Factor structure models are widely used in economics to extract latent variables, such as personality traits, and to measure their impact on outcomes of interest. The identification and inference of these models, however, highly depend on the availability of rich longitudinal data. To overcome the common problem of data scarcity, this paper proposes to combine data sets that each identify some part of the likelihood, thereby recovering the identification of the complete model. The performance of the approach is demonstrated by a Monte Carlo experiment. We apply this technique empirically to study the impact of locus of control on education and wages. Our strategy allows us to elicit the distribution of pre-market locus of control from a sample of young individuals, and to measure its impact on education and wages in a sample of adults. Our findings indicate that the effect of locus of control on wages mainly operates through education.