Nonparametric Estimation and Identification in Non-Separable Models Using Panel Data
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We present non-parametric identification results for panel models in the presence of a vector of unobserved heterogeneity that is not additively separable in the structural function. We exploit the time-invariance and finite dimension of the heterogeneity to achieve identification of a number of objects of interest with the panel length fixed. Identification does not require that the researcher have access to an instrument that is uncorrelated with the unobserved heterogeneity. Instead the identification strategy relies on an assumption that some lags and leads of observables are independent conditional on the unobserved heterogeneity and some controls. The identification strategy motivates an estimation procedure based on penalized sieve minimum distance estimation in the non-parametric instrumental variables framework. We give conditions under which the estimator is consistent and derive its rate of convergence. We present Monte Carlo evidence of its efficacy in finite samples.
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