Introduction and Overview

Personal happiness is permanently challenged by unexpected events beyond our own control: death of a family member, birth of a child, loss of job, or a promotion at the workplace are just a few examples related to the ups and downs of individual happiness. Similarly, the happiness of whole societies may also be affected by unforeseeable developments. The EU countries e.g. were recently exposed to Covid-19, the Ukrainian war, energy shortages, inflation, etc. The question is, whether these developments have a lasting negative effect on the collective happiness of the Europeans. The existing literature, mainly focused on individuals, is rather ambiguous with regard to the long-term effects of happiness shocks.Footnote 1 Cummins postulates that there is a homeostatic mechanism, which maintains happiness at the level of a so-called set point (see Cummins et al., 2012; Cummins, 2013). Veenhoven (2014), Headey et al. (2014), and Veenhoven and Kegel (2022) doubt about the temporal stability of this set point, arguing that empirical studies show a secular trend towards increased collective happiness. The critique of Easterlin (2003) is even more radical: he argues that the mentioned homeostatic stability of happiness varies with the concerned life-domain. According to him, it exists mainly for financial matters and less for non-pecuniary domains like e.g. health and family life.

In view of the controversial theoretical discussion and the lack of empirical evidence with regard to the homeostasis of collective happiness of whole societies, the present article tries to find out in which European countries there is a homeostatic mechanism at work that makes them resilient against unhappiness.Footnote 2 For this purpose, country-specific time series of annual happiness between 2007 and 2019 are analyzed by linear and quadratic regressions, where the current national happiness is the independent and the related following level of happiness the dependent variable. By analyzing the resulting regression equations it is possible to identify and analyze its mathematical fixed points. If at least one of them is stable, there exists a homeostatic set point and the regression coefficients can be used in order to calculate the strength of the equilibrating mechanism, which brings the country back to this set point. If there is no stable equilibrium at all, the country is probably not resilient against external shocks of happiness. Furthermore, unstable fixed points can be used in order to identify the limits of resilience, below which the homeostatic self-stabilization does not work anymore.

Methodological Considerations

Analyses Based on Linear Regression Functions

The simplest regression function for identifying homeostatic self-stabilization is the linear equation

$${\mathrm{H}}_{+} =\mathrm{ f}(\mathrm{H}) =\mathrm{ a }+\mathrm{ b }*\mathrm{ H}$$
(1)

where H is the current and H+ the future happiness and a and b are coefficients, which have to be estimated from observational data. The intersection of the lines H+  = H and H+  = f(H) (see Fig. 1a, b) defines the mathematical fixed point where the equality H = f(H) holds. If b < 1, the fixed point is generally a stable equilibrium (see Fig. 1a) and corresponds to the homeostatic set point of happiness. Any deviance from this set point by a positive or negative shock triggers a stepwise return to this equilibrium, as the dynamics of Fig. 1a show. Thus, in Fig. 1a there is unlimited resilienceFootnote 3 against unhappiness. In Fig. 1b with b > 1 this is obviously not the case, as the intersection of the lines H+  = H and H+  = f(H) is an unstable equilibrium: any disturbance in the form of a small positive or negative shock drives happiness away from this point.

Fig. 1
figure 1

a An exemplary linear function f(H) with a homeostatic return to the set point. Legend: H+  = f(H) = a + b * H, where b < 1. b An exemplary linear function f(H) with no homeostatic set point. Legend: H+  = f(H) = a + b * H, where b > 1

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It is important to note that happiness shocks are generally at random (white noise) and not correlated with the level of happiness. To the contrary, homeostatic correction is systematic: the farther away from the set point the stronger the compensatory change of happiness (see Fig. 1a, b). This is crucial for the statistical separation of the two processes: regression coefficients are mainly influenced by the homeostatic correction and less by positive or negative happiness shocks.

Analyses Based on Quadratic Regression Functions

A more complex regression function for identifying homeostatic self-stabilization is the quadratic polynomial

$${\mathrm{H}}_{+} =\mathrm{ f}(\mathrm{H}) =\mathrm{ a }+\mathrm{ b }*\mathrm{ H }+\mathrm{ c }* {\mathrm{H}}^{2}$$
(2)

where H is again the current and H+ the future happiness and a, b, and c are coefficients, which have to be estimated from observational data. For Eq. (2) there are generally two intersections of the lines H+  = H and H+  = f(H) (see Fig. 2a, b), which are mathematical fixed points with varying forms of (in)stability. In Fig. 2a where the quadratic coefficient c < 0, only the upper fixed point is stable and consequently defines a homeostatic set point. However, in this case homeostasis is not unlimited: the second, lower fixed point is an unstable equilibrium. Below this critical lower limit, the homeostatic mechanism does not work anymore and consequently there is only limited resilience.

Fig. 2
figure 2

a An exemplary quadratic function f(H) with c < 0. Legend: H+  = f(H) = a + b * H + c * H2, where c < 0. b An exemplary quadratic function f(H) with c > 0. Legend: H+  = f(H) = a + b * H + c * H2, where c > 0

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If c > 0 like in Fig. 2b, the homeostatic set point corresponds to the first, lower fixed point. Thus, there is no lower limit where the buffering of negative shocks of happiness fails. There is however an upper limit for the functioning of homeostasis, which is represented by the second, upper fixed point of Fig. 2b. Since we are in this paper mainly interested in negative shocks of happiness, this unstable equilibrium is not considered anymore.

Synthesis of the Two Types of Analysis

In principle it is possible to use for the analysis of homeostatic self-stabilization also higher order polynomials of the degree three and more. This opens the possibility to find other set points, which stop the race to the bottom or the top of happiness that implicitly exists in Fig. 2a and b. In view of the limited length of the available time series from 2007 to 2019 and the related risk of overfitting the scarce data, we limit the analyses to the previously discussed linear and quadratic Eqs. (1) and (2). The one that yields for a given country the better statistical fit in terms of the adjusted r-square is used for further interpretation. If in spite of sufficient variation of H, none of the equation gives a significant adjusted r-square, we assume that for the analyzed country there is no homeostasis of happiness. Similarly, also the absence of an intersection between the lines H+  = H and H+  = f(H) suggests the absence of a homeostatic mechanism with an associated set point.

Returns from the Analyses

The most important return from the previous analyses is the distinction between countries with homeostasis of happiness (e.g. Figure 1a) and without this property (e.g. Figure 1b). If there is homeostatic resilience, the set point can be time-invariant or changing over time. It is assumed to be changing if the respective intersection between of H+  = H and H+  = f(H) deviates from the mean happiness of a country by more than 2 standard errors of this mean value. Thus there are cases where there is an old set point (= mean observed happiness) and a new one (= intersection of H+  = H and H+  = f(H)). Furthermore, the empirical analyses allow to distinguish between unlimited homeostasis (e.g. Figure 1a) and homeostasis with a lower limit (e.g. Figure 2a), below which the homeostatic mechanism fails. The distance between this lower limit and the (old or new) set point is called the critical distance. Finally, the empirical analyses allow to determine the strength of resilience that is the homeostatic correction of an infinitesimal deviation from the set point f(H) = H. Hence, the strength of resilience is equal to the first derivative

$$\mathrm{d}(\mathrm{H}-\mathrm{f}(\mathrm{H})) /\mathrm{ dH }=\mathrm{ dH }/\mathrm{ dH }-\mathrm{ df}(\mathrm{H}) /\mathrm{ dH }= 1 -\mathrm{ df}(\mathrm{H}) /\mathrm{ dH}$$
(3)

of the difference between the curves H+  = H and H+  = f(H) at the set point f(H) = H.

In sum, based on the different types of homeostatic processes, there are four mutually exclusive categories of resilience against unhappiness:

  • Category 0: No resilience, due to missing intersections between the curves H+  = H and H+  = f(H) or a statistically insignificant auto-regression f(H). The latter may however also be the result of the absence of negative or positive shocks of H, in spite of functioning resilience.Footnote 4

  • Category 1: Limited resilience. As compared to category 0 there is a homeostatic mechanism. However, there is also a lower limit, below which this mechanism fails.

  • Category 2: Unlimited resilience, with a changing set point. In comparison with category 1, there is no lower limit for the functioning of homeostasis. However, the position of the set point changes over time such that the respective intersection between H+  = H and H+  = f(H) deviates from the mean happiness of a country by more than 2 standard errorsFootnote 5 of this mean value.

  • Category 3: Unlimited resilience, with a stable set point. As compared to category 2, the position of the set point does not deviate by more than 2 standard errors from the mean happiness of a country. Category 3 is an operationalization of the classical definition of homeostasis (Marks, 2018: chap. 2).

Empirical Analyses

Data Source and Method

The empirical analyses of the present Sect. "Empirical analyses" are based on annual figures about national happiness on a 0 to 10 scale, which are published in the World Database of Happiness (Veenhoven, 2020) for the years between 2007 and 2019.Footnote 6 The data were calculated by the editors of the World Database of Happiness by means of satisfaction-related interview questions in the Gallup World Polls. For technical details see Veenhoven and Fraquet (2021).

The data processing was performed with the module Regression – Curve Estimation of SPSS-25. The current satisfaction (happiness H) was used to explain the satisfaction (happiness H+) one year later, first on the basis of the linear hypothesis of Eq. (1) and then on the basis of the quadratic hypothesis of Eq. (2). The equation with the better r-square was subsequently used for analysing the homeostatic process. As explained earlier in Sect. "Analyses based on linear regression functions", this was possible, because homeostatic correction follows systematic patterns, whereas the confounding external shocks of happiness are at random.

The Example of the UK

For illustrative purposes, this section explores the existence and the nature of the homeostasis of happiness in the UK. The data used for this analysis are given in Fig. 3 and circle around a set point represented by a dotted line, which is determined in Fig. 4. As expected for homeostatic resilience, nearly half of the observed data points are within the narrow band H = 7.38 ± 0.1 enclosing the set point (see dashed lines of Fig. 3). There are two valleys in 2008 and 2015. The first might be the economic sub-prime crises and the second the constitutional crises of the proposed independence of Scotland. It is followed by a peak of temporary happiness after the Brexit referendum in 2016, probably boosted by (illusionary) hopes for a better future of Britain outside the EU.

Fig. 3
figure 3

The observed dynamics of happiness in the UK between 2007 and 2019. Legend: Dotted horizontal line: Set point at H = 7.38, based on Fig. 4. Dashed horizontal lines: Limits 7.38 ± 0.1 of the band enclosing the set point

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Fig. 4
figure 4

The empirical relation between happiness H and H+ of the UK. Legend: Linear: Empirically estimated function H+  = 2.177 + 0.705 * H (adj-rs = 0.38, p = 0.019). Diagonal line: Zero change H+  = H. Continuous vertical line: Mean value of H, based on all years. Dotted vertical line: Set point at the intersection of H+  = f(H) and H+  = H

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The analysis of the British time series in Fig. 3 yields for the linear approach a better adjusted r-sq (0.380) than for the quadratic function, where the corresponding value is only 0.340. Consequently, we continued the analyses with the linear equation

$${\mathrm{H}}_{+} = 2.177 + 0.705 *\mathrm{ H}$$
(4)

which is visualised in Fig. 4. The latter diagram shows at H = 7.38 an intersection with the main diagonal that defines the set point of an unlimited homeostasis. There is only an insignificant difference to the general mean value H = 7.28, such that the UK belongs to resilience category 3 with a stable set point. According to Eq. (3) the strength of resilience is 1–0.705 = 0.295. Consequently, it takes after a happiness shock about 1 / 0.295 = 3.39 years until the original set point is regained.

This exemplary analysis of the UK has been performed for 25 other countries of the EU. The results are given in the appendix Tables 2 and 3 and visualized in the Figs. 5, 6, 7 and 8.

Fig. 5
figure 5

Categories of resilience: Names of related countries and absolute frequencies. Legend: Category of Resilience: 0 = No resilience; 1 = Limited resilience; 2 = Unlimited resilience with changing set point; 3 = Unlimited resilience with stable set point

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Fig. 6
figure 6

Change of the set point by type of resilience. Legend: Category of Resilience: 1 = Limited resilience; 2 = Unlimited resilience with changing set point; 3 = Unlimited resilience with stable set point. Grey dotted horizontal line: Global mean

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Fig. 7
figure 7

The resulting current set point by type of resilience. Legend: Category of Resilience: 1 = Limited resilience; 2 = Unlimited resilience with changing set point; 3 = Unlimited resilience with stable set point. Grey dotted horizontal line: Global mean

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Fig. 8
figure 8

The strength of different types of resilience. Legend: Category of Resilience: 1 = Limited resilience; 2 = Unlimited resilience with changing set point; 3 = Unlimited resilience with stable set point. Grey dotted horizontal line: Global mean

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The Categorization of Countries by Resilience

A first overview of the different categories of resilience is given in Fig. 5, which presents a histogram on the basis of the typology at the end of Sect. "Returns from the analyses". The stacks have lengths that correspond to the absolute frequencies of the related countries and point to their names. (Tufte, 1992: 141).

By far the most important type of resilience is category 0: according to Fig. 5, 14 out of 26 countries have no homeostatic mechanism that protects their happiness against external shocks. All three countries of the next following category 1 belong to the former Soviet bloc. By definition of category 1 they have only limited resilience: as long as their happiness remains within the critical distance from the set point, homeostasis will return deviant happiness to this equilibrium point. Otherwise homeostasis is destroyed. This limitation does not exist for the remaining two categories 2 and 3. However, category 2 has set points that change over time. Only a rather small category 3 corresponds to the classical definition of homeostasis: a set point that does not change over time and an unconditional homeostasis maintaining this set point. This category comprises only five rather heterogeneous countries: UK, Sweden, Portugal, Lithuania, and Cyprus.

The Temporal Stability of the Set Points

As mentioned in the previous Sect. "The categorization of countries by resilience" there are many countries where the set point of homeostasis changes over time. Figure 6 gives an overview of this phenomenon for the different categories of resilience. First of all, it is remarkable that there are no countries with negative change. This is an adaptation to the increased general happiness that was observed by Veenhoven (2014) and Veenhoven and Kegel (2022). By definition (see Sect. "Returns from the analyses") countries in resilience category 3 did no change their set point at all. Category 2 is with regard to the change of the set point on the average. Figure 6 shows the highest changes for category 1. This is insofar rational as the countries in this category have only limited resilience and according to Table 1 the critical distance to the old set point was rather small. As shown in Table 1, the increase of their set point slightly reduced the risk of a breakdown of their homeostasis of happiness.

Table 1 The critical distances to the lower limit of resilience
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Figure 7 displays the current set points after the previously described changes. Not so surprisingly, category 3 with no changes has the lowest mean of set points, although its dispersion is remarkably high. Category 2, defined by a change of the set point, has the highest mean value. Category 1 is between the mentioned two groups of countries. The mean set point of all groups of countries together is slightly above 7.0, which corresponds to the respective value mentioned by Cummins (2003).

The Strength of the Resilience

The essence of homeostasis is the rapid correction of positive or negative deviations from the set point. This principle holds for all categories of resilience of Fig. 8. On the average – as the dotted line of Fig. 8 shows – only ca. 40% (= 0.40) of an (infinitesimal) deviation from the equilibrium is corrected in the next following time-step. Consequently, on the average it takes at least 2 to 3 time-steps until a happiness shock is more or less annihilated.

In category 1, with countries having only limited homeostasis, the strength of resilience is much higher than the global average. This level of strength is a supplementary safeguard against the risk of a loss of homeostasis: even after the previously discussed increase of the set-point (see Fig. 6) the new critical distance is still rather low (see Table 1). In sharp contrast the countries of category 2 with unlimited homeostasis but a new set point have a strength of resilience that is below the global mean. A disequilibrium with regard to the newly established set point represents for category 2 a normal situation that consequently does not mobilize additional forces for adaptation. Thus the strength of their resilience is smaller than in category 3, where the set point does not change and substantial deviations from the homeostatic equilibrium are consequently less common.

Summary, Methodological Limitations, and Outlook

The main lesson from the empirical analyses in Sect. "Empirical analyses" is the absence of any homeostatic mechanism for the maintenance of happiness in more than 50% of the analyzed cases. In three other countries belonging to category 1 there is only limited homeostasis with a rather small critical distance. In spite of their exceptional strength of resilience and the increase of the set point these cases are not really prepared for externally induced downturns of happiness. In sum, homeostasis is not a reliable mechanism, which protects the happiness of the European countries in turbulent times.

For future research there remains the question of the factors insuring the resilience of the remaining countries in categories 2 and 3 (see Fig. 5). Is it a strong welfare state, like in the case of Sweden? A strong and efficient welfare state is for poorer people a buffer against economic shocks, guaranteeing their happiness also in times of crisis (Easterlin & Switek, 2014; Ott, 2013). In Mediterranean cultures the structural equivalent of the welfare state is often the social support by the family (Leontopoulou, 2013; Moreno, 2006). That might explain the resilience of Portugal, Cyprus, and Malta. Perhaps resilience against unhappiness is also based on high confidence in others like in Finland and Sweden (Mackie, 2001: 248 ff.). Due to this confidence, fellow citizens are not considered to make one unhappy by theft, burglary, or other forms of criminality. Finally, as a residual explanation for homeostatic happiness, there may be the national character, as proposed by Inkeles (1997: chap. 1). The optimism of some Mediterranean cultures could perhaps fit to this category and explain the resilience of Portugal, Cyprus, and Malta.

Obviously, these explanatory factors could also influence countries, which display in our analyses no homeostasis of happiness: Italy and Spain are examples of Mediterranean countries with strong family bonds. Nonetheless they seem to belong to category 0 with no homeostasis. Thus, there are cases, where the theoretically expected homeostasis is inhibited by special factors. One of them might be the methodological limitations of the present work. Among others we are assuming that the set point of homeostasis is disturbed by a sufficient number of external shocks, which should be at random and consequently uncorrelated with the level of happiness. The absence of such shocks obviously hinders the identification of an objectively existing homeostatic mechanism. Similarly, the correlation between the deviance from the set point and the amount of the subsequent homeostatic correction can be spoiled if the level of happiness and the related shocks are not independent. Finally, we considered in this work only functional relations between the current and the next following level of happiness that were either linear or quadratic. In future empirical investigations, other mathematical relations like e.g. logistic functions would certainly deserve consideration and might reveal homeostatic processes.