class: center, middle, inverse, title-slide # Present Bias I ## EC895; Fall 2022 ### Prof. Ben Bushong ### Last updated September 14, 2022 --- layout: true <div class="msu-header"></div> <div style = "position:fixed; visibility: hidden"> `$$\require{color}\definecolor{yellow}{rgb}{1, 0.8, 0.16078431372549}$$` `$$\require{color}\definecolor{orange}{rgb}{0.96078431372549, 0.525490196078431, 0.203921568627451}$$` `$$\require{color}\definecolor{MSUgreen}{rgb}{0.0784313725490196, 0.52156862745098, 0.231372549019608}$$` </div> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ TeX: { Macros: { yellow: ["{\\color{yellow}{#1}}", 1], orange: ["{\\color{orange}{#1}}", 1], MSUgreen: ["{\\color{MSUgreen}{#1}}", 1] }, loader: {load: ['[tex]/color']}, tex: {packages: {'[+]': ['color']}} } }); </script> <style> .yellow {color: #FFCC29;} .orange {color: #F58634;} .MSUGreen {color: #14853B;} </style> --- class: inverseMSU name: Overview # Today ### **Our Outline:** (1) [The Standard Model](#section1) (2) [A Model of Present Bias](#section2) (3) [Procrastination](#section3) (4) [Evidence of Present Bias](#section4) --- class: MSU name: section1 # Choice over Time *from (Samuelson, 1937)* ### Exponential discounting When a person receives utility at different points in time, she seeks to maximize her *intertemporal utility*: `$$U \equiv u_{1}+\delta u_{2}+\delta ^{2}u_{3}+...+\delta ^{T-1}u_{T}$$` -- or put another way: `$$= \sum_{t=1}^{T}\delta ^{t-1}u_{t}\text{.}$$` -- - `\(u_{t}\)` is her **instantaneous utility** in period `\(t\)` (or her "well-being" in period `\(t\)`). -- - `\(\delta\)` is her **discount factor**, where `\(\delta \in (0,1]\)`. --- class: MSU # The Standard Model ### What are some of the implied assumptions of this model? - Consumption independence - Stationary instantaneous utility - Independence of discounting from consumption -- - **Constant discounting and time consistency** ### Is this realistic? --- class: MSU # Constant discounting **Empirical question:** How do people weight utility now vs slightly later vs even later? -- A common technique: **Calibration exercise**. (Here, magnitudes don't fit with intuition, as we'll see) - Evidence of systematic "preference reversals" - (Sometimes) demand for commitment --- class: MSU # A Calibration Argument If we discount utils tomorrow by `\(1\%\)`, -- - then the one-year discount factor is `\(.99^{365}\)`. -- - 100 utils in 1 year are worth 2.6 utils today. - 100 utils in 10 year are worth `\(1\)` x `\(10^{-14}\)` utils today. -- If we discount utils in a year by `\(5\%\)`, -- - then the one-day discount factor is `\(0.95^{1/365}\)`. - 100 utils tomorrow are worth 99.99 utils today. -- ### Something here seems amiss. --- class: MSU # Diminishing Impatience (Thaler, 1981a): > "What amount of money in one month / one year / ten years would make you indifferent to receiving $15 now? -- ### Finding: the implicit (annual) discount rate decreases in time horizons. - 345 percent over one-month horizon - 120 percent over one-year horizon - 19 percent over ten-year horizon --- class: MSU # Diminishing Impatience General pattern of diminishing impatience well-replicated. <img src="graphics/Frederick_discount1.png" width="550px" style="display: block; margin: auto;" /> (Frederick, Loewenstein, and O'Donoghue, 2002) Figure 1a: Discount Factor as a Function of Time Horizon (all studies) --- class: MSU # Preference Reversals People's time preferences (predictably) change over time. -- Asking today: - Do you prefer $50 today or $60 tomorrow? - Do you prefer $50 in 30 days or $60 in 31 days? -- Asking in 30 days: - Do you prefer $50 today or $60 tomorrow? - Do you prefer $50 in 30 days or $60 in 31 days? --- class: MSU # Present-Biased Preferences The **quasi-hyperbolic discount function** as in Phelps and Pollak (1968), O'Donoghue and Rabin (1999), and Laibson (1997): `$$D(\tau) = \begin{cases} 1 & \text{ if } \tau = 0 \\ \beta \cdot \delta^{\tau} & \text{ if } \tau \in \{1, 2, \ldots\} \end{cases}$$` where `\(\beta \leq 1\)` -- - We can then write the utility function as: `$$U^{t} = u_{t} + \beta \sum_{\tau = 1}^{T-t} \delta^{\tau} u_{t+\tau}$$` --- class: MSU # Visualizing Discount Functions <img src="graphics/Laibson_discount_functions.png" width="550px" style="display: block; margin: auto;" /> Comparison of exponential, hyperbolic, and quasi-hyperbolic discount functions; from Angeletos, Laibson, Repetto, Tobacman, and Weinberg (2001a). --- class: MSU # Building Intuitions Discount function for `\(\beta=1/2\)` and `\(\delta\simeq1\)`: `$$D(\tau) = 1,\beta\delta,\beta\delta^{2},\beta\delta^{3},\ldots$$` $$ = 1,\frac{1}{2},\frac{1}{2},\frac{1}{2},\ldots $$ -- Relative to present period, all future periods worth less (weight 1/2). -- - All discounting takes place between the present and the immediate future. -- - In the *long-run*, we are relatively patient: utils in a year are just as valuable as utils in two years. `\(\Rightarrow\)` Decisions are sensitive to the timing of benefits and costs. --- class: MSU # Intuitive Examples ### Leisure goods: immediate rewards with delayed costs. -- **Eating candy** - Immediate utility benefits `\(B_{\text{PLEASURE}}=2\)` - Delayed health costs `\(C_{\text{HEALTH}}=3\)` - (Let `\(\beta=1/2\)` and `\(\delta=1\)`.) -- ### Planning not to eat candy next week: `$$\beta\cdot(B_{\text{PLEASURE}}-C_{\text{HEALTH}})=\frac{1}{2}\cdot(2-3)<0$$` -- ...but eating candy today: `$$B_{\text{PLEASURE}}-\beta\cdot C_{\text{HEALTH}}=2-\frac{1}{2}\cdot3>0$$` -- `\(\Rightarrow\)` Over-consume leisure goods relative to long-run plans --- class: MSU # Intuitive Examples ### Investment goods: immediate costs with delayed rewards. -- **Going to the gym** - Immediate effort costs `\(C_{\text{EFFORT}}=2\)` - Delayed health benefits `\(B_{\text{HEALTH}}=3\)` - (Continue with `\(\beta=1/2\)` and `\(\delta=1\)`). -- ### Planning to go to the gym next week: `$$\beta\cdot(-C_{\text{EFFORT}}+B_{\text{HEALTH}})=\frac{1}{2}\cdot(-2+3)>0$$` -- ...but not going going today: `$$-C_{\text{EFFORT}}+\beta\cdot B_{\text{HEALTH}}=-2+\frac{1}{2}\cdot3<0$$` -- `\(\Rightarrow\)` Under-consume investment goods relative to long-run plans --- class: MSU # The Devil (Is in the Details) ### Might a person with present bias: - Build up $5,000 of debt on a credit card at 20% interest? **Yes.** -- - Take out a home equity loan at 5% interest requiring three hours of paperwork and a two-week processing delay? **I'll do it next week.** -- - Take out a home equity loan at 10% interest, *pre-approved with no paperwork required*? **Yes.** -- - Buy a new car, making $4,000 down-payment? **No thanks.** -- - Buy a new car, without a down-payment? **Ooh.** --- class: MSU # Working with the Model ## Doing it Now or Later (*Courtesy of Matthew Rabin*) Suppose there is a task that you must complete on one of the next four days. -- To complete this task, you incur costs as follows: - If you complete the task in period 1, the cost is 3. - If you complete the task in period 2, the cost is 5. - If you complete the task in period 3, the cost is 8. - If you complete the task in period 4, the cost is 13. -- Suppose there is no reward, that you value costs linearly, and that you have `\(\beta =1/2\)` and `\(\delta =1\)`. --- class: MSU # The Importance of Awareness *A critical issue*: Are you aware of your future self-control problems (or your future present bias)? -- Note that your period-1 preferences are: `$$(\text{period 2})\succ (\text{period 1})\succ (\text{period 3})$$` while your period-2 preferences are: `$$(\text{period 3})\succ (\text{period 2}).$$` -- If you were asked to commit yourself in period 1, you'd commit yourself to do the task in period 2. -- Suppose instead that in period 1 you only choose whether or not to do the task then. Then your choice will depend on what you expect to do in period 2 (if you were to wait). --- class: MSU # Sophistication vs Naivité Two extreme assumptions about people's awareness of their own future self-control problems: -- **Sophisticates** are *fully aware* of their future self-control problems and thus correctly predict future behavior. To solve for sophisticates: - Treat each period-self as a separate agent, and solve for the subgame-perfect Nash equilibrium to the game played between these agents (using backward induction). -- - Sophisticates always stick to their plans. -- **Naifs** are *fully unaware* of their future self-control problems and thus expect to behave in future exactly as they currently would like themselves to behave in future. To solve for naifs: - Each period, derive the optimal lifetime path, and follow this period's component. But when next period arrives, reassess this plan. - **Obviously:** Naifs may not stick to their plans. --- class: MSU # Doing it Now or Later (also known as Fibonacci's Fine Arts Cinema; thanks Matthew). -- - Week 1: mediocre movie, 3 utils - Week 2: good movie, 5 utils. - Week 3: great movie, 8 utils. - Week 4: **Moonfall** (obviously the best movie ever), 13 utils. -- Assume `\(\delta =1,\)` `\(\beta =\frac{1}{2}.\)` -- ### Suppose you must miss one movie, and thus get 0 utils that day. --- class: MSU # Doing it Now or Later Your (cinematic) life choices are `\((u_{1},u_{2},u_{3},u_{4})=\)`. -Choose `\((0,5,8,13)\)` or `\((3,0,8,13)\)` or `\((3,5,0,13)\)` or `\((3,5,8,0)\)`. -- *Rules:* You cannot commit to which movie to miss. You must decide incrementally each week whether to see that movie or skip it. -- (This assumption **matters**.) -- What movie should you miss? -- What movie *will* you miss? --- class: MSU # Doing it Now or Later Have to consider two cases: naive vs sophisticated decision-maker. ### Case 1: What will a sophisticate do? -- - Because `\(8+\frac{1}{2}0>0+\frac{1}{2}13,\)` the sophisticate won't skip Week 3. -- - Because `\(0+\frac{1}{2}(8+13)>5+\frac{1}{2}(8+0),\)` the sophisticate *will* skip Week 2 (if she has not already skipped Week 1). -- - Because `\(3+\frac{1}{2}(0+8+13)>0+\frac{1}{2}(5+8+13),\)` the sophisticate *won't*\ skip Week 1. -- Hence: The sophisticate will miss the 2nd movie. --- class: MSU # Doing it Now or Later ### Case 2: What will a naif do? -- - Because `\(3+\frac{1}{2}(0+8+13)>0+\frac{1}{2}(5+8+13),\)` won't skip Week 1. -- - Because `\(5+\frac{1}{2}(0+13)>0+\frac{1}{2}(8+13),\)` won't skip Week 2. -- - Because `\(8+\frac{1}{2}0>0+\frac{1}{2}13,\)` the naif won't skip Week 3. -- Hence: The naif will miss Moonfall. -- Note that even given `\(\beta =\frac{1}{2},\)` all four selves agree that missing the moon literally fall into the earth is a bad thing to happen. Yet the naif does so. --- class: MSU # Doing it Now or Later **Calibrational exercise:** Let us see what we would infer from the observed behavior if we were an anachronistic economist who believed in `\(\beta =1.\)` -- An exponential discounter would have to have a **weekly** discount factor `\(\widetilde{\delta }\leq Min[\sqrt[3]{\frac{3}{13}},\sqrt[2]{\frac{5}{13}},\frac{8}{13}]\approx .61\)` to be willing to miss that gem of a film. -- | | Letting `\(\beta <1\)` | Insisting `\(\beta =1\)` | |:-------- |:---------:|:---------:| | Week 1 weight on `\(u_{2}\)` vs. `\(u_{1}\)` | `\(.61\)` | `\(.61\)` | | Week 1 weight on `\(u_{4}\)` vs. `\(u_{1}\)` | `\(.61\)` | `\(.23\)` | -- Lesson: Some behavior looks more (absurdly) impatient if (mis)interpreted through the lens of exponential discounting. --- class: MSU # Procrastination ### Procrastination: Doing It `\(\dots\)` Tomorrow Procrastination involves the *immediate gratification* of not doing something optimally onerous -- - Often the main "cost" of doing some beneficial task is primarily the opportunity cost of doing something gratifying. - Procrastination is in fact a wonderful vice: You can, **and ideally should** do it concurrently with other vices! -- - Note: quitting smoking, etc. qualitatively similar to procrastination. -- But what *is* it? -- - Not just delaying unpleasant tasks, which is often right thing to do. - It is delaying beyond when you yourself want to complete them. --- class: MSU # Procrastination Example Suppose that, with 120 minutes of effort today, you could reduce the effort by 10 minutes needed to undertake a task every day for rest of your life. -- E.g., learn some short cuts or tricks with your word-processing package, or "fix" some annoying problem in the current user set-up. -- - So, within 2 weeks, you will on net save time. In a year, 58 hours, and in a decade, 600 hours. - Suppose that value of time the same each day. No deadlines, no commitment devices. -- - Do you do the task? If so, when? --- class: MSU # Procrastination Example If do the task today your intertemporal well-being is: `$$U^{t}=-120+\beta \delta \cdot 10+\beta \delta ^{2}\cdot 10+\beta \delta ^{3}\cdot 10+...$$` -- `$$=-120+\beta \frac{\delta }{1-\delta }10,$$` ...relative to the utility of doing nothing. --- class: MSU # Procrastination Example Suppose time consistent, no taste for immediate gratification. -- E.g., `\(\beta =1,\)` `\(\delta =.999\)`. Then: `$$U^{t}\text{(fix today)}=-120+\frac{.999}{1-.999}10=9,870.$$` -- `$$U^{t}\text{(fix tomorrow)}=.999(-120+\frac{.999}{1-.999}10)=9,861$$` -- `$$U^{t}\text{(fix next day)}=.999^{2}(-120+\frac{.999}{1-.999}10)=9,852$$` -- ...and so on -- `$$U^{t}\text{(never)}=0$$` So: Person will do it right away. --- class: MSU # General "Theorem" ### The Fundamental Theorem of Time-Consistent Task-Assessment in Stationary Environments: -- Either: - `\(U^{t}(today)\succ\)` - `\(U^{t}(tomorrow)\succ\)` - `\(...\succ\)` - `\(U^{t}(never)\)` -- or - `\(U^{t}(never)\succ\)` - `\(...\succ\)` - `\(U^{t}(tomorrow)\succ\)` - `\(U^{t}(today).\)` --- class: MSU # Relationship to Procrastination This is the combination we are interested in: - `\(U^{t}(today)\succ U^{t}(never),\)` but `\(U^{t}(tomorrow)\succ U^{t}(today).\)` -- This would never happen for a time-consistent person, by the FT-TC-TASE. -- - In a stochastic or non-stationary environment, could be that a TC person happens to not want to do it today - But the systematic congruence of these two inequalities is the feature of interest for present bias. -- **If a task is worth doing, it is worth doing right away.** -- - Day-to-day variation in opportunity cost, etc., then there may be particular reason to do tomorrow than today - or today rather than tomorrow. - But no systematic tendency to put off tasks. --- class: MSU # Back to the Example Suppose some taste for immediate gratification (present bias). E.g., `\(\beta =.9,\)` `\(\delta =.999.\)` -- `$$U^{t}(today)=-120+.9\frac{.999}{1-.999}10=8,871$$` -- (And of course, `\(U^{t}(never)=0\)`) -- So even with a taste for immediate gratification: - Feels to you like you are saving about 150 hours in the future with the two hours today. - Indeed, you would prefer doing the task today to never doing it even if it would take you 24 hours, not just 2 hours. --- class: MSU # Example End So... - Do you do the task? - If so, when? -- If your choices were Today vs. Never, then you'd **obviously do it today**. -- - But you could also plan to do the task tomorrow: `$$U^{t}(tomorrow)=.9\cdot .999(-120+\frac{.999}{1-.999}10)=8,874$$` -- You'd prefer to learn tomorrow rather than today. --- class: MSU # Exercise What does the agent do **as a function of their beliefs about themselves?** -- In a related context, O'Donoghue and Rabin (2001) introduce a formal model of *partial naivete* - Since `\(\beta\)` captures the magnitude of the person's self-control problem, we can think of the person as having a perception `\(\hat \beta\)` of future self-control problems -- 1. Sophisticates have `\(\hat \beta = \beta\)` 2. Naifs have `\(\hat \beta = 1\)` 3. Partial naifs have `\(\hat \beta \in (\beta, 1)\)` -- - As before, the solution concept: subgame perfect equilibrium, assuming that all future selves behave with `\(\hat \beta\)`, while current self uses `\(\beta\)`. --- class: MSU # Another "Theorem" **Severe** procrastination for "one-shot" tasks requires some naivety. -- ### Why? Intuitions? -- Simple style of rationality argument in economics. - Sophisticates predict their future behavior correctly, and always have one simple action available to them ... doing the action now. - That means their utility from their now perspective is bounded below by the utility of doing it right away. --- class: MSU # A Calibration Exercise As before, let's explore a mispecification/calibration exercise: -- - A **deltoid** will never do task only if `\(-120+\frac{\delta }{1-\delta }10\leq 0,\)` so she would choose the action *never do the task* only if `\(\delta \leq \frac{12}{13}\Rightarrow \delta ^{365}\leq .000000000002.\)` -- Hence, to reconcile behavior with the exponential model if we are confident in our assessment of the disutilities of effort, we would need a yearly `\(\widetilde{\delta }\leq (\frac{12}{13})^{365}=.000000000002.\)` -- By contrast, we're explaining this with very modest (first-)yearly discounting. --- class: MSU # Calibration (cont) Of course, effort costs probably increasing rather than linear. -- - And we shouldn't assume we know utility function when inferring discount factors. -- ### Principle: continue to take the exercise seriously. Suppose we didn't know `\(\widetilde{\mu }=\frac{u(120\text{ minutes})}{u(10\text{ minutes})}.\)` -- **Exercise:** What locus of `\((\widetilde{\delta },\widetilde{\mu })\)` would explain avoiding 2 hours of effort immediately to save 10 minutes every day rest of your life? -- - This is (a little) challenging, but worth exploring for "fun". Impress your friends and neighbors! --- class: MSU # The Neverending Example ### "New" Example Consider `\(\beta =.9,\)` `\(\delta =.999\)` naif again. But now: -- - Suppose that the only choice available is a "quick fix": 1 minute of effort today `\(\Longrightarrow 9\frac{1}{2}\)` minutes saved each day forever. -- - Would she do this? If so, when? -- Answer: Yes, she would. No temptation to put off the 1 minute of work until tomorrow. -- `$$U^{t}(today)=-1+.9\frac{.999}{1-.999}9.5=8540$$` `$$U^{t}(tomorrow)=.9\cdot .999(-1+\frac{.999}{1-.999}9.5)=8532$$` --- class: MSU # The Neverending Example Ends Now suppose **both** the 120/10 task and 1/9.5 task are available. -- Assume could do both sequentially, but don't save time on days when fixing. -- The naif will compare her four choices: - `\(\quad U^{t}\text{(quick fix today)}=8540\)` - `\(\quad U^{t}\text{(quick fix tomorrow)}=8532\)` - `\(\quad U^{t}\text{(full fix today)}=8871\)` - `\(\quad U^{t}\text{(full fix tomorrow)}=8874\)` -- So she'll perpetually **plan** to do the full fix tomorrow. And meanwhile she will **never do either of them**. -- ### The unfortunate guiding credo of the naif: If you are going to do something, do it right `\(\dots\)` tomorrow. --- class: MSU # Calibration (concluded) Somebody who is unwilling to take 120 minutes of effort to save 10 minutes *or* to take 1 minute of effort to save 9$\frac{1}{2}$ minutes every day for the rest of her life seems, **interpreted through the lens of exponential discounting**, as if she is discounting at rate of -- `\(\tilde{\delta}_{\text{yearly}}<.0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(0000000000\)` `\(00000000001.\)` --- Acknowledging the possibility that `\(\beta <1,\)` `\(\hat{\beta }>\beta\)` reconciles such behavior to reasonable long-term patience. --- class: MSU # April is the Cruelest Month ## Cumulative Procrastination -- Suppose you *must* read 30 pages in 30 days. That is, `\(\sum_{t=1}^{30}p_{t}\geq 30\)`. If you spend `\(h_{t}\)` hours reading on day `\(t\)`, then `\(u_{t}=-h_{t},\)` and get `\(p_{t}=\sqrt{h_{t}}\)` pages read. -- **Key feature:** It is more efficient to spread out work regularly rather than doing it all in the space of a few days. - (Other models with this qualitative feature would yield similar results.) -- **Obvious solution for deltoid** If `\(\delta =\beta =\widehat{\beta }=1\)`, `\(p_t = h_t = 1\)` for all `\(t\)`. --- class: MSU # April is the Cruelest Month Consider *April Mae*: `\(\delta =\widehat{\beta }=1, \beta =\frac{1}{2}.\)` -- Day 1: April Mae will `\(Max\)` `\(_{h_{1}}\)` `\(U^{1}\equiv -h_{1}+\frac{1}{2} \left[ -29\left( \frac{30-\sqrt{h_{1}}}{29}\right) ^{2}\right].\)` If she reads `\(h_{1}\)` hours on Day 1, she'll need to read `\(\frac{30-\sqrt{h_{1}}}{29}\)` pages each remaining day, spending `\(\left( \frac{30-\sqrt{h_{1}}}{29}\right) ^{2}\)` hours each day. -- So on Day 1, April Mae reads for 15$\frac{1}{2}$ minutes (planning to read 62 minutes each of the remaining 29 days). -- That is, she is planning to increase future `\(h\)` by 58 minutes to decrease `\(h\)` today by 45 minutes. -- Day 2: Day 2: `\(Max\)` `\(_{h_{2}}\)` `\(U^{2}\equiv -h_{2}+\frac{1}{2}\left[-28\left( \frac{29.5-\sqrt{h_{2}}}{28}\right) ^{2}\right]\)`. That is, on Day 2: April Mae reads for 16 minutes (and plans to read 64 minutes each day from now on). --- class: MSU # April is the Cruelest Month Day 3: ...reads 17 minutes ... (and plans for 67 minutes each remaining day). -- Day 10: ... 22 minutes (and ... 90 minutes ...). -- With a week left: Has read 16 pages in 11 hours. -- Day 24: 72 minutes (and ... more than 4 hours ...). -- Day 30: April Mae reads for 23$\frac{3}{4}$ hours. --- class: MSU # Research Question ### Is the previous example misleading? -- Put another way: Present bias leads us to do things last minute. In line with procrastination, people often complete tasks last minute. For example: - Parking tickets (Heffetz et al., 2016); health care plan choice (Brown and Previtero, 2018); taxes (Martinez et al., 2017); patent officers' fillings (Frakes and Wasserman, 2016) -- **A natural idea:** if task completion is driven by the tendency to procrastinate, use data on task completion to identify time preference. "Common wisdom" (as n Frakes and Wasserman, 2016): observed bunching at the deadline is evidence of time-inconsistency. -- Implicit argument: inconsistent with `\(\delta \approx 1\)`. -- Suppose an analyst observes a sequence of actions over a month. Can the analyst conclude with any confidence that the person suffers (naive) present bias? --- class: MSU # Identifying Present Bias Think of *preparing your taxes* or *paying a parking ticket*. -The agent needs to complete the task before the deadline `\(T\)`. -- -If she did not complete the task by the end of period `\(T\)`, the agent gets a penalty of `\(\frac{y}{(\beta \delta)} \leq 0\)` in period `\(T+1\)` - So `\(y\)` is the period-$T$ continuation value when not having done the task. -- In every period `\(t \leq T\)`, the instantaneous utility of completing the task is drawn independently from a given payoff distribution `\(F\)`. - Think of this as the instantaneous benefit of completing the task net of opportunity costs. - Assume `\(F\)` is known to the agent. - Instantaneous utility of not doing the task is normalized to zero. --- class: MSU # Identifying Present Bias The analyst can observe agent's stopping probabilities at every point in time. -- Either observes infinitely many homogeneous agents, - or the same agent infinitely many times. - Obviously homogeneity facilitates identifying time preferences. -- It is known that opportunity costs are drawn independently from a given stationary distribution. - (Otherwise can rationalize any data by assuming cost are either one or zero, with the probability that they are zero being equal to a period's stopping probability.) - Stationarity is a natural starting point. -- Note: This is **the absolute best case scenario for identification!** --- class: MSU # Identifying Present Bias <img src="graphics/bar-plot-stopping-probabilities.png" width="550px" style="display: block; margin: auto;" /> Red bar plot: time-consistent agent with log-normally distributed cost ($\mu=1$ and variance `\(\eta=1\)` ) Blue bar plot: sophisticated time-inconsistent agent with `\(\beta = 0.7\)` and parameters `\(\mu=0, \eta=2.3\)` . --- class: MSU # Punchline: Caution. *from Heidhues and Strack (2021)* Despite strong stationary, homogeneity, and observability assumptions, and restriction to quasi-hyperbolic discounting: -- Both, the degree of present bias as well as the discount factor are, **for any data set of stopping times** not identifiable. - Importantly, present bias parameter is unidentified even when fixing the long-run discount factor. - *Naivite* vs *sophistication* are also not identifiable. -- - With a stationary net-benefit distribution, a hyperbolic discounter never sets an earlier deadline. --- class: inverseMSU # Coming Soon Next time: real evidence of present bias. -- ### Please read: 1. DellaVigna and Malmendier (2006): "Paying Not To Go To the Gym" and 2. Kaur, Kremer, and Mullainathan (2015): "Self-Control at Work"