ANALES | ASOCIACION ARGENTINA DE ECONOMIA POLITICA XLIII Reunión Anual Noviembre de 2008
ISSN 1852-0022 ISBN 978-987-99570-6-6
Deconstructing the Hedonic Treadmill
Nicolas Luis Bottan Ricardo Pérez Truglia Deconstructing the Hedonic Treadmill*
Nicolas Luis Bottan Ricardo Pérez Truglia Department of Economics Department of Economics Universidad de San Andrés Harvard University and Universidad de San Andrés
Abstract There is consent among psychologists and some economists that satisfaction from some events, like income and marriage, is adaptive. We propose a subtle but vital difference: happiness may itself be adaptive. First we present a model to explain the emergence of adaptive stimuli. We test our hypothesis running dynamic happiness regressions based on data from the German Socio-Economic Panel Study, the British Household Panel Survey and the Swiss Household Panel. Surprisingly, the autoregressive component is positive and significant in most specifications considered. However, we propose that the hedonic treadmill may be mixed with what we call the “scale treadmill”.
Resumen Muchos psicólogos y algunos economistas sostienen que la satisfacción que retribuye ciertos eventos (e.g. ingreso, casarse) es adaptativa: luego de un aumento inicial, en unos años la felicidad reportada por individuos retorna a los valores iniciales. Proponemos una diferencia sutil pero importante: la felicidad misma podría ser adaptativa. Presentamos un modelo teórico en el cual los estímulos son costosos, y por lo tanto la adaptación de los mismos resulta óptima. Corremos regresiones dinámicas utilizando datos de la GSOEP, la BHPS y la SHP. Sorprendentemente, la mayoría de los modelos econométricos propuestos sugieren que el componente autoregresivo es positivo (y significativo).
JEL Codes: D0, I31 Keywords: happiness, adaptation, dynamic panel.
* We thank Walter Sosa Escudero and Daniel Heymann for their valuable discussions. The usual disclaimer applies. Corresponding author: [email protected]. Universidad de San Andrés, Vito Dumas 284, (B1644BID) Victoria, Provincia de Buenos Aires, Argentina. 1. Introduction Economists are embracing the idea that income is adaptive (e.g. Di Tella et al., 2007). This refers to the fact that a rise in current income generates greater happiness today. As time goes by, the individual will get used to the new life standard attained, resulting in the loss of the initial increase in happiness. Furthermore, there is vast evidence of adaptation to diverse life events, such as unemployment (Clark et al., 2007), health disabilities (Oswald et al., 2006), and even cosmetic surgery (Lowestein et al., 1999). We propose a subtle but important difference: raising today’s consumption may worsen tomorrow's well-being not only because individuals will desire a higher level of consumption, but partly because having experienced moments of happiness today will make them more prone to feelings of unhappiness tomorrow. That is, happiness itself may be adaptive. In terms of Kahneman (2000), we are distinguishing two sources of treadmill effects: a satisfaction treadmill, which invokes the notion of a changing aspiration level; and a hedonic treadmill, based on the notion of adaptation of Helson (1964). Furthermore, we will discuss the existence of a third treadmill effect which we shall call “scale treadmill”. It relates to the way in which individuals select the scale used to report happiness. There is a variety of explanations for such adaptive phenomenon. For example, some argue that habit formation might have originated for evolutive reasons (Rayo et al., 2005 ; Smith et al., 2007). Wilson et al. (2005) suggest that affective habituation is provoked by the need and ability that humans have to make sense of the stimuli around them. And Graham et al. (2006) proposed that bad life-shocks are smoothed by the drawing down of what they call “hedonic capital”. The aforementioned models are interesting, but they do not capture a very essential aspect: the intensity regulation of our stimuli. When economists formulate an individual’s utility function, the levels do not make much sense: for example, it could be normalized to some value arbitrarily close to zero. But in the real world we observe that stimuli do make sense in absolute value. Our explanation is related to the fact that some stimuli serve secondary functions different to that of providing relative incentives (e.g. pain serves as an alert system), and therefore Nature can not “multiply” these by an arbitrarily small number without incurring in an efficiency cost. A very strong stimulus has fitness costs: feeling extreme pain or pleasure would not let an individual function normally. As a direct consequence, Nature could develop an adaptive mechanism in order to minimize the cost associated with the provision of stimuli. We test our hypotheses by running dynamic happiness regressions using individual- level panel data from the German Socio-Economic Panel Study, the British Household Panel Survey and the Swiss Household Panel.1 The main challenge is estimating consistently a dynamic model with fixed effects in presence of a short-T, for which we use a variety of models. Results are fairly robust between models and strongly robust between databases (even though two of the panels are very short). The paper proceeds as follows: Section 2 presents the theoretical model describing the dynamics of happiness. Section 3 discusses the empirical strategy employed and presents the data used. Empirical findings are detailed and discussed in Section 4, followed by a methodological discussion in Section 5. The final section concludes.
2. Sources of Adaptation The quest for happiness is thought as the main concern of every individual. Nevertheless, we must bear in mind that happiness has been an evolutive means and not an end for the human race: nature hard-wired mankind in order to maximize the performance of our species. In particular, adaptive challenges have played a central role in evolution through the domain of positive and negative emotions (Nesse, 2004).
1 In the next draft you may find results for the Household, Income and Labour Dynamics in Australia (HILDA) Survey. 1 Nature developed an incentive scheme of prizes and punishments to drive human behavior. Think of evolution itself as a central planner who chooses the utility function maximized by individuals. This is done in such a way as to maximize Nature’s own utility: reproduction and survival of mankind. The complexity arises from the fact that this is a problem of imperfect information: when Nature hard-wires an individual, she knows that he may be exposed to diverse scenarios (i.e. abundance of scarcity of food, bad or good weather). Thus, the design must work optimally under any possible context. To achieve this, Nature must write optimal contracts with the individual in order to minimize the incidence of the problem of asymmetric information. Contracts with adaptive goals seem to be a fair solution. Two works have been able to capture this idea. In Rayo et al. (2005) the optimal utility function is based on a time- varying reference point that is updated in a statistically optimal way. Habits and peer comparisons are special cases of this process. Furthermore, this results in level of happiness continuously reverting to its long-term mean. In a similar spirit, Smith et al. (2007) provide a biological foundation and a characterization of specifying conditions under which it is optimal to form a habit.2 Wilson and Gilbert (2005), both psychologists, argue that affective habituation is provoked by the need and ability that humans have to make sense of the stimuli around them. Their theory, represented by the acronym AREA, states that human beings must walk down the following path: attend to self-relevant, unexplained events, react emotionally to these events, explain or reach an understanding of the events, and thereby adapt to the events (i.e. they attend less and have weaker emotional reactions to them). Graham et al. (2006) sets out a model of the dynamics of wellbeing in which bad life- shocks are smoothed by the drawing down of hedonic capital. The model fits the patterns found in the empirical literature: the existence of a stable level of wellbeing and a tendency to return gradually towards that baseline level. The abovementioned models are interesting, but they do not capture a very essential aspect: the intensity regulation of our stimuli. This feature will be covered by the model presented in the next subsection. 2.1. Happiness as a lens The concept of a hedonic treadmill was first coined by Brickman et al. (1971) as a process in which people adapt to emotional stimulus brought on by life events. This is similar to the biological adaptation of, for example, the lens of an eye adapting to the light’s brightness in a room, a nose quickly adapting to distinct scents and awareness of these thereafter disappear. They stated that the emotional system adapts to individual experiences and all stimuli received are relative to those received in the past. We economists usually think of happiness as something abstract, disregarding its physical correlate. Regardless, it is well known that stimuli exist and they cannot be normalized. When a person feels pain, it is felt in absolute value. Additionally, when individuals feel very strong positive or negative stimulus they lose their ability to function correctly. People that walk around with either constant orgasms or terrible pain all day cannot possibly perform well in everyday life. For instance, there was an experiment where rats received electronic brain stimulation by pressing down on a lever. The pleasure caused by this electronic stimulus was so great that rats would press the lever up to 7000 times in an hour and forgo feeding and mating if allowed (Olds et al., 1954). A stimulus is costly; we observe that Nature didn’t normalize utility to some capriciously low level. And the reason is that some stimuli have secondary functions. For example, when someone feels pain the electric signal in the nervous system takes on 2
2 In these models future happiness depends on past consumption. These can be reformulated to depend on past happiness instead, since in it there is embedded information about past consumption (storing directly detailed information about consumption could be costly for the organism). 2 roles: i. Informs the individual that the organism is being harmed; ii. provides disincentives to repeat the action. For the latter, what matters is the relative level compared to the stimulus provided by the other available actions (e.g. relative to eating, sex). But only the absolute value is relevant for the former. The stronger the signal, the faster the individual will react and therefore increase the chances of preventing a greater harm. In addition, an individual would suffer more with a stronger stimulus, which would be an impediment to carrying out activities optimally. Nevertheless, there is a design which may accomplish both goals: adaptive stimuli may reduce the loss without affecting the efficiency of its secondary role. Suppose that Nature must choose a utility function for an individual, xU )( , where x is the effort the individual places into given activity. The fitness function for Nature is given by zxV ),( (globally concave in both arguments), where z characterizes the environment (only known to the individual). To this point, under a few conditions we can show that Nature must simply choose z zxVExU ),()( . Suppose now that feeling pain or pleasure is costly. As a consequence, the fitness function is now: xUzxV )(),( 2 (where is the shadow cost in fitness of producing stimuli). Therefore, Nature would simply pick z zxVExU ),()( , where is a scalar arbitrarily close to zero. As we introduced before, Nature can solve the problem just by normalizing the individual’s utility function. However, now there are certain stimuli which play a secondary role. For the sake of simplicity, their utility is fixed in absolute terms and cannot be modified. The fitness function now takes the form: xUzxCzxV )(),(),( 2 , where zxC ),( is the non-scalable utility. To simplify, let’s restrict the analysis to individual utility functions of type:
z xCExUxR )()()( . Now we cannot multiply xU )( by a constant, since it would be very inefficient: the relation between xU )( and xC )( would change dramatically. Nonetheless, we can change the level of xU )( . Define zx )( as the x that (given z ) maximizes zxR ),( . So, Nature could change the level of xU )( in the following way: z z zzxVEzxVExU )),((),()( . By doing so, in expected value Nature will face a zero cost in stimuli. But nature can do even better if taking advantage of past information. Consider an extremely simple case: an individual lives two periods, and z does not change from one period to another. As a consequence, x remains constant. Nature can use
2 )()( UxUxU 1 as utility function in the second period, where U1 is the utility attained in the first period. Note that U1 does not modify the maximization problem, and that U1 is exactly the utility achieved by maximizing xU )( in the second period. This implies that an individual behaving optimally in the second period will receive a utility exactly equal to zero. There is no need for z to be constant: given time regularity, we could find an adaptive mechanism to exploit this idea. If the problem to be solved is similar thorough time, changing the current level of utility using yesterday’s utility will save a great expense on stimuli. It is in this sense that happiness may work as a lens: when an individual achieves greater consumption, Nature “learns” about the new situation (the latest z ) and updates the utility function to minimize the stimuli-related cost. The intriguing question is whether or not people incorporate this effect in their rational behavior. Riis et al. (2005) suggest that people do not. They find that hemodialysis patients have a level of happiness similar to that of healthy people, but at first, when trying to forecast, they fail to anticipate this bounce-back in wellbeing. The key difference between our framework and the other ideas introduced at the beginning of the section relies on the interpretation behind the empirical facts. For example, when an individual breaks his leg, he suffers a drop in current happiness. A model like that of 3 a satisfaction treadmill (Kahneman, 2000) or that of Wilson et al. (2005) would say that in the future, the individual will accept his new condition and therefore his situation will no longer inspire him unhappiness. On the contrary, the adaptation suggested here proposes that the individuals still has reasons to be unhappy, but the nature of his utility function will force his happiness to be normalized towards zero (i.e. given that he does not change his situation, Nature “learns” that his level of stimulus is the new benchmark and thus re-mean it to zero).
3. Econometric Model and Data A large portion of the literature tries to identify the effects of current and past life events on happiness. Brickman et al. (1971) is considered one of the precursors in this literature where they find that lottery winners were not significantly happier after the event. Additionally, there is vast evidence on adaptation to health events3, like in the case of severe burn victims (Patterson et al., 1993). Di Tella et al. (2007) find evidence in favor of adaptation to income. Clark et al. (2007) on layoffs, marriage, birth of child, Oswald et al. (2006) on disabilities. Many more studies could be listed for the fields of economics as well as in psychology (see Easterlin, 2003 for an extensive survey). However, the actual source of adaptation has never been identified in the aforementioned studies. For example, they observe that when an individual experiences a permanent raise in income, happiness increases initially, but later returns to its baseline level. Nevertheless, there have been attempts to explain this phenomenon. For example, Kahneman (2000) divides the treadmill effects in two. On one side, the hedonic treadmill described in Brickman and Campbell (1971), which is based on the notion of adaptation level in Helson (1964). Their idea is easily illustrated by the following example: if someone immerses their foot in a cold lake, the initial sensation would be very strong pain which will gradually disappear. In terms of the theoretic model presented in section 2.1, the sensation of happiness adapts and is normalized to zero. The most important point is that the sensation felt by the individual changes, but the perception of what is cold or not remains unchanged. The second effect is the hypothesis of a satisfaction treadmill, which invokes the notion of a changing aspiration level. Running 100 meters in 12 seconds might make anyone very happy, except for an Olympic runner. Aspirations vary between individuals and throughout time: people learn new information about the environment and themselves; information that is used to update what they expect of themselves. It is important to note that people’s perceptions, values, beliefs and preferences are at stake, but their primitive sensations are not. We propose that besides including lags for relevant life events (such as income, marriage, divorce, etc.) we must include lagged happiness. With the inclusion of happiness lags we will capture the effect of the hedonic treadmill on people’s general sense of happiness. There is an array of sensations that make people feel “accomplished” or “satisfied” with life in general, and we believe that these are themselves adaptive. On the other hand, when lags of other events are studied (e.g. income), the coefficients will capture the effects of a hedonic treadmill (e.g. adaptive sensations linked to consumption4) as well as a satisfaction treadmill (e.g. consumption aspirations increases as consumption raises5).6 Furthermore, we will later discuss the existence of a third treadmill
3 Although in some cases adaptation is incomplete. 4 For Example, eating and sex release hormones which are addictive. Even money itself activates similar reward areas (Camerer et al., 2005). 5 What we perceive as greed may be hard-wired (Brosnan et al., 2003, 2005), or it may even have arisen as a social or cultural arrangement (Pérez Truglia, 2007). 6 There is a subtle difference between hedonic treadmill applied to rewarding stimulus associated to income (captured by lagged income) and applied to happiness in general (captured by lagged happiness). In the first case you are addicted to income, while in the second case you are addicted to “happiness”. 4 effect which we define as “scale treadmill”. It relates to the way in which individuals select the scale used to report happiness. 3.1. Main Framework To test our hypothesis empirically, we will make use of the German Socio-Economic Panel Study7 (GSOEP), the British Household Panel Survey8 (BHPS) and the Swiss Household Panel9 (SHP). In what follows we present the regressions for the GSOEP as A- Table, and in the B- and C-Table the same information is available for the SHP and BHPS respectively. The challenge in estimating a dynamic model with fixed effects is that, for well-known reasons, it yields inconsistent estimates with large N but short T. The panel lengths are 22, 8 and 10 for the GSOEP, SHP and BHPS, respectively.10 Since the GSOEP is the longest and largest panel, we will analyze its coefficients and will comment on those of the other data sets when differences are considerable. The baseline least squares model is:
Q K R H ,ti H , qtiq y , ktik X , rtir ,titi q1 k 0 r0 where H ,ti is self reported happiness of the individual, y ,ti is income, X ,ti is a vector of time varying individual controls, Q , K and R are the number of lags to be included for each of the former variables, i is individual fixed effects, t corresponds to year effects and ,ti is the error term. If coefficient was negative, then happiness would be adaptive: feeling of happiness today makes you prone to feeling of unhappiness tomorrow. If was instead negative, happiness would then be “reinforcing”. For detailed information on all data sets along with descriptive statistics, please refer to Appendix 2. Variable definitions on happiness and all variables used are available in Appendix 3. In the GSOEP, for instance, the question on happiness is: “How satisfied are you with your life, all things considered?” where responses range from 0 (completely dissatisfied) to 10 (completely satisfied). The measure of income used is the logarithm of gross total annual household income, deflated to prices of a baseline year. Some of the control variables used are: age, household size, education indicators, employment and marital status indicators. We use a linear specification for reasons detailed in Appendix 1: Methodological Questions. In that same appendix we discuss how income scale elasticities are calculated. Standard errors are clustered by individual in all estimations. We do so to account for other possible idiosyncratic shocks affecting individuals which may persist throughout time. It is important to consider the fact that income and other variables may be potentially endogenous. For instance, there could possibly be some simultaneous causality in income: being happy may make people earn more, and not just the other way around (Lyubomirsky et al., 2005). There have been attempts trying to identify a causal link, as in natural experiments (Becchetti et al., 2007) and controlled lab experiments (see Charness et al., 2001; McBride, 2007).
7 Data was made available to us by the German Institute for Economic Research (DIW), Berlin. 8 University of Essex. Institute for Social and Economic Research, British Household Panel Survey: Waves 1-15, 1991- 2006 [computer file]. 3rd Edition. Colchester, Essex: UK Data Archive [distributor], June 2007. SN: 5151. 9 Data has been collected in the "Living in Switzerland" project, which is based at the Swiss Foundation for Research in Social Sciences FORS, University of Lausanne (a project is financed by the Swiss National Science Foundation). 10 However, there is a jump in the middle of the BHPS for data on happiness. This causes the loss of 2 periods (instead of one) whenever a lag of happiness is included. 5 The identification strategy of depends crucially on the error term not being persistent. We are forced to rely on controlling for “enough” individual time varying covariates and semi-parametric controls, such as time and fixed effects, region-specific time effects and individual-specific trends.11 This approach has the benefit of being applicable to many data sets, covering a wide array of time and countries, which will allow us to check the external validity. The following section will introduce the different models in a one by one basis.
4. Results Consider the following model:
, titi ZHH ,,1, titi
Suppose that Z ,ti is left constant in Z at some moment. This is equivalent to considering that the “fundamentals” of happiness (income, marital state, etc.) remains ~ unchanged. The steady state of happiness would then be: i ZH )1( . An individual who has “instantaneous happiness by fundamentals” Z really reaches a happiness of
Z )1( in the long run. Therefore, the model should be: , HH titi 1, )1( Z ,ti so that the steady state would be Z . Define )1( as the coefficient obtained from the regressions. The direct implication of this is that would be the instantaneous impact of the fundamentals on current happiness, and )1/( the impact of Z on the steady state value. This provides a very useful calculation: dividing the coefficients for control variables by )1( to obtain long run effects. If we find a negative (positive) , this would imply that the impact on the steady state is less (greater) than current impact. Moreover, for a negative (positive) , a transitory rise in Z for one period will produce an initial change in H of )1( , which will be reinforcing (adapting) until reaching the long run change of . If we additionally have adaptive Z ’s (e.g. income being adaptive), the equation would be: , HH titi 1, Z ,1 ti )1()1( Z ti 1,2 . Note that the steady state is now:
Z ,21 ti )1()( . That is, there is an interaction between adaptation of Z and H . 4.1. Income-Satisfaction Treadmill Consider the following basic model where we suppose that happiness depends 12 linearly on present and past income ( y ,ti and y ti 1, , respectively):
it ti yyH ,1,2,1 titi (1)
The fact that in (1) we did not include, for example, time effects or controls does not mean that they are not included in the regressions. Since including them in the equations does not alter results, we omit them to convey the ideas clearly. Note that including lagged variables is also important if one is interested only in current effects. Suppose, for instance, that income were autocorrelated: ti yy 1,1, tti . If (1) were true and we did not include ˆ 13 y ti 1, as a regressor, then the estimation of 1 would be seriously biased. As a matter of
11 However, including further control variables may cloud the interpretation for certain coefficients of interest. For instance, income improves life satisfaction through expenditures on health and education. If you include these variables you will downward bias the coefficient on income, since you will not be capturing its impact through health and education. The introduction of an extra variable may even bias a formerly unbiased estimate in the presence of measurement error. 12 The obvious effect of income is through consumption, although it could also affect happiness via “esteem”. 13 Notice that we may reproduce everything using income’s first difference instead of its lagged level. 6 fact, comparing columns (1) and (2) of Table 1A we can observe that income lags effectively reduces coefficient of current income. Di Tella et al. (2007) studied adaptation to income using the GSOEP. See the evolution of average happiness and income plotted for all 3 data sets in Figure 1. Evidently, the sustained increase in average income does not correspond with an increase in average happiness. The first model is given by:
K H it , ktik Xy ittiit k 0
Results for this specification are presented in the first two columns of Table 1A. The coefficient on income is positive and statistically significant, as expected. An increase in current income of one standard deviation would increase happiness in 7,5% of a standard deviation. Column (2) arbitrarily reports three income lags ( K 3), and the results do not vary using a larger K (consider that it involves a substantial loss of observations). We find that there is adaptation to income based on an F-test for lagged income at a level of 5%.14 And we cannot reject the null hypothesis of complete adaptation to income (at a 1% level). 4.2. Hedonic treadmill: Autoregressive Happiness As we have largely discussed, current happiness may depend directly on past happiness. Consider the following case:
, titi ti yyHH ,1,2,11, titi (3)
ˆ If model (1) were to be estimated and 0 , 2 would be biased (and so would ˆ ), since H ti 1, would be in the error component and then correlated to y ti 1, . As we have already introduced, using the within transformation for (3) would involve a short-T inconsistency. There is Monte Carlo evidence suggesting that Anderson and Hsiao (1981) estimator show smaller biases than GMM, and its efficiency compares favorably (Judson and Owen, 1999; Kiviet, 1995). Supposing that all available lags are valid instruments in these models is too strong of an assumption in the context of happiness. Including all lags as instruments of the second difference does not only sum a lot of weak instruments, but we would surely include some invalid ones: the relation between HH titi 2,1, and H ti 19, is undoubtedly noisy. In that sense, Arellano-Bover (1995) is no different than Arellano-Bond (1991). Therefore, we are inclined to use Anderson and Hsiao. In particular, using only the second lag as instrument (it is well know that instrumenting by second difference is worse in terms of efficiency). Later on we discuss the use of an exogenous instrument. After introducing lagged happiness in OLS specification (column (3), Table 1A) the effect of current income is still statistically significant and positive. In terms of magnitude, introducing lagged happiness increases the negative effect of past income on current happiness. The coefficient on past happiness is 0.142 and it is statistically different from zero at the 1% level. For the SHP and BHPS, this coefficient is negative (as expected), but we know that OLS estimates are biased towards the left. Estimations for Anderson and Hsiao are presented in column (4). Now introducing lagged happiness cuts the effect of current income by half. As a consequence of this, there is almost full adaptation in only one period. Now ˆ =0.109 and is still statistically different from
K K 14 As in Di Tella et al. (2007), we test: H0: k 0 vs. HA: k 0 . k1 k1 7 zero at the 1% level. These results are almost identical to those obtained using Arellano and Bond, presented in column (5). However, we were expecting the coefficient on past happiness to be negative. We reject the null hypotheses of second order autocorrelation in first differences, which suggests that the model is wrongly specified. We must then continue exploring further specifications. 4.3. Lagged observables As stated previously, there is evidence on happiness also depending linearly on other lagged observables. For instance, it depends on lagged marriage, divorce, widowhood, birth of a child and layoffs (Clark et al, 2007). Therefore, we should also include lags for these other variables:
, titi ti ti ti XXyyHH ,1,4,31,2,11, titi (4)
If the former model were true, estimating by (3) would be biased, since X ti 1, is correlated by construction to H ti 1, . The results are presented in column (7) of Table 1A, where coefficients are similar to those of column (5). Many of the coefficients for lagged controls are significantly different form zero. An important result is that most coefficients for lagged controls have the opposite sign to the current level (that is, they suggest adaptation instead of reinforcement). The autocorrelation test is about the same. 4.4. Second order autoregressivity Consider the following model:
ti ti HHH 2,21,1, ,tiiti When we take first difference we obtain:
( HH titi () HH titi () ti HH ti 3,2,22,1,11,, titi 1,, )() (5)
Where H ti 2, can be used as an instrument for ( HH titi 2,1, ) . Estimating (3) if (5) was true would undoubtedly bias ˆ . The results are presented in column (6) of Table 1A. The coefficient for the second lag of happiness is also positive and small, but including it increases the coefficient for the first lag (around 40%). Furthermore, the coefficient on past income is no longer significant (i.e. happiness being itself adaptive explains all what other authors considered as income adaptation). Now we cannot reject the null hypotheses of second order autocorrelation in first differences (the p-value is 0.84), which leads us to the conclusion that the second lag of happiness should be in some way included in the specification. 4.5. Lagged Unobservables
Suppose that happiness also depends linearly on lagged unobservables ( St1 ). Introducing this would yield the following expression:
,ti ti ti ti ti SSXXHH ,1,6,51,4,31, titi (6)
Now take first differences:
titi 1,, ( HHHH titi () XX titi () XX titi 2,1,41,,32,1, ) (7) SS titi ()( SS titi 2,1,61,,5 titi 1,, )()
8 If (6) is true and (5) were to be estimated, St and St1 would be both part of the error term.
That is, the whole second line in (7) would be part of the error term. The H ti 2, and S ti 2, are correlated by construction, therefore, the instrument in Anderson and Hsiao is invalid.
But in order to have an invalid instrument we do not necessarily need H ,ti to depend on S ti 1, , since having it depend on S ,ti would be sufficient and S ,ti being persistent (i.e. the error term in levels being autocorrelated). It is clear that the identification strategy consists in: including all variables containing S ti 1, , and all only containing S ,ti (but being persistent). In particular, we could use non-parametric strategies to control for most time varying variables. For example, we include region-specific time effects and the results remain unaltered. But this is not a dead-end. The easiest case to analyze is when the error term follows a MA(1). The H t2 would no longer be a valid instrument (the difference of the error is
MA(2)), but H t3 and longer lags remain valid. By using further lags we face a tradeoff between potential bias and efficiency (since a longer lag is a weaker instrument). The result is presented in column (8) of Table 1A. The coefficient for past happiness is now very large (0.514) and statistically different from zero at 1% level. Fortunately, it is not a weak instrument according to Stock and Wright LM statistic (we reject the null hypothesis of B1=0 at the level of 1%; Chi-Sq(1)=78.41).
Suppose that the errors in the model now are AR(1), therefore 1, ittiit . Using Anderson and Hsiao in this context would produce a biased estimate of past happiness when using H ti 2, as instrument. Check the first difference:
( HH tiit 1, () HH titi 2,1, () ti ti 2,1, tiit 1, )() (8)
But, above all, any lag of H used as instrument will be correlated with the error term.
In particular, any lag smaller or equal to H t2 would be negatively correlated to the error term. For example, if we use H t2 as an instrument, the bias would be given by:
Cov H ),( bias titiit 2,1, (9) ,( HHHCov tititi 2,1,2, )
If the effect of past happiness on current happiness were positive (negative), the bias would in turn be negative (positive). That is, our theory in which the coefficient is negative is consistent with finding a positive estimate but with severe autoregressive error. We will deal with this problem using exogenous instruments, which will be discussed later on. In the meantime, we will try to control for the largest amount of variables that may make the error term persistent. 4.6. Individual Specific Time Trends A straightforward way of capturing the effect of individual specific time-varying variables is with individual-specific time effects. If, for example, individuals had a positive trend for happiness, past happiness could be capturing that effect. Individual trends may be related to the fact that individuals could be “learning” how to answer the household survey, and this learning could be different between individuals. Imagine an individual who is asked to report his/her subjective level of happiness for the first time. Since they have never done this exercise before, the level of aspirations used in the evaluation may force an undervaluation of subjective happiness. As time goes by, individuals better calibrate their evaluation and may be more perceptive of their relative position with regards to the reference group (as well as being conscious of previous reported scores). This learning process generates heterogeneous trends in the level of happiness. 9 Suppose the first-order version of our model now takes the following form:
it HH 1, ititti (10)
where the model includes an interaction of time and individual effects ( it ). Taking the first difference of this model produces:
( HH tiit 1, () HH titi 2,1, () 1 tiititit 1, )() (11)
Since the model has individual specific time trends, taking first difference of baseline model does not eliminate individual fixed effects. Since we are not controlling for these “transformed” individual effects, the estimation for will be biased. However, we can take the following quasi-differences:
( HH titit 1, () 1, HH titti 2, () titit 1, ) (12)
where / ttt 1 . Using this strategy does not eliminate the individual effects. We could design a GMM strategy to estimate all parameters in the previous equation, or we could simply select a functional form for t . For the sake of simplicity, we go for the second option: we suppose t t . The results are presented in column (9) of Table 1A. The coefficient for past happiness is 0.182 (67% larger than AH with lagged controls) and statistically relevant at a level of 1%. The coefficient for current income is also significantly larger than in previous estimates (28% larger than AH with lagged controls) and also significant at 1% level. The larger coefficients are possibly the result of poorly specifying the model. The model should really include both aspects: individual-specific time trends and individual-specific intercepts:
, HH t ,211, tiiititi (13)
Therefore, when taking pseudo-differences, the 1i remains in the equation. So taking first differences:
titi 1,, ( HHHH titi titii 1,,22,1, )() (14)
If we construct the variable HHR tititi 1,,, , it is clear that the equation above is a dynamic model with fixed effects, subject to the well known bias for small-T. Thus, we must take first differences again:
, 2( HHH tititi 2,1, ti 1, 2() ti HHH ti 3,2, 2() tititi 2,1,, ) (15)
We can use as H ti 3, an instrument. Results for this model are reported in column (10) of Table 1A. Past happiness is still statistically different to zero at a level of 1%, but the coefficient is now about half of that obtained in most of the previous specifications. Therefore, not accounting for individual-specific time trends and intercepts bias the coefficient on past happiness upwards. 4.7. Rethinking the model Instead of depending on previous happiness, current happiness depends on how it changed from the previous period:
,ti ( HHH titi 1,, ) ,tii (16)
Note that this is a recursive definition (since H ,ti is on both sides of the equation). For a positive , if happiness between yesterday and today rose, then what is reported as
10 happiness adjusts upwards. If we reduce the temporal interval to zero, this would correspond to a differential equation: i i i tZdttdHtH )()()( . The first difference of (16) is:
( HH titi 1,, , 2() HHH tititi 2,1, titi 1,, )() (17)
And we calculate this using H ti 2, as an instrument. The results are available in column (11) of Table 1A (note that this is reported as “Happiness in t-1”). The coefficient for
, 2( HHH tititi 2,1, ) is -0.109 and statistically different from zero at a 1% level. Hence, under this specification we find that happiness is indeed adaptive. A similar model would be the following, where the change in happiness takes a period to adapt:
,ti ( HHH titi 2,1, ) ,tii (18) For a positive (negative) , if yesterday happiness was rising (with respect to the day before yesterday), then today’s happiness pulls upward (downward). The first difference of (18) yields the following expression:
( HH titi 1,, ti 1, 2() ti HHH ti 3,2, titi 1,, )() (19) we can instrument using H ti 2, and H ti 3, . The result for this specification is presented in column (12) of Table 1A. We can see that is again positive (0.019) and significantly different from zero at the 1% level. The coefficient is smaller due to the fact that the independent variable is a first difference, contrasted with a variable in levels as in previous subsections. 4.8. Loss aversion There is a possibility that happiness might adapt differently when it increases or decreases. That is:
, HHH titipti 1,, HH titin 1,, ,tii (20) HH titi 1,, HH titi 1,, Where the first difference is:
HH HH HH titi 1,, titip 1,, HH ti ti 2,1, HH titi 1,, titi 2,1, (21) HH titin 1,, ti HH ti 2,1, titi 1,, HH titi 1,, HH titi 2,1, and we use HH titi 2,1, and HH titi 2,1, as instruments. We can do HH titi 2,1, HH titi 2,1, something similar as with the second model in the previous subsection. The results are shown in columns (13) and (14) of Table 1A, respectively. The coefficients of interest are all statistically different from zero at the 1% level. We reject the null hypothesis of np at the 1% level of significance in both cases. Coefficients suggest that when individuals experience a positive shock to happiness, in the future their happiness adjusts downwards (that is, there is adaptation). But for negative changes in past happiness there is reinforcement: happiness adjusts downward the next period. This behavior is very interesting: what happens in average is not relevant, since the importance lies upon adaptation for positive shocks and reinforcement for negative shocks. 4.9. Future happiness We have widely discussed the importance of including lagged controls when including lagged happiness (or when variables may be autocorrelated like in the case of income). The same reasoning exposed previously applies when including a lead of happiness. If lead controls are omitted, the coefficient for future happiness will be biased by construction.
11 There is evidence that happiness is not predictable, not even in very short time horizons, like one day. For example, Kahneman et al. (1992) conducted an experiment in which individuals were given ice cream to consume whilst listening to pleasant music at the same time, every day, for eight days. After each experience, they were asked how satisfied they were with it and had to predict their rating for the following day and the last day. In these conditions, the correlation between predicted and actual satisfaction ratings was nearly zero. In another work, Gilbert et al. (1998) asked voters in the state of Texas how they would feel after the election if their favorite candidate lost. As expected, respondents claimed they would be unhappy in that scenario, but when asked a month later, they were just as happy whether their favorite candidate won or not. Consider the model:
, 1, HHH 1, ,tiitiptifti (23) If individuals could predict their happiness, then they would be happier with the news of a good future event (e.g. starting to feel happy before getting married), and maybe current happiness will adapt/reinforce in some way. The first difference is:
HH 1,, ( HH ,1, () HH titiptitiftiti ) titi 1,,2,1, (24) where we use H ti 2, and H ti 3, as instruments. However, the instruments are very weak, because of the watered down relation of ( i HH ,1, tit ) with H ti 2, and H ti 3, . Additionally, the results are not robust between data sets. This model requires a very exhaustive analysis, and we are therefore forced to leave it for a future version of the paper. 4.10. Exogenous instrument Consider the equation:
, titi YXHH 1,1,11, ,tiititi (25) where Y ti 1, can include lagged elements of X ,ti . Suppose that we want to use the lag of an explicative variable ti Xz ti 1,1, as an instrument for H ti 1, . Also, we need z ti 1, not to be a determinant of present happiness (not more than through its effect on past happiness). That is, we do not want that variable being part of the satisfaction treadmill. For example, part of the negative effect of past income on current happiness is that a greater income raises our aspirations, a reason why income is less satisfying. When studying adaptation to disabilities, we see a similar effect: an individual is used to being able to carry out certain activities, but after becoming disabled (with the passing of time) the individual accepts that those activities may no longer be carried out. This is why income nor disabilities in t 1 could not be used as instruments for H ti 1, .
On the other hand, we need z ti 1, not to be correlated with relevant omitted variables. We know that many of the controls used may have endogeneity problems, for example: there is potential simultaneity in income (happier people may work more) and with marriage
(happier people get married). Since z ti 1, is not only used as a control, but the identification of lies upon it, we must pay very close attention to this. Our answer is using variables associated to random events. For example, in the BHPS we use the number of serious accidents in the current year, defined as those accidents that require medical treatment by a doctor or a hospital visit (e.g. falling down stairs and breaking a leg, attacks by animals or humans resulting in injury). We know that there is no special satisfaction treadmill for this variable since an accident is a transitory state (as opposed to a shock in permanent income, or a disability). People do not change their aspiration because the probability of having another accident is the same. For the SHP we use a dummy indicating whether the household was a victim of a robbery as an instrument. In the meantime, we did not come up with an instrument for the GSOEP.
12 The results are presented in column (15) of Table 1B and 1C. The coefficients are positive, but not statistically significant. In addition, the instruments are very weak according to the Stock and Watson rule of thumb. 4.11. Scale treadmill Even though individuals tend to report that they frequently think about their happiness, the answer to the question “how happy are you?” is probably somewhat spontaneous. Even though what is going on may be 80% heuristics, we will try to think about what happens inside an individual’s head when facing such deep inquiry.
Let’s suppose that a level of happiness exists ( H ,ti ), defined as an arrangement of electronic impulses in the brain which individuals perceive. But this perception cannot be transformed into a number to answer “How is life overall?”, reason behind the need to place this value in a scale. That is, individuals really respond “How is life compared to sometime/someone?”. To generate the scale, individuals can base it on how they felt in the past, or how they suppose the rest of the individuals they know feel. Let’s adopt a simple functional form: the process behind the decision of happiness score is giving H1 ,ti a lower bound reference and
H10 ,ti a superior reference, and giving a measure of how far from H1 ,ti (and close to
H10 ,ti ) they feel. For example: )( )( )( r ,ti , , HHHfH ,tititi )10,1,( r where H ,ti is reported happiness. A possibility is that this function measures the relative r distance to the boundaries: ,ti ,, titi i, HHHHH ,tit )110()10( . That is, if individuals use a more demanding scale (larger H1 ,ti and H10 ,ti ), their reported happiness will fall, and it would rise if using a less demanding scale. For example, an individual could use information on levels of happiness of other individuals to form such boundaries: H1 ,ti could be the unhappy individual known and H10 ,ti the happiest within an individual’s reference group: H min1 H and H max10 H ,ti ,tj tiGj ),( ,ti ,tj tiGj ),( where tiG ),( denotes the reference group of i in t .15 A study conducted among students in California and in the Midwest was designed to examine both the reality of regional effects in life satisfaction and beliefs about these effects (Schkade and Kahneman, 1998). The results showed no trace of a difference between Californians and Midwesterners in overall life satisfaction. However, they revealed a widespread expectation, shared by residents of both regions, that the self-reports of Californians would indicate more happiness than the self- reports of Midwesterners. That is, the fact that the rest of the Californians are happier makes each one use a more demanding scale than that used by Midwesterners. Alternatively, boundaries can be formed by internal comparison: the lower bound reference could be based on the worst situation that individual experienced and the upper limit on the best experience: H min1 H and H max10 H ,ti ,ri tr ,ti ,ri tr A group of papers (see for example Kahneman, 2000) finds strong support for what they define as the “peak-end rule”: the greatest predictor of wellbeing during an experiment is the average of the most intense level of pain reported during the procedure, and of the mean
15 If reference group is geographical, we could partially control for this effect using region-specific time effects. Individuals do not need to “infer” how happy the rest of them are. There is evidence that individuals can directly distinguish the “true” happiness of others, for example, by the Duchenne Smile (Pavot et al., 1991). 13 pain level reported over the last period of time. Essentially, the mechanism operating here may be exactly what we propose: holding the average happiness constant, the peak 16 determines H10 ,ti and then modifies reported happiness. We obviously know that the scale will arise from some combination of the aforementioned criteria.17 What is certain is that the scale for happiness aspirations is probably largely determined by past happiness: therefore, lagged happiness could capture not only the effect of true happiness, but also the changes in scale. If an individual experiences greater unhappiness in a previous year, we could have a wide variety of effects: for instance, the individual may know that it is possible to be worse than what he/she thought (and H1 ,ti drops), or the individual could realize that in that unfortunate situation he/she is better off than thought ( H1 ,ti increases). Consider the simple r case where: i i i i tHtHtHtH )(10)(1)()( . In this case, we can write: r i tdH )( i tH )(1 i tH )(10 i tdH )( 1 dt tH )( tH )( dt i i i t)(
Therefore, if i t)( is close to zero: any increase in current happiness will not be reflected in happiness reported. Many have claimed that in the last 50 years self-reported happiness has not increased in developed countries. Happiness scores may show a constant behavior over time, but this does not mean that happiness has not changed over the years. If we consider models in which is negative, this suggests that the happiness scale is more demanding and consistent with this story. In itself, the coefficient for lagged happiness estimated is a combination of both effects: the effect on actual happiness (through the hedonic treadmill) and the effect on reported happiness (through the scale treadmill).
5. Discussion 5.1. Robustness of Happiness One of the objectives of this paper is to assess whether including autoregressive happiness in regressions modifies the main results of the happiness literature. Table 2 contains a selection of variables usually considered important determinants of happiness, these are: income, unemployment, marriage, widowhood and number of kids. The first two columns correspond to estimating the model without lagged happiness. Columns (3) and (4) belong to estimating the model by AH including 2 lags for happiness (like column (6) in Table 1A). Including lagged controls usually reduces the magnitude of the coefficients, which would signal to the possible existence of hedonic treadmill effects. For example, coefficient for number of kids goes from being 0.045 and statistically different from zero at 1% to 0.018 and not relevant statistically, while its lag is 0.032 and significant at the level of 5%. Consider the case of marriage and widowhood: the coefficients are positive and negative respectively (as expected) and statistically different from zero. When lags are included but they increase significantly in magnitude (and there is almost full adaptation to marriage after 1 year!). The effects of including lagged controls when including lagged happiness in AH are much closer to what is expected.
5.2. Robustness Checks
16 Additionally, the importance of happiness during the last period of time could be indicating some type of adaptation in the very short run. 17 As time goes by, an individual’s past happiness (income, etc.) changes, as well as that of the reference group. Regardless if the impact is via scale or true happiness, separating both effects if very difficult. 14 An additional aspect to take into consideration is that when respondents evaluate current situation to rank their life satisfaction, income is taken into consideration. A problem arises in that each individual evaluates income conditional to their context (i.e. number of children in the household, number of working adults). Therefore, correcting income by elasticity to household size is necessary in order to avoid this possible source of bias. Following Schwarze (2003) and Pérez Truglia (2007), we found that results are robust to corrected income (See Appendix 1 for detailed description). Accomplishing the proposed goals usually takes a certain amount of time. When formulating aspirations, individuals set objectives with a finite time to achieve goals. They may re asses the current situation with respect to aspirations every 3, 6, 9 months or every year. Since all 3 panels are surveyed yearly, the information on happiness may capture the individual’s autoregressive component within his/her own ‘happiness cycle’. Using a panel where respondents are surveyed more frequently (i.e. quarterly) would be desirable. An additional benefit of this would be having a larger T (and therefore break free of the problems related to short panel) and at the same time identify fluctuations in happiness in a shorter time horizon. A problem is that life is divided into a wide variety of domains. Happiness is just a one-dimensional measure. To identify happiness adaptation, we should study income satisfaction, health satisfaction, etc. separately. As suggested by Easterlin (2005), there are probably different rates of habituation across different domains of life. Due to this, we present the autoregressive coefficient for different types of satisfaction in Table 3. The coefficients are very similar to those obtained when using general life satisfaction. This strongly suggests that the process of habituation exists across different domains of life.
6. Conclusions The psychology literature that began with Brickman et al. (1971) asserts that the effects of a stimulus causing happiness (or unhappiness) will tend to balance each other out. As a consequence, the feeling of greater happiness today is only transitory. Some papers explored adaptation in particular events of life, but none of them truly explored the adaptation to happiness itself. The basic models indicate that the coefficient on lagged happiness is positive and statistically significant. However, the coefficients on the most common explanatory variables when it comes to happiness regressions do not suffer dramatic changes when we introduce a dynamic model. We addressed a variety of strategies, and the results are fairly robust between models and strongly robust between databases (even though two of the panels are very short). Nevertheless, the most sophisticated models suggested a negative coefficient or even a mixed behavior (adaptation for positive changes, and reinforcement for negative changes). This inconclusiveness suggests that future studies must find either a “clean” identification strategy, or a richer data set. In addition to the model of costly stimuli, we provided another explanation to the results obtained. Individuals use a scale to report happiness which can be susceptible to constant updating. Many authors interpret the stagnation of reported happiness as evidence that true happiness has not increased in the last years in some countries. If the scale treadmill idea were true, then stagnated reported happiness would not imply that actual happiness has not increased. Nearly all people believe (or would like to believe) that they can move in an “upward spiral” toward ever greater happiness (Sheldon et al., 2001). The theoretical models may be reinterpreted in an optimistic way: even though satisfaction has been autoregressive in the past, modern man may have finally found the path to perpetuate happiness.
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18 Figure 1 Evolution of Average Happiness and Income
a. German Socieconomic Panel Survey 12 11 10 9 8 7
6 5 Black: happiness. Grey: log(income). Solid line: Mean Dotted lines: 25% and 75% percentiles 4
0 1 2 3 4 92 93 94 05 985 986 987 988 989 99 99 9 9 9 998 999 000 001 00 00 00 0 1984 1 1 1 1 1 1 1 1 1 1 1995 1996 1997 1 1 2 2 2 2 2 2
b. Swiss Household Panel 13 12 11 10 9 8 7 6 Black: happiness. Grey: log(income). Solid line: Mean 5 Dotted lines: 25% and 75% percentiles 4
2 3 00 01 20 20 200 200 2004 2005 2006
c. British Household Panel Survey* 12
10
8
6
4
2 Black: happiness. Grey: log(income). Solid line: Mean Dotted lines: 25% and 75% percentiles 0
9 0 96 97 98 19 19 19 199 200 2001 2002 2003 2004 2005 *Happiness is missing in Wave-5, so w e replaced the values for the mean of the w ave 4 and 6 to provide a better picture.
19 TABLE 1A
Effects of Income and Past Happiness on Current Happiness for GSOEP
OLS AH AB AH Dep. Var.: Happiness (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14)
Happiness in t-1 0.142 0.109 0.111 0.138 0.106 0.514 0.182 0.056 -0.109 0.019 -0.127º -0.091² [0.004]*** [0.006]*** [0.005]*** [0.008]*** [0.006]*** [0.072]*** [0.005]*** [0.012]*** [0.008]*** [0.003]*** [0.003]*** [0.025]***
Happiness in t-2 0.04 0.889¹ 0.089³ [0.006]*** [0.003]*** [0.016]***
Current Income 0.223 0.21 0.201 0.077 0.078 0.087 0.09 0.057 0.115 0.053 0.101 0.094 0.047 0.1 [0.016]*** [0.018]*** [0.016]*** [0.020]*** [0.017]*** [0.021]*** [0.020]*** [0.026]** [0.021]*** [0.027]** [0.023]*** [0.020]*** [0.013]*** [0.024]***
Income in t-1 -0.023 0.001 -0.047 -0.062 -0.06 -0.023 -0.016 -0.071 -0.007 -0.043 -0.015 -0.003 0.044 -0.014 [0.013]* [0.015] [0.014]*** [0.017]*** [0.015]*** [0.019] [0.018] [0.027]*** [0.018] [0.025]* [0.020] [0.018] [0.013]*** [0.022]
Income in t-2 -0.014 0.001 0.01 0.011 0.001 [0.015] [0.020] [0.022] [0.019] [0.021]
Income in t-3 -0.031 [0.014]**
No. of Lags for Controls 0 0 0 0 0 2 1 1 1 1 2 2 1 2 Observations 143473 105145 140325 117462 117462 98273 117093 98581 117093 98273 98545 98273 98581 69396 Individuals 15327 12779 15052 13389 13389 11972 13305 12050 13305 11972 11983 11972 12050 9709 Max Time 21 19 21 20 20 19 20 20 20 19 19 19 20 19 Avg. Time 9.4 8.2 9.3 8.8 8.8 8.2 8.8 8.8 8.8 8.2 8.2 8.2 8.8 8.2
Notes: Fixed effects, time effects and Individual time-varying controls included in all estimations (+ lags specified). HH income is ln(household annual income). Columns (1) to (3) contain OLS estimates, Columns (4) to (15) were estimated using Anderson & Hsiao (except for (5) which was estimated by Arellano & Bond), coefficients reported belong to the first difference of variables described. (8): instrumented by 3rd lag; (9)&(10): Individual Specific Time Trend Models; (11)&(12): difference instead of level in baseline model; (13)&(14): Loss Aversion [Coefficients for loss aversion to happiness when: º: ΔH(t) is positive; ¹: ΔH(t) is negative; ²: ΔH(t-1) is positive; ³: ΔH(t-1) is negative]. Clustered standard errors by individual reported in parentheses. * significant at 10%; ** significant at 5%; *** significant at 10%
20 TABLE 1B
Effects of Income and Past Happiness on Current Happiness for SHP
OLS AH AB AH IV Dep. Var.: Happiness (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
Happiness in t-1 -0.147 0.103 0.098 0.142 0.094 0.736 0.215 0.039 -0.124 0.024 -0.112º -0.022² 0.016 [0.011]*** [0.020]*** [0.015]*** [0.040]*** [0.020]*** [0.386]* [0.015]*** [0.043] [0.028]*** [0.011]** [0.010]*** [0.122] [0.452]
Happiness in t-2 0.04 0.878¹ 0.036³ -0.119 [0.023]* [0.009]*** [0.075] [0.070]*
Current Income 0.136 0.124 0.146 0.119 0.119 0.192 0.147 0.15 0.16 0.2 0.177 0.154 0.078 0.188 0.144 [0.031]*** [0.048]*** [0.035]*** [0.042]*** [0.039]*** [0.058]*** [0.043]*** [0.072]** [0.042]*** [0.068]*** [0.056]*** [0.057]*** [0.032]** [0.075]** [0.044]***
Income in t-1 0.009 -0.023 0.001 0.016 0.017 0.056 0.033 0.033 0.041 0.156 0.073 0.042 0.051 0.033 0.025 [0.027] [0.044] [0.032] [0.039] [0.037] [0.056] [0.041] [0.071] [0.039] [0.060]** [0.052] [0.059] [0.029]* [0.085] [0.069]
Income in t-2 -0.08 -0.075 -0.033 -0.051 -0.087 -0.05 [0.045]* [0.053] [0.049] [0.058] [0.072] [0.057]
Income in t-3 -0.017 [0.039]
No. of Lags for Controls 0 0 0 0 0 2 1 1 1 1 2 2 1 2 2 Observations 32303 14854 25847 15559 15559 8964 14929 9821 14929 8964 12075 7986 9821 3740 14900 Individuals 10912 4900 9472 6093 6093 3444 5855 3785 5855 3444 4075 3096 3785 2097 5843 Max Time 7 5 6 5 5 4 5 5 5 4 5 4 5 4 5 Avg. Time 3 3 2.7 2.9 2.6 2.7 2.9 2.9 2.9 2.7 3 2.6 2.9 2.7 2.6
Notes: Fixed effects, time effects and Individual time-varying controls included in all estimations (+ lags specified). HH income is ln(household annual income). Columns (1) to (3) contain OLS estimates, Columns (4) to (15) were estimated using Anderson & Hsiao (except for (5) which was estimated by Arellano & Bond), coefficients reported belong to the first difference of variables described. (8): instrumented by 3rd lag; (9)&(10): Individual Specific Time Trend Models; (11)&(12): difference instead of level in baseline model; (13)&(14): Loss Aversion [Coefficients for loss aversion to happiness when: º: ΔH(t) is positive; ¹: ΔH(t) is negative; ²: ΔH(t-1) is positive; ³: ΔH(t-1) is negative]; (15): IV (OLS) instrumented by whether household was robbed. Clustered standard errors by individual reported in parentheses. * significant at 10%; ** significant at 5%; *** significant at 10%
21 TABLE 1C
Effects of Income and Past Happiness on Current Happiness for BHPS
OLS AH AB AH IV Dep. Var.: Happiness (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15)
Happiness in t-1 -0.053 0.063 0.061 0.137 0.061 1.643 0.143 -0.025 -0.087 0.009 -0.446 0.293 0.494 [0.006]*** [0.010]*** [0.008]*** [0.025]*** [0.010]*** [0.896]* [0.009]*** [0.024] [0.019]*** [0.006] [0.087]*** [0.024]*** [0.418]
Happiness in t-2 0.055 0.849 -0.482 0.077 [0.015]*** [0.059]*** [0.021]*** [0.055]
Current Income 0.033 0.035 0.041 0.007 0.007 0.026 0.007 0.025 0.01 0.007 0.029 0.027 0.063 0.083 0.022 [0.009]*** [0.012]*** [0.010]*** [0.013] [0.012] [0.019] [0.013] [0.040] [0.014] [0.021] [0.020] [0.017] [0.035]* [0.038]** [0.022]
Income in t-1 -0.023 -0.015 -0.022 -0.016 -0.016 0.013 -0.011 0.02 -0.009 0.014 0.017 0.015 0.02 0.029 -0.004 [0.008]*** [0.011] [0.009]** [0.012] [0.011] [0.020] [0.013] [0.040] [0.013] [0.021] [0.021] [0.019] [0.031] [0.037] [0.018]
Income in t-2 -0.01 -0.019 -0.018 -0.017 -0.014 -0.005 [0.011] [0.018] [0.019] [0.017] [0.036] [0.015]
Income in t-3 -0.023 [0.010]**
No. of Lags for Controls 0 0 0 0 0 2 1 1 1 1 2 2 1 2 2 Observations 92218 56593 78528 48069 48069 25539 47954 25635 47954 25539 25539 25539 6484 6446 47825 Individuals 20478 15707 20285 16501 16501 14179 16474 14226 16474 14179 14179 14179 14179 6446 16463 Max Time 8 6 7 5 5 3 5 5 5 3 3 3 5 3 5 Avg. Time 4.5 3.6 3.9 3.3 2.9 2 3.3 3.3 3.3 2 2 2 3.3 2 2.9
Notes: Fixed effects, time effects and Individual time-varying controls included in all estimations (+ lags specified). HH income is ln(household annual income). Columns (1) to (3) contain OLS estimates, Columns (4) to (15) were estimated using Anderson & Hsiao (except for (5) which was estimated by Arellano & Bond), coefficients reported belong to the first difference of variables described. (8): instrumented by 3rd lag; (9)&(10): Individual Specific Time Trend Models; (11)&(12): difference instead of level in baseline model; (13)&(14): Loss Aversion [Coefficients for loss aversion to happiness when: º: ΔH(t) is positive; ¹: ΔH(t) is negative; ²: ΔH(t-1) is positive; ³: ΔH(t-1) is negative]; (15): IV (OLS) instrumented by number of serious accidents. Clustered standard errors by individual reported in parentheses. * significant at 10%; ** significant at 5%; *** significant at 10%
22 TABLE 2
Robustness of Happiness GSOEP SHP BHPS OLS AH OLS AH OLS AH Dep. Var.: Happiness (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4)
Current Income 0.21 0.186 0.1 0.087 0.11 0.136 0.096 0.192 0.037 0.036 0.023 0.026 [0.015]*** [0.016]*** [0.022]*** [0.021]*** [0.026]*** [0.032]*** [0.049]** [0.058]*** [0.008]*** [0.010]*** [0.018] [0.019] Income in t-1 0.045 -0.023 0.04 0.056 -0.01 0.013 [0.015]*** [0.019] [0.029] [0.056] [0.010] [0.020] Unemployed -0.67 -0.672 -0.595 -0.237 -0.27 -0.322 -0.352 -0.338 -0.283 -0.256 -0.301 -0.232 [0.103]*** [0.104]*** [0.118]*** [0.153] [0.069]*** [0.082]*** [0.113]*** [0.143]** [0.026]*** [0.034]*** [0.057]*** [0.060]*** Unemployed in t-1 0.062 0.172 -0.196 0.05 0.059 0.126 [0.099] [0.133] [0.077]** [0.149] [0.031]* [0.060]** Married 0.113 0.357 0.154 0.143 0.237 0.286 -0.035 -0.035 0.068 0.138 0.095 0.107 [0.029]*** [0.036]*** [0.051]*** [0.050]*** [0.062]*** [0.078]*** [0.131] [0.147] [0.025]*** [0.037]*** [0.071] [0.072] Married in t-1 -0.323 -0.238 -0.115 -0.103 -0.108 -0.049 [0.035]*** [0.046]*** [0.072] [0.125] [0.035]*** [0.069] Widowed -0.343 -0.749 -0.507 -0.452 -0.367 -0.531 -0.794 -0.815 -0.178 -0.349 -0.101 -0.094 [0.064]*** [0.090]*** [0.129]*** [0.126]*** [0.204]* [0.341] [0.535] [0.536] [0.063]*** [0.091]*** [0.150] [0.151] Widowed in t-1 0.549 0.516 0.157 -0.612 0.171 0.25 [0.086]*** [0.113]*** [0.342] [0.607] [0.085]** [0.157] Number of kids 0.045 0.018 -0.031 -0.024 0.032 0.068 0.036 0.034 0.029 0.059 0.009 0.009 [0.011]*** [0.016] [0.023] [0.022] [0.019] [0.026]*** [0.045] [0.054] [0.010]*** [0.015]*** [0.028] [0.028] Number of kids in t-1 0.032 -0.006 -0.018 -0.092 -0.039 -0.044 [0.015]** [0.022] [0.026] [0.049]* [0.015]** [0.029]
Observations 168108 140271 98828 98273 43730 30960 10751 8964 112906 78256 25737 25539 Individuals 17161 14995 12102 11972 16310 10611 4091 3444 20767 20255 14272 14179 Max Time 22 21 19 19 7 7 4 4 9 7 3 3 Avg. Time 9.8 9.4 8.2 8.2 2.7 2.9 2.7 2.7 5.4 3.9 2 2 Notes: Fixed effects, time effects and Individual time-varying controls included in all estimations. Columns (1) & (2) correspond to OLS without lagged happiness; (3) & (4) are Anderson & Hsiao estimates using 2 lags of happiness and instrumenting first lag by 2nd lag of itself. Clustered standard errors by individual reported in parentheses. * significant at 10%; ** significant at 5%; *** significant at 10%
23 TABLE 3
Other Subjective Measures
German Socio Economic Panel Study
Satisfaction with: Health spare time Scale: 0 to 10 (1) (2) (1) (2) Satisfaction at t-1 0.139 0.025 0.154 0.008 [0.008]*** [0.011]** [0.015]*** [0.017] Satisfaction at t-2 0.051 0.065 [0.006]*** [0.009]***
Swiss Household Panel
Satisfaction with: Health Free time Scale: 1 to 7 (1) (2) (1) (2) Satisfaction at t-1 0.114 0.037 0.171 0.044 [0.027]*** [0.033] [0.026]*** [0.034] Satisfaction at t-2 0.029 0.062 [0.018] [0.017]***
British Household Panel Survey
Satisfaction with: Health Social Life Scale: 0 to 10 (1) (2) (1) (2) Satisfaction at t-1 0.109 0.062 0.191 0.004 [0.022]*** [0.026]** [0.024]*** [0.025] Satisfaction at t-2 0.03 0.069 [0.013]** [0.013]***
Notes: Fixed effects, time effects and Individual time-varying controls included in all estimations (+ lagged controls). Columns (1) correspond to Anderson & Hsiao using 2 lags of happiness from model presented in section 4.4. Columns (2) correspond to the second individual time trend model presented in section 4.6. Standard errors clustered by individual presented in brackets. * significant at 10%; ** significant at 5%; *** significant at 10%
24 Appendix 1: Methodological Discussion Linear vs. nonlinear specifications Due to the discrete nature of happiness variable, some authors suggest using nonlinear models to run happiness regressions, in particular ordered logit/probit instead of OLS. Basically they say that you must treat the life satisfaction variable as ordinal instead of cardinal (Ferrer-i-Carbonell, 2005, 2002). Suppose that aiV ),( measures the happiness change for individual i when moving from a happiness score of a to a happiness score of a 1. Then, the happiness score is cardinal if aiV ),( is the same for every i,a . Firstly, for a given individual, the subjective value for the distance between some scores (say 7 to 8) should be equal to that of another interval of the same length (say 3 to 4). In other words, the change in “true” happiness when someone moves from score 3 to 4 should be the same than moving from 7 to 8. However, if this condition does not hold, it would not be necessary to abandon linear regressions since it is possible to transform the variable in such a way as to make the condition hold (e.g. applying a concave function to the variable and then giving more value to changes in the bottom of the satisfaction scale). We ran regressions testing some transformations and found no relevant changes in the main results. Secondly, the subjective value of a certain score interval (say 5 to 6) should be the same between all individuals. This is certainly not the case. However, introducing individual fixed effects may capture the best part of this unobservable effect.18 Regardless of these issues, it has been shown that assuming ordinality or cardinality of happiness scores makes little difference as long as fixed effects are taken into account (Ferrer-i-Carbonell and Frijters, 2004). Income Corrected by Household Elasticity We estimate elasticity to household size using the method proposed by Schwarze (2003). The data sets contain questions satisfaction with income of the household. This variable is scaled from 0 to 10 for GSOEP and SHP; 1 to 7 for BHPS (with the lowest number meaning least satisfied and the highest: most satisfied). The model proposed takes the form of:
e it it lnYXS it itt
Where Sit is individual satisfaction with income, X it is a vector of control variables
(age, employment state, education and a constant), t are year effects and it corresponds e to error component. Finally, Yit is the scaled income where
e Yit Yit k 0 hitk k H it
Household size, H it , is corrected by equivalence scale elasticity made up of 0 , a constant, and a linear combination between number of: kids, teenagers, employed and k retired individuals in household ( hit ). This is used to scale Yit , annual total household income. After some rearranging it is possible to obtain the following expression:
k k it it 0 lnYXS it 1 H it )ln( it Hh it )ln( itt k
18 As long as j i j i bVbVaVaV )()()()( . It may be written as: j j i i bVaVbVaV )()()()( , which should be true if the first condition holds.
25 19 Where 001 and k 0 k . Rearranging these expressions we can obtain the elasticity to household size by solving / 010 and k k / 0 for each k. Estimation results for data sets are presented in Table A1. Household income is statistically significant and has a positive coefficient, just as one would expect. The elasticities obtained from estimations are consistent with the ranges obtained by Schwarze (2003) and those suggested by the OECD. Some examples of household weights and elasticities according to household composition are available in Table XXXb, along with OECD and Schwarze’s scales. Our results for GSOEP differ from those originally obtained by Schwarze because Schwarze uses years 1992-1999 for the full sample while we use the complete series for the original sample.
Table A1 Elasticity to Household Size Dep. Var.: Satisfaction with Household Income GSOEP BHPS SHP ln(HH income) 1.236 0.764 1.405 [0.056]*** [0.017]*** [0.030]*** ln(HH size) -0.038 -0.407 -0.747 [0.113] [0.044]*** [0.072]*** ln(HH size)*Number of kids 0.033 0.029 0.064 [0.023] [0.009]*** [0.011]*** ln(HH size)*Number of teens -0.068 0.037 [0.029]** [0.010]*** ln(HH size)*Number of adults -0.136 -0.016 0.031 [0.022]*** [0.008]** [0.016]*
Notes: Ordered logit estimates including time effects and Individual time- varying controls included in estimation. Definitions of variables differ between data sets: see Data Appendix for detailed description. Clustered standard errors reported in brackets. * significant at 10%; ** significant at 5%; *** significant at 1%
Table A2 Elasticity to Household Size 2 Adults 4 Adults 2 Adults 2 Kids Elasticity Weight Elasticity Weight Elasticity Weight
OECD 0.58 1.50 0.66 2.50 0.53 2.10 Schwarze 0.35 1.28 0.35 1.63 0.24 1.47
Our estimates: GSOEP 0.27 1.20 0.48 1.96 0.22 1.37 SHP 0.49 1.40 0.44 1.85 0.40 1.73 BHPS 0.58 1.49 0.62 2.36 0.50 2.00
Notes: Results for OECD were taken from Schwarze (2003). Reported elasticities and weights for Schwarze correspond to the estimate with fixed effects. Our weights and elasticities for GSOEP differ from those obtained by Schwarze due to the use of different time periods and observations in the GSOEP.
19 0 from original expression 26 Appendix 2: Data description German Socio-Economic Panel Study (GSOEP) The GSOEP is a longitudinal data set which is representative of the German population. It began randomly sampling households for the west states of the Federal Republic of Germany in 1984. The original sample size was around 6000 households yielding a sample of above 12,000 individuals. With the fall of the Berlin Wall in 1989, Germany was reunited and the sample was expanded to represent Germany as a whole. For more detailed information on the history of the GSOEP please refer to Wagner et al. (2007). Due to the empirical nature of this work we use the original sample (West Germany only) covering the years 1984 to 2005 in order to maximize panel length.20 This results in an average of 15 waves per respondent. Our dependant variable (happiness) is defined as the individual’s overall life satisfaction. In the survey, this question is only responded by individuals age 16 and over. Our variable for household income is taken from the Cross- National Equivalent File (1984-2005) where it is defined as “Real Household Post- Government Income”. This variable corresponds to total household income (i.e. labor income, pensions, etc.) after taxes and other transfers (combines payments of all household members). Data on CPI was taken from OECD. British Household Panel Survey (BHPS) The BHPS is a random representative sample of the population of the United Kingdom. It began in 1991 surveying some 5,500 households and additional household were incorporated in 1999 and 2001 yielding a sample of over 10,000 household containing over 24,000 individuals aged 15 onwards. Individuals who left original household to form a new one were followed and all adults were consequentially interviewed. We make use of data from wave 6 to 15 due to the fact that questions on life satisfaction were introduced as of wave 6. In wave 11 the question on life satisfaction was dropped from the survey because space constraints in Self Completion Schedule, and replaced by the Quality of Life module (introduced every 5 years). Data for wave 11 is then included with missing values for happiness. This yields a panel with a maximum length of 10 waves and a mean of 7 waves per respondent. Data on CPI was taken from the UK Office of National Statistics. Swiss Household Panel (SHP) Not widely used in Economics of Happiness literature, the SHP is a relatively new longitudinal data set which was started in 1999. It is surveyed annually covering more than 5000 representative households, with a sample size of over 13000 respondents. All individuals over the age of 14 in the household are surveyed. In comparison to the BHPS or GSOEP, the SHP collects data on a wider variety of topics which are of interest in social science. For more information on the SHP refer to Budowski et al. (2001). We use data covering waves 1 through 8 (1999 to 2006) with a mean of 5 waves per respondent. Questions on life satisfaction were included as of the year 2000; therefore we include all relevant data for 1999, as well as happiness (with missing values). Data on CPI was taken from OECD.
20 For instance, Di Tella et al. (2007) undertake the same strategy. Results are robust to including whole sample. 27 Table A3 Descriptive Statistics
German Socio Economic Panel Study (1984-2005) Variable Mean Std. Dev. Min. Max. No. of Obs. Happiness (0 - 10 Scale) 7.11 1.87 0.00 10.00 N = 172642 Between 1.50 0.00 10.00 n = 17688 Within 1.37 -1.97 15.11 T (avg) = 9.76
Total household income (year 2000 th. Euros) 25.04 16.91 0.00 421.23 N = 172642 Between 14.03 0.00 228.59 n = 17688 Within 11.00 -200.04 277.46 T = 9.76
Swiss Household Panel (1999-2006) Variable Mean Std. Dev. Min. Max. No. of Obs. Happiness (0 - 10 Scale) 8.06 1.50 0.00 10.00 N = 52895 Between 1.41 0.00 10.00 n = 18305 Within 0.81 -0.27 14.73 T (avg) = 2.89
Total household income (year 2000 Euros) 108.53 80.13 0.00 3755.39 N = 46118 Between 83.96 0.00 3755.39 n = 16724 Within 37.27 -1200.92 1512.48 T = 2.76
British Household Panel Survey (1996-2006) Variable Mean Std. Dev. Min. Max. No. of Obs. Happiness (1 - 7 Scale) 5.23 1.31 1.00 7.00 N = 118551 Between 1.12 1.00 7.00 n = 24893 Within 0.81 -0.10 10.23 T (avg) = 4.76
Total household income (year 2005 th. GB Pounds) 28.10 22.72 0.00 1205.21 N = 117611 Between 19.09 0.00 332.24 n = 24811 Within 13.78 -242.71 1061.76 T = 4.74
28 Appendix 3: Data Definitions British Household Panel Survey Happiness / Satisfaction with Life: Individual response to question: "How satisfied or dissatisfied are you with your life overall?” [1 Not satisfied at all] - [7 Fully satisfied] Satisfaction with Household Income: Individual response to question: " How satisfied or dissatisfied are you with the income of your household?” [1 Not satisfied at all] - [7 Fully satisfied] Household Income: Household Gross Income deflated to prices of 2005 using information on CPI from UK Statistics. Including all income perceived by household: labor, transfers, welfare, etc. Income value is reported in GB Pounds. Equivalence corrected Income: elasticity to household size correction for income, using equivalence scale elasticity obtained by regressing variables against satisfaction with household income. No. of Serious Accidents: number of accidents which require medical treatment by a doctor or a hospital visit. Health Satisfaction: respondent’s answer to the question: “How dissatisfied or satisfied are you with your health?” [1 Not satisfied at all] - [7 Fully satisfied] Satisfaction with Social Life: respondent’s answer to the question: “How dissatisfied or satisfied are you with your social life?” [1 Not satisfied at all] - [7 Fully satisfied] Control Variables: Household Composition variables: includes number of children, employed, retired individuals in household. Household Size: number of people in household. Employment state: set of dummies for different employment states derived from the following question: “Which best describes your current situation?” [1 Self Employed], [2 Paid Employment], [3 Unemployed], [4 Retired], [5 Maternity Leave], [6 Looking After Family], [7 Attending Classes], [8 Sick or Disabled] and [9 Government Training]. Plus dummy for having a second job. Age: age in years derived from date of interview and individual responses to the question about the birth dates. Marital State: set of dummies (Married, Separated, Divorced, Widowed and Never Married) obtained from question: "What is your legal marital status? [1 Married], [2 Separated, [3 Divorced], [4 Widowed] and [5 Never married] Education: set of dummy variables derived from individual responses to the question: "Which is the highest qualification he/she has got? [1 Training Certificate], [2 Trade Apprenticeship], …, [11 University Diploma], …, [13 University Higher Degree]". Health State: a set of dummies on diverse health problems obtained from question: "Have any of the health problems listed on this card? (i.e. difficulty seeing, diabetes, breathing problems, etc.)" Smokes: a dummy variable derived from the individual responses to the question: "Do you smoke cigarettes? [1 Yes] [2 No]". No of Cigarettes: derived from question: “How many cigarettes did you smoke in the last 7 days?” Days in Hospital: number of days respondent spent in hospital derived from question: “Since (date), in all, how many days have you spent in a hospital or clinic as an in –patient?” German Socio-Economic Panel Study Happiness / Satisfaction with Life: Individual response to question: "How satisfied are you with your life, all things considered?” [0 Completely Dissatisfied] - [10 Completely Satisfied] Satisfaction with Household Income: Individual response to question: “How satisfied are you with your household income?” [0 Completely Dissatisfied] – [10 Completely Satisfied] Household Income: “Real Household Post-Government Income” from the CNEF. It includes all income perceived by ALL household members (i.e. labor income, pensions, windfalls, etc.). Since all income data is reported as monthly average, the data has been annualized. Government tax burdens were estimated by the DIW using calculation routines developed by Schwarze. Values reported are in EURO deflated to prices of the year 2000 using data from the OECD. Equivalence corrected Income: elasticity to household size correction for income, using equivalence scale elasticity obtained by regressing variables against satisfaction with household income. Health Satisfaction: respondent’s answer to the question: “How satisfied are you with your health?” [0 Completely Dissatisfied] - [10 Completely Satisfied] Satisfaction with Spare Time: respondent’s answer to the question: “How satisfied are you with your spare time?” [0 Completely Dissatisfied] - [10 Completely Satisfied] Control Variables: Household Composition variables: number of children, household size (number of individuals in household). Age: in years and age squared.
29 Employment state: set of dummies for different employment states derived from a generated variable by the DIW using data on labor force participation and non-employment characteristics. Hours worked: annual. Constructed by DIW using information on employment status, average number of hours worked per week and the number of months worked in the previous year. No corrections for vacations were made. Marital State: set of dummies (Married, Separated, Divorced, Widowed, Single, Not living with a partner) derived from variable constructed in CNEF where categories indicate legal marital status. Education: number of years. Variable constructed by assigning years according to type of education. For example: Individuals with a school leaving degree are assigned a minimum of between 9 and 12. Days Spent in Hospital: Individuals were asked: “How many nights in total did you spend in the hospital last year?”. Since this question was not included in the questionnaire for years 1990 and 1993, this control is not included in results presented in order to maximize panel length. Regardless, results are robust to including this variable. Swiss Household Panel Happiness / Satisfaction with Life: Individual response to question: "In general, how satisfied are you with your life if 0 means “not at all satisfied” and 10 means “completely satisfied”?” Satisfaction with Household Income: Individual response to question: “Overall how satisfied are you with the financial situation of your household. If 0 means “not at all satisfied” and 10 “completely satisfied”?” Household Income: “Yearly Household Income, Net” variable constructed in the SHP. It includes all income perceived by ALL household members (i.e. labor income, pensions, windfalls, etc.) after deduction of social security contributions. Taxes not deducted. Values reported are in EURO deflated to prices of the year 2000 using data from the OECD. Equivalence corrected Income: elasticity to household size correction for income, using equivalence scale elasticity obtained by regressing variables against satisfaction with household income. Robbed: respondent’s answer to “Since [last interview] with your household, was your accommodation (house) burglured?” Yes or No. Health Satisfaction: respondent’s answer to “How satisfied are you with your state of health, if 0 means ‘not satisfied at all’ and 10 ‘completely satisfied’?” Free Time Satisfaction: respondent’s answer to “How satisfied are you with the amount of free time you have, if 0 means ‘not satisfied at all’ and 10 ‘completely satisfied’?” Control Variables: Household Composition variables: number of children, household size (number of individuals in household). Age: in years and age squared. Hours worked: individual response the question: “How many hours do you usually work each week for your main job?” Employment State: set of dummies for different employment states derived from variable generated by SHP from diverse question on employment. Marital State: set of dummies (Married, Separated, Divorced, Widowed, Never Married) indicating actual civil status in year of interview. Education: set of dummy variables indicating respondent’s highest level of education achieved: ranging from incomplete compulsory school to university, higher specialized school. Health State: set of dummies indicating different health problems such as: back problems, weakness/weariness, sleeping problems, headaches, chronic illness or long-term health problem.
30