Empirical Methods In Economics - Swedish Teenagers - Economics Assignment Help

Assignment Task:

Questions

1 Counterfactual
Suppose you have a random sample of 1500 Swedish teenagers who have all attended preschool, but di↵er in the amount of total time (in months) in preschool. You want to know if preschool attendance a↵ects schooling results later in life, and regress average grade at the end of high school on number of months in preschool: Gradei = 0 + 1Preschool i + ui. Let’s say you ?nd that 1 =0 .10 and statistically signi?cant, i.e. one extra month of preschool attendance is associated with 0.1 points higher average high school grade. Do you think this e↵ect is causal? Why/why not?

2 Exogeneity
You run the regression Yi = 0 + 1X1i + ui, but the true regression is Yi = 0 + 1X1i + 2X2i + ei.
a) Derive the omitted variable bias. Tip: Start from ˆ 1 p! cov(Xi,Yi) var(Xi) and plug in the true model for Yi. Now you run the regression Yi = 0 + 1Xi + ui, butY causes X too: Xi = 0 + 1Yi + vi
b) Derive the simultaneous causality bias. Tip: Start from ˆ 1 p! cov(Xi,Yi) var(Xi) and plug in the model for Yi.

Standard errors in parentheses.
a) Construct a 90 % con?dence interval for 1 given your estimate ˆ 1.
b) Calculate the t-statistic and the p-value for the two-sided test of the null hypothesis: H0 : 1 =0 vs. H1 : 1 6=0 . Do you reject the null hypothesis at the 5 % level? At the 1 % level? c) ˆ 1 will probably be a biased estimator of the e↵ect on crime rates of increasing the prison population. Why? Do you think ˆ 1 is biased upwards or downwards? Why?

3.Causality assumptions
A municipality in Sweden wants to test the e↵ect of o↵ering long term unemployed a temporary 4 months apprenticeship. Since there is limited funding for this, the municipality randomly assigns 30 % of the unemployed ”old population” to the treatment group and 50 % of unemployed newly arrived immigrants to the treatment group. Those who do not get an apprenticeship o↵er, constitute the control group.
Two years later, the municipality do a follow-up study looking at the wage income of those who were part of the study (treatment and control groups). Let Yi denote the wage for individual i, X1i denote a binary variable that equals 1 if the individual is o↵ered an apprenticeship (and 0 otherwise), and X2i denote a binary variable that equals

•  if the individual is a newly arrived immigrant (and 0 otherwise). Let 1 denote the e↵ect on wage of being o↵ered an apprenticeship.

a) Consider the regression Yi = 0 + 1X1i + ui. Write down the conditional mean zero assumption.
b) Do you think that the conditional mean zero assumption hold for X1i in a)? Explain.
c) Consider the regression Yi = 0 +1X1i +2X2i +ui. Write down the conditional mean independence assumption for X1i.
d) Does 1 estimate a causal relationship in c)? Does 2 estimate a causal relationship in c)? Explain.

4. Stata assignment
Use the data set CPS92 081 and carry out the following exercises.

• Produce a summary table of average hourly earnings (ahe), age (Age) and one other variable of your choice. The summary table should show the variables means, standard deviations, minimum and maximum values, and the number of observations.
• Run a regression of average hourly earnings (ahe) on age (Age), i.e. estimate:
• Earningsi = 0 + 1Agei + "i
• What is the estimated slope? Illustrate this in a (?tted) line plot.
• Include some additional regressors to control for characteristics of the worker. What is the estimated e↵ect of age on hourly earnings now?
• Produce a table with the outcome from both the regression without control variables and the regression with control variables. Is the estimated e↵ect of age in the regression in c) substantively di↵erent from the regression in b)? Based on this, does the regression in b) seem to su↵er from important omitted variable bias?

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