I show that the Parameterized Expectations Algorithm (PEA) can be naturally generalized via the bias-corrected Monte Carlo (bc-MC) operator, initially proposed to solve economic models using neural networks. When combined with a parameterized …
This paper provides a comprehensive review of the fast-expanding literature on household heterogeneity in macroeconomic models. It not only examines the main mechanisms through which household heterogeneity affects the transmission of monetary …
Artificial Neural Networks (ANNs) are powerful tools that can solve dynamic programming problems arising in economics. In this context, estimating ANN parameters involves minimizing a loss function based on the model's stochastic functional …
We develop an urban search-and-matching model. There is a central city, where all firms and jobs are located, and a continuum of peripheral cities. The population endogenously splits between migrants (who relocate from their hometown to the central …
In my previous post, I discussed how the the simulated method of moments can be used to estimate parameters without using the likelihood function. This method is useful because many “real-life” applications result in untractable likelihood functions. In this post, I use the same toy example (estimation of the mean of a mutlivariate normal random variable) and show how to use the parallel computing capabilities of Julia and MomentOpt to speed-up the estimation.
As Thomas Sargent said:
“A rational expectations equilibrium model is a likelihood function”
However in many cases, the likelihood function is too complicated to be written down in closed form. To estimate the structural parameters of a given model, one can still use Monte-Carlo methods. In this post, I would like to describe the simulated method of moments (SMM), which is a widely used simulation-based estimation technique.
A Simple Setting I want to illustrate the SMM in one of the simplest settings you could think of: the estimation of the mean of a normal density with known variance. Let’s say we have access to a (bi-dimensional) time series and we suspect it to be normally distributed with mean \([a,\,b]'\) and variance the identity matrix \(\mathcal{N}([a,\,b]',\,I_2)\). Let’s pretend that we have no idea on how to write down the associated likelihood function. The good news is that if we have access to a “black box” that generates \(i.i.d\) draws from the law \(\mathcal{N}([c,\,d]',\,I_2)\), it is enough for us to do inference.
A large class of economic models involves solving for functional equations of the form:
A well known example is the stochastic optimal growth model. An agent owns a consumption good \(y\) at time \(t\), which can be consumed or invested. Next period’s output depends on how much is invested at time \(t\) and on a shock \(z\) realized at the end of the current period. One can think of a farmer deciding the quantity of seeds to be planted during the spring, taking into account weather forecast for the growing season.
Dynare is a rich software to solve, estimate and analyse rational expectation models. While it was originally designed to solve and estimate DSGE models, Dynare has also recently been used to solve and simulate heterogeneous agents models (see Winberry and Ragot for two very different approaches). Below is a simple example on how to solve and simulate a simple RBC model using Dynare.
A simple model The economy is composed of a representative agent who maximizes his expected discounted sum of utility by choosing consumption \(C_t\) and labor \(L_t\) for \(t=1,...,\infty\)
This paper explores some of the potential determinants of efficiency and contestability in the banking systems of major emerging countries, using a sample of 24 countries over the period 2004 -2013. Efficiency is estimated using both stochastic …