# 统计代写|线性回归分析代写linear regression analysis代考|When it is not necessary to control for a variable

## 统计代写|线性回归分析代写linear regression analysis代考|When it is not necessary to control for a variable

If a potential control variable does not meet the criteria for being included, based on the three scenarios $I$ just discussed, then it would actually be okay to exclude it from a model.

Let me commit econometric heresy and make the argument that there are some cases in which it is not necessary to control for demographic characteristics. Let’s return to the issue of how the state unemployment rate affects teenage drug use, and let’s suppose that we have individual-level data on teenagers from each state over ten years and assess whether it meets any of the criteria above.

Demographic characteristics could affect the outcome – for example, teen males are more likely to use drugs than teen females. But such characteristics should not affect nor be correlated in any meaningful way with the state unemployment rate, which is based on hundreds of thousands or even millions of people over age 16 in the state. Furthermore, the demographic characteristics are in no way representative of a replacement action. And, with a large-enough sample, there should not be any meaningful incidental correlation between the demographics of the subject and the state unemployment rate. Thus, there should not be any omitted-factors bias by excluding demographic characteristics as control variables.

That said, controlling for demographic characteristics would not harm the model, as they are not mediating factors. Basically, you could control for these characteristics or not, and it shouldn’t make that much difference.

## 统计代写|线性回归分析代写linear regression analysis代考|Criteria to use and not use for deciding whether

I will now lay out criteria here for whether to include a control variable in a model that has the objective of estimating causal effects. These criteria mostly follow from the discussion so far, particularly from the PITFALLS and the example just discussed. The criteria are:

1. Theory suggests that one of the following could be the case:
a. the control variable could affect the outcome and the key-explanatory variable(s)
b. the control variable could affect the outcome and be incidentally correlated with the keyexplanatory variable
c. the control variable represents a replacement action from not receiving the treatment, or having low exposure to the treatment
d. the control variable helps towards establishing the optimal reference group for the keyexplanatory variable.
2. The control variable is not a product of the key-explanatory variable and is not an outcome itself.
3. For quantitative variables, the coefficient estimate on the control variable is not in an inconceivable direction or of an inconceivable magnitude. (This is less of an issue with dummy variables, as they merely involve estimating within-group coefficient estimates.)
4. The control variable is not too highly correlated with the key-explanatory variable.
5. The control variable does not violate these PITFALLS:
• It is not affected by the outcome (reverse causality)
• People do not select different values of the control variable based on expectations of the effects of that variable on the outcome (self-selection bias)

The first criterion is the basis for including any control variable, with (a) – (c) addressing omitted-factors bias and (d) addressing improper reference groups. If the variable should not affect the outcome or is not possibly correlated with the key-explanatory variable, then there is no need to control for the variable. The second criterion just speaks to whether the control variable would be a mediating factor or outcome for the key-explanatory variable (PITFALL #5).

The third criterion is a bit controversial. The idea here is that, for a quantitative variable that could only have a positive effect (if any), according to theory, a few non-representative outlying observations could cause its coefficient estimate to be negative. The incorrect estimate may exacerbate any omitted-factors bias. The important part of this criterion is being certain that the coefficient estimate cannot conceivably be in the direction it is. Also, if a variable has an inconceivably large estimated effect, then give some thought as to whether this apparently-overstated estimate would affect other estimates and whether it is best to exclude the variable from the model. This is part of the “art” in regression modeling.

# 线性回归代考

## 统计代写|线性回归分析代写linear regression analysis代考|Criteria to use and not use for deciding whether

1. 理论表明可能出现以下情况之一：
a. 控制变量可能影响结果和关键解释变量
b．控制变量可能会影响结果并与关键解释变量
c 偶然相关。控制变量表示未接受治疗或低暴露于治疗的替代行动
d。控制变量有助于为关键解释变量建立最佳参考组。
2. 控制变量不是关键解释变量的产物，也不是结果本身。
3. 对于定量变量，控制变量的系数估计不是不可想象的方向，也不是不可想象的大小。（这对于虚拟变量来说不是什么问题，因为它们只涉及估计组内系数估计值。）
4. 控制变量与关键解释变量的相关性不是太高。
5. 控制变量不违反这些陷阱：
• 它不受结果的影响（反向因果关系）
• 人们不会根据对该变量对结果的影响的预期来选择控制变量的不同值（自我选择偏差）

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