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Anàlisi estocàstica --- Stochastic approximation.

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Prediction (Logic) --- Stochastic approximation. --- Approximation stochastique --- Aristotle.

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A wide range of empirical applications rely on linear approximations to dynamic Euler equations. Among the most notable of these is the large and growing literature on precautionary saving that examines how consumption growth and saving behavior are affected by uncertainty and prudence. Linear approximations to Euler equations imply a linear relationship between expected consumption growth and uncertainty in consumption growth, with a slope coefficient that is a function of the coefficient of relative prudence. This literature has produced puzzling results: Estimates of the coefficient of relative prudence (and the coefficient of relative risk aversion) from regressions of consumption growth on uncertainty in consumption growth imply estimates of prudence and risk aversion that are unrealistically low. Using numerical solutions to a fairly standard intertemporal optimization problem, our results show that the actual relationship between expected consumption growth and uncertainty in consumption growth differs substantially from the relationship implied by a linear approximation. We also present Monte Carlo evidence that shows that the instrumental variables methods commonly used to estimate the parameters correct some, but not all, of the approximation bias.

Consumption (Economics) --- Stochastic approximation. --- Tax incidence. --- Mathematical models.

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Stochastic processes --- Random variables --- Variables aléatoires --- 519.245 --- Stochastic approximation. Monte Carlo methods --- 519.245 Stochastic approximation. Monte Carlo methods --- Variables aléatoires --- Variables aléatoires. --- Variables aléatoires.

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Digital computer simulation --- 519.245 --- Digital simulation --- Computer simulation --- 519.245 Stochastic approximation. Monte Carlo methods --- Stochastic approximation. Monte Carlo methods --- Artificial intelligence. Robotics. Simulation. Graphics