Question

2. When studying the impact of immigrants on wages of natives, we use the percentage of immigrants in cities from 10 years earlier as the instrumental variable.

a. What are outcome Y, treatment status D, and instrument T?

b. Why is OLS biased? In other words, can you come up with an omitted variable that may bias the OLS result?

c. Who are always-takers, never-takers, compliers and defiers?

d. Specify the first stage regression (don’t include controls)

e. Specify the reduced form regression (don’t include controls)

f. Explain what LATE are in this example (What they mean, which parameters they correspond to)

Answer 1

(a)

Y: wages of natives D: number of immigrants

T: percentage of immigrants in cities from 10 years earlier

(b)

An example would be a larger city attracting a wider range of foreigners which citizens tend to have a higher wage in larger cities compared to smaller and isolated cities.

(c)

1. Always-takers: subpopulation with D=1 regardless of the value of T.Immigrants in cities no matter the percentage of immigrants in cities from 10 years earlier2. Never-takers: subpopulation with D=0 regardless of the value of T.Few immigrants in cities no matter the percentage of immigrants from 10 years earlier3. Compliers: subpopulation with D=1 if T=1 and D=0 if T=0.A lot of immigrants because the percentage of immigrants was high 10 years ago and vice versa4. Defiers: subpopulation with D=1 if T=0 and D=0 if T=1.Few immigrants because the percentage of immigrants was high 10 years ago and vice versa.

(d)

First stage: D=α+γT+ε,

In this case,

it would be represented as; # of the immigrants =α + γimmigrant10yearsago + ε

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