Gramática del creer: de las evidencias y los motivos.
2) La gramática del creer en contextos de creencia religiosa
A.1 Adults
In this section, I assess the economic signi…cance of my results by estimating the impact of a ten-hour per week per adult increase in work hours on adult obesity, as well as the percentage of the recent rise in adult obesity that can be explained by changing employment patterns.
Since the results in table 6, where I split the sample into women and men, are inconclusive, in this section I assume that the work hour e¤ect and spouse work hour e¤ect are the same for both genders. Additionally, since I was unable to reach a de…nitive conclusion about whether or not the work hour e¤ect is di¤erent for singles and married people, I assume that the work hour e¤ect does not depend on marital status. Finally, since I found that the work hour e¤ect was similar for married people whose spouses work and those whose spouses do not work, I assume the same e¤ect for the two groups. Therefore, I calibrate the equations in this section using the results from column (3) in table 3, in which I estimated that ten work hours per week increases P(Obese) by 0.012 percentage points, and that ten spouse work hours decreases P(Obese) by 0.0002 percentage points.
The overall e¤ect of an increase in women’s work hours on obesity is equal to its e¤ect on women plus its e¤ect on men. The derivative of the obesity rate with respect to women’s work hours is therefore:
dO dHW =PW dO dH +PMMM dO dHS (17)
where O is the obesity rate, HW is the average hours worked per week for women, PW is the proportion of the adult population that is female,PM is the proportion of the adult population that is male, MM is the proportion of adult men who are married, anddO=dH and dO=dHS are the derivatives of the obesity rate with respect to own work hours and spouse’s work hours. Similarly, the change in obesity with respect to a change in men’s work hours is:
dO dHM =PM dO dH +PWMW dO dHS (18)
(17) and (18) reduce to:
dO dH = dO dH +M dO dHS (19)
whereH is average hours worked by all adults andM is the proportion of the adult population that is married. After calibrating (19) using the estimates from this paper along with the marriage rate from the 2000 census, it becomes:
dO
dH = 0:012 + 0:54( 0:0002) = 0:0119
Dividing this result by the 2004 obesity rate of 0.322 shows that a ten-hour-per-week increase in the average adult’s weekly hours worked would increase the obesity rate by 3.7%. Using the estimated costs of obesity from the introduction, these numbers translate to 4,144 deaths and $4.33 billion in medical expenditures per year.
I next estimate the percentage of the increases in adult obesity (from 1961-2004) that can be explained by changes in work hours during the periods.24 The proportion of adults who
are obese because of women’s work hours (OHW) in periodtis simplydO=dHW multiplied by the average hours worked by women in t:
OHW t =HW t
dO
dHW
(20) I approximate average weekly work hours for adult women using the percentage of single and married women employed part- and full-time combined with the average work hours for part- and full-time workers:
HW t =WSt(SWF tHF +SWP tHP) +WM t(M WF tHF +M WP tHP) (21)
wheretis 1961 or 2004, WS is the proportion of women who are single,SWF is the proportion of single women who are employed full time, HF is the average weekly work hours (in units of 10) for full-time employees,SWP is the proportion of single women who are employed part time,HP is the average weekly work hours for part-time employees, and married (M) replaces single in the second half of the expression. Combining (17), (20), and (21), I obtain:
OHW t = [WSt(SWF tHF +SWP tHP) +WM t(M WF tHF +M WP tHP)] PW dO dH+PMMM dO dHS (22) The equation for men is analogous. Calibrating the parameters using data from the Current Population Survey yields the following set of equations:25
OHW;1961 = [(0.34)(0.34*4.48+0.11*2.15)+0.66(0.23*4.48+0.08*2.15)] [0.53*0.012+0.47*0.69*-0.0002] = 0:009 OHM;1961 = [(0.31)(0.49*4.48+0.04*2.15)+0.69(0.83*4.48+0.07*2.15)] [0.47*0.012+0.53*0.66*-0.0002] = 0:019 OHW;2004 = [(0.49)(0.40*4.48+0.14*2.15)+0.51(0.43*4.48+0.15*2.15)] [0.52*0.012+0.48*0.56*-0.0002] = 0:023 OHW;1961 = [(0.44)(0.55*4.48+0.07*2.15)+0.56(0.67*4.48+0.08*2.15)] [0.48*0.012+0.52*0.51*-0.0002] = 0:017
Between 1960 and 2004, the adult obesity rate rose by 19.4 percentage points. The percentages of this rise explained by changes in female and male employment patterns are:
OHW;2004 OHW;1961
0:194 100% = 7:2% and
OHM;2004 OHM;1961
0:194 100% = 1:0%
Therefore, the rise in female employment accounted for 7.2% in the rise in adult obesity
24The initial period was actually 1960-62, so I use the midpoint. 251960 marriage rates are taken from the 1960 census.
between 1961 and 2004, while the concurrent drop in male employment o¤set about one- seventh of this increase. In total, changes in work hours accounted for 6.2% of the rise in obesity during the period.
A.2 Children
I next conduct a similar analysis for children. Given the lack of conclusive results when adding the interaction terms and splitting the sample into girls and boys, in this section I assume that the work hour e¤ect is the same for girls and boys, as well as children of single and married mothers and children of married mothers whose husbands work and married mothers whose husbands do not work. Therefore, I calibrate the equations in this section using the results from the third column of table 12. The e¤ect of a mother working ten hours per week on her children’s P(Overweight) is 0.016, while the e¤ect for the mother’s spouse is 0.001.
The following equation expresses the change in the percentage of children who are over- weight if women’s work hours increase by ten per week:
dOC
dHW
=PCW
dOC
dH (23)
whereOC is the proportion of children who are overweight,PCW is the proportion of children who live with their mothers (or another female guardian), and dOC=dHW K is the change in the "overweight rate" of children who live with their mothers with respect to a change in women’s work hours. The e¤ect of a change in men’s work hours is, similarly:
dOC
dHM
=PCM
dOC
dHS (24)
where dOC=dHSP is the mother’s spouse work hour e¤ect. Calibrating (23) and (24), again using data from the 2000 census, yields:
dOC
dHW
= 0:95(0:016) = 0:015 and dOC
dHM
= 0:76(0:001) = 0:00008
Dividing by the 0.135 rate of overweight children, I …nd that a 10 hour rise in the average woman’s work hours increases the prevalence of overweight children by 11.1%, while such a rise in men’s hours increases it by only 0.06%.
I next estimate the percentage of the rise in overweight children from 1968-2001 that can be explained by changes in adult work hours.26 The proportion of children who are overweight
because of maternal employment (OCHW) in period t is:
OCHW t =HW Ct
dOC
dHW
(25) where HW KW C is the average weekly hours worked by women who live with children.
HW Ct =W CSt(SWF tHF +SWP tHP) +W CM t(M WF tHF +M WP tHP) (26)
where W CS is the proportion of women with children who are single and W CM is the pro- portion who are married. Combining (23), (25), and (26) yields:
OCHW t= [W CSt(SWF tHF +SWP tHP) +W CM t(M WF tHF +M WP tHP)]PCW
dOC
dH (27)
The equation for men is analogous. I calibrate (27) using data from the Current Population Survey:
OCHW;1968 = [0:11(0:36 4:48 + 0:12 2:15) + 0:89(0:26 4:48 + 0:09 2:15)] 0:99 0:016 = 0:022
OCHM;1968 = [0:01(0:48 4:48 + 0:04 2:15) + 0:99(0:81 4:48 + 0:07 2:15)] 0:89 0:001 = 0:003
OCHW;2001 = [0:26(0:41 4:48 + 0:14 2:15) + 0:74(0:45 4:48 + 0:15 2:15)] 0:95 0:016 = 0:035
OCHM;2001 = [0:26(0:41 4:48 + 0:14 2:15) + 0:74(0:45 4:48 + 0:15 2:15)] 0:95 0:001 = 0:002
The proportion of children who are overweight rose by 11.5 percentage points between 1968 and 2001. The percentages of this increase that can be explained by changes in female and male employment are:
OCHW;2001 OCHW;1968
0:115 = 11:3% and
OCHM;2001 OCHM;1968
0:115 = 0:9%
Limitations in the data force me to make three potentially problematic assumptions in the calculations in table 18. First, I assume that average hours worked per week for both full- and part-time workers are constant over time. Popular consensus is that the work week has lengthened; this would mean my results understate the true e¤ect. Also, I assume that people work the same number of hours regardless of whether or not they have children. Since having children often causes one or both parents to reduce work hours, the change in mothers’ work hours may be smaller than the change in women’s work hours; therefore, my results for children may be exaggerated. Finally, I assume that the derivatives estimated in this paper are constant over time. People today have far greater access to fast food and other unhealthy pre-prepared food than they did forty years ago, suggesting that the work hour e¤ect may be stronger today, and that the impact of changes in labor force participation in the 1960’s and 1970’s on body weight may have been smaller than my results suggest. On the other hand, it is possible that increased work hours induced demand for convenience food that, once created, was consumed by all. If this is the case, my derivatives understate the true e¤ect of changing labor markets on obesity. Because of these limitations, the results in table 18 should be viewed as rough estimates and not exact calculations. Nonetheless, the sizeable magnitudes suggest that the contribution of rising work hours to America’s growing obesity problem has been nontrivial.
Figure 1 – Trends in Labor Force Participation, Adult Obesity, and Overweight Children 0 10 20 30 40 50 60 70 80 90 1960 1965 1970 1975 1980 1985 1990 1995 2000 Year P er cent
Men's Labor Force Participation Rate Women's Labor Force Participation Rate Adult Obesity Rate Rate of Overweight Children (age 6-11) Rate of Overweight Adolescents (age 12-19)
Sources: Bureau of Labor Statistics, 2007; Flegal et al, 1998; Ogden et al 2006; and Hedley et al, 2004. Obesity and overweight data are not reported annually; values for missing years
Table 1 – Summary Statistics – Adults
Variable Description Mean (Std. Dev.)
BMI Body mass index = weight in kilograms divided by height in meters squared 25.966 (5.381) Obese Binary variable that equals 1 if BMI 30 kg/m2 and 0 otherwise 0.179 (0.384) Pct(Restaurants) Proportion of household food expenditures spent on food eaten in restaurants or delivered 0.263 (0.191) Exercise Estimated number of times the respondent exercises per week 3.836 (2.596) Work Hours Average number of hours, in tens, worked per week since the respondent’s previous interview 3.411 (1.933) Spouse’s Work Hours Average number of hours worked per week by the respondent’s spouse in the previous year 2.151 (2.165)
set equal to 0 if the respondent is unmarried.
Health Limitations Binary variable that equals 1 if amount or type of work is limited by health and 0 otherwise 0.074 (0.262) Real Household Wage Real (1982-84 dollars) household income divided by the sum of "Work Hours" and "Spouse’s 14.824 (71.919)
Work Hours;" set equal to 0 if this sum is 0
Real Household Income Real (1982-84 dollars) household income in units of $10,000 3.574 (6.187) Highest Grade Completed Respondent’s highest grade completed 13.388 (2.443) AFQT Score Score on the Armed Forces Qualifying Test, an IQ test administered to all survey participants 49.608 (28.815) Married Binary variable that equals 1 if the respondent is married 0.603 (0.489)
Age Respondent’s age in years 33.167 (6.063)
Number of Children Number of children the respondent has ever had 1.358 (1.296) Race: Black Binary variable that equals 1 if the respondent’s race is black 0.132 (0.338) Race: Other Binary variable that equals 1 if race is neither white nor black 0.025 (0.156) Female Binary variable that equals 1 if the respondent is female 0.490 (0.500) Pregnant Binary variable that equals 1 if the respondent is pregnant 0.063 (0.242) White Collar Binary variable that equals 1 if the respondent works in a "white collar" occupation 0.479 (0.500) Blue Collar Binary variable that equals 1 if the respondent works in a "blue collar" occupation 0.265 (0.441) Service Binary variable that equals 1 if the respondent works in a "service" occupation 0.106 (0.308)
N o te : A ll su m m a ry sta tistic s a re w e ig hte d u sin g th e N L S Y sa m p lin g w e ig hts.
Table 2 – Summary Statistics – Children
Variable Description Mean (Std. Dev.)
Overweight Binary variable that equals 1 if the child is classi…ed as "overweight" and 0 otherwise 0.147 (0.354)
Child’s Age Child’s age in years 9.740 (4.115)
Mother’s Age Mother’s age in years 35.325 (5.322)
Number of Children Number of children under age 18 living in the household of the mother 2.423 (1.154) Child’s Race: Black Binary variable that equals 1 if the child’s race is black and 0 otherwise 0.150 (0.357) Child’s Race: Hispanic Binary variable that equals 1 if the child’s race is Hispanic and 0 otherwise 0.070 (0.255) Child: Female Binary variable that equals 1 if the child is female and 0 otherwise 0.487 (0.500) Order of Birth Respondent’s order of birth to mother; 1 indicates mother’s …rst child, etc. 1.864 (1.007) Mother is Overweight or Obese Binary variable equal to 1 if the child’s mother is overweight of obese 0.476 (0.499) Mother is Obese Binary variable equal to 1 if the child’s mother is obese 0.214 (0.410)
N o te : A ll su m m a ry sta tistic s a re w e ig hte d u sin g th e N L S Y sa m p lin g w e ig hts. O th e r va ria b le s in th e ch ild re n ’s re g re ssio n s re p re se nt th e m o th e r’s va lu e s o f th e va ria b le s in ta b le 1 .
Table 3 – E¤ect of Explanatory Variables on Adults’ BMI/P(Obese)
BMI Obese
(1) (2) (3) (1) (2) (3)
Work Hours (units of 10) 0:061
(0:015) (00:178:072) (00:193:106) (00:007:001) (00:012:005) (00:020:011)
Unmarried*Work Hours 0:131
(0:137) (00:012:014)
Spouse’s Work Hours (units of 10) 0:014
(0:018) (00:108:059) 0:041(0:113) (0:002)0:006 (00:0002:006) 0:004(0:011)
Work Hours*Spouse’s Work Hours 0:021
(0:027) (00:001:003)
Health Limitations 1:111
(0:124) (01:169:416) (01:158:415) (00:061:012) 0:068(0:041) 0:067(0:041)
Real Household Wage 0:0003
(0:0003) (00:0003:0004) (00:0003:0004) (00:00006:00003) (00:0006:0004) (00:0006:0004)
Highest Grade Completed 0:116
(0:022) 0:102(0:116) 0:111(0:116) (0:002)0:014 0:001(0:010) 0:001(0:010) AFQT Score 0:008 (0:002) (00:0002:0002) Married 0:436 (0:074) 0:348(0:217) (00:094:552) (00:031:007) (00:054:024) 0:012(0:047) Age 0:043 (0:017) (00:064:054) (00:064:054) (00:004:001) (00:004:006) (00:004:006) Number of Children 0:160 (0:028) (0:097)0:307 (0:096)0:308 (00:003:003) (00:009:010) (00:009:011) Race: Black 1:488 (0:155) (00:085:010) Race: Other 0:531 (0:306) 0:030(0:020) Female 1:160 (0:101) (00:014:007) Pregnant 0:505 (0:037) (00:583:105) (00:569:105) (00:019:004) (00:022:009) (00:021:009) Number of Observations 85,298 24,758 24,758 85,298 24,758 24,758 R2 0.092 0.009 0.009 0.053 0.003 0.003
N o te s: (1 ) R a n d o m e ¤ e c ts, (2 ) L o n g d i¤ e re n c e s, (3 ) L o n g d i¤ e re n c e s w ith inte ra c tio n te rm s, * * * re p re se nts sta tistic a lly sig n i… c a nt a t th e 1 % le ve l; * * 5 % le ve l; * 1 0 % le ve l. A ll re g re ssio n s in c lu d e a se rie s o f b in a ry va ria b le s th a t re p re se nt inte rv ie w ye a rs; th e y a re d i¤ e re n c e d in (2 ) a n d (3 ). H e te ro ske d a stic ity -ro b u st
Table 4 – E¤ect of Working an Additional 10 Hours per Week on Adults’ BMI and P(Obese)
BMI Obese
Person is single 0:063
(0:104) 0(0::008008)
Person is married; spouse does not work 0:193
(0:106) (00::011)020
Person is married; spouse works 40 hours per week 0:277
(0:102) (00::007)015
Table 5 – E¤ect of Spouse Working an Additional 10 Hours per Week on Adults’ BMI and P(Obese)
BMI Obese Person does not work 0:041
(0:113) 0(0::004011)
Person works 40 hours per week 0:125
(0:061) (00:006):001
N o te s fo r ta b le s 4 a n d 5 : S ta n d a rd e rro rs a re in p a re nth e se s. * * * re p re se nts sta tistic a lly sig n i… c a nt a t th e 1 % le ve l; * * 5 % le ve l; * 1 0 % le ve l.
Table 6 – E¤ect of Work Hours Variables on the BMI and P(Obese) of Women and Men
Women Men
BMI Obese BMI Obese Work Hours (units of 10) 0:259
(0:108) 0(0::005007) (00::138095) (00::009)017
Spouse’s Work Hours (units of 10) 0:083
(0:116) 0(0::004009) (00::081060) (00:008):002
Number of Observations 12,510 12,510 12,248 12,248
R2 0.014 0.018 0.006 0.003
Table 7 – E¤ect of Work Hours Variables on the BMI and P(Obese) of Adults – Hours Grouped by Occupation Types
BMI Obese Work Hours*White Collar (units of 10) 0:158
(0:085) (00::005)012
Work Hours*Blue Collar (units of 10) 0:147
(0:072) 0(0::009007)
Work Hours*Service (units of 10) 0:048
(0:094) (00:009):002
Number of Observations 24,739 24,739
R2 0.009 0.003
Table 8 – E¤ect of Work Hours Variables on the BMI of "At Risk" and "Not At Risk" Individuals
At Risk Not At Risk Work Hours (units of 10) 0:357
(0:139) 0(0::037052)
Spouse’s Work Hours (units of 10) 0:189
(0:106) 0(0::043058)
Number of Observations 13,351 11,407
R2 0.010 0.015
N o te s fo r ta b le s 6 , 7 , a n d 8 : * * * re p re se nts sta tistic a lly sig n i… c a nt a t th e 1 % le ve l; * * 5 % le ve l; * 1 0 % le ve l. B o th re g re ssio n s a re lo n g d i¤ e re n c e s ave ra g e s w ith o u t inte ra c tio n te rm s. A ll re g re ssio n s in c lu d e a se rie s o f b in a ry va ria b le s th a t re p re se nt inte rv ie w ye a rs; th e se va ria b le s a re d i¤ e re n c e d . S ta n d a rd e rro rs a re in p a re nth e se s; a ll sta n d a rd e rro rs a re h e te ro ske d a stic ity -ro b u st a n d c lu ste re d by in d iv id u a l. O b se rva tio n s a re w e ig hte d u sin g th e N L S Y sa m p lin g w e ig hts; w e ig hts a re th e ave ra g e o f th e w e ig hts fro m th e tw o p e rio d s u se d to c re a te th e d i¤ e re n c e s.
Table 9 – Regression Output for First Stage of Instrumental Variables Analysis – E¤ect of Explanatory Variables on the Proportion of Food Expenses Spent on
Restaurants and the Frequency of Exercise
Pct(Restaurants) Exercise
(1) (2) (1) (2)
Work Hours (units of 10) 0:010
(0:001) (00:001):009 (0:0020):103 (0:019)0:110
Spouse’s Work Hours (units of 10) 0:010
(0:001) (00:001):009 (00:023):050 0(0::036023)
Health Limitations 0:006
(0:005) (00::007)007 (0:1114):078 (0:100)1:053
Real Household Wage 0:0003
(0:0001) 0(0::001002)
Real Household Income 0:003
(0:000) (00:010):069
Highest Grade Completed 0:005
(0:001) (00:001):004 (00:017):172 (00:015):152 AFQT Score 0:0002 (0:0001) (00:0001):0002 (00:002):007 (00:002):006 Age 0:002 (0:001) (0:0001):002 (00:013):022 (00:015):023 Number of Children 0:031 (0:001) (0:0002):031 (00:031):036 (00:031):035 Race: Black 0:014 (0:004) (00:004):014 (0:0080):415 (0:092)0:401 Race: Other 0:010 (0:007) 0(0::009006) (00:162):096 (00:157):113 Female 0:019 (0:004) (0:0004):018 (0:0098):689 (0:088)0:676 Pregnant 0:008 (0:004) (00:005):009 (00:123):091 (00:159):111 Number of Observations 17,758 17,727 6,361 6,350 R2 0.125 0.130 0.088 0.094
N o te s: * * * re p re se nts sta tistic a lly sig n i… c a nt a t th e 1 % le ve l; * * 5 % le ve l; * 1 0 % le ve l. B o th re g re ssio n s in c lu d e a lin e a r tim e tre n d . S ta n d a rd e rro rs a re in p a re nth e se s; a ll sta n d a rd e rro rs a re h e te ro ske d a stic ity -ro b u st. O b se rva tio n s