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• #### Law of large numbers for large economies, a

Creator: Uhlig, Harald, 1961- Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) 342 [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 Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know 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 vector-valued version of the law of large numbers for economies. Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers C10 - Econometric and statistical methods : General - General
• #### Law of large numbers for large economies, a

Creator: Uhlig, Harald, 1961- Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) 342 [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 Riemann-type version of this integral, we establish (*) and interpret it as an L2-law of large numbers. Intuitively, the main idea is to integrate before drawing an W, thus avoiding well-know 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 vector-valued version of the law of large numbers for economies. Random variable, Khinchines law of large numbers, L2 law of large numbers, Riemann integral, Pettis integral, and Large numbers C10 - Econometric and statistical methods : General - General
• #### Note on the truncated normal distribution, a

Creator: Supel, Thomas M. Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) Truncated normal variate, Extreme value problem, Probability models, and Random variables C10 - Econometric and statistical methods : General - General
• #### Two difficulties in interpreting vector autoregressions

Creator: Hansen, Lars Peter. and Sargent, Thomas J. Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) 227 Rational expectations model, Continuous time analysis, and Vector autoregression C10 - Econometric and statistical methods : General - General and C62 - Mathematical methods and programming - Existence and stability conditions of equilibrium
• #### Linear optimal regulator problem with periodic coefficients, the

Creator: Todd, Richard M. Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) 207 Convergence theorem, Time-invariant system, and Time-varying system C10 - Econometric and statistical methods : General - General
• #### Demand uncertainty and decentralization : a simple pure transaction model of money

Creator: Bryant, John B. Working paper (Federal Reserve Bank of Minneapolis. Research Dept.) 168 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. Contracts, Commodity money, and Fiat money C10 - Econometric and statistical methods : General - General and E40 - Money and interest rates - General
• #### Estimating nonlinear dynamic equilibrium economies : a likelihood approach

Creator: Fernandez-Villaverde, Jesus. and Rubio-Ramírez, Juan Francisco. Joint committee on business and financial analysis This paper presents a method to perform likelihood-based 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 likelihood-based inference, either searching for a maximum (Quasi-Maximum 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 Kullback-Leibler 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. Dynamic equilibrium economies, Nonlinear filtering, Sequential Monte Carlo methods, and Likelihood-based inference 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