Quiz Answers (Week 6 and On)

When there is heteroskedasticity, this means that: The OLS estimates are biased You can no longer interpret the in the same way The estimate of the standard error is no longer valid. The usual t-statistic is still valid.

The estimate of the standard error is no longer valid.

Data that is used to create a predictive model is known as Test data Training data Cross-validated data Cross-sectional data

Training Data FEEDBACK: We refer to the data that we use to build the predictive model as training data

An instrumental variable is considered to be weak when the first stage F-statistic is less than 10 True False

True

The linear probability model is a multiple linear regression model with a binary dependent variable. True False

True

When a series has the same average growth rate from period to period, then it can be approximated by an exponential trend. True False

True

When estimating the equation: change in crimerate(i) = B0 + B1*change in unemployment(i) + change in U(i) The estimate of is only causal if there is no correlation between change in crimerate(i) and change in U(i) True False

True Response Feedback: We need to assume that there is no correlation between

Two-period panel data can be used for program evaluation and policy analysis. True False

True Response Feedback: Two-period panel data is used for program evaluation and policy analysis. In the simplest program evaluation setup, a sample of individuals, firms, cities, and so on is obtained in the first time period. Some of these units, those in the treatment group, then take part in a particular program in a later time period; the ones that do not are the control group.

Dummy variables can be used to address the problem of seasonality in regression models. True False

True FEEDBACK: Dummy variables can be used to account for seasonality in the dependent variable, the independent variables, or both and thus, address the problem of seasonality in regression models.

Time series data should be thought of as a sequence of random variables True False

True FEEDBACK: Economic time series are outcomes of random variables.

As the tuning parameter increases, the value of coefficients in the model typically decrease. True False

True FEEDBACK: It will typically decrease, but not always

The dummy variable coefficient for a particular group represents the estimated difference in intercepts between that group and the base group. True False

True FEEDBACK: The dummy variable coefficient for a particular group represents the estimated difference in intercepts between that group and the base group.

The R^2 never decreases as more explanatory variables are added to the regression True False

True Response Feedback: Including more explanatory variables in the regression can only lead to an increase in the , even if they are uncorrelated with the outcome variable. This is an important limitation of the for evaluating goodness of fit.

The Intent to Treat effect is equal to the Average Treatment Effect if there is full compliance, i.e. if everyone assigned to Treatment takes it up. True False

True Response Feedback: The ITT is the same as the ATE if there if full compliance. They are different if there is partial compliance

Define as Yi0 the profits of a firm if it receives a tax break. Define as Yi1 the profits of a firm is it does not receive a tax break. You have data for a sample of firms. For each single firm in your data you will observe either Yi0 or Yi1 depending on whether they received the tax break or not. True False

True Response Feedback: You can never observe both potential outcomes for the same subject

You have a cross-sectional dataset on a sample of families. For each family, you have data on the characteristics of two siblings (e.g. their education and wages). This is an example of a matched pairs sample True False

True The answer is True, since we have pairs of employees within each firm

As you add more variables to the model, the prediction mean squared error in the training sample will never increase True False

True The training MSE will never increase -- at worst, if the variable is not predictive at all, it will stay the same.

You have a five-year panel of firms and are interested in studying the effect of number of employees on profits. In the first year of the panel, the dataset includes 1000 firms, but you notice that by year five 30% of the firms have left the sample. You inquire with the organization which collected the data and they tell you that the only reason for attrition is that the organization was running low on budget, and so they scaled down the survey and randomly selected only a subset of the initial 1000 firms to be followed over time. All the firms that they tried to interview were indeed found and interviewed. Should you be worried about this type of attrition biasing the results of Fixed Effects estimation on this data? 1. Yes 2. No 3. Not enough information to decide

2. No Response Feedback: You should not be worried, because attrition is random

You have a five-year panel of firms and are interested in studying the effect of number of employees on profits. In the first year of the panel, the dataset includes 1000 firms, but you notice that by year five 30% of the firms have left the sample. You inquire with the organization which collected the data and they tell you that the reason for attrition is that 30% of the firms went out of business during the sample period. Should you be worried about attrition biasing the results of Fixed Effects estimation on this data? 1. Yes, this type of attrition will always create bias 2. Yes, unless the attrition is due solely to time-invariant firm characteristics (e.g. the personality of the owner) 3. Yes, unless the attrition is due solely to time-variant firm characteristics (e.g. demand shocks) 4. No

2. Yes, unless the attrition is due solely to time-invariant firm characteristics (e.g. the personality of the owner) You should be worried, unless the attrition is due solely to time-invariant firm characteristics (e.g. the personality of the owner), since any time-invariant firm characteristics will be differenced out by the fixed effects estimator

An NGO provided free textbooks and school uniforms in 10 schools in Kampala in 2017, but not in 20 other nearby schools. You measure test scores in each school in the school year before (2016) and after (2017) these were distributed. The average test scores are: Textbook/uniform schools: 2016 - 20, 2017 - 90 Non-textbooks/uniform schools: 2016 - 30, 2017 - 70 The differences-in-differences estimate of the effect of this policy is: 70 20 0 30

30 Response Feedback: (90-20) - (70-30) = 70-40 = 30

Contemporaneous Exogeneity Strict Exogeneity No Serial Correlation

Contemporaneous Exogeneity: E(ut | xt) = 0 Strict Exogeneity (needed to satisfy TS.3): E(ut | X) = 0 No Serial Correlation: Corr(ut, us | X) = 0, t =/ s

A data set is called a balanced panel if it has data missing in some years for at least some of the individuals/units in the sample. True False

False

An advantage of the linear probability model relative to logit and probit is that it never implies a probability more than 1 or less than 0. True False

False

Homoskedasticity is present when there is a relationship between the variance of the outcome variable and the independent variables True False

False

Machine learning methods are more useful for inference than for prediction True False

False

You collect data from a sample of USC students on past classes that they have taken, including the number of times during the semester that they skipped that class and whether they passed that class. You then estimated the relationship between passing the class and classes skipped using a logit model. The estimated relationship is: Pi = 1/(1 + e^-(2.75 - 0.05*skipi)) True or false: The correct interpretation of this model is that for each additional class skipped, the likelihood of passing a class declines by 5 percent.

False

A natural experiment always has a control group, which is affected by the policy change, and a treatment group, which is not affected by the policy change. True False

False Response Feedback: A natural experiment always has a control group, which is not affected by the policychange, and a treatment group, which is thought to be affected by the policy change.

You are working as a consultant for a company that has just begun a new advertising campaign for one of its flagship products. In the three months prior to the advertising campaign, average sales for this product were $1 million per month. In the four months after the campaign, the average sales were $1.2 million. We can attribute the $200,000 increase in sales per month as a causal impact of the advertising campaign. True False

False Response Feedback: No. It may be that sales would have gone up in the absence of the advertising campaign in those months (e.g. the advertising campaign began right before Christmas, when sales would have already been higher). There needs to be some sort of comparison group in order to draw such a conclusion.

You are a state Commissioner of Education and want to evaluate the effect of a new instructional method. The new instructional method is implemented in 10 counties of the state (not selected randomly), but not in the other counties. You see that test scores in those 10 counties were decreasing in the three years prior to the instructional method being implemented, but were increasing in the remaining counties. This is an example where using differences-in-differences will produce good causal estimates of the effect of the instructional method True False

False Response Feedback: The prior trends indicate that the two sets of schools are on different trajectories so the remaining schools are not a good comparison group. Thus differences-in-differences is not appropriate to use.

If you have a matched pairs sample of siblings, you can use the random effects estimator to get rid of omitted variable bias due to common family background True False

False The answer is False. You need to use the fixed effects or difference estimator. The random effects estimator does not get rid of the unobserved differences that are fixed

A binary variable is a variable whose value changes with a change in the number of observations. True False

False FEEDBACK: A binary variable is one whose value depends on the event taking place.

For predictive models, it is always better to have a higher R-squared in the training data set True False

False FEEDBACK: False, sometimes a higher R-squared indicates that the model has been overfit to the training data.

In a random effects model, we assume that the unobserved effect is correlated with each explanatory variable. True False

False FEEDBACK: In a random effects model, we assume that the unobserved effect is not correlated with each explanatory variable.

When using a tree-based method, the predicted value of the outcome variable in each region is selected to maximize the mean squared error. True False

False FEEDBACK: It is selected to minimize, not maximize, the mean squared error.

In the first stage of two stage least squares, we create a new variable containing only the endogenous component of the independent variable that we are interested in the effect of. True False

False Response Feedback: In the first stage of two stage least squares, we create a new variable containing only the exogenous component of the independent variable that we are interested in the effect of.

To test if the instrumental variable is a weak instrument, you regress the outcome variable (y) on the instrumental variable (z) and examine the F-statistic True False

False Response Feedback: To test if the instrumental variable is a weak instrument, you regress the endogenous variable (x) on the instrumental variable (z) and examine the F-statistic

If treatment status is assigned randomly, we expect treatment and control observations to be similar on characteristics that we cannot observe ("unobservables"), but different on characteristics that we can observe ("observables"). True False

False Response Feedback: If treatment is assigned randomly we expect treatment and control observations to be similar both on observables and on unobservables

Randomized experiments where treatment status is assigned randomly are possible only in a laboratory, not in the real world. True False

False Response Feedback: Randomized experiments are possible both in the laboratory but also in the real world. For example, there are many real life studies assigning training scholarships randomly.

You are interested in estimating the effect of receiving a scholarship to attend college on wages at age 35. Scholarships are assigned on the basis of financial need, so less affluent students are more likely to receive scholarships. You have information on student gender and parental education. You control for these observable characteristics in an OLS regression of wages on whether the student received a scholarship. This regression identifies the Average Treatment Effect of receiving a scholarship. True False

False Response Feedback: Since scholarships are not assigned randomly, students receiving a scholarship are likely to be different on unobservable characteristics from those not receiving a scholarship. Therefore, simply controlling for observable characteristics of the students will not recover the ATE. It will recover a mix of Treatment on the Treated and Selection Bias.

Supervised learning problems have no outcome variable, just a set of variables from a sample True False

False Unsupervised learning problems have no outcome variable, just a set of variables from a sample

If the R-squared value is low, then using the OLS equation to predict y will yield highly accurate predictions. True False

False. FEEDBACK: If the R-squared value is low, then using OLS equation is difficult to predict individual future outcomes on y given a set of values for the explanatory variables.​

Which of the following leads to a model being selected with the fewest number of variables? Lasso Forwards stepwise variable selection Ridge regression It is not possible to say with the given information

It is not possible to say with the given information

TS.1: Linear in parameters TS.2: No perfect colinearity TS.3: Zero Conditional Mean (Contemporaneous/Strict Exogeneity) TS.4: Homoskedasticity TS.5: No Serial Correlation TS.6: Normality

TS Assumptions

Suppose you are constructing a tree via a top-down, greedy method with binary splits. At each step, you will select the predictor and cut point such: That a split along that cut-point leads to the greatest increase in the sum of squared residuals That a split along that cut-point leads to the greatest reduction in the sum of squared residuals That a split along that cut-point does not affect the sum of squared residuals None of the above

That a split along that cut-point leads to the greatest reduction in the sum of squared residuals

Refer to the following model: yt = a0 + B0st + B1s(t-1) + B2s(t-2) + B3s(t-3) + ut B0 + B1 + B2 + B3 represents: a. the long-run change in y given a permanent increase in s. b. the short-run change in y given a permanent increase in s. c. the short-run change in y given a temporary increase in s. d. the long-run change in y given a temporary increase in s.

a. the long-run change in y given a permanent increase in s. FEEDBACK: In the model, the sum of the coefficients on current and lagged z, 0 + 1 + 2 + 3 represents the long-run change in y given a permanent change in s.

Suppose that the income of an individual depends on her religion and several other factors. The other factors which can be measured quantitatively, while religion is a discrete variable. You want to regress income on religion and the other factors that determine income levels. If there is a total of 5 religious groups in your data set, how many dummy variables for religion should be included? a. 5 b. 4 c. 1 d. 6

b. 4 FEEDBACK: If a regression model is to have different intercepts for, say, g groups or categories, we need to include g -1 dummy variables in the model along with an intercept. In this case, the regression equation should include 5-1=4 dummy variables since there are 5 religious groups.

Consider the following simple regression model y = B0 + B1*x + u. Suppose z is an instrument for x and you estimate this model using an instrumental variables regression. If Cov(z, u) = 0 and Cov(z, x) =/ 0, the value of the IV estimator 1 in terms of population covariances is _____. a. Cov(z, u) b .Cov(z, y) / Cov(z, x) c. Cov(z, u) / Cov(z, x) d. Cov( z, x)

b. Cov(z, y) / Cov(z, x)

Which of the following correctly identifies a difference between cross-sectional data and time series data? a. Cross-sectional data is based on temporal ordering, whereas time series data is not b. Time series data is based on temporal ordering, whereas cross-sectional data is not c. Cross-sectional data consists of only qualitative variables, whereas time series data consists of only quantitative variables d. Time series data consists of only qualitative variables, whereas cross-sectional data does not include qualitative variables.

b. Time series data is based on temporal ordering, whereas cross-sectional data is not

If each variable in an equation is differenced over time, then this is called the: a. instrumental variable equation b. ​ first differences equation. c. ​ unobserved effects equation. d. ​ fixed effects equation.

b. first differences equation Response Feedback: If each variable in a single cross-sectional equation is differenced over time, then it is called the first differences equation.

The model: Yt = B0 + B1ct + ut, t = 1,2,......., n is an example of a(n): a. Auto regressive conditional heteroskedasticity model. b. static model. c. finite distributed lag model. d. infinite distributed lag model.

b. static model.

The following simple model is used to determine the annual savings of an individual on the basis of her annual income and education. Savings = β0 + D0*edu + β1*Inc + u The variable 'Edu' takes a value of 1 if the person has a college education, and 0 if they do not. The variable 'Inc' measures the income of the individual. ​ Refer to the model above. The benchmark group in this model is _____. a. the group of college educated people b. the group of non-college educated people c. the group of individuals with a low income d. the group of individuals with a high income

b. the group of non-college educated people FEEDBACK: The benchmark group is the group against which comparisons are made. In this case, the savings of a college-educated person is being compared to the savings of a non- college-educated person; therefore, the group of non- college-educated people is the base group or benchmark group.

In a regression model, which of the following will be described using a binary variable? a. The volume of rainfall during a year b. Whether it rained on a particular day or it did not c. The concentration of dust particles in air d. The percentage of humidity in air on a particular day

b. whether it rained on a particular day or not FEEDBACK: A binary variable is used to describe qualitative information in regression model. Therefore, such a variable will be used to describe whether it rained on a particular day or it did not.

Consider the following regression equation: y = B0 + B1*x1 + ... + Bk*xk + u In which of the following cases is the dependent variable is binary? a. y indicates the number of children in a family b. y indicates whether an adult is a college dropout c. y indicates the gross domestic product of a country d. y indicates household consumption expenditure

b. y indicates whether an adult is a college dropout

ou are interested in estimating the probability that an individual thinks that climate change is real and human-made in origin as a function of their education and political ideology. You estimate that: ClimateChange = .25-0.25educ+.12polview+.02educ*polview Where polview = 0 if Tea Party, 1 if Rep, 2 if Ind, 3 if Dem; educ =1 if HS, educ = 2 if some college, educ=3 if college, educ=4 if post-graduate. What is the estimated probability that someone believes climate change is real and man-made if they are a Republican with some college education? a. 0.44 b. 0.32 c. 0.36 d. 0.52

c. 0.36 Response Feedback: .25-.025(2)+.12(1)+.02(1)(2)= .36

Consider the following simple regression model: y = B0 + B1x + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument exogeneity? a. Cov(z, x) = 0 b. Cov(z, u) > 0 c. Cov(z, u) = 0 d. Cov(z, x) > 0

c. Cov(z, u) = 0 FEEDBACK: The condition Cov( z, u) = 0 denotes instrument exogeneity in this case.

Which of the following correctly identifies an advantage of using adjusted R^2 over R^2? a. Adjusted R^2 is easier to calculate than R^2. b. Adjusted R^2 corrects the bias in R^2. c. The penalty of adding new independent variables is better understood through adjusted R^2 than R^2. d. The adjusted R^2 can be calculated for models having logarithmic functions while R^2 cannot be calculated for such models.

c. The penalty of adding new independent variables is better understood through adjusted R^2 than R^2.

An estimator that is based on subtracting the mean across time from the variables is called the _____. :a. random effects estimator b. least absolute deviations estimator c. fixed effects estimator d. instrumental variable estimator

c. fixed effects estimator

In the following regression equation, y is a binary variable: y = B0 + B1x1 + ... + Bk*xk+ u In this case, the estimated slope coefficient, B1, measures _____. a. the predicted change in the value of y when x1 increases by one unit, everything else remaining constant b. the predicted increase in the probability that y=1 when x1 decreases by one unit, everything else remaining constant c. the predicted increase in the probability that y=1 when x1 increases by one unit, everything else remaining constant d. the predicted change in the value of y when x1 decreases by one unit, everything else remaining constant

c. the predicted increase in the probability that y=1 when x1 increases by one unit, everything else remaining constant

The sample size for a time series data set is the number of: a. time periods over which we observe the variables of interest minus the number of variables b. time periods over which we observe the variables of interest plus the number of variables c. time periods over which we observe the variables of interest d. variables being measured.

c. time periods over which we observe the variables of interest FEEDBACK: The sample size for a time series data set is the number of time periods over which we observe the variables of interest.

The systematic differences between the control and treatment groups can be controlled by taking two years of data, _____.​ a.​ one year of data for the control group before the policy change and one year of data for the control group after the change b. one year of data for the control group and one year of data for the treatment group both before the change c.​ one year of data before the policy change and one year of data after the change, for both the treatment and control group d.​ one year of data for the treatment group before the policy change and one year of data for the treatment group after the change

c.​ one year of data before the policy change and one year of data after the change, for both the treatment and control group Response Feedback: The systematic differences between the control and treatment groups can be controlled by taking two years data, one before the policy change and one after the change , for both the treatment and control group

Suppose you still want to know the causal effect of attendance at office hours on midterm exam scores. You randomly allocate tickets to office hours and only allow students with tickets to come. Not everyone who is given a ticket comes to office hours. You compute the average score of those allocated a ticket and subtract the average score of those not allocated a ticket. What have you estimated? a. Average Treatment Effect b. Selection Bias c. Treatment on the Treated d. Intent to Treat

d. Intent to Treat Response Feedback: You have estimated the Intent to Treat Effect since tickets are allocated randomly but there is partial compliance

Suppose you want to know the causal effect of attendance at office hours on midterm exam scores. You compute the average score of office hour attenders and subtract the average score of NON- attenders. What have you estimated? a. Average Treatment Effect b. Treatment on the Treated c. Selection Bias d. None of the Above

d. None of the Above Response Feedback: You have estimated a mix of Treatment on the Treated and Selection Bias. The reason is that those students coming to office hours are likely to be different from those not not coming to office hours

Consider the following simple regression model y = B0 + B1 x + u. Suppose z is an instrument for x. Which of the following statements is true? a. The condition Cov(z, u) = 0 can be tested statistically b. The condition Cov(z, x) =/ 0 cannot be tested statistically c. The ordinary least squares estimator is unbiased if Cov(x, u) =/ 0. d. None of the above

d. None of the above

You are interested in the effect of job search support on unemployment duration. You randomly assign a first group of job seekers to receive job search support by a job center (this is the "Treatment" group), while another group of job-seekers is not given access to the job center (this is the "Control" group). Only 30% of the job seekers assigned to the job search support group actually show up at the job center at least once. You compare the average unemployment duration of those individuals from the Treatment group who show up at least once, to the average unemployment duration of those individuals from the Control group. What parameter does this strategy identify? a. Average Treatment Effect b. Intent to Treat c. Treatment on the Treated d. None of the above

d. None of the above Response Feedback: The subset of treated individuals who shows up at the job center is likely to be different from the average individual in Control. So this strategy identifies a mix of Treatment on the Treated and Selection Bias.

Which of the following assumptions is required for obtaining unbiased fixed effect estimators? a. The errors are heteroskedastic b. The unobserved effect is correlated with the explanatory variables c. The errors are serially correlated d. The explanatory variables are strictly exogenous.

d. The explanatory variables are strictly exogenous. FEEDBACK: Under a strict exogeneity assumption on the explanatory variables, the fixed effects estimator is unbiased

What will you conclude about a regression model if the Breusch-Pagan test results in a small p-value? a. The model contains dummy variables b. The model omits some important explanatory factors c. The model contains homoskedasticty d. The model contains heteroskedasticty.

d. The model contains heteroskedasticty.

Which of the following assumptions is required for obtaining unbiased random effect estimators? a. The unobserved effect is correlated with the explanatory variables b. The idiosyncratic errors are heteroskedastic c. The idiosyncratic errors are serially correlated d. The unobserved effect is independent of all explanatory variables in all time periods.

d. The unobserved effect is independent of all explanatory variables in all time periods. Response Feedback: Rationale: FEEDBACK: The unobserved effect is independent of all explanatory variables in all time periods.

The effect of which of following types of variables cannot be estimated in a fixed effects model? a. Discrete dependent variable b. Dummy variable c. Time-varying independent variable d. Time-constant independent variable

d. Time-constant independent variable Rationale: FEEDBACK: A fixed effects model cannot include a time-constant independent variable

In a regression model, which of the following will be described using a binary variable? a. The concentration of dust particles in air b. The percentage of humidity in air on a particular day c. The volume of rainfall during a year d. Whether it rained on a particular day or it did not

d. Whether it rained on a particular day or it did not

We postulate a 'static' model if: a. a change in the independent variable at time 't' is believed to have an effect on the dependent variable at period 't + 1'. b. a change in the independent variable at time 't' is believed to not have any effect on the dependent variable. c. a change in the independent variable at time 't' is believed to have an effect on the dependent variable for all successive time periods. d. a change in the independent variable at time 't' is believed to have any effect on the dependent variable at time 't' but not other times

d. a change in the independent variable at time ' t' is believed to have any effect on the dependent variable at time 't' but not other times FEEDBACK: A static model is postulated when a change in the independent variable at time ' t' is believed to have an immediate effect on the dependent variable.

A regression model exhibits unobserved heterogeneity if _____ a. the independent variables are correlated with the dependent variables b. there are unobserved factors which are correlated with the observed independent variables but are uncorrelated with the dependent variable c. there are no unobserved factors affecting the dependent variable d. there are unobserved factors affecting the dependent variable that do not change over time

d. there are unobserved factors affecting the dependent variable that do not change over time Response Feedback: A regression model exhibits unobserved heterogeneity if there are unobserved factors affecting the dependent variable but they do not change over time.

If a1 > 0, then yt ​in the linear function of time E(yt) = a0 + a1t displays a(n):​ a. exponential trend . b. quadratic trend . c. ​ downward trend. d. ​ upward trend.

d. upward trend

Which of the following is true about the LPM (linear probability model), logit, and probit models? a. LPM, logit and probit models all imply constant marginal effects for all the independent variables b.LPM, logit and probit models all imply that the marginal effect of the independent variables changes as the independent variables change c.​ the logit and probit models assume constant marginal effects for all the independent variables, while the LPM implies that the marginal effect of the independent variables changes d.​ the LPM assumes constant marginal effects for all the independent variables, while the logit and probit models imply that the marginal effect of the independent variables changes

d.​ the LPM assumes constant marginal effects for all the independent variables, while the logit and probit models imply that the marginal effect of the independent variables changes

Which of the following are examples of regularization methods? Ordinary Least Squares k-fold cross-validation Lasso Ridge regression

Lasso Ridge regression FEEDBACK?: Regularization is a technique used for tuning the function by adding an additional penalty term in the error function

Which of the following correctly represents the equation for adjusted R^2? a. = 1 - [SSR/(n -k - 1)]/[SST/(n - 1)] b. = 1 - [SSR/(n -k - 1)]/[SST/(n+1)] c. = 1 - [SSR]/[SST/(n - 1)] d. = 1 - [SSR/(n -1)]/[SST/(n+1)]

a. FEEDBACK: = 1 - [SSR/(n -k - 1)]/[SST/(n - 1)]

Suppose you still want to know the causal effect of attendance at office hours on midterm exam scores. You randomly allocate tickets to office hours and only allow students with tickets to come. Everyone who is assigned a ticket comes to office hours. You compute the average score of office hour attenders and subtract the average score of NON-attenders. What have you estimated? a. Average Treatment Effect b. Selection Bias c. Omitted Variable Bias d. None of the Above

a. Average Treatment Effect (ATE) Response Feedback: You have estimated the Average Treatment Effect since the tickets are randomly assigned and there is full compliance

You are running the regression: yi = B0 + B1xi + ui Instrumental variables zi are useful in situations where: a. Cov(xi, ui) =/ 0 b. Cov(xi, ui ) = 0 c. Cov(xi, zi) = 0 d. Cov(xi, zi ) = 0

a. Cov(xi, ui) =/ 0 Response Feedback: Instrumental variables are useful in the case of omitted variable bias

Consider the following simple regression model y = B0 + B1x + u. Suppose z is an instrument for x. Which of the following conditions denotes instrument relevance? a. Cov(z, x) =/ 0 b. Cov(z, u) = 0 c. Cov(z, y) < 0 d. Cov(z, u) > 0

a. Cov(z, x) =/ 0

You have data from a field experiment studying the impact of managerial training on business profits. Managers in the Treatment group were offered the training. 50% took it up. Managers in the Control group were not offered the training. You run a regression of business profits (Y) on whether the manager was assigned to Treatment or Control, as follows:, where Treat is equal to 1 if they were randomly assigned to be offered the training and equal to 0 if they were not randomly assigned to be offered the training. Which of the following is true about the error term in this regression? a. E(u | Treat = 1) = E(u | Treat = 0) because of randomization b. E(u | Treat = 1) =/ E(u | Treat = 0) because of selection bias c. E(u | Treat = 1) =/ E(u | Treat = 0) because there is no full compliance d. None of the above

a. E(u | Treat = 1) = E(u | Treat = 0) because of randomization Response Feedback: Randomization ensures that Treatment and Control observations are similar on both observables and unobservables.

Consider the following simple regression model y = B0 + B1 x 1 + u. The variable z is a weak instrument for x if _____ a. There is a low correlation between z and x b. There is a high correlation between z and x c. There is a low correlation between z and u d. There is a high correlation between z and u

a. There is a low correlation between z and x

Which of the following is an advantage of panel data? a. We can difference the dependent variable, y, across time for the same individuals/units. b. We can add the dependent variable, y, across time for different individuals/units. c. We can add the dependent variable, y, across time for the same individuals/units. d. ​We can difference the dependent variable, y, across time for different individuals/units

a. We can difference the dependent variable, y, across time for the same individuals/units. Response Feedback: An advantage of panel data is that we can difference the dependent variable, y, across time for the same cross-sectional units.

Refer to the following model: yt = a0 + B0 s(t) + B1 s(t-1) + B2 s(t-2) + B3 s(t-3) + ut This is an example of a(n): a. finite distributed lag model of order 3. b. finite distributed lag model of order 1. c. infinite distributed lag model. d. finite distributed lag model of order 2.

a. finite distributed lag model of order 3.

Consider the following simple regression model: y = B0 + B1x + u. In order to obtain consistent estimators of 0 and 1, when x and u are correlated, a new variable z is introduced into the model which satisfies the following two conditions: Cov(z, x) =/ 0 and Cov (z, u) = 0. The variable z is called a(n) _____ variable. a. instrumental b. random c. dummy d. lagged dependent

a. instrumental FEEDBACK: Variable z is called an instrumental variable since Cov(z, x) =/ 0 and Cov (z, u) = 0