{"title":"Renegotiation and Dynamic Inconsistency: Contracting with Non-Exponential Discounting","authors":"Doruk Cetemen, F. Z. Feng, Can Urgun","doi":"10.2139/ssrn.3442367","DOIUrl":"https://doi.org/10.2139/ssrn.3442367","url":null,"abstract":"This paper studies a continuous-time, nite-horizon contracting problem with renegotiation<br>and dynamic inconsistency arising from non-exponential discounting. The<br>problem is formulated as a dynamic game played among the agent, the principal and<br>their respective future \"selves\", each with their own discount function. We identify<br>the principal optimal renegotiation-proof contract as a Markov Perfect Equilibrium<br>(MPE) of the game, prove such a MPE exists, and characterize the optimal contract<br>via an extended Hamilton-Jacobi-Bellman system. We solve the optimal contract in<br>closed form when the discount functions of the selves are related by time di erence,<br>a property that is satis ed by common forms of non-exponential discounting such as<br>quasi-hyperbolic discounting and anticipatory utility. In particular, quasi-hyperbolic<br>discounting leads to a U-shaped action path and anticipatory utility leads to a humshaped<br>path, both are qualitatively di erent from the monotonic action path that<br>would arise under exponential discounting.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121127374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tapping Home Equity: Income and Spending Trends Around Cash-Out Refinances and HELOCs","authors":"Diana Farrell, Fiona Greig, Chen Zhao","doi":"10.2139/ssrn.3742341","DOIUrl":"https://doi.org/10.2139/ssrn.3742341","url":null,"abstract":"Approximately two thirds of American families own a home and for most homeowners, their house is also their most important source of wealth. Homeowners are currently sitting on historically high levels of home equity and the potential withdrawal of this home equity has important implications for consumption at the macroeconomic and household levels. In this report, we examine the extent to which liquidating home equity boosts consumption, as well as how income dynamics around equity extraction may play a role in influencing households’ decision to draw from this source of wealth. Using loan-level servicing data from Chase mortgage customers combined with corresponding Chase deposit account data from 2012 to 2018, we create a sample of more than 50,000 homeowners who either obtained a cash-out refinance or drew on a home equity line of credit (HELOC). We find that for homeowners who cash-out refinanced, most refinanced into a lower interest rate but a higher monthly payment because of a larger loan balance. Also, after controlling for secular trends, homeowners who obtained a cash-out refinance had no change in income whereas homeowners who extracted equity via a HELOC experienced declining income. For both groups, consumption spiked considerably as soon as the liquidated equity flowed into the bank account but quickly settled to steady state-levels at a higher level, 5 percent and 7 percent above baseline for HELOCs and cash-out refinances, respectively. After one year, cash-out refinance homeowners spent 33 percent of their total equity extracted while those with a HELOC spent 47 percent overall. For both sample groups, these marginal propensities to consume (MPCs) were highest for younger homeowners and those with higher loan-to-values (LTVs). Taken together, these findings have important implications for macroeconomic and housing policies.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133478847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How Preferences for Round Numbers Affect Choices: Stickiness and Jumpiness in Credit Card Payments","authors":"Hiroaki Sakaguchi, John Gathergood, Neil Stewart","doi":"10.2139/ssrn.3564728","DOIUrl":"https://doi.org/10.2139/ssrn.3564728","url":null,"abstract":"We explore the effects of round number preferences in credit card payments. Payments at round numbers are very common: 70% of manual non-full credit card payments are at round numbers. Using minimum payment amounts as a natural experiment for the lower bound on payments, we show stickiness in payment amounts when the minimum payment varies in the wide interval between round number bounds yet jumpiness in payment amounts when the minimum payment varies in the narrow interval across round number bounds. Round number preferences can therefore lead to over-estimation of both inattention, and responsiveness, to policies. Our findings have implications for models of inattention and for policy evaluation methods.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126574962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Do Dual Discounting Equations Reconcile Exponential Banks with Their Hyperbolic Customers?","authors":"Michael Osborne","doi":"10.2139/ssrn.3600507","DOIUrl":"https://doi.org/10.2139/ssrn.3600507","url":null,"abstract":"There is an apparent rift between the way banks calculate and the way humans think.<br><br>On the one hand, exponential discounting has played a centuries-long, lead role in financial analysis. On the other hand, experiments by behavioral economists demonstrate that hyperbolic discounting is better than exponential at explaining human inter-temporal behavior. The result is scope for misunderstanding between financial institutions and their customers because many financial products involve calculations alien to consumer thinking. Calls for improving consumer financial literacy are symptoms of this disconnect.<br><br>This article queries past experimental results by examining the underlying theory using the concept of duality. Two dual expressions are derived: one expression is dual to the exponential discounting equation and the other is dual to the hyperbolic. Each dual contains the full array of interest rates implied by every root solving its source equation. An array includes the negative and complex-valued interest rates ignored for centuries on the grounds that they lack economic meaning. Recent research, however, demonstrates that an array of rates does possess economic meaning. This finding legitimizes the duals, removing a barrier to their inclusion in financial analysis. <br><br>Duality offers possible reconciliation between the two approaches to discounting. The two dual expressions display a similarity and a difference. The similarity is in their structure, implying the two approaches to discounting are not as different as experimentalists suppose. The difference is in their components, this difference suggesting new experiments that may support or deny the proposed reconciliation.<br><br>Dual equations also suggest policy advice.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"162 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128628188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Present Bias","authors":"Anujit Chakraborty","doi":"10.2139/ssrn.3474231","DOIUrl":"https://doi.org/10.2139/ssrn.3474231","url":null,"abstract":"Present bias is the inclination to prefer a smaller present reward to a larger later reward, but reversing this preference when both rewards are equally delayed. Such behavior violates stationarity of temporal choices, and hence exponential discounting. This paper provides a weakening of the stationarity axiom that can accommodate present‐biased choice reversals. We call this new behavioral postulate \u0000 Weak Present Bias and characterize the general class of utility functions that is consistent with it. We show that present‐biased preferences can be represented as those of a decision maker who makes her choices according to conservative present‐equivalents, in the face of uncertainty about future tastes.\u0000","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124492765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Everything in Moderation: Foundations and Applications of the Satiation Model","authors":"Manel Baucells, Lin Zhao","doi":"10.2139/ssrn.3340643","DOIUrl":"https://doi.org/10.2139/ssrn.3340643","url":null,"abstract":"Models in which current utility depends solely on current consumption (a.k.a. time-separable preferences) are widely acknowledged to be unrealistic, especially when attempting to describe preferences over consumption rates. Alternatively, one may stipulate that instant utility also depends on a state, for example, some stock of past consumption. Escaping the gravitational pull of time separability, however, is difficult because (1) the behavioral axioms that characterize the state and the instant utility are not known, (2) how to elicit the preference parameters—most notably the initial level of the state and the decay rate—is not known, and (3) managerial applications where state-dependent preferences produce interesting insights and solutions are scarce. This paper makes advances on these three fronts by proposing a novel set of axioms that characterize the satiation model, a proof of concept on how to elicit all preference parameters using consumption rates, and a mixed-integer linear formulation to solve the optimal design of experiential services under satiation. Our preferences introduce a de-satiation motive, absent in separable preferences, and we explore how to optimally manage this motive. This paper was accepted by David Simchi-Levi, decision analysis.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"119 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127581146","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Social Rate of Time Preference and the Social Discount Rate","authors":"Mark A. Moore, A. Vining","doi":"10.2139/ssrn.3297241","DOIUrl":"https://doi.org/10.2139/ssrn.3297241","url":null,"abstract":"This paper explains the conceptual basis for the social rate of time preference (STP) and why it is the appropriate method of choosing the social discount rate (SDR), compared to the most prominent alternative method: the social opportunity cost of capital (SOC). We recommend that for intragenerational projects in the United States, a rate of 3.5 percent is appropriate. For long-term intergenerational effects, we recommend using declining rates. <br><br>Obtaining the SDR is intrinsically a normative exercise in a second-best world. Policymakers should maximize a social welfare function that equals the present value of current and future utility from per capita consumption. In the presence of economic growth, there will be greater future consumption possibilities. Given the assumption of diminishing marginal utility of income, the consumption of a wealthier, future society should be discounted. Displaced private investment should be accounted for by first multiplying by the shadow price of capital, but this will not generally be necessary as most government interventions mainly affect consumption. Systematic risk should be handled by conversion of expected net benefits into certainty equivalents before discounting at the risk-free SDR, but empirically this effect is typically too small to matter. <br><br>Among governments there is increased adoption of both the STP method and the use of time-declining rates. Even governments using other approaches are lowering their rates, and most OECD countries now apply rates in the 3 to 5.5 percent range.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131074431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thomas Mariotti, Nikolaus Schweizer, Nora Szech, Jonas von Wangenheim
{"title":"Information Nudges and Self Control","authors":"Thomas Mariotti, Nikolaus Schweizer, Nora Szech, Jonas von Wangenheim","doi":"10.2139/ssrn.3162013","DOIUrl":"https://doi.org/10.2139/ssrn.3162013","url":null,"abstract":"We study the optimal design of information nudges directed to present-biased consumers who make consumption decisions over time without exact prior knowledge of their long-term consequences. For any distribution of risks, there exists a consumer-optimal information nudge that is of cutoff type, recommending abstinence if the risk is high enough. Depending on the distribution of risks, more or fewer consumers have to be sacrificed, as they cannot be credibly warned even though they would like to be. Under a stronger present bias, the target group receiving a credible warning to abstain must be tightened, but this need not increase the probability of harmful consumption. If some consumers have a stronger present bias than others, traffic-light nudges turn out to be optimal and, when subgroups of consumers differ sufficiently, the optimal traffic-light nudge is also subgroup optimal. We finally compare the consumer-optimal nudge with those that a health authority or a lobbyist would favor. This paper was accepted by Manel Baucells, behavioral economics and decision analysis.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130502503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Time Consistency and Utility Weighted Discount Rates","authors":"O. Mbodji","doi":"10.2139/ssrn.3101522","DOIUrl":"https://doi.org/10.2139/ssrn.3101522","url":null,"abstract":"The discount rate is a tool used to measure the preference for immediate gratification or utility over delayed gratification. This paper considers the modified Merton problem of an economic agent maximizing his utility from consumption and final wealth when his discount rate is not constant. The question we answer is the following: if we allow the individual to update his decisions, will he stick to his original strategy or will he switch? We show that there are cases in which the agent's strategy keeps changing thus his behaviour becomes time inconsistent. We introduce two notions to solve this inconsistency problem. The agent can pre commit i.e. he does not change his original optimal strategy. He can also plan for his future changes of strategy and adopt time consistent strategies also known as subgame perfect strategies. We show that the subgame perfect strategy can be obtained from the pre commitment strategy if we replace the agent's discount rate by his utility weighted discount rate. This last quantity is shown to be the solution of a fixed point problem.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126281725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sunk Cost as a Self-Management Device","authors":"Fuhai Hong, Wei Huang, Xiaojian Zhao","doi":"10.2139/ssrn.2830409","DOIUrl":"https://doi.org/10.2139/ssrn.2830409","url":null,"abstract":"The sunk cost effect has been widely observed in individual decisions. Building on an intra-personal self-signaling game, the paper provides an economic model to show that the sunk cost effect may stem from an attempt to overcome the under-investment problem associated with present bias. The current self may take a costly action (which is a sunk cost for the future self) to signal the individual's ability that motivates his future self-disciplining behaviors. In equilibrium, a higher level of sunk cost gives rise to a higher probability for the individual to continue the project. We then conduct a laboratory experiment, which supports our theoretical implications.","PeriodicalId":443703,"journal":{"name":"ERN: Intertemporal Choice & Discounting (Topic)","volume":"41 5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126197847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}