Fixed, random and between effects, time series and panel data

Question 1

What is the HAC strategy for handling serial correlation in regerssion errors for time series?

Answer 1

1) Assume that error terms more than delta time periods apart are uncorrelated.
2) This allows you to assume the covariance are zero if (t-s) > delta and allows you to calculate the variance of the OLS coefficient using UtUs as an estimator when (t-s) < delta
3) Standard errors using this approach are called Newey Wes or HAC standard errors

Question 2

What are time variant group-level characteristics? Does fixed effects address time-variant group-level characteristics?

Answer 2

Group-level time-variant characteristics are characteristics that vary over time, such as family income or the health of parents or number of siblings.

Fixed effects does not handle these well– you need to control for them in your regression specification if they vary according to the regression you specify.

Question 3

What is the quasi-differencing approach to handling serial correlation with time data?

Answer 3

1) Assume a model with AR(1) errors
2) Take quasi difference (1-rho), because the quasi-differenced error is homoskedastic

Question 4

What does the Dickey-fuller test do?

Answer 4

It tests whether there is a stationary mean aka that rho does not equal 1.

Null hypothesis of dickey-fuller is that rho equals 1, so if your t value is greater than the df critical value you can reject the null of non stationarity