Table 3.

Summary of simulations for decomposition of trends in the correlation between husbands’ and wives’ earnings among prevailing marriages

Trend or Simulation	By Cohort and Marital Duration		By Year
(1) Observed	n/a		${\tilde{r}}_t={\displaystyle \sum _i{r}_{ti}{w}_{ti}}$
(2) Correlation for Newlyweds –From 1970–2013 Fixed –at 1970 Values	$r_{ci}^{\text{'}}=r_{1970,1}+\left(r_{ci}-r_{c1}\right)$	where i = 1 to 30 and (c > 1970, else $r_{ci}^{\text{'}}=r_{ci}$)	$r_t^{\text{'}}={\displaystyle \sum _i{r}_{ti}^{\text{'}}{w}_{ti}}$
(3) Correlation at All Marital –Durations from 1970–2013 –Fixed at 1970 Values	$r_{ci}^{"}=r_{1970,i}$	where i = 1 to 30 and (c > 1970, else $r_{ci}^{\text{'}}=r_{ci}$)	$r_t^{\text{'}\text{'}}={\displaystyle \sum _i{r}_{ti}^{\text{'}\text{'}}{w}_{ti}}$
(4) Correlation at All Marital –Durations From 1940–2013 –Fixed at 1970 Values	$r_{ci}^{\text{'}\text{'}\text{'}}=r_{1970,i}$	where i = 1 to 30 and c ≥ 1940	$r_t^{\text{'}\text{'}\text{'}}={\displaystyle \sum _i{r}_{ti}^{\text{'}\text{'}\text{'}}{w}_{ti}}$
(5) Correlation at All Marital –Durations from 1940–2013 –Fixed at 1970 Values and –Constant Marital Duration –Distribution	n/a		$r_t^{\text{'}v}={\displaystyle \sum _i{r}_{ti}^{\text{'}\text{'}\text{'}}{w}_{1970i}}$

Note: See the text for notation.