1. 考虑表 1 中的简单假设示例。该示例涉及
11 名患者，每人都感染了冠状病毒。有两种治疗方法：

1 1 10 29
2 1 5 35
3 1 4 19
4 5 6 45
5 5 1 65
6 6 7 50
7 7 8 77
8 7 10 18
9 8 2 85
10 9 6 96
11 10 7 77

a) 计算每个单元的处理效果。

b) 与卧床相比，呼吸机的平均处理效果 (ATE) 是多少？

c) 假设“完美医生”知道每个患者的潜在结果，并且作为

d) 计算如果治疗将获得的平均结果的简单差异

e) 提供一个示例，说明在治疗 covid-19 时可能会违反 SUTVA 的规定。

Problem Set 1
1. Consider the simple hypothetical example in Table 1. This example involves
eleven patients each of whom is infected with coronavirus. There are two treatments:
ventilators Y 1 and bedrest Y 0. Table 1 displays each patient’s potential outcomes in
terms of years of post-treatment survival under each treatment. Larger outcome values
correspond to better health outcomes. [20 points]

Table 1: Hypothetical Example
Patient Y 1 Y 0 Age
1 1 10 29
2 1 5 35
3 1 4 19
4 5 6 45
5 5 1 65
6 6 7 50
7 7 8 77
8 7 10 18
9 8 2 85
10 9 6 96
11 10 7 77

a) Calculate each unit’s treatment e ect.

b) What is the average treatment e ect (ATE) for ventilators compared to bedrest?
Which type of intervention is more e ective on average?

c) Suppose the \perfect doctor” knows each patient’s potential outcomes and as a
result chooses the best treatment for each patient. If she assigns each patient to
the treatment more bene cial for that patient, which patients will receive ventilators

d) Calculate the simple di erence in average outcomes that would obtain if treatment
assignment happened as in part (c). How similar is it to the ATE?

e) Provide an example of how SUTVA might be violated for treatments of covid-19.

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