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N·格里高利·曼昆的博客

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富人的后代更聪明?  

2009-08-30 17:40:41|  分类: 默认分类 |  标签: |举报 |字号 订阅

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The Least Surprising Correlation of All Time


qianlaoda[译]

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富人的后代更聪明? - 曼昆 - N·格里高利·曼昆的博客

 

富人的后代更聪明? - 曼昆 - N·格里高利·曼昆的博客

 

The NY Times Economix blog offers us the above graph, showing that kids from higher income families get higher average SAT scores.

 

NY Times Economix blog,给出了上面的图形,说的是:高收入家庭后代的平均SAT成绩比较高。

Of course! But so what? This fact tells us nothing about the causal impact of income on test scores. (Economix does not advance a causal interpretation, but nor does it warn readers against it.)

当然如此!但是,又怎么样呢?这个事儿,并没有说明收入与考试成绩之间的因果关系。(Economix也没有给出一个因果解释,但是,它也没有让读者不要去找其中的因果关系。)

This graph is a good example of omitted variable bias, a statistical issue discussed in Chapter 2 of my favorite textbook. The key omitted variable here is parents' IQ. Smart parents make more money and pass those good genes on to their offspring.

这个图形是典型的“遗漏变量偏差”,在我所喜欢的教科书的第二章里,讨论了这个统计问题。这里遗漏的关键变量就是“父母的智商”。聪明的父母会挣更多的钱,而且,会将那些好的基因传给自己的后代。

Suppose we were to graph average SAT scores by the number of bathrooms a student has in his or her family home. That curve would also likely slope upward. (After all, people with more money buy larger homes with more bathrooms.) But it would be a mistake to conclude that installing an extra toilet raises yours kids' SAT scores.

假设我们想画出平均SAT成绩与学生家里的洗手间数量之间的关系。这个曲线也很可能是斜向上的。(毕竟,有钱人,买的大房子拥有的洗手间的数量也会更多。)但是,如果说“安装多余的洗手间,能够小孩的SAT成绩”,那一定是谬之千里了。

It would be interesting to see the above graph reproduced for adopted children only. I bet that the curve would be a lot flatter.

如果对领养的小孩,也画出上面的这个图形,肯定挺有意思。我估计,曲线会平坦很多很多1

 

 

注释:

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1.因为剔除了智商相关的遗传因素。

2.克鲁格曼注意到了这篇文章,显然他还是认为”收入具有一定的作用“。下面是他的回应:

                      Heredity, environment, justice

                             遗传、环境、正义

Oh, Kay. Greg Mankiw looks at a graph showing that children of high-income families do better on tests, and suggests that it’s largely about inherited talent: smart people make lots of money, and also have smart kids.

嗯啊!曼昆研究了一个图,图的意思是:高收入家庭的后代,考试情况更好一些。他还说,这种情况主要与遗传的天分有关:聪明人挣到好多钱,也有了聪明的小宝贝。

But, you know, there’s lots of evidence that there’s more to it than that. For example: students with low test scores from high-income families are slightly more likely to finish college than students with high test scores from low-income families.

但是,大家知道吗?有很多证据表明还有更多的故事没有讲。譬如:相比于收入贫寒、考试高的学生来说,家境优裕、考试成绩不好的小孩,他们完成大学学业的可能性要更大一些。

It’s comforting to think that we live in a meritocracy. But we don’t.

想到我们生活于一个精英政体之中,就会心里舒坦一些。但是,事实却非如此。

3.关于克鲁格曼的这篇争论,曼昆给出了一个更进一步的说明,语气还是一如既往的和缓.


And I thought I was being boring


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My previous blog post on SAT scores and income generated a surprising amount of blogosphere pushback. See, for example, this post by Paul Krugman.

我前面关于SAT考试成绩与收入之间的文章,想不到引来了博客空间的强烈反对。譬如,克鲁格曼就写了一篇文章与我讨论。

I say "surprising" because I almost did not post the piece at all, thinking that it was a bit pedantic and pedestrian. In other words, a big yawn. I did not think my point about omitted variable bias was particularly new or controversial.
我说我自己“想不到”,是因为我差不多没有贴那篇文章,是因为我觉得那篇东西学究气太重,也缺乏想象力。让人要打呼噜睡着的。我觉得,我说它有“遗漏变量偏差”,也不是特别新颖,也没有什么争议性。


In essence, what I said was

本质上,我的意思是:

1. People vary in their innate talents, as measured by, say, IQ tests.

人们天生的才华有差异,譬如,可以IQ测试来检测。

2. More talented people tend to earn higher incomes.

更聪明的人,挣到大钱的可能性更大。

3. More talented people tend to have more talented biological children--that is, talent is partially heritable.
更聪明的人,可能会有生理上更聪明的小孩,即:聪明具有部分的遗传性。


4. As a logical implication of the above three points, the raw correlation of kids' SAT scores and family income conflates the true effects of family income with the biological transmission of talent.
以上三点的逻辑结论就是:小孩的SAT成绩与家庭收入之间的粗糙的相关性,将家庭收入的真实效应与天分的生物遗传,混在了一起。


I would be curious which of the above four points Paul does not agree with.
我不知道克鲁格曼对于以上四点,有什么不同意见。


Paul himself is a good case illustrating my point. He is smart, and he has high income. I don't think those two facts are a mere coincidence. Instead, his innate talent is a large element of his success. I would bet that if he had had children, they would likely have been smart as well, even if he spent only average resources rearing them (such as, for example, if he put them up for adoption).

克鲁格曼本身就是一个能够说明我观点的好例子啊。他很聪明,他的收入也很高。我觉得,这两个事实不只是简单的巧合。相反,他遗传的天分,是其成功的很大因素呢。我敢说,如果他有后代,他们也很有可能是很聪明的,即使他在养育小孩上面只花与一般人相同的费用或资源(譬如,如果他把小孩送给人家抱养。)

By the way, the conjecture in the final sentence of my last post about adopted kids was in part based on existing evidence in the nature-nurture debate. See, for instance, this paper.

顺便说一句,我那个文章最后一句中关于“领养小孩”的猜想,一部分是基于“先天条件-后天条件”的现在证据,而给出的。譬如,可以看(上面链接中的)那篇文章。


4.显然,曼昆的直觉是正确的。他在原文中说:“养子女与亲生父新之间”的关系也具有原来的“收入-成绩”关系。下面是David Cesarini给他写来的信,证明了这个结论:


Test Scores and Biological Father's Income

考试成绩与生父的收入

 

富人的后代更聪明? - 曼昆 - N·格里高利·曼昆的博客

 

MIT's David Cesarini sends me the above chart with this note:

MITDavid Cesarini给我发来上面的图形,并写了下面的便条:

Dear Professor Mankiw,

亲爱的曼昆教授:

I prepared a graph which I think nicely illustrates the simple point you made in your blogpost on the spurious association between SES and test scores. The graph is attached. The dataset is comprised of a large sample of men born in Sweden between 1955 and 1970 who took an IQ test at conscription, at the age of 18. Income is measured as the biological father's income in the 1970 census.

我画了上面的这个图,我想,它会很好地说明你在文章里写的SES与考试成绩之间的伪关系问题.图在附件里.这个数据的样本很大,1955-1970年间出生的男性,他们在18岁应征入伍时进行了IQ测试.收入是1970年普查中亲生父亲的收入.

The red line is the average measured IQ of the non-adoptees, plotted against the biological father's income decile. The blue line shows the same relationship for adoptees and their biological fathers. The patterns are remarkably similar,even though the biological fathers of adoptees did not raise these children.The fact that the biological father's income is almost an equally strong predictor of a child's test scores even when the biological father was not present in the household clearly suggests that most of the association between income and test scores does indeed arise because of omitted variable bias. Of course, an important caveat here is that it is quite likely that non-random assignment of adoptees may explain some of the similarity between the two lines.

红线是非养子女所测得的平均IQ,横线为亲生父亲的收入十分制指数.蓝线表示是养子女与其生父之间的关系,与上面相同。虽然养子女的生父没有养育自己的小孩,但是,曲线的形式是极为相似的。即使生父并没有明显地出现在他的生活环境之中,但是,生父的收入,依然是小孩考试成绩的一个很强的预测指标。这个事实说明:大人收入与小孩成绩之间的关系,大部分确实是因为“缺失变量偏差”所致。当然,有一个重要的说明,以防误解,即:养子女的非随机分配,这个情况很可能可以用来解释这两条曲线的某些相似性。

I hope you find this useful.

我希望这个东西对你有帮助。

Best wishes,


David Cesarini

Thanks, David.

感谢David的来信!


编辑手记:

* 按Eugene的指导,对其中的两处误译进行了修正.so what句,和and also句.(8月31日)

* 又新增了曼昆关于“成绩-收入”关系的一篇新文章。(9月1日)


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