Wednesday, September 28, 2011

Simpson's Paradox in Texas

I am not a fan of Rick Perry. Unlike President Obama, Perry is not smart. Perry is the worst of both worlds: he unnecessarily alienates leftists and moderates by pushing all their cultural identification buttons, at the same time as he engages in ultra-liberal open border policies with taxpayer’s money.

The media might refer to Perry's policy of using taxpayer money to pay for the college of illegal immigrants as "moderate". But a policy which is opposed by 86 percent of the public even in a rather liberal state such as Wisconsin is hardly "moderate". Compared to the views of voters, Perry's policy is extreme-left. His defense that without having their college education paid for by taxpayers illegal immigrants would live on the "government dole" is unconvincing, since illegal immigrants are not legally entitled to welfare.

Though I feel no need to defend Perry, let me defend the state of Texas itself, which is currently under attack because of Perry's candidacy.

Texas has had rapid job growth. Leftists such as Paul Krugman argue that this is irrelevant, because we have to adjust for demography. Texas also has fast population growth (apparently supply does matter even during recessions). Fair enough, I wrote about the role of population growth for Texas a while ago.

At the same time, left-wing economists such as former U.S. secretary of labor Robert Reich attack Texas for being a state where workers are paid poorly.

“While Texas leads the nation in job growth, a majority of Texas' workforce is paid hourly wages rather than salaries. And the median hourly wage there is $11.20, compared with the national median of $12.50 an hour.”

Reich writes that the Texas model is one of “low wages“ and “lower incomes”, and therefore not right for the U.S.

However, if you want to make demographic adjustment for job growth, you need to make demographic adjustment for wages. Yes, Texas has lower average wages than the U.S. But in fact, Texas Whites, Texas Hispanics and Texas African Americans each earn higher wages than Whites, Hispanics and African Americans in the rest of the country.

The data is from 2011, hourly wages, from the Current Population Survey of the Bureau of Labor Statistics. I look at those ages 20-65. Indeed, I find that average for all groups is slightly lower in Texas than the rest of the country.

But as you see, each demographic groups earns higher hourly wages in Texas. The same is true for mean and median total salary, Texas is on average lower, but Whites, Blacks and Hispanics are each higher in Texas than the other States.

Each group earns more in Texas, yet the average is lower, because the state has a higher share of low-earning groups.

This is an instance of what statisticians refer to as Simpson's Paradox.

The lower wage rates in Texas are entirely due to demographic composition. Texas is 45% white, compared to 64% nationally, and Texas is 38% Hispanic, compared to 16% nationally.

Demographically adjusted, It would be more accurate to say that Texas is characterized by a high wage (and high ethnic diversity) model.

Robert Reich also complains “Texas schools rank 44th in the nation in per-pupil spending.”

Sure, but again, each ethnic group has higher high school test scores in Reading+Math in Texas than the average for the U.S. The data is from the Department of Education NAEP. The graph is truncated at 200 points, to make it easy to read.

The overall average is identical in Texas and the Nation as a whole. Yet all groups do better in Texas than the Nation as a whole. The only reason that the average is not higher in Texas is that the state has a higher share of lower than average performing Hispanics. Even though Hispanics in Texas outperform Hispanics in the rest of the country, their higher share of the overall population depresses the Texas mean and dominates the result.

The Simpson paradox in wages and the near-Simpson's paradox in test scores highlight the increasing importance of demographic composition for social outcomes.


  1. Tino,

    Are those wage numbers COLI adjusted? Texas is materially cheaper than the national average. How about the school spending numbers?

  2. Last time I checked the NAEP statistics Texas actually matched Massachusetts. Texas whites don't do as well as whites in MA. However, TX blacks and Hispanics outperform MA.

  3. The wages numbers and school spending is not cost of living adjusted, doing that would make Texas do even better. However, there is no state data which I am aware of which is considered reliable.

  4. Folks,

    I actually want to defend Perry for a change. Overall I detest the guy. However, he has caught plenty of flak for mandating the HPV vaccine in Texas. I can't comment on the alleged campaign contribution issues or allegations of (near) corruption.

    However, on substance he was responding to a very real problem. HPV infections and cervical cancer are strongly associated with early teen sexual activity. For better or worse, this type of behavior is common in Texas and may be more common in the Hispanic community. See "State Profiles Texas" (

    While, the sexual activity data isn't clear, the cervical cancer data is devastating. See

    "Invasive Cervical Cancer Among Hispanic and Non-Hispanic Women --- United States, 1992--1999" ( A quote

    "The incidence for invasive cervical cancer was 16.9 per 100,000 women (95% CI=16.2--17.5) for Hispanic women and 8.9 (95% CI=8.8--9.1) for non-Hispanic women (Table). Regardless of the stage of disease at diagnosis, incidences for Hispanic women were approximately twice those for non-Hispanic women in each year during 1992--1999."

    See also "HPV knowledge, attitudes, and cultural beliefs among Hispanic men and women living on the Texas-Mexico Border" ( The key findings are

    "Participants had little understanding about HPV and its role in the etiology of cervical cancer. Attitudes and concerns differed by gender. Women interpreted a diagnosis of HPV as a diagnosis of cancer and expressed fatalistic beliefs about its treatment. Men initially interpreted a diagnosis of HPV as an indication of their partners' infidelity, but after reflecting upon the ambiguity of HPV transmission, attributed their initial reaction to cultural ideals of machismo. Men ultimately were interested in helping their partners seek care in the event of a positive diagnosis."

    Note that sexual activity is closely tied to assimilation. In other words, Texas Hispanic teens assimilate into the underclass. See

    "English linked to promiscuity in Hispanic teens Hispanic teen sex study puzzling Increased use of new language seems to lead to a much higher level of activity" (

    "As Hispanic teens shed the language of their native countries and immerse themselves in American culture, they become dramatically more sexually active, a new study shows.

    A review of 7,300 Arizona teenagers' behavior, which should translate well to other states that border Mexico, including Texas, found that 31 percent of Hispanic teens who speak primarily English have had sex, more than twice the percentage of those who speak primarily Spanish, 14 percent."

    The bottom line is that Perry's decision will save lives and not just a few. He may have lied about meeting the dying woman before he mandated the HPV vaccine. However, considerably fewer women will die as a consequence.

  5. Tino,

    Haven't you blogged COLI adjusted state statistics in the past?

  6. Yes, but as robustness check. There is data, but not reliable enough to base an entire story on. The left can always question the cost of living estimates.

  7. Very interesting. I wonder why East Asians always do slightly better than Whites, who in turn always do better than Hispanics and Blacks? Can it be some hereditarian traits in the mix with cultural and social factors? Hmm...You should definitely read The Perils of Diversity by Byron M. Roth. It's not economics but indeed relevant for an economist.

    Regards from a Swedish multiimmigrationism skeptic.

  8. Tino,

    A paper from 2010, "The Impact Of Right-To-Work Laws On Interstate Cost Of Living Differentials" discusses COLI data. However, the paper appears to use "" as a source. Given the Top 50 website just has numbers without any supporting data or methodolgy, I wouldn't use it.

    However, the paper does mention a potential better source.

    Cebula, Richard J. And Michael Toma. “An Empirical Analysis of Determinants of Interstate Living-Cost Differentials, 2005”. Journal of Regional Analysis and Policy, 2008, 33.3, pp. 222-228.
    --- “Geographic Living-Cost Determinants: 1995”. Atlantic Economic Journal, 2000, 28.3, pp. 380.

    For years, Dr. Howard Nelson calculated COLI data on behalf of the American Federation of Teachers (AFT). You can find a set of COLI data over at (Table I-7). Note that the AFT no longer publishes this data because it was being used in a manner they didn't appreciate.

    See also for an earlier version of the AFT data.

    Note that shows drastically lower COLI deltas between the states. In my experience, the magnitude of the state vs. state deltas is driven by housing costs. Calculations based on rental-equivalence show smaller deltas. Calculations based on home ownership show much higher deltas.

  9. This comment has been removed by the author.

  10. "Taxpayers illegal immigrants would live on the "government dole" is unconvincing, since illegal immigrants are not legally entitled to welfare. "

    In fact, they are. Illegal immigrants can apply for Food Aid and Medicaid.

    71% of illegal immigrants live on some kind of Welfare. Instate tuition for illegal children cost pretty much nothing, but can make sure that an illegal immigrant becomes a productive member of society in the future.

    I'm not a Risk Perry supporter, because he is too polarizing and would make a fool out of himself on the international stage, but he is right about immigration.

  11. Vegard:

    I know Illegal immigrants get some benefits, but as I wrote they are not *legally* entitled to them. For instance other than emergency, they are not supposed to get Medicaid. If this is the problem, Perry could just vote not to give them benefits they have no right to anyway.

    The report you cite uses households. In many cases the parents are illegal, but the children American citizens.

    “Instate tuition for illegal children cost pretty much nothing’

    Don’t be ridiculous, in state tuition costs $20.000 per year for 4-5 years. That is far more than the expected cost of welfare payments for someone not eligible for welfare (and smart enough to go to college).

    In state tuition doesn’t even pay for itself for American citizens from the point of view of the state. If it did, why not give pay for the college education of all Americans?

  12. Tino, Vegard,

    I don't mean to burst anyone's bubble. However, the fact that illegals are not legally entitled to some government benefit, does not mean that they don't get it.

    In real life, legal status is almost never checked. Typically a form has a check box where the applicant simply states that they are legal.

    See for a long comment thread. Check for the word "verification". Several folks who haved actually worked in state welfare departments confirmed that no real checking takes place. Typical quote

    "Longstanding instructions in the Family Assistance Manual direct staff to accept the statement of an applicant when he declares himself and members of his household to be citizens. No further verification has been required unless we had reason to question that statement. Requiring individuals to provide proof of citizenship or immigration status because of appearance or limited English speaking proficiency may be in violation of Title VI of the Civil Rights Act. The only reasons to question an applicant's statement and require further verification are: 1) when there are inconsistencies with statements made by the applicant; 2) inconsistencies with other information on the application or previous applications; and/or 3) inconsistencies with information received by the counselor.“"

  13. Vegard,

    The in-state tuition issue is just the tip of the iceberg. Perry opposes any type of immigration enforcement that might actually work. Fences? No. E-Verify? No. Interior enforcement? No.

    Kabuki on the border? Sure. One National Guardsmen for each five miles of border is the Perry plan.

    What does Perry really want? Amnesty followed by unlimited guest workers.

  14. Skeptical: Sure, I cite illegal welfare use all the time. But in this context the legality is central. If Perry's aim is truely to duce the dole , a much cheaper way would be just to enforce the law, rather than pay for college.

  15. Speptical: Fences will not work. It is extremely easy to get past a fence, just watch this
    A fence is not going to work, especially in remote areas.

    What would be the most effective way is a strong fence in areas with lots of people, and helicopters/satellites to check rural areas.

    His other policies apart from border fence, and instate tuition, I don't know.

  16. Tino
    "Don’t be ridiculous, in state tuition costs $20.000 per year for 4-5 years. That is far more than the expected cost of welfare payments for someone not eligible for welfare (and smart enough to go to college). "
    However, this program pays for itself because they will pay higher taxes, and fewer of them will be on welfare. It is more than expected cost of welfare for one year, but not a lifetime.

    You say they should enforce the law. I agree. However, they are not allowed to enforce the law, hence instate tuition makes sense.

    BTW: I don't think instate tuition should exist. The price should be the same for all Americans

  17. I also agree with him that it is morally wrong to punish the children of the parents decisions.

    What they really need to do is to stop giving welfare to illegals. They can make exceptions for their children, but the parents should get nothing apart from food aid.

    Also, they need to crack down on employers who hire illegals, for instance by e-verify and tougher punishments.

    Lastly, they need to secure the border, but I don't think a fence will do it. I'm not soft on immigration, but I don't like populist measure which won't work, and we need to have a system which isn't inhumane.

  18. Vegard:

    1. “this program pays for itself because they will pay higher taxes”

    According to cost-benefit estimates, subsidizing college tuition doesn’t even pay for itself for American students.

    If it did, the government would pay for everyone, not just illegal immigrants.

    2. “they are not allowed to enforce the law”

    If Perry wanted to enforce the law he would have voted for E-verify, which he is against. He is lying when he claims he had no choice, he didn’t *want* to enforce the law for political reasons.

    3. “is morally wrong to punish the children of the parents decisions.”

    No one is “punishing” anyone; this is about not rewarding you for breaking the law by giving you a gift of $100.000 from the taxpayers.

    It is not the fault of the kids, but nor is it the fault of Texas taxpayers that they broke American immigration law.

    Furthermore, why are you “punishing” the kids in Mexico whose parents didn’t violate American law by not paying for their education? Are we “punishing” everyone else in the rest of the planet by not paying for their education in American

    4. A fence can be extremely effective, if big enough, and combined with manpower. Israel proved this against a much bigger problem (terrorism) than illegal immigrants. A fence worked quite well in San-Diego. Obviously nothing can ever be 100% effective, but 95% is close enough.

    Denying the potential effectiveness of border fences is one of the most pathetic pro-immigration excuses.

  19. 1. I took a look at the study, and none of the charts say anything about instate tuition. Also, instate tuition have different effects on different groups.

    If you support rich people with instate tuition, it will not make a difference. If you support poor people who otherwise wouldn't go. It will make a huge effect. Illegal immigrants are poor.

    Think about it, an average college student earns about 650K more than a non-college student. That is a lot of tax money, and we haven't even included welfare.

    2. Misdirection! We were not talking about e-verify. We were talking about welfare for illegal immigrants. The states are not allowed to check if a person is on welfare or not. That is my point.

    E-verify could reduce the inflow because they won't be able to get jobs, but it may not be possible to implement in Texas, even if Rick Perry supported it. He would lose support among hispanics.

    3. I'm no global citizen. I don't believe in equality of rights among all countries. In the US, they should take care of the ones living in the US. If they are illegal by choice, they should be punished and deported.

    But the children of these illegals didn't chose to go to America. I don't believe they should have fewer rights than other Americans.

    If the parents go home, then they should go home as well, but if America fails to deport illegal immigrants, then I think it is immoral to punish their descendants who didn't chose to go to America and have no connection with their home country.

    4. Come on! Do you seriously think that America is going to build a wall with similar effect to Israel? Each kilometer of the wall cost already about 9 billion USD per mile. I expect a big enough wall with foundations and everyting to cost at least 100 billion USD per mile. That will be 200 billion USD dollars just to build a wall. That is not going to happen.

    The wall they are currently building will not stop illegals coming to the US, especially considering that most of them come to the US legally and overstay their visa. There is no way you can prevent people from entering the US, you need to reduce the incentives to come to the US.

    This is not pathetic, it is rational thinking. US needs people that try to find solutions, not people who blindly follow an ideology.

    BTW. I said a wall will work in populated areas, but not in rural areas. In rural areas you got a lot more time to find a way to get through the wall.

  20. Vegard:

    1. You didn’t read it carefully. One section discusses “college education subsidies”, and finds that they do not pay for themselves. In state tuition is a college education subsidy. (Texas in state is even worse deal, as a lot of college graduates move out of the state, and as Texas has no income tax.)

    2. “an average college student earns about 650K more than a non-college student.”

    First, that number is wrong, since it doesn’t time discount, and doesn’t take into account income lost from not working.
    This study estimates $121.000.

    More importantly, it is a fallacy to compare non-college students and college graduates to measure the value of college, because the degree itself is not the only difference between the two groups. College graduates on average tend to be smarter and have better non-cognitive skills than non-graduates, and would therefore earn more than the average non-graduate even if they didn’t go to college.

    3. “ The states are not allowed to check if a person is on welfare or not.”

    The state is allowed to be strict about welfare to adult illegal immigrants. Perry *chose* not to do this, so he can’t blame the Federal government.

    4. “E-verify … may not be possible to implement in Texas, even if Rick Perry supported it. He would lose support among hispanics.”

    In 2008 Hispanics were still only 20% of voters in Texas, and not all of them support illegal immigration. Texans are conservative. In fact voters in Texas, even including Hispanics, are slightly more strongly against illegal immigration than the average for the U.S.

    5. “But the children of these illegals didn't chose to go to America. I don't believe they should have fewer rights than other Americans.”

    So if the parents manage to sneak someone under 18 into the country, you believe that the U.S is obligated to immediately and automatically grant that child all the rights of U.S citizen?

    4. ”Each kilometer of the wall cost already about 9 billion USD per mile.”

    I don’t know where you got those numbers,
    but they are completely wrong. The Israeli fence cost 2 *million* per kilometer.

    A state of the art U.S fence would cost $4-8 billion to build, not $200.

    5. “most of them come to the US legally and overstay their visa.”

    Not most, 40%, according to the Federal government. This figure is also quite misleading, since many of those 40% overstayers are only here illegally for a short time rather than permanently like the southern border crossers.

    6. “In rural areas you got a lot more time to find a way to get through the wall.”

    You can *combine* a fence with patrols. One thing you can do is 2 walls, with space between. Once people are crossed, the border patrols are notified, and catch you before you cross the second one.

  21. 1. After what I see it only compares the subsidy cost with the GDP of the country. Not a very scientific way is it?

    You dispute my numbers, and say I don't take into account lost earnings. Certinally lost earnings are not 550K. For instance this study show arond the same

    High driven individuals are the ones who want to go to college, but they won't be able to if they can't afford it. Hispanics need more people who set a good example.

    2. No they are not. Or else, Arizona would have done it.

    It's not politically possible to implement in Texas. They would angle it, so that Perry would hate hispanics. I don't see any reason to discuss it.

    3. Yes, I don't want to punish the children for the parents decision. If we take your views to the logical conclusion, they shouldn't be able to attend elementary schools either.

    If US fails to deport the parents, then the next generations shouldn't be punished for that.

    4. The cost of the wall is not 2 million per km. The cost in the US and Israel is not the same. They don't even have to care about the wall in rural areas in Israel, since they are not trying to stop illegal immigration, but they are trying to stop sucide bombers. Most of them will stay home, if they can't find a easy way through.

    The cost for the San Diego border, which is inadequate in rural aeeas is 5.31 million USD dollars per mile from the same source.

    Two proper walls with foundations and everyting would be extremely expensive, and is certinally not what they are building. What they are doing right now won't work.

    They can detect people by satelites. And then they can send helicopters to find them. Video cameras could also help detecting them. With funding in America, you need to pick one of them, and a small wall by itself will do nothing. Better border security will help.

  22. You missunderstand Heckmans paper. Calling probably the best active economist in the world not “very scientific” is just silly.

    I criticized your number because it neither discounts nor includes the cost of forgone income. You answer with another measure that neither discounts nor includes the cost of forgone income? Come on.

    The value of someone going to college for the government is simply not as large as you think, on average less than the cost of tuition (and financial aid, which illegals in Texas also get). If it paid off, the government would pay for everyone’s college.

    “High driven individuals are the ones who want to go to college,”

    Yes, exactly. Therefore, estimates of the value of college cannot just compare people with and without degrees, like you did.

    “Hispanics need more people who set a good example.”

    Like illegal immigrants who want taxpayers to pay for their education?

    “The cost for the San Diego border, which is inadequate in rural aeeas is 5.31 million USD dollars per mile.”

    Sure, but you said 9000 million, not 5.

  23. Also, just to clarify. I'm in favor of a border fence in populated areas, but in rural areas it is a waste of money.

    This guy actually is arguing against the myth "The border fence is ineffective." but he still believes a border fence on the whole border is a waste of money and won't work.

    The only solution is to have border control and technology in these areas.

  24. "The value of someone going to college for the government is simply not as large as you think, on average less than the cost of tuition (and financial aid, which illegals in Texas also get). If it paid off, the government would pay for everyone’s college."

    Again, we are talking about poor people where tuition breaks helps more, and in fact most countries are paying for parts of everyone's tuition.

    My argument would rather be, why is everyone apart from the US payng for their tuition if it doesn't help. They are not just paying for poor people, they are paying for everyone.

    The paper I did show you, as far as I'm aware do show foregone earnings.
    I rather want to ask you. Do you believe in original sin. Since, you are saying that since the parents did something wrong, they can not set a good example to their peers and children.
    The wall has different cost after where it is. 9 million USD i got from one source. I gave you specific numbers for San Diego wall, which was built in the 90s. Now the cost is higher.

    If you want to create a double wall, with foundations and everything. The cost will probably be about 100 million USD per mile.

    The link I forgot to give in my previous comment.

  25. Vegard,

    The Penn & Teller video was actually funny. The "fence" in question was a vehicle barrier intended to stop cars (with drugs), not people. That fact that the Bush administration built vehicle barriers rather than fences (in many areas) should tell you a lot about Bush's motives.

    It turns out that we have a lot of information about the Israeli fence. I quote from

    "What America can learn from Israel's West Bank security barrier" by Shmuel Rosner

    "Here's one lesson Americans can definitely draw from the Israeli experience of building a fence to separate them from the Palestinians: High fences don't always make good neighbors. It didn't happen in the West Bank, and it probably won't happen in Texas. The country that builds the fence buys a sense of security, but the people prevented from getting to work, or shopping, or marrying someone on the other side will not be thankful for it. And the reason is pretty obvious: Fences work."


    "As America debates the question of erecting a fence along the U.S.-Mexico border, two precedents are mentioned by proponents and opponents: the Berlin wall and the Israeli barrier. The former is usually the negative example, the latter the more practical illustration. Most calculations of the projected cost of a U.S. fence cite the Israeli model: "[B]ased on the price of the Israeli security barrier," the National Journal estimated that 2,000 miles of fence will cost the United States $6.4 billion."


    "As such, the Israeli fence is very efficient. The number of fatalities from terror attacks within Israel dropped from more than 130 in 2003 to fewer than 25 in 2005. The number of bombings fell from dozens to fewer than 10. The cost for Israel is in money and personnel; the cost for Palestinians is in unemployment, health, frustration, and blood. The demographic benefit—keeping out the Palestinians—is just another positive side effect for the Israelis."


    "Still, some of the lessons from the Israeli experience apply. The first is one opponents don't like to hear: A wisely planned fence is capable of preventing almost every attempt to enter a country illegally.

    When Arizona Gov. Janet Napolitano declares, "You show me a 50-foot wall, and I'll show you a 51-foot ladder at the border," the answer is fairly straightforward: You show me a 51-foot ladder, and I'll show you a guardsman standing on the other side of the wall waiting to arrest the person using it. The fence is not the only thing keeping people from entering. The fence has just two objectives: slowing the intruders and making them visible to members of the border patrol. The rest of the work is done by human beings."

  26. Skeptical Economist: The costs are different in Israel, and America. Even though the fence is less effective, it cost more in America than Israel. I have already shown estimates of costs of the wall.

    Also, the wall in Israel had a different purpose, so they don't need to care that much about rural areas. Terrorist bombers won't use days to go through a rural area to get across the border.

    The rebuttals doesn't make much sense when you consider the fact that in rural areas it will take hours for police to arrive, while it will take minutes for them to pass. And you will also have to consider that a fence will go at the expense of border security.

  27. This comment has been removed by the author.

  28. I checked some data, and most of the fence (97%) is just electronic barrier, and not a wall at all. Of course it cost less, if only parts of it is a tall concrete wall.

    Which proves my point, the costs for an effective wall in rural areas with little security will be massive.

  29. where do i get state hourly wages? current population survey then what?

  30. if you want state hourly wage by race and ethnic group and state, you need to download the dataset. Click on the link.

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