1) The linear probability model is
a. the application of the multiple regression model with a continuous left- hand sidevariable 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 dependentvariable.
2) 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 modelfor values between 0.1 and 0.9.
c. forces the predicted values to lie between 0 and 1.
d. should not be used since it is too complicated.
3) In the expression Pr(deny = 1| P/I Ratio, black) = Φ (–2.26 + 2.74P/I ratio + 0.71black),the effect of increasing the P/I ratio from 0.3 to 0.4 for a white person
a. is 0.274 percentage points.
b. is 6.1 percentage points.
c. should not be interpreted without knowledge of the regression R2 . d. is 2.74 percentage points.
4) 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.
5) To measure the fit of the probit model, you should:
a. use the regression R2.
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 R2 .
6) In the probit regression, the coefficient β1 indicates
a. the change in the probability of Y = 1 given a unit change in X b. the change in the probability of Y = 1 given a percent change in X
Chapter 11:
Regression with a Binary Dependent
Variable
c. the change in the z- value associated with a unit change in X d. none of the above
7) Your textbook plots the estimated regression function produced by the probit regressionof deny on P/I ratio. The estimated probit regression function has a stretched “S” shape given that the coefficient on the P/I ratio is positive.
Consider a probit regression function with a negative coefficient. The shape would
a. resemble an inverted “S” shape (for low values of X, the predicted probability of Y would approach 1)
b. not exist since probabilities cannot be negative
c. remain the “S” shape as with a positive slope coefficient d. would have to be estimated with a logit function
8) Probit coefficients are typically estimated using
a. the OLS method
b. the method of maximum likelihood c. non-linear least squares (NLLS)
d. by transforming the estimates from the linear probability model
9) F-statistics computed using maximum likelihood estimators
a. cannot be used to test joint hypothesis
b. are not meaningful since the entire regression R2 concept is hard to apply in this situation c. do not follow the standard F distribution
d. can be used to test joint hypothesis
10) When testing joint hypothesis, you can use
a. the F- statistic
b. the chi-squared statistic
c. either the F-statistic or the chi-square statistic d. none of the above
1) The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous regressor,
a. a first stage F must be statistically significant to indicate a strong instrument.
b. a first stage F > 1.96 indicates that the instruments are weak.
c. the t-statistic on each of the instruments must exceed at least 1.64.
d. a first stage F < 10 indicates that the instruments are weak.
2) The distinction between endogenous and exogenous variables is
a. that exogenous variables are determined inside the model and endogenous variables are determined outside the model.
b. dependent on the sample size: for n > 100, endogenous variables become exogenous.
c. depends on the distribution of the variables: when they are normally distributed, they are exogenous, otherwise they are endogenous.
d. whether or not the variables are correlated with the error term.
3) The TSLS estimator is
a. consistent and has a normal distribution in large samples.
b. unbiased.
c. efficient in small samples.
d. F-distributed.
4) Weak instruments are a problem because (？)
a. the TSLS estimator may not be normally distributed, even in large samples.
b. they result in the instruments not being exogenous.
c. the TSLS estimator cannot be computed.
d. you cannot predict the endogenous variables any longer in the first stage.
5) Consider a model with one endogenous regressor and two instruments.
Then the J-statistic will be large
a. if the number of observations are very large.
b. if the coefficients are very different when estimating the coefficients using one instrument at a time.
c. if the TSLS estimates are very different from the OLS estimates.
Chapter 12:
Instrumental
Variables
Regression
d. when you use homoskedasticity-only standard errors.
6) Let W be the included exogenous variables in a regression function that also has endogenous regressors (X). The W variables can
a. be control variables
b. have the property E(ui|Wi) = 0
c. make an instrument uncorrelated with u d. all of the above
7) The logic of control variables in IV regressions
a. parallels the logic of control variables in OLS
b. only applies in the case of homoskedastic errors in the first stage of two stage least squares estimation
c. is different in a substantial way from the logic of control variables in OLS since there are two stages in estimation d. implies that the TSLS is efficient
8) For W to be an effective control variable in IV estimation, the following condition must hold
a. E(ui) = 0
b. E(ui|Zi,Wi) = E(ui|Wi) c. E(uiuj) ≠ 0
d. there must be an intercept in the regression
9) The IV estimator can be used to potentially eliminate bias resulting from
a. multicollinearity b. serial correlation c. errors in variables d. heteroskedasticity
10) Instrumental Variables regression uses instruments to
a. establish the Mozart Effect b. to increase the regression R2 c. to eliminate serial correlation
d. isolate movements in X that are uncorrelated with u
Chapter 13: Experiments and Quasi-Experiments
1) In the context of a controlled experiment, consider the simple linear regression formulation Yi=β0+β1Xi+ui . Let the Y i be the outcome, Xi the treatment level when the treatment is binary, and ui contain all the additional determinants of the outcome. Then calling ^β1
a differences estimator
a. makes sense since it is the difference between the sample average outcome of the treatment group and the sample average outcome of the control group.
b. and ^β0 the level estimator is standard terminology in randomized controlled experiments.
c. does not make sense, since neither Y nor X are in differences.
d. is not quite accurate since it is actually the derivative of Y on X.
2) The following is not a threat to external validity:
a. the experimental sample is not representative of the population of interest.
b. the treatment being studied is not representative of the treatment that would be implemented more broadly.
c. experimental participants are volunteers.
d. partial compliance with the treatment protocol.
3) Experimental data are often a. observational data.
b. binary data, in that the subject either does or does not respond to the treatment.
c. panel data.
d. time series data.
4) The following estimation methods should not be used to test for randomization when Xi, is binary:
a. linear probability model (OLS) with homoskedasticity-only standard errors.
b. probit.
c. logit.
d. linear probability model (OLS) with heteroskedasticity-robust standard errors.
5) Quasi-experiments
a. provide a bridge between the econometric analysis of observational data sets and the statistical ideal of a true randomized controlled experiment.
b. are not the same as experiments, and lessons learned from the use of the latter can therefore not be applied to them.
c. most often use difference-in-difference estimators, which are quite different from OLS and instrumental variables methods studied in earlier chapters of the book.
d. use the same methods as studied in earlier chapters of the book, and hence the interpretation of these methods is the same.
6) Testing for the random receipt of treatment a. is not possible, in general
b. entails testing the hypothesis that the coefficients on W1i, …, Wri are non-zero in a regression of Xi on W1i, …, Wr
c. is not meaningful since the LHS variable is binary
d. entails testing the hypothesis that the coefficients on W1i, …, Wri are zero in a regression of Xi on W1i, …, Wr
7) Small sample sizes in an experiment
a. biases the estimators of the causal effect
b. may pose a problem because the assumption that errors are normally distributed is dubious for experimental data
c. do not raise threats to the validity of confidence intervals as long as heteroskedasticityrobust standard errors are used
d. may affect confidence intervals but not hypothesis tests
8) A repeated cross-sectional data set is
a. a collection of cross-sectional data sets, where each cross-sectional data set corresponds to a different time period b. the same as a balanced panel data set
c. what Card and Krueger used in their study of the effect of minimum wages on teenage employment d. time series
9) In a sharp regression discontinuity design,
a. crossing the threshold influences receipt of the treatment but is not the sole determinant b. the population regression line must be linear above and below the threshold
c. Xi will in general be correlated with ui
d. receipt of treatment is entirely determined by whether W exceeds the threshold
10) Threats to internal validity of quasi-experiments include a. failure of randomization
b. failure to follow the treatment protocol c. attrition
d. all of the above with some modifications from true randomized controlled experiments
