Research Skills Part 3

Question 1

Important note on correlation

Answer 1

Zero correlation means that there is no linear relation between x and y. But it does not imply independence!!!

Correlation is not causation!!!

Question 2

Name 3 structures of correlation

Answer 2

1. x causes y
2. y causes x
3. x causes y and y causes x > self-reinforcement

Question 3

In a univariate regression…

Answer 3

Correlation determines sign of regression coefficient, and CORR^2 = R^2

Question 4

What is RSS?

Answer 4

Residual Sum of Squares = sum of all the residuals squared

Question 5

Give the formula for the beta coefficient

Answer 5

= cov(x,y) / var(x)
= (SD(y) / SD(x)) * CORR(x,y)

Question 6

What is TSS?

Answer 6

Total Sum of Squares = sum (y – y-bar)^2

Question 7

What is ESS

Answer 7

Explained Sum of Squares = sum (y-hat – y-bar)^2

Question 8

Give the formula for R2

Answer 8

TSS = ESS + RSS
R2 = 1 –RSS/TSS = ESS/TSS

Question 9

What are the drawbacks of R2?

Answer 9

1. It depends on how dep var is defined (changes versus levels, wages versus log wages, etc.). It is only comparable if the dep var is the same.
2. It always increases if you add more vars, even if they’re useless > compute Adj-R2

Question 10

Note on (adj) R2

Answer 10

(adj) R2 is useful for comparing the relative performance of 2 models with same dep var. However, it is not useful for evaluating absolute performance.

Question 11

Name 3 factors reducing the accuracy of OLS estimate

Answer 11

1. Large error variance (s^2) > large influence of other variables are not in the model > OMITTED VARIABLE BIAS!!!!!
2. Small number of observations
3. Little spread in indep var > without variation in x one cannot explain variation in y, but too much variation is also bad

Question 12

What is the F-test?

Answer 12

The F-test of overall significance indicates whether your linear regression model provides a better fit to the data than a model that contains no independent variables.

-Multiple regression: p-value of F-test equals p-value of null hypothesis that all coefficients are jointly equal to zero

Question 13

When is the Omitted Variable Bias more severe and pose a solution for this problem?

Answer 13

Problem more severe when the x variable in regression has high correlation with omitted variable z

Solution: multivariate regression

Question 14

What are the assumptions of the linear regression model?

Answer 14

1. residuals have a mean of 0 and are independent
2. residuals have a constant variance = homoskedasticity
3. residuals are uncorrelated = no autocorrelation
4. there’s no exact linear relation between the independent variables
   .
   Under these assumptions, the OLS estimators (betas) are BLUE = best linear unbiased estimator for the true beta.
   Only then are the routinely computed S.E.s and t-stats correct.
   .
5. residuals follow a normal distribution
   .
   If the errors are correlated with any of the independent vars, OLS is biased and inconsistent > wrong coefficient estimates!!

Question 15

How do you test for non-linearity and how do you fix non-linearity issues?

Answer 15

Test: Ramsey’s RESET test to examine linearity of regression

Solution: use data transformation > take logs or add a squared term

Question 16

Heteroskedasticity causes / consequences / testing / solutions

Answer 16

Causes:
- changing variance over time (time series)
- changing variance across firms (cross sectional)

Consequences:
- usual S.E. and t-stats not valid
- BUT, no impact on coefficients!!

Testing:
- visual testing
- statistical tests

Solutions:
- use corrected S.E.s
- use log transform or scale variables by size

Question 17

Autocorrelation causes / consequences / testing / solutions

Answer 17

Causes:
- seasonality effects
- lead/lag effects > over/underreaction to news
- model misspecification

Consequences:
- usual S.E.s and t-stats not valid
- positive autocorr: S.E. understated and t-stats too big
- negative autocorr: S.E. overstated and t-stats too small

Testing:
- visual testing
- statistical tests

Solutions:
- add lagged dep/indep vars
- include dummy variable
- use corrected S.E.s

Question 18

Multicollinearity causes / consequences / checking / solutions

Answer 18

Causes:
- 2 or more indep vars are highly correlated

Consequences:
- low t-stats and high S.E.s for individual coefficients
- weird signs or magnitudes of coefficient estimates

Checking:
- compute CORR matrix
- compute Variance Inflation Factor. VIF > 10 is a problem

Solutions:
- drop one variable > can lead to omitted variable bias
- collect more data to increase accuracy

Question 19

Non-normality causes / consequences / testing / solutions

Answer 19

Causes:
- extreme observations
- bounded dep var
- binary dep var
- discrete dep var

Consequences:
- large sample > no problem
- small sample > inference about coefficients wrong and t-stats invalid
- BUT, no impact on coefficients!!

Testing:
- JB statistic to test for normal distribution

Solutions:
- winsorize / truncate
- use log transformation
- use other regression model > tobit, probit/logit

Question 20

If the error term in a linear regression model is not normally distributed…

A. … the OLS estimator is biased
B. … routinely calculated S.E.s are incorrect
C. … we need to rely on asymptotic theory to perform valid tests
D. … we need to take the log of the dependent variable

Answer 20

C

Question 21

In a linear regression model, if the slope coefficient of X has a t-stat of 3.0…

A. we accept the hypothesis that X has an impact
B. we accept that X is significant
C. we reject the null hypothesis that X is insignificant
D. we reject the null hypothesis that X has no impact

Answer 21

D

Question 22

What do endogeneity and simultaneity mean?

Answer 22

Endogeneity broadly refers to situations in which an explanatory variable is correlated with the error term.

Simultaneity is another common cause of endogeneity. Simultaneity arises when one or more of the predictors (e.g., treatment variable) is determined by the response variable (Y). In simple terms, X causes Y and Y causes X.

Question 23

Which problem does make the OLS estimator biased?

A. simultaneity between x and y
B. heteroskedasticity
C. a small sample
D. all of these

Answer 23

A

Question 24

Which statement(s) is/are correct?

A. R2 is the most important statistic of a regression
B. R2 tells us how well the model fits the data
C. a larger R2 is always better
D. if R2=0, we have a useless model

Answer 24

B & D

Question 25

What increases the precision of the OLS estimator?

A. having more observations
B. having more variation in X
C. having less correlation between X and other regressors
D. having a smaller error variance

Answer 25

All of them