nep-upt New Economics Papers
on Utility Models and Prospect Theory
Issue of 2019‒06‒17
23 papers chosen by

  1. The Theory of Weak Revealed Preference By Victor H. Aguiar; Per Hjertstrand; Roberto Serrano
  2. Consistency of the Equal Split-Off Set By Dietzenbacher, Bas; Yanovskaya, E.
  3. Many-player games of optimal consumption and investment under relative performance criteria By Daniel Lacker; Agathe Soret
  4. Present bias: Definition and measurement By Alexis Direr
  5. Optimal Stopping under Model Ambiguity: a Time-Consistent Equilibrium Approach By Yu-Jui Huang; Xiang Yu
  6. Differential Impact of Uncertainty on Exporting Decision in Risk-averse and Risk-taking Firms By Haeng-Sun Kim
  7. It’s Time to Cheat! By Alessandro Bucciol; Simona Cicognani; Natalia Montinari
  8. Understanding Distributional Ambiguity via Non-robust Chance Constraint By Qi Wu; Shumin Ma; Cheuk Hang Leung; Wei Liu
  9. Are risk preferences stable ? A field experiment in Congo Basin countries. By Marielle Brunette; Jonas Ngouhouo-Poufoun
  10. Household Preferences for Load Restrictions: Is There an Effect of Pro-Environmental Framing? By Broberg, Thomas; Melkamu Daniel , Aemiro; Persson, Lars
  11. Improving Abatement Levels and Welfare by Coarse Correlation in an Environmental Game By Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta
  12. The Effects of Risk and Ambiguity Aversion on Technology Adoption: Evidence from Aquaculture in Ghana By Crentsil, Christian; Gschwandtner, Adelina; Wahhaj, Zaki
  13. The Impact of Ambiguity on the Optimal Exercise Timing of Integral Option Contracts By Luis H. R. Alvarez E.; S\"oren Christensen
  14. Counterfactual Inference for Consumer Choice Across Many Product Categories By Rob Donnelly; Francisco R. Ruiz; David Blei; Susan Athey
  15. Collective intertemporal decisions and heterogeneity in groups By Daniela Glaetzle-Ruetzler; Philipp Lergetporer; Matthias Sutter
  16. Is Prevention of Suicide Worth Less? -A Comparison of the Value per Statistical Life By Vimefall, Elin; Persson, Mattias; Olofsson, Sara; Hultkrantz, Lars
  17. Do farmers follow the herd? The influence of social norms on participation in agri-environmental schemes By Le Coent, Philippe; Preget, Raphaële; Thoyer, Sophie
  18. Equal-quantile rules in resource allocation with uncertain needs By Long, Yan; Sethuraman, Jay; Xue, Jingyi
  19. Bounded Rationality, Monetary Policy, and Macroeconomic Stability By Francisco Ilabaca; Greta Meggiorini; Fabio Milani
  20. Belief formation and belief updating under ambiguity: Evidence from experiments By Li, Wenhui; Wilde, Christian
  21. Structural changes in economic growth and well-being. The case of Italy's parabola By Pugno, Maurizio; Sarracino, Francesco
  22. The long-run effects of uncertainty shocks By Bonciani, Dario; Oh, Joonseok Jason
  23. The natural rate of interest: estimates, drivers, and challenges to monetary policy By Claus Brand; Marcin Bielecki; Adrian Penalver

  1. By: Victor H. Aguiar; Per Hjertstrand; Roberto Serrano
    Abstract: We offer a rationalization of the weak generalized axiom of revealed preference (WGARP) for both finite and infinite data sets of consumer choice. We call it maximin rationalization, in which each pairwise choice is associated with a "local" utility function. We develop its associated weak revealed-preference theory. We show that preference recoverability and welfare analysis \`a la Varian (1982) may not be informative enough, when the weak axiom holds, but when consumers are not utility maximizers. We clarify the reasons for this failure and provide new informative bounds for the consumer's true preferences.
    Date: 2019–06
  2. By: Dietzenbacher, Bas (Tilburg University, Center For Economic Research); Yanovskaya, E.
    Abstract: This paper axiomatically studies the equal split-off set (cf. Branzei et al. (2006)) as a solution for cooperative games with transferable utility. This solution extends the well-known Dutta and Ray (1989) solution for convex games to arbitrary games. By deriving several characterizations, we explore the relation of the equal split-off set with various consistency notions.
    Keywords: transferable utility games; egalitrianism; equal split-off set; consistency
    JEL: C71
    Date: 2019
  3. By: Daniel Lacker; Agathe Soret
    Abstract: We study a portfolio optimization problem for competitive agents with CRRA utilities and a common finite time horizon. The utility of an agent depends not only on her absolute wealth and consumption but also on her relative wealth and consumption when compared to the averages among the other agents. We derive a closed form solution for the $n$-player game and the corresponding mean field game. This solution is unique in the class of equilibria with constant investment and continuous time-dependent consumption, both independent of the wealth of the agent. Compared to the classical Merton problem with one agent, the competitive model exhibits a wide range of highly nonlinear and non-monotone dependence on the agents' risk tolerance and competitiveness parameters. Counter-intuitively, competitive agents with high risk tolerance may behave like non-competitive agents with low risk tolerance.
    Date: 2019–05
  4. By: Alexis Direr (LEO - Laboratoire d'Économie d'Orleans - CNRS - Centre National de la Recherche Scientifique - Université de Tours - UO - Université d'Orléans)
    Abstract: A novel definition of present bias is proposed which takes preferences as primitives. A present biased individual over-weights immediate costs and benefits relative to those occurring at any point in the future. The definition allows to sort out previous confounds, such as decreasing impatience, choice reversal or short-term impatience. It intuitively connects to usual utility representations of present bias like the quasi-hyperbolic model of Laibson (1997) or the fixed cost model of Benhabib, Bisin and Schotter (2010). Drawing on the definition, we propose two experimental methods measuring present bias at the individual level which do not require assumptions about utility or discounting, one for daily trade-offs, the other for intra-daily trade-offs. J.E.L. codes: D8, E21
    Keywords: time preferences,decreasing impatience,present bias
    Date: 2019–05–18
  5. By: Yu-Jui Huang; Xiang Yu
    Abstract: An unconventional approach for optimal stopping under model ambiguity is introduced. Besides ambiguity itself, we take into account how ambiguity-averse an agent is. This inclusion of ambiguity attitude, via an $\alpha$-maxmin nonlinear expectation, renders the stopping problem time-inconsistent. We look for subgame perfect equilibrium stopping policies, formulated as fixed points of an operator. For a one-dimensional diffusion with drift and volatility uncertainty, we show that every equilibrium can be obtained through a fixed-point iteration. This allows us to capture much more diverse behavior, depending on an agent's ambiguity attitude, beyond the standard worst-case (or best-case) analysis. In a concrete example of real options valuation under volatility uncertainty, all equilibrium stopping policies, as well as the best one among them, are fully characterized. It demonstrates explicitly the effect of ambiguity attitude on decision making: the more ambiguity-averse, the more eager to stop---so as to withdraw from the uncertain environment. The main result hinges on a delicate analysis of continuous sample paths in the canonical space and the capacity theory. To resolve measurability issues, a generalized measurable projection theorem, new to the literature, is also established.
    Date: 2019–06
  6. By: Haeng-Sun Kim (Jeju National University (KOREA), FFJ - Fondation France-Japon de l'EHESS - EHESS - École des hautes études en sciences sociales)
    Abstract: Most existing literature examining the links between firm heterogeneity and entry into exporting assumes that firms are risk neutral. In this study, we relax this strict assumption that firms are risk neutral and introduce different attitudes of firms toward risk as an additional source of firm heterogeneity. In particular, we examine how risk attitude changes the effect of uncertainty on the decision of a firm to export considering the different types of uncertainty faced by the firm, namely, firm-specific and macroeconomic. Our analysis yields two interesting findings. First, firm-specific uncertainty discourages risk-averse firms from participating in foreign markets more than risk-taking firms. One possible explanation for this finding is that risk-averse firms are more cautious in export market participation when firm-specific uncertainty increases. Second, we find that riskaverse firms are less likely to decrease their export market participation when responding to macroeconomic uncertainty. Thus, risk-averse firms are more likely to diversify their domestic risk by participating in foreign markets in responding to macroeconomic uncertainty.
    Keywords: Exports,Risk aversion,Uncertainty,Firm heterogeneity
    Date: 2019–05
  7. By: Alessandro Bucciol (Department of Economics (University of Verona)); Simona Cicognani (Department of Economics (University of Verona)); Natalia Montinari (University of Bologna)
    Abstract: We run a lab experiment testing the correlation between time preferences and cheating at the individual level, controlling for individuals' risk attitude. In our experiment cheating only entails a moral cost for the decision maker, while it imposes no externalities on others, and it is not associated to the risk of being detected and sanctioned. Our hypothesis is that cheating is higher among individuals who attribute more importance to the present. Our experiment also allows to record socio-demographic details and information on cognitive abilities of participants. We observe widespread cheating, and statistical evidence that cheating prevails among subjects who display present bias and over-confidence. Cheating also turns out to be negatively correlated with risk aversion and the discount factor, but only for men, while the impact of present bias seems to be stronger for women.
    Keywords: Cheating, Time Discounting, Quasi-hyperbolic preferences
    JEL: D91 C91 D81
    Date: 2019–06
  8. By: Qi Wu; Shumin Ma; Cheuk Hang Leung; Wei Liu
    Abstract: The choice of the ambiguity radius is critical when an investor uses the distributionally robust approach to address the issue that the portfolio optimization problem is sensitive to the uncertainties of the asset return distribution. It cannot be set too large because the larger the size of the ambiguity set the worse the portfolio return. It cannot be too small either; otherwise, one loses the robust protection. This tradeoff demands a financial understanding of the ambiguity set. In this paper, we propose a non-robust interpretation of the distributionally robust optimization (DRO) problem. By relating the impact of an ambiguity set to the impact of a non-robust chance constraint, our interpretation allows investors to understand the size of the ambiguity set through parameters that are directly linked to investment performance. We first show that for general $\phi$-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problem, where the ambiguity radius controls investor's risk preference. Based on this non-robust reformulation, we then show that when a boundedness constraint is added to the investment strategy, the DRO problem can be cast as a chance-constrained optimization (CCO) problem without distributional uncertainties. If the boundedness constraint is removed, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Our results apply to both the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, as well as those more general divergence measures which allow heavy tail ones such as student $t$ and lognormal distributions.
    Date: 2019–06
  9. By: Marielle Brunette; Jonas Ngouhouo-Poufoun
    Abstract: We compare individual risk preferences elicited through a classic Ordered Lottery Selection (OLS) procedure with five gambles, and an extended procedure composed of nine gambles. The research question is about the stability of the risk preferences across these two elicitation variants. We implemented a field experiment with 1002 rural households in the Congo Basin from December 2013 to July 2014. We show that 1/3 of the sample is extremely risk averse regardless of the procedure. We found inconsistencies in risk preferences elicited across procedures. Indeed, 45.71% are characterized by instability of preferences, either weak (34.53%) or strong (11.18%); 42.81% of the sample exhibits stable preferences and the remaining 11.48% of the sample - initially risk neutral in the classic procedure - is classified as risk loving in the extended procedure. Undereducation can be seen as the main driver of the strong instability since the incremental change brought about by the attainment of secondary school on the likelihood to remain stable is ten times greater than the other considered drivers.
    Keywords: field experiment, risk aversion, ordered lottery selection, preferences, farmers.
    JEL: C93 D81
    Date: 2019
  10. By: Broberg, Thomas (CERE - the Center for Environmental and Resource Economics); Melkamu Daniel , Aemiro (CERE - the Center for Environmental and Resource Economics); Persson, Lars (CERE - the Center for Environmental and Resource Economics)
    Abstract: In this paper we investigate if a pro-environmental framing influences households' stated willingness to accept restrictions on their electricity use. We use a split-sample choice experiment (CE) and ask respondents to choose between their current electricity contract and hypothetical contracts featuring various load controls and a monetary compensation. Our results indicate that the pro-environmental framing have little impact on the respondents' choices. We observe a significant framing effect on choices and marginal willingness-to-accept (MWTA) for only a few contract attributes. The results further suggest that there is no significant framing effect among households that engage in different pro-environmental activities.
    Keywords: Choice experiment; Demand response; Electricity contract; Load management; Pro-environmental framing; Willingness to accept
    JEL: C25 D83 Q51 Q54
    Date: 2019–06–12
  11. By: Trivikram Dokka Venkata Satyanaraya; Herve Moulin; Indrajit Ray; Sonali Sen Gupta
    Abstract: Coarse correlated equilibria (CCE, Moulin and Vial, 1978) can be used to substantially improve upon the Nash equilibrium solution of the well-analysed abatement game (Barrett, 1994). We show this by computing successively the CCE with the largest total utility, the one with the highest possible abatement levels and finally, the one with maximal abatement level while maintaining at least the level of utility from the Nash outcome.
    Keywords: Abatement game, Coarse correlated equilibrium, Efficiency gain
    JEL: C72 Q52
    Date: 2019
  12. By: Crentsil, Christian; Gschwandtner, Adelina; Wahhaj, Zaki
    Abstract: We study how aversion to risk and ambiguity aects the adoption of new tech- nologies by Ghanaian smallholder aquafarmers. We conduct a set of eld experiments designed to elicit farmers' risk and ambiguity preferences and combine it with survey- based information on their technology adoption decisions. We nd that aquafarmers who are more risk-averse were quicker to adopt the new technologies: a fast-growing breed of tilapia sh, extruded feed and oating cages. By contrast, ambiguity aversion has no eect on the adoption of the new tilapia breed and extruded feed. Furthermore, it slows down the adoption of oating cages - a technology which entails higher xed costs than the others - and the eect is diminishing in the number of other adopters in the village. We argue that these dierential eects are due to the fact that the technolo- gies are risk-reducing, with potential ambiguity about their payo distributions at the early stages of adoption. The ndings highlight the importance of distinguishing be- tween risk and ambiguity in investigating technology adoption decisions of small-holder farmers in developing countries.
    Keywords: Livestock Production/Industries, Research and Development/Tech Change/Emerging Technologies, Risk and Uncertainty
    Date: 2018–11–27
  13. By: Luis H. R. Alvarez E.; S\"oren Christensen
    Abstract: We consider the impact of ambiguity on the optimal timing of a class of two-dimensional integral option contracts when the exercise payoff is a positively homogeneous measurable function. Hence, the considered class of exercise payoffs includes discontinuous functions as well. We identify a parameterized family of excessive functions generating an appropriate class of supermartingales for the considered problems and then express the value of the optimal policy as well as the worst case measure in terms of these processes. The advantage of our approach is that it reduces the analysis of the multidimensional problem to the analysis of an ordinary one-dimensional static optimization problem. In that way it simplifies earlier treatments of the problem without ambiguity considerably. We also illustrate our findings in explicitly parameterized examples.
    Date: 2019–06
  14. By: Rob Donnelly; Francisco R. Ruiz; David Blei; Susan Athey
    Abstract: This paper proposes a method for estimating consumer preferences among discrete choices, where the consumer chooses at most one product in a category, but selects from multiple categories in parallel. The consumer's utility is additive in the different categories. Her preferences about product attributes as well as her price sensitivity vary across products and are in general correlated across products. We build on techniques from the machine learning literature on probabilistic models of matrix factorization, extending the methods to account for time-varying product attributes and products going out of stock. We evaluate the performance of the model using held-out data from weeks with price changes or out of stock products. We show that our model improves over traditional modeling approaches that consider each category in isolation. One source of the improvement is the ability of the model to accurately estimate heterogeneity in preferences (by pooling information across categories); another source of improvement is its ability to estimate the preferences of consumers who have rarely or never made a purchase in a given category in the training data. Using held-out data, we show that our model can accurately distinguish which consumers are most price sensitive to a given product. We consider counterfactuals such as personally targeted price discounts, showing that using a richer model such as the one we propose substantially increases the benefits of personalization in discounts.
    Date: 2019–06
  15. By: Daniela Glaetzle-Ruetzler; Philipp Lergetporer; Matthias Sutter
    Abstract: Many important intertemporal decisions, such as investments of firms or households, are made by groups rather than individuals. Little is known what happens to such collective deci- sions when group members have different incentives for waiting, because the economics liter- ature on group decision making has, so far, assumed homogeneity within groups. In a lab ex- periment, we study the causal effect of group members’ heterogeneous payoffs from waiting on intertemporal choices. We find that three-person groups behave more patiently than indi- viduals and that this effect is driven by the presence of at least one group member with a high payoff from waiting. We present group chat content, survey data, and additional treatments to uncover the mechanism through which heterogeneity in groups increases patience.
    Keywords: patience, time preferences, group decisions, payoff heterogeneity, experiment
    JEL: C91 C92 D03 D90
    Date: 2019–10
  16. By: Vimefall, Elin (Örebro University School of Business); Persson, Mattias (Örebro University School of Business); Olofsson, Sara (IHE-The Swedish Institute for Health Economics); Hultkrantz, Lars (Örebro University School of Business)
    Abstract: This paper compares the value per statistical life (VSL) in the context of suicide prevention to that of prevention of traffic fatalities. We conducted a contingent valuation survey with questions on willingness to pay (WTP) in both contexts by administering a web questionnaire to 1038 individuals aged 18 to 80. We conjectured that WTP for a given impact on the number of fatalities would be lower for suicide prevention because suicide, at least to some degree, is the result of individuals’ own decisions. However, this hypothesis was not supported by the within- or between-sample estimates of VSL or by responses to direct questions. Hence, no support is provided for the use of a lower valuation of the impact of suicide prevention than for risk-reducing programs in other fields, such as traffic safety.
    Keywords: Value of statistical life; Willingness to pay; Mental health; Cost-benefit; Altruism
    JEL: D61 I18 J17
    Date: 2019–06–12
  17. By: Le Coent, Philippe; Preget, Raphaële; Thoyer, Sophie
    Abstract: The economic literature on Agri-environmental Schemes (AES) largely considers that farmers participate in contracts if the payment offered is superior to their opportunity costs. Psychological and social forces may however be at play in this decision. This article analyses the role played by social norms in farmers’ decisions to enrol into AES. It develops a simple theoretical model highlighting the interplay of descriptive and injunctive norms in farmers’ utility functions. Results of this model lead us to propose few policy recommendations to counter or, in other contexts, to take advantage of the influence of social norms to increase farmers’ participation to AES.
    Keywords: Agricultural and Food Policy, Environmental Economics and Policy, Institutional and Behavioral Economics
    Date: 2019–05–29
  18. By: Long, Yan (New York University Abu Dhabi); Sethuraman, Jay (Columbia University); Xue, Jingyi (Singapore Management University)
    Abstract: A group of agents have uncertain needs on a resource, and the resource has to be divided before uncertainty resolves. We propose a class of division rules we call equal-quantile rules, parameterized by λ ∈ (0, 1]. The parameter λ is a common maximal probability of satisfaction — the probability that an agent’s realized need is no more than his assignment — imposed on all agents. Thus, the maximal assignment of each agent is his λ-quantile assignment. If the endowment of the resource exceeds the sum of the agents’ λ-quantile assignments, each agent receives his λ-quantile assignment and the resource is not fully allocated to the agents. Otherwise, the resource is fully allocated and the rule equalizes the probability of satisfaction across agents.We provide justifications for the class of equal-quantile rules from two perspectives. First, each equal-quantile rule maximizes a particular utilitarian social welfare function that involves an outside agent, who provides an alternative use of the resource, and aggregates linear individual utilities. Equivalently, it minimizes a particular utilitarian social cost function that is the sum of the aggregate expected waste and the aggregate expected deficit, weighted, respectively, by a unit waste cost and a unit deficit cost. Second, four familiar axioms, consistency, continuity, strict ranking, and ordinality, when extended to the uncertain context, characterize the class of equal-quantile rules. Thus, requiring the four axioms is equivalent to imposing either of these utilitarian objective functions.
    Keywords: Resource allocation; Fair division; Uncertain needs; Equal-quantile rules; Utilitarian social welfare function; Waste; Deficit; Ordinality
    JEL: D44 D63 D71 D82
    Date: 2019–05–09
  19. By: Francisco Ilabaca (Department of Economics, University of California-Irvine); Greta Meggiorini (Department of Economics, University of California-Irvine); Fabio Milani (Department of Economics, University of California-Irvine)
    Abstract: This paper estimates a Behavioral New Keynesian model to revisit the evidence that passive US monetary policy in the pre-1979 sample led to indeterminate equilibria and sunspot-driven fluctuations, while active policy after 1982, by satisfying the Taylor principle, was instrumental in restoring macroeconomic stability. The model assumes "cognitive discounting", i.e., consumers and firms pay less attention to variables further into the future. We estimate the model allowing for both determinacy and indeterminacy. The empirical results show that determinacy is preferred both before and after 1979. Even if monetary policy is found to react only mildly to inflation pre-Volcker, the substantial degrees of bounded rationality that we estimate prevent the economy from falling into indeterminacy.
    Keywords: Behavioral New Keynesian model; Cognitive discounting; Myopia; Estimation under determinacy and indeterminacy; Taylor principle; Active vs passive monetary policy
    JEL: E31 E32 E52 E58
    Date: 2019–06
  20. By: Li, Wenhui; Wilde, Christian
    Abstract: Decisions under ambiguity depend on both the belief regarding possible scenarios and the attitude towards ambiguity. This paper exclusively investigates the belief formation and belief updating process under ambiguity, using laboratory experiments. The results show that half of the subjects tend to adopt a simple heuristic strategy when updating beliefs, while the other half seems to partially adopt the Bayesian updates. We recover beliefs, represented by distributions of the priors/posteriors. The recoverable initial priors mostly follow a uniform distribution. We also find that subjects on average demonstrate slight pessimism in an ambiguous environment.
    Keywords: ambiguity,learning strategy,belief updates,non-Bayesian updates,pessimism,laboratory experiments
    Date: 2019
  21. By: Pugno, Maurizio; Sarracino, Francesco
    Abstract: The controversies on the relationship (or `gradient') between GDP and subjective well-being oppose those who claim that the gradient is positive and stable around the world to those who argue that long-run trends of subjective well-being are flat despite economic growth. The possible existence of structural breaks of the gradient within the same country is a challenge to both views. By focusing on the case of Italy, we show that the long-run trends of GDP and of well-being turned from increasing to decreasing, and the gradient exhibits a rise through two structural breaks. Macro and micro analyses explain why the gradient changes, and we find evidence consistent with the `loss aversion' hypothesis. In addition, the gradient changed because the erosion of trust in others, the increase of financial dissatisfaction and worsened health hinder well-being independently from income.
    Keywords: structural breaks, subjective well-being, economic growth, Easterlin paradox, trends, loss aversion
    JEL: D6 I31 O11 O12
    Date: 2019–05–22
  22. By: Bonciani, Dario (Bank of England); Oh, Joonseok Jason (European University Institute)
    Abstract: This paper argues that shocks increasing macroeconomic uncertainty negatively affect economic activity not only in the short but also in the long run. In a sticky-price DSGE model with endogenous growth through investment in R&D, uncertainty shocks lead to a short-term fall in demand because of precautionary savings and rising markups. The decline in the utilised aggregate stock of R&D determines a fall in productivity, which causes a long-term decline in the main macroeconomic aggregates. When households feature Epstein-Zin preferences, they become averse to these long-term risks affecting their consumption process (long-run risk channel), which strongly exacerbates the precautionary savings motive and the overall negative effects of uncertainty shocks.
    Keywords: Uncertainty shocks; R&D; endogenous growth
    JEL: E32 O40
    Date: 2019–06–07
  23. By: Claus Brand (European Central Bank); Marcin Bielecki (Narodowy Bank Polski); Adrian Penalver (Banque de France)
    Abstract: Using a wide range of models we document a protracted fall in the natural (or neutral) rate of interest in advanced economies, driven by ageing, waning productivity growth, arise in mark-ups, and a surge in risk aversion in the wake of the global financial crisis. While our neutral rate estimates are highly uncertain and model dependent, most of them have been negative in the wake of the financial crisis. This observation is highly relevant for assessing the monetary policy stance and the risk of monetary policy becoming constrained by the lower bound on nominal interest rates. We highlight model dependence of natural rate estimates by illustrating large differences in their stabilising properties, depending on the context chosen. We also emphasise high statistical uncertainty of natural rate estimates within models. Looking ahead, a return to higher levels would have to come from a reversal in risk aversion and flight to safety and a boost in productivity. To achieve this, structural reforms are crucial.
    Keywords: Natural rate of interest, return on capital, demographics, productivity growth, monetary policy
    JEL: E52 E43
    Date: 2019

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