## Tuesday, November 27, 2012

### Problematicity of minimum wages, part 2

Some time ago, I wrote about why I consider minimum wages unempowering and harmful to the least privileged members of society.  I contended that minimum wages shut out from the labor market - a fundamental social institution - those people whose labor is least valuable.  It prevents them from exercising what little power they have and perpetuates their disenfranchisement by preventing them from accumulating social and human capital through employment.

I'd like to revisit that topic briefly to better explain why a minimum wage effectively bars the least valuable, least privileged, and least powerful members of society from employment.

The process of establishing wages is effectively a negotiation between employer and employee.  In some cases - when the employee's power is checked by the presence of many other potential employees - the employer can set the wage.  In other cases - when the employer's power is checked by the presence of many other potential employers - the employee can set the wage.  The freer the market, the less power both employee and employer have.  All the rest of the time, employee and employer negotiate and arrive at a compromise.

Negotiations end when either the parties reach an agreement, or when one party walks away from the negotiation.  The threat of walking away without a deal is a bargaining tactic.

This illuminates the brutal consequences of a minimum wage.  In the presence of a minimum wage, the employer cannot offer a wage low enough to make the potential employee a contributing laborer.  So the employer walks away from negotiation, leaving the employee out in the cold.  The minimum wage effectively bars the least valued members of society from participating in the labor market not by outright exercise of force, but by the conjunction of freedom to walk away from negotiation and conditions on the price of labor.

In a modern, wealthy welfare state, the people most affected by the minimum wage and shut out from labor force participation move from job to job, work for cash, consume very little, and rely on friends, family, charity, and welfare.  They're not starving to death, but they are shut out of permanent participation in the labor force.  Thus they have difficulty accumulating social and human capital - they're stuck in an effective poverty trap.

So here are two general classes of solutions to this disenfranchisement.  One type of solution is to remove the ability of employers to step away from the negotiating table.  Mandate that employers take any job applicant and pay them a set wage.

The other type of solution - the type I favor: do away with the minimum wage and replace it with an anti-poverty measure that genuinely empowers the underprivileged, instead of one that merely looks nice to us upper-middle-class folks while silently disenfranchising the poorest, least valuable members of our society.

## Saturday, November 17, 2012

### 332 straight months of above-average temperatures

I ran across this on Facebook today.  It turns out that I have never, in my whole life, experienced a month with below-average temperatures:

The average temperature across land and ocean surfaces during October was 14.63°C (58.23°F). This is 0.63°C (1.13°F) above the 20th century average and ties with 2008 as the fifth warmest October on record. The record warmest October occurred in 2003 and the record coldest October occurred in 1912. This is the 332nd consecutive month with an above-average temperature.
In other words, for 332 straight months, the average temperature has been above the 20th century average temperature.

This got me thinking about just what the chances of that are.  I want to make one simple assumption and then test the hypothesis that global warming is not occurring.

Temperature Deviations

Let's look at temperature deviations.  Call the average temperature over the century $$T$$.  We should think of this as the long-haul temperature.  If global warming isn't happening, then this is the "baseline temperature" of the Earth.

Each month, the average temperature doesn't necessarily need to be the same as the long-haul temperature.  It might be above or below, depending on whether there's something like El Nino going on, or if the sun is extra-bright, and so on. Either the temperature in that month is above or below the long-run temperature$$T$$.  Whether or not the temperature is above or below -- one of those two outcomes -- is what we'll focus on.

Here's our one simplifying assumption.  The probability of monthly temperature being above or below $$T$$ in one month does not depend on whether it was above or below $$T$$ in previous months.

This lets us treat monthly temperature as a Bernoulli process.  This is a standard piece of finite mathematics which I'll proceed to explain.

Bernoulli Processes

(If you want to get to the meat, skip this section and go to the next one.)

A Bernoulli process is an experiment with the same two outcomes ("success" and "failure") and the same two probabilities (of success, of failure) repeated over and over again.  The probabilities don't change from experiment to experiment.

The standard example of a Bernoulli process is flipping a coin over and over again.  There are two outcomes each time (heads and tails), and each time the probabilities are the same ($$0.5$$) each).

The usual question in a Bernoulli process is, "What's the probability of getting this many successes in that many trials?"  For example, we might ask, "what's the probability of getting $$2$$ heads if we flip a coin $$3$$ times?"  Here's a quick explanation of where the answer comes from.  It requires two "black box facts."

We did not specify the order of the heads.  So, for example, the outcomes HHT, HTH, THH all qualify as "three heads."  Each of these outcomes has the same probability: since the probabilities don't change from experiment to experiment, the experiments are independent.  Black-box fact one: The probability of a string of independent outcomes is the product of each outcome's probability.  That is, the probability of HHT is the probability of H times the probability of H times the probability of T.

Now to get the probability of two heads (instead of HHT, say) we just have to add up the probabilities of all the different ways we can have two heads in three flips.  Each has the same probability, so we just need to multiply that probability by the number of different ways we can get two heads in three flips.  Black-box fact two: the number of ways of choosing two of the three flips to be heads (order doesn't matter) is the number $$C(3,2) = 3$$.

So the probability of flipping two heads in three tosses is $$3(0.5)^3$$.

More generally, the probability of getting $$k$$ successes in $$n$$ trials (if $$p$$ is the probability of success and $$q$$ is the probability of failure) is
$$C(n,k)p^kq^{n-k}.$$

Climate as Bernoulli Process

Our climate model is basically a series of coin flips.  If the long-haul temperature average isn't changing, then each month, the probability of above-average temperatures is just the same as the probability of below-average temperatures.  That is, there's a $$50\%$$ chance that either occurs.  We want to know the probability of $$332$$ above-average temperatures in as many trials.

This just like treating each month as a coin flip.  If you flip a coin $$332$$ times, what's the chance that you get $$332$$ heads in a row?

$$C(332,332)\bigg(\frac{1}{2}\bigg)^{332}\bigg(\frac{1}{2}\bigg)^0 = \frac{1}{2^{332}}.$$

That is an incredibly small, tiny, vanishing, eensy-weensy, little number.  It's on the order of $$10^{-100}$$, that is, one in $$10^{100}$$.  By comparison, there are roughly $$10^{80}$$ atoms in the observable universe.  So if we gathered all of those atoms into one box, colored one blue and all the rest white, and grabbed one of the atoms while blindfolded, we're billions of times more likely to pick the blue atom than we are to have $$332$$ straight months of above-average temperatures.

The tl;dr?  If global warming is not happening, and if the temperature each month is independent of the temperature the previous month, then the probability of $$332$$ straight positive deviations is a billion trillion times less likely than reaching into a bin of all the atoms in the observable universe and randomly picking the one blue atom.  So, global warming is almost certainly happening.

## Tuesday, November 13, 2012

### Libertarianism as collectivism

I want to make an odd sort of point here.  Usually, one thinks of libertarianism as an ideology focused on freedom and "collectivism" as describing an ideology which focuses on restraining freedom for the common good.  I want to compare the two and troll around for interesting similarities.

Without being so pedantic as to pull up the dictionary definition, let's identify libertarianism as an ideology of government that holds the following: The best government enforces simple rules of property ownership and contract obligations and restrains coercive behavior (i.e., threat of force to extract negotiating concessions), but does not otherwise constrain behavior.  Individual people should be (this ideology holds) free to move about and engage with each other in voluntary interactions.

Libertarian litererary works focus on freedom of action and contrast it with restrictions: Capitalism and Freedom, The Road to Serfdom, Free to Choose, Atlas Shrugged, and so on.  The greatest good is achieved when the use of force is restricted to stopping the use of force.

Whence justification for this position?  Libertarians are highly suspicious of centralized economic and social coordination for several reasons.  These are perhaps the three most cited, aside from a moral imperative that freedom be preserved.
• The Hayekian information problem: no single agent can have enough information to successfully coordinate economic activity.
• The public choice criticism: Dominant groups subvert central coordination to perpetuate their own dominance.
• The efficiency critique: A central planner will require the use of resources to centrally plan, and one large enough to direct the economy will consume a portion of economic resources that could be otherwise used for investment or consumption.

These justifications continue to claim that the well-being of society is higher with minimal government intervention.  Libertarianism is a superior ideology, then, for utilitarian reasons: Society as a whole is better off with less central intervention, even if some people are worse off.  The better-off people are better off than the worse-off people are worse off.

Collectivism is often thrown around as an epithet by libertarians: "Oh, you're a collectivist."  (Apparently, it's often leveled at less dogmatic libertarians as well as at progressives, socialists, or communists --- in one entertaining account, Ludwig von Mises stormed out of a meeting of the Mont Pelerin Society after accusing Milton Friedman of being a socialist.)  An ideology may be described as collectivist insofar as it requires the subordination of individual freedom and well-being to the collective good of all of society.

So here's the interesting comparison.  Let's grant for a moment the proposal of utilitarian libertarians that a libertarian society is better off than a non-libertarian society.  In particular, those who are less well-off than under alternative systems should accept that, for the greater good.  Laid-off steel worker?  Find a different job - your sacrifice enables lower prices for most people; they are better off than you are worse off.  Trained as a vacuum-tube computer punch-card operator?  Sorry, obsolete technology - we're all better off using semiconductor computers, except maybe you.  Low education?  Accept that minimum wage job - you're not capable of offering any more to society, and the resource use in a higher wage is better used elsewhere.  If you don't like your circumstances, you should work to improve yourself, not expect society to dump resources into your life so you can be a net drain on it.

What is this, but collectivism?  This vision of libertarianism sees humans like ants, and economic order in human society arising as spontaneously as order in an ant colony.  To distort that spontaneous order is to hurt the colony as a whole; to embrace that spontaneous order is to embrace the greater good of the colony.

Meanwhile, no ant is intrinsically worthwhile.  All ants contribute, and together create great things; but if an ant ceases to be a net contributor, it must change or cease to exist.  Same with humans - as a professor of mine once indignantly exclaimed, "Why shouldn't people have to pay the costs they impose on other people?"  (Corollary: If someone can't pay, why should they be able to exist?)

It seems to me that this libertarian perspective holds that, sometimes, in service to the greater good of society, people's livelihoods and well-being have to be sacrificed.  Society is best off when resources are directed according to free markets, and if that hurts people - so be it; they must have been net drains on society.  Thus: libertarianism as collectivism.

## Friday, November 9, 2012

### Is Indiana atypical?

Indiana consistently votes Republican.  It was a MAJOR surprise to everyone involved when Indiana barely went for Obama in 2008.  This is not typical of the Midwest: for the last twenty years, in successful Democratic election years, Indiana sticks up out of the South like a sore red thumb.  (When a Republican takes the White House, Ohio often keeps Indiana company.  While Ohio is a swing state, though, Republicans can count on Indiana for its solid dozen-or-so electoral votes.)

Short question: Is this atypical?  The question was prompted by this amusing picture:
There are five major exceptions to the pattern: New Mexico, Colorado, Virginia, Florida, and Indiana.  With the exception of Indiana, we can predict the changes based on demographics: increases in the Hispanic population, and urbanization around the District of Columbia.  But Indiana's demographics haven't significantly changed in the same way - so what's the deal?

So I compared Indiana to its close neighbor Illinois, using the New York Times' data on each state.  Glancing at county-by-county results, we see broadly similar trends: mostly red, with urban areas and some traditionally Democratic counties blue.  The glaring source of difference between Illinois and Indiana is Chicago.  I crunched a few numbers (rounding to the nearest thousand and ignoring third-party candidates - those will account for discrepancies of a few percentage points).

Illinois has 20 electoral votes, and just over 5 million votes (5,006,000) were cast in the state.  Just under 2 million (1,918,000) of them were cast in Cook County.  Obama carried Illinois with 57% of the vote, 2,916,000 votes, while Romney received 43%, or 20,990,000 votes.

Indiana, meanwhile, has 11 electoral votes.  In Indiana, 2,552,000 votes were cast, with 1,412,000 (or 54%) cast for Romney and 1,140,000 (44%) cast for Obama.

Let's suppose that Cook County just suddenly fell into Lake Michigan.  What would happen to Illinois' vote totals?  Well, instead of 5 million votes, only a handful more than 3 million votes would be cast (much closer to Indiana's 2.6 million total).  Removing the Cook County voting from the Obama-Romney statewide totals gives Romney 1,611,000 votes to Obama's 1,477,000 votes.  This is an edge of 52% - 48% to Romney (much closer to Indiana's 55%-45%).  Romney would get Illinois' electoral votes ... but there wouldn't be 20 anymore.  Crude scaling suggests there would be 12 electoral votes (hey, Indiana has 11!).

Neat, huh?  If Illinois didn't have Chicago, it would function like Indiana's twin: A state with a couple of mid-sized, moderately dense cities (Indianapolis, Fort Wayne, Evansville, South Bend, ...) in a sea of rural conservative counties.  A huge, dense urban area makes the difference between a reliable large Democratic state and a reliable mid-sized Republican state.

What about Ohio, Indiana's other neighbor?  It doesn't have any one tremendously huge, dense urban area, nor does it have only a few  - instead, it has several large, dense cities spread throughout the state (Cincinnati, Cleveland, Toledo, Columbus, Dayton, Youngstown).  The urban/rural tension is finely balanced, so Ohio functions as a swing state.

## Thursday, August 23, 2012

### Problematicity of minimum wages

We can express a minimum wage as a price floor in each labor market.  Simple models indicate that minimum wages have no effect in high-wage markets and cause unemployment in low-wage markets; the overall effect on unemployment should be relatively low, since the median hourly wage is roughly $16.50. I don't want to discuss the empirics of the minimum wage here; we'll save that for a future post. Many arguments about the minimum wage focus on its reduction of quantity of labor demanded, or increase of quantity of labor supplied. Some focus on unemployment. Others focus on the infringement of contractual freedom (a perpetual, and to me perplexing, obsession of libertarians). Rather than use those arguments, I'll argue from a moral perspective: Imposing a minimum wage marginalizes those whose labor is less valuable than the minimum wage indicates and robs them of autonomy and dignity. This imposition disproportionately affects underprivileged groups, since their lack of privilege translates into labor of lower value. If we wish to assist underprivileged and marginalized groups, we should find a way to do so that supports their autonomy and dignity, rather than effectively punishing them for having time worth less than the minimum wage. Pecuniary value exists entirely in the eye of the beholder; an asset is only and precisely as valuable as what others are willing to exchange for it. I shall refer to pecuniary value as "value." Market process discovers the pecuniary value of assets and, over time, matches assets to those who place the highest value on them. One important observation is that value can only be discovered. It cannot be declared. One cannot declare, "This home is worth$300,000!" and cause the home to be worth $300,000 --- the home's value can only be ascertained by the bids of those who are interested in purchasing. We may regard time as an asset: one exchanges time (in the form of giving up alternative uses to perform certain obligations) for money. The wage rate, reflects the value of one's time. If people are willing to pay me$35 for an hour of instruction, then an hour of my time is worth at least \$35.  (I paper over the distinction between marginal value and value.)

The labor market is an emergent social mechanism involving suppliers of labor and buyers of labor.  It acts to discover the value of each worker's time and match that worker to the employer who values her time most highly.  Each transaction is an approximate lower bound on the value of the time of the worker.

Imposing a floor on the price of labor declares that no employer may purchase time worth less than this bound.  Those whose time is worth less than the bound are shut out from participating in the labor market.  (In practice, they may participate, but will not be formally hired - hence the increase in unemployment.  Or they will participate in informal labor arrangements.)

The minimum wage declares: If your labor is worth less than this wage, you are excluded. You may not participate in this fundamental social institution.  Effectively, a minimum wage sets a minimum worthy value to time and outlaws the employment of people whose time is worth less than that minimum worthy value --- it marginalizes individuals with time less valuable than the wage.

This marginalization disproportionately impacts underprivileged groups, whose time is often worth less because of this underprivileging.  Because current employment -- by generating experience and connections, for example -- usually increases the future value of labor, effective minimum wages perpetuate the impoverishment and disenfranchisement of those groups.

In addition to blocking a mechanism that can act to correct social injustice, a minimum wage robs autonomy and dignity from those whose time is worth less than the minimum wage.  Instead of seeking the greatest value for their time, people with time worth less than the minimum wage are forced to either endure a perpetual, humiliating series of rejections, or to operate outside the law, or to simply withdraw from a fundamental social institution.  In our society, participation in the labor market confers a measure of dignity; to eject a person from the labor market, to bar him from participation, is to strip him of dignity.

Perhaps minimum wages are instituted as a mere signal of group affiliation, or in a misguided attempt to help underprivileged groups, rather than as a mechanism to perpetuate social inequity and drive underprivileged groups outside the confines of the law.  In any case, the moral impact of a minimum wage is to strip of dignity those it affects.  It serves to create outlaws and reinforces existing structures of oppression.

If we truly wish to help underprivileged groups whose labor is worth little, we should do so in a way that preserves their dignity and autonomy and does not drive them outside of the law in search of betterment.  We should do so in a way that respects basic, unquestionable human rights to shelter and sustenance without depriving already-impoverished people of more opportunities to participate in society and better themselves.

Edit 3:20 pm, 8/23:

A friend points out that in some cases --- where markets do not nearly approximate free --- there may be a power differential that acts in wage negotiations.  In this case, a minimum wage law not only shuts out those with labor worth the least, but those who have the least power.  Instead of permitting them to exercise what little power they can, it simply removes them from the process.  We create the illusion of empowerment, when in reality those who have the least power are simply barred from participation.

If we wish to empower the least privileged, most marginalized, we need a system of social insurance that actually empowers them, rather than shutting them out of a fundamentally dignifying social process.  A minimum wage removes options and strips dignity; a healthy social insurance system would give additional options, truly empowering the least privileged people in our society, giving them dignity and autonomy.

## Sunday, August 19, 2012

### Privilege informs misunderstanding of "consent"

Here at my university, we have posters up here and there indicating what "consent" means.  If she's too drunk to talk, asleep, unconscious, or does anything except explicitly indicate "yes," then sex is actually rape.

Why?  Because in a sexually charged, intimate situation, miscommunication is very easy.  If expectations are mismatched, or if there's a slight difference in body language interpretation, miscommunication can cause heady fun to disorientingly transform into violation.  Better to be a little awkward at first than to risk inadvertently hurting your partner.

Here's a simple story based on sexual dimorphism that predicts miscommunication.  Men are bigger and stronger (on average) than women.  A woman who is making out with a larger man she does not know extremely well is making risk assessments for the (low-probability, but very high-cost) case that the encounter becomes violent and balancing those against the (high-probability, high-benefit) case the encounter remains pleasant.

So let us suppose the woman does not give consent to sex.  If the man continues to press for sex, the woman's assessment that probability that the encounter becomes violent rises.*  One (common?) strategy is to continue to withhold verbal consent, but to grudgingly, unenthusiastically go along with intercourse, in order to avoid potential violence.  This is being raped, and it's probably a much more common type of rape than stereotypical home invasions or abductions.

From the man's perspective, it looks exactly like he has simply convinced her to change her mind, except she's just less enthusiastic than she was before.  He is making no threat assessments, so he judges her to not be making any either.  She goes along with it; he would not go along with sex if he didn't want to have sex, so he judges that she is consenting.  If she intended the "no" to be permanent, she would have reinforced "no" when he pressed -- that's what he would have done -- so he judges the lack of reinforcement as evidence that she has implicitly consented.

This is exactly what she intends!  Causing him to believe she is consenting, even if she does not consent, removes the possibility that he violently assaults her.  She is engaged in sex against her wishes, but has minimized harm.

Observe here that "male privilege" --- the man's perspective does not take into account the calculation the woman has to make concerning him --- leads to misinterpretation of behavior, and hence of the nature of consent.  Whereas the behavior actually communicates, "I'll do it because I don't want you to assault me," the man evaluates it to mean, "I changed my mind to 'yes.'"

* You lose all the futures where he says "Okay!" and goes back to making out.

## Thursday, August 16, 2012

### A Song of Sticky Wages (Told in Pictures)

During the recession, total income contracted:
Income from total employee wages also fell significantly:
(This is the sum of all wages and salaries paid to everyone in the country.  It's the single largest component of income.  I'll call it "total wages.")

Why did total wages fall?  Let's add another line, total number of (nonfarm, seasonally adjusted) employees:
Care: the scale of the red line is on the right hand side. Total wages fell because income fell.  Let's verify this by looking at wages per person, what I'll call "wages," computed by dividing total wages and total employment.  What happened?
Wages stagnated but did not fall.  In other words, wage growth dropped to zero and then the rest of the total wage drop manifested in layoffs.  After the recession was over, wages per person picked up right where they left off and continued growing, albeit at a slightly lower rate.

This looks to be a general phenomenon.  Here's the whole time series of per-employee wages, from 1939 to 2012, presented as quarter-on-quarter percentage change.  Observe that it has dropped below zero precisely four quarters in the last 80 years - and each time it promptly bounced back up.  Even during recessions, wage growth keeps rising.  These are called "sticky wages."

So what happens in a bad recession?  Total income falls and wages fall in proportion.  That wage drop manifests itself in a drop in per-employee wage growth to zero, and thereafter people are simply laid off.  After the recession is over, wages resume their upward trend.

Let's look at it like this.  Total wages are some (more or less fixed) fraction of total income -- roughly half.  In a recession, total income falls, so total wages have to fall as well.  First, wages stop growing.  Then, since wages don't fall and thus don't keep pace with the fall in total wages, people start getting laid off.

Let's now look at the source of the drop in total wages.  Wages fell because income fell: observe that the ratio of total wages to income (green line, right scale) stayed roughly constant over the course of the 2008 recession.  Total wages and income are red and blue, respectively, and measured on the left scale.
(As an aside, this constancy was actually a stay in a secular decline; most of the rest of income goes to capital, and income inequality fell drastically during the recession.)

Note that after the fall in incomes, they did not rise back to their initial trend.  We can measure potential income, which is what the economy could be producing if it were at full employment, and compare it to actual income:

Unemployment has been persistently high.  Why?  Wages have continued to grow a little bit more slowly than total wages, and total wages are locked in as a fraction of total income.  Thus:
Wages are at a level that produced full employment in 2007, but total income, and hence total wages, are far below that level.  The difference is made up in the misery of 5,000,000 people.

Let's examine more closely the relationship between a persistent shortfall in income and unemployment.  Let's look at the ratio of actual income to potential income.  Here's are the two graphs, one since 2000 and one since 1949.  Look at how closely unemployment tracks the income gap:

We should hypothesize that, because of sticky wages, there is a strong positive correlation between this ratio (which I'll call income shortfall or NGDP shortfall) and unemployment.  Surprise!

(Data are quarterly, 1949Q1-2012Q2.)

If we look more recently, 2000-2012, we see the same pattern:

In this case, it's tighter because over a mere decade we shouldn't see a large shift in the natural rate of unemployment.

So we see that a sharp shock to income down to a new trend is what causes persistent high unemployment.  As Scott Sumner memorably analogized:
NGDP shocks are like a game of musical chairs.  Remove 9% of NGDP relative to trend, and you'll have 9,000,000 unemployed workers sitting on the floor.  It's that simple.
Wages will slowly adjust downwards (since total wage growth has been greater than wage growth) and labor market hysteresis will reduce the workforce.  The former is incorporated in the new income trend, and the both pull potential income down to the new income trend.  The economy will return to full employment.  But at what cost?

Addendum: There may be some concern that the correlation between income shortfall and unemployment is artificial - that is, that potential income is computed using the unemployment rate, so I'm merely expressing a tautology.  For further reading, here is the CBO's explanation of their method for computing potential income.

## Wednesday, August 15, 2012

### Privilege - what is it?

So I've been thinking about what "privilege" is and how to apply recognition of the idea in everyday life.  A personal project of mine is trying to translate ideas from humanities into forms that make intuitive sense to me, giving them precise definitions.  Maybe these thoughts will be useful to other people as well.

### Definition

Here's a simple definition from Finally Feminism 101:
Privilege is an advantage conferred by the configuration of society to some groups over other groups.
What do we mean here by advantages? Let us say that an "advantage of X over Y" is a benefit X enjoys in reaching X's goals that Y does not enjoy in reaching Y's goals.  So, unwinding, privilege of some group over another means that the way society is configured gives the first group benefits in reaching their goals that the second group does not receive in reaching their goals.

(Side note: It is also interesting to remove society from the definition and make another definition:
X privilege is an advantage conferred by configuration of X to some groups over other groups.
So, "social privilege" would be a class of advantages conferred by the configuration of society.  Meanwhile, "biological privilege" would be a class of advantages conferred by the configuration of biology to some groups over others --- for instance, men are biologically privileged with strength and not-having-babies, people without disabilities are biologically privileged over people with disabilities, and so on.

This may not be a good more general definition because it conflates with an identical use: "X privilege" means, I think, "advantage conferred to group X over group not-X by the configuration of society with respect to X."  For instance, "male privilege" is advantage conferred to men over women by the configuration of society with respect to men; white privilege is advantage conferred to white people over non-white people by the configuration of society with respect to race; etc.)

### Some observations.

"Privilege" is an empirical claim.  It can be supported or disproven by observation.  For instance, "men have privilege in the workforce" makes the prediction that men should have, all else equal, higher salaries. They do.  So this is evidence for the proposition that society's configuration gives men an advantage in the workplace.

Privilege is a statement about groups, so it only extends stochastically to individuals.  Nonetheless, since individuals make decisions based on limited information and assessments of probabilities, this stochastic extension impacts individual behavior.  (Interesting implication: The perception of privilege can create privilege where none actually existed.)

Since basic human instinct is to evaluate others' situations by placing ourselves into their spots, privilege can be difficult to detect for members of the privileged group.  Because of the advantage conferred by privilege, a member of the privileged group performing simple first-order analysis on the motivations and behavior of a member of the non-privileged group will fail to detect factors for which the non-privileged person must account in optimizing well-being.  (More on this below.)

Privilege could be "intrinsic," in the sense that one group in society possesses a set of values or characteristics that give it an advantage over other groups.  For instance, suppose that upper-middle class families have a culture that emphasizes education and long-term investment in human capital, while lower class families do not.  Given a broader society that is configured to reward education and long-term investment over short-term consumption, we could say that this is an example of upper-middle class privilege over lower classes.  (If this is not an example of privilege, then the definition needs to be modified to exclude this case and others like it.)

Not all privilege is good; not all privilege is bad.  Some groups are privileged in some areas and underprivileged in other areas.  (For example, mathematicians are privileged, apparently, in precise logical thinking, but underprivileged in social subtleties.  Victorian upper-class women were privileged in their treatment by men, but severely underprivileged in freedom.)  Given a group, one can probably measure all the privilege it has and all the underprivileges it has and judge whether it is net positive or negative.

### Application

In practice, what does this mean?  While I was following a little bit of that Rebecca-Watson-got-creeped-on-in-an-elevator story (I refuse to call it "elevatorgate" because appending "-gate" to the end of every salacious outburst is just ridiculous -- it was the name of the hotel, people), I realized this: recognizing privilege is just modifying the golden rule.

We all know the golden rule.  We learn it in preschool, taking our first steps into a larger world of social interaction.  "Do to others what you want them to do to you."  We tell it to our children: "Kiddo, would you like it if he hit you?  Then don't hit him."  It has arisen in religious and philosophical teaching independently across the world.

Why is it useful?  As humans, we all have some basic beliefs in common - we want social interactions to be pleasant, we don't want to get hit, we don't want to have our stuff taken, so on.  Internalizing the golden rule amounts to recognizing this commonality: we can predict other people's reactions to our behavior by placing ourselves on the opposite ends of our interaction.

But as we pass on to interaction with broader and more diverse people, our approach needs to become a little more sophisticated.  Here's a motivating example.  Until last spring, there was an abandoned building about a block away from our apartment.  It was between us and our jobs.  I hadn't really noticed it before, but my wife drew my attention to it: she wanted me to walk her home from her job.  Why?  Because of that abandoned building.

It would never have occurred to me to be creeped out by the building.  When I put myself in her place -- which wasn't hard, because I had walked past it many times! -- I still wasn't creeped out walking past it.  It was only when I modified my analysis of her motivations to take into account differences between us that I understood why she felt the building was creepy.

She's weaker than I am and can't run as fast.  Her chances of being the target of an assault are much higher than mine.  (They're still statistically small, given our class and neighborhood, and even smaller, but still high enough, with bad enough consequences that she needs to take them into account).   So, in the exact same situation, she is rationally more cautious than I am.

To recognize privilege (if it exists), you have to modify the golden rule.  When you're evaluating someone else's motivations and behavior, you have to ask yourself not just "what would I do in his circumstance?" but "how is he different from me and how does that difference impact what I'd do in his circumstance?"

### Conclusion

A privilege is an advantage enjoyed by one group over another that is bestowed by the current configuration of society (and not by, say, biology or geography).  Privilege between individuals is stochastically inherited from groups, and manifests itself in differences in evaluation of the same situation. It can be detected by modifying the golden rule from "Put yourself in their shoes" to "Put yourself in their shoes, then ask how they're different from you and how that difference would impact your response."

## Tuesday, August 14, 2012

### Where does understanding math break down?

I received my fall teaching assignment this week.  Next Monday, I stand up in front of 80 or so nervous students who have to pass this class in order to graduate, and I start telling them about math they've probably never seen before.

Most of them already have mental blocks in place telling them that math is difficult.  Many of them struggled in their high school math classes as they moved from arithmetic to algebra and geometry.  Instead of introspecting to figure out what they were doing wrong, they decided it was too "difficult" for them.  So they enter my class with trepidation, and they're already setting themselves up to fail it.

To facilitate learning, one of my tasks is to convince my students that they actually can learn math, that it's not too difficult.  In fact, I contend that the sort of math I'm teaching is, in principle, not difficult at all.  That's what I want to ruminate about in this post.

In this type of math class, we have three basic threads interacting.  First, we have definitions: I write down symbols, I tell you what they mean, I tell you why they mean this, and I give you some simple examples.  Second, we have techniques: I tell you how and why in this class of situations, we use these symbols, and in that class of situations, we use those symbols.  Third, we have problems: I give you a problem, you figure out which class of situations it falls in, and then you use the symbols and their meaning to tell me something about the problem.

Let me give you an example.

The definition. A binomial coefficient is this symbol: for any two positive integers $$n$$ and $$k$$ with $$n > k$$,
$C(n,k) = \frac{n!}{k!(n-k)!}.$
Here $$n! = n(n-1)(n-2)\cdots 3\cdot 2\cdot 1$$, the product of all the numbers from $$1$$ to $$n$$.  In fact, we can write down
$C(n,k) = \frac{n(n-1)(n-2)\cdots(n-k+1)}{k(k-1)(k-2)\cdots 3\cdot 2\cdot 1}.$
That is, we take $$k$$ slots, start with $$n$$ and continue on down, multiplying as we go, then divide that product by $$k!$$.

What it means.  A binomial coefficient tells you how many unordered combinations of $$k$$ things you can draw from $$n$$ things.  That is, it is the number of $$k$$-element subsets in an $$n$$-element set. This is because the number of ways of picking $$k$$ things in order is counted by $$\frac{n!}{k!}$$ and the number of ways of ordering those $$k$$ things is $$k!$$, so to see how many ways there are of picking $$k$$ things without regard to order, we divide the number of total ways of picking $$k$$ things in order by the number of ways of picking the same $$k$$ things in different orders.

Example.  To see this in action, check out
$C(5,3) = \frac{5\cdot 4\cdot 3}{3\cdot 2\cdot 1} = 10.$

The general class of situations.  You use a binomial coefficient any time you want to count the number of ways of choosing $$k$$ things from $$n$$ things without regard to order.

A particular example.  Say you have five different sandwiches and you grab three of them.  How many different outcomes does this experiment have?  Well, since you're just grabbing them, you're obviously not making a point of checking what order you're taking them.  So you're just choosing $$3$$ things from $$5$$ things without regard to order.  How many ways are there of doing this?  $$C(5,3) = 10.$$

Where could the process of understanding break down?  You might have just skimmed this because you've already decided you won't ever understand math.  If that's the case, I'd encourage you to go back and read it again.  It's not as bad as you think it is.

Perhaps your eyes glossed over at the symbol $$C(n,k)$$.  If that's the case, remember: I told you what the symbol means.  I don't expect you to remember it right away, because it's unfamiliar and new -- but remember that its definition is right there!  Any time you need to remember it, you can just go back and double-check what it means.

Maybe you didn't quite catch why binomial coefficients count unordered combinations.  If so, that's all right; that's a dense paragraph and in the interest of brevity (and accuracy - the whys get short shrift in the classroom) I left out some small steps.  But if you read it a few times, I don't doubt that you'll come to understand.

(I recognize that if this is new to you, you won't catch all of it right away.  I can do this off the top of my head because I've taught this material for several years.  But if you take enough time to practice, you'll come to grasp the idea, just as if you shoot enough baskets, you'll be able to hit a free throw.)

So where else could a student's understanding break down?  There's always the possibility that the student is blowing off the class (because they don't think they're able to do it?).  I don't have too much control over that.

Perhaps students' understanding fails not for any single process, but when many new, related ideas are thrown at them very quickly.  Part of learning mathematics is building up heuristics which indicate which tool to use in a given problem.  If students do not focus sufficiently on distinguishing related ideas from each other, then their heuristics will confuse related but distinct situations and the intuition they develop will not conform to reality.

For example, related to the idea of binomial coefficients measuring unordered combinations is permutation coefficients measuring ordered combinations.  The number of ways of drawing $$k$$ items from $$n$$ items, counted in order, is $$P(n,k) = \frac{n!}{(n-k)!} = n(n-1)(n-2)\cdots (n-k+1).$$  One way we help students remember is, if there are $$k$$ items, you draw $$k$$ slots. There are $$n$$ ways of filling the first slot, $$n-1$$ ways of filling the second slot, and so on.  Then you multiply them all together.  This tool is used to count the number of ordered $$k$$-tuples that can be created from an $$n$$-element set.

If the problem is the same as above --- five sandwiches, you grab three --- a student might reason this way: There are three sandwiches, so I draw three slots.  There are five ways of filling the first slot, four ways of filling the second slot, and three ways of filling the third slot, so there must be sixty ways of drawing three sandwiches from five sandwiches.

Where did the student's reasoning go wrong?  Take a minute and figure it out.

The student's intuition is misshapen: He did not consider order.  The student has internalized that, in any problem that involves drawing items from a larger set, the number of ways of drawing items can be found by drawing a slot for each item, then counting the number of items to be included in each slot.

In principle, (this kind of) math isn't difficult.  It's no harder than learning a foreign language.  You just have to remember the meanings of new symbols, how to use them, and which situations call for using those symbols.  A computer could do it (and anything a computer can do is not difficult, just tedious).

Perhaps failing students just move too fast, gulping instead of chewing, so that their intuitions malfunction?  Or they just don't put in the time and practice necessary for remembering these new, foreign symbols?  Or is there some fundamental limitation that I just don't see?

Edit:
Addendum -- One friend asked me, "Where does 'binomial coefficient' come from?"  A binomial is the sum of two algebraic terms: $$a + b$$.  If you take an integer power of a binomial, you get the following polynomial:
$(a+b)^n = \sum_{k = 0}^n C(n,k)a^kb^{n-k}$
$= a^n + na^{n-1}b + \frac{n(n-1)}{2}a^{n-2}b^2 + \cdots + \frac{n(n-1)(n-2)\cdots 3\cdot 2}{(n-2)(n-4)\cdots 3\cdot 2\cdot 1}a^2b^{n-2} + nab^{n-1} + b^n.$
So the "binomial coefficients" are coefficients (numbers by which variable expressions are multiplied) in the polynomial you get by raising a binomial to a power.

### Sanity from the Boston Fed

Eric Rosengren, president of the Boston Fed, interviewed by Jeremy Hobson on Marketplace.  Here are some excerpts.

Whether the Fed should continue waiting and seeing:
My own expectation is that the second half of the year won't be much better than the first half, because the drivers of fiscal austerity and European problems aren't likely to be resolved in the next two quarters, and that monetary policy shouldn't wait any further before reacting to the global slowdown that we've been encountering.

Should policy actually be tied to results?
So the focus not only for quantitative easing but also on any kind of forward guidance for how long interest rates stay low should be focused on the economic outcomes that we want. So we should be focused on getting growth and income that is satisfactory, and that results in a labor market that is improving. So I would have any of our programs, whether it's forward guidance or whether it's quantitative easing, tied to getting the right kind of economic outcomes before we stopped. So I would want a substantial program if we did quantitative easing, and I would tie it to getting the kind of income growth that we want, or tie to getting clear improvements in the labor market.

"You think that you can see a direct connection at some point between the Fed pumping money into the economy essentially, and somebody getting a job somewhere?"
I do. Any of our models would indicate that some of the programs that we've already done have provided some stimulus to the economy. It's probably not the growth that we wanted, and unfortunately, the economy's been buffeted by factors that we couldn't completely offset, such as what's been going on in Europe.

What about inflation? (Probably a response to Dallas Fed president Fisher.)

One of the concerns surrounding the Federal Reserve expanding its balance sheet has been that we would induce inflation.  We first expanded our balance sheet in the fall of 2008, and then with our two quantitative easing programs.  Despite the fact that we've expanded our balance sheet quite substantially, and we've had more than four years since we started those programs, we're still seeing an inflation rate below our 2 percent target. ... That just highlights that despite the fact that we have taken expansionary policy over the last several years, we've yet to see the inflation that some are concerned about.

If you intervene now, won't you be accused of politics?
An independent Federal Reserve should be focused on the business cycle, not the political cycle, and that's what I'm focused on.

Go listen to the entire interview.  Hopefully, now that the July jobs report is in, the doves will push their case harder at the next meeting.

### Yet another reason why nominal income matters

 Nominal output gap and federal deficit. Source: St Louis Federal Reserve.

The blue line is the nominal output gap.  The orange line is the federal deficit.

Before 2008, you can see the effect of various structural policies on the deficit.  We start with Reagan's tax deficits, then Bush and Clinton raises taxes and the deficit tumbles, then W. Bush cuts taxes and the deficit rises.  All through this, the actual deficit tracks the output gap.

So what happens in 2008, when the Fed blows a GIANT HOLE in nominal income?  Exactly what happens every time nominal income falls below trend: it blows a GIANT HOLE in the federal budget, too.  The structural deficit from Obama's tax cuts is tiny compared to the cyclical deficit from the GIANT HOLE in nominal income.

Taxes are nominal.  Spending is nominal.  Debt is nominal.  Real quantities we construct are useful for prying apart the economy and studying its wriggling guts, but their purpose is just to better help us understand a nominal beast.

There's one thing in the economy that controls nominal incomes, and it's responsible for three quarters of this budget deficit.

## Monday, August 13, 2012

### Comparing the six measures of unemployment

Some two years ago, I wrote a post about comparing the six measures of unemployment the Bureau of Labor Statistics measures.  After I read Evan Soltas' post today about unemployment, and since it's been, well, two years, I thought I'd revisit the subject and add some sexy graphs to my original analysis.

### Unemployment

Unemployment can be a sticky topic.  It seems simple enough at first blush: If you have a job, you're employed.  If you don't have a job, you're unemployed.  But when you start to think about it (as you do in your first semester of macro), you realize that you have to be a little bit more careful.  Should a three-year-old count as "unemployed"?  Perhaps in the broadest sense, but probably not for macroeconomic policy-makers.

What about people with college degrees who, say, could only find work at Kroger?  If I have a BS in physics and I'm swiping items at a cash register in a supermarket, I'm obviously not unemployed, but I'm not really employed, either.

What about people who lost their jobs, looked for a new job for two years, and then gave up?  They're not even looking for jobs, but if the economic situation brightened, perhaps they would start again -- do they count as unemployed?

To answer these questions, economists have developed the notion of the "labor force" and various measurements of unemployment.  The labor force is a rough measure of how many people the economy has available for work at any given time.  If you've looked for a job in the last four weeks, or you have a job, you're in the labor force.  Usually, the labor force comprises 60-70% of the country's population.  (Note that even the definition of the labor force can be debated: should someone who has stopped looking for work because of a downturn be counted as a member of the labor force?)

"The" unemployment rate, then, is a measure of what proportion of the labor force has a job.  I put "the" in scare quotes because, as we saw, there are many different, but related, ways of defining the notion of "unemployment."  There are, correspondingly, many ways different, but related, measures of unemployment.

### The six measures of unemployment

The Bureau of Labor Statistics (BLS) maintains six different measurements of unemployment.  They are creatively named:

• U-1: The proportion of the labor force who have been unemployed for 15 weeks or longer.
• U-2: The proportion of the labor force who have lost jobs or done temp work.
• U-3: The official unemployment rate (this is the number you see in the headlines at the start of each month): The proportion of the labor force who have lost jobs.
• U-4: The proportion of workers who are in U-3, or who are not looking for a job because of economic conditions.  (These workers are called "discouraged workers.")
• U-5: The proportion of workers who are in U-4, or who would like to work and can work but are not seeking work.
• U-6: The proportion of workers who are in U-5, or who are employed part-time and would like full-time work, but cannot.
U-1, U-2, and U-3 operate in the labor force as I defined it above.  U-4, U-5, and U-6 all expand the labor force to include people who are "marginally attached" to the labor force: unemployed individuals who would like to participate in the labor force but are not currently looking for work.

Here is a graph of all six unemployment rates since 1994:

Observe that they all move more or less together.  This suggests that perhaps they all tell more or less the same story.  If I know the headline unemployment rate, just how much of the other unemployment rates can I figure out?

The BLS data are accessible from the link above.  In my previous post, I looked at the data (then, through 2010) and found the following:
$U_1 = (0.76 \pm 0.01)U_3 − (2.31 \pm 0.07)$
$U_2 = (0.78 \pm 0.01)U_3 − (1.47 \pm 0.05)$
$U_4 = (1.066 \pm 0.003)U_3 − (0.09 \pm 0.01)$
$U_5 = (1.099 \pm 0.005)U_3 − (0.43 \pm 0.03)$
$U_6 = (1.70 \pm 0.07)U_3 − (0.3 \pm 0.1)$
That is, if at any point between 1994 and 2010, you know the headline unemployment rate U-3 (currently $$8.3$$%), you can compute the other five unemployment rates with reasonably high precision.  For example, U-6 should be near 13.8%.  In fact, it is currently 15.0%.

### Graphs

I went back and grabbed the data again, but this time, instead of running regressions on them, I just made some pretty pictures.

Here is a graph of U-3 against U-1 since 1948 (which is how long the BLS has been measuring both of them):

Interesting patterns, eh?  There's definitely a positive correlation, just like you'd expect, but it does some wandering too.  I chalk that up to structural and demographic change.  What would happen on a shorter time scale?  Well, the BLS has only been measuring U-4, U-5, and U-6 since 1994.  To stay consistent, let's only consider U-1 and U-2 against U-3 from 1994.  Here is a graph measuring all five against U-3, 1994-2012:

Neat, isn't it?  You can see that there is a strong linear relationship between each of the other unemployment rates and the headline rate of unemployment.  To highlight that linear relationship, here's a graph of each of the five alternate timeseries divided by the headline rate:

### Discussion

Let's refer back to the graph of all unemployment rates as well as to the graph of the ratios of the unemployment rates to U-3 and see if we can make some sense of them.

Several interesting things have happened since 2008.  First, U-1 has risen almost exactly to U-2.  Since both use the same definition of "labor force", it suggests that the proportion of the labor force which is long-term unemployed has risen.  We might perhaps think that U-1 and U-2 are measuring the same people, but we cannot conclude that from these data.

Second, U-4 has stayed exactly proportional to U-3.  This indicates that the labor force "breathes": change in the number of discouraged workers moves in direct proportion to the change in the number of unemployed workers.  This is all the more interesting because there has not been any measurable change in this during the 2008 recession.

Meanwhile, third, there has been a visible change in the proportion of U-5 and of U-6 to U-3.  This indicates that while workers become discouraged in proportion to becoming unemployed, during a recession workers become slightly more reluctant to move further from the labor force (or to become underemployed? or workers who move beyond discouraged actually become less than marginally attached?).  The same phenomenon is visible with U-6 during the 2001 recession, when it fell in proportion to U-3 and only slowly moved back up to levels it reached during the 1990s.  It fell again in 2008, and is inching back up as the economy slowly recovers.

Evan Soltas, in the post that inspired this one, pointed out that unemployment rates do not capture changes in the labor force participation rate.  He is probably correct in this - the unemployment rates can only indirectly see labor force participation rates by measuring the spread across different definitions of the labor force, and then only as in a mirror darkly.

Later he posited that perhaps the broader definitions of unemployment, U-4, U-5, and U-6, might better catch changes in labor force participation.  They won't; they move in close to lockstep with U-3 (especially U-4).  The only glimmer of changing labor force participation rates might be in the deviations of U-5/U-3 and U-6/U-3 over the course of the business cycle.

### Conclusion

To answer the original question, since all six measures of unemployment are very tightly correlated, they all convey roughly the same information.  (This is not a vacuous statement! It is an observation about the behavior of the labor force, and working-age population in general, through the business cycle.)

By looking closely, we do see that the rates do convey information that differs in the details.  For instance, U-1 and U-2 do not track U-3 as closely as U-4 does.  Perhaps we can see underlying facts about demographics and labor force participation from these subtle differences.  But on the whole, any structural changes in the economy are only dimply reflected in these unemployment rates.  They do track each other closely!

Addendum: There is some question about whether U-3 should be "the" unemployment rate reported in headlines -- whether U-4, U-5, or U-6 more accurately captures what people mean when they informally discuss "unemployment" -- but that's not what I mean here.  What I mean to say is that if you know the relationships between the other Us and U-3, then when you hear the U-3 rate announced, you can get a good idea of what the spread of the unemployment rates looks like.

I also don't mean to imply that Evan is wrong in his assertion that the unemployment rate is incomplete information.  Declining labor force participation rates are very important pieces of information - in fact, the labor force participation rate (or the employment:population rate) should be announced in conjunction with the headline unemployment rate to indicate whether the cause of change in the rate is worker sentiment, a change in the rate of job creation, or both.

### What about the Fed and automatic stabilizers?

Here are two potential objections to my previous post on discretionary fiscal stimulus.

### If you're so skeptical of the ability of Congress to time fiscal stimulus, why aren't you skeptical of the Fed's ability to time monetary stimulus?

First, the Fed is a much smaller institution than the federal government.  Since it is (supposed to be) independent of Congress, it is not subject to intense political pressure from lobbyists and constituents.  Since it's smaller and has fewer forces pushing and pulling on it, the decision-making process is shorter and the Fed has greater discretion.
 Weekly average federal funds rate (blue) and federal funds target (red)

Second, the Fed has actually demonstrated the ability to conduct discretionary operations on a daily basis.  The Fed's open market operations keep the fed funds rate in line with its target.  (Whether the Fed's operations in the loanable funds market are justified is a matter of discussion - but there's no question it can manipulate the market.)  When has Congress ever legislated anything on a daily basis?  Let alone consistently and cleanly produced the results it wants?

Nonetheless, I do agree that this point has some merit.  The Fed is not omniscient; while it can react on the order of days or weeks, conditions can deteriorate so rapidly the Fed can't respond in time - consider that it raised the fed funds target rate the day after Lehman Brothers collapsed (that little spike in the middle of the recession).

The Fed is also subject to some political pressure.  Its mandate requires it to balance full employment and price stability.  On the right, Ron Paul and other extreme Republicans insist that it should cease to exist and the economy should return to a gold standard (what a disaster that would be, I will discuss in later posts).

And evidence suggests that it often considers the American public's visceral fear of inflation as it balances employment and inflation.  Even though monetary indicators suggested a full-blown recession was underway during the summer of 2008, one read of the September price hike is that the commodities price spike spooked the Fed into making its rates decision based on headline inflation, rather than core inflation.

So using discretionary monetary policy against the business cycle is a better bet than using discretionary  fiscal policy, but it's still not a money shot.  The institution of the Fed is subject to some political pressure and may not respond quickly enough to changing conditions to counter at its discretion. Moreover, the "counter" here is discretionary, and we've seen what damage discretion can do.

So perhaps the key here is to remove discretion from countercyclical policy, whether monetary or fiscal, which brings me to counterpoint number two ...

Automatic stabilizers are programs like unemployment insurance and welfare which by their nature increase expenditure during a recession and decrease expenditure during a boom.  The easy response to this counterpoint is: If they're automatic, they're not discretionary!  So they don't count as "discretionary fiscal policy" - technically, this is a red herring.

But it's an interesting and useful subject to discuss.  As I said in my previous post about fiscal stimulus, good policies are good regardless of whether the economy is booming or busting; bad policies are bad regardless of whether the economy is booming or busting.  When we make policy, we should regard the policy as in place for the long run, not as a momentary response to the business cycle.

One implication is that the government should operate by rules, not discretion.  The larger the institution or its impact, the less discretion it should have (at least in response to the business cycle).  Moreover, rules whose impact correlates strongly and negatively to the business cycle stand a much better chance of providing countercyclical amelioration than discretionary policy.

Automatic stabilizers, in the form of tax cuts or welfare assistance to the needy, are one form of rule-based policy that acts countercyclically.  (Mind, this also implies that we don't discretionarily tinker with automatic stabilizers during the business cycle, such as extending unemployment benefits to be more generous than in some socialist countries.)

Since the safety net functions as an automatic stabilizer (and that's usually what people mean when they talk about automatic stabilizers), I do have concerns about the impact of the post-tax, post-benefit (PTPB) income curve on long-run incentives for behavior.  The withdrawal of means-tested programs, such as food stamps, can create very high effective marginal tax rates, punishing poor people for harder work instead of helping them out of poverty.

More broadly, in the US the PTPB curve is very flat at low incomes and does not begin to increase until one has reached the middle class.  This implies that poor people face approximately effective 100% marginal tax rates.  I don't need to mention how perverse this is, but I will anyway.  This outrage will be the subject of a different series of blog posts.  Nonetheless, it's a reasonable concern about automatic fiscal stabilizers.

There is similar scope for making a case for automatic policy on the part of the Fed.  Scott Sumner points out that there are no small recessions.  I'll have more to say on this at a later date, but for now let's take it for granted that the Fed's discretion can turn small recessions into big recessions.  In fact, the Fed's discretion is directly responsible for the five largest recessions in American history:

• The great decline of 1929-1933 (as the Fed at its own discretion chose not to stop the annihilation of a third of the monetary base),
• The crash of 1937 (when the Fed at its own discretion raised reserve requirements prematurely),
• The two recessions of 1980 and 1981 (when the Fed at its own discretion sharply contracted monetary policy to kill inflation expectations and shift price growth to a lower trajectory), and
• The great recession of 2008 (when the Fed at its discretion stopped growth of the monetary base, contracted monetary policy, and then refused to engage in unconventional monetary policy in the face of the sharpest decline of nominal income since 1929-33).

Removing the Fed's discretion is not a new idea.  Milton Friedman proposed simply increasing the monetary base by some fixed percentage each year, regardless of the business cycle.  A different rule --- one I favor --- is to require the Fed to target nominal income growth at some fixed long-run percentage. The Fed would do this by either setting up a prediction market in which to conduct open-market operations, or by targeting its own internal forecasts.

The key here is to cut down the scope of the Fed's discretion, because abuse - passive or negligent - of that discretion leads to great harm.

### Conclusions

Two criticisms of my skepticism of discretionary stimulus are, "If Congress can't do countercyclical stimulus, why would the Fed be able to?" and "Wouldn't automatic stabilizers play the role of countercyclical stimulus?"

The Fed is smaller, not subject to the same political and special-interest pressures, and has a demonstrated track record of successful economic manipulation.  It can make decisions in a matter of days or weeks, while Congress often takes months to make decisions --- it didn't pass its fiscal stimulus until the recession was two-thirds over, and that fiscal stimulus took effect just as the recession ended.

Meanwhile, yes, automatic stabilizers should play the role of countercyclical stimulus, precisely because they're not discretionary.  Since they require no decision-making time, an automatic stabilizer can be tightly and negatively correlated with the business cycle, whereas discretionary fiscal stimulus has significant built-in lag time.

Even the Fed's discretion is questionable; it's directly responsible for the five greatest recessions in living memory.  We should therefore be looking at replacing the Fed's discretion with an automatically stabilizing rule, such as monetary growth or a nominal income target.

## Sunday, August 12, 2012

### Why I'm skeptical of fiscal stimulus

First, let me lay out a definition.  When I say "fiscal stimulus," I mean: discretionary countercyclical spending.  I don't mean: military spending; necessary infrastructure spending; welfare; sanitation; or any other function that government is expected to serve regardless of the economic climate.  I do mean: Tax cuts; make-work; the WPA; ARRA; extravagant (Japanese-style, bridge-to-nowhere) infrastructure spending; and other spending that occurs because the fiscal authority has identified that the economy is in the recessionary phase of the business cycle.  (Implicitly, when I say "discretionary fiscal stimulus," I really mean "expansive fiscal stimulus."  It is rare for a democratic government to engage in discretionary fiscal contraction.)

Here are two of the main reasons I'm skeptical of fiscal stimulus.

### 1: Timing

The first, due to Friedman, is very nicely laid out in this Marginal Revolution post.  I reproduce the argument here.

Let's set up a simple model.  At time $$t$$, represent total income by $$Z(t)$$, income in the absence of fiscal policy by $$X(t)$$, and the amount added to (or subtracted from) $$X(t)$$ by all the history of fiscal policy denote by $$Y(t)$$.  Here's the identity at the heart of the model:
$Z(t) = X(t) + Y(t).$
Since we hope for our policy to be countercyclical -- that is, we hope for $$Y$$ to reduce the fluctuations of $$X$$ so that $$Z$$ has low variance -- we want $$X$$ and $$Y$$ to be correlated.  The variance of a sum of correlated variables is
$V(Z) = V(X) + V(Y) + 2Cov(X,Y) = V(X) + V(Y) + 2r(X,Y)\sigma(X)\sigma(Y).$
(Here $$\sigma$$ is the standard deviation, $$\sigma^2 = V$$, and $$r$$ is the correlation of two random variables.)

Following Friedman and dividing both sides, we have
$\frac{V(Z)}{V(X)} = 1 + \frac{V(Y)}{V(X)} + 2r(X,Y)\frac{\sigma(Y)}{\sigma(X)}.$
Remember that $$X$$ measures fluctuations in the economy absent any countercyclical policy.  If the left side of the equation is $$1$$, then the countercyclical policy has no effect.  If it is less than $$1$$, the countercyclical policy has some positive effect.  If it is greater than $$1$$, the countercyclical policy has negative effect.

The key question here is, how closely does the cumulative effect of policy, $$Y$$, need to track incomes, $$X$$?  This tracking is measured by the correlation $$r(X,Y)$$; if $$Y$$ is perfectly timed and opposite to income fluctuations, $$r(X,Y) = -1$$; if $$Y$$ is independent from $$X$$, $$r = 0$$; and if $$Y$$ is perfectly harmful, so that policy is perfectly procyclical, $$r = 1$$.

Friedman goes on to show that policy is countercyclical if $$r(X,Y) < -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$, has no effect if $$r(X,Y) = -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$, and procyclical if $$r(X,Y) > -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)}$$.

The first thing to note is that it is harder to conduct countercyclical policy than procyclical policy: to be effective, we need $$r(X,Y) = -\frac{1}{2}\frac{\sigma(Y)}{\sigma(X)} < 0$$.  Why?  Note that if $$Y$$ is independent from $$X$$, then $$r = 0$$, so $$V(Z) = V(X) + V(Y)$$.  The variance of after-government income will be greater than the variance of the private economy's income because some of the time, spending will be procyclical, exacerbating the business cycle.

The next thing to note is that if policy were to attempt to mitigate, say, half the magnitude of the business cycle, one would need $$\frac{\sigma(Y)}{\sigma(X)} = \frac{1}{2}$$ so that $$-1 \leq r(X,Y)\leq -\frac{1}{4}$$.  The window of the target for effective business cycle amelioration narrows the more of the business cycle you want to eliminate.

The last thing to note is that for any correlative ability, there is an optimal level of countercyclical spending.  Using calculus to find $$\sigma(Y)$$ maximizing $$\frac{V(Z)}{V(X)}$$ for a fixed $$r(X,Y)$$, one sees that this optimum occurs at
$\sigma(Y) = -r(X,Y)\sigma(X).$
So to see the effectiveness of stabilization policy, assume the best $$\sigma(Y)$$ can be found and substitute:
$\frac{V(Z)}{V(X)} = 1 - r(X,Y)^2.$
Boom.  Right there.  This is how difficult discretionary fiscal stimulus is.  For example, if we want to cut the standard deviation of the business cycle in half with discretionary spending, the cumulative effect of all discretionary spending must be pegged to within 70% of the business cycle.

You should read both the Marginal Revolution post and Friedman's article.

This is reason number one that I'm skeptical of discretionary fiscal stimulus.  If you want to positively mitigate the business cycle, you need to be able to target your fiscal response very precisely.  Your discretionary fiscal authority has to be able to do three things:
1. Correctly identify current income - what we've been calling $$X(t)$$
2. Determine what level of spending is appropriate (including correctly estimating secondary and tertiary effects) to mitigate some of the deviation of $$X(t)$$ from its expected value
3. Enact that spending quickly enough to actually mitigate $$\sigma(X)$$.
Even correctly identifying current income is tricky enough (the BEA didn't announce the US was in a recession until December 2008, an entire year after the recession began), estimating the appropriate level of spending is almost as tricky (quarterly real GDP figures from 2008 are still being revised), and enacting that spending quickly ... well, anybody who's been watching Congress knows how tough this is.

Even when Democrats controlled both houses and the White House, fiscal stimulus wasn't even signed into law until February 2009.  The worst of the economic contraction had passed by then, and the economy returned to growth well before the bulk of stimulus spending occurred (ARRA was authorized for two years, so it was in effect until August 2011).

### 2: The Sumner Critique

As Paul Krugman said in 1997:
If you want a simple model for predicting the unemployment rate in the United States over the next few years, here it is: It will be what Greenspan wants it to be, plus or minus a random error reflecting the fact that he is not quite God.
How? I have a series of posts on the omnipotence of your local central bank coming up, so I'll save all the gory details until then. Instead, I'll just point out that the Fed controls aggregate demand by controlling the supply of money. The total amount of spending in the economy at any price level -- aggregate demand -- is a product of the Fed's policies.

If the Fed were to decide that spending was too low and needed to rise, it would increase the money supply, spending would rise, and -- depending on underlying real factors, such as unemployment, productivity, etc. -- some of that increased spending would cause an increase in output, while the rest of it would push up prices.

If the Fed were to decide that spending was too high and needed to fall, it would decrease the money supply, spending would fall, and both output and prices would fall.

(This discussion holds in the short run only; in the long run, as expectations adjust, output adjusts so that all monetary expansion and contraction translate into price changes.)

The Fed makes decisions about spending based on its assessment of monetary variables such as inflation, interest rates, unemployment.  It also (sadly) incorporates political assessments - would a policy decision hurt the independence and credibility of the Fed?

You can see where this is going.  If the government engages in discretionary fiscal policy, it also boosts total spending.  Ultimately, fiscal stimulus has the same short-run effect on total spending as monetary expansion, and hence the same short-run effects on unemployment and on inflation.

If the Fed has decided that it prefers current levels of unemployment and inflation, then it will initiate contractionary monetary policy when the government engages in discretionary fiscal stimulus and the fiscal stimulus will have no effect.  (To see the effects of this, look no further than our erstwhile Pacific protege).

If the Fed has decided that it does not prefer current levels of unemployment and inflation, then it will initiate expansionary monetary policy.  If the government engages in discretionary fiscal stimulus, the Fed will only loosen money to the extent that the fiscal stimulus does not meet the Fed's goals for unemployment and inflation.  In other words, discretionary fiscal stimulus is unnecessary: If it had not occurred, the Fed would just have instituted looser monetary policy.

This is the weakest form of the Sumner critique: one cannot measure the gains from fiscal stimulus without a counterfactual of central bank policy.  A stronger form is: the fiscal multiplier is always zero.  (The strongest form is: If the central bank targets nominal income, all macroeconomic effects are classical.)

Here's a little bit of play (inspired by these posts) using accounting identities to shore up the Sumner critique.  We know that income is consumption plus investment plus government spending plus net exports,
$Y = C + I + G + NX,$
and, by the equation of exchange,
$Y = \frac{MV}{P}.$
Therefore,
$C + I + G+ NX = \frac{MV}{P}.$
Claiming that discretionary fiscal stimulus works amounts to asserting that we can control $$G$$, and therefore at our discretion we can affect $$Y$$ by changing the right hand side of the last equation.  But the central bank exerts continuous and complete control over the right hand side of the equation.

If $$G$$ rises but the central bank does not permit the money ratio $$\frac{MV}{P}$$ to change, then necessarily the other components of $$Y$$ fall.  On the other hand, if the central bank changes $$\frac{MV}{P}$$, then the components of income will rise.

### Conclusion

There are other, weaker reasons I'm skeptical of fiscal stimulus -- how do we know that the projects being undertaken are valuable investments of time and resources?  Is it really worthwhile to pay people to dig holes and fill them back in?  And so on.  They're not so hard to reasonably answer ("They're still better than leaving resources idle," "It's the same as printing money and handing it out, and they'll spend the money and incomes will rise,"), so I'll leave considering them to a future post.

These two reasons, however, seem damning to me.  There's just no way an institution like Congress can gather enough information on the state of the economy, identify projects to engage in or taxes to cut, craft legislation, trade all the horses, and pass a bill to counteract a downturn (or counteract an upturn, but let's not get into why Congress might not want to quench a booming economy) quickly enough to correlate the economy and the government's response tightly enough to make discretionary fiscal stimulus effective.

(This begs the question of why the Fed would be able to do so, which I will answer in future posts regarding the Fed's omnipotence.)  But the central bank does control the macroeconomy, which means that either discretionary fiscal policy will be offset by contractionary monetary policy or it can simply be replaced by expansive monetary policy.

The take-home lesson from all this is, the fiscal authority should not worry itself with the business cycle.  Instead, the fiscal authority should set the monetary authority on a rule that does its best to eliminate the business cycle, because recessions are everywhere and always monetary phenomena, and focus on long-run policies that correct market failures and optimize growth against humane considerations.

Whether a policy is good or bad doesn't depend on the condition of the economy.  If a policy is a good idea in a boom, then it's a good idea in a recession: it's a good idea, period.  If a policy is a bad idea in a recession, then it's a bad idea in a boom: it's a bad idea, period.