Applied Statistics Quiz review

The confidence interval for the sample regression function slope a) can be used to compare the value of the slope relative to that of the intercept b) can be used to conduct a test about a hypothesized population regression function slope c) allows you to make statements about the economic importance of your estimate d) adds and subtracts 1.96 from the slope

b) can be used to conduct a test about a hypothesized population regression function slope

Finding a small value of the p-value (e.g. less than 5%) a) implies that the t-statistic is less than 1.96 b) indicates evidence against the null hypothesis c) will only happen roughly one in twenty samples d) indicates evidence in favor of the null hypothesis

b) indicates evidence against the null hypothesis

If the absolute value of your calculated t-statistic exceeds the critical value from the standard normal distribution, you can a) safely assume that your regression results are insignificant b) reject the null hypothesis c) reject the assumption that the error terms are homoscedastic d) conclude that most of the actual values are very close to the regression line

b) reject the null hypothesis

An example of the interaction term between two independent, continuous variables is (using the notation from Stock and Watson) a) Yi = β0 + β1D1i + β2D2i + β3(D1i * D2i) + ui b) Yi = β0 + β1X1i + β2X2i + ui c) Yi = β0 + β1Xi + β2Di + β3(Xi * Di) + ui d) Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) + ui

d) Yi = β0 + β1X1i + β2X2i + β3(X1i * X2i) + ui

You extract approximately 5,000 observations from the Current Population Survey (CPS) and estimate the following regression function: ahei_hat = 3.32 - 0.45 * Agei (1.00) (0.04) R² = 0.02, SER = 8.66 note: standard errors in parentheses where ahe is average hourly earnings and age is the individual's age. Given the specification, your 95% confidence interval for β1: a) [-0.25, -0.05] b) [-0.63, -0.40] c) cannot be determined given the information provided d) [-0.53, -0.37]

d) [-0.53, -0.37]

Assume that you had estimated the following quadratic regression model: Happiness_hat = 607.3 + 3.85 * Income - 0.0423 * Income². If Income increased from 10 to 11 (income is measured in thousands), then the predicted change in Happiness would be (round to two decimals): a) 2.96 b) 3.85 c) cannot be calculated because the function is non-linear d) 3.80

a) 2.96

The difference between an unbalanced and a balanced panel is that Select one: a. an unbalanced panel contains missing observations for at least one time period or one entity. b. you cannot have both fixed time effects and fixed entity effects regressions. c. in the former you may not include drivers who have been drinking in the fatality rate/beer tax study. d. the impact of different regressors are roughly the same for balanced but not for unbalanced panels.

a. an unbalanced panel contains missing observations for at least one time period or one entity.

Consider a regression that estimates the effect of gas taxes on car sales across the 48 contiguous U.S. states. If gas taxes were set yearly by the national government, then Select one: a. you cannot use time fixed effects and include gas tax in the model b. it would not make sense to use state fixed effect. c. you can use time fixed effects and include gas tax in the model d. all OLS coefficient estimates will certainly be biased in the model.

a. you cannot use time fixed effects and include gas tax in the model

Consider the following regression results: Yi_hat = 10 + 2.5 * X1,i + -5.5 * X2,i + 15 * X3,i What is the predicted value of Yi_hat when X1 = 2, X2 = 4, and X3 = 1? a) 52 b) 8 c) -8 d) -2

b) 8

Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient β1 changes by a large amount. This suggests that your first regression suffers from a) perfect multicolinearity b) omitted variable bias c) heteroskedasticity d) dummy variable trap

b) omitted variable bias

If the estimates of the coefficients of interest change substantially across specifications, a) then choose the specification for which your coefficient of interest is most significant b) then this often provides evidence that the original specification had omitted variable bias c) then this can be expected from sample variation d) then you should change the scale of the variables to make the changes appear to be smaller

b) then this often provides evidence that the original specification had omitted variable bias

What is the approximate correct large-sample t-critical value for a 1-sided hypothesis test of a single coefficient of an OLS regression at the 5% significance level? Select one: a. 1.28 b. 1.64 c. 1.96 d. 2.58

b. 1.64

All of the following are true, with the exception of one condition: a) a high R² always means that an added variable is statistically significant b) a high R² does not mean that there is no omitted variable bias c) a high R² does not mean that the regressors are a true cause of the dependent variable d) a high R² does not necessarily mean that you have the most appropriate set of regressors

a) a high R² always means that an added variable is statistically significant

The question of reliability/unreliability of a multiple regression depends on a) internal and external validity b) the quality of your statistical software package c) internal but not external validity d) external but not internal validity

a) internal and external validity

The analysis is externally valid if a) its inferences and conclusions can be generalized from the population and setting studied to other populations and settings b) some committee outside the author's department has validated the findings c) the study has passed a double blind refereeing process for a journal d) the statistical inferences about causal effects are valid for the population being studied

a) its inferences and conclusions can be generalized from the population and setting studied to other populations and settings

Panel data is also called a) longitudinal data b) time series data c) cross-sectional data d) experimental data

a) longitudinal data

Misspecification of functional form of the regression function a) results in a type of omitted variable bias b) is more serious in the case of homoscedasticity-only standard error c) is overcome by adding the squares of all explanatory variables d) requires alternative estimation methods such as maximum likelihood

a) results in a type of omitted variable bias

The random walk model is an example of a a) stochastic trend model b) deterministic trend model c) binomial model d) stationary model

a) stochastic trend model

In the probit regression, the coefficient β₁ indicates a) the change in the z-value associated with a unit change in X b) the change in the probability of Y = 1 given a percent change in X c) the change in the probability of Y = 1 given a unit change in X d) none of the above

a) the change in the z-value associated with a unit change in X

For the polynomial regression model, a) the techniques for estimation and inference developed for multiple regression can be applied b) you can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution c) the critical values from the normal distribution have to be changed to 1.96², 1.96³, etc. d) you need new estimation techniques since the OLS assumptions do not apply any longer

a) the techniques for estimation and inference developed for multiple regression can be applied

In the probit model Pr(Y=1 | X₁, X₂, ... Xk) = phi(β₀ + β₁X₁ + β₂X₂ + ... + βkXk), a) the β's do not have a simple interpretation b) β₀ is the probability of observing Y when all X's are 0 c) β₀ cannot be negative since probabilities have to lie between 0 and 1 d) the slopes tell you the effect of a unit increase in X on the probability of Y

a) the β's do not have a simple interpretation

Consider the regression example from your textbook, which estimates the effect of beer taxes on fatality rates across the 48 contiguous U.S. states. If beer taxes were set yearly by the national government rather than by the states, then a) you should not use time fixed effects since beer taxes are the same at a point in time across states b) it would not make sense to use state fixed effect c) you can test state fixed effects using homoscedastic-only standard errors d) the OLS estimator will be biased

a) you should not use time fixed effects since beer taxes are the same at a point in time across states

Consider the following regression output: Y_hati = 698.9 - 1.50 * X1,i - 0.75 * X2,i. You are told that STATA-generated t-statistic on X1's coefficient is -2.56. The standard error for X1's coefficient is approximately Select one: a. 0.586 b. 0.650 c. 1.96 d. 0.25

a. 0.586

To test for the significance of time fixed effects in a panel regression analysis of alcohol taxes on traffic deaths where the estimation period includes years 2010, 2012, 2013, 2014 and 2015 for the 48 contiguous U.S. states, you should calculate the F-statistic and compare it to the critical value from your Fq,∞ distribution, where q equals Select one: a. 4. b. 52. c. 48. d. 5.

a. 4.

In the panel regression analysis of beer taxes on traffic deaths, the estimation period is 1982-1988 for the 48 contiguous U.S. states. To test for the significance of time fixed effects, you should calculate the F-statistic and compare it to the critical value from your Fq,∞ distribution, where q equals Select one: a. 6. b. 53. c. 48. d. 7.

a. 6.

The following interactions between binary and continuous variables are possible, with the exception of Select one: a. Yi = (β0 / Di) + β1Xi + ui. b. Yi = β0 + β1Xi + β2(Xi × Di) + ui. c. Yi = β0 + β1Xi + β2Di + ui. d. Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui.

a. Yi = (β0 / Di) + β1Xi + ui.

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1 ln(Xi)+ ui is as follows: Select one: a. a 1% change in X is associated with a β1 % change in Y. b. a change in X by one unit is associated with a β1 change in Y. c. a change in X by one unit is associated with a 100 β1 % change in Y. d. a 1% change in X is associated with a change in Y of 0.01 β1.

a. a 1% change in X is associated with a β1 % change in Y.

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1Xi + ui is as follows: Select one: a. a change in X by one unit is associated with a 100 β1 % change in Y. b. a 1% change in X is associated with a β1 % change in Y. c. a change in X by one unit is associated with a β1 change in Y. d. a 1% change in X is associated with a change in Y of 0.01 β1.

a. a change in X by one unit is associated with a 100 β1 % change in Y.

If you had a two regressor regression model, then omitting one variable which is relevant Select one: a. can result in a negative value for the coefficient of the included variable, even though the coefficient will have a significant positive effect on Y if the omitted variable were included. b. will have no effect on the coefficient of the included variable if the correlation between the excluded and the included variable is negative. c. will always bias the coefficient of the included variable upwards. d. makes the sum of the product between the included variable and the residuals different from 0.

a. can result in a negative value for the coefficient of the included variable, even though the coefficient will have a significant positive effect on Y if the omitted variable were included.

In the simple linear regression model, the regression slope Select one: a. indicates by how many units Y changes, given a one unit increase in X. b. indicates by how many percent Y changes, given a one percent increase in X. c. when multiplied with the explanatory variable will give you the predicted Y. d. represents the elasticity of Y on X.

a. indicates by how many units Y changes, given a one unit increase in X.

The Times Series Regression with Multiple Predictors Select one: a. is the same as the ADL(p,q) with additional predictors and their lags present. b. requires that the k regressors and the dependent variable have nonzero, finite eighth moments. c. cannot be estimated by OLS due to the presence of multiple lags. d. gives you more than one prediction.

a. is the same as the ADL(p,q) with additional predictors and their lags present.

The logit model can be estimated and yields consistent estimates if you are using Select one: a. maximum likelihood estimation. b. OLS 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.

a. maximum likelihood estimation.

The OLS estimator is derived by Select one: a. minimizing the sum of squared residuals. b. minimizing the sum of absolute residuals. c. connecting the Yi corresponding to the lowest Xi observation with the Yi corresponding to the highest Xi observation. d. making sure that the standard error of the regression equals the standard error of the slope estimator.

a. minimizing the sum of squared residuals.

Correlation of the regression error across observations Select one: a. results in incorrect OLS standard errors. b. is not a problem in cross-sections since the data can always be "reshuffled." c. results in correct OLS standard errors if heteroskedasticity-robust standard errors are used. d. makes the OLS estimator inconsistent, but not unbiased.

a. results in incorrect OLS standard errors.

You have to worry about perfect multicollinearity in the multiple regression model because Select one: a. the OLS estimator cannot be computed in this situation. b. the OLS estimator is no longer BLUE. c. many economic variables are perfectly correlated. d. in real life, economic variables change together all the time.

a. the OLS estimator cannot be computed in this situation.

When there are omitted variables in the regression, which are determinants of the dependent variable, then Select one: a. the OLS estimator is biased if the omitted variable is correlated with the included variable. b. you cannot measure the effect of the omitted variable, but the estimator of your included variable(s) is (are) unaffected. c. this has no effect on the estimator of your included variable because the other variable is not included. d. this will always bias the OLS estimator of the included variable.

a. the OLS estimator is biased if the omitted variable is correlated with the included variable.

A study based on OLS regressions is internally valid if Select one: a. the OLS estimator is unbiased and consistent, and the standard errors are computed in a way that makes confidence intervals have the desired confidence level. b. you use a two-sided alternative hypothesis, and standard errors are calculated using the heteroskedasticity-robust formula. c. weighted least squares produces similar results, and the t-statistic is normally distributed in large samples. d. the errors are homoskedastic, and there are no more than two binary variables present among the regressors.

a. the OLS estimator is unbiased and consistent, and the standard errors are computed in a way that makes confidence intervals have the desired confidence level.

The regression R2 is a measure of Select one: a. the goodness of fit of your regression line. b. whether or not ESS > TSS. c. whether or not X causes Y. d. the square of the determinant of R.

a. the goodness of fit of your regression line.

Consider the estimated equation from a sample of 1000. Yi_hat= 5.25 - 3.75 * Xi (1.75) (2.50) R2 = 0.50, SER = 18.6 note: standard errors in parenthesis Perform the following hypothesis test: Ho: ß1 = 0 HA: ß1 does not equal 0 Select one: a. Reject the null hypothesis at the 5% level of significance. b. Do not reject the null hypothesis at the 5% level of significance. c. Uncertain---not enough information.

b. Do not reject the null hypothesis at the 5% level of significance.

The following are all least squares assumptions with the exception of: Select one: a. Large outliers are unlikely. b. The explanatory variable in regression model is normally distributed. c. (Xi, Yi), i = 1,..., n are independently and identically distributed. d. The conditional distribution of ui given Xi has a mean of zero.

b. The explanatory variable in regression model is normally distributed.

Simultaneous causality bias Select one: a. is also called sample selection bias. b. arises in a regression of Y on X when, in addition to the causal link of interest from X to Y, there is a causal link from Y to X. c. results in biased estimators if there is heteroskedasticity in the error term. d. happens in complicated systems of equations called block recursive systems.

b. arises in a regression of Y on X when, in addition to the causal link of interest from X to Y, there is a causal link from Y to X.

A survey of earnings contains an unusually high fraction of individuals who state their weekly earnings in 100s, such as 300, 400, 500, etc. This is an example of Select one: a. simultaneous causality bias. b. errors-in-variables bias. c. companies that typically bargain with workers in 100s of dollars. d. sample selection bias.

b. errors-in-variables bias.

Omitted variable bias Select one: a. is always there but is negligible in almost all economic examples. b. exists if the omitted variable is correlated with the included regressor and is a determinant of the dependent variable. c. will always be present as long as the regression R2 < 1. d. exists if the omitted variable is correlated with the included regressor but is not a determinant of the dependent variable.

b. exists if the omitted variable is correlated with the included regressor and is a determinant of the dependent variable.

The OLS estimators of the coefficients in multiple regression will have omitted variable bias Select one: a. only if the omitted variable is not normally distributed. b. if an omitted determinant of Yi is correlated with at least one of the regressors. c. only if an omitted determinant of Yi is a continuous variable. d. if an omitted variable is correlated with at least one of the regressors, even though it is not a determinant of the dependent variable.

b. if an omitted determinant of Yi is correlated with at least one of the regressors.

Time Fixed Effects regression are useful in dealing with omitted variables Select one: a. when there are more than 100 observations. b. if these omitted variables are constant across entities but not over time. c. if these omitted variables vary across entities and not over time. d. even if you only have a cross-section of data available.

b. if these omitted variables are constant across entities but not over time.

Stationarity means that the Select one: a. forecasts remain within 1.96 standard deviation outside the sample period. b. probability distribution of the time series variable does not change over time. c. time series has a unit root. d. error terms are not correlated.

b. probability distribution of the time series variable does not change over time.

To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, you cannot consult the regression R2 because Select one: a. ln(Y) may be negative for 0<Y<1. b. the TSS are different c. the regression R2 can be greater than one in the second model. d. the slope no longer indicates the effect of a unit change of X on Y in the log-linear model.

b. the TSS are different

The "flaw" of the linear probability model is that Select one: a. the regression R2 can be used as a measure of fit. b. the predicted values can lie above 1 and below 0. c. people do not always make clear-cut decisions. d. the actuals can only be 0 and 1, but the predicted are almost always different from that.

b. the predicted values can lie above 1 and below 0.

Heteroskedasticity means that Select one: a. homogeneity cannot be assumed automatically for the model. b. the variance of the error term is not constant. c. agents are not all rational. d. the observed units have different preferences.

b. the variance of the error term is not constant.

In a two regressor regression model, if both are determinants of Y and you exclude one then Select one: a. it is no longer reasonable to assume that the errors are heteroskedastic. b. you are no longer controlling for the influence of the omitted variable. c. the OLS estimator no longer exists. d. the remaining coefficient is certainly biased

b. you are no longer controlling for the influence of the omitted variable.

In the model Yi = β0 + β1X1 + β2X2 + β3(X1 × X2) + ui, the expected effect of changing X1 by 1 unit is Select one: a. β1. b. β1 + β3X2. c. β1 + β3. d. β1 + β3X1.

b. β1 + β3X2.

Consider a panel regression of unemployment rates for the G7 countries (United States, Canada, France, Germany, Italy, United Kingdom, Japan) on a set of explanatory variables for the time period 1980-2000 (annual data). If you included entity and time fixed effects, you would need to specify the following number of binary variables: a) 6 b) 21 c) 26 d) 28

c) 26

The error term is homoscedastic if a) Xi is normally distributed b) there are no outliers c) Var[ ui | Xi ] is constant for all i = 1, 2, ..., n d) Var[ ui | Xi] depends on Xi

c) Var[ ui | Xi ] is constant for all i = 1, 2, ..., n

The main advantage of using panel data over cross sectional data is that it a) allows you to analyze behavior across time but not across entities b) allows you to look up critical values in the standard normal distribution c) allows you to control for some types of omitted variables without actually observing them d) gives you more observations

c) allows you to control for some types of omitted variables without actually observing them

A possible solution to errors-in-variables bias is to a) use the square root of that variable since the error becomes smaller b) choose different functional forms c) mitigate the problem through instrumental variables regression d) use log-log specifications

c) mitigate the problem through instrumental variables regression

The following tools from multiple regression analysis carry over in a meaningful manner to the linear probability model, with the exception of the a) 95% confidence interval using ±1.96 times the standard error b) joint hypothesis testing c) regression R² d) significance test using the t-statistic

c) regression R²

The AR(p) model a) can be represented as follows: Yt = β₀ + β₁X₁ + βpYt-p + ut b) is defined as Yt = β₀ + βpYt-p + ut c) represents Yt as a linear function of p of its lagged values d) can be written as Yt = β₀ + β₁Yt-1 + ut-p

c) represents Yt as a linear function of p of its lagged values

When you add state fixed effects to a simple regression model for U.S. states over a certain time period, and the regression R² increases significantly, then it is safe to assume that a) the included explanatory variables, other than the state fixed effects, are unimportant b) time fixed effects are unimportant c) state fixed effects account for a large amount of the variation in the data d) the coefficients on the other included explanatory variables will not change

c) state fixed effects account for a large amount of the variation in the data

If you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should (assuming large sample) a) add and subtract 1.96 from the slope and check if that interval includes 1 b) see if the slope coefficient is between 0.95 and 1.05 c) subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96 d) check if the adjusted R² is close to 1

c) subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96

In the linear probability model, the interpretation of the slope coefficient is a) the response in the dependent variable to a percentage change in the regressor b) the change in odds associated with a unit change in X, holding other regressors constant c) the change in probability that Y = 1 associated with a unit change in X, holding other regressors constant d) not all that meaningful since the dependent variable is either 0 or 1

c) the change in probability that Y = 1 associated with a unit change in X, holding other regressors constant

In the log-log model, the slope coefficient indicates a) ΔY / ΔX b) ??? c) the elasticity of Y with respect to X d) the effect that a unit change in X has on Y

c) the elasticity of Y with respect to X

An example of a quadratic regression model is Select one: a. Yi = β0 + β1X + β2Y2 + ui. b. Yi = β0 + β1X + β2Z+ ui. c. Yi = β0 + β1X + β2X2 + ui. d. Yi = β0 + β1X + ui.

c. Yi = β0 + β1X + β2X2 + ui.

The interpretation of the slope coefficient in the model Yi = β0 + β1 ln(Xi) + ui is as follows: Select one: a. a change in X by one unit is associated with a β1 change in Y. b. a change in X by one unit is associated with a β1 100% change in Y. c. a 1% change in X is associated with a change in Y of 0.01 β1. d. a 1% change in X is associated with a β1 % change in Y.

c. a 1% change in X is associated with a change in Y of 0.01 β1.

If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then Select one: a. the F-statistic must be negative. b. the regression is always significant. c. a series of t-tests may or may not give you the same conclusion. d. all of the hypotheses are always simultaneously rejected.

c. a series of t-tests may or may not give you the same conclusion.

The first difference of the logarithm of Yt equals Select one: a. the first difference of Y. b. the growth rate of Y exactly. c. approximately the growth rate of Y when the growth rate is small. d. the difference between the lead and the lag of Y.

c. approximately the growth rate of Y when the growth rate is small.

The OLS residuals Select one: a. can be calculated using the errors from the regression function. b. are unknown since we do not know the population regression function. c. can be calculated by subtracting the fitted values from the actual values. d. should not be used in practice since they indicate that your regression does not run through all your observations.

c. can be calculated by subtracting the fitted values from the actual values.

The Fixed Effects regression model Select one: a. in a log-log model may include logs of the binary variables, which control for the fixed effects. b. has "fixed" (repaired) the effect of heteroskedasticity. c. has n different intercepts. d. the slope coefficients are allowed to differ across entities, but the intercept is "fixed" (remains unchanged).

c. has n different intercepts.

The Augmented Dickey Fuller (ADF) t-statistic Select one: a. has a normal distribution in large samples. b. is a two-sided test. c. is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1). d. has the identical distribution whether or not a trend is included or not.

c. is an extension of the Dickey-Fuller test when the underlying model is AR(p) rather than AR(1).

The construction of the t-statistic for a one- and a two-sided hypothesis Select one: a. uses ±1.96 for the two-sided test, but only +1.96 for the one-sided test. b. depends on the critical value from the appropriate distribution. c. is the same. d. is different since the critical value must be 1.645 for the one-sided hypothesis, but 1.96 for the two-sided hypothesis (using a 5% probability for the Type I error). : the t-critical values are different but the t-statistic (i.e. the calculated t-statistic or sample statistic) is the same no matter whether you have a one-sided or two-sided test.

c. is the same.

Possible solutions to omitted variable bias, when the omitted variable is not observed, include the following with the exception of Select one: a. use of randomized controlled experiments. b. panel data estimation. c. nonlinear least squares estimation. d. use of instrumental variables regressions.

c. nonlinear least squares estimation.

Multiplying the dependent variable by 100 and the explanatory variable by 100,000 leaves the Select one: a. OLS estimate of the slope the same. b. OLS estimate of the intercept the same. c. regression R-squared the same. d. variance of the OLS estimators the same.

c. regression R-squared the same.

The t-statistic is calculated by dividing Select one: a. the OLS estimator by its standard error. b. the slope by 1.96. c. the estimator minus its hypothesized value by the standard error of the estimator. d. the slope by the standard deviation of the explanatory variable.

c. the estimator minus its hypothesized value by the standard error of the estimator.

A statistical analysis is internally valid if Select one: a. its inferences and conclusions can be generalized from the population and setting studied to other populations and settings. b. statistical inference is conducted inside the sample period. c. the statistical inferences about causal effects are valid for the population being studied. d. the hypothesized parameter value is inside the confidence interval.

c. the statistical inferences about causal effects are valid for the population being studied.

You should use the QLR test for breaks in the regression coefficients, when Select one: a. the suspected break date is known. b. there are breaks in only some, but not all, of the regression coefficients. c. the suspected break date is not known. d. the Chow F-test has a p value of between 0.05 and 0.10.

c. the suspected break date is not known.

When estimating probit and logit models, Select one: a. F-statistics should not be used, since the models are nonlinear. b. you cannot have binary variables as explanatory variables as well. c. the t-statistic should still be used for testing a single hypothesis. d. it is no longer true that the adjRsq < Rsq

c. the t-statistic should still be used for testing a single hypothesis.

To test joint linear hypotheses in the multiple regression model, you need to Select one: a. compare the sums of squared residuals from the restricted and unrestricted model. b. compare the adjusted R2 for the model which imposes the restrictions, and the unrestricted model. c. use the heteroskedasticity-robust F-statistic. d. use several t-statistics and perform tests using the standard normal distribution.

c. use the heteroskedasticity-robust F-statistic.

Consider a regression that estimates the effect of beer taxes on divorce rates across the 48 contiguous U.S. states. If beer taxes were set yearly by each state government, then Select one: a. you cannot use time fixed effects and include beer tax in the model b. it would not make sense to use state fixed effect. c. you can use time fixed effects and include beer tax in the model d. all OLS coefficient estimates will certainly be biased in the model.

c. you can use time fixed effects and include beer tax in the model

The following linear hypothesis can be tested using the F-test with the exception of Select one: a. β2 =0. b. β0 = β1 and β1 = 0. c. β2 = 1 and β3= β4/β5. d. β1 + β2 = 1 and β3 = -2β4.

c. β2 = 1 and β3= β4/β5.

In multiple regression, the R² can increase whenever a regressor is a) greater than 1.96 in absolute value b) added unless there is heteroskedasticity c) added unless there is multicolinearity d) added

d) added

The true causal effect might not be the same in the population studied and the population of interest because a) the study is out of date b) of geographical differences c) of differences in characteristics of the population d) all of the above

d) all of the above

HAC standard errors and clustered standard errors are related as follows: a) clustered standard errors are the square root of HAC standard errors b) they are the same c) they are the same if the data is differenced d) clustered standard errors are one type of HAC standard error

d) clustered standard errors are one type of HAC standard error

Simultaneous causality a) means you must run a second regression of X on Y b) cannot be established since regression analysis only detects correlation between variables c) means that a third variable affects both X and Y d) leads to correlation between the regressor and the error term

d) leads to correlation between the regressor and the error term

The dummy variable trap is an example of a) something that does not happen to university or college students b) imperfect multicolinearity c) something that is of theoretical interest only d) perfect multicolinearity

d) perfect multicolinearity

Consider the following regression line: Yi_hat = 53.2 - .75 × Xi. You are told that the t-statistic on the slope coefficient is 4.38. What is the standard error of the slope coefficient? Select one: a. 0.52 b. -1.96 c. 1.96 d. 0.17

d. 0.17

Consider the following least squares specification between testscores and the student-teacher ratio: TestScores= 557.8 + 36.42 ln (Income). According to this equation, a 1% increase income is associated with an increase in test scores of Select one: a. 557.8 points b. 36.42 points c. cannot be determined from the information given here d. 0.36 points

d. 0.36 points

The critical value of F4,∞ at the 5% significance level is Select one: a. 3.84 b. Cannot be calculated because in practice you will not have infinite number of observations c. 1.94 d. 2.37

d. 2.37

Errors-in-variables bias Select one: a. is particularly severe when the source is an error in the measurement of the dependent variable. b. becomes larger as the variance in the explanatory variable increases relative to the error variance. c. is only a problem in small samples. d. arises from error in the measurement of the independent variable.

d. arises from error in the measurement of the independent variable.

The OLS residuals in the multiple regression model Select one: a. are zero because the predicted values are another name for forecasted values. b. cannot be calculated because there is more than one explanatory variable. c. are typically the same as the population regression function errors. d. can be calculated by subtracting the fitted values from the actual values.

d. can be calculated by subtracting the fitted values from the actual values.

The probit model Select one: 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 0.1 and 0.9. c. should not be used since it is too complicated. d. forces the predicted values to lie between 0 & 1.

d. forces the predicted values to lie between 0 & 1.

In a linear probability model, a predicted value of 0.6 means that Select one: a. the model makes little sense, since the dependent variable can only be 0 or 1. b. given the values for the explanatory variables, there is a 40 percent probability that the dependent variable will equal one. c. the most likely value the dependent variable will take on is 60 percent. d. given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one.

d. given the values for the explanatory variables, there is a 60 percent probability that the dependent variable will equal one.

In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2 Select one: a. is the difference in means in Y between the two categories. b. is usually positive. c. indicates the difference in the slopes of the two regressions. d. indicates the difference in the intercepts of the two regressions.

d. indicates the difference in the intercepts of the two regressions.

The linear probability model is Select one: 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. another word for logit estimation. c. an example of probit estimation. d. the application of the linear multiple regression model to a binary dependent variable.

d. the application of the linear multiple regression model to a binary dependent variable.

Sample selection bias occurs when Select one: a. data are collected from a population by simple random sampling. b. samples are chosen to be small rather than large. c. the choice between two samples is made by the researcher. d. the availability of the data is influenced by a selection process that is related to the value of the dependent variable.

d. the availability of the data is influenced by a selection process that is related to the value of the dependent variable.

E(ui|Xi) = 0 says that Select one: a. the sample mean of the Xs is much larger than the sample mean of the errors. b. the sample regression function residuals are related to the explanatory variable. c. dividing the error by the explanatory variable results in a zero (on average). d. the conditional distribution of the error given the explanatory variable has a zero mean.

d. the conditional distribution of the error given the explanatory variable has a zero mean.

Indicate for which of the following examples you cannot use Entity and/or Time Fixed Effects: a regression of Select one: a. the return of 500 stocks on the compensation for the 500 firm's CEOs for the years 2000-2016. b. The 50 US state's unemployment rates on state bankruptcy rates for the period 1970-2010 (annual data). c. the per capita income level in Canadian Provinces on provincial population growth rates, using decade averages for 1960, 1970, and 1980. d. the impact of years of experience on earnings using a survey of 20,000 households for conducted in March 2015.

d. the impact of years of experience on earnings using a survey of 20,000 households for conducted in March 2015.

Under imperfect multicollinearity Select one: a. the OLS estimator is biased even in samples of n > 100. b. the error terms are highly, but not perfectly, correlated. c. the OLS estimator cannot be computed. d. two or more of the regressors are highly correlated.

d. two or more of the regressors are highly correlated.

The maximum likelihood estimation method produces, in general, all of the following desirable properties with the exception of Select one: a. normally distributed estimators in large samples. b. efficiency. c. consistency. d. unbiasedness in small samples.

d. unbiasedness in small samples.

When testing a joint hypothesis, you should Select one: a. use t-test for each underlying hypothesis and reject the joint null hypothesis if all of the restrictions fail. b. use t-tests for each hypothesis and reject the joint null hypothesis once the statistic exceeds the critical value for a single hypothesis. c. use an F-test and reject the joint null hypothesis (and all the underlying hypotheses) if the statistic exceeds the critical value. d. use an F-test and reject the joint null hypothesis (and at least one of the underlying hypotheses) if the statistic exceeds the critical value.

d. use an F-test and reject the joint null hypothesis (and at least one of the underlying hypotheses) if the statistic exceeds the critical value.

Using the textbook example of 420 California school districts and the regression of testscores on the student-teacher ratio, you find that the standard error on the slope coefficient is 0.51 when using the heteroskedasticity robust formula, while it is 0.48 when employing the homoskedasticity only formula. When calculating the t-statistic, the recommended procedure is to Select one: a. use the homoskedasticity only formula because the t-statistic becomes larger b. make a decision depending on how much different the estimate of the slope is under the two procedures c. first test for homoskedasticity of the errors and then make a decision d. use the heteroskedasticity robust formula

d. use the heteroskedasticity robust formula

The Granger Causality Test Select one: a. is a special case of the Augmented Dickey-Fuller test. b. is a rather complicated test for statistical independence. c. establishes the direction of causality (as used in common parlance) between X and Y in addition to correlation. d. uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors.

d. uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors.