Econ Test Questions
If the Breusch-Pagan Test for heteroskedasticity results in a large p-value, the null hypothesis of homoskedasticty is rejected.
False
If the instrumental variable estimator has an upward bias, the ordinary least square estimator always has a downward bias.
False
If variance of an independent variable in a simple linear regression model, say x1, is greater than 0, or var(x1)>0, the inconsistency in β^1 (OLS estimator associated with x1) is negative, if x1 and the error term are positively related.
False
If we focus only on consistency, it is necessarily better to use IV than OLS if the correlation between z and u is smaller than that between x and u.
False
If β^1 and β^2 are estimated values of regression coefficients associated with two explanatory variables in a regression equation, then the se(β^1−β^2)=se(β^1)−se(β^2) .
False
In regression analysis, the standard errors should not always be included along with the estimated coefficients.
False
In the multiple regression model y=β0+β1x1+⋯+βkxk+u , if x1 is correlated with u but the other independent variables are uncorrelated with u, then all of the OLS estimators are generally consistent.
False
In the multiple regression model y=β0+β1x1+⋯+βkxk+u, if var(u|x1,⋯,xk)≠σ2 (a constant), then all of the OLS estimators are generally inconsistent.
False
Instrumental variables cannot be used for estimating a regression equation if the regression model suffers from the measurement error problem.
False
The coefficient of determination decreases when an independent variable is added to a multiple regression model.
False
The interpretation of goodness-of-fit measures changes in the presence of heteroskedasticity.
False
The key assumption for the general multiple regression model is that all factors in the unobserved error term be correlated with the explanatory variables.
False
The population R2 is affected when heteroskedasticity is present in var(u|x1,⋯,xk).
False
The sample covariance between the regressors and the Ordinary Least Square (OLS) residuals is always positive.
False
The variance of the slope estimator increases as the error variance decreases.
False
There are n−1 degrees of freedom in Ordinary Least Square residuals in the traditional simple linear regression model.
False
Whenever the dependent variable takes on just a few values it is close to a normal distribution.
False
Whenever there is strong heteroskedasticity, it is preferable to use OLS rather than WLS, which may use a possibly misspecified variance function
False
Experimental data are easy to obtain in the social sciences.
False
Random sampling complicates the analysis of cross-sectional data.
False
When one randomly samples from a population, the total sample variation in xl decreases without bound as the sample size increases.
False
Consider the following simple regression model y=β0+β1x+u . The variable z is a poor instrument for x if _____.
It is correlated with u and there is a low correlation between z and x.
Increasing the number of overidentifying restrictions can cause severe biases in two stage least squares estimators.
True
R^2 is the ratio of the explained variation compared to the total variation.
True
Standard errors must always be positive.
True
The Generalized Least Squares estimators for correcting heteroskedasticity are also called Weighed Least Squares estimators.
True
The dummy variable coefficient for a particular group represents the estimated difference in intercepts between that group and the base group.
True
The estimator β~1=∑i=1nyi/∑i=1nxi for the slope parameter in the linear regression model y=β1x+u where E[u|x]=0 is consistent provided E[x]≠0.
True
The linear probability model always contains heteroskedasticity when the dependent variable is a binary variable unless all of the slope parameters are zero.
True
The multiple linear regression model with a binary dependent variable is called the linear probability model.
True
The notion of ceteris paribus means "other factors being equal."
True
The parameters in a linear probability model can be interpreted as measuring the change in the probability that y=1 due to a one-unit increase in an explanatory variable.
True
The sample mean, y¯=(1/n)∑i=1nyi , from a random sample y1,y2,⋯,yn generated from the model y=β0+u satisfying assumptions MLR.1-MLR.4 is a consistent estimator of β0 .
True
The term "linear" in a multiple linear regression model means that the equation is linear in parameters.
True
The two stage least squares estimator is less efficient than the ordinary least squares estimator when the explanatory variables are exogenous.
True
What will you conclude about a regression model if the Breusch-Pagan test results in a small p -value?
The model contains heteroskedasticty.
Which of the following statements is true?
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.
Which of the following is a statistic that can be used to test hypotheses about a single population parameter?
t statistic
If β^j an unbiased estimator of βj, is also a consistent estimator of βj, then when the sample size tends to infinity:
the distribution of β^j collapses to the single point βj.
Weighted least squares estimation is used only when _____.
the functional form of the error variances is known
A test for heteroskedasticty can be significant if _____.
the functional form of the regression model is misspecified
In a multiple regression model, the OLS estimator is consistent if:
there is no correlation between the independent variables and the error term.
The order condition for identification of an equation requires that there should be _____.
at least as many excluded exogenous explanatory variables as there are included endogenous explanatory variables
Let {xi;i=1,...,n} be a sequence of positive numbers greater than b and define f(b)=∑i=1nlog(xi−b). What is the derivate of f(b) with respect to b, i.e., df(b)/db ?
df(b)/db=−∑i=1n(xi−b)−1
Consider the following simple regression model y=β0+β1x+u . Suppose corr(x,u)>0, corr(z,x)>0, and corr(z,u)<0 . Then, the IV estimator has a(n) _____.
downward bias
A _____ variable is used to incorporate qualitative information in a regression model.
dummy
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 _____.
dummy variable trap
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education, i.e., savings=β0+δ0edu+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 above model. If δ0>0, _____.
educated people have higher savings than those who are not educated
The term 'u ' in an econometric model is usually referred to as the _____.
error term
If a change in variable x causes a change in variable y, variable x is called the _____.
explanatory variable
The expression var(β^l|x1,x2)=σ2/[SSTl(1−Rl2)] treats both regressors as _____.
nonrandom
Which of the following is true of BLUE?
An estimator is linear if and only if it can be expressed as a linear function of the data on the dependent variable.
Suppose that you are interested in estimating the average impact a job training program has on wages. However, you recognize that there are some observed factors that influence wage, participation on the training program, or both. You may still get the unbiased estimate for the program effectiveness by:
Including factors that predict both wage and participation as controls and running a multiple linear regression.
Which of the following is true of standard error?
It is an estimate of the standard deviation of the OLS estimator in a regression model.
Which of the following is true?
The WLS method fails if hi is negative or zero for any observation.
Which of the following is true of time series data?
The chronological ordering of observations in a time series conveys potentially important information.
When the error term is not normally distributed, then se(β^j) is sometimes called the:
asymptotic standard error.
Consider the following simple regression model y=β0+β1x+u and z is an instrument for x . Suppose x and z are both positively correlated with u and corr(z,x)>0. Then, the asymptotic bias in the IV estimator is less than that for OLS only if:
corr(z,u)/corr(z,x)<corr(x,u).
Econometrics is the branch of economics that _____.
develops and uses statistical methods for estimating economic relationships
The square root of the quantity var^(β^l∣x1,x2,...,xn)=∑i=1nr^il2u^i2SSRl2 is called the _____ for β^l .
heteroskedasticity-robust standard error
The generalized least squares (GLS) is an efficient procedure that weights each squared residual by the:
inverse of the conditional variance of ui given xi.
A binary response is the most extreme form of a discrete random variable that takes on:
only two values, zero and one.
A cross-sectional data set consists of observations on a variable or several variables over time.
False
A dummy variable trap arises when a single dummy variable describes a given number of groups.
False
A reduced form equation expresses an exogenous variable in terms of endogenous variables.
False
A time series data is also called a longitudinal data set.
False
An explanatory variable is said to be exogenous if it is correlated with the error term.
False
Even if the error terms in a regression equation, u1,u2,⋯,un, for a fixed sample size n are not normally distributed, the estimated coefficients can be normally distributed.
False
Experimental data are sometimes called retrospective data.
False
H1: B^j>0, where β^j is an estimated regression coefficient associated with an explanatory variable xj , represents a one-sided alternative hypothesis.
False
Note: lsalary represents the natural logarithm of 209 CEOs' salaries (salary ) measured in thousands of USD and lsales represents the natural logarithm of firms' total annual sales (sales ) measured in thousands of USD. Which expression is true?
N/A Therefore y=y^+u^ by definition.
Which of the following is true of confidence intervals?
Confidence intervals are also called interval estimates.
Which of the following statements is true of confidence intervals in the Classical Linear Model (CLM)?
Confidence intervals in the CLM provide a range of likely values for the population parameter.
Sophia wants to organize an event. The cost of the rental space is $1,600 for 6 hours. After the 6 hours, Sophia has to pay $240 for each additional hour. Let x be the extra hours and y be the total cost for the event. The linear function is defined as y=1600+240x . What is the total cost required for organizing the event if Sophia has rented the space for an additional five hours?
$2,800
In the equation c=β0+β1i+u, c denotes consumption and i denotes income. What is the residual for the 5th observation if c5=$500 and c^5=$475 ?
$25
where crime measures the annual number of crimes on college campuses and enroll the total student enrollment. Using the textbook's statistical tables, a 90% confidence interval for the elasticity of crime with respect to enrollment is:
(1.0872,1.4528)
Let x0 be the initial value and x1 be the subsequent value. Then, the proportionate change in x in moving from x0 to x1 is given by:
(x1−x0)/x0=Δx/x0,x0≠0
Let {i;i=1,2,3,4} and define f(x)=∑i=14(i−x)2. Then f′′(x)≡d2f(x)/dx2 equals
-2
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?
0.27
Consider the following simple regression model y=β0+β1x+u . Suppose z is an instrument for x , and let R2 be the coefficient of determination from a simple regression of x on z. Then sampling variance for the instrumental variables (IV) estimator of β1 is larger than the variance for the ordinary least square estimators (OLS) of β1 because _____.
0<R^2<1
Based on this regression output, the wage differential between single women and single men is:
13.2%
If the explained sum of squares is 35 and the total sum of squares is 49, what is the residual sum of squares?
14
Suppose the relationship between wages (wage ) and years of formal education (educ ) is: wage=0.84+1.08educ−0.03educ2 . After how many years of education is the expected wage maximized?
18
Find the degrees of freedom in a regression model that has 10 observations and 7 independent variables.
2
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?
4
Based on this regression output, the wage differential between women and men is:
35.9%
If the R2 of an unrestricted model is 0.6873 (call this Rur2), and the R2 of a restricted model is 0.5377 (call this Rr2), after imposing 3 linear restrictions, and n−k−1=229 , the F statistic equals:
36.5
The proportion of students who play soccer in a high school is .45. This implies that:
45% of students in the high school play soccer.
The average number of crime cases registered at a station house per day has increased from 10 to 15 cases. What is the percentage change in the number of crime cases registered at the station house per day?
50%
Which of the following refers to panel data?
Data on the birth rate, death rate and population growth rate in developing countries over a 10-year period.
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)?
56
Consider the fitted regression log(cons)^=1.2+0.5inc−0.01inc2 where both consumption (cons) and income (inc) are measured in thousand US$. By how much the predicted consumption increase if income increases to US$12,000 from US$10,000?
56% log(cons)^ is Δlog(cons)^=0.5×(inc1−inc0)−0.01×(inc12−inc02) or equivalently Δlog(cons)^=0.5×(12−10)−0.01×(122−102)=0.56. Therefore the predicted consumption is expected to increase by 56%.
Which of the following is an example of time series data?
Data on the gross domestic product of a country over a period of 10 years.
Which of the following is true of dependent variables?
A dependent variable can be binary.
Which of the following is true of dummy variables?
A dummy variable takes a value of 0 or 1.
Which of the following is a difference between panel and pooled cross-sectional data?
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 under the Gauss-Markov assumptions?
Among a certain class of estimators, OLS estimators are best linear unbiased and asymptotically efficient.
The derivative of the linear equation y=β0+β1x with respect to x is:
B1
In the model log(y)=β0+β1x, the semi-elasticity is constant and approximately equal to:
B1 x 100
Which of the following terms measures the association between two variables?
Correlation
In the following econometric model, wage=β0+β1educ+u , which of the following factors would not be contained in the term u ?
Education (educ)
Why do labor economists often find it difficult to estimate the ceteris paribus return to education, in terms of wage, using non-experimental data?
Education level in non-experimental data is probably dependent on other omitted factors that also affect wage.
Which of the following is true of experimental data?
Experimental data are collected in laboratory environments in the natural sciences.
The heteroskedasticity-robust _____ is also called the heteroskedastcity-robust Wald statistic.
F statistic
A binary variable is a variable whose value changes with a change in the number of observations.
False
Note: salary represents 209 CEOs' salaries measured in thousands of USD and lsales represents the natural logarithm of firms' total annual sales measured in thousands of USD. your colleague concludes that "a 1% increase in firm sales increase CEO salaries by roughly 263 thousand USD." Is this statement true or not?
False, 2.63 thousand USD
Is the OLS estimator the most efficient estimator in this case? *picture of graph showing variance increasing
False, heteroskedastic
Which of the following null hypotheses test whether the assessed housing price is a rational valuation?
H0:β1=1,β2=0,β3=0,β4=0
Which of the following correctly identifies a reason why some authors prefer to report the standard errors rather than the t statistic?
Having standard errors makes it easier to compute confidence intervals.
Suppose the relationship between wage, years of education (educ), years of experience (exper), and participation in a job training program (train) is modeled as: log(wage)=β0+β1educ+β2exper+β3train+u . Which of the following is the most accurate interpretation of the coefficient, β3 ?
Holding education and experience constant, participating in the training program is predicted to increase the wage by 100×β3%.
If q is quantity demanded, p is price, income is measured in US$ and they are related by log(q)=4.7−1.25log(p)+0.01income, what statement is not true?
Holding p constant, 1 extra dollar of income leads to a 0.01 increase in quantity demanded.
What is the estimated increase in price for a house with one more bedroom, holding squared footage constant?
Holding square footage constant, Δprice^=15.198Δbdrms, and so price^ increases by 15.198, which means US $15,198.
If δ1=cov(x1,x2)/var(x1) where x1 and x2 are two independent variables in a regression of y on x1 and x2, which of the following statements is true?
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.
_____ has a causal effect on _____.
Income; consumption
Given the following econometric model, wage=β0+β1educ+u, can we eliminate the error term u entirely?
No, because many factors affect wage, that we cannot even list, let alone observe.
Consider the following regression equation: y=β0+β1x1+u. Which of the following indicates a functional form misspecification in E[y|x]?
Ordinary Least Squares estimates are positive while Weighted Least Squares estimates are negative.
Which of the following is the first step in empirical economic analysis?
Specification of an econometric model when an economic model is not needed.
Which of the following statements is true?
Taking a log of a non-normal distribution yields a distribution that is closer to normal.
Which of the following is true of two-stage least squares (2SLS) estimators?
The 2SLS estimators are biased if the regression model exhibits multicollinearity.
Consider the relationship between monthly expenditure on health and monthly income which is defined as health expenditure=125+.39 income . Which of the following statements is true about marginal propensity to consume (MPC) and average propensity to consume (APC)?
The APC is not constant, it is always larger than the MPC, and it gets closer to the MPC as income increases.
Which of the following tests helps in the detection of heteroskedasticity?
The Breusch-Pagan test
Which of the following statements is true?
The F statistic is always nonnegative as SSRr is never smaller than SSRur.
Which of the following is true of heteroskedasticity?
The Ordinary Least Squares estimators are not the best linear unbiased estimators if heteroskedasticity is present.
Which of the following is true of the White test?
The White test assumes that the square of the error term in a regression model is uncorrelated with all the independent variables, their squares and cross products.
Which of the following Gauss-Markov assumptions is violated by the linear probability model?
The assumption of constant variance of the error term.
Which of the following assumptions is known as exclusion restrictions?
The assumption that an exogenous explanatory variable is excluded from a regression model and is uncorrelated with the error term.
Which of the following will cause Ordinary Least Square (OLS) estimates of a simple regression model, y=β0+β1x+u to be biased?
The conditional mean E(u|x) is a function of x.
Which of the following assumptions is required for two-stage least squares (2SLS) estimation method?
The error term has zero mean.
Consider a simple linear regression model y=β0+β1x+u . What does the zero conditional mean assumption imply?
The expected value of the error term, u, is zero, regardless of what the value of the explanatory variable, x, is.
What can we conclude about the endogeneity of an explanatory variable if the OLS and 2SLS estimates are significantly different? Assume that the instrument used was exogenous.
The explanatory variable is endogenous and therefore using 2SLS should be considered.
Consider the following simple regression model y=β0+β1x+u . Suppose z is an instrument for x . Which of the following statements is true?
The instrumental variables estimator is always biased if cov(x,u)≠0 .
Which of the following is true?
The notion of 'ceteris paribus' plays an important role in causal analysis.
Which of the following is a difference between the White test and the Breusch-Pagan test?
The number of regressors used in the White test is larger than the number of regressors used in the Breusch-Pagan test.
Identify the difference between percentage point change and percentage change value.
The percentage point change is just the change in the percentages. The percentage change is the change relative to the initial value.
Consider the following regression equation graduate=β0+β1female+β2score+u where graduate is a dummy variable (1 if the person graduated from college, and 0 otherwise), female is a dummy variable (1 if the person is female, and 0 otherwise), and score is the college admission test score. What does β1 measure?
The predicted difference in probability of graduating between male and female students, all else equal.
What does the equation y^=β^0+β^1x denote if the regression equation is y=β0+β1x+u ?
The sample regression function
Which of the following is assumed for establishing the unbiasedness of Ordinary Least Square (OLS) estimates?
The regression equation is linear in the explained and explanatory variables.
Which of the following statements is true?
The upper bound of the confidence interval for a regression coefficient, say βj, is given by β^j+critical value×s.e.(β^j) .
A larger error variance makes it difficult to estimate the partial effect of any of the independent variables on the dependent variable.
True
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
An economic model consists of mathematical equations that describe various relationships between economic variables.
True
Everything else the same "If the fifth observation is dropped, then the sum of squared residuals will be smaller." *fifth point is very far out top right of graph
True
Identification fails when there are more included endogenous variables than excluded exogenous variables in the structural equation.
True
If cov(z,x)≠0, then z and x are correlated.
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
If the p -value of an F statistic 2.63 is 0.034, then we can say that the problem of interest is significant at the 5% level.
True
A standard linear model which is supposed to measure a causal relationship is called a structural equation.
True
Note: lsalary represents the natural logarithm of 209 CEOs' salaries measured in thousands of USD and sales represents the firms' total annual sales measured in thousands of USD. Your boss tells you "it seems that on average firms without annual sales pay their CEOs 941 thousand USD." Is this statement true or not?
True exp(lsalary^)≈941.05
In a regression model, which of the following will be described using a binary variable?
Whether it rained on a particular day or it did not
where colGPA is explained by high school GPA, hsGPA , the ACT scores, and the average number of lectures skipped per week, skipped by 141 college students. Is there evidence that after controlling for hsGPA and skipped , the ACT scores plays no role in explaining colGPA ?
Yes, at the 5% level of significance.
Given the sequence {xi:i=1,...,n}, then ∑i=1n(xi−x¯)=
Zero
Consider a simple linear regression model, wage=β0+β1male+u , where male is a binary variable (1 if a person is male, and 0 otherwise). Now suppose that we know being a male means there is a lower probability of attaining higher education, another factor that is also expected to affect wage. Which of the key assumptions made to establish unbiasedness of OLS estimates do not hold?
Zero conditional mean
If the model y=β0+β1x1+β2x2+v satisfies the first four Gauss-Markov assumptions, then v has:
a zero mean and is uncorrelated with x1 and x2.
The linear probability model contains heteroskedasticity unless _____.
all the slope parameters are zero
If the error term is correlated with any of the independent variables, the OLS estimators are:
biased and inconsistent.
If two variables x and y are related by y=β0+β1x , then marginal effect of x on y is:
constant and equal to β1.
Consider the following simple regression model: y=β0+β1x+u . Suppose z is an instrument for x . Which of the following conditions denotes instrument exogeneity?
cov(z, u) = 0
Consider the following simple regression model y=β0+β1x+u . Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance?
cov(z,x) does not equal 0
Consider the following simple regression model y=β0+β1x+u . Suppose z is an instrument for x . if cov(z,u)=0 and cov(z,x)≠0 , the value of β1 in terms of population covariances is _____.
cov(z,y)/cov(z,x)
Data on the income of law graduates collected at different times during the same year is _____.
cross-sectional data
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) _____.
cross-sectional data set
An empirical analysis relies on _____ to test a theory.
data
The parameters of an econometric model _____.
describe the strength of the relationship between the variable under study and the factors affecting it
If β^j an unbiased estimator of βj, is consistent, then the:
distribution of β^j becomes more and more tightly distributed around βj as the sample size grows.
If xi and yi are positively correlated in the sample then the estimated slope is _____.
greater than zero
Suppose the variable x2 has been omitted from the following regression equation y=β0+β1x1+β2x2+u , β~1 is the estimator obtained when x2 is omitted from the equation. If E(β~1)>β1 , β~1 is said to _____.
have an upward bias
Consider the following simple regression model: y=β0+β1x+u . In order to obtain consistent estimators of β0 and β1 , when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: cov(z,x)≠0 and cov(z,u)=0 . The variable z is called a(n) _____ variable.
instrumental
In the equation y=β0+β1x+u, β0 is the _____.
intercept parameter
The population parameter in the null hypothesis _____.
is not always equal to zero
In the regression model Yi=β0+β1Ci+β2Fi+β3(Ci×Fi)+ui , where Y denotes earnings, C a dummy variable for having a college degree and F a gender dummy variable, β2
is the gender difference in earnings for someone without a college degree.
The value of R2 always _____.
lies between 0 and 1
Note: lsalary represents the natural logarithm of 209 CEOs' salaries measured in thousands of USD and lsales represents the natural logarithm of firms' total annual sales measured in thousands of USD. What is the correct way to report the following regression output?
lsalary^=4.822+0.257lsales^ one reports y^=β^0+β^1x
Exclusion of a relevant variable from a multiple linear regression model leads to the problem of _____.
misspecification of the model
High (but not perfect) correlation between two or more independent variables is called _____.
multicollinearity
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.
n<k+1
Nonexperimental data is called _____.
observational data
The necessary condition for identification of an equation is called the _____.
order condition
The quarterly increase in an employee's salary depends on the rating of his work (1 to 5) by his employer and several other factors as shown in the model below: increase in salary=β0+δ0rating+other factors. The variable 'rating ' in this case is a(n) _____.
ordinal variable
The procedure of comparing different instrumental variables estimates of the same parameter is an example of testing _____.
overidentifying restrictions
The constants of econometric models are referred to as _____.
parameters
In the linear equation y=150+.29x1+.34x2 with Δx1=0 , the value .34 represents the:
partial effect of x2 on y .
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 _____.
perfect collinearity
A dependent variable is also known as a(n) _____.
response variable
Let β^1 and β^2 be the OLS estimates of the slope parameters in the multiple linear regression model y=β0+β1x1+β2x2+u . What is the correct expression for the se(β^1−β^2)?
se(β^1−β^2)= square root(var^(β^1)+var^(β^2)−2cov^(β^1,β^2))
If β^j is an OLS estimator of a regression coefficient associated with one of the explanatory variables, such that j=1,...,n, asymptotic standard error of β^j will refer to the:
square root of the estimated variance of β^j when the error term is not normally distributed.
Which of the following is true of R2 ?
shows what percentage of the total variation in the dependent variable, y, is explained by the explanatory variables.
A useful rule of thumb is that standard errors are expected to shrink at a rate that is the inverse of the:
square root of the sample size.
In the equation y=β0+β1x1+β2x2+u, β2 is a(n) _____.
slope parameter
A normal variable is standardized by:
subtracting off its mean from it and dividing by its standard deviation.
The general t statistic can be written as:
t=(estimate - hypothesized value)/standard error
The following simple model is used to determine the annual savings of an individual on the basis of his annual income and education, i.e., savings=β0+δ0edu+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 _____.
the group of uneducated people
The Gauss-Markov theorem will not hold if _____.
the independent variables have exact linear relationships among them
The normality assumption implies that:
the population error u is independent of the explanatory variables and is normally distributed with mean zero and variance σ2.
In the following regression equation, y is a binary variable: y=β0+β1x1+⋯+βkxk+u. In this case, the OLS estimated slope coefficient, β^1, measures _____.
the predicted change in the probability of success when x1 increases by one unit, everything else remaining constant
The significance level of a test is:
the probability of rejecting the null hypothesis when it is true.
The test for overidentifying restrictions is valid if _____.
the regression model exhibits homoskedasticity
If OLS estimators satisfy asymptotic normality, it implies that:
they are approximately normally distributed in large enough sample sizes.
A data set that consists of observations on a variable or several variables over time is called a _____ data set.
time series
An auxiliary regression refers to a regression that is used:
to compute a test statistic but whose coefficients are not of direct interest.
Consider the following simple regression model y=β0+β1x+u . Suppose corr(x,u)>0, corr(z,x)>0, and corr(z,u)>0 . Then, the OLS estimator has a(n) _____.
upward bias
Consider the following regression model: yi=β0+β1xi+ui. If the first four Gauss-Markov assumptions hold true, we say that the error term contains heteroskedasticity if its variance is also reported to be _____.
var(ui|xi)=i2
In the regression of y on x , the error term exhibits heteroskedasticity if _____.
var(y|x) is a function of x
The log function y=log(x) is defined only for:
x>0
Consider the following regression equation: y=β0+β1x1+⋯+βkxk+u In which of the following cases, the dependent variable is binary?
y indicates whether an adult is a college dropout
Consider the following regression equation: y=β0+β1x1+⋯+βkxk+u In which of the following cases, is 'y' a binary variable?
y indicates whether there are children in a family
Which of the following is a nonlinear regression model?
y=1/(α0+α1x)+u
From the equation y=β0+u , what is the estimated value of β0 ?
y^-
What is the estimated increase in price (in thousand of US $) for a house with an additional bedroom that is 140 squared feet bigger in size? ⚠ Please use all the decimals in your calculations.
Δprice^=.128Δsqrft+15.20Δbdrms=.128(140)+15.198=33.118 which is US $33,118.
Consider the following regression equation y=β0+β1x1+β2x2+u. What does β1 imply?
β1 measures the ceteris paribus effect of x1 on y.
Consider the model: log(wage)=β0+β1female+β2graduate+β3female×graduate+u, where graduate is a dummy variable (1 if the person has graduated from college, and 0 otherwise), and female is a dummy variable (1 if the person is female, and 0 otherwise). Which of the following measures the return of graduating from college for men?
β2
Suppose the variable x2 has been omitted from the following regression equation y=β0+β1x1+β2x2+u , β~1 is the estimator obtained when x2 is omitted from the equation. The bias in β~1 is negative if _____.
β2<0 and x1 and x2 are positively correlated
Suppose the variable x2 has been omitted from the following regression equation y=β0+β1x1+β2x2+u , β~1 is the estimator obtained when x2 is omitted from the equation. The bias in β~1 is positive if _____.
β2>0 and x1 and x2 are positively correlated
Consider the model: log(wage)=β0+β1female+β2exper+β3female×exper+u, where exper is the years of work experience, and female is a dummy variable (1 if the person is female, and 0 otherwise). Which of the following measures the difference in the return of experience between men and women?
β3
Consider the no-intercept model, y=β1x+u, where E[u|x]=0, then the OLS estimator of β1 is _______.
β^1=∑i=1nxiyi/∑i=1nxi2
If {(xi,yi):i=1,...,n} denotes a set of n pair of numbers, then
∑i=1n(2xi+5yi)=2∑i=1nxi+5∑i=1nyi