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Conceptual Framework: 
From Multidimensional SWB Data 
to a Well-Being Index 
Daniel J. Benjamin (Cornell and USC) 
Ori Heffetz (Cornell) 
Miles S. Kimball (Michigan) 
OECD Workshop on Multidimensional SWB 
30 October 2014
Motivation 
• Revealed preference: welfare = well-informed choice 
– Despite limitations, a reasonable starting point 
• But in a policymaking context: 
– Individuals rarely directly choose policy 
– Individuals often not well-informed re consequences 
• Economists hence often rely on welfare 
indicators, such as GDP, indirectly justified by 
revealed preference (for a rep. agent) 
• However, many shortcomings, so looking for 
additional measures “beyond GDP”
Motivation 
• Candidate measures: “subjective well-being” (SWB) 
– In this talk: SWB = any subjective assessment of some 
aspect of well-being 
• Capture a wide range of experiences, including 
unrelated to market exchange (“beyond GDP”) 
• Need for more than 1 question 
– Different SWB measures have different correlates 
(e.g., Kahneman and Deaton, 2010, PNAS; Deaton, Fortson, and 
Tortora, 2010) 
– No single SWB measure captures everything people care 
about (Benjamin, Heffetz, Kimball, and Rees-Jones, 2012, AER, and 
2014, AER)
Standard Consumption Framework 
• Theory for an individual (“representative agent”). 
• u(c) depends on a vector c = (c1,…,cM)'. 
Δ푢 ≈ 
휕푢 풄 
휕푐푚 
푀 
푚=1 
푀 
Δ푐푚 ∝ 푝푚 
푚=1 
Δ푐푚 
• Governments measure c and prices. 
• For small Δc, change in the index is approximately 
proportional to Δu. 
• Perhaps main limitation: only consumption goods
Fundamental Aspects of Well-Being 
Rather than focusing on standard consumption 
goods (e.g., rice, TVs, train rides)… 
…a multidimensional SWB survey measures 
more fundamental aspects of well-being (e.g., 
health, emotional states, freedoms). 
More general approach in that fundamental 
aspects include all objects of desire. 
– Consumption goods & non-consumption 
determinants of well-being.
Our Framework 
(Benjamin, Heffetz, Kimball, and Szembrot, AER, 2014) 
• u(w) depends on a vector w = (w1,…,wJ)'. 
Δ푢 ≈ 
휕푢 풘 
휕푤푗 
퐽 
푗=1 
Δ푤푗 
• Purpose of SWB survey: measure w; can add 
“objective” measures. 
• For small Δw, change in the index approx. 
proportional to Δu. 
• Purpose of a stated-pref (SP) survey: estimate 
the missing ingredient: the marginal utilities.
Step 1: Choosing the Aspect List 
Two key criteria: 
1. Exhaustive (i.e., cover all elements of w) 
• Otherwise, same problem as GDP: not a 
comprehensive measure of well-being. 
2. Non-overlapping (i.e., don’t cover an element of 
w more than once) 
• If overlapping, then will “double count” some 
aspects of well-being in the index. 
• Like including cars and BMWs as separate categories 
that enter GDP.
Step 2: Conduct SWB+SP Survey and 
Construct Well-Being Index 
• Theoretical ideal: 
– Conduct SWB+SP survey regularly on each individual. 
– Track individual-level well-being index:
• What if limited to N < J questions? 
– Find best predictor of “full index” → need to 
construct and track full index for a few waves. 
• Conceptually, regress full index on sets of N questions 
to max R2 (sophisticated methods avoid overfitting). 
• Optimal weights for “abridged index” generally ≠ MUs. 
• Optimal Qs and weights may change if Qs’ covariances 
change → should track full index periodically. 
• What if need to pool respondents? 
– E.g., to estimate weights for full index. 
– Justified theoretically only if same slope of indiff 
surfaces; testable via SP survey.
Step 3: Aggregate Across Individuals 
for National Well-Being Index 
• If willing to assume aspect levels and survey 
responses are interpersonally comparable: 
– Can take the average across individuals of reported 
SWB levels, or the average of the individual well-being 
indices. 
• Commonly done today. 
– But we suspect this assumption is problematic, so 
prefer approaches that do not rely on it. 
• Two approaches that assume merely ordinal and 
interpersonally non-comparable aspect levels and 
survey responses:
• Money-metric approach (see Fleurbaey and Blanchet, 2013): 
– Include money amounts in SP survey. 
– Enables denominating change in well-being index in terms of 
income change that would leave the individual indifferent. 
– Can aggregate the monetary changes. 
• Could sum up (as in cost-benefit analysis). 
• We prefer a social welfare function aggregation that puts more 
weight on poorer individuals. 
• Normalized Gradient Addition mechanism: 
(Benjamin, Heffetz, Kimball, and Szembrot, 2013, AER P&P; Benjamin, 
Carroll, Heffetz, and Kimball, 2014): 
– Not enough time to explain here. 
– Essentially uses estimated effects of policies on individuals’ 
well-being indices to calculate how people would optimally 
vote for adjusting various policies. 
– Recommends adjusting policies by (multidimensional) net 
vote margin.
Actionable Lessons for OECD 
1. Promote adoption of SP surveys to estimate weights 
for creating indices. 
2. Assess overlap in existing list of SWB questions. 
3. Implement a much broader list of SWB questions, at 
least in a subsample. (cf., Deaton, Kahneman, Krueger, 
Schkade, Schwarz, and Stone, 2011) 
– Enables assessing comprehensiveness of existing list. 
– Enables estimating optimal weights for the shorter, 
existing SWB questions. 
4. Promote estimation of policy effects on a well-being 
index for well-defined demographic subgroups in a 
consistent way across policies. 
– Enables studying the policy recommendations implied by 
alternative aggregation methods.

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HLEG thematic workshop on "Multidimensional Subjective Well-being", Dan Benjamin

  • 1. Conceptual Framework: From Multidimensional SWB Data to a Well-Being Index Daniel J. Benjamin (Cornell and USC) Ori Heffetz (Cornell) Miles S. Kimball (Michigan) OECD Workshop on Multidimensional SWB 30 October 2014
  • 2. Motivation • Revealed preference: welfare = well-informed choice – Despite limitations, a reasonable starting point • But in a policymaking context: – Individuals rarely directly choose policy – Individuals often not well-informed re consequences • Economists hence often rely on welfare indicators, such as GDP, indirectly justified by revealed preference (for a rep. agent) • However, many shortcomings, so looking for additional measures “beyond GDP”
  • 3. Motivation • Candidate measures: “subjective well-being” (SWB) – In this talk: SWB = any subjective assessment of some aspect of well-being • Capture a wide range of experiences, including unrelated to market exchange (“beyond GDP”) • Need for more than 1 question – Different SWB measures have different correlates (e.g., Kahneman and Deaton, 2010, PNAS; Deaton, Fortson, and Tortora, 2010) – No single SWB measure captures everything people care about (Benjamin, Heffetz, Kimball, and Rees-Jones, 2012, AER, and 2014, AER)
  • 4. Standard Consumption Framework • Theory for an individual (“representative agent”). • u(c) depends on a vector c = (c1,…,cM)'. Δ푢 ≈ 휕푢 풄 휕푐푚 푀 푚=1 푀 Δ푐푚 ∝ 푝푚 푚=1 Δ푐푚 • Governments measure c and prices. • For small Δc, change in the index is approximately proportional to Δu. • Perhaps main limitation: only consumption goods
  • 5. Fundamental Aspects of Well-Being Rather than focusing on standard consumption goods (e.g., rice, TVs, train rides)… …a multidimensional SWB survey measures more fundamental aspects of well-being (e.g., health, emotional states, freedoms). More general approach in that fundamental aspects include all objects of desire. – Consumption goods & non-consumption determinants of well-being.
  • 6. Our Framework (Benjamin, Heffetz, Kimball, and Szembrot, AER, 2014) • u(w) depends on a vector w = (w1,…,wJ)'. Δ푢 ≈ 휕푢 풘 휕푤푗 퐽 푗=1 Δ푤푗 • Purpose of SWB survey: measure w; can add “objective” measures. • For small Δw, change in the index approx. proportional to Δu. • Purpose of a stated-pref (SP) survey: estimate the missing ingredient: the marginal utilities.
  • 7.
  • 8.
  • 9. Step 1: Choosing the Aspect List Two key criteria: 1. Exhaustive (i.e., cover all elements of w) • Otherwise, same problem as GDP: not a comprehensive measure of well-being. 2. Non-overlapping (i.e., don’t cover an element of w more than once) • If overlapping, then will “double count” some aspects of well-being in the index. • Like including cars and BMWs as separate categories that enter GDP.
  • 10. Step 2: Conduct SWB+SP Survey and Construct Well-Being Index • Theoretical ideal: – Conduct SWB+SP survey regularly on each individual. – Track individual-level well-being index:
  • 11. • What if limited to N < J questions? – Find best predictor of “full index” → need to construct and track full index for a few waves. • Conceptually, regress full index on sets of N questions to max R2 (sophisticated methods avoid overfitting). • Optimal weights for “abridged index” generally ≠ MUs. • Optimal Qs and weights may change if Qs’ covariances change → should track full index periodically. • What if need to pool respondents? – E.g., to estimate weights for full index. – Justified theoretically only if same slope of indiff surfaces; testable via SP survey.
  • 12. Step 3: Aggregate Across Individuals for National Well-Being Index • If willing to assume aspect levels and survey responses are interpersonally comparable: – Can take the average across individuals of reported SWB levels, or the average of the individual well-being indices. • Commonly done today. – But we suspect this assumption is problematic, so prefer approaches that do not rely on it. • Two approaches that assume merely ordinal and interpersonally non-comparable aspect levels and survey responses:
  • 13. • Money-metric approach (see Fleurbaey and Blanchet, 2013): – Include money amounts in SP survey. – Enables denominating change in well-being index in terms of income change that would leave the individual indifferent. – Can aggregate the monetary changes. • Could sum up (as in cost-benefit analysis). • We prefer a social welfare function aggregation that puts more weight on poorer individuals. • Normalized Gradient Addition mechanism: (Benjamin, Heffetz, Kimball, and Szembrot, 2013, AER P&P; Benjamin, Carroll, Heffetz, and Kimball, 2014): – Not enough time to explain here. – Essentially uses estimated effects of policies on individuals’ well-being indices to calculate how people would optimally vote for adjusting various policies. – Recommends adjusting policies by (multidimensional) net vote margin.
  • 14. Actionable Lessons for OECD 1. Promote adoption of SP surveys to estimate weights for creating indices. 2. Assess overlap in existing list of SWB questions. 3. Implement a much broader list of SWB questions, at least in a subsample. (cf., Deaton, Kahneman, Krueger, Schkade, Schwarz, and Stone, 2011) – Enables assessing comprehensiveness of existing list. – Enables estimating optimal weights for the shorter, existing SWB questions. 4. Promote estimation of policy effects on a well-being index for well-defined demographic subgroups in a consistent way across policies. – Enables studying the policy recommendations implied by alternative aggregation methods.