Relative Wage Changes and Fertility in the US

Abstract

During the last several decades, the US wage structure experienced substantial changes because of energy price shocks, increased international competition, and technological change. Katz and Murphy, among others, argued that these changes reflected a rise in demand for skilled workers and women. I use these types of relative wage changes to identify the effects of women's and men's earnings on fertility rates. Measurement error in grouped regressions is addressed by applying the Devereux unbiased-error-in-variables estimator. I find that higher earnings of men increase fertility among younger married women. Holding men's earnings constant, increased wages of married women reduce fertility among the younger women and increase it among the older women.

APPENDIX

Data Appendix 1: Construction of the wage series from CPS/ORG

Observations on wage/salary are limited to workers aged 16–64 with 1–40 years of experience, who are not self-employed, or who worked without pay, or who never worked fulltime, or who are in school. NBER methodology is used to construct a consistent hourly wage series during the entire period by dividing earnings per week by usual hours per week. This calculation gives the imputed hourly wage for weekly workers and the actual hourly wage for hourly workers. Usual weekly hours are restricted to between 1 and 99. Top-coded earnings observations are multiplied by 1.5. Full-time earnings below $67 per week in 1983 and hourly earnings below $1.675 per hour in 1983 are dropped, as are hourly wages exceeding 1/35th of the top-coded value of weekly earnings. All earnings are deflated by a monthly consumer price index deflator, base period October 1983.

Data Appendix 2: Imputation of newborns to mothers in IPUMS-CPS

In households (HH) with only one newborn who was unmatched to a mother, the potential mother was identified as the only woman aged 15–49 whose reported age of her youngest own child was missing (Step 1). In the remaining HHs, women were excluded from the set of potential mothers using family inter-relationships: the woman was excluded if the woman was the head/head spouse of the HH and newborn was not a child/stepchild of the HH head; if the woman was a sibling of the HH head and the newborn was a child of the HH head; if the woman and the newborn were both children of the HH head; and if the woman and the newborn were both grandchildren of the HH head. If only one woman remained in the HH after these exclusions, she was assigned as the mother of this newborn (Step 2). In the remaining HHs with more than one potential mother, a woman was assigned to be the mother if she was the only woman to satisfy the criterion of higher priority from a list of criteria (Step 3). Criterion priority was assigned in the following order, from most important to least important: if the woman was the only child of the HH head and the newborn was a grandchild of the HH head; if the woman was the only spouse/partner/roommate of the HH head and the newborn was a child of the HH head; if the woman was the only woman in the same family unit as the newborn; if the woman received Special Supplemental Nutrition Program for Women, Infants, and Children (WIC); if the woman reported the age of the youngest child as 1; if the woman was absent from work because of maternity leave; if the woman received child-care assistance; if the woman reported child-care problems; if the woman received alimony or child-support income; if the source of the woman's welfare income was Aid to Families with Dependent Children (AFDC)/Temporary Assistance to Needy Families (TANF); if the woman received income from alimony, contributions, other; if the woman was covered by Medicaid last year; if the woman had welfare (public assistance) income; if the woman was the only married woman in the HH; if the woman was a teenager not in school. The remaining unmatched newborns were assigned to women in accordance with the national likelihood of being a mother at a certain age, based on NCHS birthrates by age of mother.²⁹

In HHs with at least two women and at least two newborns, assignment of the women to the newborns was done in a similar manner. The only potential mother of multiple newborns was assigned as the mother of all of them (Step 4). All women in HHs with at least as many newborns as the number of potential mothers were assigned to be mothers since the national incidence of twin births was less than 3% during this period [Martin and Park 1999] (Step 5). Step 6 followed the rules of Step 2, and Step 7 followed the rules of Step 3. This imputation rendered complete assignment of newborns to potential mothers. The numbers of women identified as mothers of newborns at each imputation step are as follows:

illustration

Technical Appendix 1. The relationship between the EWALD and the 2SLS estimators

When the groups are indexed by g instead of ct, the EWALD estimator takes the form for g=1, …, G:

EWALD estimator of β was shown in Angrist [1991] to be identical to the two-stage least squares estimator, where group indicators are used as the instruments for individual-level observations on x _ict , that is,

where , , P _g =l _g (l _g ′l _g )⁻¹l _g ′, l _g is n _g dimensional vector of ones, and n _g is the number of observations in group g. Here, vectors l _g enter in the columns of the diagonal matrix of instruments Z, which is a set of dichotomous (0–1) indicators for each group g after the data are ordered by g=1, …, G:

Technical Appendix 2. The Errors-in-Variables Estimator (UEVE) [Devereux 2007]

When the groups are indexed by g instead of ct, the UEVE estimator takes the form for g=1, …, G:

where G is the number of groups, K is the number of independent variables, is the sampling error variance of x _ig , and is the sampling error covariance between x _ig and y _ig estimated from the sample of individual-level joint observations on x _ig and y _ig .

In the modified UEVE,

the measurement error in the dependent variable is assumed to be uncorrelated with the sampling error in the independent variables, that is, . In this case, EWALD is still biased because of a sampling error in the right-hand side variables with variance , which is estimated from samples of monthly individual-level CPS/ORG data.

Table A1

Table A1 Robustness checks of UEVE regressions of log age-specific fertility rates on log women's and men's earnings, married women

Table A2

Table A2 Robustness checks of UEVE regressions of log age-specific fertility rates on log women's and men's earnings, married women

Table A3

Table A3 Robustness checks of UEVE regressions of log age-specific fertility rates on log women's and men's earnings, married women