Deck 9: Prediction for a Dichotomous Variable

Question 1

One of the merits of the linear probability model is that it:

A) is a stronger model of causality than two-stage least squares.
B) does not require defining a determining function.
C) is easy to summarize and use traditional linear regression model techniques.
D) does not suffer from small sample issues.

Answer 1

C

Question 2

A dependent variable whose range of possible values has consequential constraints is known as a(n):

A) limited dependent variable.
B) instrumental variable.
C) control variable.
D) linear estimator.

Answer 2

A

Question 3

If one ran the regression on whether a mortgage applicant was approved for a loan or not (Approved_i) on their income to debt ratio, this would be an example of what sort of model?

A) A two-stage least squares model
B) A fixed-effects model
C) A within estimator model
D) A linear probability model

Answer 3

D

Question 4

If you were to estimate the linear probability model for whether or not a student passed their econometrics class and how that relates to if they are a business major (1 if yes, 0 if other), what will the coefficient on the dichotomous business major variable be?

A) The econometrics class pass rate of business majors
B) The econometrics class pass rate of non-business majors
C) The average pass rate of all students
D) The difference in pass rates of business majors and non-business majors

Question 5

Which of the following variables is most likely to be a limited dependent variable, assuming that each variable will be featured as a dependent variable?

A) GDP growth
B) Change in the number of faulty units
C) Labor productivity
D) Weekly number of complaints

Question 6

A linear probability model is regression analysis applied to what sort of variable?

A) An instrumental variable
B) A variable found in a likelihood function
C) A dichotomous dependent variable
D) A fixed effect variable

Question 7

Which of the following variables would be natural outcomes for a linear probability model?

A) Income
B) GDP
C) Wages
D) Click-through or no click-through

Question 8

In the event that you are modeling weekly advertising spend (as a dependent variable), and you notice that several weeks have no spending-it is likely your analysis will have to handle what?

A) A selected sample problem
B) A small sample problem
C) A limited dependent variable
D) An endogeneity problem

Question 9

If the regression results for a linear probability model of mortgage application are given by: Approved_i = 0.6(0.12) + -0.05(0.001)Debt2IncomeRatio_i, with standard errors reported in parenthesis. How should we interpret the coefficient on the debt-to-income ratio variable?

A) Increasing your debt to income ratio by 1 decreases your probability of being approved by 0.05.
B) Increasing your debt to income ratio by 1 decreases your probability of being approved by 0.55.
C) The probability of being approved for a mortgage is 0.05.
D) The probability of being approved for a mortgage is 0.6.

Question 10

If you are modeling shopping decisions at the grocery store, and construct an outcome variable that is coded as 0 for no soup purchases, 1 for soup purchased of only one brand, and 2 for soup purchase of multiple brands, it would be appropriate to model this outcome as limited dependent variable because the:

A) outcome variable is ordinal.
B) outcome variable is cardinal.
C) range of possible values has consequential constraints.
D) variable is dichotomous.

Question 11

How does the interpretation of the coefficient on the income to debt ratio change in the linear probability model of whether a mortgage applicant was approved for a loan or not if the outcome variable was Denied_i instead of Approved_i?

A) It won't change.
B) The coefficients will be the same, but the standard errors will change.
C) One will be a model of causality, the other will be purely about correlation.
D) One coefficient will be the change in probability of being denied, while the other will be the change in probability of being approved.

Question 12

A limit-violating prediction is a predicted value that:

A) only is normally distributed in the limit.
B) is heteroscedastic.
C) is measured with noise.
D) does not fall within that variables limits.

Question 13

The primary distinction between a linear probability model and linear regression model is:

A) you can't interpret the coefficients in a linear probability model.
B) a linear probability model never suffers from heteroscedasticity.
C) the standard errors of a linear probability model will be larger.
D) the outcome is dichotomous in a linear probability model.

Question 14

All of the following variables are likely to be limited dependent variables except for which one?

A) Consumer trips that include an ice cream purchase
B) Seasons in which a team wins their national championship
C) Average wholesale electricity price for state of Indiana
D) Whether a mortgage applicant is approved or not

Question 15

If you are planning on running the regression model given by Tenure_i = β₀ + β₁Salary_i + β₂Years of Education_i + U_i, which of the following situations would cause this model to have a limited dependent variable?

A) No one in the company earns more $130,000 a year.
B) Everyone in the company earns at least $65,000 a year.
C) No one can have negative years of education.
D) No one can have negative tenure at the company.

Question 16

Which of the following statistics or conditions has an interpretation in the linear probability model that is unique/distinct to the standard linear regression model?

A) 95% confidence interval
B) T-statistic
C) P-value for an estimated coefficient
D) None of the answers is correct.

Question 17

A dichotomous dependent variable is a variable that:

A) leads to biased estimates of the coefficient of interest.
B) can take on just two values, typically recorded as 0 and 1.
C) requires that you use OLS to estimate any determining function.
D) cannot be used to identify causal effects.

Question 18

For a linear probability model all of the following are true except for which condition?

A) You can conduct causal analysis.
B) You can conduct hypothesis testing.
C) You can calculate marginal effects of control variables.
D) The outcome can take a large range of values.

Question 19

If you are modeling shopping decisions at the grocery store, and construct a control variable that is coded as 0 for not a store loyalty program member, 1 for an individual store loyalty program member, and 2 for a family store loyalty program member, it would be appropriate to model this as limited dependent variable because:

A) the outcome variable is ordinal.
B) the outcome variable is cardinal.
C) the range of possible values has consequential constraints.
D) None of the answers is correct.

Question 20

If one was attempting to build a model that predicted a person's height-which has to be positive, why might it still be the case that you wouldn't consider this as a limited dependent variable?

A) The sample of heights will always be a selected sample.
B) You need an appropriate instrumental variable for height.
C) It is very unlikely that the 0 boundary for height is a binding restriction in any sample of individuals.
D) It will depend on your sample size.

Question 21

After estimating a probit model to determine the effect of salary offers on whether or not the offer is accepted; Y_i^* = β₀ + β₁SalaryOffer_i + U_i, what would be the marginal effect associated with β₁?

A) The probability of accepting an offer
B) The probability of increasing the salary offered
C) The increase in the probability of an offer being accepted from a unit increase in the salary
D) The increase in salary associated with the offers that were accepted

Question 22

In the standard regression formula of Y_i = β₀ + β₁X_i + U_i, which object is most closely tied to the marginal effect of X on Y?

A) β₀
B) Y_i
C) β₁
D) U_i

Question 23

After estimating a probit model for the likelihood of a website visitor clicking through conditional on if the visit occurred on a weekday or not, you get the following results: ClickThrough_i = -1.2(0.4) + 0.8(0.2)WeekDay_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of a visit moving from a weekend to a weekday on click-throughs?

A) -1.2 + 0.8 = -0.4
B) 0.8
C) Φ(-1.2 + 0.8) - Φ(-1.2)
D) Φ(-1.2)

Question 24

In estimating a probit or logit model it is typical to maximize which objective function?

A) T-statistic
B) Likelihood
C) Least squares
D) Adjusted R-squared

Question 25

A consequence of the linear probability model always having heteroscedastic errors will be which of the following?

A) The coefficient estimates will be biased.
B) The R-squared measure will be above 1.
C) The intercept will be negative.
D) None of the answers is correct.

Question 26

In estimating the linear probability model for whether an individual clicked through on an advertisement based off how much time the individual spent on the website, the regression results are as follows: ClickThrough_i = 0.4(0.08) + 0.07(0.01)TimeSpent_i, where the standard errors of each coefficient are reported in parenthesis. Why would the fact that someone in the sample was on the website for 10 hours be problematic?

A) It suggests the outcome is measured with error.
B) It suggests that you have a non-representative sample.
C) The prediction for that individual will fall above 1 (the maximum of ClickThrough).
D) It suggests that the errors are heteroscedastic.

Question 27

The primary difference between the probit and logit model is the:

A) probit model uses a latent variable convention that the logit model does not.
B) probit model suffers from a heteroscedasticity problem while the logit does not.
C) choice of distribution for the unobservables.
D) probit model identifies causal effects, while the logit model identifies correlations.

Question 28

The probit model assumes what sort of distribution for the unobservables?

A) Standard normal distribution
B) T-distribution
C) Logistic distribution
D) The probit distribution

Question 29

In estimating the linear probability model for whether an individual clicked through on an advertisement based off whether the individual is on a mobile device or not, which of the following conditions may not hold from the resulting regression (ClickThrough_i = β₀ + β₁Mobile_i + U_i)?

A) The sum of the residuals will be zero.
B) The sum of the residuals for the mobile observations will be zero.
C) The sum of the residuals for the non-mobile observations will be zero.
D) The sum of the predictions will be zero.

Question 30

What condition will fail to hold in a linear probability model?

A) The determining function will be linear in parameters.
B) The moment conditions will define the estimate of the coefficients.
C) The errors will be homoscedastic.
D) The coefficient estimates will minimize the sum of squared residuals.

Question 31

In estimating the linear probability model for whether an individual clicked through on an advertisement based off how much time the individual spent on the website, which of the following conditions must hold from the resulting regression (ClickThrough_i = β₀ + β₁TimeSpent_i + U_i)?

A) The sum of the residuals will be zero.
B) All the predictions will fall between 0 and 1.
C) The estimate for β₁ will be negative.
D) The estimate for β₀ will be positive.

Question 32

A latent variable is one that:

A) can be used instead of an instrumental variable in two-stage least squares.
B) will cause multi-collinearity problems.
C) cannot be observed, but information about it can be inferred from other observed variables.
D) will create endogeneity problems in your regression model.

Question 33

One of the limitations of the linear probability model is that it:

A) is difficult to interpret the resulting coefficient estimates.
B) suffers from multicollinearity.
C) may generate predictions that fall outside of the range of the outcome variable.
D) may lead to homoscedastic errors.

Question 34

The logit model assumes what sort of distribution for the unobservables?

A) Standard normal distribution
B) T-distribution
C) Logistic distribution
D) Exponential distribution

Question 35

After estimating a probit model for whether an individual purchases a particular product as a function of income, which of the following conditions must hold?

A) The r-squared will be one.
B) The intercept will be positive.
C) The predictions will fall between zero and 1.
D) The predictions will sum to zero.

Question 36

After estimating a probit model for the likelihood of a website visitor clicking through conditional on the average income from the county in which the visit's IP address came from, you get the following results: ClickThrough_i = -1.8(0.75) + 0.06(0.005)Income_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of income moving from $40,000 to $41,000 on the click-through rate?

A) -1.8 + 0.06 = -1.74
B) Φ[0.06(41 - 40)]
C) Φ(-1.8 + 0.06 × 41) - Φ(-1.8 + 0.06 × 40)
D) 0.8

Question 37

Why is a cumulative distribution function a natural choice for the modeling of a limited dependent variable-particularly a dichotomous one?

A) Cumulative distribution functions are smooth.
B) Cumulative distribution functions are nonlinear.
C) Cumulative distribution functions are easy to calculate.
D) Cumulative distribution functions have a range between 0 and 1.

Question 38

A natural latent variable for a probit model for modeling the purchase of a good by consumers would be which of the following?

A) Profits
B) Net revenues
C) Costs
D) Utility

Question 39

Which of the following limitations of the linear probability is not problematic in the event that the only treatment variable in your regression (X or right-hand side), is a binary variable?

A) The errors of the model have to be heteroscedastic.
B) The errors of the model have to be homoscedastic.
C) The predictions might not fall between zero and 1.
D) The coefficients might be negative.

Question 40

A marginal effect summarizes the:

A) change in a coefficient from altering the sample size.
B) estimated size of the variance for the model residuals.
C) rate of change in the probability of a dichotomous dependent variable equaling one with a one-unit increase in an independent variable.
D) size of the p-value on a coefficient.

Question 41

A potential shortcoming of the probit/logit models is that to get consistent estimates of the parameters:

A) the unobservables must be distributed via the standard normal (for probit) and logistically (for the logit).
B) coefficient estimates cannot be evaluated against alternative hypotheses.
C) the determining function must be linear.
D) moment conditions are required for each parameter to be estimated.

Question 42

After estimating a logit model for the likelihood of a website visitor clicking through conditional on if the visit occurred on a weekday or not, you get the following results: ClickThrough_i = -1.2(0.4) + 0.8(0.2)WeekDay_i, where standard errors are reported in parenthesis. What would be the calculation that yields the marginal effect of a visit moving from a weekend to a weekday on click-throughs?

A) -1.2 + 0.8 = -0.4
B) 0.8
C) $\frac { 1 } { 1 + e ^ { - 1.2 + 0.8 } }$
D) $$\frac { 1 } { 1 + e ^ { - 1.2 + 0.8 } }$$ - $$\frac { 1 } { 1 + e ^ { - 1.2 } }$$

Question 43

When you estimate parameters by finding those that make the observed outcomes as likely as possible for a given model, you are using which method?

A) Generalized method of moments
B) Maximum likelihood estimation
C) Instrumental variables
D) Least absolute deviations

Question 44

Estimating a probit or logit model via maximum likelihood involves all of the following except for what?

A) Choosing a determining function
B) Characterizing a likelihood function given choices about the distribution of observables
C) Setting up the moment conditions
D) Finding the coefficient estimates that maximize the likelihood function

Question 45

For probit/logit models the size of the marginal effect calculated will be a function of the estimated coefficient in addition to the:

A) size of the independent variable change.
B) standard error on that coefficient estimate.
C) r-squared of the regression.
D) adjusted r-squared.

Question 46

A shortcoming of potentially using the probit/logit model when attempting to identify causal effects can include:

A) software to estimate the probit/logit model is not widely available.
B) the use of instrumental variables with probit/logit is difficult.
C) probit/logit models have a difficult time incorporating binary control variables.
D) hypothesis testing is all but impossible in probit/logit models.

Question 47

Which of the following is a merit of using the probit/logit model over the linear probability model for a limited dependent variable?

A) By construction predictions from the model will fall within 0 and 1.
B) The marginal effects are easier to calculate.
C) The probit/logit model can be estimated using similar OLS.
D) The probit/logit model is better at finding causal estimates.

Question 48

Which of the following correctly summarizes one of the differences in calculating marginal effects of probit/logit models relative to linear probability models?

A) Probit/logit models' marginal effects are causal; linear probability models are not.
B) Probit/logit models' marginal effects will not be constant for all values of X, while (strictly) linear probability models' marginal effects will be constant.
C) Probit/logit marginal effects cannot be positive since predictions need to be between zero and 1, while linear probability models can be positive.
D) Probit/logit marginal effects are stable, while linear probability models tend to be noisier.

Question 49

A common method to estimate probit and logit models is:

A) moment conditions.
B) within estimator.
C) maximum likelihood estimation.
D) OLS.

Question 50

Aside from the sample being a random sample from the target population, and the latent variable model determining function is correct, what critical assumption guarantees the consistency of the maximum likelihood probit and logit estimates for the coefficients?

A) The sample size is large.
B) The model errors and the treatment variables are independent.
C) The predictions need to be between zero and one.
D) The coefficients are jointly statistically significant.