Econometrics Exercise session for midterm preparation


Problem 1

Suppose that X is the number of free throws made by a basketball player out of two attempts and
assume that the individual probabilities for each outcome of X are the following:

pr(x=0)=0.2; pr(x=1)=0.44 and pr(x=2)=0.36

i)                    Define the random variable.

ii)                  Draw the probability distribution associated to the above random variable.

iii)                Calculate the expected value of the above random variable.

iv)                Calculate the probability that the player makes at least one free throw


Problem 2

We have a dataset containing data about births to women in the United States. Two variables of
interest are the dependent variable, infant birth weight in onces (bw), and an explanatory
variable, average number of cigarettes the mother smoked per day during pregnancy (cigs). The
following simple regression was estimated using data on 1,388 births:

i)                     Think about possible factors contained in the error term 𝑢[𝑖] .

ii)                   Interpret the above regression results.

iii)                 What is the predicted birth weight when cigs =10? What about when cigs = 20
(one pack per day)? Comment on the difference.



Problem 3

We have information about mortality rates (MORT=total mortality rate per 100,000 population) in a
specific year for 51 States of the United States combined with information about potential
determinants: INCC (per capita income by State in Dollars), POV (proportion of families living
below the poverty line), EDU (proportion of population completing 4 years of high school), TOBC
(per capita consumption of cigarettes by State) and AGED (proportion of population over the age of
65). Estimation results are presented in the following table:

i)                    Interpret the slope coefficient in Model 1 and validate it at 1% significance
level.

ii)                   Validate the joint significance of Model 2 in comparison to model 1 at 1%
significance level?

iii)                 Comment on the effect of INCC on MORT in the second model. Why do you think is
a positive and significant effect?

iv)                 In Model 3 we add two new explanatory variables: POV and TOBC. Test whether
this inclusion helps to improve the quality of the model at 1% significance level. Is model 3 the
best in terms of goodness-of-fit?

v)                   Are the effects of these two new variables the expected ones? Are they
individually significant at 1% significance level?

vi)                 What about the individual significance of EDU in model 3 if compared with model
2? Why?


Problem 4

consider a simple model to compare the returns to education at junior colleges and four-year
colleges; for simplicity, we refer to the latter as “universities.” The population includes working
people with a high school degree, and the model is:

                                                     (1)

where

jc  is number of years attending a two-year college, univ is number of years at a four-year
college. exper  is months in the workforce.

Note that any combination of junior college and four-year college is allowed, including

jc =0 and univ = 0. Use the data twoyear.dta

a)   Test the hypothesis that . The hypothesis of interest is whether one year at a junior college
is worth one year at a university.

 (ii) The variable phsrank is the person’s high school percentile. (A higher number is

better. For example, 90 means you are ranked better than 90 percent of your graduating

class.) Find the smallest, largest, and average phsrank in the sample.

 (iii) Add phsrank to regression (2) and report the OLS estimates in the usual form. Is

phsrank statistically significant? How much is 10 percentage points of high school

rank worth in terms of wage?

(i)                  Does adding phsrank to regression (2) substantively change the conclusions on
the returns to two- and four-year colleges? Explain.



Problem 5


A soda vendor at Louisiana State University football games observes that more sodas are sold the
warmer the temperature at game time is. Based on 32 home games covering five years, the vendor
estimates the relationship between soda sales and temperature to be

 where  y is the number of sodas she sells and x is temperature in degrees Fahrenheit,

(a) Interpret the estimated slope and intercept. Do the estimates make sense? Why,

or why not?

(b) On a day when the temperature at game time is forecast to be 80^0F, predict how

many sodas the vendor will sell.

(c) Below what temperature are the predicted sales zero?

(d) Sketch a graph of the estimated regression line.