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on Utility Models and Prospect Theory |
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Issue of 2020‒11‒16
twenty-one papers chosen by |
| By: | Aase, Knut K. (Dept. of Business and Management Science, Norwegian School of Economics) |
| Abstract: | We address how recursive utility affects important results in the theory of economics of uncertainty and time, as compared to the standard model, where the focus is on dynamic models in discrete time. Several puzzles associated with the standard theory are less puzzling with recursive utility, even if this type of preference representation seems close to the standard one at first sight. An inconsistency with the axioms behind the standard, separable and additive expected utility representation is pointed out and extended to also be relevant for recursive utility. The basic difference from the standard model is that recursive utility allows a form of separation of consumption substitution from risk aversion. This also means that the timing of resolution of uncertainty matters. In dynamic models, however, this turns out to be a rather crucial step. |
| Keywords: | Recursive utility; axioms; scale invariance; utility gradients; the equity premium puzzle; precautionary savings |
| JEL: | D51 D53 D90 E21 G10 G12 |
| Date: | 2020–10–30 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:nhhfms:2020_013&r=all |
| By: | Sarah Bensalem; Nicolás Hernández Santibáñez (UCHILE - Universidad de Chile = University of Chile [Santiago]); Nabil Kazi-Tani |
| Abstract: | This paper deals with an optimal linear insurance demand model, where the protection buyer can also exert time-dynamic costly prevention effort to reduce her risk exposure. This is expressed as a stochastic control problem, in which the agent maximizes an exponential utility of her terminal wealth. We assume that the effort reduces the intensity of the jump arrival process, and we interpret this as dynamic self-protection. We solve the problem using a dynamic programming principle approach, and we provide a representation of the value function using a particular backward SDE. This allows us to solve the problem explicitly: we identify the dynamic certainty equivalent of the agent, and prove that the dynamic effort is actually constant, for a large class of loss processes. This shows in particular that the Lévy property is preserved under exponential utility maximization. We also characterize the constant effort as a the unique minimizer of an explicit Hamiltonian, from which we can determine the optimal effort in particular cases. Finally, after studying the dependence of the BSDE on the linear insurance contract parameter, we prove the existence of an optimal linear cover, that is not necessarily zero or full insurance. |
| Keywords: | Self-Protection,Prevention effort,Dynamic programming,Continuation utility,Backward SDEs |
| Date: | 2020–10–22 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-02974961&r=all |
| By: | Daniel J. Benjamin; Mark Alan Fontana; Miles S. Kimball |
| Abstract: | Risk aversion is typically inferred from real or hypothetical choices over risky lotteries, but such “untutored” choices may reflect mistakes rather than preferences. We develop a procedure to disentangle preferences from mistakes: after eliciting untutored choices, we confront participants with their choices that are inconsistent with expected-utility axioms (broken down enough to be self-evident) and allow them to reconsider their choices. We demonstrate this procedure via a survey about hypothetical retirement investment choices administered to 596 Cornell students. We find that, on average, reconsidered choices are more consistent with almost all expected-utility axioms, with one exception related to regret. |
| JEL: | D63 D81 G11 H8 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:28007&r=all |
| By: | Takahiko Kan |
| Abstract: | Adam Smith is the author of An Inquiry into the Nature and Causes of the Wealth of Nations. He is known mainly as a pioneer of political economy. However, he was not only an economist but also a moral philosopher. He published The Theory of Moral Sentiments (TMS) in 1759. In TMS, he explained an establishment of a social order based on sympathy between people in a society. Sympathy is sharing of sentiments with others by imaginarily swapping situations with others. People in TMS form the impartial spectator and regulate their conduct to be sympathized by the impartial spectator. The impartial spectator is often considered as an important concept in TMS. However, even if people formed the impartial spectator, this does not mean that they can always regulate their conduct. To regulate their conduct absolutely, people need general rules of morality (GRM). People can establish a social order thanks to GRM. Some preceding studies have reinterpreted TMS with various research results in contemporary economics. For example, Meardon & Ortmann (1996) reinterprets self-command by using a repeated game theory model. Ashraf et al. (2005) indicates that Smith foresaw some research findings of behavioral economics. Tajima (2007) reinterprets TMS from a perspective of institutional economics. Breban (2012) formularizes a behavior of people in TMS with a utility function, and compares this function with utility functions in behavioral economics. Khalil (2017) reinterprets TMS from a perspective of rational choice theory. These reinterpretations have shed light on modern significance of TMS. However, there is room for reinterpreting important concepts in TMS with research results in contemporary economics. Following the preceding studies, this paper reinterprets the GRM formation process and the corruption of moral sentiments (CMS) by using a replicator dynamics model, which is a basic model of evolutionary game theory. GRM are the social norms in TMS that concern what is fit and proper either to be done or to be avoided. In TMS, people form GRM through interactions with others. They continually observe conduct of others, and this can lead them to form certain GRM. This paper interprets this observation process as a trial-and-error learning process. To formularize this process, this paper uses a replicator dynamics model. The results of the model clarify the character of sympathy in the CRM. The more sympathetic players exist in a player set, the more corrupted situation is likely to be realized. This result mathematically supports an interpretation in preceding studies (Brown 1994, Griswold 1999) that sympathy involves risk that CMS is progressing. The paper is organized as follows. In the section 2, we briefly describe GRM and the CMS. In the section 3, we construct a model of replicator dynamics. In the section 4, we discuss the results of the model. In the last section, we conclude this paper. |
| Date: | 2020–09–11 |
| URL: | http://d.repec.org/n?u=RePEc:toh:tergaa:432&r=all |
| By: | Christopher Dobronyi; Christian Gouri\'eroux |
| Abstract: | We introduce two models of non-parametric random utility for demand systems: the stochastic absolute risk aversion (SARA) model, and the stochastic safety-first (SSF) model. In each model, individual-level heterogeneity is characterized by a distribution $\pi\in\Pi$ of taste parameters, and heterogeneity across consumers is introduced using a distribution $F$ over the distributions in $\Pi$. Demand is non-separable and heterogeneity is infinite-dimensional. Both models admit corner solutions. We consider two frameworks for estimation: a Bayesian framework in which $F$ is known, and a hyperparametric framework in which $F$ is a member of a parametric family. Our methods are illustrated by an application to a large panel of scanner data on alcohol consumption. |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2010.13937&r=all |
| By: | Alex Dickson (Department of Economics, University of Strathclyde); Ian MacKenzie (School of Economics, University of Queensland); Petros G Sekeris (Montpellier Business School) |
| Abstract: | This article investigates rent dissipation—the total costs of rent seeking in relation to the value of the contested rent—in share contests. We consider preferences that are more general than usually assumed in the literature, which allow for contestants to have diminishing marginal utility. With sufficiently concave preferences the equilibrium will feature over-dissipation if the rent is small, and under-dissipation if the rent is large: if contestants have strong diminishing marginal utility and they are contesting a small rent they are highly sensitive to changes in their allocation of the rent so are relatively effortful in contesting it; by contrast when the rent is large they are less effortful relative to the size of the rent. Thus, the inclusion of diminishing marginal utility allows us to reconcile the Tullock paradox—where rent-seeking levels are observed to be relatively small compared to the contested rent—with observed over-dissipation of rents in, for example, experimental settings. We also propose a more general rent dissipation measure that applies to any contest and is suitable for general preferences. |
| Keywords: | Rent seeking; rent dissipation; share contests. |
| JEL: | C72 D72 H40 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:str:wpaper:2014&r=all |
| By: | Carmine De Franco; Johann Nicolle; Huy\^en Pham |
| Abstract: | We study a discrete-time portfolio selection problem with partial information and maxi\-mum drawdown constraint. Drift uncertainty in the multidimensional framework is modeled by a prior probability distribution. In this Bayesian framework, we derive the dynamic programming equation using an appropriate change of measure, and obtain semi-explicit results in the Gaussian case. The latter case, with a CRRA utility function is completely solved numerically using recent deep learning techniques for stochastic optimal control problems. We emphasize the informative value of the learning strategy versus the non-learning one by providing empirical performance and sensitivity analysis with respect to the uncertainty of the drift. Furthermore, we show numerical evidence of the close relationship between the non-learning strategy and a no short-sale constrained Merton problem, by illustrating the convergence of the former towards the latter as the maximum drawdown constraint vanishes. |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2010.15779&r=all |
| By: | Tobias Holmsgaard Larsen (Department of Food and Resource Economics, University of Copenhagen); Thomas Lundhede (Department of Food and Resource Economics, University of Copenhagen); Søren Bøye Olsen (Department of Food and Resource Economics, University of Copenhagen) |
| Abstract: | This report summarizes the main results from a choice experiment survey addressing peoples’ willingness to pay (WTP) for improvements in surface water quality as well as groundwater quality. A particular novel focus is on estimating the extent to which WTP is impacted by the time lags and outcome uncertainties that commonly occur in practice when implementing new policies to improve water quality. The survey is conducted across four different case areas in four different countries, involving responses from more than 3000 respondents. Results generally confirm previous findings that people on average have quite high WTP for improvements in water quality, both in relation to surface water and groundwater. In addition, the results show that the WTPs reduce significantly with increasing time lags and outcome uncertainty in relation to the actual water quality improvements. |
| Keywords: | Economic Valuation, Choice Experiment, Water Quality, Outcome Uncertainty, Time Lags |
| JEL: | C83 D60 Q51 Q53 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:foi:wpaper:2020_12&r=all |
| By: | Marie-Louise Leroux; Pierre Pestieau |
| Abstract: | This paper studies the design of the optimal linear taxation of bequests when individuals differ in wage as well as in their risks of both mortality and old-age dependance. We assume that the government cannot distinguish between bequests motives, that is whether bequests resulted from precautionary reasons or from pure joy of giving reasons. Instead, we assume that it only observes the timing of bequests, that is whether they are made early in life or late in life. We show that, if the government is utilitarian, whether the taxation of early bequests should be given priority over the taxation of late bequests depends on the magnitude of insurance and redistributive concerns. While the efficiency concern unambiguously recommends taxation of early bequests, redistributive concerns yield ambiguous results. This indeterminacy comes from the fact that, in case of late death, the government cannot observe the health status of the deceased. Whether the taxation of early bequests should be given priority depends on the specific relationships between wages and both risks of early death and of old-age dependence, as well as on the concavity of the joy of giving utility function. If the government is Rawlsian, it is optimal to tax early bequests if the survival chances of the poorest agents are very low. If they survive, but their chances to remain autonomous are very low, it is then optimal to tax early bequests if the poorest agents contribute relatively less to the taxation of early bequests than to the taxation of late bequests or if the joy of giving utility is extremely concave. |
| Keywords: | Bequest taxation, Long term care, Utilitarianism, Rawlsian welfare criterion, Old-age dependency. |
| JEL: | H21 H23 I14 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:rsi:creeic:2007&r=all |
| By: | Gaurab Aryal; Eduardo Fajnzylber; Maria F. Gabrielli; Manuel Willington |
| Abstract: | We use data on annuities to study and evaluate an imperfectly competitive market where firms have private information about their (annuitization) costs. Our data is from Chile, where the market is structured as first-price-auction-followed-by-bargaining, and where each retiree chooses a firm and an annuity contract to maximize her expected present discounted utility. We find that retirees with low savings have the highest information processing cost, and they also care about firms' risk-ratings the most. Furthermore, while almost 50% of retirees reveal that they do not value leaving bequests, the rest have heterogeneous preference for bequest that, on average, increases with their savings. On the supply side, we find that firms' annuitization costs vary across retirees, and the average costs increase with retirees' savings. If these costs were commonly known then the pensions would increase for everyone, but the increment would be substantial only for the high savers. Likewise, if we simplify the current pricing mechanism by implementing English auctions and "shutting down" the risk-ratings, then the pensions would increase, but again, mostly for the high savers. |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2011.02899&r=all |
| By: | Ma, Sai (Federal Reserve Board of Governors); Zhang, Shaojun (Ohio State U) |
| Abstract: | When households consume both nondurable goods and housing services, external habit preference over nondurable consumption generates procyclical demand for housing. Marginal utility falls when housing demand rises and innovations to housing demand arise as a risk factor. Motivated by theory, we use shocks to the ratio of residential-to-aggregate investment to capture the housing demand risk. The single-factor model exhibits strong explanatory power for expected returns across various equity characteristic-sorted portfolios and non-equity asset classes with positive risk price estimates that are similar in magnitude. The model is robust to controlling for other factor models based on durable consumption, financial intermediaries, household heterogeneity, and return-based multifactor models designed to price these assets. |
| JEL: | G10 G11 G12 |
| Date: | 2020–05 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:ohidic:2020-08&r=all |
| By: | Giulio Bottazzi; Daniele Giachini |
| Abstract: | This paper studies whether, and to what extent, trading in an incomplete competitive market rewards the CAPM portfolio rule over alternative rules. We find that, if a mean-variance trader faces an agent who invests in each asset proportionally to expected relative payoffs, in the long-run only two scenarios are possible: either the mean-variance trader vanishes or both agents survive with fixed and constant wealth shares. In both cases, asymptotic prices are proportional to assetsù expected payoff, and the relation between prices and returns implied by the CAPM does not generally hold. Conversely, when a mean-variance trader faces a generic fixed-mix investor, several long-run outcomes are possible, such as dominance of one trader, survival of both, and generic path-dependency. We provide sufficient conditions to assess such outcomes. We find that the different outcomes can be effectively discussed in terms of the effective risk aversion of the trading strategies, as implied by their portfolio choices conditional on prevailing market prices. In general, a larger effective risk aversion constitutes a survival advantage. |
| Keywords: | Selection; Evolution; Capital Asset Pricing Model; Incomplete Markets. |
| Date: | 2020–10–29 |
| URL: | http://d.repec.org/n?u=RePEc:ssa:lemwps:2020/29&r=all |
| By: | Agostino Capponi; Zhaoyu Zhang |
| Abstract: | We propose a novel approach to infer investors' risk preferences from their portfolio choices, and then use the implied risk preferences to measure the efficiency of investment portfolios. We analyze a dataset spanning a period of six years, consisting of end of month stock trading records, along with investors' demographic information and self-assessed financial knowledge. Unlike estimates of risk aversion based on the share of risky assets, our statistical analysis suggests that the implied risk aversion coefficient of an investor increases with her wealth and financial literacy. Portfolio diversification, Sharpe ratio, and expected portfolio returns correlate positively with the efficiency of the portfolio, whereas a higher standard deviation reduces the efficiency of the portfolio. We find that affluent and financially educated investors as well as those holding retirement related accounts hold more efficient portfolios. |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2010.13928&r=all |
| By: | Hang Bai; Lu Zhang |
| Abstract: | Labor market frictions are crucial for the equity premium in production economies. A dynamic stochastic general equilibrium model with recursive utility, search frictions, and capital accumulation yields a high equity premium of 4.26% per annum, a stock market volatility of 11.8%, and a low average interest rate of 1.59%, while simultaneously retaining plausible business cycle dynamics. The equity premium and stock market volatility are strongly countercyclical, while the interest rate and consumption growth are largely unpredictable. Because of wage inertia, dividends are procyclical despite consumption smoothing via capital investment. The welfare cost of business cycles is huge, 29%. |
| JEL: | E32 E44 G12 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:28001&r=all |
| By: | Becker, Christoph K. (Heidelberg University); Melkonyan, Tigran (University of Alabama); Proto, Eugenio (University of Glasgow); Sofianos, Andis (Heidelberg University); Trautmann, Stefan T. (Heidelberg University) |
| Abstract: | Bayesian Updating is the dominant theory of learning in economics. The theory is silent about how individuals react to events that were previously unforeseeable or unforeseen. Recent theoretical literature has put forth axiomatic frameworks to analyze the unknown. In particular, we test if subjects update their beliefs in a way that is consistent "reverse Bayesian", which ensures that the old information is used correctly after an unforeseen event materializes. We find that participants do not systematically deviate from reverse Bayesianism, but they do not seem to expect an unknown event when this is reasonably unforeseeable, in two pre-registered experiments that entail unforeseen events. We argue that participants deviate less from the reverse Bayesian updating than from the usual Bayesian updating. We provide further evidence on the moderators of belief updating. |
| Keywords: | reverse Bayesianism, unforeseen, unawareness, Bayesian Updating |
| JEL: | C11 C91 D83 D84 |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp13821&r=all |
| By: | Anastasios Xepapadeas; Athanasios Yannacopoulos |
| Abstract: | Spatiotemporal dynamics are introduced in a standard Ramsey model of optimal growth in which capital moves towards locations where the marginal productivity of capita is relatively higher. We extend Pontryagin's maximum principle to account for transition dynamics governed by a nonlinear partial differential equation emerging for spatial capital flows. The potential spatial heterogeneity of optimal growth as seen from the point of view of an optimizing social planner is examined. Our results suggest that for high utility discount rate the spatial capital flows induce the emergence of optimal spatial patterns while hor low utility discount a flat-earth steady state is socially optimal. Furthermore, when spatial heterogeneities exist due to total factor productivity differences across locations, we identify conditions under which the spatial capital flows could intensify or weaken spatial inequalities. |
| Keywords: | Ramsey model, spatiotemporal dynamics, flat earth, pattern formation. |
| JEL: | O41 R11 C61 C62 |
| Date: | 2020–10–30 |
| URL: | http://d.repec.org/n?u=RePEc:aue:wpaper:2033&r=all |
| By: | Roman M. Sheremeta (Weatherhead School of Management, Case Western Reserve University and Economic Science Institute, Chapman University); Neslihan Uler (Agricultural and Resource Economics, University of Maryland) |
| Abstract: | We examine how taxes impact charitable giving and how this relationship is affected by the degree of wasteful government spending. In our model, individuals make donations to charities knowing that the government collects a flat-rate tax on income (net of charitable donations) and redistributes part of the tax revenue. The rest of the tax revenue is wasted. The model predicts that a higher tax rate increases charitable donations. Surprisingly, the model shows that a higher degree of waste decreases donations (when the elasticity of marginal utility with respect to consumption is high enough). We test the model’s predictions using a laboratory experiment with actual donations to charities and find that the tax rate has an insignificant effect on giving. The degree of waste, however, has a large, negative and highly significant effect on giving. |
| Keywords: | charitable giving, tax, waste, redistribution, experiment, public goods provision, neutrality, income inequality |
| JEL: | C93 D64 H21 |
| Date: | 2020 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:20-32&r=all |
| By: | Szymon Peszat; Dariusz Zawisza |
| Abstract: | We consider a consumption-investment problem in which the investor has an access to the bond market. In our approach prices of bonds with different maturities are described by the general HJM factor model. We assume that the bond market consist of entire family of rolling bonds and the investment strategy is a general signed measure distributed on all real numbers representing time to maturity specifications for different rolling bonds. The investor's objective is to maximize time-additive utility of the consumption process. We solve the problem by means of the HJB equation for which we prove required regularity of its solution and all required estimates to ensure applicability of the verification theorem. Explicit calculations for certain particular models are presented. |
| Date: | 2020–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2010.13915&r=all |
| By: | Stephen L. Ross (University of Connecticut); Tingyu Zhou (Florida State University) |
| Abstract: | Many studies document loss aversion in the housing market, where expected losses lead to higher sales prices. However, exposure to expected losses may correlate with unobservables that influence housing prices. Under the assumption that multiple psychological biases appear together, we estimate loss aversion by identifying sellers who appear psychologically biased by exhibiting focal point or round number bias in their choice of mortgage amount at purchase. Using both difference-in-differences and regression discontinuity approaches, we find evidence of loss aversion on sales prices based on a stronger correlation between loss and sales price for our subsample of sellers who exhibited round number bias, but our estimated effects are substantially smaller than the results that arise from directly estimating the effects of expected loss on the sales price. In addition, lumpy sellers are less likely to sell relative to the control group. We show that expected loss correlates strongly with predetermined mortgage, housing unit, and census tract attributes, but the interaction between a round mortgage amount and expected loss exhibits far fewer failures of balance. Further, the magnitude of the sample-wide relationship between expected loss and sales price is eroded substantially by the inclusion of balancing test controls, as well as by the inclusion of a running variable for the mortgage amount, while the magnitude of the relative estimates for the round mortgage amount subsample is quite stable. Evidence from an earlier experiement showing a positive relationship between reporting round numbers and loss aversioin provide supports for our identification strategy. |
| Keywords: | loss aversion, anchoring, mortgage, behavioral bias, round number bias, focal point, house prices, sale likelihood |
| Date: | 2020–11 |
| URL: | http://d.repec.org/n?u=RePEc:uct:uconnp:2020-17&r=all |
| By: | Canta, Chiara; Cremer, Helmuth |
| Abstract: | We study the design of social long-term care (LTC) insurance when informal care is exchange-based. Parents do not observe their children's cost of providing care, which is continuously distributed over some interval. They choose a rule specifying transfers that are conditional on the level of informal care. Social LTC insurance is designed to maximize a weighted sum of parents' and children's utility. The optimal uniform public LTC insurance can fully cover the risk of dependence but parents continue to bear the risk of having children with a high cost of providing care. A nonlinear policy conditioning LTC benets on transfers provides full insurance even for this risk. Informal care increases with the children's welfare weight. Our theoretical analysis is completed by numerical solutions based on a calibrated example. In the uniform case, public care should represent up to 40% of total care but its share decreases to about 30% as the weight of children increases. In the nonlinear case, public care increases with the children's cost of providing care at a faster rate when children's weight in social welfare is higher. It represents 100% of total care for the families with high-cost children. |
| Keywords: | Long-term care; informal care; strategic bequests; asymmetric information |
| JEL: | H2 H5 |
| Date: | 2020–11–02 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:124871&r=all |
| By: | YiLi Chien; Yi Wen |
| Abstract: | A key feature of the infinite-horizon heterogeneous-agents incomplete-markets (Inf-HAIM) framework is that the equilibrium interest rate of public debt lies below the time discount rate (regardless of capital). This happens because of a positive liquidity premium on asset returns due to imperfect risk sharing. This fundamental property of standard Inf-HAIM models, however, implies that the Ramsey planner's fiscal policy may be time-inconsistent---because the planner has a dominate incentive to issue plenty of debt such that all households are fully self-insured against idiosyncratic risk whenever the interest rate of government borrowing is lower than the household time discount rate. But such a full self-insurance allocation may be infeasible---because to achieve it the optimal quantity of debt may approach infinity or the optimal labor tax rate may approach 100%. This is puzzling from an intuitive perspective because near the point of full self-insurance the marginal gains of increasing debt should be less than the marginal costs of financing the debt under distortionary taxes. We show that this puzzling behavior originates from the assumption that the planner must commit to future plans at time zero. Under such a full commitment, the Ramsey planner opts to exploit the low interest cost of borrowing to front load consumption by sacrificing future consumption in the long run---because future utilities are heavily discounted compared to the inverse of the interest rate on government bonds. We demonstrate our points analytically using a tractable Inf-HAIM model featuring non-linear preferences and a well-defined distribution of household wealth. |
| Keywords: | Time Inconsistency; Optimal Debt; Ramsey Problem; Incomplete Markets |
| JEL: | E13 E62 H21 H30 |
| Date: | 2020–10–29 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedlwp:88991&r=all |