ECON/STAT 2123 Homework 1

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ECON/STAT 2123

Homework 1

due Thursday, January 26

You may work together with others in the class but you must write up your answers separately. Copying another student’s work is not allowed.  Please provide thoughtful and thorough answers. Some of these questions are intentionally open-ended.

1.   According to one study, 28% of Black applicants for mortgages are denied while only 9% of white applicants for mortgages are denied.  This is a correlation, not a causal effect.  How would you define the causal effect of race on the probability of being denied a mortgage, using one of the two definitions introduced in class? Does the causal effect coincide with the idea of “racial bias”? That is, is it possible that there is a causal effect but no racial bias or that there is racial bias but no causal effect?

2.   Suppose that y is determined by y = (x1  − 100)2 + 3x2 .  (a) Does x1  have a causal effect on y?  (b) Suppose I conduct an experiment where x2  is controlled (i.e., held fixed) and x1 is assigned a value of either 125 or a value of 75.  What is the outcome of this experiment? Relate this answer to your answer to part (a).

3.   Suppose we have a sample of skydiving instructors and piano teachers from California and Kansas. The skydiving instructors in California earn more than the piano teachers in Califor- nia. Also, the skydiving instructors in Kansas earn more than the piano teachers in Kansas. If we combine the data and compare skydiving instructors to piano teachers, ignoring which state they are from, is it possible that piano teachers earn more than skydiving instructors? Explain.

4.   Suppose I have a nationally representative dataset on educational outcomes for adults in the U.S. Suppose one variable in this dataset is a binary variable that is equal to 1 if the individual has a 4-year college degree and is equal to 0 if they don’t. Call this variable college. Next, suppose I aggregate this dataset to the state-level by averaging the variables. How do you think the distribution (e.g., the mean, variance, a histogram, etc.)  of college in the individual-level data compares to the distribution in the state-level data.