Marjorie Drysdale: Even When You Can Do Math, You May Not Love It

Marjorie Balgooyen Drysdale is a classical soprano, music teacher, conductor, and the author of the book Tagalong Kid.

Not all of the emails Noah Smith and I received in response to our column “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t” agreed with us. Some people said they had tried as hard as they could and still couldn’t do math. In a few cases, genuine dyscalculia might be at issue. But more often, I suspect the problem is with the quality of the math teaching. Elizabeth Green had a fascinating New York Times article “Why Do Americans Stink at Math?” a few days ago that pointed the finger squarely at the lack of adequate instruction for math teachers in how to teach math.

Marjorie Drysdale, who received a Master’s degree in Music from the University of Michigan, graciously agreed to share this email she made in response to Noah’s and my column. In addition to the issue of how math is taught, and where one is at when the math is taught, she points out that just because you can do something doesn’t mean you will love it. I agree. There are always tradeoffs in life, and time spent doing math is time away from doing something else that you may love more–maybe a lot more. But at least if you know how to do math, you can make the choice. And if math is taught well, what you learn will have some value for your life.

Dear Miles and Noah,

Regarding your essay, “There’s one key difference between kids who excel at math and those who don’t,” I have to disagree with your assertion that “For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.”

I was an excellent high school student. I worked hard, prepared, and was self-confident.  I always made the high honor roll. I graduated 2nd in my class.

I went on to a competitive college and graduated with highest honors, phi beta kappa.  I had two majors. I was always on the Dean’s List.

I went on to get a master’s degree and graduated with honors there, too. I became a professional musician. Supposedly, math and music go together. Not with me.

After geometry, I simply “didn’t get it." I took one more year of math—a course which, in the 60’s, was called "fusion." It was a combination of trigonometry and advanced geometry. That did me in. Until then, I had always earned A’s in math. I barely passed "fusion.”

It might have made a difference that I had skipped a grade and then was put into the “honors group”—an accelerated class. (In those days, classes were “tracked.”) In that class, we were taking courses a year ahead of our peers. Therefore, I was taking courses two years ahead of my peers. Perhaps I simply had a “readiness” problem. 

I “hit a wall” and never went back to math. It had nothing to do with lack of effort, believe me.

Oddly, when I took my GRE exams after college and two years of work, my verbal and math scores were both in the 700’s. This truly surprised me. I hadn’t taken a math course in seven years.

I think that “readiness” in my case was more of a determining factor than “hard work.”

As I grew older, I understood it better, but I still didn’t like it. There are people who adore math. They light up about it. They enjoy it from the get-go. Therefore, I do think there is an innate element to these differences. Some people love math; others don’t.

I adore classical music. Most people couldn’t care less about it. The first time I heard it, I was hooked. That had nothing to do with hard work, either. Succeeding in it required hard work, of course, but the love came first.

Kate Owino: Kenyan Women Can Love Math Too

I have been thinking more about the issues Noah Smith and I raised in our column “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t.” So I asked permission to publish a few more of the comments Noah and I received by email. Here is a note I liked from Kate Owino:

I’d like to thank Quartz and Profs. Kimball and Smith for the wonderful article on math capabilities in kids released on October 27th, 2013. Reading it reminded me of my personal relationship with mathematics, as a subject and as a life/job-related skill.

I was born and raised in Kenya, and here the attitude toward math takes on a sexist connotation in favor of male students. It’s rare to hear of a female student saying that she excelled in math not only for the sake of passing the exams and getting into a good school or university, but also because she LOVES the subject.

From my personal experience, I was one of a handful of students in secondary school who fell in the latter category. This has proved (to date) to be a slight challenge whenever the topic of attitude towards math arises in a discussion with my female friends - they talk about how poorly they performed especially in secondary school, to the point where it comes across like they’re actually proud of the grades they got (Cs and below). I cannot contribute to the self-mockery because I got As all the way to my final exam…and the same applies to Chemistry.

Reading about the criticism-to-work-harder approach employed by students in China reminded me of my mother’s toughness towards my performance in math. From the age of 8 she would literally slap my wrists if I worked sloppily at a sum, and it was worsened by my teachers’ constant comments in my report book about my propensity to make careless mistakes.

As I look back now I cannot help but be proud of my love for math (and the sciences in general), even though I ended up pursuing a different academic path - studied literature in my undergraduate, and currently work in web content management. I hope to find a way to help do away with that sexist attitude in schools in my country especially since, as it was indicated in the article, poor attitude toward math makes many people lose out on critical life skills and lucrative career paths.

Thanks once again for the wonderful article. Have a wonderful week!

Provo High School and the 1977 National Speech Tournament

Newpapers.com is a great resource for things like this.

Newpapers.com is a great resource for things like this.

I tell the story of our Provo High School Forensics Team at the 1977 National Speech Tournament starting on page 2 of the storified tweets in “A More Personal Bio: My Early Tweets.” Here is the relevant newspaper article from 1977 to back up my story.

In the newspaper article, you can see my name at the top of the second column.

Noah Smith: Why Do Americans Like Jews and Dislike Mormons?

I am delighted to host another guest religion post by Noah Smith. Don’t miss Noah’s other religion posts on supplysideliberal.com:

  1. God and SuperGod
  2. You Are Already in the Afterlife
  3. Go Ahead and Believe in God
  4. Mom in Hell
  5. Buddha Was Wrong About Desire
  6. Noah Smith: Judaism Needs to Get Off the Shtetl

Here is Noah:

The Pew Research Center recently did an interesting survey asking Americans how they felt about various religious groups.Here are the findings in a single table, shown above.

I was actually surprised by the low numbers across the board - there was almost no category in which more than 70% of people of one religion felt warmly toward people of another religion. But I wouldn’t put too much stock in that, actually - answers to these surveys usually tend to change a lot depending on how you phrase the question. The relative ratings are more interesting. Some of the findings are easily explained–the low ratings given to Muslims, for example are obviously an unfortunate result of the current political troubles with jihadist terrorist groups. But other findings are more surprising and intriguing. Here are some thoughts I had, looking at the numbers. 

Why do Americans like Jews?

As many have noticed, Jews received the most positive ratings of any religious group in America. This confirms that American society is not in any meaningful way anti-Semitic, which is good news. But why do people like Jews so much?

Hypothesis 1: Nobody knows what Jews even are. When I was in high school in a medium-sized Texas town, another kid asked me about my religion. He asked: “Are you…Hanukkah?” So maybe people just have no idea what Judaism is, and figure it must be a minor thing that is no threat to their own faith.

Hypothesis 2: Jews are no threat. Jewish culture has a strong stigma against proselytization. I’ve criticized that insularity, but maybe it’s paying dividends. People don’t like threats - that’s why Japan and Germany are such popular countries these days. Judaism is not going to knock on your door and ask you if you’ve heard about Yahweh.

Hypothesis 3: The entertainment industry. There are lots of Jewish actors, comedians, etc. If you ask the average American to name someone Jewish, she’ll probably think of a funny guy like Jerry Seinfeld or a cute girl like Natalie Portman, or maybe a musician like Bob Dylan. If people knew that Drake, Scarlett Johansson, and James Franco were Jewish, they’d probably like us even more!

In addition, the two main drivers of anti-Semitism–European conspiracy theories and Muslim anger about Palestine–are both notably absent in America.

Why don’t Americans like Mormons more?

Mormons get middling low ratings in the poll. I guess this shouldn’t be surprising, given the prevalence of anti-Mormon discrimination in America. But what is the cause of the discrimination? David Smith, a political scientist at the University of Sydney (and no relation to Yours Truly, though we have clinked a few glasses over the years), finds that many Americans consider Mormons as an “outsider” group, which is strange considering that Mormonism is the only major religion to begin on American soil. Why do people see Mormons as outsiders?

Hypothesis 1: Proselytizing. One possibility is that the rapid spread of Mormonism poses a threat to other, more established religions. In this respect, Mormonism is the polar opposite of Judaism–every Mormon man must go out and convert people. That’s threatening, no matter how politely it’s done.  

Hypothesis 2: The perception of secrecy. There is a perception of secrecy and exclusivity surrounding Mormonism. Anyone can go participate in any Jewish prayer service. But not even all Mormons can enter “dedicated” Mormon temples! Some Mormon weddings exclude non-Mormons. And there’s a perception that many other aspects of the religion are secret. Secrecy seems alien, and exclusivity is suspicious.

I think anti-Mormonism is a bad thing, but I don’t know how to combat it.

Why don’t Jews like Evangelicals?

One interesting finding from the poll is that although 69% of Evangelical Christians expressed positive feelings toward Jews (one of the highest ratings given), only 28% of Jews expressed positive feelings toward Evangelical Christians (one of the lowest ratings given). This is weird, since Evangelical Christian sects - unlike, say, the Catholic Church - have no history of anti-Semitism or persecution of Jews. Also, the asymmetry itself is strange. Why don’t Jews like Evangelicals more?

What’s going on?

Hypothesis 1: Instinctive fear of dominant religion. Jews in Europe and the Mideast had a long history of being persecuted by whatever the dominant religious sect in the area happened to be - the Catholic Church, Islam, or the Eastern Orthodox Church. Jewish culture may have simply inherited an instinctive distrust of whatever the most powerful religious group seems to be. 

Hypothesis 2: Politics. American Jews are generally liberal, while Evangelicals are generally conservative. In America, politics is often a stronger religion than actual religion. In addition, some Jews may be afraid that Evangelicals only like them because of a millenarian desire to see Israel recreated and then destroyed (in accordance with Biblical prophecy), or perhaps a cynical desire to use Israelis as expendable shock troops against the Muslims. This is probably not a motivating factor for most Evangelicals, but it does get some play in the media.

Hypothesis 3: Anxiety about the end of Judaism. Non-Orthodox Judaism is a dying religion. In America (and Britain), Jews are marrying non-Jews and ditching their ancestral religion at an astounding rate. It turns out that integration and assimilation destroys Judaism, while pogroms, ostracism, and oppression keep it going (someone might have bothered to mention this to Hitler!). Many Jews are naturally anxious about the end of their distinctive culture, and may tend to displace this anxiety by feeling bad about America’s “dominant” religion - Evangelical Christianity.

I think this attitude is a bad one. Evangelical Christianity is far more pro-Jewish than any other branch of Christianity has ever been. Furthermore, Evangelical Christianity has been an important factor in the creation of American society, the most philo-Semitic Western society in history. Jews should have a more positive view of Evangelicals.

Von Günter Heismann in the Süddeutsche Zeitung: Economists Ken Rogoff and Miles Kimball Want to Abolish Cash →

Ökonomen wie Kenneth Rogoff oder Miles Kimball wollen das Bargeld abschaffen. 

I made it into the German press for wanting to demote–not abolish–cash, along with Ken Rogoff, who does indeed want to get rid of cash. (i wrote about Ken Rogoff’s views here.) Google Translate works fine on this article. Thanks to Rudi Bachmann for letting me know about this article. 

See what I have to say about breaking through the zero lower bound with electronic money in “How and Why to Eliminate the Zero Lower Bound: A Reader’s Guide.” The article in the Süddeutsche Zeitung should have mentioned that I visited the European Central Bank and three of its associated national banks (France, Germany and Italy) to talk about how to keep paper currency from creating a zero lower bound. 

The Medium-Run Natural Interest Rate and the Short-Run Natural Interest Rate

Note: This post was the lead-up to my post “On the Great Recession.” After reading this one, I strongly recommend you take a look at that post.

Online, both in the blogs and on Twitter, I see a lot of confusion about the natural interest rate. I think the main source of confusion is that there is both a medium-run natural interest rate and a short-run natural interest rate. Let me define them:

  • medium-run natural interest rate: the interest rate that would prevail at the existing levels of technology and capital if all stickiness of prices and wages were suddenly swept away. That is, the natural rate of interest rate is the interest rate that would prevail in the real-business cycle model that lies behind a sticky-price, sticky-wage, or sticky-price-and-sticky-wage model.
  • short-run natural interest rate: the rental rate of capital, net of depreciation, in the economy’s actual situation. From here on, I will shorten the phrase “real rental rate of capital, net of depreciation” to  "net rental rate.“ 

Both the short-run and medium-run natural interest rates are distinct from actual interest rate, but in the short run, the short-run natural interest rate is much more closely linked to the actual interest rate than the medium-run natural interest rate is.

The Long Run, Medium Run, Short Run and Ultra Short Run

Introductory macroeconomics classes make heavy use of the concepts of the "short run” and the “long run.” To think clearly about economic fluctuations at a somewhat more advanced level, I find I need to use these four different time scales:

  • The Ultra Short Run: the period of about 9 months during which investment plans adjust–primarily as existing investment projects finish and new projects are started–to gradually bring the economy to short-run equilibrium. 
  • The Short Run: the period of about 3 years during which prices (and wages) adjust gradually bring the economy to medium-run equilibrium.
  • The Medium Run: the period of about 12 years during which the capital stock adjusts gradually to bring the economy to long-run equilibrium. 
  • The Long Run: what the economy looks like after investment, prices and wages, and capital have all adjusted. In the long run, the economy is still evolving as technology changes and the population grows or shrinks.  

Obviously, this hierarchy of different time scales reflects my own views in many ways. And it is missing some crucial pieces of the puzzle. Most notably, I have left out entry and exit of firms from the adjustment processes I listed. I don’t know have fast that process takes place. It could be an important short-run adjustment process, or it could be primarily a medium-run adjustment process. Or it could be somewhere in between.

The Medium-Run Natural Interest Rate

The importance of the medium-run natural interest rate is this: it is the place the economy will tend to once prices and wages have had a chance to adjust–as long as those prices and wages adjust fast enough that the capital stock won’t have changed much by the time that adjustment is basically complete. (I called that last assumption the “fast-price adjustment approximation” in my paper “The Quantitative Analytics of the Basic Neomonetarist Model”–the one paper where I had a chance to use the name of my brand of macroeconomics: Neomonetarism. See my post “The Neomonetarist Perspective” for more on Neomonetarism. The fast-price adjustment approximation is what makes good math out of the distinction between the short run and the medium run.)  The medium-run natural interest rate is not a constant. Indeed, at the introductory macroeconomics level, the standard model of the market for loanable funds is a model of how the medium-run natural interest rate is determined. Here is the key graph for the market for loanable funds, from the Cliffsnotes article on “Capital, Loanable Funds, Interest Rate”:

A common mistake students make is to try to use the market for loanable funds graph to try to figure out what the interest rate will be in the short run. That doesn’t work well. Although technically possible, it would be confusing, since how far the economy is above or below the natural level of output has a big effect on both the supply and the demand for loanable funds that using the market for loan. To understand the short-run natural interest rate, it is much better to use a graph designed for that purpose–a graph that focuses on how the short-run natural interest rate is determined by the demand for capital to use in production and by monetary policy.

The Short-Run Natural Interest Rate

Above, I defined the short-run natural interest rate as the "rental rate of capital, net of depreciation,“ or "net rental rate,” for short. What does this mean?

Renting Capital. First, to understand what it means to rent capital, think of those ubiquitous office parks. If the capital a company or other firm needs is an office to work in, it can rent one in an office park like this:

In retail, the capital a firm needs to rent might be retail space in a strip mall:

If a firm is in construction or landscaping, the capital it needs might be a bulldozer, which it can rent from the Cat Rental Store, among other places.

Of course, sometimes a firm needs specialized machine that it has to buy, because those machines are hard to rent. In that case, let me treat it as two different firms: one that buys the specialized machine and puts it out for rent, and another firm that rents the machine. The same trick works for a specialized building that is hard to rent, such as a factory designed for a particular type of manufacturing. When firms that own buildings or machinery are short of cash, sometimes they separate themselves into exactly these two pieces, and sell the piece that owns the specialized buildings or machines so the other piece of the firm can get the cash from the sale of those buildings or machines, while still being able to use those buildings and machines by paying to rent them.  

The (Gross) Rental Rate. I will call the gross rental rate simply “the rental rate." The rental rate is equal to the rent paid on a building or piece of equipment divided by the purchase price of that building or piece of equipment.  Because this is one price (expressed for example in dollars per year) divided by another price (dollars per machine), the rental rate is a real rate–that is, it does not need to be adjusted for inflation. The rental rate is usually expressed in percent per year, meaning the percent of the purchase price that has to be paid every year in order to rent the machine.  

The Net Rental Rate. It is useful to adjust the rental rate for depreciation, however. The paradigmatic case of depreciation is physical depreciation: a machine or building wearing out. More generally, a machine or building might become obsolete or start to look worse in comparison with newer machines. I am going to treat obsolescence as a form of depreciation. Obsolescence shows up in the price of new machines or buildings of that type falling relative to the prices of other goods in the economy. There are other things that can affect the prices of machines and buildings that will matter for the story below, but the rate of physical depreciation and the rate of obsolescence measured by declines in the real price of new machines and buildings of given types at the long-run trend rate are the two to subtract from the rental rate to get the net rental rate.

The Determination of Physical Investment

Physical investment is the creation of new capital–such as machines, buildings, software, etc.–that can be used as factors of production to help produce goods and services. Notice that I am using the phrase "physical investment” to distinguish what I am talking about from “financial investment.” So in this case, at some violence to the English language, I include writing new software in “physical investment." 

The amount of physical investment is determined by the costs and benefits of creating new machines, buildings, software, etc. now instead of later. Say we are talking about whether to create or purchase a building or machine now, or a year from now. The benefit of creating a new building or machine a year earlier is the rent that building or machine could earn in that year. In the absence of capital and investment adjustment costs (to which I return below), the cost of creating a new building or machine a year earlier is 

  • interest on the amount paid to create or purchase the building or machine.
  • physical depreciation
  • obsolescence

Dividing all of the costs and benefits by the amount paid to create or purchase the building or machine, the costs and benefits per dollar spent on the machine are 

benefit relative to amount spent = rental rate

cost relative to amount spent = real interest rate + physical depreciation rate + obsolescence rate

The reason it is the real interest rate in the cost relative to amount spent is because the obsolescence rate is being measured in terms of a real price decline.

In the absence of capital and investment adjustment costs, the rule for physical investment is:

  • If the rental rate is less than (the real interest rate + physical depreciation rate + obsolescence rate), invest later.
  • If the rental rate is more than (the real interest rate + physical depreciation rate + obsolescence rate), invest now.

If I move the physical depreciation rate and the obsolescence rate to the other side of the comparison, I can say the same thing this way: 

  • If the rental rate net of net of physical depreciation and obsolescence is below the real interest rate, invest later.
  • If the rental rate net of physical depreciation and obsolescence is above the real interest rate, invest now.

Or more concisely: 

  • If the net rental rate is less than the real interest rate, invest later.
  • If the net rental rate is more than the real interest rate, invest now.

Finally, using the definition of the short-run natural interest rate as the net rental rate and flipping the order, I can describe the rule for investment this way:

  • If the real interest rate is above the short-run natural interest rate (the net rental rate), invest later.
  • If the real interest rate is below the short-run natural interest rate (the net rental rate), invest now.

The Determination of the Short-Run Natural Interest Rate: Capital Equilibrium (KE) and Monetary Policy (MP)

Susanto Basu and I have a rough working paper on the determination of the short-run natural interest rate and about very-short-run movements of the actual interest rate in relation to the short-run natural interest rate: 

"Investment Planning Costs and the Effects of Fiscal and Monetary Policy” by Susanto Basu and Miles Kimball.

 We also have a set of slides to go along with the paper:

Slides for “Investment Planning Costs and the Effects of Fiscal and Monetary Policy” by Susanto Basu and Miles Kimball.

The short-run natural interest rate is determined by (a) equilibrium in the rental market for capital and (b) monetary policy.

Capital Equilibrium (KE): Supply and Demand for Capital to Rent

The Supply of Capital to Rent: The supply of capital to rent cannot change very fast. It takes time to create enough new machines, buildings, software, etc. through physical investment to affect the total amount of capital available to rent in any significant way. Wikipedia has an excellent article “Stock and flow” about this relationship between capital and physical investment. The canonical illustration is this picture of a bathtub:

Turning the tap on full blast might double the flow of water, but it will still take time for that flow to significantly affect the overall level of water in the tub. Similarly, turning investment on full blast may double the rate of physical investment creating new machines, buildings, software, etc., but it will still take time to significantly affect the overall amount of capital that exists in the form of machines, buildings, software, etc.

The Demand for Capital to Rent: The most important thing to understand about the demand for capital to rent is that it is higher in booms than in recessions. The more goods and services people want to buy, the more capital firms will want to rent at any given rental price in order to produce those goods and services. Ask any business person who has been involved in a decision to buy capital and they will tell you that they are more eager to get hold of capital to use when business is good than when business is bad.

The way I think of why the demand for capital to rent is higher in a boom than in a recession is this:

  • Since profit is revenue minus cost, whatever amount of output a profit-maximizing firm decides to produce to sell or inventory, it should try to produce that amount of output at the lowest possible cost. 
  • In a boom a firm will produce more output than in a recession (other things equal).
  • Since the stock of capital can’t change very fast, when the economy booms and firms add worker hours, a typical firm will not have as much capital per unit of labor as before. 
  • The more the economy booms, the higher wages  will be. (How much depends on whether wages are sticky or not. On sticky wages, if you are prepared for a hardcore economics post, see “Sticky Prices vs. Sticky Wages: A Debate Between Miles Kimball and Matthew Rognlie.”)
  • What is true of labor is also true for intermediate goods firms use as material inputs into production: when the economy booms and firms buy more materials to use, a typical firm will not have as much capital per unit of material inputs as before. 
  • Also, the more the economy booms, the higher the price of intermediate goods used as material inputs will be. (How much depends on whether the prices of the material inputs are sticky or not.) 
  • When the typical firm has less capital per unit of other inputs, it will be more eager to rent capital at any given rental price. 
  • If the firm is employing more labor and using more of other inputs despite wages and other input prices being high, it will be especially eager to rent additional capital at a given rental price, since capital then is relatively cheaper than other inputs.

The math behind this story is in the Basu-Kimball paper “Investment Planning Costs and the Effects of Fiscal and Monetary Policy.” There, although it is not needed to get these results, for simplicity we use the fact that for Cobb-Douglas production functions, the ratio of how much a cost-minimizing firm spends on labor and on capital is fixed. (See the relatively hardcore post “The Shape of Production: Charles Cobb’s and Paul Douglas’s Boon to Economics.”) Using the letters

  • R for the the rental rate,
  • K for the amount of capital,
  • W for the wage, and
  • L for the amount of total worker hours,

that means

RK = constant * WL.

Dividing both sides of this equation gives an equation for the rental rate:

R = constant * WL/K.

Since the total amount of capital K in the economy can’t change very fast, the total amount of capital in the typical firm also can’t change fast, so increases in wages W and total worker hours will push up the rental rate. And the net rental rate will parallel the overall gross rental rate very closely.  

The KE Curve. With the supply of capital relatively fixed (or technically “quasi-fixed”) at any moment in time, a higher demand for capital means a higher equilibrium rental rate in the market for renting capital. How much a  typical firm chooses to produce is closely related to how much output the economy as a whole produces.  (Indeed, the amount firms produce must add up to the amount of output in the economy as a whole.) So the overall gross rental rate–and the net rental rate–will be increasing in the amount of output the economy as a whole produces. And of course, the amount of output the economy as a whole produces is GDP, for which we will use the single letter y.  Thus, the graph below, which has GDP on the horizontal axis, and like the graph at the top of this post, shows an upward slope for the KE curve:

The KE Curve vs. the IS Curve. The IS curve has no microfoundations. The KE curve does. That is, I just explained where the KE curve comes from. The explanations of where the IS curve comes from are either incoherent, or really imply something very different from the IS curve taught in introductory and intermediate macroeconomics classes. Let me critique several ways people convince themselves the IS curve is OK. (Don’t worry if you haven’t heard of some of the interpretations I am critiquing.)

  • The consumption Euler equation as an IS curve: The consumption Euler equation is an equation about changes rather than levels. Much more seriously, the consumption Euler equation acts like some sort of IS curve only in models that don’t have investment or other durables. Investment and other durables play such a big role in economic fluctuations that it It is hard to take a model of economic fluctuations that leaves out investment and other durables seriously. Bob Barsky, Chris House and I show how big a difference it makes to sticky price models to bring in investment or other durables goods in our paper “Sticky-Price Models and Durables Goods,” which appears in the American Economic Review.
  • Q-theory as a foundation for the IS curve: Like the consumption Euler equation, Q-theory yields a dynamic equation, instead of one that can be drawn as a simple curve with output on the horizontal axis and the real interest rate on the vertical axis. Q-theory says that firms might invest now even if the interest rate is above the net rental rate as long as the level of investment is increasing over time. The reason is that it will be harder to invest later when investment is proceeding faster, so it could make sense to get a jump on things and invest now. On the other hand, firms might delay investment even if the interest rate is below the net rental rate if the level of investment is decreasing over time. The reasons is that it will be easier to invest later when investment is proceeding more slowly, so it could make sense to wait until later when investment can be done in a more leisurely way. Suppose that we show the short-run equilibrium in terms of output and the real interest rate (rather than the net rental rate) and that higher investment is associated with higher GDP, as is usually the case. Then in relation to the KE curve, what Q-theory means is that the short-run equilibrium can be above the KE curve if that equilibrium point is moving to the right (GDP is increasing along with investment), while the short-run equilibrium can be below the KE curve if the equilibrium point is moving to the left (GDP is decreasing along with investment). But the slower the equilibrium point is moving, the closer it has to be to the KE curve. So when the “short-run” lasts a long time, as it has in the last five years since the bankruptcy of Lehman Brothers, the short-run equilibrium needs to be quite close to the KE curve. I discuss how the speed with which the economy is headed toward the medium-run equilibrium affects what can be gotten out of the Q-theory story in “The Quantitative Analytics of the Basic Neomonetarist Model.”
  • Heterogeneity of investment projects as a foundation for the IS curve: Heterogeneous investment projects, with some being able to clear a high interest-rate hurdle and some only being able to clear a low-interest-rate hurdle is the traditional story for the IS curve. This is actually a very interesting story, and one my coauthors Bob Barsky, Rudi Bachmann and I have been thinking about for a project in the works, but it actually points to something much more complex than an IS curve. For example, if potential investment projects are heterogeneous, then in general, one needs to keep track of how many are still available of each type. In any case, there is nothing simple about such a story.

The MP Curve. Central banks periodically meet to determine the interest rate they will set. The rate they set is a nominal interest rate, where “nominal” just means it is the interest rate that non-economists think of. The real interest rate is the nominal interest rate minus expected inflation. Inflation expectations tend to change quite slowly and sluggishly, so the nominal interest rate the central bank chooses determines the real interest rate in the short run and the very short run. Central banks ordinarily raise their interest rate target when the economy is booming and lower it when the economy is in recession, so the interest rate (both nominal and real) will be upward sloping in output. Indeed, in order to make the economy stable, the central bank should make sure that the real interest rate goes up faster with output than the net rental rate does, so that, going from left to right, the MP curve showing how the central banks target interest rate depends on output cuts the KE curve from below, as shown in the complete KE-MP diagram:

In the KE-MP model, the intersection of the KE and MP curves is the short-run equilibrium of the economy. In short-run equilibrium, the real interest rate equals the net rental rate, or equivalently, the real interest rate equals the short-run natural interest rate.

The Ultra Short Run

What brings the economy to short-run equilibrium is the adjustment of investment based on the gap between the net rental rate determined by the KE (capital rental market equilibrium) curve and the real interest rate determined by the MP (monetary policy) curve. But it takes time for firms to adjust their investment plans. Indeed, the level of investment is unlikely to adjust much faster than existing investment projects are completed and a new round of investment projects is started, as Susanto Basu and I discuss in “Investment Planning Costs and the Effects of Fiscal and Monetary Policy.” In the meanwhile, before investment has had time to full adjust, output can be away from its short-run equilibrium level, and the interest rate determined by the MP curve can be different from the net rental rate determined by the KE curve.   

For example, suppose that the economy starts out in short-run equilibrium, but then the central bank decides to make a change in the interest rate change for some reason other than a change in the level of output. Since output is unchanged, the change in the interest rate corresponds in the KE-MP model to a shift in the MP curve. The graph below, taken from Slides for “Investment Planning Costs and the Effects of Fiscal and Monetary Policy,” shows the effects of a monetary expansion.

The movement up along the MP’ curve reflects the ultra-short-run adjustment of investment to get to the new short-run equilibrium–a process that might take about 9 months. The movement back along the unchanging KE curve reflects the short-run adjustment of prices to get back to the original (and almost unchanged) medium-run equilibrium. Since the real interest rate is on the axis, the point representing first ultra-short-run equilibrium, and then short-run equilibrium, is always on the MP curve. (The graph does not show the gradual shift of the MP curve back to return the economy to the medium-run equilibrium. One way for that adjustment of the MP curve to happen is if there is some nominal anchor in the monetary policy rule so that the level of prices matters for monetary policy, not just the rate of change of prices.)

Why It Matters: Remarks About the KE-MP Model

  1. The reason I wrote this post is because many people don’t seem to understand that low levels of output lower the net rental rate and therefore lower the short-run natural interest rate. Leaving aside other shocks to the economy, monetary policy will not tend to increase output above its current level unless the interest rate is set below the short-run natural interest rate. That means that the deeper the recession an economy is in, the lower a central bank needs to push interest rates in order to stimulate the economy. In the Q-theory modification of the KE-MP model, the belief that the economy is going to recover fast could generate extra investment even if interest rates are somewhat higher, but when such confidence is lacking, the remedy is to push interest rates below the net rental rate that is the short-run natural interest rate.
  2. As discussed in “Investment Planning Costs and the Effects of Fiscal and Monetary Policy” and the Slides for “Investment Planning Costs and the Effects of Fiscal and Monetary Policy,” fiscal policy and technology shocks have counterintuitive effects on the KE curve. This is grist for another post. Also grist for another post is the way a version of the Keynesian Cross comes into its own in the ultra short run, but only during the 9 months or so of the ultra short run.  
  3. If a country makes the mistake of having a paper currency policy that prevents it from lowering the nominal interest rate below zero, then the MP curve has to flatten out somewhere to the left. (The zero lower bound on the nominal interest rate puts a bound of minus expected inflation on the real interest rate. That makes the floor on the real interest rate higher the lower inflation is.) The lower bound on the MP curve might then make it hard to get the interest rate below the net rental rate (a.k.a. the short-run natural interest rate). In my view, this is what causes depressions. QE can help, but is much less powerful than simply changing the paper currency policy so that the nominal interest rate can be lowered below the short-run natural interest rate, however low the recession has pushed that short-run natural interest rate.  (See the links in my post “Electronic Money, the Powerpoint File” and all of my posts on my electronic money sub-blog.)

Clay Christensen, Jerome Grossman and Jason Hwang on the Three Basic Types of Business Models

In The Innovator’s Prescription, Clay Christensen, Jerome Grossman and Jason Hwang make good use of a typology of business models laid out by C. B. Stabell and Øystein Fjeldstad in their May, 1998 Strategic Management Journal article “Configuring Value for Competitive Advantage: On Chains, Shops and Networks.” Modifying Stabell and Fjeldstad’s terminology a bit for clarity, Clay and his coauthors call the three types of business models solutions shops, value-adding processes, and facilitated networks. Clay, Jerome and Jason argue that these three types of business models are so different that it is difficult to efficiently house them under one roof. They give these definitions for these three types of business models (from about location 360):

Solution Shops

These “shops” are businesses that are structured to diagnose and solve unstructured problems. Consulting firms, advertising agencies, research and development organizations, and certain law firms fall into this category. Solution shops deliver value primarily through the people they employ—experts who draw upon their intuition and analytical and problem-solving skills to diagnose the cause of complicated problems. After diagnosis, these experts recommend solutions. Because diagnosing the cause of complex problems and devising workable solutions has such high subsequent leverage, customers typically are willing to pay very high prices for the services of the professionals in solution shops. 

The diagnostic work performed in general hospitals and in some specialist physicians’ practices are solution shops of sorts. …

Value-Adding Processes

Organizations with value-adding process business models take in incomplete or broken things and then transform them into more complete outputs of higher value. Retailing, restaurants, automobile manufacturing, petroleum refining, and the work of many educational institutions are examples of VAP businesses. Some VAP organizations are highly efficient and consistent, while others are less so.

Many medical procedures that occur after a definitive diagnosis has been made are value-adding process activities….

Facilitated Networks

These are enterprises in which people exchange things with one another. Mutual insurance companies are facilitators of networks: customers deposit their premiums into the pool, and they take claims out of it. Participants in telecommunications networks send and receive calls and data among themselves; eBay and craigslist are network businesses. In this type of business, the companies that make money tend to be those that facilitate the effective operation of the network. They typically make money through membership or user fees.

Networks can also be an effective business model for the care of many chronic illnesses that rely heavily on modifications in patient behavior for successful treatment. Until recently, however, there have been few facilitated network businesses to address this growing portion of the world’s health-care burden. …

Clay, Jerome and Jason’s central idea is that medicine will be more efficient if there is one medical institution designed for inherently expensive “solution shop” activities such as difficult diagnoses, other much more convenient and inexpensive clinics for the routine treatment of well-diagnosed diseases, and online networks for patients to discuss their contribution as patients to disease management with others who have the same disease. What wouldn’t survive would be the current hospital model where the solution shop aspect of what they do confers high expense on many other activities that don’t have to be so expensive. Here is the way Clay, Jerome and Jason say it:

The two dominant provider institutions in health care—general hospitals and physicians’ practices—emerged originally as solution shops. But over time they have mixed in value-adding process and facilitated network activities as well. This has resulted in complex, confused institutions in which much of the cost is spent in overhead activities, rather than in direct patient care. For each to function properly, these business models must be separated in as “pure” a way as possible.

This is not just a matter of static efficiency:

The health-care system has trapped many disruption-enabling technologies in high-cost institutions that have conflated two and often three business models under the same roof. The situation screams for business model innovation. The first wave of innovation must separate different business models into separate institutions whose resources, processes, and profit models are matched to the nature and degree of precision by which the disease is understood. Solution shops need to become focused so they can deliver and price the services of intuitive medicine accurately. Focused value-adding process hospitals need to absorb those procedures that general hospitals have historically performed after definitive diagnosis. And facilitated networks need to be cultivated to manage the care of many behavior-dependent chronic diseases. Solution shops and VAP hospitals can be created as hospitals-within-hospitals if done correctly.

Further Musings: Even apart from this application to health care, I have found the typology of solution shop, value-adding process and facilitated network very interesting to think about for understanding my own work life (as a complement to the kind of analysis I talked about in my post “Prioritization”).  

I work at the University of Michigan. Universities combine research–which is quintessentially a solution shop activity–with teaching, which has a big component of value-adding processes. And of course, Tumblr, Twitter and Facebook, where I put in effort as a blogger, are facilitated networks.

The idea of a value-adding process highlights the gains to be had from routinizing something. It is good to periodically ask oneself if there is anything in my daily activities that I can make more routine and streamlined.  

The idea of a facilitated network highlights the gains to be had by having users do a lot of the work. That in turn is related both to the benefits of laissez faire under a decent system of rules and the idea of delegation, which typically involves giving up some control at the detailed level.  

I find for me, however, that I love the “solution-shop” aspect of life so much that I think I resist routinization. I don’t know if this is what I should be doing, but I would rather keep thinking about how I am doing things than have everything fade into the background of routine. That does cost me extra time, as I do things inefficiently because I am thinking too much about them as I do them.  

Here is a link to a sub-blog of all of my posts tagged as being about Clay Christensen’s work

Rich People Who Believe in Behavioral Economics

From Harvard Magazine, July-August 2014:

… the [Harvard] Faculty of Arts and Sciences disclosed a $17-million donation from the Pershing Square Foundation–founded by Bill (William A.) Ackman ‘88, M.B.A. '92, CEO of the Pershing Square Capital Management hedge fund, and Karen Ackman, M.L.A. '93–for a “foundation of human behavior” initiative grounded in behavioral economics and other disciplines. That gift provides for three new professorships and a research fund.

Math Camp in a Barn

Image created by Miles Spencer Kimball. I hereby give permission to use this image for anything whatsoever, as long as that use includes a link to this post. For example, t-shirts with this picture (among other things) and http://blog.supplysidelibe…

Image created by Miles Spencer Kimball. I hereby give permission to use this image for anything whatsoever, as long as that use includes a link to this post. For example, t-shirts with this picture (among other things) and http://blog.supplysideliberal.com/post/92400376217/math-camp-in-a-barn on them would be great! :)

I like Naomi Schefer Riley’s account in the Wall Street Journal of Ben Chavis’s math camp in North Carolina’s poorest county: “Math Camp in a Barn: Intensive Instruction, No-Nonsense Discipline” (googling the title of a Wall Street Journal article jumps over the paywall, so my link is to the search page). Naomi’s article illustrates two related principles I have written about. First, almost anyone can learn math with enough hard work and a can-do attitude, as Noah Smith and I write in “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t.” Second, a key element of learning is simply time spent learning, as I write about in “Magic Ingredient 1: More K-12 School.” Lengthening the school year is one of the most straightforward ways to increase learning, especially in hard subjects. Naomi points out the arithmetic of math instruction: 

From 8:30 a.m. to 4 p.m. Monday through Friday the children learn math, interspersed with some reading, physical education and lunch. Each gets 120 hours of instruction during the three weeks, equivalent to what they would get in a year at a typical public school.

Among many other serious problems with education in the United States, our attachment to the idea of summer vacation is an important one.

John Stuart Mill's Rejection of Anarcho-Capitalism

The Anarcho-Capitalism of Murray Rothbard does not recognize the legitimacy of taxation even to fund police protection. John Stuart Mill has a broader view of what a state can legitimately do. In On Liberty, Chapter IV, “Of the Limits to the Authority of Society over the Individual” paragraphs 1-3, he writes:

What, then, is the rightful limit to the sovereignty of the individual over himself? Where does the authority of society begin? How much of human life should be assigned to individuality, and how much to society?

Each will receive its proper share, if each has that which more particularly concerns it. To individuality should belong the part of life in which it is chiefly the individual that is interested; to society, the part which chiefly interests society.

Though society is not founded on a contract, and though no good purpose is answered by inventing a contract in order to deduce social obligations from it, every one who receives the protection of society owes a return for the benefit, and the fact of living in society renders it indispensable that each should be bound to observe a certain line of conduct towards the rest. This conduct consists first, in not injuring the interests of one another; or rather certain interests, which, either by express legal provision or by tacit understanding, ought to be considered as rights; and secondly, in each person’s bearing his share (to be fixed on some equitable principle) of the labours and sacrifices incurred for defending the society or its members from injury and molestation. These conditions society is justified in enforcing at all costs to those who endeavour to withhold fulfilment. Nor is this all that society may do. The acts of an individual may be hurtful to others, or wanting in due consideration for their welfare, without going the length of violating any of their constituted rights. The offender may then be justly punished by opinion, though not by law.

John’s argument that “every one who receives the protection of society owes a return for the benefit” is one that Elizabeth Warren has been echoing to argue for the legitimacy of taxation to support a wide range of government activities. E. J. Dionne’s review of her book A Fighting Chance in the Washington Post offers these quotations from the book:

1. “There is nobody in this country who got rich on his own,” she said. “Nobody. You built a factory out there? Good for you. But I want to be clear: You moved your goods to market on the roads the rest of us paid for. You hired workers the rest of us paid to educate. You were safe in your factory because of police forces and fire forces that the rest of us paid for.” …

2. “There’s nothing pro-business about crumbling roads and bridges or a power grid that can’t keep up,” she writes. “There’s nothing pro-business about cutting back on scientific research at a time when our businesses need innovation more than ever. There’s nothing pro-business about chopping education opportunities when workers need better training.”

Although her specific examples of government action in these quotations sound fairly benign, the way Elizabeth is using the argument that "every one who receives the protection of society owes a return for the benefit" does not provide any obvious principle for putting a bound on what the government can legitimately raise taxes for. I suspect that, if magically revived in the modern world, John Stuart Mill would argue for a more limited government than the one Elizabeth Warren advocates. (And it is clear from the passage in On Liberty quoted above that he would not go along with her invocation of a “social contract.”)

Count to ten when a plane goes down... →

John Beck is a friend of mine from middle school and high school. At the link above, he tells this story of Korean Airlines flight 007, which may have lessons for today. 

Just a little under 31 years ago, I played a key role in a conspiracy theory that grew up around a passenger plane downed by a Russian missile. Trust me, I did not mean to be involved. …

Update: Quartz picked this blog post up here.

Bruce Bartlett on Access to Research Results

Bruce Bartlett, who also appears in the post “Bruce Bartlett on Careers in Economics and Related Fields” gave this reaction to my presentation “On the Future of the Economics Blogosphere”:

I think you missed an opportunity to criticize academic journals for excessive cost and severe paywall constraints. The inability of many readers to access the underlying research is a major problem for blogs to advance serious debate. While in many cases, working paper versions can be located, this applies to only a fraction of the research that is out there. You should criticize academics who don’t post their work in places like SSRN or on personal web sites. My understanding is that unless you literally sign away your rights, you have the right to post your own work on your own web site.

In other words, each of us who produces published research has a lot of discretion to make the results of our research available inexpensively. Let’s do it.

Clay Christensen, Jerome Grossman and Jason Hwang on Intuitive Medicine vs. Precision Medicine

I found the passage below from The Innovator’s Prescription (location 333), by Clay Christensen, Jerome Grossman and Jason Hwang especially insightful. It puts diagnosis at the center of medicine, especially when viewing medicine from a business point of view. Better and better diagnosis opens up the possibility of more cost-efficient treatments for those diseases that are precisely identified. But that possibility must be seized.

Our bodies have a limited vocabulary to draw upon when they need to express that something is wrong. The vocabulary is comprised of physical symptoms, and there aren’t nearly enough symptoms to go around for all of the diseases that exist—so diseases essentially have to share symptoms. When a disease is only diagnosed by physical symptoms, therefore, a rules-based therapy for that diagnosis is typically impossible—because the symptom is typically just an umbrella manifestation of any one of a number of distinctly different disorders.

The technological enablers of disruption in health care are those that provide the ability to precisely diagnose by the cause of a patient’s condition, rather than by physical symptom. These technologies include molecular diagnostics, diagnostic imaging technology, and ubiquitous telecommunication. When precise diagnosis isn’t possible, then treatment must be provided through what we call intuitive medicine, where highly trained and expensive professionals solve medical problems through intuitive experimentation and pattern recognition. As these patterns become clearer, care evolves into the realm of evidence-based medicine, or empirical medicine—where data are amassed to show that certain ways of treating patients are, on average, better than others. Only when diseases are diagnosed precisely, however, can therapy that is predictably effective for each patient be developed and standardized. We term this domain precision medicine.

… disruption-enabling diagnostic technologies long ago shifted the care of most infectious diseases from intuitive medicine (when diseases were given labels such as “consumption”) to the realm of precision medicine (where they can be defined as precisely as different types of infection, different categories of lung disease, and so on). To the extent that we know what type of bacterium, virus, or parasite causes one of these diseases—and when we know the mechanism by which the infection propagates—predictably effective therapies can be developed—therapies that address the cause, not just the symptom. As a result, nurses can now provide care for many infectious diseases, and patients with these diseases rarely require hospitalization. Diagnostics technologies are enabling similar transformations, disease by disease, for families of much more complicated conditions that historically have been lumped into categories we have called cancer, hypertension, Type II diabetes, asthma, and so on.

When I was a kid, we talked about “curing cancer” as the prototypical world-shaking accomplishment. The reason there is no one “cure for cancer” is that cancer is not one disease but hundreds of different diseases involving different genes going awry in the direction of too much growth. A cure needs to be found for each one of those diseases in order for there to be a cure for the amorphous notion of “cancer.” Many of these diseases have been cured and others are well on their way to being cured. But other diseases under the general heading of “cancer” have not even been identified yet (in the sense of carefully distinguishing them from other diseases with similar symptoms). Once they have been identified at the level of the particular gene that goes awry to produce that particular disease, they will be halfway to being cured.

The term “personalized medicine” is sometimes used for what I would call “treating the disease someone actually has instead of some other disease.” A better phrase for that is the phrase Clay, Jerome and Jason use: “precision medicine.”