Deck 7: Specifying Models

Question 1

The following is an example of a polynomial OLS model.
$$Y _ { i } = \beta _ { 0 } + \beta _ { 1 } ^ { 2 } X _ { 1 i } + \epsilon _ { i }$$

Answer 1

False

Question 2

Given the model Y_i=20+30X_1i+5X_2i², a one unit increase in X_1i will lead to 40 unit increase in Y_i.

Answer 2

False

Question 3

In a linear log model with only one independent variable, we interpret as a 1% increase in X₁ is expected to lead to a $\beta$ ₁ change in Y.

Answer 3

False

Question 4

When variables are not on the same scale, it makes it harder to compare them with each other. To deal with this problem, we standardize the variables by logging the variables.

Question 5

When conducting an F-test, the unrestricted model is the one that includes all of the independent variables that are in the full model, while the restricted model include only the variables that conform with our null hypothesis.

Question 6

One of the main reasons for using a polynomial OLS model is:

A) In order to estimate non-linear relationships.
B) In order to estimate linear relationships.
C) In order to account for measurement error.
D) In order to estimate a model where we suspect there is a measurement error in both the independent and dependent variables.

Question 7

Which of the following models should be used if we want to estimate the relationship between years of education and income if we expect the relationship to be non-linear.

A) Income= $\beta$ ₀₊B₁Education
B) Income =B₀₊B₁²Education
C) Income =B₀₊B₁Education + B₁²Education
D) Income =B₀₊B₁Education +B₁Education²

Question 8

Given log linear model that says Ln Income =B₀₊B₁Education, we interpret the results as:

A) A one year increase in education is expected to lead to a B₁ change in income.
B) A one year increase in education is expected to lead to a B₁% change in income.
C) A one year increase in education is expected to lead to a B₁/100 change in income.
D) A one percent increase in education is expected to lead to a B₁/100 change in income

Question 9

Given a log log model lnY_i=B₀B₁lnX_i, we interpret the results as:

A) A one unit increase in X is expected to lead to a B₁ change in Y_i.
B) A one unit increase in X is expected to lead to a B₁% change in Y_i.
C) A one unit increase in X is expected to lead to a B₁/100 change in Y_i.
D) A one percent increase in X is expected to lead to a B₁ percent change in Y_i.

Question 10

Given the model Income = 10,000 + 1,000YearsofExperience + 100YearsofExperience², a one year increase in years of experience from 10 years is expected to lead to a:

A) 1,100 increase in income
B) 1,000 increase in income
C) 3,000 increase in income
D) 11,100 increase in income

Question 11

Given Y_i = B₀ + B₁X₁ + B₂X₂ + B₃X₃ + B₄X₄ + e_i, the restricted model for an F-test where H₀: B₁= B₂= B₄=0 is:

A) Y_i = B₀ + B₁X₁ + B₂X₂ + B₃X₃ + B₄X₄ + e_i
B) Y_i = B₀ + B₁X₁ + B₂X₂ + B₄X₄ + e_i
C) Y_i = B₀ + B₃X₃ + B₄X₄ + e_i
D) Y_i = B₀ + B₃X₃ + e_i

Question 12

Given the model Income = 20,000 + 1,500YearsofExperience + 150YearsofExperience² - 10 YearsofExperience³, a one year increase in years of experience from 10 years is expected to lead to a:

A) 1,500 increase in income
B) 1,650 increase in income
C) 1,800 increase in income
D) 1,770 increase in income
E) None of the above, need more information

Question 13

Given a model where the variables are on a different scale, in order to make them comparable we need to:

A) Standardize the model by dividing the difference of the variable from its average by its standard deviation.
B) Don't need to do anything and can run the model in its unaltered form.
C) Standardize the model by taking the log/ln of each variable.
D) Standardize the model by dividing the coefficient of each variable by its standard deviation.

Question 14

Given Y_i = B₀ + B₁X₁ + B₂X₂ + B₃X₃ + B₄X₄ + e_i, the restricted model for an F-test where H₀: B₁= B₂= B₃ is:

A) Y_i=B₀+B₁X₁+B₂X₂+B₃X₃+B₄X₄+e_i
B) Y_i=B₀+B₁(X₁+ X₂+ X₃) + B₄X₄ + e_i
C) Y_i=B₀+B₄X₄+e_i
D) Y_i=B₀+B₁X₁+B₂X₂+B₃X₃ +e_i

Question 15

Explain how to conduct F-tests in both of the possible scenarios, describing both the purpose of the F-test and the criteria for rejecting the null hypothesis.

Question 16

Explain how one can use OLS in order to estimate non-linear effects, and describe what has to be done with the data in order to do so.

Question 17

Given the following results
Life expectancy = 1+2GDP - 0.01GDP²
where GDP is in thousands (meaning a GDP of $60 signifies a GDP of $60,000), answer the following:
a.The predicted increase in life expectancy of GDP increase by $1 from $40.
b. The predicted increase in life expectancy if GDP increase by $1 from $100.
c. The predicted life expectancy in a country with a GDP of 50.
d. Give a simple explanation for the use of a polynomial model in order to model the relationship between life expectancy and GDP.

Question 18

Describe the appropriate interpretation of the following log models - specify the values:
a. lnY_i=0.5+0.33X_i
b. Y_i=2300+450ln X_i
c. lnY_i=4.5+17 ln X_i

Question 19

Describe the challenge faced when it comes to comparing the effects of variables with different units, and describe how one can deal with this challenge.