate LS within areas was stationary. The tests strongly reject the null hypothesis that all the panels contain unit roots (p < 0.01). Although the LS of individuals may not be stationary over the course of a lifetime, we do not use individual LS but aggregate LS in this paper. Aggregated data is prone to be more stationary as individuals within the aggregated data vary in age and may migrate between areas. Regardless, we acknowledge that unobserved area level fixed effects could be present. Nevertheless, our main interest lies in variation between areas rather than within areas over time. Most importantly, the aim of this paper requires us to examine how the preciseness of the estimates changes as we move up the spatial scale. We do not make strong causal or correlational inferences on the relationships.

Aggregation and empirical model

The three samples analyzed include, (1) all individuals within the 16 waves that responded to the LS question, (2) individuals that replied that their LS was equal or less than five, and (3) individuals that replied that their LS was greater than five. The latter two samples enable us to examine how information relevant to individuals, or small groups, particularly for those at opposing ends of the LS Likert scale, is lost as we aggregate.

For each of our samples, we aggregate individual level data to five spatial scales. The spatial scales used in this paper are based on the Australian Statistical Geography Standard (ASGS) hierarchical scales to allow for future comparison. Listed in ascending order, they include Statistical Area Level 1 (SA1), Statistical Area Level 2 (SA2), Statistical Area Level 3 (SA3), Statistical Area Level 4 (SA4), and State and Territory (State).

The Australian Bureau of Statistics designed the SA geographic structure specifically for the release of statistical information (http://www.abs.gov.au/websitedbs/D3310114.nsf/home/geography). Their sizes are based on population, not area, and each SA level aggregate up to the next SA level. SA1s have populations of approximately 400 (between 200 and 800) people and aim to separate differing geographical characteristics. SA2s have average populations of about 10,000 (between 3,000 and 25,000) people and were designed to represent communities that interact economically and socially. SA3s have between 30,000 and 130,000 people and were designed to include an entire region that contains a small town or suburb. SA4s have between 100,000 and 300,000 people and were setup to reflect labor markets within regions. States and territories boundaries are defined by the federal government.

Table 2 presents the total number of areas at each scale and the average number of individuals within a given area at each scale. For all years, our sample includes 87 SA4 areas and eight states/territories. The number of SA1, SA2, and SA3 areas vary from year to year, depending on location of respondents. On average there are 4,581 SA1 areas, 1,509 SA2 areas, and 317 SA3 areas. The SA1s, on average, include 3 (±3.99 SD) individuals, SA2s include 9 (±10.21 SD) individuals, and SA3s include 46 (±32.44 SD). The variation in the number of individuals within an area increases as we move up the spatial scale and consider larger areas. These deviations impact aggregation from individual level data within an area. There is greater dispersion in individual responses as the number of individuals within an area increases along with spatial scale.

Descriptive statistics

To understand the relationships between objective variables and average LS at different spatial scales, it is important to examine how the aggregation of these objective variables differs across the spatial scales. Table 3 presents the mean and standard deviation (reported in parentheses) of the average LS for the three samples.

As we aggregate over larger areas, the population within an area becomes more diverse, but the diversity between the areas decreases. At SA1, the average LS is 7.81 with a standard deviation of ±1.24 between the SA1 scales, compared to the standard deviation of LS within an SA1 area, which is ±0.69. This implies that at the SA1 level, individual LS scores between areas are more dispersed than the aggregated scores within an area. This is reversed as the scale increased. The standard deviation of average LS decreases between areas as the spatial scale increases in size, being largest at SA1 and smallest at the state level. The states and territories have fairly similar average LS scores to each other (average of 7.92 ± 0.087). This also indicates that key information about dispersion of individual LS scores is lost as we aggregate across larger spatial scales (and more individuals). This is an important finding that is reflected in our regression results.

This can be seen when the average LS is mapped across Australia at the five different spatial scales (Figs. 1A–1E). The differences between the different areas are significantly decreased as the aggregation areas grow. Populations seen in Fig. 1A (SA1) that report average LS between 0 and 5.61 no longer show up in Fig. 1E (state/territory scale).

Average LS for the “Unsatisfied” sample is around 4.2 and 8.1 for the “Satisfied” sample, at all spatial scales. The “Satisfied” sample has greater standard deviation in individual LS within areas compared to the “Unsatisfied” sample at all scales except state. In contrast, the “Unsatisfied” sample as greater standard deviation between areas compared to the “Satisfied” sample.

Table S1 presents the descriptive statistics for the objective variables used in this paper. Similar to the standard deviation of average LS, the standard deviation of the objective variables between the areas decreases as the spatial scale increase. In some cases, large differences exist in the averages between the two samples. For example, the average household disposable income for the “Unsatisfied” sample is around $60,000 (±$59,000) at the SA1 level, while for the “Satisfied” sample it is around $80,000 (±$75,000). While at the state/territory scale, the average household disposable income for the “Unstatisfied” sample is about $63,000 (±$27,500) and $84,000 (±$23,000) for the “Satisfied” sample. The “Satisfied” sample is fairly similar to the full sample, which is expected as the “Satisfied” sample comprises 94% of the “All” sample.

Other variables seem to have major differences between the “Unsatisfied” and “Satisfied” samples. For example, at SA1, in the “Unsatisfied” sample the average portion of individuals that don’t exercise at all is about 0.2% and in the “Satisfied” sample, this is around 0.08%.These averages are similar at all scales. We also see that the proportion if individuals with a bachelor’s degree or higher qualification is great in the “Satisfied” sample as is the proportion of individual’s in a relationship, and the number of hours worked per week. The objective variables that seem to be smaller at all scales in the “Satisfied” sample include the proportion of individuals that are unemployed, divorced, engage in no physical activity at all (as discussed above), and having a long-term health condition.

Regression results

The objective variables chosen for this regression were based on those that had a highly significant correlation to subjective LS at the individual level (p ≤ 0.05) based on previous research, and at SA1 scales. The number of observations that are stated in Table 4 indicate the number of SAs over the 16 years which contain respondents to the overall LS question in the HILDA Survey. There are 62,499 SA1s that have at least one person that responded to the LS question in the HILDA Survey. There are 9,484 SA1s over the 16 years that have at least one person with a LS equal or less than 5 and 60,141 with at least one person with a LS of greater than 5.

The model goodness of fit as measured by the adjusted R² increased with each increase in spatial scale (from 0.156 at SA1, through to 0.686 at state level for the full sample) (Table 4). This increase is to be expected as more information is being included in the model, increasing model fitness (Costanza & Maxwell, 1994). Moreover, as seen from Table 2, there is little deviation in average LS at the state level. Thus, the total sum of squares residuals is lower compared to smaller scales.

As the resolution of the scale decreases (aggregation area becomes larger), so does the uncertainty of our model as the estimated coefficients lose precision. This is seen in the higher robust standard errors relative to the coefficients. The increase in uncertainty is due to a larger number of people being aggregated in larger areas, overlooking individuals on the extremes. Further as evident from the standard deviations of the variables between areas (Table 3), there is little disparity between area level aggregates at higher scales.

Comparing life satisfaction of the dissatisfied and the satisfied

Aggregating LS scores, and estimating the models separately, for satisfied and unsatisfied individuals shows how the relationship between objective variables and LS differs between the two groups (Table 4). Separating these individuals shows that information is being lost when aggregating measures for the entire population. We highlight some important examples below.

Future wellbeing indicators

Objective variables that are significant at the SA1 level often cease to be significant at the higher levels, especially at the state level. By focusing on only a single scale, information about objective factors that contribute toward LS may be lost through aggregation. For example, decisions regarding environmental policy based on state level indicators may fail to reflect the important contribution that the local environment, like community parks, makes to individual wellbeing at the local area level. As seen in regression 2 and 3 in Table 4 (“Unsatisfied” and “Satisfied”), the variables most significant to individuals with a lower LS differ from the variables most significant to individuals with a higher LS. By averaging the population over sub-national scales, individuals that are most vulnerable and most at risk within a population may be lost within the averages. Small areas that are excessively low (or high) in LS will be overlooked when averaging the entire population. Understanding the distribution and identifying regions where there is a dearth of critical contributors of LS, allows for targeted policies. Policies at the state, regional, and neighborhood scales take on different forms and produce different outcomes (Gabriel et al., 2010; Termeer, Dewulf & Van Lieshout, 2010; Gale, 2016).

When creating national or subnational wellbeing indicators, it is critical to understand the differences in the value sets that different portions of the population hold, arguing for focusing on finer and more appropriate scales. These value sets can vary due to a person’s age, where they grew up, whether they immigrated, and many other factors. For example, in Australia, the Indigenous population comprises 3.3% of the total population, just fewer than 800,000 individuals according to the 2016 census. However, the values they hold and the type and relative importance of factors that contribute to their LS has been found to differs greatly from others in Australia (Biddle, 2011; Yap & Yu, 2016). Even in countries without a large indigenous population, immigrants hold different value sets and recognize different contributors to their LS (Graham & Markowitz, 2011). This is also not restricted to cultural differences; males and females perceive contributors to wellbeing differently, as do the rich vs the poor, or old vs young. Aspects like safety, money, or family are perceived very differently in these different portions of the population.

Many wellbeing indicators are created based on information only from the sub-national or national scales. This creates a situation in which society is focusing on variables that may not be significant to individuals, and omitting those factors crucial at local level, such as the environment. Often, policies are set based on the assumption of improving variables contributing to human wellbeing. However, the scale of these policies is not often aligned with the most appropriate scale of the variable, potentially reducing the effectiveness of the policy intervention.

By only considering very fine scales of wellbeing, critical information around overall wellbeing of a nation may also be overlooked. Assessing wellbeing at a national scale illustrates the overall progress of the entire nation. A series of national level goals can provide a dashboard of wellbeing indicators; however, an aggregated overall indicator is also essential in measuring the wellbeing of the entire population (Costanza et al., 2016). A national level indicator is also important for comparing countries to determine which are moving toward or away from this goal.