Assignment 1: Empirical Methods of Economics
Instructions:
• Work in groups of maximum 2 students.
• Please submit your answers through Brightspace no later than Thursday,
September 28 at 13:00. If you are late, your assignment will be graded with
0.
• The empirical exercises (questions 4 and 5) require the use of Stata. Please
submit also the do-files and log-files for these exercises.
1. You have data on time spent training per week (x), measured in hours, and
time to run a marathon (y), measured in minutes, for 10 amateur runners.
Runner
1
2
3
4
5
6
7
8
9
10
x
8.5
9
9.1
9.5
10
10.6
10.5
11.5
12
12.5
y
240
237
236
230
235
220
225
220
216
210
You want to estimate the model:
yi = β1 + β2 xi + εi
(a) Write the model in matrix notation.
(b) Using matrix notation and the data provided in the table, find estimates
(by hand) for β1 and β2 . Please show your calculations, not only the final
result.
(c) What is the predicted time to run a marathon for runner number 6? What
is the value of the residual?
Empirical Methods of Economics Assignment 1
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2. [This exercise is without Stata]. You write a model to explain the logarithm of
wage, the annual salary of NBA players, using the average points per game
(points), the average number of games played per year (games), the number
of years as a professional basketball player (years) and the age of the player
(age):
ln (wagei ) = β1 + β2 pointsi + β3 gamesi + β4 yearsi + β5 agei + εi
(a) Suppose that agei = 3 × yearsi − 4. What will happen?
(b) Suppose that the model is estimated with points∗i = 5 × pointsi − 10 rather
than pointsi . How are the coefficients related to those of the original
model? And the R2 ? Please motivate your answer.
3. Define M as follows:
0 −1 0
M =I −P =I −X X X
X
Show that M is idempotent.
4. The following model is a simplified version of the model used by Biddle and
Hamermesh (Journal of Political Economy, 1990) to study the trade-off between
time spent sleeping and working:
sleepi = β1 + β2 totwrki + β3 educi + β4 agei + εi
where sleep and totwrk (total work) are measured in minutes per week and
educ and age are measured in years.
(a) What signs do you think β2 , β3 and β4 will have and why?
(b) Download the dataset SLEEP75.dta and estimate the model.
(c) Provide an economic interpretation of the estimated coefficients. Are the
results in line with your predictions in (a)?
(d) Generate for each of the observations the residual and the predicted value.
Calculate the average of the residuals and of the predicted values of y.
Compare the average of the predicted values of y with the average of y.
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5. In the dataset BIRTHWEIGHT you have information on the weight at birth of
1832 infants, obtained from the National Center for Health Statistics natality
and mortality data.
(a) Estimate a linear model (model A) that explains bweight using the gender
of the baby (male), the age of the mother (mage), the square of the age of
the mother, a dummy variable no smoker equal to 1 if the average daily
number of cigarettes smoked by the mother during pregnancy is 0, the
total number of prenatal visits (npvis) and a constant. Interpret the results.
What is the marginal effect of the age of the mother on the weight at birth
of the baby?
(b) Estimate a model (model B) that explains the logarithm of bweight on the
basis of the same variables as before. Interpret the results. What is now
the marginal effect of the age of the mother on the weight at birth of the
baby?
(c) Add now the square of the total number of prenatal visits. What can
you say about the effect of the number of prenatal visits on the weight at
birth? Does it make sense?
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