Econometrics

You estimate the following sample regression function: Daily Earnings_hat = 80 + 10*Years_of_Education Donald has 8 years of education and earns $140 a day. What is his sample residual? A. -$60 B. -$20 C. $20 D. $160

B. -$20 80 + 10 * 8 = 160 Donald earns $20 less than the model predicts.

You obtain the following sample regression function: GDP_hat = 5367 - 32*ForeignAid +76*ExportValue + 8*PercentHigherEducation What is the change in predicted GDP per capita associated with an increase of $26 per capita in foreign aid? Assume the current foreign aid is $70 per capita, the current value of exports is 90, and the current percent of individuals with higher education is 33 percent. A. 1820 B. -832 C. 10,231 D. -1976 E. None of the above.

B. -832 The predicted change in GDP is $26 * (-32, which is a coefficient on Foreign Aid) = -$832.

You estimate the following relationship between a house's price and its number of bedrooms: log price_hat = 12 + .3*bedrooms How would interpret the coefficient on bedrooms? A. Each additional bedroom is associated with a 0.3 percent increase in price. B. Each additional bedroom is associated with a 30 percent increase in price. C. Each additional bedroom is associated with a 30 percentage point increase in price. D.Need more information on the units of the price variable.

B. Each additional bedroom is associated with a 30 percent increase in price. When the outcome is a logarithm, coefficents have percent change interpretation.

You estimate the following relationship between household income and time spent working (in hours): log(income_hat) = 30,000 + 2*timespent How would interpret the coefficient on timespent? A. Each additional hour is associated with a 0.2 percent increase in income. B. Each additional hour is associated with a 20 percent increase in income. C. Each additional hour is associated with a 20 percentage point increase in income. D. Need more information on the units of the timespent variable.

B. Each additional hour is associated with a 20 percent increase in income.

Data reveal the following relationship between life expectancy (years) and gender, the number of days per week a person exercises, and the interaction of gender and exercise: LifeExpectancy = 75 - 5*male + 2*ExerciseDays + 3*MaleExerciseDays Each additional day of exercise per week is associated with life expectancy A. Increasing by 2 years for women and increasing 3 years for men. B. Increasing by 2 years for women and increasing 5 years for men. C. Increasing by 3 years for women and decreasing 5 years for men. D. Increasing by 3 years for women and increasing 3 years for men.

B. Increasing by 2 years for women and increasing 5 years for men. Because of the interaction term, the coefficient on ExerciseDays (2) represents the relationship for women and the interaction coefficient (3) represents the additional relationship for men.

You estimate the following quadratic sample regression function: Daily Earnings_hat = 450 + 50*Education - 2*Education^2 Assuming this relationship is causal, what do these estimates suggest about the marginal return to a year of education? A. It is increasing with education. B. It is decreasing with education. C. It is constant. D. None of the above.

B. It is decreasing with education. The negative coefficient on the quadratic term means the slope of the curve gets more negative as education levels increase (i.e. diminishing marginal returns).

In the handedness research that you read, I estimated this: ln(Earnings) = 10.2 - 0.1*LeftHanded Which of these statements about this regression is correct? A. Lefties earn 0.1 percent less than righties. B. Lefties earn 10 percent less than righties. C. Lefties earn 0.1 percentage points less than righties. D. Lefties earn 10 percentage points less than righties.

B. Lefties earn 10 percent less than righties. Coefficients from log-level regressions can be interpreted as 100*beta percent changes.

You want to know whether a new juice diet introduced this year helps people sleep well. You have observational data on sleep and eating habits and other personal characteristics. What regression has the greatest internal validity? A. Sleep = B0_hat + B1_hat*juicediet + u_hat B. Sleep = B0_hat + B1_hat*juicediet + B2_hat*sleeplastyear + u_hat C. Sleep = B0_hat + B1_hat*juicediet + B2_hat*lastdigitofphonenumber+ u_hat D. Juice Diet= B0_hat + B1_hat*sleeplastyear+ u_hat

B. Sleep = B0_hat + B1_hat*juicediet + B2_hat*sleeplastyear + u_hat

Which of the following is NOT true for a probit model?A. The outcome variable Y must be a dummy variable. B. The independent variable X must be a dummy variable. C. The probit results tell you whether the relationship between Y and X is statistically significant. D. The probit results tell you the sign of the relationship between Y and X

B. The independent variable X must be a dummy variable.

Some people claim that instrumental variable models may lack external validity. This would be the case when: A. The instrument is exogenous for only certain types of people B. The instrument is relevant for only certain types of people C. The instrument is relevant for everyone D. None of the above

B. The instrument is relevant for only certain types of people

Which of these is an advantage of probits over linear probability models? A. The coefficients are easier to interpret. B. You can only get predictions between 0 and 1. C. They give you causal evidence, not just associations. D. None of the above.

B. You can only get predictions between 0 and 1.

You would like to understand how political leanings affect whether or not people vote. You decide to specify a linear probability model. What criticism may people raise: A. You may get predicted probabilities that are greater than 0. B. You may get predicted probabilities that are greater than 1. C. It is hard to assess the magnitude of the relationship with a linear probability model. D. It is hard to assess the significance of the relationship with a linear probability model.

B. You may get predicted probabilities that are greater than 1.

A researcher estimates the following quadratic relationship between daily earnings (in dollars) and years of education: earnings_hat = 10 + 5*education + 1*education^2 What is the estimated change in earnings associated with moving from 6 to 8 years of education? A. $6 per day B. $12 per day C. $38 per day D. Need more information.

C. $38 per day

A researcher estimates the following quadratic relationship between daily earnings (in dollars) and years of education: earnings_hat = 36 + 8*education + 2*education^2 What is the estimated increase in earnings associated with moving from 9 to 10 years of education? A. $8 per day B. $10 per day C. $46 per day D. Need more information.

C. $46 per day Estimated earnings for 9 years of education = 36 + 8*(9) + 2*(9)^2 = 270 Estimated earnings for 10 years of education = 36 + 8*(10) + 2*(10)^2 = 316

You are very certain that providing families with subsidized housing improves children's outcomes. Which study should most change the mean and variance of your beliefs? A. A randomized trial showing that subsidized housing no impact on children. B. A randomized trial showing that subsidized housing improves children's outcomes. C. A randomized trial showing that subsidized housing hurts children's outcomes. D. An observational study showing that subsidized housing hurts children's outcomes.

C. A randomized trial showing that subsidized housing hurts children's outcomes. This study has high internal validity and is most at odds with your current beliefs.

Randomized experiments can be analyzed with bivariate regressions (of Y on the treatment X) because... A. Outcomes are not correlated with potential omitted variables. B. Assignment to treatment is not correlated with outcomes. C. Assignment to treatment is not correlated with potential omitted variables. D. The sample is representative of the population.

C. Assignment to treatment is not correlated with potential omitted variables. Adding further control variables should make little difference because random assignment guarantees such variables are not correlated with treatment.

You have a dataset of blood pressure and chocolate consumption for a sample of dogs and cats. Which model allows you to determine whether the association between chocolate consumption and blood pressure is different for dogs and for cats? A. bloodpressure_hat= B0_hat + B1_hat*cat + B2_hat*chocolate + B3_hat*dog*chocolate B. bloodpressure_hat= B0_hat + B1_hat*dog + B2_hat*chocolate + B3_hat*dog*chocolate C. Both A and B D. Neither A and B

C. Both A and B In both cases, the statistical significance of the interaction coefficient answers this question.

You have been asked to determine whether playing violent video games makes teenagers more likely to commit crimes. What is the theoretically correct counterfactual comparison to make? A. Compare the crime rates of teenagers who play video games with the crime rate of teenagers who do not play video games. B. Compare the video game playing habits of teenagers who commit crimes with teenagers who do not commit crimes. C. Compare the crime rate of teenagers who play video games with their own crime rate had they not played video games. D. Compare the video game playing habits of teenagers who commit crimes with their own video playing habits had they not committed crimes. E. None of the above.

C. Compare the crime rate of teenagers who play video games with their own crime rate had they not played video games. In the theoretically correct counterfactual, you would want to compare the outcome (crime rates) for the same person in the absence of the treatment (video games).

In a regression of quantity_sold on number_of_tv_ads, the coefficient on number_of_tv_adsis 1.3 and statistically insignificant. What can one learn from this information? A. It is unlikely that the true effect of the number_of_tv_ads is greater than zero. B. It is likely that the true effect of the number_of_tv_ads is greater than zero. C. It is likely that we'd see an effect this large, even if the true coefficient on the number_of_tv_ads is zero. D. An increase in predicted sales of 1.3 is not a large number when it comes to quantity_sold.

C. It is likely that we'd see an effect this large, even if the true coefficient on the number_of_tv_ads is zero.

A sibling fixed effects model shows the Head Start pre-school program improves children's high school graduation rates. Which of these is a valid argument that this might be an underestimate of the program's impacts on the population studied? A. Families who use Head Start care more about education than families who do not. B. Families who use Head Start are lower income than families who do not. C. Parents are more likely to use Head Start for a child with academic challenges. D. Parents are more likely to use Head Start for a child with academic strengths.

C. Parents are more likely to use Head Start for a child with academic challenges. That five percentage point impact might be even higher if the data could account for the fact that the Head Start sibling had lower academic skills to begin with.

An analyst proposes using how far a person lives from the nearest hospital (distance) as an instrument for the amount of time between first signs of a stroke and being treated (time). He shows you his first stage regression and the coefficient on the distance variable is not significant. Which IV assumption has the instrument failed? A. Endogeneity B. Exogeneity C. Relevance D. Magnitude

C. Relevance

A researcher, using a sample of lottery players, regresses life expectancy on a dummy variable for randomly winning a jackpot in the lottery. The researcher considers adding education as another explanatory variable. What is likely to be true? A. The coefficient on winning a jackpot will change because education affects life expectancy. B. The coefficient on winning a jackpot will not change because education does not affect life expectancy. C. The coefficient on winning a jackpot will not change because education and winning a jackpot are not correlated. D. The coefficient on winning a jackpot will not change because education and life expectancy are not correlated.

C. The coefficient on winning a jackpot will not change because education and winning a jackpot are not correlated.

You evaluate the effect of a micro-finance program on income by comparing areas that chose to receive the program to those that did not, both before and after the program was introduced. What do you need to determine to ensure that your comparison is valid: A. Income levels looked similar in the program and non-program areas in the pre-treatment period. B. Income levels looked similar in the program and non-program areas in the post-treatment period. C. The pre-period trend in income between the program and non-program is constant over time D. The post-period trend in income between the program and non-program areas is constant over time

C. The pre-period trend in income between the program and non-program is constant over time

In a randomized control trial, spillover effects between the treatment and control groups imply that the estimated impact of the treatment is... A. ... underestimated. B. ... overestimated. C. ... correctly estimated. D. Impossible to choose A, B or C with certainty.

D. Impossible to choose A, B or C with certainty. Spillovers make the control and treatment groups' outcomes more similar than they should be.

A researcher wants to know if the association between education and life expectancy varies by gender. Which is the simplest regression that can help answer this question? A. LifeExpectancy = B0 + B1*female + E B. LifeExpectancy = B0 + B1*educ+ E C. LifeExpectancy = B0 + B1*female + B2*Educ + E D. LifeExpectancy = B0 + B1*female + B2*Educ + B3*female*educ + E

D. LifeExpectancy = B0 + B1*female + B2*Educ + B3*female*educ + E The interaction coefficient (B3) measures the difference in the association of life expectancy and education between females and males. The female coefficient (B1) just measures the difference in average life expectancy between males and females (conditional on education).

A researcher wants to know if the association between phone usage and price per minute varies by gender. Which is the simplest regression that can help answer this question? A. Phone Usage = B0 + B1*female + E B. Phone Usage = B0 + B1*price+ E C. Phone Usage = B0 + B1*female + B2*price + E D. Phone Usage = B0 + B1*female + B2*price + B3*price*female + E

Phone Usage = B0 + B1*female + B2*price + B3*price*female + E

To evaluate the impact of family income on child outcomes, a researcher proposes to use maternal (mother's) education as an instrumental variable for family income. A critic argues that this instrumental variable isn't exogenous, claiming that A. Maternal education is not strongly related to family income. B. Maternal education is not strongly related to child outcomes. C. Family income may affect child outcomes for many reasons. D. Maternal education may affect child outcomes through channels other than family income.

D. Maternal education may affect child outcomes through channels other than family income. Answer A suggests the instrument isn't relevant. Answer B suggests the instrument isn't related to the outcome. Answer C isn't a flaw of the instrument, just a question of interpreting results. Answer D is an exogeneity concern, namely that the instrument affects child outcomes through channels other than family income.

Which is false for a probit model? A. The dependent variable Y must be a dummy variable. B. Predicted values from the model fall between 0 and 1. C. Estimates from the model convey statistical significance clearly. D. The magnitudes of coefficients from the model can be easily interpreted.

D. The magnitudes of coefficients from the model can be easily interpreted. Coefficients have to be plugged into normal distribution functions for magnitudes to be interpreted properly.

Prof. Shoag regresses your Metrics midterm score on your Stats score. Your positive residual means: A. Your Metrics score is the average score of the whole class. B. Stats scores are poor predictors of Metrics scores. C. You scored lower on this test than last semester's score would have predicted. D. You scored higher on this test than last semester's score would have predicted.

D. You scored higher on this test than last semester's score would have predicted. A residual is defined as the difference between an actual outcome and a predicted outcome.

You collect data on the number of children a person has, whether or not they have graduate degrees (dummy) and their income (in thousands). You estimate the following SRF: Children_hat = 3.5 - 0.01*Income - 1.1*Grad_Degree What is the predicted number of children for someone with a graduate degree earning $60,000?A. 1.8 B. 2 C. -598 D. 2.9

A. 1.8

Assume all people have black, brown, blond or red hair. Which of the following regressions immediately tells you whether redheads are smarter than the average non-redhead? A. B0_hat + B1_hat*Red + u_hat B. B0_hat + B1_hat*Red + B2_hat*Blond + u_hat C. B0_hat + B1_hat*Red + B2_hat*Black+ B3_hat*Brown +u_hat D. B0_hat + B1_hat*Red + B2_hat*Blond+ B3_hat*Black + B4_hat*Brown +u_hat

A. B0_hat + B1_hat*Red + u_hat This regression is the only for which all non-redheads are the omitted/reference group.

Assume all coffee comes from Dunkin Donuts, Starbucks, or Peets. Which of the following regressions most easily allows you to test whether Starbucks coffee has significantly more caffeine than all other coffees? A. Caffeine = B0_hat + B1_hat*Starbucks + u_hat B. Caffeine = B0_hat + B1_hat*Starbucks + B2_hat* Peets + u_hat C. Caffeine = B0_hat + B1_hat*Starbucks + B2_hat* Dunkin+ u_hat D. Caffeine = B0_hat + B1_hat*Starbucks + B2_hat* Peets + B3_hat*Dunkin + u_hat

A. Caffeine = B0_hat + B1_hat*Starbucks + u_hat

To estimate the impact of attending pre‐school on the probability of attending college, a researcher proposes to use a sibling fixed effects approach. Which of the following sources of omitted variable does this eliminate? A. Children who attend pre‐school are from more educated families than children who do not. B. Families send children to pre‐school only if those children are healthy. C. Families send children to pre‐school when the economy is doing well. D. None of the above.

A. Children who attend pre-school are from more educated families than children who do not. Sibling fixed effects eliminated sources of bias from differences across families. Answer A is one such difference. Answers B and C could still be problems, as the outcomes of siblings might be driven not only by differences in their pre-school status but also in their health status or financial support when they're young.

You present results from a regression of weight on a dummy variable for a new weight loss drug. Someone criticizes the internal validity of the regression, claiming that gender is associated with both weight and taking the drug. What should you do to improve internal validity? A. Control for gender in a multiple regression model B. Interact the gender with a dummy for taking the drug C. Restrict the sample only to men D. None of the above

A. Control for gender in a multiple regression model

Which of the following is a threat to internal validity in a randomized control trial? A. Crossovers B. Random sampling C. Both A and B D. Neither A nor B

A. Crossovers Random sampling helps external validity. Crossovers cause underestimation of true impacts.

Random sampling improves a study's: A. External validity B. Internal validity C. Precision D. Omitted Variable Bias

A. External validity

The correlation of Y and X and the coefficient from the bivariate regression of Y on X: A. Have the same signs but different magnitudes. B. Have the same signs and same magnitudes. C. Have different signs but the same magnitudes. D. Have different signs and different magnitudes. E. None of the above.

A. Have the same signs but different magnitudes. Bivariate regression coefficients and correlation coefficients will have the same sign, since the numerators for both are the same. However, the magnitudes will differ: regression coefficients have units, while the correlation coefficients do not.

Random assignment, if done properly, guarantees that a study has A. High internal validity B. High external validity C. Both A and B D. Neither A nor B

A. High internal validity Random assignment makes causality clearer but doesn't guarantee generalizability to other contexts.

The government has a new jobs training program. They want to evaluate it using an RCT and ask you to help with the design. They choose 200 US counties and randomly assign 100 counties to receive the program to minimize the risks of spillovers. Under what circumstance would spillovers still be a problem? A. If some people in the control counties moved to the treatment counties to take the training. B. If some people in the treatment countries decided not to take the training program C. If more companies open up in the treatment area D. If some people in the control areas set up their own training program

A. If some people in the control counties moved to the treatment counties to take the training.

You run a regression of child test scores on their parent's income level and find a positive effect. You believe that due to an omitted variable, you have an underestimate of this effect. If you have a relevant and exogenous instrument for parental income, what would you expect to happen to the coefficient on parent's income when you instrument for it? A. It should get bigger B. It should stay the same C. It should get smaller D. It should flip sign

A. It should get bigger

A new study is released in which the authors state that individuals who have a lot of debt start fewer new businesses. The authors did not, however, control for the education levels of individuals in the study. Individuals with higher education levels have more debt due to student loans and are more likely to start new businesses. Omitting education thus creates a: A. Positive bias, so the study is understating the true impact of debt on entrepreneurship. B. Positive bias, so the study is overstating the true impact of debt on entrepreneurship. C. Negative bias, so the study is understating the true impact of debt on entrepreneurship. D. Negative bias, so the study is overstating the true impact of debt on entrepreneurship. E. None of the above.

A. Positive bias, so the study is understating the true impact of debt on entrepreneurship. By the OVB formula, beta two (higher education is a determinant of "more" new businesses) is positive, and gamma one (higher education and having a lot of debt is positively correlated) is positive. If you use the 2x2 table from class, this translates to the scenario where X1 & X2 are positively correlated and Beta 2 >0. Thus, positive x positive = positive bias. We also know that the sign of beta one is negative when we omit education (those with a lot of debt start fewer businesses), which tells us that the absolute value of coefficient on debt in the short regression is smaller in magnitude (i.e. closer to zero) than the absolute value of coefficient on debt in the long regression (which would be a more negative number). Thus, we have understated the true impact of debt on entrepreneurship. The proportion of the sample variation in Y (hours worked) is entirely explained by the explanatory variable (hours not worked). In other words, X was the perfect predictor of Y, and therefore, this regression will have the highest R-squared.

Which of the following characteristics of an instrumental variable can be verified with certainty in the data? A. Relevance B. Exogeneity C. Both A and B D. Neither A nor B

A. Relevance We can verify with our data whether the instrument is strongly related to treatment (relevance). We can not totally verify that it affects outcomes only through that treatment (exogeneity). Those receiving assistance were more likely to get jobs but took those jobs away from others.

Which of these could cause a randomized experiment to generate an overestimate? A. Spillover effects. B. Crossovers. C. No-shows. D. Attrition.

A. Spillovers OR D. Attrition Certain types of attrition can cause overestimation (see the problem sets). Same is true for spillovers.

We randomly select half of econometrics students to attend extra office hours with a faculty member. At the end of the semester, we find no evidence that this affects the final exam scores. The Dean argues that this means faculty members are ineffective teachers. I argue that spillover effects led to these small estimates because... A. Students who attended the extra office hours passed their knowledge onto others. B. Not everyone who was selected to attend the extra office hours did so. C. Some people who were not selected nonetheless demanded and received extra office hours. D. We screwed up the randomization and were more likely to give extra office hours to students with lower midterm grades.

A. Students who attended the extra office hours passed their knowledge onto others. Answer B represents no-shows. Answer C represents cross-overs. Answer D represents imperfect randomization. Answer A represents a spillover effect from treatments to controls.

In the Michelle Rhee IMPACT case, which control variable was the most important for minimizing the bias in estimates of teachers' impacts on students' test scores? A. Students' prior year test scores. B. Students' current year test scores. C. Students' poverty status. D. Students' parental education levels.

A. Students' prior year test scores. We argued that controlling for students' prior year test scores was actually a fairly effective way at controlling for many (though not all) non-teacher factors that affect student achievement.

In an instrumental variables study, the first stage regression tests whether A. The instrument (Z) is related to the treatment variable (X). B. The instrument (Z) is related to the outcome (Y). C. The treatment variable (X) is related to the outcome (Y). D. The instrument is exogenous.

A. The instrument (Z) is related to the treatment variable (X). The first stage tests whether there is a "strong" quasi-experiment to exploit for the study.

Steve is exploring the relationship between the price of a house, its number of rooms, and its distance from the subway. When Steve regresses house prices on the number of rooms, he finds a positive coefficient. Steve then regresses house prices on both the number of rooms and the distance to the subway. He gets a positive coefficient on both variables, though the coefficient on rooms is smaller than before. What does he know about the correlation of rooms and distance? A. They are positively correlated B. They are negatively correlated C. We cannot infer the direction of their correlation D. They are not correlated

A. They are positively correlated

You are asked to evaluate four studies that look at the relationship between participation in a jobs training program and wages earned after the program. Which regression has the highest level of internal validity? A. The researchers took a random sample of households in the state and regressed wages on whether the individual participated in the jobs training program. B. The researchers took a random sample of households in the state and regressed wages on whether the individual participated in the jobs training program, as well as gender, race, and previous job experience. C. The researchers took a sample of men between the ages of 18 to 22. They randomly assigned half of the men to the job trainings program, and then regressed wages on whether the individual participated in the jobs training program. D. The researchers took a sample of men and women between the ages of 18 to 22. They assigned the men to participate in the job trainings program, and then regressed wages on whether the individual participated in the jobs training program.

C. The researchers took a sample of men between the ages of 18 to 22. They randomly assigned half of the men to the job trainings program, and then regressed wages on whether the individual participated in the jobs training program. A study has internal validity if it estimates the causal effect of interest for the population represented by our sample. The study would have high internal validity if the participation in the jobs training program is unrelated to any background characteristics; the only study that does this is study C, where the jobs training program is randomly assigned.

You regress the log of house prices on pollution and obtain the following results: ln(house prices_hat) = 5 + 0.03*Pollution This means that a one unit increase in pollution is associated with a ... A. ... 3 percentage point increase in house prices. B. ... 0.30 percentage point increase in house prices. C. ... 30 percent increase in house prices. D. ... 3 percent increase in house prices.

D. ... 3 percent increase in house prices.

You regress a dummy for being unemployed on a dummy for being male. The constant (β0) from that regression is 0.2. This means that... A. Men are 0.2 percent more likely to be unemployed than women. B. Men are 20 percent more likely to be unemployed than women. C. Men are 20 percentage points more likely to be unemployed than women. D. 20 percent of women are unemployed.

D. 20 percent of women are unemployed. The constant in a bivariate regression represents the average value of the dependent variable (unemployment) for the omitted group (in this case women).

You run a linear probability model of admission to college on SAT scores. You find a coefficient of 0.004 on SAT score, with a p-value of 0.02. You can conclude that: A. Taking the SATs is associated with a 0.4% increase in admission that is significant at the 5% level. B. There is an increase in the probability of admission that is significant, but you cannot interpret the magnitude. C. A one point increase in SAT scores raises the predicted probability of admission by 0.4%. D. A one point increase in SAT scores raises the predicted probability of admission by 0.4 percentage points.

D. A one point increase in SAT scores raises the predicted probability of admission by 0.4 percentage points.

You run a linear probability model on a sample of Americans, regressing an indicator for gun ownership on income (measured in tens of thousands of dollars). You find a coefficient of 0.06 on income, with a standard error of 0.04. You can conclude that: A.An additional $10,000 of income is associated with a 0.06 percentage point increase in the probability of owning a gun, a relationship that is statistically significant. B. An additional $10,000 of income is associated with a 0.06 percentage point increase in the probability of owning a gun, a relationship that is statistically insignificant. C. An additional $10,000 of income is associated with a 6 percentage point increase in the probability of owning a gun, a relationship that is statistically significant. D. An additional $10,000 of income is associated with a 6 percentage point increase in the probability of owning a gun, a relationship that is statistically insignificant.

D. An additional $10,000 of income is associated with a 6 percentage point increase in the probability of owning a gun, a relationship that is statistically insignificant. Linear probability model coefficients can be interpreted as 100 * beta percentage point changes in the likelihood of an outcome occurring. The coefficient (0.06) divided by its standard error (0.04) is 1.5, which is less than 1.96, hence the relationship is statistically insignificant.

Your analyst runs the following probit regression model: Voted_hat = 0.35 + 0.21*Male + 0.18*Black + 0.05*Hispanic Where voted is a dummy variable that equals 1 if the individual voted, and black and Hispanic are dummy variables for census demographic categories (the omitted category is white). He wants to interpret the magnitude of the coefficient on the male dummy. What do you suggest he does? A. Re-run the model using two-stage least squares B. Re-run the model without including black or Hispanic C. Calculate the correlation coefficient D. Calculate the marginal effects

D. Calculate the marginal effects

Suppose you have repeated observations for participants in an experiment on the relationship between exercise and weight. What technique would help you address serial correlation in their measurements? A. Heteroskedastic robust standard errors B. Probit regressions C. Clustering the standard error by observation D. Clustering the standard error by person

D. Clustering the standard error by person Serial correlation is dependence over time in the error terms. To address this you have to treat all observations for a person as a single cluster.

You want to know if listening to music makes you solve puzzles quickly. What is the theoretically correct counterfactual comparison to make? A. Compare the music listening habits of people who solve puzzles quickly with those who do not B. Compare the puzzle solving ability of those who listen to music with those who do not. C. Compare the listening habits of the same people while they solve and do not solve puzzles D. Compare the puzzle solving ability of the same people while they listen and do not listen to music

D. Compare the puzzle solving ability of the same people while they listen and do not listen to music

A randomized trial finds that treatment and control group patients taking a new drug had similar cholesterol levels after one year. The drug was thus deemed ineffective. Patients who died during the trial could not have their cholesterol measured. A critic argues that the drug is successful but that this form of attrition has biased the results. Which of these facts would best support his argument? A. Many patients in the treatment and control groups died during the trial. B. Many patients with particularly high cholesterol in the treatment and control groups died during the trial. C. More patients with high cholesterol died in the treatment group than in the control group. D. More patients with high cholesterol died in the control group than in the treatment group.

D. More patients with high cholesterol died in the control group than in the treatment group. Answers A and B don't necessarily create bias, as the attrition may be balanced across the two groups. Answer C would make the treatment group look like it had lower cholesterol than the control group (i.e. because high cholesterol patients aren't counted), but the question said the two groups actually looked similar. Answer D is correct because if the drug was effective, the control group would have ended up with higher cholesterol, but the death of those patients made the control group look "normal", just as the question suggested.

In a regression with country fixed effects, which could you also include as controls? A. An indicator for whether the country is landlocked. B. A measure of the country's GDP in 1960. C. Both A and B D. Neither A nor B

D. Neither A nor B Both controls are constant characteristics of countries and thus would be collinear with the country fixed effects (and hence dropped by Stata).

You regress a dummy variable for employment on a dummy variable for high school graduation or higher, a dummy variable for male, and your father's log(earnings). To estimate the model, you use ordinary least squares. Which of the following statements is correct: A. You should have used a probit since you included your father's log(earnings) B. You should have used log(employment) as the dependant variable since you included your father's log(earnings). C. Both are correct D. Neither are correct

D. Neither are correct

Using wage data for North Americans, you regress wages on a Canadian dummy, a Mexican dummy, and a constant. What does the Canadian dummy represent? A. The average wages of Canadians. B. The difference in average wages between Mexicans and Canadians. C. The difference in average wages between Mexicans and U.S. Americans. D. None of the above.

D. None of the above. The Canadian dummy represents the difference in average wages between Canadians and U.S. Americans (the omitted group).

Does earning an BA at CWRU improve your future income? What theoretically correct counterfactual must you observe to know this? A. The incomes of students rejected from CWRU. B. Your income prior to starting the BA. C. Your income after completing the BA. D. None of these.

D. None of these. You need to observe your income in a world where you didn't earn an BA, which is impossible.

You would like to know how having health insurance affects how many years one lives after having a heart attack (the variable "Survival"). You obtain the following SRF (Sample Regression Function): Survival_hat = 60.7 + 5.5*Insured - 3.8*Uninsured + 4.3*Income What can you conclude? A. Holding all else constant, being insured results in longer survival after a heart attack. B. Holding all else constant, being uninsured is associated with shorter survival after a heart attack. C. Nothing, the income variable must have an error. D. Nothing, the insurance variables must have an error. E. None of the above.

D. Nothing, the insurance variables must have an error. Individuals should either belong to the insured or the uninsured category. If they only belong to one category, one of the dummies will be dropped as the omitted category. However, since it is not dropped, it must be the case that at least one person is wrongly coded as both insured and uninsured.

We observe this relationship in adults: Weight = -20 + 30 *height + 2 *height^2 Which statement is true? A. Each additional foot of height is associated with 30 pounds more of weight. B. Each additional foot of height is associated with 34 pounds more of weight. C. On average, 6-foot tall people weigh 32 pounds more than 5-foot tall people. D. On average, 6-foot tall people weigh 52 pounds more than 5-foot tall people.

D. On average, 6-foot tall people weigh 52 pounds more than 5-foot tall people. The quadratic terms means there's no single, constant relationship between height and weight. If you plug in 6 and 5 into this formula, the difference is 52 pounds.

To estimate the impact of state income taxes on labor supply, a researcher runs a regression of labor force participation rates on tax rates, controlling for state and year fixed effects. She concludes that higher taxes lower labor supply. What might be a valid objection to her conclusion, given her empirical approach? A. States that raise taxes have more liberal voters than states that do not raise taxes. B. States often raise taxes at the same time as each other. C. States raise taxes more when their local labor force participation is low, making it harder to balance their budgets. D. States raise taxes more when their local labor force participation is high, when voters are well‐employed and thus more willing to support public projects.

D. States raise taxes more when their local economies are doing well, when voters are well-employed and thus more willing to support public projects. State fixed effects eliminate bias from across-state differences, such as A. Year fixed effects eliminate bias from across-time differences, such as B. If answer D were true, tax increases would be associated with increases in labor supply. Only answer C would generate an association between increased taxes and lower labor supply that was not causal.

In a difference‐in‐difference framework, the parallel trends assumption means that A. The treatment and control groups look similar in the pre‐treatment period. B. The treatment and control groups look similar in the post‐treatment period. C. The treatment and control groups look similar in both periods. D. The difference between the treatment and control groups in the post‐period would have been the same as in the pre‐period if not for the treatment.

D. The difference between the treatment and control groups in the post-period would have been the same as in the pre-period if not for the treatment. D-in-D doesn't depend on levels being the same, as in answer A. Nor would it make sense for outcomes to be identical, so answers B and C are wrong. D describes the assumption that makes the D-in-D estimator unbiased, that the counterfactual is clearly identified.

True or False: In a Linear Probability Model, you can interpret magnitude and statistical significance, but not sign.

False

True or False: In a randomized control trial, no-shows generally lead to an overestimate of true effects.

False

True or False: An IV model can include additional control variables.

True

True or False: In a randomized control trial, a cross-over is a person from the control group who chose to get treated.

True

True or False: Randomized experiments removed omitted variable bias by forcing the correlation between your treatment variable and other variables to be zero.

True

True or False: To include sibling fixed effects, you must have data on multiple siblings for at least some families.

True