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. Author manuscript; available in PMC: 2012 Jan 1.
Published in final edited form as: Biodemography Soc Biol. 2011;57(1):88–141. doi: 10.1080/19485565.2011.580619

Table 12.

Univariate, bivariate ACE and ACE-β models for schooling and fertility

Univariate ACE Bivariate ACE ACE-β ACE-β with Meas. Err. ACE-β with IV ACE-β with IV & eyx:= 0
Model (1) (2) (3) (4) (5) (6)
axx 0.68** (0.072) 0.682** (0.072) 0.682** (0.072) 0.618** (0.068) 0.721** (0.076) 0.721** (0.076)
ayx −0.231* (0.115) −0.073 (0.14) −0.071 (0.15) 0.517 (0.38) −0.001 (0.143)
ayy 0.611** (0.105) 0.565** (0.108) 0.565** (0.107) 0.559** (0.111) 0.458** (0.138) 0.481** (0.126)
cxx 0.424** (0.106) 0.421** (0.107) 0.421** (0.107) 0.501** (0.079) 0.384** (0.131) 0.384** (0.131)
cyx — 0.094 (0.179) 0.192 (0.162) 0.196 (0.124) 0.459 (0.284) 0.155 (0.190)
cyy 0.114 (0.474) −0.069 (0.89) 0.069 (0.873) 0.108 (0.532) 0.345+ (0.184) 0.297 (0.201)
exx 0.574** (0.021) 0.574** (0.021) 0.574** (0.021) 0.471** (0.021) 0.573** (0.022) 0.573** (0.022)
eyx — −0.133 (0.037) — — 0.448 (0.298) 0†
eyy 0.745** (0.026) 0.733** (0.026) 0.733** (0.026) 0.734** (0.026) 0.742** (0.027) 0.742** (0.027)
β — — −0.232** (0.064) −0.275** (0.088) −1.025* (0.512) −0.265** (0.068)
δ — — — — 0.126** (0.045) 0.126** (0.045)
γ — — — 0.972** (0.019) — —
σ2(xo) — — — 0.114** (0.013) — —
σ2(xs) — — — 0.08** (0.012) — —
hx2
 0.476 0.478 0.478 0.446 0.515 0.515
cx2
 0.185 0.183 0.183 0.294 0.144 0.144
hy2
 0.397 0.395 0.395 0.393 0.280 0.292
cy2
 0.014 0.014 0.014 0.016 0.099 0.090
N 1,364 1,364 1,364 1,364 1,188 1,188

p-values (for model coefficients only):

**

p < .01,

*

p < .05,

+

p < .1. N refers to individuals. All variables have been converted to z-scores with mean zero and a variance of one using cohort-specific estimates of both mean and variance of each variable. The subscripts x, y indicate the variables as: x = schooling; y = fertility. The instrument for schooling used in the extended ACE IV model is a linear combination of a twin’s birth weight and the interaction of birth weight with the mother’s age at the birth of the twins and an indicator of whether the twin’s mother died before the twins reached age 20. The weights for this linear combination were obtained from a within-MZ fixed-effect regression of schooling on birth weight and its interactions (i.e., the first-stage regression of the within-MZ IV approach).

†

The coefficient eyx in Model 6 is set to zero.