Yield Curve

Below, Corrections depicts the daily yield curve from Jan1990-Aug2012 (click to enlarge).

Below, Corrections takes each day's yield curve and breaks it up into a constant, slope (by duration), and quadratic (by duration squared) term (click to enlarge):

Finally, we normalize each components to have mean zero and standard deviation one, and graph them together (click to enlarge).  Insofar as interest rates predict bad times, the three components point to lower growth (the low level, shallow slope, and less curvature).   

Joint Distribution of Coke and Pepsi Stock Returns

For fun, Corrections displays the joint distribution of daily Coke and Pepsi stock returns from 1990 to present, from two different angles (click to enlarge).

We might also graph the joint distribution of what Coke's daily return was yesterday against what Pepsi's return is today, in the hopes that we can generate an actively-managed portfolio that buys and sells Pepsi based on Coke's conditional return (click to enlarge):

No such luck.  The two are slightly negatively correlated, with a slope of 0.01% return and an insignificant coefficient (even without correcting for serial correlation).  Note that while concurrent returns are moderately positively correlated, the two have no forecasting power for one another.

Entertaining. 

When the Crowd Isn't Wise

David Leonhardt writes a rather painful article in the New York Times "When the Crowd Isn't Wise" (July 7th, 2012).  He notes that Intrade thought Obamacare was more likely to be ruled unconstitutional than constitutional:

[Intrade markets] continued to show about a 75 percent chance that the law's so-called mandate would be ruled unconstitutional, right up until the morning it was ruled constitutional.

The market-the wisdom of crowds-turned out to be wrong. 

Corrections sees risk premia and self-insurance everywhere, but let's take the common view of Intrade markets, that the price/10 is equivalent to the probability the market puts on an event.

Are political writers like Leonhardt so ignorant of statistics to know what "wrong" means?  75% represents a distribution of outcomes!  If you looked at all Intrade markets that were at and around 75%, and then looked at the outcomes, if they were "right" (by Leonhardt's incorrect statistic) 100% of the time we should conclude these are poorly functioning markets.

No.  If you predict something should happen with 75%, then it should not happen 25% of the time, and happen 75% of the time.  Not happening 25% of the time means you are correct in your guess about the distribution.  75% represents a distribution of outcomes.  A 90% guess would be more wrong than 75% in general, when the outcome actually happens 75% of the time.  The relative entropy of the distributions is what helps us differentiate them statistically.

New York Times quality article.

Are Some Forecasters Really Better Than Others?

From the Journal of Money, Credit and Banking, (D'Agostino, McQuinn, and Whelan), the paper "Are Some Forecasters Really Better Than Others?" is entertaining.  (Sadly, not many easy-to-excerpt figures).  The abstract:

In any data set with individual forecasts of economic variables, some forecasters will perform better than others. However, it is possible that these ex post differences reflect sampling variation and thus overstate the ex ante differences between forecasters. In this paper, we present a simple test of the null hypothesis that all forecasters in the U.S. Survey of Professional Forecasters have equal ability. We construct a test statistic that reflects both the relative and absolute performance of the forecaster and use bootstrap techniques to compare the empirical results with the equivalents obtained under the null hypothesis of equal forecaster ability. Results suggest little support for the idea that the best forecasters are actually innately better than others, though there is evidence that a relatively small group of forecasters perform very poorly.

Corrections believes it.

10-year Eurozone Bond Yields: January 1993-April 2012

Below, Corrections displays 10-year Eurozone Bond Yields from January 1993-April 2012 (click to enlarge).  Did Ireland's "austerity" measures work like Iceland's did?  10-year bond yields have fallen dramatically.

The Religious Right Turns 33: What Have We Learned?

Jonathan Merritt writes an embarassingly wrong op-ed in The Atlantic:  The Religious Right Turns 33:  What Have We Learned? (June 8th, 2012).  In it, he attacks the Religious Right, arguing that the movement into politics of Evangelicals and the Religious Right has diminished interest in Christianity.

Economics has special ways of dealing with time-series theses like "The Christian Right got into politics, and their share of the population went down.  Therefore, it must have been because of the politics."  On its own, this has little empirical content:  post hoc ergo propter hoc.  But a good analysis can be convincing by showing parallel data.  We can examine other religions that didn't get into politics (or didn't change their relative immersion into politics), or look at factions of Christianity that went into politics more.

In other words, we can say "if that thesis is true, then it has testable implications."  Corrections offers two testable implications:

• Other branches of Christianity haven't gone into politics as much as Evangelicals:  therefore, Evangelicals should be suffering the most.
• Judaism, a religion strongly tied to the left for more than a century, has not changed its political position very much.  Therefore, it should be untouched by the last twenty years.

Obviously these aren't the only stories one can tell: Corrections is glad to entertain other testable hypotheses of Merritt's otherwise empty theory.  First, we use the Statistical Abstract of the United States to depict the proportions of different religions with a logarithmic scale (otherwise, Evangelicals, Muslims, and Jewish proportions are too small to distinguish) (click to enlarge).

One can see that Christianity and Judaism have declined while Athiests, Muhammadans, and Evangelicals have seen an increase in their proportions.  It would be easier to compare them all to their 1990 proportion, to see the change (click to enlarge):

This figure tells our whole story:  if being political has hurt Christians, then why has Judaism, which hasn't changed its political orientation seen a larger fall, while the subset of Evangelicals in Christianity seen the largest rise?  

As a note, it is true one can begin to tell stories (ex:  Evangelicals rose by draining other Christians while the rest left, Judaism has its own thing going on, etc.) to make sure Merritt's claim is devoid of testable hypotheses.  Such a tack would ironically and safely bring one's own politics into a religious (non-testable) sphere.

Balance Sheet of U.S. Households and Nonprofit Organizations 1949-2011

Below, Corrections displays the Balance Sheet of Households and Nonprofit Institutions in the United States from 1949-2011, in real 2011 U.S. dollars (click to enlarge).

The Labor Wedge

The labor wedge is a difference between the marginal rate of substitution (MRS) between consumption and leisure, and the marginal product of labor (MPL).  That is, how willing you are to trade off leisure for consumption, and the degree to which you are able to do it.  If an individual may do so perfectly, then the labor wedge is zero.  It is given its name because all real taxes have distortionary effects, and most, if not all, have effects on labor.  If we look at measures of MRS and MPL, we can say "what tax rate explains this gap?"  This is what the labor wedge is:  essentially a structural "this is what taxes seem to be, given distortions in the economy."

Below, Corrections offers the labor wedge as offered in Rob Shimer's book, with data from Cociuba, Prescott, and Ueberfeldt (Simona Cociuba's website).  We graph two possible labor wedges:  one with a low Frisch elasticity of 0.5, and one with a Frisch elasticity of 4 (used for most macro settings).   The Labor Wedge is depicted graphically below (click to enlarge).

U.S. Employment and Hours as Percent of Previous Peak

Below, Corrections plots U.S. Employment (nonfarm and total private) and Hours (aggregate hours of nonsupervisory and production employees), along with dated NBER recessions (click to enlarge).

Business Employment Dynamics: Where Jobs Losses and Gains Come From

Below, Corrections graphically depicts transformed Business Employment Dynamics data.  The two data series are the proportion of gross job losses generated by closing establishments, rather than contracting establishments (click to enlarge).  Similarly for gross job gains generated by opening establishments, rather than expanding establishments.

Three things seem to jump out of the figure:

• Generally, around 20% of gross job gains and losses come from opening and closing establishments.
• Compared to the proportion of gross job losses that come from closings, generally a higher proportion of gross job gains come from openings.
• There has been a secular downward trend in the impact of closings and openings on employment.

The last point is probably bad news for the U.S. economy.

Business Employment Dynamics: 1992:Q3-2011:Q2

Below, Corrections shows Business Employment Dynamics data from 1992:Q3-2011:Q2.  We index to 1992:Q3=1, from data originally in levels.

• Gross job gains are the total people hired in a quarter (not subtracting losses).  U.S. generally has around 7.6 million total gains in a given quarter.  
• Expansions are businesses that reported more jobs than last quarter.  U.S. generally has around 6.1 million firm expansions in a given quarter.
• Openings are businesses that did not exist in the previous quarter.  U.S. generally has around 1.6 million firm openings in a given quarter.
• Gross job losses are the total separations in a quarter (not adding gains).  U.S. generally has around 7.4 million total losses in a given quarter.
• Contractions are businesses that reported fewer jobs than last quarter.  U.S. generally has around 6.0 million firm contractions in a given quarter.
• Closings are businesses that reported last quarter but are no longer active.  U.S. generally has around 1.5 million closings in a given quarter.

We generally think of having both gross job gains and gross job losses high as creative destruction:  while not much is moving, there's a lot of churn in the economy, generally very good.  We generally think of having both gross job gains and gross job losses low as stagnation or sclerosis:  not much is flowing in the economy.

The 1990's and the Great Recession both show prominently in the figure of BED data, depicted graphically below (click to enlarge).

US GDP, Log GDP, and Percent Deviations from Trend

GDP from 1947-2011, log GDP for the same period, and deviations from that log trend (which can be interpreted as percent deviations).

John Cochrane is now blogging

John Cochrane is now blogging.

Labor Force Participation by Gender

Below we plot the labor force participation rate of men and women over time. The share of women who are either working or looking for work has nearly doubled since 1948, while the share of men has fallen by nearly 20 percent in the same time-period.

Despite the entrance of women into the labor market, the unemployment rate of men has hardly changed over time.

The huge increase in competition for work was not met with any notable difficulty finding work among men. In general, a larger labor force does not imply more difficulty finding work. This holds both when women enter the labor market and when immigrants enter the labor market.

Unemployment Flows from Labor Force

Below, Corrections displays the four places the unemployed go, from month to month (click to enlarge). They either find employment, stay unemployed, leave the labor force, or "other" (a very, very tiny category that would include dying, or immigrating, for instance).

AAA vs. BAA Bond Spreads

Below, Corrections takes the difference between daily AAA and BAA rated bonds (Moody's, from the FRED database) and displays recessions (click to enlarge).

When the data from Operation Twist and the subsequent days become available, we'll put those graphs up too.

Ratio of Job Seekers to Job Openings

Below, Corrections displays the number of unemployed, the number of job openings, and the ratio between the number of unemployed and the number of job openings (e.g. number of seekers per position that month) up until July 2011.   If job openings increased to where they were in 2007, then 70% gap between today and the average of the seeker-opening ratio would be closed.   

Three Charts (not) to Email to Your Right-Wing Brother-In-Law

Truth-out.org suggests “Three Charts to Email to Your Right-Wing Brother-In-Law". Here are a few pictures to think about before you do so.

The graphs created by truth-out.org select the last year of the Bush presidency (not his entire term) to note that the recession started in 2008. Recessions actually happen very frequently in the US economy. This gives us a wealth of data with which to compare the current President’s performance. The first graph in the picture below plots the trends of many recessions. We evaluate using the same basis as truth-out.org--national employment statistics. In particular, we plot the employment as a percentage of its lowest value during a recession over time, for a number of recessions (from 1950 on). We can look at the growth of employment after the trough of a recession. Usually, the economy recovers rather quickly; in the graph, this corresponds to a steep uptick after hitting 0.

The current recession is the very bottom black line on the graph. This means that currently, we’re doing worse than any recession in the past 60 years in terms of recovery. Since Obama had been president for months before the trough, it wouldn’t seem natural to blame Bush alone for the slowest recovery that we have seen in the last 60 years. Just below the first graph, there is a comparison our recession--the blue line--with the average recovery after a recession. We are doing a poor job relative to the average.

In the second column, we look at another interesting trend: job growth before and after the passage of Obamacare. While the country seemed to be recovering at a reasonable rate and coming out of the recession before the passage of this bill, job growth slowed dramatically immediately following the passage of Obamacare in April 2010. Below this, the last graph depicts the actual stimulus rollout. The solid black line depicts funds received by organizations from the stimulus. Contrary to the deceptive picture painted by truth-out.org, the stimulus has been doled out at a fairly constant, increasing rate since the beginning of 2009. The article from truth-out.org, however, makes the ridiculous suggestion that the slowing of job growth and the constant unemployment rate is caused by the stimulus “winding down”. That is false. Just because there is no bill on the table doesn't mean that our economy isn't being "stimulated," and these are the results.

Reported Satisfaction with Life across Countries

A look into life satisfaction across countries yields interesting regional and historic patterns. In the graph below (click here to enlarge), we plot average reported life satisfaction against national GDP per capita (2006 figures). Responses to the question "are you satisfied with your life?" were on a scale from 1-10, with 10 indicating "satisfied."

From this, one trend stands out starkly--the similarity of response across formerly communist and eastern european nations as well as the similarity of response across developed western economies (in particular across largely Protestant nations). There is a great gulf, however, between the reported life satisfaction of these formerly communist nations and western nations. The graph below (click here to enlarge) gives the distribution of satisfaction with life from 8 formerly communist eastern european nations and 8 western, non-communist nations. The countries are ordered by GDP per-capita. Numbers are in terms of deviations from average reported levels, in order to make the differences more stark. A green area indicated a higher concentration of responses than a red area. We see that the concentration of reported life satisfaction is increasing with GDP and in general is fairly uniform across formerly communist nations and across western non-communist nations.

Imprisonment, Torture, Killings and Assassinations

There have been several interesting stories about the cost of imprisonment, torture, killing and assassinations in the U.S.'s War on Terror.  For example, in Afghanistan one often hears of an ineffective criminal justice system causing the U.S. military to release captured militants in the hopes that they can kill them next time.  Similarly, this news article discusses the Obama administration's increased reliance on assassination attempts in, for example, Yemen, Afghanistan, and Pakistan.

Corrections suggests that this is in accordance with the Obama administration's decreased reliance on torture and the substitutability between targeted assassinations and capture and torture.  This is depicted graphically below (click to enlarge).  The straight red line depicts the Bush administration's capability to substitute capture and torture for assassinations.  The curved line depicts their preferences, and the red dot depicts the best mix of capture and killing.  We can imagine that the Obama administration through rhetoric has decreased its capacity to capture and torture terrorists (if only due to political ramifications).  They retain the same ability to kill as the Bush administration, so their budget line is the straight blue line.  If killings and assassinations are substitutable enough (for example) then it's possible the Obama administration will not only substitute away from torture and toward assassination but will actually have more assassinations (rather than less of both), which can be seen as the blue dot.