Category Archives: Deep Questions

The Apostle of Negative Interest Rates

Miles Kimball is a Professor at the University of Michigan, and a vocal and prolific proponent of negative interest rates. His Confessions of a Supply-Side Liberal is peppered with posts on the benefits of negative interest rates.

March 2 Even Central Bankers Need Lessons on the Transmission Mechanism for Negative Interest Rates, after words of adoration, takes the Governor of the Bank of England (Mark Carney) to task. Carney’s problem? Carney wrote recently that unless regular households face negative interest rates in their deposit accounts.. negative interest rates only work through the exchange rate channel, which is zero-sum from a global point of view.

Kimball’s argument is a little esoteric, but promotes three ideas.

First, negative interest rates central bank charge member banks on reserves should be passed onto commercial and consumer customers with larger accounts – perhaps with an exemption for smaller checking and savings accounts with, say, less than $1000.

Second, moving toward electronic money in all transactions makes administration of negative interest rates easier and more effective. In that regard, it may be necessary to tax transactions conducted in paper money, if a negative interest rate regime is in force.

Third, impacts on bank profits can be mitigated by providing subsidies to banks in the event the central bank moved into negative interest rate territory.

Fundamentally, Kimball’s view is that.. monetary policy–and full-scale negative interest rate policy in particular–is the primary answer to the problem of insufficient aggregate demand. No need to set inflation targets above zero in order to get the economy moving. Just implement sufficiently negative interest rates and things will rebound quickly.

Kimball’s vulnerability is high mathematical excellence coupled with a casual attitude toward details of actual economic institutions and arrangements.

For example, in his Carney post,  Kimball offers this rather tortured prose under the heading -“Why Wealth Effects Would Be Zero With a Representative Household” –

It is worth clarifying why the wealth effects from interest rate changes would have to be zero if everyone were identical [sic, emphasis mine]. In aggregate, the material balance condition ensures that flow of payments from human and physical capital have not only the same present value but the same time path and stochastic pattern as consumption. Thus–apart from any expansion of the production of the economy as a whole as a result of the change in monetary policy–any effect of interest rate changes on the present value of society’s assets overall is cancelled out by the effect of interest rate changes on the present value of the planned path and pattern of consumption. Of course, what is actually done will be affected by the change in interest rates, but the envelope theorem says that the wealth effects can be calculated based on flow of payments and consumption flows that were planned initially.

That’s in case you worried a regime of -2 percent negative interest rates – which Kimball endorses to bring a speedy end to economic stagnation – could collapse the life insurance industry or wipe out pension funds.

And this paragraph is troubling from another standpoint, since Kimball believes negative interest rates or “monetary policy” can trigger “expansion of the production of the economy as a whole.” So what about those wealth effects?

Indeed, later in the Carney post he writes,

..for any central bank willing to go off the paper standard, there is no limit to how low interest rates can go other than the danger of overheating the economy with too strong an economic recovery. If starting from current conditions, any country can maintain interest rates at -7% or lower for two years without overheating its economy, then I am wrong about the power of negative interest rates. But in fact, I think it will not take that much. -2% would do a great deal of good for the eurozone or Japan, and -4% for a year and a half would probably be enough to do the trick of providing more than enough aggregate demand.

At the end of the Carney post, Kimball links to a list of his and other writings on negative interest rates called How and Why to Eliminate the Zero Lower Bound: A Reader’s Guide. Worth bookmarking.

Here’s a YouTube video.

Although not completely fair, I have to say all this reminds me of a widely-quoted passage from Keynes’ General Theory –

“Practical men who believe themselves to be quite exempt from any intellectual influence, are usually the slaves of some defunct economist. Madmen in authority, who hear voices in the air, are distilling their frenzy from some academic scribbler of a few years back”

Of course, the policy issue behind the spreading adoption of negative interest rates is that the central banks of the world are, in many countries, at the zero bound already. Thus, unless central banks can move into negative interest rate territory, governments are more or less “out of ammunition” when it comes to combatting the next recession – assuming, of course, that political alignments currently favoring austerity over infrastructure investment and so forth, are still in control.

The problem I have might be posed as one of “complexity theory.”

I myself have spent hours pouring over optimal control models of consumption  and dynamic general equilibrium. This stuff is so rarified and intellectually challenging, really, that it produces a mindset that suggests mastery of Portryagin’s maximum principle in a multi-equation setup means you have something relevant to say about real economic affairs. In fact, this may be doubtful, especially when the linkages between organizations are so complex, especially dynamically.

The problem, indeed, may be institutional but from a different angle. Economics departments in universities have, as their main consumer, business school students. So economists have to offer something different.

One would hope machine learning, Big Data, and the new predictive analytics, framed along the lines outlined by Hal Varian and others, could provide an alternative paradigm for economists – possibly rescuing them from reliance on adjusting one number in equations that are stripped of the real, concrete details of economic linkages.

The Arc Sine Law and Competitions

There is a topic I think you can call the “structure of randomness.” Power laws are included, as are various “arcsine laws” governing the probability of leads and changes in scores in competitive games and, of course, in winnings from gambling.

I ran onto a recent article showing how basketball scores follow arcsine laws.

Safe Leads and Lead Changes in Competitive Team Sports is based on comprehensive data from league games over several seasons in the National Basketball Association (NBA).

“..we find that many …statistical properties are explained by modeling the evolution of the lead time X as a simple random walk. More strikingly, seemingly unrelated properties of lead statistics, specifically, the distribution of the times t: (i) for which one team is leading..(ii) for the last lead change..(and (iii) when the maximal lead occurs, are all described by the ..celebrated arcsine law..”

The chart below shows the arcsine probability distribution function (PDF). This probability curve is almost the opposite or reverse of the widely known normal probability distribution. Instead of a bell-shape with a maximum probability in the middle, the arcsine distribution has the unusual property that probabilities are greatest at the lower and upper bounds of the range. Of course, what makes both curves probability distributions is that the area they span adds up to 1.


So, apparently, the distribution of time that a basketball team holds a lead in a basketball game is well-described by the arcsine distribution. This means lead changes are most likely at the beginning and end of the game, and least likely in the middle.

An earlier piece in the Financial Analysts Journal (The Arc Sine Law and the Treasure Bill Futures Market) notes,

..when two sports teams play, even though they have equal ability, the arc sine law dictates that one team will probably be in the lead most of the game. But the law also says that games with a close final score are surprisingly likely to be “last minute, come from behind” affairs, in which the ultimate winner trailed for most of the game..[Thus] over a series of games in which close final scores are common, one team could easily achieve a string of several last minute victories. The coach of such a team might be credited with being brilliantly talented, for having created a “second half” team..[although] there is a good possibility that he owes his success to chance.

There is nice mathematics underlying all this.

The name “arc sine distribution” derives from the integration of the PDF in the chart – a PDF which has the formula –

f(x) = 1/(π (x(1-x).5)

Here, the integral of f(x) yields the cumulative distribution function F(x) and involves an arcsine function,

F(x) = 2/(π arcsin(x.5))

Fundamentally, the arcsine law relates to processes where there are probabilities of winning and losing in sequential trials. The PDF follows from the application of Stirling’s formula to estimate expressions with factorials, such as the combination of p+q things taken p at a time, which quickly becomes computationally cumbersome as p+q increases in size.

There is probably no better introduction to the relevant mathematics than Feller’s exposition in his classic An Introduction to Probability Theory and Its Applications, Volume I.

Feller had an unusual ability to write lucidly about mathematics. His Chapter III “Fluctuations in Coin Tossing and Random Walks” in IPTAIA is remarkable, as I have again convinced myself by returning to study it again.


He starts out this Chapter III with comments:

We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted motions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued. For example, in various applications it is assumed that observations on an individual coin-tossing game during a long time interval will yield the same statistical characteristics as the observation of the results of a huge number of independent games at one given instant. This is not so..

Most pointedly, for example, “contrary to popular opinion, it is quite likely that in a long coin-tossing game one of the players remains practically the whole time on the winning side, the other on the losing side.”

The same underlying mathematics produces the Ballot Theorem, which states the chances a candidate will be ahead from an early point in vote counting, based on the final number of votes for that candidate.

This application, of course, comes very much to the fore in TV coverage of the results of on-going primaries at the present time. CNN’s initial announcement, for example, that Bernie Sanders beat Hillary Clinton in the New Hampshire primary came when less than half the precincts had reported in their vote totals.

In returning to Feller’s Volume 1, I recommend something like Sholmo Sternberg’s Lecture 8. If you read Feller, you have to be prepared to make little derivations to see the links between formulas. Sternberg cleared up some puzzles for me, which, alas, otherwise might have absorbed hours of my time.

The arc sine law may be significant for social and economic inequality, which perhaps can be considered in another post.

Our Next President is a Wrestling Giant – Trump

Greetings, and I thought you would all enjoy this bit of rough-and-tumble involving the leading Republican candidate so far for US President – Donald Trump.

Make sure you watch past the 42 second mark to see Trump lambast his billionaire buddy. 

So this is really happening. Trump apparently has hired people to work on his campaign for President, and he has taken an early lead over Scott Walker and Jeb Bush, and the other more minor candidates.

Failures of Forecasting in the Greek Crisis

The resounding “No” vote today (Sunday, July 5) by Greeks vis a vis new austerity proposals of the European Commission and European Central Bank (ECB) is pivotal. The immediate task at hand this week is how to avoid or manage financial contagion and whether and how to prop up the Greek banking system to avoid complete collapse of the Greek economy.


Thousands celebrate Greece’s ‘No’ vote despite uncertainty ahead

Greece or, more formally, the Hellenic Republic, is a nation of about 11 million – maybe 2 percent of the population of the European Union (about 500 million). The country has a significance out of proportion to its size as an icon of many of the ideas of western civilization – such as “democracy” and “philosophy.”

But, if we can abstract momentarily from the human suffering involved, Greek developments have everything to do with practical and technical issues in forecasting and economic policy. Indeed, with real failures of applied macroeconomic forecasting since 2010.

Fiscal Multipliers

What is the percent reduction in GDP growth that is likely to be associated with reductions in government spending? This type of question is handled in the macroeconomic forecasting workshops – at the International Monetary Fund (IMF), the ECB, German, French, Italian, and US government agencies, and so forth – through basically simple operations with fiscal multipliers.

The Greek government had been spending beyond its means for years, both before joining the EU in 2001 and after systematically masking these facts with misleading and, in some cases, patently false accounting.

Then, to quote the New York Times,

Greece became the epicenter of Europe’s debt crisis after Wall Street imploded in 2008. With global financial markets still reeling, Greece announced in October 2009 that it had been understating its deficit figures for years, raising alarms about the soundness of Greek finances. Suddenly, Greece was shut out from borrowing in the financial markets. By the spring of 2010, it was veering toward bankruptcy, which threatened to set off a new financial crisis. To avert calamity, the so-called troika — the International Monetary Fund, the European Central Bank and the European Commission — issued the first of two international bailouts for Greece, which would eventually total more than 240 billion euros, or about $264 billion at today’s exchange rates. The bailouts came with conditions. Lenders imposed harsh austerity terms, requiring deep budget cuts and steep tax increases. They also required Greece to overhaul its economy by streamlining the government, ending tax evasion and making Greece an easier place to do business.

The money was supposed to buy Greece time to stabilize its finances and quell market fears that the euro union itself could break up. While it has helped, Greece’s economic problems haven’t gone away. The economy has shrunk by a quarter in five years, and unemployment is above 25 percent.

In short, the austerity policies imposed by the “Troika” – the ECB, the European Commission, and the IMF – proved counter-productive. Designed to release funds to repay creditors by reducing government deficits, insistence on sharp reductions in Greek spending while the nation was still reeling from the global financial crisis led to even sharper reductions in Greek production and output – and thus tax revenues declined faster than spending.

Or, to put this in more technical language, policy analysts made assumptions about fiscal multipliers which simply were not borne out by actual developments. They assumed fiscal multipliers on the order of 0.5, when, in fact, recent meta-studies suggest they can be significantly greater than 1 in magnitude and that multipliers for direct transfer payments under strapped economic conditions grow by multiples of their value under normal circumstances.

Problems with fiscal multipliers used in estimating policy impacts were recognized some time ago – see for example Growth Forecast Errors and Fiscal Multipliers the IMF Working Paper authored by Oliver Blanchard in 2013.

Also, Simon Wren-Lewis, from Oxford University, highlights the IMF recognition that they “got the multipliers wrong” in his post How a Greek drama became a global tragedy from mid-2013.

However, at the negotiating table with the Greeks, and especially with their new, Left-wing government, the niceties of amending assumptions about fiscal multipliers were lost on the hard bargaining that has taken place.

Again, Wren-Lewis is interesting in his Greece and the political capture of the IMF. The creditors were allowed to demand more and sterner austerity measures, as well as fulfillment of past demands which now seem institutionally impossible – prior to any debt restructuring.

IMF Calls for 50 Billion in New Loans and Debt Restructuring for Greece

Just before to the Greek vote, on July 2, the IMF released a “Preliminary Draft Debt Sustainability Analysis.”

This clearly states Greek debt is not sustainable, given the institutional realities in Greece and deterioration of Greek economic and financial indicators, and calls for immediate debt restructuring, as well as additional funds ($50 billion) to shore up the Greek banks and economy.

There is a report that Europeans tried to block IMF debt report on Greece, viewing it as too supportive of the Greek government position and a “NO” vote on today’s referendum.

The IMF document considers that,

If grace periods and maturities on existing European loans are doubled and if new financing is provided for the next few years on similar concessional terms, debt can be deemed to be sustainable with high probability. Underpinning this assessment is the following: (i) more plausible assumptions—given persistent underperformance—than in the past reviews for the primary surplus targets, growth rates, privatization proceeds, and interest rates, all of which reduce the downside risk embedded in previous analyses. This still leads to gross financing needs under the baseline not only below 15 percent of GDP but at the same levels as at the last review; and (ii) delivery of debt relief that to date have been promises but are assumed to materialize in this analysis.

Some may view this analysis from a presumed moral high ground – fixating on the fact that Greeks proved tricky about garnering debt and profligate in spending in the previous decade.

But, unless decision-makers are intent upon simply punishing Greece, at risk of triggering financial crisis, it seems in the best interests of everyone to consider how best to proceed from this point forward.

And the idea of cutting spending and increasing taxes during an economic downturn and its continuing aftermath should be put to rest as another crackpot idea whose time has passed.

More on Negative Nominal Interest Rates

The European Central Bank (ECB) experiment with negative interest rates has not occurred in a vacuum. The concept has been discussed with special urgency since 2008 in academic and financial circles.

Recently, Larry Summers and Paul Krugman have developed perspectives on the desirability of busting through the zero bound on interest rates to help balance aggregate demand and supply at something like full employment.

Then, there is Ken Rogoff’s Costs and Benefits to Phasing Out Paper Currency, distributed by the National Bureau of Economic Research (NBER).

Rogoff notes,

If all central bank liabilities were electronic, paying a negative interest on reserves (basically charging a fee) would be trivial. But as long as central banks stand ready to convert electronic deposits to zero-interest paper currency in unlimited amounts, it suddenly becomes very hard to push interest rates below levels of, say, -0.25 to -0.50 percent, certainly not on a sustained basis. Hoarding cash may be inconvenient and risky, but if rates become too negative, it becomes worth it.

Rogoff cites Buiter’s research at the London School of Economics (LSE) which dates to a decade earler, but has been significantly revised in the 2009-10 timeframe.

For example, there is Negative Nominal Interest Rates: Three ways to overcome the zero lower bound, which sports the following abstract:

The paper considers three methods for eliminating the zero lower bound on nominal interest rates and thus for restoring symmetry to domain over which the central bank can vary its policy rate. They are: (1) abolishing currency (which would also be a useful crime-fighting measure); (2) paying negative interest on currency by taxing currency; and (3) decoupling the numéraire from the currency/medium of exchange/means of payment and introducing an exchange rate between the numéraire and the currency which can be set to achieve a forward discount (expected depreciation) of the currency vis-a-vis the numéraire when the nominal interest rate in terms of the numéraire is set at a negative level for monetary policy purposes.

Buiter notes the “scrip” money developed locally during the Great Depression (also see Champ) effectively involved a tax on holding this type of currency.

Stamp scrip, sometimes called coupon scrip, arose in several communities. It was denominated in dollars, in denominations from 25 cents to $5, with $1 denominations most common. Stamp scrip often became redeemable by the issuer in official U.S. dollars after one year.

What made stamp scrip unique among scrip schemes was a series of boxes on the reverse side of the note. Stamp scrip took two basic forms—dated and undated (often called “transaction stamp scrip”). Typically, 52 boxes appeared on the back of dated stamp scrip, one for each week of the year. In order to spend the dated scrip, the stamps on the back had to be current. Each week, a two-cent stamp needed to be purchased from the issuer and affixed over the corresponding week’s box on the back of the scrip. Over the coming week, the scrip could be spent freely within the community. Whoever was caught holding the scrip at week’s end was required to attach a new stamp before spending the scrip. In this scheme, money became a hot potato, with individuals passing it quickly to avoid having to pay for the next stamp.

Among the virtues of eliminating paper currency and going entirely to electronic transactions, thus, would be that the central bank could charge a negative interest rate.

Additionally, by eliminating the anonymity of paper money and coin, criminal activities could be more effectively controlled. Rogoff offers calculations suggesting the percentages of US currency held in Europe in ratio to overall economic activity are suspicious, especially since there are apparently a surfeit of 100 dollar bills in these foreign holdings.

These ideas go considerably beyond the small negative interest charged by the ECB on banks holding excess reserves in the central bank accounts. What is being discussed is an extension of negative nominal interest, or a tax on holding cash, to all business agents and individuals in an economy.

Video Friday – The Present Can Influence the Past?

In forecasting, the common assumption is that the present influences the future, but the opposite does not occur.

Oh to be sure, one develops expectations and, yes, predictions which may influence present actions. But these are not realized, but projected. What actually occurs tomorrow, however, is not usually considered to directly influence what transpires today, particularly chance events. Thus, if Roger flips a coin tomorrow and it comes up heads, that is not supposed to have any material effect on physical processes occurring today.

But this turns out to happen at the level of quantum reality – in other words, at a more fundamental level of physical reality, as the quantum eraser experiment proves.

OK, it is a good idea to begin with the classic double slit experiment, as a lead-in. Here are two videos, one with a comic strip professor, and the second with Professor Brian Greene of Columbia University and several of his collegues.


So you immediately get into what I would call metaphysics – issues of whether consciousness can impinge on what is being observed, thus changing it.

Again, Professor Brian Greene on the double slit experiment, another narrative.

 OK, so then there is the “quantum eraser.”

 I’m still thinking about this. It’s profound, experimental metaphysics. Time is not what we think it is, just as space is not what it seems.

Quantum entanglement, incidentally, is what Einstein called “spooky action at a distance.”

Links – late August 2014

Economics Articles, Some Theoretical, Some Applied

Who’s afraid of inflation? Not Fed Chair Janet Yellen At Jackson Hole, Yellen speech on labor market conditions states that 2 percent inflation is not a hard ceiling for the Fed.

Economist’s View notes a new paper which argues that deflation is simply unnecessary, because the conditions for a “helicopter drop” of money (Milton Friedman’s metaphor) are widely met.

Three conditions must be satisfied for helicopter money always to boost aggregate demand. First, there must be benefits from holding fiat base money other than its pecuniary rate of return. Second, fiat base money is irredeemable – viewed as an asset by the holder but not as a liability by the issuer. Third, the price of money is positive. Given these three conditions, there always exists – even in a permanent liquidity trap – a combined monetary and fiscal policy action that boosts private demand – in principle without limit. Deflation, ‘lowflation’ and secular stagnation are therefore unnecessary. They are policy choices.

Stiglitz: Austerity ‘Dismal Failure,’ New Approach Needed

US housing market loses momentum

Fannie Mae economists have downgraded their expectations for the U.S. housing market in the second half of this year, even though they are more optimistic about the prospects for overall economic growth.

How Detroit’s Water Crisis Is Part Of A Much Bigger Problem

“Have we truly become a society to where we’ll go and build wells and stuff in third world countries but we’ll say to hell with our own right here up under our nose, our next door neighbors, the children that our children play with?”

Economic harassment and the Ferguson crisis

According to .. [ArchCity Defenders] recent report .. the Ferguson court is a “chronic offender” in legal and economic harassment of its residents….. the municipality collects some $2.6 million a year in fines and court fees, typically from small-scale infractions like traffic violations…the second-largest source of income for that small, fiscally-strapped municipality….

And racial profiling appears to be the rule. In Ferguson, “86% of vehicle stops involved a black motorist, although blacks make up just 67% of the population,” the report states. “After being stopped in Ferguson, blacks are almost twice as likely as whites to be searched (12.1% vs. 7.9%) and twice as likely to be arrested.” But those searches result in the discovery of contraband at a much lower rate than searches of whites.

Once the process begins, the system begins to resemble the no-exit debtors’ prisons of yore. “Clients reported being jailed for the inability to pay fines, losing jobs and housing as a result of the incarceration, being refused access to the Courts if they were with their children or other family members….

“By disproportionately stopping, charging, and fining the poor and minorities, by closing the Courts to the public, and by incarcerating people for the failure to pay fines, these policies unintentionally push the poor further into poverty, prevent the homeless from accessing the housing, treatment, and jobs they so desperately need to regain stability in their lives, and violate the Constitution.” And they increase suspicion and disrespect for the system.

… the Ferguson court processed the equivalent of three warrants and $312 in fines per household in 2013.


Astronauts find living organisms clinging to the International Space Station, and aren’t sure how they got there


A Mathematical Proof That The Universe Could Have Formed Spontaneously From Nothing

What caused the Big Bang itself? For many years, cosmologists have relied on the idea that the universe formed spontaneously, that the Big Bang was the result of quantum fluctuations in which the Universe came into existence from nothing.


Big Data Trends In 2014 (infographic – click to enlarge)