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1 Regret Aversion & Dynamic Choice PhD Upgrade Presentation 29th February 2008 Stephen Lovelady Department of Economics 2 Why Regret Aversion? ~ The undergraduate approach... “You can't regret what you can't remember.” Lisa Birnbach (author) ~ Unfortunately little economic content ~ But probably quite enjoyable ~ Some explanatory power ~ Explains presenter's sobriety Introductio 3 Why Regret Aversion? ~ The PhD approach “Regret is insight that comes a day too late.” Anonymous ~ Considerations of regret are part of the decision making process ~ But do they come “a day too late”? ~ If we can anticipate regret, how does our decision making change? Introductio 4 Motivation for the research ~ Paper for Behavioural Economics ~ “Thoughts on Extending Present Bias Preferences to Continuous Time” ~ Highlighted two problems ~ How do you define the “present”? ~ When can individuals make decisions? ~ Can psychological factors play a role? ~ Specifically regret of a wrong decision Introductio 5 Parallels in the literature ~ Concept of “preference reversal” ~ Can occur in quasi-hyperbolic discounting models ~ What is optimal in one time period is not in the next ~ Can occur with regret theory ~ Cyclical preferences caused by anticipated regret ~ Behavioural Economics paper suggests they may be related Introductio 6 Primary Questions “Is it possible to construct a theoretically stable and empirically useful model of continuous time quasi-hyperbolic discounting?” “Is it possible to construct a dynamic framework for decision making with regret aversion?” Introductio 7 Secondary Questions “Is it possible to create a definition of the 'present' for use in quasi-hyperbolic discounting models, based on psychological factors?” “By what method are individuals able to learn and adapt their decision making process in a repeated dynamic context?” Introductio 8 Plan for the presentation ~ Outline the development of Regret Theory ~ Outline existing problems in the literature ~ Introduce the mechanisms of Regret Theory ~ Outline the development of Discounting Models ~ Propose how to bring the models together ~ Suggest examples where the model is relevant Introductio 9 Non-EUT Models ~ Empirical evidence suggests systematic violations of Expected Utility Theory (EUT) ~ Whole class of models (Non-EUT) which relax assumptions of EUT ~ Excellent summary by Starmer (JEL, 2000) ~ Makes several points which support my work ~ Regret Theory is just one proposed model ~ Disappointment Aversion ~ Complementary to Regret Theory Regret Theory 10 Regret Theory ~ Simultaneous work by Bell (1982) and Loomes & Sugden (1982) ~ Based on modifying the utility function to include a psychological “regret” term ~ Both papers use the same approach ~ I use the Loomes & Sugden framework without loss of generality ~ The model can explain the EUT violations suggested by Kahneman & Tversky (1979) Regret Theory 11 Regret Theory – The Model ~ Modified Utility Function mijk = cij + R(cij – ckj) ~ Decisions made by comparing Expected MU n ∑ p j mEkijik = j= 1 => Ai is preferred to Ak if n ∑ j= 1 pj [ cij – ckj + R(cij – ckj) – R(ckj – cij) ] ≥ 0 ~ Regret Aversion => for all z R''(z) > R''(-z) Regret Theory 12 Regret Theory - Implications ~ Individuals are willing to trade off now to avoid future potential regret ~ Individuals are disproportionately influenced by large potential regrets (regret aversion) ~ Not necessarily the same predictions as risk aversion ~ A descriptive, behavioural model ~ Though axiomatic foundation has been found by Sugden (1993) Regret Theory 13 Regret Theory - Development ~ However... ...regret is the result of comparing one's outcome with a better outcome that would have occurred had a different alternative been selected (Tsiros and Mittal, 2000, p.402) ~ Non-EUT is just one situation where regret occurs ~ What about dynamic models? ~ What about certainty models? Regret Theory 14 Regret Theory - Problems ~ Information regarding resolution of uncertainty ~ Simonson (1992) ~ What happens if you can't observe the missed opportunity? ~ Tsiros and Mittal (2000) ~ Counterfactual thinking ~ Feedback Conditional Regret Theory ~ Humphrey (2000) ~ Outcome resolution vs State of the world resolution ~ How are situations resolved dynamically? ~ Important consideration for my research Problems in Regret Theory 15 Regret Theory - Problems ~ Status Quo Bias ~ Tsiros and Mittal (2000) ~ Regret is greatest when deviating from the “status quo” option ~ Omissions versus Commissions ~ Spranca et al. (1991) ~ Individuals can judge an action with the same outcome differently depending on whether it is an omission or a commission ~ Suggests more regret for commissions ~ Is there a reference point in dynamic decisions? Problems in Regret Theory 16 Regret Theory - Problems ~ Framing effects ~ Starmer and Sugden (1998) ~ Uses “juxtaposition effects” to test Regret Theory versus other Non-EUT models ~ Results are sensitive, however, to: ~ Event splitting effects ~ Presentation framing effects ~ Hence tough to empirically test such models ~ Is it possible to construct a model to take account of such “mental shortcuts”? Problems in Regret Theory 17 Regret Theory - Mechanisms ~ Consider the “Money-Pump” argument ~ Regret Theory can generate cyclical preferences ~ A is preferred to B is preferred to C is preferred to A ~ Loomes & Sugden (1987) consider this a static problem ~ More likely to be a case for dynamic modelling ~ How do we make choices psychologically? ~ Can you learn from past mistakes? ~ Richard, van der Pligt & de Vries (1996) ~ Consider the difference between “evaluative” and “affective” components, ~ Also consider how they can be anticipated ~ Is regret the “affective” component? Mechanisms of Regret Theory 18 Discounting Models ~ Second part of my research ~ Excellent summary by Frederick, Loewenstein and O'Donoghue (2002) ~ Development of a discount rate to encompass all intertemporal choice parameters ~ Samuelson (1937) described the constant rate exponential model T− t t U (ct,....cT) = ∑D k= 0 k u ct 1 k k where D(k) = 1 ~ Implies Time Consistency of preferences Discounting & Time Consistency 19 Discounting Models ~ Empirical evidence, however, points to falling discount rate, not constant ~ Strotz (1955) called this the “intertemporal tussle” ~ Development of a discount rate to encompass all intertemporal choice parameters ~ Most constant formulation is the “quasihyperbolic” discount model T− t Ut(ct,....cT) = if k=0 ∑D k= 0 k u ct k where D(k) = 1 ~ Potential for Time of preferences βδkInconsistency if k>0 Discounting & Time Consistency 20 Discounting Models ~ Like Regret Theory, there has been “sideways” discussion and application ~ Illiquid Assets – Laibson (1997) ~ Procrastination - O'Donoghue and Rabin (1999) ~ Noticeable failure to develop the model in new contexts ~ Primarily moving from discrete to continuous time ~ Exhaustive list of papers on the topic ~ Karp (Journal of Economic Theory, 2007) ~ ...... ~ I aim to reintroduce economics to the area Discounting & Time Consistency 21 Discounting Models ~ Can we combine elements of discrete and continuous time? ~ More realistic economic context ~ Discrete decision making, but continuous utility? ~ How do we define “the present”? ~ Graph from Laibson (1997) ~ Highlights the problem faced ~ How do we “join the dots”? Discounting & Time Consistency 22 Creating the model ~ First start by expanding the “choiceless” or “basic” utility function ~ We can have an instantaneous utility function ~ eg. a lottery ticket ~ Or have a path of utility ~ receiving xir1, xir2 and xir3 at t=1,2,3 ~ xirt can itself be instantaneous or distributed over the period ~ Hence cir is now a function of xir1, xir2 and xir3 Creating the Model 23 Creating the model ~ The Loomes & Sugden (1982) framework suggests Ai is preferred to Ak if ∑ pj [ C(xij1, xij2, xij3) – C(xkj1, xkj2, xkj3) + R(C(xij1, xij2, xij3) – C(xkj1, xkj2, xkj3)) j= r ,b – R(C(xkj1, xkj2, xkj3) – C(xij1, xij2, xij3)) ] ≥ 0 ~ Now introduce a decision period, t=0 ~ no utility gained at t=0 ~ exists one period prior to t=1 => u(xaj0) = 0 for all a = i,k and j = r,b ~ It is clear that the method of disconting matters for decision making Creating the Model 24 Consider the discounting ~ Firstly consider an exponential discounting model 3 Cτ(xijt=0,1,2,3) =∑ cijτ =t− τ u(xijt) t= τ ~ Are preferences still time consistent with the additional regret term? ∑ 0 j= r ,b [ cij0 – ckj0 + R(cij0 – ckj0) – R(ckj0 – cij0) ] ≥ if and only if ∑ 0 pj j= r ,b pj [ cij1 – ckj1 + R(cij1 – ckj1) – R(ckj1 – cij1) ] ≥ Creating the Model 25 Resulting questions ~ Furthermore: ~ Does the definition of regret aversion still hold with exponential discounting? ~ What conditions are needed on u(.) and R(.) for regret aversion and time consistency? ~ Do the same results hold if the uncertainty is removed from the model? ~ Can we anticpiate and be averse to regret without uncertainty? Creating the Model 26 Consider the discounting ~ Now consider a quasi-hyperbolic model Cτ(xij t=0,1,2,3 τ 3 ) = cij = u(xij∑τ) + t− τ u(xijt) t τ ~ What conditions on u(.) and R(.) give time consistency of preferences? ~ What conditions on u(.) and R(.) give time inconsistency of preferences? ~ Does regret aversion hold with quasihyperbolic discounting? Creating the Model 27 Further Questions ~ Consider the model from the perspective of “evaluative” and “affective” choice ~ Richard, van der Pligt and de Vries (1996) ~ Is the same discounting function necessarily used for the evaluative and affective components? ~ What happens if not? ~ Are the evaluative and affective components necessarily aligned at the same time points? ~ Do we consider the evaluative component first, and then think about the affective consequences? ~ Introduce a time delay into the model Creating the Model 28 Relevant Examples ~ Alcohol consumption ~ Richard, van der Pligt and de Vries (1996) “...people may like the idea of going out with friends, drinking alcohol, and having a good time, but may also realize that they will regret it early the next morning when having to get up for work." ~ 3 stage process ~ Precommitment phase ~ Drive, walk or get the bus ~ Drinking phase ~ High level of utility if drunk, low if not ~ Hangover phase Relevant Examples 29 Relevant Examples ~ How is the decision reached? at ~ Precommitment device (car) prevents getting drunk the next stage ~ Present bias preference reversal when getting drunk ~ “I said I wasn't getting drunk tonight, but....” ~ Potential peer pressure effects? ~ Does the hangover induce regret aversion? ~ Being hungover is much worse than not getting drunk the previous night(?) Answering the question requires an integrated model, where none currently exists Relevant Examples 30 Next Steps ~ Start with pairwise decision ~ Begin with uncertainty ~ look to remove eventually ~ Introduce time into Regret Theory ~ Introduce regret into Exponential and QuasiHyperbolic discounting ~ Develop continuous time Quasi-Hyperbolic discounting economically rather than mathematically ~ Remain aware of the problems identified Next Steps 31 Questions... Questions