Showing posts with label fun with numbers. Show all posts
Showing posts with label fun with numbers. Show all posts

Thursday, August 6, 2009

The way we count stuff matters

NYU Law professor Anthony Thompson points out an interesting quirk in the way the census works: prison inmates are counted as living in the same county as their prision, even if they will be released within a year or two. Why does this matter? It has a direct impact on how federal and state congressional districts are drawn and how government money is channeled:
"...the district of State Senator Elizabeth O'C. Little, a Republican in upstate New York, has 13 prisons, adding approximately 13,500 incarcerated "residents." Without the inmate population, Ms. Little would face an uncertain future. Her district would probably have to be redrawn because it wouldn't have enough residents to justify a Senate seat.

The residence rule raises two fundamental issues:

First, inmates in nearly all states aren't allowed to vote, yet their presence affects electoral representation in places where they do not live permanently.

Second, a disproportionate number of state prison inmates are from urban areas. Most state prisons, however, are in rural areas. As a result, resources and electoral authority are transferred from inner cities to rural jurisdictions.

The effects are plain to see. Cities lose out on funds that could be used both for crime prevention and prisoner rehabilitation; rural areas do their best to thwart reform because they don't want to lose the benefits that prisons confer on them."
As I've written before, most American live in what the Census classifies as urban areas. So the residence rule will skew public funds in an inefficient and non-representative way.

Conducting a census presents myriad conceptual issues, and no strategy is perfect. But there's something fundmentally wrong with counting incarcerated citizens who are legally barred from voting towards a district's population total. This will ultimately give voters in those districts disproportionate voting power and will result in policy choices that do not reflect the will of the majority.

Monday, June 15, 2009

Poverty and income inequality over time

Justin Wolfers posted this graph at Freakonomics, showing income growth by quintile since the 1970s:


His analysis was that economic growth has done little for the poor, accruing mostly (almost entirely) to the upper incomes.

Russ Roberts, however, takes issue with this analysis. In two separate posts (here and here), he criticizes Wolfers' interpretation:
"This alas, is a meaningless chart. It tells you nothing about who got the gains of the last 35 years. Why? Because they're not the same people in the quintiles. Starting in 1973, and it's not a coincidence, the divorce rate in the United States began to rise. The number of families increased dramatically simply because of divorce. There was also an increase in the number of families headed by single women with children. The quintile breaks-points changed, not because the economy was growing or shrinking but simply because of changes in the types of families."
In a sense, Roberts is not wrong. Looking at static graphs of quintiles does not account for differences in composition. If people move up the income ladder, then we will mistake static income growth among the groups for static income growth among individuals. The key here is the degree of social mobility. Basically, what are the odds that a person who is poor today will be poor next year, or in ten years?

Emmanuel Saez, the most recent winner of the John Bates Clark Medal, looks at this question in depth. Using Social Security data, Seaz tracked individuals over time to assess income growth and social mobility in the US over time. He concludes:
"We found that changes in short-term mobility have not substantially affected the evolution of inequality, so that annual snapshots of the distribution provide a good approximation of the evolution of the longer term measures of inequality. In particular, we find that increases in annual earnings inequality are driven almost entirely by increases in permanent earnings inequality with much more modest changes in the variability of transitory earnings. However, our key finding is that while the overall measures of mobility are fairly stable, they hide heterogeneity by gender groups. Inequality and mobility among male workers has worsened along almost any dimension since the 1950s: our series display sharp increases in annual earnings inequality, slight reductions in short-term mobility, large increases in long-term inequality with slight reduction or stability of long-term mobility.

Against those developments stand the very large earning gains achieved by women since the 1950s, due to increases in labor force attachment as well as increases in earnings conditional on working. Those gains have been so great that they have substantially reduced long-term inequality in recent decades among all workers, and actually almost exactly compensate for the increase in inequality for males."
Certainly, some longitudinal studies have found larger amounts of social mobility, but the bulk of the literature has not found the degree of mobility that Roberts implies.

So while the graph posted by Wolfers is static, there is evidence that it is a good approximation of reality. Income growth has accrued largely to wealthier individuals and families over the past 30 years, and it has not been sufficiently counterbalanced by social mobility.

Curiously, Roberts says that liberals lack a causal mechanism for changes in inequality and stagnant incomes among the poor. However, Wolfers was explicitly citing one of the most powerful arguments for this phenomenon, namely "skill-biased technological change". As Harvard's Larry Katz and Claudia Goldin explain, technological change has raised the productivity of skilled workers relative to less skilled workers, causing changes in relative incomes. In manufacturing, for example, advanced machinery has decreased demand for assembly line workers, but increased demand for engineers and mechnical operators. At the same time, the supply of educated workers has not kept up, resulting in large income gains in the upper half of the income distribution and much lower gains at the bottom.

Roberts is correct, however, in asserting that there is a difference between income inequality and absolute well-being. A rising tide can lift all boats, even while it lifts some faster than others. But it's important not to minimize slow income growth among lower income Americans; they may be better off than they were 30 years ago, but they are still struggling.

In a follow-up post, I'll delve more into the measurement, economics and politics of inequality.

Tuesday, April 28, 2009

Putting things in perspective (or trying, at least)

I came across this article from CNN on the current swine flu outbreak. Trying to contextualize the possibility of an influenza pandemic, the author wrote:
"In 1968, a 'Hong Kong' flu pandemic killed about 1 million people worldwide. And in 1918, a 'Spanish' flu pandemic killed as many as 100 million people. Putting those figures into perspective about 36,000 people die from flu-related symptoms each year in the United States, according to the Centers for Disease Control and Prevention."
The first two numbers are world-wide totals, while the third figure is US-specific. Since the US has roughly 5% of the world's population, the yearly world death toll from the seasonal flu would be about 750,000. That would put it close to the 1968 Hong Kong flu and far below the Spanish flu. If you read the paragraph quickly, however you come away with the impression that the 1968 pandemic was significantly worse than the average flu season, while the 1918 pandemic was exponentially worse; in reality, only the latter is true.
Clearly, not all pandemics are equal, ranging from catastrophic to roughly equivalent to a seasonal flu. Either way, if you're going to provide context, it's good to put everything on the same scale.

Thursday, January 29, 2009

Getting mugged by a girl named Apple

There must be something about being famous that compels parents to give their children stupid names. These crazy celebrity offspring appellations range from place names (like David and Victoria Beckham's child "Brooklyn") to fake-profession titles (Jason Lee's child "Pilot Inspektor") to the obviously drug-induced (Bob Geldof's child "Fifi Trixibell").

Are stupid baby names a problem? According a new study from two economists at Shippensberg University in Pennsylvania, these oddly-named children are more likely to commit crimes than those of us with boring names, like John or Dan. The authors find that:
"The distribution of first names in the state’s population is different from the names of juvenile delinquents. Our results show that unpopular names are positively correlated with juvenile delinquency for both blacks and whites."
The authors note that it is unlikely that having an unpopular name causes juvenile delinquency, but rather that unpopular names are "correlated with factors that increase the tendency toward juvenile delinquency, such as a disadvantaged home environment and residence in a county with low socioeconomic status." This seems strange to me. Why would they embark on a study to show that something correlated with factors that increase crime also are linked with more crime? It seems a little roundabout.

Further, Steven Levitt critiques the questionable methods used in this paper:

"The authors first compute criminality for each name by taking the ratio of the number of juvenile delinquents with that name and dividing it by the number of children total with that name. The higher that ratio, the more criminal the name. But then the authors take the log of that ratio. The problem is that the log of zero is equal to negative infinity, so any name for which that ratio is equal to zero gets dropped from the analysis.

The kinds of names that will have a ratio of zero are uncommon names for which no one with that name is a juvenile delinquent.

If I understand correctly what they are doing, if exactly one person has a particular name, the only way that the observation for that name will be included in their sample is if that person is a juvenile delinquent! This leads to a powerful bias toward mistakenly concluding that people with uncommon names are more likely to be criminals."
Quantitative research is fraught with pitfalls that can bias your results. It seems weird to me that they would have missed something like that, but then again, this study makes little sense to begin with.

Since the success of Malcom Gladwell's "The Tipping Point" and Levitt's "Freakonomics", there has been a tendency for researchers to look for novel and completely unexpected relationships in data. But if you look hard enough (and use certain methods) you can find almost anything. It's really important to ground this sort of research in some sort of theory that one is trying to prove.

The good news is that we don't have to fear the wave of kids with unusual names eminating out of Hollywood.

Saturday, January 17, 2009

Monopoly Money

This week's issue of Rolling Stone features an open letter from Paul Krugman to Barack Obama. In it, Krugman outlines the case for a mammoth stimulus package:
How much spending are we talking about? You might want to be seated before you read this. OK, here goes: "Full employment" means a jobless rate of five percent at most, and probably less. Meanwhile, we're currently on a trajectory that will push the unemployment rate to nine percent or more. Even the most optimistic estimates suggest that it takes at least $200 billion a year in government spending to cut the unemployment rate by one percentage point. Do the math: You probably have to spend $800 billion a year to achieve a full economic recovery. Anything less than $500 billion a year will be much too little to produce an economic turnaround.
Krugman advises sitting down before listening to the price tag; I had to go get a beer.

No one can really visualize the vast sums of money currently being discussed. Our brains didn't evolve to deal with numbers larger than hundreds, or maybe thousands. But public spending is orders of magnitude higher. So how much is the nearly $1 trillion package Krugman suggests? According to Barbara Kiviat, a stack of 1 trillion dollar bills would reach a quarter of the way to the moon.

And yet, Krugman articulates a compelling case for such a large stimulus package and helps put the gargantuan sums into perspective:
It's possible that reviving the economy might cost as much as a trillion dollars over the course of your first term. But the Bush administration wasted at least twice that much on an unnecessary war and tax cuts for the wealthiest; the recovery plan will be intense but temporary, and won't place all that much burden on future budgets. Put it this way: With long-term federal debt paying the lowest interest rates in half a century, the interest costs on a trillion dollars in new debt will amount to only $30 billion a year, about 1.2 percent of the current federal budget.
In fact, Krugman is being conservative with his estimate on the war in Iraq.  Joseph Stiglitz puts the total cost of the war (including indirect costs) at $3 trillion.  I don't know that that completely alleviates my sticker shock, but it helps.   

Monday, January 12, 2009

It's all relative

When a movie is referred to as the "highest grossing of all time", the figure is never adjusted for inflation.  That's why roughly half the films on the list of the highest grossing movies were made after 2000, and why the top ten includes such cinema classics as Shrek 2 and Pirates of the Caribbean.  It's hard to make the comparison when movies are $10 a ticket today and were 25 cents half a century ago.

But it's not just movies.  That's why when job reports come out, it's useful to have some reliable historical data for comparison.  Courtesy of the Minneapolis Federal Reserve Bank, here are some charts that show the current recession relative to past ones:

As you can see, the level of job loss has just reached that of the median post World War II recession.  However, the trend is clearly downward and many economists believe that job losses will continue for months.  The good news is that were still well above where we would be were we 11 months into one of the harshest recessions.

So when you read articles claiming the US economy lost more jobs last month that at any time since 1945, remember that that is a gross number, not adjusted for the larger size of the economy today.  It's bad out there, but it's good to keep some perspective.

Tuesday, January 6, 2009

This just in: 18 year olds talk about sex!

If you want to frighten parents and educators, mention "MySpace". The social networking site has become public enemy number one in the fight against teenage vice. Now, even the medical community is getting involved. According to a study published in the Archives of Pediatrics & Adolescent Medicine, "54 percent of teens talk about behaviors such as sex, alcohol use, and violence on the social networking giant MySpace".

Actually, that quote is a bit misleading. A few paragraphs down, we find out:
The study looked at MySpace profiles of 500 people who identified themselves as 18-year-old males and females in the United States. References to risky behaviors included both words and photos, the authors said.
So this means that 54% of 18-year-olds on MySpace reference sex or drugs (there's no mention of "rock-n-roll" in the study) in their profiles. Let's put aside for a moment the fact that 18-year-olds are legal adults. Studies of the sexual behavior of Ameircan teens reveal that 58% of 18-year-olds in this country have had sex. If you believe these statistics, MySpace users are actually less likely to have sex than the general population.

You may be wondering why anyone would be interested in this (I know I was). Accodring to one of the authors:

Even if teens have not actually engaged in risky behaviors but merely brag about them online, this can still affect their future behavior, said study co-author Dr. Dimitri Christakis, professor of pediatrics at the University of Washington and director of the Center for Child Health, Behavior and Development at Seattle Children's Hospital.

Those who lie about the behaviors to show off may receive positive feedback from others -- comments such as "that's great" or "I do the same thing" -- that encourage them to actually try out the behaviors, he said.

So the danger here is not MySpace, per se, but rather peer pressure--pressure that results from essentially any contact with peers.  That means that if MySpace is dangerous, then so are cell phones, or any other communication device.  If MySpace is dangerous, so is talking.

Interestingly, one of the researchers makes this point, though it is buried in the article:
"It's really not that MySpace is bad or good. I think the lesson is that it's a tool, and how you use it determines the kinds of outcome you're going to get," Moreno said.
Technology changes, but people typically stay the same.  Teenagers--in this case, young adults--think about, and talk about, sex.  It's easier to see that now that social networking sites have gained popularity.  But just because it's more apparent, doesn't mean it's new.