SJTU CMGPD 2012Methodological Lecture

Day 4

Household and Relationship Variables

Outline

• Existing household variables– Identifiers– Characteristics– Dynamics– Household relationship

• Creation of new variables– Use of bysort/egen

• Household relationship variables

Identifiers

• HOUSEHOLD_ID– Identifies records associated with a household in the current

register• HOUSEHOLD_SEQ

– The order of the current household (linghu) within the current household group (yihu)

• UNIQUE_HH_ID– Identifies records associated with the same household across

different registers– New value assigned at time of household division

• Each of the resulting households gets a new, different

Characteristics

• HH_SIZE– Number of living members of the household– Set to missing before 1789

• HH_DIVIDE_NEXT– Number of households in the next register that the

members of the current household are associated with.– 1 if no division– 0 if extinction– 2 or more if division– Set to missing before 1789

histogram HH_SIZE if PRESENT & HH_SIZE > 0, width(2) scheme(s1mono) fraction ytitle("Proportion of individuals") xtitle("Number of members")

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• This isn’t particularly appealing• A log scale on the x axis would help• In STATA, histogram forces fixed width bins, even

when the x scale is set to log• We can collapse the data and plot using twoway bar

or scatter

table HH_SIZE, replacetwoway bar table1 HH_SIZE if HH_SIZE > 0,

xscale(log) scheme(s1mono) xlabel(0 1 2 5 10 20 50 100 150)

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0 1 2 5 10 20 50 100 150Household size

• What if we would like to convert to fractions?• Compute total number of households by summing table1,

then divide each value of table 1 by the total• sum(table1) returns the sum of table 1 up to the current

observation• total[_N] returns the value of total in the last observation

drop if HH_SIZE <= 0generate total = sum(table1)generate hh_fraction = table1/total[_N]twoway bar hh_fraction HH_SIZE if HH_SIZE > 0, xscale(log) scheme(s1mono) xlabel(0 1 2 5 10 20 50 100 150) ytitle("Proportion of households")

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Households as units of analysis• The previous figures all treated individuals as the units of an

analysis• Every household was represented as many times as it had

members– A household with 100 members would contribute 100 observations

• In effect, the figures represent household size as experienced by individuals

• Sometimes we would like to treat households as units of analysis– So that each household only contributes one observation per

register

Households as units of analysis• One easy way is to create a flag variable that is set to 1 only

for the first observation in each household• Then select based on that flag variable for tabulations etc.• This leaves the original individual level data intact

bysort HOUSEHOLD_ID: generate hh_first_record = _n == 1

histogram HH_SIZE if hh_first_record & HH_SIZE > 0, width(2) scheme(s1mono) fraction ytitle("Proportion of households") xtitle("Number of members")

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Another approach to plotting trends

• We can plot average household size by year of birth without ‘destroying’ the data with TABLE, REPLACE or COLLAPSE

bysort YEAR: egen mean_hh_size = mean(HH_SIZE) if HH_SIZE > 0

bysort YEAR: egen first_in_year = _n == 1twoway scatter mean_hh_size YEAR if first_in_year & YEAR >= 1775, scheme(s1mono) ytitle("Mean household size of individuals") xlabel(1775(25)1900)

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Mean household size of individuals by age

keep if AGE_IN_SUI > 0 & SEX == 2 & YEAR >= 1789 & HH_SIZE > 0

bysort AGE_IN_SUI: egen mean_hh_size = mean(HH_SIZE)

bysort AGE_IN_SUI: generate first_in_age = _n == 1twoway scatter mean_hh_size AGE_IN_SUI if

first_in_age & AGE_IN_SUI <= 80, scheme(s1mono) ytitle("Mean household size of individuals") xlabel(1(5)85) xtitle("Age in sui")

lowess mean_hh_size AGE_IN_SUI if first_in_age & AGE_IN_SUI <= 80, scheme(s1mono) ytitle("Mean household size of individuals") xlabel(1(5)85) xtitle("Age in sui") msize(small)

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bandwidth = .8

Lowess smoother

Household divisionIndividuals by next register

. tab HH_DIVIDE_NEXT if PRESENT & NEXT_3 & HH_DIVIDE_NEXT >= 0

Number of | household in | the next | available | register | Freq. Percent Cum.---------------+----------------------------------- 1 | 789,250 94.98 94.98 2 | 33,000 3.97 98.95 3 | 5,815 0.70 99.65 4 | 1,812 0.22 99.87 5 | 383 0.05 99.91 6 | 314 0.04 99.95 7 | 196 0.02 99.98 8 | 34 0.00 99.98 9 | 82 0.01 99.99 10 | 86 0.01 100.00---------------+----------------------------------- Total | 830,972 100.00

Household divisionHouseholds by next register

. bysort HOUSEHOLD_ID: generate first_in_hh = _n == 1

. tab HH_DIVIDE_NEXT if PRESENT & NEXT_3 & HH_DIVIDE_NEXT >= 0 & first_in_hh

Number of | household in | the next | available | register | Freq. Percent Cum.---------------+----------------------------------- 1 | 117,317 97.80 97.80 2 | 2,287 1.91 99.71 3 | 272 0.23 99.94 4 | 57 0.05 99.98 5 | 8 0.01 99.99 6 | 7 0.01 100.00 7 | 2 0.00 100.00 9 | 1 0.00 100.00 10 | 1 0.00 100.00---------------+----------------------------------- Total | 119,952 100.00

Household divisionExample of a simple analysis

generate byte DIVISION = HH_DIVIDE_NEXT > 1

generate l_HH_SIZE = ln(HH_SIZE)/ln(1.1)

logit DIVISION HH_SIZE YEAR if HH_SIZE > 0 & NEXT_3 & HH_DIVIDE_NEXT >= 0 & first_in_hh

logit DIVISION l_HH_SIZE YEAR if NEXT_3 & HH_DIVIDE_NEXT >= 0 & first_in_hh

. logit DIVISION HH_SIZE YEAR if HH_SIZE > 0 & NEXT_3 & HH_DIVIDE_NEXT >= 0 & first_in_hh

Iteration 0: log likelihood = -15419.716 Iteration 1: log likelihood = -14310.848 Iteration 2: log likelihood = -14127.244 Iteration 3: log likelihood = -14126.276 Iteration 4: log likelihood = -14126.276

Logistic regression Number of obs = 132688 LR chi2(2) = 2586.88 Prob > chi2 = 0.0000Log likelihood = -14126.276 Pseudo R2 = 0.0839

------------------------------------------------------------------------------ DIVISION | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- HH_SIZE | .0882472 .0016549 53.32 0.000 .0850036 .0914908 YEAR | -.0122989 .0005941 -20.70 0.000 -.0134633 -.0111345 _cons | 18.23519 1.087218 16.77 0.000 16.10428 20.3661

. logit DIVISION l_HH_SIZE YEAR if NEXT_3 & HH_DIVIDE_NEXT >= 0 & first_in_hh

Iteration 0: log likelihood = -15419.716 Iteration 1: log likelihood = -13953.268 Iteration 2: log likelihood = -13468.077 Iteration 3: log likelihood = -13463.036 Iteration 4: log likelihood = -13463.032 Iteration 5: log likelihood = -13463.032

Logistic regression Number of obs = 132688 LR chi2(2) = 3913.37 Prob > chi2 = 0.0000Log likelihood = -13463.032 Pseudo R2 = 0.1269

------------------------------------------------------------------------------ DIVISION | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- l_HH_SIZE | .1341566 .0023316 57.54 0.000 .1295867 .1387265 YEAR | -.0130866 .0005775 -22.66 0.000 -.0142185 -.0119547 _cons | 17.75924 1.048066 16.94 0.000 15.70507 19.81342------------------------------------------------------------------------------

Creating household variables• bysort and egen are your friends• Use household_id to group observations of the same

household in the same register• Let’s start with a count of the number of live individuals in

the household

bysort HOUSEHOLD_ID: egen new_hh_size = total(PRESENT)

. corr HH_SIZE new_hh_size if YEAR >= 1789(obs=1410354)

| HH_SIZE new_hh~e-------------+------------------ HH_SIZE | 1.0000 new_hh_size | 1.0000 1.0000

Creating measures of age and sex composition of the household

bysort HOUSEHOLD_ID: egen males_1_15 = total(PRESENT & SEX == 2 & AGE_IN_SUI >= 1 & AGE_IN_SUI <= 15)

bysort HOUSEHOLD_ID: egen males_16_55 = total(PRESENT & SEX == 2 & AGE_IN_SUI >= 16 & AGE_IN_SUI <= 55)

bysort HOUSEHOLD_ID: egen males_56_up = total(PRESENT & SEX == 2 & AGE_IN_SUI >= 56)

bysort HOUSEHOLD_ID: egen females_1_15 = total(PRESENT & SEX == 1 & AGE_IN_SUI >= 1 & AGE_IN_SUI <= 15)

bysort HOUSEHOLD_ID: egen females_16_55 = total(PRESENT & SEX == 1 & AGE_IN_SUI >= 16 & AGE_IN_SUI <= 55)

bysort HOUSEHOLD_ID: egen females_56_up = total(PRESENT & SEX == 1 & AGE_IN_SUI >= 56)

generate hh_dependency_ratio = (males_1_15+males56_up+females_1_15+females56_up)/HH_SIZE

bysort AGE_IN_SUI: generate first_in_age = _n == 1bysort AGE_IN_SUI: egen mean_hh_dependency_ratio =

mean(hh_dependency_ratio)twoway line mean_hh_dependency_ratio AGE_IN_SUI if first_in_age &

AGE_IN_SUI >= 16 & AGE_IN_SUI <= 55, scheme(s1mono) ylabel(0(0.1)0.5) xlabel(16(5)55) ytitle("Household dependency ratio (Prop. < 15 or >= 56 sui)") xtitle("Age in sui")

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Numbers of individuals who co-reside with someone who holds a position

. bysort HOUSEHOLD_ID: egen position_in_hh = total(PRESENT & HAS_POSITION > 0)

. tab position_in_hh if PRESENT & YEAR >= 1789

position_in | _hh | Freq. Percent Cum.------------+----------------------------------- 0 | 1,177,575 90.23 90.23 1 | 87,517 6.71 96.94 2 | 24,204 1.85 98.79 3 | 8,019 0.61 99.41 4 | 4,893 0.37 99.78 5 | 1,712 0.13 99.91 6 | 651 0.05 99.96 7 | 241 0.02 99.98 8 | 136 0.01 99.99 9 | 101 0.01 100.00------------+----------------------------------- Total | 1,305,049 100.00

. replace position_in_hh = position_in_hh > 0(49183 real changes made)

. tab position_in_hh if PRESENT & YEAR >= 1789

position_in | _hh | Freq. Percent Cum.------------+----------------------------------- 0 | 1,177,575 90.23 90.23 1 | 127,474 9.77 100.00------------+----------------------------------- Total | 1,305,049 100.00

RELATIONSHIP

• String describes relationship of individual to the head of the household– Before 1789, describes relationship to head of

yihu• This is the basis of our kinship linkage

– Automated linkage of children to their parents– Automated linkage of wives to their husband’s– All based on processing of strings describing

relationship

RELATIONSHIPCore

• e is household head• w is a household head’s wife• m is household head’s mother• f is household head’s father (usually dead)• 1yb, 2yb, 2ob etc. are head’s brothers

– Older brothers of the head are unusual• 1yz, 2yz, 2oz etc. are head’s unmarried sisters• 1s, 2s, etc. are head’s sons• 1d, 2d, etc. are the head’s unmarried daughters

RELATIONSHIPCombining codes

• More distant relationships are built up from these core relationships by combining them

• Examples– ff is grandfather of head– fm is grandmother of head– f2yb is an uncle: father’s second younger brother

• f2ybw is his wife– f2yb1s is a cousin: father’s 2nd younger brother’s 1st son– 3yb2s is a nephew: 3rd younger brother’s 2nd son– 3s2s is a grandson: 3rd son’s 2nd son

• 3s2sw is his wife

RELATIONSHIPLinking wives to husbands

• Strip the w off of a married woman’s relationship and search the household for the remaining string. – f2yb1sw -> search for f2yb1s

• Exceptions– For w, search for e– For f, search for m– For fm, search for ff– Etc.

• Basically prepare a target string, and then make use of merge on HOUSEHOLD_ID and the target

RELATIONSHIPLinking children to fathers

• In most cases, strip off the last relationship code and look for the remainder.– 1s1s -> look for 1s– ff2yb3s2s -> look for ff2yb3s

• Exceptions– e look for f– 2yb look for f– f2yb look for ff

• To link married women to their fathers-in-law, strip off w first, then convert to father’s relationship

RELATIONSHIPIndicators of specify basic relationships to head

generate head = RELATIONSHIP == “e”

generate head_wife = RELATIONSHIP == “w”

generate mother = RELATIONSHIP == “m”

generate father = RELATIONSHIP == “f”

. tab head SEX if PRESENT & SEX >= 1, row col

+-------------------+| Key ||-------------------|| frequency || row percentage || column percentage |+-------------------+

| Sex head | Female Male | Total-----------+----------------------+---------- 0 | 539,935 671,972 | 1,211,907 | 44.55 55.45 | 100.00 | 98.69 78.90 | 86.64 -----------+----------------------+---------- 1 | 7,148 179,658 | 186,806 | 3.83 96.17 | 100.00 | 1.31 21.10 | 13.36 -----------+----------------------+---------- Total | 547,083 851,630 | 1,398,713 | 39.11 60.89 | 100.00 | 100.00 100.00 | 100.00

RELATIONSHIPProcessing for distant relationships

• Strip out numbers, seniority modifiers y and b, etc.

• In a .do file, this will create a new variable with a stripped relationship

generate new_RELATIONSHIP = RELATIONSHIPlocal for_removal "1 2 3 4 5 6 7 8 9 o y w"foreach x of local for_removal {

replace new_RELATIONSHIP = subinstr(new_RELATIONSHIP,"`x'","",.)

}

ExamplesRELATIONSHIP new_RELATIONSHIPe ewf fm m1ob b1obw b1ob1s bs3yb b3ybw b3yb1s bs3yb1d bd4yb b4ybw bf2yb fbf2ybw fb

RELATIONSHIP new_RELATIONSHIPf2yb1d fbdf3yb fbf3ybw fbf3yb1s fbsf3yb1sw fbsf3yb1s1s fbssf3yb1s1d fbsdf3yb2s fbsf3yb2sw fbsf3yb2s1d fbsdf4ybw fbf4yb1sw fbsf4yb1s1d fbsdf4yb1d fbdf4yb2d fbd

generate brother = new_RELATIONSHIP = “b” & SEX == 2

generate brothers_wife = “b” & SEX == 1 & MARITAL_STATUS !=2 & MARITAL_STATUS > 0

generate sister = new_RELATIONSHIP = “z” & SEX == 1

generate male_cousin = new_RELATIONSHIP = “fbs” & SEX == 2

generate nephew = new_RELATIONSHIP = “bs” & SEX == 2

Proportions of different relationships by age

generate brother = new_RELATIONSHIP == "b"bysort AGE_IN_SUI: egen males = total(SEX == 2 & PRESENT)bysort AGE_IN_SUI: egen brothers = total(SEX == 2 & brother & PRESENT)generate proportion_brothers = brothers/malesby AGE_IN_SUI: generate first_in_age = _n == 1twoway line proportion_brothers AGE_IN_SUI if AGE_IN_SUI >= 1 & AGE_IN_SUI <= 80

& first_in_age, ytitle("Proportion of males who are brother of a head") scheme(s1mono)

bysort AGE_IN_SUI: egen heads = total(SEX == 2 & RELATIONSHIP == "e" & PRESENT)generate proportion_heads = heads/malestwoway line proportion_heads AGE_IN_SUI if AGE_IN_SUI >= 1 & AGE_IN_SUI <= 80 &

first_in_age, ytitle("Proportion of males who are household head") scheme(s1mono)bysort AGE_IN_SUI: egen sons = total(SEX == 2 & new_RELATIONSHIP == "s" & PRESENT)generate proportion_sons = sons/malestwoway line proportion_sons AGE_IN_SUI if AGE_IN_SUI >= 1 & AGE_IN_SUI <= 80 &

first_in_age, ytitle("Proportion of males who are son of a head") scheme(s1mono)

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Relationship at first appearancebysort PERSON_ID (YEAR): generate fa_nephew = new_RELATIONSHIP[1] == "bs" & AGE[1] <= 10 &

SEX == 2 & PRESENTbysort PERSON_ID (YEAR): generate fa_son = new_RELATIONSHIP[1] == "s" & AGE[1] <= 10 & SEX == 2

& PRESENTgenerate fa_nephew_head = fa_nephew & headgenerate fa_son_head = fa_son & headbysort AGE_IN_SUI: egen fa_sons = total(fa_son)bysort AGE_IN_SUI: egen fa_nephews = total(fa_nephew)bysort AGE_IN_SUI: egen fa_sons_head = total(fa_son_head)bysort AGE_IN_SUI: egen fa_nephews_head = total(fa_nephew_head)generate p_fa_sons_head = fa_sons_head/fa_sonsgenerate p_fa_nephews_head = fa_nephews_head/fa_nephewstwoway line p_fa_sons_head p_fa_nephews_head AGE_IN_SUI if AGE_IN_SUI >= 1 & AGE_IN_SUI <=

80 & first_in_age, ytitle("Proportion") scheme(s1mono)twoway line p_fa_sons_head p_fa_nephews_head AGE_IN_SUI if AGE_IN_SUI >= 1 & AGE_IN_SUI <=

80 & first_in_age, ytitle("Proportion now head") scheme(s1mono) legend(order(1 "Appeared as sons of head" 2 "Appeared as nephews of head"))

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