2,612 research outputs found

    Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity

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    This paper investigates identification and inference in a nonparametric structural model with instrumental variables and non-additive errors. We allow for non-additive errors because the unobserved heterogeneity in marginal returns that often motivates concerns about endogeneity of choices requires objective functions that are non-additive in observed and unobserved components. We formulate several independence and monotonicity conditions that are sufficient for identification of a number of objects of interest, including the average conditional response, the average structural function, as well as the full structural response function. For inference we propose a two-step series estimator. The first step consists of estimating the conditional distribution of the endogenous regressor given the instrument. In the second step the estimated conditional distribution function is used as a regressor in a nonlinear control function approach. We establish rates of convergence, asymptotic normality, and give a consistent asymptotic variance estimator.

    Feedback control of unstable cellular solidification fronts

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    We present a numerical and experimental study of feedback control of unstable cellular patterns in directional solidification (DS). The sample, a dilute binary alloy, solidifies in a 2D geometry under a control scheme which applies local heating close to the cell tips which protrude ahead of the other. For the experiments, we use a real-time image processing algorithm to track cell tips, coupled with a movable laser spot array device, to heat locally. We show, numerically and experimentally, that spacings well below the threshold for a period-doubling instability can be stabilized. As predicted by the numerical calculations, cellular arrays become stable, and the spacing becomes uniform through feedback control which is maintained with minimal heating.Comment: 4 pages, 4 figures, 1 tabl
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