Chapter 17 Econometrics

1
Chapter 17 Econometrics

• This series of slides will cover a subset of
  Chapter 17
• Autocorrelated Error
• Lagged Variables
• The Backshift Operator
• Adjustment Models

2
Repeated Firm or Consumer Data

• Time Structured Data - Examples - (y1, y2, , yt,
  , yT)
• Misspecification - Missing Exogenous Variables
• Error Structure - Not Gauss-Markov (?2I)

3
Autocorrelated Error
et ?et-1 ?t
? N(0,??2I)
4
Recursive Substitution in Time Series
et ?et-1 ?t ?(?et-2 ?t-1) ?t
??(?et-3 ?t-2) ?t-1 ?t
5
Now We Leverage the Pattern
et ??(?et-3 ?t-2) ?t-1 ?t
?t ???t-1 ?2?t-2 ?3?t-3
6
Time to Figure Out E()
7
And Now Of course V()
V(et) Eet - E(et)2
V(et) Eet2
The previous slide showed that E(et) 0
8
Now We Use the Pattern (Squared)
9
A Big Mess, Right?

• V(et) E(et2) (1 ?2 ?4 )?2

Uh-oh an infinite series
10
Lets Define the Infinite Series s

• s 1 ?2 ?4 ?8
• ?2s ?2 ?4 ?8 ?16

What is the difference between the first and
second lines?

• s - ?2s 1

11
Putting It Together
Since
12
Applying the Same Logic to the Covariances
For any pair of errors one time unit apart we have
and in general
13
Instead of the Gauss-Markov Assumption (?2I) we
have
V(e)
So how do we estimate ? now?
14
Lagged IndependentVariables
Consumer behavior and attitude does not
immediately react to changes in marketing
variables
yt ?0 xt-1?1 et
Or more generally
yt ?0 xt-1?1 xt-2?2 xt-s?s et
15
Lagged effects can take on many forms
Koyck and others have come up with ways of
estimating different shaped impacts