Category Archives: Uncategorized

Some Fun Stuff: Seinfeld and Optimal Stopping Times

Sometimes while you are proctoring exams, you realize that an episode of Seinfeld can be understood as an optimal stopping time problem and you write a short paper about it. Enjoy.

Review of Piketty’s Capital in the 21st Century

My review of Piketty’s Capital in the 21st Century will run in the May 5 issue of National Review. In the meantime, here is a link to a longer version of the review.

What I’m Reading

1. The New Dynamic Public Finance by Narayana Kocherlakota

2. The Redistribution Recession by Casey Mulligan

3. The Bretton Woods Transcripts, edited by Kurt Schuler and Andrew Rosenberg

4. Misunderstanding Financial Crises by Gary Gorton

Forecasts and Standard Errors

Via John Whitehead, I was led to this discussion of climate change by the EPA. The EPA repeats the following claim from the IPCC:

The average surface temperature of the Earth is likely to increase by 2 to 11.5°F (1.1-6.4°C) by the end of the 21st century, relative to 1980-1990, with a best estimate of 3.2 to 7.2°F (1.8-4.0°C) (see Figure 1). The average rate of warming over each inhabited continent is very likely to be at least twice as large as that experienced during the 20th century.

Does the standard error on this century-long forecast seem small to anyone else? (I’m not being facetious, I’m genuinely asking in the hopes that those will greater knowledge of the issue will answer.)

Thank You, Steve

I remember sometime in 2003, I was still an undergrad and I was working in retail. I showed up for work one day and one of my fellow workers said to me, “I have to show you something really cool.” We walked back to the electronics department, he opened up the case and said, “check this out. It’s from Apple. They call it an iPod.” I played around with the iPod for about 15 minutes, looked at him it said, “this is really cool, but it’s a bit pricey. Is anybody going to buy it?”

That was the genius of Steve Jobs. He didn’t invent the graphical user interface, but he perfected it like no other. I still remember seeing Mac OS X for the first time and it convinced me that I needed to switch back to using Apple’s products. It was so much more fluid and user friendly than Windows, but in quintessential Jobs fashion, it was also elegant and beautiful. And this says nothing about reliability. I have first generation MacBook Pro on my desk at home. First generation means that it’s 5 1/2 years old. It still runs like new and even if it crashed tomorrow (which it won’t), it would still be the longest-lasting and most reliable computer I have ever owned.

The creation of the iPod in an of itself was a remarkable innovation (thousands of songs on one device!), but Steve Jobs did so much more than simply create a new way to listen to music; he revolutionized the way we purchase music. It also revolutionized the way that we access content. Do you want to listen to NPR or ESPN Radio or EconTalk? The iPod and the iTunes store enabled you to listen to many of your favorite radio programs anywhere you want whenever you want. And would programs like EconTalk even exist without the creation of the iPod or iTunes? The iPhone allowed us the same functionality while simultaneously offering the ability to make phone calls, but it was also so much more. In doing so, it revolutionized the way we think about and use our phones.

In my mind, though, perhaps the best creation, and what will turn out to be the most revolutionary, is the iPad. While I do not yet own an iPad (donations are accepted), I really see the iPad and tablets in general as being the new laptop. It is so much more enjoyable to surf the internet, watch digital content, and read journal articles, newspapers and magazines on a tablet. What the iPod did for the way we listen to music, the iPad will do to the way we read and consume other digital content, like movies and television shows.

Steve Jobs had perhaps the most innovative mind of the last century. Since the founding of Apple, Jobs created more value and perhaps did more to improve the everyday lives of individuals than perhaps any other. The world has lost a great mind. Thanks for everything, Steve.

Econo-blogosphere Inquiry

Before his retirement Neil Skaggs was working on a monograph about the influence of Henry Thornton on monetary thought. Does anybody know if this was completed?

Commodity Money: A Primer

Much has been said recently about commodity money.  Unfortunately, a number of the things that have been said have been misleading or misinformed.  Similarly, it is fairly strange that so many people assert the benefits OR the costs of a commodity standard as evidence for or against.  A careful analysis would suggest a comparison of benefits AND costs.  Given that the commodity money research cupboard has laid bare – for the most part – for some time, it might be useful to dust off the theory and address it in a meaningful fashion.

In order to discuss the gold standard, I will address the specific case of a pure gold standard.  Under this scenario, it is true that either gold coins circulate as money or that bank notes are backed 100 percent by gold.  If we neglect the costs associated with coining, deterioration, and debasement, these are essentially equivalent from a macroeconomic perspective.  Once this framework is discussed I will proceed to a discussion of a fractional reserve gold standard (perhaps in a subsequent post).

Suppose that resources can be used to produce consumer goods and gold.  For a given amount of resources, Rfixed, we can write a production possibilities frontier:

Rfixed = R(C, G)

Where C is consumer goods and G is gold.  The marginal productivities can be of producing consumer goods and gold are, respectively, Rc > 0 and Rg > 0.

Resource owners earn income:

Y = (Pc/Pg) C + G

Where Y is income and P­c and Pg are the prices of consumer goods and gold, respectively.

Equilibrium necessarily requires that

Rc/Pc = Rg/Pg


Rc/Rg = Pc/Pg

This implies that the price of consumer goods in terms of gold is equal to the marginal opportunity cost (marginal rate of transformation).  Price changes in either industry would lead to resources shifting from one industry to another.

Under a gold standard, the price of gold is fixed.  In addition, we will assume that there is free coinage provided that the individual pays the resource cost.  With the price of gold fixed, there is a corresponding price level for consumer goods.  This highlights the main benefit of a gold standard.  With the price of gold fixed, the purchasing power of gold is fixed.  Holding everything else constant, this implies that the purchasing power of money in terms of consumer goods is fixed as well.  In other words, absence changes, the price level for consumer goods is constant.

Given this basic framework, we can summarize the mechanisms of the gold standard.

First, consider the case of a growing economy in which all industries are growing at the same rate as the overall economy.  In this case, there would be no change in the ratio of productivities.  Equilibrium implies that the ratio of prices would remain unchanged as well.  Since the price of gold is fixed, this means that the price level would remain constant.

Second, suppose that there is technological progress in gold mining, the discovery of a new mine, or that the gold mining industry is growing at a faster rate than that of consumer goods.  If we imagine a production possibilities frontier with gold on the x-axis and consumer goods on the y-axis, this implies that the production possibilities frontier gets flatter.  This implies that Rc/Rg rises as the opportunity cost of producing gold relative to consumer goods declines.  This necessarily requires that Pc/Pg rises as well.  Since the price of gold is fixed, this means that consumer prices will rise.

Third, it follows that if the rate of technological progress in consumer goods outpaces that of gold mining or if there is simply a lack of gold discoveries to keep the pace of gold mining in line with the rate of growth in consumer goods, the opposite change would occur.  In this case the opportunity cost of producing consumer goods would fall relative to that of producing gold.  This implies that Pc/Pg would fall.  With the price of gold fixed, consumer prices decline.

Each of these three examples described above concerns a change in flows.  It is possible, however, that a change in stocks might also have influence on the gold standard.  In order to discuss the role of stocks in this analysis we need to extend the framework as follows.  First, define the quantity of gold as the sum of monetary and non-monetary gold:

G = (M/Pg) + Gnm

Where G is gold, M is the quantity of money, and Gnm is the quantity of non-monetary gold.

In addition, monetary equilibrium is defined as when the supply of monetary gold (M/Pg) is equal to the demand for monetary gold:

M/Pg = L[Y, (Pc/Pg)]

Now, suppose there is an increase in the demand for money.  The effects can be considered in the context of stock/flow equilibrium.  An increase in the demand for money is an increase in the demand for the stock of monetary gold.  The increase must be offset by a reduction in the demand for non-monetary gold, consumer goods, or a combination of both.  If the increase in money demand corresponds with a reduction in the demand for non-monetary gold, there is no further adjustment necessary.  The individual essentially just takes non-monetary gold to the mint.

If, however, the increase in the demand for gold corresponds with a reduction in the demand for consumer goods, the prices of these goods decline thereby increasing the purchasing power of gold.  It follows that an increase in the purchasing power gold encourages an increase in gold production.  However, since gold production is (usually) a small proportion of the existing stock of gold it takes an extended period of time for the adjustment to take place.

This adjustment likely results in reduced total output and lower prices, which is to some extent why deflation has been considered a poor outcome.  It is important to note, however, that in the first three examples we were concerned with flows rather than stocks.  In the case of flows, the fact that gold production is a fraction of the total stock of gold makes the adjustment process smoother.  Thus, when there is an increase in productivity in the consumer goods industry relative to the gold industry, the prices of consumer goods fall and deflation is associated with economic growth rather than economic contraction.

Finally, the last possible change to consider is a change in the price of gold.  As the model has been written, an increase in the price of gold would not affect the real side of the economy and therefore would only result in a corresponding increase in the price level of consumer goods.  In reality, however, the increase in the price of gold would result in a relative price change making consumer goods cheaper, which would increase the demand and production in consumer goods.  This would therefore entail temporary real effects that would ultimately result in a higher price level for consumer goods.

This discussion of commodity money, while somewhat long-winded, should highlight several important concepts.  First, it should be clear that the primary advantage of commodity money is that by setting the price of gold (or any such asset), the price level remains constant – absent any changes.  If gold production and consumer goods production grow at the same average rate over a period of time, the average price level will remain unchanged.  Second, the demand for money is important because if changes in the demand for money correspond with changes in the demand for consumer goods, these changes produce changes in the price level of consumer goods.  Since the gold mining is small relative to the stock of gold, this implies a long adjustment process.  Finally, changes in relative productivity across industries induce changes in the flow of consumer goods and the flow of gold.  These similarly entail an adjustment process, but that process is mitigated to some extent by the fact that the flow of newly mined gold is a fraction of the total stock.

A careful discussion of commodity money would require consideration of the costs and benefits.  Since much of the framework that I described above was based on that found in Niehans’s The Theory of Money, I would conclude the post with a quote from that text (p. 140):

“Commodity money does not exist today.  It is also not ideal in the sense that it is relatively easy to imagine non-commodity systems that are intellectually more satisfying than commodity money.  In fact, a non-commodity system, since it gives monetary policy more freedom, can if it is ideally managed, always do at least as well as any commodity money system and probably better.  Commodity money has therefore been denounced as a ‘barbaric relic’ from less enlightened stages of human society.  Yet, from a practical point of view, commodity money is the only type of money that, at the present time, can be said to have passed the test of history in market economies.”