Chapter 3.3 No Autocorrelation/ Expected Value ...

Question 1

Explain Gauss-Markov assumption 4 and 5.

Answer 1

4. No autocorrelation: No correlation between ith and jth residual terms.
5. Expected value of the residual vector given X is zero.

Question 2

Autocorrelation
Examining the residuals over time, …
Autocorrelation can be detected by …, or Durbin- Watson statistic.

Answer 2

no pattern should be observed if the errors are independent.

graphing the residuals against time

Question 3

How can autocorrelation happen?

Answer 3

Reasons leading to autocorrelation:
* Omitted an important variable
* Functional misfit
* Measurement error in independent variable

Question 4

• 𝐷 = 2 – no autocorrelation
• 𝐷 = 0 – perfect positive autocorrelation
• 𝐷 = 4 – perfect negative autocorrelation

Explain.

Answer 4

Use Durbin-Watson (DW) statistic to test for first-order autocorrelation. DW takes values within [0, 4]. For no serial correlation, a value close to 2 (e.g., 1.5-2.5) is expected.

Question 5

Breusch-Godfrey test

Answer 5

slide 37

Question 6

A regression can estimate both…
* Create … which indicate the season.
* Regress on …
* Use the multiple regression model to forecast.

Answer 6

the trend and additive seasonal indexes.

dummy variables
time and the seasonal variables

For any season, e.g. season 1, create a column with 1 for time periods which are season 1 and zero for other time periods (only season – 1 dummy variables are required).

Question 7

When modelling for seasonality, explain how to use dummy variables in that instance.

Answer 7

Model only 3 quarters explicitly. Otherwise there is multicollinearity as Q1 = 1 - (Q2+Q3+Q4)

This allows to test for seasonality

Question 8

What does endogeneity mean?

Answer 8

Correlation between error terms given Xi is not equal to zero

Simple test: analyze the correlation of the residuals and an independent variable.

• Reason for endogeneity: measurement errors, variables that affect each other,
  omitted variables(!)

(show this in an omitted variable context)

Question 9

Panel Data vs. Cross-Section Data
Cross-section data collected in observational studies refers to …, or without regard to differences in time.
A panel data set, or longitudinal data set, is one where there are …
* A balanced panel is one where …
* In an unbalanced panel some individuals have not been recorded in some time period.

Answer 9

data observing many subjects (such as individuals, firms or countries/regions) at the same point of time

repeated observations on the same units, which makes it possible to overcome an omitted variable bias.

every unit is surveyed in every time period.

Question 10

Modeling & estimating fixed effects

Answer 10

Fixed effects
* assume 𝜆 are constants (there is endogeneity) 𝑖
* effects are correlated with the other covariates

Least squares dummy variable estimator
* uses a dummy variable for each individual (or firm, etc.), which we assume to
have a fixed effect

Within estimator –> take deviations from individual means and apply least squares, relies on variations within individuals