The Time Use of Mothers in the United States at the Beginning of the 21st Century

Appendix D: Theoretical Model Used in Chapter 4

143 Appendix D Theoretical Model Used in Chapter 4 Maximize individual utility, U(tmL , tfL , CS, G) Subject to: Household production function: G = G(tmhp , tfhp , X; θ) Child Services production function: CS = CS(tmcc , tfcc , tcc , CX; φ) Money budget constraint: PX X + Pcctcc + PCXCX = wmtmem + wf tfem + V Mother’s time constraint: T = tmem + tmhp + tmcc +tmL+ tms Husband’s time constraint: T = tfem + tfhp + tfcc +tfL+ tfs Child time constraint: CT = tmcc + tfcc + tcc + tscc G denotes adult consumption goods. CS denotes child services. T is total adult time while CT is total child time. tiL is leisure, tihp is home production time, and ticc is caregiving time of the parent , tiem is time in employment, and tis is time in all other time uses (mainly sleep and personal care but also time in human capital investments and unpaid work-related activities) for i = m or f where m denotes mother and f denotes father. tcc is paid nonparental child care time (purchased at price Pcc) and tscc is secondary child caregiving time (time when the parent is engaged in another primary time use activity but is also watching the child). X is purchased goods which are inputs in the production of adult consumption goods. q is an efficiency parameter for the production of adult consumption goods. PX is the price of X goods. CX is purchased goods that are inputs in the production of child services. φ is an efficiency parameter for the production of child services. PCX is the price of CX goods. wi is the hourly wage of each parent. V is nonearned income. 144 Connelly and Kimmel Note that often in models involving paid child care tcc = tmem but that is not the case here. However, some adult must be with the child at all times unless self care is included in secondary child care. The model results in mother’s time use demand equations that depend on the price of her time, the price of the husband’s time, and the spouse’s time use in the same activity. tj = f(Em, Ef| D, S)for j = hp, cc, L Em denotes economic factors of the mother. Ef denotes economic factors of her husband (i.e., the father). D denotes demographic factors. S denotes time/spatial factors. ...