Econ Midterm 2

Beta coefficients are always greater than standardized coefficients.

False

4. Standardized coefficients are also referred to as: a. beta coefficients. b. y coefficients. c. alpha coefficients. d. j coefficients.

a

The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education. Savings = β0+∂0 Edu + β1Inc+u The variable 'Edu' takes a value of 1 if the person is educated and the variable 'Inc' measures the income of the individual. Refer to the model above. The benchmark group in this model is _____. a. the group of educated people b. the group of uneducated people c. the group of individuals with a high income d. the group of individuals with a low income

b

Which of the following models is used quite often to capture decreasing or increasing marginal effects of a variable? a. Models with logarithmic functions b. Models with quadratic functions c. Models with variables in level d. Models with interaction terms

b

Which of the following is true of Chow test? a. It is a type of t test. b. It is a type of sign test. c. It is only valid under homoskedasticty. d. It is only valid under heteroskedasticity.

c

A normally distributed random variable is symmetrically distributed about its mean, it can take on any positive or negative value (but with zero probability), and more than 95% of the area under the distribution is within two standard deviations.

true

A problem that often arises in policy and program evaluation is that individuals (or firms or cities) choose whether or not to participate in certain behaviors or programs.

true

If a new independent variable is added to a regression equation, the adjusted R2 increases only if the absolute value of the t statistic of the new variable is greater than one.

true

If the calculated value of the t statistic is greater than the critical value, the null hypothesis, H0 is rejected in favor of the alternative hypothesis, H1.

true

Predictions of a dependent variable are subject to sampling variation.

true

Standard errors must always be positive.

true

The dummy variable coefficient for a particular group represents the estimated difference in intercepts between that group and the base group.

true

The multiple linear regression model with a binary dependent variable is called the linear probability model.

true

7. If OLS estimators satisfy asymptotic normality, it implies that: a. they are approximately normally distributed in large enough sample sizes. b. they are approximately normally distributed in samples with less than 10 observations. c. they have a constant mean equal to zero and variance equal to σ2. d. they have a constant mean equal to one and variance equal to σ.

a

A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the: a. square root of the sample size. b. product of the sample size and the number of parameters in the model. c. square of the sample size. d. sum of the sample size and the number of parameters in the model.

a

Changing the unit of measurement of any independent variable, where log of the dependent variable appears in the regression: a. affects only the intercept coefficient. b. affects only the slope coefficient. c. affects both the slope and intercept coefficients. d. affects neither the slope nor the intercept coefficient.

a

In a regression model, which of the following will be described using a binary variable? a. Whether it rained on a particular day or it did not b. The volume of rainfall during a year c. The percentage of humidity in air on a particular day d. The concentration of dust particles in air

a

Residual analysis refers to the process of: a. examining individual observations to see whether the actual value of a dependent variable differs from the predicted value. b. calculating the squared sum of residuals to draw inferences for the consistency of estimates. c. transforming models with variables in level to logarithmic functions so as to understand the effect of percentage changes in the independent variable on the dependent variable. d. sampling and collection of data in such a way to minimize the squared sum of residuals.

a

Which of the following Gauss-Markov assumptions is violated by the linear probability model? a. The assumption of constant variance of the error term. b. The assumption of zero conditional mean of the error term. c. The assumption of no exact linear relationship among independent variables. d. The assumption that none of the independent variables are constants.

a

Which of the following correctly identifies a reason why some authors prefer to report the standard errors rather than the t statistic? a. Having standard errors makes it easier to compute confidence intervals. b. Standard errors are always positive. c. The F statistic can be reported just by looking at the standard errors. d. Standard errors can be used directly to test multiple linear regressions.

a

Which of the following statements is true? a. In large samples there are not many discrepancies between the outcomes of the F test and the LM test. b. Degrees of freedom of the unrestricted model are necessary for using the LM test. c. The LM test can be used to test hypotheses with single restrictions only and provides inefficient results for multiple restrictions. d. The LM statistic is derived on the basis of the normality assumption.

a

Which of the following statements is true? a. Taking a log of a nonnormal distribution yields a distribution that is closer to normal. b. The mean of a nonnormal distribution is 0 and the variance is σ2. c. The CLT assumes that the dependent variable is unaffected by unobserved factors. d. OLS estimators have the highest variance among unbiased estimators.

a

6. Refer to the above model. If ∂0 > 0, _____. a. uneducated people have higher savings than those who are educated b. educated people have higher savings than those who are not educated c. individuals with lower income have higher savings d. individual with lower income have higher savings

b

8. Which of the following statements is true when the dependent variable, y > 0? a. Taking log of a variable often expands its range. b. Models using log(y) as the dependent variable will satisfy CLM assumptions more closely than models using the level of y. c. Taking log of variables make OLS estimates more sensitive to extreme values. d. Taking logarithmic form of variables make the slope coefficients more responsive to rescaling.

b

Consider the equation, Y = β1 + β2X2 + u. A null hypothesis, H0: β2 = 0 states that: a. X2 has no effect on the expected value of β2. b. X2 has no effect on the expected value of Y. c. β2 has no effect on the expected value of Y. d. Y has no effect on the expected value of X2.

b

Consider the following regression equation: y = β0+β1x1+...βk xk+ u In which of the following cases, the dependent variable is binary? a. y indicates the gross domestic product of a country b. y indicates whether an adult is a college dropout c. y indicates household consumption expenditure d. y indicates the number of children in a family

b

If ^β j, an unbiased estimator of β j, is consistent, then the: a. distribution of ^β j becomes more and more loosely distributed around the sample size grows. b. distribution of ^β j becomes more and more tightly distributed around the sample size grows. β j as β j as c. distribution of ^β size grows. d. distribution of ^β

b

If a regression equation has only one explanatory variable, say x1, its standardized coefficient must lie in the range: a. -2 to 0. b. -1 to 1. c. 0 to 1. d. 0 to 2.

b

If δ1 = Cov(x1/x2) / Var(x1) where x1 and x2 are two independent variables in a regression equation, which of the following statements is true? a. If x2 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. b. If x2 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive. c. If x1 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is negative. d. If x1 has a positive partial effect on the dependent variable, and δ1 > 0, then the inconsistency in the simple regression slope estimator associated with x1 is positive.

b

In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment. log(gdp) = 2.65 + 0.527log(bankcredit) + 0.222FDI (0.13) (0.022) (0.017) Which of the following statements is then true? a. If gdp increases by 1%, bank credit increases by 0.527%, the level of FDI remaining constant. b. If bank credit increases by 1%, gdp increases by 0.527%, the level of FDI remaining constant. c. If gdp increases by 1%, bank credit increases by log(0.527)%, the level of FDI remaining constant. d. If bank credit increases by 1%, gdp increases by log(0.527)%, the level of FDI remaining constant.

b

The quarterly increase in an employee's salary depends on the rating of his work by his employer and several other factors as shown in the model below: Increase in salary= β0+∂0Rating + other factors. The variable 'Rating' is a(n) _____ variable. a. dependent variable b. ordinal variable c. continuous variable d. Poisson variable

b

Two equations form a nonnested model when: a. one is logarithmic and the other is quadratic. b. neither equation is a special case of the other. c. each equation has the same independent variables. d. there is only one independent variable in both equations.

b

Which of the following correctly defines F statistic if SSRr represents sum of squared residuals from the restricted model of hypothesis testing, SSRur represents sum of squared residuals of the unrestricted model, and q is the number of restrictions placed? (SSRur−SSRr)/q SSRur/(n−k−1) (SSRr−SSRur)/q SSRur/(n−k−1) (SSRur−SSRr)/q SSR r/(n−k−1) a. F = b. F = c. F = (SSRur−SSRr)/(n−k−1) SSRur/q

b

Which of the following is a statistic that can be used to test hypotheses about a single population parameter? a. F statistic b. t statistic c. χ2 statistic d. Durbin Watson statistic

b

Which of the following problems can arise in policy analysis and program evaluation using a multiple linear regression model? a. There exists homoscedasticity in the model. b. The model can produce predicted probabilities that are less than zero and greater than one. c. The model leads to the omitted variable bias as only two independent factors can be included in the model. d. The model leads to an overestimation of the effect of independent variables on the dependent variable.

b

Which of the following statements is true of confidence intervals? a. Confidence intervals in a CLM are also referred to as point estimates. b. Confidence intervals in a CLM provide a range of likely values for the population parameter. c. Confidence intervals in a CLM do not depend on the degrees of freedom of a distribution. d. Confidence intervals in a CLM can be truly estimated when heteroskedasticity is present.

b

Which of the following statements is true when the dependent variable, y > 0? a. Taking log of a variable often expands its range. b. Models using log(y) as the dependent variable will satisfy CLM assumptions more closely than models using the level of y. c. Taking log of variables make OLS estimates more sensitive to extreme values. d. Taking logarithmic form of variables make the slope coefficients more responsive to rescaling.

b

Which of the following statements is true? a. If the calculated value of F statistic is higher than the critical value, we reject the alternative hypothesis in favor of the null hypothesis. b. The F statistic is always nonnegative as SSRr is never smaller than SSRur. c. Degrees of freedom of a restricted model is always less than the degrees of freedom of an unrestricted model. d. The F statistic is more flexible than the t statistic to test a hypothesis with a single restriction.

b

Which of the following statements is true? a. The standard error of a regression, σ^ , is not an unbiased estimator for σ , the standard deviation of the error, u, in a multiple regression model. b. In time series regressions, OLS estimators are always unbiased. c. Almost all economists agree that unbiasedness is a minimal requirement for an estimator in regression analysis. d. All estimators in a regression model that are consistent are also unbiased.

b

7. In the following equation, gdp refers to gross domestic product, and FDI refers to foreign direct investment. log(gdp) = 2.65 + 0.527log(bankcredit) + 0.222FDI (0.13) (0.022) (0.017) Which of the following statements is then true? a. If FDI increases by 1%, gdp increases by approximately 22.2%, the amount of bank credit remaining constant. b. If FDI increases by 1%, gdp increases by approximately 26.5%, the amount of bank credit remaining constant. c. If FDI increases by 1%, gdp increases by approximately 24.8%, the amount of bank credit remaining constant. d. If FDI increases by 1%, gdp increases by approximately 52.7%, the amount of bank credit remaining constant.

c

A change in the unit of measurement of the dependent variable in a model does not lead to a change in: a. the standard error of the regression. b. the sum of squared residuals of the regression. c. the goodness-of-fit of the regression. d. the confidence intervals of the regression.

c

A normal variable is standardized by: a. subtracting off its mean from it and multiplying by its standard deviation. b. adding its mean to it and multiplying by its standard deviation. c. subtracting off its mean from it and dividing by its standard deviation. d. adding its mean to it and dividing by its standard deviation.

c

A variable is standardized in the sample: a. by multiplying by its mean. b. by subtracting off its mean and multiplying by its standard deviation. c. by subtracting off its mean and dividing by its standard deviation. d. by multiplying by its standard deviation.

c

An auxiliary regression refers to a regression that is used: a. when the dependent variables are qualitative in nature. b. when the independent variables are qualitative in nature. c. to compute a test statistic but whose coefficients are not of direct interest. d. to compute coefficients which are of direct interest in the analysis.

c

If R2ur = 0.6873, R2r = 0.5377, number of restrictions = 3, and n - k - 1 = 229, F statistic equals: a. 21.2 b. 28.6 c. 36.5 d. 42.1

c

If ^β j, an unbiased estimator of β j, is also a consistent estimator of then when the sample size tends to infinity: β j, a. the distribution of b. the distribution of c. the distribution of d. the distribution of

c

If the error term is correlated with any of the independent variables, the OLS estimators are: a. biased and consistent. b. unbiased and inconsistent. c. biased and inconsistent. d. unbiased and consistent.

c

Refer to the model above. The inclusion of another binary variable in this model that takes a value of 1 if a person is uneducated, will give rise to the problem of _____. a. omitted variable bias b. self-selection c. dummy variable trap d. heteroskedastcity

c

The LM statistic follows a: a. t distribution. b. f distribution. c. χ 2 distribution. d. binomial distribution.

c

The significance level of a test is: a. the probability of rejecting the null hypothesis when it is false. b. one minus the probability of rejecting the null hypothesis when it is false. c. the probability of rejecting the null hypothesis when it is true. d. one minus the probability of rejecting the null hypothesis when it is true.

c

Which of the following correctly identifies an advantage of using adjusted R2 over R2? a. Adjusted R2 corrects the bias in R2. b. Adjusted R2 is easier to calculate than R2. c. The penalty of adding new independent variables is better understood through adjusted R2 than R2. d. The adjusted R2 can be calculated for models having logarithmic functions while R2 cannot be calculated for such models.

c

Which of the following correctly represents the equation for adjusted R2? a. R ́ 2 = 1 - [SSR/(n -1)]/[SST/(n+1)] b. R ́ 2 = 1 - [SSR/(n -k - 1)]/[SST/(n+1)] c. R ́ 2 = 1 - [SSR/(n -k - 1)]/[SST/(n - 1)] d. R ́ 2 = 1 - [SSR]/[SST/(n - 1)]

c

Which of the following is true of dependent variables? a. A dependent variable can only have a numerical value. b. A dependent variable cannot have more than 2 values. c. A dependent variable can be binary. d. A dependent variable cannot have a qualitative meaning.

c

Which of the following is true of dummy variables? a. A dummy variable always takes a value less than 1. b. A dummy variable always takes a value higher than 1. c. A dummy variable takes a value of 0 or 1. d. A dummy variable takes a value of 1 or 10.

c

Which of the following statements is true of hypothesis testing? a. The t test can be used to test multiple linear restrictions. b. A test of single restriction is also referred to as a joint hypotheses test. c. A restricted model will always have fewer parameters than its unrestricted model. d. OLS estimates maximize the sum of squared residuals.

c

Which of the following statements is true under the Gauss-Markov assumptions? a. Among a certain class of estimators, OLS estimators are best linear unbiased, but are asymptotically inefficient. b. Among a certain class of estimators, OLS estimators are biased but asymptotically efficient. c. Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient. d. The LM test is independent of the Gauss-Markov assumptions.

c

Which of the following tools is used to test multiple linear restrictions? a. t test b. z test c. F test d. Unit root test

c

8. In a regression model, if variance of the dependent variable, y, conditional on an explanatory variable, x, or Var(y|x), is not constant, _____. a. the t statistics are invalid and confidence intervals are valid for small sample sizes b. the t statistics are valid and confidence intervals are invalid for small sample sizes c. the t statistics confidence intervals are valid no matter how large the sample size is d. the t statistics and confidence intervals are both invalid no matter how large the sample size is

d

A _____ variable is used to incorporate qualitative information in a regression model. a. dependent b. continuous c. binomial d. dummy

d

A predicted value of a dependent variable: a. represents the difference between the expected value of the dependent variable and its actual value. b. is always equal to the actual value of the dependent variable. c. is independent of explanatory variables and can be estimated on the basis of the residual error term only. d. represents the expected value of the dependent variable given particular values for the explanatory variables.

d

Consider the following regression equation: y = β0+β1x1+...βk xk+ u In which of the following cases, is 'y' a discrete variable? a. y indicates the gross domestic product of a country b. y indicates the total volume of rainfall during a year c. y indicates household consumption expenditure d. y indicates the number of children in a family

d

If ^β j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j= 1, 2, ...., n, asymptotic standard error of ^β j will refer to the: a. estimated variance of ^β j when the error term is normally distributed. b. estimated variance of a given coefficient when the error term is not normally distributed. c. square root of the estimated variance of distributed. d. square root of the estimated variance of distributed.

d

In the following regression equation, y is a binary variable: y= β0+β1x1+...βk xk+ u In this case, the estimated slope coefficient, ^β1 measures _____. a. the predicted change in the value of y when x1 increases by one unit, everything else remaining constant b. the predicted change in the value of y when x1 decreases by one unit, everything else remaining constant c. the predicted change in the probability of success when x1 decreases by one unit, everything else remaining constant d. the predicted change in the probability of success when x1 increases by one unit, everything else remaining constant

d

The general t statistic can be written as: Hypothesized value Standard e rror estimate - hypothesized value ) ¿ (estimate - hypothesized value) variance (estimate - hypothesized value) standard error

d

The income of an individual in Budopia depends on his ethnicity and several other factors which can be measured quantitatively. If there are 5 ethnic groups in Budopia, how many dummy variables should be included in the regression equation for income determination in Budopia? a. 1 b. 5 c. 6 d. 4

d

The n-R-squared statistic also refers to the: a. F statistic. b. t statistic. c. z statistic. d. LM statistic.

d

The normality assumption implies that: a. the population error u is dependent on the explanatory variables and is normally distributed with mean equal to one and variance σ2. b. the population error u is independent of the explanatory variables and is normally distributed with mean equal to one and variance σ. c. the population error u is dependent on the explanatory variables and is normally distributed with mean zero and variance σ. d. the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance σ2.

d

Which of the following statements is true? a. When the standard error of an estimate increases, the confidence interval for the estimate narrows down. b. Standard error of an estimate does not affect the confidence interval for the estimate. c. The lower bound of the confidence interval for a regression coefficient, say βj, is given by ^β J - [standard error × ( ^β J)] d. The upper bound of the confidence interval for a regression coefficient, say βj, is given by ^β J + [Critical value × standard error ( ^β J)]

d

n a multiple regression model, the OLS estimator is consistent if: a. there is no correlation between the dependent variables and the error term. b. there is a perfect correlation between the dependent variables and the error term. c. the sample size is less than the number of parameters in the model. d. there is no correlation between the independent variables and the error term.

d

A binary variable is a variable whose value changes with a change in the number of observations.

false

A dummy variable trap arises when a single dummy variable describes a given number of groups.

false

Even if the error terms in a regression equation, u1, u2,....., un, are not normally distributed, the estimated coefficients can be normally distributed.

false

F statistic can be used to test nonnested models.

false

H1: βj ≠ 0, where βj is a regression coefficient associated with an explanatory variable, represents a one-sided alternative hypothesis.

false

If ^β 1 and ^β 2 are estimated values of regression coefficients associated with two explanatory variables in a regression equation, then the standard error ( ^β 1 - ^β 2) = standard error ( ^β 1) - standard error ( ^β 2).

false

If variance of an independent variable in a regression model, say x1, is greater than 0, or Var(x1) > 0, the inconsistency in ^β 1 (estimator associated with x1) is negative, if x1 and the error term are positively related.

false

The F statistic is also referred to as the score statistic.

false

The LM statistic requires estimation of the unrestricted model only.

false

To make predictions of logarithmic dependent variables, they first have to be converted to their level forms.

false

Whenever the dependent variable takes on just a few values it is close to a normal distribution.

false