Can adjustment costs of intangible capital explain the decline in the labor share?

Economics master project by Pierre Coster, Pia Ennuschat, Raquel Lorenzo, Giacomo Stazi, and Robert Wojciechowski ’20

Two tiny figurines of construction workers stand on an asphalt road

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


Labor share, once thought to be a constant, has experienced a secular decline in many developed economies. We investigate whether adjustment costs to intangible capital can be used to explain this trend. We develop a simple partial equilibrium model with a profit maximizing firm that produces using a three factor CES production function and faces convex adjustment costs to intangible capital. We find an intuitive expression for the steady state labor share as a function of parameters and the steady state level of investment in intangible capital.

We then run simulations to better understand the behaviour of the labor share in our model. Somewhat surprisingly, we find that adjustment costs do not affect the steady state labor share for any given elasticity of substitution. However, their presence creates a strong relationship between the labor share and the elasticity of substitution. We also find a number of short-run dynamics that are affected by the level of adjustment costs.

Labor share trends over the last 60 years in the United States. Source: AMECO


We find that our model with adjustment costs leads to a very clear relationship between the elasticity of substitution and the labor share. Therefore, one could use it to explain the secular decline in the labor share as a result of a falling elasticity of substitution in presence of convex adjustment costs to intangible capital. However, in our simple model there does not appear to be a meaningful relationship between the level of convex adjustment and the steady state labor share. Moreover, adjustment costs affect a number of interesting short-run dynamics. The level of adjustment costs changes the responsiveness of the labor share to variations in the price of inputs. Lastly in our simple model the volatility of the price process does not alter the steady state labor share, even though it does matter for short-run dynamics.

We see room for further research in the following directions. Our analysis assumes perfectly competitive markets. A model of monopolistic competition in the goods market could lead to long-run effects of the level of adjustment costs on the labor share. Karabarbounis and Neiman, 2013 showed that in such a model price decreases can explain part of the decrease in the labor share. Therefore, analysing the effect of adjustment costs in the context of monopolistic competition seems promising. Another potential avenue is the generalization of the analysis to a general equilibrium setting.

Understanding endogenous changes in wages that were set to be fixed throughout our analysis, could be important in explaining the changes in the labor share.

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About the Barcelona GSE Master’s Program in Economics

Broadstreet: a blog for inter-disciplinary conversation about Historical Political Economy

Vicky Fouka ’10 (Economics) is an editor of this new meeting point for HPE researchers

A map shows the original location of the Broad Street Pump

About the project

Broadstreet is a blog dedicated to the study of historical political economy (HPE). Its goal is to foster conversations across disciplines in the social sciences, namely economics and political science, but also history, sociology, quantitative methods, and public policy. Correspondingly, its editors (and guest contributors) are drawn from these respective disciplines. 

Given the boundaries that typically exist across academic disciplines, scholars who work on similar subjects – like HPE – rarely talk to one another or read each other’s work. Our hope in starting Broadstreet is to break down some of these artificial boundaries, generate true cross-disciplinary dialogues, and produce better and more wide-ranging HPE research.

The blog’s name, Broadstreet, is a nod to the legendary John Snow and his study of the 1854 cholera outbreak in London. Snow found convincing evidence for a previously unproven water-born theory of cholera transmission, with a rigorous yet interdisciplinary approach — using detailed socio-economic data, ethnography, historical patterns of disease transmission, and early techniques of causal inference. The Broad Street water pump in London’s Soho district was not only a meeting place for the diverse residents of the neighborhood, but served as the focal point for Snow’s interdisciplinary breakthrough. While the Broad Street pump is no more, the legacy of this innovative research lives on. We hope that Broadstreet will be go-to location for all those with interests in HPE.

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Vicky Fouka ’10 (Economics) is Assistant Professor of Political Science at Stanford University. She is an alum of the Barcelona GSE Master’s in Economics and earned her PhD in Economics at GPEFM (UPF and Barcelona GSE).

Check out her most recent post on Broadstreet, “The Great Northward Migration and Social Transformation, Part I” which looks at the mass exodus of more than 5 million Black Americans from the Southern United States between 1915 and 1970.

The Effectiveness of Debt Relief in Mitigating the Macroeconomic Consequences of Natural Disasters

ITFD master project by Emma Howard, Kean Murphy, Wouter Nientker, Karim El-Ouaghlidi, and Harry Schmidt ’20

land affected by severe drought
Photo: CNN

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


Using a dynamic panel fixed effects model, we find that increases of ODA of above 2% of GDP have significant effects on the economic growth of African countries in the immediate aftermath of severe natural disasters. This is a surprising result because we do not find that ODA in times of relative stability has a significant effect on GDP. This suggests that debt relief, at least through the channel of significant increases in ODA, is an effective instrument in promoting post-disaster recovery, even though its effectiveness in raising economic growth more generally is limited. Since increases in ODA inflows of above 2% of GDP only occurred after 1/3 of the disasters we studied, we recommend that international financial institutions concentrate ODA flows on countries that had been afflicted by severe disasters. 


One of the biggest challenges facing developing Sub-Saharan African economies is their vulnerability to severe natural disasters such as droughts and floods. Not only do they face on average over 50 disasters a year, but their economies’ over-reliance on agricultural production and weak institutional capacity cause them to experience the effects of these disasters particularly acutely. Worryingly, this vulnerability is likely to rise in the coming years, as the earth warms and climate change increases the number and severity of extreme climatic events. 

While it is difficult for countries to prevent natural disasters, since they tend to arise from exogenous climate conditions, they can take steps to mitigate these adverse consequences through post-disaster rehabilitation. To do so, governments require sufficient fiscal space so that they can borrow and spend without jeopardising budgetary sustainability. However, many African countries suffer from persistently high levels of debt, with 33 of the 39 countries in the Heavily Indebted Poor Countries scheme located on the continent. This constrains government spending on humanitarian relief and reconstruction, which can leave countries unable to recover from the devastation. 

In view of these twin trends – African economies’ vulnerability to natural disasters and their crippling levels of debt – any channel that reduces a country’s debt burden and hence increases its fiscal space should theoretically encourage faster economic recovery. This suggests that debt relief can be a vital policy instrument in mitigating the negative effects of natural disasters. However, corruption and inefficient resource allocation mean that its effectiveness may be constrained in practice. To explore the role of debt relief further, we employ a dynamic panel fixed effects model across the most severe 25 floods and 68 droughts in Africa from 1978 to 2013. As a robustness check, we also include an Anderson-Hsiao style GMM estimation procedure. We define debt relief as any policy that reduces the need for governments to issue new debt or repay existing debt, particularly in the aftermath of a natural disaster. In the context of this paper, this includes debt forgiveness, debt rescheduling and/or increased official development assistance (ODA). Furthermore, we run two different specifications of debt relief: first, using a dummy variable which indicates any instance of the aforementioned forms of debt relief; and second, using a continuous variable for ODA inflows alone. 

Main findings

Surprisingly, when we run our first specification, we find that debt relief in general does not have a statistically significant impact on economic growth. Additionally, ODA inflows in times of relative stability do not have significant effects on economic growth. Instead, they only reduce debt-to-GDP growth, suggesting that they are merely used by governments to pay off existing debt. This is in line with previous research by both Mejia (2014) and Raddatz (2009), who found at most weak evidence that either debt relief in the aftermath of disasters or ODA in general is effective in boosting economic growth. 

In contrast, we find that increases in inflows of ODA of above 2% of a country’s annual GDP, when provided in the year of or immediately after severe disasters, do have statistically significant positive effects on economic growth (see Figure 1). These findings are similarly observed when we interact our ODA variable with the continuous measure of disaster severity. For a given level of ODA, the effectiveness of post-disaster ODA increases in the severity of the underlying disasters. Furthermore, ODA inflows no longer have statistically significant effects on debt-to-GDP growth. This suggests that, unlike in regular times, ODA flows are used fruitfully by governments after disasters to bolster economic recovery rather than to pay off existing debt. 

Figure 1

This is a notable result because it suggests that debt relief, at least through the channel of ODA, is an effective instrument to promote post-disaster recovery. This result differs from that found by previous research because we focus on ODA increases that a) were larger than 2% of GDP and b) occurred in the aftermath of severe natural disasters. This helps us isolate the specific role of ODA in promoting post-disaster recovery from its general effectiveness as a form of economic stimulus to boost growth. 

Policy implications

Our findings suggest that policymakers in international financial institutions such as the OECD or IMF should step up efforts to increase ODA inflows to developing countries when severe natural disasters hit. This not only has the direct effect of reducing the loss of lives, but is also vital for poverty reduction by ensuring that these countries return rapidly to their existing balanced growth path. Otherwise, countries risk experiencing persistent economic slowdown and skyrocketing debt due to the disasters, which would in turn lead to a vicious cycle of mounting debt and stagnant growth. Instead, increased ODA flows can substitute for the domestic shortfall in resources available to countries to rehabilitate the economy by providing emergency relief to citizens and rebuilding damaged infrastructure. 

Current attempts at mitigating such disasters are relatively limited: in our sample of 92 severe disasters in Africa between 1978 and 2013, large increases of ODA greater than 2% of GDP only occurred after 32 of these disasters. This is surprisingly infrequent, especially considering that we focus only on the largest of disasters which should have ample international media coverage. As highlighted above, larger increases in ODA have greater cumulative effects on the economy, especially for more severe disasters. As this effect is not observed when we study ODA inflows in times of stability or inflows below 2% of GDP, we recommend that existing ODA programmes prioritise large flows to countries which have just suffered from severe natural disasters. This is because the marginal benefit of these targeted flows in promoting development is likely higher than general flows to countries that are relatively stable. 

Finally, although our paper focuses on floods and droughts in Africa, we believe that our results can be generalized to other types of disasters. Although further research is needed to fully establish the causal mechanism by which debt relief improves post-disaster outcomes, it is likely that it will have a similar positive impact in rehabilitating economies that face disasters which leave them with high levels of debt and significantly lower budgetary revenue. Most notably, it suggests that significant increases in ODA flows can play a vital role in helping developing economies devastated by the COVID-19 pandemic by allowing them to mitigate its adverse effects. 


Mejia, S. A. (2014, July). Debt, Growth and Natural Disasters A Caribbean Trilogy (IMF Working Papers No. 14/125). International Monetary Fund. Retrieved from 14-125.html 

Raddatz, C. (2009). The Wrath of God: Macroeconomic Costs of Natural Disasters. The World Bank. Retrieved from 

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About the Barcelona GSE Master’s Program in International Trade, Finance, and Development

Eliciting preferences for truth-telling in a survey of politicians

Publication in PNAS by Katharina Janezic ’16 (Economics) and Aina Gallego (IBEI and IPEG)


Honesty is one of the most valued traits in politicians. Yet, because lies often remain undiscovered, it is difficult to study if some politicians are more honest than others. This paper examines which individual characteristics are correlated with truth-telling in a controlled setting in a large sample of politicians. We designed and embedded a game that incentivizes lying with a non-monetary method in a survey answered by 816 Spanish mayors. Mayors were first asked how interested they were in obtaining a detailed report about the survey results, and at the end of the survey, they had to flip a coin to find out whether they would be sent the report. Because the probability of heads is known, we can estimate the proportion of mayors who lied to obtain the report.

We find that a large and statistically significant proportion of mayors lied. Mayors that are members of the two major political parties lied significantly more. We further find that women and men were equally likely to lie. Finally, we find a negative relationship between truth-telling and reelection in the next municipal elections, which suggests that dishonesty might help politicians survive in office.

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6 Real Policy Solutions to the U.S. Mental Health Crisis

Article by Patricia Paskov ’18 (Economics) on Medium

image: piranka / Getty Images

In a post on Medium’s Elemental, Patricia Paskov outlines six mental health policy recommendations for the United States during Covid-19 and beyond:

  • Destigmatize mental health
  • Widen accessibility of mental health care
  • Break down barriers to telehealth care
  • Strengthen labor policies for low-skilled workers
  • Build a body of rigorous data and research
  • Harness artificial intelligence and predictive analytics

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Patricia Paskov ’18 is an Impact Evaluation Analyst at The World Bank. She is an alum of the Barcelona GSE Master’s in Economics.

A Flexible Fix? Assessing the Labour Market Penalties to Flexible Working in Britain

EPP master project by Charley Lamb, Jana Eir Víglundsdóttir and Alessandro Zicchieri ’20

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


Our paper examines the wages and career prospects of employees in flexible work arrangements (FWAs). Using the British Household Panel Survey, we analyse the effect of being in a FWA on hourly wages and the likelihood of promotion. We use the occupational share of employees in FWAs before and after the introduction of “Right to Request” (R2R) legislation as an instrument to control for sample selection. Applying our instrument in pooled OLS and linear regression models, we find that flexible workers, particularly women, may receive higher wages than their non-flexible counterparts. This supports theoretical arguments that FWAs could increase labour productivity.


Our findings imply that there may be no penalty associated with workers adopting flexible working practices. Our instrumental variables wage model implies there could in fact be a reverse effect: coefficients changed from negative. In particular, the effect of FWAs was significant and large for women, leading to an approximately 9 percent increase in their wages. Those in FWAs have higher wages than those in conventional working arrangements, controlling for variables such as occupational choice, hours worked, and personal circumstances (including number of children and educational background). Similarly, we cannot reject the hypothesis that FWA has no impact on career progression, when modelling promotions as a 10 percent pay rise versus the previous year.

Income Distribution and FWA

We do find some evidence that working flexibly decreases the difference in wage outcomes between men and women. The approximately 9 percent increase in wages associated with our FWA variable in our women-only specification compares to a 5 percent increase in our men-only specification. We cannot reject the hypothesis that FWAs have no effect on men’s wages. We find evidence women in FWAs are paid significantly more than their non-flexible counterparts.

This begs the question: why do those in FWAs appear to achieve better labour market outcomes than those not in FWAs? This appears to contradict some findings of economic theory on compensating wage differentials and the effects of similar working arrangements, such as part-time work. Further, the fact that our wage findings were highly significant for women (and not for men) appears to go against the gendered difference in how men and women use flexible working; men are more likely to use FWAs to improve their career outcomes, whilst women use FWAs to accommodate care needs.

First, we could have captured a range of productivity benefits that often come alongside flexible working practices. The increase in schedule control may improve worker satisfaction and hence productivity in itself, but is also often associated with better workplace practices such as improved management (Bloom et al, 2010). The increase in flexible working seen across many sectors (such as services) following the R2R reforms may have disproportionately benefited them ahead of other, less “flexible” sectors. The UK, with more than two-thirds of its labour force in the service sector, may have seen a productivity rise associated with more employees having greater scheduling control. Increases in productivity may then have been passed on to flexible-working employees in the form of pay rises above the mean.

Second, our model may neglect important social trends. The R2R legislation may have accompanied shifting attitudes towards flexible working, which spurred an increase in the compensation afforded to flexible workers. Future research examining historical trends in the remuneration of employees in FWAs could provide more detail on this.

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About the Barcelona GSE Master’s Program in Economics of Public Policy

The Impact of the Sharing Economy on Housing Rental Prices: The Case of Airbnb in Barcelona

Economics master project by Marc Agustí, Magnus Asmundsson, Christof Bischofberger, Pablo de Llanos, Alberto Font, and Lucía Kazarian ’20

Source: Airbnb

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

Peer-to-peer home-sharing platforms such as Airbnb are a new phenomenon which many researchers consider to be responsible for significant disruptions in the housing market. Prior to the introduction of these platforms into the rental market, hotels were the primary supplier of short-term rentals, while residential properties almost exclusively operated on the long-term rental market. The introduction of short-term rental platforms like Airbnb, allows homeowners to choose either to supply on the short-term or the long-term rental markets. As a result, when residential properties are moved to the short-term rental market, the quantity of housing supplied on the long-term rental market decreases, inducing an upward pressure on long-term rents.

In our paper, we offer a novel approach to investigate the extent to which the expansion of the sharing economy is responsible for increases in long-term rents and prices on the housing market. To this end, we construct a theoretical framework for the housing market that allows for spillover effects between neighborhoods, and other local externalities caused by tourism. The model allows for the short-term housing market devoted to tourism to impact both long-term rental rates and housing prices. Using a panel of quarterly data on newly signed rental contracts and transaction prices in Barcelona from 2015-Q2 to 2018-Q4, we implement a fixed-effects spatial 2SLS method allowing for endogeneity in the variable which measures the presence of Airbnb.

Airbnb listings in Barcelona (2018-Q2)

Barcelona, which hosts the sixth largest concentration of Airbnb listings in the world, serves as a prime case study to investigate these effects because our dataset covers growth rates in contractual rental rates, transaction prices and the number of active Airbnb listings of 27.42%, 27.41% and 29.38%, respectively.

Key results

The theoretical model predicts that a change in the level of Airbnb activity might affect both long-term rents and housing prices. In fact, if negative externalities generated by tourists are sufficiently small, Airbnb leads to increases in long-term rental prices. Yet, these effects ultimately depend on the values of parameters such as the size of the stock of housing units and the level of externalities emerging from tourism. In addition, the model bears upon the effects of Airbnb on gentrification and displacement: we find that for a positive increase in the negative externalities generated by tourism, the proportion of homeowners renting in the short-term market will increase. As the degree to which residents are harmed by negative externalities increases, more of them will decide to abandon their neighborhood, reducing the local demand for long-term housing. As a result, rents will suffer a downward pressure, increasing the relative profitability of the short-term rental market for homeowners. Besides, this effect will be aggravated if the degree of inter-neighborhood dependence generated by externalities is high. Residents will be prone to move to other neighborhoods in which not only the presence of Airbnb is low, but also in which the penetration of this marketplace is low in the surrounding areas.

We refer to this process as Airbnb-induced gentrification. Similarly, if the profitability of renting a property on Airbnb increases, a similar process as the one we have just described above would arise, which would also lead to gentrification.

For another thing, our main empirical results show that Airbnb positively and significantly affects rents, even when accounting for spatial dependence and inter-neighborhood spillovers. In a given neighborhood (as classified in this paper), for every additional 100 Airbnb listings, rents increase by an average of 2.1% when indirect spillovers coming from adjacent neighborhoods are included. In particular, the direct effect of Airbnb within a given neighborhood accounts for much of this effect: the own-neighborhood effect is to induce a 1.7% increase in rents. The maximum average indirect effect found in the sample data accounts for 35% of the total effect. The implications of these findings are far reaching and suggest that spillover effects can indeed explain a large portion of rent increases. Likewise, we identify a potential bias in the previous literature in that the total effect is falsely interpreted as the direct effect, thereby misinterpreting the direct effect of Airbnb on long-term rents.

Empirical Results: Main Impact Measures

In contrast, our empirical results show that Airbnb has had no significant effect on transaction prices. The most plausible explanation for the non-significant results for prices is that homeowners do not believe that Airbnb is sustainable in the long-run, and therefore they do not adjust their predicted future cash flows when valuing their properties.

Finally, we believe that future research could delve into more detailed theoretical models, especially with respect to the price setting by homeowners in light of the establishment of Airbnb. Additionally, we think that making a distinction between direct and indirect neighborhood effects is vital in order to truly understand the dynamics of the housing markets, especially in the growing metropoles. Accordingly, we encourage scholars to further apply and develop spatial econometric methods that measure indirect spillover effects in studies related to housing markets.

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About the Barcelona GSE Master’s Program in Economics

The Asymmetric Unemployment Response of Natives and Foreigners to Migration Shocks

Working Paper by Nicolò Maffei Faccioli (Macro ’15 and IDEA) and Eugenia Vella (Sheffield)

What is the macroeconomic impact of migration in the second-largest destination for migrants after the United States? 

In this paper, we uncover new evidence on the macroeconomic effects of net migration shocks in Germany using monthly data from 2006 to 2019 and a variety of identification strategies in a structural vector autoregression (SVAR). In addition, we use quarterly data in a mixed-frequency SVAR.

While a large literature has analyzed the impact of immigration on employment and wages using disaggregate data, the migration literature in the context of macroeconometric models is still limited due to a lack of data at high frequency. Interestingly, such data is available for Germany. The Federal Statistical Office (Destatis) has been collecting monthly data on the arrivals of foreigners by country of origin on the basis of population registers at the municipal level since 2006. The figure below shows the net migration rate by origin. 


Key takeaways

Migration shocks are persistently expansionary, increasing industrial production, per capita GDP, investment, net exports and tax revenue. 

Our analysis disentangles the positive effect on inflation of job-related migration from OECD countries from the negative effect of migration (including refugees) from less advanced economies. In the former case, a demand effect seems prevalent while in the latter case, where migration is predominantly low-skilled and often political in nature (including refugees), a supply effect prevails.

In the labor market, migration shocks boost job openings and hourly wages. Unemployment falls for natives, driving a decline in total unemployment, while it rises for foreigners (see figure below). Interestingly, migration shocks (blue area in the first row) play a relevant role in explaining fluctuations in industrial production and unemployment of both natives and foreigners, despite the bulk of these being explained by other shocks (red area in the first row), like business cycle and domestic labor supply.


We also shed light on the employment and participation responses for natives and foreigners. Taken together, our results highlight a job-creation effect for natives and a job-competition effect for foreigners.


The COVID-19 recession may trigger an increase in migration flows and exacerbate xenophobic sentiments around the world. This paper contributes to a better understanding of the migration effects in the labor market and the macroeconomy, which is crucial for migration policy design and to curb the rise in xenophobic movements. 

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

Multi-Armed Bandit Approach to Portfolio Choice Problem

Finance master project by Güneykan Özkaya and Yaping Wang ’20

Image by bibblio

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


Historically, there have been many strategies implemented to solve the portfolio choice problem. An accurate estimation of optimal portfolio allocation is challenging due to the non-deterministic complexities of financial markets.  Due to this complexity, investors tend to resort to the mean-variance framework. If we consider the mean-variance framework, there are several drawbacks to this approach. The most pivotal one could be normality assumption on returns so that we could depict the behavior of returns only by mean and variance.  However, it is well known that returns possess a heavy-tailed and skewed distribution, which results in underestimated risk or overestimated returns. 

In this paper, we rely on a distribution of different metrics other than returns to optimize our portfolio. In simple terms, we combine several parametric and non-parametric bandit algorithms with our prior knowledge that we obtain from historical data. This framework gives us a decision function in which we can choose portfolios to include in our final portfolio. Once we have our candidate portfolio weights, we apply the first-order condition over portfolio variances to distribute our wealth between 2 candidate set of portfolio weights such that it minimizes the variance of the final portfolio. 

Our results show that if contextual bandit algorithms applied to portfolio choice problem, given enough context information about the financial environment, they can consistently obtain higher Sharpe ratios compared to classical methodologies, which translates to a fully automated portfolio allocation framework.

Key results

We conduct the experiments on 48 US value-weighted industry portfolios and consider the time range 1974-02 to 2019-12; The table below reports extensive evaluation criteria of following strategies by order; Minimum Variance Portfolio (MVP), Constant Weight Rebalance portfolio (CWR), Equal Weight portfolio (EW), Upper Confidence Bound 1 (UCB1), Thompson Sampling (TS), Maximum Probabilistic Sharpe ratio (MaxPSR), Probability Weighted UCB1 (PW-UCB1). Below the table, one can observe the evaluation of cumulative wealth through the whole investment period.

Table 1. Evaluation Metrics

One thing to observe here, even UCB1 and PW-UCB yield the highest Sharpe ratios. They also have the highest standard deviation, which implies bandit portfolios tend to take more risk than methodologies that aim to minimize variance, but this was already expected due to the exploration component. Our purpose was to see if the bandit strategy can increase the return such that it offsets the increase in standard deviation. Thompson sampling yields a lower standard deviation because TS also consists of portfolio strategies that aim to minimize variance in its action set.

Figure 1. Algorithm Comparison

We also include the evaluation of cumulative wealth throughout the whole period and in 10 year time intervals. One interesting thing to notice is that bandit algorithms’ performance diminishes during periods of high momentum followed by turmoil. The drop in the bandit algorithms’ cumulative wealth is more severe compared to classic allocation strategies such as EW or MVP. Especially PW-UCB1, this also can be seen from standard deviation of the returns. This is due to using the rolling window to estimate moments of the return distribution. Since we are weighing UCB1 with the Sharpe ratio probability, and since this probability reflects the 120-day window, algorithm puts more weights on industries that gain more during high momentum periods, such as technology portfolio. During the bubble (1995-2002) period, UCB1 and PW-UCB1 gain a lot by putting more weight on technology portfolio, but they suffer the most, during the turmoil that followed high momentum period. One can solve this issue by using more sophisticated prediction model to estimate returns and the covariance matrix.

Figure 2. 1974-1994 Algorithm Comparison
Figure 3. 1994-2020 Algorithm Comparison

To conclude, our algorithm allows dynamic asset allocation with the relaxation of strict normality assumption on returns and incorporates Sharpe ratio probability to better evaluate performances. Our algorithm could appropriately balance the benefits and risks well and achieve higher returns by controlling risk when the market is stable.

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About the Barcelona GSE Master’s Program in Finance

Scalable Inference for Crossed Random Effects Models

Data Science master project by Maximilian Müller ’20

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


Crossed random effects models are additive models that relate a response variable (e.g. a rating) to categorical predictors (e.g. customers and products). They can for example be used in the famous Netflix problem, where movie ratings of users should be predicted based on previous ratings. In order to apply statistical learning in this setup it is necessary to efficiently compute the Cholesky factor L of the models precision matrix. In this paper we show that for the case of 2 factors the crucial point to this end is not only the overall sparsity of L, but also the arrangement of non-zero entries with respect to each other. In particular, we express the number of flops required for the calculation of L by the number of 3-cycles in the corresponding graph. We then introduce specific designs of 2-factor crossed random effects models for which we can prove sparsity and density of the Cholesky factor, respectively. We confirm our results by numerical studies with the R-packages Spam and Matrix and find hints that approximations of the Cholesky factor could be an interesting approach for further decrease of the cost of computing L.

Key findings

  • The number of 3-cycles in the fill graph of the model are an appropriate measure of the computational complexity of the Cholesky decomposition.
  • For the introduced Markovian and Problematic Design we can prove sparsity and density of the Cholesky Factor, respectively.
  • For precision matrices created according to a random Erdös-Renyi-scheme the Spam algorithms could not find an ordering that would be significantly fill-reducing. This indicates that it might be hard or even impossible to find a general ordering rule that leads to sparse Cholesky factors.
  • For all observed cases, many of the non-zero entries in the Cholesky factor are either very small or exactly zero. Neglecting these small or zero values could spare computational cost without changing the Cholesky factor ‘too much’. Approximate Cholesky methods should therefore be included in further research.
Fill-in-ratio (a measure of relative density of the Cholesky factor) vs. matrix size for the random Erdös-Renyi scheme. For all permutation algorithms the fill-in-ratio grows linearly in I indicating that in general it might be hard to find a good, fill-reducing permutation.

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About the Barcelona GSE Master’s Program in Data Science