Econometrics Midterm

Front 1

what is a single independent variable model?

Back 1

an equation with only one independent variable

Y = β0 + β1X

Front 2

what is a multivariate regression model?

Back 2

an equation with two or more independent variables

Y = β0 + β1X1 + β2X2

Front 3

how do you evaluate the quality of a regression equation? (8 questions)

Back 3

is the equation supported by sound theory?

how well does the estimated regression fit the data?

is the dataset reasonable large and accurate?

is OLS the best estimator for the equation?

how well do the estimated coefficients correspond to expectations developed by the researcher before the data were collected?

are all the obviously important variables included in the equation?

has the most theoretically logical functional form been used?

does the regression appear to be free of major econometric problems?

Front 4

what is r-squared?

Back 4

r-squared is the ratio of explained sum of squares to total sum of squares

or the amount of change in the dependent variable explained by the changes in the independent variable/s

adding another independent variable will at least keep R2 constant, but generally increases it

Front 5

what is r?

Back 5

r is the simple correlation coefficient, a measure of the strength and direction of the linear relationship between two variables

in single independent variable models, r*r == R2

meaning

r = 1 - perfectly positively correlated

r = -1 - perfectly negatively correlated

r = 0 - totally uncorrelated

Front 6

what is adjusted r-squared?

Back 6

adjusted r-squared is r-squared taking into account degrees of freedom

it fixes the problem of new independent variables increasing r-squared even if they don't add anything to the equation

Front 7

what are the steps in regression analysis? (6 steps)

Back 7

1. review the literature and develop the theoretical model

2. specify the model: select the independent variables and the functional form

2.1 choosing independent variables and how they should be measured

2.2 choosing functional form of variables

2.3 choosing properties of the stochastic error term

3. hypothesize the expected signs of the coefficients

4. collect, inspect, and clean the data

5. estimate and the evaluate the equation

6. document results

Front 8

what are the classical assumptions? (6 required, 1 optional)

Back 8

1. the regression model is linear, is correctly specified, and has an additive error term

2. the error term has a zero population mean

3. all explanatory variables are uncorrelated with the error term

4. observations of the error term are uncorrelated with the each other (no serial correlation)

5. the error term has a constant variance (no heteroskedasticity)

6. no explanatory variable is a perfect linear function of any other explanatory variables (no perfect multicollinearity)

7. the error term is normally distributed (optional, but usually invoked)

Front 9

what are the properties of the sampling distribution of OLS estimators? (4 properties)

Back 9

mean and unbiasedness - an estimator is unbiased if its sampling distribution has as its expected value, the true value of β; E(β) = β

properties of the variance - desirable for the sample distribution to be as narrow as possible; as sample size increases, variance decreases

standard error - since this is square root of variance, a larger sample size will cause it to fall

standard deviation - same as standard error, but used for population measurements, not sample measurements

Front 10

what is the Gauss-Markov Theorem?

Back 10

given classical assumptions 1-6 are true, then the OLS estimator of a coefficient is the minimum variance estimator from among the set of all linear unbiased estimators

means that estimators are BLUE (best [min. variance], linear, unbiased, estimators)

Front 11

what are the properties of OLS estimators?

Back 11

unbiased: E(β) = β, OLS estimates are centered around the true value

minimum variance: distribution of coefficient estimates around the true parameter values is as tightly distributed as possible

consistent: as sample size approaches infinity, estimates converge to true population parameters

normally distributed: due to distribution, various statistical tests based on the normal distribution may be applied to the estimates

Front 12

what are the steps of a hypothesis (t) test?

Back 12

1. set up null and alternative hypotheses

null: opposite of what you believe

alternative: what you believe to be true

2. choose level of significance, which gives you a critical t-value

3. run the regression and obtain an estimated t-value

4. apply the decision rule by comparing calculated t to the critical t in order to reject the null hypothesis or not

Front 13

what are the different types of errors in a hypothesis test?

Back 13

Type 1: you reject a null hypothesis that is true

Type 2: you do not reject a null hypothesis that is false

Front 14

what is a t-test?

Back 14

used to test significance of a hypothesis about a single coefficient

appropriate when stochastic error term is normally distributed and when variance of distribution must be estimated

Front 15

what is a confidence interval?

Back 15

a range that contains the true value of an item a specified percentage of the time (percentage is level of confidence)

Front 16

what is an F-test?

Back 16

an f-test is a way to test multiple coefficients simultaneously; two main types:

1. Joint Hypothesis Test - a null hypothesis that contains multiple hypotheses or a single hypothesis about a group of coefficients; appropriate when underlying economic theory specifies values for multiple coefficients simultaneously

2. Test of Overall Significance - null hypothesis in an f-test of overall significance is that all the slope coefficients in the equation equal zero simultaneously; used to show that overall fit of an equation is statistically significant

Front 17

what is a p-value?

Back 17

the probability of observing a t-score that size or larger if the null hypothesis were true

it is two times area under the curve of the t-distribution between the absolute value of the t-score and infinity

need a small p-value to reject null hypothesis

decision rule: reject H0 if p-value(k) < the level of significance and βk has the sign implied by HA

Front 18

what is omitted variable bias? what are its effects?

Back 18

omitted variable bias takes place when a relevant independent variable is left out of a regression equation; it causes inaccurate estimates of all included coefficients

classical assumption III (all explanatory variables are independent of the error term) is violated with an omitted variable because all variables are generally correlated in some way, making included variables and the error term take on changes that would have been attributed to the omitted variable

Front 19

what are irrelevant variables?

Back 19

an irrelevant variable has no place in an equation; it increases the variances of the estimated coeffcients

Front 20

what are the 4 specification criterion for independent variables?

Back 20

theory: is the variable's place in the equation unambiguous and theoretically sound?

t-test: is the variable’s estimated coefficient significant in the expected direction?

Adj. R2: does the overall fit of the equation improve when the variable is added to the equation?

bias: do other variable’s coefficients change significantly when the variable is added to the equation?

Front 21

what is a constant term? what are its components?

Back 21

constant term: expected value of Y when all explanatory variables and the error term are zero

3 components:

1. the true value of the constant

2. the constant impact of any specification errors (like omitted variables)

3. the mean of the error term for the correctly specified equation (if not equal to zero)

Front 22

what is the linear functional form?

Back 22

Y=β0+β1X1

Front 23

what is double log functional form?

Back 23

lnY= β0+ β1(ln X1)

Front 24

what is semi-log functional form?

Back 24

lnY= β0+ β1X1

AND

Y= β0+ β1(ln X1)+β2X2

Front 25

what is polynomial form?

Back 25

Y= β0+ β1X1+β2(X1)^2

Front 26

what is inverse form?

Back 26

Y= β0+ β1(1/X1)+β2X2

Front 27

what is a lagged independent variable?

Back 27

in time series models, effects are not always instant, you want to sometimes lag independent variables, represented by subscript (t-1)

Front 28

what is a dummy variable? what are the two types?

Back 28

dummy variable: a binary condition that is represented by a 1 if true, or 0 otherwise

slope dummies:

- Y= β0+ β1X1+β2D1+β3D1X1

- slope dummies allow the slope of of the relationship between the dependent variable and an independent variable to be different depending on if the dummy condition is met

intercept dummies:

- Y= β0+ β1X1+β2D1

- slope stays constant if dummy condition is met, but changes intercept