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Creator: Uhlig, Harald, 1961 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 342 Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers () Xdl = U. In this paper we propose to interpret () as a Pettis integral. Using the corresponding Riemanntype version of this integral, we establish (*) and interpret it as an L2law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding wellknow measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vectorvalued version of the law of large numbers for economies.
Keyword: Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers Subject (JEL): C10  Econometric and statistical methods : General  General 
Creator: Uhlig, Harald, 1961 Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 342 Abstract: [Please note that the following Greek lettering is improperly transcribed.] If [0,1] is a measure space of agents and X a collection of pairwise uncorrelated random variables with common finite mean U and variance a , one would like to establish a law of large numbers () Xdl = U. In this paper we propose to interpret () as a Pettis integral. Using the corresponding Riemanntype version of this integral, we establish (*) and interpret it as an L2law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding wellknow measurability problems. We discuss distributional properties of i.i.d. random shocks across the population. We given examples for the economic interpretability of our definition. Finally, we establish a vectorvalued version of the law of large numbers for economies.
Keyword: Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers Subject (JEL): C10  Econometric and statistical methods : General  General 


Creator: Todd, Richard M. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 207 Keyword: Convergence theorem, Timeinvariant system, and Timevarying system Subject (JEL): C10  Econometric and statistical methods : General  General 
Creator: Bryant, John B. Series: Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Number: 168 Abstract: A simple model of backed money without a store of value function is presented, discussed, and defended. The function of money in the model is to replace complex contingent contracts traded on a centralized exchange with simple trades in decentralized markets.
Keyword: Contracts, Commodity money, and Fiat money Subject (JEL): C10  Econometric and statistical methods : General  General and E40  Money and interest rates  General 
Creator: FernandezVillaverde, Jesus. and RubioRamírez, Juan Francisco. Series: Joint committee on business and financial analysis Abstract: This paper presents a method to perform likelihoodbased inference in nonlinear dynamic equilibrium economies. This type of models has become a standard tool in quantitative economics. However, existing literature has been forced so far to use moment procedures or linearization techniques to estimate these models. This situation is unsatisfactory: moment procedures suffer from strong small samples biases and linearization depends crucially on the shape of the true policy functions, possibly leading to erroneous answers. We propose the use of Sequential Monte Carlo methods to evaluate the likelihood function implied by the model. Then we can perform likelihoodbased inference, either searching for a maximum (QuasiMaximum Likelihood Estimation) or simulating the posterior using a Markov Chain Monte Carlo algorithm (Bayesian Estimation). We can also compare different models even if they are nonnested and misspecified. To perform classical model selection, we follow Vuong (1989) and use the KullbackLeibler distance to build Likelihood Ratio Tests. To perform Bayesian model comparison, we build Bayes factors. As an application, we estimate the stochastic neoclassical growth model.
Keyword: Dynamic equilibrium economies, Nonlinear filtering, Sequential Monte Carlo methods, and Likelihoodbased inference Subject (JEL): C13  Econometric and statistical methods : General  Estimation, C11  Econometric and statistical methods : General  Bayesian analysis, C15  Econometric and statistical methods : General  Simulation methods, and C10  Econometric and statistical methods : General  General