Question 1

A control variable is a variable included in a regression equation whose purpose is to:

Accepted Answer

A control variable is included in a regression equation to address endogeneity Issues. Endogeneity problems arise when there is a correlation between the dependent variable and one of the independent variables. This can lead to biased estimates of the coefficients of the independent variables. By including control variables, we can try to isolate the relationship between the dependent variable and the independent variable of interest, thereby improving the accuracy of the regression coefficients.

Question 2

It is often times necessary to make reference to a base group in regression analysis, which denotes what?

Accepted Answer

A base group, also known as a reference group, is the group that is excluded when creating dummy variables to represent a categorical, ordinal, or interval variable in regression analysis. This allows for comparisons to be made between the other groups and the base group. Therefore, choice C is the correct answer. Choices A, B, and D are not related to the concept of a base group in regression analysis.

Question 3

What are the two primary criteria for identifying "good" controls?

Accepted Answer

D

Question 4

What condition best describes the endogeneity problem?

Accepted Answer

Endogeneity problem arises when one or more independent variables are correlated with the error term in a regression model. Option D describes this condition. This problem can cause biased and inconsistent estimates of the coefficients and standard errors, which can lead to invalid hypothesis testing and incorrect conclusions. Solutions to the endogeneity problem include instrument variables, control variables, and structural equation modeling. Options A, B, and C describe other potential problems in regression analysis but do not relate to endogeneity specifically.

Question 5

In determining the causal effect of Price on Sales, if advertising spend is a good control variable, how will the correlation of the error terms from the regression, Sales_i = β₀ + β₁Price_i + U_i, and Sales_i = α₀ + α₁Price_i + α₂Advertising_i + V_i and price be related?

Accepted Answer

Including advertising spend as a control variable in the regression model aims to isolate the effect of price on sales by accounting for advertising's influence. If advertising is a good control, it means that any correlation between price and the error term in the model without advertising (U) should be due to omitted variable bias, which is reduced when advertising is included. Therefore, before controlling for advertising, the error term (U) may be correlated with price because advertising affects both sales and is correlated with price. After including advertising in the model, the new error term (V) should not be correlated with price if advertising adequately controls for the omitted variable, leading to the conclusion that Cor(U, Price) ≠ 0 and Cor(Price, V) = 0.

Question 6

Sometimes including independent variables in a regression serve as a "data sanity check," in so much as they facilitate a:

Accepted Answer

Including independent variables in a regression allows for a comparison between the estimated coefficient for that variable and the value for that coefficient as predicted by theory. This can help ensure the data is consistent with expectations and provide a data sanity check.

Question 7

A selected sample is one that is:

Accepted Answer

A selected sample refers to a nonrandom sample, where the sampling method is not based on randomization. Therefore, choice B is the best answer option.

Question 8

If the decision to include average tenure at the company as a control variable in an attempt to estimate if West coast store locations are outperforming store locations in the rest of the country (i.e., the regression, StoreProfits_i = β₀ + β₁West Coast_i + β₂Avg.Tenure_i + U_i), which of the following conditions need to be true in order for the estimate of β₁ to be the same regardless of whether Avg. Tenure is used as a control or not?

Accepted Answer

If the variables of interest (West Coast) and the potential control variable (Avg. Tenure) are uncorrelated, then the estimate of β₁ will be the same regardless of whether Avg. Tenure is used as a control or not. This is because the effect of West Coast on Store Profits is not confounded by Avg. Tenure in this case. The p-value on average tenure or the semi-partial correlation of Store Profits on West Coast holding Avg. Tenure fixed do not necessarily have an impact on the estimate of β₁.

Question 9

A dummy variable is:

Accepted Answer

A dummy variable is a type of binary variable that represents the presence or absence of a characteristic. It is typically used in regression analysis to model the effect of that characteristic on some outcome of interest.

Question 10

In attempting to estimate the causal effect of employee hours worked on total units produced, you include the age of the production equipment as a control variable. Which of the following conditions would not be a good reason to include this control variable?

Accepted Answer

The age distribution of the plants being non-normal would not be a good reason to include age of the production equipment as a control variable. Non-normality would not affect the relationship between employee hours worked and total units produced nor would it affect the relationship between age of the equipment and total units produced. It would only affect the distribution of the age variable itself. A, B, and D are all good reasons to include age of the production equipment as a control variable because they suggest that age of the equipment may be associated with total units produced and could potentially confound the relationship between employee hours worked and total units produced.

Question 11

Suppose you are estimating the following model: Y_i = β₀ + β₁X_i + U_i. Suppose also that you only observe values of Y that are above 50. What is the consequence of this selection on the values of Y?

Accepted Answer

The selection of values of Y that are above 50 creates a sample selection bias, which can lead to biased estimates for coefficients. In this case, since we are only observing values of Y that are above 50, we are missing information on the lower end of the distribution. This can lead to biased estimates for the coefficient on the interaction term β₁X_i, which may have a different effect on values of Y below 50. The selection of values of Y above 50 does not necessarily cause the heteroscedasticity problem.

Question 12

A representative sample is one whose:

Accepted Answer

A representative sample is one where the distribution of the sample approximately matches the distribution of the population for key variables, ensuring that the sample accurately reflects the population characteristics.

Question 13

An ordinal variable is one that contains categories that:

Accepted Answer

Ordinal variables have categories with a meaningful order, but the difference between the values is not necessarily equal. For example, a rating scale from 1 to 5 has an obvious order, but it is not necessarily the case that the difference between a rating of 1 and 2 is the same as the difference between a rating of 4 and 5. Thus, choice A is the best answer.

Question 14

Suppose you know the determining function for what drives restaurant sales is of the following form WeeklySales_i = β₀ + β₁WeeklyPromoSpend_i + β₂HolidayWeek_i + U_i. Suppose further that your client told you that she is spending $1,000 per week on weekly promotions, except during the summer where she doubles it. Which statement best describes the role of "summer weeks" in estimating the causal effect of weekly promotion spent using the determining function above?

Accepted Answer

If summer weeks are included in the error term (U_i), then they will be correlated with the promotional spend variable (β₁). This creates an endogeneity problem as the promotional spend is no longer exogenous and will bias any estimates of the causal effect of weekly promotion spent on sales.

Question 15

Irrelevant variables are ones that:

Accepted Answer

Irrelevant variables do not have any effect on the outcome, neither in the population nor in the sample.

Question 16

Which step is not involved with constructing a representative sample?

Accepted Answer

Running a t-test is not involved in constructing a representative sample. The correct steps involved in constructing a representative sample are A) choosing the independent variables you want to match, B) collecting the sample by randomly sampling from each stratum (defined by your pre-chosen independent variables), and C) using information about the population to stratify (categorize) each of the chosen variables.

Question 17

The presence of a confounding factor will lead to failure of which of the critical assumptions used to justify claiming your estimates consistently estimate a causal effect?

Accepted Answer

The presence of a confounding factor, which is a variable that is associated with both the treatment and outcome, means that the model's error terms and treatments are no longer uncorrelated. This violates the critical assumption that the model's error terms and treatments are uncorrelated, which is necessary for consistently estimating a causal effect. The other critical assumptions (linear determining function, random sample, and homoscedastic errors) may still hold in the presence of a confounding factor.

Question 18

Assuming that you are trying to determine the true effect of how years of education affect career earnings (Earnings_i = β₀ + β₁Education_i + U_i), and that this effect is positive . What would be the likely induced correlation between Education and U_i of receiving a sample that only had individuals that made over $85,000?

Accepted Answer

In a sample with individuals making over $85,000, those with less education likely have other factors (U) compensating for their lower education to still achieve high earnings. This suggests a negative correlation between education and U, as higher U is needed for those with less education to reach the earnings threshold.

Question 19

Suppose you are estimating the following model: Y_i = β₀ + β₁X_i + U_i. You believe the variance of the unobserved factors (U) varies with X. If this is true, what is the consequence?

Accepted Answer

If the variance of the unobserved factors (U) varies with X, it affects the efficiency of the estimates but does not necessarily bias the estimates of β0 or β1. The key issue here is heteroskedasticity, which affects the standard errors of the estimates, making them inefficient, but not biased.

Question 20

Suppose you have estimated the following regression: Refrigerator Sales_i = β₀ + β₁Price_i + U_i. However, when presenting your results, someone in the audience claims your estimate is biased because your sample only contains sales figures for refrigerators that are priced over $300. Their point is:

Accepted Answer

The answer of Suppose you have estimated the following regression:...

Quiz 7: Basic Methods for Establishing Causal Inference