Ch. 8 - econometrics

A polynomial regression model is specified as: A) Yi = β0 + β1Xi + β2X^2 + ∙∙∙ + βrX^r + ui. B) Yi = β0 + β1Xi + β Xi + ∙∙∙ + β Xi + ui. C) Yi = β0 + β1Xi + β2Y + ∙∙∙ + βrY + ui. D) Yi = β0 + β1X1i + β2X2 + β3 (X1i × X2i) + ui.

A

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

A

Consider the population regression of log earnings [Yi, where Yi = ln(Earningsi)] against two binary variables: whether a worker is married (D1i, where D1i=1 if the ith person is married) and the worker's gender (D2i, where D2i=1 if the ith person is female), and the product of the two binary variables Yi = β0 + β1D1i + β2D2i + β3(D1i×D2i) + ui. The interaction term: A) allows the population effect on log earnings of being married to depend on gender B) does not make sense since it could be zero for married males C) indicates the effect of being married on log earnings D) cannot be estimated without the presence of a continuous variable

A

In the model Yi = β0 + β1X1 + β2X2 + β3(X1 × X2) + ui, the expected effect of (delta)Y/(delta)X1 is A) β1 + β3X2. B) β1. C) β1 + β3. D) β1 + β3X1.

A

The interpretation of the slope coefficient in the model ln(Yi) = β0 + β1 ln(Xi)+ ui is as follows: 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

For the polynomial regression model: A) you need new estimation techniques since the OLS assumptions do not apply any longer. B) the techniques for estimation and inference developed for multiple regression can be applied. C) you can still use OLS estimation techniques, but the t-statistics do not have an asymptotic normal distribution. D) the critical values from the normal distribution have to be changed to 1.96^2, 1.96^3, etc.

B

The best way to interpret polynomial regressions is to: A) take a derivative of Y with respect to the relevant X. B) plot the estimated regression function and to calculate the estimated effect on Y associated with a change in X for one or more values of X. C) look at the t-statistics for the relevant coefficients. D) analyze the standard error of estimated effect.

B

The following are properties of the logarithm function with the exception of: A) ln(1/ x) = -ln(x). B) ln(a + x) = ln(a) + ln(x). C) ln(ax) = ln(a) + ln(x). D) ln(xa)= a ln(x).

B

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

B

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

B

To decide whether Yi = β0 + β1X + ui or ln(Yi) = β0 + β1X + ui fits the data better, you cannot consult the regression R2 because: A) ln(Y) may be negative for 0<Y<1. B) the TSS are not measured in the same units between the two models. C) the slope no longer indicates the effect of a unit change of X on Y in the log-linear model. D) the regression R2 can be greater than one in the second model.

B

In the log-log model, the slope coefficient indicates

B (the elasticity of Y with respect to X)

10) An example of a quadratic regression model is: A) Yi = β0 + β1X + β2Y^2 + ui. B) Yi = β0 + β1ln(X) + ui. C) Yi = β0 + β1X + β2X^2 + ui. D) = β0 + β1X + ui.

C

In nonlinear models, the expected change in the dependent variable for a change in one of the explanatory variables is given by: A) △Y = f(X1 + X1, X2,... Xk). B) △Y = f(X1 + △X1, X2 + △X2,..., Xk+ △Xk)- f(X1, X2,...Xk). C) △Y = f(X1 + △X1, X2,..., Xk)- f(X1, X2,...Xk). D) △Y = f(X1 + X1, X2,..., Xk)- f(X1, X2,...Xk).

C

In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β3: A) indicates the slope of the regression when D=1. B) has a standard error that is not normally distributed even in large samples since D is not a normally distributed variable. C) indicates the difference in the slopes of the two regressions. D) has no meaning since (Xi × Di) = 0 when Di = 0.

C

Including an interaction term between two independent variables, X1 and X2, allows for the following except: A) the interaction term lets the effect on Y of a change in X1 depend on the value of X2. B) the interaction term coefficient is the effect of a unit increase in X1 and X2 above and beyond the sum of the individual effects of a unit increase in the two variables alone. C) the interaction term coefficient is the effect of a unit increase in sqrt(X1*X2) D) the interaction term lets the effect on Y of a change in X2 depend on the value of X1.

C

The following interactions between binary and continuous variables are possible, with the exception of: A) Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui. B) Yi = β0 + β1Xi + β2(Xi × Di) + ui. C) Yi = (β0 + Di) + β1Xi + ui. D) Yi = β0 + β1Xi + β2Di + ui.

C

16) To test whether or not the population regression function is linear rather than a polynomial of order r: A) check whether the regression R2 for the polynomial regression is higher than that of the linear regression. B) compare the TSS from both regressions. C) look at the pattern of the coefficients: if they change from positive to negative to positive, etc., then the polynomial regression should be used. D) use the test of (r-1) restrictions using the F-statistic.

D

5) In the case of regression with interactions, the coefficient of a binary variable should be interpreted as follows: A) there are really problems in interpreting these, since the ln(0) is not defined. B) for the case of interacted regressors, the binary variable coefficient represents the various intercepts for the case when the binary variable equals one. C) first set all explanatory variables to one, with the exception of the binary variables. Then allow for each of the binary variables to take on the value of one sequentially. The resulting predicted value indicates the effect of the binary variable. D) first compute the expected values of Y for each possible case described by the set of binary variables. Next compare these expected values. Each coefficient can then be expressed either as an expected value or as the difference between two or more expected values.

D

7) An example of the interaction term between two independent, continuous variables is: A) Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui. B) Yi = β0 + β1X1i + β2X2i + ui. C) Yi = β0 + β1D1i + β2D2i + β3 (D1i × D2i) + ui. D) Yi = β0 + β1X1i + β2X2i + β3(X1i × X2i) + ui.

D

Assume that you had estimated the following quadratic regression model TestScore = 607.3 + 3.85 Income - 0.0423 Income^2. If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on testscores would be: A) 3.85 B) 3.85-0.0423 C) Cannot be calculated because the function is non-linear D) 2.96

D

Consider the polynomial regression model of degree Yi = β0 + β1Xi + β2X^2 + ...+ βr^r + ui. According to the null hypothesis that the regression is linear and the alternative that is a polynomial of degree r corresponds to: A) H0: βr = 0 vs. βr ≠ 0 B) H0: βr = 0 vs. β1 ≠ 0 C) H0: β3 = 0, ..., βr = 0, vs. H1: all βj ≠ 0, j = 3, ..., r D) H0: β2 = 0, β3 = 0 ..., βr = 0, vs. H1: at least one βj ≠ 0, j = 2, ..., r

D

In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, to test that the two regressions are identical, you must use the: A) t-statistic separately for β2 = 0, β2 = 0. B) F-statistic for the joint hypothesis that β0 = 0, β1 = 0. C) t-statistic separately for β3 = 0. D) F-statistic for the joint hypothesis that β2 = 0, β3= 0.

D

The binary variable interaction regression: A) can only be applied when there are two binary variables, but not three or more. B) is the same as testing for differences in means. C) cannot be used with logarithmic regression functions because ln(0) is not defined. D) allows the effect of changing one of the binary independent variables to depend on the value of the other binary variable.

D