Term Paper
FEEDBACK ON YOUR ANALYSIS TASKS SO COMMON I DIDN’T TRY TO WRITE IT ON EVERY PAPER:
Always report p-values. This means you’ll want to do at least some regressions, since that is the easiest way to get p-values. Report the raw p-values, then do the Benjamini-Hochberg FDR adjustment for multiple hypothesis testing if appropriate. (It is confusing if you don’t also report the raw p-values.)
Always give the full details of the wordings of the questions and the response options. You can always get these by doing the survey again, but when I am doing that sort of thing I don’t give real answers to the questions, I just click anything until I get to the questions I wanted to look at.
I said I love scatterplots, but there is an exception: when one of the two variables has only a few possible values, box plots for the other variable given each of those few possible values are a better way to show the relationship. Note that box plots are a lot like bar charts—but they have more total information in them than bar charts.
If you have income in the regression, always use log(income). When it is income ranges (bins) that people say, you should use log(midpoint of the range) as log(income). Using non-logged income is almost guaranteed to get you weird results. And using bin number gives a coefficient that is hard to interpret.
If you have log(income) in a regression (and I think it will be household income—all the adult incomes should be counted), I highly recommend using putting log(household size) in as another variable in the regression. That makes sure that you are accounting for a given amount of income being spread over more people while being fairly agnostic about economies of scale in the household.
Make sure to discuss causality and to discuss causality in the context of your particular analysis, not just in general terms. What are the likely biases? What is their likely direction? What are some things that are possible but that you don’t think are issues in your particular case?
Carefully use non-causal words where you aren’t actually claiming causality. You don’t want to use causal words until you are really ready to discuss causality.
Due by 11 PM Wednesday, April 30, 2025.
Your term paper should incorporate a revised version of what you wrote for your Analysis Task and be 4-6 pages longer than that revision of what you wrote for your Analysis Task. That is, the rest of your paper beyond what you wrote for the Analysis Task should be 4-6 pages.
Here are some of the main things I’ll look for in your term paper:
Write well: have a thesis statement and a theme that you follow through
Critique a paper in the academic literature on topics related to things we have discussed in class. Don’t choose one of my papers. But the references lists in my papers on happiness and of the other papers listed below are good places to find a paper.
(Drilling down on point 2.) Assume that the paper has flawed statistical interpretation. (In particular, results are typically overinterpreted to make them sound more exciting.) Do better on the statistical interpretation front. Use all of the things you learned about statistical interpretation in class that are relevant. (I’ll subtract points if a statistical interpretation principle was clearly relevant to what you are critiquing or to your own analysis and you don’t discuss it and add points if you do a great job discussing an issue.) The goal is not to solve everything but to show your awareness of the issues and do what can readily be done to think about what the issue implies. (For example, it is great if you can say which direction a bias is.)
Weave in a revision of your analysis task. The integration of this with your critique of a paper in the literature doesn’t have to be perfect, but it is a plus if you can make the critique of a paper in the literature and your own statistical analysis fit together with a theme.
Be timely: because of the exigencies of making grades for this and my other course, it is especially important that I get these term papers by the due date. However, I will still accept them, but with some points off, up to two days late.
The main idea for the term paper is to discuss an academic journal article on well-being skeptically. Chat GPT and other AI are great ways to find academic articles related to the analysis you did, though if you have real trouble finding something closely related, more distantly related is fine.
When I ask ChatGPT for a book or article on the topic, I use a prompt like this: Please find 10 articles on [TOPIC}. You often hallucinate articles and books that don’t exist, so please check online to make sure each one of them really exists and give me a link for each.
How to be skeptical. Here are some ways you might want to be skeptical (and there are many others):
Scale-use differences might be creating an illusion. (How?)
There is likely to be statistical bias relative to what the author or authors seem to be claiming or implying. (Make sure to explain which direction you think any story of possible statistical bias would bias things. Is the estimate in the paper likely to be higher than the truth or lower than the truth? What does that say about the truth?)
A result that has a nominal p-value of 5% (t-statistic of 2 or so) really has about a 50% chance of being spurious, as indicated by replication studies. (By contrast, a result with a nominal p-value of 1/2 % (t-statistic of 3 or more) has only about a 5% chance of being spurious, and so is relatively trustworthy. Here though, “trustworthy” had to be taken in a narrow sense. Something is probably going on with that coefficient, but what is going on may be very different from what the authors claim. (See for example the rest of this list of reasons to be skeptical!)
Happiness is not the same as utility. As my coauthored papers “Utility and Happiness,” “What Do You Think Would Make You Happier? What Do You Think You Would Choose?” “Can Marginal Rates of Substitution Be Inferred from Happiness Data? Evidence from Residency Choices” and “Beyond Happiness and Satisfaction: Toward Well-Being Indices Based on Stated Preference” suggest, there are many distinct meaning of happiness. Among them are:
utility
feeling happy
what people report on a survey about their happiness, life satisfaction or position on the ladder of life (all of which have a lot of data available)
Aristotelian noble happiness, often called “eudaimonia” or “eudaemonic well-being” in the literature
Other theoretical issues
In Addition to Getting Help from AI, There Are a Lot of References in Your Textbook to Papers that Would Be Good to Critique. And Here are Some Papers with References Lists in which You Can Find a Paper to Critique (Note: Don’t Critique a Paper with Miles as a Coauthor—those papers are only included because they have highly relevant references lists):
“Challenges in Constructing a Survey-Based Well-Being Index,” by Dan Benjamin, Kristen Cooper, Ori Heffetz and Miles Kimball
“A Well-Being Snapshot in a Changing World,” by Dan Benjamin, Kristen Cooper, Ori Heffetz and Miles Kimball
“What Do You Think Would Make You Happier? What Do You Think You Would Choose?” by Dan Benjamin, Ori Heffetz, Miles Kimball and Alex Rees-Jones
“Can Marginal Rates of Substitution Be Inferred from Happiness Data? Evidence from Residency Choices,” by Dan Benjamin, Ori Heffetz, Miles Kimball and Alex Rees-Jones
“Beyond Happiness and Satisfaction: Toward Well-Being Indices Based on Stated Preference,” by Dan Benjamin, Ori Heffetz, Miles Kimball and Nichole Szembrot
“Happiness Dynamics, Reference Dependence and Motivated Beliefs in US Presidential Elections,” by Miles Kimball, Collin Raymond, Jiannan Zhou, Junya Zhou, Fumio Ohtake and Yoshiro Tsutsui
“What Do Happiness Data Mean: Theory and Survey Evidence,” by Dan Benjamin, Jakina Debnam Guzman, Marc Fleurbaey, Ori Heffetz and Miles Kimball
“Adjusting for Scale-Use Heterogeneity in Self-Reported Well-Being,” by Dan Benjamin, Kristen Cooper, Ori Heffetz, Miles Kimball, Jiannan Zhou.
“Utility and Happiness,” by Miles Kimball and Bob Willis
“The Paradox of Declining Female Happiness” by Betsey Stevenson and Justin Wolfers
“The Female Happiness Paradox” by David Blanchflower and Alex Bryson
Quiz #2, 2025, Wednesday, April 23
Translation of Raw Score to Letter Grade Equivalent
If I had to base your final grade on only this exam, here is what I would do:
25-26 A
24 A-
21-23 B+
20 B
18-19 B-
17 C+
14-16 C
11-13 C-
Blog Posts and Articles to Read to Prepare for 2025 Quiz #2:
“Desiderata,” by Max Ehrmann (Optional: Wikipedia article on “Desiderata”)
Alan Watts: How to Come Back from Alienation with the Universe and with Ourselves
“Measuring the Essence of the Good Life,” by Dan Benjamin, Kristen Cooper, Ori Heffetz and Miles Kimball
“Judging the Nations: Wealth and Happiness Are Not Enough,” by Miles Kimball
“What Do People Want?” by Tushar Kundu, Dan Benjamin, Kristen Cooper and Miles Kimball
“Let's Set Half a Percent as the Standard for Statistical Significance,” by Miles Kimball
*************************
Here is what I had about Quiz #2 two years ago:
Statistical Interpretation Principles to be Tested on the Quiz
Whether the direction of bias is 0, +, - or ? given an arrow diagram with +’s and -’s on the arrows
Multicollinearity in practice
Note: Using the false discovery rate (FDR) approach to deal with multiple hypothesis testing will not be tested on this quiz, but you will be expected to use it where appropriate in your term paper. Note that “Who Leaves Mormonism?” and “A Well-Being Snapshot in a Changing World” use the false discovery rate approach.
(1) Life Purpose Statement and (2) Reflections on Your Meditation App Experience (Due 11 PM Friday, April 18)
Due 11 PM Friday, April 18
This is really 2 short assignments, but just for logistical simplicity, please put it in one document.
(1) Life Purpose Statement
One of the exercises I do with people as a life coach is to help them craft a life purpose statement. You can do it any way that works for you, but many people find this framework helpful:
I am the NOUN who VERB in order to PHRASE.
For example, here is my life purpose statement, which does things twice, with some variation on the pattern:
I am the WARRIOR who CHAMPIONS TRUTH to SAVE THE WORLD,
and the WILD ARTIST who RENEWS AND REVEALS the WORLD IN BEAUTY.
This life purpose statement is tentative. You can change it whenever you like! This assignment is meant you to get a first draft that I think you will find the beginning of something that will make a difference in your life.
(2) Reflections on your meditation app experience.
Refer to the earlier post for the assignment itself.
For these reflections, write less than a page about what your experience was like in using the meditation app. What did you notice about what was going on in your head (in your consciousness)?
Positive Intelligence Training
I do free positive intelligence training for economists. I am extending that invitation all those who have completed my Economics 4060 class, once you have a bachelor’s degree. Take a look at the description in these two posts:
How Economists Can Enhance Their Scientific Creativity, Engagement and Impact
Reactions to Miles’s Program For Enhancing Economists’ Scientific Creativity, Engagement and Impact
If you are interested, just send me an email after you graduate.
In the meanwhile, I highly recommend the book Positive Intelligence, by Shirzad Chamine. And I think you will find taking this “saboteur assessment” interesting, you’ll get a report describing what your results mean.
Reflections on What You Learned from JP's Big 5 Assessment (Due 11 PM Tuesday April 11)
Report Due 11 PM Tuesday, April 15
****** You have the option of trading this due date with the due date for the Analysis Task. That is, if you choose, you can upload these reflections on April 10 and the Analysis Task on April 15 if you choose.
Take the Big 5 assessment you will find at this link (https://www.understandmyself.com/)
WHEN YOU DO THE QUESTIONS, MAKE SURE TO COMPARE YOURSELF TO EVERYONE IN YOUR HIGH SCHOOL, NOT JUST TO YOUR COLLEGE CLASSMATES. EVERYONE IN COLLEGE TENDS TO BE MORE CONSCIENTIOUS THAN AVERAGE, SO IF YOU COMPARE YOURSELF TO YOUR COLLEGE CLASSMATES, YOUR CONSCIENTIOUSNESS SCORE WILL BE INACCURATELY LOW.
(Let me know if you have trouble paying the $10. We can work something out.)
Note that there may be a little delay in getting your report back, so don’t wait until the last minute.
Write less than a page about the most interesting things you learned from the report.
(I’ll set this up on Canvas well before the time. Don’t worry if it isn’t there yet.)
Your essay on what you learned from this Big 5 assessment can be much shorter, but you can think of this post of mine as me doing this assignment:
Miles's Personality in 10 Facets of the Big Five
Distance to College Contributes to Educational Disparities →
This is a good example of instrumental variables (IV). Having to travel more than 30 minutes to the nearest community college is treated as an instrument for going to college. This is not a perfect instrument, but this is definitely a good analysis to do.
Gifted Education Boosts Achievement of Disadvantaged Boys →
This is a nice example of the regression discontinuity (RD) strategy for getting causal identification. The difference between a 115 IQ and a 116 IQ is too small to affect outcomes much other than the fact that 116 is the lowest score for getting into the gifted program being studied.
The Well-Being Index Initiative →
You might be interested in seeing what my well-being research team is doing. Here is our public-facing website.
Analysis Task: Due 11 PM Thursday, April 10, 2025
FOR ACCESS TO THE DATA, LOOK AT THIS README FILE
Do the Survey Links assignment before trying to think about the analysis task. You need to know what kind of data will be available. (You could use other data sets related to well-being or Behavioral Economics, but I don’t recommend it. We’re set up to help you with this data, and all of it is highly related to the course.) Our goal is to get the data available for you by the Wednesday of Spring Break, but that timeline might slip.
Your Analysis Task needs to report the analysis with tables or figures and also have text that clearly explains the analysis. The idea is that this is like one section of a paper.
If you have an idea of what to do for the analysis task, just send me and Colby (colbychambers4@gmail.com) an email and I'll give a reaction of how interesting I think it is, and maybe a suggestion for a tweak.
Seeing the analysis and its explanation as one section of your term paper. (Your term paper is due later, at 11 PM on Wednesday, May 3—the evening after the last class.) The idea is to make this analysis part of a larger discussion.
Including figures and tables, the analysis task should be at least 5 pages. I'll take a risk and not put an upper limit on the length of the analysis task. (The term paper beyond the analysis task should be between 5 and 10 pages, with closer to 5 being preferred.)
How to structure your writeup of the Analysis Task:
You can design a different structure, but a typical writeup could look like this:
Here is an interesting question or questions. The answers matter (people care or should care) because: …
Here is a statistical analysis that seems to have some bearing on this question or questions:
On the surface the statistical results seem to say: …
However, the following confounding factors could be giving rise to an illusion, making it seem like something is there that isn’t or that something is bigger or different than it really is.
Don’t forget to talk about the confounding factors! (4.)
Here is a Q&A about the analysis task:
Q:
What is the level of analysis you are expecting for this assignment? I’ve taken some stats classes, so I’m familiar with hypothesis testing and regression, but since this class doesn’t have a stats prerequisite I’m not sure how in depth I should go for this assignment.
Since most aspects of wellbeing are correlated with each other, it seems to difficult to use regression to analyze relationships between these aspects without running into reverse causality, cousin causality, or both. My knowledge of stats isn’t sufficient to avoid these problems in cases where instrumental variable regression isn’t a viable alternative. I’m wondering what you would suggest that I do to avoid this issue.
A:
At the low end, it could be simply some scatter plots or bar charts or other interesting graphs.
I don't expect you to have consistent estimates of anything, rather to be able to discuss any biases there might be in the estimates you do get, relative to something interesting. Please make the attempt to figure out the sign (+ or -) of any bias you discuss, and say what that would mean for the truth of the interesting thing one might care about. If there are multiple biases, try to figure out the sign of each one, even if all the biases put together can't be signed because some biases are likely to be + and others are likely to be -. Also, discuss whether you think a bias is likely to be large or small.
Advice for the Analysis Task:
Use lots of graphs. I love scatterplots, but other types of graphs and figures can be good, too.
It’s fine to do some statistics on individual variables, but make sure you do something that relates pairs of variables to each other.
Do some formal statistical tests.
When you test more than one hypothesis, set it up so you can do the multiple hypothesis test correction using the False Discovery Rate procedure!
Make a distinction between being significant at the 5% level and being significant at the 1/2 % level.
If something isn’t statistically significant, you say “I can’t reject the null hypothesis that …” NOT “I reject the alternative hypothesis.” If you want to reject a hypothesis, you have to set it up as a null hypothesis.
Recognize reverse causality and cousin causality, including the consumer-theory-esque model I gave in class of how resources broadly construed help all good things, leading to the general principle (with only a few exceptions) that “All good things are positively correlated.” (This is a statement about the cross section.
Define variables in full. You need to act like your reader doesn’t know what the abbreviations mean. So write out the full text of the aspects, and describe fully all other variables. (You will see that we do this in our papers.)
Don’t order response categories alphabetically! They need to be ordered logically. For example, political leanings should be ordered from Left to Right and levels of education should be ordered from less to more.
When you have interesting results for several variables that are along the same lines, think of creating a simple index to get more statistical power. That is, take simple averages of similar variables and treat that simple average as an index.
Think about how nearly statistically exogenous your right-hand-side variables are. Other things equal, regressions with more nearly statistically exogenous right-hand-side variables are more interesting. That doesn’t mean you can’t do other things. Just think about this dimension.
Think seriously about scale use. Any statistical analysis you do with aspect-of-well-being data you can probably do both with the raw aspect ratings and with (aspect rating - average of calibration questions). Doing both of those analyses will be much more interesting than just the one analysis.
Shirzad Chamine on the War Inside
“The war raging inside our mind between the Saboteurs and Sage, is ultimately a war between the two primal forces that make life possible. The two primal forces are—you guessed it: Fear and Love.
All saboteurs are rooted in fear: fear of failure, fear of poverty, fear of abandonment, fear of rejection, fear of harm, fear of not mattering—and ultimately, fear of death.
On the other hand, the Sage operates entirely on love. When you think about it, the Sage Perspective, that everything can be turned into a gift and opportunity, is based on love for the unfolding mystery of life, and finding the gift in whatever happens.
Of the 5 Sage powers, Empathize is love for yourself and others. Explore is love for discovery. Innovate is love for possibilities. Navigate is love for meaning and purpose. And Activate is love for making things happen.
Today, whenever you feel any negative emotion, ranging from anxiety and stress to anger, shame, guilt or blame, ask yourself what the underlying fear might be. And then, choose something to love instead: something to love about yourself or the situation or person in front of you, so you begin to shift to Sage. Today, choose Love!”
Survey Links
Please take each of these surveys so you can see what kind of data is available for you. Take all of UAS, Baseline and Life & Psyche. (The Bottomless link takes you to just one block of the survey. The actual Bottomless survey is very long, with many different aspects of well-being and many different calibration questions (CQs) so there is more data on Bottomless than what you’ll see here.)
This is an assignment. I’ll have a couple of Quiz 2 questions that will be easy if you have done it, hard if not.
If you run into trouble with any of these links, email our predoctoral research assistant Colby Chambers: colbychambers4@gmail.com
We’re working on writing up full instructions for accessing the data. The goal is to have that for you by next Wednesday.
UAS
https://uas.usc.edu/survey/playground/uas571/test/index.php
Baseline
https://wiagl.gitlab.io/survey-baseline/?workerId=[EXAMPLE ID]
- (replace EXAMPLE ID with something like your full name without spaces)
Bottomless
https://wiagl.gitlab.io/survey-bottomlessA/?workerId=[EXAMPLE ID]
- (replace EXAMPLE ID with something like your full name without spaces)
Life and Psych
https://ucla.qualtrics.com/jfe/form/SV_8kK2HMh6YrGSEF8
EVERYTHING FROM HERE ON IS OPTIONAL
Aspect Flagging (these are the Qualtrics links to the surveys Colby owns)
- 1.1: https://cuboulder.qualtrics.com/jfe/form/SV_bORDu08uzL5aQf4
- 2.1: https://cuboulder.qualtrics.com/jfe/form/SV_3wu8fWJFuoj5Q6q
- 2.2: https://cuboulder.qualtrics.com/jfe/form/SV_6Rl1LME8k4n98j4
- 2.3: https://cuboulder.qualtrics.com/jfe/form/SV_8enmSl5SFjgA0nk
- 2.4: https://cuboulder.qualtrics.com/jfe/form/SV_eLPpy2G1aTKzedw
- 3.1: https://cuboulder.qualtrics.com/jfe/form/SV_blWFfIUkvLD1vzE
- 3.2: https://cuboulder.qualtrics.com/jfe/form/SV_2nrNlcuAqmi0fum
- 3.3: https://cuboulder.qualtrics.com/jfe/form/SV_5olxMQl9DaNAtJI
- 3.4: https://cuboulder.qualtrics.com/jfe/form/SV_8waQyVU3cpqidIG
- 4.1: https://cuboulder.qualtrics.com/jfe/form/SV_5vCARkRhqbWfEcC
- 4.2: https://cuboulder.qualtrics.com/jfe/form/SV_cBKvaiuO5oF80om
- 4.3: https://cuboulder.qualtrics.com/jfe/form/SV_3jxeDYvKyrtohFk
- 4.4: https://cuboulder.qualtrics.com/jfe/form/SV_1BO0MbaxkhNucjI
- 5.1: https://cuboulder.qualtrics.com/jfe/form/SV_8wSQmff0JdKEQL4
- 5.2: https://cuboulder.qualtrics.com/jfe/form/SV_0wGxqQnjOWnkSt8
- 5.3: https://cuboulder.qualtrics.com/jfe/form/SV_3C0pxd18kfx5nBs
- 5.4: https://cuboulder.qualtrics.com/jfe/form/SV_3EMVDhnAm4u9nv0
Super Responder (life and psych in its first iteration)
http://wiagl.gitlab.io/survey-super/
Prescreen
https://cumc.co1.qualtrics.com/jfe/form/SV_3fLA5sW2a4QIDjg
Bottomless – Preview (This is the screen workers see before accepting the assignment)
https://wiagl.gitlab.io/survey-bottomless/?assignmentId=ASSIGNMENT_ID_NOT_AVAILABLE&
UAS:
https://uas.usc.edu/survey/playground/uas571/test/index.php
Baseline:
https://cuboulder.qualtrics.com/jfe/form/SV_78tDltCPOcalvuK
Note: this is a version of baseline contained in a Qualtrics account Colby owns (which is itself a copy of a version Tushar owns). It has a little less elaboration on things in the instructions (e.g. public goods), as well as fewer demographic questions at the end, but the ratings and tradeoffs are the same as the traditional baseline survey.
Life and psych:
https://ucla.qualtrics.com/jfe/form/SV_3eiDxyBZnHLwF7g
Bottomless:
https://wiagl.gitlab.io/survey-bottomless/
Note: while the aspects in each block of the survey seem to match those in our tracking spreadsheet, the alternative scale frame aspect and CQs don't perfectly correspond to those we have tracked as being in each block (e.g. cuteness appears with the block 3 aspects even though it is recorded as being a block 12 CQ trio). Beyond this, the structure of the survey is identical to the traditional bottomless survey.
Paper on "Positive Intelligence" by Shirzad Chamine
Due: 11 PM Tuesday, April 3, 2025
3-5 Pages
In addition to reading the book, this assignment asks you to do the saboteur assessment at this link and read the report you are sent about your own saboteurs. DO THIS RIGHT AWAY: IT MIGHT TAKE A DAY TO GET YOUR REPORT BACK.
As usual, provide evidence in your paper that you have read the whole book, and if you use ChatGPT, follow the clear citation rules for ChatGPT that I set out early on in the class. (See “Ideas for Using ChatGPT.” Using ChatGPT is optional, but it is an interesting thing to try.)
This paper is meant to be a personal essay. The objective is to help you think through things that can help make you happier.
For your paper, think about the following questions:
What did you learn from reading the report on your Saboteur assessment? Focus only on the things that resonated with you; ignore things you thought were off-track for you personally.
What Sage strengths do you have that are associated with the Saboteurs you have? Here are examples of Sage strengths associated with each Saboteur. (There are more sage strengths associated with Saboteurs than these.) Below I have it notated as (bad: good). Saboteurs are often a strength going overboard, and going bad as a result:
Judge: blameless discernment
Pleaser: empathy
Avoider: peacefulness, peacemaking, flexibility
Stickler: meticulousness
Victim: self-knowledge, especially knowledge of what you want
Controller: leadership, making things happen
Restless: fun, creativity
Hyper-Achiever: achievement
Hyper-Rational: rationality
Hyper-Vigilant: vigilance
In your own religious or non-religious background, how was what Shirzad calls “The Sage Perspective” taught or expressed? Reading my post “'Everything Happens for a Reason' for Nonsupernaturalists” will help clarify what I mean by this. This post is my personal answer to this question.
What do you want to do in the area of developing the five Sage Powers to a greater extent?
What role do you think Shirzad’s bag of psychological tricks and techniques could have in society in general?
Steps for Applying the Benjamini-Hochberg "False-Discovery-Rate" (FDR) Procedure for Multiple-Hypothesis-Test Correction
Identify a group of hypotheses among which you would shift emphasis according to how good the results look. Note: anything that you would want to talk about if it had strong statistical results counts!
How do you identify groupings of hypotheses? Groups of hypotheses can be handled separately if you will keep the same level of emphasis between groups. For example, you will focus in on Group A and focus in on Group B and discuss them equally regardless of what the results are.
Now, focusing in on one particular group, call the number of hypotheses in this set n. Multiply all reported p-values by n. Let’s call these “adjusted p-values.”
Order all the hypotheses from the smallest adjusted p-value at the top to the largest adjusted p-value at the bottom. (Note that having the numbers in Excel makes this easy to do and then later restore your original order.) Call the hypothesis with the smallest adjusted p-value #1, the one with the second-smallest adjusted p-value #2, etc. And call the m with the smallest adjusted p-values the “top m hypotheses.”
The conventional significant level for a False Discovery Rate is .1 (=10%). Let’s go with that, although it is easy to use other values.
If the #m hypothesis has an adjusted p-value less than .1 m, then the top m hypotheses are all significant at a false discovery rate (FDR) threshold of 10%.
Find the largest m for which the #m hypothesis had an adjusted p-value less than .1 m. This gives you the set of hypotheses within this group that are significant at the FDR 10% level.
Documents for Review of Statistics Drawn from My “Monetary and Financial Theory” Class at the University of Michigan
I recommend that you print these documents out and bring them to class (except for the class notes—those won’t be needed in class).
Well-Being Possibility Frontier/Indifference Curves AND The Corresponding Supply and Demand Graphs
WBPF = Well-Being Possibility Frontier (Orange)
Green is for preferences (indifference curves above, demand below)
MRT = Marginal Rate of Transformation: the opportunity cost of the other things that must be sacrificed to get one point more of happiness
MRS = Marginal Rate of Substitution: amount of other things the individual is willing to sacrifice to get one point more of happiness
Notes:
The Supply Curve is a graph of minus the slop of the WBPF. It has the level of the highlighted aspect on the horizontal axis and the marginal utility (MU) of the highlighted aspect (which is technically the marginal rate of substitution (MRS) relatve to an amalgam of all other aspects (“all else”).
The Demand Curve is a graph of minus the slope of the indifference curve an individual is on. That means that any shift that puts an individual onto a different indifference curve shifts the demand curve, unless all the indifference curves are parallel vertical shifts of each other (quasi-linearity). That is not a good assumption. The shift of the demand curve occasioned by ending up on a new indifference curve is analogous to income effects on demand for market goods. Because it isn’t literally income, I don’t call these income effects, I call them prosperity effects. The demand curve has the level of the highlighted aspect on the horizontal axis and the marginal rate of transformation (MRT) of “all else” into the highlighted aspect.
Comparative Statics Exercise #1:
Comparative Statics Exercise #2:
Comparative Statics Exercise
Comparative Statics Exercise #4:
