Novel Avenues for Monetary Policy: Insights from Heterogeneous Agent Models

PhD Track master project by Simone Cigna, Isabel Figueiras, Antonio Giribaldi, and Franziska Schwingeler ’22

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


This literature review focuses on the contribution of the heterogeneous agents framework to the empirical robustness of macroeconomic models. 

First, we focus on the transmission of monetary policy in an economy characterized by heterogeneous agents. We do this by analyzing both the quantitative HANK model and an analytical representation (THANK). 

Secondly, we illustrate the greater suitability of heterogeneous agent models for economic and welfare analysis in a developing country context. 

Finally, we analyze agent-based models as a potential avenue to address a higher degree of heterogeneity and complexity in the data.

HANK and THANK models

We see that the HANK model delivers a more accurate representation of the wealth and consumption distribution of households, but it still lacks important dimensions of household heterogeneity. For instance, the distribution of capital gains is crucial to match the empirical evidence on movements of capital and equity prices. 

The THANK model attempts to give a tractable representation of the HANK model, keeping a certain degree of idiosyncratic uncertainty. Yet, in contrast with the latter, it is not able to address issues related to wealth distribution and welfare.

The challenges of working with macroeconomic simulations

Even with heterogeneous agents, it is unclear whether macroeconomic simulations of the scaling up of micro-evaluations can really do more than making us aware and cautious of forces in general equilibrium that might alter the effects found in RCTs. 

Given the data-challenges in developing countries, the dimension of the informal economy, and in general the immense complexity that remains beyond what is captured in the models, the model predictions might still be inaccurate. 

The introduction of agent-based models attempts to represent more complex and richer economic dynamics. However, this enhancement comes with some drawbacks. First, researchers are left with almost arbitrary freedom in choosing the inputs of the models (e.g., behavioral equations governing agents’ behavior). Second, causal mechanisms in the model are unclear (“black box” critique).

Better models for complex, real-world economies

Despite these challenges, the introduction of the heterogeneous agents’ framework makes macroeconomic models more suitable to capture the complex dynamics in real-world economies.

We conclude that such development in the macroeconomic field is key to enhance the relevance of the models’ policy prescriptions and to improve the ability of their empirical performance.

Connect with the authors

Simone Cigna, Isabel Figueiras, Antonio Giribaldi, and Franziska Schwingeler ’22 are PhD students in Economics in the doctoral program organized jointly by Universitat Pompeu Fabra and the Barcelona School of Economics.

Author info is current as of May 2023.

About the BSE PhD Track Master’s Program

Stacking Ensemble: a quick review

Maxim Fedotov ’22 (Data Science Methodology)

Stacking Ensemble diagram
Stacking Ensemble


Stacking is an ensemble method that is used widely in supervised learning. As always, we have some training data, and the goal is to predict target variable in new data. The basic structure of the method consists in two levels of learners: base and meta. The main idea is that the meta learner combines predictions of the base learners to provide final response. That is, predictions of the base learners are used to calibrate the meta learner. The beauty of ensemble techniques in general is that they allow to capture various aspects of patterns in data using heterogeneous machine learning models. It explains why ensembles often happen to exhibit strong predictive power. For peak performance, it is recommended to have some degree of diversity in the base learners and sufficiently small correlation among their predictions.

Of course, at first sight, this algorithm might seem to be prone to overfitting. However, stacking is constructed in a way that helps to avoid it. In fact, it is the most subtle part of the technique. In short, while calibrating the meta learner, one uses cross-validation type of procedure to combine predictions of the base learners.

Along the text, I will use some pseudo-code notation which I will be defining on the go. Also, the text was prepared having in mind the stacking ensemble implementations from scikit-learn and mlens Python packages.

The purpose of this text is to describe meta learner calibration and base learners training separately to avoid any misinterpretations that could arise when mixing these components together.

I start with a short description of a basic supervised learning setup to define some notation. Then, I proceed to how the meta learner is trained. Finally, I explain how one obtains predictions for new data. Take a coffee, and let’s jump in!


In this text, we consider a basic numerical data setup. That is, we have a target which we want to predict, and the feature matrix which carries information about some features of n observations.

Let’s quickly setup some notation:

  1. Data: X_train (feature matrix), y_train (target).
  2. Number of rows (observations) in the training data: n.
  3. Cross-validation folds (disjoint): cv_folds = [fold_1, …, fold_K], such that union(cv_folds) = {1, … , n}.
  4. Base learners: base_learners = [base_learner[1], ..., base_learner[B]].
  5. Meta learner: meta_learner.
  6. New data: X_new.

The learners here are generic objects that define a learning model, that can be fitted on data via applying a generic method .fit() and predict a target via method .predict(). Whenever the learners are trained, I mention it explicitly. With this setup, we proceed to describing how one trains the meta learner.

Stacking Ensemble Training

Now, we are ready to discuss how we can train a stacking ensemble and then obtain predictions for new data.

Meta learner calibration

One first fits the base learners on the training data using a cross-validation approach. Remember, our final goal here is to train the meta learner, which will be producing final target predictions. So, we do not want to propagate information about target realisation of the i-th observation into a base learner prediction for it since doing this will cause extreme overfitting of the meta learner. That is why we use a cross-validation type of procedure. Then, when we have predictions of the base learners obtained via the cross-validation approach, we can concatenate them with our initial feature matrix, i.e. considering them as new features for the meta learner. So, to train the meta learner one simply fits it to the target given the extended feature matrix. That is it!

Now, let’s summarise the procedure into a piece of pseudo-code:

Algorithm for meta learner training

Note that construction of X_meta may vary from one implementation to another. For example, one may choose a subset of features to use (propagate) in the meta-learner. Attention: do not confuse it with a concept of feature propagation that was introduced to cope with a problem of missing data in learning on graphs by Rossi, E., Kenlay, H., Gorinova, M.I., Chamberlain, B.P., Dong, X. and Bronstein, M.M. in the paper “On the unreasonable effectiveness of feature propagation in learning on graphs with missing node features.” Learning on Graphs Conference; PMLR, 2022.

As we can see, the structure is not complex. Of course, there are some technicalities that do not appear in this demonstrative pseudo-code. For example, one might want to do the cross-validation and base learners training in parallel to speed up performance. For a reference on the state-of-the-art implementation in Python, check out scikit-learn and mlens packages.

Meta learner training

Base learners training

I describe this step after meta learner calibration on purpose so that we do not confuse the former with a part of the latter. So far, we have calibrated the meta learner. However, to predict the target for new data we also need to train the base learners so they are able to produce base predictors for the unseen dataset.

The procedure is straightforward. One can just fit each base learner on the whole training dataset X_train, y_train. Again, when training the meta learner we were using the cross-validation approach to avoid excessive overfitting of the meta learner. Here, we do not have to do this since we will use the base learners to obtain base predictions for newly occurred data that was never seen by the model. So, we can utilize all the data that we have.

Stacking Ensemble prediction

At this point, we have the meta learner calibrated and the base learners trained. So, to predict target values for newly occurred data, we first obtain the base target predictions, and then use the meta learner.

Algorithm for Stacking Ensemble prediction.


Ensemble methods are particularly known for their decent prediction performance in supervised-learning setups if used appropriately. Stacking ensembles exhibit hierarchical structure with two levels: base and meta. Meta learner combines responses of base learners to provide final prediction of a target variable. To avoid overfitting, meta learner is trained involving cross-validation type of procedure used to obtain base-learner predictions.

I discuss how stacking ensembles can be trained and used for prediction in supervised learning problems. I decided to maintain some level of generality in the method description while providing pseudo-code examples.

Hope it helps!


Connect with Maxim

Portrait of Maxim Fedotov

Maxim Fedotov ’22 is an MRes student in Statistics at Universitat Pompeu Fabra. He is an alum of the BSE Master’s in Data Science Methodology.

Burning Growth: Rising Temperatures in a Growth-at-Risk Approach

A case study of Colombia. Macroeconomic Policy and Financial Markets master project by Camila Camilo, Angie Rozada, and Carlos Sanz ’22

A hydroelectric plant in Colombia

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


The rise in global temperatures has been a growing source of concern for policy makers given its potential impact for sustainable economic activity. 

This paper explores the effects of a temperature shock on the distribution of economic growth in Colombia. Specifically, we focus on the impact of these shocks on economic risks. 

Our findings suggest the existence of asymmetries on the lower and upper tail of the distribution, indicating that higher temperatures leads to less optimistic outcomes for GDP growth. We also found negative and significant effects of temperature shocks on non-agricultural sectors. 

The results are obtained using quantile regressions under the growth-at-risk (GaR) approach and local projections.

Temperature shocks on climate-exposed sectors

The analysis of the effects of temperature shocks on climate-exposed sectors suggest that several components of GDP are affected by increased heating.

  • Manufacturing activity seems to be negatively affected after a temperature shock, specially on the upper tail.
  • The entire distribution of construction shows a strong response to temperature shocks, suggesting that labor productivity could be severely affected by heat stress in this sector.
  • The generation of electricity by hydro-powers in Colombia could be explaining the negative effects on the energy sector after an increase in temperatures.
  • Results for agriculture are not statistically significant, possibly capturing the national attempt to increase resilience of this sector in Colombia.

Protecting Colombia’s economy from the impacts of global warming

Colombia has taken some steps in the mitigation and adaptation of its economy to rising temperatures. Especially, it has adopted the National Adaptation Program, whose principal objective is to reduce the country’s vulnerability and increase its response capacity to the impacts of global warming on economic growth, especially for the agricultural sector.

The findings for this sector and the mitigating measures adopted suggest that these efforts could reduce the country’s vulnerability to rising temperatures. However, the country should take complementary strategies with a broader scope of sectors such as energy and construction, that appear to be more vulnerable to warming.

For example, in the energy sector some of 18 the adaptation measures that could be taken are optimization of the conventional energies and improvement of efficiency and diversification of energy sources and promotion of renewal energy.

Further research

Further analysis about the channels and causes of the effects of temperature shocks on GDP growth could be done for a regional level. The heterogeneity on temperature levels and on the reliance on climate-exposed sectors across different regions in Colombia could imply differential effects depending the geographical area analyzed.

Connect with the authors

Camila Camilo ’22 is a Division Chief at the Central Bank of the Dominican Republic in Santo Domingo, DR.

Angie Rozada ’22 is an Expert in the Financial Stability Department at Banco de la República (Central Bank of Colombia).

Carlos Sanz Pérez ’22 is a Trainee at the European Central Bank in Frankfurt, Germany.

Author info is current as of March 2023.

About the BSE Master’s Program in Macroeconomic Policy and Financial Markets

A Short Literature Review on Workplace Discrimination

PhD Track master project by Maddalena Grignani, Wei-Liang Hsu, Jiaxun Liu, and Georgii Zherebilov ’22

People icons in a variety of colors

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


In this literature review, we focus on workplace discrimination with particular attention paid to the hiring process. We classified the hiring process into two stages: CV-screening and interview. 

Following the theoretical discussion of stereotypes supporting the existence of discrimination, two empirical pieces of research are introduced: 

  • The first paper shows that race affects applicants’ callback rate during the screening process
  • The second study shows that the probability of a female musician being hired increases with the introduction of blind auditions. 

Lastly, from a sociological aspect, we claim that cultural similarities can affect employers’ hiring decisions, from which workplace discrimination might also appear.

Connect with the authors

All four of the authors are currently PhD students in Economics in the doctoral program organized jointly by Universitat Pompeu Fabra and the Barcelona School of Economics. (March 2023)

About the BSE Master’s Program in Economics

Sam Juthani ’13 on crypto, DLT, and digital regulation

Economics of Public Policy alum Sam Juthani ’13 recently wrote about the maturing digital assets market in a blog post for Flint Global, where he works in the Markets and Investor Advisory practice.

BSE Economics of Public Policy alum Sam Juthani ’13 recently wrote about the maturing digital assets market in a blog post for Flint Global, where he works in the Markets and Investor Advisory practice.

Sam shared an overview of his post on LinkedIn:

“I’ve blogged about the outlook for crypto and DLT (distributed ledger technology). While crypto assets might have hogged the headlines, the big story is the investment in the underlying infrastructure. And that’s where there’s a huge amount of commercial possibility – from payments, digital bonds, tokenisation, and safe, stable ways to access a wider digital economy.”

He pointed out that “2023 is a major year for digital regulation, and there’s a risk that innovation is stopped in its tracks by policymakers who are rightly trying to stop cases of abuse and fraud. This isn’t a question of balance so much as understanding – and businesses have an important role to play in helping policymakers understand that world.”

You might also like to check out Sam’s post on the collapse of FTX from November 2022: History repeats itself – first as banking, then as crypto (with Conor Sewell).

Connect with BSE authors

Portrait of Sam Juthani

Sam Juthani ’13 is a Manager at Flint Global in the UK. He is an alum of the BSE Master’s in Economics of Public Policy.

Machine learning model to predict mental health crises from electronic health records

Publication in Nature Medicine by Roger Garriga ’17 and Javier Mas ’17 (Data Science) et al

Article cover in Nature Medicine

The use of machine learning in healthcare is still in its infancy. In this paper, we describe the project we did to predict psychotic episodes together with Birmingham’s psychiatric hospital. We hope to see these sorts of applications of ML in healthcare become the new standard in the future. The technology is ready, so it’s just a matter of getting it done!

Paper abstract

The timely identification of patients who are at risk of a mental health crisis can lead to improved outcomes and to the mitigation of burdens and costs. However, the high prevalence of mental health problems means that the manual review of complex patient records to make proactive care decisions is not feasible in practice. Therefore, we developed a machine learning model that uses electronic health records to continuously monitor patients for risk of a mental health crisis over a period of 28 days. The model achieves an area under the receiver operating characteristic curve of 0.797 and an area under the precision-recall curve of 0.159, predicting crises with a sensitivity of 58% at a specificity of 85%. A follow-up 6-month prospective study evaluated our algorithm’s use in clinical practice and observed predictions to be clinically valuable in terms of either managing caseloads or mitigating the risk of crisis in 64% of cases. To our knowledge, this study is the first to continuously predict the risk of a wide range of mental health crises and to explore the added value of such predictions in clinical practice.

(You can also read about the project in more detail in this article from UPF)


Garriga, R., Mas, J., Abraha, S. et al. Machine learning model to predict mental health crises from electronic health records. Nat Med (2022).

Connect with BSE authors

Roger Garriga ’17 is a Research Data Scientist at Koa Health. He is an alum of the BSE Master’s in Data Science.

Javier Mas ’17 is Lead Data Scientist at Kannact. He is an alum of the BSE Master’s in Data Science.

Application of bagging in day-ahead electricity price forecasting and factor augmentation

Publication in Energy Economics by Kadir Özen ’21 (PhD Track) and Dilem Yıldırım

Illustration of an energy plant and city lights with market graph

This paper has been published in the November 2021 issue of the journal Energy Economics.


The electricity price forecasting (EPF) is a challenging task not only because of the uncommon characteristics of electricity but also because of the existence of many potential predictors with changing predictive abilities over time. In such an environment, how to account for all available factors and extract as much information as possible is the key to the production of accurate forecasts. To address this long-standing issue in a way that balances complexity and forecasting accuracy while facilitating the traceability of the predictor selection procedure, we propose the method of Bootstrap Aggregation (bagging). To forecast day-ahead electricity prices in a multivariate context for six major power markets, we construct a large-scale pure price model and apply the bagging approach in comparison with the popular Least Absolute Shrinkage and Selection Operator (LASSO) estimation method. Our forecasting study reveals that bagging provides substantial forecast improvements on daily and hourly scales in almost all markets over the popular LASSO estimation method. The differentiation in the forecast performances of the two approaches appears to arise, inter alia, from their structural differences in the explanatory variables selection process. Moreover, to account for the intraday hourly dependencies of day-ahead electricity prices, all our models are augmented with latent factors, and a substantial improvement is observed only in the forecasts from models covering a relatively limited number of predictors.


  • We forecast day-ahead electricity prices for major markets with a large-scale model.
  • The method of Bootstrap Aggregation (bagging) is applied to generate forecasts.
  • Bagging appears to be very competitive and promising compared to the popular LASSO.
  • Factor augmentation is proposed to capture intraday hourly dependencies of prices.
  • Augmentation improves forecasts only for models with limited number of predictors.

Connect with BSE authors


Kadir Özen ’21 is a student in the PhD Program at UPF and BSE. He is an alum of the BSE Master’s in Economics and Finance (PhD Track).

Marta Morazzoni and Andrea Sy win EEA Young Economist Award

Their paper, “Female entrepreneurship, financial frictions and capital misallocation in the US,” has also been published in the Journal of Monetary Economics.

A photo of the two BSE alumni who wrote the award-winning paper, Marta Morazzoni and Andrea Sy, posing together at UPF Ciudatella Campus where they are both PhD candidates.
EEA Young Economist Awardees Marta Morazzoni ’18 and Andrea Sy ’18

BSE alumni Marta Morazzoni and Andrea Sy (both Economics Class of 2018) received the 2021 Young Economist Award from the European Economic Association and Unicredit Foundation for their paper, “Female entrepreneurship, financial frictions and capital misallocation in the US.”

The paper has also just been published in the Journal of Monetary Economics. (It originally appeared as a Barcelona School of Economics Working Paper.)

“New empirical evidence, highly relevant policy implications”

The EEA Young Economics award committee consisted of Philipp Kircher, Giacomo Ponzetto and Antonella Trigari. They noted that “the paper addresses an extremely important topic, offers new empirical evidence from micro-level data cleverly identifying informative moments, and builds a state-of-the-art general equilibrium model to rationalize the evidence and to provide highly relevant policy implications.”

Read the award committee’s report on the EEA website

Paper abstract

We document and quantify the effect of a gender gap in credit access on both entrepreneurship and input misallocation in the US. Female entrepreneurs are found to be more likely to face a rejection on their loan applications and to have a higher average product of capital, a sign of gender-driven capital misallocation that decreases in female-led firms’ access to finance. These results are not driven by differences in observable individual or businesses characteristics. Calibrating a heterogeneous agents model of entrepreneurship to the US economy, we show that the observed gap in credit access explains the bulk of the gender differences in capital allocation across firms. Eliminating such credit imbalance is estimated to potentially increase output by 4%, and to reduce capital misallocation by 12%.

Key findings

  • In the US, female entrepreneurs receive less business funding compared to male entrepreneurs.
  • Female-owned firms operate with lower levels of assets, resulting in gender-driven capital misallocation.
  • Female-led businesses are nonetheless relatively more profitable and have better credit risk scores.
  • Removing the gender gap in business financing is estimated to potentially increase output by 4%.

Connect with BSE authors


Marta Morazzoni ’18 is a PhD candidate at Universitat Pompeu Fabra and BSE. She is an alum of the BSE Master’s in Economics.


Andrea Sy ’18 is a PhD candidate at Universitat Pompeu Fabra and BSE. She is an alum of the BSE Master’s in Economics.

Economic gains from global cooperation in fulfilling climate pledges

Publication in Energy Policy by Sneha Thube ’16 (Economics) et al

Co2, Carbon Dioxide, Carbon, Oxygen, The Atmosphere
Image by Gerd Altmann from Pixabay

My paper “Economic gains from global cooperation in fulfilling climate pledges” (with Ruth Delzeitab and Christian H.C.A. Henning) is now available online.

Paper Abstract

Mitigation of CO2 emissions is a global public good that imposes different regional economic costs. We assess the distributional effects of cooperative versus non-cooperative CO2 markets to fulfil the Nationally Determined Contributions (NDCs), considering different CO2 permit allocation rules in cooperative markets. We employ a global computable general equilibrium model based on the GTAP-9 database and the add-on GTAP-Power database. Our results show the resulting winners and losers under different policy scenarios with different permit allocation rules. We see that in 2030, we can obtain gains as high as $106 billion from global cooperation in CO2 markets. A cooperative CO2 permit market with equal per capita allowances results in considerable monetary transfers from high per capita emission regions to low per capita emission regions. In per capita terms, these transfers are comparable to the Official Development Assistance (ODA) transfers. We also disaggregate the mitigation costs into direct and indirect shares. For the energy-exporting regions, the largest cost component is unambiguously the indirect mitigation costs.


With regard to the initial NDCs, aggregate economic gains from jointly achieving the NDCs are $106bn (i.e. 60% of costs with unilateral action) in 2030. Mobilizing cooperation via Article 6 is important.

When the costs are disaggregated into direct (i.e. domestic mitigation) and indirect (i.e. due to changes in international markets) within the energy-exporters (e.g., Russia, Canada, Middle East and North Africa) the dominant cost share arises from indirect costs.

We also model a scenario using where regional allowances allocated in proportion to the regional population (aka Carbon Egalitarianism) within a global ETS. This approach addresses global equity issues, aligns incentives of all countries & eliminates free-riding problem.

Large financial transfers (~$114bn in 2030) are generated via the carbon markets are leads to welfare improvements in the developing regions. These transfers are comparable to the per capita ODA received by some countries esp. in Sub-Saharan Africa.

The approach based on per capita emission benchmarking has also been suggested by Dr. Raghuram Rajan

If global justice is considered as a global public good, which similar to GHG mitigation, is underprovided, then the principle of carbon egalitarianism could promisingly combine an additional aspect to welfare, giving an important message for policymakers.

Connect with the author


Sneha Thube ’16 is a researcher at the Kiel Institute for World Economy. She is an alum of the Barcelona GSE Master’s in Economics.

Two Macro alumni publish in the same volume of European Economic Review

Publications by Nicolò Maffei-Faccioli ’15 and Alessandro Ruggieri ’12

The September 2021 volume of the journal European Economic Review includes two publications by alumni of the BSE Macroeconomic Policy and Financial Markets Program:

Does immigration grow the pie? Asymmetric evidence from Germany

by Nicolò Maffei-Faccioli ’15 (with Eugenia Vella)

We provide empirical evidence suggesting that net migration shocks can have substantial demand effects, potentially acting like positive Keynesian supply shocks. Using monthly administrative data (2006–2019) for Germany in a structural VAR, we show that the shocks stimulate vacancies, wages, house prices, consumption, investment, net exports, and output. Unemployment falls for natives (dominant job-creation effect), driving a decline in total unemployment, while rising for foreigners (dominant job-competition effect). The geographic origin of migrants and the education level of residents matter crucially for the transmission. Overall, the evidence implies that the policy debate should focus on redistributive strategies between natives and foreigners.

(Featured on this blog as a working paper last year)

Twin Peaks: Covid-19 and the labor market

by Alessandro Ruggieri ’12 (with Jake Bradley and Adam Hal Spencer)

This paper develops a choice-theoretic equilibrium model of the labor market in the presence of a pandemic. It includes heterogeneity in productivity, age and the ability to work from home. Worker and firm behavior changes in the presence of the virus, which itself has equilibrium consequences for the infection rate. The model is calibrated to the UK and counterfactual lockdown measures are evaluated. We find a different response in both the evolution of the virus and the labor market with different lockdown policies. A laissez-faire approach results in lives lost and acts as negative shock to the economy. A lockdown policy, absent any other intervention, will reduce the lives lost but increase the economic burden. Consistent with recent evidence, we find that the economic costs from lockdown are most felt by those earning the least. Finally, we introduce a job retention scheme as implemented by the UK Government and find that it spreads the economic hardship more equitably.

Connect with BSE authors

Nicolò and Alessandro are both alumni of the Barcelona School of Economics Master’s Program in Macroeconomic Policy and Financial Markets. They both got their PhDs from the IDEA Program (UAB and BSE).


Nicolò Maffei-Faccioli ’15 is a Senior Economist at Norges Bank.


Alessandro Ruggieri ’12 is an Assistant Professor at the University of Nottingham.