SOME EXAMPLES OF LINEAR PROBABILITY MODELS

Q.1

SCENARIO 1: 400 driver’s license applicants were randomly selected from the DVLA database and asked whether they passed their driving test (Passi =1) or failed their test (Passi =0): data was also collected on their gender (Malei =1, if male and =0 if female) and their years of driving experience (Expi in years).

An estimated linear probability model yielded the following: (standard errors in brackets)

(0.034)(0.002)

a.Does the probability of passing the test depend on experience? Explain

b.Richmond has 10 years of driving experience. What is the probability that he will pass the test

c.Sarah is a new driver, what is the probability she will pass the test?

Q.2

SENARIO 2: Let Ti represent a dummy dependent variable =1 if church member donates to the collection box (tithe) every Sunday and 0 otherwise. Fi = 1 if ith church member is a female and 0 otherwise and Siis the number of years of schooling of the ith church member.

Given the linear functional form:

An estimate of this model gives: (standard errors in brackets)

(0.15) (0.03)

  1. Think of an omitted variable that might bias the regression coefficient(s) above. What is it and how would it bias the results?
  2. Are the coefficients significant in the expected direction? Explain
  3. Interpret the estimated coefficients. Do the estimated coefficients make economic sense?
  4. What is the estimate of Di for a male with 16 years of schooling? Does it make sense?
  5. You obtained an R2 = 0.36. Is this meaningful? Why or why not?

Q.3

Consider the linear probability model

Where

  1. Show that E(|
  2. Show that the var(|

Q. 4 SOME EXAMPLES OF PROBIT

SCENARIO 1: 400 driver’s license applicants were randomly selected from the DVLA database and asked whether they passed their driving test (Passi =1) or failed their test (Passi =0): data was also collected on their gender (Malei =1, if male and =0 if female) and their years of driving experience (Expi in years).

An estimated PROBIT model yielded the following: (standard errors in brackets)

(0.200) (0.259) (0.156) (0.019)

  1. The sample included values for Experience between 0 and 40 years, and only 5 people in the sample had more than 30 years of driving experience. Moses is 95 years old and has been driving since he was 16. What is the model prediction for the probability that Moses will pass the test? Do you think this prediction is reliable? Why or why not?
  2. Jane is woman with 2 years’ experience, what is the probability that she will pass the test?
  3. Compute the estimated probability of passing the test for men and for women (use same experience of 10 years
  4. Does the effect of experience on test performance depend on gender?

Q.5

Suppose you were hired by the University of Ghana to study the factors that determine whether students admitted to the university actually come to the university. You are given a large random sample of students that were admitted the previous year. You have information on whether each student chose to attend, high school performance, family income, financial aid offered, race and geographical variables.

Create a model to fulfill your job duties and explain how you would go about estimating the model.

Q.6 A study investigated the impact of house price appreciation on household mobility. The underlying idea was that if a house were viewed as one part of the household's portfolio, then changes in the value of the house, relative to other portfolio items, should result in investment decisions altering the current portfolio. Using 5,162 observations, the probitequation was estimated as shown in the table, where the limited dependent variable is one if the household moved in 2010 and is zero if the household did not move:

Regression / Probit
model
constant / -2.077
(-0.113)
Male / -0.354
(-0.263)
Black / -0.596
(-0.322)
Married78 / 0.034
(-0.258)
marriage / 0.478
change / (-0.260)
A1115 / -160.625
(-0.576)
PURN / -2.841
(-2.096)
Pseudo-R2 / 0.010

wheremale, black, married78, and marriage change are binary variables. They indicate, respectively, if the entity was a male-headed household, a black household, was married, and whether a change in marital status occurred between 2009 and 2010. A1115 is the appreciation rate for each house from 2011 to 2015 minus the SMSA-wide rate of appreciation for the same time period, and PNRN is a predicted appreciation rate for the unit minus the national average rate.

(a) Interpret the results. Comment on the statistical significance of the coefficients. Do the slope coefficients lend themselves to easy interpretation?

(b) The mean values for the regressors are as shown in the table below.Taking the coefficients at face value and using the sample means, calculate the probability of a household moving

Variable / Mean
male / 0.82
black / 0.09
married78 / 0.78
marriage change / 0.03
A1115 / 0.003
PNRN / 0.007

.

(c)Given this probability, what would be the effect of a decrease in the predicted appreciation rate of 20 percent, that is A1115= –0.20?

(d)What is the meaning of the pseudo-R2? What other measures of fit might you want to consider?