Publications by Barci & Martínez
Gibbs Sampler
Gibbs Sampler Author Andres Martinez Published May 1, 2023 Introduction Gibbs sampler is an example of the Markov Chain - Monte Carlo (MCMC) technique used to estimate Bayesian models when analytical solution is not feasible. Prior distributions reflect your knowledge of the phenomenon prior to the experiment. They are part of the model. Init...
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Problem Set 2 - QSMI
Problem 1. We estimate the following linear regression model with a sample of \(n\) observations. \[ Model \quad (1): \quad y= \beta_1 + \beta_2 x_2 + \beta_3x_3+\epsilon \] Consider a change of unites of measurement of regressor \(x_2\) (only this regressor), wher enow, each new value of this regressor is, \(x^*_2 = a\cdot x_2\) . Define \(X\...
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QSMI - Problem Set 3
Exercise 1 One of the classical assumptions is strict exogeneity. This assumption is usually presented as: \[ E(\epsilon_i|X)=0 \] (a) Re-write the assumption without using matrix \(X\), but using instead vectors xi and xj, which include, respectively, observation i and observation j of all regressors: \(E(\epsilon_i|x_i, x_j)\) Where: \(x_i=[1...
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R Markdown Households Representative household": all households are identical, both ex ante and ex post. The household maximizes \[ max \quad E[\sum_{t=0}^{\infty} \beta^t (log(c) +\eta\cdot log(1-L)) ] \\s.t. \quad K_t=(1+r_t)K_{t-1} + w_tL_t-C_t\\lim_{k\rightarrow \infty} = 0 \] We rewrite the household’s problem into Bellman equation form...
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Markov Chains Our focus is to understand a framework where the effect of the past on the future is summarized by a state. This state changes over time according to given probabilities. Discrete time Markov Chains We will first consider discrete-time Markov chains, in which the state changes at certain discrete time instants, indexed by an intege...
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VAR Implementation
Identification of Redistributive shocks and Productivity Shocks Working example: Redistributive Shocks and Productivity Shocks by Rios-Rull and Santaeulalia-Llopis (2010). The authors document the dynamic effects of productivity shocks on labor share. The so called overshooting is the situation when a productivity innovation produces a reduction ...
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knitr::opts_chunk$set(echo = TRUE) Notebook on VAR Consider the following bivariate VAR representation \[ y_t = \mu + \Gamma y_{t-1} + \epsilon_t \] where yt = [y1,t , y2,t] , µ = [µ1, µ2] , Γ is a 2-by-2 matrix with generic element γij , and ε = [ε1, ε2] with εt ∼ N(0, Σ),that is, ε1 and ε2 are potentially correlated. • For s...
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