econometrics Final
A time series data is also called a longitudinal data set. (True/False)
False
The notion of ceteris paribus means "other factors being equal."
True
In the equation, y=β_0+β_1 x_1+β_2 x_2+u, β_2 is a(n) _____. a. independent variable b. dependent variable c. slope parameter d. intercept parameter
c. slope parameter
A cross-sectional data set consists of observations on a variable or several variables over time. (True/False)
False
The term 'u' in an econometric model is usually referred to as the _____. a. error term b. parameter c. hypothesis d. dependent variable
a. error term
The term _____ refers to the problem of small sample size. a. micronumerosity b. multicollinearity c. homoskedasticity d. heteroskedasticity
a. micronumerosity
If the total sum of squares (SST) in a regression equation is 81, and the residual sum of squares (SSR) is 25, what is the explained sum of squares (SSE)? a. 64 b. 56 c. 32 d. 18
b. 56
The sample covariance between the regressors and the Ordinary Least Square (OLS) residuals is always positive (True/False)
False
A data set that consists of a sample of individuals, households, firms, cities, states, countries, or a variety of other units, taken at a given point in time, is called a(n) _____. a. cross-sectional data set b. longitudinal data set c. time series data set d. experimental data set
a. cross-sectional data set
Suppose the variable x2 has been omitted from the following regression equation, y=β_0+β_1 x_1+β_2 x_2+u. (β_1 ) ̃ is the estimator obtained when x2 is omitted from the equation. If E((β_1 ) ̃ ) >β1, (β_1 ) ̃ is said to _____. a. have an upward bias b. have a downward bias c. be unbiased d. be biased toward zero
a. have an upward bias
If an independent variable in a multiple linear regression model is an exact linear combination of other independent variables, the model suffers from the problem of _____. a. perfect collinearity b. homoskedasticity c. heteroskedasticty d. omitted variable bias
a. perfect collinearity
In the equation y = β0 + β1 x + u, what is the estimated value of β0 ? a. y−β^1 x b. y+β1 ́x c. y yi−¿¿ ¿ (xi− ́x)¿ ∑n ¿i=1¿ d. ∑i=1n xy
a. y−β^1 x
Suppose the variable x2 has been omitted from the following regression equation, y=β_0+β_1 x_1+β_2 x_2+u. (β_1 ) ̃ is the estimator obtained when x2 is omitted from the equation. The bias in (β_1 ) ̃is positive if _____. a. β_2 >0 and x 1 and x 2 are positively correlated b. β_2 <0 and x 1 and x 2 are positively correlated c. β_2 >0 and x 1 and x 2 are negatively correlated d. β_2 = 0 and x 1 and x 2 are negatively correlated
a. β_2 >0 and x 1 and x 2 are positively correlated
Which of the following is a difference between panel and pooled cross-sectional data? a. A panel data set consists of data on different cross-sectional units over a given period of time while a pooled data set consists of data on the same cross-sectional units over a given period of time. b. A panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time c. A panel data consists of data on a single variable measured at a given point in time while a pooled data set consists of data on the same cross-sectional units over a given period of time. d. A panel data set consists of data on a single variable measured at a given point in time while a pooled data set consists of data on more than one variable at a given point in time.
b. A panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time
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. Confidence intervals in a CLM provide a range of likely values for the population parameter.
Which of the following refers to panel data? a. Data on the unemployment rate in a country over a 5-year period b. Data on the birth rate, death rate and population growth rate in developing countries over a 10-year period. c. Data on the income of 5 members of a family on a particular year. d. Data on the price of a company's share during a year.
b. Data on the birth rate, death rate and population growth rate in developing countries over a 10-year period.
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? a. F = ((SSRur - SSRr)/q)/(SSRur/(n-k-1)) b. F = ((SSRr - SSRur)/q)/(SSRur/(n-k-1)) c. F = ((SSRur - SSRr)/q)/(SSRr/(n-k-1)) d. F = ((SSRur - SSRr)/(n-k-1))/(SSRur/q)
b. F = ((SSRr - SSRur)/q)/(SSRur/(n-k-1))
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. The F statistic is always nonnegative as SSRr is never smaller than SSRur.
Which of the following is true? a. A variable has a causal effect on another variable if both variables increase or decrease simultaneously. b. The notion of 'ceteris paribus' plays an important role in causal analysis. c. Difficulty in inferring causality disappears when studying data at fairly high levels of aggregation. d. The problem of inferring causality arises if experimental data is used for analysis.
b. The notion of 'ceteris paribus' plays an important role in causal analysis.
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. X2 has no effect on the expected value of Y
The parameters of an econometric model _____. a. include all unobserved factors affecting the variable being studied b. describe the strength of the relationship between the variable under study and the factors affecting it c. refer to the explanatory variables included in the model d. refer to the predictions that can be made using the model
b. describe the strength of the relationship between the variable under study and the factors affecting it
Econometrics is the branch of economics that _____ a. studies the behavior of individual economic agents in making economic decisions b. develops and uses statistical methods for estimating economic relationships c. deals with the performance, structure, behavior, and decision-making of an economy as a whole d. applies mathematical methods to represent economic theories and solve economic problems.
b. develops and uses statistical methods for estimating economic relationships
The error term in a regression equation is said to exhibit homoskedasticty if _____. a. it has zero conditional mean b. it has the same variance for all values of the explanatory variable. c. it has the same value for all values of the explanatory variable d. if the error term has a value of one given any value of the explanatory variable
b. it has the same variance for all values of the explanatory variable
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. subtracting off its mean from it and dividing by its standard deviation.
The Gauss-Markov theorem will not hold if _____. a. the error term has the same variance given any values of the explanatory variables b. the error term has an expected value of zero given any values of the independent variables c. the independent variables have exact linear relationships among them d. the regression model relies on the method of random sampling for collection of data
c. the independent variables have exact linear relationships among them
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. the probability of rejecting the null hypothesis when it is true.
Which of the following is a nonlinear regression model? a. y = β0 + β1x1/2 + u b. log y = β0 + β1log x +u c. y = 1 / (β0 + β1x) + u d. y = β0 + β1x + u
c. y = 1 / (β0 + β1x) + u
Consider the following regression equation: y=β_1+β_2 x_1+β_2 x_2+u. What does β1 imply? a.β_1 measures the ceteris paribus effect of x_1on x_2. b. β_1 measures the ceteris paribus effect of y on x_1. c. β_1 measures the ceteris paribus effect of x_1on y. d. β_1 measures the ceteris paribus effect of x_1on u.
c. β_1 measures the ceteris paribus effect of x_1on y.
Which of the following is true of R2? a. R2 is also called the standard error of regression. b. A low R2 indicates that the Ordinary Least Squares line fits the data well. c. R2 usually decreases with an increase in the number of independent variables in a regression. d. R2 shows what percentage of the total variation in the dependent variable, Y, is explained by the explanatory variables.
d. R2 shows what percentage of the total variation in the dependent variable, Y, is explained by the explanatory variables.
Consider the following regression model: y = β0 + β1x1 + u. Which of the following is a property of Ordinary Least Square (OLS) estimates of this model and their associated statistics? a. The sum, and therefore the sample average of the OLS residuals, is positive. b. The sum of the OLS residuals is negative. c. The sample covariance between the regressors and the OLS residuals is positive. d. The point ( x , y ) always lies on the OLS regression line.
d. The point ( x , y ) always lies on the OLS regression line.
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. The upper bound of the confidence interval for a regression coefficient, say βj, is given by β ̂J + [Critical value × standard error (β ̂J)]
In the equation y = β0 + β1 x + u, β0 is the _____. a. dependent variable b. independent variable c. slope parameter d. intercept parameter
d. intercept parameter
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. the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance σ2.
Experimental data are sometimes called retrospective data. (True/False)
False
Which of the following is an example of time series data? a. Data on the unemployment rates in different parts of a country during a year. b. Data on the consumption of wheat by 200 households during a year. c. Data on the gross domestic product of a country over a period of 10 years. d. Data on the number of vacancies in various departments of an organization on a particular month.
c. Data on the gross domestic product of a country over a period of 10 years.
Which of the following is the first step in empirical economic analysis? a. Collection of data b. Statement of hypotheses c. Specification of an econometric model d. Testing of hypotheses
c. Specification of an econometric model
What does the equation ^y=^β0+^β1x denote if the regression equation is y = β0 + β1x1 + u? a. The explained sum of squares b. The total sum of squares c. The sample regression function d. The population regression function
c. The sample regression function
An empirical analysis relies on _____to test a theory. a. common sense b. ethical considerations c. data d. customs and conventions
c. data
High (but not perfect) correlation between two or more independent variables is called _____. a. heteroskedasticty b. homoskedasticty c. multicollinearity d. micronumerosity
c. multicollinearity
Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS) estimates? a. The error term has an expected value of 1 given any value of the explanatory variable. b. The regression equation is linear in the explained and explanatory variables. c. The sample outcomes on the explanatory variable are all the same value. d. The error term has the same variance given any value of the explanatory variable.
d. The error term has the same variance given any value of the explanatory variable.
Data on the income of law graduates collected at different times during the same year is_____. a. panel data b. experimental data c. time series data d. cross-sectional data
d. cross-sectional data
The assumption that there are no exact linear relationships among the independent variables in a multiple linear regression model fails if _____, where n is the sample size and k is the number of parameters. a. n>2 b. n=k+1 c. n>k d. n<k+1
d. n<k+1
A dependent variable is also known as a(n) _____. a. explanatory variable b. control variable c. predictor variable d. response variable
d. response variable
The general t statistic can be written as: a. t = (Hypothesized value)/(Standard error) b. t = (estimate -hypothesized value) c. t = ((estimate - hypothesized value) )/variance d. t = ((estimate - hypothesized value) )/(standard error)
d. t = ((estimate - hypothesized value) )/(standard error)
Exclusion of a relevant variable from a multiple linear regression model leads to the problem of _____. a. misspecification of the model b. multicollinearity c. perfect collinearity d. homoskedasticity
a. misspecification of the model
R2 is the ratio of the explained variation compared to the total variation. (True/False)
True
The variance of the slope estimator increases as the error variance decreases. (True/False)
False
A larger error variance makes it difficult to estimate the partial effect of any of the independent variables on the dependent variable. (true/false?)
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/false?)
true
A natural measure of the association between two random variables is the correlation coefficient. (True/False)
True
An economic model consists of mathematical equations that describe various relationships between economic variables. (True/False)
True
In the regression of y on x, the error term exhibits heteroskedasticity if _____. a. it has a constant variance b. Var(y|x) is a function of x c. x is a function of y d. y is a function of x
b. Var(y|x) is a function of x
10. 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. F test
_____ has a causal effect on _____. a. Income; unemployment b. Height; health c. Income; consumption d. Age; wage
c. Income; consumption
The value of R2 always _____. a. lies below 0 b. lies above 1 c. lies between 0 and 1 d. lies between 1 and 1.5
c. lies between 0 and 1
A data set that consists of observations on a variable or several variables over time is called a _____ data set. a. binary b. cross-sectional c. time series d. experimental
c. time series
An explanatory variable is said to be exogenous if it is correlated with the error term. (true/false?)
false
The coefficient of determination (R2) decreases when an independent variable is added to a multiple regression model. (true/false?)
false
Standard errors must always be positive. (true/false?)
true
The key assumption for the general multiple regression model is that all factors in the unobserved error term be correlated with the explanatory variables. (true/false?)
false
Whenever the dependent variable takes on just a few values it is close to a normal distribution. (true/false?)
false
There are n-1 degrees of freedom in Ordinary Least Square residuals. (True/False)
False
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. t statistic
Nonexperimental data is called _____. a. cross-sectional data b. time series data c. observational data d. panel data
b. time series data
Suppose the variable x2 has been omitted from the following regression equation, y=β_0+β_1 x_1+β_2 x_2+u. (β_1 ) ̃ is the estimator obtained when x2 is omitted from the equation. The bias in (β_1 ) ̃ is negative if _____. a. β_2 >0 and x 1 and x 2 are positively correlated b. β_2 <0 and x 1 and x 2 are positively correlated c. β_2 =0 and x 1 and x 2 are negatively correlated d. β_2 =0 and x 1 and x 2 are negatively correlated
b. β_2 <0 and x 1 and x 2 are positively correlated
The explained sum of squares for the regression function, yi=β0+β1x1+u1 , is defined as _____. a. ∑i=1n (yi− ́y)2 b. ∑i=1n (yi−^y)2 c. ∑i=1n ^ui d. ∑i=1n (ui)2
b. ∑i=1n (yi−^y)2
What is the estimated value of the slope parameter when the regression equation, y = β0 + β1x1 + u passes through the origin? a. ∑n yi i=1 b. y¿¿¿∑n ¿ i=1) c. ∑n xi yi i=1∑n xii=12 d. ∑n (yi− ́y)2 i=1
c. ∑n xi yi i=1∑n xii=12
In the equation c = β0 + β1 i + u, c denotes consumption and i denotes income. What is the residual for the 5th observation if c5 =$500 and ^c5 =$475? a. $975 b. $300 c. $25 d. $50
c. $25
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. 36.5
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. A restricted model will always have fewer parameters than its unrestricted model.
If a change in variable x causes a change in variable y, variable x is called the _____. a. dependent variable b. explained variable c. explanatory variable d. response variable
c. explanatory variable
If the residual sum of squares (SSR) in a regression analysis is 66 and the total sum of squares (SST) is equal to 90, what is the value of the coefficient of determination? a. 0.73 b. 0.55 c. 0.27 d. 1.2
c. 0.27
H1: βj ≠ 0, where βj is a regression coefficient associated with an explanatory variable, represents a one-sided alternative hypothesis. (true/false?)
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). (true/false?)
false
The term "linear" in a multiple linear regression model means that the equation is linear in parameters. (true/false?)
true
Which of the following is true of experimental data? a. Experimental data are collected in laboratory environments in the natural sciences. b. Experimental data cannot be collected in a controlled environment. c. Experimental data is sometimes called observational data. d. Experimental data is sometimes called retrospective data.
a. Experimental data are collected in laboratory environments in the natural sciences.
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. Having standard errors makes it easier to compute confidence intervals.
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. Taking a log of a nonnormal distribution yields a distribution that is closer to normal.
14. Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables. a. 17 b. 2 c. 3 d. 4
b. 2
If the explained sum of squares is 35 and the total sum of squares is 49, what is the residual sum of squares? a. 10 b. 12 c. 18 d. 14
d. 14
