## Abstract

I examine the relationship between economic position relative to local neighbors and life satisfaction in rural Bangladesh. In particular, I exploit a novel household level census of three villages that includes the geospatial coordinates of every household and a perception measure of economic position relative to neighbors. This allows for exploring the sensitivity of the aforementioned relationship to (1) different objective definitions of neighborhood, and (2) the type of positional measure used, objective or perceived. I find that a higher perceived position improves life satisfaction while objective position has no statistically significant effect. This difference stems from a very low correlation between the objective and perceived positional measures. The low correlation can be explained by individual specific heterogeneity in definitions of neighbor. However, observable socioeconomic and demographic variables cannot explain the difference.

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## Notes

- 1.
- 2.
However, there is little empirical evidence for such a causal relationship (Rosenzweig 1988).

- 3.
Indeed, psychologists and behavioral scientists have documented numerous instances where individuals’ reported perceptions deviate systematically from objective realities (Kahneman 2011).

- 4.
It is possible that some of the households got mislabeled into the wrong village which may explain the lower number of households in S and higher number of households in B.

- 5.
Principal component analysis indicates that there is only one underlying factor with an eigenvalue greater than 1 explaining about 37% of the total variance of these eight factors. All eight components are positively correlated with the composite index with household type, number of rooms, ownership of television and ownership of fridge being the most important components.

- 6.
The HES of household

*i*(\(HES_i\)) is generated using the formula \(HES_i =\frac{CI_i - {\text {min}}(CI)}{{\text {max}}(CI) - {\text {min}}(CI)}\) where \(CI_i\) is the composite index (*CI*) of household*i*and \({\text {max}}(CI)\) and \({\text {min}}(CI)\) are the maximum and minimum values of*CI*in the data, respectively. Roughly eight percent of the households (112 households) have \(HES_i=0\) which is set to 2. - 7.
Figure 1b illustrates such a case where household B and household C have 5 and 2 neighbors, respectively, for the same DB.

- 8.
Calculation of economic position has some limitations related to missing information from neighbors due to non-response and the location of neighboring households outside the three villages surveyed. Given the refusal rate of participation in the TS is less than one percent, the first issue is at most marginal. The second issue is more problematic since the three villages surveyed share a border with other non-surveyed villages.

- 9.
Mean comparison tests of HES between the 1301 respondents who answered the perceived position question versus the 94 who did not, does not raise reason for concern. In particular, the null hypothesis that the difference in mean HES between the two groups is zero cannot be rejected at the 95% confidence interval.

- 10.
I included household size and employment status in my preliminary analysis but eventually dropped them because they are not significant and do not change the main results.

- 11.
Religiosity is measured as a response to the question, “How religious are you?” on the 3-point scale of 1-not, 2-moderately, 3-very while health condition is based on responses to the question, “How satisfied are you with your current health” on the scale 1-not at all, 2, 3, 4, 5-completely satisfied.

- 12.
Boes and Winkelmann (2004) underscore the importance of using generalized choice models instead of standard Ologits in estimating life satisfaction regressions. Indeed they find the relationship between life satisfaction and absolute income varies considerably when a GOlogit is used instead of an Ologit.

- 13.
For OLS and Ologit the least life satisfaction age are 40.6 and 39.6 years respectively. For GOlogitF, this age varies between 35.8 and 42.2 years based on reported life satisfaction category.

- 14.
Although it is possible that education affects life satisfaction indirectly by improving economic well-being, health status, and etc.

- 15.
Results from the baseline regressions run on the constrained sample have not been included here but will be made available for those interested.

- 16.
All the signs and approximate magnitude of the odds ratio also remain the same.

- 17.
Interestingly, the proportionality odds constraint is violated for the perceived position variable

- 18.
With the exception of age and squared-age, the variance inflation factor for all regressors, including logarithm of HES, in the perception regressions is less than 2 suggesting multi-collinearity is not responsible for this insignificance.

- 19.
Note that a smaller number of clusters imply a bigger reference group.

- 20.
Marital status and gender seems to affect perceived position in some categories of the GOlogitPs. Measures of fit do not improve much either when compared to the regression of perceived position on objective position only.

- 21.
I do not present the more than 9000 regression results (one for each objective measure) here but can provide the result for those interested.

- 22.
I choose this broad measure out of the six possible considered in this paper, since it offers the highest correlation between objective and perceived measures.

- 23.
I also constructed the HES index by adding households’ reported income as an additional factor. The two HES measures shared a correlation of 0.95; however, there is a significant drop in observations when household income is used as a factor.

- 24.
This method is called the “average link” method and involves taking an arithmetic mean of all distances between each pair of households situated in the two clusters.

- 25.
For a detailed explanation and a discussion of the pros and cons of hierarchical clustering see Chapter 8 of Tan et al. (2006).

- 26.
Note that the average HES of neighbors or the reference economic state used here is the same for everyone when \(J=1\).

- 27.
The \((M-1)\) associated odds ratios indicate how the odds of falling into higher

*y*categories compared to lower categories go up when \(\theta\) goes up by a unit. For instance, if the third odds ratio related to \(\theta\) is 2, it implies that when \(\theta\) increases by one, the odds of \(y>3\) compared to \(y\le 3\) doubles.

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## Appendices

### Appendix 1: Brief Explanation of Hierarchical Clustering with an Average Link

I choose the hierarchical clustering procedure since it is a popular method of clustering with a long history in the literature. It also provides some objectivity by not requiring me to make any subjective choice of initial seeding that some other clustering techniques necessitate (e.g. K-means). Assuming there are *N* distinct households, the hierarchical clustering technique involves *N* iterative steps with each step producing a unique way of dividing all the households into separate clusters. The first step defines each of the *N* household as a cluster. The second step calculates the distance between every pair of households (or clusters) and then identifies the two households with the shortest distance between them as a single cluster while the rest of the households continue being treated as their own cluster (leading to \((N-1)\)-cluster neighbors). In the third step, the “average” distance between every cluster is calculated and the two clusters with the shortest average distance between them merged into one cluster.^{Footnote 24} This process is repeated until all households form a single cluster in the *N*th step. Thus, the *J*-cluster neighbors refer to neighbors defined in the \((N-J+1)\)th step and comprising of *J* clusters.^{Footnote 25}

There are 1395 possible *J*-cluster neighbors (where \(J = 1,2,\ldots ,1395\)) associated with the hierarchical iterative process explained before in the data used for this paper. However, for higher values of *J* these are not very useful because there are too many single household clusters. Hence, I do not consider *J*-clusters where \(J > 200\). Under the 200-cluster neighbors, there are 27 households that form singleton clusters while 43% of the households are located in clusters with less than 10 households. I also do not use 1-cluster because this makes HES and the ratio of HES to average neighbors’ HES perfectly collinear.^{Footnote 26}

### Appendix 2: Generalized Ordered Logits

Equation (3) summarizes the GOlogit associated with Eq. (1):

Note that the model parameters \(\rho _0,\rho _1,\ldots ,\rho _K\) from Eq. (1) have an additional subscript of *j* in Eq. (3). This embodies the generalization that the parameters may vary across reported \(y_i\) i.e. the “proportional-odds” assumption that is standard in ordered logits (Ologits) is relaxed. Indeed, relaxing the proportional-odds constraints (POCs) is equivalent to assuming the threshold cut-offs in ordered logits are heterogeneous and are weighted linear combinations of the independent variables. If the POCs are imposed for all variables, it becomes the standard Ologit. The interpretation of the regression coefficients and related odds ratio of GOlogits can be a bit tricky. Without loss of generality, for each regressor \(\theta\), the GOlogit estimates \((M-1)\) different regression coefficients.^{Footnote 27}

Generally, if the dataset has a large number of observations using a GOlogit without imposing any POCs (GOlogitF) is preferred to implementing the more parametrically parsimonious Ologit. Given the TS has a limited number of observations, running a GOlogitF entails estimation of additional parameters that may reduce efficiency unnecessarily if the true data generating process (DGP) imposes all of the POCs. However, if the true DGP is one where some of the POCs do not hold, then Ologits produce biased estimates.

A GOlogit which relaxes only those POCs that are violated (GOlogitP) is a practical compromise between an Ologit and a GOlogitF. Brant (1990) proposes using Wald tests to identify which POCs do not hold. I use the iterative *autofit* process developed by Williams (2007), an extension of the “Brant” test, to choose which POCs to relax when running the GOlogitPs. In particular, running the baseline regressions and the perception regressions with *autofit* reveal that only POCs associated with the village dummies and the perceived position variables are violated. Consequently, I relax the POCs for only the village dummies and the objective position measures when running the objective regressions.

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Bhuiyan, M.F. Life Satisfaction and Economic Position Relative to Neighbors: Perceptions Versus Reality.
*J Happiness Stud* **19, **1935–1964 (2018). https://doi.org/10.1007/s10902-017-9904-8

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### Keywords

- Subjective well-being
- Life satisfaction
- Relative consumption
- Bangladesh
- Perception
- Spatial analysis