Thoughts on Economics Seminars

My Twitter feed has recently been filled with people arguing about whether economics seminars are conducive to improving research in the field. For those unfamiliar with academic economics, our seminars tend to encourage active participation from the audience. While it varies across individuals, many economics professors have no problem interrupting a presentation to ask a question (or voice their displeasure) about something in your presentation. Fabio Ghironi, a professor at the University of Washington, recently compared economics seminars to a fencing match. Professors try to stab with you by asking you challenging questions about your models and methods and it is up to you to defend yourself.

I like this analogy and I think it perfectly describes my experience in macroeconomics at UCLA so far. Especially in the student seminars it is a rare occurrence to see somebody make it past their first slide without somebody chiming in. In general, I like this style of seminar. Rather than waiting until the end to answer a bunch of questions at once, it allows the presenter to deal with confusion and make clarifications as they go. Being forced to defend your work against criticism also helps make the parts that need improvement immediately clear.

I do see some problems with the current format of economics seminars, however. One issue arises when the questions seem aimed at proving the questioners intelligence rather than helping understand or improve the research. Especially for early work in progress where the paper is unpolished, too often have I seen audience members shaking their heads or making faces at ideas that are undeveloped but might still have potential. I think I am probably guilty of this as well. Another problem is when questions try to anticipate the rest of the presentation. The introduction slide should not be the place to figure out the identification strategy or the specifics of the model.

The biggest problem though is that being a good researcher and being able to sell your work in a presentation are not necessarily correlated. Many people are great at coming up with ideas and writing down interesting models, but not so good at presenting these ideas in a way that convinces other people that they are interesting. Of course, there is some truth to the idea that if you cannot present your idea well it may actually just not be that interesting, but the opposite is also true. Do we want economics to be dominated by used car salesmen that can make any idea sound great in an hour long seminar? Confidence and the ability to think on your feet are certainly valuable skills for any job, but shouldn’t they be less important for researchers whose goal is to seek out the truth, not just sell their own idea?

Too often it seems that communication ability and value as a researcher are conflated. But if we really want economics to stand as a science beside physics and chemistry (I’m not sure we do, but some people seem to want to), then we should avoid making this mistake. Research should be judged based on how well it improves our understanding of the real world. If a paper makes accurate predictions or useful methodological advances it shouldn’t matter if it’s presented or even written well or not.

The obvious objection to this point is that if research cannot be communicated well, how do we know if it’s good or not? We can’t carefully read every paper and spend time figuring out what it really means. A presentation is supposed to provide a quick overview of the main results to prove that the full paper is actually worth reading. How can we keep this benefit without throwing out good research done by poor presenters?

My solution is to separate research and the communication of research. Why does the person that wrote the model or collected the data have to be the one that presents it? It seems to me that current economics academics actually have two jobs. First, they have to write a paper that they know is interesting, often with fancy math that is difficult to understand for anyone not closely related to their field. Their second job is then to convince others that their idea is worth looking at, explaining complex ideas in a short amount of time to those who aren’t heavily invested in the literature. Why do both of these jobs have to be done by the same person? Manufacturers hire marketing firms to sell their product. Why can’t economists do the same thing?

One way around this problem comes through co-authoring papers. By forming a pair where at least one author is a relatively good communicator, researchers who lack communication skills can leverage their other skills and still be successful. However, this strategy can’t work for students looking to be hired since they need to prove they have value as a researcher on their own. With a co-authored paper it is impossible to tell how much each of the authors actually contributed. But what if they could hire somebody just to present? The economist writes the model, deals with the data, and produces all of the results. The presenter then turns that into something others can understand and evaluate.

I can see why some people wouldn’t like this setup. There is something pure about research being an individual project from start to finish. Coming up with a great idea, answering it in a clever way, and then explaining it to colleagues in the best possible way. But the goal of the profession should not be to find the most well-rounded researcher, but to advance our understanding of economics. If good ideas are being pushed aside simply because they aren’t communicated well enough, we should do everything we can to correct that.

Blackboard Economics and the Coase Theorem

Introductory economics is often criticized for providing an overly idealized version of the world. The price system functions perfectly, markets are competitive, and information is freely available. A well known result from microeconomics, the First Welfare Theorem, says that under certain assumptions, a competitive equilibrium is Pareto efficient. Government intervention in the market cannot make anybody better off without making somebody else worse off. Critics of neoclassical economics point out that the conditions under which this result holds are incredibly unrealistic. As soon as those assumptions are relaxed, the door opens for government to improve upon the market.

The classic example of these kinds of “market failure” are externalities like pollution where the total cost to society is more than the private cost faced by the producer. Our modern treatment of such problems in introductory classes is essentially unchanged from Pigou’s analysis of the problem almost 100 years ago in The Economics of Welfare. He outlined a simple solution to the problem of externalities. If producers impose costs (like pollution or noise) on others through their production activities, we can simply tax them to force them to internalize the social cost of their actions. Unlike standard taxes that introduce inefficiencies to a market economy, these “Pigovian taxes” actually improve efficiency.

Much of economics tends to follow a similar pattern. We begin with the perfect world, the benchmark economy of full information and a perfectly competitive economy. We then show that relaxing some of these assumptions, putting in asymmetric information, or monopoly power, or externalities, can mess up this perfect benchmark. Finally, we outline how government can solve these problems. The left loves to complain about how we too often stop at step 1 (especially in intro courses) and forget about all the problems of markets that government really needs to fix.

I also take issue with this kind of economics, but for a different reason. To understand my view, we need to take a look at an incredibly famous, but sometimes misunderstood paper, called “The Problem of Social Cost” by Ronald Coase.

Coase begins his paper by responding to Pigou. He shows, in several numerical examples, that Pigovian taxes or other government solutions are entirely unnecessary if the price system functions costlessly. This argument has been summarized in what is now known as “The Coase Theorem.” Private actors will always find the most efficient solution as long as transaction costs are not too high. Although perhaps unintuitive at first, Coase’s intuition is actually quite simple. If bargaining is costless, there is no reason why private agents wouldn’t be able to work out a solution that is beneficial for everyone. I recommend reading the article for many numerical examples of how this kind of bargaining could work to produce an outcome just as good as that produced by the Pigovian solution.

Unfortunately, most discussions of Coase tend to stop there. Supporters of free markets use Coase to argue against any form of government intervention. Detractors respond that of course transaction costs are not zero and therefore Pigovian solutions are still needed. Both sides miss Coase’s broader point. As Deirdre McCloskey puts it, “Something like a dozen people in the world understand that the “Coase” theorem is not the Coase theorem…One of this select few is Ronald Coase himself so I expect we blessed few are right.”

Here’s what I think is a better “Coase theorem” (from Coase’s paper): “All solutions have costs and there is no reason to suppose that government regulation is called for simply because the problem is not well handled by the market or the firm. Satisfactory views on policy can only come from a patient study of how, in practice, the market, firms and governments handle the problem of harmful effects”

Coase’s use of a world without transaction costs was not an attempt to make a statement about the real world, but rather to demonstrate the emptiness of doing analysis in a world without transaction costs. His article serves a deeper purpose than simply a criticism of Pigou’s treatment of externalities. It more importantly acts as a response to what Coase called “blackboard economics.” He thought the exercise of comparing “a state of laissez-faire and some kind of ideal world” to be entirely pointless. Economics without some consideration of the set of institutions, of the laws and the legal system that govern agents actions, is just an analysis of some imaginary world that will never exist. He wanted to bring economics back to reality.

For Coase, “a better approach would seem to be to start our analysis with a situation approximating that which actually exists, to examine the effects
of a proposed policy change and to attempt to decide whether the new situation would be, in total, better or worse than the original one. In this way, conclusions for policy would have some relevance to the actual situation.”

Shifting lines on a blackboard makes for nice undergraduate exercises. It is less useful for real policy analysis. Coase’s approach is less elegant. Blackboard economics gives nice simple answers to a wide range of policy questions. Unfortunately those answers don’t always tell us much about the much more complicated questions of the real world.

Coase’s argument against blackboard economics is essentially the same as Hayek’s criticisms of economic analysis. If we assume away all the hard stuff like who sets prices and who possesses knowledge of relevant economic information then of course we can come up with solutions to all sorts of economic problems. But those answers only hold in a world that looks nothing like our own and more importantly in a world where those policy choices are completely unnecessary in the first place. To get any kind of policy answers that our actually relevant for the world we actually live in, we occasionally need to ask these much harder questions about institutions and the economic environment in which economic actions take place.

Star Wars: The Last Jedi Review

Spoiler Warning: This post contains major spoilers for The Last Jedi. Don’t read it if you haven’t seen it yet (but do go see it – it’s good)


I’ve never been a die-hard Star Wars fan, but I have always enjoyed the movies. Even the poorly written and acted prequels offer a glimpse into a cool world with interesting characters and lore. So when I started to see claims that the new movie was the worst in the series and almost ruined the franchise I couldn’t imagine how that was possible. A series that survived “I’ll try spinning, that’s a good trick” and “I don’t like sand” would really need to do something awful to get these reactions. Was Supreme Leader Snoke secretly Jar Jar Binks? Did Luke break out in song halfway through the movie?

After watching the movie, I can’t say I fully understand any of the extreme criticism. The Last Jedi ranks among the best of the Star Wars movies. It tells a fast paced story centered around the strength of its two main leads, Kylo Ren and Rey. It subverts expectations when it makes sense while still offering fans plenty of the moments implicitly promised by the setup in Episode 7. Most importantly, it goes beyond the simple light vs dark conflict that drives much of the Star Wars story by adding some much needed nuance to characters on both sides of the conflict.

That’s not to say everything about the movie was perfect. Leia floating back to the ship was unnecessary and goofy. There was no reason why Poe had to be kept in the dark about the plan to have the escape pods flee to the nearby planet. Some plot points seemed a bit too convenient (How did the codebreaker make a deal with the First Order so quickly? Why does it take so long to shoot down the rebel escape pods? Why did they wait to close the blast door just long enough for Finn and Rose to get through? Why can a ship entering hyperspace destroy another ship and why has nobody ever done that before?). But these are minor complaints that have little effect on the broader story and themes of the movie. Deeper criticism of the plot and characters misses the mark in my opinion.

Luke’s Character: One major complaint about The Last Jedi was its treatment of the last Jedi himself (including a statement from Hamill himself saying he disagreed with the direction). Luke’s motivations seemed perfectly clear to me. He tried to train the next generation of Jedi, but instead he saw history repeat itself. The dark side lured away one of the strongest students and destroyed everything he had built. Is it that hard to believe he wouldn’t immediately want to try again? Perhaps a more fitting criticism comes from Luke’s fleeting desire to kill Kylo Ren in his sleep. Would the Luke we know from the original trilogy ever do something like that? Some say no. But rather than see this as a rejection of Luke’s character, I think of it more as an evolution. Nobody is entirely free from darkness. Doing bad in the interest of the greater good is a temptation everybody faces and I didn’t find it unreasonable that Luke would briefly consider going down that path. A perfectly benevolent Luke is also a boring one.

Kylo Ren Killing Snoke: Based on the setup in the Force Awakens, some people assumed that Supreme Leader Snoke would have a major part to play in the trilogy. It is understandable, then, that his quick end would be disappointing. Wouldn’t it have been better to see more of Snoke’s origin, how he lured Kylo to the dark side, and how he became the most powerful man in the universe? I’m not so sure. We already saw that story with Palpatine and receiving more of his backstory in the prequels arguably diminished his character from the original trilogy. Why retread the same ground? Killing off Snoke so early in the trilogy allows the focus to be on the more interesting Kylo Ren. I think that’s the right choice. Not every question raised by episode 7 needs to be answered.

Kylo Ren’s Motivation: But why did Kylo Ren even want to kill Snoke? Does it make sense that he would turn so quickly on his master? I think it does. It’s clear that Kylo has always been ambitious and confident in his abilities. He sees himself as better than others and therefore well-suited to lead the world to what he views as a better, more orderly, place. Just like Anakin, the light side didn’t offer enough power on its own and so he looked for alternatives. Initially, Snoke offered him that alternative. But it’s also clear that he has a connection with Rey. He sees in Rey many of the same features  he sees in himself. Power, ambition, drive. He thinks he needs to only show Rey the error of her ways, that the light side is weak and that by using the dark they can lead together. And so when faced with a choice between Rey and Snoke, his choice is simple. Snoke will only constrain him. Rey could work alongside him. When she rejects him, he does not turn to light, but rather occupies some gray area in the middle, taking the steps he feels are necessary to create (what he views as) a better world even when it requires destroying what came before. I’m definitely interested in seeing how his character progresses in the next movie.

Rey’s Parents: Did anyone really want any of the fan theories about Rey’s parents to be true? Did we need some convoluted explanation of Luke or Han and Leia somehow having a daughter that they abandoned and forgot? Would it really add anything to the story if Obi-Wan secretly had a granddaughter? Would it be better if she was created by midichlorians? There just aren’t that many important characters left who could feasibly be Rey’s parents. Having Rey come from nobody was the best choice. The mistake was building it up as a question to be answered in the first place, but compounding that error and shoehorning in some forced connection to existing characters would have been much worse.

Finn and Rose’s Story: It’s true that Finn and Rose’s excursion to the casino planet ends up being essentially meaningless for the rest of the story. But, as my 12th grade english teacher liked to tell us (every class), “if it doesn’t contribute to plot, it contributes to theme.” Maybe it’s hard for some people to believe that Star Wars actually has a theme beyond good vs evil, but Finn and Rose’s storyline demonstrates what the rebels are fighting for. Why should we see the rebels as something other than terrorists fighting against what could very well be a benevolent dictatorship? Finn and Rose show the oppression caused by the First Order and why a resistance is needed at all. It also develops Finn’s character from somebody ready to abandon the resistance at the beginning to one who is willing to sacrifice himself for it at the end and provides context for Rose’s line at the end that the good guys need to differentiate from the bad by focusing on saving what they love.

Other criticisms make even less sense to me. The porgs added humor and had very little effect on the plot. Compared to Jar-Jar becoming a senator they are completely inoffensive. Some jokes might not have hit the mark for everyone, but has Star Wars ever been a series that took itself completely seriously? Has anyone watched the Yoda scenes or the Ewok scenes from the original trilogy lately? Humor has always been a part of the series. And I won’t even get into the people claiming the movie is full of left-wing propaganda. Come on guys.

Overall I felt that the movie added some complexity to the standard Star Wars formula. The original trilogy was a relatively simple story of good vs evil. The Last Jedi makes you think a little bit about what those words mean. That it opened such a fierce controversy about Luke’s character or Kylo Ren’s motivations shows me that it succeeded in doing that. And, for me at least, taking some risks with Star Wars was a welcome change.

Here We Go Again Once More on DSGE Models

A day may come when the old guard of macroeconomics convinces this starry eyed graduate student to give up his long battle against the evils of DSGE models in macroeconomics. But it is not this day.

Shockingly, it seems like many top economists have not yet discovered my superior critique of macroeconomics (because obviously if they had they would be convinced to stop defending DSGE). Instead, we get statements like:

Macroeconomic policy questions involve trade-offs between competing forces in the economy. The problem is how to assess the strength of those forces for the particular policy question at hand. One strategy is to perform experiments on actual economies. Unfortunately, this strategy is not available to social scientists. The only place that we can do experiments is in dynamic stochastic general equilibrium (DSGE) models

That’s from the recent paper “On DSGE Models” written by three prominent DSGE modelers, Lawrence Christiano, Martin Eichenbaum, and Mathias Trabandt (who I’ll call CET). As you might suspect, I disagree. And I expect their defense will be about as effective at shifting the debate as my critique was (and since my readership can be safely rounded down to 0, that’s not a compliment). Unlike Olivier Blanchard’s recent thoughts on DSGE models, which conceded that many of the criticisms of DSGE models actually contained some truth, CET leave no room for alternatives. It’s DSGE or bust and “people who don’t like dynamic stochastic general equilibrium (DSGE) models are dilettantes.” So we’re off to a good start.

But let’s avoid the ad hominem as much as we can and get to the economics. Beyond the obviously false statement that DSGE models are the only models where we can do experiments, CET don’t offer much we haven’t heard before. Their story is by now pretty standard. They begin by admitting that yes, of course RBC models with their emphasis on technology shocks, complete markets, and policy ineffectiveness were woefully inadequate. But we’re better now! Macroeconomics has come a long way in the last 35 years! They then proceed to provide answers to the common criticisms of DSGE modeling.

Worried DSGE models don’t include a role for finance? Clearly you’ve never heard of Carlstrom and Fuerst (1997) or Bernanke et al. (1999) which include financial accelerator effects. Maybe you’re more concerned about shadow banking? Gertler and Kiyotaki (2015) have you covered. Zero lower bound? Please, Krugman had that one wrapped up all the way back in 1998. Want a role for government spending? Monetary policy? Here’s 20 models that give you the results you want.

Essentially, CET try to take everything that critics of DSGE models say is missing and show that actually many researchers do include these features. This strategy is common in any rebuttal to attacks on DSGE models. Every time somebody points out a flaw in one class of models (representative agent models, rational expectations models, models that use HP-filtered data, complete markets, etc.) they point to another group of models that purports to solve these problems. In doing so they miss the point of these critiques entirely.

The problem with DSGE models is not that they are unable to explain specific economic phenomenon. The problem is that they can explain almost any economic phenomenon you can possibly imagine and we have essentially no way to decide which models are better or worse than others except by comparing them to data that they were explicitly designed to match.  It’s true there were models written before the recession that contained features that looked a lot like those in the crisis. We just had no reason to look at those models over the hundreds of other ones that had entirely different implications.

Whatever idea you can dream up, you can almost be sure that somebody has written a DSGE model to capture it. Too much of what DSGE models end up being is mathematical justifications for ideas people have already worked out intuitively in their minds (often stripped of much of the nuance that made the idea interesting in the first place). All the DSGE model itself adds is a set of assumptions everybody knows are false that generate those intuitive results. CET do nothing to address this criticism.

Take CET’s defense of representative agent models. They say “It has been known for decades that restrictions like (1)[the standard Euler equation] can be rejected, even in representative agent models that allow for habit formation. So, why would anyone ever use the representative agent assumption? In practice analysts have used that assumption because they think that for many questions they get roughly the right answer.”

Interesting. If they already knew the right answer, what was the model for again? Everybody agrees the assumptions are completely bogus, but it gets the result we wanted so who cares? That’s really the argument they want to make here?

But this is the game we play. Despite CET’s claims to the contrary, I am almost certain that most macroeconomics papers begin with the result. Once they know what they want to prove, it becomes a matter of finagling a model that sounds somewhat like it could be related to how an actual economy works and produces the desired result (and when this task can’t be done, it becomes a “puzzle”). The recession clearly demonstrated the importance of finance on the economy? Simple. Let’s write a DSGE model where finance is important. If in the end the model actually shows that finance is unimportant rewrite it until you get the answer you want.

Almost every DSGE macroeconomics paper follows pretty much the same outline. First, they present some stylized facts from macroeconomic data. Next, they review the current literature and explain why it is unable to fit those facts. Then they introduce their new model with slightly different assumptions that can fit the facts and brag about how well the model (that they designed specifically to fit the facts) actually fits the facts.  Finally they do “experiments” using their model to show how different policies could have changed economic outcomes.

In my view, macroeconomics should be exactly the opposite. Don’t bother trying to exactly match macroeconomic aggregates for the United States economy with a model that looks nothing like the United States economy. Have a little more humility. Instead, start by getting the assumptions right. Since we will never be able to capture all of the intricacies of a true economy, the model economy should look very different from a real economy. However, if the assumptions that generate that economy are realistic, it might still provide answers that are relevant for the real world. A model that gets the facts right but the assumptions wrong probably does not.

I spent 15 posts arguing that the DSGE paradigm gets the assumptions spectacularly wrong. CET provide many examples of people using these flawed assumptions to try to give us answers to many interesting questions. They do not, however, provide any reason for us to believe those answers.

But, then again, I am but a dilettante, so you probably shouldn’t believe me either.

Talking Past Each Other on Math in Economics

Trump’s recently proposed plan to cut corporate taxes has opened a debate about whether corporate tax cuts are good for workers. Opponents of the plan argue that it will only help corporations increase their profit while supporters believe a large portion of the benefits will accrue to workers through increased wages. I don’t want to comment on that debate. Instead, I want to discuss a point made by John Cochrane in his attempt to prove that a lower corporate tax can increase wages (responding to a post by Greg Mankiw). You can find his post here. Please read it before continuing.

Cochrane shows in a simple model that a decrease in taxes will cause an increase in wages of \frac{1}{1-\tau} where \tau is the current tax rate. In other words, if the tax rate is 1/3, a decrease in taxes of one dollar increases wages by $1.50. Cochrane then says something that I find incredibly misleading:

“This is also a lovely little example for people who decry math in economics. At a verbal level, who knows? It seems plausible that a $1 tax cut could never raise wages by more than $1. Your head swims. A few lines of algebra later, and the argument is clear. You could never do this verbally.”

There are two issues with Cochrane’s statement. The first is that it is pretty easy to prove that a $1 tax cut could raise wages by more than $1. Assume the only two inputs are labor and capital and profits are zero. Assume the rental price of capital is fixed. Any change in taxes must therefore cause a change in wages. If production doesn’t change, this change has to be the exact amount of the tax (otherwise profit would change). Now assume that the tax caused some deadweight loss so lowering it will also increase production. Again wages increase so they must have increased more than one for one with the increase in tax.

Now you might say those assumptions are a bit ridiculous and I would agree. But Cochrane actually used the exact same assumptions (and more). He just hid them behind some math. And that brings me to the second problem with Cochrane’s statement. A few lines of algebra later, the argument is actually not clear at all unless you already know what’s going on (even Greg Mankiw admits he doesn’t have intuition for the result in the post that Cochrane is expanding on).

Let’s take Cochrane’s “proof” piece by piece and outline the assumptions he needed to get his result.

He writes: the production technology is

    \[Y = F(K,L) = f(k)L ; k=K/L\]

To just write this line, we need three strong assumptions

Assumption 1: There are only two productive inputs, labor and capital

Assumption 2: We can represent this economy by an aggregate production function (which is almost certainly impossible)

Assumption 3: The aggregate production function exhibits constant returns to scale (multiplying each of its inputs by some factor also multiplies its output by that factor)

The last assumption is necessary to write the function in its f(k)L form and also ensures that firms have zero profit.

Next we have that firms maximize

    \[\max (1-\tau\)[F(K,L) - wL] - rK\]

Again, we are implicitly making more assumptions here

Assumption 4: Firms maximize profits every period (the setup of the problem guarantees that this behavior also maximizes lifetime profits, but another model might not have that property)

Assumption 5: All workers get paid the same wage, which is taken as given by individual firms (i.e. labor markets are perfectly competitive)

Assumption 6: The rental rate of capital is exogenously set. Mankiw set up the problem as a small open economy so that the interest rate (the price of capital) is constant. Note that the US is obviously not a small open economy.

Continuing, the firm’s first order conditions are

    \[(1-\tau)f'(k) = r\]

    \[f(k) - f'(k)k = w\]

Again, more assumptions

Assumption 7: Workers get paid their marginal product (technically this one follows from 4 and 5 above so maybe I shouldn’t count it).

Assumption 8: Firms know their production function as well as the marginal products of labor and capital.

Assumption 9:  Wages are fully flexible and can be changed at any time.

Assumption 10: Capital can move costlessly between countries.

I’ll stop there but I’m sure there are plenty more (including the assumptions of no involuntary unemployment, no money of any kind, and that the economy is always in equilibrium – assumptions common to many macro models). My point in doing this exercise is to demonstrate that in order to even begin to write an economic model using math you need to make strong assumptions. Without them the problem quickly becomes either impossible to solve or impossible to interpret. By hiding these assumptions (either intentionally or not) behind fancy equations, they often go unnoticed.

Nobody that criticizes math in economics is literally criticizing the use of algebra or calculus to provide intuition about an economic result. What we criticize are the restrictions that using math places on the economic problem. Mises described math in economics as a “vicious method, starting from false assumptions and leading to fallacious inferences. Its syllogisms are not only sterile; they divert the mind from the study of the real problems and distort the relations between the various phenomena.”

I can’t help but think that diverting the mind from the real problem is exactly what’s happening here. The corporate tax debate is really about the incidence of the tax. Do workers bear most of the burden, or does it primarily serve to prevent monopoly profits and rents? Cochrane’s example avoids this question by assumption. Rather than being a nail in the coffin for people who want less math in economics, it serves as a perfect example of why those criticisms exist. In some ways math provides clarity over verbal reasoning, but it can also be deceiving. Behind the formal logic and the proofs is a fragile set of assumptions that in many cases drive the results.


P.S. I don’t usually agree with Paul Krugman but I think he gets this one right in this post. He also shows which assumptions are driving the result, and that they are not ones that make much sense.

P.P.S. Larry Summers has a nice response to the debate as well

P.P.P.S. Casey Mulligan claims Krugman and Summers still get it wrong. I haven’t fully wrapped my head around his argument. What was Cochrane saying about algebra making everything clear?

P.P.P.P.S. I’m still in favor of cutting the corporate tax precisely because it is so hard to determine the incidence. Even if we want to stop monopoly profits (and I’m not sure that we do), it seems better to me to just focus on preventing monopolies.

 

A Different Kind of Economic Modeling

In macroeconomics, research almost always follows a similar pattern. First, the economist comes up with a question. Maybe they look at data and generate some stylized facts about some aspect of the economy. Then they set out to “explain” these facts using a structural economic model (I put explain in quotes because this step usually involves stripping away everything that made the question interesting in the first place). Using their model, they can then make some predictions or do some policy analysis. Finally, they write a paper describing their model and its implications.

There is nothing inherently wrong with this approach to research. But there are some issues. The first is that every paper looks exactly the same. Every paper needs a model. Sometimes papers adapt existing models, but they need enough difference to be a contribution on their own (but not so much difference that you leave the narrow consensus of modern macroeconomic methodology). Rarely, if ever, is there any attempt to compare models, to evaluate their failures and successes. It’s always: previous papers missed this and that feature while mine includes it.

This kind of iterative modeling can give the illusion of progress, but it really just represents sideways movement. The questions of macroeconomics haven’t really changed much in the last 100 years. What we have done is develop more and more answers to those questions without really making any progress on figuring out which of those answers is actually correct. Thousands of answers to a question is in many ways no better than none at all.

I don’t think it’s too much of a mystery why macroeconomics looks this way. Everybody already knows how an evaluation of our current answers to macroeconomic questions would go. The findings: we don’t know anything and all our models stink. I’d be surprised if even 10% of economists would honestly suggest a policymaker to carry out the policy that their papers suggest.

Academics still need to publish of course so they change the criteria that describes good macroeconomic research. Rarely is a paper evaluated on how well it answers an economic question. Instead, what matters is the tool used to answer the question. An empirical contribution without a model will get yawns in a macro seminar. A new mathematical contribution that uses a differential equations derived from a heat diffusion equation from physics? Mouths will be watering.

The claim is that these tools can then be used by other researchers as we continue to get closer and closer to the truth. The reality is that they are used by other researchers, but they only use the tools to develop their own slightly “better” tool in their own paper. In other words, the primary consumer of economic papers is economists who want to write papers. Widely cited papers are seen as better. Why? Because they helped a bunch of other people write their own papers? When does any of this research start to actually be helpful to people who aren’t responsible for creating it? Should we measure the quality of beef by how many cows it can feed?

Again there is an easy explanation for why economists are the only ones who can read economics papers. They would be completely unintelligible to anybody else. Reading and understanding the mechanism behind a macroeconomic paper is often a herculean task even for a trained economist. A non-expert has no chance. There could be good reasons for this complexity. I don’t expect to be able to open a journal on quantum mechanics and get anything out of it. But there is one enormous difference between physics and economics models. The physics ones actually work.

Economics didn’t always look this way. Read a paper by Milton Friedman or Armen Alchian. Almost no equations, much less the giant dynamic systems in models today. Does anybody think modern economic analysis is better than the kind done by those two?

The criticism of doing economics in words rather than math is that it is harder to be internally consistent. An equation has fewer interpretations than a sentence. I’m sympathetic to that argument. But I think there are better ways to add transparency to economics than by writing everything out in math that requires 20 years of school to understand. There are ways to formalize arguments other than systems of equations, ways to explain the mechanism that generates the data other than structural DSGE models.

The problem with purely verbal arguments is that you can easily lose your train of logic. Each sentence can make sense on its own but completely contradict another piece of the argument. Simultaneous systems of equations can prevent this kind of mistake. They are just one way. Computer simulations can provide the same discipline. Let’s say I have some theory about the way the world works. If I can design a computer simulation that replicates the kind of behavior I described in words, doesn’t that prove that my argument is logically consistent? It of course doesn’t mean I am right, but neither does a mathematical model. Each provides a complete framework that an outside observer can evaluate and decide whether its assumptions provide a useful view of the world.

The rest of the profession doesn’t seem to agree with me that a computer simulation and a system of equations serve the same purpose. I’m not exactly sure why. One potential worry is that it’s harder to figure out what’s actually happening in a computer simulation. With a system of equations I can see exactly which variables affect others and the precise channel of each kind of change. In a simulation, outcomes are emergent. Maybe I develop a simulation where an increase in taxes causes output to fall. Simply looking at the rules I have given each agent of how to act might not tell me why that fall occurred. It might be some complex interaction between these agents that generates that result.

That argument makes sense, but I think it only justifies keeping mathematical models rather than throwing out computer models. They serve different purposes. And computer models have their own advantages. One, which has yet to be explored in any serious way, is the potential for visual results. Imagine that the final result of an economic paper was not a long list of greek symbols and equals signs, but rather a full moving mini economic world. Agents move around, trade with each other. Firms set prices, open and close. Output and unemployment rise and fall. A simple version of such a model is the “sugarscape” model of Axtell and Epstein which creates a simple world where agents search for and trade sugar in order to survive.

Now imagine a much more complicated version of that that looked a lot more like a real economy. Rather than being able to “see” the relationships between variables in an equation, I could literally see how agents act and interact visually. My ideal world of economic research would not be writing papers, but creating apps. I want to download your model on my computer and play with it. Change the parameter values, apply different shocks, change the number and types of agents. And then observe what happens. Will this actually tell us anything useful about the economy? I’m not sure. But I think it’s worth a try. (I’m currently trying to do it myself. Hopefully I can post a version of it here soon)

Keynesian Economics Part 2 Investment and Output

In my last post on Keynesian economics I outlined a simple example that I think captures the core of Keynes’s economics. It will help to understand this post if you read that one first.

Keynes’s key insight was that an attempt to save by an individual does not always lead to an increase in aggregate saving. I showed how using a simple example in the last post, but we can also generalize the problem. Imagine that each consumer consumes only a fraction of their income (it does not have to be the same across individuals, but I will assume it is for simplicity). Then total consumption spending is given by

    \[C = bY\]

Where C is consumption, Y is income (and total output), and b is the fraction of income spent on consumption (the marginal propensity to consume).

Let’s say that the only spending in the economy is consumption spending. You might already be able to see that we have a problem. Total spending must always equal total income in the economy so that

    \[Y = C = bY\]

Which can only be true if Y=0, so the economy breaks down. Perhaps this scenario is easiest to see if we imagine the case where there is one worker and one firm. The worker works for the firm and gets paid Y. He then decides to buy bY of the output he just produced. The firm realizes he made too much stuff, so he cuts back on production. But this means he reduces his demand for the worker’s labor and cuts his hours. But now the worker makes less so he spends even less and the process continues until no production is carried out at all. The only way we could sustain production through consumption alone would be if nobody wanted to save at all.

If consumption spending isn’t enough to keep firm production positive, we need some demand from another source. One source could be other firms in the form of investment. If we fix income at Y and assume again households only want to consume bY, it is still possible that firms can make up the additional spending by investing (1-b)Y. Keynes argued that there is no reason to expect that investment would always exactly fill gap. If desired investment by firms is less than the difference between consumption and income, they won’t be able to sell all of their product and will cut back on production. We can see that if we write out our equation again, now with investment, it becomes

    \[Y = C + I = bY + I\]

And solving for Y gives

    \[Y = \frac{I}{1-b}\]

So the level of investment determines the level of income. It was through this logic that Keynes concluded that it was the “animal spirits” of firms that determined the state of the economy. It’s possible that the level of investment exactly corresponds to the full employment level of output of an economy, but there is nothing that guarantees that it will.

There are still a few subtleties we need to consider. The first is the role of interest rates. In the classical view of the economy, when people try to save more, they increase the supply of loanable funds, which pushes down interest rates (think of banks having excess money to lend and the only way they can get rid of it is by lowering the interest rate). That lower interest rate then makes previously unprofitable investment projects become profitable and investment rises. If the interest rate falls enough, it’s possible that the increase in investment would be enough to offset the decrease in consumption.

Keynes didn’t deny this possibility. However, he argued (I think correctly), that interest rates are certainly not the only, and likely not even the primary, factor that goes into a firms investment decision. If a firm expects demand to be low due to a recession, there is no interest rate where it will be profitable for them to make that investment. And, as we saw in the last post, by failing to make those investments, firms’ expectations become self-fulfilling and their pessimism is proven correct. Interest rate adjustments alone therefore cannot save us from a Keynesian recession.

Another potential question comes from the assumptions of the Keynesian consumption function. It is obviously unrealistic to assume that each household wants to consume the same constant fraction of their income. People like Milton Friedman have argued that what people really care about when making consumption decisions is their permanent income. If my income falls today, but I expect it to return to its previous level tomorrow, I will borrow in the bad times to keep a constant level of consumption. I think this criticism is valid, but I don’t think it stops Keynes’s story. As long as aggregate consumption is less than total output (which it almost certainly will be), we still need investment to fill the gap. We still rely on expectations of firms to be correct regarding their future demand.

By focusing on the case where investment was exactly enough to move the economy to full employment, Keynes argued that “classical” economists implicitly restricted the economy to a special case. Keynes set out to correct that theory by proposing a “general theory” where investment fluctuated unpredictably and could (and often is) less than the level that would sustain full employment. I think this contribution is extremely valuable and unfortunately often overlooked. Even modern “New Keynesian” models bear little resemblance to the economy Keynes described. Models with money at all are rare and ones that allow the type of monetary disequilibrium in Keynes’s theory are all but nonexistent.

What has been emphasized instead have been the policy implications of Keynes’s work. In my next post I will provide an argument that Keynesian policies do not solve the problem Keynes described.

 

Fixing the NBA Draft

The NBA recently voted to change the way it decides the order teams draft college players. If you aren’t familiar with basketball, the current system determines the order by assigning different probabilities of drafting in each position to each of the 30 teams based on the standings. For example, under the old system, the team that finished last had a 25% chance of receiving the top overall pick, while the 14th worst had only a 0.5% chance to land in the top spot (playoff teams are not part of the lottery – they just pick in reverse order of standings).

This system is distinct from other sports like the NFL, which deterministically sets the draft order as the reverse of the standings. The worst team always picks first in football. The reason the NBA does not follow the NFL is to discourage “tanking,” which is when one team attempts to lose on purpose to get the number one pick and improve their team for the future. A new proposal that was just approved by a majority of owners punishes tankers even more, reducing the odds of the worst team getting the first pick to 14% and giving the exact same 14% chance to the second and third worst teams.

At first, it might seem like the lottery system accomplishes its goal of reducing the incentives to tank. The benefit of coming in last place is obviously higher if you have a 100% chance of getting the first pick rather than a 25% chance or a 14% chance.

But there’s something wrong with this logic. The decision to tank or not does not depend on the overall benefit of coming in last, but rather its relative benefit compared to any other strategy. In other words, the only reason a team wouldn’t tank is if its benefit of playing hard every game outweighs the benefit of losing and moving down the standings. It seems clear to me that under any system that gives any draft advantage to the worst teams will always encourage tanking.

There is simply no benefit at all to being the 24th or 23rd best team in the NBA. If your team cannot realistically compete for a title, you are always better off being dead last than somewhere in the middle. With the new system, that calculation changes so that you become indifferent between any of the bottom 3 spots, but does anybody really care much if a team only has to tank to 28th instead of 30th? They are still better off losing as many games as possible.

This flaw in any lottery system has led to even more radical proposals that decouple draft order and standings completely. The most famous of these is “the wheel,” which would replace the lottery entirely with a draft order set years in advance. Each team would pick in each of the 30 draft slots exactly once every 30 years. And they would know exactly when. No randomness. No relation to the standings at all.

The virtue of this system is that it removes all incentive to tank. If your draft order is unconnected to your record, you might as well do your best to win. This feature has given it a large following of NBA fans hoping for more competition in the league and it has been seriously considered as an alternative to the lottery.

I think it’s a terrible idea. By removing the link between record and draft order, the wheel solves the tanking problem. But it deepens another major issue with the NBA: how do bad teams get better? And what happens when a team like the Warriors ends up with the first pick in the draft? Imagine the current Warriors roster plus Markelle Fultz and you can immediately see why the wheel can end up producing some incredibly undesirable results.

In the article I linked above, Zach Lowe acknowledges both of these issues, but writes them off by arguing that they would be a part of any draft system that offers a chance for good teams to get good picks. And he’s absolutely right. Any measure that discourages tanking will necessarily make it harder for bad teams to get better. And any attempt to give some advantage to bad teams will always encourage tanking. There is no perfect system.

My proposal is a bit different. Rather than try to fix the draft, fix the system that makes tanking one of the few ways for a team in a bad situation to improve. Tanking is not the the root of the problem. The issue is that teams like the Warriors can have 4 superstar players on the roster, making it nearly impossible for teams with less talent to compete. What’s the point of trying to win when you know you won’t? Even a tiny advantage in the draft is enough for any team to see some value in tanking when their probability of beating the teams at the top falls close to zero.

We can solve that problem in a much easier way. Remove the cap on player salaries. Let LeBron and Durant make $50 million a year. The market would make it impossible for the Warriors to have multiple top 5 players. Somebody would offer enough that one of them would want to leave. And let bad teams tank. Get rid of the lottery. The worst team gets the first pick. Would tanking increase? Possibly, but so would parity in the league. Nobody watches bad teams anyway. At least this system would give them a path to being good again.

Keynesian Economics and Monetary Disequilibrium

What is Keynesian Economics about? Even if you’ve never taken an economics class you might still have some idea. The 2008 stimulus package was frequently referred to as a Keynesian policy. Government intervention and Keynesian economics often go hand and hand. If you have taken a macroeconomics class you might have an even deeper knowledge of Keynesian economics. Maybe you know about the multiplier, the Keynesian cross, the IS-LM model. And all of those are certainly related to Keynesian economics, but none really capture the heart of Keynes’s contribution.

Part of the trouble with people’s understanding of Keynes’s work is that secondary sources frequently distort what he actually said. For example, if you read Mankiw’s intermediate macroeconomics textbook you will come away with the impression that Keynesian economics is about sticky prices. We get unemployment because wages don’t adjust downward quickly enough. So called “New Keynesian” models, the modern analogue to IS-LM are also predicated on slower than optimal price adjustments to shocks. It is true that Keynes assumed sticky prices for part of his analysis, but he was careful to emphasize that “The essential character of the argument is precisely the same whether or not money-wages, etc., are liable to change” (General Theory Ch. 3).

So if not sticky prices or wages, what is it that causes unemployment in Keynes’s world? In my reading, Keynes’s story is all about monetary disequilibrium and a failure to coordinate savings and investment in a monetary economy.

Keynes famously stated that his theory refuted “Say’s Law,” which can be simply stated as “supply creates its own demand.” Now, whether or not that’s what Say actually said remains a point of contention even today, but  it’s that formulation that Keynes attempts to refute, which I think is worth exploring on it’s own. What Keynes really wants to do is draw a distinction between a barter economy and a monetary economy. I recently taught an intermediate economics class and I developed a simple example that I think helps illustrate the main points.

Let’s start with an economy with no money and only two goods, apples and bananas. There are two people in the economy. Person A can only produce apples and person B can only produce bananas. For simplicity, I will assume a fixed price ratio of 2:1. One banana is worth as much as two apples. The story gets more complicated if we allow this price to change, but I don’t think the main implications would be any different. In this economy with no money, the only trade that can occur is bananas for apples. If A wants to demand 10 bananas from B, he needs to produce 20 apples. It is in this sense that supply creates its own demand. Without money, demand for one good is precisely supply of another. The diagram below illustrates what is happening (I arbitrarily fixed prices in dollar terms, but remember there is still no money. Dollars operate only as a unit of account)

In this kind of barter setup, Say’s law is trivially true. Any demand for bananas is supply of apples so supply creates its own demand. In this case, demand for bananas is $10(20) = 200 and supply is $20(10), which are obviously equal. However, when we start to add in money, the relationship between supply and demand is not as clear.

For a second example we will assume now that bananas and apples cannot be directly traded. Instead, each good will have to be sold for dollars, which can then be used to purchase the other good. Of course, we could still have the exact same situation as above. If all transactions happen instantaneously and every time an apple is produced it is immediately sold and the proceeds immediately used to purchase an apple. However, now there is another possibility.

Imagine that for some reason the apple producer wants to consume more bananas tomorrow than today and decides to save in dollars (I assume apples cannot be saved directly – this might be a strong assumption but it will make sense later). He still wants to consume 10 bananas (so he needs to produce 20 apples), but he also wants to save $100, so he produces an additional 10 apples (30 apples total). But what if the banana producer still only wants to buy 20 apples. He doesn’t want to pay an extra $100 for the additional 10 apples that are being produced.

If you’re an economist the first question that comes to your mind should be why the price doesn’t just adjust. If demand for apples is less than supply for apples, the price of apples should fall until the market is equilibrated. So in this case, apples could fall in price to $6.67 so that 10 bananas buy 30 apples and supply equals demand again. Except then we run into a problem. After the price adjustment producer A still isn’t happy. He didn’t get to save his $100. So really this can’t be an equilibrium at all (it’s possible that the change in prices would also affect his desired saving, but as long as it’s still positive it’s still not an equilibrium).

The problem with the logic above is that we are still trying to think of the economy as a barter economy with one market (trade between apples and bananas), when it is actually a monetary economy with 2 markets (money for apples and money for bananas). Finding a single equilibrium price for two markets is not enough. We need equilibrium in both markets. What we have in the example above is an excess supply of apples and an excess demand for money. The banana producer can’t supply additional money, so he is unable to help return to equilibrium. So who can help? Who supplies money? The Fed! If the Fed simply prints money to buy the excess apples we are back to equilibrium at the same prices as before.

So what does any of this have to do with unemployment? Let’s change the example slightly. Instead of apples, assume now that A provides labor. They work for B to produce bananas. If this is a barter economy then their wage is paid in bananas (I still fix arbitrary dollar values) and demand and supply are always equal as above:

But what if the worker wants to save? He obviously can’t save labor directly (which is why I assumed no saving of apples above) and I will assume he doesn’t have the storage to save bananas either. Instead, he will try to save in dollars by buying fewer bananas (but working the same amount). If he wants to save $100 the picture becomes:

Since the worker still worked 20 hours, production of bananas didn’t fall, but demand for bananas did. The firm is forced to put the extra bananas into its inventories. Is this a problem? Maybe not. If the firm realizes that the worker will use his savings to purchase more bananas in the future, they are happy to increase their investment now in order to produce more bananas next period (an equivalent story could be told where they are building machines to increase production, but the inventory version is the simplest I think). We could then imagine a second period of this economy where the worker uses his savings from the first period to buy the bananas from the inventory in the second.

This story gives us a nice equilibrium outcome with no unemployment. The worker works his desired amount in each period, saving $100 in the first to buy five additional bananas in the second. The banana producer invests in 5 extra bananas to prepare for the increase in demand in the second period. Saving and investment are perfectly coordinated. Say’s Law holds.

But it is easy to imagine another equilibrium. What if the firm does not realize demand for its product will increase next period? All it knows is that consumers want to buy 5 fewer bananas right now. In this simple example where there is only one option for the worker to spend his money that’s hard to believe, but in the real economy with thousands of firms and millions of products, an individual producer has no idea whether increased savings will translate to future demand for its own product. If demand falls today, they might predict lower demand tomorrow as well. In this case they will not want to increase investment today. Instead they simply cut production. So we have a worse equilibrium that looks like

Here the firm doesn’t expect the decline in demand today to translate into an increase in demand tomorrow. They see demand for 5 bananas today so they only hire the worker for long enough to produce those 5. The worker still wants to work 20 hours to save an additional $100, but nobody will hire him so he only works 10 and is therefore underemployed (if we think about this as representing many people we would have some employed and some unemployed). Keynes referred to this situation as involuntary unemployment. People want to work at the prevailing wage, but since firms don’t expect their consumption of their product to compensate the cost of their wages, they don’t want to hire.

There are two interesting points here. First, note that wage cuts will not help. The worker wants to save regardless of his wage. Cutting it will only make him want to work more, which actually makes the problem even worse. Second, the firm’s prediction actually comes true. Since the worker was actually unable to save anything in the first period, his demand for bananas actually won’t increase in the future either. By expecting lower demand tomorrow, the firm actually caused that future to be realized. In this way, expectations are self-fulfilling and we get multiple equilibria.

This example is highly stylized, but I think it demonstrates Keynes’s main point. When somebody wants to save, there is no magical process that instantly transforms their saving into investment. Investment decisions are driven primarily by firms’ expectations about demand for their own products. Without perfect foresight, they must rely on cruder measures of prediction (like animal spirits). If they don’t expect increased saving to translate into future demand, we get unemployment.

I will have more to say on Keynesian economics in at least one future post (including some criticism of Keynes), but this is already getting long so I will stop here for now.

 

Seeing Like a State

I recently finished reading Seeing Like a State, an interesting book by James Scott, a political scientist at Yale. Scott argues that many attempts to coordinate and control from the top down necessarily leave out many important details that are essential to the workings of an organically developed process. In his words “Designed or planned social order is necessarily schematic; it always ignores essential features of any real, functioning social order.” His thesis is essentially a Hayekian one. Because they can never fully collect the local knowledge of individuals, state programs often forget important features of society, in some cases leading to tragic results.

Scott begins the book with an example that I think perfectly encapsulates his broader point. He describes the story of the forestry industry in late 18th century Prussia and Saxony. In order to optimize lumber yields, states decided that there was no need to keep the seemingly unordered naturally grown forest. Instead, they could optimize forest growth, planting only the most valuable trees in a grid-like setup to enable easy access. You can probably guess what comes next.

While the managed forests worked well for one generation, soon the trees stopped growing quite as large or even dying before they could be used for lumber. Without the natural habitat they had evolved to survive in, the trees no longer received the nutrients they needed from the soil. Scientists attempted to replicate the essential features of the forest, to provide the trees with the nutrients they needed while maintaining their controlled environment. As Scott describes, “given the fragility of the simplified production forest, the massive outside intervention that was required to establish it – we might call it the administrators’ forest – is increasingly necessary in order to sustain it as well.” Just as we see in countless cases of government intervention, a single intervention ends up requiring even more intervention and government becomes necessary to maintain the system despite being itself the original source of the problem.

Scott summarizes the situation:

“The metaphorical value of this brief account of scientific production forestry is that it illustrates the dangers of dismembering an exceptionally complex and poorly understood set of relations and processes in order to isolate a single element of instrumental value…Everything that interfered with the efficient production of the key commodity was implacably eliminated. Everything that seemed unrelated to efficient production was ignored. Having come to see the forest as a commodity, scientific forestry set about refashioning it as a commodity machine. Utilitarian simplification in the forest was an effective way of maximizing wood production in the short and intermediate term. Ultimately, however, its emphasis on yield and paper profits, its relatively short time horizon, and, above all, the vast array of consequences it had resolutely bracketed came back to haunt it.” (21)

It is hard to read the excerpt above without immediately thinking of other examples where governments have attempted to replace complex natural systems with more intelligible, but far simpler systems. The remainder of the book goes through many such examples, from the design of cities and languages, to the failed communist experiments of the Soviets and the Chinese and many more. Scott picks out four features that his research suggests lead to poor results of state control. They are, in his words

  1. “Administrative ordering of nature and society”
  2. “High modernist ideology”
  3. “Authoritarian state that is willing and able to use the full weight of its coercive power to bring these high-modernist designs into being”
  4. “Prostrate civil society that lacks the capacity to resist these plans”

1, 3, and 4 are pretty straightforward, but 2 deserves some further discussion. By “high modernist ideology,” Scott refers to the belief that scientists and other experts know how to design a society in a more efficient way than ones that develop without any top down intervention. It is the belief that a centralized plan can trump decentralized spontaneous order. Hayek frequently called this attitude “scientism” in his work. Both Scott and Hayek argue that high modernist thinking is too arrogant. Ancient traditions may look backwards to a modern scientist. Customs may seem strange, cultures don’t always make sense.

But it is important to remember that just because you don’t understand the reason behind something doesn’t mean there isn’t one. To the central planner who only cared about lumber production, natural forests seemed incredibly inefficient. So the solution is simple. Cut out everything we don’t need and just keep the good stuff. In doing so, however, those seemingly useless features often reveal themselves to be essential.

Overall, I found the book to be full of interesting historical examples that each serve to illustrate this theme again and again. One point that I did wish had gotten more attention was the role of corporations and their similar top down nature. Scott briefly mentions that “large-scale capitalism is just as much an agency of homogenization, uniformity, grids, and heroic simplification as the state is.” He is quick to note that there is a major difference that “for capitalists, simplification must pay.” Still, in cases like the German forests, if the results were profitable in the short run and the problems only observable after dozens of years, it is easy to imagine capitalist firms falling into the same trap. I would have liked to see some examples of historical corporations that have also failed to simplify complex systems, but I guess that would require a much longer book. As it stands, the book serves as a useful warning for any attempt to improve a natural process that is not fully understood. Well worth the read.