U.S. Family Household Momentum and Dynamics: Projections at the National Level

Abstract

In this chapter, we apply the ProFamy extended cohort-component model to project U.S. households by race from 2000 to 2050. We address important questions such as: How may demographic changes alter the number and proportion of different types and sizes of households in future years? How may demographic changes affect the living arrangements of elderly persons? We also provide evidence of “family household momentum,” which is similar to the well-known phenomenon of population momentum.

Appendices

Appendix 1: A Procedure to Adjust the o/e Rates of Marital/Cohabiting Union Status Transitions Based on the NSFH and NSFG Data to Be Consistent with the o/e Rates of Marital Status Transitions Based on the CPS, SIPP, NSFH, and NSFG Data

Although we perform adjustments for each of the race groups, men and women, respectively, we omit race and sex dimensions in the formulas for simplicity of presentation.

Let m4 _ij (x) denote the o/e rate of transition from marital status i to marital status j between age x and x + 1 based on the CPS, SIPP, NSFH, and NSFG data, using a classic 4 marital status model (i,j = 1,2,3,4, represent never-married, married, widowed, and divorced, respectively, excluding cohabitation).

m* _ij (x), observed and unadjusted age-specific o/e rates of transitions from marital/union status i to j (i,j = 1,2,3,4,5,6,7, including cohabitation, see the definitions and flow chart in Fig. 2.2 of Chap. 2), based on NSFH and NSFG data;

m _ij (x), the final adjusted age-specific o/e rates of transitions from marital/union status i to j (i,j = 1,2,3,4,5,6,7, including cohabitation) based on pooled survey data and adjusted to be consistent with m4 _ij (x);

P _ij (x), age-specific probabilities of transitions from marital/union status i to j; m _ij (x) can be analytically transferred into P _ij (x) using the standard formula in multistate demography (see, e.g., Willekens et al. 1982; Schoen 1988; Preston et al. 2001).

l _i (x), life table number of persons aged x with marital/union status i;

L _i (x), number of person-years lived in marital/union status i between ages x and x + 1;

$$ {l}_i\left(x+ 1\right)={\displaystyle \sum_k{l}_k(x){P}_{ki}(x),\kern0.5em k=1,2,\dots, 7} $$

(8.1)

$$ {L}_i(x)= 0.5\left[{l}_i(x)+{l}_i\left(x+ 1\right)\right] $$

(8.2)

The goal of the adjustment is to make the average number of marriages (including first and re-marriages) (AM7) and average number of divorces (AD7) in the life time in the 7-status life table (including cohabitation) based on NSFH and NSFG data equal to the corresponding average numbers (AM4 and AD4) in the 4-status life table (excluding cohabitation) based on all of the data from CPS, SIPP, NSFH, and NSFG.

We use the m4 _ij (x) to compute P4 _ij (x), age-specific probabilities of marital status transitions based on CPS, SIPP, NSFH, and NSFG data, using the standard formula. Based on P4 _ij (x), we construct a multi-state life table to get L4 _i (x), using formulas (8.1) and (8.2). We then use m4 _ij (x) and L4 _i (x) to compute the AM4 and AD4 in the 4 marital status model based on CPS, SIPP, NSFH, and NSFG data.

$$ AM 4=\frac{{\displaystyle \sum_{x=\partial}^{\omega}\left[L{4}_i(x)m{4}_{i2}(x)\right]}}{100,000},\kern0.5em i=1,3,4 $$

$$ AD 4=\frac{{\displaystyle \sum_{x=\partial}^{\omega}\left[L{4}_2(x)m{4}_{24}(x)\right]}}{100,000} $$

We then employ the following two-step procedure to adjust the observed o/e rates of first marriage, divorce, and remarriages (m* ₁₂ (x), m* ₅₂ (x), m* ₂₄ (x), m* ₃₂ (x), m* ₆₂ (x), m* ₄₂ (x) and m* ₇₂ (x)), but do not need to adjust the observed o/e rates of cohabitation union formation and dissolution (m* ₁₅ (x), m* ₃₆ (x), m* ₄₇ (x), m* ₅₁ (x), m* ₆₃ (x), m* ₇₄ (x)) based on NSFH and NSFG.

• Step 1. Adjustment for the o/e rates of first marriage, remarriage, and divorce

• We use the unadjusted survey-based m* _ij (x) to compute P* _ij (x), and we then use P* _ij (x) to construct an initial multi-state life table and get the initial L* _i (x) using formulas (8.1) and (8.2); we then use m* _ij (x) and L* _i (x) to compute the initial AM7* and AD7* in the 7 marital/union status model based on the NSFH and NSFG data.

  $$ AM{ 7}^{*}=\frac{{\displaystyle \sum_{x=\partial}^{\omega}\left[{L^{*}}_i(x){m^{*}}_{i2}(x)\right]}}{100,000},\kern1em i=1,3,4,5,6,7 $$

  (8.3)
  $$ AD{ 7}^{*}=\frac{{\displaystyle \sum_{x=\alpha}^{\omega}\left[{L^{*}}_2(x){m^{*}}_{24}(x)\right]}}{100,000} $$

  (8.4)

• We use AM4/AM7*, AD4/AD7* as adjustment factors (not age-specific) to adjust the corresponding age-specific o/e rates of first marriage, remarriage, and divorce for not-cohabiting and cohabiting persons at ages x (x = α to ω).

  $$ m^{\prime}_{12}(x)={m^{*}}_{12}(x) AM 4/ AM{ 7}^{*} $$

  (8.5)
  $$ m^{\prime}_{52}(x)={m^{*}}_{52}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.6)
  $$ m^{\prime}_{32}(x)={m^{*}}_{32}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.7)
  $$ m^{\prime}_{62}(x)={m^{*}}_{62}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.8)
  $$ m^{\prime}_{42}(x)={m^{*}}_{42}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.9)
  $$ m^{\prime}_{7 2}(x)={m^{*}}_{7 2}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.10)
  $$ m^{\prime}_{24}(x)={m^{*}}_{24}(x)\ AM 4/ AM{ 7}^{*} $$

  (8.11)

• Step 2. Check whether the goal of the adjustment is achieved

• We use the first adjusted m’ _ij (x) to compute the first adjusted P’ _ij (x), and use m’ _ij (x) to replace m* _ij (x) in the formulas (8.3) and (8.4) to get the first adjusted AM7’ and AD7’. If the absolute values of the relative difference between AM7’ and AM4 and between AD7’ and AD4 are all less than a selected criterion (e.g., 0.5 %), we have completed Step 2 and have the final estimates of the o/e rates (m _ij (x)). Otherwise, we will have to use the first adjusted AM7’ and AD7’ to replace AM7* and AD7* in formulas (8.5), 8.6, 8.7, 8.8, 8.9, 8.10 and (8.11) to repeat the iterative procedures described in Step 1 and Step 2 until the selected criterion is achieved.

Appendix 2: Comparisons of Summary Measures of Marital Status Life Tables (Excluding Cohabitation) Between Our Estimates Based on the Pooled Survey Data and Schoen’s Estimates Based on Vital Statistics, All Races Combined

Data set	Schoen	Surveys	Abs. Diff	% Diff
Period	1995	1990s
Women
Lifetime proportion of first marriage	0.887	0.878	−0.009	−1.0
Lifetime proportion of divorce	0.425	0.430	0.005	1.2
Lifetime proportion of remarriage of widows	0.048	0.049	0.001	2.1
Lifetime proportion of remarriage of divorcees	0.687	0.619	−0.068	−9.9
Men
Lifetime proportion of first marriage	0.831	0.841	0.01	1.2
Lifetime proportion of divorce	0.437	0.392	−0.045	−10.3
Lifetime proportion of remarriage of widows	0.123	0.132	0.009	7.3
Lifetime proportion of remarriage of divorcee	0.781	0.723	−0.058	−7.4

1. Sources: “Schoen” refers to: Schoen, R. and N. Standish (2001); “Surveys” refer to our estimates based on pooled data sets of the CPS, SIPP, NSFH and NSFG

Appendix 3: Major Parameters of Medium Forecasts, Smaller and Larger Family Household Scenarios

	White and non-Hispanic			Black and non-Hispanic			Hispanic			Asian and other non-Hispanic
	2000	2025	2050	2000	2025	2050	2000	2025	2050	2000	2025	2050
Medium mortality
Male e 0	74.9	77.8	81.1	68.7	73.6	78.5	77.4	80.0	83.0	79.7	81.9	84.6
Female e 0	80.3	83.6	86.4	75.4	80.5	84.6	83.8	86.1	88.4	85.9	87.6	89.7
Low mortality
Male e 0	74.9	79.2	83.5	68.8	75.3	81.3	77.4	81.5	85.5	79.7	83.4	86.9
Female e 0	80.3	84.5	88.0	75.5	81.7	86.5	83.9	87.1	90.0	86.0	88.6	91.2
High mortality
Male e 0	74.8	76.9	79.5	68.5	72.4	76.6	77.2	79.0	81.4	79.6	81.0	83.0
Female e 0	80.2	82.6	84.8	75.3	79.3	82.7	83.8	85.1	86.8	85.8	86.6	88.0
Medium fertility
TFR-all births	1.84	2.03	2.04	2.08	2.12	2.11	2.97	2.68	2.56	2.26	2.18	2.16
TFR(1)-1st birth	0.80	0.87	0.88	0.82	0.77	0.77	0.95	0.94	0.90	0.96	0.91	0.91
TFR(2)-2nd birth	0.66	0.71	0.71	0.67	0.66	0.66	0.90	0.81	0.77	0.73	0.70	0.69
TFR(3)-3rd birth	0.26	0.30	0.31	0.38	0.39	0.39	0.55	0.50	0.48	0.37	0.35	0.35
TFR(4)-4th birth	0.09	0.10	0.10	0.14	0.18	0.18	0.28	0.25	0.24	0.12	0.13	0.13
TFR(5)-5+ birth	0.03	0.05	0.05	0.07	0.12	0.12	0.20	0.18	0.18	0.08	0.08	0.08
Low fertility
TFR-all births	1.82	1.73	1.67	2.06	1.80	1.73	2.96	2.28	2.09	2.23	1.86	1.76
TFR(1)-1st birth	0.79	0.74	0.72	0.81	0.66	0.63	0.94	0.80	0.73	0.95	0.78	0.74
TFR(2)-2nd birth	0.65	0.60	0.58	0.67	0.56	0.54	0.89	0.69	0.63	0.72	0.59	0.57
TFR(3)-3rd birth	0.26	0.26	0.25	0.37	0.33	0.32	0.55	0.42	0.39	0.37	0.30	0.29
TFR(4)-4th birth	0.09	0.09	0.08	0.14	0.15	0.14	0.28	0.21	0.20	0.12	0.11	0.11
TFR(5)-5+ birth	0.03	0.04	0.04	0.07	0.11	0.10	0.20	0.16	0.14	0.08	0.07	0.07
High fertility
TFR-all births	1.86	2.33	2.42	2.10	2.44	2.50	2.99	3.08	3.03	2.28	2.51	2.56
TFR(1)-1st birth	0.81	0.95	0.95	0.82	0.89	0.91	0.95	0.95	0.95	0.96	0.95	0.95
TFR(2)-2nd birth	0.67	0.84	0.90	0.68	0.76	0.78	0.90	0.90	0.90	0.74	0.86	0.89
TFR(3)-3rd birth	0.26	0.36	0.38	0.38	0.45	0.46	0.56	0.66	0.63	0.38	0.43	0.45
TFR(4)-4th birth	0.09	0.12	0.13	0.14	0.20	0.21	0.28	0.33	0.32	0.13	0.16	0.17
TFR(5)-5+ birth	0.03	0.05	0.06	0.07	0.14	0.15	0.20	0.24	0.23	0.08	0.10	0.11
Medium marriage/union formation and dissolution
General marriage rate	0.0704	0.0704	0.0704	0.0362	0.0362	0.0362	0.0593	0.0593	0.0593	0.0676	0.0676	0.0676
General divorce rate	0.0292	0.0292	0.0292	0.0308	0.0308	0.0308	0.0184	0.0184	0.0184	0.0214	0.0214	0.0214
General cohabiting rate	0.1094	0.1094	0.1094	0.0775	0.0775	0.0775	0.0996	0.0996	0.0996	0.1187	0.1187	0.1187
General union break rate	0.2992	0.2992	0.2992	0.3612	0.3612	0.3612	0.2013	0.2013	0.2013	0.3341	0.3341	0.3341
Male mean age first mar.	27.59	28.45	28.45	29.99	30.57	30.57	27.38	28.14	28.14	30.54	31.12	31.12
Female mean age first mar.	25.45	26.16	26.16	28.57	29.18	29.18	25.83	26.68	26.68	28.25	28.92	28.92
Mean age at births	27.56	28.07	28.07	25.74	26.19	26.19	26.88	27.61	27.61	28.77	29.22	29.22

1. Note: The medium/low/high mortality and medium/low/high fertility parameters are those assumed in the Census Bureau’s latest population projection (Hollmann et al. 2000)