This subproject is one of many research subprojects utilizing theresources provided by a Center grant funded by NIH/NCRR. The subproject andinvestigator (PI) may have received primary funding from another NIH source,and thus could be represented in other CRISP entries. The institution listed isfor the Center, which is not necessarily the institution for the investigator.This project investigates the dynamics of cognitive and noncognitive skill acquisition during childhood and their responses to parental inputs into their child's development. We rely on extensive data gathered in the National Longitudinal Study of Youth to estimate the parameters of a dynamic state space model of skill acquisition. The knowledge of these model parameters enable us to conduct various counterfactual ('what if') analyses that quantify to which extent skill deficits at early stages of a child's life can be overcome by parental inputs at later stages. This project expands upon the most recent studies in this field (i) by considering two types of mutually interacting skills (cognitive and noncognitive) (ii) by exploring the dynamics via a division of childhood in multiple periods (iii) by allowing for nonlinearities in the model of skill formation to enable a quantification of the level of substitutionability between different inputs or skills (iv) by anchoring the skills in a absolute scale based on objective adult outcomes (instead of arbitrarily scaled test scores) and (v) by accounting for the fact that skills and parental inputs are not perfectly measured by explicitly modeling the noisy nature of this data. This project's substantial computational requirements arise from the need to infer the true distribution of each skill and parental investments at each time period from a large number of imperfect measures of them. In earlier work, we have formally established realistic sufficient conditions that ensure that the joint distribution of the unobserved variables is uniquely determined by the type of data reported in the dataset used. However, solving the requisite equations involve high-dimensional integrals that are best carried out using Monte Carlo simulations methods, due to the highly nonlinear and high-dimensional nature of the problem. The dynamic aspect of the model calls for a specific approach called particle filtering based on Sampling Importance Resampling. We have already implemented the necessary algorithms in a FORTRAN code designed to run on a serial architecture. However, our approach offers substantial avenues for efficient parallelization that will be explored in this allocation. Our implementation of particle filtering generates a 'swarm' of particles representing specific values of the unobserved skills and inputs that are then evolved over time under the dynamic model's random disturbances. A natural parallelization scheme would devote one processor per particle. The probability of each particle path conditional on the observed but noisy data is constantly monitored in order to calculate the so-called likelihood function of the model conditional on the data and given the values of model parameters. The latter are optimized so as to obtain the maximum likelihood estimator of the model's parameters. For maximum efficiency, particles that wander in regions of very low probability are periodically removed and replaced by noisy clones of more successful particles. This 'survival-of-the-fittest' process in combination with gathering each component of the likelihood function will demand most of the interprocess communication. We expect that the parallel implementation will be straightforward and that our requested allocation should, in addition, enable us to initiate our main project, including the preliminary estimation of all model parameters and a few preliminary counterfactual analyses.
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