Table 5.

Factor Loadings of the Measurements of Expectation of Human Capital at Age 2 Subjective Probability-Elicitation Form

Equation Number	Latent Variable	MSD Item	Factor Variances
			1	2	3	4	5	6
			2.951	2.608	2.538	2.362	2.320	0.733
			Factor Loadings
			1	2	3	4	5	6
1	μψ,3	1	0.008	−0.034	−0.041	−0.886	−0.044	0.170
2	μψ,3	2	−0.043	−0.053	−0.842	−0.062	−0.048	0.257
3	μψ,3	3	−0.048	−0.070	−0.033	−0.031	−0.861	0.277
4	μψ,3	4	−0.056	−0.831	−0.081	−0.030	−0.056	0.249
5	μψ,2	1	0.693	−0.047	−0.040	0.489	−0.100	−0.033
6	μψ,2	2	0.777	−0.054	0.369	−0.061	−0.047	0.008
7	μψ,2	3	0.827	−0.059	−0.068	−0.057	0.381	−0.002
8	μψ,2	4	0.767	0.401	−0.043	−0.051	−0.073	0.015
9	μψ,1	1	−0.024	0.054	0.045	0.841	0.056	0.300
10	μψ,1	2	0.029	0.076	0.826	0.036	0.035	0.341
11	μψ,1	3	0.008	0.056	0.046	0.045	0.841	0.347
12	μψ,1	4	0.011	0.801	0.052	0.068	0.103	0.336

Notes: This table displays the factor loadings when we estimate the latent variable model (18) in Section 2.7. The data come from the subjective elicitation form. The MSD Item 1 is “Speaks partial sentence”; MSD Item 2 is “Counts three objects correctly”; MSD Item 3 is “Knows own age and sex”; and MSD Item 4 is “Says first and last names together.” See Figure 1 for a full description of the MSD items and scenarios. We order MSD items according to their difficulty, from easiest (“speaks partial sentence”) to hardest (“says first and last name together”). The bolded factor loadings highlight the equations which factor loads. Factor 1 loads in equations 5–9 in the latent variable model (18). These equations contain identifying information for the MSE parameter μ_ψ,2. Factors 2 and 5 load on MSD item-specific equations, reflecting measurement error that correlates across scenarios within MSD items. Factor 6 loads in the equations that contain identifying information for the MSE parameters μ_ψ,1 and μ_ψ,3, thus indicating that these parameters are potentially highly correlated.