Ed Herbst


The goal of this course is to understand Bayesian methods used in macroeconometrics with an emphasis on the estimation of Dynamic Stochastic General Equilibrium (DSGE) models. The course will cover posterior simulation from linear and nonlinear DSGE models. We’ll start will linear(ized) models and cover the Kalman filter, importance sampling, Markov chain monte carlo (MCMC), the Metropolis-Hastings (MH) algorithm, and Sequential Monte Carlo (SMC) for static parameters. Next, we will cover the estimation of nonlinear models via the particle filter using either (particle) Markov chain monte carlo (PMCMC) or SMC\(^2\). Finally, we’ll discuss piecewise linear models. Where possible, we’ll establish high level theoretical results for the various methodologies including laws of large numbers, central limit theorems, and unbiasedness properties. (Part 2 will cover practical implementation.)

Some Background

The course will be taught via internet lectures. I’ll distribute slides before each one and hopefully technology will cooperate. The material draws from my academic research, especially monograph with Frank Schorfheide, and courses taught at Georgetown and Indiana Universities. The material should be self-contained on the slides, but I’ve added background readings and academic papers to each of the lectures.


Macroeconometrics is an intensely computational field. It is important to be proficient in at least one interpeted programming language popular in economics. While the first part of the course we’ll mainly focuse on theory, some of concepts are best illustrated using simulation, so expect some demos. I’ll talk more about this on the first day.


(Tentative) Calendar

Lecture 1: Hello, Welcome to Bayesian inference

[2020-11-09 Mon 10:00]–[2020-11-09 Mon 12:00]

Slides: A Crash Course

Topics: Introduction, decision theory, prior, posterior, credible sets, hypothesis testing.

Some background readings: HerbstSchorfheide2015; Robert1994

A few related papers:

Lecture 2: (Linear) Bayesian DSGE Models

[2020-11-10 Tue 10:00]–[2020-11-10 Tue 12:00]

Topics: State space models, the kalman filter, prior specification, prior and posterior predictive checks, linear rational expectations, impulse response functions, variance decompositions

Some background readings: HerbstSchorfheide2015

A few related papers:

Lecture 3: Monte Carlo Simulation

[2020-11-11 Wed 10:00]–[2020-11-11 Wed 12:00]

Topics: approximation of moments via posterior simulation, monte carlo methods, rejection sampling, particle systems, importance sampling, variance reduction, effective sample size

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 4: Markov Chain Monte Carlo Simulation

[2020-11-11 Wed 02:00] Topics: markov chain basics, the Metropolis-Hastings (MH) algorithm, random walk, parameter blocking

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 5: Importance Sampling on Steriods: Sequential Monte Carlo

[2020-11-12 Thu 10:00]

Topics: sequential monte carlo, correction-selection-mutation, transition kernels, tempering, generalized tempering

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 6: Estimating a Linear DSGE Model

[2020-11-13 Fri 10:00]

Topics: bimodality, model selection, variance decomposition, impulse response, effective number of draws, chain length.

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 7: Nonlinear DSGE Models

[2020-11-13 Fri 02:00]

Topics: global approximation methods, perturbation methods, stochastic volatility, Markov switching, asymmetries, occasionally binding constraints

Some background reading: HerbstSchorfheide2015; JuddBOOK

A few related papers:

Lecture 8: The Particle Filter

[2020-11-17 Tue 10:00]

Topics: nonlinear filtering, unbiasedness, bootstrap particle filter, auxiliary particle filter, conditionally-optimal particle filter, particle impoverishment, degeneracy, deterministic filters, tempering.

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 9: Bayesian Estimation of Nonlinear Models

[2020-11-18 Wed 10:00]

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 10: SMC^2

[2020-11-18 Wed 02:00]

Some background reading: HerbstSchorfheide2015

A few related papers:

Lecture 11: Piecewise Linear Model

[2020-11-18 Wed 10:00]

Lecture 12: The Next Frontier in Estimation (?)

[2020-11-19 Thu 10:00] Topics: hamiltonian dynamics, Rao-Blackwellization, automatic differentiation

A few related papers:


[HerbstSchorfheide2015] Edward Herbst & Frank Schorfheide, Bayesian Estimation of DSGE Models, Princeton University Press (2015).

[Robert1994] Christian Robert, The Bayesian Choice, Springer-Verlag (1994).

[Schorfheide2008a] @inbookSchorfheide2008a, author=“Schorfheide, Frank”, editor=“Durlauf, Steven N. and Blume, Lawrence E.”, title=“Bayesian methods in macroeconometrics”, bookTitle=“The New Palgrave Dictionary of Economics: Volume 1 - 8”, year=“2008”, publisher=“Palgrave Macmillan UK”, address=“London”, pages=“402-406”, abstract=“Macroeconometrics encompasses a large variety of probability models for macroeconomic time series as well as estimation and inference procedures to study the determinants of economic growth, to examine the sources of business cycle fluctuations, to understand the propagation of shocks, to generate forecasts, and to predict the effects of economic policy changes. Bayesian methods are a collection of inference procedures that permit researchers to combine initial information about models and their parameters with sample information in a logically coherent manner by use of Bayes' theorem. Both prior and post-data information is represented by probability distributions.”, isbn=“978-1-349-58802-2”, doi=“10.1007/978-1-349-58802-2_109”, url=“https://doi.org/10.1007/978-1-349-58802-2_109"

[delnegroschorfheide2010] @INCOLLECTIONdelnegroschorfheide2010, author = Del Negro, Marco and Schorfheide, Frank, title = Bayesian Macroeconometrics, booktitle = Handbook of Bayesian Econometrics, publisher = Oxford University Press, year = 2011, editor = Herman van Dijk and Gary Koop and John Geweke, pages = 293-389, owner = schorf, timestamp = 2010.06.25

[Sims2002] Sims, Solving Linear Rational Expectations Models, Computational Economics, 20, 1-20 (2002).

[An2007b] An & Frank Schorfheide, Bayesian Analysis of DSGE Models, Econometric Reviews, 26(2-4), 113-172 (2007). doi.

[KloekVanDijk] Kloek & van Dijk, Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo, Econometrica, 46(1), 1-19 (1978). link.

[Geweke_1989] Geweke, Bayesian Inference in Econometric Models Using Monte Carlo Integration, Econometrica, 57(6), 1317 (1989). link. doi.

[Chib1995a] Chib & Greenberg, Understanding the Metropolis-Hastings Algorithm, The American Statistician, 49, 327-335 (1995).

[ChibR08] Chib & Srikanth Ramamurthy, Tailored Randomized Block MCMC Methods with Application to DSGE Models, Journal of Econometrics, 155(1), 19-38 (2010).

[Chopin2004a] Nicolas Chopin, A Sequential Particle Filter for Static Models, Biometrika, 89(3), 539-551 (2004).

[Herbst_2014] Herbst & Schorfheide, Sequential Monte Carlo Sampling for DSGE Models, Journal of Applied Econometrics, 29(7), 1073 1098 (2014). link. doi.

[Cai_2019] Cai, Del Negro, Herbst, , Matlin, Sarfati, Schorfheide & Frank, Online Estimation of DSGE Models, SSRN Electronic Journal, (2019). link. doi.

[Smets2007] Smets & Wouters, Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach, American Economic Review, 97, 586-608 (2007).

[Schmitt-Grohe2008] Schmitt-Groh'e & Uribe, What’s News in Business Cycles?, Econometrica, 80, 2733-2764 (2012).

[JuddBOOK] Kenneth Judd, Numerical Methods in Economics, The MIT Press (1998).

[Fern_ndez_Villaverde_2016] Fernandez-Villaverde, Rubio-Ramirez, & Schorfheide, Solution and Estimation Methods for DSGE Models, Handbook of Macroeconomics, 527 724 (2016). link. doi.

[Schorfheide2005b] Schorfheide, Learning and Monetary Policy Shifts, Review of Economic Dynamics, 8(2), 392-419 (2005).

[Bora_an_Aruoba_2017] Aruoba, Cuba-Borda, & Schorfheide, Macroeconomic Dynamics Near the ZLB: A Tale of Two Countries, The Review of Economic Studies, 85(1), 87 118 (2018). link. doi.

[Gordon_1993] Gordon, Salmond & Smith, Novel approach to nonlinear/non-Gaussian Bayesian state estimation, IEE Proceedings F Radar and Signal Processing, 140(2), 107 (1993). link. doi.

[Pitt_2001] Pitt & Shephard, Auxiliary Variable Based Particle Filters, Sequential Monte Carlo Methods in Practice, 273 293 (2001). link. doi.

[Malik_2011] Malik & Pitt, Particle filters for continuous likelihood evaluation and maximisation, Journal of Econometrics, 165(2), 190 209 (2011). link. doi.

[Herbst_2019] Herbst & Schorfheide, Tempered particle filtering, Journal of Econometrics, 210(1), 26 44 (2019). link. doi.

[Fernandez-Villaverde2007a] Fern'andez-Villaverde & Rubio-Ram'irez, Estimating Macroeconomic Models: A Likelihood Approach, Review of Economic Studies, 74(4), 1059-1087 (2007).

[Andrieu_2010] Andrieu, Doucet, & Holenstein, Particle Markov chain Monte Carlo methods, Journal of the Royal Statistical Society: Series B (Statistical Methodology), 72(3), 269 342 (2010). link. doi.

[Pitt2012] Pitt, Silva, Giordani & Kohn, On some properties of Markov chain Monte Carlo simulation methods based on the particle filter, Journal of Econometrics, 171(2), 134-151 (2012). link. doi.

[Gust_2017] Gust, Herbst, , López-Salido & Smith, The Empirical Implications of the Interest-Rate Lower Bound, American Economic Review, 107(7), 1971 2006 (2017). link. doi.

[ChopinJacobPapas2012] Chopin, Jacob & Papaspiliopoulos, $SMC^2$: An Efficient Algorithm for Sequential Analysis of State-Space Models, arXiv:1101.1528, (2012).

[Neal_2011] Neal, MCMC Using Hamiltonian Dynamics, Handbook of Markov Chain Monte Carlo, (2011). link. doi.

[Hoffman_Gelman_2014] Hoffman & Gelman, The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo, Journal of Machine Learning Research, 15, 1351-1381 (2014).