No Bubble #2

An old paper from Greg Mankiw and David Weil, "The Baby Boom, The Baby Bust, and the Housing Market" (1989) offers one possible reason for the transitions we've seen in housing prices: an anticipated baby boom.  The paper offers nice depictions in dynamics that Corrections wishes were present in more papers.  If the boom is transitory, we have supply and demand temporarily moving and falling back down along the same supply curve (click to enlarge)

Or, offers a graph that might be informative about our current housing issues: what would happen to housing prices in a forward-looking and a naïve world under a baby boom (click to enlarge):

Look familiar? (In shape, not in magnitude!)  Almost like a partially-anticipated, rational boom that dissipated when the state of the world turned out to be different.

Bridging the achievement gap

Los Angeles Times opinion editorial "Bridging the achievement gap" (September 22nd, 2010) discusses the achievement gap between black males and all other students (black females and white males being the primary groups of comparison). It speaks only of educational means to fix the graduation gap, while discussing crime. Corrections would like to entertain a different possibility that might help solve both. The Times also confuses correlation and causation.

These disparities aren't new — the Schott report could have been published a generation ago. What is new and noteworthy is solid evidence that this gap can be bridged, with well-tested approaches that don't require massive changes in public education and don't depend on superhero teachers and administrators.

An economic idea might be that individuals, both black and white, make decisions about education today based on what they believe their income differentials will be tomorrow. One way to encourage education is to ensure higher wages for the educated. Another is to ensure lower wages for the uneducated.

The Times suggests that some of these students might be on the "prison track." "All too often they're on what educators privately dub 'the prison track.'"

If the Times is concerned that black males (or, for that matter, individuals of any race or gender) are opting out of educations and into lives of crime, one way of reducing their involvement in crime and increasing their graduation rates might be to lower their future wages as criminals.

We do a quick back-of-the-envelope calculation to test this hypothesis. We should see a correlation between an increase in law enforcement officers tomorrow and an increase in graduation rates. For the 50 states from 1998-2003, we plot the two, and offer a fitted least squares line. This is displayed graphically below (click to enlarge).
The relationship is indeed positive, which is itself phenomenal. If high schoolers were myopic and unresponsive to future police presence, we would have expected a drop in graduation rates to result in an increase in police next period--an increase in bad high school students should make more police next period a necessity. The fact that we see this indicates that the difference between our two effects is rather large. At a first glance, while the relationship is only near significant, it would appear tantalizing. For those concerned about the outliers, the relationship remains positive dropping them from a fixed effects panel data regression.

The Times discusses young black males, their graduation rates, and crime. Following our above analysis, we might think that a way to increase the graduation rates of young black males (who head into crime at higher rates than young white men or young black women) might be to decrease their wage differential between crime and legitimate employment through the hiring of more law enforcement officials over the course of several years. This would have the added effect of decreasing crime. Indeed, if individuals are forward looking and we have a believable commitment mechanism, we needn't wait to see the effects.

Clearly the analysis Corrections provides is both preliminary and inconclusive--it is merely suggestive. Nevertheless, it offers an interesting avenue to improve education by rational forward-looking individuals of all races and genders.

Beyond this discussion of heterogeneous impacts by race of an increase in future police presence on future crime and graduation rates, we might also add a particularly offensive quote by the Times:

A large-scale study in Chicago found that 74% of the boys who attended preschool graduated from high school, compared with 57% of those who didn't.

This is a correlation. It is not clearly causal.

3-D girl a reminder for B.C. drivers in school zone

Toronto Star article "3-D girl a reminder for B.C. drivers in school zone" (September 9th, 2010) describes the decision of Vancouver officials to put an optical illusion of a girl playing in the road to slow drivers down. Corrections thinks this is a mistake.

The visual image of the girl is believed to be the first time a child is being used to drive home the message of the dangers in excessive speeding. In 2008, the city of Philadelphia began using virtual images of fake speed humps of white, blue and orange triangles to get drivers there to slow down.

Vancouver officials are "crying wolf." The lesson to be learned from hyperinflation or the story of the boy who cried wolf is rational expectations. Individuals are not fooled over the long run. Drivers get a signal of a child playing in the road. They then make a decision on whether or not to slow down, and if so by how much. Normally, the stronger the signal the more a driver would break. By "muddying" the signal by making it unclear whether or not it is a trick or a real child, drivers are rationally less likely to slow down. This, in turn, is likely to be a mistake.

Depicted graphically below is the ordinary relationship between signals of kids playing (balls in the street, summer days, hockey nets in garage ways) and the likelihood that kids are actually playing--that they are going to rapidly dart out into the street from behind a car, or are in the street playing already (click to enlarge).

Vancouver's optical illusions change that relationship by making strong signals mean less (click to enlarge).

Consequently, drivers break less when their signal means less--when the cry of "wolf" is less likely to yield a wolf (click to enlarge). The blue line indicates the original regime, the red line indicates the new regime, and the mixed line is the two lines overlapping.


Corrections notes that this is our own application of the "Lucas Critique" to almost all "behavioralist" policy advisements. Too often policy is suggested by small-scale experiments, when macro conditions change, given the adoption of certain policies. While experimentation yields valuable results, its generalizability outside the localized field (in which the policy it is testing has not been adopted) should always be in question.

What if the end isn't near?

USA Today article "What if the end isn't near?" (August 23rd, 2010) discusses a large subpopulation in America that ostensibly believes that the Second Coming of Christ will occur within the next forty years. The article is deeply concerned about this and its effects on public policy (e.g. if Nuclear Disarmament or Global Warming are long-term threats, we need spend resources on them, as the world ends before they become problems).

A new poll from the Pew Research Center for the People and the Press finds that roughly four in 10 Americans believe the Second Coming will happen by 2050.

and

Thankfully, Wigg-Stevenson and many new-breed evangelicals like him are refusing the kind of end-times bait that lets believers off the hook — off the hook of inspired social action that can make their faith a powerful blessing to their society and their time.

Corrections, from its own a priori beliefs, finds this statistic difficult to believe. The proper economic method for discerning beliefs is to watch what individuals do, not what they say. Our a priori beliefs are so strong that Corrections suggests that individual economic activity simply doesn't match up with these beliefs--people are professing things to pollsters that they don't believe.Corrections ventures out of its area of expertise into christian eschatology to understand this poll figure. Any corrections are welcome; the purpose here is just to get a grasp on what individuals might believe, as various interpretations impact economic behavior.There are five important events or periods that are relevant to the Christian End Times: 1) The First Coming, 2) Tribulation 3) The Second Coming 4) The Millenial Reign 5) The Last Judgement.

1. The First Coming kicks off the sequence of events, bounding the sequence of events and marking the beginning of the "countdown".
2. The Tribulation is a period of time after the Rapture (taking of Christians to Heaven, and their disappearance on Earth). In this period of time, for many, the Four Horsemen of the Apocalypse come, many individuals die.
3. The Second Coming is the arrival of Christ on earth.
4. The Millennial Reign is the Thousand-Year Reign of Christ before Judgement Day.
5. Judgement Day is the point at which all economic activity ceases (e.g. August 29, 1997 as Judgement Day would signal the cessation of all economic activity, as individuals are separated into good and bad, and sent to the afterlife).

First, we stipulate all individuals believing in the Second Coming are Christians. In our understanding, there are several ways to interpret "The Millennium," mentioned in the bible before the Last Judgement (after which we suppose all economic activity to cease). These beliefs can be broken down into two categories and two sub-categories within those.The first is Premillennialism, which includes both Post-tribulational Premillennialism and Pre-tribulational Premillenialism. These believers hold that there is economic activity after the Second Coming--that the Second Coming occurs before the Millennial Reign.

In this case, these individuals do not believe that economic activity will cease upon the second coming. (Though Pre-tribulational Premillennialists may believe that the rapture will remove them or others from economic activity upon the Second Coming. Neither of these allows for the end of the world before 2040, requiring at least a Millennial Reign.

The second category are individuals who believe the Second Coming and the Last Judgement will be concurrent--in this case, all economic activity ceases. Included in this are Postmillennialists and Amillennialists, the former thinking that the Millennial Reign will occur before the Second Coming (and may have been happening for some time) and Amillennialists believing that the Bible only refers to a "symbolic" Millennial Regin. Both allow for the end of the world to occur in or before 2040.In any case, the article can only be concerning itself, as far as Corrections can see, with Postmillennialists and Amillennialists, as it would be difficult for either Premillenialists to believe the Second Coming will happen, due to the requirement of the Millennial Reign which has not happened--these people should still be willing to invest in their futures or their children's futures, as the Second Coming may happen in 2040, the world doesn't end.

Do people act as if the world will end by 2040 rather than at an indeterminate time? Corrections suggests not. To understand why, we merely need to understand that individuals would have starkly different consumption patterns. To understand why, take two individuals, starting out with the same consumable resource. They enjoy consuming it, but given they don't consume it, it grows or reproduces at some rate. An example of this might be any animal herding, or saving money (which grows at the real interest rate). Individuals are impatient, but also want to smooth consumption. One individual believes in an infinite-horizon world, where they save for themselves and future generations. Another believes the world will end in forty periods. How would their consumption patterns look? We solve the dynamic programming problem for when to sell a herd stock for both individuals. Their stock of animals and number of animals sold is displayed graphically below (click to enlarge):


As one can see, savings and consumption patters are starkly different in the two groups quite quickly--people who have dynastic preferences and solve an infinite-horizon problem (or something approximating it) are able to take advantage of exponential growth in a way that finite-horizoned individuals cannot. The question is whether or not we see this sort of behavior among the 40% of the population the Pew Research Center claims. It is also worth noting that the difference seen would be enlarged further by any comparison before today's date (we assume the same resources today--were individuals to have started with the same resources five years ago, a difference would be even more noticeable, because there is more time for divergence).

How might we see this in public policy? Any individual believing that Judgement Day would happen before 2050 and born after 1983 will not see any social security benefits, while paying in for social security and other retirement programs. Indeed, individuals born before 1983 will not come remotely close to being paid their contributions, and should rebel equally agianst this program.

Such individuals should not be saving for retirement, and certainly not be taking care of their bodies--many of this 40% who believe the world will end by 2050 should begin smoking, and planning for a family may be seen as mildly short-sighted.

In summary, Corrections believes that the lack of evidence on this 40% of the population, the lack of articles noting the incredible rise of unhealthy behavior and savings is evidence of individuals not believing what they claim to believe in surveys. Corrections might further note that while one may joke about short-sightedness among Americans today, the question is about whether or not people are behaving with the degree of extremity necessary to act as if the world was going to end in 40 years.

How to Lose an Election Without Really Trying

New York Times opinion "How to Lose an Election Without Really Trying" (August 7th, 2010) discusses political "amnesia", a concept that sounds particularly non-economical. Corrections suggests an alternative model.

Betting on amnesia is almost always a winning, not a losing, wager in America. Angry demonstrators at health care town-hall meetings didn’t remember that Medicare is a government program, and fewer and fewer voters of both parties recall that the widely loathed TARP was a Bush administration creation supported by the G.O.P. Congressional leadership.

There may be a real reason for political "amnesia." We might take a "regime switching" model as an explanation. The republican party can take on two values. One in which most Republicans want to reduce government intervention, and one in which they do not.  Individuals do not know what state or "regime" Republicans are in, but have signals.  (regular readers will see the familiarity between this Regime Switching model and our earlier article introducing the Kalman Filter).

In any case, we can generate a random variable in which Republicans are in a "regime."  They have a 95% chance of staying in whatever regime they are currently in next period, and a 5% chance of switching regimes.  In our case, we have a signal with noise which broadly tracks the true regime (because of the noise, we can get "false" signals).  In this case, we observe the following signal.  As the blue line is close to one, we see high legislative activity and Republicans are likely to be in a pro-government mood, though they may or may not be.  Using the blue line, our probabilities, and a standard regime switching model, as James Hamilton outlines here (gated) and here (ungated), we can make a "best guess" of what our regime is.  Graphically below, we display our signal in blue and our "best guess" as a red dotted line.  The red line is the "probability"we assign to each state (click to enlarge).

A measure of our success is the following graphical display, in which we again graph the probability that we assign to each state, while also graphing the "truth" (something we wouldn't ordinarily observe) (click to enlarge).  We call this a 'Hamiltonian' Regime Switch simply because we're following Hamilton's outline, not in relation to the mathematical concept.  Note that times when our guess (red dotted line) spikes and our regime (solid blue) doesn't change  were noise that lead us to believe regimes switched when they did not.  Also note that we are (asymptotically) efficient with our estimator--linear weightings cannot do better, ex ante.

This modeling situation appears to be more appropriate than suggesting "amnesia."  We can extend this situation in the case of having no signal as well.  In the case of having no data and predicting what regime or state we are in, or the case of forecasting what state we will be in at some future period, probabilities will slowly converge to our unconditional probabilities--a 50/50 probability of being in Regime 1 or Regime 2.

This seems to be an adequate story for voter "amnesia."  Voters observe strong signals of the regime Republicans are in when they have legislative power.  This may be the Medicare Prescription Drug Improvement and Modernization Act of 2003, for instance.  In such a case, voters understand with a clear signal "where" Republicans are.  When they are out of power for a time, or with a noisy signal, they may be less sure than they were two years ago--they recognize the regime can switch.

Corrections suggests that this sort of model is more satisfactory and economical than a model positing "amnesia" in voters.

A Sin and a Shame

New York Times editorial "A Sin and a Shame" (July 30th, 2010) offers another installation of Bob Herbert painfully writing about concepts he does not understand, and quoting figures that do not support his point.

The recession officially started in December 2007. From the fourth quarter of 2007 to the fourth quarter of 2009, real aggregate output in the U.S., as measured by the gross domestic product, fell by about 2.5 percent. But employers cut their payrolls by 6 percent.

Herbert then suggests that these figures mean that "cruel, irresponsible, shortsighted policy" has taken hold in American corporations. However, using a simple bread-and-butter real business cycle model involving investment-specific technological change, solved with Matlab program Dynare (this is a DSGE model, or Dynamic Stochastic General Equilibrium Model), we can show the relative movements can the result of far-sighted optimizing behavior, rather than the result of capital in the hands of individuals destined for the Fourth Circle of Dante's Inferno for their avarice, as Herbert perpetually suggests in various columns.

Below, we plot the impulse-response functions of one such model, in which firms maximize profits from a Cobb-Douglas production function, households have log-preferences, capital depreciates, produced goods are either invested or consumed, and both technology and quality of investment good are independent stochastic first-order autoregressive processes. (For the interested, this flavor of model is prototypically described in "The Role of Investment-Specific Technological Change in the Business Cycle", published in the European Economic Review (2001) by Greenwood, Hercowitz and Krusell). We examine what happens when we have a negative investment quality shock. The impulse-response functions to a are plotted below (click to enlarge):

How should we interpret these figures? First, for those unfamiliar, impulse-response functions plot the response of all other related variables to an exogenous shock over time. Here, we plot the reactions of all other variables in percentage points of their own standard deviations to a one-standard deviation negative shock to investment good quality. The "direction" of reaction can be seen by comparing the black line, which is the reaction of a variable to our shock, to the red line, which is a "baseline." We forgo concern about the size of the shocks and focus on the qualitative reactions of each variable.

Specifically, we see that when investment in durable goods this period gives less (lower quality investment goods), we see a decline in both production and labor (increasing back to steady state (or stable growth path) over time), while seeing an increase in productivity, precisely the sort of reaction Herbert pretends is irrational. This is a product not of shortsighted policy, but of perfect foresight (though not perfect information).

Indeed, one doesn't need to examine even simple real business cycle models to explain why we should see productivity rise, labor fall, and production fall by less than labor in the short run. In the United States, labor can be treated as a consumable good. Labor is more flexible than durable goods. In a simple analysis, we can hold capital as fixed and labor is flexible in the short run, while in the long run, both are flexible.

We might imagine our aggregate production function is Cobb-Douglas, using labor and capital, depicted graphically below (click to enlarge). We also denote a dark black line, indicating a schedule for production given fixed capital. Therefore, we might consider any point on this graph viable combinations for inputs and corresponding output in the long run, while considering only the dark black line viable in the short run (were we to have that specific level of capital, .5 in this case).

We could simply graph the dark black line in two dimensions (click to enlarge). This represents production along a fixed capital stock, as we would see in the short run:

On this graph, we can see our whole story: output, labor supply, and productivity. Marginal labor productivity, which may be defined as $$\Delta$$output/$$\Delta$$labor, is the slope of any point on this line. Average productivity is simply the ratio of output to labor. We can see that any time we shift downward along the supply schedule, labor will, on average, be more productive. Note that this is not true in the long run, because capital will shift as well (this Cobb-Douglas is constant returns to scale in the long run, decreasing returns to scale in the short run). We can display this on the same graph, also writing out productivity below two sample points (click to enlarge):

All this is to say that if we make less, our average productivity increases when we are in a regime with decreasing marginal returns to scale. It appears Bob Herbert's real complaint is about decreasing marginal returns, or his ignorance of economics, rather than "corporate greed" or "shortsightedness."

As a last point, Crypto-Marxists like Herbert appear to adopt the poor understanding of capital and labor that Marx shared with Malthus. The belief that capital (land, in Malthus's case) is fixed, and labor is elastic (people have more children and "soak up" any wage higher than subsistence living).

Productivity tells the story. Increases in the productivity of American workers are supposed to go hand in hand with improvements in their standard of living. That’s how capitalism is supposed to work. That’s how the economic pie expands, and we’re all supposed to have a fair share of that expansion.

Corporations have now said the hell with that.

This is incorrect. If corporations could always just say "to hell with that" and not pay workers as much, they would have done so at some point in the past 150 years. Over the last 150 years, the return on invested capital has remained unchanged, while real wages have continued to rise. The mistake that Marx, Malthus and Herbert make is to believe that capital is fixed (inelastically supplied) while labor is flexible (elastic), and so capital gains all benefits from a shift in productivity.

To be clear, the mistaken idea is as follows. Society has a productivity gain. There is a large excess pool of labor that will compete away any higher wages, while capital remains fixed. Therefore, because labor competes all gains away, capital gets all the benefits of a productivity gain.

The reason this idea is mistaken is that there is a large excess pool of possible capital--its primary "input" is simply foregone consumption, and that can be supplied rather easily, if the real interest rate is high enough. Real wages have gone up over time, while real return on capital has not.

The opposite is true--capital is elastic, while labor is relatively inelastic, explaining why real wages have been the claimant on all increases in productivity over the last 150 years.

Building Is Booming in a City of Empty Houses

New York Times article "Building Is Booming in a City of Empty Houses" (May 15th, 2010) suggests that the country has too many houses. While it gives some reasoning for this argument, the evidence for a bubble is not clear-cut to Corrections.

Simply put, the country already has too many houses, the legacy of wide-scale overbuilding during the boom. The Census Bureau says there are two million vacant homes for sale, about double the historical level. Fewer new households, moreover, are being formed as families double up for economic reasons, putting a further brake on demand.

Was there a housing bubble in prices? Was there a housing bubble in construction? One might ask, as Casey Mulligan has (our analysis is indebted to him), whether or not these oft-cited bubbles are really bubbles--the answer is not immediately apparent to Corrections. There does not appear to have been a particularly spectacular housing boom in terms of new housing units or housing completion, judging from the biannual American Housing Survey. The housing bubble is often cited to have started in 1996, when the Case-Shiller Housing Index first began to rise dramatically. However, it appears as though half of the dramatic rise in prices from 1996 has survived the "bubble's" burst--indicating that at least some portion of the bubble was not a bubble at all, but driven by some fundamentals. Housing Units from the American Housing Survey are displayed below, along with the composite Case-Shiller Index, Housing Completions from the Census, and Residential Investment from the Bureau of Economic Analysis's National Economic Accounts (click to enlarge). Housing Units for 2009 is due Summer 2010--the value displayed is imputed from housing completions over a period of 20 years, and some interstitial data points are similarly linearly imputed. An update will be offered when the American Housing Survey for 2009 is released Summer 2010.



As one can see, the stock of housing units never increased dramatically--15% at their peak. The flow of housing completions and residential investment both grew and have fallen from their peak. However, prices have not fallen completely, which indicates to Corrections that the "bubble" was not necessarily a bubble, but simply a housing boom, driven at least in some part by fundamentals--were it not, prices would be even lower than they are now, given an increased housing stock.

The Liberal Democrat eruption is not finished yet

The Guardian article "Liberal Democrat eruption is not finished yet" (April 25th, 2010) offers a corrupted version of the median voter theorem, suggesting that but one in twenty-five marginal voters decides the ruling party in Britain.

Elections are determined by remarkably few voters. These are those voters who choose to vote (in the past two elections only six in 10); who have little party loyalty (about one in five); and who live in marginal seats. As few as one voter in 25 decides who rules the land.

This might appear to be true, and it might appear that the marginal voter is one twenty-fifth of the eligible voting population. However, it's not clear that this is actually the case. For any given election, there may be 75% of the population supporting the candidate that wins. Two-thirds of that 75% have an incentive to free-ride on the other 25% plus one that can win the election for them without having to vote, something that might be considered to be costly.

In such a situation, the defection of every single individual who was going to vote for the winning party would mean nothing--there is a vast resovoir of previously supra-marginal, now-marginal agents willing to vote for the winner. Voting is endogenous to chances of winning, and the Guardian appears to have missed this.

Media’s mendacity should be news to all

Boston Herald article "Media’s mendacity should be news to all" (April 10th, 2010) by Bill O'Reilly discusses individual American's discovery that United States newspapers are politically biased, and appears surprised. Corrections suggests that far from being surprising, this is a natural occurrence, and we should see media bias in a different way.

While many Americans believe the national press is biased toward the left, a more damning charge is now being debated: Are U.S. media outlets actually corrupt? Those who believe they are point to the cheerleading during Barack Obama’s presidential campaign and to the recent reportage on the Tea Party movement.

As you may know, the Tea Party people have been branded in some media quarters as a bunch of racist, far-right loons. TV commentators on MSNBC and CNN have actually called the Tea Party folks dirty names on the air - all in an attempt to diminish the growing influence of the movement.

But a funny thing happened on the way to the gutter. Regular Americans have apparently opted to decide for themselves about the Tea Party, and the polling is interesting.

Corrections suggests that January 2010 Econometrica article "What Drives Media Slant? Evidence from U.S. Newspapers" by Jessie Shaprio and Matt Gentzkow has a more appropriate manner of examining media bias. In order to understand its relevance, we first note that in Shapiro and Gentzkow's 2006 Journal of Political Economy paper "Media Bias and Reputation", they posit consumers who do not know the quality of a news source with certainty. Their consumers have prior beliefs about the truth, read news articles, and sometimes the truth is revealed to them at a later time (so they can update, finding that the newspaper has deceived them, or not). The article finds that newspapers will optimally slant their news to their consumer bases's biases.

Returning to the original paper Corrections referred to, the authors find that, "consumer demand responds strongly to the fit between a newspaper's slant and the ideology of potential readers, implying an economic incentive for newspapers to tailor their slant to the ideological predispositions of consumers. We document such an effect and show that variation in consumer preferences accounts for roughly one-fifth of the variation in measured slant in our sample."

Corrections suggests that the cycle O'Reilly was referring to makes quite a bit of sense, in this light. First, individuals had some signal about Barack Obama as a Presidental candidate. News sources respond to that bias (and perhaps the two feed one another, though that conjecture is by no means clearly going to happen). Individuals vote for Obama, and perhaps discover, given a relatively monotonic downward trend, that they were deceived by media slant. Corrections offers Gallup Approval Rating Polling data below (click to enlarge). They bayesian update on the slant media stations have, just as the Tea Party, borne out of individual's discovery of deception by the media, occurs.



Corrections suggests that Mr. O'Reilly's article was not necessarily off-base, but was grasping at the model suggested by Shapiro and Gentzkow without explicitly mentioning it. It is in this clarifying manner that Corrections offers a clarification.

College tuition is expensive enough, let alone the textbooks

Los Angeles Times article "College tuition is expensive enough, let alone the textbooks" (March 15th, 2010) offers an interesting but empirically faulty conjecture concerning textbook revisions. Textbooks are durable goods that may be bought, used, and sold. Furthermore, they are in monopolistic competition with one another. The Times suggests that editors come out with new editions to generate revenue.

A US Government Accounting Office report shows that textbook prices rose 40 percent between 2002 and 2007, and 186 percent between 1986 and 2004, so that a college student’s annual book bill averages $900!

Publishers claim sky-high prices are necessary to offset losses from used-book businesses that recirculate titles, killing sales of new books.

So publishing reps compete for their piece of the multibillion-dollar pie, throwing book release parties with refreshments and gifts for faculty, including free examination copies. Additionally, they lure professors to tweak and rewrite new editions each year, to render obsolete the slightly used copies and create new demand.

In an NBER Working Paper, "Are Durable Goods Consumers Forward Looking?" Judith Chevalier and Austen Goolsbee find that students do indeed spend approximately $900 purchasing textbooks every year. Chevalier and Goolsbee examine student sensitivity to price. Students buy books and often sell them back, used, at the end of the term. They are able to sell them for a fraction of the price (between 50%-75%) if no new edition has come out, and a smaller sum (approximately 20%) if a new edition has come out. Corrections notes in passing that this indicates students are not paying $900 net, but quite a bit less than that.

A student's willingness-to-pay, absent discounting (which Goolsbee and Chevalier do not neglect) for a book will be equal to the difference of price paid and cost recovered through resale, plus the gain a student gets from using the book in the meantime. If companies accelerate their revision cycle, a student's willingness to pay will go down.

Indeed, Goolsbee and Chevalier find just that: students are patient and forward-looking, and become more sensitive to price as the likelihood of a new revision increases. Indeed, they find that textbook firms cannot increase profits by accelerating their product cycle--the decrease in value to a patient student causes fewer sales.

They find that students are not myopic in their purchase decisions, and their sensitivity to reap greater profits appears to be incorrect, due to the patience and rational expectations of college students.

The argument offered by the Times, that textbook companies accelerate their revision cycles to gain profit, appears to be contradicted by empirical evidence.