A Partisan Nonpartisan Blog: Cutting Through Confusion Since 2012
This is a thoughtful piece. The worries and prescriptions are unsurprising, but Uri Dadush’s and Moises Naim’s discussion of the underlying strengths of the U.S. economy is a useful antidote to alarmism.
The title of this post is the original working title of the column.
In early drafts, I related what I say in the Quartz column to Jonathan Haidt’s six moral tastes in his book The Righteous Mind: Why Good People Are Divided by Politics and Religion. Here is a New York Times book review by William Saletan, and here is a good passage from Jonathan Haidt summarizing his theory, chosen by Bill Vallicella, in Bill’s post “Jonathan Haidt on Why Working Class People Vote Conservative.”
There is a key chunk of text making the link to Jonathan Haidt’s theory that was appropriately cut for being too wonkish, but that I think you might find valuable
Here it is:
The most important boon people want for the nation as a whole is freedom. In the words we used for the choices we gave them, the #1, #2, #10, #13, #18 and #23 things people want for the nation are
- freedom from injustice, corruption, and abuse of power in your nation
- people having many options and possibilities in their lives and the freedom to choose among them;
- freedom of speech and people’s ability to take part in the political process and community life;
- the amount of freedom in society;
- people’s ability to dream and pursue their dreams; and
- people’s freedom from emotional abuse or harassment.
The next most important boons people want for the nation are goodness, truth, loyalty, respect and justice. On our list, the #3, #6, #8, #17, #19 and #21 most highly-valued aspects of the good society are
- people being good, moral people and living according to their personal values;
- people’s freedom from being lied to, deceived or betrayed
- the morality, ethics, and goodness of other people in your nation; and
- people having people around them who think well of them and treat them with respect
- the quality of people’s family relationships
- your nation being a just society.
The exact picture of “goodness” and “justice” might differ from one person to the next, but it is clear that they represent more than just money and happiness. University of Virginia psychologist Jonathan Haidt, in his brilliant book The Righteous Mind: Why Good People Are Divided by Politics and Religion argues that morality comes in six flavors (“The righteous mind is like a tongue with six tastes.”):
- liberty vs. oppression,
- fairness vs, cheating,
- sanctity vs. degradation,
- loyalty vs. betrayal,
- authority vs subversion, and
- care vs. harm.
The first five of Haidt’s flavors of morality are well represented above. The fourth flavor of morality, care vs. harm, is the one many authors focus on, to the exclusion of the others. It is the bread and butter aspects of people’s lives. In our findings, care vs. harm is reflected in 11 of the top 25 (numbers 4, 7, 9, 11, 12, 13, 16, 18, 22, 24, 25), including “the overall well-being of people and their families” in your nation, people’s health, financial security, and freedom from pain; “people having people they can turn to in time of need” and a “sense of security about life and the future in general” and balance, as reflected in the items “people’s mental health and emotional stability,” “how much people enjoy their lives” and “how peaceful, calm and harmonious people’s lives are.”
In addition to all of these, people want meaning, as reflected by #5 and #14 on our list: “people’s sense that they are making a difference, actively contributing to the well-being of other people, and making the world a better place, and “people’s sense that their lives are meaningful and have value.” In addition to his discussion of key dimensions of morality, in The Righteous Mind: Why Good People Are Divided by Politics and Religion, Jonathan Haidt emphasizes the importance of meaning—in particular, the importance of feeling one is a part of a larger whole. One of his central metaphors is “We are 90 percent chimp and 10 percent bee.” That is, Haidt believes that perhaps 90% of the time we are out for ourselves, however gently, but perhaps 10% of the time we are out for a higher cause (like the general good of everyone in our group) to the deepest level of our beings. A sense of “meaning” often comes from making that connection to something greater than ourselves.
You can see my other posts on happiness in the happiness sub-blog linked at my sidebar, and here:
In my post “The True Story of How Economics Got Its Nickname ‘The Dismal Science,’” I told how economics got its nickname “the dismal science” as a result of the opposition of John Stuart Mill (who was a noted economist as well as philosopher) to slavery. But the nickname sticks partly because people think of economists as bearers of bad news. But in fact, economists are prominent among those who remind people that over the long haul “Things Are Getting Better.” Steven Johnson’s article “We’re Living the Dream, We Just Don’t Realize It” has the same message. For a book-length treatment of this theme, I recommend The Progress Paradox: How Life Gets Better While People Feel Worse.
The economic slump we are in will someday be over. We should not let it falsely color our picture of the broad, progressive sweep of modern history.
Debora Spar has what I feel is good advice for modern women in her Daily Beast essay “Why Women Should Stop Trying to Be Perfect.” I have no first-person authority on dilemmas that women face, but having been born in 1960, I watched the Second Wave of Feminism and the Third Wave of Feminism with interest from their inceptions. I recommended this essay to my daughter.
Debora has useful things to say about how inequality in the sharing of household burdens–and in particular, the unequal sharing of child care–affects how women fare in the workforce as well:
…women who juggle children and jobs will still face a discrete and serious set of tensions that simply don’t confront either men (except in very rare cases) or women who remain childless….
Another piece of the puzzle sits closer to home, where parity remains frustratingly elusive and women still consistently log more hours than their mates. Between 1965 and 2000, the number of working mothers in the United States rose from 45 to 78 percent of all mothers, and the average time that an American woman spent in the paid labor force increased from 9 to 25 hours a week. Yet women were still devoting nearly 40 hours a week to family care: housework, child care, shopping. Men, by contrast, spent only 21, most of which were devoted to fairly discrete and flexible tasks like mowing the lawn, washing the car, and tossing softballs with the kids. (Try this. See who in any household schedules the kids’ dental appointments. My own husband, lovely though he is, seems not to be aware that our children even have teeth.)
At work, Debora points out how the true marginal products of women are often underestimated because women are less boastful than men and because the ways in which they contribute to balanced decision-making and the output of others are not fully counted:
Let me say what is often forbidden: women may differ from men in a whole range of important ways. In the aggregate, as research has shown, they may be less comfortable with outsize risk than men, and more inclined toward caution. They may be less directly confrontational, and slower to boast of their talents and successes. They may prize consensus over discord and favor personal relationships over hierarchical ones. Rather than wishing these differences away, or pretending they don’t exist, we need to analyze them, understand them, and then talk to one another about how best to create a world shaped by a diversity of styles and patterns; a world driven by women’s skills and interests and passions as much as by men’s.
Debora also has some wise words about the costs of political correctness:
Thankfully, the time for this evolution is now ripe. Millions of men have watched their daughters play soccer, their mothers launch companies, their sisters struggle to compete. They have invested in female employees who subsequently quit and have wondered, later in their own lives, whether they asked their wives to sacrifice too much on their behalf. Most of these men genuinely want women to succeed.
But they don’t know how to make the right changes and are generally not party to the conversations that women have among themselves. All too often, women are scared of raising the topic of gender with men, thinking it will brand them as radicals or troublemakers, while men are terrified of saying or doing anything that might classify them as politically incorrect. The result, of course, is that no one says anything productive at all. Women mutter to themselves about their continued exploitation, men mumble platitudes and hire high-priced diversity consultants, and nothing changes.
Finally, Debora has two key pieces of advice for women juggling both work and children in the world as it is now:
I like both of these points. On the first point, let me add this thought of my own:
If you think “setting priorities” is a pleasant platitude, you don’t understand what it really is. “Setting priorities” is the brutal process of deciding which things won’t get done.
In my latest column on Quartz, “Second Act: Obama Could Really Help the US Economy by Pushing for More Legal Immigration,” I wrote:
Additional immigration may cause a problem for native-born Americans who don’t complete high school, but the kind of education reform that will help solve that problem is already one of the president’s strong suits and something strongly supported by Republicans.
Jennifer Hunt, in her recent NBER Working Paper “The Impact of Immigration on the Educational Attainment of Natives,” finds evidence that the impact of additional immigration on high school dropouts is mitigated by the fact that many of the native born come to realize they need more schooling to avoid being in competition with immigrants. Jennifer’s paper was considered of enough general interest that it was featured in the NBER Digest. Here is the NBER Digest’s summary of her paper:
An increase of one percentage point in the share of immigrants aged 11-64 in the population increases the probability that natives aged 11-17 eventually complete 12 years of schooling by 0.3 percentage points.
In The Impact of Immigration on the Educational Attainment of Natives (NBER Working Paper No. 18047), Jennifer Hunt finds that, contrary to the popular notion that immigrants may have a negative impact on the public education experience of native-born children, the net effect of immigrant children in schools is positive. Using the 1940-2000 censuses and the pooled 2008-2010 American Community Surveys, Hunt focuses on the impact of immigration on the probability of natives’ completion of 12 years of schooling. She finds that an increase of one percentage point in the share of immigrants aged 11-64 in the population increases the probability that natives aged 11-17 eventually complete 12 years of schooling by 0.3 percentage points.
There are at least two ways in which immigration could affect schooling outcomes for natives. Immigrant children could compete for schooling resources with native children, lowering the return to native education and discouraging native high school completion. Conversely, native children might be encouraged to complete high school in order to avoid competing with immigrant high-school dropouts in the labor market. Hunt finds evidence that both channels are operative and that the net effect is positive, particularly for native-born blacks, but not for native-born Hispanics.
Compared to natives, immigrants to the United States are much more likely to be poorly educated, and also more likely to be highly educated. Immigrants are underrepresented among workers with an intermediate level of education, such as a high school diploma. –Matt Nesvisky
The Digest is not copyrighted and may be reproduced freely with appropriate attribution of source.
The one finding that is worrisome is the less positive effect on education for the native-born Hispanics, who are most similar to the bulk of the immigrants. This suggests that it might be wise for a policy increasing legal immigration to aim for increased immigration from a wide range of different countries. This would be consistent with having a large number of legal immigration slots for those coming from Latin American countries, if most of those slots were reserved for those who already have a strong connection to the United States–for example, by having resided here for a long time.
Here is the link to my 6th column on Quartz. My original working title was “How Obama Can Put the Republicans in a Box and Secure His Legacy.”
This column is in honor of Barack Obama, President of the United States, on the occasion of his reelection.
Miles gives a delayed response to Jean-Paul Sartre on Twitter
Jean-Paul Sartre said:
The best work is not what is most difficult for you, it is what you do best.
From my own observation, of others as well as myself, let me say this:
When you are good at something, the way it looks to you is that you are OK at it, but everyone around you is messing up.
When things look that way, be patient with those around you and realize that you may have found your comparative advantage–a comparative advantage that might help you go far.
Thanks to Scott Sumner for highlighting this interesting and accessible piece by Garrett Jones here. To see if you want to read it, start by taking a look at the graphs.
In the title “National IQ and National Productivity: The Hive Mind Across Asia," having read Noah Smith’s diatribe against the Asian "hive mind” stereotype, I recommend ignoring the phrase “Hive Mind.” Also, since IQ depends a lot on how hard people study, I interpret “IQ” as a measure of human capital that may be superior in many ways to just counting years of schooling. In any case, this set of facts is quite intriguing.
Here is one more in my selection of what I think are especially good posts by Noah Smith. This one might be controversial, but it is well argued. I like Noah’s take on history here.
A few years back, economists and other social scientists and technical experts at RAND and the University of Michigan put together a grant proposal focused on seeing what can be done with web surveys. Thanks to funding provided by the National Institute on Aging (part of the National Institute of Health), we were able to find out the answer. Leaving out many details, the basic answer is that, except for a few things that have to be done in person, web surveys are at least as good, and usually better, than other survey methods. RAND’s American Life Panel arose out of that collaboration (though it is now an independent RAND survey that has a wide range of clients other than government research agencies). I can’t pretend to be objective about the American Life Panel. As part of a large team, I have been involved in it from the beginning and I love it.
An important distinction has to be made between commercial web surveys, which use samples of convenience (often trying to match certain broad demographic frequencies to the population as a whole) and scientific web surveys that make great efforts to get as close to a representative sample as possible–even on characteristics that are unmeasured. The American Life Panel is just such a scientific web survey. Every effort is made not only to draw respondents randomly from the population as a whole, but also to give web access to those randomly chosen who don’t already have web access.
By contrast to most surveys, which fairly soon became calcified under the weight of a standard set of questions that are asked again and again, taking up most of the available survey time, under Arie Kapteyn’s leadership, the American Life Panel (ALP) has grown in power and reach under a unique philosophy of experimental modules initiated in a relatively decentralized way that over time add up to much more than the sum of the parts. At this point, data from a huge variety of experimental modules can now be compared to data on ALP respondents that duplicates most of what is collected from respondents to Michigan’s Health and Retirement Study and data that duplicates a big subset of what is collected from respondents to Michigan's Cognitive Economics Study. Arie’s commitment to supporting “bold, persistent experimentation” in surveys augurs well for the future of the American Life Panel.
Because the American Life Panel has only recently come into its own, most economists don’t realize what is there, what can be done with the existing data on the ALP, and what can be done by collecting new experimental data to combine with the ALP’s existing data. For young economists in particular, I am confident there are many, many dissertations hiding in the data already collected, aside from everything that is coming.
Just for fun, I have put a link under the illustration to the ALP’s election forecast webpage, based on survey questions that probe for probabilities as opposed to discrete answers–a style of survey question that has been advocated most forcefully by Chuck Manski and his coauthors. Also, unlike typical election polls, the results you see above and at the election forecast webpage are based on panel data: the same people are asked the questions repeatedly, so that the changes you see are more likely to be genuine changes in opinion, instead of random fluctuations in the set of people surveyed. (Note: the election polling behind the picture above is not supported by any government agency.)
Update: Brad DeLong tweeted to me this interesting comment:
RAND’s reinterview method is a treatment that over time turns low-info voters into high info voters. That’s a powerful bias…
My reaction is that if Brad is right, the views of a high-information sample of otherwise typical voters from a representative sample is itself very interesting. The question that Brad raises is a good example of the value of an experimental survey–to be able to discover and investigate, or rule out, effects such as that.
At this link, Bryan Caplan does a great job of framing Joshua Muravchik’s account of Robert Owen’s utopian socialist experiments. Bryan sums up his take in this way:
Until now, I’d always thought that despite his pretensions, Marx was no better than the Utopian socialists. Now I realize that this was entirely unfair. Marx was decidedly inferior to his “Utopian” rivals. They were wrong, but at least they had the common sense and common decency to beta test their radical proposals on a small scale with consenting subjects.
This op/ed by Nicholas Kristof is a classic that Greg Mankiw links to. I use it in my class to make two points:
A number of policies recommended by those who say they care about the poor have the common element of saying, in effect:
If you can’t or won’t create a good job, don’t create a job at all.
For some people, a “bad job” is a lifeline. And if we insist that only good jobs should exist, they will have no job.
I think there is another element behind opposition to sweatshops. When people in poor countries are suffering before the arrival of an American company in their backyard, that hideous suffering from poverty is out of sight for us in America. But as soon as the American company arrives to give the opportunity of taking what look like bad jobs to us, if they choose to, the somewhat lesser suffering of their poverty after taking the “bad job” seems like the fault of the American company for not making the jobs nicer. In fact the company has helped them, but we only see the suffering from poverty after, not the hideous suffering from worse poverty before.
One factor that can make it easier to blame the American company for the suffering left after providing the job is that some of the corporate executives involved in setting up and running the new factory in a poor country may, in fact, be uncaring, unfeeling people (though I doubt this is true anywhere near as often as people suppose). But even if many of the corporate executives involved in setting up and running the new factory are uncaring, unfeeling people, it doesn’t change the fact that, by their actions of setting up and running the factory, they have made people’s lives better. They could have made people’s lives better still if they had taken a bigger fraction of their personal earnings and donated it to helping the poor than they actually did, but that is something that can be said for almost every American.
One policy change that could increase what Americans do to help the desperately poor in other countries is the program of “public contributions” I recommend in my post “No Tax Increase Without Recompense.” That program of public contributions would dramatically increase the amount of assistance American give to the desperately poor in other countries. Government-funded foreign aid is very unpopular–and often is relatively ineffective because much of it is channeled through corrupt foreign governments. But many individuals (with whatever money they have set aside to donate to good causes) are attracted by the idea of helping the desperately poor.
Mancur Olson, an economist who studied The Rise and Decline of Nations
Last Saturday, Holman Jenkins had a very interesting op/ed in the Wall Street Journal: “Hey Mitt, Voters Aren’t the Obstacle.” What is the obstacle in Holman’s view? The political influence of organized labor. The theory Holman bases his analysis on is from the brilliant economist Mancur Olson, who focused on the forces that change institutions over time. Holman:
Mancur Olson, the late and admired social thinker, described the lobbying incentives created by policies that concentrate benefits on the few and disperse the costs to the many. Recipients of federal entitlements aren’t highly motivated to oppose the kind of long-term reforms actually required by our fiscal dilemma. Organized labor is.
I encountered Mancur Olson through his book The Rise and Decline of Nations. Here is wikipedia’s summary of The Rise and Decline of Nations in its article on Mancur Olson:
In 1982, [Mancur Olson] expanded the scope of his earlier work in an attempt to explain The Rise and Decline of Nations. The idea is that small distributional coalitions tend to form over time in countries. Groups like cotton-farmers, steel-producers, and labor unions will have the incentives to form lobby groups and influence policies in their favor. These policies will tend to be protectionist and anti-technology, and will therefore hurt economic growth; but since the benefits of these policies are selective incentives concentrated amongst the few coalitions members, while the costs are diffused throughout the whole population, the “Logic” dictates that there will be little public resistance to them. Hence as time goes on, and these distributional coalitions accumulate in greater and greater numbers, the nation burdened by them will fall into economic decline.
The most interesting thing in Holman’s piece is his list of bipartisan and Democratic initiatives that were thwarted by union lobbying. I have added bullets and combined three different quotation blocks here, but the words are Holman’s:
Holman summarizes as follows:
We don’t dismiss the power of AARP, but organized labor dominates the Democratic Party on Capitol Hill. Organized labor has been the force, decade after decade, carefully tending the creation of the many liabilities and excesses that now threaten the Republic.
Let me say this on my own behalf. No one should blithely assume that unions will support liberal policies, if by liberal policies one means policies to help the poor and the suffering. Most unions are middle-class organizations that in their political activities are ready and willing to sacrifice the interests of the poor to benefit their members and their leaders. (Here I am distinguishing the political activities of unions from the wage-and-benefit-raising and worker-voice activities of unions that I discuss in my post “Adam Ozimek on Worker Voice.”)
Detroit Metro Times mockup of the card for my Federal Lines of Credit Proposal
This is an update of my post “Miles’s Best 7 “Save-the-World” Posts, as of July 7, 2012”– a title with a bit of gentle self-mockery at my own presumption. This time, inspired by the U.S. presidential campaign, I want to think of my most important policy recommendations as a kind of shadow political platform. I have neither the odd talents, the drive, nor the sheer stamina required to be a political candidate. But if I were a political candidate, this is the platform I would run on.
Let me organize some key posts for each policy area. Within each policy area, I have arranged them in a recommended reading order. Many of the proposals are the proposals of others, but if I put a post in this list, it is something I have signed on to, with whatever caveats are in my post.
There are three areas where I don’t have as much in the way of specific proposals (with the one exception of Charter Cities), but the posts hint at an approach. I have signaled these by using the word “perspectives” in the area heading.
Until I do another update, you will be able to access this post at any time by the “‘Save the world’ posts” link at my sidebar. Or you should be able to reach it by using the searchbox further down on the sidebar.
Question from tommlu
Hi. I’m an undergraduate in my senior year, and I was wondering if you could any topics for an economic thesis, particularly in the area of taxation. Let me say that I am unconvinced that taxes has an effect on economic growth in the short run or the long run. There’s no doubt that taxes create a disincentive to work, but is that effect really so large as to decrease overall economic activity (productivity, demand, income,). If you could offer any suggestions for me, I would love to hear them. Thanks.
Answer
To me, the more interesting question is the long-run question. Here, I think there is something very useful you could do in an undergraduate thesis. Tax and benefit systems of different countries are complex enough that it is not easy to research all the details to compare how different tax and benefit systems lead to different effects. (I have seen this done more comprehensively for tax and benefit policies that would affect retirement decisions than for tax and benefit policies for younger workers). Doing thorough case studies of the tax and benefit systems of various countries and looking for the predicted effects would be a great service. For example, do many of the French take August off because of the details of their tax and benefit system? Is there something about Germany’s tax code and benefit code that helps explain why so few German women work? Don’t forget advanced Asian economies, such as Japan.
You would have the most impact if you concentrate first and foremost on providing clear summaries of how the tax and benefit codes of different countries work and what the details are. I know I would learn a lot from that. I think most economists would.
What I am suggesting might have been impossible before Google Translate, but nowadays, your computer will give you a translation that is probably good enough to figure out most of what is going on.
During my first year in Harvard’s Economic Ph.D. program (1983-1984), I thought to myself I could never be a macroeconomist, because I couldn’t figure out where the equations came from in the macro papers we were studying. In my second year, I focused on microeconomic theory, with Andreu Mas-Colell as my main role model. Then, during the first few months of calendar 1985, I stumbled across Martin Weitzman’s paper “Increasing Returns and the Foundations of Unemployment Theory” in the Economics Department library. Marty’s paper made me decide to be a macroeconomist. (I took the macroeconomics field courses and began working on writing some macroeconomics papers the following year, my third year–the year Greg Mankiw joined the Harvard faculty–and went on the job market in my fourth year.) I want to give you some of the highlights from “Increasing Returns and the Foundations of Unemployment Theory”, not only so you can see what affected me so strongly, but also because it includes ideas that every serious economist should have in his or her mental arsenal. Marty’s paper is a “big-think” paper. It has a lot to say, even after all of the equations were stripped out of it.
There is one important piece of background before turning to Marty’s paper: Say’s Law. In Say’s own words, organized by the wikipedia article on Say’s Law:
In Say’s language, “products are paid for with products” (1803: p. 153) or “a glut can take place only when there are too many means of production applied to one kind of product and not enough to another” (1803: p. 178-9). Explaining his point at length, he wrote that:
It is worthwhile to remark that a product is no sooner created than it, from that instant, affords a market for other products to the full extent of its own value. When the producer has put the finishing hand to his product, he is most anxious to sell it immediately, lest its value should diminish in his hands. Nor is he less anxious to dispose of the money he may get for it; for the value of money is also perishable. But the only way of getting rid of money is in the purchase of some product or other. Thus the mere circumstance of creation of one product immediately opens a vent for other products. (J. B. Say, 1803: pp.138–9)
Say’s Law is sometimes expressed as “Supply creates its own demand.” Say’s law seems to deny the possibility of Keynesian unemployment–unemployed workers who are identical in their productivity to workers who have jobs, and are willing to work for the same wages, but cannot find a job in a reasonable amount of time. The argument of Say’s law needs to be countered in some way in order to argue for the existence of Keynesian unemployment. Marty paints of picture of Keynesian unemployment in this way:
In a modern economy, many different goods are produced and consumed. Each firm is a specialist in production, while its workers are generalists in consumption. Workers receive a wage from the firm they work for, but they spend it almost entirely on the products of other firms. To obtain a wage, the unemployed worker must first succeed in being hired. However, when demand is depressed because of unemployment, each firm sees no indication it can profitably market the increased output of an extra worker. The inability of the unemployed to communicate effective demand results in a vicious circle of self-sustaining involuntary unemployment. There is an atmosphere of frustration because the problem is beyond the power of any single firm to correct, yet would go away if only all firms would simultaneously expand output. It is difficult to describe this kind of ‘prisoner’s dilemma’ unemployment rigorously, much less explain it, in an artificially aggregated economy that produces essentially one good.
Marty mentions one economic fact that has big implications even outside of business cycle theory. A remarkable fact about the political economy of trade is that trade policy often favors the interests of producers over the interests of consumers. Why are producer lobbies more powerful than consumer lobbies? The key underlying fact is that “Each firm is a specialist in production, while its workers are generalists in consumption.” So particular firms and the workers of those firms care a huge amount about trade policy for the good that they make, while the many consumers who would each benefit a little from a lower price with free imports are not focused on the issue of that particular good, since it is only a small share of their overall consumption. The exceptions, where consumer interests take the front seat in policy making, are typically where the good in question is a very large share of the consumption bundle (such as wheat or rice in poor countries) or where trade policy for many different goods has been combined into an overall trade package that could make a noticeable difference for an individual consumer. Other political actions that depart from the free market often follow a similar principle–either favoring a producer or favoring households interests in relation to a good that is a large share of the household’s budget, such as rent, or a very salient good such as gasoline, which seems to consumers as if it is even more important for their budgets than it really is.
After painting the picture of the world that he wants to provide a foundation for, Marty dives into his main argument–that increasing returns is essential if one wants to explain unemployment.
In this paper I want to argue that the ultimate source of unemployment equilibrium is increasing returns. When compared at the same level of aggregation, the fundamental differences between classical and unemployment versions of general equilibrium theory trace back to the issue of returns to scale.
More formally, I hope to show that the very logic of strict constant returns to scale (plus symmetric information) must imply full employment, whereas unemployment can occur quite naturally with increasing returns
He argues that much the same issues would arise from increasing returns to scale from a wide variety of difference causes:
The reasons for increasing returns are anything that makes average productivity increase with scale - such as physical economies of area or volume, the internalisation of positive externalities, economising on information or transactions, use of inanimate power, division of labour, specialisation of roles or functions, standardisation of parts, the law of large numbers, access to financial capital, etc., etc.
Marty lays out a sequence of three models. Here are the first two models or “stages”:
III. STAGE I: SELF SUFFICIENCY
Suppose each labourer can produce α units of any commodity. In such a world the economic problem has a trivial Robinson Crusoe solution. A person of attribute type i simply produces and consumes α units of commodity i.
IV. STAGE II: SMALL SCALE SPECIALISATION
Now suppose a person of type (i,j) prefers to consume i but has a comparative advantage in producing j.
In such an economy there can be no true unemployment because there are no true firms. If anyone is declared 'unemployed’ by a firm, he can just announce his own miniature firm, hire himself, and sell the product directly on a perfectly competitive market.
In the context of the “Stage II” model, Marty points to increasing returns to scale not only as the explanation for unemployment, but also as what makes plants discrete entities (in this paper he does not distinguish between plants and firms):
In a constant returns economy the firm is an artificial entity. It does not matter how the boundary of a firm is drawn or even if it is drawn at all. There is no operational distinction between the size of a firm and the number of firms.
Also, increasing returns to scale is the reason it is typical for a firm, defined in important measure by its capital, to hire workers, rather than the other way around. With constant returns to scale, workers could easily hire capital and there would be less unemployment:
When unemployed factor units are all going about their business spontaneously employing themselves or being employed, the economy will automatically break out of unemployment.
One reason increasing returns to scale is so powerful in its effects is that it is closely linked to imperfect competition–as constant returns to scale is closely linked to perfect competition.
The seemingly institution-free or purely technological question of the extent of increasing returns is a loaded issue precisely because the existence of pure competition is at stake.
To emphasise a basic truth dramatically, let the case be overstated here. Increasing returns, understood in its broadest sense, is the natural enemy of pure competition and the primary cause of imperfect competition. (Leave aside such rarities as the monopoly ownership of a particular factor.)
After laying out a particular macroeconomic model with increasing returns to scale, Marty directly addresses Say’s law, writing this:
Behind a mathematical veneer, the arguments used in the new classical macroeconomics to discredit steady state involuntary unemployment are implicitly based on some version or other of Say’s Law. It is true that under strict constant returns to scale and perfect competition, Say’s Law will operate to ensure that involuntary unemployment is automatically eliminated by the self interested actions of economic agents. Each existing or potential firm knows that irrespective of what the other firms do it cannot glut its own market by unilaterally expanding production, hence a balanced expansion of the entire underemployed econorny in fact takes place. But increasing returns prevents supply from creating its own demand because the unemployed workers are essentially blocked from producing. Either the existing firms will not hire them given the current state of demand, or, even if a group of unemployed workers can be coalesced effectively into a discrete lump of new supply, it will spoil the market price before ever giving Say’s Law a chance to start operating. When each firm is afraid of glutting its own local market by unilaterally increasing output, the economy can get trapped in a low level equilibrium simply because there is insufficient pressure for the balanced simultaneous expansion of all markets. Correcting this 'externality’, if that is how it is viewed, requires nothing less than economy-wide coordination or stimulation. The usual invisible hand stories about the corrective powers of arbitrage do not apply to effective demand failures of the type considered here.
To this day–more than 27 years later–I stand convinced that increasing returns to scale are essential to understanding macroeconomics in the real world. Much of what we see around us stems from the inability of half a factory, staffed with half as many workers, to produce half the output. Despite the difficulty of explaining Marty’s logic for why increasing returns to scale matters and what its detailed consequences are, I believe Intermediate Macroeconomics textbooks–and even Principles of Macroeconomics textbooks–need to try. Anyone who learns much macroeconomics at all should not be denied a chance to hear some of Marty’s logic.
Paul Douglas, Economist and Senator from Illinois Paul Douglas was not only an economist, but one of the most admirable politicians I have ever read about. See what you think: here is the wikipedia article on Paul. I would be interested in whether there are any skeletons in his closet that this article is silent on. If the Devil’s Advocate’s case is weak, he may qualify as a Supply-Side Liberal saint. (He was divorced, so a Devil’s Advocate might have something to work with. See my discussion of saints and heroes in “Adam Smith as Patron Saint of Supply-Side Liberalism?”) Paul was one of Barack’s predecessors as senator of Illinois, serving from 1949-1967, but chose not to run for president when he was given the chance.
In 1927, before he dove fully into politics, Paul teamed up with mathematician and economist Charles Cobb to develop and apply what has come to be called the “Cobb-Douglas” production function. (The wikipedia article on Charles Cobb is just a stub, so I don’t know much about him.) Here is the equation:
A very famous economist, Knut Wicksell, had used this equation before, but it was the work of Charles Cobb and Paul Douglas that gave this equation currency in economics. Because of their work, Paul Samuelson–a towering giant of economics–and his fellow Nobel laureate Robert Solow, picked up on this functional form. (Paul Samuelson did more than any other single person to transform economics from a subject with many words and a little mathematics, to a subject dominated by mathematics.)
In the equation, the letter A represents the level of technology, which will be a constant in this post. (If you want to think more about technology, you might be interested in my post “Two Types of Knowledge: Human Capital and Information.”) The Greek letter alpha, which looks like a fish (α), represents a number between 0 and 1 that shows how important physical capital, K–such as machines, factories or office buildings–is in producing output, Y. The complementary expression (1-α) represents a number between 0 and 1 that shows how important labor, L, is in producing output, Y. For now, think of α as being 1/3 and (1-α) as being 2/3:
As long at the production function has constant returns to scale so that doubling both capital and labor would double output as here, the formal names for α and 1-α are
What Makes Cobb-Douglas Functions So Great. The Cobb-Douglas function has a key property that both makes it convenient in theoretical models and makes it relatively easy to judge when it is the right functional form to model real-world situations: the constant-share property. My goal in this post is to explain what the constant-share property is and why it holds, using the logarithmic percent change tools I laid out in my post “The Logarithmic Harmony of Percent Changes and Growth Rates.” If any of the math below seems hard or unclear, please try reading that post and then coming back to this one.
The Logarithmic Form of the Cobb-Douglas Equation. By taking the natural logarithm of both sides of the defining equation for the Cobb-Douglas production function above, that equation can be rewritten this way:
log(Y) = log(A) + α log(K) + (1-α) log(L)
This is an equation that holds all the time, as long as the production engineers and other organizers of production are doing a good job. If two things are equal all the time, then changes in those two things must also be equal. Thus,
Δ log(Y) = Δ log(A) + Δ {α log(K)} + Δ {(1-α) log(L)}.
Remember that, for now, α= 1/3. The change in 1/3 of log(K) is 1/3 of the change in log(K). Also, the change in 2/3 of log(L) is 2/3 of the change in log(L). And quite generally, constants can be moved in front of the change operator Δ in equations. (Δ is also called a “difference operator” or “first difference operator.”) So
Δ log(Y) = Δ log(A) + α Δ log(K) + (1-α) Δ log(L).
As defined in “The Logarithmic Harmony of Percent Changes and Growth Rates,”the change in the logarithm of X is the Platonic percent change in X. In that statement X can be anything, including Y, A, K or L. So as long as we interpret %Δ in the Platonic way,
%ΔY = %ΔA + α %ΔK + (1-α) %ΔL
is an exact equation, given the assumption of a Cobb-Douglas production function.
Percent Changes of Sums: An Approximation. Now let me turn to an approximate equation, but one that is very close to being exact for small changes. Economists call small changes marginal changes, so what I am about to do is marginal analysis. (By the way, the name of Tyler Cowen and Alex Tabarrok’s popular blog Marginal Revolutionis a pun on the “Marginal Revolution” in economics in the 19th century when many economists realized that focusing on small changes added a great deal of analytic power.)
For small changes,
%Δ (X+Z) ≈ [X/(X+Z)] %ΔX + [Z/(X+Z)] %ΔZ,
where X and Z can be anything. (Those of you who know differential calculus can see where this approximation comes from by showing that d log(X+Z) = [X/(X+Z)] d log(X) + [Z/(X+Z)] d log(Z)], which says that the approximation gets extremely good when the changes are very small. But as long as you are willing to trust me on this approximate equation for percent changes of sums, you won’t need any calculus to understand the rest of this post.)
The ratios X/(X+Z) and Z/(X+Z) are very important. Think of X/(X+Z) as the fraction of X+Z accounted for by X; and think of Z/(X+Z) as the fraction of X+Z accounted for by Z. Economists use this terminology:
By the way they are defined, the shares of X and Z in X+Z add up to 1.
The main reason the rule for the percent changes of sums is only an approximation is that the shares of X and Z don’t stay fixed at their starting values. The shares of X and Z change as X and Z change. Indeed, if one changed X and Z gradually (avoiding any point where X+Z=0), the approximate rule for the percent change of sums would have to hold exactly for some pair of values of the shares of X and Z passed through along the way.
The Cost Shares of Capital and Labor. Remember that in the approximate rule for the Platonic percent change of sums, X and Z can be anything. In thinking about the production decision of firms, it is especially useful to think of X as the amount of money that a firm spends on capital and Z as the amount of money the firm spends on labor. If we write R for the price of capital (the "Rental price” of capital) and W for the price of labor (the “Wage” of labor), this yields
For the issues at hand, it doesn’t matter whether the amount R that it costs to rent a machine or an office and the amount W it costs to hire an hour of labor is real (adjusted for inflation) or nominal. It does matter, though, that nothing the firm can do will change R or W. The kind of analysis done here would work if what the firm does affects R and W, but the results, including the constant-share property, would be altered. I am going to analyze the case when the firm cannot affect R and W–that is, I am assuming the firm faces competitive markets for physical capital and labor. Substituting RK in for X and WL in for Z, the approximate equation for percent changes of sums becomes
%Δ (RK+WL) ≈ [RK/(RK+WL)] %Δ(RK) + [WL/(RK+WL)] %Δ(WL)
Economically, this approximate equation is important because RK+WL is the total cost of production. RK+WL is the total cost because the only costs are total rentals for capital RK and total wages WL. In this approximate equation
The two shares always add up to 1 (as can be confirmed with a little algebra), so
s_L = 1 - s_K.
Using this notation for the shares, the approximation for the percent change of total costs is
%Δ (RK+WL) ≈ {s_K} %Δ(RK) + {s_L} %Δ(WL).
The Product Rule for Percent Changes. In order to expand the approximation above, I am going to need the rule for percent changes of products. Let me spell out the rule, along with its justification twice, using RK and WL as examples:
%Δ (RK) = Δ log(RK) = Δ {log( R ) + log(K)} = Δ log( R ) + Δ log(K) = %ΔR + %ΔK
%Δ (WL) = Δ log(WL) = Δ {log(W) + log(L)} = Δ log(W) + Δ log(L) = %ΔW + %ΔL
These equations, reflecting the rule for percent changes of products, hold exactly for Platonic percent changes. Aside from the definition of Platonic percent changes as the change in the natural logarithm, what I need to back up these equations is the fact that the change in one thing plus another, say log( R ) + log(K), is equal to the change in one plus the change in the other, so that Δ {log( R ) + log(K)} = Δ log( R ) + Δ log(K). Using the product rule,
%Δ (RK+WL) ≈ {s_K} (%ΔR + %ΔK) + {s_L} (%ΔW+ %ΔL).
Cost-Minimization. Let’s focus now on the firm’s aim of producing a given amount of output Y at least cost. We can think of the firm exploring different values of capital K and labor L that produce the same amount of output Y. An important reason to focus on changes that keep the amount of output the same is that it sidesteps the whole question of how much control the firm has over how much it sells, and what the costs and benefits are of changing the amount it sells. Therefore, focusing on different values of capital and labor that produce the same amount of output yields results that apply to many different possible selling situations (=marketing situations=industrial organization situations=competitive situations) a firm may be in. That is, I am going to rely on the firm facing a simple situation for buying the time of capital and labor, but I am going to try not to make too many assumptions about the details of the firm’s selling, marketing, industrial organization, and competitive situation. (The biggest way I can think of in which a firm’s competitive situation could mess things up for me is if a firm needs to own a large factory to scare off potential rivals, or a small one to reassure its competitors it won’t start a price war. I am going to assume that the firm I am talking about is only renting capital, so that it has no power to credibly signal its intentions with its capital stock.)
The Isoquant. Economists call changes in capital and labor that keep output the same “moving along an isoquant,” since an “isoquant” is the set of points implying the same (“iso”) quantity (“quant”). To keep the amount of output the same, both sides of the percent change version of the Cobb-Douglas equation should be zero:
0 = %ΔY = %ΔA + α %ΔK + (1-α) %ΔL
Since I am treating the level of technology as constant in this post, %ΔA=0. So the equation defining how the Platonic percent changes of capital and labor behave along the isoquant is
0 = α %ΔK + (1-α) %ΔL.
Equivalently,
%ΔL = -[α/(1-α)] %ΔK.
With the realistic value of α=1/3, this would boil down to %ΔL = -.5 %ΔK. So in that case, %ΔK= 1% (a 1 % increase in capital) and %ΔL = -.5 % (a one-half percent decrease in labor) would be a movement along the isoquant–an adjustment in the quantities of capital and labor that would leave output unchanged.
Moving Toward the Least-Cost Way of Producing Output. To find the least-cost or cost-minimizing way of producing output, think of what happens to costs as the firm changes capital and labor in a way that leaves output unchanged. This is a matter of transforming the approximation for the percent change of total costs by
After Step 1, the result is
%Δ (RK+WL) ≈ {s_K} %ΔK + {s_L} %ΔL.
After doing Step 2 as well,
%Δ (RK+WL) ≈ {s_K} %ΔK - {s_L} {[α/(1-α)] %ΔK}.
Then after Step 3, and collecting terms,
%Δ (RK+WL) ≈ {s_K - (1-s_K) [α/(1-α)]} %ΔK
= { [s_K/(1-s_K)] - [α/(1-α)] } [(1-s_K) %ΔK].
Notice that since the
1-s_K = s_L = the cost share of labor
is positive, the sign of (1-s_K) %ΔK is the same as the sign of %ΔK. To make costs go down (that is, to make %Δ (RK+WL) < 0), the firm should follow this operating rule:
1. Substitute capital for labor (making %ΔK > 0)
if [s_K/(1-s_K)] - [α/(1-α)] < 0.
2. Substitute labor for capital (making %ΔK < 0)
if [s_K/(1-s_K)] - [α/(1-α)] > 0.
Thus, the key question is whether s_K/(1-s_K) is bigger or smaller than α/(1-α). If it is smaller, the firm should substitute capital for labor. If s_K/(1-s_K) is bigger, the firm should do the opposite: substitute labor for capital. Note that the function X/(1-X) is an increasing function, as can be seen from the graph below:
X
Since X/(1-X) gets bigger whenever X gets bigger (at least in the range from 0 to 1 (which is what matters here),
So the firm’s operating rule can be rephrased as follows:
1. Substitute capital for labor (making %ΔK > 0)
if s_K < α.
2. Substitute labor for capital (making %ΔK < 0)
if s_K > α.
This operating rule is quite intuitive. In Case 1, the importance of capital for the production of output (α) is greater than the importance of capital for costs (s_K). So it makes sense to use more capital. In Case 2, the importance of capital for the production of output (α) is less than the importance of capital for costs (s_K), so it makes sense to use less capital.
Proof of the Constant-Share Property of Cobb-Douglas. So what should the firm do in the end? For fixed R and W, the more capital a firm uses, the bigger effect a 1% increase in capital has on costs. So if the firm is using a lot of capital, the cost share of capital will be greater than the importance of capital in production α and the firm should reduce its use of capital, substituting labor in place of capital. If the firm is using only a little capital, the cost share of capital will be smaller than the importance of capital in production α, and it will be a good deal for the firm to increase its use of capital, allowing it to reduce its use of labor. At some intermediate level of capital, the cost share of capital will be exactly equal to the importance of capital in production α, and there will be no reason for the firm to either increase or reduce its use of capital once it reaches that point. So a firm that is minimizing its costs–a first step toward optimizing overall–will produce a given level of output with a mix of capital and labor that makes the cost share of capital equal to the importance of capital in production:
cost-minimization ⇒ s_K = α.
Concordantly, one can say
cost-minimization ⇒ 1-s_K = 1-α.
That is, the firm will use a mix of capital and labor that makes the cost share of labor equal to the importance of labor in production as well. Since the Cobb-Douglas functional form makes the importance of capital in production α a constant, a cost-minimizing firm will continually adjust its mix of capital and labor to keep the cost share of capital equal to that constant level α, and the cost share of labor equal to another constant, 1-α. This is the constant-share property of Cobb-Douglas. The constant-share property is something that can be tested in the data, and often seems to hold surprisingly well in the real world. So economists often use Cobb-Douglas production functions.
Another Application of the Cobb-Douglas Idea: Achieving a Given Level of Cobb-Douglas Utility at Least Cost. Note that similar logic will work for utility functions as well. For example, in my post “The Flat Tax, The Head Tax and the Size of Government: A Tax Parable,” since the importance of consumption and leisure for utility is equal (both equal to 1/3), adjusting consumption C and leisure L so that %ΔC = - %ΔL will leave utility unchanged. Then,
On the other hand,
This means that if consumption is too high, it should be reduced, while if consumption is too low, it should be increased, until the amount of spending on consumption equals the amount of spending on leisure.
Two of the most fundamental choices people make are how to spend their money and their time. Economists talk about a “budget constraint” for money and a “budget constraint” for time. Here is a set of links to well-done graphs on how Americans deal with those two budget constraints:
Thanks to my brother Joseph Kimball for pointing me to this series of posts by Lam Thuy Vo and Jacob Goldstein.
Human Capital and Information. Knowledge can be either “human capital” or “information.” The difference is the resource cost of transferring a body of knowledge from one person to another. Here is the classification scheme I have in mind:
Human capital is knowledge that is hard to transfer.
Information is knowledge that is easy to transfer.
(This is a specific technical meaning of the word “information” for economics. I use the word “information” in a more general philosophical sense in my post “Ontology and Cosmology in 14 Tweets.”) Note that a given body of knowledge can shift from one category to another when technology changes. The words of the Iliad and the Odyssey were “human capital” when the only means of transferring this knowledge was oral transmission and memorization. When printing arose, the words of the Iliad and the Odyssey became “information." (See Albert Lord's The Singer of Tales on the original oral transmission of the Iliad and the Odyssey.)
Now comes the mid-post homework problem. Read Daniel Little’s description of the knowledge of how to fix machines or my abridged version of it just below, and classify the knowledge of how to fix machines as human capital or information. Here is Daniel Little’s opening paragraph:
There is a kind of knowledge in an advanced mechanical society that doesn’t get much attention from philosophers of science and sociologists of science, but it is critical for keeping the whole thing running. I’m thinking here of the knowledge possessed by skilled technicians and fixers – the people who show up when a complicated piece of equipment starts behaving badly. You can think of elevator technicians, millwrights, aircraft maintenance specialists, network technicians, and locksmiths.
Here is Daniel’s account of the level of difficulty of transferring this knowledge, based on his conversations with a fixer of mining machinery:
I said to him, you probably run into problems that don’t have a ready solution in the handbook. He said in some amazement, "none of the problems I deal with have textbook solutions. You have to make do with what you find on the ground and nothing is routine.” I also asked about the engineering staff back in Wisconsin. “Nice guys, but they’ve never spent any time in the field and they don’t take any feedback from us about how the equipment is failing.” He referred to the redesign of a heavy machine part a few years ago. The redesign changed the geometry and the moment arm, and it’s caused problems ever since. “I tell them what’s happening, and they say it works fine on paper. Ha! The blueprints have to be changed, but nothing ever happens.”
I would trust Tim to fix the machinery in my gold mine, if I had one. And it seems that he, and thousands of others like him, have a detailed and practical kind of knowledge about the machine and its functioning in a real environment that doesn’t get captured in an engineering curriculum. It is practical knowledge: “If you run into this kind of malfunction, try replacing the thingamajig and rebalance the whatnot.” It’s also a creative problem-solving kind of knowledge: “Given lots of experience with this kind of machine and these kinds of failures, maybe we could try X.” And it appears that it is a cryptic, non-formalized kind of knowledge. The company and the mine owners depend crucially on knowledge in Tim’s head and hands that can only be reproduced by another skilled fixer being trained by Tim.
In philosophy we have a few distinctions that seem to capture some aspects of this kind of knowledge: “knowing that” versus “knowing how”, epistime versus techne, formal knowledge versus tacit knowledge. Michael Polanyi incorporated some of these distinctions into his theory of science in Personal Knowledge: Towards a Post-Critical Philosophy sixty years ago, but I’m not aware of developments since then.
As a practical matter, Polanyi’s distinction between “knowing how” (formal knowledge) and “knowing that” (tacit knowledge) is so important for the costs of transferring knowledge from one person to another that it closely parallels the distinction between human capital and information.
Pure Technology. Let me assume that your answer to the homework problem is the same as mine: knowledge of how to fix machines has a large element of human capital. This has an important consequence: “technology” as we usually think of “technology” is not just made of the easily copied “recipes” that Paul Romer talks about in his Concise Encyclopedia of Economics article “Economic Growth.”
Suppose for the purposes of economic theory, we insist on defining “pure technology” as a recipe that can be cheaply replicated. Then “technology” in the ordinary sense has an element of human capital in it as well as “pure technology,” much as “profit” in the ordinary sense has an element of return to capital in it as well as “pure profit.” The pure technology for mining would include not only
The “technology” in the ordinary sense is human capital for using and repairing the machines–that is, already embedded knowledge produced from 1, 2 and learning time.
Economic Metaknowledge. In addition to straight ideas or recipes, Paul Romer emphasizes the importance of meta-ideas:
Perhaps the most important ideas of all are meta-ideas. These are ideas about how to support the production and transmission of other ideas. The British invented patents and copyrights in the seventeenth century. North Americans invented the agricultural extension service in the nineteenth century and peer-reviewed competitive grants for basic research in the twentieth century.
There are many meaning of the prefix “meta.” Paul is using “meta” so that “meta-X” means “things in category X to foster the production and transmission of things in category X.” When another meaning of “meta-” might otherwise intrude, let’s use “economic meta-X” for this meaning. Then with the distinction between human capital and information in hand, there are at least four types of economic metaknowledge–knowledge to foster the production and transmission of knowledge:
Extra Credit: Figure out how Paul Romer’s meta-ideas listed above–patents and copyrights, agricultural extension services, and peer-reviewed competitive grants–fit into this fourfold division of economic metaknowledge.
Rumsfeldian Metaknowledge. According to Colin Powell (as excerpted in the Appendix below and given more fully at this link) we can blame Donald Rumsfeld’s unchecked insubordination in disbanding the Iraqi Army for some portion of the long hard slog we faced in the War in Iraq since 2003, but Donald did coin a memorable description of another kind of metaknowledge. Here is the 21-second video, and here is the transcript:
[T]here are known knowns; there are things we know that we know.
There are known unknowns; that is to say there are things that, we now know we don’t know. But there are also unknown unknowns–there are things we do not know, we don’t know.
Metaknowledge in this sense of knowing what one knows and knowing what one doesn’t know often has great economic value, whether in daily life, business and policy making. But metaknowledge in this Rumsfeldian sense–even economically valuable Rumsfeldian metaknowledge–should be distinguished from “economic metaknowledge” as I define it above.
Appendix.Here is what Colin Powell wrote:
When we went in, we had a plan, which the president approved. We would not break up and disband the Iraqi Army. We would use the reconstituted Army with purged leadership to help us secure and maintain order throughout the country. We would dissolve the Baath Party, the ruling political party, but we would not throw every party member out on the street. In Hussein’s day, if you wanted to be a government official, a teacher, cop, or postal worker, you had to belong to the party. We were planning to eliminate top party leaders from positions of authority. But lower-level officials and workers had the education, skills, and training needed to run the country.
The plan the president had approved was not implemented. Instead, Secretary Donald Rumsfeld and Ambassador L. Paul Bremer, our man in charge in Iraq, disbanded the Army and fired Baath Party members down to teachers. We eliminated the very officials and institutions we should have been building on, and left thousands of the most highly skilled people in the country jobless and angry—prime recruits for insurgency. These actions surprised the president, National Security Adviser Condi Rice, and me, but once they had been set in motion, the president felt he had to support Secretary Rumsfeld and Ambassador Bremer.
This link gives a taste of the kind of thing you can read in a book I highly recommend: The Talent Code: Greatness Isn’t Born, It’s Grown by Daniel Coyle. In order to learn a lot, you need to
To study effectively, you need to do a lot more than “going over things” several times. You need to identify what you don’t completely understand and zero in on it to figure it out. You need to wonder how each idea relates to everything else you have learned. You need to get to the point where you can write your own exam questions and answer them, carefully thinking through what it would make sense for the instructors to test.
The human mind has a natural tendency to skitter away from things that are hard to understand. Effective study requires you to resist that tendency like a bad addiction. You need to turn toward the ideas that are hardest, not away from them.
