Econometrics - Panel/TS & hetero/autocorrelation

Question 1

What is heteroskedasticity and why is it a problem?

Answer 1

Non-constant variance in errors - violates a classical assumption

Question 2

What are 6 reasons heteroskedasticity occurs?

Answer 2

1. Error-learning models
2. Real income grows through time
3. Improved data collection over time
4. Outliers in a sample of data
5. An incorrectly specified model
6. Skews in distribution in an X variable

Question 3

What are the consequences of heteroskedasticity?

Answer 3

No longer minimum variance so inefficient estimator, not BEST anymore so there can be another estimator that can produce smaller variance, there will be a breakdown in inference (std errors no longer unbiased so issues w t-tests)

Question 4

What are the 3 main tests for heteroskedasticity?

Answer 4

1. Goldfeld-Quandt Test (GQ test)
2. Breusch-Pagan Test (BP test)
3. White’s Test

Question 5

How does the Breusch-Pagan test work?

Answer 5

Fit regression, then calculate the squared residuals, and fir a new model using the squared residuals, then calculate the chi-square test stat and p-value, and compare to sig level. Null hypothesis is homoskedasticity.

Question 6

How can you correct for heteroskedasticity?

Answer 6

1. Transform model e.g. logs/squares/inverse
2. Robust standard errors
3. Generalised Least Squares/Weighted Least Squares (GLS/WLS)

Question 7

What is autocorrelation/serial correlation and why is it a problem?

Answer 7

Errors correlated with their previous value - violates classical assumption

Question 8

When does serial correlation occur?

Answer 8

1. Time-series data
2. Spatially organised data
3. Can be in cross section but less common

Question 9

What causes serial correlation?

Answer 9

1. Omitted lagged variables
2. Economic shocks that have persistent effects
3. Transformations applied to data
4. Model misspecification
5. Error term being truly dynamic

Question 10

What is first-order autocorrelation?

Answer 10

Assume that the errors is correlated linearly only with its value in the previous period

Question 11

What are the consequences of autocorrelation?

Answer 11

Residuals don’t have minimum variances so OLS isn’t BLUE.
R-squared may seem high
Standard errors may be baised downwards - OLS is inefficient and incorrect inferences may be made

Question 12

What does the Durbin Watson Test test for?

Answer 12

First-order correlation

Question 13

What values of the Durbin Watson test statistic indicate first-order autocorrelation?

Answer 13

DW -> 0 = positive autocorrelation
DW -> 2 = no autocorrelation
DW -> 4 = negative autocorrelation

Question 14

What are 3 limitations of the Durbin Watosn test?

Answer 14

1. Not valid in dynamic models as test stat biased to 2
2. Only applies to first-order autocorrelation
3. Bounds test doesn’t offer exact critical values so an element of doubt

Question 15

What is a better test for serial correlation?

Answer 15

Bresuch-Godfrey Lagrange Multiplier Test

Question 16

How is a Bresuch-Godrey LM test conducted?

Answer 16

Estimate OLS and obtain residuals, estimate auxiliary regression and then either compute LM test stat and compare to ch-squared dist OR use an F-test

Question 17

What can be done to correct for serial correlation?

Answer 17

Employ robust standard errors (HAC standard errors)

Question 18

What do hetertoskedasticity autocorrelated consistent (HAC) standard errors do?

Answer 18

Larger standard errors so less statistical significance

Question 19

What is the difference between a True and Natural experiment

Answer 19

True = observations randomly assigned to different groups
Natural = not randomly assigned

Question 20

What is the equations for a Difference-in-Difference model?

Answer 20

Y = b0 + b1Gi + b2Ri + b3(G.R) + error, where G=1 in treatment group, otherwise 0, and R=1 if observation is observed in period 2, otherwise 0

Question 21

What is the interpretation of b3 in a general D-in-D?

Answer 21

Average treatment effect (ATE), captures the policy effect

Question 22

What are the advantages of using panel data? (5)

Answer 22

1. More information, more variability, less collinearity, greater degrees of freedom - hence more efficient
2. Consider dynamic changes
3. Detect/measure effects that can’t be observed in other data types
4. Better model specific types of economic behaviour
5. Large panels less likely to produce biased estimates

Question 23

What are the 4 main types of panel models?

Answer 23

1. Pooled OLS
2. Fixed Effects Least Squares Dummy Variable Model (LSDV)
3. Fixed Effects Within-Group Model
4. Random Effects Model

Question 24

Explain pooled OLS?

Answer 24

Pools data and estimates simple OLS - disregards time and entity dimensions

Question 25

Explain LSDV model?

Answer 25

Pools data and gives each entity its own intercept dummy

Question 26

Explain fixed effects (within group) ?

Answer 26

Each entity given its own intercept, but each variables is expressed as deviation from mean value

Question 27

Explain random effects model?

Answer 27

Assumes intercepts are random draws from a bigger population

Question 28

Problems of LSDV model?

Answer 28

1. Time-invariant - can't consider variables over time 2. Too many dummies can reduce degrees of freedom 3. Lots of dummies = multicollineaity 4. Can have issues with error term

Question 29

How is random effects different from fixed effects?

Answer 29

Random effects doesn't estimate an individual effect for each observation, it estimates an overall estimate of the intercept that captures the average effect within the sample of data

Question 30

What are the 2 error terms in a random effects model?

Answer 30

1. cross section/individual specific error component 2. combine time series and cross section error comportment - idiosyncratic error term (always in a regression)

Question 31

When should REM be used over FEM?

Answer 31

If you think differences across firms influence dependent variables

Question 32

What does the Hasuman test test for? What is the null/alternate hypothesis?

Answer 32

Tests whether the unique errors are correlated with the regressors. The null hypothesis is that there is no correlation and so estimates are consistent and REM is preferred.

Question 33

What type of estimator is used for REM and why?

Answer 33

Generalised Least Squares (GLS) - cannot use OLS as would yield inefficient estimators.

Question 34

What models can be employed if you have a binary/limited dependent variable?

Answer 34

1. Linear Probability Model 2. Logit Model 3. Probit Model 4. Tobit Model

Question 35

What type of estimation the is Probit Model?

Answer 35

Maximum-Likelihood estimator

Question 36

What is the interpretation of a Probit Model?

Answer 36

Have to calculate marginal effects and the results are a change in probability, in software marginal effects are the slope value

Question 37

What is the interpretation of a Logit Model?

Answer 37

Coefficients are a partial slope coefficient, the measure change in logit for a unit change in X

Question 38

How do you decide between a Logit and a Probit?

Answer 38

1. Measure of fit, R-squared 2. Hypothesis test 3. Model interpretation (marginal effects)

Question 39

What is a Tobit Model used for?

Answer 39

Limited dependent variables, where the value is continuous but is cut-ff/censored at a particular value

Question 40

How does the Tobit Model work?

Answer 40

Uses maximum likelihood estimation that treats the cutoff/censor values differently

Question 41

What is the general equation for a simultaneous equation model?

Question 42

How do you estimate a reduced form equation?

Answer 42

Use the relationship between the 2 simultaneous equations e.g. Qd = Qs and rearrange to get a reduced form equation. Treat as a normal simultaneous equation

Question 43

What is the problem with using OLS with simultaneous equation models? What is the solution?

Answer 43

Simultaneity bias, use two stage least squares (2SLS) instead

Question 44

How do you conduct a 2SLS

Answer 44

Identify exogenous and endogenous variables, use an instrumental variables approach where regressors = endogenous variables and the instruments = exogenous variables

Question 45

What makes a good instrument?

Answer 45

Z (insturment) must be exogenous in the equation , but related to X (endogenous variable)

Question 46

What is the difference between static and dynamic time series data?

Answer 46

Static =change in X at time t has an immediate effect on y e.g. Phillips curve Dynamic = where change in X at time t doesn't have an immediate effect on y, lags are included in the model to account for the time it takes for the change in X to be full absorbed by Y

Question 47

In TS data - what additional classical assumption is needed?

Answer 47

Strict exogenity = for each time period the expected value of the error term given all explanatory variables for all time periods is 0

Question 48

What problem will you have if stricy exogeneity is not achieved?

Answer 48

biased OLS estimates

Question 49

How can you prove consistency?

Answer 49

Stationarity and weak dependence

Question 50

What does stationarity mean?

Answer 50

Probability distribution is stable over time - the statistical properties of a process generating a time series do not change over time. (the series changes over time but the WAY it changes does not itself change over time)

Question 51

What are 2 problems with dynamic models?

Answer 51

1. High mutlicollinearity 2. Loss of degrees of freedom

Question 52

What is an autoregressive model? Why is it used?

Answer 52

Replace lagged values of independent variables with lagged dependent variables. Used to mitigate issues with dynamic models

Question 53

What happens when TS data is not weakly dependent?

Answer 53

Random walk - which is highly persistent and non-stationary

Question 54

What is it called when you have highly persistent TS data with a trend?

Answer 54

Random walk with drift

Question 55

How can you make a problematic series stationary and have weak dependence?

Answer 55

First-differencing the data series

Question 56

What model can you employ if you have serial correlation in TS?

Answer 56

Feasible Generalized Least Squares

Question 57

How do you test for a unit root? What is the null/alternate hypothesis?

Answer 57

Dickey-fuller test (uses special DF critical values) H0 = there is a unit root, data is non-stationary H1 = there is not a unit root, the data is stationary