Estimation

Question 1

What is y?

Answer 1

Dependent variable

Question 2

What is Bo?

Answer 2

Intercept/constant coefficient

Question 3

What are B1-Bk?

Answer 3

Slope coefficients

Question 4

What are X1-Xk?

Answer 4

Explanatory/independent variables

Question 5

What is u?

Answer 5

Error term

Question 6

What is the definition of the causal effect of x on y (under notion of ceteris paribus)?

Answer 6

How y changes if variable x changes, when all other relevant factors are held constant

Question 7

What does linearity imply about effect of x on y?

Answer 7

Implies a one unit change in x always the same effect on y
- y increases by same value with each 1 unit change in x

Question 8

What assumptions must hold to ensure the estimators are unbiased in the simple regression model?

Answer 8

• model is linear in parameters
• data is from a random sample
• there must be some variation in our explanatory variable
• no perfect Collinearity between explanatory variables
• there should be no statistical relationship between the error term and regressor (Zero conditional mean assumption)

Question 9

What is E(U)?

Answer 9

Zero

Question 10

What is the zero conditional mean assumption?

Answer 10

E(U/X1,X2,……,Xk = 0
- explanatory variables must not contain info about the mean of the unobserved factors

Question 11

What is the aim of the line/plane of best fit?

Answer 11

We want the residuals to be as small as possible

Question 12

What does the estimated error term equal?

Answer 12

Estimated u = true value of y - estimated y

Question 13

What are the algebraic properties of OLS?

Answer 13

• Sum of residuals = 0
• sample covariance between regressors and OLS residuals is zero
• sample averages of y and regressors lie on regression line

Question 14

What is SST?

Answer 14

Total sum of squares
- represents total variation in dependent variable

Question 15

What is SSE?

Answer 15

Explained sum of squares
- represents variation explained by regression

Question 16

What is SSR?

Answer 16

Residual sum of squares
- represents variation not explained by regression

Question 17

What is SST equal to?

Answer 17

SST = SSE + SSR

Question 18

What is R-squared?

Answer 18

• measures the proportion of the sample variation in y that is explained by the regression model/explanatory variables

Question 19

What does R-squared equal?

Answer 19

R-squared = SSE/SST = 1 - SSR/SST

Question 20

What is the definition of an unbiased estimator?

Answer 20

The expected value of the estimated coefficient = true population value

Question 21

What assumptions must hold on MLR model so that OLS estimators are unbiased?

Answer 21

MLR.1- Linear in parameters
MLR.2- Random Sampling
MLR.3- No Perfect Collinearity
MLR.4-Zero conditional mean

Question 22

Describe MLR.1?

Answer 22

• Linear in parameters
• model must be correctly specified
• error term is additive

Question 23

Describe MLR.2

Answer 23

• Random Sampling
• observations in the sample are randomly selected from the population

Question 24

Describe MLR.3

Answer 24

• No Perfect Collinearity
• must be variation on all of the independent variables
• there are no exact relationships among the independent variables

Question 25

Describe MLR.4

Answer 25

-Zero conditional mean - value of the explanatory variables must contain no info about the mean of the unobserved factors

Question 26

What is meant by an endogenous explanatory variable?

Answer 26

- an explanatory variable that is correlated with the error term - endogeneity is a violation of MLR.4

Question 27

What is meant by an exogenous explanatory variable?

Answer 27

- explanatory variable is uncorrelated with error term - if all explanatory variables are exogenous MLR.4 holds

Question 28

What is simultaneity?

Answer 28

When causality doesn’t just run from the regressors to the regressand but also in the other direction

Question 29

Interpret unbiasedness

Answer 29

It is an average property in repeated samples. - on average the estimated coefficient will equal the true value

Question 30

What is omitted variable bias?(OVB)

Answer 30

- occurs when one or more explanatory variables are correlated with a relevant omitted variable subsumed in the error term) - results in biased estimated coefficients - more generally, in MLR if omitted variable is correlated with only one explanatory variable all estimates coefficients are likely to be biased

Question 31

What is MLR.5?

Answer 31

Homescedasticity - the value of the explanatory variables must contain no info about the variance of the unobserved factors

Question 32

What is the effect of a high error variance on the sampling variance?

Answer 32

- High error variance leads to an increase in sampling variance. - As a result a large error variance makes estimates more imprecise. - error variance does not decrease with sample size

Question 33

What is the effect of a higher sample variation in the explanatory variable on the OLS estimates?

Answer 33

- More sample variation leads to more precise estimates - total sample variation increases with sample size

Question 34

Effect of a high Rj-Squared.

Answer 34

High Rj-Squared means there is a strong correlation between explanatory variable Xj and the other explanatory variables - higher Rj-Squared increases variance of estimate Bj - problem of almost linearly dependent explanatory variables is called multi Collinearity - Occurs as Rj approaches 1

Question 35

Is multi Collinearity a violation of our assumptions?

Answer 35

- does not violate any of our assumptions - but troublesome

Question 36

How can we lessen effect of multi Collinearity?

Answer 36

Increase sample size

Question 37

What is Gauss-Markov theorem?

Answer 37

Under assumptions MLR.1-MLR.5 Bo, B1……. Are the Best Linear Unbiased Estimators (BLUE) of the true population values

Question 38

How to tell if a regression suffers from multi Collinearity.

Answer 38

- VIF > 10 indicates m/c in regression - t-tests reject the individual significance of several coefficients but overall R-Squared of regression is still high - Estimates are imprecise - Estimates will be sensitive to changes in specification of the model