Chapter 9 Regression with a Binary Dependent Variable. Multiple Choice. 1) The binary dependent variable model is an example of a

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1 Chapter 9 Regression with a Binary Dependent Variable Multiple Choice ) The binary dependent variable model is an example of a a. regression model, which has as a regressor, among others, a binary variable. b. model that cannot be estimated by OLS. c. limited dependent variable model. d. model where the left-hand variable is measured in base 2. 2) (Requires Appendix Material) The following are examples of limited dependent variables, with the exception of a. binary dependent variable. b. log-log specification. c. truncated regression model. d. discrete choice model. 3) In the binary dependent variable model, a predicted value of 0.6 means that a. the most likely value the dependent variable will take on is 60 percent. b. given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one. c. the model makes little sense, since the dependent variable can only be 0 or. d. given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one. 4) k E( Y X,..., X ) = Pr( Y = X,..., X ) means that k a. for a binary variable model, the predicted value from the population regression is the probability that Y=, given X. b. dividing Y by the X s is the same as the probability of Y being the inverse of the sum of the X s. c. the exponential of Y is the same as the probability of Y happening. d. you are pretty certain that Y takes on a value of given the X s.

2 5) The linear probability model is a. the application of the multiple regression model with a continuous left-hand side variable and a binary variable as at least one of the regressors. b. an example of probit estimation. c. another word for logit estimation. d. the application of the linear multiple regression model to a binary dependent variable. 6) In the linear probability model, the interpretation of the slope coefficient is a. the change in odds associated with a unit change in X, holding other regressors constant. b. not all that meaningful since the dependent variable is either 0 or. c. the change in probability that Y= associated with a unit change in X, holding others regressors constant. d. the response in the dependent variable to a percentage change in the regressor. 7) The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the a. F-statistic. b. significance test using the t-statistic. c. 95% confidence interval using ±.96 times the standard error. d. regression R 2. 8) (Requires Material from Section 9.3 possibly skipped) For the measure of fit in your regression model with a binary dependent variable, you can meaningfully use the a. regression R 2. b. size of the regression coefficients. c. pseudo R 2. d. standard error of the regression. 9) The major flaw of the linear probability model is that a. the actuals can only be 0 and, but the predicted are almost always different from that. b. the regression R 2 cannot be used as a measure of fit. c. people do not always make clear-cut decisions. e. the predicted values can lie above and below 0. 2

3 0) The probit model a. is the same as the logit model. b. always gives the same fit for the predicted values as the linear probability model for values between 0. and 0.9. c. forces the predicted values to lie between 0 and. d. should not be used since it is too complicated. ) The logit model derives its name from a. the logarithmic model. b. the probit model. c. the logistic function. d. the tobit model. 2) In the probit model Pr( Y = = Φ ( β0 + βx), Φ a. is not defined for Φ (0). b. is the standard normal cumulative distribution function. c. is set to.96. d. can be computed from the standard normal density function. 3) In the expression Pr( Y = = Φ( β0 + βx), a. ( β0 + βx ) plays the role of z in the cumulative standard normal distribution function. b. β cannot be negative since probabilities have to lie between 0 and. c. β0 cannot be negative since probabilities have to lie between 0 and. d. min ( β0 + βx ) > 0 since probabilities have to lie between 0 and. 4) In the probit model Pr( Y = X, X2,..., X ) = Φ ( β0 + βx+ β X β X ), 3 k x k k a. the β s do not have a simple interpretation. b. the slopes tell you the effect of a unit increase in X on the probability of Y. c. β 0 cannot be negative since probabilities have to lie between 0 and. d. β 0 is the probability of observing Y when all X s are 0. 5) In the expression Pr(deny = P/I Ratio, black) = Φ( P/I ratio + 0.7black), the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person a. is percentage points.

4 b. is 6. percentage points. c. should not be interpreted without knowledge of the regression R 2. d. is 2.74 percentage points. 6) The maximum likelihood estimation method produces, in general, all of the following desirable properties with the exception of a. efficiency. b. consistency. c. normally distributed estimators in large samples. d. unbiasedness in small samples. 7) The logit model can be estimated and yields consistent estimates if you are using a. OLS estimation. b. maximum likelihood estimation. c. differences in means between those individuals with a dependent variable equal to one and those with a dependent variable equal to zero. d. the linear probability model. 8) When having a choice of which estimator to use with a binary dependent variable, use a. probit or logit depending on which method is easiest to use in the software package at hand. b. probit for extreme values of X and the linear probability model for values in between. c. OLS (linear probability model) since it is easier to interpret. d. the estimation method which results in estimates closest to your prior expectations. 9) (Requires Advanced Material) Nonlinear least squares a. solves the minimization of the sum of squared predictive mistakes through sophisticated mathematical routines, essentially by trial and error methods. b. should always be used when you have nonlinear equations. c. gives you the same results as maximum likelihood estimation. d. is another name for sophisticated least squares. 20) (Requires Advanced Material) Only one of the following models can be estimated by OLS : α β a. Y = AK L + u. 4

5 b. Φ β0 β Pr( Y = X) = ( + X). c. Pr( Y = X) = F( β0 + β X) =. ( 0 X ) + e β + β α β d. Y = AK L u. 2) (Requires Advanced Material) Nonlinear least squares estimators in general are not a. consistent. b. normally distributed in large samples. c. efficient. d. used in econometrics. 22) (Requires Advanced Material) Maximum likelihood estimation yields the values of the coefficients that a. minimize the sum of squared prediction errors. b. maximize the likelihood function. c. come from a probability distribution and hence have to be positive. d. are typically larger than those from OLS estimation. 23) (Requires Advanced Material) To measure the fit of the probit model, you should: a. use the regression R 2. b. plot the predicted values and see how closely they match the actuals. c. use the log of the likelihood function and compare it to the value of the likelihood function. d. use the fraction correctly predicted or the pseudo R 2. 24) When estimating probit and logit models, a. the t-statistic should still be used for testing a single restriction. b. you cannot have binary variables as explanatory variables as well. c. F-statistics should not be used, since the models are nonlinear. 2 2 d. it is no longer true that the R < R. 25) The following problems could be analyzed using probit and logit estimation with the exception of whether or not a. a college student decides to study abroad for one semester. b. being a female has an effect on earnings. c. a college student will attend a certain college after being accepted. d. applicants will default on a loan. 5

WISE International Masters

WISE International Masters ECONOMETRICS Instructor: Brett Graham INSTRUCTIONS TO STUDENTS 1 The time allowed for this examination paper is 2 hours. 2 This examination paper contains 32 questions. You are