Saturday, November 06, 2010
On Income "Inequality"
I stumbled upon an article lately on my Google Reader feed that ranted somewhat predictably about how income "inequality" has risen significantly in the United States and how the middle class in the US has stagnated over the past 2-3 decades. Here's the link
It is a very provocative article as most poorly reasoned articles are. The worst part of it is that the author attempts to place the blame for "inequality of incomes" on Corporate America without rhyme or reason. In this post, I ponder on the possible reasons for stagnation of middle-class incomes. There are several of them and the most obvious ones have nothing to do with Corporate America or conservative economic policies.
Let's look at certain portions of the article that are worthy of repudiation.
globalization's significant profits were captured by a small corporate elite in the U.S. and a new corporate elite and rising middle class in China and India. The American middle class got very little of it. No wonder people are mad.......Americans accept income and wealth inequality to a much larger degree than Europe........... Looking at the stats on inequality gives us an idea of why so many are angry at the business elite — it's the highest since the 20's and getting worse
Okay. So the moot point is that while incomes have soared in the top bracket, the "median" income of the "representative" Middle American has stagnated over the last few decades notwithstanding the outstanding economic growth during the same period.
I checked up the income stats on wikipedia and it appears that this contention is quite compelling on the surface.
We observe that while the 95th %ile income has risen by nearly 40% between 1979 and 2003, the median incomes have remained quite stagnant. On the surface, this might seem like an indictment of Reagan era deregulation and the increasing preponderance of economic conservatism in the US since the late seventies.
But there are several problems with this story.
Think about Individuals and not some mythical "Middle American" : Anybody with an iota of sense can readily see that the 50th %iler who earned a median income of $38,649 in 1979 is not necessarily from the same household as the 50th %iler who earned $43,318 in 2003. It is quite possible that someone who was at 50th %ile in 1979 now has a gainfully employed son who is closer to the 80th %ile on the income distribution curve.
The American Middle class has changed in constitution since the late seventies. Several households have moved up the economic ladder as one would expect in any society bustling with private economic activity. Then, the natural question is that if most households have been upwardly mobile over the past three decades, why have median incomes remained stagnant?? The answer could well be immigration.
Immigration likely to push down median Incomes: A lot of people emigrate to the US with the hope of working their way out of poverty in their native lands and entering the "middle class". These immigrants are often unskilled and poorly educated and hence unlikely to land up with jobs that fetch them more than the median US income.
Households that have immigrated in the eighties and nineties did not feature in the dataset that generated a median income of $38,649 in 1979. Which is why it is highly irregular and inappropriate to compare two very distinct datasets from 1979 and 2003 and make sweeping statements about stagnant "middle class" incomes in the country.
So, does that mean the US should place restriction on immigration to help solve this "problem" of seeming income inequality? No. Reducing inequality of incomes should never be an end in itself. Most recent immigrants to US earning less than the median income are quite happy with their adopted country and wouldn't want to return to their roots. Take for instance a waiter in an ethnic Indian restaurant in NYC (Saravana Bhavan for eg). The guy probably earns $20,000 in his present role which perhaps places him at the 40th %ile on the income distribution curve. It is quite likely that percentile-wise he was much better off in his native country, prior to immigration (given that median income in India is barely $500 p.a). Yet, immigration makes sense for this guy as he is better off being a 40th %iler in NYC than an 80th %iler in Trichy, TN.
The Tamil waiter's immigration to US has contributed to a drop in the median American income. Nevertheless, it is welcome as the waiter's immigration was a personal preference and leaves him better off than he otherwise would've been in his native town.
"Inequality" could be an outcome of personal choices : Let's consider Bob, a successful corporate executive of yesteryear who used to earn the equivalent of $300,000 back in 1979. He has a daughter - Alice who has led a rather comfortable life thanks to her father's affluence. Unlike her father, Alice has little aptitude for business. She has always evinced keen interest in Native American history and wants to specialize in the same and eventually end up as a professor of Native American history in one of the eastern colleges. Alice is 30 years old now in 2003 and is well settled in a Boston college enjoying her role thoroughly. Her annual income is in the vicinity of $50,000, not even one-fifth of what her father used to earn in 1979!!
Is this an instance of downward intergenerational mobility? Yes. Nevertheless, it is an outcome of personal preferences and shouldn't be bemoaned. Alice is less well off than her parents in terms of monthly cash-flow. But she loves her job and probably enjoys more leisure than her father ever did in all his working life!
This little story emphasises an important point that's often overlooked by liberals who bemoan income inequality :
"It is quite likely that the 50th %iler enjoys more leisure and leads a less stressful life than the 95th %iler!"
Distribution of Leisure fairer in recent decades : Back in 1900, the distribution of Leisure was terribly unfair in the Western world. The rich were not just wealthy in terms of cash but also leisure, with little accountability. The workers who slogged 18 hours a day in unwholesome sweatshops, had neither the income nor the leisure to compensate for the lack of income.
Today, the distribution of leisure is distinctly fairer. The clerk in a Federal office may languish at the 50th %ile of the income curve, but he is quite probably placed much better (perhaps 90th %ile+) on the leisure distribution curve! The corporate executives of today enjoy far less leisure and peace of mind than the landed gentry who constituted the affluent class in the 19th century.
Disclaimer : This is only a hypothesis. But I do wish someone undertakes a study that examines how the distribution of leisure has shifted over the past 100 years in favour of the lower income groups.
Writers in the press who talk about rising income inequality in America seldom think about the points discussed in this post because of their obsession with aggregate nation-wide statistics and an indifference to what the statistics actually mean in the context of average individuals and households. Which is why we keep reading pieces where "pundits" use statistics such as the ones used in this post to launch a tirade on outsourcing and corporate executive compensation.
Inequality of outcomes need not necessarily always be a plot hatched by Wall Street wolves or neo-conservative policy makers. People who think so misunderstand not just economics but also human nature. Economics is a social science that concerns real people gifted with a free will. To reduce these people to a statistical abstraction is not just downright unfair, but bad science.
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I stumbled upon an article lately on my Google Reader feed that ranted somewhat predictably about how income "inequality" has risen significantly in the United States and how the middle class in the US has stagnated over the past 2-3 decades. Here's the link
It is a very provocative article as most poorly reasoned articles are. The worst part of it is that the author attempts to place the blame for "inequality of incomes" on Corporate America without rhyme or reason. In this post, I ponder on the possible reasons for stagnation of middle-class incomes. There are several of them and the most obvious ones have nothing to do with Corporate America or conservative economic policies.
Let's look at certain portions of the article that are worthy of repudiation.
globalization's significant profits were captured by a small corporate elite in the U.S. and a new corporate elite and rising middle class in China and India. The American middle class got very little of it. No wonder people are mad.......Americans accept income and wealth inequality to a much larger degree than Europe........... Looking at the stats on inequality gives us an idea of why so many are angry at the business elite — it's the highest since the 20's and getting worse
Okay. So the moot point is that while incomes have soared in the top bracket, the "median" income of the "representative" Middle American has stagnated over the last few decades notwithstanding the outstanding economic growth during the same period.
I checked up the income stats on wikipedia and it appears that this contention is quite compelling on the surface.
| Sluggish Growth in Median American Incomes | ||
|---|---|---|
| Data | 2003 | 1979 |
| Median (50th) | $43,318 | $38,649 |
| 95th percentile | $154,120 | $111,445 |
We observe that while the 95th %ile income has risen by nearly 40% between 1979 and 2003, the median incomes have remained quite stagnant. On the surface, this might seem like an indictment of Reagan era deregulation and the increasing preponderance of economic conservatism in the US since the late seventies.
But there are several problems with this story.
Think about Individuals and not some mythical "Middle American" : Anybody with an iota of sense can readily see that the 50th %iler who earned a median income of $38,649 in 1979 is not necessarily from the same household as the 50th %iler who earned $43,318 in 2003. It is quite possible that someone who was at 50th %ile in 1979 now has a gainfully employed son who is closer to the 80th %ile on the income distribution curve.
The American Middle class has changed in constitution since the late seventies. Several households have moved up the economic ladder as one would expect in any society bustling with private economic activity. Then, the natural question is that if most households have been upwardly mobile over the past three decades, why have median incomes remained stagnant?? The answer could well be immigration.
Immigration likely to push down median Incomes: A lot of people emigrate to the US with the hope of working their way out of poverty in their native lands and entering the "middle class". These immigrants are often unskilled and poorly educated and hence unlikely to land up with jobs that fetch them more than the median US income.
Households that have immigrated in the eighties and nineties did not feature in the dataset that generated a median income of $38,649 in 1979. Which is why it is highly irregular and inappropriate to compare two very distinct datasets from 1979 and 2003 and make sweeping statements about stagnant "middle class" incomes in the country.
So, does that mean the US should place restriction on immigration to help solve this "problem" of seeming income inequality? No. Reducing inequality of incomes should never be an end in itself. Most recent immigrants to US earning less than the median income are quite happy with their adopted country and wouldn't want to return to their roots. Take for instance a waiter in an ethnic Indian restaurant in NYC (Saravana Bhavan for eg). The guy probably earns $20,000 in his present role which perhaps places him at the 40th %ile on the income distribution curve. It is quite likely that percentile-wise he was much better off in his native country, prior to immigration (given that median income in India is barely $500 p.a). Yet, immigration makes sense for this guy as he is better off being a 40th %iler in NYC than an 80th %iler in Trichy, TN.
The Tamil waiter's immigration to US has contributed to a drop in the median American income. Nevertheless, it is welcome as the waiter's immigration was a personal preference and leaves him better off than he otherwise would've been in his native town.
"Inequality" could be an outcome of personal choices : Let's consider Bob, a successful corporate executive of yesteryear who used to earn the equivalent of $300,000 back in 1979. He has a daughter - Alice who has led a rather comfortable life thanks to her father's affluence. Unlike her father, Alice has little aptitude for business. She has always evinced keen interest in Native American history and wants to specialize in the same and eventually end up as a professor of Native American history in one of the eastern colleges. Alice is 30 years old now in 2003 and is well settled in a Boston college enjoying her role thoroughly. Her annual income is in the vicinity of $50,000, not even one-fifth of what her father used to earn in 1979!!
Is this an instance of downward intergenerational mobility? Yes. Nevertheless, it is an outcome of personal preferences and shouldn't be bemoaned. Alice is less well off than her parents in terms of monthly cash-flow. But she loves her job and probably enjoys more leisure than her father ever did in all his working life!
This little story emphasises an important point that's often overlooked by liberals who bemoan income inequality :
"It is quite likely that the 50th %iler enjoys more leisure and leads a less stressful life than the 95th %iler!"
Distribution of Leisure fairer in recent decades : Back in 1900, the distribution of Leisure was terribly unfair in the Western world. The rich were not just wealthy in terms of cash but also leisure, with little accountability. The workers who slogged 18 hours a day in unwholesome sweatshops, had neither the income nor the leisure to compensate for the lack of income.
Today, the distribution of leisure is distinctly fairer. The clerk in a Federal office may languish at the 50th %ile of the income curve, but he is quite probably placed much better (perhaps 90th %ile+) on the leisure distribution curve! The corporate executives of today enjoy far less leisure and peace of mind than the landed gentry who constituted the affluent class in the 19th century.
Disclaimer : This is only a hypothesis. But I do wish someone undertakes a study that examines how the distribution of leisure has shifted over the past 100 years in favour of the lower income groups.
Writers in the press who talk about rising income inequality in America seldom think about the points discussed in this post because of their obsession with aggregate nation-wide statistics and an indifference to what the statistics actually mean in the context of average individuals and households. Which is why we keep reading pieces where "pundits" use statistics such as the ones used in this post to launch a tirade on outsourcing and corporate executive compensation.
Inequality of outcomes need not necessarily always be a plot hatched by Wall Street wolves or neo-conservative policy makers. People who think so misunderstand not just economics but also human nature. Economics is a social science that concerns real people gifted with a free will. To reduce these people to a statistical abstraction is not just downright unfair, but bad science.
Labels: economics, statistics
Friday, January 29, 2010
On the Misjudgment of Probabilities
A somewhat rambling, indulgent post. I'm writing a blogpost after quite a while which may account for the rather stodgy turns of phrase.
Finished reading Nassim Taleb's bestsellers Fooled by Randomness and Black Swan lately. One among the several insights in the books is that in the real world, it is difficult to assess the degree of uncertainty as risks are not easily computable. The tools of Probability theory come in mighty handy to help compute odds in controlled environments like a casino. But they are of little use once we step out of such regulated environs.
Also, even when we are in a position to reliably compute the odds, we do not consciously use the odds while taking decisions.
Suppose an insurance salesman presents you with two policies.
- Death on account of a terrorist strike
Covered Amount: $50,000
Annual Premium: $50(for 5 years)
- Death on account of any cause
Covered Amount: $50,000
Annual Premium: $2500(for 5 years)
Now, I find Policy A just as attractive as Policy B if not even better. Yes, we would all expect the premium on a special-case death policy to be a lot lower than a "normal" life insurance policy.
A premium of $50 as opposed to $2500 seems fair enough as it appears to account for the relative rarity of a death on account of a terrorist strike.
However, though a ratio of 1/50 ($50/$2500) sounds very good, Policy A is terribly overpriced! (I'm assuming ofcourse that Policy B is reasonably priced)
Death on account of a terrorist strike is an extremely rare event. Surely, fewer than one in fifty deaths is caused due to a terrorist strike. Even if Policy A were priced at $10, I'd still regard it as overpriced!
This reminded me of the law trial in the memorable Otto Preminger classic - Angel Face starring Robert Mitchum and Jean Simmons (who passed away last week) that I watched the other day on DVD. A 20 year old girl kills her step mother by tampering with the gear and break system of the latter's convertible. She succeeds quite spectacularly in her attempt as her victim hurtles to her death along with the vehicle which falls off a cliff.
In the trial that ensues, the ruins of the vehicle are examined. An automobile engineer concludes that the gear shaft was manipulated. The defence lawyer asks whether the gear shaft may have reached its present position due to the impact of the fall. The engineer replies that it is a one in a million event. The shrewd lawyer rejoins - why not one in a thousand? or even one in ten!
So now the case rests on the jury's assessment of probabilities. The higher the likelihood of the gear shaft reaching its present position during the fall, the better the chance of the step daughter getting acquitted. Here's a case where there is no way one can judge the likelihood of the event, no matter how sophisticated you are in your knowledge of statistics and probability. Juries tend to play safe in scenarios like these (i.e over-estimate the likelihood of the rare event) and let the criminal go scot-free.
PS: Jean Simmons does get acquitted in the movie, somewhat predictably.
I've seldom seen a mainstream Hollywood movie demonstrate our inability to come to terms with randomness. Angel Face is an honourable exception.
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A somewhat rambling, indulgent post. I'm writing a blogpost after quite a while which may account for the rather stodgy turns of phrase.
Finished reading Nassim Taleb's bestsellers Fooled by Randomness and Black Swan lately. One among the several insights in the books is that in the real world, it is difficult to assess the degree of uncertainty as risks are not easily computable. The tools of Probability theory come in mighty handy to help compute odds in controlled environments like a casino. But they are of little use once we step out of such regulated environs.
Also, even when we are in a position to reliably compute the odds, we do not consciously use the odds while taking decisions.
Suppose an insurance salesman presents you with two policies.
- Death on account of a terrorist strike
Covered Amount: $50,000
Annual Premium: $50(for 5 years)
- Death on account of any cause
Covered Amount: $50,000
Annual Premium: $2500(for 5 years)
Now, I find Policy A just as attractive as Policy B if not even better. Yes, we would all expect the premium on a special-case death policy to be a lot lower than a "normal" life insurance policy.
A premium of $50 as opposed to $2500 seems fair enough as it appears to account for the relative rarity of a death on account of a terrorist strike.
However, though a ratio of 1/50 ($50/$2500) sounds very good, Policy A is terribly overpriced! (I'm assuming ofcourse that Policy B is reasonably priced)
Death on account of a terrorist strike is an extremely rare event. Surely, fewer than one in fifty deaths is caused due to a terrorist strike. Even if Policy A were priced at $10, I'd still regard it as overpriced!
This reminded me of the law trial in the memorable Otto Preminger classic - Angel Face starring Robert Mitchum and Jean Simmons (who passed away last week) that I watched the other day on DVD. A 20 year old girl kills her step mother by tampering with the gear and break system of the latter's convertible. She succeeds quite spectacularly in her attempt as her victim hurtles to her death along with the vehicle which falls off a cliff.
In the trial that ensues, the ruins of the vehicle are examined. An automobile engineer concludes that the gear shaft was manipulated. The defence lawyer asks whether the gear shaft may have reached its present position due to the impact of the fall. The engineer replies that it is a one in a million event. The shrewd lawyer rejoins - why not one in a thousand? or even one in ten!
So now the case rests on the jury's assessment of probabilities. The higher the likelihood of the gear shaft reaching its present position during the fall, the better the chance of the step daughter getting acquitted. Here's a case where there is no way one can judge the likelihood of the event, no matter how sophisticated you are in your knowledge of statistics and probability. Juries tend to play safe in scenarios like these (i.e over-estimate the likelihood of the rare event) and let the criminal go scot-free.
PS: Jean Simmons does get acquitted in the movie, somewhat predictably.
I've seldom seen a mainstream Hollywood movie demonstrate our inability to come to terms with randomness. Angel Face is an honourable exception.
Labels: movies, statistics
Saturday, February 03, 2007
On Conservatives, Liberals and.....Hypothesis Testing
What makes a person conservative or liberal? I don't know.
But the theory of Hypothesis Testing does help us gain insight into a person's political predilections. Gobsmacked, eh? Read on.
Suppose, for the sake of argument, that youth from the Middle East/N.Africa are more likely to resort to terrorism than any other race. To strengthen this supposition, we have to reject the hypothesis that terrorism finds no special favour among any specific group of people.
H0 : Youth from the Middle East/North Africa are no more inclined/indifferent towards Terrorism than youth from any other part of the world.
The alternative hypothesis is that youth in certain parts of the world are indeed more likely to turn into terrorists. Hence, racial profiling can help apprehend potential terrorists and debar entry to dubious immigrants.
For instance, assume that 5% of the youth wanting to immigrate to US are of Middle Eastern/N.African extraction. Going by the Null Hypothesis, in any sample of immigrant terrorists, the proportion hailing from M.E/N.A shouldn't exceed 5%. Right?
Now, consider a random sample of immigrant terrorists wherein 20% are Arabs/N.Africans and the probability of more than 20% of a random sample of immigrant terrorists being N.Africans/Arabs, given that the null hypothesis holds, is 5%.
Does this figure justify racial profiling? This is where your political predilection comes into play. A liberal might be wary of rejecting a true hypothesis (Type I error) and may be unwilling to disregard it even if the figure was as low as 1%. A conservative right-winger on the other hand, would not want to run the risk of accepting a false hypothesis (Type II error). He may be tempted to ditch the hypothesis for any figure less than 15%!
This has to be one of the great debates in public policy. What is the most appropriate significance level? Should policy makers opt for a high significance level and aggressively pursue racial profiling to weed out the slightest possibility of terrorist infiltration at the expense of civil liberties? Or should they refrain from 'profiling' altogether, and thereby run the risk of terrorist attacks?
The answer would vary depending on whether you're a fan of George Bush or Michael Moore ;)
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What makes a person conservative or liberal? I don't know.
But the theory of Hypothesis Testing does help us gain insight into a person's political predilections. Gobsmacked, eh? Read on.
Suppose, for the sake of argument, that youth from the Middle East/N.Africa are more likely to resort to terrorism than any other race. To strengthen this supposition, we have to reject the hypothesis that terrorism finds no special favour among any specific group of people.
H0 : Youth from the Middle East/North Africa are no more inclined/indifferent towards Terrorism than youth from any other part of the world.
The alternative hypothesis is that youth in certain parts of the world are indeed more likely to turn into terrorists. Hence, racial profiling can help apprehend potential terrorists and debar entry to dubious immigrants.
For instance, assume that 5% of the youth wanting to immigrate to US are of Middle Eastern/N.African extraction. Going by the Null Hypothesis, in any sample of immigrant terrorists, the proportion hailing from M.E/N.A shouldn't exceed 5%. Right?
Now, consider a random sample of immigrant terrorists wherein 20% are Arabs/N.Africans and the probability of more than 20% of a random sample of immigrant terrorists being N.Africans/Arabs, given that the null hypothesis holds, is 5%.
Does this figure justify racial profiling? This is where your political predilection comes into play. A liberal might be wary of rejecting a true hypothesis (Type I error) and may be unwilling to disregard it even if the figure was as low as 1%. A conservative right-winger on the other hand, would not want to run the risk of accepting a false hypothesis (Type II error). He may be tempted to ditch the hypothesis for any figure less than 15%!
This has to be one of the great debates in public policy. What is the most appropriate significance level? Should policy makers opt for a high significance level and aggressively pursue racial profiling to weed out the slightest possibility of terrorist infiltration at the expense of civil liberties? Or should they refrain from 'profiling' altogether, and thereby run the risk of terrorist attacks?
The answer would vary depending on whether you're a fan of George Bush or Michael Moore ;)
Labels: economics, politics, statistics
Wednesday, November 09, 2005
An Update...
I was way too gullible in the previous post. Got carried away by the good Professor's number crunching. Micheal Higgins has demystified the statistical quirk since then.
Can somebody point out why it is much more likely for a batsman to have a round figure strike rate of 50 or 100 than 49.88 or 99.74?
Post your answers without reading Higgins' elementary explanation.
Read the article here to know what I'm talking about.
Current Mood - Embarassed.
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I was way too gullible in the previous post. Got carried away by the good Professor's number crunching. Micheal Higgins has demystified the statistical quirk since then.
Can somebody point out why it is much more likely for a batsman to have a round figure strike rate of 50 or 100 than 49.88 or 99.74?
Post your answers without reading Higgins' elementary explanation.
Read the article here to know what I'm talking about.
Current Mood - Embarassed.
Labels: cricket, statistics
Tuesday, November 08, 2005
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