Reversing the Causality- Does Happiness Reduce Income Inequality? Satya Paul University of Western Sydney

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1 Reversng the Causalty- Does Happness Reduce Income Inequalty? Satya Paul Unversty of Western Sydney 3 Contact detals: Satya Paul, Professor of Economcs School of Busness Parramatta Campus, Room # EDG 36 Unversty of Western Sydney Loced Bag 797, Penrth, NSW 75, Australa. Emal: s.paul@uws.edu.au Phone: Moble: Fax:

2 Reversng the Causalty- Does Happness Reduce Income Inequalty? March 3 Abstract Ths paper nvestgates the effect of happness (self reported lfe satsfacton) on ncome nequalty by explorng the causalty from happness to ncome based on the panel data from the frst fve waves (-5) of Household Income and Labour Dynamcs n Australa (HILDA) survey. Happness s hypotheszed to mpact upon the ncome generatng capacty of an ndvdual drectly by stmulatng worng effcency and ndrectly through ts effect on the allocaton of tme for pad wor. Both these effects of happness on ncome are tested n a model consstng of an ncome generatng functon and wor hour equaton. The ncome flows of happness and other varables obtaned from the model are nserted nto the ncome nequalty decomposton equatons to obtan ther relatve nequalty contrbutons. The emprcal results reveal that happness has a postve effect on ncome generaton and contrbutes to the reducton of nequalty. Keywords: Happness, ncome generatng functon, wor hours, nequalty decomposton. Introducton The happness or lfe satsfacton studes are gettng ncreasngly more attenton among economsts, psychologsts and polcy maers. The frst promnent study of happness was undertaen by Easterln (974) to nvestgate whether economc growth has any postve mpact on happness n the Unted States. He noted that whle at a pont of tme rcher are happer, overtme ncome growth does not rase happness. Ths apparent nconsstency between these two phenomenons s now nown as the Easterln paradox. The effect of ncome on happness n the subsequent studes of other developed economes vares from postve to nsgnfcant or even negatve. There are other related contrbutons on the effects on happness of unemployment, nflaton and ncome nequalty, see, e.g. Clar and Oswald (994), D Tella et al () and Alesna et.al. (4). Ferrer--Carbonell and

3 3 Frjters (4) and Clar et al (8) have provded excellent revews of happness lterature. In ths paper, we explore the possblty of a reverse causaton,.e., happness may lead to hgher ncome/earnng. Economst and other socal scentsts now very lttle of the mechansm through whch happness affects human performance. However, there s a vast lterature n psychology revealng that worers who experence postve emotons (a term used to reflect happness) show less emotonal exhauston and low absenteesm at wor (Iverson et al, 998; Wrght and Cropanzano, 998; George, 989; Gl et al, 4). The happy people have hgher self-esteem and are more dscplned n ther actons (Guven, 7; Fran, 997 and Kenny, 999). Amable et al (5) provde some evdence that happness nctes greater creatvty. In an nterestng expermental study, Oswald et al (8) desgned a randomzed tral at the Unversty of Warwc to see how emotons affect human productvty. They ran the experment twce, both tmes worng wth 8 subjects. The frst tme, they nduced happness n a group of people by showng them mnutes of comedy clps. Another group saw no clps. Then, both groups too a short math test. They were told they would be pad based on how many questons they answered correctly. The group that had watched the clps answered % more questons correctly than the group that hadn't. The ln between good emotons (feelng of happness) and wor performance s also evdent across dverse wor envronments. For nstance, happy crcet players show superor performance durng games (Totterdell, 999, ). Insurance agents wth a postve dsposton have been found to sell more nsurance polces than ther less postve counterparts (Selgman and Schulman, 986). On the contrary, Sanna et al (996) suggest that ndvduals n negatve mood put forth the most effort. Ths s consstent wth the generally held vew that academcs produce a large and of hgh qualty research output under stress whle gong for tenure at the North Amercan Unverstes. To the best of my nowledge, no prevous economcs study, wth the excepton of Graham et al (4), has used large sample survey data to nvestgate the effect of happness on ncome. The study of Graham at al s based on the panel data for Russa for 995 and. These researchers frst regress happness on log ncome and other

4 4 conventonal varables usng data for 995 and obtan resdual happness as the dfference between observed happness and estmated happness. Then, they regress the log ncome n on resdual happness n 995. The study reports that a one per cent ncrease n the unexplaned (resdual) happness n 995 yelds approxmately 3 percent ncrease n ncome n. The study provdes no explanaton why effect of happness on ncome occurs after fve years. If happness has a sgnfcant effect on ncome, then varatons n levels of happness among ndvduals are lely to affect the level of ncome nequalty. Ths s an nterestng and mportant ssue wth whch ths paper s manly concerned. More specfcally, we frst nvestgate the effect of happness on ncome generatng capacty of an ndvdual n a regresson model and then examne the extent to whch ncome flow from happness contrbutes to nequalty. An emprcal exercse based on panel data from the frst fve waves ( to 5) of Household Income and Labour Dynamcs n Australa (HILDA) surveys s presented. The results reveal that happness has a postve sgnfcant effect on ncome generaton and contrbutes about 9% to the reducton of nequalty. The paper s structured as follows. Secton dscusses the analytcal framewor that we use for explorng the mpact of happness on ncome nequalty. We specfy a model that captures the channels through whch happness may affect the ncome generatng capacty of an ndvdual and then dscuss the methodology for assgnng nequalty contrbutons to ncome flows assocated wth happness and other relevant varables such as age, educaton, and wor hours. Secton 3 dscusses the data and the emprcal results for Australa. Secton 4 concludes the study.. The Analytcal Framewor At least two major ssues are nvolved n nvestgatng the effect of happness on ncome nequalty. The frst ssue relates to the explorng of channels through whch happness may affect the ncome generatng capacty of an ndvdual. Gven the results of experments conducted by Andrew Oswald and hs team at Warwc Unversty, we hypothesse that happness drectly enhances the performance of an ndvdual n earnng actvtes. We shall call ths the drect or productve effect of happness on ncome generaton. Happness may also affect ncome ndrectly va ts mpact on the tme

5 5 allocaton of an ndvdual. An ndvdual allocates her total tme between three actvtes: () pad wor () mantenance of health (such as sleepng and restng etc) and () consumpton of relatonal goods. An ndvdual wors some hours n the wee to earn ncome whch she spends for buyng conventonal and postonal consumpton goods. Each ndvdual devotes some mnmum tme for mantanng health. The relatonal goods are the nteractons wth famly members, frends and relatves. These goods are tme consumng and thus have opportunty cost. These goods are jontly produced and are nown to be benefcal to ndvduals. People go on holdays to recharge ther energy essentally by consumng relatonal goods. The consumpton of relatonal goods may neutralse or more than neutralse the relatonal bads (tense). The latter are consumed whle nteractng wth some unpleasant colleagues and customers at wor or wth unnown persons n the maret place. A happy person may prefer to wor more hours per wee and produce/earn more. Or, alternatvely, a happy person may le to enjoy more lesure tme to consume relatonal goods and thus wor less hours per wee. The resultng ncome loss s the cost of consumng relatonal goods (lesure) a happy person may le to ncur/ bear. We shall call t the ndrect effect of happness on ncome. Thus, the total effect of happness on ncome wll depend on the magntude and sgns of both the drect and ndrect effects. They may renforce or neutralse each other. A second ssue relates to the choce of an approprate methodology to assgn nequalty contrbutons to the ncome flows from happness and other ncome generatng varables. A standard procedure s to choose one or more nequalty measures and use ther decompostons for assgnng nequalty contrbutons to ncome flows from dfferent regresson varables. Snce the nequalty measures dffer n terms of ther dstrbutonal weghts, ther decomposton rules (equatons) dffer from each other. Hence, the choce of decomposton equatons becomes mportant for assgnng unambguous nequalty contrbutons to dfferent ncome flows. We return to ths ssue latter n ths Secton. Another related ssue that s equally crucal and requres menton at the very outset relates to the possblty of bdrectonal causalty between happness and ncome whch can lead to smultaneous/ endogenety bas n the coeffcent of happness varable n ncome generatng functon. One effectve way to resolve ths problem s to use an nstrument whch s correlated wth happness varable but s uncorrelated wth the error term. In a

6 6 recent attempt to examne the effect of happness on consumpton, savng and rs tang behavour wth panel data for Germany and the Netherlands, Guven (7) overcomes the problem of ndogenety n each regresson equaton by nstrumentng ndvdual happness wth regonal sunshne. However, whle worng wth tme seres data, the lagged value of the varable serves as a natural nstrument n the model (Greene, 3, pp ).. An Income Generatng Model Consder the followng ncome generatng functon Y t Ht g(at ) xt s () where Y t s the ncome of ndvdual durng perod t. H t- s one year lagged selfreported overall lfe satsfacton (happness) tang values (scores) between zero ( totally dssatsfed wth lfe) and ( totally satsfed wth lfe) as reported n HILDA le most western surveys on lfe satsfacton. These happness scores are assumed to be the cardnal numbers. One year lagged values of happness serve as an nstrument for happness to overcome the problem of endogenety. Paul and Gulbert (3) have reported statstcally nsgnfcant effect of current and lagged ncomes on happness based on the same data set we use here. Hence, we do not confront wth any ssues related to causalty runnng from ncome to happness. t The functon g(a t ) represents the age-ncome profle. x t s a vector of wor hours and dummes for educaton, gender, locaton, poor health and occupatons. The choce of these varables s dctated largely by the avalablty of data. s s the tme nvarant ndvdual-specfc effect of unobservable varables le sll, drve, luc and taste and s assumed to have zero mean and constant varance. t represents the general effect of transtory factors and s also assumed to have zero mean and constant varance. We also assume that the varance of combned random term ( = s + t ) s also constant, = s +. s t The human captal theory suggests a hump-shaped age-ncome profle, whch n often represented by regressng log ncome (or log wages) on age and age (see e.g. Murphy and Welch, 99 and Wlls, 986). But snce we are nterested n decomposng the

7 7 nequalty of ncome rather than of log ncome, we approxmate age-ncome hump profle by a pece-wse functon of age. The functon s assumed to consst of three peces correspondng to three age groups, namely, () below 5, () 5 and less than 35, and () 35 and above. We specfy lnear forms for the frst two age groups and a quadratc form for the thrd age group durng whch ncome reaches the maxmum level and then starts declnng. To ensure a smooth transton, the rght hand dervatve of the second functon wll be equated to the left-hand dervatve of the thrd functon, both beng evaluated at age 35. If we assume that the worng age of an ndvdual starts at age 5 (whch s the mnmum age we observed n the sample), then the hump-shaped pattern of age-ncome profle could be specfed as g(a ) V V V () t t t where A t s the age of ndvdual at tme t and V t = (A t - 5) d t + (d t + d 3t ) V t = (A t - 5) (d t + d 3t ) V 3t = (A t - 35) d 3t wth d t = f A t < 5, zero otherwse d t = f 5 A t < 35, zero otherwse d 3t = f A t 35, zero otherwse Substtutng () and the elements of vector x t nto (), we have 3 3t Y t 7 H t Graduate V t Whle collar t 3 t PH 8 t V t 4 3 Female Blue collar t V 3t WH 9 5 Cty t Others t t 6 s Professonal t t (3) where Graduate, Poor health (PH), Cty, Females and four occupatons are the dummy varables wth Managers as a default category. WH represents the average wor hours per wee. Gven the panel data from waves -5 of HILDA, equaton (3) can be estmated wth generalzed least squares (GLS) wth random effects. Note that, and ( + 3 (A t -35)) reveal the annual margnal changes n ncome durng 5 A t < 5, 5 A t < 35 and A t 35 respectvely. The coeffcent represents the effcency (drect) effect of happness on ncome generaton.

8 8 The wor hours mght be nfluenced by the level of happness and poor health of an ndvdual. If ths s the case, then both these varables can also ndrectly affect the level of ncome. To explore ths, we specfy a wor hour equaton and estmate by GLS random effects. In the absence of any gudance from economc theory, the wor hour, for smplcty, s assumed to be a lnear functon of happness and poor health. WH t H PH e (4) t t t where η and e t are respectvely ndvdual tme-nvarant and general random effects, each s assumed to have zero mean and constant varance. If and are statstcally sgnfcant, then the second and thrd terms n (4) wll represent those portons of wor hours that are nduced (or constraned) by happness and poor health respectvely. The remanng part e ) represents what we call here the oblgatory wor hours ( t (OWH) of a healthy but totally unsatsfed person. Substtutng (4) nto (3) we have Y t ( 7 ( )H 3 )PH t Whle collar t t V 4 8 t Female Blue collar t V 5 t Cty 9 t 3 V 3t 6 Others t OWH t t Professonal s t Graduate t (5) Note that and ( ) are respectvely the drect and ndrect effects of happness on ncome, and 3 and ( ) are the drect and ndrect effects of poor health on ncome. From model (3), one can obtan the combned resdual term separate estmates of s and t. However, gven t, s and mnmum varance estmate of s as (Kng and Dcs-Mreaux, 98, p. 54): t (= s + t ) but not the t one can obtan the ŝ (s ) ( ) (6) t t t where s /( s ). Snce s s assumed to be a tme nvarant ndvdual random effect, we obtan the estmate of s by multplyng wth the combned resdual term averaged over the tme perods,.e., we get ~ s ( ) and then ~ ˆ ~ s. t t

9 9 For expostonal reasons, equaton (5) may be rewrtten convenently as Y t Yt bzt Ztb (7) where Y t = (b Z t ) represent the ncome flow from the -th varable. Z t = [ H t- H t- V t V t V 3t OWH t Graduate t PH t PH t Female Cty t Professonal t Whte collar t Blue collar t Others ~ t s ~ t ]. b [ ]. The ncome flow from age wll be represented by ( V t + V t + 3 V 3t ) and that from occupatonal factors by ( + 6 Professonal t + 7 Whte collar t + 8 Blue collar t + 9 Others t ).. Regresson based Decomposton of Income Inequalty: The Choce of Decomposton Rules The methodology that forms the bass of our nequalty decomposton follows the lead wors of Fe, Rans and Kuo (978), Pyatt, Chen and Fe (98), Shorrocs (98), Lerman and Ytzha (985), Morduch and Secular () and Paul (4). In ths secton, we suppress the tme subscrpt t from all the varables for the same of smplcty. If the dstrbuton vector of ncomes among n ndvduals s represented by Y = (Y, Y,...,Y n ), then a measure of nequalty, say I, can be wrtten as the weghted sum of ncomes. I w (Y,I) Y (8) where w (Y, I) s the dstrbutonal weght assocated wth Y. On substtutng Y = b Z I for Y, we have w (Y,I) Y = w (Y,I)b Z. (9) Ths s nown as a natural decomposton of ncome nequalty. The replacement of Y by bz n (9) mantans the lnear structure of decomposton gven that ncome components sum to total ncome. Whle our methodology (dscussed n Secton.) allows us to fnd out the contrbuton of each ndvdual varable, our nterest les n nowng how age and occupatonal dfferences contrbute to nequalty.

10 The contrbuton of the -th explanatory varable to ncome nequalty s represented by v (I) w (Y,I) Y = w (Y,I)bZ. () Ths, when expressed as a proporton of total nequalty, s called the decomposton rule for nequalty measure I. v~ (I) v (I) / I. () All measures of nequalty, except the Atnson ndces, are decomposable as n (9). The natural decomposton of Gn coeffcent proposed by Fe, Rans and Kuo (978) and elaborated and extended by Pyatt, Chen and Fe (98) and Lerman and Ytzha (985) has formed the bass of analyss n most of the earler studes. Paul (4) provded decomposton rules for the entre class of entropy measures. Snce the nequalty measures dffer n terms of dstrbutonal weghts, ther decomposton rules dffer from each other. The expressons for the decomposton rules of dfferent nequalty measures are presented n Table. It s convenent for appled researchers to conduct ther research based on a sngle decomposton rule. In hs desre to get a decomposton rule (equaton) ndependent of the functonal form of the nequalty measures, Shorrocs (98) mposed certan strngent constrants on the decomposton procedure and arrved at a unque decomposton rule whch turned out to be the decomposton equaton for varance. Ths so called unque decomposton rule s based on the requrement that a gven ncome source maes no contrbuton to aggregate nequalty f every ndvdual receves equal ncome from that source. Ths requrement s untenable because f each person receves a constant postve ncome from a source, then the aggregate nequalty declnes. That s, a decomposton rules must assgn a negatve nequalty contrbuton to any source ncome that s equally dstrbuted and s postve. Ths condton s called the property of negatvty n Paul (4) 3 and s satsfed f the sum of dstrbutonal weghts s less than zero,.e. w (Y, I). See, for example, Star et al (986), Paul and Dasgupta (989), Garner (993) and Ytzha (99). 3 Morduch and Secular () have called ths the property of equal addtons.

11 As shown n Paul (4), only a sub-class of the entropy measures wth nequalty averson parameter < c < (whch ncludes Thel s T ) meets the negatvty requrement and hence can be used for assgnng nequalty contrbutons to ncome sources unambguously. The Gn ndex and the generalzed entropy ndces for c and c (whch nclude half of the squared coeffcent of varaton and Thel s T ) fal to satsfy ths test and thus be consdered unsutable for decomposng nequalty. For our emprcal analyss, we rely on two decompostons rules satsfyng the negatvty requrement, though experments are also made wth unacceptable rules to see ther relatve performance. 3. An Emprcal Illustraton wth Australan Data 3. Data The panel data for 93 ndvduals from the fve waves ( to 5) of the Household Income and Labour Dynamcs n Australa (HILDA) surveys s used to examne the effects of happness on ncome generaton and nequalty. In these surveys, the respondents are ased detaled questons about economc and subjectve wellbeng as well as labour maret dynamcs. The varables used n the estmaton of models (3) and (4) are defned as follows. Happness (lfe satsfacton 4 ) s measured on a scale numbered from zero to ten accordng to each person s response to the followng queston: All thngs consdered, how satsfed are you wth your lfe? 5 A score of zero means that the person s completely unsatsfed wth lfe and the score of means that the person s completely satsfed wth lfe. The annual ncomes of ndvduals are converted nto constant prces usng consumer prce ndces avalable from the Australan Bureau of Statstcs (ABS, 7). To prevent zero ncome values from beng treated as mssng data by STATA, $ s added to all ncomes. An added advantage of ths s that t facltated the computaton of Thel s entropy measures whch requre log values of ncome. 4 We use the terms happness and lfe satsfacton nterchangeably throughout ths paper. 5 Whle the valdty of self-reported happness statstcs has been a source of consderable debate n recent years, exstng emprcal studes appear to suggest that there s a lot of mportant and relable nformaton contaned wthn these fgures, see, e.g., Layard (5), Glbert (6) and Schmmac (6).

12 In the HILDA survey, the tme spent by an ndvdual n the pad wor s recorded as the average wor hours per wee, and the age s measured n years. Bnary varables are generated for females, graduates (unversty degree holders), those who suffer from poor health, and those who lve wthn a major cty. People are labelled as sufferng from poor health f they have a long-term health condton. For the occupatonal status, dummy varables are used for professonals, whte collars, blue collars and others (managers serve as the reference group). Tables through 4 present summary statstcs on varables used n estmatng equatons 3 and 4. The real mean ncome of ndvduals ncreased from $547 n wave to $794 n wave 5 showng a growth of 7.7 per cent over the entre perod. The rse n ncome s accompaned by a declne n nequalty as revealed by Gn and generalzed entropy measures (Table ). The number of unversty graduates ncreased by less than percentage ponts. The number of ndvduals wth poor health has ncreased by percentage ponts. The average wor-hours per wee show a tendency to ncrease, though margnally, over the years. The average self reported lfe satsfacton (happness) score has margnally declned or remaned constant. The dstrbuton of lfe satsfacton scores s qute sewed. Only 3 percent of ndvduals report a lfe satsfacton score of 4. A large proporton of ndvduals report happness scores n the range of 7- each year (Table 3). Ths, however, does not mean that ndvduals have not moved upward or downward on the happness scale. The moblty statstcs presented n Table 4 show that over tme about one-thrd of ndvduals move downwards on the lfe satsfacton scale, less than one-thrd move upwards and all others stay at the same level of lfe satsfacton. 3. Emprcal Results Tables 5 and 6 present the random effect GLS estmates of ncome generatng functon (3) and wor hours equaton (4). R for the ncome generatng functon s.36, and for the wor hours equaton.9. All the estmated coeffcents seem to be reasonable n terms of ther sgns and magntude and are statstcally dfferent from zero at hgh levels of sgnfcance. In the ncome generatng model, the coeffcents of V and V are postve but the coeffcent of latter s lower than the former. Ths ndcates that the rate of change

13 3 n ncome decelerates for the age group, Snce the coeffcent of V 3 s negatve and sgnfcant, our data provde a strong support for a hump shaped pattern of agencome profle. The age at whch the ncome level reaches the hghest 6 turns out to be 5. The coeffcent of happness n ncome generatng model s postve (α = 4.8), whch suggests that happness enhances the performance of an ndvdual n earnng actvtes. The postve coeffcent of wor hours suggests that an addtonal wor hour (per wee) adds $95.78 to the ncome of an ndvdual. Snce the happness has a negatve effect on wor hours ( = -.4), the ndrect effect on ncome of one pont rse n lfe satsfacton s negatve ( = -7.4). Ths s the opportunty cost of lesure an ndvdual s wllng to ncur as she moves one pont upward on lfe satsfacton scale. Clearly, the drect effect of happness on ncome s stronger that the ndrect effect. Hence, the net effect on ndvdual s ncome of one pont rse n lfe satsfacton s postve $76.67 = Ths mples that, other thngs remanng the same, an ndvdual who s completely satsfed wth lfe earns $766.7 more than the one who s completely unsatsfed wth lfe. The elastcty of ncome wth respect to happness calculated at the mean levels of ncome and happness s.56 [ Y ( H / Y ) Y / H (7.9/547) ( )],H whch s the sum total of the drect (.64) and ndrect (-.8) elastcty estmates. Ths suggests that percent ncrease n happness leads to.56 percent ncrease n ncome. Ths elastcty s much lower than the one (3 per cent) obtaned n Graham et al (4) for Russa. Ths dfference n elastcty estmates between the two countres could be due to dfferences n model specfcaton, data, and the length of perod used for calculatng the response. We explore drect and ndrect effects of happness on ncome generaton responses whereas no such dstncton s made n Graham et.al. The latter study examnes the effect of 995 resdual happness on ncome generaton n. It should also be noted that the data set used for Russa belongs to a perod of drastc socal change whch mght have been reflected n the effects of happness on ncome and other varables. The Australan data set relate to a normal perod. All these factors should also be ept n mnd whle comparng our results wth those of Graham at al. 6 Ths s wored out by equatng ( + 3 (A t -35)) to zero (frst order condton).

14 4 Poor health adversely affects the productve effcency leadng to a declne of ncome by $ per year. Indvduals wth poor health wor per wees 3.33 hours less than those who are healthy (Table 6). Thus, the ndrect effect of poor health on ncome (through a reducton n worng hours) s also negatve ( = ). Summng these drect and ndrect effects, one can say that, other thngs remanng the same, an ndvdual wth poor health earns $ less than one who s healthy. There are other nterestng ponts that emerge from the estmated models. Cetrs perbus, the unversty degree holders earn per year $848 more than others. Females earn about $878 less than males. Those who lve n bg ctes earn about $77 more than those who lve n smaller ctes. Three are sgnfcant dfferences n ncome between occupatons, wth managers (default) at the top and blue collars at the lower end. We now turn to the decomposton of nequalty by ncome flows from dfferent varables. Three entropy decomposton rules, namely, v~ (Tc.), v~ (Tc. ) and v~ (Tc ), and the Gn decomposton rule v~ (G) are presented n Table 7. The frst two decomposton rules satsfy the negatvty condton, whereas the other two volate ths condton. The entropy decomposton rules that satsfy the negatvty condton provde qute a consstent and plausble pcture. Durng, happness reduces ncome nequalty (measured by entropy measure, T c= ) by.4 per cent through ts drect (effcency) effect, but enhances t by.5 per cent through ts ndrect effect (va reducton n wor hours). Thus, happness leads to 9.7 per cent net reducton n ncome nequalty among ndvduals. Ths result seems qute sensble n vew of the fact that happness-nduced ncome share n aggregate ncome declnes as we move to hgher quntle groups of ndvduals (see Appendx Table A) 7. Happness s seen to be playng a smlar role n reducng nequalty n the subsequent years, see Table 7. Other varables that are found to be nequalty reducng based on v~ (Tc. ) are age, lvng n bg ctes and oblgatory wor hours. 7 Ths s consstent wth the result for Russa presented n Graham et al (4, ) when these authors report (p.33), In comparson to those respondents n the lowest quntles, happness matters less to future ncome for those n wealther quntles, although the dfference s just short of sgnfcant. In other words, happness matters to future ncome to those at lower levels of ncome.

15 5 Durng, poor health contrbutes.75 per cent to ncome nequalty measured by entropy ndex T c=. Ths s qute explcable as poor health causes a greater percentage reducton n ncome n lower quntles groups than the upper quntles (see Appendx Table A). We further note that the drect effect of poor health on ncome nequalty s stronger than ts ndrect effect. Both these effects have ncreased sgnfcantly over the years (Table 7) whch s consstent wth the rsng ncdence of poor health n Australa (Table ). Other varables that are found to be nequalty enhancng based on the acceptable decomposton rules are graduates, females, occupatonal structure and ndvdual-specfc and general random varables. A smlar pcture s seen based on the decomposton rule ~ v (T ) c.. The nequalty contrbutons of happness and other varables based on decomposton rules that volate the negatvty property are often qute dfferent n magntude and even opposte n sgn n few cases. For example, the entropy decomposton rule v~ (Tc ) and Gn decomposton rule v~ (G) reveal that even though the drect contrbuton of happness to nequalty s negatve, t s very low (less than -. %). The ndrect contrbuton of happness to nequalty s revealed almost zero by these decomposton rules. Smlarly, the contrbuton of poor health based on these rules s even less than oneffth of what acceptable entropy measures have revealed. As opposed to acceptable rules, both v~ (Tc ) and v~ (G) assgn postve contrbuton to age whch s hard to explan especally when we now that share of age-generated ncome n the overall ncome declnes as we move to hgher quntle groups (Appendx Table A). Thus, the nequalty contrbutons based on decomposton rules volatng negatvty condton are both unappealng and msleadng. 4. Concludng Remars Ths paper has examned the effect of happness (self reported lfe satsfacton) on ncome nequalty by explorng the causalty from happness to ncome based on panel data from

16 6 the frst fve waves (-5) of HILDA survey. Happness s hypotheszed to mpact upon the ncome generatng capacty of an ndvdual drectly by nducng effcency n earnng actvtes and ndrectly through ts effect on tme allocaton for pad wor. Both these effects of happness on ncome are tested n a model consstng of an ncome generatng functon and wor hour equaton. The ncome flows of happness and other varables obtaned from the model are nserted nto the ncome nequalty decomposton equatons (rules) to obtan ther relatve nequalty contrbutons. The drect effect of happness on ncome s postve but ts ndrect ncome effect (va wor hours) s negatve. Snce the drect effect s stronger than the ndrect effect, the net effect of happness on ncome generaton s both postve and sgnfcant. Other thngs remanng the same, an ndvdual who s completely satsfed wth lfe earns n a year $766.7 more than the one who s completely unsatsfed wth lfe. The elastcty of ncome wth respect to happness s.56 whch s much lower than the one reported n Graham et al (4) for Russa. Poor health adversely affects both the productve effcency and the wor hours of an ndvdual, leadng to a declne n ncome. Other thngs remanng the same, degree holders earn more than others, females earn less than males and those who lve n bg ctes earn more than those who lve n small ctes. The occupatonal factors affect ncome sgnfcantly. The data also provde a strong support for a hump shaped pattern of age-ncome profle. The age at whch ncome reached the hghest level turns out to be 5. The relatve nequalty contrbutons of happness and other varables are obtaned by nsertng ther ncome nflows nto the ncome nequalty decomposton equatons (rules). The results based on nequalty decomposton rules that satsfy the property of negatvty are qute sensble and consstent. Happness does reduce ncome nequalty among ndvduals. Other varables that are found to be nequalty reducng are age, lvng n bg ctes and oblgatory wor hours. Poor health, occupatonal structure and few other varables are found to be nequalty enhancng. The results based on decomposton rules that volate the property of negatvty are dfferent n magntude and even opposte n sgn n few cases and thus dstort the pcture.

17 Acnowledgements: For comments on earler drafts, the author s thanful to several partcpants at the Oxford Conference on New Drectons n Welfare and Fourth Meetng of the Socety for the Study of Economc Inequalty at Catana, Italy. The remanng errors, f any, are mne. 7

18 8 Gn Coeffcent Table : Decomposton Rules for Gn and Generalzed Entropy Measures Inequalty Measure If we arrange the ncome unts n an ascendng order (Y Y...Y n ), then the Gn coeffcent can be wrtten as the weghted sum of ncomes. G w (Y,G) Y n where w (Y, G) w (Y ; G) - s the weght assocated wth Y. μ n s mean ncome. On substtutng Y for Y we have n G S - Y S G n where Y = b Z s the regresson based ncome flow from the explanatory varable Z. v ( G) = S. S ( / ) (b Z / ) s the contrbuton of -th G regresson varable to aggregate ncome. G s the pseudo Gn whch s dfferent from the conventonal Gn snce the weght attached to Y n G corresponds to the ran of ndvdual n the dstrbuton of Y whch s, n general, not the same as her ran n the dstrbuton of Y. The Generalzed Entropy Measures c T {/ nc(c )} {(Y / ) } c, c w (Y ;Tc )Y w (Y,Tc )Y w (Y,Tc )bz v (Tc ) c c c w(y,tc ) [/{nc(c ) }](Y and c s the nequalty where ) averson parameter. v~ (G) v Decomposton rule (G) / G S G c c / G c (n ) / (n ) / Y (Y )Y v~ (Tc ) c, c (Y )Y Y

19 9 For c = : T (Y n w (Y / )ln(y,t )Y / ) w (Y where w (Y,T ) (/ n)ln (Y / ).,T )Y w (Y,T )b Z v (T ) v~ (T ) (ln Y (ln Y ln )Y ln )Y For c = : T (/ n) w (Y ln( / Y,T )Y ) w (Y,T )Y w (Y,T )b Z v (T ) ( v~ (T ) / )ln (/ n) ln (/ n) Y ln Y / Y ln Y where w (Y,T ) (/ n){(ln / ) (ln Y / Y )}. T and T are Thel s frst and second entropy measures. For c =, the generalzed entropy reduces to the half of squared coeffcent of varaton: T (/ n ) (Y )Y w (Y,T )Y w (Y,T )b where w(y,t ) (/ n )(Y ). T s the half of the squared coeffcent of varaton. Z v (T ) v~ (T ) Cov(Y,Y )/ (Y ). Ths s Shorrocs so called unque decomposton rule. Ths s also the decomposton rule of varance. Note that varance s nown for even not satsfyng the basc desrable propertes of an nequalty measure.

20 Table : A Summary Statstcs of Data and Varables Statstcs of Interest (Wave ) 3 (Wave 3) 4 (Wave 4) 5 (Wave 5) Mean Real Income (Aus$) Gn coeffcent (G) Generalsed Entropy Measures of Inequalty (T c= ) (T c=. ) (T c= ) Age (n years) Average Happness( year lagged ) Wor Hours (Average wor hours per wee) Graduates (%) Female (%) Cty (Indvduals lvng n major ctes) (%) Indvduals n Poor Health (%) Occupatonal Dstrbuton (%) Manager Professonal Whtecollar Bluecollar Other Occupatons Source: Author s calculatons

21 Table 3: Dstrbuton of Indvduals by Lfe Satsfacton Scores Happness Scores Wave Wave Wave 3 Wave 4 Wave Average Score Source: Author s calculatons Perod Table 4: Moblty of Happness (Lfe Satsfacton) Rgdty n Happness (Stayers) Downward Moblty (Downward Movers) (Percentage of Indvduals) Upward Moblty (Upward Movers) Source: Author s calculatons. Note that stayers are those whose levels of lfe satsfacton have not changed from year t to year t+. The downward (upward) movers are those who have moved downward (upward) on the lfe satsfacton scale from year t to year t+.

22 Table 5: Random Effects GLS Estmates of Income Generaton Functon Explanatory varable Coeffcent Value Robust Standard Error Happness (-) V V V Wor Hours Graduate Poor Health Female Cty Professonal Whtecollar Bluecollar Other Occupatons Constant R : Wthn =. Between =.36 Overall =.9 σ s = σ = 5.99 (fracton of varance due to s) =.6 No of observatons = 3783 Table 6 Random Effects GLS Estmates of Wor Hours Equaton Explanatory Varable Coeffcent Value Robust Standard Error Happness Poor Health Constant R : Wthn =. Between =.4 Overall =.9 σ η =8.7 σ e = 9.57 (fracton of varance due to ) =.78 Number of observatons = 3783

23 3 Table 7 Percentage Contrbutons to Income Inequalty: The Decomposton Rules based on Generalsed Entropy Indces and Gn coeffcent Contrbutory Factors Entropy Decomposton Rules satsfyng negatvty condton Entropy Decomposton Rules volatng negatvty condton ~ v (T Gn Decomposton Rules volatng negatvty condton v (G ~ v (Tc ) ~ v (Tc.) c ) ~ ) (Wave ) Age Happness: Drect Happness: Indrect Graduates Females Cty Poor Health: Drect Poor Health: Indrect Occupatonal Structure Oblgatory Wor Hours Indvdual Random 7.73 Effects General Random Effects Total 3 (Wave 3) Age Happness: Drect Happness: Indrect Graduates Females Cty Poor Health: Drect Poor Health: Indrect Occupatonal Structure Oblgatory Wor Hours Indvdual Random 8.3 Effects General Random Effects Total 4 (Wave 4) Age Happness: Drect Happness: Indrect Graduates Females Cty Poor Health: Drect Poor Health: Indrect Occupatonal Structure Oblgatory Wor Hours

24 4 Indvdual Random 8.33 Effects General Random Effects Total 5 (Wave 5) Age Happness: Drect Happness: Indrect Graduates Females Cty Poor Health: Drect Poor Health: Indrect Occupatonal Structure Oblgatory Wor Hours Indvdual Random 74.4 Effects General Random Effects Total

25 5 Income Quntles Wave Appendx Table A: Contrbutons of Explanatory Varables to Income (Percentages) Age Happness Happness nduced Wor loss Graduates Females Cty Poor Health Poor Health nduced Wor loss Occupatonal Structure Oblgatory Wor Hours Indvdual Random Effects General Random Effects All Wave 3 4 Wave 4 5 Wave All All All

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