Wednesday, April 29, 2009

Today's class

For those who missed class today, I handed back the in-class quiz (mean 49, median 53 -- slightly lower, but not terribly lower than I was hoping for), went over the answers, finished the discussion from Monday (on hiring and training costs) and discussed asymmetric information (lecture slides available here).

Tuesday, April 28, 2009

Questions to ponder

Tomorrow, we will discuss asymmetric information problems in class. In our discussion of neoclassical labor markets, lurking throughout was an assumption of perfect information. Firms knew the quality of potential workers and workers knew the quality of potential jobs. This is clearly unrealistic. Firms and workers do not start with perfect information about each other. As we will see tomorrow, this can create problems in the labor market.

One potential solution to these problems is signaling. For instance, imagine there are two types of workers -- good and bad. Firms can't distinguish among them. As such, they offer a single wage to both types. However, firms would gladly pay more to good workers if they could identify them. This creates an incentive for good workers to distinguish themselves from bad workers. Signaling is one way to do this. The key assumption for signaling to separate good and bad workers is that obtaining the signal is sufficiently more expensive for bad workers than good, so only good workers want to obtain it.

College is the classic example of a signal. The assumption is that good workers find education cheaper than bad workers, so good workers go to college and bad workers do not. One implication of this view, however, is that college is not necessarily about skill acquisition. Rather, it is a form of ability revelation.

What do you think? Setting aside the consumption aspects of college (e.g., it is fun, you like learning stuff), do you think that college (for you) is primarily about signaling or investment in skills? That is, do you think that you needed to come to college to acquire valuable skills that you couldn't have obtained as cheaply otherwise (e.g., through on the job training/experience or self-study) or is your attendance here really just about separating yourself from others for whom the effort to complete college is too expensive?

This is an important question. College is very expensive (in terms of both time and money). If it is really just about signaling, is it conceivable that we could develop alternative methods of providing workers with credible signals of their abilities with far lower costs (and thus improve total welfare)?

Compensating Wage Differential Materials

Monday's lecture slides are available here.

Some other, perhaps more complete, materials are available here and here.

Also, additional information on my aside on the value of a statistical life is available here.

Monday, April 27, 2009

Hmm ... sick days and pandemics

This strikes me as a bit troublesome:
Currently, nearly 50 percent of private-sector workers have no paid sick days. For low-income workers, the number jumps to 76 percent, and climbs to 86 percent for food service workers. These workers have to decide between the health of themselves and their co-workers, and the wages that they lose by staying home.
On one hand, I can certainly understand why firms -- particular food service firms -- don't want paid sick days. Food service operations can be seriously impacted if workers don't show up on short notice. Furthermore, it would not surprise me if low wage employees prefer higher regular wages to lower wages and sick days.

However, these statistics don't answer the key question lurking in the last sentence of the quote -- what share of sick people actually show up to work. Still, this pattern is troublesome because it is not hard to imagine that an inefficiently high number of workers choose to show up at work while sick.

Workers who work while sick impose negative externalities on their co-workers, employers, and customers. Recall, that the presence of negative externalities, suggests that an inefficiently high number of workers will work while sick. As such, discouraging workers from showing up to work sick -- particularly in occupations where there is lots of contact/interaction with other people -- is good policy. Allowing workers who are sick to stay home ans still get paid is one way to encourage this (so perhaps the government should subsidize sick days in high interaction occupations), but there may be other ways to achieve better results.

Sunday, April 26, 2009

From the Archive: Nagging

Within couples or families, when our partners reduce the relationship surplus by shirking their responsibilities or engaging in "annoying" activities, we frequently resort to nagging in order to change the undesirable behavior. Nagging (or the threat of nagging) serves to raise the cost of the undesirable behavior, thus encouraging one's partner to "behave." While the basic economics of this strategy are ok (raise the price of undesirable activity => reduction in undesirable activity), nagging never struck me as a very effective relationship bargaining strategy.

Certainly, nagging will inevitably be part of any relationship, and it will even work sometimes. The problem with nagging is its overuse -- particularly at the expense of more efficient (and effective) strategies.

Nagging is popular because it is cheap. When someone engages in behavior that reduces our welfare, we get upset (typically in proportion to how much welfare we've lost). When we feel bad, it is normal to want to "let off some of the steam." Nagging is an easy way to do this (while also trying to prevent the situation from arising in the future). As such, it is common.

However, this does not imply that it is efficient. While I will assume that nagging is rational for the nagger (i.e., the expected benefits of nagging outweigh the costs), the relationship as a whole may be worse off because the costs imposed on the nagged may be greater than the net benefit to the nagger. Further, because nagging is frequently not effective at eliminating unwanted behaviors (e.g., the threat of nagging is not enough to overwhelm habits), the nagging escalates which only increases the net loss to the relationship by reducing the net benefit to the nagger and imposing larger costs on the nagged. Inevitably the loss of relationship surplus associated with this puts the relationship on a trajectory toward larger blow ups and potential break-up.

In light of nagging's limited potential, it is important to think about other strategies for altering relationship behaviors because no matter how hard you search there is no perfect mate this stuff is gonna come up. This article from the NYTimes describes some nice substitutes for nagging that the author, Amy Sutherland, learned while writing a book on animal training. As she puts it:
The central lesson I learned from exotic animal trainers is that I should reward behavior I like and ignore behavior I don't. After all, you don't get a sea lion to balance a ball on the end of its nose by nagging. The same goes for the American husband.

She describes three lessons in the article:

1) Instead of changing behavior through nagging (raising costs), raise the benefits associated with not doing the undesirable thing (e.g., kiss your partner for picking up their clothes -- a win-win for everyone)
2) Create incompatible behaviors which make engaging in the annoying task impossible (obviously this won't work in all situations, but in the article she describes creating tasks on the other side of the kitchen to occupy her husband in order to prevent him from crowding her while cooking).
3) Ignore stuff (Least Reinforcing Syndrome) -- "The idea is that any response, positive or negative, fuels a behavior. If a behavior provokes no response, it typically dies away."

Ultimately, all three of these strategies are themselves limited. The point, though, is to think creatively about how to deal with thoughtless or annoying partners. Nagging is natural and cheap, but can be destructive to the relationship. Try and figure out if there is an alternative response which might produce the desired outcome with lower long term costs on you and the relationship.

From the Archive: Outside the Fairy Tale

Growing up, I am certain all of you encountered, and perhaps embraced, the notion of fairy tale romance. This view posits the existence of some perfect mate who we are destined to meet and live with happily ever after.

That is, one can find love without costs. Somewhere out there a perfect match awaits us -- someone who is a far better match than any alternatives (i.e., the relationship product from pairing you with this person far exceeds the relationship product from any other possible pairing). Further, this person is so perfect that you will never have to engage in costly bargaining (because they have no traits you find annoying or vice versa and you agree completely on who should do what and how things should be allocated). Finally, you WILL meet this person (there are no search costs). You need only keep an eye out and overcome the few obstacles that stand in the way.

There is a reason we describe such romance as a fairy tale. Real love comes with a variety of costs -- search costs, forgone opportunities, bargaining costs. The importance we assign to these costs plays an enormous role in determining how we date and marry.

Some people believe strongly that a Mr. or Ms. Right exists and can be found with appropriate searching . Such people essentially assume that partnering with the "wrong" person imposes large costs because they forego the option of pairing with someone substantially better (more productive) and staying with the wrong person requires lots of extra bargaining and negotiation.

This approach to dating makes sense if one believes that people are very complicated and very hard to change. Under these assumptions, pairing with the "wrong" person substantially lowers an individual's welfare. As such, it makes sense to incur large search costs (date alot) in order to find the "ideal" mate. Further, we want to make dissolving imperfect matches fairly easy because resolving incompatibilities whenever they are found may be extremely costly.

The alternative view assumes people are relatively simple and capable of change. As such, relationship success hinges not on finding Mr. or Ms. Right, but rather it hinges on people having the right attitude and being able to figure out how to make things work. Under this view, searching wastes of energy and awareness that someone better exists only makes it more difficult to come to terms with what is, in fact, a good relationship.

The extreme version of this approach is arranged marriage. In arranged marriages two relative strangers are paired off and essentially told to "make it work." Many do, although it is important to note that such success does not indicate that imperfect matches and bargaining costs are irrelevant. Indeed, such "make it work" approaches to relationships are typically accompanied by large barriers to divorce and strong gender norms which govern the relationship. This suggests that people need to be pushed in order to "make it work."

So which assumptions are correct? Which approach to dating produces the best outcome for individuals? for society?

I don't know. Part of me worries that people make themselves worse off by consistently worrying about if there might be someone better available, and worse, people quit otherwise successful relationships because they view it as cheap (don't have to incur bargaining costs and a better match exists). If people overestimate the cost of bargaining with their partner or their chances of finding someone substantially better, then people might be made better off in the long run if we made it more difficult for them to break-up. On the other hand, if most people don't make these mistakes regularly, then making it more difficult to break-up only forces many people to stay in bad relationships longer then is necessary (imposing a big loss on social welfare).

From the Archives: Relationship Gift Giving

Part of the process of developing and maintaining relationships involves gift giving. Why? There are lots of reasons, I am sure, but here is a very simplistic use of economic tools which offers a compelling explanation.

For simplicity, I will just describe gift giving while courting. Two people, Dave and Diana, are getting to know each other. Dave realizes that he quite likes Diana and would like to keep seeing her. He wants to let Diana know how he feels. He's said it too her, but talk is cheap. Diana has heard how great she is from lots of suitors. Dave wants to strongly signal his interest. What can he do?

He can give Diana a gift. By giving Diana a gift, Dave signals Diana that he is enjoying a large net benefit from being with her (that is, the benefits of the time he spends with her exceed the costs). Dave would not be willing to spend resources signaling his affection if he were only marginally interested. Diana realizes that Dave would not want to spend resources if he were only marginally interested, and thus now trusts that he is really interested (of course there is the looming question about what exactly Dave is interested in, but, for now, assume that Dave is an upstanding young gentleman).

What exactly should Dave give?

This article suggests that he should give "an extravagant gift that has no resale value." This is because "women feel confident that they have found a strong and committed mate when they receive an extravagant gift. And men avoid gold-diggers by giving only gifts that have no intrinsic value."

I agree with this premise in many ways, but I actually have some slightly different views on what kinds of gifts Dave should give. I will save this discussion for class, but feel free to discuss your own thoughts on gift giving in the comments.

From the Archives: Is Hooking Up Optimal?

Last Spring, Diversity and Distinction heard about our class, and interviewed me for an article (scroll to page 18) about "hook ups."

The reporter was kind enough to send me prepared questions. Here is my complete response to her question "is hooking up optimal?":

Well, that really depends on what you mean. You can think about it at two levels: the individual level and the social level.


Amongst the individuals actually hooking up, if we assume that they are rational (in the economic sense) and fully informed, arguing that their behavior is sub-optimal is difficult. They choose to do it, so it must be their best available option (otherwise they would have chosen the alternative).

If the effects of hooking up are felt only by those involved, then the social planner should only intervene if he/she feels that the decision is not based on full information or that he/she somehow "knows better" then these individuals what is good for them.

On the information issue, as long as both sides are fully aware of the situation (e.g., that this is just short-term consumption -- a random hook-up), then I don't see grounds for concern. If information is asymmetric, i.e., one party is just looking to hook-up while the other is thinking that this is part of developing a lasting relationship, then maybe we should care (depending on how you trade off one party's gains versus the other's losses).

Another potential information problem arises if individuals do not understand the long run consequences of their actions. It is possible, although I have no idea to what extent, that the effort that is invested in hooking-up could be spent in some alternative manner which would produce better lifetime outcomes. That is, hooking up may have large opportunity costs that people don't fully account for. For example, some argue that dating is a learning process. When you date you learn about yourself, about what you desire in a partner, about how to effectively bargain in relationships, etc. If the effort spent hooking-up crowds out investments in dating, then the individuals might be making themselves worse off in the long run.

[Note -- One could also argue the complete opposite. Dating has nothing to do with personal growth. When people are ready for a "real" relationship they settle down. Dating in college, which has a low probability of producing a long term mate, is purely consumptive and may distract people from making productive long run investments in their human (classes) and social (friends and activities) capital. So allowing people to satisfy physical urges by hooking up rather then involving themselves in distracting relationships is a good thing.]

Alternatively, one might argue that individuals don't care enough about their future selves relative to their current self and they take actions which effectively "screw" their future selves (this is known as hyperbolic discounting).

So if individuals lack perfect information, or if they are hyperbolic discounters, then society might decide that hooking-up is sub optimal and want to reduce it -- even though no one other then those choosing to hook up is affected.


The above analysis assumes those engaing in hook-ups pay all of the costs and reap all of the benefits. This may not be the case. If hooking up produces spillovers (positive or negative), then these necessarily must be accounted for and included in the analysis before establishing the efficiency (which I prefer to the term optimality) of hook-up culture.

As such, we must ask, "how are those not engaging in hook up culture affected by it?"

At the most basic level, one might raise concerns about public health and safety. If hook up culture spreads diseases, that is bad and wasteful for society. More subtly, hook up culture may (and I stress that this is purely speculation) spawn clearly undesirable behavior like rape or other sexual misconduct. Also, hooking up potentially increases the probability of people abusing alcohol (because alcohol is very effective at lowering "prices" in the hook-up market). In all three of these examples, those seeking to hook up do not bear the full cost of behavior. As a result of people seeking to hook up, others must incur costs preventing the spread of disease, discouraging sexual misconduct and caring for its victims, and keeping drunk people under control.

Slightly less obvious are the effects of a large hook up market on the traditional dating market. As the market for hook ups grows stronger, it becomes more attractive to the marginal dater (either because the price of hooking up falls or peer pressure to particpate in hook ups grows). This reduces the supply in the dating market and makes that market less productive (e.g., it is harder to meet people, there are fewer events designed to facilitate dating matches, ...). If, for some reason, the dating market is better then the hook up market (or that it is more important to have a large functioning dating market then a large hook up market), then a growing hook up market might be bad.

Even more problematic, if it is impossible to distinguish people who want to date from people who want to hook-up, the dating market can fail. If people interested in hook-ups don't care if the hook-up with a dater or player (or even worse if they prefer daters), then they might show up in both markets. If an unsuspecting dater gets "preyed" upon by a player, they may be more hesitant to enter the dating market. Eventually, this can lead the entire dating market to unravel. So all the would-be daters are made substantially worse off by the inability to distinguish players. If there are ways to separate people (and this is hard), then this is not a problem.

Ultimately, I think the key to determining the efficiency of hook ups is understanding how dating versus hooking up affects people. If dating is important for personal development (i.e., it develops human capital that can be employed to improve all relationships) and one needs to be dating consistently to maximize this development, then it is important to, at least, make sure that those who would be interested in dating can do so. Further, one may also want to actively discourage hook ups to improve the overall dating market and prevent people from making "a mistake."

Here are some additional articles on high school hook-ups:

In comments below, Jenny points us to two interesting pieces on current trends in "dating" among high school students. Try and read them, I'd like to discuss them in class (probably next week).

As you read them ask yourself a few questions. First, do the authors convince you that things are really different from how they used to be? Why or why not? If you think that there are real trends, what is causing them? That is, why are people engaging relationships differently than they used to? How are the incentives different? Finally (and this gets back to the previous post on hook ups), are you at all concerned by this description? Do you think that these behaviors will have long term consequences for how these people will approach relationships in the future?

From the Archives: Overview of Relationship Economics

The economics of dating focuses on a few key questions:

Basically, we want to know who meets whom; after meeting, who dates whom; once dating, who continues to date/get married, etc., and why. We are also interested in understanding when this market may fail – i.e., what prevents potentially good matches from being formed?

To figure this out, one needs to understand some basic features of the social network, understand the sources of relationship productivity, and understand the bargaining process within relationships.

Understanding the social network helps us understand who is likely to meet whom and what information are they likely to have (or to lack) about potential partners.

Relationship productivity is usually referred to as “chemistry”, but it is really productivity. In dating economics one focuses on what makes one pairing of people more productive then another. This is very important because ultimately we will only consider being in relationships with people with whom we can achieve a certain level of satisfaction (or utility).

Finally, dating economics focuses on how the relationship product is allocated through bargaining. (E.g., I will go shopping with you and endure you trying on 27 pairs of jeans in exchange for you not nagging me during the game -- this is massively over simplified, but you get the idea. In reality, most relationship bargaining is not this explicit, but it still goes on.)

Ultimately, two things lead to the end of the relationship: breakdowns in relationship productivity and breakdowns in intra-relationship bargaining. Once an individual no longer believes that they will be better off staying in the relationship versus reentering the market, they leave, and the relationship ends.

The economics of dating is about exploring and understanding the myriad of issues which affect this process.

Tuesday, April 21, 2009

PS 1 Hint

I've received the same question from several people, so let me offer a brief refresher on solving for optimal quantities given an MRS and a budget constraint.

Typically, these types of problems ask you to solve for the optimal amounts of two variables. In the labor supply world, we are interested in total consumption (C) and total Leisure (L).

Recall from algebra that to solve for two unknowns, we need two equations. We have two. We know that MRS = w and we know that the agent faces a budget constraint (wT + a = C + wL -- this says the total value of time and unearned income = the total value of consumption and leisure). With these two equations we can solve for the two unknown quantities.

Assuming an MRS of C/L and the above budget constraint, we can solve for C in terms of L (and the other variables):

C = wL (from the first equation)

C = wT + a - wL (from the budget constraint)

Since the left hand side of both equations is C, we know that the right hand sides are equal:

wL = wT + a - wL

or (solving for L)

L = (wT + a) / 2w

Which in turn (plugging back into the equations above) implies

C = w * [(wT + a) / 2w]

And the total number of hours worked = T - L

One other thing. On the problem set, I note that I don't penalize late assignments until they impose costs on me. Late problem sets typically impose two potential costs. First, it is seriously annoying to have to grade assignments after having graded all the others because the grade rhythm is gone. Second, for similar reasons, it is annoying to answer student questions about the problem set well after having dealt with others students' questions.

Thus, if you want to avoid penalties, you should (a) turn in your assignment before I start grading and (b) not ask for any problem set related help after the deadline. Technically, I can start grading anytime after the assignment is due, but grading is not one of my favorite activities so I am seldom eager to do it.

Compensating Wage Differentials

In class yesterday, I briefly discussed compensating wage differentials (aka compensating differential or equalizing difference). A compensating wage differential is the extra compensation that must be offered to a worker in order for them to accept a risky, dangerous, or dirty job.

E.g., how much extra do you think needs to be offered to:

The answers are here, here, and here.

How much would winning the lottery affect your labor supply?

Winning the lottery can provide a big boost to your unearned income. From what we've discussed in class, we know increasing unearned income shifts out your budget constraint and should prompt reductions in work via income effects.

But how big are these effects? Are income effects big or small? Would you change how much you work if given $15,000 a year for 20 years? What about $80,000 a year for 20 years?

The beauty of the lottery is that winning is random, so we can actually investigate the magnitude of these effects given appropriate data. Guido W. Imbens, Donald B. Rubin, and Bruce Sacerdote performed such an analysis using a data from a survey of 496 Massachusetts lottery winners. They found:
winning $15,000 a year for 20 years would not have a major effect on your life. However, if you instead won $80,000 a year for 20 years, it would affect your labor force participation, automobile expenditures, the value of the home you own, and your savings, according to the study.

Imbens, Rubin, and Sacerdote, in Working Paper 7001 from the National Bureau of Economic Research, analyzed a survey that they conducted of 496 Massachusetts lottery winners. The survey participants were divided into three groups: winners of one-time prizes between $100 and $5,000; winners of a yearly amount of less than $25,000 for 20 years, with an average annual prize of $15,000; and winners of at least $25,000 a year for 20 years with an average prize of $80,000 annually.

The researchers found that a prize of $15,000 a year had little effect on the labor supply of the winners. However, they also found that winning $80,000 rather than $15,000 reduced labor supply significantly. Additionally, estimates by Imbens, Rubin, and Sacerdote indicated that, in this case, car values rose (by at least $5,500 on average), home values increased (by $30,000 on average), and savings went up (especially in the form of bonds and mutual funds).

Friday, April 17, 2009

Random Question

Which is better: The power of flight or the power of invisibility? Listen here for more details.

Take Home Assingment 1

Due Next Wednesday -- available here. (Updated with question 6).

Friday, April 10, 2009

Labor Demand

Some good slides and additional reading on labor demand are available here and here. (Other slides are available here and here).

Next Week (4/13 and 4/15)


We will not have class on Monday (4/13).

We will have a quiz followed by a guest lecture by Prof. Whitelaw on Wednesday (4/15).

The quiz will take approximately 30 minutes to complete. It will consist of a few fill in the blank or complete the figure type questions and a few "identify the core assumption" questions (like we've discussed in class). It will cover everything we've seen to date. This includes:

(1) Basic Micro-Theory (i.e., the stuff you learned in 311)

Core elements of micro -- agent, objectives, constraints, incentives/tradeoffs, equilibrium -- and associated tools -- utility function, indifference curves, budget constraints, supply and demand curves, etc.).

(2) Econometric/statistical intuition

In our class this largely boils down to understanding, interpreting, and evaluating statistical evidence. The key phrase to latch onto is, "correlation is not causation." Frequently, people present evidence of a correlation between two variables and interpret the relationship as causal (X causes Y). You should be skeptical of such claims.

Two major questions to consider when presented with evidence of a correlation between two variables:

(A) What else might explain this relationship?

(B) What sort of comparison would produce convincing estimates of any causal relationship? (Hint -- ideally convincing comparison should rule out the alternative explanations identified in (1) using randomized controls or some other quasi-experimental method.)

(3) Labor Supply

The core questions (hint -- a reasonable way to study would be to answer these questions):

(a) What decision(s) are we interested in examining? That is, what must agents choose?

(b) What are the benefits associated with the available choices?

(c) What constrains agents from infinitely pursuing all the available choices? That is, why can't agents consume as much as they would like of all the available options?

(d) For a given set of preferences, what defines the agent's optimal choice? [Stated differently -- Why is an agent's optimal choice defined where MRS = w?]

(e) How do agents respond to an increase in unearned income?

(f) How do agents respond to a change in the wage?

(g) How do you identify/calculate the substitution effect? How to you identify/calculate the income effect?

(4) Beginning of Labor Demand

The core questions we've considered so far:

(a) In a competitive market where firms take prices (for output and inputs) as given, why do firms hire workers up until the value of a worker's marginal product equals the wage?

(b) What causes firms to change the number of workers they hire?

(c) Why do labor demand curves typically slope downward?

Sunday, April 05, 2009

A nice example of why you need to learn empirical skills

Conventional wisdom holds that breastfeeding is vastly superior to bottle feeding. The superiority of breast milk is supposedly supported by scientific evidence. Upon closer examination, though, the evidence does not appear that overwhelming. Why?
most of the claims about breast-feeding’s benefits lean on research conducted outside the lab: comparing one group of infants being breast-fed against another being breast-fed less, or not at all. Thousands of such studies have been published, linking breast-feeding with healthier, happier, smarter children. But they all share one glaring flaw.

An ideal study would randomly divide a group of mothers, tell one half to breast-feed and the other not to, and then measure the outcomes. But researchers cannot ethically tell mothers what to feed their babies. Instead they have to settle for “observational” studies. These simply look for differences in two populations, one breast-fed and one not. The problem is, breast-fed infants are typically brought up in very different families from those raised on the bottle. In the U.S., breast-feeding is on the rise—69 percent of mothers initiate the practice at the hospital, and 17 percent nurse exclusively for at least six months. But the numbers are much higher among women who are white, older, and educated; a woman who attended college, for instance, is roughly twice as likely to nurse for six months. Researchers try to factor out all these “confounding variables” that might affect the babies’ health and development. But they still can’t know if they’ve missed some critical factor. “Studies about the benefits of breast-feeding are extremely difficult and complex because of who breast-feeds and who doesn’t,” says Michael Kramer, a highly respected researcher at McGill University. “There have been claims that it prevents everything—cancer, diabetes. A reasonable person would be cautious about every new amazing discovery.”

The article continues to describe some very clever ways researchers have attempted to tease out the "true" effects of breastfeeding. Economists call these types of clever approaches "identification strategies", and a significant share of graduate training in labor economics consists of learning how to come up with these kinds of clever strategies.

Thursday, April 02, 2009

Basic Labor Supply Model

One of the questions we will focus on next week is: how many hours to people choose to work?

The main model economists use to explain this decision is the neoclassical labor supply model. This model explains the decision to work as a tradeoff between labor (working for pay ) and leisure (all time spent not working for pay).

In order to augment our discussion in class, you can find additional materials on this topic in a number of places. First, many intermediate micro texts contain a discussion of this model (so you may want to check the books on your shelf or in the library). Alternatively, there are a number of discussions available online. E.g., here, here, and here.

Additional Resources on Necessary and Sufficient Conditions

In class on Wednesday, we discussed necessary and sufficient conditions -- a framework for identifying and evaluating the assumptions lurking in arguments. I find that thinking about things in terms of necessity and sufficiency helps clarify the most important aspects of any argument, so I encourage you to incorporate these logic rules into your intellectual toolkit.

Some additional resources on these concepts (e.g., additional definitions and examples) are available here and here.

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