Midterm

Question 1

Causal relationship

Answer 1

a change in one variable (action) CAUSES change in another variable (result)

Question 2

Correlation

Answer 2

the change between X and Y can partially be explained by other factors

Question 3

Error Term

Answer 3

• Deviation of the observed Y from the true line
• Represented by εi in structural equation
• A theoretical representation of unobserved variables that explains for the remaining change not interpreted by the model (omitted variable absorbed by error term)

Question 4

Residual

Answer 4

• Deviation of the observed Y from the estimated line
• Calculated by e_i = Y_i – (Y_i )̂
• *Oberserved - Estimated**

Question 5

R^2

Answer 5

Goodness of Fit

• Ranges from 0 – 1
• Closer to 1 = better fit
• Adjusted R2: Includes “penalty” for adding additional regressors

Question 6

null hypothesis

Answer 6

The null hypothesis states “no difference” or “no effect”

Question 7

alternative hypothesis

Answer 7

The alternative hypothesis states there is a difference/effect

Question 8

T-test

Answer 8

• If the absolute value of the t-stat is bigger than the critical value (e.g. 1.96) it means we can reject the null hypothesis and accept the alternative that the true coefficient is not zero
• *our variable is statistically significant at the 5% level of significance
• This also means the p-value is smaller than 5% (0.05).

Question 9

T-test formula

Answer 9

Divide the coefficient by the standard error to get the t-value

Question 10

F-test

Answer 10

Test a set of regression coefficients for joint significance

• H0: β1 = β2 = β3= 0 (ALL coefficients = 0)
• HA: β1 ≠ 0 OR β2 ≠ 0 OR β3 ≠ 0 (at least 1 coefficient NOT equal to 0)

F-stat > Critical Value = Reject the Null
(p-value of F lower than the level of significance)

Question 11

F-test formula

Answer 11

You want the F-stat high & probability low

Question 12

Interpreting Coefficients:

Level-Level

Answer 12

Y = β1 X1

on average a one-unit increase in X is associated with a β1-unit increase in Y, holding all else constant

Question 13

Interpreting Coefficients:

Log-Level

Answer 13

lnY= β1 X1

on average a one-unit increase in X is associated with a β1% increase in Y, holding all else constant

Question 14

Interpreting Coefficients:

Level-Log

Answer 14

Y= β1 lnX1

on average a 1% increase in X is associated with a β1-unit increase in Y, holding all else constant

Question 15

Interpreting Coefficients:

Log-Log

Answer 15

lnY= β1 lnX1

on average, a 1% increase in X is associated with a β1% increase in Y, holding all else constant

Question 16

Dummy/binary variable

Answer 16

Only has two possible values – e.g. X = 1 if female; X= 0 is male

Y = B0 + B1female

Ex: On average, being female is associated with a B1 difference in Y compared to male, holding all else constant

Question 17

Categorical Variable

Answer 17

A variable like “region” has multiple values (south, west, northeast, midwest) that should be transformed into individual dummy (0 or 1) variables

Y = B0 + B1south + B2west + B3 northeast

Ex: On average, living in the South is associated with a B1 change in Y compared to the Midwest, holding all else constant.

Question 18

Interaction term

Answer 18

An independent variable in a regression equation that is the multiple of two or more other independent variables. Each interaction term has its own regression coefficient

Does the effect of work experience on salary differ between males and females?

Y = B0 +B1Experience + B2Female + B3(Experience*Female) + e

Ex: On average, a one-unit increase in experience has a B3 difference in Y for females compared to males, holding all else constant

This allows the effect of experience on income to vary by gender

B3 now measures the effect of an additional year of experience for females relative to males

Question 19

7 Classical Assumptions

Answer 19

1. Regression model is linear (in B’s), correctly specified, and has an additive error term
2. The error term has a population mean of zero
3. The explanatory variables are not correlated with the error term
4. Observations of the error term are not correlated
5. The error term has a constant variance
6. The regressors are uncorrelated with each other
7. Error term is normally distributed

Question 20

Omitted Variable Bias

Answer 20

Y = β0 + β1X1 +e

where error term absorbs an omitted variable X2

Question 21

Variable Inclusion Criteria

Answer 21

Theory: is there sound justification for including the variable?

Bias: do the coefficients for other variables change noticeably when the variable is included?

T-Test: is the variable’s estimated coefficient statistically significant?

R-square: has the R-square (adjusted R-square) improved?

Question 22

First-order serial correlation

Answer 22

occurs when the value of the error term in one period is a function of its value in the previous period; the current error term is correlated with the previous error term.

Question 23

DW Test

Answer 23

compare DW(d) to the critical values (𝐝_𝐋, 𝐝_𝐔)

Question 24

Newey-West Standard Errors

Answer 24

-Designed to correct for the consequences of first-order serial correlation; they are technically still biased, but are more accurate than OLS standard errors so they can be used for t-tests and other hypothesis tests

Newey-West SE > OLS SE

-Larger standard errors produce lower t-scores, so coefficients won’t be as statistically significant

Question 25

Heteroskedasticity

Answer 25

happens when the standard errors of a variable, monitored over a specific amount of time, are non-constant. With heteroskedasticity, the tell-tale sign upon visual inspection of the residual errors is that they will tend to fan out over time, as depicted in the image below.

Question 26

Pure Heteroskedasticity

Answer 26

occurs in correctly specified equations

Question 27

Impure Heteroskedasticity

Answer 27

arises due to model misspecification

Question 28

Multicollinearity

Answer 28

state of very high intercorrelations or inter-associations among the independent variables. It is therefore a type of disturbance in the data, and if present in the data the statistical inferences made about the data may not be reliable.

Question 29

Perfect Multicollinearity

Answer 29

virtually always the result of a definitional relationship between the independent variables, and is solved by dropping variables from the regression.

Question 30

Imperfect Multicollinearity

Answer 30

describes the existence of a strong (but not exact) linear relationship between two or more independent variables that can significantly affect the estimates of coefficients. 

Question 31

Multicollinearity

Answer 31

Multicollinearity exists in every equation & the severity can change from sample to sample.  There are no generally accepted true statistical tests for multicollinearity. VIF > 5 as a rule of thumb

Question 32

Outliers

Answer 32

A distinctly unusual observation or extreme value 

Question 33

Unbiased

Answer 33

Parameter estimates are, on average, equal to the parameter's true value in the population model

Question 34

Unbiased Equation

Answer 34

E(Bhat)=B | Distrobution of Bhat is centered around B

Question 35

Efficient

Answer 35

Has the lowest variance among unbiased estimators

Question 36

Multicollinearity

Answer 36

strong (but not exact) linear relationship between two or more regressors

Question 37

Best Linear Unbiased Estimator

Answer 37

If first 6 classical assumptions are met

Question 38

OLS stands for

Answer 38

Ordinary least squares

Question 39

Most Common remedies for multicollinearity

Answer 39

1. Do Nothing 2. Drop a redundant variable 3. Increase the sample size

Question 40

Impure Serial Correlation

Answer 40

Serial correlation that is caused by a specification error such as an omitted variable or an incorrect functional form

Question 41

Pure Serial Correlation

Answer 41

This type of serial correlation occurs when the error in one period is correlated with the errors in other periods. The model is assumed to be correctly specified.

Question 42

Best remedy for impure serial correlation

Answer 42

attempt to find the ommitted variable or the correct functional form for the equation

Question 43

Stochastic Error Term

Answer 43

term that is added to aregression equation to introduce all the variation in the dependent variable that cannot be explained by the independent variables that have been included Equation: Y = B0+B1X+e

Question 44

Residual Error Term

Answer 44

The difference between the estimated value of the dependent variable and the actual value of the dependent variable (observered-estimated) Equation: ei=Yi-Y^i

Question 45

Durbin-Watson d statistic test

Answer 45

Used to determine if there is first-order serial correlation in the error term of an equation by examining residuals. Includes dL(lower bound) and dU (upper bound).

Question 46

Durbin-Watson assumptions

Answer 46

1. regression model includes an intercept term 2. serial correlation is first-order in nature 3. regression model does not include a lagged dependent variable as an independent variable

Question 47

What if Durbin-Watson d-statistic is outside of upper limit?

Answer 47

We do not reject the null hypothesis of no autocorrelation since there is no statistical evidence of first order positive serial correlation

Question 48

White Test

Answer 48

Used to test for heteroskedasticity

Question 49

t-test formula

Answer 49

coefficient divided by standard error

Question 50

r2 formula

Answer 50

ess(model) divided by tss (total)

Question 51

Sign of bias = sign of OVB x sign correlation

Answer 51

sign of bias

Question 52

5% confidence

Answer 52

1.96

Question 53

1% confidence

Answer 53

2.787

Question 54

Omitted Variable (issue)

Answer 54

``` Bias in the coefficient estimates of the included X's #3 OLS classical assumption ```

Question 55

Omitted Variable (correction)

Answer 55

``` Include the ommitted variable or a proxy #3 OLS classical assumption ```

Question 56

Irrelevant variable

Answer 56

Inclusion of a variable that does not belong in the equation

Question 57

Incorrect Functional Form (issue)

Answer 57

``` The function form is inappropriate #1 OLS classical assumption ```

Question 58

Incorrect Functional Form (correction)

Answer 58

``` Transform the variable or the equation to a different functional form #1 OLS classical assumption ```

Question 59

Multicollinearity (issue)

Answer 59

``` Some of the ind. variables are imperfectly correlated #6 OLS classical assumption ```

Question 60

Multicollinearity (correction)

Answer 60

``` Drop the redudant variables but often doing nothing is best #6 OLS classical assumption ```

Question 61

Serial Correlation (issue)

Answer 61

``` Observations of the error term are correlated #4 OLS classical assumption ```

Question 62

Serial Correlation (correction)

Answer 62

``` if impure, fix the specification. consider Geralized Least Squares or Newey-West standard errors #4 OLS classical assumption ```

Question 63

Heteroskedasticity (issue)

Answer 63

``` The variance of the error term is not constant for all observations #5 OLS classical assumption ```

Question 64

Heteroskedasticity (correction)

Answer 64

if impure, fix the specification. Use the HC standard errors or reformulate the variables