There Is No Such Thing as Decreasing Returns to Scale

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There is no such thing as decreasing returns to scale. Everything people are tempted to call decreasing returns to scale has a more accurate name. The reason there is no such thing as decreasing returns to scale was explained well by Tjalling Koopmans in his 1957 book Three Essays on the State of Economic Science. The argument is the replication argument: if all factors are duplicated, then an identical copy of the production process can be set up and output will be doubled. It might be possible to do better than simply duplicating the original production process, but there is no reason to do worse. In any case, doing worse is better described as stupidity, using an inappropriate organizational structure, or X-inefficiency rather than as decreasing returns to scale. 

The replication argument is extremely valuable as a guide to thinking about production since it often identifies a factor of production that might otherwise be ignored, such as land, managerial time, or entrepreneurial oversight. Thinking through what difficulties there might be in practice in duplicating a production process at the same efficiency helps to identify key factors of production if those factors of production were not already obvious.  

The nonexistence of decreasing returns to scale implies that the U-shaped average cost curve still taught routinely to most economics students, with its decreasing returns to scale region, is not what it seems. I got into a debate about this on Twitter, which I storified in "Is There Any Excuse for U-Shaped Average Cost Curves?" A U-shaped average cost curve might be justifiable as a cost-curve per top-level manager, or perhaps as a cost-curve per entrepreneur. But including all inputs, including both managerial and entrepreneurial time and effort, production must still be at least constant returns to scale if not increasing returns to scale. 

In addition to crowding out the clarity of the replication argument, the emphasis in many economics classes on the so-called U-shaped average cost curve makes it harder for students to get the idea of increasing returns to scale clearly in their minds. Much better would be to use something like the graph below to teach students about increasing returns to scale:  

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Given the replication argument, there is no scale of operation that is beyond efficient scale. There may be ample reason to make different plants or divisions quasi-independent so they do not interfere with one another's operations. But that is not an argument against scale per se. There may even be reason to set up incentives so that different divisions are almost like separate firms, headed by someone in an entrepreneurlike position. But that still is not, properly speaking, an example of diseconomies of scale. 

Even those who disagree with me on some of the points above should agree that a debate on these issues, beginning with the challenges I have made above, would be good for student understanding of production. 

Besides pedagogical inertia—enforced to some extent by textbook publishers—I am not quite sure what motivates the devotion in so many economics curricula to U-shaped average cost curves. Let me make one guess: there is a desire to explain why firms are the size they are rather than larger or smaller. To my mind, such an explanation should proceed in one of three ways, appropriate to three different situations. 

1. If returns to scale are constant, then everything can be done on a per manager or per entrepreneur basis. This might still use diagrams similar to U-shaped average cost curves, but would be quite explicit about the fact that one factor was held constant, so that the upward-sloping part of the U-shaped average cost curve does not represent true decreasing returns to scale, but rather decreasing returns to scale in all other factors when managerial or entrepreneurial input is held constant.

2. If returns to scale are increasing, the size of the firm can be made determinate by having a downward-sloping demand curve. (I discuss in some detail the relationship between increasing returns and imperfect competition in "Next Generation Monetary Policy" and hope to return to discussing this relationship in a future blog post.)

3. If the firm is large enough relative to its suppliers and labor force that increasing its scale noticeably increases factor prices, that may limit a firm's scale. This is not properly decreasing returns to scale simply because returns to scale is defined over quantities, and so when translated into cost terms is effectively defined for given factor prices. In any case, to my mind, the analytical distinction between the production function and interaction with factor markets is an analytical distinction worth highlighting.

What I am most confident of is that microeconomic teaching of production as we know it, with the U-shaped average cost curve in center stage, is suboptimal. Let's change it. The way I think about production may not be the best way, but the way it is now taught is definitely not the best way.  

Don't miss the followup post: "Returns to Scale and Imperfect Competition in Market Equilibrium."

Update: In addition to the comments below (visible when you go to the post itself or click on the post title), this post has sparked a vigorous debate on Twitter, which I organized in this Storify story: "Up for Debate: There Is No Such Thing as Decreasing Returns to Scale."  In these storified tweets, I answer many questions you may have as well. I will try to keep that story updated. And here is a link to the debate on my Facebook page. 

Here are some of the most instructive comments, and some of my replies:

Chris Kimball: The replication argument is so obviously correct that every "diminishing return to scale" presentation is implicitly or explicitly holding one or more factor constant. That much seems near tautological. As a result, this strikes me as a pedagogy discussion. What's the preferred way to tease out these concepts? Given the fact that in the real world there really are constraints both internal and external, factors really are limited, and perfect replication is a thought experiment more than an observation.

Miles: Absolutely. We are thinking along very much the same lines. 

mike: But isn't franchising an example of where people realize that to get a local manager that cares at 2,000 locations, its better to seperate ownership interests. You talk about territory distribution etc, but I would argue that is an example of needing that remedy to overcoming decreasing returns to scale.

Miles: I love your example of a franchising system. This is exactly what I mean by having a firm organization that allows one to replication owner/entrepreneurs. The franchisees become one more input in the system from the point of view of headquarters. I wish I had thought of this example!

Patrick Neal Russell Julius: My favored way of explaining this is describing the last factor of production as "planets". If you were to copy the Earth in its entirety, in every detail, it strains all credulity to imagine that you could do any less than double total output. So there must be SOME factor of production that would allow you to have at least constant returns to scale—though if it is indeed planets, obtaining more of that factor might be quite prohibitive even in what we normally call the "long run".

Chris Makler: ... workers being homogenous fails ... If your production function only involves computer servers, fine; double the servers, double the traffic (or even more, but you get the point). But once you start hiring humans it's completely different. By definition if you have 10 slots to fill and 30 applicants, you fill the slots with the 10 people who are the best match. If you have 20 slots to fill, you go down the list. So DRS follows directly from some form of match-specific productivity.

Miles: This is very interesting. After adjusting for input quality, the amount of labor doesn't really double when the firm goes from 10 employees to 20. But "quality" of a worker may be firm specific, and so not visible in other data that isn't specific to the firm. 

In the Twitter debate storified in "Up for Debate: There Is No Such Thing as Decreasing Returns to Scale," the most interesting discussions to me were about communications within the firm and the production of software. Here is my summary of the issues and what I think is their resolution:

Communication Within a Firm: If every employee is encouraged to talk to every other employee, then the number of communication lines goes up with the square of the number of employees. A vast volume of communication could start to drag down production. The answer I give is that as an organization grows it needs siloing: groups with a lot of communication within the group, but limited communication between groups. Siloing is usually only mentioned in order to criticize it, but siloing has the huge benefit of helping to keep people from being overwhelmed with emails, for example. The trick is to get interaction between groups where that interaction is likely to be helpful, and avoid interaction between groups where that communication is a cost with little benefit. 

The Writing of Software and Books, Recording of Songs and Shows, etc.:  Sam Vega asks "Doesn't throwing more programmers at a software project qualify as "decreasing returns of scale"?" There are two perspectives one can take here: thinking about copies of the software, book, song, shows, etc. (whether physical or digital copies) and thinking about different software programs, texts, songs, shows etc.

From the perspective of copies of the software, book, song, show, etc., the writing and recording is a fixed cost. Throwing more programmers at writing the software to try to do things faster raises the fixed costs and increases the returns to scale for the copies. 

From the perspective of distinct software programs, books, songs, shows etc., the key point is that the replication argument only applies to the production of identical items. Leaving aside copies, you only need one of the code for each type of software. If you are only going to produce one, then returns to scale don't apply.  On the other hand, if you are willing to consider an array of different computer games, say, as distinct but on par (a symmetry assumption), then it should be possible to create 10 distinct games in the same amount of time if one has ten times the input.  

Another way to put it is that cutting the time it takes to produce something in half is not at all the same as producing twice as much of something in the same amount of time. 

Don’t miss the follow-up post “Returns to Scale and Imperfect Competition in Market Equilibrium.”

Polygenic Prediction and its Application in Social Science Conference|Center for Economic and Social Research, University of Southern California, April 13 and 14, 2017 →

This was a fascinating conference. The link above takes you to separate links for each presentation in the conference. My coauthor Dan Benjamin is heavily involved in genoeconomics as well as well-being research. I hope to get more involved in genoeconomics myself, as I mentioned in "Restoring American Growth: The Video."

My Objective Function

A key aspect of higher religion—that holds for nonsupernaturalist religion as well as supernaturalist religion—is serious attention to choosing the governing goals for human action. Economists spend a lot of time studying how to make choices in order to best achieve their goals given the limitations of the situations they are in. But (perhaps because of the kind of modeling difficulties I discuss in "Cognitive Economics") economists spend much less time studying metachoice: the choice of the goals themselves. This is particularly true for the choice—based in part on goals that then might be fully superseded—of those goals that become an individual's ultimate goals.

Someone who successfully proposes goals for others that they had never before conceived of can be thought of as a kind of prophet—whether a supernaturalist prophet or nonsupernaturalist prophet. The possibility of a future prophet identifying a new goal that many people would gladly take on makes it impossible to circumscribe the universe of all attractive human objectives. People want more than the things money can buy. They want more than happiness and life satisfaction. And they potentially want many things that they have never even dreamed of. 

In addition to prophets, who successfully propose goals for others, there are coaches who help people choose objectives for themselves. Such coaches might be friends, teachers, clergy, psychotherapists, leaders of human growth workshops, or people who call themselves "life coaches." Metachoice is so important that most people should seek out some coach to help them think through what they want their goals to be. Those who can't find such a coach in someone else competent to do that job need to coach themselves on a careful choice of their own objective function; but that is more difficult. 

In the mid-1990's I attended a series of excellent personal growth workshops by Landmark Education. In the "Advanced Communication Course" I was encouraged to identify my personal objectives and create a symbolic reminder of them. The star whose two sides are shown at the top of this post is the result. One side of the star—which I show first—gives headings for the objectives that are designed to spark curiosity. The other side gives the objectives themselves. In the Landmark Education courses, each of these objectives is typically preceded by the stem "I am the possibility of ..." as an expression of personal identification with that goal. The relationship between the heading on one side and the objective on the other side is clear for most. For those without the Mormon upbringing I had, the meaning of "Zion" might be unclear. I explain it this way in "Teleotheism and the Purpose of Life":

Zion, the ideal society—that we and our descendants can build.

The expression of my own personal objective function that I created in that Landmark course has had an important effect on my life. I want to illustrate that in relation to my career, this blog, and my personal life.

The reason I am writing about how my career, this blog, and my personal life have been shaped by my personal objective function today is that today is the 5th anniversary for supplysideliberal.com: my first post, "What is a Supply-Side Liberal," appeared on May 28, 2012. I have had an anniversary post every year since:

1. A Year in the Life of a Supply-Side Liberal
2. Three Revolutions
3. Beacons
4. Why I Blog

Now, on to how my objective function plays out in my career, this blog and my personal life. 

Profound Relationship

My most profound relationship is my marriage. I have two Valentine's Day posts about marriage:

• Marriage 101
• Marriage 102

My relationships with my children are different, but profound in their own way. After my mother died in Fall of 2012, I made a point of visiting my Dad often, fearing he would also die soon, and was gratified to have four years to deepen that relationship. As a bonus, since the rest of my brothers and sisters lived close to my Dad, my visits to my Dad also provided occasions for my brothers and sisters and I to get together and deepen those relationships. 

I have a set of wonderful relationships that are quite intentional. Men often need more friends than they would have without intentionally setting out to have friends. In Ann Arbor, I belonged to a group of Mormon and formerly Mormon men that met every two weeks in its heyday and sporadically in more recent years to the present day. Given the closeness of the group, they were OK with my decision to leave Mormonism in 2000. I also joined a Men's Circle established by the Men's Movement within my Unitarian-Universalist Congregation in Ann Arbor that meets every two weeks. The meetings of our Unitarian-Universalist Men's Circle are consciously designed to encourage self-disclosure: sharing true stories and ruminations about our lives. My Mormon Men's Group and Unitarian-Universalist Men's Circle fostered some of the closest relationships I have outside of my own family. In particular, my friend Kim Leavitt is the one other person who belongs to both groups and my friend Arland Thornton is the one who now holds my Mormon Men's Group together.

Professionally, my most profound relationships are those with my coauthors and others I am working with. One sign of a profound relationship is when working through strong disagreements makes the relationship stronger, rather than disagreements causing the relationship to disintegrate. That describes the relationships I have had with others in what we have called the "Well-Being Measurement Initiative": Dan Benjamin, Ori Heffetz and Kristen Cooper. In the work of the Well-Being Measurement Initative, which absorbs the bulk of my research time these days, I also treasure the relationships I have had with our amazing research assistants (Samantha Cunningham, Pierre-Luc Vautrey, Becky Royer, Robbie Strom, and Tuan Nguyen), then-graduate-student coauthors (Alex Rees-Jones, Nichole Szembrot, Derek Lougee and Jakina Debnam) and other more senior coauthors (Marc Fleurbaey and Collin Raymond), but those relationships have not had occasion to weather any serious disagreements. 

My blog has led to some surprisingly deep relationships. Here are some examples:

• Beginning my blog with his encouragement added another dimension to my relationship with my student Noah Smith, which has deepened in very interesting ways as Noah has become an important economic journalist. 
• Joshua Hausman is one of my best friends. As you can see from "Brad DeLong and Joshua Hausman on Federal Lines of Credit," I was first introduced to Joshua by Brad DeLong in response to one of my posts.
• I have never met Matthew Rognlie in person, but I feel I know him well from our electronic discussions, prompted by things I had said here on this blog. (See for example "Sticky Prices vs. Sticky Wages: A Debate Between Miles Kimball and Matthew Rognlie.")
• Ruchir Agarwal was a star student in my intermediate macro class a while back, but it was Ruchir's interest in the discussion of negative interest rates I had on this blog that got us back together to write "Breaking Through the Zero Lower Bound" and do other work together on negative interest rate policy.
• I feel I know Tom Grey well because of his frequent comments.
• My Twitter arguments with John Davidson help me to know him much better.
• I do Facebook as an extension of my blog, and can't help getting to know those I interact with better than I otherwise would.
• Finally, I am always gratified when those I know in real life read a few things on my blog. It probably helps them understand me a bit better.
• All this is in addition to the much more obvious ability of blogging to generate many relationships that may not qualify as deep, but are still quite meaningful. 

Human Connection and Justice and Welfare

When I write of "making the world a better place"—or more extravagantly of "saving the world"—I mean advancing human connection and justice and welfare. These three are very closely related. In particular, now that humanity as a whole has gained some power over nature, the greatest evils in the world come from a failure of "human connection," as groups of other human beings are seen as something less than fully human. I explore this phenomenon in "Us and Them," "The Hunger Games" Is Hardly Our Future--It's Already Here," "'Keep the Riffraff Out!'" Nationalists vs. Cosmopolitans: Social Scientists Need to Learn from Their Brexit Blunder," and "The Aluminum Rule."

Professionally, my two biggest efforts to make the world a better place right now are my work on negative interest rate policy and my work with the Well-Being Measurement Initiative to build national well-being indices that can help identify what people want and what policies are most successful in helping them get there. On my blog I also advocate many other ways to make the world a better place. To see one of my favorites, take a look at "How and Why to Expand the Nonprofit Sector as a Partial Alternative to Government: A Reader’s Guide." (I hope to give a better rundown of policies I have advocated in a bibliographic post sometime this Summer.)

I have felt some psychological pull toward more direct government service, but at this point in my life any significant direct government service seems increasingly unlikely. 

For advancing human connection and justice and welfare, I consider religion and philosophy as well as science and public policy. It has been very interesting blogging about religion every other Sunday and blogging my way through John Stuart Mill's On Liberty and John Locke's Second Treatise on the other Sundays.

Overall, there are three moral principles that keep coming up as I think about making the world a better place:

1. Doing good rather than harm.
2. Treating all human beings as equals, regardless of their origin.
3. Truth.

On the third point, I find myself especially distressed when someone in an academic position cares more about advancing their career than they do about the truth. 

In my personal life, my efforts to advance human connection and justice and welfare are random but real. I don't notice everything around myself, but when I do notice an injustice, I want to do something about it. I don't mean it is all to the good, but I think the fact that I don't notice everything around myself keeps me from burning out. 

All People Being Empowered by Math and Other Tools of Understanding

Professionally, a big part of my teaching (for undergraduates as well as graduate students) is helping students to understand math. I hope I can both make potentially hard things easy and also instill some enthusiasm for math and related tools of understanding such as logic and graphs. I hope some of my papers accomplish the same job of making what could be difficult math a little easier. 

Without consciously setting out to make math a theme of my blog, it has become one. "There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t," which I wrote with Noah is by far my most read piece, and my follow-up pieces also did well (though at least an order of magnitude less in readerships): "How to Turn Every Child into a 'Math Person'" and "The Coming Transformation of Education: Degrees Won’t Matter Anymore, Skills Will." I also have many minor posts on this theme; one recent post in this category is "You, Too, Are a Math Person; When Race Comes Into the Picture, That Has to Be Reiterated." 

In my personal life, I hope I transmit a bit of my love for math through my dabbling with number theory. I have had some success in inveigling my wife Gail in memorizing hotel room numbers by factoring them. I make Archimedean solids and other geometrical shapes with Magnetix

and try to show how each number is interesting in the birthday signs I draw for my children, such as this one for my daughter Diana:

Adventure into the Unknown

Intellectually, I am a contrarian, which does a lot to bring me into new territory. I try hard to think up new angles on questions in front of me and to combine ideas from different sources. I love to dive into fields and subfields I haven't done research on before. (You can see this in the REPEC ranking analysis I have a link for here: one of the dimensions I rank highest among economists in the world is in "breadth of citations across fields.") 

On my blog, I delight in tackling new topics. I arranged my bibliography of "key posts" to show the variety of subjects I have written on.

Attending seminars and reading tweets continually introduces me to new ideas. 

My travels to talk about negative interest rate policy have had the fortunate side effect of letting me explore many places in the world (1, 2). Those travels have also given me a chance to see great works of art in some of the greatest museums in the world. I hope a little bit of the visual sensibility from that time in art museums comes across in this blog. 

In my personal life, I manage to do "adventures into the unknown" without being particularly daring. I like to do urban hiking to explore nooks and crannies of cities I am visiting or of my home city (which is now Superior, Colorado). I often try one of the more exotic dishes on a restaurant menu. And I read science fiction. 

Lately, I have realized that a willingness to "adventure into the unknown" is important in preserving a commitment to truth. The truth is not always what one thought at first. So a willingness to go someplace new is a prerequisite in many cases for arriving at the truth. 

A willingness to "adventure into the unknown" is also crucial for arriving at "profound relationship." One of the best ideas from the Landmark Communications courses was the idea that one should listen to those close to you as if you don't know what they are going to say next. The opposite of acting as if you always know what someone is going to say next is a surefire way to wear away any understanding you have of them. 

Fun

I started out my life as quite a serious kid. So having fun is something I have needed to work on. But now, I have a lot of fun. In my professional life, I get to spend a lot of time talking to people. In all that talk, there is both a social element and a delicious competitive element of arguing one's points. Much the same is true of my blog, and Twitter and Facebook and my writing for Quartz, which I see as extensions of my blog. Often, when I sound very confident of what I am saying, what I am really thinking is "There is no way for me to be wrong without it being interesting." And that thought is almost always borne out: either I get the joy of being right, or I get the joy of seeing things from a new angle I hadn't thought of before. 

In my personal life, fun comes in more varieties. I love the beauty of the landscape here in Colorado. I love learning new languages (something that contributed to my getting a Linguistics MA before I got an Economics PhD). I love vocal music, and often combine it with my love of foreign languages by listening to vocal music with non-English lyrics. I love reading both fiction and non-fiction. I love the great dramatic form of our age: TV. I love having friends and family come to visit. 

I am not sure I understand how to make things fun for other people. I remember once at a men's retreat all the men going around the circle and telling a little about their hobbies. The variety was astounding. People are truly different in the leisure-time activities they love. I know many of my tastes are minority tastes. I seldom fall into the trap of pretending to like something I don't really like in order to appear more cultured or cool, though I do try to stretch to get an angle to understand why other people like something. It is a rare occurrence but fun for me when I run into someone who happens to share my tastes in some leisure-time pursuit.  

Managing for Completion and Fulfillment-->All People Being Joined Together in Discovery and Wonder

The overall summary of all the objectives above is in the center of the star: "all people being joined together in discovery and wonder." After two decades or so since I took the Landmark Education courses, I still respond emotionally to that phrase. But the path to "all people being joined together in discovery and wonder" runs through "managing for completion and fulfillment." There are tasks that must be done, one by one, in order to get where I want us all to get to. 

Professionally, teaching the classes I am scheduled to teach, keeping promises (explicit and implicit) to caouthors, and the deadlines imposed by conferences and journals often provide plenty of structure to propel things forward. Other times, self-discipline must be applied to get key things done. Overall, I feel if I complete all of the research projects I have already begun, plus their obvious spinoffs, I will have had a wonderful career. 

On my blog, the rules and structures I have made up for myself have helped greatly in creating a set of blog posts I am very proud of. Trying to balance my other time demands with a determination that my blog continues to become richer and richer in its content, I have settled on the target of two substantial posts during the five weekdays (usually on Tuesday and Thursday) and a post on religion or philosophy on Sunday. It has turned out to be very easy to have a good link for the other days, including frequent links to Twitter debates that I have organized on Storify. (I would like to do many more Quartz columns than I have been doing lately. In addition to my own time constraints, current events seem to be running the editors I work with ragged on other fronts.) 

In my personal life, trying to be a good husband, father, friend and family member provides most of the structure I need to do good things on a regular basis. 

The back and forth between grand objectives and the determination to complete the day-to-day tasks needed to achieve those goals often seems counterintuitive and strange. But grand objectives without accomplishment of the crucial daily tasks along the way won't get anyone anywhere. And hard work without grand objectives is likely to get one a long way in the wrong direction. So that counterintuitive and strange back and forth between grand objectives and the determination to complete daily tasks is the only way to have much hope of saving the world—or even of making one's own corner of it a little better.   

Related Posts:

• Breaking the Chains
• Leaving a Legacy

Eric Turkheimer, Kathryn Paige Harden, and Richard E. Nisbett: Charles Murray Is Once Again Peddling Junk Science about Race and IQ →

I had some excellent comments on this article on my Facebook page. Here is the link. 

Travis Bradberry: Ten Guaranteed Ways To Appear Smarter Than You Are

Link to the article above

I like Travis Bradberry's 10 ways to appear smarter than you are better after I arrange them into two lists: laudable and gimmicky. Here is my arrangement:

Laudable, in order from least to most laudable:

1. Skip that drink.
2. Speak expressively.
3. Believe in yourself.
4. Make graphs.
5. Write simply.

Gimmicky, in order from least to most gimmicky:

1. Look 'em in the eye.
2. Keep pace with the crowd. ("If you want to look smarter, you need to stop dawdling, but you also need to stop scurrying around like some crazed robot.")
3. Dress for success.
4. Use a middle initial.
5. Wear nerd glasses.

On the third laudable way to look smarter, "believe in yourself," I say this in "Calculus is Hard. Women Are More Likely to Think That Means They’re Not Smart Enough for Science, Technology, Engineering and Math":

In addition to discouragement, low confidence in oneself also causes other people to underestimate one’s skills. It is quite difficulty to know how skilled someone is, but typically quite easy to tell how skilled they think themselves to be. So people use a job candidate’s opinion of herself or himself as a shortcut for judging her or his skills. 

For those who need to come across as more confident I highly recommend the weekend personal growth workshops conducted by Landmark Education Corporation, beginning with the Landmark Forum. In my view, almost everyone entering the dissertation writing and then job-hunting phases of getting a PhD in economics should do the Landmark Forum because of how much it will help the psychology of being able to focus on dissertation research and then the psychology of self-presentation for getting a job. I am sure that the same advice would apply to students in many other fields, at many stages of education. 

My biggest disagreement with Travis is not my discomfort with gimmicky ways to appear smarter. It is with his conclusion

Intelligence (IQ) is fixed at an early age. You might not be able to change your IQ, but you can definitely alter the way people perceive you. 

Au contraire: your intelligence is not fixed at all. It is possible to become much smarter by serious, well-focused effort. If you don't believe that, read these three columns on education:

1. There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t
2. How to Turn Every Child into a “Math Person”
3. The Coming Transformation of Education: Degrees Won’t Matter Anymore, Skills Will

What is said there about math also applies to many other mental skills. 

In Praise of Partial Equilibrium

image source

I have had it verified by those in a position to know that among many economists in the city of Minneapolis, there is a view that can be summarized as

General equilibrium good, partial equilibrium bad.

I would like to contest the second half of this view, and qualify the first half. Here, when I speak of general equilibrium, I am thinking of a typical dynamic, stochastic general equilibrium model. When I speak of partial equilibrium, I am including models of a single agent's decision problem, such as the model of household decision-making that leads to the empirical consumption Euler equation. In both cases, I am thinking of models being taken to the data as opposed to models that are pure theory.  

Why Partial Equilibrium Has an Advantage over General Equilibrium Models for Empirical Analysis

The basic problem with a general equilibrium model is that if any part of the model is misspecified, then inference (formal or informal) about the relationship between any other part of the model and the data is likely to be messed up. If that is not true, then the general equilibrium model is equivalent, or nearly equivalent to a partial equilibrium model, putting that partial equilibrium model and the general equilibrium model on an equal footing. (If a general equilibrium model is equivalent to a partial equilibrium model, then the general equilibrium aspect of the general equilibrium model is just window dressing.)

By contrast, a partial equilibrium model—say one that makes predictions conditional on observed prices—can be robust to ignorance about big chunks of the economy. For example, given key assumptions about the household (rational expectations, maximization of a utility function of a given functional form, absence of preference shocks, no liquidity constraints, etc.) the consumption Euler equation should hold regardless of how the production side of the economy is organized.

That statement about the robustness of the consumption Euler equation to ignorance about big chunks of the economy holds true for a variety of different functional form assumptions. For example, if labor hours (or equivalently, leisure hours) are nonseparable from consumption, there is still a well-specified consumption Euler equation in which one only needs to know labor hours to condition on them. Here, for the purposes of understanding the determination of consumption, one need not know the structure of the labor market for the equation to hold, only the actual magnitudes of labor hours ground out by the labor market. (Susanto Basu and I talk about this in our still-in-the-works paper "Long-Run Labor Supply and the Elasticity of Intertemporal Substitution for Consumption.") 

As another example, I have begun supervising a potential dissertation chapter looking at a model that combines many sides of the economy, but derives results that are robust to ignorance about the stochastic processes of the shocks to the economy. 

One way to think about partial equilibrium is that a partial equilibrium model represents a class of general equilibrium models. Showing that something is true for an entire class of general equilibrium models can be quite useful. Therefore, partial equilibrium can be quite useful. 

Where General Equilibrium Models Come In

Because of their robustness to ignorance in other parts of the economy, partial equilibrium models have a real advantage over general equilibrium models for breaking the task of figuring out how the world works into manageable pieces. This is empirical analysis, in the literal sense of analysis as breaking things down. 

Once one understands (to some reasonable extent) how the world works, general equilibrium models are the way to understand what the effects of different policies would be. The motto that "Everything affects everything else" is a useful reminder that studying the effects of policies often requires a general equilibrium approach. But that comes after one understands what the right model is. Partial equilibrium is often a better way to figure out, piece by piece, what the right model and the right parameter values are. 

Price Theory

Even in policy analysis, sometimes a more partial equilibrium approach can be helpful. In policy analysis, a partial equilibrium approach can be called "price theory," in line with Glen Weyl's definition in his Marginal Revolution guest post "What Is 'Price Theory'?":

... my own definition of price theory as analysis that reduces rich (e.g. high-dimensional heterogeneity, many individuals) and often incompletely specified models into ‘prices’ sufficient to characterize approximate solutions to simple (e.g. one-dimensional policy) allocative problems.

Glen gives some examples:

To illustrate my definition I highlight four distinctive characteristics of price theory that follow from this basic philosophy. First, diagrams in price theory are usually used to illustrate simple solutions to rich models, such as the supply and demand diagram, rather than primitives such as indifference curves or statistical relationships. Second, problem sets in price theory tend to ask students to address some allocative or policy question in a loosely-defined model (does the minimum wage always raise employment under monopsony?), rather than solving out completely a simple model or investigating data. Third, measurement in price theory focuses on simple statistics sufficient to answer allocative questions of interest rather than estimating a complete structural model or building inductively from data. Raj Chetty has described these metrics, often prices or elasticities of some sort, as “sufficient statistics”. Finally, price theory tends to have close connections to thermodynamics and sociology, fields that seek simple summaries of complex systems, rather than more deductive (mathematics), individual-focused (psychology) or inductive (clinical epidemiology and history) fields. 

I view most of the economics I do on this blog as price theory in Glen Weyl's sense: "analysis that reduces rich and often incompletely specified models into 'prices' sufficient to characterize approximate solutions to simple allocative problems." My analysis of negative interest rate policies—and in particular what I wrote in "Even Central Bankers Need Lessons on the Transmission Mechanism for Negative Interest Rates" and "Negative Rates and the Fiscal Theory of the Price Level"—is a good example. 

Conclusion

The moral is don't put unnecessary constraints on the tools you use. Use the tool that best fits the purpose. Sometimes that will be general equilibrium; sometimes it will be partial equilibrium. 

Related posts:

• Defining Economics

• Economics Needs to Tackle All of the Big Questions in the Social Sciences

• Breaking the Chains

John Locke: When the Police and Courts Can't or Won't Take Care of Things, People Have the Right to Take the Law Into Their Own Hands

image source

I have watched enough cop and detective shows to know the standard line against vigilantism: some version of "You can't take the law into your own hands." But John Locke begs to differ. In section 19 of his 2d Treatise on Government: “On Civil Government,” he says quite explicitly that in situations where the police and courts won't do their jobs or are unable to do their jobs in time, that it is appropriate to take the law into one's own hands:

And here we have the plain difference between the state of nature and the state of war, which however some men have confounded, are as far distant, as a state of peace, good will, mutual assistance and preservation, and a state of enmity, malice, violence, and mutual destruction, are one from another. Men living together according to reason, without a common superior on earth, without authority to judge between them, is properly the state of nature. But force, or a declared design of force, upon the person of another, where there is no common superior on earth to appeal to for relief, is the state of war: and it is the want of such an appeal gives a man the right of war even against an aggressor, though he be in society and a fellow subject. Thus a thief, whom I cannot harm, but by appeal to the law for having stolen all that I am worth, I may kill, when he sets on me to rob me but of my horse or coat; because the law, which was made for my preservation, where it cannot interpose to secure my life from present force, which, if lost, is capable of no reparation, permits me my own defence, and the right of war, a liberty to kill the aggressor, because the aggressor allows not time to appeal to our common judge, nor the decision of the law, for remedy in a case where the mischief may be irreparable. Want of a common judge with authority, puts all men in a state of nature: force without right, upon a man’s person, makes a state of war, both where there is, and is not, a common judge.

There are three reasons to let the state take care of justice rather than taking the law into one's own hands that do not involve any mystical respect for the state. The first is the principle that "People Must Not Be Judges in Their Own Cases." And by the same token, my family, friends, close allies or someone in my pay should not judge my case either. There is too much chance of bias. But other than one's family, friends and close allies, whom can I convince to take an interest in justice for me? One can hope the state will. 

Second, even if an impartial vigilante is available to take an interest in justice for me, there is a good chance that the vigilante's procedures for determining the facts and appropriate disposition of my case will be less accurate, and therefore less just than the state. 

Third, even when a wise, impartial vigilante with excellent investigative skills is available to take an interest in justice for me, the state may object, simply as a power play. If the state isn't too much worse than the vigilante at securing justice, it might make sense to allow a modest degradation of justice in order to avoid getting in practical trouble with a state jealous of its own prerogatives. 

All of these reasons to let the state take care of justice are a matter of degree. I consider the first the most compelling; people often do misjudge their own cases and the cases of those close to them, and even the cases of those in their own ethnic group, when the opposing side in the case is someone from another ethnic group. But once an impartial vigilante is in play, it is easy to get sympathy for that vigilante and the person who needs justice simply by portraying a situation in which the state is doing a bad job. 

Moreover, when they are otherwise in the right, vigilantes who take the law into their own hands often get away with only light punishments. To me, this reflects the respect prosecutors and juries have for the principles John Locke writes of, whether those prosecutors and juries realize it or not. 

Update: After reading this post, Dwight Allman makes a very interesting comment on Facebook about John Locke's shifting views of the state of nature. Here is a link.  

Nick Timiraos and Andrew Tangel: In the Long Term, an Economy Can’t Expand Faster than the Combined Growth Rates of Its Working Population and Their Output Per Hour

Link to Nick Timiraos's and Andrew Tangel's May 17 Wall Street Journal article "Can Trump Deliver 3% Growth? Stubborn Realities Stand in the Way" shown above

Nick Timiraos and Andrew Tangel's Wall Street Journal article on productivity and number of workers in the US explores many of the same themes as my talk "Restoring American Growth." One of the most basic truisms in the article is the one I made into the title of this post: 

In the long term, an economy can’t expand faster than the combined growth rates of its working population and their output per hour.

Let me talk about each of these in turn, as they do. 

The Drift of Policy is Against Growth in Number of Workers Because It Focuses on Prohibiting People from Working for the US Economy

Nick and Andrew write:

The president is pushing some policies that work against economic growth. Relatively low birthrates and an aging population mean immigration is the source of nearly all of the work force’s net increase, so its growth rate would be even lower if legal immigration were curbed. 

For the most part, economic growth is judged in terms of income per person. But there is one exception: potential military power depends in important measure on total GDP, not just GDP per person. In "Benjamin Franklin's Strategy to Make the US a Superpower Worked Once, Why Not Try It Again?" and "Why Thinking about China is the Key to a Free World," I wrote of how allowing more immigration could add greatly to the military and therefore geopolitical strength of the US. Thus, allowing more immigration is the obvious way to "Make America Great Again" in the geopolitical sense. Conversely, treating being American as a closely guarded privilege that only those born to that privilege are allowed is a path to greatly reduced American power and influence. Of course, allowing more immigration is also extremely valuable to the immigrants themselves, as I talk about in "Us and Them" and "'The Hunger Games' Is Hardly Our Future--It's Already Here." But many people have a "Keep the Riffraff Out!" attitude that trumps concern with the America's power and the well-being of people who want to join us in our fair land. 

Aggregate Demand Is No Longer Scarce

Other than immigration, is there room for expanding the number of workers in the US economy? NIck and Andrew argue this is difficult:

With the unemployment rate now at 4.4% and operating at a level economists consider to be “full employment,” meaning the economy produces as many jobs as it can without spurring inflation, the labor market provides little room for the kind of economic surge that marked the 1980s.

But there is a contrary argument:

White House Budget Director Mick Mulvaney ... pointed to millions of prime-age workers who aren’t in the labor force. “If you created economic opportunity and jobs that they want, they would come back,” Mr. Mulvaney said. “So I’m not worried about the tightness of the labor supply.”

This argument should not be dismissed too quickly. It is quite similar to arguments made by Narayana Kocherlakota in our storified Twitter debate "Narayana Kocherlakota and Miles Kimball Debate the Size of the US Output Gap in January, 2016."

When Monetary Policy Keeps the Economy at the Natural Level, the Supply Side Determines What Happens

Some people think that monetary policy alone can create growth miracles. It can't; not for long. Good monetary policy can readily cut short potential disasters such as the Great Depression or Great Recession, which is in itself quite valuable, but when monetary policy has done its job, then it takes other policies to raise the growth rate of the economy in a sustainable way. 

And indeed, if monetary policy is done well, the remaining story will about the supply side. In my view, one of the best ways to get people to focus on the supply side—or what is sometimes called "structural reform"—is to do monetary policy so well that the economy stays at the natural level, or very close. What would this look like? Something like this description from Nick and Andrew, only more so:

If growth advances and productivity does too, policy makers may be able to keep interest rates lower for longer because productivity growth holds down inflation. Companies can boost profit margins and hold down costs, and thus inflation, when they can produce more goods and services with fewer workers.

If, on the other hand, the administration’s policies boost demand without drawing in new workers or raising their productivity, the growth that results could be harder to sustain because it would produce inflation. The Fed would feel additional pressure to raise interest rates to prevent the economy from overheating.

The Overall Trends in Productivity Growth Are Disappointing

Nick and Andrew include a graph showing how the growth rate of output per work hour has declined in recent years: 

I made a similar graph in the slides for my talk "Restoring American Growth." But where Nick and Andrew's graph gives credit for growth in the next 5 years and the last 5 years, my graph gives credit only for growth in the next 5 years after a given date, and so shows the decline in productivity growth after 2003 much more clearly:

A capsule history of productivity growth since World War II goes like this: 

1. Fast from the end of World War II in 1945 to 1973
2. Slow from 1973 to 1995
3. Fast from 1995 to 2003
4. Slow from 2003 to the present and maybe beyond (2017+) 

But to provide some perspective, however wrenching they have been politically, the "slow" growth rates from 1973 to 1995 and from 2003 to the present still represent the productivity growth rate that existed during the Industrial Revolution. The fast periods from the end of World War II in 1945 to 1973 and 1995-2003 made many people expect those productivity growth miracles to continue. 

Productivity Growth Is Miserable in Construction

One of the big puzzles for productivity—one that deserves to have many more economists studying it—is why productivity growth in construction has been so miserable. Productivity growth has been quite high in manufacturing. Construction is also a seemingly straightforward physical activity involving the assembly of tangible materials. Why is its productivity growth trend so different from that of manufacturing? 

Look at the difference in the productivity trends between construction ("Structures") and manufacturing (the other two):

Nick and Andrew also note the low productivity growth in construction. Here is their discussion:

Camden uses efficiencies such as prefabricated concrete building panels and roof trusses, “but there hasn’t been a huge breakthrough yet where we can lower costs dramatically,” said Mr. Campo. “You have a nail gun instead of a hammer, OK? But you still have to line it up and pull the trigger.”

Productivity in construction has contracted at a 1% annual rate since 1995, according to a study by McKinsey Global Institute, the research arm of McKinsey & Co., due in part to reliance on unskilled workers and in part to government red tape.

Joel Shine, chief executive of builder Woodside Homes Inc., visited Kyoto, Japan, to see how firms there use automation in home construction. He thinks it would take at least a decade for the innovations to become mainstream in the U.S., in part because they would require building-code changes.

State and local rules often play as big a role for his business as the federal government. Higher permitting fees, for instance, have raised construction costs in California towns. “There are a lot of places if you gave me a raw lot for free—for free!—I could not even come close to building an entry-level house,” Mr. Shine said.

I think this passage is part of the story. But I think there is more to the story of why construction productivity has gotten worse instead of better. I hope someone does more digging to find out. 

Prospects for Productivity Growth Elsewhere are Unclear

There is hope that productivity growth—that is, growth in output per work hour—will pick up. But the prospects are unclear. Nick and Andrew counterpose these two views:

Some productivity optimists say gains from new technology will build in the years ahead. They see businesses incorporating a backlog of innovations in artificial intelligence, from self-driving vehicles to the processing of routine clerical work.

A paper from four growth specialists published by the Brookings Institution in March takes a dimmer view. It maintains that almost the entire shortfall in output during the recent expansion reflects long-term forces unrelated to the financial crisis and recession, including a drop in a measure of economic dynamism called “total factor productivity.” That measure reflects how efficiently labor and capital are used.

Of course, the future of technology is unavoidably difficult to know; to know enough to predict it well, we would have to know the future technology itself. I talk about that difficulty in "The Unavoidability of Faith." 

What Can Be Done?

The question of what can be done is a difficult one. I know I don't have all of the answers, but I tried in my talk "Restoring American Growth" to make progress on this issue. I would be honored to have anyone reading this post listen to the video of that talk. 

David Roberts's Extreme Psychological Theory of Donald Trump →

A clear refutation of this theory would be very interesting. 

Economics Is Unemotional—And That's Why It Could Help Bridge America's Partisan Divide

Here is a link to my 68th Quartz column, "Economics is unemotional—and that's why it could help bridge America's partisan divide."    Note: You can see all of my previous Quartz columns listed in order of popularity here.

In order to keep things tight, my editor for this column, Sarah Todd, suggested cutting two passages that might interest you: my original introduction, which defines the concept of "politicism," and a passage about the politics of financial stability. I reproduce them below from my early draft of this column:

Original Intro Defining 'Politicism':

Among friends considering where to live, I hear a concern these days I don’t remember hearing when I was younger: “I could never live there because people are too conservative there politically.” A series of social psychology studies by Jarret Crawford, Mark Brandt, Yoel Inbar, John Chambers and Matt Motyl back up the idea that this kind of distaste for those with different political beliefs is common. They have two main findings, based on detailed surveys of 4912 people. First, liberals look down on conservatives just as much as conservatives look down on liberals. Second people look down on others more for discordant beliefs on social issues than they do for discordant beliefs on economic issues.

It is handy having a word for “looking down on a group of people because of their politics.” The word “politicism” seems available. The online Oxford Dictionary defines it as “A concern with or emphasis on the political,” which is close enough for me. The online Urban Dictionary defines it as “voting in a politic election simply based on religion, sex, or ethnicity.” In my definition I am turning that around: politics itself has become a quasi-ethnicity that many people have intense prejudices about. Using my definition of “politicism,” one can say liberals as well as conservatives show a great deal of politicism, and politicism is stronger for social issues than for economic issues.

Original Passage on the Politics of Financial Stability

For a political strategy in which rhetoric focuses on social issues and easy-to-understand economic issues, there is a role for hard-to-understand aspects of economic policy. Hard-to-understand aspects of economic policy are perfect for pleasing sophisticated special interests who understand—while others don’t—that some opaque bit of economic policy will enrich them at the expense of everyone else. A prime example is the hope of banks and other financial firms to get themselves in line for more bailouts in the future by gutting requirements that stockholders put up enough money for banks that stockholders take the hit in a crisis rather than taxpayers. Regular voters know they don’t like bailouts, but their eyes glaze over at discussions of the capital requirements needed to avoid bailouts. Even Elizabeth Warren, who is better at making this kind of thing interesting to the average voter than anyone else, often has to quickly shift the subject to the easier-to-understand issue of people being ripped off by deceptive consumer finance in order to keep her listeners awake.

Edward Lawrence Kimball on Mormonism, Part 1

Link to the video above on YouTube

My Dad, Edward Lawrence Kimball, died on November 21, 2016, a little less than six months ago. I have posted my tribute to my Dad and the tributes of my brothers and sisters, as well as by my Dad's colleague Jack Welch:

• My Dad
• Christian Edward Kimball on Edward Lawrence Kimball
• Joseph Ellsworth Kimball on Edward Lawrence Kimball
• Paula Kimball Gardner, Mary Kimball Dollahite and Sarah Camilla Kimball Whisenant on Edward Lawrence Kimball
• Jordan Andrew Kimball on Edward Lawrence Kimball
• One for All: John Woodland "Jack" Welch on Edward Lawrence Kimball

Today, and four weeks from today, I am posting videos of John Dehlin's two interviews of my Dad about my Dad's views on Mormonism. (If you can't wait, here is a link to Part 2.) These interviews are excellent at showing how my Dad thought about religion—something he cared deeply about. If you want to see the best face of Mormonism I know of, take a look at these videos.