ECO 4000 Quizzes

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Baruch College, CUNY *

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Economics

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Jan 9, 2024

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Question 1 The interpretation of the slope coefficient in the log-log model is as follows: a 1% change in X is associated with a change in Y of 0.01 β 1 . a 1% change in X is associated with a β 1 % change in Y. a change in X by one unit is associated with a 100 β 1 % change in Y. a change in X by one unit is associated with a β 1 change in Y. Question 2 To test whether or not the population regression function is linear rather than a polynomial of order r: compare the TSS from both regressions. use the test of (r-1) restrictions using the F-statistic. check whether the regression R 2 for the polynomial regression is higher than that of the linear regression. look at the pattern of the coefficients: if they change from positive to negative to positive, etc., then the polynomial regression should be used. Question 3 Consider the regression equation The t-test for the siginificance of the coefficients at 95% confidence yield t 1 =2.53, t 2 =4.04 and t 3 = 3.59. The F statistic was 4.72. Answers: The regressors are not individually significant but jointly significant. The regressors are neither individually significant nor jointly significant. The regressors are individually significant but not jointly significant. The regressors are both individually significant and jointly significant.

 Question 4 In the model Y i = β 0 + β 1 X 1 + β 2 X 2 + β 3 (X 1 × X 2 ) + u i , the expected effect of a unit change in X 1 on Y Answers: depends on both X 1 and X 2 depends on X 2 only depends on both X 1 and Y depends on X 1 only   Question 5 The interpretation of the slope coefficient in the lin-log model is as follows: Answers: a 1% change in X is associated with a change in Y of 0.01 β 1 . a 1% change in X is associated with a β 1 % change in Y. a change in X by one unit is associated with a β1 change in Y. a change in X by one unit is associated with a β 1 100% change in Y.  Question 6 To decide whether Y i = β 0 + β 1 X + u i or ln(Y i ) = β 0 + β 1 X + u i fits the data better, you cannot consult the regression R 2 because: Answers: the TSS are not measured in the same units between the two models. the slope no longer indicates the effect of a unit change of X on Y in the log- linear model. ln(Y) may be negative for 0<Y<1. the regression R 2 can be greater than one in the second model.  Question 7

If you estimate the Californian school district test-score~STR model using a polynomial model with high degree, then there is a possibility that: Answers: the model will be closely aligned to the data points and will not give the general trend of the relationship between the two variables. the higher powers will increase the variance of the estimated coefficients and make the model less reliable. It is not possible to conduct t-tests or F-test with high degree polynomial model, and hypothesis tests cannot be performed to test the significance of the coefficients. R-squared will go down and the model will have a lower predictive power.  Question 8 Given the following equation, Y i =β 0 +β 1 X i +β 2 D i +u i , assume X i is a continuous variable and D i is a binary variable that can take on the values 0 or1. Select the correct Y-axis intercepts when D i =1 and when D i =0, and select the accurate description regarding the slope Answers: β 0 +β 2 whn D i =1 and β 0 when D i =0; the slope is the same whether D i =1 or 0 and equals β 1 . β 0 +β 2 whn D i =1 and β 0 when D i =0; the slopes depend on the value of D i =1 or 0 but equals β 1 . β 0 +β 2 whn D i =1 and β 1 when D i =0; the slope is the same whether D i =1 or 0 and equals β 1 . β 0 +β 1 whn D i =1 and β 0 when D i =0; the slope is the same whether D i =1 or 0 and equals β 2 .  Question 2

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If you reject a joint null hypothesis using the F-test in a multiple hypothesis setting, then: Answers: individual t-tests will give you the same conclusion. a series of t-tests may or may not give you the same conclusion. the F-statistic must be negative. all of the hypotheses are always simultaneously rejected.  Question 3 If you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should: Answers: add and subtract 1.96 from the slope and check if that interval includes 1. check if the adjusted R2 is close to 1. subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96. see if the slope coefficient is between 0.95 and 1.05.  Question 4 When testing joint hypothesis, you should: Answers: use the F-statistics and reject at least one of the hypothesis if the statistic exceeds the critical value. use t-statistics for each hypothesis and reject the null hypothesis is all of the restrictions fail. use t-statistics for each hypothesis and reject the null hypothesis once the statistic exceeds the critical value for a single hypothesis.

use the F-statistic and reject all the hypothesis if the statistic exceeds the critical value.  Question 5 A 95% confidence set for two or more coefficients is a set that contains: Answers: the population values of these coefficients in 95% of randomly drawn samples. the sample values of these coefficients in 95% of randomly drawn samples. integer values only. the same values as the 95% confidence intervals constructed for the coefficients.  Question 6 You have estimated the relationship between test scores and the student-teacher ratio under the assumption of homoskedasticity of the error terms. The regression output is as follows: Testscore= 698.9 - 2.28×STR, and the standard error on the slope is 0.48. The homoskedasticity-only "overall" regression F- statistic for the hypothesis that the Regression R2 is zero is approximately: Answers: 4.75. 1.96. 0.96. 22.56.       Question 7 The standard error of regression coefficients while moving from a single regressor model to multiple regressor model:

Answers: changes, unless the second explanatory variable is a binary variable. changes changes, unless you test for a null hypothesis that the addition regression coefficient is zero. stays the same.  Question 1 In the Californian school example, based on the estimates obtained from the regression of test_score on STR only, the policymakers hired additional instructors so that STR reduced by 2. The test scores improved but by less than anticipated. What is most likely have happened? Answers: The omitted variables bias led to underestimation of the true effect of STR on test score. The omitted variables bias led to overestimation of the true effect of STR on test score. The estimated coefficient ? 1 is a large value, and the true coefficient must also have been large, thus it is simply by chance. There can be no omitted variables bias existing in this case.  Question 2 When referring to an effective control variable, which one of the following is incorrect ? Answers: While in the regression, the variable of interest is not correlated with the error term. The variables of interest can be labeled as ‘as if’ which are randomly assigned while there is a hold on control variables. When the entries match the value of control variables, the variable of interest is uncorrelated with the omitted determinants. None of the above are incorrect.  Question 3

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Under imperfect multicollinearity: Answers: the error terms are highly, but not perfectly, correlated. two or more of the regressors are highly correlated. the OLS estimator is biased even in samples of n > 100. the OLS estimator cannot be computed.  Question 4 A researcher is trying to estimate the effect of rainfall on crop yield. After regressing rainfall variable on the yield variable using R, he runs a second estimation by regressing rainfall and humidity variables on yield. This time he gets an error from R. What might have been the problem? Answers: Heteroscedasticity Multicollinearity Omitted variables bias Presence of large outliers  Question 5 When you have an omitted variable problem, the assumption that E(ui| Xi) = 0 is violated. This implies that: Answers: there is another estimator called weighted least squares, which is BLUE. the sum of the residuals is no longer zero. the sum of the residuals times any of the explanatory variables is no longer zero. the OLS estimator is no longer consistent.

 Question 6 The reason for including control variables in multiple regressions is to: Answers: increase the regression R-squared. reduce heteroskedasticity in the error term. reduce imperfect multicollinearity. make the variables of interest no longer correlated with the error term, once the control variables are held constant.  Question 7 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 changes by a large amount. This suggests that your first regression suffers from: Answers: omitted variable bias. perfect multicollinearity. dummy variable trap. heteroskedasticity.  Question 8 In the multiple regression model, the adjusted R-squared Answers: cannot decrease when an additional explanatory variable is added. equals the square of the correlation coefficient r. will never be greater than the regression R-squared. cannot be negative.

 Question 9 You are trying to identify at which high school grade level class size matters the most in determining test score and you run the equation: Test_score i = β 0 +β 1 STR i + β 2 D 1 +β 3 D 2 + β 4 D 3 +u i where D 1 , D 2 and D 3 are respectively dummies for grade levels sophomores, juniors and seniors respectively and the freshman year is used as baseline. What would be the differential impact on test score between juniors and freshmen? Answers: β 3 - β 1 β 3 β 3- β 2 β 0

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