A Structural Investigation of Quantitative Easing
Review of Economics and Statistics, forthcoming
We provide evidence that the Federal Reserve's large-scale asset purchases actually reduce inflation. Using nonlinear Bayesian methods that fully account for the binding zero lower bound (ZLB), we estimate a macro-finance DSGE model. Counterfactual analysis suggests that by easing financing conditions, quantitative easing facilitated an increase in aggregate investment. The resulting expansion of firms’ production capacities lowered their marginal costs. These disinflationary supply side effects dominated over the inflationary effects coming from the higher aggregate demand. At the ZLB, the concomitant rise in real interest rates in turn induced a net fall in aggregate consumption.
Estimation of DSGE Models with the Effective Lower Bound
Journal of Economic Dynamics and Control, 2024
We propose a set of tools for the efficient and robust Bayesian estimation of medium- and large-scale DSGE models while accounting for the effective lower bound on nominal interest rates. We combine a novel nonlinear recursive filter with a computationally efficient piece-wise linear solution method and a state-of-the-art MCMC sampler. The filter allows for fast likelihood approximations, in particular of models with large state spaces. Using artificial data, we demonstrate that our methods accurately capture the true model parameters even with very long lower bound episodes. We apply our approach to analyze post-2008 US business cycle properties.
Monetary Policy and Speculative Asset Markets
European Economic Review, 2022
I study monetary policy in an estimated financial New-Keynesian model extended by behavioral expectation formation in the asset market. Credit frictions create a feedback between asset markets and the macroeconomy, and behaviorally motivated speculation can amplify fundamental swings in asset prices, that potentially cause endogenous, nonfundamental bubbles and bursts. Booms in asset prices improve firms financing conditions and are therefore deflationary. These features significantly improve the power of the model to replicate empirical key moments. A monetary policy that targets asset prices can dampen financial cycles and reduce volatility in asset markets (dampening effect). This comes at the cost of creating an additional channel through which asset price fluctuations transmit to macroeconomic fundamentals (spillover effect). I find that unless financial markets are severely overheated, the undesirable fluctuations in inflation and output caused by the spillover effect more than outweigh the benefits of the dampening effect.
Efficient Solution and Computation of Models with Occasionally Binding Constraints
Journal of Economic Dynamics and Control, 2022
Structural estimation of macroeconomic models and new HANK-type models with extremely high dimensionality require fast and robust methods to efficiently deal with occasionally binding constraints (OBCs). This paper proposes a novel algorithm that solves for the perfect foresight path of piecewise-linear dynamic models. In terms of computation speed, the method outperforms its competitors by more than three orders of magnitude. I develop a closed-form solution for the full trajectory given the expected duration of the constraint. This allows to quickly iterate and validate guesses on the expected duration until a perfect-foresight equilibrium is found. A toolbox, featuring an efficient implementation, a model parser and various econometric tools, is provided in the Python programming language. Benchmarking results show that for medium-scale models with an occasionally binding interest rate lower bound, more than 150,000 periods can be simulated per second. Even simulating large HANK-type models with almost 1000 endogenous variables requires only 0.2 milliseconds per period.
Revisions & Working Papers
An Ensemble MCMC Sampler for Robust Bayesian Inference
R&R @ Journal of Econometrics
This paper proposes a Differential-Independence Mixture Ensemble (DIME) sampler for the Bayesian estimation of structural models. DIME allows the estimation of models that are computationally expensive to evaluate with challenging, multimodal, high-dimensional posterior distributions and ex-ante unknonw properties. It combines the advantages of gradient-free global multi-start optimizers with the properties of Monte Carlo Markov chains to quickly explore the typical set. DIME is used to estimate a two-asset heterogeneous agent New Keynesian ("HANK") model, for the first time including the households' preference parameters. The results point towards a less accentuated role of household heterogeneity for the empirical macroeconomic dynamics.
The Hockey Stick Phillips Curve and the Zero Lower Bound
R&R @ Journal of Economic Dynamics and Control
We show that the interplay between a binding effective lower bound (ELB) and the costs of external financing weakens the disinflationary effect of financial shocks. In normal times, factor costs dominate firms' marginal costs and hence inflation; credit spreads and the nominal interest rate, which together constitute external financing costs, balance out. When nominal rates are constrained by the ELB, larger spreads can in parts offset the effect of lower factor costs on firms' price setting. The Phillips curve is hence flat at the ELB, but features a positive slope in normal times and thus an overall hockey stick shape. This mechanism also weakens the effects of forward guidance on inflation, since such policy reduces spreads and thereby financing costs.
HANK on Speed: Robust Nonlinear Solutions using Automatic Differentiation
Building on the technique of automatic differentiation, I propose an iterative method to quickly and accurately find nonlinear perfect foresight solutions for models with heterogeneous agents and many aggregate equations. The method allows to account even for strong nonlinearities such as, e.g., several aggregate and disaggregate occasionally binding constraints, and the transition dynamics of the full cross-sectional distribution. The canonical heterogeneous agent New Keynesian (HANK) model can typically be solved within a few seconds. I provide a powerful and easy-to-use reference implementation which levers the virtues of modern open source software. The importance of this paradigm for the future progress in economic research is highlighted and discussed. The method is used to study a permanent shift in redistribution policy in a large-scale HANK model featuring households portfolio choice, capital formation and many aggregate frictions. Since firms wish to deplete their capital stock, the transition path is characterized by a long-lasting deflationary episode. This effect may be intensified by a binding lower bound on interest rates or downward wage rigidity.
Rational vs. Irrational Beliefs in a Complex World
Can rational and boundedly rational agents co-exist in a competitive asset market? To answer this question, we build a highly nonlinear asset pricing model where agents hold heterogeneous beliefs. Our model features fully rational forward looking agents versus boundedly rational backward looking agents whose market shares evolve endogenously. We develop a novel numerical method to be able to solve for rational expectations equilibrium paths which are characterized by complex bubble and crash dynamics. This method is highly efficient with negligible approximation errors by construction and does not require an ex-ante truncation of the expectation horizon. Applying our method, we find that trend-extrapolators amplify small deviations from fundamentals, while rational agents anticipate market crashes after large bubbles and drive prices back to the fundamental. The interaction of different beliefs produces complex endogenous dynamics, even without any exogenous shocks.
The Empirical Performance of the Financial Accelerator since 2008
We evaluate the empirical performance of financial frictions á la Bernanke et al. (1999) during and after the Global Financial Crisis. We document that in an ex-post analysis, these frictions do not improve the canonical medium-scale DSGE model's ability to explain macroeconomic dynamics during the Great Recession. The reason is that in the estimated model with financial frictions, the drastic post-2008 collapse of investment causes firms' leverage to decline, which in the model would trigger a counterfactual narrowing of the credit spread. This would imply financial decelerator effects for the post-2008 period. Additionally, the estimated model only attributes a minor role to the associated financial shocks. These findings are confirmed independently for US and euro area data. Our analysis is based on nonlinear Bayesian methods, which account for the binding effective lower bound on nominal interest rates.
The Micro & Macro of (Unconventional) Monetary Policy: the Role of the Banking Sector
Macroeconomic theory assigns a central role to the risk free savings rate, which in reality corresponds to the banks' deposit rate that is only indirectly controlled by the central bank. Backed by Euro-Area evidence, this paper shows that the pass-through of central bank reserves and interest-on-reserves policy on equilibrium rates may be state-dependent. I develop an industrial organization model of the banking sector where loans are financed by deposits and banks use reserves to hedge against liquidity risk from holding deposits. Swapping assets and reserves (i.e. central bank asset purchases) compresses the liquidity premium between lending and deposit rate, thereby stimulating lending. If the lending rate falls by less than the liquidity premium (if investment demand is elastic, e.g. in a recession), deposit rates may increase, thereby dampening consumption. Additionally, inflation may remain subdued as lower lending rates reduce firms' financing costs. Incorporated into a DSGE model, the estimated model suggests that the effects of the ECB policy amount to 0.25 percent of quarterly GDP, and the effects on inflation is negligible.
(Unconventional) Fiscal Policy at the ELB
[work in progress, with Ralph Luetticke]
We document that the effects of the zero lower bound on nominal interest rates (ZLB) on inequality dynamics can be decomposed in two channels:
(i) the real rate channel compounds the effects of a recessionary shock on inequality while (ii) the liquidity premium channel compresses the spread between liquid and illiquid assets, therby reducing inequality. We find that the real rate channel dominates for income inequality whereas wealth inequality is driven by the liquidity premium channel. Large-scale asset purchases (LSAPs) and helicopter money drops (HDs) are moderately effective in stimulating the economy.
Their effects are greatly amplified by the duration for which the ZLB is expected to bind.
HDs are always egalitarian. For LSAPs, short ZLB durations cause a hike in consumption inequality and a longer binding ZLB causes wealth inequality to increase.
The Quantitative Effects of Taxation on Inequality Dynamics
[work in progress]
We use a novel identification strategy of functional-coefficient structural inference to estimate the relationship between different forms of taxation and the concentration of income and wealth. We find that overall, the degree of taxation has a very high explanatory power on the dynamics of top shares, in particular so the series of income taxes. This regularity holds for the US, UK, France and Sweden. We estimate that an 1 percent increase of taxation reduces the concentration of wealth in the long run by approximately 0.5 percent and concentration of income by 0.25 percent. This effect is more emphasized in the US and less so for Sweden.
Helicopter Money and the Cross-Section of Households
Low nominal rates and the saver: The dark side of lower(ing) interest rates
Policy, Media and Other Work
The Federal Reserve and quantitative easing: A boost for investment, a burden on inflation
The ETACE Virtual Appliance: An Exploratory for the Eurace@Unibi model
This paper presents the Etace Virtual Appliance. The purpose of the software package is, among others, to provide researchers the possibility to explore the dynamics of the Eurace@Unibi agent-based macroeconomic model and to encourage the reproducibility and transparency of research. The package contains various components that allow the user to initialize, simulate and analyze the model. We also give a short overview of what can be done with the Etace Virtual appliance.
In brief, my current position is fully funded by the German Reserach Foundation (DFG) as part of my reserach project on nonlinear Bayesian estimations.
With the OSE initiative I also successfully raised funding for teaching and research infrastructure.
Prior to joining the University of Bonn I spent two years as a Postdoc at the
Goethe University Frankfurt
in cooperation with the
Hoover Institution at
Stanford University (longer-term visits in Stanford in 2018 and 2019).
I completed my PhD at the
University of Amsterdam
Bielefeld University, supervised jointly by
Cars Hommes and
I won the 2017 Student Price of the Society for Computational Economics.
During my PhD I was financed by scholarships from the Bielefeld Graduate School in Economics and the DFG.
I obtained my MSc in economics from the University of Granada (top of class) and studied economics at Humboldt University Berlin at undergraduate level. I have worked as a professional guitar player and as an IT consultant for several start-up companies.
I am an enthusiast user of
Arch Linux and Python.
I support the use of free and open source software in science.
As such, I think that the access to software must be unrestrained by expensive and restrictive licenses. Implementations should be tractable, and libraries easily extensible. Openness is a booster for performance and flexibility.
I am in particular sceptical towards closed ecosystems like
and think it is a
towards future scientific
advancement ("writing reusable code in matlab is like ordering food in Klingon").
collection of links
below for some references on this issue.
As code is getting more and more important, I advertise code sharing and cooperation on new implementations. To that end I encourage the use of
(they can also be
version control systems.
Most of my codes can be found in my repositories on
My packages on
(the python packages can be installed via `pip`):
econpizza is a generic nonlinear solver for general equilibrium models, including heterogenous agent models (and including exressing and parsing models).
It uses an alternative shooting algoritm that is faster and more robust than the extended path method implemented in Dynare.
Example heterogenous agents models (and representative agent models) are provided. The package is documented in
pydsge is a Python based solution and simulation toolbox, specifically targeted to provide tools for nonlinear filtering and estimation of models with occasionally binding constraints. Its back-end for nonlinear filtering is
econsieve, a hybrid between the Particle filter and the Kalman filter. Both packages are explained in the respective
method paper above.
DIMESampler.jl (Julia) and
provide the differential-independence mixture ensemble (DIME) MCMC sampler from my paper on ensemble MCMC sampling. DIME MCMC is a (very fast) global multi-start optimizer and, at the same time, a MCMC sampler that converges to the posterior distribution. This makes any posterior mode density maximization prior to MCMC sampling superfluous. The DIME sampler is pretty robust for odd shaped, multimodal distributions. DIME MCMC is parallelizable: many chains can run in parallel, and the necessary number of draws decreases almost one-to-one with the number of chains.
I maintain a
compilation of unsolved problems in macroeconomics, please be invited to browse or
(or shoot me a short email).
Some useful econ-related links:
Why I use (and endorse) Python:
This interactive online textbook (by Roger Labbe) gives an excellent and hands-on introduction into Bayesian filtering.
This post explains very nicely how the Hamiltonian Monte Carlo (HMC) Sampler works and, en passant, shows why using Metropolis Hastings might not be a good idea for many problems in practice. Note that HMC is also behind the NUTS sampler used in Stan (a widely used sampling package), but not very feasible for many applications in structural (macro-)econometrics. The reason is that HMC requires the evaluation of the gradient at each draw, which is relatively costly for most of our likelihood functions. Have a look at the DIME sampler if you are looking for a powerful multi-purpose sampler.
Some more handy Python packages:
jax) is incredibly fast
Python is easy to debug and provides meaningful error messages
Python is a general purpose language, and (truely) object-oriented
Python is free and open source. There are no limiting licences or any additional costs
Python is matured: updates don't tend to break things and bugs are very rare.
Mayor tech firms just recently invested heavily into Python (jax by google, PyTorch by Meta, amazon, ...), so it will probably be around for longer
Python is well documented and has a huge active user base. The answers to many questions can be found on Stack Overflow
Python enforces a high code quality and readability
Knowing python is also an asset outside of academia. It is the industry standard in machine learning and big data
There are a trillion well documented and well tested packages out there for essentially any purpose
Python is very well integrated into modern software development workflows (version control and continuous integration using github, automatic documentation using sphinx)
numba - probably by now the first address to speed up your code.
jax - emerging to be the new numba.
Developed and endorsed by google.
Different philosophy featuring automatic differenciation.
emcee provides very powerful and easily paralellizable MCMC sampler.
chaospy - for quasi-random numbers and uncertainty quantification.
filterpy (by Roger Labbe, see above) is a collection of linear and nonlinear Bayesian filters.
interpolation.py (also by Pablo Winant) provides fast-as-light interpolation tools.
mail [ät] gregorboehl [döt] com
gboehl [ät] uni-bonn [döt] de
Dr. Gregor Boehl
Institute for Macroeconomics and Econometrics
University of Bonn