# 统计代写|线性回归分析代写linear regression analysis代考|Self-selection bias

## 统计代写|线性回归分析代写linear regression analysis代考|The basics of self-selection bias

Recall from Section 2.11 that everyone has (or all subjects have) their own effect(s) rather than there being a single effect of a treatment on an outcome that everyone would experience if given the treatment. One of the examples I gave was that a parental divorce could affect children differently, depending on the situation and the child.

Self-selection bias involves the individual effect being a factor in determining whether the subject receives the treatment or how much of the treatment they get. It reminds me of a Yogi Berra quote (slightly modified): “When you come to a fork in the road, take it … rather than choosing your path randomly, as this will vex academic researchers who aim to estimate the causal effects of your choices.”

There are various forms of what is called “selection bias.” I will address “sample-selection bias” in Section 6.12. Self-selection bias, sometimes called just “selection bias,” occurs when the following two conditions occur: the subject (a person or entity such as a city or state) can, to some extent, select him/her/itself into a category (i.e., choose a value) for the key-explanatory variable; and the reason(s) for that choice or determination of the key-explanatory variable are related to the individual benefits or costs of that factor on the dependent variable.
For the case of estimating how parental divorce affects children’s outcomes:

It’s not exactly the subject (the child) who chooses but the parents do Parents might make that choice based on how much the divorce would benefit or harm their children’s well-being (and outcomes).

Of course, subjects would not always know what their impact would be from the treatment, but as long as there is some connection between their perceived impact and the true impact, along with that being an input in the decision for receiving the treatment, there could be self-selection bias. What results from self-selection bias is that those with more-beneficial or less-harmful impacts would be more likely to receive the treatment (or have greater exposure to the treatment). Thus, the bias would be in the direction of overstating beneficial effects and understating harmful effects of a treatment. Because the expected benefits/costs of the treatment are not known to the researcher, there would be bad-operative variation in the treatment and result in a biased estimated treatment effect.

## 统计代写|线性回归分析代写linear regression analysis代考|A basic two-person example of the effects of a college degree on income

Consider the following example, in Table 6.5, based on a sample of two people: Charlie (who wants to work in Silicon Valley for a big tech company) and David (who wants to do a construction job or some other manual labor). The big tech firms in Silicon Valley typically do not consider people for programming jobs if they do not have a college degree, so Charlie needs to go to college to land such a job and would be handsomely rewarded if he does so. David, on the other hand, would receive much less of a benefit for going to college; maybe a college degree would boost his earnings a little by improving his business sense and networking skills.

The Average Treatment Effect we would hope to estimate would be $\$ 50,000$, which is the average of the effects of$\$80,000$ for Charlie and $\$ 20,000$for David. However, the likely scenario would be that Charlie gets his college degree and David does not because the expected effect of college on his income may not be worth the costs of college for David. And so we would likely observe$\$110,000$ for the person who went to college and $\$ 40,000$for the person who did not go to college, translating to an estimated$\$70,000$ effect of college. Thus, we would be overstating the true average effect of college on income (which was $\$ 50,000$) for this sample because the person who chose college did so because he (correctly) expected to receive the larger effect. (There could also be omitted-factors bias here, as earning potential without a college degree could determine who goes to college and affect income.) In this case, assignment to different levels of education is not random, but rather tied to something related to the benefits of the education in terms of future earnings potential. Of course, people do not always know what the effect of college would be for them, but many people have a sense of how their income potential would be affected based on what type of career they plan on pursuing. There would be bad variation from “expected benefit of college” determining whether people get their college degree. This, of course, is not an observable trait in any data, and so it would be bad-operative variation. More generally on this issue of the effects of years-of-schooling on income, there is a distribution of individual effects, and people choose the level of schooling for which their individual expected net benefit is maximized (considering the individual costs of schooling as well). Thus, the benefit of schooling (or average effect) for those who actually acquire more schooling is likely higher than the average effect for those who have less schooling. This contributes to a positive bias on the estimated effect of schooling on income. # 线性回归代考 ## 统计代写|线性回归分析代写linear regression analysis代考|The basics of self-selection bias 回忆一下 2.11 节，每个人都有（或所有受试者都有）自己的效果，而不是治疗对每个人在接受治疗时都会经历的结果的单一影响。我举的一个例子是，父母离婚对孩子的影响可能不同，这取决于情况和孩子。 自选偏差涉及个体效应作为决定受试者是否接受治疗或他们接受多少治疗的一个因素。这让我想起了 Yogi Berra 的一句话（略有修改）：“当你来到岔路口时，选择它……而不是随机选择你的路径，因为这会让旨在估计你的选择的因果效应的学术研究人员感到烦恼” 所谓的“选择偏差”有多种形式。我将在第 6.12 节中解决“样本选择偏差”。自我选择偏差，有时简称为“选择偏差”，发生在以下两种情况时：主体（个人或实体，如城市或州）在某种程度上可以选择他/她/自己进入一个类别（即选择一个值）为关键解释变量；选择或确定关键解释变量的原因与该因素对因变量的个别收益或成本有关。 对于估计父母离婚如何影响孩子结果的案例： 选择的不完全是主体（孩子），而是父母。父母可能会根据离婚对孩子的福祉（和结果）的好处或损害程度来做出选择。 当然，受试者并不总是知道他们会从治疗中产生什么影响，但只要他们感知到的影响和真实影响之间存在某种联系，并且将其作为接受治疗决定的输入，就可以是自我选择偏差。自我选择偏差的结果是，那些影响更有益或危害更小的人更有可能接受治疗（或更多地接触治疗）。因此，偏见将倾向于高估治疗的有益影响和低估有害影响。由于研究人员不知道治疗的预期收益/成本，因此治疗中会出现不良的手术变异，并导致估计的治疗效果有偏差。 ## 统计代写|线性回归分析代写linear regression analysis代考|A basic two-person example of the effects of a college degree on income 考虑以下表 6.5 中的示例，该示例基于两个人的样本：查理（想在硅谷的一家大型科技公司工作）和大卫（想从事建筑工作或其他体力劳动）。硅谷的大型科技公司通常不会考虑没有大学学位的人从事编程工作，因此查理需要上大学才能找到这样的工作，如果他这样做，他将获得丰厚的回报。另一方面，戴维上大学的好处要少得多；也许大学学位可以通过提高他的商业意识和网络技能来增加他的收入。 我们希望估计的平均治疗效果是$50,000，这是影响的平均值$80,000对于查理和$20,000对于大卫。然而，可能的情况是查理获得了大学学位而大卫没有，因为大学对他收入的预期影响可能不值得大卫的大学费用。所以我们可能会观察到$110,000对于上过大学的人和$40,000对于没有上过大学的人，转化为估计$70,000大学的影响。因此，我们夸大了大学对收入的真实平均影响（这是$50,000) 对于这个样本，因为选择大学的人这样做是因为他（正确地）预期会收到更大的效果。（这里也可能存在遗漏因素偏差，因为没有大学学位的收入潜力可能决定谁上大学并影响收入。）

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