Notes

In the Luttmer study, a region is defined as a public use microdata area (PUMA), with an average population of 150,000. PUMAs are used by the U.S. Census Bureau to partition a state into sub-state areas for statistical reporting purpose. A PUMA is generally the aggregate of small counties or the aggregate of census tracts in large metropolitan areas, with at least 100,000 people.

Barrington-Leigh and Helliwell (2008) have also addressed this issue. However, their study is based on a much smaller sample. For instance, only about 9000 respondents in their study are nesting simultaneously in neighbourhoods, local communities, and municipalities, while the sample size in the current study is 15 times larger. More importantly, the present study differs from that of Barrington-Leigh and Helliwell in modelling approaches, particularly in terms of the sequence of entering control variables.

Happiness also protects health (Diener and Chan 2011; Siahpush et al. 2008; Veenhoven 2008). The reciprocal relationship between SWB and health cannot be sorted out with cross-sectional survey data.

In analysis with both individual-level and group-level variables, the estimation of the effects of group-level variables is equivalent to that from a grouped data model. That is, the group means of the individual-level outcome variables, after adjusting for group differences in individual-level control variables, are regressed on the group-level variables. The reliability of grouped data analysis strongly depends on the average size of observations within each group and the number of groups (Devereux 2007; Raudenbush et al. 2000).

A CMA or CA contains one or more adjacent municipalities situated around a major urban core. A CMA must have a total population of at least 100,000, of which 50,000 or more live in the urban core. A CA must have an urban core population of at least 10,000.

The distribution of the sample across surveys is the following: 12,581 cases from the 2008 GSS, 12,214 cases from the 2009 GSS, 9,777 cases from the 2010 GSS, 14,308 cases from the 2011 GSS, 30,609 cases from the 2009 CCHS, 31,573 cases from the 2010 CCHS, and 31,718 cases from the 2011 CCHS. Together, there are about 5 respondents per immediate neighbourhood, 29 respondents per local community, and 332 respondents per municipality.

The number of children younger than age 18 is defined differently in the GSS and the CCHS. In the GSS, it is the number of respondents' single (never married) children 0 to 17 years of age living in the household. In the CCHS, it is the number of persons in the household less than 18 years of age. The mean of the variable is larger in the CCHS (0.62) than in the GSS (0.51).

The square root of family size is a conventional scale that discounts the consumption needs of additional family members. Controlling for this factor, the effect of household income on life satisfaction tends to increase. For instance, the coefficients for the lowest and lower middle household income groups (as relative to the higher middle) are -0.47 and -0.19, respectively, without controlling for family size in a model including all other individual-level socio-demographic variables. With the control, they change to -0.50 and -0.21, respectively (as in Model 2, Table 4).

This is computed by dividing the after-tax income by a scale that assigns a decreasing value to the second and subsequent family members. In the census microdata file, the scale is the sum of the following values: 1.0 is assigned to the oldest person in the family; 0.4 is assigned to each of the other family members aged 16 and over; and 0.3 is assigned to each of family members under age 16. For persons not in families, the value is set to 1.0. Empirically, this scale is close to the square root of family size.

The next-higher geographic level is province, which is too broad. For instance, North Bay CMA in northern Ontario is drastically different from Toronto CMA in southern Ontario in terms of population size, economic scales, population diversity, and climate.

This is because log odds ratios or odds ratios from logit or probit regression are affected by unobserved heterogeneity that may be reduced when an additional variable is added to the model even though the added variable is unrelated to the independent variables already in the model.

In the GSS, the average weight ranges from 1500 to 2000 depending on the survey year. In the CCHS, the average weight is about 640. Standardizing these weights avoids an overestimation of the critical level while maintaining the same distributions as those of non-standardized weights. Alternatively, the weights could be standardized so that the sum of the standardized weights is the same in each survey year and type and equal to the sample size of the smallest survey year and type. Additional analysis (not shown) suggests that there is no substantive difference in model estimates from using either weighting method.

Out of the 31,024 immediate neighbourhoods, 3,301 contain at least 10 respondents. Thus, each quintile comprises about 660 neighbourhoods.

An additional model is estimated in which DA-level demographic and socioeconomic characteristics are included but the fixed effects of local communities are not. The R-squared of this model is 0.0785, which is slightly larger than that of Model 2. In this additional model, the coefficient of log locality income is 0.083. Among the included DA-level characteristics, population density and share of new immigrants are negatively and significantly associated with life satisfaction. These results suggest that part of the locality income estimated in Model 2 is attributable to low density and fewer new immigrants in high-income neighbourhoods.

In the current data, neighbourhood income is strongly correlated with community income (Pearson r = 0.81).

In these models, community average income is calculated by excluding a respondent's immediate neighbourhood, and municipality average income is calculated by excluding a respondent's local community (Barrington-Leigh and Helliwell 2008). The purpose of this procedure is to reduce correlation between locality incomes at various geographic levels. The nested models with three levels of locality income are not affected by multicolinearity. In all models, no coefficient has a variance inflation factor (VIF) value over 2.5. A general rule is that a VIF value of 10 or higher indicates considerable collinearity.

In a model similar to Model 3 in Table 5 but one that uses self-reported health as the outcome, the coefficient is 0.16 for neighbourhood income and 0.11 for community income, and both are significant at p<0.001. The coefficient for municipality income is not significant.

Luttmer did control for the size of metropolitan area population and fraction of blacks in PUMA. He also performed an additional test to control for PUMA housing price. These controls, however, may not fully capture other PUMA attributes that may be negatively associated with happiness. The negative coefficient of municipality income in Model 2 in the present study hardly changes when controlling only for other area-level attributes; it changes to positive and significant only when the fixed effects of CMAs/CAs are controlled for.

While the causal direction between self-reported health and life satisfaction is in doubt, it is reasonable to assume that chronic physical and mental illnesses can affect individuals' evaluation of their current SWB. Veenhoven (2008) suggests that happiness protects one against falling ill but that it does not cure diseases. Chronic physical and mental illnesses include asthma, arthritis, back problems, high blood pressure, migraine, chronic bronchitis, diabetes, heart disease, cancer, stomach or intestinal ulcers, effects of a stroke, urinary incontinence, bowel disorders, Alzheimer's disease or other dementia, mood disorders (such as depression, bipolar disorder, mania, or dysthymia), and anxiety disorders (such as a phobia, obsessive-compulsive disorder, or panic disorder). The mastery scale measures the extent to which people believe that their life-chances are under their control.

Model results are available on request. The 2008 GSS contains only 12,580 respondents nested within 9,538 neighbourhoods, 4,119 communities, and 378 municipalities. Likely as a result of the small sample size and the corresponding larger coverage errors and measurement errors, none of the coefficients of community income in Models 1, 2, 3, and 4 are statistically significant, although the size of the coefficients is similar to that reported in Table 5.