Lecture 20

Question 1

If the explanatory variable(s) of interest vary little over time and, hence, are correlated with the time-invariant unobservables, what model would be best for significant results

Answer 1

• OLS on a cross section may yield significant results, while
• OLS on the first differenced model may not

Question 2

Why is having data from more time periods useful

Answer 2

• more observations
• potentially, more variation in variables of interest
• greater opportunity to investigate how relationships change over time

Question 3

When working with more than 2 time periods, what issue needs further consideration

Answer 3

the non-independence issue relating to having more than one observation for each cross-section element in the sample needs further consideration

Question 4

Can we use the first differencing method for eliminating time-invariant unobservables for 3 or more time periods

Answer 4

The first differencing method for eliminating time-invariant unobservables can still be applied but, for our conclusions to be valid, we require that a very specific assumption relating to the time dimension of the data be valid

Question 5

Example model for three period panel data

Answer 5

Question 6

Example of differencing the the three-period panel data model

Answer 6

Question 7

What are the two issues with this differenced model

Answer 7

This differenced model contains differences in the year dummies…
when 𝑡=2”,” ∆〖𝑑2〗_𝑖𝑡=1 and ∆〖𝑑3〗_𝑖𝑡=0
when 𝑡=3”,” ∆〖𝑑2〗_𝑖𝑡=−1 and ∆〖𝑑3〗_𝑖𝑡=1
…and no intercept

Question 7

What do we need to assume for our standard errors and test statistics to be valid

Answer 7

Need to assume that the differenced idiosyncratic errors, ∆𝑢𝑖𝑡, are serially uncorrelated, i.e., uncorrelated over time

Question 8

Example process of fixed effects estimation as a method of eliminating time-invariant unobservables

Answer 8

Question 9

What can we now label our dependent and explanatory variable

Answer 9

Question 10

How were time invariant observables able to be eliminated in this method

Answer 10

The time invariant unobservables have been eliminated because 𝑎_𝑖 does not vary over time => it is always equal to its within 𝑖 mean

Question 11

What do we call this transformation

Answer 11

This transformation is called
the fixed effects transformation or
the within transformation

Question 12

What is required, across all time periods to get an unbiased estimate of B1 by applying OLS to fixed effects model

Answer 12

If 𝑢_𝑖𝑡 is uncorrelated with 𝑥_1𝑖𝑡 across all time periods

Question 14

To get unbiased estimates of the standard error of 𝛽̂1 either:

Answer 14

• we need the idiosyncratic errors, 𝑢_𝑖𝑡, to be homoscedastic and serially uncorrelated; or
• we need to adjust the standard errors to account for the heteroscedasticity and/or serial correlation

Question 15

What are the degrees of freedom for T and F tests for fixed effects estimation method

Answer 15

When conducting t- and F- tests, we need to use the correct degrees of freedom: 𝑑𝑓=𝑁𝑇−𝑘−𝑁