Results for “solow” 90 found
Teaching the Solow Model
The Solow model is a foundational model for understanding economic growth. Yet it’s typically not taught to principles students because it’s considered too difficult. In Modern Principles, however, Tyler and I develop a super simple version of the model that is fun to teach and accessible to students of all levels. I’ll be talking about the Super Simple Solow model in a short webinar tomorrow (Tuesday March 26) at 1pm est. Register here.
Bob Solow, RIP
Here is Alex’s MRU video on the Solow model, one of the best things Alex has done, on the best thing Solow did. Here are previous MR mentions of Solow.
Robert Solow on the future of leisure
…there is no logical or physical reason that the work year of a machine should not actually increase, say. But it would seem more likely that increased leisure over the next century should be accompanied by a smaller stock of capital (per worker), smaller gross investment (per worker), and thus a larger share of consumption in GDP. Of course, this tendency will almost certainly be offset by an ongoing increase in capital intensity, even in the service sector. Obviously there are other, totally moot, considerations. Will leisure time activities be especially capital intensive (grandiose hotels, enormous cruise ships) or the opposite (growing marigolds, reading poetry)? Show me an economist with a strong opinion about these things, and I will show you that oxymoron: a daredevil economist.
Of course if you really do think the capital-labor ratio will be falling, investment behavior is going to disappoint for a long time to come. The shift to intangible capital will strengthen that tendency all the more.
p.s. Leisure will become especially capital-intensive, at least in the United States.
Here is the full essay, from a few years ago, but I think new on-line, and from this MIT Press book of collected essays, now forthcoming in paperback.
Georgescu-Roegen vs. Henry George vs. Wakefield vs. Solow
For Georgescu-Roegen, the ultimate fixed factor is the laws of physics, due to entropy. Economic systems cannot receive an ongoing influx of both energy and matter indefinitely, and so eventually they reach limits to growth. At that margin substitutability breaks down and catastrophe ensues. To check this outcome, we must find a way to live with slower rates of economic growth, and eventually a zero or negative rate of economic growth. For him this is as much a criticism of Marxism as of capitalism, and he wrote about making do with agrarianism. Consistent with this view, his consumer theory portrayed wants as hierarchical rather than smoothly substitutable. He would have liked this Alex post on not all gdp being created equal.
For Henry George, the ultimate fixed factor is land, due to the nature of space. There is always enough energy, due to Julian Simon-like arguments that allow capital and ingenuity to be substituted for all other fixed resources, except for land. Economic systems cannot create or activate more land indefinitely, and thus the marginal benefits of growth are captured mostly by landowners, to the detriment of social welfare. At this final margin substitutability breaks down and widespread poverty ensues. To check this outcome, the returns to land must be redistributed to the rest of society, ideally through a single tax. Unlike many environmentalists, he wasn’t worried about soil erosion because land is land.
For 19th century colonial theorist Edward Gibbon Wakefield, human beings and the positive externalities from human contact are the ultimate scarcity. If you let people settle the countryside, you will have an underpopulated republic of deplorables — there is no substitute for city life! So the price of external farm land has to be kept high, so that settlers cluster in the city and as wage laborers contribute to ongoing innovation, urbanity, and economic growth. Wakefield worked in New Zealand — did they listen? If Wakefield were around today, maybe he would want to cut off broadband to large swathes of the Midwest and Appalachia. Justly or not, he cited rural French Canadians as an example of what he was worried about, whereas Georgescu-Roegen might have appreciated their agrarianism.
For Robert Solow, ultimate fixed factors do not come into play and substitutability reigns at all relevant margins. If some resources become scarce, just substitute in more capital. Growth continues forever, though it can be accelerated by investing more in the ultimate growth driver, namely new ideas. Georgescu-Roegen argued that Solow did not incorporate the idea of entropy or insights from science.
Is it proper that Solow’s model should have so dominated in the economics profession?
You cannot understand or evaluate environmentalism without revisiting these debates. One reason many environmental critiques do not seem so strong is that they are trying to measure costs in a Solow-like framework, when in fact the underlying model might involve core non-substitutabilities, a’la the other thinkers. Unless you stress how not all gdp is created equal, the costs of bad environmental outcomes won’t show up as very high, not relative to total wealth. It will appear as if you always can substitute away from bearing those costs full on, even though perhaps you cannot.
My own view is that the ultimate scarcity in today’s system comes from what the political economy of our societies and polities can bear, but that must await another day.
The Solow Model and Ideas
The fifth video in the Solow series from our Principles of Macroeconomics course is really the capstone. It explains how ideas drive growth on the cutting edge. A key insight of the model, however–one which many people still don’t really get–is that ideas increase output and by doing so they also drive capital accumulation so both forces are always at play.
The Solow Model Animated!
Modern Principles of Economics was the first principles textbook to make the Solow model of economic growth easily accessible to undergraduates. By focusing on simple mathematics that the students already know, like the square root function, we made the Solow model easy to understand without losing the power of the model to explain the world.
Modern Principles is the only textbook with the Super Simple Solow model! And now we’ve brought the model to life with a series of fun videos in our Principles of Macroeconomics class at MRUniversity. You’ve never seen the Solow model taught like this!
Introduction to the Solow Model introduces the questions and the “characters” that drive the story. Physical capital and diminishing returns explains the idea of a production function and diminishing returns. We then introduce capital depreciation and focus in on the most important idea for understanding the Solow model, the steady state:
I’ll cover some more videos in the Solow series later this week.
Is Chinese economic growth Solow catch-up growth?
Forget about the current troubles, or for that matter the current innovations, I’m talking about the earlier golden years. It seems obvious to many people that Chinese growth is Solow-like catch-up growth, as the country was applying already-introduced technologies to its development.
But how many other economies have grown at about ten percent for so long? Was there not a secret ingredient added to the mix?
Increasing returns to scale? Understanding the importance of having networks which allow an employer to assemble so many engineers so quickly for a new project? Something about Communist Party governance which enabled the corruption to be channeled productively into building more infrastructure rather than holding up progress? Tiger Mom parenting combined with a relatively meritocratic exam system?
I do not find it unreasonable to postulate that two to three percentage points of that yearly growth were in fact due to innovation and increasing returns to scale in some manner. Note that most of these innovations are useful only at China’s (previous) ppf and they are less valuable to the West, or perhaps simply not transferable.
More radically, is there some “natural,” culture-neutral rate at which innovations trickle down from the world leaders to the poorer countries? The diversity of growth rates would seem to indicate not. Is each country then not innovating — with varying degrees of success — by building its culture-specific net for catching and transmitting global innovations throughout the nation?
In which case we are back to catch-up growth not being entirely well-defined.
Livestream of Solow and DeLong vs. Cowen and Roberts debate on Piketty
Friday, 1:15, EST. The LiveStream is here. I commend the Center for Equitable Growth for sponsoring this event.
Piketty v. Solow
Krusell and Smith lay out the Solow and Piketty growth models very nicely but perhaps not in a way that is immediately transparent if you are not already familiar with growth models. Thus, in this note I want to lay out the differences using the Super Simple Solow model that Tyler and I developed in our textbook. The Super Simple Solow model has no labor growth and no technological growth. Investment, I, is equal to a constant fraction of output, Y, written I=sY.
Capital depreciates–machines break, tools rust, roads develop potholes. We write D(epreciation)=dK where d is the rate of depreciation and K is the capital stock.
Now the model is very simple. If I>D then capital accumulates and the economy grows. If I<D then the economy shrinks. Steady state is when I=D, i.e. when we are investing just enough each period to repair and maintain the existing capital stock.
Steady state is thus when sY=dK so we can solve for the steady state ratio of capital to output as K/Y=s/d. I told you it was simple.
Now let’s go to Piketty’s model which defines output and savings in a non-standard way (net of depreciation) but when written in the standard way Piketty’s saving assumption is that I=dK + s(Y-dK). What this means is that people look around and they see a bunch of potholes and before consuming or doing anything else they fill the potholes, that’s dK. (If you have driven around the United States recently you may already be questioning Piketty’s assumption.) After the potholes have been filled people save in addition a constant proportion of the remaining output, s(Y-dk), where s is now the Piketty savings rate.
Steady state is found exactly as before, when I=D, i.e. dK+s(Y-dK)=dK or sY=sdK which gives us the steady level of capital to output of K/Y=s/(s d).
Now we have two similar looking expressions for K/Y, namely s/d for Solow and s/(s d) for Piketty. We can’t yet test which is correct because nothing requires that the two savings rates be the same. To get further suppose that we now allow Y to grow at rate g holding K constant, that is over time because of better technology we get more Y per unit of K. Since Y will be larger the intuition is that the equilibrium K/Y ratio will be lower, holding all else the same. And indeed when you run through the math (hand waving here) you get expressions for the Solow and Piketty K/Y ratios of s/(g+d) and s/(g+sd) respectively, i.e. a simple addition of g to the denominator in both cases (again bear in mind that the two s’s are different.)
We can now see what the models predict when g changes–this is a key question because Piketty argues that a fall in g (which he predicts) will greatly increase K/Y. Here is a table showing how K/Y changes with g in the two models. I assume for both models that d=.05, for Solow I have assumed s=.3 and for Piketty I have calibrated so that the two models produce the same K/Y ratio of 3.75 when g=.03 this gives us a Piketty s=.138.
As g falls Piketty predicts a much bigger increase in the K/Y ratio than does Solow. In Piketty’s model as g falls from .03 to .01 the capital to output ratio more than doubles! In the Solow model, in contrast, the capital to output ratio increases by only a third. Remember that in Piketty it’s the higher capital stock plus a more or less constant r that generates the massive increase in income inequality from capital that he is predicting. Thus, the savings assumption is critical.
I’ve already suggested one reason why Piketty’s saving assumption seems too strong–Piketty’s assumption amounts to a very strong belief that we will always replace depreciating capital first. Another way to see this is to ask where does the extra capital come from in the Piketty model compared to Solow? Well the flip side is that Solow predicts more consumption than Piketty does. In fact, as g falls in the Piketty model so does the consumption to output ratio. In short, to get Piketty’s behavior in the Solow model we would need the Solow savings rate to increase as growth falls.
Krusell and Smith take this analysis a few steps further by showing that Piketty’s assumptions about s are not consistent with standard maximizing behavior (i.e. in a model in which s is allowed to vary to maximize utility) nor do they appear consistent with US data over the last 50 years. Neither test is definitive but both indicate that to accept the Piketty model you have to abandon Solow and place some pretty big bets on a non-standard assumption about savings behavior.
Robert Solow on Hayek and Friedman and MPS
The TNR essay is here, prompted by the publication of Angus Burgin’s The Great Persuasion: Reinventing Free Markets Since the Great Depression. Excerpt:
The MPS was no more influential inside the economics profession. There were no publications to be discussed. The American membership was apparently limited to economists of the Chicago School and its scattered university outposts, plus a few transplanted Europeans. “Some of my best friends” belonged. There was, of course, continuing research and debate among economists on the good and bad properties of competitive and noncompetitive markets, and the capacities and limitations of corrective regulation. But these would have gone on in the same way had the MPS not existed. It has to be remembered that academic economists were never optimistic about central planning. Even discussion about the economics of some conceivable socialism usually took the form of devising institutions and rules of behavior that would make a socialist economy function like a competitive market economy (perhaps more like one than any real-world market economy does). Maybe the main function of the MPS was to maintain the morale of the free-market fellowship.
Solow neglects to mention that Milton Friedman turned out to be right on most of the issues he discussed (though targeting money doesn’t work), that MPS economists shaped at least two decades of major and indeed beneficial economic reforms across the world, or that some number of the economists at MIT envied the growth performance of the Soviet Union and that such remarks were found in the most popular economics textbook in the profession. You can consider this essay a highly selective, error-laden, and disappointing account of a topic which could in fact use more serious scrutiny.
By the way, if you read Solow’s own 1962 review of Maurice Dobb on economic planning (JSTOR gate), it shows very little understanding of Hayek’s central points on these topics, which by then were decades old. Arguably it shows “negative understanding” of Hayek.
Or to see how important Friedman’s work on money and also expectations was, try comparing it with…um…the Solow and Samuelson 1960 piece on the Phillips Curve (JSTOR), which Friedman pretty much refuted point by point. Here is the closing two sentences of that piece:
We have not here entered upon the important question of what feasible institutional reforms might be introduced to lessen the degree of disharmony between full employment and price stability.These could of course involve such wide-ranging issues as direct price and wage controls, antiunion and antitrust legislation, and a host of other measures hopefully designed to move the American Phillips’ curves downward and to the left.
And Solow wonders why the Mont Pelerin Society and monetarism were needed. Solow should have started his piece with a sentence like “Milton Friedman was not right about everything, but most of his criticisms of my earlier views have been upheld by subsequent economic theory and practice….”
Greg Ransom…telephone!
For the pointer I thank Peter Boettke.
The Solow Model
The Solow Model is a workhorse model of economic growth. Many subsequent papers in growth theory and in business cycle theory build on this model. A model of growth helps us to structure our thinking. Why is it, for example, that China is growing faster than the United States despite having much poorer institutions such as the rule of law? Surprisingly, even a simple version of the Solow model offers some useful predictions and ways to interpret aspects of the the growth data. At MRUniversity this week we have four videos on the Solow model. These videos are a bit more technical than many of our previous videos and we think they will be useful in many other classes such as macroeconomics, especially if you are using a truly excellent textbook. The videos will also be useful for anyone who wants to read more of the literature on growth theory or the empirics of growth (such as can be found, for example, in Barro and Sala-i-Martin’s Economic Growth or David Weil’s textbook Economic Growth). Even if you don’t want to study the theory in more depth, we think these videos will be useful for understanding development and how economists use theory and data to understand the sources of growth (and its absence).
Good thing he didn’t ask Alex to explain the Solow growth model (in French)
He asked an Air Canada fight attendant for 7Up and he got Sprite.
“I’m a little bit disappointed with the lower amount awarded,” Thibodeau said. “But the positive note is that the court recognized our rights were violated on several occasions.”
…So, in 2009, when Thibodeau ordered a 7Up in French, and the English-speaking attendant brought him a — gasp! — different brand of lemon-lime soda, he sued.
“If I take a flight and I’m not served in the language of my choice, and I don’t do anything about it, then my right is basically dead,” Thibodeau told The Globe and Mail. “I was not asking for anything other than what I was already entitled to. I have a right to be served in French.”
It’s a right that Thibodeau — who is a federal employee and happens to speak perfect English — takes very, very seriously.
The full story is here. I suppose one could make a living this way. Which are the French questions most likely to be misunderstood by an English-speaking Canadian? From another article:
It is Thibodeau’s second successful legal action against the airline and its subsidiaries. In 2000, he was refused service in French when he tried to order a 7Up from a unilingual English flight attendant on an Air Ontario flight from Montreal to Ottawa.
Thibodeau filed suit in Federal Court for $525,000 in damages. The court upheld his complaint, ordered the airline to make a formal apology and pay him $5,375.95. Thibodeau was later honoured by the French-language rights group, Imperatif Francais.
For the pointers I thank Graham Rowe. Alex and I explain the Solow growth model — in English — here. Chinese, Spanish, and other editions are on the way.
The Solow Model with Mathematica
In Modern Principles Tyler and I explain the Solow model of economic growth and show how the model can easily be run using Excel. I have also written a fun Mathematica demonstration of the Solow model.
You can see a quick animation of what the demonstration does by clicking "watch web preview" at the link above but anyone can also run the demo interactively by downloading a free copy of Mathematica Player. The Player is actually a stripped down version of Mathematica so what you see in the demo is not an animation but a computation of the equilibrium on the fly. Many of the other demonstrations in science, math, economics and other fields are also of interest.
Solow on Schumpeter
Mark Thoma offers some excerpts. I should note that the TNR web-site still refuses to let me — a paid subscriber — in.
Addendum: This link now seems to be working for all.
Saturday assorted links
1. Interview with Mark Dybul about PEPFAR.
2. Women’s tears! Worth a sniff?
3. Macmillan Learning spotlight on Tyler Cowen. Excerpt: “I’ve been working with Alex for over 33 years,” Dr. Cowen said, “and after all of those years, I can still speak about him with affection in my voice.”
4. AI-written novel wins Chinese science fiction prize.
5. “Argentina is one of the most regulated countries in the world and has gotten worse over time. On regulation, it has fallen to a rank of 143 out of 165 countries in the Human Freedom Index.” Link here.
7. Cass Sunstein on free speech on campus. And Cass on Knightian uncertainty.