28 April 2015

Unit roots in English and Pictures

After my unit roots redux post, a few people have asked for a nontechnical explanation of what this is all about.


Suppose there is an unexpected movement in any of the data we look at -- inflation, unemployment, GDP, prices, etc.  Now, how does this "shock" affect our best estimate of where this variable will be in the future? The graph shows three possibilities.


First, green or "stationary."  There may be some short lived dynamics, the little hump shape I drew here. Then, given enough time, the variable will return to where we thought it was going all along. For unemployment, suppose your best guess of unemployment in 2050 was 5%. Then you see an upward unexpected 1% spike in today's unemployment. Ouch, that means that we're going back to a recession. But perhaps this news does not change your view of 2050 unemployment at all.

Second, blue or "pure random walk." That's more plausible (though no longer thought to be true) of stock prices. If the price goes up unexpectedly, your expectation of where the (log) price will be in the future goes up one-for-one, for all time.

Third, black, "unit root." This option recognizes the possibility that a shock may give rise to transitory dynamics, and may come back towards, but not all the way towards your previous estimate. As you can see the "unit root" is the same as a combination of a stationary component and a bit of a random walk. Perhaps seeing unemployment rise 1%, you think most of it will work itself out, but that even in the long run labor markets will be sticky and we'll never quite get back.

The "unit root" is most plausible and verified in the data for log GDP. Recessions and expansions have a lot of transitory component that will come back. But there are permanent movements too. Unemployment, being a ratio, strikes me as one that eventually must come back. But it can take a longer time than we usually think, which is interesting.

This is very simplified. A few of the issues:

For GDP the question is whether it will come back to a linear trend extrapolated from past data, not back to a level as I have shown.

Most of the issue is how standard statistical procedures work in these circumstances.

As you can see from the graph, the pure question whether the series will come back in an infinite time period is not really knowable. It could be that the series will come back eventually, but take a very long time. It could be stationary plus a second very slow moving stationary component. This is a statistical problem but not really an economic problem. The appearance of unit roots are economically interesting as they show a lot of "low frequency" movement, series that are coming back slowly -- even if they do come back eventually. The economics of "slumps" and (we hope, someday) "booms" is hot on the agenda, and this is one indication of the fact.

This is all much more interesting if you look at multiple series together. For the canonical example, if you just look at stock prices, they are very very close to a random walk. A price rise or decline are permanent. However, if you see stock prices rise relative to dividends, that's almost entirely stationary. GDP and consumption have a similar relationship. As in the latest recession, if GDP declines with a big consumption decline, that looks pretty darn permanent. GDP declining and people still consuming is much more likely to go away.

I hope this helps.


26 April 2015

Ryuho Okawa's Happy Science

In February at the 13th Annual Los Angeles Conscious Life Expo, among 175 exhibitors was an organization that I hadn't heard about before — "Happy Science Reigen Channeling."  (I later learned 'Reigen' means 'spiritual messages.')  When I approached the booth, a Happy Science representative enthusiastically began talking to me about the founder of the organization, Ryuho Okawa.  When the representative learned that I was a blogger, he provided me with some introductory materials.

In the Happy Science Organization Overview (July 2013 edition), there is a short biography:

Master Ryuho Okawa

Master Okawa was born on July 7, 1956 in Tokushima Prefecture, Japan. After graduating from the prestigious University of Tokyo, he joined a Tokyo-based international trading company.  While working at the company's New York headquarters, he studied finance at the Graduate Center of the City University of New York.

On March 23, 1981, he achieved Great Enlightenment and awakened to the hidden part of his consciousness, El Cantare, whose mission is to bring happiness to all humanity.

In 1986, Master Ryuho Okawa renounced a promising career as a businessman and devoted his life to spreading the Truth.  He established "Happy Science" ("Kofuku-no-Kagaku" in Japanese), which was registered as a religious organization in 1991.  Since then, he has guided countless people to happiness, publishing over 1,300 books, giving over 2,000 lectures, creating numerous seminars and producing 8 films based on his teachings.

Furthermore, in order to guide companies and the Japanese government through today's troubling times, Master Okawa has given innumerable guidance in politics, economics and foreign affairs.

In 2009 and 2010 respectively, he laid the foundation for ideal politics and education by establishing the Happiness Realization Party and the Happy Science Academy for manifesting happiness in a tangible way.  In 2013, Happy Science Academy Kansai was also found and Happy Science University is planning to open in 2015.

A notice in the pamphlet informs about Okawa: "In 2010 alone, he published 52 books.  It was recorded by Guinness World Records as 'the most books written in one year by an individual.'"
Perusing issue 245 of the Happy Science Monthly periodical, I noticed that the total of books published by Okawa is currently reported as having surpassed 1,600.  Articles in the pamphlet included "Setting the Foundation for the Development of Japan by 2020" subtitled "Lecture on The Laws of Perseverance (Part 4)" and excerpts from one of Okawa's books in an article entitled "Spiritual Interview with Ichiru Suzuki."  An explanation about the latter article was offered: "On August 21st, 2013, Ichiru reached his remarkable 4,000 hits of his professional baseball career.  Upon hearing the news, on August 27th, 2013, Master Ryuho Okawa summoned the guardian spirit of Ichiru to interview him on his thoughts and the secrets to his success and professionalism."

A paragraph about another book mentioned that the "guardian spirit" of Russia President Vladimir Putin is the channeling source for another book.  I also learned there is also a 'Happiness Realization [political] Party.'  The Overview instructed:

The Happiness Realization Party is a new Japanese political party that was founded in May 2009 by Master Ryuho Okawa, the President of the Happiness Realization Party.  By preserving democracy and the values of freedom and prosperity, it aims to realize the happiness of the people of Japan, as well as the world, and thus create a utopian world.

At the center of Okawa's teachings is 'El Cantare,' who is described in the Overview brochure: "El Cantare is the spiritual name of the God, which means 'the light of the Earth,' whom Happy Science believers follow and worship.  He is the united consciousness of Buddha and God."  It seems that in this instance 'Buddha' expresses the same meaning as the name 'Christ' while 'El Cantare' might also be understood as another way of expressing the traditional metaphor of 'Holy Ghost'/'Holy Spirit.'

I conducted an Internet search to see if there were any Western media news articles about Okawa.  I found no in-depth articles.

The IRH Press/Happy Science imprint paperback book (an English translation) provided to me is The Secret Behind The Rape of Nanking: A Spiritual Confession by Iris Chang (2014). The book is identified at the top of the front cover as being part of the "Spiritual Interview Series."
The book has a question and answer interview style.  I am not knowledgeable about much of the Eastern historical data presented in the book yet the sentiments expressed by "the spirit of Iris Chang" seem reasonable, including some confusion about the turbulent final months of her Earth life.  Iris is the controversial author of the bestselling book The Rape of Nanking (1997). 
 
An introductory portion of the book "Publisher's Note" explains: "Happy Science's spiritual messages are not only from the spirits of people who lived in the past, but are also from the guardian spirits of living people [A guardian spirit resides in the spirit world, and is a part of the consciousness of the living person, as well as a past life of that person . . .]"  In this part of the book some assumptions are made about 'messengers of God,' reminding me of the importance of keeping the records of transcendental communication (and other interaction) from being altered or confused with passages of interpretation.  The Publisher's Note affirms about Okawa:

The majority of his spiritual messages are publicly recorded in front of a live audience.  Videos of these spiritual messages are made public, and the spiritual messages are published in books, too.
 
Okawa is conducting and publishing countless spiritual messages at an amazing pace to prove the existence of the spirit world and to enable readers to learn valuable lessons.
 
Described in the book as a "Chinese-American journalist," Iris Chang was born in New Jersey and grew up in Illinois.  She is a graduate of the University of Illinois, became a journalist and in 2004 at age 36 was found dead in her car after being shot in the head.  During the 2014 channeling session, three interviewers participated: Soken Kobayashi, Jiro Ayaori and Yukihisa Oikawa.  The following excerpts are from the interview transcript published in the book.  The communication of Iris Chang followed her being summoned by Okawa, who remains conscious while channeling.

They palmed off false material on me and made me write what I wrote.  I realized that some things were not as they seemed to me.


I was seeking justice.  "This is your chance to stand out, to become famous.  We'll give you the money and funding.  Write the book," they told me.  "We'll advertise it to make sure you get publicity," they said.  They told me all these good things.

But later, when I was criticized about various things, a lot of different pictures started to emerge.


I found that no matter how much I investigated, the materials were inconclusive.


It became increasingly agonizing.


It really struck me that I'd been misled when I realized that I had relied too heavily on the material provided by anti-Japanese groups of China and had written too much from their point of view, yet I'd sold 500,000 copies of my book and couldn't retract it.  After that it started to hurt my conscience to continue writing as a writer or journalist.


I had received a number of work requests and was interacting with a variety of people.  And in the middle of all that, I sometimes revealed my doubts about the content.


The doctor said that I had some type of psychological abnormality, so I had to take some medicine.  I think I was being given too much medication.  After that, I believe that maybe they did me in and made it look as if I had spontaneously committed suicide . . .


I feel that maybe I was made sick and made to look as if I had committed suicide.  This is probably because if I were still alive and were to hold a press conference denying the authenticity of the book, it would cause problems.


AYAORI: It has been 10 years now since your death . . .

IRIS CHANG: It's been that long?

AYAORI: Yes.

IRIS CHANG: Oh I see.


There actually is a hell.


AYAORI: So you have been gathering various information for the past ten years?

IRIS CHANG: Yes, and I feel like I'm also running around nightmarish war zones. Or I feel like I'm being hounded by someone in the United States. It seems like I'm running from place to place in the United States. Various things like those.

In the case of the United States, I often have nightmares in which it seems like I'm involved in something like mafia wars and being targeted with guns. When I go to China, there is something like a hell of war and I also gather information there, but it seems like things somehow don't make sense.

Also, after seeing the destruction of the World Trade Center in which 3,000 people died, I lost track of what is what, and I'm no longer sure about what justice is anymore.


I can't rest in peace unless this book is taken out of print.


Whatever the circumstances . . . you mustn't lie. Lies are wrong.


And furthermore, to the writers and journalists who are still using my words for their business, I want to say, "This is all fabricated. It is foolish to think that unreported facts about that time could be discovered in 1997" . . .


I'm very sorry . . .

There is a Happy Science website in English with information about Ryuko Okawa and his organizations.  Although numerous books have been published, it is reported that donations are the main source of funding.  A variety of articles about Okawa may be read at The Liberty Web, including about his own 'guardian spirit' and 'El Cantare.'  Here is an excerpt from the article "How to Understand the Importance of El Cantare's Love".

El Cantare has a cosmic characteristic.  El Cantare’s cosmic expression of love has been interwoven within the very fabric of the consciousness of the universe.  As I’ve explained in many of my books, humanoids and human-like beings live all throughout space and on other planets.

These beings are significantly different from humans in appearance, but they also receive teachings on "The Origin of Love," which directly flow from the Spring of Love.  El Cantare is the name of this "Spring of Love," which I liken to a tree-like structure in the universe.  El Cantare appears to me as a tree of universal life-force.  El Cantare exists at the heart of the birthplace of every human-like being.

Okawa being conscious while channeling differentiates him from trance-channelers, who are unconscious as another entity speaks through their bodies.  I conducted a You Tube search to see what videos of Okawa are available.
In addition to an 11-minute introductory video, I discovered there are available a few videos of Okawa speaking English.  A Happy Science Australia video entitled "The Law of Salvation Master Ryuho Okawa" shows that he is inexperienced speaking English.  A subtitled video about seven and a half minutes in length contributed to my introduction to Okawa's perspective (as he expressed at the time) — the following are the subtitles of the first portion of the discourse seen in "Can you handle the Truth?"

When I was speaking in Hawaii there were about 150 local members with an additional 50 people that those members brought along with to hear me.  The Hawaii branch was jam-packed, with people sitting along the sides, and even people sitting up beside the podium.  About half of the local members were crying, but the non-believers, those who call themselves Christians, received quite a shock.  What was it that shocked them?  It was when I declared that the one whom Jesus called 'Father' was me.  Now, for a Christian believer, this is like having someone split your head open with an axe.  I declared that I guided Him, that Jesus prayed every day to His Father, and that it was I who guided Him in what He would preach each day, telling Him that He need not worry about it . . .

Okawa said this with some humor, reminding how each person's spiritual reality is determined by one's own synthesis of understanding.  Eventually the wry rationale for Okawa's hypothetical perspective is stated:  "I am able to call out any god, or high spirit, or angel . . . they would come if called, and would have to speak to me.  I can call down the revelation.  What does that mean?  It means exactly that it reflects the position of El Cantare, as is taught in our teachings.  Because I'm master of them all . . ."

Reminding me of the 'Ra-Ta' conundrum in the Edgar Cayce channeled reading transcripts, the expression "brother souls" and the circumstances concerning Okawa learning about "past incarnations" are aspects of Okawa's case about which I would like to learn more.  A portion of the opening message of the aforementioned video—a quotation of Okawa—provides a means of comprehending the basis of his perspective of himself: "I am just a storyteller or liar or a savior . . . I must be, I want to be, I desire to be the third one.  Because, I love everybody . . ."  Perhaps Okawa was referring to Gautama Siddhartha and Jesus on this occasion yet there have been many people through the ages who have been subjects for scriptures that have inspired religions.  Other channelers have allowed their bodies to be used for transcendental communication explaining the Christian prophecy of the Second Coming — (through Edgar Cayce) as "that influence in the earth known as the Christ Consciousness, the coming of that force or power into the earth that has been spoken of through the ages"; (through JZ Knight) "The Coming of Christ is the awakening of that principle of that divinity in all people."

A video with the odd title "The Mayan Calendar Prophecy for 2012 and Its Connection with President Obama" presents Okawa commenting about apocalyptic fears and stating in English: "I now came down to here to stop [the] worrying of the world, to stop the destroying of the world, to stop the bad prediction of the world . . ."

There is a short clip of Okawa in a video entitled "Master Ryuko Okawa" in Malaysia".  Okawa is seen speaking in English:

The time has come.  You need new religion which combine all the religion, all the differences, all the — and overcome all the discommunications of the world.  We are One.  Asia is One.  The world is One.  We are living in the Age of Mercy.  Mercy's a different name of God.  Mercy means God stand by you everyday.

Among Happy Science data (FAQ Ryuho Okawa) is the identification of Okawa's soul as "the core part of El Cantare's consciousness" with details about Okawa's past lives.
 
The past incarnations of Ryuho Okawa's brother souls over the last 20,000 years are: La Mu on the Mu continent, Thoth in Atlantis, Rient Arl Croud in the ancient kingdom of the Incas, Ophealis and Hermes in Greece, Gautama Siddhartha (Shakyamuni Buddha) in India.  The core consciousness of El Cantare has descended only three times in the 300 million years of the history of humanity, the third being in the present day as Master Ryuho Okawa.  The two previous descents were under the name Alpha and then later Elohim.
 
It seems evident that when one studies the annals of unexplained phenomena, there are no two personal spiritual or religious orientations of people that are precisely the same as each individual's perspective derives from one's own experiences, family traditions and perceptions encompassing interpretations and beliefs.  My evaluation of the 'El Cantare' cryptogram is that the relationship of Ryuho Okawa to the spiritual Force is analogous for each human soul as an individual 'consciousness unit'/iota of 'God.'

Beyond the 'Spiritual Interview Series,' many books by Okawa offer philosophical topics with a prominent trilogy mentioned at the Happy Science website: The Laws of the Sun (1990), The Laws of Eternity (1998) and The Golden Laws (2000).
The first book of the trilogy concludes with some autobiographical details of Okawa's life.  Here are some excerpts from this part.

After having studied nothing but law, I encountered the "Right Law of God's Truth" instead of the six codes of law.  Then, in January of 1981 I began reading a volume called God's Truth out of Shinji Takahashi's trilogy, The Discovery of Mind.  When I reached somewhere around page 57, I realized that my heart was beating very quickly and my body began to sway back and forth.
 
Something was bound to happen.  I kept reading the books one after another by the same author and found myself always saying, "I already know this Truth.  I have learned it before."
 
On the twenty-third of March of the same year, a Sunday, I was suddenly struck by the feeling that somebody was trying to speak to me.  I hurried to get a card and a pencil.  My hand which held the pencil started to move as if it had its own life and wrote, "Good news, good news" on one card after another.  When I asked who it was, it signed "Nikko"; It was the Buddhist monk Saint Nikko.
 
After a while, St. Nichiren started to send messages.
 
 
Finally, a decisive moment arrived.  It was an evening in June of 1981.  A voice as solemn as I had never heard before suddenly echoed in my heart.  A person named Shinji Takahashi started to send messages to me.  He had passed away five years before.  I had never met him personally while he was alive, nor had I been aware of his existence.
 
Takahashi: "Ryuho Okawa, I come here to tell you of your vocation.  You must teach the laws of salvation to save humankind."
 
Okawa: "My Master, I'm only an ordinary business man at a trading house.  I am even a freshman at that.  What do you think I can do?  Or, do you mean that I should cooperate with the GLA (God Light Association), the body which your daughter has succeeded from you?"
 
Takahashi: "GLA does not need you.  You have to clear your own way.  You have to go your own way."
 
At that time, the spirit, named Shinki Takahashi, told me what my vocation was and who I was.
 
The person most surprised by this story came rushing from my home town.  It was Saburo Yoshikawa, the current Advisor to The Institute for Research in Human Happiness [the organization that has evolved into Happy Science].  Then, in the same month, June, 1981, Jesus Christ spoke to Saburo Yoshikawa through myself.  It was a very shocking event.
 
Since then, Yoshikawa and I have been researching God's Truth, sometimes being surprised at or wondering about innumerable spiritual phenomena unfolding one after another in front of us.  In the meantime, St. Nichiren informed us that Mr. Yoshikawa was St. Nichero in his past life, one of Nicheren's six senior disciples.
 
 
In August, 1985, we presented our  first publication of communications with the spiritual world, Spiritual Messages of St. Nichiren, for public judgment.  We were elated that the reaction was much greater and the criticisms much fewer than we had expected.  As more of our books were published; Spiritual Messages of Kukai, in October; Spiritual Messages of Jesus Christ, in December; Spiritual Messages of Amaterasu-O-Mikami, in February, 1986, the response from readers grew bigger and bigger.
 
While publishing these spiritual messages, I continued to work for the trading house.  I was in charge of international finance in one of the international general trading houses in Tokyo.
 
 
Eventually, in June, 1986, I was struck a hard blow.  Saint Nichiren, Jesus Christ, Ame-no-Minakanushi-no-Mikoto (the Lord God of the Heavenly Center, principal god in Japanese Shintoism), Amaterasu-O-Mikami (the Sun Goddess in Shintoism), Moses and Shinji Takahashi descended one after the other and sternly advised me to immediately leave the company.  After three sleepless nights, I finally tendered a letter of resignation to the company.  And on the fifteenth of July of that year, I formally resigned the trading house I had spent some years with, just after I had turned thirty on the seventh of July.
 
In September, 1986, I established "The Institute for Research in Human Happiness" in Tokyo and have dedicated my whole life to spreading God's Truth.
 
Previous blog articles about channeling include: "Taking a Closer Look at 'Unexplained Phenomena'", "Paulina Peavy Interview on Long John Nebel Radio Show 1958", "Ramtha's 2014 Interview", "Case Profile: Edgar Cayce""'The Dr. Fritz Phenomenon'""An Introduction to Healer John of God", "Mark Probert and The Inner Circle""Rosemary Brown and the Media", "The Coming of Seth" and "Chico Xavier: Medium of the Century by Guy Lyon Playfair".

24 April 2015

Unit roots, redux

Arnold Kling's askblog and Roger Farmer have a little exchange on GDP and unit roots. My two cents here.

I did a lot of work on this topic a long time ago, in How Big is the Random Walk in GNP?  (the first one)  Permanent and Transitory Components of GNP and Stock Prices” (The last, and I think best one) "Multivariate estimates" with Argia Sbordone, and "A critique of the application of unit root tests", particularly appropriate to Roger's battery of tests.

The conclusions, which I still think hold up today:

Log GDP has both random walk and stationary components. Consumption is a pretty good indicator of the random walk component. This is also what the standard stochastic growth model predicts: a random walk technology shock induces a random walk component in output but there are transitory dynamics around that value.

A linear trend in GDP is only visible ex-post, like a "bull" or "bear" market.  It's not "wrong" to detrend GDP, but it is wrong to forecast that GDP will return to the linear trend or to take too seriously correlations of linearly detrended series, as Arnold mentions.  Treating macro series as cointegrated with one common trend is a better idea.

Log stock prices have random walk and stationary components. Dividends are a pretty good indicator of the random walk component. (Most recently, here.)

Arnold asks  "In stock market returns, econometricians have been able to identify long-term mean reversion even though the short run is a random walk. Can something similar be done with GDP data?" Answer: Yes, and  Permanent and Transitory Components is it.

Both Arnold and Roger claim that unemployment has a unit root. Guys, you must be kidding. Actually, this makes a great test case for my point in "A critique", that it is a bad idea it is to blindly run unit root tests and then impose that structure.

A unit root means a random walk component. A random walk will eventually pass any upper and lower limit. Look at it. That's as stationary a series as you're going to find in economics. ("Look at the plot" and "think about the units" are the Cochrane unit root tests.)

Yes, unemployment like other stationary ratios in macro (consumption/GDP, hours/day, etc.)  have important and frequently overlooked low-frequency movements. But they are far from random walks, and they like unemployment have a very large transitory component at business cycle frequencies. When unemployment is above 8%, it is a good bet that it will decline over the next 5 years.

If you apply unit root tests to an hour of second by second temperature data from 9 to 10 AM you will think it has both a linear trend and a unit root. Millisecond data will not help you to detect climate change.  That's why unit root tests are a problem. You have to think, and consider the span of data you have and the frequency of mean reversion that makes economic sense in your data.

The tests are about infinite horizon behavior which you can never tell with finite horizons. However, they can alert you to low-frequency movement in your data, which can make ordinary distribution theory a bad guide. So can looking at a plot.

As far as I can tell, "Potential GDP" is equivalent to a two sided filter. It looks great ex-post. None of this is inconsistent with Arnold's view that standard calculations of potential GDP gaps do little to forecast GDP growth, especially in real time.

22 April 2015

The right to herd

Just when you thought financial regulation couldn't get more expansive and incoherent, our Justice Department comes in to defend morons' right to herd.

As explained in the Wall Street Journal at least, Mr. Navinder Singh Sarao is now under arrest, fighting extradition to the US, and his business ruined, for "spoofing" during the flash crash.

What is that? The Journal's beautiful graph at left explains.

The obvious question: Who are these traders who respond to spoofing orders by placing their own orders? Why is it a crucial goal of law and public policy to prevent Mr. Sarao from plucking their pockets? Is "herding trader" or "momentum trader" or "badly programmed high-speed trading program" or just simple "moron in the market" now a protected minority?

Why is Mr. Sarao being prosecuted and not all the people who wrote badly programmed algorithms that were so easily spoofed? If this caused the flash crash (how, not explained in the article) are they not equally at fault?

I don't mean by this a defense of the crazy stuff going on in high speed trading. As explained here, I think one second batch auctions are a much better market structure.  But the whole high speed trading thing is largely a response to SEC regulations in the first place, the order routing regulation, discrete tick size regulation, and strict time precedence regulation. A fact which will probably not enter at Mr. Sarao's trial (he doesn't seem to have billions for a settlement) and will give him little comfort in jail.

And maybe, just maybe, there is something more coherent here than the Journal lets on. I'll keep reading hoping to find it and welcome comments who can.

A larger thought. We still really want to rely on regulators to spot all the problems of finance and keep us safe from more crashes?

Update: Craig Pirrong excellent commentary here via a good FT alphaville post. Great quote:
The complaint alleges that Sarao employed the layering strategy about 250 days, meaning that he caused 250 out of the last one flash crashes. [my emphasis] I can see the defense strategy. When the government expert is on the stand, the defense will go through every day. “You claim Sarao used layering on this day, correct?” “Yes.” “There was no Flash Crash on that day, was there?” “No.” Repeating this 250 times will make the causal connection between his trading and Flash Clash seem very problematic, at best.
Update 2: Reading various commentaries that I can't find to cite any more, I realize that "front running" more than "herding" is the protected class. You "spoof" by putting in a bunch of orders just outside the current spread. The algorithms that respond to that think this behavior means some big orders coming, so try to front run those by buying. They cross the spread to take the small order you put on the other side. Or so the story goes. In any case, viewed as spoofers vs. front-runners it's harder still to have sympathy for the latter.

Update 3: Good Bloomberg View coverage from Matt Levine  and John Arnold, the source of the above front-running observation.

20 April 2015

Consumption-based model and value premium

The consumption based model is not as bad as you think. (This is a problem set for my online PhD class, and I thought the result would be interesting to blog readers.)

I use 4th quarter to 4th quarter nondurable + services consumption, and corresponding annual returns on 10 portfolios sorted on book to market and the three Fama-French factors. (Ken French's website)
The graph is average excess returns plotted against the covariance of excess returns with consumption growth. (The graph is a distillation of Jagannathan and Wang's paper, who get any credit for this observation.  The lines are OLS cross-sectional regressions with and without a free intercept.)


By comparison, the CAPM is the usual disaster. If we plot average returns against the covariance of returns with the market (rmrf) or against market betas, there is very little pattern. In particular, the hml portfolio, which by itself captures almost all the pricing information in the ten b/m portfolios (that's the point of the Fama-French model) has a 5% average return and a slightly negative market beta. The fact that the hml portfolio is right on the line in the previous graph is the main point of that graph.
There is an essentially correct story in the consumption-based model: value stocks and small stocks have higher average returns. And they have correspondingly higher covariance with consumption growth. Value and small stocks tend to do poorly in years of bad consumption growth, though they have little systematic correlation with the market.

Is this perfect? No. The model is \(E(R^e) = cov(R^e, \Delta c)) \times \gamma\) where \(R^e\) = excess return, \(\Delta c\) is consumption growth and \( \gamma\) is the risk aversion coefficient. The mean returns are so large -- and the volatility of consumption growth so small -- that the slope coefficient = risk aversion coefficient is 80, a bit hard for most people to swallow.

Also, this is the linearized model. The true nonlinear model is \(E(R^e) = -cov(R^e_{t+1}, (c_{t+1}/c_t)^{-\gamma})\), and raising things to the 80th power is a lot different than multiplying by 80. On the other hand, perhaps this is the key to good performance. If you think the underlying correct model works in continuous time,  which is linear, \( E_t(dR^e) = -E_t(dR^e, dc)  \gamma \), then perhaps the linearized model is a better approximation to annual time-averaged data than is the discrete-time model that pretends all consumption happens in one big lump every December 31. Furthermore, if you raise consumption growth to the 80th power, all the covariance of returns with marginal utility comes in one or two big spikes. The model becomes a model of rare disasters in marginal utility, not one of repeated events. Perhaps, but life would be so much easier if markets were about repeated risks not once per century disaster covariances.

The larger point: Very few researchers have really given the consumption model a good go to see just how full the glass might be. Hansen and Singleton famously rejected the model, but they used monthly seasonally adjusted consumption data, a bunch of low-power instruments, and no treatment of time aggregation (consumption is sum for the month, returns are 30th to 30th), or the durability of most "nondurable" goods. (Shirts are "nondurable." I get all mine at Christmas, hence 4th quarter to 4th quarter works pretty well for me!) Their point was mostly an illustrative example of GMM methodology not a serious Fama-French style empirical investigation of just how far a model can go. (The Fama-French model is also rejected!) It took 25 years before Jagannathan and Wang produced this simple graph. Can we do even better?

Sure, the consumption-based model won't work at a 5 minute interval. But is there some essence of truth in it, that stocks which fall more in business cycles, as measured by consumption, must pay a higher rate of return.  Just how far does that truth go? I think one could do far better by thinking hard about time aggregation,  data construction, durability, seasonal adjustment, and the appropriate frequency to evaluate such a model. And by trying to see just how far the model can go, rather than statistically rejecting its perfection.

In the end  "why are people afraid of value stocks and leave attractive returns on the table?" must come down to 1) they're morons, they haven't figured it out 2) the value premium isn't really there or 3) value stocks do badly in bad times, so make a portfolio riskier. That consumption is also low in these bad times seems pretty natural.

Update




From "Cross-Sectional Consumption-Based Asset Pricing: A Reappraisal" by Tom Engsted and Stig Vinther Møller at University of Aarhus. Thanks to Stig for the link. BOP and EOP are beginning of period and end of period consumption. In a discrete time model, do you treat the sum of consumption over the year as happening at the beginning of the year, or the end of the year? Treating it at the beginning produces the dramatic graph on the left.

This is a small instance of the many explorations one can do to see if there is some power to the consumption-based model, rather than just take it literally and reject it.

A bigger point. Means are pretty insensitive to timing. But covariances and correlations of white noise series are exquisitely sensitive to timing, measurement error, and so forth. \(cov(a_t,b_t)\) may be large, and \( cov(a_{t-1} b_t)=0\). Another approach is to create time averaged returns. I did this a long time ago here. Average january-january, feburary-february, march-march, etc. returns and compare them to the growth of annual macro data. The right thing to do is to explicitly model time aggregation -- the fact that consumption is reported as an annual average -- along with seasonal adjustment.


19 April 2015

Seances with Matylda in Poland 1930s

Alexander Imich in middle age



Alexander Imich (1903-2014) described witnessing seances with diverse manifestations of unexplained phenomena in Poland during the 1930s.  The medium is known as 'Matylda S.'  Imich is the editor of Incredible Tales of the Paranormal: Documented Accounts of Poltergeist, Levitations, Phantoms, and Other Phenomena (1995).  The book includes articles about the mediums known as Mirabelli and Franek Kluski by Guy Lyon Playfair and Dr. Roman Bugaj, respectively.  Imich contributed the chapter "Matylda."  Some biographical information about Imich is presented in the book:

Dr. Alexander Imich is a chemical consultant, a contributing editor to Psychological Abstracts, to Parapsychology Abstracts International, and in the past to Chemical Abstracts.  His articles were published in British, French, German, Italian, Indian, and USA periodicals.  Imich describes adventurous personal experiences with a little-known but powerful Polish medium, Matylda S.  This music teacher's late psychic career started after the death of the well-known Polish medium Jan Guzik.

Impressive experiments with Guzik were reported in Clairvoyance and Materialisation (1927) by Dr. Gustave Geley. 

Matylda was the widow of a medical doctor.  Imich wrote: "She had two sons to raise.  A graduate of a piano class of the conservatory, she loved music and turned to giving music lessons."  Imich never observed any indication of Matylda entering a trance state during seances.

Imich mentioned that documents connected with Matylda were lost during World War II and only the original paper he published in the German Zeitschrift für Parapsychologie (1932) was saved.  A college professor who was president of a Polish parapsychological society had informed Imich about 'Matylda S.'  Imich wrote to her, asking for permission to participate in a seance.  She invited him to come to Wloclawek from his home in the Polish town of Czestochowa.  The first two seances Imich witnessed would be recalled as being among "the strongest experiences of my adolescence."

The year was 1932 "shortly after Christmas."  Imich traveled by train and went directly from the train station to the indicated address, where the other participants were gathered.  He described Matylda as "a middle-aged woman, whose corpulence might have surprised those who would expect an intermediary between this world and the other to be more ethereal.  Only one feature lived up to the most exciting phantasy: the medium's eyes which were large, green and resembled the eyes of a nocturnal bird."

The seance participants were "mostly young people" and he decided, "In such a gay group there was no possibility of applying necessary controls."  However, a more significant realization would follow.  Imich recalled: "I did not know yet that there are phenomena which simply cannot be faked, and which make control, in its usual meaning, superfluous."

The phenomena began nearly at once after Matylda turned off the lights —

They were so explicit and so violent, at first I had no doubt they were faked.  I even admired the confidence—nay, the effrontery—of the person responsible for their production.  They were exceptionally numerous, one could say crowded, and appeared simultaneously at different locations.

Very soon, however, I understood that they were authentic.  Some were altogether inimitable.

Imich commented that "a feeling of eeriness pervaded my whole being."  The seance was being held in a small room of a ground floor apartment with thirteen participants.  The shutters were closed and the door was shut to the next room.  The sitters were gathered around a very large table three meters long and they formed a chain by linking their small fingers.  Imich was seated on the right side of the medium.

The seance participants "heard sounds and felt vibrations of the table caused by strong blows coming from underneath."  An extension board under the table was knocking against it.  Lights momentarily appeared — one of a bluish color appeared behind one person and a half minute later a light with a greenish tinge monetarily appeared in a corner of the room.  "From that moment on, such a great number of phenomena began to happen that I was quite unable to memorize them and still less able to remember the order in which they appeared."  He listed the occurrences with categorical headings.

Telekinesis included chairs moving from under participants with great force and noise that sent the chairs "flying" to the walls as "people frequently fell on the floor" — six chairs in one or two seconds.  A piece of chalk earlier placed on the table by the medium was heard by the sitters to "scribble with violence on the table" (the letter "O" was written and "three small crosses").  Then Imich's own chair was "strongly pushed."  The movement and transportation of objects left objects to be found on the table: a wooden riding horse for children, a chair, a shaving blade, keys and a pocket knife from Matylda's pocket, and a loaf of bread from the cupboard.

A cushion from the sofa was so strongly pressed against me that I was forced to defend myself with both hands.  A sweater fell on my head, a cracker on my chest, then—on the request of the medium—another cracker; then a doll was put to my lips.  In the red glow of my flashlight I saw a chair extracted from under one of the participants.  The heavy table around which we were sitting rose first on two legs, then violently on all four, then softly descended to the floor.  The height of the levitation did not exceed three inches.

The list of observed phenomena in the category Touches compiled by Imich begins with the recollection that soon after the beginning of the seance a participant exclaimed that something or somebody was pushing him.  "Matylda asked the spirits to show their strength."  Fifteen minutes later, Imich described feeling fingers lightly scratch his head.

Then something pulled my hair, touching my eyelids quite strongly at the same time.  During one of the heavy knocks against the table the end of my thumb was struck with great power; it continued hurting for a long while.  I heard some noises of the medium being touched or struck and of her struggle with the invisible powers wanting to strip her of different articles of clothing.  Time and time again one or another of the participants cried for help, beset by the invisible powers, so that it was frequently necessary to turn on the light.  Illuminated by my flashlight, during a fraction of a second, I saw the tousled hair of the girl sitting next to me who was defending herself against something.  Another girl had been dragged upon the table and was lying face down with her hands stretched out.  Another one had been lifted from her chair and was found sitting on the table.

The category Acoustic phenomena includes the descriptions of scratching upon the table, a rhythmical drumming on the table and "blows against the table so strong, it seemed surprising the massive table could withstand them."  He explained, "Those sounds were sometimes heard in such rapid sequence that it took only a second to make a complete round of the table — a terrifying cannonade."  Sounds heard from around the room were "boots stomping, then a fist knocking against the door. and unknown objects scratching and rapping the walls."

Invisible lips whistled in the air above us, and there were sounds of blowing with the accompanying air currents.  In addition to the croaking of a frog, were many other sounds difficult to describe or identify.

Considering Optical phenomena, among the approximately twelve times white, bluish or greenish lights "went on in different locations," three instances the lights appeared below the table near to Imich.  At one point when Matylda asked that the light should present itself, Imich saw an elliptically shaped light appear momentarily at the other end of the table at a height parallel with the head of one of the sitters; then the light "went off with a metallic sound."

The Apports (materialized objects) identified by Imich are a pine branch with a thick candle (the candle was from the fir Christmas tree in another room) and—also brought from nearby rooms—artificial flowers, one galosh, a strainer, a doll, a whip and a sheet of paper with greetings signed "Guzik."  When Imich requested Matylda to get out of her chair, she stood behind his chair and then "a deluge of events fell upon us so that the participants started screaming for light."  An apport of "freshly cut alpine flowers" appeared and—with the participants having heard coughing toward the end of the seance—there was noticed on the table "a half ounce of clear fluid."

There was also an incident with a radio loudspeaker.  Imich explained: "At that time loudspeakers were still a separate part of the receiving set; thus, a loudspeaker, in the form of an elegantly carved trumpet, stood on the wardrobe, while the receiver was inside of it."  During the seance, the wardrobe door was closed and could not be opened because of the position of a chair of one of the participants.  "Somebody asked for spoken words to come from the loudspeaker . . . After maybe ten or fifteen minutes, the loudspeaker started with music." Then:

I asked for another station and the tune actually changed.  This happened at once and without the whistles  that in the early radio receivers accompanied tuning in to a station.  I made one more request, asking for German speech; I had in mind a man's voice.  While German language did come out of the speaker, it was, however, feminine.  The characteristic noises of a distant radio transmitter accompanied this reception.

Alexander Imich's second seance with Matylda took place in the ground floor apartment of 'Lieutenant L.'  The lieutenant was present along with the medium, Imich and seven other participants.

The seance was being held in the middle room of three adjacent rooms, without doors in the doorways.  Entrances to the two rooms were from the street and from the courtyard.  Those two entrances and the shutters had been locked before the seance started. 
 
This time Imich sat at the end of the table opposite Matylda.
 
When the light was turned off, raps against the table were heard at once.  A vase with flowers was put into my lap; a crystal paperweight was thrown on the table with a grumble and a picture from the wall suddenly appeared on the table.  When the girl sitting next to me cried for help, I stretched out my hand to encounter a warm and soft hand which vanished instantaneously.  Then the "ghosts" began to annoy the young lieutenant who was attending a seance for the first time in his life.  As a gallant officer, he had taken a bold attitude towards ghosts in whose existence he did not believe.  Soon after the seance began, he seemed to become more and more excited.  First we heard the keys in his pocket jingling, then the chain on which his sabre was suspended.  Then he declared he was feeling the approach of a heavy mass and started to scream so loudly that we had to interrupt the seance and turn the light on.  This did not quiet the warrior.  His eyes were staring; he appeared to be in a trance.  He fought with whoever tried to approach him, and when I attempted to calm him, he attacked me with raised fists.  When he finally recovered consciousness, he left the seance, declaring he would never take part in any experiments with ghosts.  I was told later that he did not feel well and stayed in bed for several days.
 
A direct voice was a new phenomenon.  From the neighboring room a basso voice sounded near the floor.  Approaching the doorway leading to our room, it introduced itself as the spirit of the well-known Polish medium, the deceased Jan Guzik.  He spoke of my visit and bade me a friendly welcome.  The voice was particularly low and pronounced words with difficulty.  Suddenly, a bright light appeared on the chest of one of the participants, and I thought he was being dragged into the next room.  Guzik's voice fell silent, and we heard from the next room a loud noise as if the door had been slammed violently.  All that happened in just a few seconds.  The light was turned on.  From the next room our participant returned and declared that, in order to uncover a fake, he had suddenly lit his flashlight and run into the next room.  There was nobody there; he found the entrance door locked, the key in the lock inside the apartment.  In an agitated mood we returned to the seance.  We heard the squeak of the door as if opening very slowly, and suddenly we heard a crash as loud as a pistol shot, followed by the noise of broken glass, as if a large glass vessel had been thrown on the floor.  Terrified by this assault, we again interrupted the seance.  There was no trace of glass in the next room, and the door leading outside was locked, key in the lock.

The tension mounted still higher, but we decided to continue the seance.  In all three rooms undefined noises were heard simultaneously.  Again the squeak of the opening door and, in the next room, the sound of steps or two or more persons.  Then, some groaning and the sound of heavy breathing approached from the next room.  The narrow strip of light penetrating the crack in the shutter disappeared for a moment, as if obscured by a moving body.  The groans and heavy breathing now were near our table.  Matylda exclaimed that something heavy was lying on her.  In the darkness, through the change of acoustics, the presence of an additional body in the room could be sensed.  The tension became unbearable and cries for light sounded.  Imagine our terror when, in the full light of the chandelier, we saw on the floor a long body in a military trenchcoat.  What powers did we rouse?  What were we going to do now?  Light, that until now had been saving us from the dread of the unknown, suddenly lost its power.  As apprentices of the supernatural, we were now forced to face a great mystery.  I quickly glanced at all present with the last faint hope that the body on the floor was one of them.  My hope was futile; everybody was in his or her place.  In the meantime, somebody recognized the prostrated form as the owner of the apartment.  He had left town a few days ago.  We lifted him up and seated him on a chair.  He was unconscious but slowly recovering, looking with surprised eyes at the people assembled around him.  He told us he had just returned from his trip, had gone directly from the railroad station to a cafe to say hello to his friends, had then gone out into the street in the direction of his home—and he remembered no more.  He had no idea how he had entered the apartment.  I checked the entrance door again; it was locked from the inside.
 
After a lengthy interruption, we once more returned to the seance.  Of the many phenomena that followed, I will mention the apport of a letter.  It was accompanied by a noise—as if a roll of paper many feet long was being unrolled.  When the light was turned on, we found a small sheet of paper folded in four: "Matylda, your power is great" was written upon it.  I snatched the paper as a precious item for future archives.  Guzik's voice sounded again and made a false prediction [expectation?] that Gandhi would die in a prison.  I asked Guzik to materialize, but he declared that he was tired from yesterday's seance.  Some of those present said they could see a foggy person in a turban.  I, personally, did not see it.
 
At a certain moment, the voice began to predict an erotic episode to the medium; I learned later that, in the past, this had happened many times.  Matylda interrupted the voice, asking him to stop such prophecies.  When this did not help, she reiterated her request more forcefully, trying to dumbfound the basso voice and telling him in not-complimentary epithets what she thought of such enunciations.  The voice, however,  was not to be persuaded or silenced; it was growing louder and faster every moment.  The medium began to scream, and so did the voice.  The whole incident  resembled an ordinary quarrel between two mortals, yet extraordinary since it was taking place between a living person and an assumed spirit of a deceased being.  It would be doubly interesting for Freud—not only for its erotic content, but because of this unique assignation of roles.  Again light had to be turned on, and that's how the weird quarrel ended.

Considering the message left for Matylda, the question of what constitutes 'power' on Earth is a complex one.  I shared in a previous article an understanding of my own regarding earthly 'power' — If any exercise of power, influence or authority has a negative result then the perceived 'power' is a misconception.

Imich provided details about how Matylda became a medium.  She had attended a seance with the medium Jan Guzik a short time before his passing.  Imich wrote:

The wonders she saw, the existence of which she did not suspect, delighted her.  "I liked it most when a beautiful little light moving under the ceiling drifted down, lifted a bunch of keys from the dresser and put them very, very softly in my hand.  I was so delighted with the pranks played by the spirits that I simply began to like them and could not forget them."

One evening when she was playing cards with a woman friend, the doorbell was intermittently heard at her home  with nobody found to be outside each time.  Matylda suddenly deduced: "It was Jan (Guzik's first name) calling on me.  His spirit has come to me and will appear during seances."
 
Matylda professed her awareness that some of the people who had witnessed her seances didn't believe in 'spirits.'  She told Imich what had occurred after one of her grown-up sons declared, "I will believe in spirits when they bring me 1000 zlotys." 

"And, just imagine!  At the next seance we heard noise as if scores of bank notes were being counted by the fingers of an expert cashier.  We turned the light on.  On the table, before my son, lies a bank note—but one from the German occupation during World War I and without any value today.  It's strange, but that's how it is.  No great help can be expected from the spirits.  They help with small things.  They will bring an egg, a dinner role, an apple or few tomatoes.  They will gladly bring flowers, but money or other more valuable things—nothing doing.  They know how difficult my life is, apparently they are not allowed to help too much.  In the land of spirits there also must exist laws that cannot be broken." 
 
Imich left Wloclawek after experiencing the two seances and informed a psychical research society in London that Matylda was willing to participate in experiments.  He reported that Harry Price replied immediately with a formal invitation and a check for 300 pounds sterling to cover the expenses for Imich to accompany Matylda to London. 

He met her in Warsaw and recalled about the beginning of their railway journey: ". . . Matylda prayed frequently and addressed short invocations to Mr. Jan, her leading spirit."  They continued via boat from Ostend to Dover.  When the customs officer learned about the purpose of their visit he told them that Rudi Schneider had been in the United Kingdom just before them.  Imich commented, "He appeared to know something about parapsychology.  We were pleasantly surprised."  Matylda was quoted as having hopefully said, "Here they really love spirits."  It seems that Imich had no awareness of Price's unconvincing repudiation of Scottish medium Helen Duncan's seances in 1931. 

During three weeks in London, Matylda conducted seventeen uneventful sittings.

She complained that the spirits had let her down mercilessly, that she had exposed herself to the greatest shame of her life.  She explained that this was an exceptional opportunity to do what the spirits had always wanted—to let them be known by the entire world.  The actual opportunity might be the only one forever.  She implored, encouraged and threatened the spirits.  All in vain; the spirits had a deaf ear.

Imich learned about the resumption of anomalous manifestations during Matylda's seances after she returned home.   He soon went to Wloclawek accompanied by two of his friends.  The again tumultuous events he then witnessed included levitation, apports of candy, whistles/"whistling fragments of a tune," "words or broken sentences, sighs, groans; smacks were heard . . . meowing of cats, croaking of frogs . . . sounds of panting or blowing, accompanied by cool breezes on our faces or hands"; touches, raps, jerks. 
 
When Imich arranged for Matylda to conduct a series of twenty seances at his parents' house in Czestochowa, the perhaps still unexpected result was silence as had been experienced in London.  She could only theorize that the spirits needed time to learn her new location.

Imich reported that after he moved to Warsaw, he  convinced Matylda to visit her sister there for a longer stay.  After waiting many weeks, Imich arranged a trial seance in the apartment where she was staying.  A series of eventful and "wild" seances ensued with all the previously observed different aspects of phenomena: apports, touches, transports of objects, light phenomena, diverse sounds including raps and scraping, and "powerful blows in the table or floor."   

When the medium declared "Spirits, Dr. Imich loves you very much!" the basso voice replied, "And we love him too."

Unable to support herself in Warsaw, Matylda returned to Wloclawek and Imich could only occasionally visit her.

I was at the beginning of my professional career.  I had to establish my position, gain experience in my industrial specialty, and start saving money for an extended series of future experiments.

Then came World War II.

It destroyed millions of human lives.  Do I have to mention that it also ruined my project?  When the disastrous times were over, I could not find Matylda anymore.

In 2014 Alexander Imich was the topic of media news reports worldwide when he became the world's oldest validated living male.  When he passed in June 2014 at the age of 111, an AP article described him as "The world's oldest man, a retired chemist and parapsychologist" and a New York Times article described him as "a Polish-born psychic researcher."  The latter article mentioned Matylda and encapsulated what had happened to Imich during World War II —

With the outbreak of World War II, he and his wife fled to Soviet-occupied Bialystok, Poland, where they were sent to a Soviet labor camp.  Once freed, they moved to Samarkand, in what is now Uzbekistan, and then back to Poland, where they found many family members had died in the Holocaust.  In 1951 they immigrated to Waterbury, Conn.

Video footage of the elderly Imich may be seen on You Tube.

Some of the media coverage reveals the social conditioning of contemporary people who may not have personally read any original case studies of unexplained phenomena.  One 2014 article about Imich is even entitled "The World's Oldest Man is an Occult-Obsessed Weirdo." 

A close examination of the various manifestations detailed by Imich includes occurrences that offer parallels with what may be read in some well-known paranormal case studies, including the 'Bell Witch' Tennessee 'talking poltergeist' case.  Manifestations of Direct Voice (disembodied) communication has been documented in other cases of mediums who found this phenomena consistently happening in their presence.  The Leslie Flint case (1, 2, 3, 4, 5, 6) offers evidence in the form of Direct Voice audio recordings that afford researchers a precise understanding of moods and temperaments expressed with the transcendental communication.

Incredible Tales of the Paranormal is available from Bramble Books.
 

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