Stats Final
The observation on the time series variable Y made at date t is denoted as Yt and the total number of observations is denoted as T. 1. Which of the following statements are true? (Check all that apply.) A reputed car manufacturing company wants to study its returns on its 100th anniversary. For this purpose, it uses data on its yearly reported profits (Y) for the past 10 years from 2007 to 2017. Complete the following table by finding the autocorrelation values. The values suggest that reported profit is
1. a)The percentage change of a time series Yt between periods t−1 and t is approximately 100ΔlnYt, where the approximation is most accurate when the percentage change is small. c)The first difference of a series of the logarithm of Yt is its change between periods t−1 and t and is given by the expression lnYt−lnYt−1 PT Q25
Consider the following multiple regression model 1. Which of the following explains why two perfectly collinear regressors cannot be included in a linear multiple regressions? (Check all that apply) Suppose you are interested in estimating the effect of the student-teacher ratio (STR) on test performance using the model 2. Which of the following regressors, if added to the model, would be perfectly collinear with STR? (Check all that apply)
1. a)Intuitively, if one regressor is a linear function of another, OLS cannot identify the partial effect of one while holding the other constant. c)For the case of two regressors and homoskedasticity, it can be shown mathematically that the variance of the estimated coefficient β1 goes to infinity as the correlation between X1 and X2goes to one. 2. a)The teacher-security officer ratio if the student-security officer ratio is 1:10. c)The student-faculty parking ratio, if every teacher has a parking spot. d)The number of teachers expressed as a percentage of the number of students. PT Q8
Consider the following multiple regression The numbers in parentheses below each estimated coefficient are the estimated standard errors. A detailed description of the variables used in the data set is available here Suppose you wanted to test the hypothesis that BDR equals zero. That is, Report the t-statistic for this test. 1. Is the coefficient on BDR statistically different from zero at the 5% significance level? (Y/N) 2. Typically five-bedroom houses sell for much more than two-bedroom houses. Is this consistent with your previous answer and with the regression more generally? (Y/N) A homeowner purchases 1936 square feet from and adjacent lot. Construct a 95% confidence interval for the change in the value of her house. 3. Lot size is measured in square feet. Do you think that measuring lot size in thousands of square feet might be more appropriate? 4. The F-statistic from the joint test of BDR and Age is F = 0.14. Are the coefficients on BDR and Age statistically different from zero at the 10% level?
1. No 2.Yes 3.Yes, because small differences in square footage between two houses is not likely to have a significant effect on differences in house prices. 4. No PT Q14
The index of industrial production (IPt) is a monthly time series that measures the quantity of industrial commodities produced in a given month. Using the data on this index for the United States over the sample period 1986:M1 to 2013:M12 (that is, January 1986 through December 2013), a researcher tests for a stochastic trend in ln(IPt) using the following regression: where the standard errors shown in parentheses are computed using the homoskedasticity-only formula and the regressor t is a linear time trend. Calculate the ADF statistic to test for a stochastic trend (unit root) in ln(IP). 1.Does the ADF test reject the null hypothesis that ln(IP) contains a stochastic trend (unit root) at a 10% significance level? 2. Do these ADF test results support an AR(4) specification to forecast the monthly percentage change in IPt?
1. No, since the computed ADF is less negative than the critical value of −3.12. 2. Yes, the use of first differences eliminates a random walk trend in ln(IP). HW15 Q9
8. This problem is inspired by a study of the "gender gap" in earnings in top corporate jobs [Bertrand and Hallock (2001)]. The study compares total compensation among top executives in a large set of U.S. public corporations in the 1990s. (Each year these publicly traded corporations must report total compensation levels for their top five executives.) Let Female be an indicator variable that is equal to 1 for females and 0 for males. A regression of the logarithm of earnings onto Female yields Calculate the average hourly earnings for top male and female executives. 1. Looking at the t-statistic, does this regression suggest that female top executives earn less than top male executives? 2.Does this imply that there is gender discrimination? Two new variables, the market value of the firm (a measure of firm size, in millions of dollars) and stock return (a measure of firm performance, in percentage points), are added to the regression: If MarketValue increases by 4.22%, what is the increase in earnings? 3. The coefficient on Female is now − 0.28. Why has it changed from the first regression?
1. Yes 2. No 3.All of the above. HW8 Q8
Refer to the table of estimated regressions below, computed using data for 1999 from all 420 K-6 and K-8 districts in California, to answer the following question. The variable of interest, test scores, is the average of the reading and math scores on the Stanford 9 Achievement Test, a standardized test administered to fifth-grade students. School characteristics (average across the district) include enrollment, number of teachers (measured as "full-time equivalents"), number of computers per classroom, and expenditure per student Results of Regressions of test scores on the Student-Teacher Ratio and Student Characteristic Control Variables Using California Elementary School Districts. Compute the R^2 for each of the regressions. Construct the homoskedasticity-only F-statistic for testing β3=β4=0 in the regression shown in column (5) 1. Is the homoskedasticity-only F-statistic significant at the 5% level? (Y/N) Test β3=β4=0 in the regression shown in column (5) using the Bonferroni test. Note that the 1% Bonferroni critical value is 2.807. 2) Is the Bonferroni test significant at the 1% level?
1. Yes 2. No PT Q15
The data set consists of information on 4700 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let Using the regression results in column (2): 1. Is age an important determinant of earnings? Sally is a 32-year-old female college graduate. Betsy is a 35-year-old female college graduate. Predict Sally's and Betsy's earnings.
1. Yes, because wages are not consistent across different age groups. PT Q3
The data set consists of information on 4400 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using Data from the Current Population Survey 1. Do there appear to be important regional differences? 2. Why is the regressor West omitted from the regression? What would happen if it was included?
1. Yes, because wages are not consistent across the region. 2.The regressor West is omitted to avoid perfect multicollinearity. If West is included, then the OLS estimator cannot be computed in this situation. PT Q9
Suppose that ΔYt follows the AR(1) model ΔYt=β0+β1ΔYt−1+ut The model for Yt can be written as: 1. If ΔYt follows the AR(1) model ΔYt=β0+β1ΔYt−1+ut
1. an AR (2) model. PT Q27
A researcher carries out a QLR test using 25% trimming, and there are q = 5 restrictions. Answer the following questions using the values in Table 14.5 ("Critical Values of the QLR Statistic with 15% Trimming")
1. should reject 2. should not reject 3. should be uncertain about HW15 Q10
Look at the plot below of the logarithm of the index of industrial production for Japan. 1. Does this time series appear to be stationary? Explain. 2. Suppose that you calculated the first difference of this series. Would it appear to be stationary?
1.Both (a) and (c) are true. a)It does not appear stationary because the series has an upward trend. c)It does not appear stationary. Observations at the end of the sample are somewhat larger than observations at the beginning, implying that the mean of the series is not constant. 2. The first difference of the series is nonstationary because the slope of the original plot, which is the level of the first difference series, is steeper at the beginning than at the end. HW15 Q5
Consider the following multiple regression model 1.Which of the following describes how to test the null hypotheses that either B1 = 0 or B2 = 0? 2.Suppose you want to test the null hypothesis that two separate tests B1 = 0 and B2 = 0. Is the result of the joint test implied by the result of the two separate tests?
1.Compute the standard errors, the correlation between 1 and 2, the F-statistic, and the p-value associated with the F-statistic. Reject the null hypothesis if the p-value is less than some relevant significance level. 2.No HW7 Q5
1. Suppose you run a regression of test scores against parking lot area per pupil. Is the R^2 likely to be high or low? 2. Are the OLS estimators likely to be biased and inconsistent
1.High, because parking lot area is correlated with student teacher ratio, with whether the school is in a suburb or a city, and possibly with district income. 2.The OLS estimators are likely biased and inconsistent because there are omitted variables correlated with parking lot area per pupil that also explain test scores, such as ability. HW 7 Q7
Consider the following multiple regression The numbers in parentheses below each estimated coefficient are the estimated standard errors. A detailed description of 1 the variables used in the data set is available here . Suppose you wanted to test the hypothesis that BDR equals zero. That is, Report the t-statistic for this test. 1. Is the coefficient on BDR statistically different from zero at the 5% significance level? 2.Typically five-bedroom houses sell for much more than two-bedroom houses. Is this consistent with your previous answer and with the regression more generally? 3.A homeowner purchases 1539 square feet from and adjacent lot. Construct a 95% confidence interval for the change in the value of her house. 4.Lot size is measured in square feet. Do you think that measuring lot size in thousands of square feet might be more appropriate? 5.The F-statistic from the joint test of BDR and Age is F = 0.14. Are the coefficients on BDR and Age statistically different from zero at the 10% level?
1.No 2. Yes 4.Yes, because small differences in square footage between two houses is not likely to have a significant effect on differences in house prices. 5.No HW 7 Q4
An independent researcher is interested in finding out whether there exists a positive relationship between the number of years of formal education received by an individual and the number of years of formal education received by each of his parents. It is assumed that the number of years of formal education received by one parent of an individual is positively correlated with that of the other parent. The researcher randomly selects 130 individuals and estimates the following regression function: Since the researcher only incorporates the educational attainment of an individual's father in the regression, and not that of the individual's mother, omitted variable bias will occur. 1.Which of the following statements correctly describes the omitted variable bias? 2.As the sample size increases, the value to which the slope estimator will converge to with high probability is 3.In this case, the direction of the omitted variable bias is Assume a father's weight is correlated with his years of eduction, but is not a determinant of the child's years of formal education. 4. Which of the following statements describes the consequences of omitting the father's weight from the above regression?
1.Omitted variable bias arises when the omitted variable is correlated with a regressor and is a determinant of the dependent variable. 3. Positive 4.It will not result in omitted variable bias because the omitted variable, weight, is not a determinant of the dependent variable. PT Q1
Read the box "The Return to Education and the Gender Gap ." The sample size is 52,970 observations for each regression. Female is an indicator variable that equals 1 for women and 0 for men. Midwest, South, and West are indicator variables denoting the region of the United States in which the worker lives: For example, Midwest equals 1 if the worker lives in the Midwest and equals 0 otherwise (the omitted region is Northeast). Standard errors are reported in parentheses below the estimated coefficients. Individual coefficients are statistically significant at the *5% or **1% significance level. Scenario A Consider a man with 15 years of education and 4 years of experience who is from a western state. Use the results from column (4) of the table and the method in Key Concept 8.12 to estimate the expected change in the logarithm of average hourly earnings (AHE) associated with an additional year of experience. Scenario B Consider a man with 15 years of education and 12 years of experience who is from a western state. Use the results from column (4) of the table and the method in Key Concept 8.13 to estimate the expected change in the logarithm of average hourly earnings (AHE) associated with an additional year of experience. The expected change in the logarithm of average hourly earnings (AHE) associated with an additional year of experience is 0.85 %. (Round your response to two decimal places.) 1.Why are the answers to Scenario A and Scenario B different? 2.How would you change the regression if you suspected that the effect of experience on earnings was different for men than for women?
1.The regression is nonlinear in experience. 2.Include interaction terms Female X Potential Experience and Female x (Potential Experience)^2 HW8 Q7
Suppose the researcher realises that she may have missed an important variable while processing the data. She now estimates the following regression equation: where CCTV denotes the number of CCTV cameras installed in the district. With the revised estimates, the expected change in the cost to the state due to the increase in the number of inmates would be $ 1.The initial regression model suffered from
1.omitted variable bias PT Q6
Suppose that ΔYtfollows the AR(1) model ΔYt=β0+β1ΔYt−1+ut The model for Yt can be written as: 2.If ΔYt follows the AR(1) model ΔYt=β0+β1ΔYt−1+ut, Yt follows:
2. an AR (2) model. HW15 Q2
The critical value of F4,infinity at the 5% significance level is:
2.37 Quiz 7 Q4
Assume that you had estimated the following quadratic regression model: If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores would be:
2.96 HW 8 Q2
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: The homoskedasticity-only "overall" regression F-statistic for the hypothesis that the regression R^2 is zero is approximately:
22.56 Quiz 7 Q1
A "Cobb-Douglas" production function relates production (Q) to factors of production, capital (K), labor (L), raw materials (M), and an error term u using the equation Suppose that you have data on production and the factors of production from a random sample of firms with the same Cobb-Douglas production function. Which of the following regression functions provides the most useful transformation to estimate the model?
A logarithmic regression function. HW8 Q6
Which of the following variables are likely useful to add to the regression to control for important omitted variables? (Check all that apply)
A. The average income per capita of the county. B. The fraction of young males in the county population D. The average level of education in the county. HW 6 Question 1
In the model the elasticity of E(Y\X) with respect to X is:
B1X Quiz 8 Q4
The data set consists of information on 4800 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let
HW 6 Question 4
Suppose that crime rate is positively affected by the fraction of young males in the population, and that counties with high crime rates tend to hire more police. Use the following expression for omitted variable bias to determine whether the regression will likely over or underestimate the effect of police on the crime rate.
HW 6 Q1
Sally is a 29-year-old female college graduate. Betsy is a 42-year-old female college graduate. Predict Sally's and Betsy's earnings.
HW 6 Q3
The data set consists of information on 3500 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let
HW 6 Q3
Juanita is a 25-year-old female college graduate from the South. Jennifer is a 25-year-old female college graduate from the Midwest. Calculate the expected difference in earnings between Juanita and Jennifer.
HW 6 Q8
A multiple regression includes two regressors: Use the tool palette to the right to answer the following questions. What is the expected change in Y if X1 increases by 5 units and X2 is unchanged?
HW 6 Q9
The data set consists of information on 4300 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let
HW 7 Q1
Sales in a company are $186 million in 2009 and increase $200 million in 2010. Compute the percentage increase in sales using the usual formula Compare this value to the approximation Now, assume that sales in a company are $186 million in 2009 and increase $262 million in 2010.
HW 8 Q4
Suppose that Yt follows the stationary AR(1) model Yt=2.4+0.7Yt−1+ut, where ut is i.i.d.with Eut=0 and varut=9. Compute the first two autocovariances of Yt Compute the first two autocorrelations of Yt.
HW15 Q4
Consider the AR(1) model Yt=β0+β1Yt−1+ut. Suppose that the process is stationary. Which of the following statements must be true? Which of the following statements is the correct expression for E(Yt)?
HW15 Q6
The Akaike Information Criterion (AIC) is given by the following formula:
HW15 Q8
The adjusted R^2 , or R , is given by
HW6 Q 6
The data set consists of information on 4400 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let
HW6 Q8
Sally is a 30-year-old female college graduate. Betsy is a 39-year-old female college graduate. Construct a confidence interval of 99% for the expected difference between their earnings.
HW7 Q1
Consider a regression with two variables, in which X1i is the variable of interest and X2i is the control variable. Conditional mean independence requires:
HW7 Q6
A standard "money demand" function used by macroeconomists has the form Where m is the quantity of (real) money, GDP is the value of (real) gross domestic product, and R is the value of the nominal interest rate measured in percent per year. Supposed that 1 = 1.96 and 2 = − 0.05. What is the expected change in m if GDP increases by 8%? What is the expected change in m if the interest rate increases from 3% to 9%?
HW8 Q3
Consider the following regression function to answer the questions below. *graph* Which of the following specifies a nonlinear regression that model this shape?
HW8 Q5
The data set consists of information on 3900 full-time full-year workers. The highest educational achievement for each worker was either a high school diploma or a bachelor's degree. The worker's ages ranged from 25 to 45 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. For the purposes of these exercises, let Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using Data from the Current Population Survey Is the college-high school earnings difference estimated from this regression statistically significant at the 10% level? Construct a confidence interval of 90% for the college-high school earnings difference. Is the male-female earnings difference estimated from this regression statistically significant at the 10% level?
PT Q10
A medical student at a community college in city Q wants to study the factors affecting the systolic blood pressure of a person (Y). Generally, the systolic blood pressure depends on the BMI of a person (B) and the age of the person A. She wants to test whether or not the BMI has a significant effect on the systolic blood pressure, keeping the age of the person constant. For her study, she collects a random sample of 175 patients from the city and estimates the following regression function: Keeping BMI constant, she now wants to test whether the age of a person (A) has no significant effect or a positive effect on the person's systolic blood pressure. At the 5% significance level, the student will
PT Q11
An independent researcher wants to investigate if the factors which determine the house rent (Y, measured in dollars), such as the distance of the house from the airport (X1), the time since the house was built (X2), are significant or not. He collects data from 120 prospective locations and estimates the following regression equation: The 95% confidence interval for the slope coefficient β1, keeping the other variables constant will be Based on the calculated confidence intervals, we can say that at the 5% significance level, we will The 99% confidence interval for the slope coefficient β2, keeping the other variables constant will be Based on the calculated confidence intervals, we can say that at the 1% significance level, we will
PT Q12
A researcher is interested in finding out the factors which determined the yearly spending on family outings last year (Y, measured in dollars). She compiles data on the number of members in a family (X1), the annual income of the family (X2), and the number of times the family went out on an outing in the last year (X3). She collects data from 152 families and estimates the following regression: The researcher wants to check if neither X1 nor X2 have a significant effect on Y or at least one of them has a significant effect, keeping X3 constant. She calculates the value of the F-statistic for the test with the two restrictions The p-value for the test will be At the 10% significance level, we will
PT Q13
Assume that you had estimated the following quadratic regression model: If income increased from 10 to 11 ($10,000 to $11,000), then the predicted effect on test scores would be:
PT Q17
The researcher wants to test the hypothesis that the relationship between number of members in the house and the electricity consumption by households is linear, against the alternative that it is nonlinear. The test statistic associated with the test the researcher wants to conduct is
PT Q18
A market analyst is interested in estimating the relationship between the miles per gallon of fuel for motorcycles (Mileage, measured in mpg) and the age of that vehicle (Age, measured in years). She collects information on 300 motorcycles across the automobile industry and estimates the following regression equation: The standard errors are given in parentheses. She wants to find the effect on mileage of a change in age (ΔAge) of motorcycles. So, when the age of a motorcycle increases from 7 to 8 years, the decrease in total mileage will be We reject or fail to reject a hypothesis using the criterion does the hypothesized value fall in our 95% confidence interval. Based on the calculated confidence interval, we can say that at the 5% significance level, we will
PT Q19
A multiple regression includes two regressors: Use the tool palette to the right to answer the following questions. What is the expected change in Y if X1 increases by 10 units and X2 is unchanged?
PT Q2
A "Cobb-Douglas" production function relates production (Q) to factors of production, capital (K), labor (L), raw materials (M), and an error term u using the equation Suppose that you thought that the value of β2 was not constant, but rather increased when K increased. Which of the following regression functions captures this dynamic relationship?
PT Q20
A student wants to study the impact of the number of kilometers (K) run by a car on its resale price (P, measured in dollars). For her study, she selects a random sample of 100 second hand car sellers from her city and estimates the following regression equation: P=62.75−278.50ln(K) where P and K denote the predicted value of the resale price of the car and the number of kilometers run by that car, respectively. A researcher is interested in finding out the relationship between the price of house (H, measured in hundred dollars) and its distance from the highway (D, measured in kilometers) passing through her district. She estimates the following regression using 300 observations on prices of house and their corresponding distance from the highway: where ln(H)is the predicted value of the logarithm of house prices and Dis the value of the distance of the house from the highway. A survey was conducted to study the impact of per capita gross national product or GNP (X, measured in thousand dollars) on life expectancy at birth (Y). Data across 100 countries was collected and the following regression was estimated:
PT Q22
A study compares the total earnings of senior officials of 120 large corporations in the U.S. Let Female be an indicator variable that equals 1 for females and equals 0 for males, and let Age be an indicator variable that equals 1 if the age of the person is greater than 45 and equals 0 otherwise. The estimated regression equation is as follows: where Earnings denotes the yearly earnings of the officials (measured in thousand dollars). The predicted mean earnings of males below the age of 45 are If Sheila, a senior official at a global firm, turns 46 this year, her predicted mean earnings would
PT Q23
A researcher is interested in finding out how the past average daily values of the stock prices of a firm A determine the current average daily value of its stock price. Let pt (measured in dollars) denote the average daily value of the stock price of firm A at time t. The researcher collects data on the average daily values of the stock prices of the last quarter of 2017, i.e., t=1, 2,..., 90 and estimates the following autoregressive model with 1 lag of pt: The standard errors are given in parentheses. Suppose that the actual average daily value of the stock price on January 2, 2018 was $504.48 and the average daily value of the stock price on December31, 2017 was $445.12. The forecast error in the estimation of the average daily value of the stock price on January 2, 2018 will be Suppose that the researcher wants to check the causal effect of pt−1 on the current average daily value of the stock price, pt. Let β1 denote the population slope coefficient on pt−1. Suppose the researcher now estimates the following AR(2) model by adding a second lag of the average daily value of the stock price (pt−2): The standard errors are given in parentheses. Let β2 denote the population slope coefficient on pt−2.
PT Q29
Data were collected from a random sample of 280 home sales from a community in 2003. Let Price denote the selling price (in $1,000), BDR denote the number of bedrooms, Bath denote the number of bathrooms, Hsize denote the size of the house (in square feet), Lsize denote the lot size (in square feet), Age denote the age of the house (in years), and Poor denote a binary variable that is equal to 1 if the condition of the house is reported as "poor." Suppose that a homeowner converts part of an existing family room in her house into a new bathroom. What is the expected increase in the value of the house? Suppose that a homeowner adds a new bathroom to her house, which increases the size of the house by 105 square feet. What is the expected increase in the value of the house? What is the loss in value if a homeowner lets his house run down so that its condition becomes "poor"? Compute the R^2 for the regression.
PT Q4
Suppose the population multiple regression model is of the form: Suppose that a local law enforcement chief wants to decide whether or not to hire more law enforcement officers to patrol area X. For this, the chief wants to know about the current presence of law enforcement officers in area X and the reduction in the incidence of crime in that area. In the last 3 years, the total number of law enforcement officers hired for patrolling area X increased from 1,410 to 1,820. In the same span, the number of crime incidents recorded in area X decreased from 11,522 to 10,155. The relationship the chief wants to estimate is: where β0, βOfficers, and βUnemployed are the coefficients of the regression line, Officers denotes the number of law enforcement officers who were patrolling area X in the last 3 years, Unemployed denotes the number of people living in area X who were unemployed for more than 2 months within the last 3 years, and Uother is the error term which includes all other factors which could affect the number of reported crimes apart from the presence of law enforcement officers and the number of unemployed people. From the given information, the partial effect of changing the number of law enforcement officers on the number of reported crimes, βOfficers, holding the number of unemployed individuals fixed, is
PT Q5
Refer to the table of estimated regressions below, computed using data for 1998 from the CPS, to answer the following question. The data set consists of information on 4000 full-time full-year workers. The highest educational achievement of each worker was either a high school diploma or a bachelor's degree. The worker's age ranged from 25 to 34 years. The data set also contained information on the region of the country where the person lived, marital status, and number of children. A detailed description of the variables used in the data set is available here Results of Regressions of Average Hourly Earnings on Gender and Education Binary Variables and Other Characteristics Using 1998 Data from the Curren Population Survey.
PT Q7
The Bayes-Schwarz information criterion (BIC) is given by the following formula:
Quiz 15 Q2
The following OLS assumption is most likely violated by omitted variables bias:
Quiz 6 Q4
Consider the polynomial regression model of degree According to the null hypothesis that the regression is linear and the alternative that is a polynomial of degree r corresponds to:
Quiz 8 Q1
The formulas for the AIC and the BIC are different.
The BIC is preferred because it is a consistent estimator of the lag length. Quiz 15 Q1
Why is the regressor West omitted from the regression? What would happen if it was included?
The regressor West is omitted to avoid perfect multicollinearity. If West is included, then the OLS estimator cannot be computed in this situation. HW6 Q8
A researcher plans to study the causal effect of police crime using data from a random sample of U.S. counties. He plans to regress the county's crime rate on the (per capita) size of the country's police force. Why is this regression likely to suffer from omitted variable bias?
There are other important determinants of a country's crime rate, including demographic characteristics of the population, that if left out of the regression would bias the estimated partial effect of the (per capita) size of the county's police force. HW 6 Question 1
Does this imply that age is an important determinant of earnings?
Yes, age is an important determinant of earnings because the low p-value implies that the coefficient on age is statistically significant at the 1% level. HW7 Q1
Is age an important determinant of earnings?
Yes, because wages are not consistent across different age groups. HW 6 Q3
Do there appear to be important regional differences?
Yes, because wages are not consistent across the region. HW6 Q8
A researcher estimates an AR(1) with an intercept and finds that the OLS estimate of β1 is 0.95, with a standard error of 0.02. Does a 95% confidence interval include β1=1?
Yes, since the value of the t-statistic for the null hypothesis β1=1 is −2.50 and the 5% critical value of the augmented Dickey-Fuller statistic is −2.86, the null hypothesis is not rejected. Thus β1=1 is in the 95% confidence interval. HW15 Q1
The interpretation of the slope coefficient in the model ln Yi = B0 + B1ln Xi + (mean)i is as follows:
a 1% change in X is associated with a B1% change in Y. HW8 Q1
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 A. H0: r=0vs.H1: r≠0.B. H0: 1=0vs.H1: 1≠0.C. H0 : 2=0, 3=0,..., r=0vs.H1 :atleastone j≠0,j=2,...,r. D. H0 : 2=0, 3=0,..., r=0vs.H1 :all j≠0,j=2,...,r. person is female), and the product of the two binary variables The interaction term:
allows the population effect on log earnings of being married to depend on gender. Quiz 8 Q3
Under the least squares assumptions for the multiple regression problem (zero conditional mean for the error term, all Xi and Yi being i.i.d., all Xi and i having finite fourth moments, no perfect multicollinearity), the OLS estimators for the slopes and intercept:
are unbiased and consistent. HW 6 Q10
The interpretation of the slope coefficient in the model lnYi=β0+β1lnXi+μi is as follows:
a 1% change in X is associated with a β1% change in Y. PT Q16
In the multiple regression model, the t-statistic for testing that the slope is significantly different from zero is calculated:
by dividing the estimate by its standard error. Quiz 7 Q5
If you had a two-regressor regression model, then omitting one variable that is relevant:
can result in a negative value for the coefficient of the included variable, even though the coefficient will have a significant positive effect on Y if the omitted variable were included. Quiz 6 Q1
The homoskedasticity-only F-statistic and the heteroskedasticity-robust F-statistic typically are:
different Quiz 7 Q3
When there are two coefficients, the resulting confidence sets are:
ellipses Quiz 7 Q2
Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. When omitting X2 from the regression, there will be omitted variable bias for B1:
if X1 and X2 are correlated. Quiz 6 Q3
Imperfect multicollinearity:
implies that it will be difficult to estimate precisely one or more of the partial effects using the data at hand. Quiz 6 Q5
A nonlinear function:
is a function with a slope that is not constant. Quiz 8 Q5
Imperfect multicollinearity:
means that two or more of the regressors are highly correlated. Quiz 6 Q2
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 1 changes by a large amount. This suggests that your first regression suffers from:
omitted variable bias. HW 6 Q2
The best way to interpret polynomial regressions is to:
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. PT Q21
The best way to interpret polynomial regressions is to:
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. Quiz 8 Q2
The AR(p) model:
represents Yt as a linear function of p of its lagged values. HW15 Q3
The AR(p) model:
represents Yt as a linear function of p of its lagged values. PT Q28
If you wanted to test, using a 5% significance level, whether or not a specific slope coefficient is equal to one, then you should:
subtract 1 from the estimated coefficient, divide the difference by the standard error, and check if the resulting ratio is larger than 1.96. HW7 Q2
One reason for computing the logarithms (ln) or the changes in the logarithms of economic time series is that:
they often exhibit growth that is approximately exponential. PT Q24
One reason for computing the logarithms (ln) or the changes in the logarithms of economic time series is that:
they often exhibit growth that is approximately exponential. Quiz 15 Q3
When testing a joint hypothesis, you should:
use the F-statistics and reject at least one of the hypotheses if the statistic exceeds the critical value. HW7 Q3
The AIC is a statistic:
used to help a researcher choose the number of lags in a time series with multiple predictors. HW15 Q7
The BIC is a statistic:
used to help the researcher choose the number of lags in an autoregression. Quiz 15 Q4
The Granger causality test:
uses the F-statistic to test the hypothesis that certain regressors have no predictive content for the dependent variable beyond that contained in the other regressors. Quiz 15 Q5
In the multiple regression model, the adjusted R , R :
will never be greater than the regression R^2 . HW 6 Q5
