Consumption Theory

Which of the following confidence intervals is associated with the highest level of confidence?

(0,1)

In a regression with a very large sample (ie one can use the Z table as opposed to the t table) the estimated slope is 0.1 and the standard error is 0.03. Which of the following is the 95% confidence interval for the true regression slope?

(0.1-1.96(0.03),0.1+1.96(0.03))

In a sample it is found that x and y have sample means that are zero. This implies that the intercept is equal to what?

0

Which of the following is the p-value associated with an F statistic equal to 4 where we are testing 3 restrictions the sample size is n=100 and the number of regressors in the unrestricted model is k=6?

0.0223

I add an irrelevant variable x2 to a regression model that also includes the variable x1. The correlation between x2 and x1 equals 0.5. The variance of the coefficient of x1 in the simple regression of y on x1 was 0.2. What will be the variance of the coefficient of x1 in the multiple regression?

0.2/0.75

We are given a coin and we know that either it is fair (ie probability of heads is 0.5) or unfair (probability of heads is 0.6). The null hypothesis is that the coin is fair and the alternative hypothesis is that it is unfair. The decision rule is to reject the null if we flip the coin and we get heads. What is the probability of a Type II error?

0.4

In a regression of y on x1 the slope is 0.5. In a regression of y on x1 and x2 the respective slopes are 0 and 1 respectively. Which of the following gives the slope in the regression of x2 on x1.

0.5

We are given a coin and we know that either it is fair (ie probability of heads is 0.5) or unfair (probability of heads is 0.6). The null hypothesis is that the coin is fair and the alternative hypothesis is that it is unfair. The decision rule is to reject the null if we flip the coin and we get heads. What is the probability of a Type I error?

0.5

The estimated regression of log wage on education has an intercept of 0.6 and a slope of 0.083. Which of the following gives the predicted value for the log wage for someone who has 12 years of education?

0.6+0.083(12)

Using house price data (n=88) a regressed the price on the assessed value. If the assessed value is an unbiased predictor then one would expect an intercept of 0 and a slope on assess equal to 1. The estimated slope coefficient is 0.976 with a standard error of 0.049. Which of the following is the p-values for a test that the slope is 1 against a two sided alternative that is not equal to 1 (rounded to 4th decimal place)?

0.9274

In wage data the correlations between lwage and the three variables education, experience and job tenure (all measured in years) are respectively 0.4, 0.1 and 0.3. Which regression will have the highest R squared.

1) Regression of lwage on job tenure 2) Regression of lwatge on education 3) Regression of lwage on experience R squared is the square of the correlation so the pair that have the highest correlation will also have the highest R squared in a regression involving the two variables. Answer: Regression of lwage on education

What critical value should I use if I am doing a one sided test with 25 degrees of freedom and a significance level (alpha) equal to 0.1?

1.316

In a regression of y on x1 and x2 with 103 observations I find that the SSR is equal to 100. The total variation in x1 is 10 and the correlation between x1 and x2 is 0.1. Which calculation will give the estimated variance of the coefficient on x1?

1/9.9

Suppose instead of regressing y on x I instead regress 100y on 10x. How would the new slope look compared to the slope in the regression of y on x.

10 times the original

In a house price regression of sale price (in thousand of dollars) of houses on the characteristics bdrms (number of bedrooms) lotsize (size of the lot on which house is located) and sqrft (size of house in square feet) the slopes are respectively 13.85, 0.002 and 0.122. Which of the following provides the appropriate estimated partial effect on house price (holding bdrms and lotsize fixed) of increasing sqrft by 100 units?

100*0.122 thousand dollars

A fitted regression line is given by log(wage)^=0.3+0.09educ+0.002exper+0.04tenure. The effect of increasing experience by 2 years with the same firm is given by which calculation.

2*(0.002+0.04)

The fitted regression of log wage on education, experience and the square of experience is as follows: log(wage)=0.13+0.09educ+0.04exper−0.0007expersq. Which of the following is the return to experience at experience = 10 years?

2.6%

For a regression with k=5 and n-k-1=100 the R squared equals 0.5. Which of the following gives the F statistic for the overall goodness of fit of the regression?

20

For a data set consisting of high schools I have measures of percentage of students who passed a standardized math test, math10 and percentage of students who qualify for a free lunch at the school lnchprg. The fitted regression is: math10^=32−0.3lnchprg and the R squared is 0.17. What is the effect of a 10 percentage point increase (as opposed to 10 percent increase) in lnchprg on math10.

3 percentage point decrease Note the difference between percentage point increase and percent increase. A 10 percentage point increase would be going from 30% to 40% whereas a 10 percent increase at 30 would be increasing from 30% to 33% since 10% of 30 is 3.

An estimated regression coefficient is equal to 0.5. What is the confidence level associated with the one sided interval (0.5,∞) ?

50%

Consider the regression of log wage on a dummy for being female, education and the interaction between female and education: logwage=1.5+0.1educ−0.23female−0.002female∗educ Which of the following gives the return to education for females?

9.8%

In the regression of math10 on the log of expenditure per student lexpend I get a slope of 11. Which of the following is a correct interpretation?

A 1% increase in expenditure is predicted to increase math10 by 0.11 units (percentage points)

Consider the following regressions of individual labor market earnings in 1998 on whether or not that individual received job market training in 1997 (train = 1 if they received training train =0 if they did not): earn98^=10−2.0train Suppose I also include earnings from 1996 as an additional control: earn98^=4+2.5train+0.4earn96 Based on these regressions which of the following statements is correct?

An individual was more likely to receive training if they had low earnings in 1996

In a fitted regression none of the slopes equals 0 exactly. It is still possible for the R squared to be exactly 0.

False

In a regression of wage on experience and the square of experience the coefficient on experience gives me the partial effect of experience holding fixed experience squared.

False

In the MLRM if Assumption MLRM5 is not satisfied then the residuals will be heteroskedastic. This will result in the coefficients being biased.

False

From the regression in the previous question one can plausibly conclude that participating in the lunch program causes students to do worse in the math test? True

False The ZCM is questionable here as schools with higher participation in the lunch program have more student from poor families with less resources to help their students academically and we have omitted this factor so it is in the residual.

Since the fitted residuals are perfectly uncorrelated with the regressor then the ZCM assumptions is satisfied?

False ZCM is about the residual - not the fitted residual. The algebraic result holds regardless of the relationship between the residual and the regressor.

In a simple regression of y on x including an intercept (ie not restricted to being zero) it is possible for all residuals to be strictly negative

False, residuals average to 0 so they cannot be negative.

In the population regression of y on x1 and x2 the population slope coefficient on x2 is positive. If I omit x2 and just regress y on x1 then the slope coefficient on x1 will:

Have a negative bias if x1 and x2 are negatively correlated

Assume that education and ability are positively correlated and that ability has a positive effect on log wage if I also control for education. If I do not have a measure of ability and just regress log wage on education then which of the following statements is correct.

I would expect on average to get an coefficient on education that is larger than if I could control for ability

Using the same regression as the previous question suppose I wanted to test the hypothesis that the effect of spending by candidates has equal but opposite (or off setting) effects on voteA. It is known that the covariance between the coefficients lexpendA and lexpendB is -0.0027. Variable Coef. Std. Err. lexpendA 6.1 0.38 lexpendB - 6.6 0.38 prtystr 0.15 0.062 _cons 45.08 3.92 Which of the following is correct concerning the test of this hypothesis? I would reject the null at 10% but not at 5% I would reject the null at 5% but not 1%. I would not reject the null hypothesis at the 10% level.

I would not reject the null hypothesis at the 10% level.

Suppose the value a is inside the 90% confidence interval for a coefficient in an estimated regression. Suppose one were to test the hypothesis that the coefficient is equal to a against the two sided alternative that it is not equal to a. Which of the following is a correct statement?

I would not reject the null hypothesis at the 5% level of significance

The p-value for a test for a specific hypothesis concerning a slope coefficient is 0.08. Which of the following statements is correct?

I would reject the null at the 10% level but not the 5% level.

Suppose a hypothesized slope value is not contained in the 95% confidence interval. If one were test the hypothesis at the 10% level which of the following statements are correct?

I would reject the null hypothesis

Which of the following will not result in a lower variance for the coefficient on x1 in a regression of y on x1 and x2?

Increasing the correlation between x1 and x2

Suppose instead of using log of wage in dollars I instead used the log of wage in cents (ie wagecents = 100 * wage). Which of the following describes what will happen to the slope and intercept? (Hint log(c*x)=log(c)+log(x) )

Intercept changes slope is unaffected

In a simple regression of y on x suppose both variables are measured with error that is mean zero and uncorrelated with the variables that were measured with error. Which statement is correct concerning the slope coefficient in the the simple regression?

It will be biased towards 0.

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. What can we say about the coefficient on x1 in the multiple regression?

It will be exactly the same as b1

If I add a measure of individual's IQ to a regression of lwage on educ what is the most plausible effect on the coefficient on educ? ie How does the slope on educ in the MLRM with educ and IQ compare to the slope in the SLRM with just educ?

It will decrease

Suppose people can have one of 3 political affiliations: Labor, Liberal and Independent. In a regression of wage on political affiliation I get: wage=6.0−1.0Labor+1.2Liberal Which of the following is not a correct statement concerning the implications of this regression?

Liberals earn 1.2 more than Labor

Which of the following variables cannot have a normal distribution?

Number of cigarettes smoked during pregnancy

Which of the following are not a consequence of heteroskedasticity?

OLS is biased and inconsistent

In a regression of lwage (log wage) on tenure (job tenure) the slope is 0.02. Which of the following is a correct interpretation?

One additional year of job tenure is predicted to increase the wage by 2%

In a regression of y on x it is found that the SSE is 3700 while the SSR is 6300. What will be the R squared for this regression.

R Squared = SSE/SST SST = SSE + SSR

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. What is the relationship between the R squared in SLRM and R squared in MLRM?

R squared for MLRM will be same as for SLRM

In the MLRM (with at least 2 regressors) which of the following is not necessarily true?

R squared will be the square of the correlation between y and the regressors

Note that the 5% critical value for the t distribution with df larger than 120 is between 1.658 and 1.645. The t statistic on experience 2.4 in the regression (with n=526) of lwage on education, experience and tenure. Therefore if I was doing a 5% level test of the null hypothesis that the coefficient on experience is zero vs the alternative that the coefficient is positive what would be my decision?

Reject the null hypothesis

If MLRM.5 is satisfied which of the following statements will be correct?

Robust standard errors will be different from the usual default standard errors but they will be similar in large samples

Compare the SLRM with y on x1 only with the MLRM that regresses y on x1 and x2. If x1 and x2 have zero correlation then what can we say about the relationship between the standard error on the coefficient of x1 in the SLRM as compared to the standard error on the coefficient on x1 in the MLRM?

Standard errors will be smaller for the model that has the lower estimated residual variance

If I add a variable to a regression which of the following statements is NOT correct concerning the R squared in the new regression compared to the original regression without that variable?

The R squared will be smaller after I add the regressor

Instead of regressing y on x suppose we do the reverse regression of x on y. In the reverse regression the slope coefficient will have what relationship to the slope in the original regression?

The original slope is Cov(x,y)} / Var{x} which has a different denominator than the reverse regression Cov(x,y)/ Var(y) So they will generally be different but have the same sign.

If I run a regression of voteA (percentage of votes received by candidate A) on lexpendA (log expenditure of candidate A) ;expendB (log of expenditure on candidate B) and prtystr (percentage of the most recent presidential election that went to A's party) I get the following results in table form: Variable CoefStd. Err. lexpendA 6.1 0.38 expendB - 6.6 0.38 prtystrA 0.15 0.062 _cons 45.08 3.92 The sample size is 173. Which of the following statements is incorrect regarding the slope coefficients?

The slopes are all statistically significant at the 1% level

Consider regression on a constant'': y=β0+u The OLS estimator is simply the sample average of the y's in the sample β0^=1n(y1+y2+y3+.....+yn) Consider an alternative estimator which is obtained as a weighted average of the y's with weights that add up to 1 but which are not necessarily the same: β0~=w1y1+w2y2+.....+wnyn Which statement is correct concerning these estimators assuming the the five assumptions MLRM1-5 are satisfied (here MLRM3 is not needed and MLRM4 is just E(u)=0)?

The variance of OLS is no larger than the variance of the weighted estimator

In a regression of sleep hours on total work hours, education and age it is found that the R squared is equal to 0.113. When I drop education and age the R squared is 0.103. The sample size is 706. What do I conclude concerning the joint significance of education and age?

They are jointly significant at 5%

Suppose I start with the simple regression of y on x1 where the slope is given by b1. I add an additional variable x2 to the regression and find that in the multiple regression the slope cofficient on x2 is exactly zero. This implies that the fitted values in SLRM and MLRM will be exactly the same?

True

The students in my ECO441K classes can be considered a random sample from the population of students at UT

True or False Answer: False

Suppose that x and u are statistically independent and E(u)=0. Does this imply that the ZCM assumption is satisfied?

True, since x and u are independent then E(u|x) = E(u) = 0 so ZCM is true.

The p-value for a t test of a null hypothesis against a two sided alternative is 0.00010578. The degrees of freedom are 45. Which of the following is correct concerning the possible values for the t statistic?

We need more information to determine the value of the t statistic.

Prof Donald creates a data set consisting of the demographic and grades of an ECO441K class from Fall 2019. What type of data is this?

a ) Pooled Cross-Sections b ) Panel Data c )Time Series d ) Cross-section (Correct)

For a cross section of observation units a sample of 30 observations reveals that a variable x has a sample variance of 4, y has a sample variance of 1 and the variables x and y have a sample covariance of 0.5. The correlation between x and y must be equal to what?

a) 0 b) 0.125 c)0.25 (Correct) d)0.5 Explanation: Mary Vu is mid and r is found by dividing sample covariance (0.5) by the square root of x sample variance (4) times the square root of y sample variance (1) 0.5 / squareroot(4) * squareroot(1)

A data set is constructed containing daily Covid cases and deaths for every country in the world for which data is available. The data contains daily case and death totals from March 1 until August 31. What type of data is this?

a) Pooled Cross-Section b) Time Series Data c) Cross-Section Data d) Panel Data (Correct)

Which of the following would (generally) not lead to a reduction of the variance of the slope coefficient?

dropping half the sample

In regression of log wage on education the intercept is 0.6 and the slope is 0.083. The residual variance is equal to 0.23. Which of the following gives the predicted value for the wage for someone with 12 years of education?

exp(0.23/2)exp(0.6+0.083(12))

Consider the following regression of sleep (minutes per week) on totwork (total work in minutes per week) education and age. The sample size is 706 Which of the following statements is incorrect regarding the coefficients and significance (against a two sided alternative)? Var. Coef. Std. Err. totwork 0.148 0.017 educ -11.13 5.88 age 2.2 1.45 -cons 3640 112.28

neither educ or age are significant at 10% level

In a regression of y on x it is found that the slope is equal to 0.5. This implies that the predicted change in y due to a 4 unit increase in x is equal to what value?

predicted change is coefficient b1 * change in x

Suppose people can have one of 3 political affiliations: Labor, Liberal and Independent. In a regression of wage on political affiliation I get: wage=6.0−1.0Labor+1.2Liberal Suppose I instead used the Independent dummy rather than the Labor dummy. Which of the following gives the new regression of wage on Independent and Liberal?

wage=5.0+1.0Independent+2.2Liberal

In a sample it is found that the averages for the 4 groups based on marital status and gender are in the table below. Which of the regressions would be valid if I regressed wage on a female indicator, a married indicator and an interaction between female and married? Gender Male Female Marital Status Single 5.17 4.61 Married 8.00 4 .56

wage=5.17-0.56female+2.83married-2.88female*married

The sample average y¯ is consistent for the population average μ. Which of the following is also a consistent estimator for μ?

y hat * (2n/n+1)