“Injuries, therefore, should be inflicted all at once, that their ill savor being less lasting may the less offend; whereas, benefits should be conferred little by little, that so they may be more fully relished.” – Niccolò Machiavelli, The Prince
Ceteris paribus, would one inflict bad things all at once or spread them out? And would one do the same or the opposite with positive events? Machiavelli urges us to bunch the bad and space the good. We address this question empirically by looking at the non-linearity in the effects of positive and negative events on self-reported life satisfaction in a large panel of Australians observed since 2002, to shed light on the shape of the utility function. If our empirical life-satisfaction function turns out to be in line with classic economic assumptions on the shape of the utility function, life satisfaction could be interpreted as a suitable proxy for utility, which would further motivate its use for policy analysis.
In classic economic parlance, Machiavelli's reasoning assumes an S-shaped utility function that is concave in positive and convex in negative shocks, much like the shape of the value function by Kahneman and Tversky (1979). Then, the average absolute impact of negative shocks would decrease in their size (or number), with the same holding for positive effects. Under classic economic assumptions, on the other hand, there is concavity everywhere (diminishing marginal utility), which means that the average absolute impact of negative shocks would increase in their size. Fig. 1 illustrates the shapes of these different functions.
Implicit in Machiavelli's argument is adaptation to shocks: when he suggests inflicting all injuries at once rather than conferring them little by little, Machiavelli argues that, in doing so, “their ill savor [would be] less lasting”, which implies that these different strategies would exhibit different adaptation profiles over time. The same holds, in the opposite direction, for benefits.
The notion of ‘hedonic adaptation’ has a long tradition in psychology, dating back at least as far as Brickman's and Campbell's Hedonic Relativism and Planning the Good Society (Brickman and Campbell, 1971). There is now an established body of evidence on adaptation to various positive or negative life events in the psychology and applied economics literature, most of which uses individuals’ self-reported life satisfaction as outcome. It covers changes in marital status (Lucas, 2005; Lucas and Clark, 2006; Oswald and Gardner, 2006; Stutzer and Frey, 2006), disability (Menzel et al., 2002; Oswald and Powdthavee, 2008), income (Di Tella et al., 2010; Kuhn et al., 2011), or unemployment (Clark et al., 2008), as well as studies using measures of life satisfaction to look at anticipation and adaptation to life shocks in relative comparison (Clark et al., 2008; Frijters et al., 2011; Clark and Georgellis, 2013). Adaptation is also central to the idea of a set point of life satisfaction around which individuals fluctuate, and often thought to be one reason (besides relative comparisons) behind the lack of a strong relation between GDP and life satisfaction in rich countries over time.1 If we want to study Machiavelli's prescript empirically by looking at non-linearity in the effects of positive and negative life events on life satisfaction, we must, therefore, pay attention to the phenomenon of hedonic adaptation in order to separate that issue from the issue of non-linearity that determines the optimal spacing of events.
Apart from these studies, which have a particular focus on hedonic adaptation, there is a large literature on how individuals’ life satisfaction (or subjective wellbeing more generally) reacts to various positive or negative life shocks, including, for example, shocks to income and wealth (Gardner and Oswald, 2007; Adda et al., 2009; Schwandt, 2018), war time experiences (Johnston et al., 2016), crime victimization (Johnston et al., 2018), own criminal behavior (Corman et al., 2011), homelessness (Curtis et al., 2013), and various other life shocks (Lindeboom et al., 2002). However, despite the large interest in this topic, the question of optimal spacing of events has never been posed, to our knowledge. This reflects, in part, the inherent difficulty in finding random variation in enough life events simultaneously to be certain about their cumulative effect. Researchers, therefore, have typically restricted themselves to look at single events in isolation, such as unemployment or marital breakdown, or else have been interested in particular psychological mechanisms that hold for many events, such as adaptation or the relation between decisions and experiences (Kahneman et al., 1997).
Yet, the question of spacing, in particular its optimality, is important: to the extent that individuals may have control over certain life events (for example, getting married or divorced, retiring, or going for promotion), they may make ‘clean breaks’ (all at once), ‘bite the bullet’ (all at once), ‘take it one at a time’ (one by one), and so on. Often, policy-makers must decide when to implement certain reforms with negative or positive wellbeing consequences over the legislative period. Is it better to implement all reforms at once, or rather spread them out? Hence, it would be insightful for such deliberations to know whether – as Machiavelli's puts it – it is better if ‘injuries’ or ‘benefits’ are bunched or spread out, ceteris paribus.
We use the analogy of life events and test Machiavelli's prescript empirically, by specifying and estimating various life-satisfaction functions with life events as arguments. We find evidence that life satisfaction is concave in both positive and negative domains: accounting for selection, anticipation, and adaptation, and holding the number of negative events constant over an individual's life, we show that overall life satisfaction decreases when negative events occur all at once as opposed to being spread out. For positive events, the same holds, meaning that – from a welfare perspective – it is better if both the good and the bad are spread out. The findings from our empirical life-satisfaction functions, therefore, reject Machiavelli's prescript. If data on life satisfaction are anything to go by (an issue discussed more later on), our findings are suggestive of a utility function that is globally concave, in line with classic economic assumptions.
We use data on six positive and twelve negative life events in the Household, Income and Labour Dynamics in Australia (HILDA) panel. HILDA has several advantages over comparable datasets: it uniquely tracks the 18 life shocks we use for the entire duration of the panel (2002-now), has a large numbers of individuals (about 20,000), consistently measures life satisfaction in every survey year, and records life events on a quarterly basis. The panel dimension allows us to look at within-person variation in life events and life satisfaction, reducing some of the bias resulting from selection into particular events. The availability of quarterly event information allows us to account for the adaptation profile of each event on a precise level.
In our most simple specification, we pool all positive life events into a single count variable and all negative events into another, finding clear evidence of a non-linear effect of life events on life satisfaction. This specification assumes that all events have equal magnitude and the same temporal effect profile, which are both unlikely. So in our extended specification, where each event has its own anticipation and adaptation profile, we use empirical indices of negative and positive events, finding the same overall pattern.
Another legitimate worry is that events might arise from choice behavior rather than befalling individuals randomly. In sensitivity analyses, we show that the results remain qualitatively the same when following the literature and looking only at a specific subset of more exogenous and unanticipated events in our data (like winning the lottery, experiencing the death of a close friend, or being a victim of crime). Further robustness checks, including tests for selective attrition, respondents’ fidelity and engagement with the survey questions, and alternative estimation procedures, are all in line with our main findings.
We then ask: how much does the non-linearity in life events matter when it comes to overall welfare, measured as the sum of life satisfaction over the population over time? We find that if losses were spread evenly in a given period of time, the overall welfare loss from these losses would reduce by about 10%. If gains were spread evenly, the overall welfare gain would rise by about 2%. In sum, this would yield an overall net welfare gain of about 12% relative to the status quo. Note that this is 12% of the status quo effects of all positive and negative events, not 12% of welfare or life-satisfaction variation.
Our findings add to two streams of literature: first, there is a literature in applied economics and psychology that exploits data on subjective wellbeing (in particular on self-reported life satisfaction) focussed on the non-linearity around the reference point. A general finding is that financial worsening looms larger for life satisfaction than financial improvement of the same absolute size, which would be in line with prospect theory and the kink at the reference point of value functions experimentally identified by Kahneman and Tversky (1979). Using nationally representative longitudinal household data from the British Household Panel Survey (BHPS) and the SOEP panel, Boyce et al. (2013) find that, over a relatively long time horizon, positive changes in income from one year to another yield a lower absolute change in life satisfaction than negative changes. A similar asymmetry is found by De Neve et al. (2018) at the macro level when it comes to positive and negative fluctuations in economic growth. Likewise, Vendrik and Woltjer (2007) provide evidence of a globally concave life-satisfaction function in the context of relative income, with a (slight) kink at a zero relative income gap. Gonza and Burger (2017) also claim an S-shaped function in some of their estimates for the effects of the economic downturn of 2008 on life satisfaction.
Second, there is an established literature studying anticipation and adaptation in self-reported life satisfaction to various life events, both positive and negative. Clark et al. (2008) use annual data on four negative (unemployment, divorce, widowhood, and lay-off) and two positive life events (marriage and childbirth) from the German Socio-Economic Panel Study (SOEP), showing that respondents anticipate and later fully adapt to most life events when it comes to their life satisfaction. Frijters et al. (2011) extend this analysis by studying life satisfaction dynamics around changes in employment status (being promoted and being laid off), changes in family life (births, deaths, and divorce), and changes related to the physical person (victimization and health) in the HILDA panel. The authors confirm that respondents hedonically adapt to most changes in life circumstances. Dore and Bolger (2018) extend that methodology to allow for heterogeneous response patterns to negative shocks they call ‘stressors’.
We join both streams of literatures, allowing for a non-linearity at the reference point while focussing primarily on non-linearities further away from it. Most importantly, we account for the dynamics of life events by explicitly modeling anticipation and adaptation regarding each life event at a precise quarterly level.
The rest of this paper is organised as follows: Section 2 gives an overview of the data we use and provides summary statistics on the life events we study. Section 3 introduces the empirical strategy, including different types of estimation and different ways to operationalise the occurrence of life events in a given period of time. Section 4 presents our main findings and scrutinises their robustness regarding alternative operationalisations and explanations. Section 5 calculates overall welfare counterfactuals. Finally, Section 6 concludes and discusses potential implications for individual and policy choices.
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