Issues with the Bayes estimator of a conjugate normal hierarchy model

Someone asks for an instability issue in R's integrate program:

Hello everyone,

I am supposed to calculate the Bayes estimator of a conjugate normal hierarchy model. However, the Bayes estimator does not have a closed form,

The book "Theory of Point Estimation" claims that the numerical evaluation of  this estimator is simple. But my two attempts below both failed.

1. I tried directly using the integration routine in R on the numerator and denominator separately. Maybe because of the infinite domain, occasionally the results are far from reasonable.

2. I tried two ways of change of variables so that the resulting domain can be finite. I let


But the estimator results are very similar to the direct integration on the original integrand. More often than it should occur, we obtain quite large evaluation of the Bayes estimator, up to 10^6 magnitude.

I wonder if there is any other numerical integration trick which can lead to a more accurate evaluation.

I appreciate any suggestion.


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xxx
Some State University
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Well, what happens here? Her program have a part that says:

[Bayes(nu,p,sigma,xbar) is the ratio of both integrals, "f", and "g" are the integrals, f is the numerator, g the denominator, so Bayes = f/g]

Now, executing Bayes(2,10,1,9.3) fails:

> Bayes(2,10,1,9.3)
[1] 1477.394

, which is much greater than the expected approx. 8.


I tried this with the same program, integrate, to do this simple case (dnorm is the normal distribution density):

> integrate(dnorm,0,1)
0.3413447 with absolute error < 3.8e-15
> integrate(dnorm,0,10)
0.5 with absolute error < 3.7e-05
> integrate(dnorm,0,100)
0.5 with absolute error < 1.6e-07
> integrate(dnorm,0,1000)
0.5 with absolute error < 4.4e-06
> integrate(dnorm,0,10000000000)
0 with absolute error < 0



As we can see, the last try, with a very large value, fails miserably, value is 0 (instead of 0.5) and absolute error is negative.

The program "integrate" uses code that is part of supposedly "a Subroutine Package for Automatic Integration", as it is advertised, but it cannot anticipate everything -- and we hit an instability we cannot solve.

My suggestion was to use integrate(f,0,1) and integrate(g,0,1) always until we get results outside what is reasonable. In those cases, we should try integrate(f,0,.999) and integrate(g,0,.999) with as many nines as we can (I got problems with just .9999, that's why I wrote .999 there).

Of course, you can always try a different method. Since this function is well-behaved, any simple method could be good enough.

Basel: Consultative document on recognising the cost of credit protection purchased

Basel Committee issues consultative document on recognising the cost of credit protection purchased
March 22, 2013
http://www.bis.org/press/p130322.htm

The Basel Committee on Banking Supervision has today published a proposal that would strengthen capital requirements when banks engage in certain high-cost credit protection transactions.

The Committee has previously expressed concerns about potential regulatory capital arbitrage related to certain credit protection transactions. At that time it noted that it would continue to monitor developments with respect to such transactions and would consider imposing a globally harmonised minimum capital Pillar 1 requirement if necessary. After further consideration, the Committee decided to move forward with a more comprehensive Pillar 1 proposal.

While the Committee recognises that the purchase of credit protection can be an effective risk management tool, the proposed changes are intended to ensure that the costs, and not just the benefits, of purchased credit protection are appropriately recognised in regulatory capital. It does this by requiring that banks, under certain circumstances, calculate the present value of premia paid for credit protection, which should be considered as an exposure amount of the protection-purchasing bank and be assigned a 1,250% risk weight.

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Recognising the cost of credit protection purchased

http://www.bis.org/publ/bcbs245.htm

The proposal set out in this consultative document would strengthen capital requirements when banks engage in certain high-cost credit protection transactions. The Committee has previously expressed concerns about potential regulatory capital arbitrage related to certain credit protection transactions. At that time it noted that it would continue to monitor developments with respect to such transactions and would consider imposing a globally harmonised minimum capital Pillar 1 requirement if necessary. After further consideration, the Committee decided to move forward with a more comprehensive Pillar 1 proposal.

While the Committee recognises that the purchase of credit protection can be an effective risk management tool, the proposed changes are intended to ensure that the costs, and not just the benefits, of purchased credit protection are appropriately recognised in regulatory capital. It does this by requiring that banks, under certain circumstances, calculate the present value of premia paid for credit protection, which should be considered as an exposure amount of the protection-purchasing bank and be assigned a 1,250% risk weight.

 

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Full text of the consultative doc: http://www.bis.org/publ/bcbs245.pdf

Basel Committee: supervisory guidance on external audits of banks (consultation)

Basel Committee publishes for consultation supervisory guidance on external audits of banks
March 21, 2013
http://www.bis.org/press/p130321.htm

The Basel Committee on Banking Supervision has today published supervisory guidance on External audits of banks for consultation along with a letter to the International Auditing and Assurance Standards Board (IAASB).

The consultative paper aims to enhance and supersede the existing guidance that was published by the Basel Committee in 2002 on the relationship between banking supervisors and banks' external auditors and in 2008 on external audit quality and banking supervision. The evolution of bank practices and the introduction of new standards and regulations over the last 10 years warranted a thorough revision of the Committee's supervisory guidance. In addition, the recent financial crisis has highlighted the need to improve the quality of external audits of banks. The proposed enhanced guidance sets out supervisory expectations of how:

• external auditors can discharge their responsibilities more effectively;
• audit committees can contribute to audit quality in their oversight of the external audit;
• an effective relationship between external auditors and supervisors can lead to regular communication of mutually useful information; and
• regular and effective dialogue between the banking supervisory authorities and relevant audit oversight bodies can enhance the quality of bank audits.

The Committee's letter to the IAASB calls for enhancing the International Standards on Auditing (ISAs) to include more authoritative guidance relating to the audit of banks. It sets out specific areas where the Committee believes the ISAs should be improved.

Commenting on today's publications, Stefan Ingves, Chairman of the Basel Committee and Governor of Sveriges Riksbank, said, "The Committee has developed guidance that builds on recent experience and will help raise the bar with regard to what supervisors expect of banks' external auditors and audit committees. We also recognise the great importance of audit standards and are keen to support the IAASB in enhancing audit quality."

Comments on the proposals should be submitted by Friday 21 June 2013 by e-mail to: baselcommittee@bis.org. Alternatively, comments may be sent by post to: Secretariat of the Basel Committee on Banking Supervision, Bank for International Settlements, CH-4002 Basel, Switzerland. All comments may be published on the website of the Bank for International Settlements unless a comment contributor specifically requests confidential treatment.

Tracking Global Demand for Advanced Economy Sovereign Debt

Tracking Global Demand for Advanced Economy Sovereign Debt. Prepared by Serkan Arslanalp and Takahiro Tsuda
IMF Working Paper No. 12/284
December 2012
http://www.imf.org/external/pubs/cat/longres.aspx?sk=40135.0

Recent events have shown that sovereign, just like banks, can be subject to runs, highlighting the importance of the investor base for their liabilities. This paper proposes a methodology for compiling internationally comparable estimates of investor holdings of sovereign debt. Based on this methodology, it introduces a dataset for 24 major advanced economies that can be used to track US$42 trillion of sovereign debt holdings on a quarterly basis over 2004-11. While recent outflows from euro periphery countries have received wide attention, most sovereign borrowers have continued to increase reliance on foreign investors. This may have helped reduce borrowing costs, but it can imply higher refinancing risks going forward. Meanwhile, advanced economy banks’ exposure to their own government debt has begun to increase across the board after the global financial crisis, strengthening sovereign-bank linkages. In light of these risks, the paper proposes a framework— sovereign funding shock scenarios (FSS)—to conduct forward-looking analysis to assess sovereigns’ vulnerability to sudden investor outflows, which can be used along with standard debt sustainability analyses (DSA). It also introduces two risk indices—investor base risk index (IRI) and foreign investor position index (FIPI)—to assess sovereigns’ vulnerability to shifts in investor behavior.

In service of the country: Ted van Dyk

My Unrecognizable Democratic Party. By Ted van Dyk
The stakes are too high, please get serious about governing before it's too late.
http://online.wsj.com/article/SB10001424127887324128504578344611522010132.html 
The Wall Street Journal, March 18, 2013, on page A13

As a lifelong Democrat, I have a mental picture these days of my president, smiling broadly, at the wheel of a speeding convertible. His passengers are Democratic elected officials and candidates. Ahead of them, concealed by a bend in the road, is a concrete barrier.

They didn't have to take that route. Other Democratic presidents have won bipartisan support for proposals as liberal in their time as some of Mr. Obama's are now. Why does this administration seem so determined to head toward a potential crash and burn?

Even after the embarrassing playout of the Obama-invented Great Sequester Game, after the fiasco of the president's Fiscal Cliff Game, conventional wisdom among Democrats holds that disunited Republicans will be routed in the 2014 midterm elections, leaving an open field for the president's agenda in the final two years of his term. Yet modern political history indicates that big midterm Democratic gains are unlikely, and presidential second terms are notably unproductive, most of all in their waning months. Since 2012 there has been nothing about the Obama presidency to justify the confidence that Democrats now exhibit.

Mr. Obama was elected in 2008 on the basis of his persona and his pledge to end political and ideological polarization. His apparent everyone-in-it-together idealism was exactly what the country wanted and needed. On taking office, however, the president adopted a my-way-or-the-highway style of governance. He pursued his stimulus and health-care proposals on a congressional-Democrats-only basis. He rejected proposals of his own bipartisan Simpson-Bowles commission, which would have provided long-term deficit reduction and stabilized rapidly growing entitlement programs. He opted instead to demonize Republicans for their supposed hostility to Social Security, Medicare and Medicaid.

No serious attempt—for instance, by offering tort reform or allowing the sale of health-insurance products across state lines—was made to enlist GOP congressional support for the health bill. It passed, but the constituents of moderate Democrats punished them: 63 lost their seats in 2010 and Republicans took control of the House.

Faced with a similar situation in 1995, following another GOP House takeover, President Bill Clinton shifted to bipartisan governance. Mr. Obama did not, then blamed Republicans for their "obstructionism" in not yielding to him.

Defying the odds, Mr. Obama did become the first president since Franklin Roosevelt to be re-elected with an election-year unemployment rate above 7.8%. Yet his victory wasn't based on public affirmation of his agenda. Instead, it was based on a four-year mobilization—executed with unprecedented skill—of core Democratic constituencies, and on fear campaigns in which Mitt Romney and the Republicans were painted as waging a "war on women," being servants of the wealthy, and of being hostile toward Latinos, African Americans, gays and the middle class. I couldn't have imagined any one of the Democratic presidents or presidential candidates I served from 1960-92 using such down-on-all-fours tactics.

The unifier of 2008 became the calculated divider of 2012. Yes, it worked, but only narrowly, as the president's vote total fell off sharply from 2008.

Other modern Democratic presidents have had much more success with very different governing strategies. In 1961-62, John Kennedy won Republican congressional and public support with the proposals of his Keynesian Council of Economic Advisers chairman, Walter Heller, to cut personal and business taxes "to get America moving again," and for the global free movement of goods, services, capital and people.

In 1965, Lyndon Johnson had Democratic congressional majorities sufficient to pass any legislation he wanted. But he sought and received GOP congressional support for Medicare, Medicaid, civil rights, education and other Great Society legislation. He knew that in order to last, these initiatives needed consensus support. He did not want them re-debated later, as ObamaCare is being re-debated now.

Johnson got bipartisan backing for deficit reduction in 1967, when he learned that the deficit had reached an unthinkable $28 billion. Faced with today's annual deficits of $1 trillion and federal debt between $16.7 and $31 trillion, depending on whether you count off-budget obligations, LBJ no doubt would appoint a bipartisan Simpson-Bowles commission and use it to get a tax, spending and entitlements fix so that he could move on to the rest of his agenda. Bill Clinton took the same practical approach and got to a balanced federal budget as soon as he could, at the beginning of his second term.

These former Democratic presidents would also know today that no Democratic or liberal agenda can go forward if debt service is eating available resources. Nor can successful governance take place if presidential and Democratic Party rhetoric consistently portrays loyal-opposition leaders as having devious or extremist motives. We really are, as Mr. Obama pointed out in 2008, in it together.

It's not too late for the president to take a cue from his predecessors and enter good-faith budget negotiations with congressional Republicans. A few posturing meetings with GOP congressional leaders will not suffice. President Obama's hype about the horrors of fiscal-cliff and sequestration cuts, and his placing of blame on Republicans, have been correctly viewed as low politics. His approval ratings have plunged since the end of the sequestration exercise.

But time is running out for Democrats to get serious about governance. That concrete barrier—in the form of the 2014 midterm—lies just ahead on the highway, and they're joy riding straight toward it.

Mr. Van Dyk served in Democratic national administrations and campaigns over several decades. His memoir of public life, "Heroes, Hacks and Fools," was first published by University of Washington Press in 2007.

A Framework for Macroprudential Bank Solvency Stress Testing: Application to S-25 and Other G-20 Country FSAPs

A Framework for Macroprudential Bank Solvency Stress Testing: Application to S-25 and Other G-20 Country FSAPs. By Andreas A Jobst, Li Ong, and Christian Schmieder

IMF Working Paper No. 13/68
March 13, 2013
http://www.imf.org/external/pubs/cat/longres.aspx?sk=40390.0

Summary: The global financial crisis has placed the spotlight squarely on bank stress tests. Stress tests conducted in the lead-up to the crisis, including those by IMF staff, were not always able to identify the right risks and vulnerabilities. Since then, IMF staff has developed more robust stress testing methods and models and adopted a more coherent and consistent approach. This paper articulates the solvency stress testing framework that is being applied in the IMF’s surveillance of member countries’ banking systems, and discusses examples of its actual implementation in FSAPs to 18 countries which are in the group comprising the 25 most systemically important financial systems (“S-25”) plus other G-20 countries. In doing so, the paper also offers useful guidance for readers seeking to develop their own stress testing frameworks and country authorities preparing for FSAPs. A detailed Stress Test Matrix (STeM) comparing the stress test parameters applie in each of these major country FSAPs is provided, together with our stress test output templates.

The Real Women's Issue: Time. By Jody Greenstone Miller

The Real Women's Issue: Time. By Jody Greenstone Miller
Never mind 'leaning in.' To get more working women into senior roles, companies need to rethink the clock
The Wall Street Journal, March 9, 2013, on page C3
http://online.wsj.com/article/SB10001424127887324678604578342641640982224.html


Why aren't more women running things in America? It isn't for lack of ambition or life skills or credentials. The real barrier to getting more women to the top is the unsexy but immensely difficult issue of time commitment: Today's top jobs in major organizations demand 60-plus hours of work a week.

In her much-discussed new book, Facebook Chief Operating Officer Sheryl Sandberg tells women with high aspirations that they need to "lean in" at work—that is, assert themselves more. It's fine advice, but it misdiagnoses the problem. It isn't any shortage of drive that leads those phalanxes of female Harvard Business School grads to opt out. It's the assumption that senior roles have to consume their every waking moment. More great women don't "lean in" because they don't like the world they're being asked to lean into.

It doesn't have to be this way. A little organizational imagination bolstered by a commitment from the C-suite can point the path to a saner, more satisfying blend of the things that ambitious women want from work and life. It's time that we put the clock at the heart of this debate.

I know this is doable because I run a growing startup company in which more than half the professionals work fewer than 40 hours a week by choice. They are alumnae of top schools and firms like General Electric GE +0.38% and McKinsey, and they are mostly women. The key is that we design jobs to enable people to contribute at varying levels of time commitment while still meeting our overall goals for the company.

This isn't advanced physics, but it does mean thinking through the math of how work in a company adds up. It's also an iterative process; we hardly get it right every time. But for businesses and reformers serious about cracking the real glass ceiling for women—and making their firms magnets for the huge swath of American talent now sitting on the sidelines—here are four ways to start going about it.

Rethink time. Break away from the arbitrary notion that high-level work can be done only by people who work 10 or more hours a day, five or more days a week, 12 months a year. Why not just three days a week, or six hours a day, or 10 months a year?

It sounds simple, but the only thing that matters is quantifying the work that needs to get done and having the right set of resources in place to do it. Senior roles should actually be easier to reimagine in this way because highly paid people have the ability and, often, the desire to give up some income in order to work less. Flexibility and working from home can soften the blow, of course, but they don't solve the overall time problem.


Break work into projects. Once work is quantified, it must be broken up into discrete parts to allow for varying time commitments. Instead of thinking in terms of broad functions like the head of marketing, finance, corporate development or sales, a firm needs to define key roles in terms of specific, measurable tasks.

Once you think of work as a series of projects, it's easy to see how people can tailor how much to take on. The growth of consulting and outsourcing came precisely when firms realized they could carve work into projects that could be done more effectively outside. The next step is to design internal roles in smaller bites, too. An experienced marketer for a pharma company could lead one major drug launch, for example, without having to oversee all drug launches. Instead of managing a portfolio with 10 products, a senior person could manage five. If a client-service executive working five days a week has a quota of 10 deals a month, then one who chooses to work three days a week has a quota of only six. Lower the quota but not the quality of the work or the executive's seniority.

One reason this doesn't happen more is managerial laziness: It's easier to find a "superwoman" to lead marketing (someone who will work as long as humanly possible) than it is to design work around discrete projects. But even superwoman has a limit, and when she hits it, organizations adjust by breaking up jobs and adding staff. Why not do this before people hit the wall?

Availability matters. It's important to differentiate between availability and absolute time commitments. Many professional women would happily agree to check email even seven days a week and jump in, if necessary, for intense project stints—so long as over the course of a year, the time devoted to work is more limited. Managers need to be clear about what's needed: 24/7 availability is not the same thing as a 24/7 workload.


Quality is the goal, not quantity. Leaders need to create a culture in which talented people are judged not by the quantity of their work, but by the quality of their contributions. This can't be hollow blather. Someone who works 20 hours a week and who delivers exceptional results on a pro rata basis should be eligible for promotions and viewed as a top performer. American corporations need to get rid of the notion that wanting to work less makes someone a "B player."

Promoting this kind of innovation, where companies start to look more like puzzles than pyramids, has to become part of feminism's new agenda. It's the only way to give millions of capable women the ability to recalibrate the time that they devote to work at different stages of their lives.

We have been putting smart women on the couch for 40 years, since psychologist Matina Horner published her famous studies on "fear of success." But the portion of top jobs that go to women is still shockingly low. That's the irony of Ms. Sandberg's cheerleading for women to stay ambitious: She fails to see that her own agenda isn't nearly ambitious enough.

"Leaning in" may help the relative handful of talented women who can live with the way that top jobs are structured today—and if that's their choice, more power to them. But only a small percentage of women will choose this route. Until the rest of us get serious about altering the way work gets done in American corporations, we're destined to howl at the moon over the injustice of it all while changing almost nothing.

—Ms. Greenstone Miller is co-founder and chief executive officer of Business Talent Group.

Rules, Discretion, and Macro-Prudential Policy. By Itai Agur and Sunil Sharma

Rules, Discretion, and Macro-Prudential Policy. By Itai Agur and Sunil Sharma
March 08, 2013
IMF Working Paper No. 13/65
http://www.imf.org/external/pubs/cat/longres.aspx?sk=40379.0

Summary: The paper examines the implementation of macro-prudential policy. Given the coordination, flow of information, analysis, and communication required, macro-prudential frameworks will have weaknesses that make it hard to implement policy. And dealing with the political economy is also likely to be challenging. But limiting discretion through the formulation of macro-prudential rules is complicated by the difficulties in detecting and measuring systemic risk. The paper suggests that oversight is best served by having a strong baseline regulatory regime on which a time-varying macro-prudential policy can be added as conditions warrant and permit.